From Dr. Spencer’s Global Warming Blog
Dr. Roy Spencer
It took the better part of two years to satisfy the reviewers, but finally our paper Urban Heat Island Effects in U.S. Summer Surface Temperature Data, 1895–2023 has been published in the AMS Journal of Applied Meteorology and Climatology.
To quickly summarize, we used the average temperature differences between nearby GHCN stations and related those to population density (PD) differences between stations. Why population density? Well, PD datasets are global, and one of the PD datasets goes back to the early 1800s, so we can compute how the UHI effect has changed over time. The effect of PD on UHI temperature is strongly nonlinear, so we had to account for that, too. (The strongest rate of warming occurs when population just starts to increase beyond wilderness conditions, and it mostly stabilizes at very high population densities; This has been known since Oke’s original 1973 study).
We then created a dataset of UHI warming versus time at the gridpoint level by calibrating population density increases in terms of temperature increase.
The bottom line was that 65% of the U.S. linear warming trend between 1895 and 2023 was due to increasing population density at the suburban and urban stations; 8% of the warming was due to urbanization at rural stations. Most of that UHI effect warming occurred before 1970.
But this does not necessarily translate into NOAA’s official temperature record being corrupted at these levels. Read on…
What Does This Mean for Urbanization Effects in the Official U.S. Temperature Record?
That’s a good question, and I don’t have a good answer.
One of the reviewers, who seemed to know a lot about the homogenization technique used by NOAA, said the homogenized data could not be used for our study because the UHI-trends are mostly removed from those data. (Homogenization looks at year-to-year [time domain] temperature changes at neighboring stations, not the spatial temperature differences [space domain] like we do). So, we were forced to use the raw (not homogenized) U.S. summertime GHCN daily average ([Tmax+Tmin]/2) data for the study. One of the surprising things that reviewer claimed was that homogenization warms the past at currently urbanized stations to make their less-urbanized early history just as warm as today.
So, I emphasize: In our study, it was the raw (unadjusted) data which had a substantial UHI warming influence. This isn’t surprising.
But that reviewer of the paper said most of the spurious UHI warming effect has been removed by the homogenization process, which constitutes the official temperature record as reported by NOAA. I am not convinced of this, and at least one recent paper claims that homogenization does not actually correct the urban trends to look like rural trends, but instead it does “urban blending” of the data. As a result, which trends are “preferred” by that statistical procedure are based upon a sort of “statistical voting” process (my terminology here, which might not be accurate).
So, it remains to be seen just how much spurious UHI effect there is in the official, homogenized land-based temperature trends. The jury is still out on that.
Of course, if sufficient rural stations can be found to do land-based temperature monitoring, I still like Anthony Watts’ approach of simply not using suburban and urban sites for long-term trends. Nevertheless, most people live in urbanized areas, so it’s still important to quantify just how much of those “record hot” temperatures we hear about in cities are simply due to urbanization effects. I think our approach gets us a step closer to answering that question.
Is Population Density the Best Way to Do This?
We used PD data because there are now global datasets, and at least one of them extends centuries into the past. But, since we use population density in our study, we cannot account for additional UHI effects due to increased prosperity even when population has stabilized.
For example, even if population density no longer increases over time in some urban areas, there have likely been increases in air conditioning use, with more stores and more parking lots, as wealth has increased since, say, the 1970s. We have started using a Landsat-based dataset of “impervious surfaces” to try to get at part of this issue, but those data only go back to the mid-1970s. But it will be a start.
Interesting paper but not surprising.
Interesting that it took two years to get past the gatekeepers, but not surprising (maybe a bit of a surprise that it did get through).
It would be interesting to know what the picture looks like for Tmin and Tmax separately. Would that take another two years?
It got through, because the study is “in progress”, per the author, and is a slow process of educating away from the accepted truths of the “standard operating procedures” used at present, id est, no boats were rocked, no crockery was broken
The east coast has an heat island from Portland, Maine to Norfolk, Virginia, about 700 miles, that was forested not so long ago, but now is covered with all sorts of heat retaining, human detritus.
Congratulations on passing a tough peer review and getting this important work published in an AMS journal. My daughter Sarah studied heat islands for a 7th-grade science fair project. Her main data came from a car trip across Texas and New Mexico. She employed a thermistor-style sensor connected to a data logger. The sensor was placed inside a shielded tube placed outside her back seat window. She found that even highway intersections in rural West Texas form heat islands. Likewise, a gravel road parallel to the asphalt paved IH-10 was slightly cooler. A gas station in the middle of nowhere is also a heat island. I once published an article in MAKE magazine on the temperature measured atop a pole mounted on my pickup that showed a very distinct increase while driving across San Antonio well after sunset. There’s a graph in the article.
FWIW, the gridded weather forecast for Las Vegas NV shows the “Strip” as being 4 to 5ºF warmer than the less dense areas of Las Vegas. This matches my experience of driving on I-15 though LV, with the outside air temp being up to 5º warmer in the vicinity of the strip than the other parts of the city.
I think it is important to understand the difference between local warming and global warming as mitigation is substantially different for the two cases.
Isn’t it easier to simply gather all the data from verified pristine rural stations around the world and look at those in isolation? By ”pristine” stations I mean those which have remained removed from urban influence and with at least 60-80 years of regular temp records. You would not need many of them. Dr Bill Johnston from bomwatch has found no trend in Australian data.
I think this is what scientists at CERES recently published and the results were in line basically with this new paper.
The GHCN is garbage. But we do have the USCRN, which shows no significant warming in the US since 2005 (when observations began).
Since all anthropogenic energy production and use creates ephemeral “waste heat” which is eventually radiated to space, it is not at all surprising that thermometers respond to this increased heat.
And of course, Urban Heat Island —> National Heat Island —> Global Warming.
No need for a GHE.
This isn’t the reason for UHI. I don’t have time to explain to you why not, but there are many people on here who I hope will oblige.
The ephemeral “waste heat” is four orders of magnitude lower than what the sun hits the earth with every day and it’s not all concentrated in cities. Think tarmac and concrete, etc. for UHI.
Of course, your last point is correct and, indeed, there’s no mention of CO2 anywhere to be found.
Of course it is.
Of course you don’t.
and your data is where, exactly?
You are not commenting in good faith, just trying to disparage me.
“Of course you don’t.”
Getting on a plane to London today. Meeting up with my daughter there. Lots to catch up on in organizing stuff. Got my car booked and tickets for the Arsenal v. Newcastle game on Sunday printed though.
Have a nice weekend. I will.
But you had time to write a pointless comment aimed at disparaging me, didn’t you?
Greetings from London.
No it was aimed at educating you and stopping you from continuously making incorrect claims about waste heat, where the citations appear to be voices in your head.
Well, if you’re going to accuse me of disparaging you ……
If you would get your head out of your you know what, you would see that I did have a point and it was to educate you, or at least have people who know more about it than I educate you.
Thank you for your interest.
Well, that’s informative, isn’t it? Unsolicited advice from someone who admits to their lack of knowledge.
Well done.
Waste heat is not trivial. A few years ago on this very site Willis did some calculations for some large cities.
https://wattsupwiththat.com/2020/01/16/the-cities-are-cooking/
Yes, that’s a primary reference to my comment to Mr Flynn, who appears to not want to learn something new every day, thereby deserving the dislikes. Willis starts off with the following:
I got to thinking about the phenomenon known as the “Urban Heat Island” effect, or UHI. Cities tend to trap heat due to the amount of black pavement and concrete sidewalks, the narrow canyons between buildings that slow down the wind, and the sides of the buildings reflecting sunlight downwards.
As a result, cities are often warmer than the surrounding countryside. In some cities, it’s hot enough that it affects the local weather. Here’s a simplified diagram: (Followed by a nice diagram).
Enough solar energy hits Earth every second to power multiple Katrina sized hurricanes. Katrina unleashed 14 to 20 years (depending on whose numbers are used) equivalent of all human energy use.
What the entire human race can do with heat producing energy use is as nothing compared to the solar energy smackdown Earth gets every second.
And after four and a half billion years of continuous sunlight, the surface has cooled.
You seem to have given yourself a serious smackdown.
You were implying?
Gregg, the points are not incompatible.
Human energy use has a trivial effect on *global* temperatures;
Human energy use has a non-trivial effect on *local* temperatures.
When they are claiming a energy imbalance of less that 1%, it becomes a factor.
The devil is in the details. Dismiss orbital mechanics and precession. They are trivial. Dismiss solar cycles. They are trivial. Dismiss this and that until you get the results you want and then calculated it to decimal precisions that would necessarily show how those dismissed factors would play in.
How much of lunar gravity is taken into account. Tides are water swells are kinetic energy.
How much sun does the moon block when it is on the sun side and how much is reflected when the moon is on the dark side. Not much. Probably as significant as CO2.
The medieval warm period, that lasted 150 years was “regional,” so dismiss it, but the CO2 from a power plant covers the globe in hours. Likewise the more recent mini ice age. Dismiss it as regional even though it lasted decades.
Yes. Concrete, glass, brick, tarmac, all play in. But also the change in surface area when putting up 3D structures atop a 2D surface. It all has to be taken into account.
There are so many things dismissed merely by handwaving. Not science.
“There are so many things dismissed merely by handwaving. Not science.”
You nailed it.
But there is no “increased heat” at the surface. If you think there is, what is its source?
Take off your shoes and socks. Go outside. Put one foot on blacktop and the other on grass.
Dear Sparta Nova 4,
A totally dumb analogy. Leave your socks on and put your pinkie on the roof of a black car, then a white car – then so what.
What has that got to do with a weather station?
You want UHI? Fly across a city in a small plane or even a big plane and feel the effect of hot air rising. Then wonder how all that heat buffeting the plane that has been transferred by advection to the air, and carried away vertically by convection, becomes measured by thermometers held 1.2m above the ground in a Stevenson screen. It simply isn’t.
If anything, a well-maintained Stevenson screen over grass on the city’s outskirts, like Sydney Observatory, or even in a park in the city, like at Cranbourne Gardens Melbourne, or a little triangle beside La Trobe Street in Melbourne, is probably the coolest place around on a stinking hot day. You want heat, its above the buildings being blown into the sky by all the AC heat exchanges (that advection word again) …
I think UHI is the most over-rated and least well-understood of all the factors affecting terrestrial temperature data. Furthermore, if it exists it should be measurable in single-site long-term temperature datasets, after unbiasedly adjusting for inhomogeneties caused by site and instrument changes.
Yours sincerely,
Dr Bill Johnston
http://www.bomwatch.com.au
You have not asked that question in good faith, have you?
and your answer is a non-answer ???
Are you trying to be disparaging, or are you really asking me to tell you something you don’t know? Do want me to educate you? Just tell me what you don’t know, and I will do my best to help.
I don’t know everything, obviously.
You are correct in that waste heat from energy production is not taken into account.
I did a calculation a couple of years ago. Just coal. The heat released burning coal (and electricity ultimately become heat) infused sufficient energy to raise the bottom 105 feet (specific heat capacity calculation) by 1 C.
No claims the analysis covered everything. No natural gas. No oil. But it does suggest an area that needs attention.
Or take the body’s internal temperature – if it’s not above ambient, the body is probably defunct.Heat times 8 billion or so – particularly at night.
Anything between a pendulum coming to rest, and the Tsar Bomba fusion explosion result in ephemeral heat, which can make thermometers hotter before it flees to space.
Instead of just blathering why don’t you just show us your math? The siting of the thermometers is a huge issue on this and if you were capable of learning something new you should know that scientists on here are the world leaders in this specific field and you could ask them.
Why should I? What math are you blathering about?
I’d guess a next step could be to look at surrounding geography that acts as a trap for urban heat.
I know the Blue Mountains can have a very large trapping effect on the air in the Penrith/Windsor region.. Air quality and urban heat can be badly affected. Also, its far enough from the ocean not to get much ocean effect
Had to visit a friend out there once on a really hot summer day.. Was horrendous !
I hate the word trap. Heat is the flow of thermal energy across a temperature gradient (hot to cold). If heat is trapped, it is not flowing and therefore is not heat.
That aside, your point is valid and points to a new avenue for research.
Recall part of the LA smog problem decades ago is due to the city being in a geological “bowl.”
“I hate the word trap.”
I keep stating the thermodynamic definition of heat and people keep ignoring it. At least you didn’t.
Ok, the energy that causes the heat cannot escape as easily, so it builds up.
bnice 2000,
Heat trapping on windless days, which is common in the Penrith area in summer (typically when a slow-moving high pressure cell sits directly over Sydney), is a different process to UHI.
Because the Penrith valley is solidly blocked to the west by the Great Dividing Range, it is also almost peculiar to that area. The phenomenon was mentioned by Henry Chamberlain Russell in his 1877 book on the Climate of New South Wales: Descriptive, Historical, and Tabular.
Whereas at other places along the range, the Hunter Valley for example, the geography allows hot air to be replaced by cooler air from the coast, when conditions prevail, it does not happen immediately east of the range around Penrith.
Yours sincerely,
Bill Johnston
“is a different process to UHI.”
But it still allows the UHI effect to build up to even higher levels.
Penrith is far enough away from the coast not to get much benefit from coastal breezes.
As you say, the Hunter region doesn’t have the escarpment feature to the immediate west that Penrith has…
… more a dip in the Great Dividing Range and a shallower slope through the Singleton, Muswellbrook, Scone area.
“Heat trapping . . . .”
Clearly Dr. Johnston doesn’t know the definition of heat.
Silly man Jim Masterson,
Sometimes measured as temperature, heat is when you go out in the yard or parking lot and, in case your body is not working, your app tells you it is HOT. Heat is also when you burn your mouth on a gulp of near-100 degC freshly brewed coffee.
In case you the only person in the universe who has not experienced it, heat is also the 210 degC oven that your mother might have used to cook the Sunday roast!
Under windless conditions in summer or even when there is a high altitude westerly wind, heat trapped by the sandstone walls of Great Dividing Range west of Penrith causes temperatures to rise toward the degF century, which is most unconformable.
(Trigger warning: remember to drink plenty of water, wear a hat, slap on some goo, stay in the shade and don’t get shot, stabbed or run-over by a gassed-up pre-teen driving some car they stole from a pregnant mum balancing groceries and babies at the nearest supermarket … Don’t have bad thoughts either; its fun!)
Get it?
All the best,
Bill
Once again, to quote my thermodynamics textbook:
“Heat is defined as the form of energy that is transferred across the boundary of a system at a given temperature to another system (or the surroundings) at a lower temperature by virtue of the temperature difference between the two systems. That is, heat is transferred from the system at the higher [temperature] to the system at the lower temperature, and the heat transfer occurs solely because of the temperature difference between the two systems. Another aspect of this definition of heat is that a body never contains heat. Rather heat can be identified only as it crosses the boundary. Thus, heat is a transient phenomenon.”
Oh Jim you have a textbook. Your quoted text must be WRONG. It mentions the word TEMPERATURE six times.
How do you measure HEAT without a thermometer again? Oh you hold your pinkie up and start counting … or go outside and see if it is hot!
Why don’t you stick to the point:
Even though, as I have explained, I have reason to believe that by-and-large, all raw temperature data are compromised by site and instrument changes, the paper by Spencer et al., which is what this post is about, uses temperature to measure UHI effects – to quote:
Urban Heat Island Effects in U.S. Summer Surface Temperature Data, 1895-2023.
Cheers,
Bill
Heat is energy. Temperature is not.
Oh, how profound is that???
Like Tim Gorman would say, temperature is not climate!!
b.
The ideal gas law is:
pV = nRT
The term on the left is pressure times volume which gives you an energy result. If pressure is in newtons per square meter and volume is in meters cubed then the result is in joules (actually newton-meters which is the same thing). The term on the right is moles times the ideal gas constant times temperature. This also gives an energy result. Notice that temperature is not equal to energy. You must multiply two constants together to get an energy result.
Dear Jim,
I have a physics book too, possibly older than yours. Wading through “The kinetic theory of the ideal gas”, is quite a slog, and well beyond anything that I want to do now, or that could be summarised here.
Dr Google AI says “The Ideal Gas Law (PV=nRT) describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of an ideal gas.
It’s a fundamental equation in physics and chemistry, providing a way to predict the behavior of gases under various conditions ….
also,
“Applications:
The Ideal Gas Law is used in various applications, including calculating gas densities, stoichiometry, and understanding phenomena like hot air balloons and internal combustion engines.”
In Australia air pressure is measured in hectopascals (hPa) equivalent to millibars (mb) = mb*100 Newtons/sqM, reduced to mean sea-level. At STP (1atm, 0.0 degC), 1.00 mole of any gas takes up 22.4 litres.
Ummm, without doing some numerical calesthetics, like converting pressure and moles from STP to the altitude of the station, picking the right R, and expressing T in Kelvin ….
Why bother when all you want to know is whether T is increasing over time; or in the case of Spencer et al, whether it is warmer over here, than over there.
Why not stick to the issue or go out and water the garden.
Yours sincerely
Dr Bill Johnston
http://www.bomwatch.com.au
Temperature doesn’t define “warmer”, enthalpy does. 77F in Miami will seem *much* warmer than 77F in Las Vegas.
“Why not stick to the issue or go out and water the garden.”
I live in Western Washington State. Currently the convergence zone is watering my garden.
Good for you.
Unlike southwest of the divide, here on the north coast of NSW, we have had buckets of rain. I’m waiting for the ground to dry a little so I can cart a trailer-load of garden prunings to the tip without getting bogged there.
I’m also working on several outstanding weather stations datasets they used to homogenise the ACORN-SAT site at Rabbit Flat in the Northern Territory, also Alice Springs, Tennant Creek and Camooweal (Qld).
All the best,
Bill
“I have a physics book too . . . .”
What amazes me is that you have a physics book in your library. By the way, what subject is your supposed PhD in?
I don’t have a supposed PhD I have a real one. Agronomy mainly, but also hydrology, soils and climatology. Some modelling too. Masters in biology, plant cultivar selection and palatability.
So of course undergrad physics, chem, biochem and stats (and other stuff including climatology). Most of my old texts are just over there, and Dr Google is right here.
What about yours …..
Cheers,
Bill
I’m not as narcissistic as most PhD types. I have several degrees, and I suppose I could use the Master title since I have a masters degree. After completing my degree, I asked my class advisor if I should get a PhD. He said, “It depends. Are you going to teach or do research?” I said, “No.” My favorite degree is after 18 months of flight training, I earned my Navy pilot wings in October of 1973. Have you ever flown a P-3 through a thunderstorm at night? I have. (So have numerous NOAA pilots–I imagine.) It’s essentially a class “E” ticket ride (back when amusement parks used class tickets).
Dear Jim,
Nor am I in fact. I only use the title Dr when establishing my formal qualifications.
I am also not interested in whether mine is better, bigger or brighter than yours, As a navy pilot (or any pilot) you would know the value of meteorological data to day-to-day operations. I’ve been particularly interested in Aeradio in Australia – the combined met-radio service set up in 1939 along our major air routes. I also vividly remember as a kid being violently sick, flying seemingly backwards in a DC3 from Sydney to Dubbo against a strong westerly with bushfires burning across the Blue Mountains below.
Aerado met-data formed the backbone of ACORN-SAT, mainly due to their dispersion – 300-500 km apart mainly north from Tasmania to then Dutch New Guinea and Timor, along the west and east coasts and up the centre through Alice Springs.
And no, I would not fly in anything through a thunderstorm at night!
All the best,
Bill
Speaking of rain, thanks to an almost stationary high-pressure ridge across Bass Strait (40 degS), the central and north coast of NSW received around 8-inches of rain in 24-hours to 9AM. Floods predicted, another couple of inches this morning with 8-inches forecast over the next couple of days – cold, windy and raining steadily at the moment
Some sunny weather would be welcome!
b
The ideal gas law only applies to dry air and sensible heat.
I remember a couple of my profs saying that the ideal gas law only applies to ideal gases.
In the courses I have taken it is assumed that the atmosphere is “close” to an ideal gas. “Close” is in the eye of the beholder! Is being within a degree “close” enough? Is 1 psi “close” enough?
Come on now. An ideal gas has infinitesimally small particles that have no inter-particle forces. A real gas can condense and deposition. Obviously, when that happens, it really departs from ideal.
That is not exactly true. Heat is absorbed energy that changes the internal energy. Internal energy has two parts, kinetic (sensible) and potential or latent (not sensible). That is why steam tables are important in steam driven turbines.
The first law in simple differential form is:
dU = δQ – δW
where U is internal energy, Q is heat, and W is work. The total derivative “d” in front of U is because U is a state variable. The squiggly d’s in front of Q and W is because heat and work are path variables. Q is positive if heat is added to a system, and Q is negative if heat is removed from a system. Likewise, work done by a system is positive, and work done on a system is negative. (This is the Clausius standard. Chemists use a slightly different standard.)
The definition of entropy for a reversible process is
dS = δQ/T
where S is entropy, Q is heat, and T is temperature. Here, again, S is a state variable. Entropy can be positive or negative, because heat can be positive or negative. Temperature is always positive.
Sometimes you will see the first law written as follows:
dU =TdS – PdV
where U is internal energy, T is the absolute temperature, S is entropy, P is pressure, and V is volume.
So you can add heat to a system and you can remove heat from a system. I don’t understand the purpose of your comment.
In the mid-ranges, the Tuhi/Tave trend in the last column of table 3 was kind of a shock.
“I still like Anthony Watts’ approach of simply not using suburban and urban sites for long-term trends.”
And how about not averaging them all together.
Let’s see.
25C and 5C average is 15C.
30C and 0C average is 15C.
So they both have the same micro climate.
Neither case is likely in meteorology – they are useless numbers plucked out of your ear that make no sense.
Neither case is likely in meteorology – they are useless numbers plucked out of your ear that make no sense.
This only highlights the fact that temperature is a piss poor metric for actual heat. Climate science should be using enthalpy.
Look at this from chatgpt
average june temps
las vegas high = 100F
low = 75F
miami high = 88F
low = 77F
average june atmospheric enthalpy
las vegas 54 kJ/kg
miami 83 kJ/kg
Enthalpy is the scientific measure of heat. Miami’s atmosphere contains much more heat than Las Vegas, at least in June.
It is also interesting that Las Vegas and Miami both cool to about the same temperature at night. The CO2 densities in June are pretty close to the same, 4.5×10^-4 kg/m^3 for Las Vegas and 4.8×10^-4 kg/m^3 for Miami. Water vapor, however, is vastly higher in Miami. It would appear that it is water vapor that slows the cooling in Miami vs Las Vegas. Yet CO2 density is not related to WV density in either location according to chatgpt.
Just for comparison the average june enthalpy in Bismarck, ND is 41.4 kJ/kg.
Temperature would indicate that Las Vegas is much “hotter” than Miami even though when actual *heat* is considered Miami is clearly warmer than Las Vegas. When discussing thermodynamics of the biosphere it would seem to be obvious that it is enthalpy which needs to be considered, not temperature.
chatgpt doesn’t return any climate science papers with monthly or annual enthalpy values for any location over any timespan. Wonder why?
Having yourself on again Tim and you need a bot to help.
You say:
“chatgpt doesn’t return any climate science papers with monthly or annual enthalpy values for any location over any timespan. Wonder why?”
They use temperature, that’s why. If you want to know if temperature is increasing, you grab some temperature data.
And oh, by the way, if you want to measure enthalpy, you need a thermometer, and also a calorimeter and some way to squeeze the environment you are interested into it.
Oh, from Dr Google’s AI overview: “In essence, measuring enthalpy change involves quantifying the heat absorbed or released during a process, and relating it to the change in temperature and other physical properties of the system.
Good luck with that. See you on the other side!
Cheers,
Bill
“They use temperature, that’s why. If you want to know if temperature is increasing, you grab some temperature data.”
They are attempting to define CLIMATE! Thus “CLIMATE CHANGE”.
As I showed, temperature is a piss poor metric for climate. Enthalpy is a much better metric.
Why doesn’t climate science want to use the best possible metric for climate?
“ “In essence, measuring enthalpy change involves quantifying the heat absorbed or released during a process, and relating it to the change in temperature and other physical properties of the system.”
Latent heat is obtained from a PROCESS, the process known as evaporation. Latent heat is given up by a PROCESS. The process known as condensation.
Latent heat is not just a change in temperature, it is a QUANTITY. See your quote “quantifying the heat absorbed”. See your quote “other physical properties”.
The quantity of latent heat in a volume of air is related to the mass of water vapor in that volume of air. That latent heat is a component of the enthalpy of that volume of air. You get a much higher quantity of latent heat in the same volume of air in Miami than you do in Las Vegas – because of the different amount of water vapor in the air at each location.
Using temperature alone you would typically conclude that Miami is a “cooler” climate than Las Vegas. Using enthalpy you would typically conclude just the opposite – Miami is *warmer” than Las Vegas.
Guess what most people will tell you about each? (hint: Las Vegas & “dry heat”.)
It may be more uncomfortable because of humidity, but Its only warmer if the temperature is warmer!
And if you want to know if the climate is warming, temperature is the correct metric.
Why don’t you write a paper about your favorite theory, or at least explain how you would fit Las Vegas into a calorimeter. Oh wait, with a thermometer – always a thermometer.
Why not save the trouble and just use temperature?
Cheers,
Bill
“uncomfortable” “climate” ????
It’s not my theory, I don’t need to publish anything. Go look up the name “Köppen“.
Miami = climate Af
Las Vegas = climate BWh
Higher precipitation levels typically coincide with higher humidity which, in turn, typically coincide with higher enthalpies.
Thus while temperatures would tell you Miami is “cooler” than Las Vegas, enthalpy tells a different story.
Temperature is a factor in climate but it isn’t the best metric for climate, enthalpy is.
BS Tim, look up Köppen up for yourself. (For his original papers you need to be able to read German!) I don’t think you have any real knowledge of climate classifications.
Until I had a tidy-up I had a collection of English versions of papers relating to his most important contributions. Climate classifications, which were largely descriptive have been superseded by more objective methods based on data – numbers, Tim, numbers that quantify the climate, not feelings about the climate. See: http://www.bom.gov.au/jshess/docs/2000/stern_hres.pdf.
You and your incoherent snippets of useless information are not even a distraction. You have published nothing and you have no message to sell other than repetitive idiotic concepts that lack any semblance of common sense.
Want to know if its getting warmer, then grab some temperature data and work it out yourself.
Cheers,
Bill
“BS Tim, look up Köppen up for yourself. (For his original papers you need to be able to read German!) I don’t think you have any real knowledge of climate classifications.”
Bill, this is nothing more than the argumentative fallacy of Argument by Dismissal. You don’t actually refute anything.
The Köppen classification considers these major factors: Temperature, Precipitation, and Vegetation. It is highly correlated with natural vegetation zones.
Again, high precipitation areas generally have high enthalpies, as indicated by the comparison of Las Vegas and Miami. You have yet to refute that assertion.
Compare the summer temps in Topeka, KS with Lincoln, NE., about 150 miles apart. Both have their average temp in the mid-70’s degF (25C vs 24C), very little difference. Yet the average summer enthalpy in Topeka is 61 and in Lincoln 57. Significant difference. – due to a higher average humidity in Topeka. And the enthalpy difference is a big reason for the different ag products in both. Topeka: Soybeans, corn, winter wheat. Lincoln: Corn, soybeans, hay.
Temperature simply doesn’t tell the difference in climate. Enthalpy is a much better metric.
“You have published nothing”
I’ve given you the numbers on temperatures, enthalpies, ag products, etc. I don’t have to publish them. They are already published. This is nothing more than an ad hominem attack which is all you have because you can’t refute the numbers.
Temperatures don’t distinguish the difference in climates for Miami/Las Vegas or Topeka/Lincoln. Enthalpies give a much better metric for the differences in climate. It’s up to you to refute that – the numbers are what they are!
Dear Tim,
If you want to know if the climate is warming, grab some temperature data and work it out for yourself.
If you want to know the Köppen classification or enthalpy for a place you ask Ai or some other source. I am unconvinced that you personally could work either index out for yourself.
If you are so full of your latest theory, then prepare and publish a post on WUWT – Changes in enthalpy since 1900 at Topeka, KS – for example.
Multi-character (multi-numeric) indices like Köppen or enthalpy are too blunt to adequately derive sensitive time series and I’m sure your stretchy tape measure is not that useful to measure or estimate them either!
Do you know (are you sufficiently proficient) to describe a vegetation type and thereby from your own knowledge, derive a Köppen classification, which is actually based in vegetation type more-so than climate considerations? By definition, semi-arid vegetation types are typical of low, intermittent rainfall, high temperatures and low humidity for example. Thus vegetation type is the leading index.
Aside from blabbing-on not once have you published anything regarding temperature (or enthalpy) trends or change.
Then you cover your lack of skill and knowledge with some fallacious argument such as “Bill, this is nothing more than the argumentative fallacy of Argument by Dismissal. You don’t actually refute anything.” Until you publish something worthwhile and defendable, consider yourself refuted. Otherwise you are tied to the BS fallacy, the lots of nonsense argument.
Again, if you want to know if the climate at Topeka, KS is warming, grab some temperature data and work it out for yourself. Many examples of the protocols you need are available at http://www.bomwatch.com.au
Publish something about your theory or go away!
Cheers
Bill
I did about four years ago. I sampled over 100 sites with 20 years worth of cooling-degree day values spread over all of the continents.
Most showed no significant changes in the annual cooling-degree dey values (365 degree-days per year). About 10% showed some warming and another 10% showed some actual cooling. Some of the stations were rural, some were at airports, and some were urban.
I didn’t use them. I used cooling-degree days. Neither did I use warming-degree days. Just cooling-degree days.
“By definition, semi-arid vegetation types are typical of low, intermittent rainfall, high temperatures and low humidity for example. “
No kidding? That’s what I live in, a semi-arid desert. The bread-basket of the US.
“Aside from blabbing-on not once have you published anything regarding temperature (or enthalpy) trends or change.”
Again, I don’t need to have published anything. Others have done it for me! This is just an attempt to cast my assertions as being untrue because they haven’t been published – when they don’t *have* to have been published by me!
You keep saying temperature is a good metric for climate. I’ve shown you that it isn’t by offering Köppen classifications as refutation. And all you can do is say I don’t know how to calculate the Köppen index. I DON’T NEED TO CALCULATE IT! IT’S ALREADY PUBLISHED! All you are doing is dismissing my assertion of the Köppen index as showing that climate is based on more than temperature without actually refuting it at all.
I have. I’ve been recording my own data since 2012 using a Vantage View sensor suite. It isn’t “warming” here.
Dear Jim,
So how does Köppen classifications trend over time? They don’t.
The classification is a geographically aggregated index that incorporates vegetation type with a limited assessment of climatic influences such as seasonality, aridity, humidity and temperature. (my words).
According to https://en.wikipedia.org/wiki/K%C3%B6ppen_climate_classification, Köppen divides Earth’s climates into only 5 major climate groups …. “As Köppen designed the system based on his experience as a botanist, his main climate groups represent a classification by vegetation type.” ….
How useful is that for studying enthalpy, which you have been badgering about for the last year or so?
You can look up the classification for a region, but it tells you little about specific aspects, such as actual rainfall, temperature (Tmax & Tmin), humidity, cloud and other parameters for a specific site. Neither does it track changes over time in any of those parameters.
Why you would drag Köppen classifications into a discussion about UHI as measured by thermometers, is incomprehensible. Just because you can look it up, does not make it handy for a discussion about temperature. I can only conclude that you are extremely skilled at seeking attention by wasting everyone’s time.
While climate of a location is described by elements in addition temperature, if you want to know if the climate is warming grab some temperature data and work it out for yourself.
Further, why would you calculate cooling-degree days (using what base) over 20-years, if you are interested in warming at time scales of a century or more. Did you correct your data for site and instrument changes that had nothing to do with the climate? Do you know how to do that? If you used any Australian data, it is probably sufficiently faulty to result in spurious trends.
You say “I don’t need to have published anything. Others have done it for me!” Really, where is the reference that refers to your specific contribution?
Where is your enthalpy stuff?? Did you take into account heat fluxes within the environment – soil, roads, buildings; or just use cooling-degree days (using what base) over 20-years?
My final word of advice is that ff you want to know if the climate is warming, grab some temperature data and work it out for yourself.
Cheers,
Dr Bill
Sticking your head in a 176 degree F oven while standing in a bucket of ice water produces a balmy 72 degree F average. People the world around love living in 72 degree F weather.
Fantastic! Congratulations on your excellent and outstanding peer reviewed study!
In 1989 NOAA looked at about 100 years of data for the USA and concluded there was no trend. Unless the data has been fiddled with the same data should still show no trend.
You can see the New York Times article reporting this almost at the bottom of this one page website:
https://www.juststopnetzero.com/
Thanks for that link.
It says there that this is a NOAA study published in a 1987 issue of the Geophysical Research Letters, covering the period from 1895 to 1987.
And what they say is the same thing the U.S. regional temperature chart shows, that it was just as warm in the recent past as it is today, which means, even though CO2 has increased during this period, the temperatures are no warmer and CO2 has had no apparent effect on temperatures.
Does anyone have access to Geophysical Research Letters for 1987?
We should ask NOAA why they are singing a completely different tune today.
Money, control, and prestige.
“We should ask NOAA why they are singing a completely different tune today.”
Accuracy.
The bottom line was that 65% of the U.S. linear warming trend between 1895 and 2023 was due to increasing population density at the suburban and urban stations
How could that be?
Climate change: Ditching dark roofs in Sydney will reduce temperatures, UNSW study finds
PS: Just stop these things and get painting-
Truck carrying wind turbine gets stuck under Mount Crosby Bridge closing Warrego Highway
Man dies in Japan after blade falls from wind turbine | RenewEconomy
U.S. Senate Minority Leader Chuck Shumer calls Trump a Dictator for stopping further construction of windmills off the coast of New York.
And I call Biden a dictator for starting the construction of windmills off the coast of New York
They are recycling that again? bwahahaha
A while back and US Congressman proposed the same thing along with painting the roads white and everyone driving white cars.
If I live in the north where there is snow, I want a dark roof. A collapsing roof is a much more near term risk than the runaway greenhouse effect.
I’m personally sick and tired of this data analyses. Where’s the laboratory physico-chemical data that proves CO2 is warming up the earth’s atmosphere? Nowhere? Who’s doing lab research on this? CO2 warming up the atmosphere is unlikely, because 1) quantum thermodynamics explicitly says that what CO2 does with IR energy is alter molecular vibrational modes; the energy absorbed is consumed in KINETIC ENERGY OF MOTION, not on THERMAL ENERGY OF HEATING. There’s no proof in the literature, nor from IPCC that this quantum thermodynamics is being violated by CO2. 2) although the apparent additions of human-made CO2 to the atmosphere, CO2 in air is still 0.04%, unchanged. There’s no evidence in the literature nor by IPCC that this analytical chemistry quantification is being violated by CO2. That should end the discussion of CO2 warming up the earth. JBVigo, PhD Environmental Science & Engineering, MS/BS Chemist.
Yes that is all very good Dr Jim, but what does Greta say about it? That is what the BBC and the other mainstream media are focused on.
All this science based fact/talk is great but is secondary to the ‘settled science’ of man made climate change.
When the settled science believers want to really advance their credibility they invite the head hype leader of the UN to tell everyone the world is burning up and seas are boiling.
The inconvenient truth is, Al Gore and too many others have become very wealthy from promoting natural variation is something to do with humanity and caused by CO2?.
I am just off to fashion my new hockey stick, I have a bristle cone pine tree to talk to while I am out there,…
“Settled Science” is the logic fallacy of Appeal to Authority.
The observational basis is thousands of laboratory spectroscopic measurements made over the last 50+ years that quantify how CO2 (or water vapor or methane, etc) absorbs IR energy at different IR wavelengths, air pressures, and temperatures. Those measurements go into the IR radiative codes developed by a number of groups over the years. The theory of what happens on a molecular level is pretty well understood. Importantly, any gas that absorbs IR also emits IR (generally NOT at the same rate, though, because IR emission has a strong temperature dependence while absorption does not). All that is needed for a “greenhouse effect” in a planetary atmosphere is to have IR absorption/emission: the GHE is a necessary consequence of those processes, causing warmer temperatures in the lowest layers and cooler temperatures in the upper layers compared to if those GHGs did not exist. Handwaving arguments about quantum thermodynamics do not change the fact that GHGs absorb and emit IR, and that is all that is required for a greenhouse effect to exist. Here’s my suggestion for directly observing the greenhouse effect using a handheld IR thermometer: https://www.drroyspencer.com/2013/04/direct-evidence-of-earths-greenhouse-effect/
‘The theory of what happens on a molecular level is pretty well understood. Importantly, any gas that absorbs IR also emits IR (generally NOT at the same rate, though, because IR emission has a strong temperature dependence while absorption does not).’
Agreed, but do IR ‘radiative codes’ take into account that IR active trace gases that have been excited by thermal radiation from the Earth’s surface are then predominantly returned to their ground states by collisions with non-IR active gas species, thereby converting their energy into sensible heat and contributing to convection?
Much of the greenhouse theory is based on heat loss being slowed. But it doesn’t seem to always consider that heat loss is an exponential while temperature rise is linear. At some point the heat loss (T^x) sets a boundary condition for the rise of the temperature (T). If the heat loss over time doesn’t equal the heat gained from the sun then the earth eventually becomes a sterile rock. Since CO2 in the atmosphere has been higher in the past and that didn’t happen then the alarm over it happening now would seem to be way overplayed.
“All that is needed for a “greenhouse effect” in a planetary atmosphere is to have IR absorption/emission: the GHE is a necessary consequence of those processes, causing warmer temperatures in the lowest layers and cooler temperatures in the upper layers compared to if those GHGs did not exist. “
As this gradient between the lower and upper atmosphere increases, the heat loss propagated across the gradient also increases. It does so using both radiative and convective transports. It’s not obvious in any of the radiative budgets associated with the greenhouse effect exactly how this is accounted for. It’s the same issue as using the average radiative flux to calculate the heat loss from the earth to space. The heat loss is the integral of the temperature curve and since the curve is an exponential you get much higher heat loss at the start of the decay than the average value will indicate. This heat loss occurs both during the day and during the night.
‘It’s not obvious in any of the radiative budgets associated with the greenhouse effect exactly how this is accounted for.’
All of the energy ‘budgets’ I’ve ever encountered only allocate a small portion of tropospheric energy transport to convection. This seems odd to me given what we can all observe looking skyward, not to mention what David Dibbell, among others, repeatedly points out what the satellites show is happening from space.
At some point I’d like to see some of the ‘heavy hitters’ who are skeptical of CAGW come forth to explain exactly why we should think that radiative transfer models are uniquely applicable to a highly convective lower troposphere.
“At some point I’d like to see some of the ‘heavy hitters’ who are skeptical of CAGW come forth to explain exactly why we should think that radiative transfer models are uniquely applicable to a highly convective lower troposphere.”
It’s similar to the excuse that since the top of the atmosphere is caused to be colder by increased CO2, less energy is radiated to space since cooler molecules radiate a lower flux level. That totally ignores the fact that there would be more CO2 molecules to radiate so the total radiation may not change at all or it may only change a little (maybe a little more, maybe a little less). I’ve yet to see any actual analysis of this based on actual observations and measurements.
According to Happer and van Wijngaarden, CO2 doesn’t effectively emit to space until 80+ km (panel b in the attached figure). The same graphic shows that H2O (WV) is doing most of the heavy lifting well below that level, and we all know that there’s effectively an infinite reservoir of WV in the form of liquid water that covers 70% of the Earth’s surface to a depth of 2+ miles. In other words, CO2 is a nothing burger, which is why there is no geological evidence that it has ever been the ‘control knob’ of the Earth’s climate.
It also totally ignores the fact that it is colder because the air is much less dense. Those molecules could well have the same kinetic energy as molecules at much lower levels.
All true.
Plus:
The earth is an oblate sphere.
The solar energy at the day-night terminator is substantially less than when that same surface area is at high noon.
In addition, the optical depth of the atmosphere at the day-night terminator is substantially deeper than at high noon just due to spherical geometry versus a EM wave vector.
Greenhouse effect does not exist. Greenhouse gasses only exist in greenhouses.
We really need to use correct scientific terminology. Every time we parrot the climate alarmist vocabulary, we raise their credibility.
Unfortunately, there are lots of badly named scientific terminologies that we are stuck with–for example: heat capacity. They named x-rays expecting to have them given a better name when it was discovered what they were. The same is true with alpha, beta, and gamma rays.
Congratulations on your paper, and for having the best available unbiased available temperature dataset! I knew that before your paper was published.
Yes, CO2 is a greenhouse gas, but it’s not affecting global temperature. CO2 concentrations lag temperature and [CO2] is integrally related to temperature. I won’t defend those statements right now, but would be happy to.
Because of that integral relationship I’ve found a single equation, in integral and differential forms, can be used to predict temperature from [CO2] and [CO2] from temperature.
This equation works well with unbiased data. UAH Globe and Glob_Ocean produce similar results with Ocean working ever so slightly better — as it should.
With land and UHI bias, predicted temperatures appear low, and [CO2] predictions are high and have more curvature.
It’s H2O.
Dr. Spencer, here is my nit to pick.
When one examines land rural areas since 1900, Tmax has changed very little. Tmin was the same until about 1980 when a noticeable increase in monthly averages started in the U.S.
It would seem that Tmax would be the most affected by CO2 since that is when the maximum insolation occurs. Yet, there doesn’t appear to be a large change. Not even high temperature records are being overwhelmingly set.
Water vapor doesn’t affect temperature (sensible heat) so something is amiss.
Here is a representative graph from NOAA.
Jim makes an interesting point. A reason that TMIN might be higher at night in rural areas than it was pre-1980 is possibly the change of farming methods to use continuous cropping, and more crop vegetation due to fertilization. The same amount of daylight heat would be released more slowly to outer space at night if there is more vegetation covering the surface….thus causing local rural weather stations to read a degree or two warmer….
Actually I think it may have to do with the advent of ASOS devices in the U.S.
The assertion that “Water vapor doesn’t affect temperature ” is misleading. WV is an IR active gas that has been increasing about 1.4 % per decade, on average, since before it started being accurately measured globally in Jan 1988 by NASA/RSS using satellite-based instrumentation. Part of the WV increase can be calculated from planet warming. The rest is from increasing population and especially from increasing irrigation. The increasing WV can account for all climate change attributable to humanity. https://watervaporandwarming.blogspot.com
Absolutely. More WV between the Sun and the surface results in lower temperatures, as John Tyndall (a keen alpinist) pointed out more than a century ago.
Lower the WV, and you get Death Valley or Lut desert temperatures. Remove the whole atmosphere, and temperatures really soar! 127 C or so on the Moon after the same exposure time.
The moon’s day is 14 Earth days so the heating you refer to takes place over a much longer exposure time. At sunrise on the moon the temperature is about 100K.
After the same exposure time. Basic physics.
Water vapor also intercepts IR from the sun thus keeping it from heating the surface by redirecting a portion of it back toward space. That’s a cooling process as far as the earth’s surface is concerned.
Why do you keep showing that Kansas graph when making a point about the difference between TMax and TMin? Your graph is showing TMean. How can you tell from it whether minimum of maximum temperatures are warming faster?
Here’s my graph based on ClimDiv data for Kansas, showing TMin and TMax annual averages.
The trend from 1895-2024 is
TMin: +0.09 ± 0.03°C / decade
TMax: +0.07 ± 0.04°C / decade
So TMin has been warming slightly faster, not significantly so.
What about since 1980.
TMin: +0.15 ± 0.15°C / decade
TMax: +0.32 ± 0.20°C / decade
A lot more uncertainty, but if anything it seems that TMax has been warming faster than TMin.
“the fact that GHGs absorb and emit IR, and that is all that is required for a greenhouse effect to exist”.
That poses the question: how much of that GHE is at work in the atmosphere?
I would like people to consider this seriously as opposed to the old: without the GHE it would be 18 degrees cooler..
Dear Dr Roy Spencer
Your paper is not about the atmosphere at large, but specifically about temperatures measured 1.2m (4-feet or so) above the ground.
From the many Australian datasets I have examined (some reported on in detail at http://www.bomwatch.com.au) no UHI effect is detectable. Furthermore, all sites are affected by site and instrument changes many of which are not reported in Bureau of Meteorology metadata. Combining all the available data into one great big beautiful dataset hides the reality that resulting trends are spurious.
As I have already said, despite all the blather and hypothesizing mostly by people who have never undertaken weather observations, while the US data may be different, I believe UHI is the least-well understood factor likely to impact trend at any Australian weather station sites.
Yes we have changes at airports, new runways, houses near-by, spraying-out the grass, security fences going up entrapping heat, Stevenson screen changes, and roads being sealed nearby, but their effects are not UHI. Bundling data together without taking those factors, and data quality considerations into account is my experience, is a mistake.
I would like to see data for one single long-term weather station analysed for step-changers, cross-referenced with independent site data/aerial photographs etc, and checked for consistency (quality), before I would view the data as useful for depicting trend. This is what BomWatch protocols are all about! One set of procedures that can be applied universally across all Australian datasets (I have not analysed any US data so I’m sticking to what I know).
What is needed is an assessment of data quality, analysis of co-variables, verification of the outcome and post-hoc analysis of residuals, on a site-by-site basis. If the work is thorough enough, no Australian Journal will publish it!
See for example https://www.bomwatch.com.au/climate-of-gbr-townsville/, and for a full report, https://www.bomwatch.com.au/wp-content/uploads/2025/03/Bomwatch-Halls-Creek-backstory-edited-1.pdf
Yours sincerely,
Dr Bill Johnston
http://www.bomwatch.com.au
Roy, you wrote –
Completely irrelevant, sorry. All matter absorbs IR, all matter above absolute zero emits IR.
You link about “evidence of Earth’s Greenhouse Effect” states –
Unfortunately this is simply ignoring the part of reality you refuse to acknowledge – removing the atmosphere during the day would allow the full intensity of the Sun’s rays to reach the surface – resulting in maxima the same as those on the Moon after the same exposure time – about 127 C.
Hence the highest surface temperatures on Earth are found where the poorly named “greenhouse gases” are least – places like Death Valley and the Lut desert.
No, Roy, adding CO2 (or H2O) does not make it hotter.
You also ask in your link –
The answers, in fact, are quite simple, and not requiring a GHE. Before you make any disparaging remarks, I invite you to provide a consistent and unambiguous description of this “Greenhouse Effect” which you talk about.
Sorry, there is no GHE. Four and a half billion years of continuous sunlight has not made the surface hotter – atmosphere, CO2, H2O, or any other gas notwithstanding.
You are on the right track with your latest paper. Thermometers respond to heat – not CO2 in the air.
“Completely irrelevant, sorry. All matter absorbs IR, all matter above absolute zero emits IR.”
Not true, that doesn’t apply to gases!
Yes it does, unless you can demonstrate it doesn’t by experiment.
KINETIC ENERGY OF MOTION is THERMAL ENERGY OF HEATING.
They have hijacked and redefined thermalization. It’s true meaning is to move towards or achieve thermal equilibrium. The bastardized meaning is IR hits a CO2 molecule and is thermalized heating the atmosphere.
And you have a Ph.D? I very much doubt it…if so, you missed the majority of molecular thermodynamics somehow….
Indeed, and talking about vibrational modes, CO2 has only one, water vapour 3. Given its proportionality it gives tiny mouse CO2 no chance to move the elephant H2O yet that is what the warministas say..
At this point, UHI is so ubiquitous that we should just ignore using it for measuring global temperature averages/trends, or for very large countries like the USA, Australia etc. Individual stations can still be used to produce the moving 30 year averages, for the interest of people living or traveling there. For everything else, just use the satellite data.
Satellite data has its own problems. It can’t measure path loss through the atmosphere at sampling time. Varying path losses over the satellite path can only be partially compensated by using a parameterized value as a constant for adjustment thus adding measurement uncertainty to the data. The measurement uncertainty of the satellite data is never actually put forth, only the sampling error. The measurement uncertainty, like most temperature data sets, probably overwhelms the possibility of actually identifying anything in the tenths or hundredths digit. You simply can’t reduce inaccuracy in the data by averaging since you are measuring different things in different environments.
Huzzah.
Dear Dr Spencer,
It is not my understanding that “Homogenization looks at year-to-year [time domain] temperature changes at neighboring stations, not the spatial temperature differences [space domain] like we do”.
The consensus homogenization paper (Petersen et al 1996 – Homogeneity adjustments of in situ atmospheric climate data: a review; https://doi.org/10.1002/(SICI)1097-0088(19981115)18:13%3C1493::AID-JOC329%3E3.0.CO;2-T) makes clear that first differenced (monthly) data are only used to select data for stations that are highly correlated with target-site data, in order to derive a multi-site comparator dataset to use to detect and adjust for site-change effects. The combined multi-site correlated comparator dataset is assumed to reflect “the climate”, while deviations (differences) between the target and comparators evidence “non-climate” effects (BS of-course).
If you read the Petersen article carefully, you will find that it is a complicated way of making arbitrary changes, and applying adjustments that are disproportionate to the effect they aim to correct.
On the other-hand, as most long-term raw datasets are compromised by site and instrument changes, many of which are time-correlated, they should not be used for any serious study without careful verification that each dataset is fit-for-purpose. Eyeballing your study, I can’t see quality control routines applied to any datasets you have used.
How do you know that any of the data in your study are truly homogeneous?
What is the use of using “spatial temperature differences”, if all data are compromised to some extent?
Yours faithfully,
Dr Bill Johnston
http://www.bomwatch.com.au
Bill,
As you know, I have prepared several articles about properties at weather stations that could be classed as “pristine” for UHI studies. I have not promoted these with any enthusiasm because each version has drawbacks. A version that is starting to approach publication quality requires a great deal of work, almost like studying millions of individual daily temperature observations to create a data base for 50 or so stations that could be regarded as representative and not anomalous.
I am now close to getting the data in a form that supports my emerging contention that the bulk of the historic raw data curated by BOM is unfit for the study of UHI. The BOM official homogenisation of this raw data into ACORN-SAT is unsafe to use.
This is not in conflict with your conclusions that there is no significant warming signal in the dozens of BOM stations, pristine or urban, that you have studied in a different way. If no overall warming signal is present, there is no UHI signal strong enough to show itself. Geoff S
Nice response!
“highly correlated with target-site data”
Since when does correlation imply “equal”?
I did not say anything about equal – read the paper!
Stop being disparaging! Someone might take offence!
Take all the offense you want; have a tanti if you wish. At least butt-out of other people’s conversations.
Tim Gorman specifically said “Since when does correlation imply “equal”?
Who said anything about “equal”. Tim’s a silly non-answer to an issue that was not mentioned in the first place!
I also referenced the primordial paper dealing with homogenisation. The paper describes comparator site selection based on correlation of first differenced data. You know about first differencing and why it is done don’t you? You know it is still done don’t you?
It is that paper you should both read to get a grip on homogenisation methods.
Cheers,
Bill
Hang on, it’s only me that’s allowed to be offensive and disparaging, isn’t it?
Oh, sorry – you mean everybody else but me is allowed to be offensive and disparaging, is that it?
You wrote –
And precisely why should I do that? Do you imagine I care about “homogenisation”? Where have I even mentioned the word? You’re a strange one – giving me unsolicited advice about something I haven’t even mentioned!
At least you don’t believe in the GHE, so that’s something.
All my best to you.
m.
You said: “makes clear that first differenced (monthly) data are only used to select data for stations that are highly correlated “
The issue is whether homogenization is a legitimate methodology. In order to use interpolation of a temperature value from Location1 at Location2 the value supplied from Location1*has* to be considered to be equal to the value expected at Location2. Otherwise you are just creating garbage data.
Correlation does *NOT* imply equality. It is truly just that simple. It simply doesn’t matter if the data at Location1 is “highly correlated” to the data at Loaction2. Correlation does not imply equality.
Had you said: “used to select data for stations that are close in value” it would have raised even more questions since stations even a kilometer apart can have significantly different temperatures.
Dear Tim,
You obviously have not read the paper or if you have, you have not understood it. You probably did not read or understand Roy Spencer’s paper either.
Correlation of first differences aims to find stations that closely mimic the behavior of the target station. Nothing to do with equality, everything to do with ‘pattern’.
First differencing is usually used to remove (minimise) autocorrelation caused by seasonal or other cycles. In some cases, if first-differenced data are not independent, second-differencing may be necessary.
Pearsons correlation coefficient presumes paired data are independent and not influenced by a confounded third variable such a a cycle or trend. That in essence is why they use correlation of first differences to select comparator sites.
And by the way, I did not have to rely on artificial intelligence, I used my own!
All the best,
Cheers,
Bill
P.s I find argumentative people who really have nothing to add to a conversation boring, so don’t expect any more replies.
The issue isn’t autocorrelation. The issue isn’t independence. The issue *is* equality.
If the temperature value at Location1 is not the same as at Location2 and you substitute the value for Location1 into the Location2 data then you have corrupted the data for Location2. It simply doesn’t matter if the two data set are highly correlated. Correlation does not guarantee equality!
If the value at Location2 should be 2C and you substitute 1.5C for it because that is what Location1 has for a value then you have corrupted the data for Location2. It simply doesn’t matter if the Location1 data set is highly correlated with the data set for Location2. Correlation does not provide a test of equality.
Correlation only tells you that the two data sets move similarly. Data set 1 (1,2,3,4,5) is highly correlated with data set 2 (2,4,6,8,10) yet the values are not equal and neither are the steps between the values in each data set.
Nice essay. It clearly shows that there is a UHI effect.
I’m not sure that (Tmax + Tmin)/2 is the best data item to use. My research shows that Tmin is the culprit in most warming for the last 40 – 50 years. Using Tavg lets warmists still trumpet that high temperatures are going to kill all life on the planet. That propaganda needs some actual data to oppose it.
(Tmax + Tmin)/2 does not yield an average temperature. Not to mention that an average temperature is basically useless.
Look at the hourly temperatures at your favorited weather station. The data do not comprise a sine wave. Average the 24 1-hour temperatures and compare to (Tmax – Tmin)/2. Only if you are lucky will they be the same
A global average temperature is bogus. I submit a higher information quality is achieved using the statistical median. Median is not mean is not average. Median is a value that delineates the high 50% from the low 50%. This should be done for high temps and low temps. Why? During the course of the day you might experience the average temperature twice for a few minutes. It does not define the micro climate.
The data will show a pretty good (not perfect) piece of a sine wave during daylight hours. But the average value of a sine wave is (.63)Tmax and not Tmax/2. At night the data will show a pretty good (not perfect) exponential decay. But the average value of the heat loss associated with an exponential decay is not (start+end)/2 either.
“A global average temperature is bogus.”
Yep.
Temperature is *not* a good metric for climate just as it isn’t a good metric for enthalpy. There are multiple other factors that modulate the climate just as there is for enthalpy.
The median temperature isn’t much better. It’s why other disciplines have moved to using heat accumulation associated with the degree-day values – essentially an integral of the temperature over the 24 hour period. A median value can be the same for two different climates while the integrative degree-day value will be different.
Some do some don’t. I’ve actually looked at some ground temperatures and they are as close to a sine. Closer than a monthly temperature is to a normal.
Trying to find the inflection point between a sine and a an exponential decay is difficult. It obviously occurs when insolation falls below radiation. Where that is, is hard to tell visually.
As the earth warms, part of the insolation is diffused downward meaning less upward. This may be why Tmax has not changed much. Soil temps at depth show quite a bit of warming during spring and summer, limiting the radiation going up and causing atmospheric warming. During fall and winter the soil starts to give up heat keeping temperatures a bit warmer.
Radiation budgets that simply use the scourge of averaging don’t take this into account. The earth is a heat sink, and as such, modifies the atmospheric changes.
All you have for most weather stations is daily Max & Min.
You can’t calculate a median from two values.
However, (Max+Min)/2 = average by definition.
Cheers,
Bill
Huh? In this case the average and the median are the same. You only have two values and therefore they become the middle values as well. The median is the average value of the two middle values, i..e if the number of values in the data set is even the median is the average of the two middle vales.
BS Tim. You have gone-off somewhere.
There is no “middle value” or central tendency when you only have two values. You can only calculate an average, which is the sum of the two values divided by 2. You also can’t calculate a standard deviation for two values, except of course by GUM.
Median and average have two distinctly different meanings and it is sad that you confuse the two.
Cheers,
Bill
“Average” is a vague term which could refer to any number of measures of centrality. It is often used to mean the arithmetic mean, but it ain’t necessarily so.
Of course there is. It’s half way between the 2 values.
It may not physically exist, but that’s what it is.
It’s the median of an even-numbered set of values, by definition. If there are an even number of values, the median is the mid-point of the 2 middle values.
Yes, but which average? You described the mean, which is also the mid-point, or the median, or the lower value plus half the difference, or the higher value minus half the difference.
Eh? It’s sqrt (sigma(x_i – x_bar)^2/n), same as any other populatian standard deviation.
If you’re silly enough to have a sample of size 2, it’s sqrt(sigma (x_i – x_bar)^2)
oc: I’m sorry. I didn’t read your reply before writing mine. I think we both are saying the same thing.
No worries.
I suspect it’s currently not good fishing weather up Bill’s way, so he’s after other sorts of bites 🙂
Oh dear Old Cocky,
How can you sustain an argument that “It may not physically exist, but that’s what it is” … if it does not physically exist; and how many averages are there for the string 22.3, 27.8?
As you know, the median is mostly used to find the mid-point of a string of numbers that are not normally distributed. For data that are normally distributed. the mean = the median, and the distance between the median and the 25th percentile = the distance between the median and the 75th percentile, likewise the 5th and 95th percentiles.
If you are working with medians, I was advised that the least biased measure of variation, is the median of deviations from the dataset median.
Excel calculates “average” of a string, which is actually the mean, and whatever is calculated still has to be expressed with units attached. It also calculates the median, but for two numbers, median-average = mean.
I stand corrected on the point of calculating an SD, but it has no distributional qualities (i.e. one does not know if the two numbers are from a normal distribution or not.
Looking at Stack Exchange, a useful go-to (https://stats.stackexchange.com/questions/230171/is-it-meaningful-to-calculate-standard-deviation-of-two-numbers)
“…. 95% 2-sided error bars for n = 2 data points require a multiplicative factor of 12.71 on the sample standard deviation, not the familiar factor of 1.96 based on the Normal (Student t with ∞ degrees of freedom). The corresponding multiplicative factor for n = 3 data points is 4.30.
The situation gets even more extreme for two-sided 99% error bars (confidence intervals) …”
CIs become factors higher than a mean, which makes them meaningless. Reporting CIs reflects a lack of replication, which is not the same as unsound methodologies. Better giving the two numbers rather than trying to interpret what they mean.
All the best,
Bill
Good morning to you, too, Bill.
The same way as the arithmetic mean, which is far less likely than the median to match a value from the sample or population. They are just measures of centrality. What could be more central than the middle value of a sorted data set or halfway between the two middle values?
Well, in common use, there are the arithmetic mean, the median and 2 modes. There are sure to be plenty of more exotic measures as well.
I’d put it the other way around. If the median isn’t approximately equal to the mean, we know that the distribution is skewed, and in which direction. It’s a good diagnostic tool.
Excel is a Microsoft product, so one shouldn’t expect it to be correct 🙂
For 2 numbers, the median and mean are the same.
If that was a typo, yes; for 2 numbers median == mean. “Average” is an ambiguous term, even if it’s usually conflated with the mean.
There really isn’t any point in calculating the s.d. of 2 values, but it can be done. Just because it cane be done doesn’t mean it should be done.
The s.d. is just a measure of dispersion, so it doesn’t tell you anything about the shape of the underlying distribution. Neither does the mean in isolation.
That pretty much applies to any small data set and summary statistics. Graph them first.
The median and the average having two different meanings doesn’t mean they can’t be the same value in a set of data!
And of course you can calculate the standard deviation of a data set with just two values! If you can calculate an average for the two values then you can calculate a standard deviation. What makes you think you can’t?
A data set with only two stated values is decidedly Gaussian with an equal distribution of stated values less than and greater than the average value. Except the distribution of daily temperatures is *not* Gaussian. So you have translated a non-Gaussian distribution into a Gaussian one with all of the attendant problems associated with such a translation.
It gets even more complicated when considering measurement uncertainty. There is nothing that says because the stated values of the data are Gaussian that the measurement uncertainty distribution has to be the same. If a measurement device has more measurement uncertainty when in open air and being impacted by direct sun insolation than it does at night with no sun then the measurement uncertainty is definitely not Gaussian and the measurement uncertainty should be added using root-sum-square. Think of how you handle measurement uncertainty when you are taking measurements of different things under different environments while using the same instrument for both. You can’t just assume that the measurement uncertainties will cancel because they will create a Gaussian distribution. You can only assume a partial cancellation — thus the root-sum-square.
The physical effects that cause the max-min thermometer to record a Tmax each day are not the same that record a Tmin. They are different entities with different properties. Usually, one happens in sunshine hours, the other in the night. They should not be averaged. They are samples from different populations, statistically. Taverage might be more easily available in historic data bases, but that does not justify or excuse its use. Geoff S
yep. You are averaging the heights of a mixed herd of Shetland ponies and quarter horses. Anyone that thinks that average has any real physical meaning is off in “statistical world” which has no congruence with “teal world”. Anyone that ordered saddles for that herd based on the “average height” would lose a lot of invested capital.
Tell us the one about measuring lumber with your stretchy tape measure Tim … or was it ball-bearings.
The average of a string of numbers has got meaning Tim.
The average daily temperature, is by definition (by convention if you like) Tmax + Tmin/2. However, I always work with daily Tmax and Tmin separately.
(And yes dear old cocky, due to all the rain, fishing is off the agenda. However, I’m making wooden toys as part of our woodworking group’s contribution to a charity, at Christmas. (Despite all the warming that doesn’t exist, many kids are doing it tough!) Time to get to-it!)
Cheers,
Bill
Good on you. That’s a nice thing to do.
If you think tape measures aren’t stretchy then you’ve never done precision measurements with a metal tape measure under different conditions.
If you think ball bearings don’t have measurement uncertainty then you’ve never done root cause analysis on a failed ball bearing.
“The average of a string of numbers has got meaning Tim.”
Here we go with the climate science meme of “numbers is numbers”. Measurements are not just “numbers”. The average of those measurements don’t always mean anything in the real, physical world.
Would you design a bridge span load capability using the “average” shear strength of the beams used in the construction?
Are you not going to complain about the lack of uncertainty estimates in the paper, or how many significant figures he uses?
From the paper.
I have already made note of the fact that Tavg hides information that is relevant to discovering the actual rise in temperature. Maybe you didn’t notice that.
Dr. Spencer has addressed some of the issues.
I would note that Dr. Spencer and you examine closely the cause of the increase in temperature starting ~1980. It appears very similar to many of the NOAA graphs and quite possibly show a change in measurement devices with ASOS.
I haven’t really had the time to dig into the paper but I am disappointed that measurement uncertainty in the temperatures was not dealt with adequately. I do believe that using Tavg hides too much important information and this paper has not proven otherwise.
Nothing you say here addresses my point. You keep insisting that anyone who doesn’t include uncertainties when quoting any figure, is committing a scientific fraud, as is anyone using too many significant figures. Yet here we have a paper that contains virtually no mention of uncertainty, and your response is “Nice essay. It clearly shows that there is a UHI effect.”
Measurement uncertainties in the data are not really the issue. It’s the cumulative multiple linear regressions, some using power laws, with very small correlation coefficients, that must have uncertainties, and these are going to propagate through the model. How much uncertainty should there be in the final 22% of the US summer warming trend is due to UHI?
You are hilarious. You criticize Dr. Frank’s paper that said the same the same thing you just said – uncertainty propagating through the model.
Perhaps you need to reread Dr. Frank’s paper to find the reasons he used.
As for me, I’ve already done the research into the CRN network to know the hockey stick is bogus for rural stations. And, by the way, there are many rural stations around the globe that are similar with far longer records than CRN. Australian temperatures have shown the identical lack of warming.
You have claimed to be knowledgeable concerning measurement uncertainty, so let’s see your detailed analysis!
“You criticize Dr. Frank’s paper that said the same the same thing you just said”
No. I criticized it for his nonsensical propagation of uncertainty.
“Perhaps you need to reread Dr. Frank’s paper to find the reasons he used.”
The “reason” he used is ridiculous, and inconsistent.
“As for me, I’ve already done the research into the CRN network to know the hockey stick is bogus for rural stations.”
Amazing. You were able show this based on 20 years of data. Will you be publishing this research any time soon?
And you are still avoiding my point – which is you claiming that anything stated without uncertainty is scientific fraud, yet not addressing the complete lack of uncertainty in Spencer’s paper.
“You have claimed to be knowledgeable concerning measurement uncertainty”
I’ve never cl.aimed any such thing. I just understand the statistics enough to refute your absurd claims.
“so let’s see your detailed analysis!”
Of what? If you mean Spencer’s paper, it’s not up to me to do that work for him.
You said: “You keep insisting that anyone who doesn’t include uncertainties when quoting any figure”
The operative words here are “any figure”. No, it applies to MEASUREMENTS, not just any figure.
“I just understand the statistics enough to refute your absurd claims.”
This, along with the above statement, just shows your dependence on the climate science meme of “numbers is just numbers”.
The use of uncertainties in measurements is *not* absurd. And as several experts on measurements have said (and you’ve been given the quotes) it is not possible to analyze systematic measurement uncertainties using statistical analysis. If you can’t analyze the systematic portion of measurement uncertainty then you can’t determine the size of random measurement uncertainty. The only thing you can do is propagate measurement uncertainty. And measurement uncertainty grows with every measurement added to the total.
Have you figured out yet that average measurement uncertainty is *NOT* the measurement uncertainty of the average?
“This, along with the above statement, just shows your dependence on the climate science meme of “numbers is just numbers”.”
You are dealing with numbers. If you don;t understand what the equations you use mean, you will get the wrong numbers. Pointing out that they are not “just” numbers won’t help you.
“The use of uncertainties in measurements is *not* absurd.”
I didn’t say the use of uncertainties is absurd, I said your claims about them are. Specifically the one you keep returning to, that the average of multiple measurements will grow the more measurements you include.
“…it is not possible to analyze systematic measurement uncertainties using statistical analysis”
And there’s that familiar Gorman diversion. When in trouble just change the subject. And what do you think the point of Spencer’s paper is, if not to analyze the systematic effects of UHI, using statistical analysis.
“If you can’t analyze the systematic portion of measurement uncertainty then you can’t determine the size of random measurement uncertainty.”
Of course you can. That’s the whole point of a Type A uncertainty. Measure something multiple times and take the standard deviation as size of the random measurement uncertainty. Any systematic error is irrelevant to the result.
“And measurement uncertainty grows with every measurement added to the total.”
That depends, as has been explained to you constantly for the last 4 years, on how you are combing the different measurements.
“Have you figured out yet that average measurement uncertainty is *NOT* the measurement uncertainty of the average?”
Have you forgotten the 1000 other times you have asked this same inane question, and been given the same simple answer. The average measurement uncertainty is not the measurement uncertainty of the average. I have never claimed it was, no-one with any intelligence has ever claimed such a thing. the only person who claims such a thing is Pat Frank.
‘The average measurement uncertainty is not the measurement uncertainty of the average….[T]he only person who claims such a thing is Pat Frank.’
Bellman,
Can you please save me a bit of time on this and provide a citation for what you believe Pat Frank is actually claiming re. calculating the average uncertainty of a series of measurements? Thanks.
Bellman doesn’t understand enough metrology to be able to understand the measurement uncertainty of a set of instruments and the measurement uncertainty of a set of measurements.
I’m guessing he doesn’t understand what the +/- 1.8C measurement uncertainty for ASOS stations actually means.
“Can you please save me a bit of time on this and provide a citation for what you believe Pat Frank is actually claiming ”
https://pubmed.ncbi.nlm.nih.gov/37447827/
Key point is equations (5) and (6), which convert the uncertainty of a single daily observation, into the uncertainty of a monthly average and then into an annual average. The resulting uncertainty is always the same as for a single daily value.
In effect he uses RMS, and just squares the uncertainty, multiplies it by N, then divides it by N and takes the square root. He also multiplies it by 1.96 to get the 95% expanded uncertainty, before dividing it by 1.96 to put into the next equation.
Of course, this is only the average uncertainty because all the uncertainties are the same size. It’s the average of the variances rather than the standard deviations.
Thanks, I’ll take a look, hopefully sooner rather than later…
Okay, I’ll weigh in here that there are two sources of error around any temperature measurement, the first being instrument error, which presumably is a systematic bias. and the second being measurement error, which is more optimistically presumed to be ‘random’ in nature.
If the above presumptions are true, then the latter will tail off rapidly as the number of measurements in the observation period increases, but the former will always remain constant no matter the periodicity of the average or how many observations are incorporated therein. (I’m assuming, of course, that we’re talking about a single instrument or ‘observer’ here, otherwise we have to incorporate additional errors into our estimates).
I didn’t have time to delve into Dr F’s paper, but if he’s maintaining that the same amount of uncertainty applies to both a monthly or an annual average, as opposed to a larger amount that also includes measurement error, I would agree.
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/01%3A_Introduction_to_Physics_and_Measurements/1.03%3A_Measurements_Uncertainty_and_Significant_Figures
From your site which is very correct.
This is exactly what I have already shown Bellman from Dr. Taylor’s derivation of dividing by √n. His derivation also requires the means of each measurement to be the same.
In other words, the samples need to be identical.
I’ve resounded to Frank from NoVA comment here:
https://wattsupwiththat.com/2025/05/15/dr-roy-spencer-our-urban-heat-island-paper-has-been-published/#comment-4075030
I’ve provided the link because it’s likely my response will be lost behind all the usual Gorman nonsense, due to the terrible threading here.
Now, to Jim’s point.
“This is exactly what I have already shown Bellman from Dr. Taylor’s derivation of dividing by √n.”
If you stopped trying to think you need to educate me on this, when we’ve been over it so many times in the past 4 years, you might have learn something.
Taylor is only showing what has been known for decades. The derivation is quite simple and relies only on the concept of independent random variables. You can apply them to the sum or average of any number of different random variables. The √n comes from a special case when all the random variables have the same variance, but it works regardless of whether they have the same mean or not. (This is distinct from the CLT which requires identically distributions.)
Even if they have different variances, you will still find the variance of the mean decreases with sample size.
I can write a very long explanation of how the different sums and average work if you want.
As usual, you have no concept of the necessary assumptions to perform a mathematical derivation. Let’s look at the derivation that Frank from NoVA showed. It is from a university and parallels Dr. Taylor’s derivation.
Let’s look at Rule 2, Eq. 1.3.3,
Δz = z · √[(Δx/x)² + (Δy/y)²] (Eq. 1.3.3)
Notice and keep in mind that x and y are different values, while Δx could easily equal Δy depending on the repeatable conditions.
Now look at “The Uncertainty in the Mean” section. You should notice this ends with the same derivation as Dr. Taylor. The first equation to examine is the calculation of the uncertainty of the numerator in Eq. 1.3.9
x̅ = [Σ xᵢ (1, N)] / N (Eq. 1.3.9
Using Eq. 1.3.10 we get,
√[(Δx)² + (Δx)² + … + (Δx)²] = √N · Δx (Eq. 1.3.10)
One should note that the Δx values are all the same. This means multiple measurements of the same thing under repeatable conditions (GUM 2.15) in order to obtain the exact same values. This is the exact same condition that Dr. Taylor posits in his derivation.
Replacing the numerator of Eq. 1.3.9, with (√N · Δx) we obtain,
x̅ = (√N · Δx) / N = (√N · Δx) / (√N · √N) = Δx / √N (Eq. 1.3.11)
At the end, all the “Δx” values must be the same for Eq. 1.3.3 to be satisfied and all the “x” values must also be the same.
Otherwise you end up with an equation similar to Eq. 1.3.3. You may have similar uncertainties when using repeatable conditions, but the values of the measurements are different. When this occurs, the √N disappears because you are forced into Eq 1.3.3. It will look like:
Δz = z · √[(Δx/x)² + [(Δx/y)² + …+ [(Δx/z)²]
You will have a combined uncertainty of the mean based upon fractional uncertainties just as in Eq. 1.3.3. There won’t be a √N because the denominators are all different which violates Eq. 1.3.10.
“As usual, you have no concept of the necessary assumptions to perform a mathematical derivation.”
If you disagree, then you need to show your working. Show how all your assumptions are necessary for the proof.
“One should note that the Δx values are all the same.”
Yes, because the assumption is all the measurements here have the same uncertainty. This allows for the simplification of simply multiply the variance by N. The same applies when you take a random sample from a population.
” This means multiple measurements of the same thing under repeatable conditions”
That’s the conclusion you jump to. Nothing in the equation says that each reading has been made with the same instrument by the same observer or that it is measuring the same thing. Just that the uncertainties are all the same. That might be the most likely thing you do in the laboratory, but the equation works just as well for measuring different things with different instruments, as long as the assumed absolute uncertainty is the same for each.
” and all the “x” values must also be the same. ”
where does it say that? If all the x values are the same there’s little point taking an average. Look at 1.3.9 again, the sum of N x_is. The subscript should tell you these are not all going to be the same x.
“Otherwise you end up with an equation similar to Eq. 1.3.3.”
No. 1.3.3 is specifically about multiplying and dividing values. This is your and Tim’s problem from the start, you just cannot learn to apply the correct equation top the correct circumstance. It’s really simple. When you add or subtract values you add the absolute uncertainties in quadrature. When you multiply or divide values you add the relative uncertainties in quadrature, to get the relative uncertainty.
You cannot mix and match this. To get the uncertainty of a sum you first have to use 1.3.2, then to get the uncertainty of the average use 1.3.3 – which in this case means converting the uncertainty of the sum to a relative uncertainty, adding zero, and that gives you the relative uncertainty of the average. Then convert this back to an absolute uncertainty.
The result is that the uncertainty of the mean is equal to the uncertainty of the sum divided by N. This is exactly what the article does in 1.3.11, when it applies Rule 2. It takes the uncertainty of the numerator and divides by N. It’s just that in the case where all the uncertainties are the same size, this reduces to
√NΔx / N = Δx / √N
If the uncertainties are not the same you have
√(Δx1^2 + Δx2^2 + … + Δxn^2) / N.
Except you *NEVER* do that. You just always either ignore measurement uncertainty or assume the standard deviation of the sample means is the measurement uncertainty of the average.
If you do this with the temperature databases where the values *should* be given as “stated values +/- measurement uncertainty”, what do you wind up with for total uncertainty after adding all the uncertainties in quadrature?
An average is a division. by “n”. What is the relative uncertainty of “n”? How does the relative uncertainty of “n” impact the total relative uncertainty?
My guess is that you are either going to answer that the uncertainty of the average is (population-SD)/sqrt(n) or is the average uncertainty (total-uncertainty)/n. I.e. you will leave out the word “measurement”.
“The result is that the uncertainty of the mean is equal to the uncertainty of the sum divided by N”
This is the AVERAGE MEASUREMENT UNCERTAINTY, it is not the measurement uncertainty of the average.
There is a reason why N never appears in Eq 1.3.3.
The definition of uncertainty, including the uncertainty of the average, as laid out in the GUM is: “uncertainty (of measurement) parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand”
The dispersion of the values that could reasonably be attributed to the measurand, including the average of multiple different things, is *not* the average uncertainty.
The measurement uncertainty of the average would usually be closely approximated by the combined standard deviation of all of the measurement components. The combined standard deviation of measurements of different things is highly unlikely to be the average of the standard deviations of the elements. It is far more likely to actually be greater than the root-sum-square of the standard deviations.
And after 4 years, we are back where we started, with Tim still unable to see his own mistakes.
“An average is a division. by “n”. What is the relative uncertainty of “n”?”
Depending on how it’s derived, zero, or at least close to zero.
“How does the relative uncertainty of “n” impact the total relative uncertainty?”
It doesn’t – assuming the uncertainty is zero. The relative uncertainty of the average is the same as the relative uncertainty of the sum. Hence the absolute uncertainty of the average is equal to the absolute uncertainty of the sum divided by n.
“My guess is that you are either going to answer that the uncertainty of the average is (population-SD)/sqrt(n)”
That depends on whether you are talking about just the measurement uncertainty, or the uncertainty in treating the average of a sample as an estimate for the average of the population.
“or is the average uncertainty (total-uncertainty)/n”
Nope. As I’ve explained to you enough times that someone with a half functioning brain would have understood by now. You are not dividing “total uncertainty” by n. You are dividing the uncertainty of the sum by n. The uncertainty of the sum is only equal to the sum of the uncertainties if you ignore the rule about adding in quadrature, and that only makes sense if you think the measurement uncertainty is entirely systematic, or you use something like interval arithmetic. E.g. the sort of thin Pat Frank does.
“This is the AVERAGE MEASUREMENT UNCERTAINTY”
It is not. You must surely know by now it is not. The “tell” of always using all caps when lying is evident here.
“There is a reason why N never appears in Eq 1.3.3.”
Is it becasue they are multiplying or dividing two things with different relative uncertainties?
“The measurement uncertainty of the average would usually be closely approximated by the combined standard deviation of all of the measurement components.”
As described in the law of propagation of uncertainty (Equation (10) in the GUM). But it’s not the standard deviation of the values. It’s the standard uncertainties of all the measurements. And that requires you to have finally figured out what a partial derivative is and how to use it in the equation.
If they are different then why do you never differentiate what you are talking about when you say “uncertainty of the mean”?
Again, the significant digits in the average is determined by the measurement uncertainty. Once the standard deviation of the sample means reaches that level of resolution, trying to decrease it is meaningless.
If your average value is 8′ +/- 1″ then how does trying to calculate the standard deviation of the sample means to the ten thousandths digit (i.e. +/- .0001″) helpful at all? You can’t legitimately state the average as 8.0001″ +/- 1″ because you can’t measure at that level of resolution!
You obsession with the SEM as being some kind of measurement uncertainty is not healthy. It’s preventing you from understanding the basics of metrology.
The word “add” doesn’t specify *how* you add. Adding directly or adding in quadrature. You don’t *always* add in quadrature – you only do that when you think there might be partial cancellation of uncertain values.
You basic lack of knowledge of metrology just continues. How do you add measurement uncertainties when your sample size is small? How do you add measurement uncertainties when safety considerations are in play? How do you add measurement uncertainties for correlated quantities?
Get out of your mama’s basement and go apprentice with a master carpenter/machinist or a licensed civil engineer designing a bridge carrying public traffic.
ROFL!! And exactly what *is* the “standard uncertainties of all the measurements”?
I see you *still* haven’t gotten over how I showed you the method Possolo used to get the result he did – using partial derivatives! The fact that I can do in my head what you can’t do on paper just chaps your backside to no end, doesn’t it?
“If they are different then why do you never differentiate what you are talking about when you say “uncertainty of the mean”?”
I’ve been telling you there’s a difference since the start. You just never listen.
You really need to decide what you argument is. It’s impossible to explain anything to you when you just change the subject each time.
So far today you have argued that:
That uncertainties just add.That the uncertainty if the sum is the uncertainty if the mean.That the uncertainty of the mean is the sample standard deviation.That the sample deviation increases and the sample size increasesThat the uncertainty if the mean is the population standard deviation.And finally that whilst you accept that whilst the uncertainty of the mean does reduce with sample size, it is limited by the resolution of the individual measurements.It doesn’t bother you that these are all contradictory arguments. You just want to accept any arguement as long as it agrees with your prior beliefs.
“The word “add” doesn’t specify *how* you add. Adding directly or adding in quadrature. You don’t *always* add in quadrature – you only do that when you think there might be partial cancellation of uncertain values.”
Which is why you are wrong to say I think the uncertainty if the average is the average uncertainty. You only get that identity if you directly add the uncertainties. This is what Pat Frank effectively does. It isn’t correct if the uncertainties are random.
“ROFL!! And exactly what *is* the “standard uncertainties of all the measurements”?”
That depends on how you assess each measurement. It might be a Type B estimate, or you might make repeated measurements and use the experimental standard deviation of the mean.
“I see you *still* haven’t gotten over how I showed you the method Possolo used to get the result he did”
You are such a child. You really can’t accept that you got it wrong and I had to explain it to you. You just can’t bare the fact that you made a mistake, so now have to keep rewriting history.
There’s no real mystery to calculating the uncertainty if a cylinder. You can do it using the standard rules, using equation 10 and simplifying, or using the special case law for functions that only involve multiplication and powers. Or you can get a more accurate result using Monte Carlo estimation.
“The fact that I can do in my head…”
There’s no benefit to doing something in your head if you keep getting it wrong. It doesn’t matter if the derivative of X/n is 1 in your head, it’s still wrong.
“You really can’t accept that you got it wrong “
Except *I* didn’t get it wrong. I got it right. The measurement uncertainty of a barrel is *exactly* what I gave you. And you said I didn’t include the partial differentials because I didn’t know how to do partial differentials. I had to show you in detail the cancellations that occur when using relative uncertainties! For each component, the division by the total cancels the fixed components of the individual uncertainties. For the formula ΠHR^2, the relative uncertainty component for R becomes
2 * u(R)^2/R^2 because the ΠH terms cancel when divided by the total in the relative uncertainty formula.
EXACTLY what Possolo showed and what I gave you!
I showed you from Taylor and Bevington how they get the same exact thing in their examples.
*I* did it in my head and you couldn’t so you said I was wrong.
Mostly because you don’t understand relative uncertainty let alone metrology as a whole.
“Except *I* didn’t get it wrong. I got it right.”
See what I mean.
“And you said I didn’t include the partial differentials because I didn’t know how to do partial differentials.”
No, I said you were getting the partial derivatives wrong. Specifically you were claiming that x/N had a derivative of 1, rather than 1/N.
“*I* did it in my head and you couldn’t so you said I was wrong.”
This is so childish.
For the record here’s the relevant discussion
https://wattsupwiththat.com/2022/11/03/the-new-pause-lengthens-to-8-years-1-month/#comment-3636787
No! Measurement uncertainties add. If you are going to quote me then quote me. Don’t put words in my mouth.
“That the uncertainty if the sum is the uncertainty if the mean”
The uncertainty of the sum is the MEASUREMENT uncertainty of the mean. If you are going to quote me then quote me. Don’t put words in my mouth.
“hat the sample deviation increases and the sample size increases”
I’ve *never* said that. I’ve said that as you add measurements to the data set the measurement uncertainty increases. I’ve given you quotes from Bevington that agree with me. If you are going to quote me then quote me. Don’t put words in my mouth.
“That the uncertainty if the mean is the population standard deviation.”
The MEASUREMENT uncertainty of the mean is the population standard deviation. Why do you think I keep telling you to stop using the argumentative fallacy of Equivocation? *YOU* are the only one using the term “uncertainty of the mean”. *I* use “standard deviation of the sample means” and “measurement uncertainty of the mean”. Those are description of different things. If you are going to quote me then quote me. Don’t put words in my mouth.
“And finally that whilst you accept that whilst the uncertainty of the mean does reduce with sample size, it is limited by the resolution of the individual measurements”
The *standard deviation of the sample means” reduces with sample size. But the standard deviation of the sample means has nothing to do with the accuracy of the mean – i.e. the measurement uncertainty of the mean. The standard deviation of the sample means is a metric for sampling error, not measurement accuracy.
from statisticsbyjim.com
“ Sampling error is the difference between the sample and population mean.”
The average itself can’t have more resolution than the measurements themselves. The sample means can’t have more resolution than the measurements themselves. That’s why I keep pointing out that the sample component data are actually “stated value +/- measurement uncertainty” – BECAUSE THEY ARE THE SAME DATA AS THE POPULATION.
But you and climate science just use the “all measurement uncertainty is random, Gaussian, and cancels” meme to ignore the fact that the sample data has accompanying measurement uncertainty intervals. The measurement uncertainty of the sample means is the sum of the sampling error and the measurement uncertainty of the data used to calculate the sample means. As the sample size gets larger the sampling error gets smaller and the measurement uncertainty approaches the population measurement uncertainty.
There is simply no physical way you can state that the difference between the sample mean and the population mean can be smaller than the resolution of the sample mean and the population mean. You simply don’t know anything past the resolution of the measurement. And the measurement uncertainty is a main controlling factor in the resolution you can have for the measurement value.
It’s where the “numbers is numbers” meme of you and climate science comes into play. You and climate science just assume you can have any resolution you want with no regard to whether the data represents measurements of limited resolution or are just “numbers is numbers” and a repeating decimal has infinite resolution.
Most statisticians, mathematicians, and climate scientists believe that the larger your sample size the more accurately you can determine the “average” value and use it as a true value, i.e. standard error goes to zero.
As Bevington points out in his tome this can’t be automatically assumed for measurements, not even for purely “random” error. Even when systematic uncertainty is reduced to zero the measurements will form a random distribution. That random distribution will have a variance based on the range of the values in the distribution. That variance is a metric for the uncertainty of any average. As you increase the number of measurements you get more and more values that exist further and further out in the tails thus increasing variance, thus increasing the uncertainty of the average. This is true even for a Gaussian distribution of random error (and being random doesn’t guarantee that the distribution will be Gaussian).
The statistician and climate science meme that all measurement uncertainty is random, Gaussian, and always cancels is a theoretical construct useful in mathematical derivations of statistical descriptors like the “average” and the “standard error of the mean”. That theoretical construct is an *assumption*, and is usually implicit, unstated, and is not even consciously recognized. The real world consistently violates this “theoretical” understanding. It is a significant reason for the use of “significant digit” rules.
“Most statisticians, mathematicians, and climate scientists believe…”
Does it never worry you that maybe the reason most experts believe something is because it’s correct?
“larger your sample size the more accurately you can determine the “average” value and use it as a true value, i.e. standard error goes to zero.”
They “believe”, i.e. can prove, that when you have independent random variables the standard deviation of the mean gets smaller the larger the sample size. They also sometimes believe, (on the basis of maximum likelihood, or other other arguments), that the mean of a sample is the “best estimate” for the population mean. They do not believe it is the true mean.
“As Bevington points out in his tome this can’t be automatically assumed for measurements,”
And I’ve told you he’s correct, and none of the experts you quote would disagree with the point. As the uncertainty of the mean of random uncertainties gets smaller, any systematic error will become relatively more important. You can never get to the “true” mean, even if you take infinite measurements. Nobody, has ever claimed otherwise. Maths is an abstraction, it’s results what will happen in a perfect world. The world is far from perfect. However, you still have to understand how to use the maths in order to get a simplified, approximation of the real world, and also to understand what factors might make such a result reliable or unreliable.
“As you increase the number of measurements you get more and more values that exist further and further out in the tails thus increasing variance, thus increasing the uncertainty of the average.”
And here’s the problem. You just keep trying to replace the imperfect maths, with nonsense like this. The variance does not generally increase as you add more measurements. The variance is not based on the range of values. If anything you said was true, you might wonder why Taylor, Bevington, the GUM or anyone, never mentions this.
“The statistician and climate science meme that all measurement uncertainty is random, Gaussian, and always cancels…”
is a meme that only exists in Tim Gorman’s head.
Not at all. If the statisticians and climate scientists that post here on WUWT are an indication of the disciplines as a whole, none of them are trained in metrology yet make all kinds of unjustified assumptions concerning the treatment of measurements. THAT INCLUDES YOU!
And, as usual, here you are trying to substitute the standard deviation of the sample means as the measurement uncertainty of the mean. THEY ARE NOT THE SAME! You’ve been cautioned ad infinitum that you need to use the terms “standard deviation of the sample means” and “measurement uncertainty” in your writing in order to specifically indicate which you are discussing. Yet you continue to indulge in the argumentative fallacy of Equivocation by defining the term “standard deviation of the mean” to imply whatever you need it to imply at the moment thus changing the definition of the words without specifically informing the audience that you are doing so.
YOU just did. And so do the rest that post on here.
NO! You are *still* trying to substitute the standard deviation of the sample means for the measurement uncertainty of the mean. The standard deviation of the sample means is only a metric for how precisely you have located the mean of the population. It tells you ABSOLUTELY NOTHING about the measurement uncertainty of that mean. You remain WILLFULLY IGNORANT of the difference regardless of the references given to you that show your view to be wrong.
The standard deviation of the population data *is* a metric for the measurement uncertainty of the mean. But that value is the standard deviation of the sample means multiplied by the sample size! Making the standard deviation of the sample means smaller by increasing sample size DOES NOT CHANGE THE STANDARD DEVIATION OF THE POPULATION! Therefore, making the standard deviation of the sample means smaller and smaller DOES NOT CHANGE THE MEASURMENT UNCERTAINTY OF THE MEAN as described by the statistical descriptor known as the standard deviation.
Your statement is just wrong. It shows a continued willful ignorance concerning measurement uncertainty. Determining the population mean more and more precisely simply does not change the importance of systematic measurement uncertainty one iota! As km has pointed out to you ad infinitum, the term is systematic UNCERTAINTY, not systematic error. The term error implies you know the true value – which by definition in the GUM simply isn’t known. It implies that uncertainty in measurement can be totally eliminated and made equal to zero.
“Maths is an abstraction, it’s results what will happen in a perfect world. The world is far from perfect. However, you still have to understand how to use the maths in order to get a simplified, approximation of the real world, and also to understand what factors might make such a result reliable or unreliable.”
You’ve got it exactly backward, the viewpoint of someone unconcerned with real world implications. Math exists to describe the real world. Insofar as it fails to accurately describe the real world the math introduces uncertainty into the results it provides. The operative word in your statement is “approximation” yet you refuse to understand the definition of that word. You simply cannot ignore the ramifications of that word. Whatever result you get from “the math” REQUIRES that you identify the uncertainty that approximation introduces into the result provided by “the math”.
“And, as usual, here you are trying to substitute the standard deviation of the sample means as the measurement uncertainty of the mean.”
I said “random variables”. I stated the proven fact that when you average independent random variables the standard error of the mean gets smaller. Whether you apply this to sampling, or to measurement uncertainty is up to you. You really need to understand that numbers are numbers. They don’t behave differently just because you don’t like the results.
“YOU just did.”
Stop with this eternal lying. If you can’t win an argument without resorting to strawman arguments, maybe that should tell you something about the strength of your arguments.
“NO! ”
I’m just explaining what Bevington says, and your response is “NO!.”
“You are *still* trying to substitute the standard deviation of the sample means for the measurement uncertainty of the mean.”
First, there is no such thing as “standard deviation of the sample means”, that’s just a phrase you use to sound cute. The correct term is standard error of the mean, or if you prefer standard deviation of the mean.
Secondly, I was talking about the measurement uncertainties in this case. It’s what Bevington says. You might think that you could make a measurement as precise as you want just by averaging more and more measurements, but there are a couple of problems with that. 1) as the uncertainty decreases with the square root of the number of observations, the law of diminishing returns makes it impracticable, and 2) averaging will only reduce random uncertainties, and as that becomes smaller any systematic error no matter how small will remain.
“It tells you ABSOLUTELY NOTHING about the measurement uncertainty of that mean. You remain WILLFULLY IGNORANT of the difference regardless of the references given to you that show your view to be wrong. ”
Ranting like this really doesn’t help your case. Show me the specific reference you think proves I’m wrong. And I’ll try once again to explain why you are misunderstanding it, or that it’s just saying what I’m saying.
“The standard deviation of the population data *is* a metric for the measurement uncertainty of the mean.”
No it is not. You keep claiming it, but it makes no sense and you provide no evidence to back it up.You admit that the standard error of the mean indicates how precisely you have estimated the mean – why you can’t see that you are describing the uncertainty of the mean, is your problem.
“Making the standard deviation of the sample means smaller by increasing sample size DOES NOT CHANGE THE STANDARD DEVIATION OF THE POPULATION!”
Correct, but no need to shout.
“As km has pointed out to you ad infinitum, the term is systematic UNCERTAINTY, not systematic error.”
From the GUM 0.7.
That is the only place they use the term. Throughout the rest of the document it’s always systematic error or systematic effect. E.g. B.2.22
“Math exists to describe the real world.”
And it does that by abstraction.
“The operative word in your statement is “approximation” yet you refuse to understand the definition of that word.”
Are there any other crimes you want to accuse me of? Stop pretending you know what I understand, and just stick to your argument.
“You simply cannot ignore the ramifications of that word.”
Thanks for advice. I was rather hoping that if I just closed my eyes all the world’s problems would go away.
“Whatever result you get from “the math” REQUIRES that you identify the uncertainty that approximation introduces into the result provided by “the math”.”
What do you think we’ve been doing?
So what?
Again, so what? We are concerned with MEASUREMENT UNCERTAINTY, not how precisely you can calculate the mean. Once your calculation of the sample deviation of the sample means exceeds the resolution with which you can measure you are doing nothing but mathematical masturbation as far as the real world of measurements is concerned. Who cares if you reduce the standard deviation of the sample means to the ten thousandths digit if you can’t measure it?
Measurement uncertainty is *NOT* the standard deviation of the sample means. It is the standard deviation of the population data.
SD = (n) * (standard deviation of the population means)
It’s amazing that you just continue to blow that off!
“Show me the specific reference you think proves I’m wrong.”
This is the standard deviation of the data, not of the sample means.
“I stated the proven fact that when you average independent random variables the standard error of the mean gets smaller.”
“So what” is exactly correct, this is a huge red herring. He has never grasped the fact that making measurements of a time-series is not an exercise in random statistical sampling of a population.
Who said anything about a time series?
What do you think a monthly average of daily temperatures is? What value goes on the x-axis? Are monthly and daily units defined as time periods? Are months and days independent variables of a functional relationship?
He refuses to accept that the SEM is not the measurement uncertainty of the average. He refuses to even use the term “measurement uncertainty” let alone admit that it is the measurement uncertainty that is of prime importance, not the precision with which you calculate the mean. The measurement uncertainty determines when further decrease in the SEM becomes mathematical masturbation. he knows he’s lost this argument and his only lifejacket is the use of the argumentative fallacy of Equivocation so the term “uncertainty of the mean” can be defined however he wants in the moment. The use of the words “uncertainty of the sample means” and “measurement uncertainty of the average” would immediately make his tactic transparent.
It is the standard deviation of the data that characterizes the dispersion of the values that could reasonably be attributed to the measurand. It is *not* the standard deviation of the sample means that determines the dispersion of values that could reasonably be attributed to the measurand.
Not once have you *ever* bothered to actually study and comprehend the tomes recommended to you. You just continue to cherry pick things you think validate your worldview.
The precision of the calculation of the population mean increases as you increase the number of samples. That has NOTHING, *ABSOLUTELY NOTHING*, to do with the measurement uncertainty of the average.
It is the standard deviation of the population data that determines the dispersion of the values that could reasonably be attributed to the measurand. And the standard deviation of the population data is the standard deviation of the sample means times the square toot of the sample size. The standard deviation of the population data is a given just as the average of the population data is a given. You can only estimate them via sampling. You can’t change either one by sampling. It’s why the standard deviation of the sample means is considered an estimate of *sampling error* and not of measurement uncertainty.
Bevington: “It is important to realize that the standard deviation of the data does not decrease with repeated measurement, it just becomes better determined. On the other hand, the standard deviation of the mean decreases as the square root of the number of measurements, indicating the improvement in our ability to estimate the mean of the distribution.”
As far as the temperature data sets are concerned there are three different scenarios:
So which scenario do *you* use for the temperature data sets?
Bevington:
Well done. You’ve found a quote from Bevington that confirms what I’ve been trying to tell you. Increasing the number of measurements better determines the standard deviation. That is, as sample size increases the standard deviation of the sample tends towards the population standard deviation. It does not just get bigger.
And as sample size increases your ability to estimate the mean improves, i.e, you reduce the uncertainty.
ROFL! As the sample becomes the population the standard deviation of the sample gets closer to the standard deviation of the population — AND IT IS THE STANDARD DEVIATION OF THE POPULATION THAT DETERMINES THE MEASUREMENT UNCERTAINTY.
“And as sample size increases your ability to estimate the mean improves, i.e, you reduce the uncertainty.”
You reduce the SAMPLING ERROR – meaning you can more precisely locate the mean. That does *NOT* reduce the measurement uncertainty of the mean!
from statisticsbyjim.com
(bolding mine, tpg)
The operative words here are “observation” and “sample means”. The standard deviation addresses the dispersion of the observations – i.e. the *MEASUREMENT* uncertainty of the average. The SEM addresses the dispersion of the sample means – i.e. how precisely the sample means locate the population mean – which is *NOT* the measurement uncertainty of the average.
Who do you think you are fooling on here by refusing the use the term “measurement uncertainty? You are just making a fool of yourself.
“It is the standard deviation of the data that characterizes the dispersion of the values that could reasonably be attributed to the measurand.”
We just keep going round in circles here, becasue you have this in interpretation of what the definition means, and no amount of evidence or common sense will disabuse you.
But here goes – the measurand in this case is the mean, either an exact mean of the data, or more usually the population mean. “values that could reasonably be attributed” to the measurand means what values would it be reasonable for you to say may be the value of the mean. Not, as you seem to think all the values that went into estimating the mean.
If we follow your interpretation, what would you say was the uncertainty of a sum of measurements? Would it be the standard deviation of all the values that went into the sum, or would it be the range of values you think it reasonable that the sum might be?
It’s not MY interpretation. It’s the interpretation of everyone with any knowledge of metrology. It’s right out of the GUM! It’s the interpretation that you simply can’t admit to.
The mean is a STATISTICAL DESCRIPTOR. It is not a measurand. It does not exist outside of being a statistical descriptor for data that *does* exist – in this case measurement data.
from copilot ai:
from the GUM:
GUM:
The mean is not a measurand. It is a calculated, derived statistical descriptor.
The average is *NOT* obtained by measurement.
You have been given this MULTIPLE times in the past!
GUM:
These quotes, and similar ones from other experts, have been given to you MULTIPLE times. Print them out and frame them. Hang them near your computer monitor for reference.
YOU *NEVER* BOTHER TO ACTUALLY STUDY ANYTHING! You keep trying to beat everyone over the head with your OPINIONS while ignoring accepted standards in metrology. STOP CHERRY PICKING things you think verify your misconceptions and actually *study* the tomes you’ve been given references for context and meaning.
It simply isn’t nonsense. The variance of the population of measurements DEFINITELY increases as you add more measurements. What do you think Bevington was stating in his quote?
Data points in the tails of a distribution *do* have a probability of appearance. It will be lower than those closer to the average but it will *not* be zero. The more measurements you make the more likely you are to obtain a result further and further out in the tail of the distribution. That *does* increase the variance associated with the measurement data set.
You just keep confusing the difference between the standard deviation of the sample means and the measurement uncertainty of the average. I can only conclude that for some reason you wish to remain willfully ignorant on this subject. It’s been explained often enough to you in detail yet you keep getting it wrong.
Of course it is. It is calculated using (X – X-bar). As X gets further and further from Xbar, i.e. an increased range of values, the variance grows. They are not directly proportional but they are directly related!
They *do* mention this. For instance, Bevingtton covers it in Chapter 1. “The variance σ^2 is defined as the limit of the average of the squares of the deviations from the mean μ:” The GUM gives the same definition in Equation 4. I don’t have Taylor with me right now but I’m sure you will find the same definition if you actually bother to ever study his tome instead of just cherry picking things from it.
“is a meme that only exists in Tim Gorman’s head.”
It’s the meme exhibited by everyone that never bothers to propagate measurement uncertainty in their measurement data and instead substitutes how precisely they can find the average value of the stated values only. That includes you!
“The variance of the population of measurements DEFINITELY increases as you add more measurements.”
Then you need to provide some evidenced for this. Either real world, simulation of better a mathematical proof.
You could start by trying rolling dice, or measuring all those lengths of wood you keep about the place. What should happen is that the more things you include in your sample the more the variance will tend to the population variance. It may get bigger or smaller along the way dies to chance – especially at the start, but there is no “DEFINITLY” that it will always increase.
Note, the one exception for this might be if the data is not stationary. I.e. if you measure temperatures throughout the year the variance will increase because of the average temperature is increasing.
“What do you think Bevington was stating in his quote? ”
What quote is that? I know you think you can read my mind, but don;t assume I can read yours.
“Data points in the tails of a distribution *do* have a probability of appearance.”
Yes, that’s the whole point of a probability distribution.
“It will be lower than those closer to the average but it will *not* be zero.”
Why do you always assume everything’s a normal distribution?
“The more measurements you make the more likely you are to obtain a result further and further out in the tail of the distribution.”
You have as much chance of getting such a result on the 1st as on the 1000000th measurement. The proportion of extreme results will on average always be the same. E.g, if there’s a 1% chance of an extreme result, than you might have 1 in the first 100 values, you might have 10000 in the first 1000000 values. The effect of each such extreme result on the variance will be on average the same.
“That *does* increase the variance associated with the measurement data set.”
Oh no it doesn’t.
“It’s been explained often enough to you in detail yet you keep getting it wrong.”
Or maybe, it’s your explanations that are wrong, and demonstrably wrong.
“Of course it is. It is calculated using (X – X-bar).”
You need to look at what (X – X-bar)^2/N means and explain why the occasional larger or smaller value will result in it inevitably getting larger. The occasional large value will quite likely balanced by sets of values closer to the mean.
“For instance, Bevingtton covers it in Chapter 1. “The variance σ^2 is defined as the limit of the average of the squares of the deviations from the mean μ:””
And how does that rearrange itself in your mind to “as you measure more values the variance will inevitably increase”?
Just for fun, here’s an illustration of the cumulative variance caused by adding random numbers, with a normal distribution with standard deviation 1. There are some dramatic swings for the first few numbers, but in the long run it is tending to a variance of 1.
Bevington addresses this. What more proof do you need? Any distribution with a tail will generate more values further out in the tail as you add values from the distribution. You are, once again, demonstrating absolutely no understanding of the real world. Why do you think people bet on the “long shot” coming in? Every time the long shot comes in the variance associated with distribution increases! And sometimes the long shot comes in as the winner!
Jeesh!
Adding measurements IS adding elements to the population of measurements! The POPULATION VARIANCE will change!
variance is related to the range. Adding to the range adds to the variance. Variance is a metric for uncertainty of the average. I.e. the standard deviation increases and thus the measurement uncertainty increases.
That is exactly what Bevington argues against. If you would actually study the experts instead of cherry picking you would know this. It’s why he argues that arbitrarily increasing sample size can actually increase measurement uncertainty – even if the SEM decreases.
It is the standard deviation of the POPULATION that determines the measurement uncertainty associated with the average and not the standard deviation of the sample means. The standard deviation of the sample means only tells you how precisely you have calculated the population average. It tells you nothing about the accuracy of the average value you have calculated.
You keep confusing sample and population and standard deviation of the sample means with the standard deviation of the population. It has to be on purpose. The difference had been explained often enough to you.
And you equate generating a set of random numbers with doing actual measurements of a measurand? Your argument is with Bevington.
Could you actually provide an exact quote for all your claims? You have a track record for completely misunderstanding what you read, and I wouldn’t want you to defame Bevington, by claiming he;s saying something he isn’t.
“Why do you think people bet on the “long shot” coming in?”
Because they’re idiots, and gambling can be addictive. I suspect this illustrates your problem. A gambler might keep betting on long shots, and when one comes up he think he’s winning – even though he’s bet more money than he’s won. You think that the occasional extreme value will increase the variance, but ignore the many more values that are close to the mean.
“Adding measurements IS adding elements to the population of measurements! The POPULATION VARIANCE will change!”
You really don’t understand what population means in this context.
“And you equate generating a set of random numbers with doing actual measurements of a measurand?”
I was demonstrating you are completely wrong to claim that increasing the number of random variables sampled from a population will inevitably increase variance. If you are claiming that you cannot model measurement uncertainty using random variables – then you need to explain what model you are using and demonstrate how it will increase the variance by increasing the number of measurements.
And then explain why you disagree with Bevington using Monte Carlo methods.
“Could you actually provide an exact quote for all your claims? You have a track record for completely misunderstanding what you read, and I wouldn’t want you to defame Bevington, by claiming he;s saying something he isn’t.”
More BS. Bevington: ““Removing an outlying point has a greater effect on the standard deviation than on the mean of a data sample, because the standard deviation depends on the squares of the deviations from the mean”
The corollary of this is that the odds of getting an outlying point increases with the number of observations. Sometimes the “long shot” wins!
“Because they’re idiots, and gambling can be addictive.”
Typical idiocy from you. Entrepreneurs will sometimes bet on a long shot as well. Are they idiots? Those who gambled on crypto currency a decade ago, very much a “long shot”, have won big! Those who gambled on Nvidia stock, again a “long shot”, have won bit! It’s balance of risk and return!
“You think that the occasional extreme value will increase the variance, but ignore the many more values that are close to the mean.”
I don’t ignore that fact at all! What *you* wan to do is ignore that samples are not perfect representations of the parent distribution and that the sample values themselves carry the measurement uncertainties of the parent values!
In the physical world, measurement uncertainties ADD. They *always* ADD. You can’t reduce them by finding an average measurement uncertainty. All that average measurement uncertainty does is spread the total measurement uncertainty evenly across all data elements. The measurement uncertainty of that mean remains the standard deviation of the population, not the standard deviation of the sample means.
from chatgpt:
σ: Describes variability of individual measurements.
σ/sqrt{n}: Describes uncertainty of the sample mean as an estimate of the true population mean μ.
You seem to be just unable in any way to relate these definitions to measurement uncertainty of the mean.
You seem to be arguing that because variance sometimes doesn’t change very much with an increase in the range of measurement values that you can assume that adding measurement elements to the distribution *never* changes the standard deviation. It’s a meme of the same type as assuming that all measurement uncertainty is random, Gaussian, and cancels.
You seem to be unable to grasp that when it comes to measurements the standard deviation of the measurements, i.e. the measurement uncertainty, determines the level of resolution which can be applied to the mean. Once your standard deviation of the sample means reaches that level of resolution, increasing the sample size doesn’t really buy you much if anything at all! If your measurement uncertainty of the average, i.e. the standard deviation of the population, is 1″ then trying to lower the standard deviation of the sample means to the ten thousandths of an inch buys you what? That calculated mean is *still* just an estimate of the true value, it is *not* the true value. And if you can’t measure to that resolution then how do you confirm that it is a better estimate?
Quit whining! Quit asking questions when you have no answer. All you are doing is exposing your lack of any technical or mathematical references that would show you are correct!
That means EVERYTHING you post is suspect and only amounts to an uneducated opinion.
I have shown you pages from Dr. Taylor. Frank from NoVA has shown you a web page from a university course. I’ve asked you to list the assumptions in NIST TN 1900 Ex. 2 that allows the use of the uncertainty of the mean as a basis for measurement uncertainty. You just hand wave them away and imply that they are incorrect and that your OPINION is the only truth. I am surprised that your hand hasn’t fallen off from all the hand waving.
Whining? Have you read you posts!
You didn’t answer the question. Why do you think variance will increase with sample size?
More bulls@it with no reference. You are claiming kurtosis is an invalid statistical descriptor since variance is not based on the range. Kurtosis and range are closely related.
As kurtosis increases from a normal, the tails grow. That means more values that are further and further from the mean.
You need to read this Wikipedia article. It has some good info and it also has a derivation of the standard uncertainty of the mean.
I also want to point out something about your statement:
More bulls@it.
Equation 1.3.3 is a general equation for fractional uncertainty. Fractional uncertainty converts an uncertainty value into a percent value that in effect weights uncertainties so that they can be directly added. YOU MUST USE FRACTIONAL UNCERTAINTIES WHEN FUNCTIONAL RELATIONSHIPS HAVE MULTIPLICATION OR DIVISION. You MAY use fractional uncertainties (Eq. 1.3.3) at any time. It is especially useful when reproducibility conditions exist such as measured temperatures on different days.
It is why you multiply “z” (the mean) by a total percent to obtain a stated value of Δz.
Δz = z · √[(Δx/x)² + (Δy/y)²] (Eq. 1.3.3)
Where did you learn otherwise? Cherry picking?
“More bulls@it with no reference.”
This in response to my point that the variance is not based on the range of values. The reference is the definition of variance.
Var(X) = E[(X – µ)^2]
https://en.wikipedia.org/wiki/Variance
Consider two sets of 5 values
X = {1,4,5,6,10}
Y = {1,2,3,9,10}
Same range, but var(X) = 10.7, var(Y) = 17.5.
“You are claiming kurtosis is an invalid statistical descriptor since variance is not based on the range. Kurtosis and range are closely related.”
What? This was about variance, not kurtosis – and kurtosis is not based on range either
kurtosis(X) = 2.3
kurtosis(Y) = 1.3
And as with variance, kurtosis does not tend to grow as sample size increases – it tends to the kurtosis of the population.
“As kurtosis increases from a normal, the tails grow. That means more values that are further and further from the mean.”
But that’s not the point Tim was making. He said that as your sample size increases variance increases. Having a larger variance in the population will result in a higher probability of extreme values in the sample, but that’s just saying the sample will tend to the population variance. Same with kurtosis.
“You need to read this Wikipedia article.”
Which one?
“More bulls@it.”
In relation to me saying
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/01%3A_Introduction_to_Physics_and_Measurements/1.03%3A_Measurements_Uncertainty_and_Significant_Figures
“Equation 1.3.3 is a general equation for fractional uncertainty.”
We are talking about 1.3.4.2 Rule 2, here. It starts by stating that If z = x ✕ y, or z = x / y. It is the rule you use when you multiply or divide values. Just as it is in Taylor.
“You MAY use fractional uncertainties (Eq. 1.3.3) at any time.”
Not if you want a correct answer. Look at Rule 1, just above rule 2.
Equation 1.3.2 – adding absolute uncertainties in quadrature. Not do this or use rule 2, we don’t care. These rules are different for a reason, and you use the appropriate one if you want the correct uncertainty.
“It is especially useful when reproducibility conditions exist such as measured temperatures on different days.”
In a case like that it probably won’t make much difference. The fractional uncertainties based on absolute temperatures will be very similar. But it makes a big difference if you are adding things with very different sizes. Say you add a 10cm and a 10000cm rod together, each measured with an uncertainty of 1cm. Using the correct rule the uncertainty the sum is 10010.0 ± 1.4cm.
Using rule 2 you have the relative uncertainty of √(0.1^2 + 0.0001^2) = 0.1. So you end up with
10000 ± 1000cm
“Where did you learn otherwise?”
Reading Taylor and the GUM. It follows from the general equation.
Here’s a relevant quote from Taylor, section 3.8
It’s no wonder you never show any calculations or any context. I went ahead and used both equations using the temperature data from NIST TN Ex.2, with a ±0.5 uncertainty for each measurement. Guess what?
Rule 1
Δz = √[(Δx1)² + … + (Δxn)²] = √[22 ∙ (0.5)²] = 2.35 -> 2.4
Rule 2
Δz = z ∙ √[(Δx1/x1)² + … + [(Δx₂₂/x₂₂)²] = 2.44 -> 2.4
Which do you think is more accurate?
Is your assertion that Rule 1 is more correct than Rule 2 when uncertainties are added?
What is even more interesting is when you use the standard uncertainty of 0.87 in NIST TN 1900 as the individual uncertainty of each measurement.
Rule 2 gives this.
Δz = 4.25
Rule 1
Δz = 4.08
Wow! That’s almost the same as the standard deviation of 4.1 that NIST calculated. But they are both very close.
Now let’s examine the context and assumptions used in NIST TN 1900.
Read this section of the GUM carefully.
NIST makes the assumption that the observed variance of the repeated observations on any single measurement is negligible. They then proceed to find the possible differences among the individual samples.
Why do they do this? Because they don’t have multiple observations of each daily Tmax reading. Doing a calculation of measurement uncertainty for each observation would compromise the procedure they were trying to show.
It wouldn’t be fun without showing you another reference about what constitutes measurement uncertainty.
From: Statistical distributions commonly used in measurement uncertainty in laboratory medicine – PMC
“It’s no wonder you never show any calculations or any context.”
This is getting insane. I’ve spent ages giving you calculations. I gave you an example in the comment you are replying to. You just have a blind spot, or are just making stuff up.
“I went ahead and used both equations using the temperature data from NIST TN Ex.2,”
I specifically pointed out that I. A cade such as temperatures it would make little difference. The values, using absolute temperatures are large compared to the uncertainties, so absolute or relative uncertainties are all roughly the same for each temperature.
“Is your assertion that Rule 1 is more correct than Rule 2 when uncertainties are added?”
It’s my assertion that rule 1 if the correct rule when adding or subtracting values, and that rule 2 is incorrect. I base this both on the fact that all your references state it, and on my understanding of how rule 2 is derived from the general law of propagation. This in turn results from the fact that when you multiply two values you have to take into account the size of the other value, whereas when adding it’s irrelevant.
“Read this section of the GUM carefully.”
Why don’t you try reading it carefully. You spam the same quote every other week as if it had some special meaning to you. You never seem to understand what it is actually saying.
“NIST makes the assumption that the observed variance of the repeated observations on any single measurement is negligible.”
What repeated measurements? They have at most one measurement per day, and the observed variance of those observations is the basis of the uncertainty of the mean. It is not negligible.
What they do assume is negligible is any calibration issue.
“They then proceed to find the possible differences among the individual samples.”
Again, there is only one sample, the 22 daily maximums.
“Doing a calculation of measurement uncertainty for each observation would compromise the procedure they were trying to show.”
They could do it quite easily. For a start you know the resolution is 0.25°C. That imposes a minimum uncertainty for each reading. Then they could use a Type B specified uncertainty for the instrument. But it’s not going to have much of an impact compared with variation in daily temperatures.
You have no clue do you?
Rule 1 can be used only if the uncertainties are of the same range of measured values. If they are not, then Rule 2 is more appropriate.
Percent errors are always appropriate. I showed you calculated values. They are close. Why not the same? Because the range of values range from ~18 to ~33. When the uncertainty is identical, 0.5/18 is a higher value than 0.5/33. This actually makes Rule 2 more accurate than Rule 1.
You also miss the other big issue. Uncertainties of input values ALWAYS add. The combined uncertainty never reduces in value.
“You have no clue do you?”
Rather more than you.
Clue 1 is the words used to describe Rule 1 – “if” “then”. If you are adding or subtracting, then you add the uncertainties in quadrature. Not then you can choose what rule you want.
Clue 2 is the passage from Taylor, which you ignored
Not, “uncertainties in sums or differences involve either absolute or relative uncertainties.”
Clue 3 is the Law of propagating uncertainties, as given in the GUM. Note, if you are just adding the partial derivative for each term is 1. Hence the law is just adding the uncertainties in quadrature. There is no simplification that will allow you change that to a sum of relative uncertainties.
Clue 4 is the example I gave you, and you ignored
The absurdity is that you can add two lengths each with an uncertainty of 1cm, and get an uncertainty of the sum of 1000cm.
Clue 5 is the fact that despite your continuous insistence that I provide references for the simplest fact, you so far have provided zero references to support your claim.
“Rule 1 can be used only if the uncertainties are of the same range of measured values. If they are not, then Rule 2 is more appropriate.”
That makes no sense at all. As I said, if the values are close together, than it makes little difference which rule you use when adding. That’s because the relative and absolute values will be of a similar proportion. The problem is when the values are quite different, and then Rule 2 is definitely not appropriate. See my example above.
“They are close. Why not the same? Because the range of values range from ~18 to ~33.”
You mean 291 to 306. You surely understand you have to use an absolute temperature scale when talking about relative uncertainties.
“Uncertainties of input values ALWAYS add. The combined uncertainty never reduces in value.”
Apart from all the times they do reduce – e.g. when taking an average. As we’ve discussed many, many, times before. It’s explained in 1.3.6 The Uncertainty of the Mean. Add the values using Rule 1, then use Rule 2 when you divide by N.
I ignored it because it is ridiculous. Do you really think that if you can only measure a 10 cm rod to an uncertainty of ±1 cm, that you can measure a 10,000 cm (100 m) to ±1 cm?
That is one reason fractional uncertainties are useful. If your device can give a full scale reading of (1÷10,000) ×100= 0.01%, it should do about the same on 1 cm or ±0.0001 cm. So you end up with 10,001 ± 1.0001 cm
You are displaying your lack of training in metrology and your lack of experience.
“I ignored it because it is ridiculous.”
It’s meant to be ridiculous, to illustrate your claim is wrong. Using relative uncertainties when adding or subtracting is wrong. The greater the difference between the values the more wrong it will be.
You ignored all my other arguments, and have not provided any references to support your argument.
The math is correct. It is your example that ends up with ridiculous uncertainty values. A 10% uncertainty at 10 cm and a 0.01% uncertainty at 100 m is ridiculous.
Why don’t you justify not using the device with a 0.01% uncertainty for both.
Even my 300 foot surveyor’s tape has worse uncertainty over 300 feet than at 4 inches due to tension and bending over that distance. Your example shows a1000 times better uncertainty at a longer distance.
“The math is correct. It is your example that ends up with ridiculous uncertainty values.”
Which is my point. If you claim that relative uncertainties can be used when adding values, and I give you a mathematically correct example that leads to an absurd result, that’s demonstrating that your math is wrong. You might be able to say that in some cases it will give you approximately the correct result, but why not just use the correct absolute uncertainties, just as all your references say.
“Why don’t you justify not using the device with a 0.01% uncertainty for both.”
Using Rule 1.
0.01% of 10cm is 0.001cm, 0.01% of 100m is 1cm, so adding absolute uncertainties will make the uncertainty of the sum 1cm.
Using Rule 2
Relative uncertainty of the sum is √(0.01%^2 + 0.01%^2) = 0.014%,
so uncertainty of the sum is 100.1 * 0.014% = 1.4cm.
Little difference, just one is correct and the other if exaggerating the uncertainty.
So now consider measuring 100 boards, each around 1m long with an uncertainty of 0.01%.
Using Rule 1, the uncertainty of each measurement is 0.01cm. The combined uncertainty is √100 * 0.01 = 0.1cm.
Using Rule 2, the combined relative uncertainty is 0.1%, which makes the uncertainty on the length of 100 boards 10cm.
Quite a difference, and using rule 2 the uncertainty of the sum is 10 times longer than all the uncertainties added together.
Still waiting for you to proved any reference that says you can use Rule 2 when adding or subtracting.
Quit whining. I showed you the math and a reference about your ridiculous “example”. You obviously didn’t read it. I’ll show part of the pertinent text.
That is exactly why I called your example ridiculous!
Good grief! A 100 ±0.01% m and a 10 ±10% cm! Neither the magnitudes nor the uncertainty are roughly the same.
They will *NEVER* get it. They are too tied to the memes that all measurement uncertainty is random, Gaussian, and cancels plus “numbers is just numbers” so that any number of significant digits is possible from any calculation.
The concept that the measurement uncertainty can swamp any differences attempting to be identified just doesn’t exist in their statistical world.
If you are going to quote me then quote me. Don’t put words in my mouth.
“Quit whining.”
Hilarious. How many times have you insisted I provide a referenced for the most obvious fact, yet when I ask you to provide a reference for your obviously wrong assertion, I’m whining.
“I’ll show part of the pertinent text.”
Where in that text does it say you can use relative uncertainties when adding or subtracting?
“That is exactly why I called your example ridiculous!”
You still don’t get that this is the point. You claim you can choose between relative or absolute uncertainties when adding or subtracting. Why? You know that you will generally get an incorrect result, and your only justification is that in some situations it won;t be ridiculous wrong.
Read this again.
You just won’t admit that your example was ridiculous will you? You can put lipstick on a pig, BUT, it is still a pig.
Do everyone a favor and add the two values together using significant digital rules and show what you get.
“Read this again”
In other words it doesn’t say what you are claiming. It’s saying not to add up different quantities, not that you can do it using relative uncertainties. Your passage literally starts by saying
All it is saying is there is little point in adding together things when the size of one is less than the uncertainty of the other, not that you can solve this by using relative uncertainties. True the example with relative uncertainties.
Dick’s height is 186±2cm.
Flea’s height is 0.020±0.003cm
Convert to relative uncerftainties
Dick: 186±1%
Flea: 0.020±15%
Using Rule 2, relative uncertainty of sum of Dick and Flea is
√(0.01^2 + 0.15^2) = 15%
Absolute uncertainty is
186 ± 15% = 186 ± 28cm.
And that’s the problem with using relative uncertainties when adding. You push the relative uncertainty of the smaller item onto the size of the larger one. This is exactly what you want when multiplying, but not when you are adding.
“You just won’t admit that your example was ridiculous will you?”
If you want evidence that the Gorman’s never read what I say, there it is. Scroll up a bit to see where I said
You just keep validating this statement from:
http://spiff.rit.edu/classes/phys273/uncert/uncert.html
This applies to any calculation of uncertainty, whether you realize or not.
Yes, I agree with the statement. It says nothing to back up your claim that you can use relative uncertainties when adding and subtracting.
This whole futile exercise is so typical of the Gormans. They state something that is obviously wrong, and then when challenged will just go of on these distractions rather than admit they may have been mistaken.
When you divide by N you are finding the SEM. The SEM is *not* the measurement uncertainty of the average. It is a metric for how precisely you have located the average of the data – but tells you nothing about the accuracy, i.e. the measurement uncertainty of the average.
As the GUM says:
The dispersion of the values that could reasonably be attributed to the measurand is related to the standard deviation of the data and not to the standard deviation of the data divided by N or sqrt(N).
from statisticsbyjim.com
“how closely your sample estimates the population,” should be edited to say “how closely your sample estimates the population mean”.
The statistical descriptor that is most use with temperature is the measurement uncertainty, i.e. the standard deviation of the data, not how precisely you have located the population mean, i.e. the spread of the sample means. Once you have enough sample means that the SEM matches the measurement uncertainty there really isn’t any use in going any further. You are never going to know the “true value” and since the true value of the measurand can be anywhere in the measurement uncertainty interval the measure of interest is the how large the measurement uncertainty interval is. Getting closer to the true value is a matter of lowering the measurement uncertainty of the measurements (e.g. the standard deviation of the data) thus decreasing the size of the interval in which the true value can lie. Getting closer to the true value is *NOT* how small you can make the SEM.
If you have two random variables then Var(Y) = Var(X1) + Var(X2). Thus the measurement uncertainty of Y is going to be described by Var(X1) + Var(X2) since that determines the standard deviation of the new data set.
Dividing Var(X1) + Var(X2) by 2 gives you the average variance, i.e. the average uncertainty of the two variables. All that does is spread the total variance equally across each component. The value of that equally spread total variance is *NOT* the measurement uncertainty of the combination.
It’s why I keep trying to tell you that the average uncertainty is not the uncertainty of the average. The SEM is a metric for *SAMPLING* ERROR and not for measurement uncertainty.
“The SEM is *not* the measurement uncertainty of the average”
It is if uncertainties are measurement uncertainties. Really, all you have to do is follow the rules. They are describing what happens when you propagate measurement uncertainties, and they lead to conclusion that the measurement uncertainty if an average of measurements will be smaller than the individual measurement uncertainties.
“The dispersion of the values that could reasonably be attributed to the measurand is related to the standard deviation of the data and not to the standard deviation of the data divided by N or sqrt(N).”
That’s your delusion. It’s a complete misreading of the GUM definition, and clearly makes no sense regarding measurement uncertainty.
“If you have two random variables then Var(Y) = Var(X1) + Var(X2).”
You missed the point that this is only true if Y = X1 + X2.
“Dividing Var(X1) + Var(X2) by 2 gives you the average variance”
And why would you do that. I’ve explained this to you any number if times, and either you are unwilling or incapable of remembering, but if Y = (X1 + X2) / 2, then Var(Y) = (Var(X1) + Var(X2)) / 4.
That’s 4, not 2. The variance if the average is not the average variance, at least for independent random variables.
“It’s why I keep trying to tell you that the average uncertainty is not the uncertainty of the average.”
Is it because you have severe memory loss, and keep forgetting all the times I say I agree?
“The SEM is *not* the measurement uncertainty of the average”
/*BLINK*/ What??? Are you for real???
How exactly does blindly stuffing the average formula into the GUM cancel measurement uncertainty? This is an extraordinary claim that requires extraordinary evidence.
So far you have zero evidence, just lots of words.
(It would also help if you understood was measurement uncertainty is, and what it isn’t. See above.)
These folks have no idea what an input quantity is nor any idea how to find the uncertainty of each input quantity so the uncertainty of each can be propagated through a functional relationship.
I’ll bet this statement from the GUM is unfamiliar to them.
Section 4.2.1
“This is an extraordinary claim that requires extraordinary evidence.”
Yes, it’s an extraordinary claim that the Law of propagation of uncertainty works. what evidence would be acceptable to you? Explain the maths, or a Monte Carlo estimate?
Now if you want to argue that there are cases where it doesn’t work, then we could go into details. E.g. it’s an approximation when the function isn’t linear, and it’s assuming independent uncertainties. But just rejecting it because you don’t like the results, is an extraordinary claim.
Yet another meaningless pseudo-random number generation exercise?
You claim that forming an average cancels uncertainty: then you should easily be able to demonstrate your claim for the following:
Measure four quantities and record their values, and calculate their uncertainty intervals.
Add the values together while correctly accounting for the uncertainty intervals.
Divide by 4.
Then demonstrate how the resultant uncertainty after the division is smaller than any of the individual elements.
Should be easy: do it on paper without a computer.
“Yet another meaningless pseudo-random number generation exercise?”
And to no-ones surprise the self proclaimed expert on all things metrology rejects using one of the best methods for determining uncertainty. But then if you use any statistical method he’ll say you are just blindly plugging numbers into an equation.
“You claim that forming an average cancels uncertainty”
Reduces uncertainty.
“Measure four quantities and record their values, and calculate their uncertainty intervals.”
OK, using made up values I’ll measure 4 imaginary iron rods, each with a tape measure that has a Type B standard uncertainty of 0.5cm.
20.1(0.5)cm
25.6(0.5)cm
22.2(0.5)cm
28.7(0.5)cm
“Add the values together while correctly accounting for the uncertainty intervals.”
20.1 + 25.6 + 22.2 + 28.7 = 96.6cm
Standard uncertainty of the sum is
√(0.5^2 + 0.5^2 + 0.5^2 + 0.5^2) = √4 * 0.5 = 1.0cm
“Divide by 4.”
96.6 / 4 = 24.15cm
Using the standard rule for multiplication and division, the relative uncertainty is
u(Avg) / Avg = u(Sum) / Sum + 0
Hence the absolute uncertainty of the average is
u(Avg) = Avg * u(Sum) / Sum
and as Avg = Sum / 4
u(Avg) = u(Sum) / 4
In figures
u(Avg) / 24.15 = 1.0 / 96.6
u(Avg) = 24.15 * 1.0 / 96.6 = 0.25cm
So the average is
24.15(0.25)cm,
or if you want an expanded interval, say k = 2
24.15 ± 0.50cm
The expanded uncertainty of the average is small than the expanded uncertainty of any of the individual elements.
Or this could have been done using the Law of propagation, with the partial derivative of each input value being 1/4.
“And to no-ones surprise the self proclaimed expert on all things metrology rejects using one of the best methods for determining uncertainty.”
Do those random numbers come with an attached measurement uncertainty interval?
u(Sum) = 0.5 * 4 = 2. 2/4 = 0.5
This is the AVERAGE UNCERTAINTY. It is *NOT* the uncertainty of the average!
Minimum values = 19.6 + 25.1 + 21.7 + 28.2 = 94.6
Maximum values = 20.6 + 26.1 + 22.7 + 29.2 = 98.6
98.6 – 94.6 = 4. This would give a plus/minus interval of 2. The best case would be +/- 1
So your measurement should be given 24.2 +/- 2. (worst case)
What you have done is come up with an average measurement uncertainty that gives the same total value as the propagation of the individual uncertainties. 0.25 * 4 = 1. Heck, the standard deviation of the data alone is about 3.3!
If these were measurements of the same thing they would normally be considered to be unacceptable since the variance of the measurments is greater than the measurement uncertainty. Someone should go back and redo the measurements.
If they are measurements of different things then no one is concerned about the average uncertainty calculated from the total uncertainty. They would only be interested in the propagated total uncertainty or the standard deviation. For instance, in designing a bridge, you would be more concerned with the standard deviation of 3.3 for the shear strength of the i-beams used in the spans! You might even fail the contract for the i-beams with that kind of measurement uncertainty.
“This is the AVERAGE UNCERTAINTY. It is *NOT* the uncertainty of the average!”
I give up. You’re beyond help. I hope you are getting the best medical attention.
For anyone else, the average of (0.5,0.5,0.5,0.5) is not 0.25.
Tim then proceeds to ignore every source he claims to understand and resorts to interval arithmetic, in order to claim that the uncertainty of the average 0.5, i.e. the average uncertainty.
“Heck, the standard deviation of the data alone is about 3.3!”
I was specifically talking about measurement uncertainty, that is I’m assuming you want the actual average of the 4 values, not the 4 values taken as a sample. If they are a sample it’s too small to be very useful, but the SEM would be 3.3 / 2 = 1.7.
“If these were measurements of the same thing”
They are not. I said they are 4 different rods. Obviously they are not meant to be all the same size, or there is something very wrong with the measurements.
“If they are measurements of different things then no one is concerned about the average uncertainty calculated from the total uncertainty.”
Indeed. That’s why interval arithmetic is not the correct way of doing it.
“They would only be interested in the propagated total uncertainty or the standard deviation.”
Why? What’s that going to tell you?
“For instance, in designing a bridge, you would be more concerned with the standard deviation of 3.3 for the shear strength of the i-beams used in the spans!”
Typical Gorman distraction. We were talking about the sum of different rods, not their shear strength.
“You might even fail the contract for the i-beams with that kind of measurement uncertainty.”
Tim thinks he knows what the imaginary contract said for a hypothetical toy example involving 4 non-existent rods.
“I was specifically talking about measurement uncertainty,”
No you aren’t. And you have to look at *all* the data in the real world. You can’t just blow off the fact that the standard deviation of the measurements is far greater than the propagatedmeasurement uncertainty. That’s a clear indication to anyone knowledgeable about measurement uncertainty that something is amiss. If you and climate science would take even a cursory look at the variance of the temperature data sets it would be obvious that there is an issue with trying to use the data average as a metric for anything.
“They are not. I said they are 4 different rods. Obviously they are not meant to be all the same size, or there is something very wrong with the measurements.”
Me: “And how are Shetland ponies and Quarter-horses part of the same population?”
bell: “They are the population of Shetland ponies and Quarter-horses. Why you would want to treat them as a population is your own business,”
Why are *you* making a population out of different things?
“Why? What’s that going to tell you?”
Not a lot! Why do you think people are criticizing you and climate science for making a population out of intensive properties of different things, even creating a multi-modal distribution from northern and southern hemisphere temperatures!
“Typical Gorman distraction. We were talking about the sum of different rods, not their shear strength.”
If you are using them to span a gap then the very same thing applies! Which you want to ignore. You want to make sure that if they are all on the short side of the measurement uncertainty that the length will still span the gap! So you are interested in the total measurement uncertainty and not the average uncertainty! Calculating the average uncertainty is just mathematical masturbation – you just wind up multiplying by “n” to find the total WHICH YOU ALREADY HAD IN ORDER TO FIND THE AVERAGE!
You *really* have no real world experience at all, do you?
“Tim thinks he knows what the imaginary contract said for a hypothetical toy example involving 4 non-existent rods.”
I’ll ask again. You *really* have no real world experience at all, do you?
“…the standard deviation of the measurements is far greater than the propagatedmeasurement uncertainty. That’s a clear indication to anyone knowledgeable about measurement uncertainty that something is amiss.”
You need to finally explain exactly what you mean by measurement uncertainty. If I measure the height of a bunch of people and find their heights vary by say 20cm, that variation has little to do with how I measured them. Their heights vary becasue they are different heights.
“Why are *you* making a population out of different things?”
I’m not the one doing it. You are the one who keeps asking about the average of two different species of horses. I’m just telling you what you get if you try that – the average of a population consisting of just those two species. I say that’s meaningless, you say it’s meaningless – so why do you keep insisting on doing it.
“If you are using them to span a gap…”
I’m not. We are just back to this pathetic Gorman tactic of asking for toy examples to illustrate how measurement uncertainty decreases in an average, and then trying to turn it into some completely different real world example.
“You want to make sure that if they are all on the short side of the measurement uncertainty that the length will still span the gap!”
If I’m trying to span a gap I want to know the sum of the rods, not the average. I also want to know the uncertainty of the sum. I can get that from the average by multiplying the average by 4, and the uncertainty of the average by 4. That just gets us back to the start when I pointed out that the uncertainty of the average is the uncertainty of the sum divided by 4.
“Calculating the average uncertainty is just mathematical masturbation”
Then stop doing it. I’m talking about the uncertainty of the average, not the average uncertainty. You and karlo on the other hand want to use interval arithmetic which results in you getting the average uncertainty. You are just adding up all the uncertainties and dividing by N Literally the average uncertainty.
“you just wind up multiplying by “n” to find the total WHICH YOU ALREADY HAD IN ORDER TO FIND THE AVERAGE!”
Gormless. You ask for the average I give you the average. Then you say you really want the sum. Say what you actually want, don;t blame me for giving you the answer you asked for.
“Finally”??? Incredible, you’ve been given hint after hint and lesson after lesson, but you deny them all because they don’t fit with your air temperature climatology biases.
Averaging still does not reduce air temperature measurement uncertainties — a simple basic fact you will never acknowledge.
Hints and lessons, just never an answer to the question. What in your world view defines a measurement uncertainty, as opposed to any other sort of uncertainty?
I ask because claiming the measurement uncertainty of a sample of different things is equal to the standard deviation of the sample bhas no resemblance to the word “measurement”.
I’ve told yo uwhat measurement uncertianty is. I’ve given you quotes from the GUM REEATEDLY.
GUM:
When I do an experiment I make measurements using instruments. When Joe Blow does the same experiment he makes measurements using instruments.
I get a a set of data with an average value and an uncertainty interval of values that could reasonably be assigned to the measurand.
Joe Blow gets a set of data with an average value and an uncertainty interval of values that could reasonably be assigned to the measurand.
My average doesn’t have to be the same as Joe Blow’s.
My uncertainty interval doesn’t have to be the same as Joe Blow’s.
But if both values lie in an overlap of the reasonable values then we can assume we have 1. somewhat the same measurand and, 2. we have found the same value for the property being measured.
The average is *NOT* the “expected value” that you find in statistician world. It’s a *reference* value useful in letting experimenters judge whether measurement results are similar. Joe Blow’s stated value may be way out in the positive part of my uncertainty interval but still be correct.
It’s because measurements have UNCERTAINTY. Not error. UNCERTAINTY. The average of my results is not a value from which error can be determined. You can’t use my average and Joe’s average to size “error” because neither is known to be the true value.
“I ask because claiming the measurement uncertainty of a sample of different things is equal to the standard deviation of the sample bhas no resemblance to the word “measurement”.”
What do you think we’ve been trying to tell you about the temperature data you so adamantly believe tells you something? Not only is a single station measuring different things throughout the day it is measuring an intensive property of those things! You can’t add intensive properties so how can you have an average?
“I’ve told yo uwhat measurement uncertianty is. I’ve given you quotes from the GUM REEATEDLY.“
I know what the GUM says. I’m asking what you think the words measurement uncertainty” mean. When you say you want to add the measurement uncertainty to the SEM, what actually differentiates “measurement” uncertainty from any other kind?
If you just meant the uncertainty arising from the uncertainty of the individual measurements, how does that lead you to conclude that the standard deviation of all the values making up a mean or sum is the measurement uncertainty?
“I get a a set of data with an average value and an uncertainty interval of values that could reasonably be assigned to the measurand.”
What measurand? Are you taking an average of different things? What do you mean by assigning values to the measurand?
“The average is *NOT* the “expected value” that you find in statistician world. It’s a *reference* value useful in letting experimenters judge whether measurement results are similar.”
That’s just how it’s used in statistics. Comparing the average of two samples to determine if they are from different populations.
“But if both values lie in an overlap of the reasonable values then we can assume we have 1. somewhat the same measurand and, 2. we have found the same value for the property being measured.”
That’s a bad assumption. And an even worse one if you are using the sample standard deviation as the uncertainty of the mean. Say you measure the heights of a bunch of woman and fond the average and Joe does the same for a bunch of men. You get different averages, but the range of heights overlap, so you conclude that you have found the same value for the average height of men and women.
Uncertainties add. If you have sampling error in your analysis of a set of data that *adds* to the measurement uncertainty of the result.
You are doing nothing here but throwing up a red herring trying to distract.
You’ve just offered up meaningless word salad. Different methodologies are used for assessing measurement uncertainty of different situations. If you are measuring the same measurand multiple times then you use a different methodology than if you are measuring different measurands a single time each. What is so hard to understand about this?
More red herring. The dispersion of values that can reasonably be assigned to the measurand applies to *all* measurement situations. It’s how you determine that dispersion that differs. If you can’t figure out what “assigning values to the measurand” means then you are totally lost in the fog of statistical world.
“That’s just how it’s used in statistics. Comparing the average of two samples to determine if they are from different populations.”
You are *still* showing your biases here. The mass of a fishing weight and the mass of a rubber ball can be the same. Thus their average will be the same. Their weights can’t tell you if they are from the same population or not. But the measurement of their weights can have the same measurement uncertainty!
“That’s a bad assumption”
No, it’s the whole purpose of MEASURING. If two judges timing a runner get different times but their times are within the measurement uncertainty interval what can you glean from the times? You can assume that they are both reasonable values based on the dispersion of possible values that can be assigned to the measurand. But that does *NOT* tell you if one or the other is a true value or not.
“Say you measure the heights of a bunch of woman and fond the average and Joe does the same for a bunch of men. You get different averages, but the range of heights overlap, so you conclude that you have found the same value for the average height of men and women.”
Did you read this before you hit post?
I said: “When I do an experiment I make measurements using instruments. When Joe Blow does the same experiment” (bolding mine, tpg)
How does measuring the height of men become the same experiment as measuring the height of women?
Your lack of reading comprehension skills is just atrocious.
Measurements are really fundamental. The GUM and most textbooks concentrate on how to measure THE SAME THING. In other words, obtaining a probability distribution of measurements surrounding that single thing. From that one can determine a confidence interval describing where possible values can occur.
That is known as an input value to a multivariable functional relationship. A simple example is the area of a table. A = l*w. You don’t make measurements of l1*w1, l2*w2, … ln*wn and find their uncertainty. You measurre ln multiple time and determine the probability function for “l” and its unique uncertainty. Then you measure “wn” multiple times and determine it probability function and the determine its unique uncertainty and finally add the two uncertainties.
These are denoted as Xi,k in the GUM.
As to measuring different things, you move into the realm of reproducibility, that is, changing things. The GUM introduces this in section F.
From the
This is why NIST TN 1900 declares measurement uncertainty is neglible in Example 2. That would complicate the example and its proof that part of the uncertainty is the variance arising from possible differences among samples.
“variance arising from possible differences among samples”
sampling error is an additive factor to measurement uncertainty. It is a standalone factor in only one, restrictive situation.
“Uncertainties add.”
It’s like drawing teeth. You simply refuse to address my question. What do you, personally, mean by measurement uncertainty?
Your inability to answer that question speaks volumes.
As I’ve tried to explain more than once, fundamentally measurement uncertainty is a limit to knowledge. It is a statement that the true value of a measurement result is expected to be within the uncertainty interval, but its precise location remains unknown. An excellent analogy is the Heisenburg Uncertainty Principle in QM — the wave nature of energy/matter makes it impossible to know both energy and position at the same time. Averaging cannot sneak past the HUP and gain information about both.
It is important to realize that without a measurement result, there can be no uncertainty interval, the two are intertwined. And a measurement result can only be produced as the end product a measurement process. Without these, trying to discuss measurement uncertainty isn’t very useful. If you study Annex H of the GUM, it should become apparent that each of them begins with a definition of the desired measurement result, and then gives a fairly detailed description of the corresponding measurement process that will be used.
The examples then proceed to an analysis that attempts to quantify the aspects that affect the result. This is called Uncertainty Analysis, and from these is the proper way to quantify an uncertainty interval. Depending on the measurement process, these can be quite detailed and easily run to scores of pages.
“Different things” should be understood as different measurement results from differing measurement processes.
Some people just can’t accept that there are things that are unknowable. They can’t even accept that there are unnkown unknowables. So they just assume things that make it look like they know everything.
He still has not come around to understand that propagating uncertainties is about combining multiple and diverse factors that contribute to a final uncertainty interval for a particular measurement. For him, propagation is restricted to blindly (and incorrectly) stuffing the average formula into the GUM equation.
“propagating uncertainties is about combining multiple and diverse factors that contribute to a final uncertainty interval for a particular measurement.”
I keep telling you that. Any uncertainty estimate of the global average anomaly is based on multiple diverse factors.
No, the only propagation you talk about is stuffing averages into the GUM equation and getting the answer you want.
The fact remains that averaging cannot create informations from nothing. Maybe you’ve seen too many magic image enhancements scenes on TV.
Uncertainty increases, which is not what climatology wants to hear.
You stuff any function into the Law of propagation, it’s just the only one you have a problem with is the average.
And you never explain why it is wrong, just these hand waving claims about adding information and image enhancement. All I ever point out is that it is possible for the uncertainty of an average to be less than for the individual measurements. A fact, which seems spark of some religious levels of denial.
I don’t have to explain how it is wrong, you are the one claiming that it is reality.
Explain exactly how averaging cancels effects of drift over time that can only be quantified as a Type B interval:
_________
Religion indeed.
“It is a statement that the true value of a measurement result is expected to be within the uncertainty interval, but its precise location remains unknown.”
So you keep saying, and all I can respond withnagain is – yes, I agree, that’s why it’s uncertain.
I feel the real difference is that I think the you can model that uncertainty using a probability distribution, and hence can propagate uncertainties. Whereas you see it as simply an unknown that can only be modelled as an interval of ignorance. This explains your use of interval arithmetic rather than adding in quadrature. It seems to be the same logic Pat Frank uses.
And there may be tomes when that is the most appropriate way of handling some types of uncertainties. But if you are doing that you should be clear that you are avoiding the standard interpretations as described in the GUM.
“I feel the real difference is that I think the you can model that uncertainty using a probability distribution”
What probability distribution did the IPCC use to come up with a best estimate that is not the mid-point of the interval?
“Whereas you see it as simply an unknown that can only be modelled as an interval of ignorance”
If you don’t know what the value is then it *is* an interval of ignorance. All you can do is make a guess known as a “best estimate”.
“But if you are doing that you should be clear that you are avoiding the standard interpretations as described in the GUM.”
The only one avoiding standard interpretations as described in the GUM seems to be you. You keep referencing 4.2.3 while ignoring its dependence on B.2.15. You need to follow your own advice.
“What probability distribution did the IPCC use to come up with a best estimate that is not the mid-point of the interval?”
And the distractions continue. You seem to be agreeing with me about our two world views, why not just ackowledge that rather than being so needlessly aggressive.
I’ve no idea what the actual distribution is. It isn’t a measurement but a projection in any case.
“If you don’t know what the value is then it *is* an interval of ignorance. All you can do is make a guess known as a “best estimate”.”
But if you can make a best estimate you are assuming a distribution. My interpretation of Frank’s “ignorance region” is that there is no probability associated with it. No one value is better than another, but at the same time you cannot say all are equally likely.
“You keep referencing 4.2.3 while ignoring its dependence on B.2.15. ”
I reference 4.2.3 when it’s appropriate, such as when you claim the measurement uncertainty of the average of multiple measurements of the same thing is the standard deviation. If you are not using 4.2.2 to base that claim on what are you using?
The fact is, it doesn’t matter which sub clause if the GUM you use, all roads lead in the same direction. Measure the same thing under repeatability conditions and the uncertainty of the mean is sd / √n. Average dirrent things under different conditions and Eq 10 gives you the uncertainty of the sum divided by the number if observations. Treat a number if observations as a sample from a population and the SEM gives you the sampling uncertainty of the mean. They all give essentially the same conclusion because they all realy on the same statistical theory.
Why does there need to be a probability distribution associated with an uncertainty interval?
Why is it so completely unacceptable that an average does not reduce measurement uncertainty?
And BTW, averaging cannot give you any information about distribution, in fact it throws the needed information away. Paging Dr. Histogram…
“Why does there need to be a probability distribution associated with an uncertainty interval?”
Whether there “needs” to be was the subject we were debating. I think it’s a sensible way of combining multiple uncertainties, and my world view finds it difficult to imagine what an uncertainty means without some sort of probability attached. It feels like a contradiction in terms. “This value could be anywhere within this interval, we have no idea where. But we can’t even say that means it’s equally likely to be anywhere.”
But others seem to accept that as a possibility and I’m prepared to accept there may be some types of models where it makes sense – I just don’t see the use or need for such an anodyne model when talking about independent measurement uncertainties.
“Why is it so completely unacceptable that an average does not reduce measurement uncertainty?”
It isn’t “unacceptable”. In some cases, i.e. where there’s a complete dependence between measurement uncertainties it would be correct, and at the least it’s an upper limit on measurement uncertainty. But in most cases it’s just not correct.
And you are still wrong, and unable to explain how this magic cancelation occurs.
The fact that you think adding in quadrature is “magic” says everything that needs be said about your claimed expertise. Your argument isn’t with me, it’s with every actual expert on the subject.
Again for the “lurkers”, I have never claimed to be an expert in metrology.
How does averaging cancel Type B uncertainty components?
So you claim, because you need it to be so. But you are wrong.
I claim it becasue it is the result of the equation. I can;t help it if you prefer to disbelieve this because you need the uncertainties to be larger for some reason.
Go read the title of the GUM again, what does it say?
Then read through Appendix H and think about what they are doing…
What is the probability distribution of the calibration certificate for a digital thermometer?
To what does “that uncertainty” (singular) refer?
This does not follow; exactly what are you propagating (now plural)?
Are you propagating distributions? Or intervals? Or values?
“You need to finally explain exactly what you mean by measurement uncertainty.”
You *really* can’t comprehend the difference between measuring the same thing and measuring different things, can you? It’s all just “numbers is numbers”.
“I’m not the one doing it.”
ROFL!! You just stated you gave measurements for four different rods!
“I say that’s meaningless, you say it’s meaningless – so why do you keep insisting on doing it.”
If it’s meaningless then why did you put forth the example of measuring four different rods and finding a “meaningful” average?
“I’m not.”
Then why are you summing them?
You *really* can’t understand the real world, can you?
“If I’m trying to span a gap I want to know the sum of the rods, not the average”
That’s *exactly* what I told you. Thanks for repeating what I said.
“That just gets us back to the start when I pointed out that the uncertainty of the average is the uncertainty of the sum divided by 4.”
No, it is the average uncertainty. To get the total uncertainty you had to multiply by 4. You just admitted that the average uncertainty is meaningless and here you are trying to justify it as the measurement uncertainty!
“I’m talking about the uncertainty of the average”
The uncertainty of the average is not the average uncertainty. I showed you that. The uncertainty of the average is related to the maximum and minimum values of the components in the sum used to find the average. The maximum and minimum value of the sum is related to the sum of the uncertainties, not to the average value of the uncertainties.
Which is exactly what my little example with the four intervals showed, and he pooh-poohed it because it doesn’t fit his climatology worldview.
Yep. It is *exactly* what you showed. And, as usual, he wishes to remain willfully ignorant, the worst kind of ignorance.
Using a Monte-Carlo uncertainty assessment requires you to first understand the range of each element, it is not an exercise in stats 101 sampling from a population.
“Add the values together while correctly accounting for the uncertainty intervals.”
You left out the uncertainty intervals, not a surprise. They are an integral part of the measurement, something you’ve never been able to grasp:
m1 ± u_c(m1)
m2 ± u_c(m2)
m3 ± u_c(m3)
m4 ± u_c(m4)
Adding:
m1 ± u_c(m1) + m2 ± u_c(m2) + m3 ± u_c(m3) + m4 ± u_c(m4)
Algebra:
(m1 + m2 + m3 + m4) ± u_c(m1) ± u_c(m2) ± u_c(m3) ± u_c(m4)
In the worst case, the uncertainties simply add, because the true values are expected to lay anywhere within the intervals:
(m1 + m2 + m3 + m4) ± [u_c(m1) + u_c(m2) + u_c(m3) + u_c(m4)]
Dividing:
(m1 + m2 + m3 + m4) / 4 ±
[u_c(m1) + u_c(m2) + u_c(m3) + u_c(m4)] / 4
No magic cancelation occurs through invoking the holy average.
“You left out the uncertainty intervals, not a surprise.”
quit lying. I said what the uncertainty was, I calculated the uncertainty for the sum and the average, and converted them to expanded intervals just for you.
“m1 ± u_c(m1) + m2 ± u_c(m2) + m3 ± u_c(m3) + m4 ± u_c(m4)”
And all you are doing here is ignoring all the actual rules for adding random uncertainties. You add the uncertainties in quadrature.
“No magic cancelation occurs through invoking the holy average.”
Yes, if you ignore the equations that take into account cancellation, you don;t get any cancellation. Well done.
Please to explain for all the lurkers exactly what constitutes a “random uncertainty”:
— — — —
Checking back … nope, this bizarre phrase is nowhere in my post.
The problem is even simpler using interval expression:
m1_lo … m1_hi
m2_lo … m2_hi
m3_lo … m3_hi
m4_lo … m4_hi
m1_lo + m2_lo + m3_lo + m4_lo …
m1_hi + m2_hi + m3_hi + m4_hi
(m1_lo + m2_lo + m3_lo + m4_lo) / 4 …
(m1_hi + m2_hi + m3_hi + m4_hi) / 4
These are four measurements of real-world quantities, not samples pulled out of a hat with pseudo-random numbers.
“Checking back … nope, this bizarre phrase is nowhere in my post.”
Read Taylor. He uses the “bizarre phrase” dozens of times.
“The problem is even simpler using interval expression:”
Pythagoras’ Theorem would be simpler if you just said the length of the hypotenuse is equal to the length of the other two sides. Sometimes simpler is not better.
Am I Taylor??? You will never understand what measurements are:
:These are four measurements of real-world quantities, not samples
:pulled out of a hat with a pseudo-random number generator.
I don’t think you possess even a single clue about the nature of an uncertainty interval.
???? Now you are off in k-space.
And you still can’t show how averaging reduces any of the uncertainties in this real-world example.
“You will never understand what measurements are”
So sayeth the self-proclaimed expert, who thinks random uncertainty is a bizarre term, and has never heard of adding in quadrature.
“I don’t think you possess even a single clue about the nature of an uncertainty interval.”
If you are going by the GUM, you mean an expanded uncertainty, multiplying the standard uncertainty by a coverage factor k. Otherwise you need to say what definition you are using.
“And you still can’t show how averaging reduces any of the uncertainties in this real-world example.”
I did using the conventional definitions of uncertainty and the standard equations described in every document describing measurement uncertainty. I can’t help it if adding in quadrature is too advanced for you.
“I did using the conventional definitions of uncertainty and the standard equations”
All you’ve ever shown is how to calculate the SEM and/or the average uncertainty – while claiming these are the *real* measurement uncertainties that metrology uses.
You didn’t even refute my showing you what the minimum and maximum totals of your 4 rods could be when added together- which defines the measurement uncertainty used in the real world!
“:These are four measurements of real-world quantities, not samples
:pulled out of a hat with a pseudo-random number generator.”
What measurements? You’ve just provided a list of labels. What are you actually measuring? What were the actual measurements, what was the standard uncertainty.
Throw up another smoke-screen and run away from the real issue:
Averaging does not reduce measurement uncertainty, except in special cases.
He’s whining again!
“What measurements? You’ve just provided a list of labels”
How does this refute the math?
You are whining again!
“How does this refute the math?”
We’ve already been through the math. I was just puzzled why km was making such a virtue of the fact that he’s used “real” measurements, when all he was showing was a list of labels.
Yet another smoke-screen is deployed to run away from the real issue.
And FTR, I’ve never asserted that I’m an expert in metrology, this is another one of your red herrings.
The phrase “random uncertainty” is not bizarre as used by Dr. Taylor. His purpose is to continually remind students that only “random uncertainty” is amenable to statistical analysis. Systematic uncertainty can not be identified
by a probability distribution.
Maybe you could read his book and do his problems with an open mind rather than trying to denigrate his book and his knowledge. It would behoove you to state your bona fides that qualify you to criticize a PhD Professor in Physics who has written a textbook that is still in publication.
“…than trying to denigrate his book and his knowledge”
When have I ever done that? I agree with most of what he writes. I’m not the one claiming that he’s wrong because he treats uncertainty as error, or uses the term random uncertainty. Just because I point out when you are misunderstanding the book doesn’t mean I’m denigrating Taylor – I’m denigrating you.
“most of what he writes” — oh this is telling…
He doesn’t know most of what Taylor writes. Taylor specifically states that when he uses the term “error” in his book he is speaking of UNCERTAINTY and not the difference from a true value.
Bellman is a CHAMPION cherry-picker and continually shows his ignorance of the basic concepts of metrology.
UNCERTAINTY IS NOT ERROR!!!!
As I said, to you error is the difference from a true value. Taylor specifically says he uses the term “error” to mean “uncertainty”. I’m not surprised you just don’t get it.
“As I said, to you error is the difference from a true value.”
Yes. That’s what the word means.
“Taylor specifically says he uses the term “error” to mean “uncertainty”.”
He does that at first, before he gets into the more detailed statistics. I think it’s a confusing simplification as uncertainty is not an error, it’s the range of likely errors. But by 4.3 he’s defining uncertainty as the standard deviation of measurements about a true value.
“Yes. That’s what the word means.”
More evidence of your atrocious reading comprehension skills.
Taylor: “For now, error is used exclusively in the sense of uncertainty, and the two words are used interchangeably.”
Of course, you never actually *read* anything, you just cherry pick from it. So maybe it’s not your lack of reading comprehension skills that is the problem, it’s just willful ignorance from not actually reading for comprehension.
“He does that at first, before he gets into the more detailed statistics.”
More evidence of your willful ignorance.
from Chapter 4 of Taylor:
“the random uncertainties, which can be treated statistically, and the systematic uncertainties, which cannot.”
“Most of the remainder of this chapter is devoted to random uncertainties.”
“The relation of the material of this chapter (statistical analysis) to the material of Chapter 3 (error propagation) deserves mention. From a practical point of view these two topics can be viewed as separate, though related, branches of error analysis (somewhat as algebra and geometry are separate, though related, branches of mathematics). Both topics need to be mastered, because most experiments require the use of both.”
from Chapter 5: “This chapter continues our discussion of the statistical analysis of repeated measurements.”
The rest of the book is almost totally about the statistical analysis of random error – i.e. no systematic measurement uncertainty.
Bevington’s book is basically the same.
Your ingrained meme of “all measurement uncertainty is random, Gaussian, and cancels” means you think all measurement uncertainty can be ignored because of the characteristics of Gaussian distributions. Thus the SEM *always* becomes the measurement uncertainty!
More willful ignorance.
In the real world, including climate science, systematic measurement uncertainty is endemic. If you are going to ignore it then that has to be “justified” in some manner or the other. In the real world that’s done by creating a measurement uncertainty budget allowing the judgement to be made as to whether the systematic measurement uncertainty is insignificant enough to be ignored.
You seem to be unable to relate to the real world. That makes your opinions formed in statistical world pretty much useless!
“Taylor: “For now, error is used exclusively in the sense of uncertainty, and the two words are used interchangeably.”
What part of “for now” don’t you understand?
Taylor starts of simply, introducing various concepts to be taken on trust before getting more in to the statistical underpinnings. By 4.2 he’s replacing a vague idea of an uncertainty interval with one based on the standard deviation of measurements about a true value. That is the error model of uncertainty you keep saying is no longer accepted.
Perhaps if you had ever answered any of the times I asked you to explain exactly what you meant by UNCERTAINTY IS NOT ERROR!!!! You might have figured out what you were really objecting to.
“What part of “for now” don’t you understand?”
What part of “for now” do *YOU* not understand?
“By 4.2 he’s replacing a vague idea of an uncertainty interval with one based on the standard deviation of measurements about a true value”
And can you state the assumptions he lays out for when you can do this? You’ve never been able to for Possolo’s examples. My guess is that you have no idea for Taylor either.
Did you bother to read the introduction to Chapter 4.4? You don’t need to answer, I know you didn’t. Here is what he says:
“If x1, …, xn are the results of N measurements of the same quantity x, then, as we have seen, our best estimate for the quantity x is their mean x_bar.” (bolding mine, tpg)
That restriction is what we’ve been telling you over and over and over. Yet you seem to want to ignore that and assume it applies in general. In the real world of temperature measurements IT NEVER APPLIES!
” N measurements of the same quantity x“
Yes. That’s why I said he’s defining measurement uncertainty using the standard deviation of measurements about the true value.
That’s the final comment form me for now. You can post another 20 patronizing ad hominem filled rants for all I care. Whatever I say you will just ignore it and respond to your own “gotcha” strawmen arguments.
“ I’m not the one claiming that he’s wrong because he treats uncertainty as error,”
He doesn’t treat uncertainty as error – not in the sense you are implying. This is just another artifact of your cherry-picking instead of actually studying the text.
In the third paragraph of his book he writes:
“In science, the word error does not carry the usual connotations of the term mistake or blunder. Error in a scientific measurement means the inevitable uncertainty that attends all measurements.”
“For now, error is used exclusively in the sense of uncertainty, and the two words are used interchangeably.”
You are a champion CHERRY-PICKER, and like all cherry-pickers you continually get caught out not actually understanding any base concepts!
““In science, the word error does not carry the usual connotations of the term mistake or blunder. Error in a scientific measurement means the inevitable uncertainty that attends all measurements.””
What do you think anyone has meant every time they yelled at me “UNCERTAINTY IS NOT ERROR!!”?
Error does not mean mistake in statistics. It’s the difference between the true or expected value and an observation. It’s a way of analyzing uncertainty or deviation in observations and how they propagate. The GUM tries to use a slightly different definition of uncertainty, but says you can still use the error and true value model if you prefer and that in any case the calculations will be the same.
But some here take this as a holy command to abolish all mention of the word error, without seeming to understand that the alternative definition gives you just the same results. It’s clear from the last few comments that you and KM think that abolishing the “error” model means going back to something like interval arithmetic, and ignoring all the probabilistic methods for propagating uncertainty. But it’s just dishonest to claim that that is what the GUM is doing.
No, the reason I keep pointing this out is because you and the rest of the climatology crowd do not understand the difference, and in fact deny the very existence measurement uncertainty.
You have to do so in order to protect the tiny, unmeasurable air temperature “anomalies” that you hang your hats on.
Think how much easier your life would be if you tried to engage with what I and the “rest of climatology crowd” were saying rather than argue with your own phantoms.
When you equate the “true value” and the “expected value” it is OBVIOUS what you are saying. And it is wrong!
“Error does not mean mistake in statistics. It’s the difference between the true or expected value and an observation”
You just made my point by equating the true value and the expected value!
You don’t understand uncertainty at all!
“ ignoring all the probabilistic methods for propagating uncertainty.”
No, we don’t ignore it at all. But we understand how those methods have to be applied. You don’t. You never have. And you have never bothered to learn. You just remain willfully ignorant – the worst kind of ignorance.
I didn’t equate them. I was describing different uses for the word. If you are measuring a thing with a true value the error is the difference between the measurement and the true value. If you are measuring something from a population the error can be the difference between that value and the population mean.
“No, we don’t ignore it at all.”
Then what’s you justification for using interval arithmetic?
“But we understand how those methods have to be applied.”
These arguments from authority are pretty pathetic when you never demonstrate any of this expertise. Your only arguments are “we’re the experts” or “you don’t know nothing”. If you really wanted to impress me with your experience, provide evidence that the best way of propagating independent uncertainties is to just add them all up. Then explain why every source form Taylor to the GUM is wrong.
“I was describing different uses for the word. If you are measuring a thing with a true value the error is the difference between the measurement and the true value.”
GUM: “Although these two traditional concepts are valid as ideals, they focus on unknowable quantities: the “error” of the result of a measurement and the “true value” of the measurand (in contrast to its estimated value), respectively.”
If the true value and error are UNKNOWABLE then they are of no use in the real world.
“If you are measuring something from a population the error can be the difference between that value and the population mean.”
Nope! Here again you are assuming the population mean is a “true value”. The population mean is nothing more than an *estimate*. The true value is an UNKNOWABLE. If, and I emphasize *IF*, the measurements form a normal distribution, then the difference between the mean and the measured value is part of the DISPERSION of REASONABLE values that can be assigned to the measurand. If the distribution is not normal then the dispersion around the mode may very well be a better measure of the reasonable values that can be assigned to the measurand.
“Then what’s you justification for using interval arithmetic?”
Because there is no guarantee that the measurement dispersion is not asymmetric. You can *assume* a distribution but it should *always* be justified. I just left you a message about an asymmetric uncertainty interval used in the IPCC report. The use of the INTERVAL doesn’t imply *anything* about the distribution. You don’t have to assume a Gaussian distribution the way you and climate science do.
“These arguments from authority are pretty pathetic when you never demonstrate any of this expertise.”
You have absolutely no understanding of the basics and can’t judge expertise at all.
“Your only arguments are “we’re the experts” or “you don’t know nothing”. “
You are CONTINUALLY provided references to any assertions I, Jim, or KM make. And you CONTINUALLY demonstrate that you “don’t know nothing”. All you ever offer are cherry picked pieces that you think confirm your misconceptions – and they *are* misconceptions, of how the real world works!
“If you really wanted to impress me with your experience, provide evidence that the best way of propagating independent uncertainties is to just add them all up.”
Taylor covers this in detail in his Chapter 3. I just left you a message with quotes as to why he says Chapter 3 is so essential. In Chapter 9 he says about direct addition of uncertainties vs root-sum-square: “We also stated, without proof, that whether or not the errors are independent and random, the simpler formula (9.1) always gives an upper bound on ẟq; that is, the uncertainty ẟq is never any worse than is given by (9.1).” No one is saying that direct addition is always the *best* way, that’s just you and your lack of reading comprehension skills. But direct addition can also *NOT* be considered as the best way. Direct addition many times is the best way to demonstrate a principle even if it wouldn’t actually be used in a specific real world situation.
And I have given you MULTIPLE examples from my own life. From designing foot bridges to span a gully to designing stairs to designing beams to support the upper floors and roof structure of a house. Working with financial budgets and safety budgets in each and every case. Why do you think I’m always using 2″x4″ board examples? And those are just from my personal life. I’ve given you examples like designing microwave links for carrying telephone circuits – where the success/failure of the links under adverse conditions carry professional liabilities, both civil and criminal if the circuits are carrying public safety communications.
STOP WHINING!
He opts to yap about the for the GUM because he thinks it gives him the answer he wants, but of course ignores the title and scope of the document.
He denies that uncertainty always increases, which is a symptom of his deeper denial of the existence of measurement uncertainty. It is a threat to his air temperature time-series graphs. Thus he only agrees with Taylor in part.
I suspect that underneath all the smoke and noise, he doesn’t believe uncertainty intervals even exist. This is all in line with standard climatology thats treats all real measurement uncertainty as zeros.
The old line still holds: “The error can’t be this big!”
I have no idea what he’s going to do the first time he runs into a paper where “best estimate” is not provided, only the interval in which it is believed the property of the measurand actually lies.
I expect he’ll do what anyone would do, and assume the best estimate is the mid point of the interval. Do you think it’s likely that at some point there will be a new set of standards that forbid the use of stated value with uncertainty? You’ve been claiming this is about to happen for years, but have never provided any evidence.
Personally, I think this would interesting as long as there was a requirement to provide a probability distribution. Maximum likelihood as best estimate can be very misleading.
But if you are suggesting you want to start using these ignorance intervals with no supposed probability distribution, you really need to provide a reference for when you think this absurd change will happen.
An you would be wrong, as usual. Your denial of measurement uncertainty includes denying that uncertainty limits can be non-symmetrical.
And you still don’t understand that an uncertainty interval does not necessarily imply knowledge of any specific distribution.
Couldn’t have said it better myself. I have no problem assuming the *mid-point” might be the best estimate. What I have a problem with is assuming that the distribution of the uncertainty is always Gaussian and therefore the mean is the mid-point – with *NO* justification for the assumption.
For instance, TTL logic levels have a “gray” area. Ground to about 0.8v is considered a 0. 2v to 5v is considered a one. What happens when the voltage is between 0.8v and 2v is not certain for any specific situation – it is UNCERTAINTY, part of the Great Unknown. CMOS has a similar gray area but are different voltage levels.
What you *do* know is that those voltage levels are asymmetric so the uncertainties from such equipment will be asymmetric as well, just based entirely on the physics of the equipment. So when a voltmeter using CMOS logic is used and the measurement uncertainty is given as 1% of full-scale indication why would you assume the mid-point of a set of measurements would form a Gaussian distribution?
Assuming that the average of a set of measurements from such an instrument is the “best estimate” is a crutch of a statistician, not of someone familiar with metrology. Since for TTL the voltage for a 1 has an interval of 3 volts and for a zero is 0.8v I would usually, at least for precision measurements, assume a right-skewed distribution uncertainty distribution.
Of course I don’t expect bellman to understand any of this. He lives in statistical world where everything is random and Gaussian.
TTL (transistor-transistor-logic) usually uses power supplies at 5 volts. CMOS (complementary metallic oxide semiconductor) is less demanding on voltage requirements.
But they both still have a “gray” area where the response of the device is uncertain. And that gray area is not symmetric so the uncertainty won’t be symmetric either.
bellman can’t get it into his head that the SEM is the standard deviation of the sample means – it is a metric for SAMPLING EROR and not for measurement uncertainty.
The standard deviation for measurement uncertainty is the variation in the *data points*, i.e. the measurements.
The SEM is the metric for variation between samples taken from a population. Technically the SEM requires having *multiple* samples. A single sample can only be used if it is ASSumed that the single sample has exactly the same characteristics as the population, in which case the SEM *still* doesn’t apply since the average would be the same for both as well as the standard deviation, thus there is no sampling error! If that single sample is *not* exactly the same as the population then trying to calculate an SEM from it *adds* additional measurement uncertainty because it is a guess!
When asked whether the temperature data sets are *a* (one) sample or a population those defending climate science are so reticent to answer that I have yet to have anyone actually tie themselves to one or the other.
He desperately needs it to keep his air temperature trends meaningful, at this point he is way too invested in this averaging reduces uncertainty meme that he cannot let go of it. It is all so in line with climatology —with the answer is already known, let us spend $200 billion trying anything to justify the answer.
Nope.
Nope. Measurement uncertainty always grows. It never gets smaller. The average measurement uncertainty is *NOT* the measurement uncertainty of the data. Being an average means there will be individual measurement uncertainties that are smaller and individual measurement uncertainties that are greater than the average.
If you have z = (x +/- u1) + (y +/- u2) then the measurement uncertainty is the addition of u1 and u2 whether the addition is done directly or in quadrature. The measurement uncertainty is *NOT* (u1 + u2)/2
If the data set is (x1 +/- u1), (x2 +/- u2), …, (xn +/- un)
The measurement uncertainty is the addition of u1 through un whether it is done directly or in quadrature. It is *NOT* (Σu_i)/n or the average uncertainty.
The fact that you have never provided a single quote from the GUM in support of your assertion that the SEM is the measurement uncertainty proves that this is just your misguided opinion.
GUM:
…………………………………………
………………………………………….
It is the variability of the data that determines the measurement uncertainty, i.e. the dispersion of OBSERVED values around the mean.
Of course it is. SO WHAT? It’s the AVERAGE variance divided by “n” again! Avg = [ Var(X1) + Var(X2)/2. Then you divide by 2 again!
That is the variance of the average! The SEM again! You just can’t get away from that can you?
“The variance if the average is not the average variance, at least for independent random variables.”
The variance of the average is the SEM! That is not the measurement uncertainty!
How many times do you have to be told that how precisely you locate the mean has nothing to do with the measurement uncertainty of the average. The average is the best ESTIMATE of the value of the measurand and the measurement uncertainty associated with that ESTIMATE is the dispersion of the values that could reasonably be attributed to the measurand. *NOT* the standard deviation of the sample means!
“s it because you have severe memory loss, and keep forgetting all the times I say I agree?”
Every time you claim the SEM is the measurement uncertainty associated with a set of measurements YOU DISAGREE!
“Measurement uncertainty always grows. It never gets smaller.”
That’s your religion – it’s demonstrably false. You even accept it’s false for the case of averaging measurements of the same quantity.
“If you have z = (x +/- u1) + (y +/- u2) then the measurement uncertainty is the addition of u1 and u2 whether the addition is done directly or in quadrature. ”
And we are back to square one – with Tim still ignoring the fact that an average is not a sum.
“It is *NOT* (Σu_i)/n or the average uncertainty.”
Correct. It is not.
“The fact that you have never provided a single quote from the GUM in support of your assertion that the SEM is the measurement uncertainty proves that this is just your misguided opinion.”
My point is that the definition of measurement uncertainty given in the GUM is that it characterizes the dispersion of the values that
could reasonably be attributed to the measurand. And that if the mean is the measurand then that defines the range of values it’s reasonable to ascribe to the mean.
Whereas you seem to read it as the range of all the values that went into the calculation of the mean.
Given a random sample my interpretation is compatible with the SEM being the uncertainty of the mean, whereas your interpretation is that it’s the standard deviation of all the observations.
But your interpretation is incompatible with your claim that the measurement uncertainty of the average is the same as that for the sum. Hence your desperate attempts to claim that the SD increases with sample size.
“Gum 4.2.2”
Yes, that’s describing a Type A estimate of the standard uncertainty for a single measurement.
Now read the next section where it describes how to work out the uncertainty of the mean of those N observations.
“Of course it is. SO WHAT? It’s the AVERAGE variance divided by “n” again! Avg = [ Var(X1) + Var(X2)/2. Then you divide by 2 again!”
Dividing an average by N does not give you an average. You really need to get rid of this obsession that anything that involves dividing something by N, or a power of N, or by the root of N means you are taking an average.
“That is the variance of the average! The SEM again!”
No. The SEM is the root of the variance of the average. But well done, you are getting there.
“That is not the measurement uncertainty!”
You said “Thus the measurement uncertainty of Y is going to be described by Var(X1) + Var(X2)”. You are happy to calculate measurement uncertainty in terms of the variance of a random variable. Yet as soon as you realize it gives you the result you don’t want, you just stamp your foot and go “nah! not going to accept that”.
“How many times do you have to be told that how precisely you locate the mean has nothing to do with the measurement uncertainty of the average.”
Once if you could offer a rational justification, as many times as you like if you can’t.
“The average is the best ESTIMATE of the value of the measurand and the measurement uncertainty associated with that ESTIMATE is the dispersion of the values that could reasonably be attributed to the measurand.”
I know the GUM is badly worded at times, but please try to understand what the words “dispersion of the values that could reasonably be attributed to the measurand.” means. If the measurand is the population mean and your best estimate is 100, and you’ve located it reasonably to within ±2, but the standard deviation of all the values was 10, is it reasonable to attribute a value of 80, or 120 to the mean?
“And we are back to square one – with Tim still ignoring the fact that an average is not a sum.”
The average is *NOT* a functional relationship. It is a statistical descriptor. A statistical descriptor can have sampling error but it doesn’t have measurement uncertainty. The data values in the data set can be used to establish the measurement uncertainty associated with the best estimate of the average.
“And that if the mean is the measurand then that defines the range of values it’s reasonable to ascribe to the mean.”
Give us a reference stating that the mean is a measurand and not just a statistical descriptor of a set of measurements.
from copilot ai:
From GUM, Sec 5.1.2
The propagation of uncertainty is associated with MEASUREMENTS, not with statistical descriptors of the measurements.
Again, from copilot:
You keep wanting to define sampling error as measurement uncertainty. It isn’t. It never will be. And you have not one single reference to offer stating otherwise.
“The average is *NOT* a functional relationship.”
It is a functional relationship. I really don’t know why you keep misunderstanding this. It’s just another case where you don;t understand what the terms mean.
And you are sidestepping my point, which is that average is not the sum.
” A statistical descriptor can have sampling error but it doesn’t have measurement uncertainty.”
Then stop claiming you know what the measurement uncertainty of a mean is.
“The data values in the data set can be used to establish the measurement uncertainty associated with the best estimate of the average.”
What do you mean by a measurement uncertainty associated with something you don’t think is a measurand?
“Give us a reference stating that the mean is a measurand and not just a statistical descriptor of a set of measurements. ”
NIST TN1900 Ex 2.
“from copilot ai”
Seriously? BTW, if you are going to use your imaginary friend to do you home work, please specify what prompt you used. Here I typed “can a population mean be a measurand?” into copilot and it said:
“The propagation of uncertainty is associated with MEASUREMENTS, not with statistical descriptors of the measurements.”
What do you think the uncertainty of a measurement is? The GUM defines standard uncertainty in terms of a standard deviation of a probability distribution.
GUM 3.3.5
“You keep wanting to define sampling error as measurement uncertainty.”
No, I’m happy to just call it uncertainty. You keep whining about how you want measurement uncertainty, despite claiming the mean isn’t a measurement.
Not even the copilot ai agrees with this. I gave you what it said. The average is a statistical descriptor. It is not a measurand. Since it isn’t a measurand it can’t be part of a functional relationship.
A statistical descriptor is no different than a color. Saying a car is blue does not mean the color blue is a functional relationship with the car, it is a descriptor of the car.
Does it ever sink into your head that metrology is heading toward *NOT* using a “best estimate” any longer but just defining the interval endpoints?
You’ll no longer see “stated value +/- uncertainty”. Instead of 10 +/- 1 you’ll just see “the measurement has an uncertainty interval from 9 to 11”.
The use of a “best estimate” was just a carry-over from the use of “true value +/- error”. Where in the uncertainty interval the actual true value or “best estimate” actually is part of the GREAT UNKNOWN.
What are you going to do when I tell you the measurement interval for the temperature at my location right now is between 55F and 56F? Are you going to assume you know where in that interval the “true value” or “best estimate” actually is?
“What do you mean by a measurement uncertainty associated with something you don’t think is a measurand?”
Perhaps I’ve been unclear. Measurements have an uncertainty interval. Choosing the mid-point of that interval as the “best estimate” and defining the interval in terms of the mid-point as a reference point is meaningless. As an *estimate” you don’t actually even know which point in the interval is the “best”. You are just choosing it as a reference point. If the measurement uncertainty is asymmetric the mid-point isn’t even the “best estimate”.
You always seem to forget that in all the references the use of the “average” as the best estimate assumes that all measurement uncertainty is random, Gaussian, and cancels. Those are *always* stated as assumptions. That assumption rarely applies when you are measuring different things with different things at different times – which what most real world data is, especially when it comes to temperature.
ROFL! You seem to have missed this from copilot! As usual, your lack of reading comprehension skills is apparent.
Most of us live in metrology world and not in your statistical world.
Uncertainty of a measurement is that area of the Great Unknown that can’t be penetrated!
GUM:
*YOU* seem to want to take the “average” as the “true value” which is *not* what the GUM says.
In statistical world the average may be your “true value”. In the real world it is just a probability expectation. It might be the most common result but that does not mean that it is the “true value”. The probability of the average being the true value is *NOT* 100% except in your statistical world.
“No, I’m happy to just call it uncertainty”
It is *sampling* uncertainty, not measurement uncertainty. It is a statistical artifact, not a measurement value.
“Not even the copilot ai agrees with this.”
This is why a fear ai might be the end of civilization as we know it. Not only are they likely to be wrong, but people will just believe them as they lose any ability for critical thinking.
Seriously though – as I already told you, you need to say what your prompt was. It’s easy to trick a generative AI into agreeing with you. Here for the record is what I get when I ask copilot “is an average a functional relationship”
“It is not a measurand. Since it isn’t a measurand it can’t be part of a functional relationship. ”
That’s quite a non-sequitur. What definition of functional relationship requires something to be a measurand?
“Saying a car is blue does not mean the color blue is a functional relationship with the car”
Why do you think the relationship is between the car and the colour. The functional relationship is between the inputs that determine the colour.
“Does it ever sink into your head that metrology is heading toward *NOT* using a “best estimate” any longer but just defining the interval endpoints?”
Do you ever realise you fail to answer the questions I ask, and just try to cause another distraction. Again, if the mean is not a measurand how can it have a measurement uncertainty?
“You’ll no longer see “stated value +/- uncertainty”. Instead of 10 +/- 1 you’ll just see “the measurement has an uncertainty interval from 9 to 11”.”
Citation required. And why keep going on about the GUM if you think all it’s statements on how to report measurements and uncertainty are wrong.
“What are you going to do when I tell you the measurement interval for the temperature at my location right now is between 55F and 56F? Are you going to assume you know where in that interval the “true value” or “best estimate” actually is?”
I’m going to assume the best estimate is 55.5, unless you tell me that the uncertainty is not symmetric.
“Measurements have an uncertainty interval. Choosing the mid-point of that interval as the “best estimate” and defining the interval in terms of the mid-point as a reference point is meaningless.”
You mean that thing everyone of your sources has been saying to do since forever? When do we start burning all these books?
“As an *estimate” you don’t actually even know which point in the interval is the “best”.”
Of course you do. That;s the first thing you work out. You can justify it in terms of maximum likelihood or some such.
“You are just choosing it as a reference point. If the measurement uncertainty is asymmetric the mid-point isn’t even the “best estimate”.”
Which is why it’s important to state what the best estimate is along with the interval. If you just say that the interval is between 1 and 3, and it’s asymmetric you have no way of kn owing that. If you say the best estimate is 1.5, with an interval of 1 to 3, you have a better idea of what the spread of likely values is.
“You seem to have missed this from copilot!”
You seem to forget that I don;t give a toss what copilot says.
“Uncertainty of a measurement is that area of the Great Unknown that can’t be penetrated! ”
Your thinking of your own mind there. If measurement uncertainty is so impenetrable, why do it? Who cares what the measurement uncertainty is, it’s unknowable?
Which is not describing measurement uncertainty as the “GREAT UNKNOWN”. The dispersal of an infinite number of values is specifically referring to a probability distribution, which allows you to know how certain or not you are about the measurement.
“In statistical world the average may be your “true value”. In the real world it is just a probability expectation.”
Which average are you talking about? The sample average is not the “true value”, it’s the best estimate of the population mean. You can call the population mean the “true value” if you want, but that’s only in the sense it’s the value you are trying to estimate. The GUM doesn’t like the term “true value” becasue it’s redundant – by definition the measurand is the “true” value. And also because you have to define exactly what you mean by true.
From the GUM
This is what you always do. You state your opinion with no supporting references. I guess you hope people will see you as an expert.
Your own reference supports what I’ve just said. But if you insist, yes, I should have said a true value to be consistent with the GUM world view.
I’m still waiting for your reference that says you can use relative uncertainties when adding or subtracting.
Read Dr. Taylor Sections 2.7 and 2.8.
Here is how Section 2.9 begins.
Nowhere does it say you CAN NOT use fractional uncertainties when adding measurements.
You keep asking for a positive statement saying to use fractional uncertainties when measurements are added. I do not have that. BUT, neither do you have a positive statement that says one CAN NOT use them.
Dr. Taylor also says.
Very appropo to your ridiculous example.
“Nowhere does it say you CAN NOT use fractional uncertainties when adding measurements.”
I’ve already given you a direct quote where he says adding and subtraction use absolute uncertainties. 3.8
You keep saying you need to do all the exercises. Try doing any of them using relative uncertainties and see if you get the correct result. E.g. 3.17(d)
(5.6 ± 0.7) + (1.9 ± 0.3)
Assuming independent uncertainties.
Using absolute uncertainties I get
7.5 ± 0.8
Using relative uncertainties
7.5 ± 20% = 7.5 ± 1.5.
What does Taylor give as the correct result?
7.5 ± 0.8
“BUT, neither do you have a positive statement that says one CAN NOT use them.”
If every source says if you add use absolute uncertainties and if you multiply use relative uncertainties, don’t you think that’s trying to tell you what you should do.
And again, if you really understood the subject, you could work out for yourself why fractional uncertainties are used when multiplying and not for adding. You can start with the general rule of propagation and see what happens when you apply it to adding or multiplying.
“Seriously though – as I already told you, you need to say what your prompt was”
Look to *YOUR* own prompt! It resulted in copilot telling you that in metrology science the average is not a measurand!
from YOUR OWN PROMPT:
“hen dealing with measurement science, such as metrology, measurands usually refer to physical quantities that can be directly observed or experimentally determined.””
Go whine to someone else about how copilot is wrong.
“ It’s easy to trick a generative AI into agreeing with you.”
DID *YOU* TRICK COPILOT? I quoted the answer it gave to *YOUR* prompt!
copilot from your prompt: ““hen dealing with measurement science, such as metrology, measurands usually refer to physical quantities that can be directly observed or experimentally determined.””
“Yes, an average can be considered a functional relationship in mathematical terms”
Look to your own prompt! The operative words here are “in mathematical terms”. IT DOES NOT SAY IN METROLOGY TERMS.
As usual your reading comprehension skills are atrocious. This is just one more proof of your meme “numbers is just numbers”.
“That’s quite a non-sequitur. What definition of functional relationship requires something to be a measurand?”
METROLOGY!
GUM:
————————————————–
4.1 Modelling the measurement
4.1.1 In most cases, a measurand Y is not measured directly, but is determined from N other quantities X1, X2, …, XN through a functional relationship f :
Y = f (X1, X2, …, XN ) (1)
NOTE 1 For economy of notation, in this Guide the same symbol is used for the physical quantity (the measurand) and for the random variable (see 4.2.1) that represents the possible outcome of an observation of that quantity. When it is stated that Xi has a particular probability distribution, the symbol is used in the latter sense; it is assumed that the physical quantity itself can be characterized by an essentially unique value (see 1.2 and 3.1.3).
NOTE 2 In a series of observations, the kth observed value of Xi is denoted by Xi,k; hence if R denotes the resistance of a resistor, the kth observed value of the resistance is denoted by Rk .
NOTE 3 The estimate of Xi (strictly speaking, of its expectation) is denoted by xi.
—————————————- (bolding mine, tpg)
“physical quantity”, “measurand”, “observation”, “functional relationship”
I’ve continually asked you to show me a physical average or an observation of an average. You’ve failed every single time!
You live in someplace other than the real world – I’ve named it statistical world. Where numbers is numbers. It explains why you think an average is a measurand. It explains why you think that significant digit rules are a joke. It explains why you think an SEM is a measurement uncertainty instead of a sampling error metric. It explains why you think all measurement uncertainty is random, Gaussian, and cancels so it can be ignored. It explains why you think you don’t have to weighted averages for measurements. It explains why you think the average uncertainty is the uncertainty of the average. It explains why you can’t figure out the difference between accuracy and precision. It explains why you think average uncertainty is important in a collection of dissimilar things.
And you are trying to suck everyone into your statistical world in the belief that it is true metrology.
You’ve even failed to read the very last paragraph in the explanation by colpilot of a functional relationship.
“However, if you’re asking whether an average represents a functional dependence in a broader sense—like in physics or economics—it depends on the context. In some cases, an average is just a statistical summary and doesn’t necessarily imply a direct cause-and-effect relationship.
In what context is the average a direct cause-effect relationship in metrology?
You just can’t stop cherry picking without understanding the basic concepts.
“Do you ever realise you fail to answer the questions I ask, and just try to cause another distraction. Again, if the mean is not a measurand how can it have a measurement uncertainty?”
The average doesn’t have an inherent measurement uncertainty. It carries the measurement uncertainty of the measurement data. it’s a BEST ESTIMATE, a concept that is being gradually left behind. If the true value can be anywhere in the interval then a “best estimate” is just a fools errand!
As usual you just ignore the hard issues.
“Citation required. And why keep going on about the GUM if you think all it’s statements on how to report measurements and uncertainty are wrong.”
Go look at the IPCC reports on future climate. You’ll find no stated values, only confidence intervals.
Nor have I said the GUM is wrong. I have said the methods of reporting measurements is evolving, that does *not* mean current methods are wrong. As usual, your reading comprehensions skills are atrocious.
“I’m going to assume the best estimate is 55.5, unless you tell me that the uncertainty is not symmetric.”
The word “uncertainty” just has no meaning whatsoever for you, does it? How do you *know* what the uncertainty profile is?
The interval 55 to 56 means it can be ANYWHERE in between. Where it actually lies is part of the Great Unknown, unless you are bellman I guess!
“Go look at the IPCC reports on future climate. You’ll find no stated values, only confidence intervals. ”
OK, just did that. From the Synthesis Report (SYR) (AR6) Note 30.
That’s five best estimates for different scenarios.
“1.8 [1.3 to 2.4]°C”
An interval doesn’t imply a symmetric uncertainty interval the way +/- 0.6 would. The actual temperature can be anywhere from 1.0 to 1.8. Making this into a symmetric statement would turn out to be 1.9 +/- 0.6C so specifying the interval instead avoids having to assume a Gaussian distribution the way you would do.
“A.1.2 The likely range of total human-caused global surface temperature increase from 1850–1900 to 2010–20197 is 0.8°C to 1.3°C, with a best estimate of 1.07°C. Over this period, it is likely that well-mixed greenhouse gases (GHGs) contributed a warming of 1.0°C to 2.0°C8 , and other human drivers (principally aerosols) contributed a cooling of 0.0°C to 0.8°C, natural (solar and volcanic) drivers changed global surface temperature by –0.1°C to +0.1°C, and internal variability changed it by –0.2°C to +0.2°C. {2.1.1, Figure 2.1}”
note carefully the last sentence: “Over this period, it is likely that well-mixed greenhouse gases (GHGs) contributed a warming of 1.0°C to 2.0°C8″” I don’t see a “best estimate” in this statement, just an interval size.
Note carefully that
1.3C – 1.07C = 0.23C
1.07C – 0.8C = 0.27C
An asymmetric best estimate. The actual statement of possible values is given as a range, 0.8C to 1.3C, not as 1.05C +/- 0.25C.Giving the interval doesn’t mean you *can’t* give a best estimate. It only means you aren’t trying to always assume a symmetric uncertainty around a Gaussian mean. It’s why there is a move away from specifying a best estimate +/- uncertainty interval. Giving the endpoints or the interval size is far more useful to those doing the same experiment. If a subsequent experiment gets 0.9C that is considered to be accurate enough to confirm the prior experiment.. If a subsequent experiment gets 1.2C then it is also considered to be accurate enough to confirm the prior experiment.
As usual, your reading comprehenion skills are atrocious.
Are you capable of ever acception you were wrong? You claim that the new standard is to only quote an interval, you claim that the IPCC does this for future projections. Then when I show you they do specify a best estimate, you go of on another distracting rant.
“An interval doesn’t imply a symmetric uncertainty interval the way +/- 0.6 would”
You wouldn’t know it wasn’t symmetric if you just quite an interval. It’s the fact that the best estimate is not the mid pint that indicates the unsymetric nature.
Did you see a +/- u in anything you quoted or in what I quoted?
“Then when I show you they do specify a best estimate, you go of on another distracting rant.”
The intervals they use stand alone. It is not referenced to a “best estimate” in any manner whatsoever. It’s *EXACTLY* what I stated. Your lack of reading comprehension skills is showing again.
“You wouldn’t know it wasn’t symmetric if you just quite an interval. It’s the fact that the best estimate is not the mid pint that indicates the unsymetric nature.”
You don’t NEED to know if it is asymmetric or not as long as your measurement falls within the interval! You have continued to fail in absorbing what a measurement is given *for*. It’s to allow someone measuring the same thing to duplicate the measurement and judge if it is the same as yours! If that is *not* what the measurement is for then just say “cut to fit” so no one needs to know the measurement!
“Did you see a +/- u in anything you quoted or in what I quoted?”
So let me get this straight. All this time you’ve been claiming the standard was going to abolish the use of best estimate and insist all that should be quoted wax an interval, what you really meant was everyone was going to have to quote a best estimate and an interval. Is that your point? Or are you just doing your usual dissembling to avoid admitting you were wrong?
Simply unfreakingbelievable. I cannot explain your lack of reading comprehension skills. I told you the move is to start quoting the interval in which a measurement might lay. That is what the quotes show the IPCC did. When asked if you could see a +/- anywhere you make up words to put in my mouth. What I told you was that there was a move *from* using stated value +/- measurement uncertainty to just giving the interval – exactly what the IPCC did.
If you have the interval you don’t *need* a “best estimate”. That “best estimate” is a guess at the true value. It’s irrelevant when trying to judge whether two measurements are similar. Someone else doing the same measurement doesn’t need the best estimate. All they need to know is that their measurement is inside the interval of possible reasonable values.
I cant let this lie slip by. Tim says:
“Simply unfreakingbelievable. I cannot explain your lack of reading comprehension skills. I told you the move is to start quoting the interval in which a measurement might lay. That is what the quotes show the IPCC did. When asked if you could see a +/- anywhere you make up words to put in my mouth. What I told you was that there was a move *from* using stated value +/- measurement uncertainty to just giving the interval – exactly what the IPCC did.”
What he actually said was
and
and
The IPCC show a best estimate – he claims this supports his claim becasue the have an interval along with the best estimate.
Where is the uncertainty analysis attached to the IPCC “projections”?
Hint — it doesn’t exist.
“Of course you do. That;s the first thing you work out. You can justify it in terms of maximum likelihood or some such.”
This is *NOT* the first thing you work out. Again, you know NOTHING about metrology yet come on here trying to act like one. Can you GUESS at what the first thing you work out actually is?
“Which is why it’s important to state what the best estimate is along with the interval. If you just say that the interval is between 1 and 3, and it’s asymmetric you have no way of kn owing that. If you say the best estimate is 1.5, with an interval of 1 to 3, you have a better idea of what the spread of likely values is.”
Did you actually read this for meaning before you posted it?
Even if you say the best estimate is 1.5 THAT’S BASED ON A WILD ASS GUESS! You just stated that if the uncertainty is asymmetric you have no way of knowing what the interval is (which is wrong, you *can* know the interval without knowing the best estimate) so how can you know what the best estimate is?
The *interval* gives you the spread of likely values, not the reference value! Using the mid-point as the best estimate is based on the unjustified assumption that the distribution is normal. You and climate science are just chock-full of unjustified assumptions!
“You seem to forget that I don;t give a toss what copilot says.”
Then why did you quote it as a justification for claiming the average is a functional relationship? And why did you not read the entire quote for meaning?
“Your thinking of your own mind there. If measurement uncertainty is so impenetrable, why do it? Who cares what the measurement uncertainty is, it’s unknowable?”
You are *never* going to get it! It isn’t the measurement uncertainty interval that is unknowable, what is going on inside it is unknowable. If what is going on inside the uncertainty interval is known then you don’t have an uncertainty interval!
Don’t you *ever* get tired of coming on here and showing your ignorance of basic concepts?
Yes, several references call the mean a “point estimate” to remove the inference that it is “the probable answer”. That inference removes the importance of what the uncertainty interval actually is. The GUM D.5.2 makes that very plain with its reference to an infinite number of values.
Gum 4.2.2”
You state:
“Values” is plural. Is “single measurement” plural too?
The GUM describes qₖ as observations for a unique input quantity. An “input quantity” is a variable in a functional description.
For example,
Area = length × width or A = l×w
Length is a unique input variable.
Width is a unique input variable.
What are you calling a single measurement in this context?
While you are at it, define what Xᵢ,ₖ truly means in GUM 4.2.1.
Nonsense, it is impossible to perform a Type A evaluation without multiple observations of the same quantity under identical conditions.
How many times has this been explained to you?
You lack even Clue One about uncertainty analysis.
Sigh. Just try to understand what I’m saying rather than going on these rants every time you see my name.
A type A estimate is perform by taking multiple measurements of the same thing using the same instrument etc. it’s the standard deviation of these multiple measurements that is used to estimate the standard uncertainty of those measurements. That is telling you how much uncertainty there is in any single measurement.
It is not telling you the uncertainty is in the average if those multiple measurements. The standard uncertainty of the mean is given by the standard deviation divided by root N.
It is telling you the UNCERTAINTY OF THE DATA SET! Since the data set has uncertainty so does the average. And the uncertainty of the average is the uncertainty of the data set!
“That is telling you how much uncertainty there is in any single measurement.”
Unfreakingbelievable! Each measurement has its own, separate measurement uncertainty. That is what is used to propagate measurement uncertainty.
In Eq 10 from the GUM what do you think u^2(x_i) is? The “average” uncertainty? How do you find the average uncertainty if you don’t add up all the u^2(x_i) values first?
“The standard uncertainty of the mean is given by the standard deviation divided by root N.”
You are stuck trying to use the arguemtnative fallacy of Equivocation.
The SEM is *NOT* the measurement uncertainty of anything. It is the sampling error – pure and plain.
u_c characterizes the dispersion of the values that could reasonably be attributed to the measurand. The “average” of the stated values is *NOT* the only value that could reasonably be assigned to the measurand so the precision with which the average is calculated is irrelevant to the measurement uncertainty. The SEM is only an estimate of the sampling error – WHICH IS AN ADDITIVE FACTOR TO THE MEASURMENT UNCERTAINTY!
When you make a statement like this you are saying that you *always* assume that measurement uncertainty is random, Gaussian, and cancels. You deny that you have that meme stuck in your head but it just comes shining forth every time you discuss measurement uncertainty!
“It is telling you the UNCERTAINTY OF THE DATA SET!”
You really need to stop pressing that Caps Lock key. It’s such a tell that you know you are talking nonsense.
“Since the data set has uncertainty so does the average. And the uncertainty of the average is the uncertainty of the data set!”
No it is not. Read the GUM, specifically 4.2.3.
“Each measurement has its own, separate measurement uncertainty.”
But you need multiple measurements to estimate what it is.
“That is what is used to propagate measurement uncertainty.”
No. What you use is the mean of those measurements, and use the uncertainty of that mean in the propagation.
“In Eq 10 from the GUM what do you think u^2(x_i) is?”
It’s the squared uncertainty of the ith input element.
“The “average” uncertainty?”
Average of what uncertainty?
“How do you find the average uncertainty if you don’t add up all the u^2(x_i) values first?”
Your rambling again. This obviously means something to you – but you seem to be obsessed with finding average uncertainties, and have a blind spot in terms of understanding what equation 10 says.
“The SEM is *NOT* the measurement uncertainty of anything. It is the sampling error – pure and plain.”
Read 4.2.3 again. It doesn’t matter if you call it the SEM or the experimental standard deviation of the mean – it’s still the standard deviation divided by root N.
“u_c characterizes the dispersion of the values that could reasonably be attributed to the measurand.”
So all you have to do is calculate u_c and you have the measurement uncertainty. But you won;t because you’ll keep claiming some nonsense about average uncertainties, misunderstand what a partial derivative is, and try to change everything to relative uncertainties, rather than accept the inevitable conclusion that if the “f” used in Eq 10 is the function for the average, the uncertainty will be smaller than the average uncertainty of the input values.
“The “average” of the stated values is *NOT* the only value that could reasonably be assigned to the measurand”
That’s why it’s uncertain.
“so the precision with which the average is calculated is irrelevant to the measurement uncertainty.”
Why is it that whenever you use the word “so” the next statement does not follow from the previous one?
“The SEM is only an estimate of the sampling error – WHICH IS AN ADDITIVE FACTOR TO THE MEASURMENT UNCERTAINTY!”
There’s that tell again. Using equation 10 is not given you the SEM of the average – it is giving you (what I would call) the measurement uncertainty. If you want to calculate both the SEM and the measurement uncertainty you could. But adding the measurement uncertainty will be generally smaller than that of the sample standard deviation, so will likely be close to irrelevant.
“When you make a statement like this you are saying that you *always* assume that measurement uncertainty is random, Gaussian, and cancels.”
What statement? Most of your comment was you arguing with yourself. I simply pointed out what the GUM 4.2.3 says, and what Eq 10 says, and yes they are assuming random effects, but there’s no assumption of a Gaussian distribution.
“No it is not. Read the GUM, specifically 4.2.3.”
As usual, you are CHERRY PICKING without understanding the context!
From 4.2.1:
(bolding mine, tpg)
You keep wanting to make the exception case into the general case! It’s idiotic.
Do you measure the shear strength of one i-beam out of a pile to determine the shear strength of all of them? Do temperature measurements at different locations meet the requirement of “the same location”? Does the use of different instruments meet the requirement of “same measuring instrument”?
Why do you ALWAYS just adamantly refuse to study the whole context of the subject? Why do you *ALWAYS* just cherry pick things you think support your misconceptions? Why do you *ALWAYS* remain willfully ignorant?
“Read 4.2.3 again. It doesn’t matter if you call it the SEM or the experimental standard deviation of the mean – it’s still the standard deviation divided by root N.”
*YOU* read 4.2.3 again. And then go look at the reference to B.2.15 in 4.2.3!
And then come back and tell us how 4.2.3 even applies to the daily average temperature taken at the same station.
“But you won;t because you’ll keep claiming some nonsense about average uncertainties, misunderstand what a partial derivative is, and try to change everything to relative uncertainties, rather than accept the inevitable conclusion that if the “f” used in Eq 10 is the function for the average, the uncertainty will be smaller than the average uncertainty of the input values.”
This whole forum is about temperatures. The discussion about measurement uncertainty focuses on temperature measurement. And you keep wanting to drag the discussion into statistical world where you can use your meme of “all measurement uncertainty is random, Gaussian, and cancels” to claim that is how measurement uncertainty in the real world should be handled.
You can deny you have that meme embedded in your brain but it just comes shining through in every assertion you make!
Bevington has a point in Example 4.1.
He ends the example by finding an appropriate interval using the equation:
|Tₑₓₚ – Tₑₛₜ| / σᵤ (where σᵤ is the standard deviation of the mean.)
This calculation ends up with a determination of 1.4 standard deviations. Not standard deviations of the means.
“I simply pointed out what the GUM 4.2.3 says, and what Eq 10 says, and yes they are assuming random effects, but there’s no assumption of a Gaussian distribution.”
Without any understanding whatsoever for when 4.2.3 applies. NONE. Zero. NADA.
For the average to be considered a “best estimate” the distribution is typically considered to be Gaussian. For most other distributions the mode would be considered the best estimate.
You don’t even realize when you are applying the meme that “all measurement uncertainty is random, Gaussian, and cancels”.
Thus, for an input quantity Xi estimated from n independent repeated observations Xi,k, the arithmetic mean i X obtained from Equation (3) is used as the input estimate xi in Equation (2) to determine the measurement result y; that is, xi = X̅i. Those input estimates not evaluated from repeated observations must be obtained by other methods, such as those indicated in the second category of 4.1.3.
There is a lack of understanding of what input quantities are. In the simple functional relationship f(l,w) = l × w.
“l” is represented by X1
“w” is represented by X2
Xi,k -> X1k (k) multiple measurements
Xi,k -> X2k (k) multiple measurements
4.1.3 (second category)
It is your delusion. The uncertainty of the mean as the uncertainty of a single measurand applies in one and only one instance. You have been shown by Dr. Taylor what is required in his Section 5.7.
One must assume multiple experiments, each with a large number of observations OF THE EXACT SAME MEASURAND. Each experiment becomes a sample with size “n”. One must also have experiments (samples )with the same means and standard deviation.
You continually fail to identify a measurement model that you are discussing. Here is a simple question for you to answer.
A monthly average has 30 observations. Are those observations:
That is where you need to start in analyzing the measurement uncertainty.
Here is a good document from the Rochester Institute of Technology. This University offers PhD courses of study isn’t a “trade school”.
http://spiff.rit.edu/classes/phys273/uncert/uncert.html
Note,
“You have been shown by Dr. Taylor what is required in his Section 5.7.”
And on numerous occasions people have tried to explain to you that just because Taylor describes measuring the same thing multiple times, does not mean the proof only works for measuring the same thing multiple times. He’s just applying the concept of the SEM to the task of measuring a thing. It is not a requirement that everything you measure has to be the same thing for the statistics to work.
“One must assume multiple experiments, each with a large number of observations OF THE EXACT SAME MEASURAND.”
And again, you do not have to actually make multiple experiments. That’s just what you imagine. And you need to decide if you think a mean of a population is a measured. If it is then when you take a sample you are taking observations of the exact same measurand. And if you think it can’t be a measurand, then by definition it can’t have a measurment uncertainty, so you might as well stick to the standard statistical analysis.
“Each experiment becomes a sample with size “n”.”
You still don’t get what the word “imagine” means. He starts by saying you have taken N measurements, and from that works out the SEM or SDOM.
“You continually fail to identify a measurement model that you are discussing”
The model I’m discussing is when you take a random sample from a population and use the mean of that sample as the best estimate of the population mean.
“A monthly average has 30 observations.”
Is more complicated, becasue the observations will not be IID.
“2. a single sample with 30 observations,”
Is the one you want, but as I’ve said in relation to TN1900 Ex2, you could argue that the average of the 30 observations is the monthly average, in which case maybe that’s what you are leaning to with option 3.
“That is where you need to start in analyzing the measurement uncertainty.”
It might be if I was interested. But you have to start with the basics, and the basic point is that the uncertainty of the mean is not the standard deviation of all the observations.
“Here is a good document”
Not another one. OK, did you want me to read this bit
So I can measure the properties (e.g. volume) of a piece of coal and a piece of lead and statistical descriptors like the average and standard deviation will work to tell me something useful in the real world?
“And you need to decide if you think a mean of a population is a measured.”
I’ve asked you before to post a picture of an object in your backyard that is an average you could measure. You finally admitted you couldn’t.
The mean is a statistical descriptor of a population. That is all that it is. Statistical descriptors describe the features of a population but is *not* part of the population itself.
“If it is then when you take a sample you are taking observations of the exact same measurand. “
Again, the mean is not a measurand. It is a calculated statistical descriptor. You are not measuring the average. If you were then every observation would be exactly the same – the average!
“he model I’m discussing is when you take a random sample from a population and use the mean of that sample as the best estimate of the population mean.”
“take a random sample” And how do you know if the sample mean is the same as the population mean? How do you know from one sample that the standard deviation of the sample is the same as the standard deviation of the population, especially if the data is multi-modal like temperature data is?
“So I can measure the properties (e.g. volume) of a piece of coal and a piece of lead and statistical descriptors like the average and standard deviation will work to tell me something useful in the real world?”
I doubt it will tell you anything useful. Why did you want to do that?
“I’ve asked you before to post a picture of an object in your backyard that is an average you could measure.”
And I replied that there is nothing in any definition of a measurand that requires it t be something you can take a picture of.
“The mean is a statistical descriptor of a population.”
Finally you might be getting it.
“Statistical descriptors describe the features of a population but is *not* part of the population itself.”
Well, there’s a philosophical question. Is a property of something not a part of that thing?
“If you were then every observation would be exactly the same – the average! ”
You still don’t understand what an average is.
“And how do you know if the sample mean is the same as the population mean?”
You don’t, and it almost certainly won’t be. That’s why it’s uncertain.
you said: ““It is not a requirement that everything you measure has to be the same thing for the statistics to work.””
If the statistics work then they must tell you something useful. Otherwise they are just mathematical masturbation, i..e numbers is just numbers.
If you can’t measure it then how can it be a measurand?
GUM:
A distribution is a collection of things, it is not a “thing” on its own. Is a distribution of the heights of horses with wings really a distribution?
I understand it perfectly – IN THE REAL WORLD. It is a central TENDENCY. But it does not have a probability of 1 – except in your statistical world.
“You don’t, and it almost certainly won’t be. That’s why it’s uncertain.”
That’s because of SAMPLING uncertainty, not because of measurement uncertainty.
“If the statistics work then they must tell you something useful.”
You still don’t get the fact that it’s possible to construct meaningless sums, but that doesn’t make all sums meaningless. If I tell you that 2 + 2 = 4, and you respond with, “then whats two gooseberries added 2 two helicopters” you are not making a very good argument.
“If you can’t measure it then how can it be a measurand? ”
A) You don’t need to take a picture of something to measure it.
B) “In most cases, a measurand Y is not measured directly, but is determined from N other quantities X1, X2, …, XN through a functional relationship f”
I can measure the average temperature in a garden by sticking thermometers about the place and taking an average. The average temperature, or any temperature is not an object I can take a photo of. It doesn’t mean I can’t measure it.
“A distribution is a collection of things”
And the mean is not a distribution of things.
“It is a central TENDENCY. But it does not have a probability of 1 – except in your statistical world.”
You are going to define what probability you are using, frequentist or Bayesian.
“That’s because of SAMPLING uncertainty, not because of measurement uncertainty.”
What are you on now? You do not know the mean of a population. That’s because of all the sources of uncertainty – including random sampling and measurement error.
Then show your mathematical derivation where different means and different standard deviations in the samples can be simplified to σ/√n.
Hint: Consider the standard deviation of the sample means and how it is derived.
bellman has never *studied* any of the tomes he’s been given as references. If the standard deviations are different then when finding the best estimate value you can’t simply do a simple average, you must use weighted values based on the variances to find the best estimate. There is simply no guarantee that when measuring different things those measurement distributions are all going to have the same variance. You can’t fix that by just assuming that all variances are the same.
“Then show your mathematical derivation where different means and different standard deviations in the samples can be simplified to σ/√n.”
You can’t just do that by sampling. But that’s not the point I was making. The SEM describes a situation where all your values in the sample are taking from an identical distribution. That distribution is the defined by the population, and the derivation is the same as described by Taylor.
If you want to break the population down into sub-populations, each with it’s own mean and standard deviation, then that’s a whole new game.
And this applies to measurements of different things using different instruments under different conditions how?
If the distribution of each data element is different that is going to be reflected in the sample data. How do you take an average of data elements that have different variances?
Can it be? Are you finally waking up to what people have been trying to tell you for years when it comes to metrology?
Are you now able to see why people say the SEM of temperature data is *not* the measurement uncertainty of the average, i.e. the GAT?
“And this applies to measurements of different things using different instruments under different conditions how?”
the way I said, by treating everything as part of the same population. Of course, if you want to take into account different conditions and instruments you can, but it isn’t going turn the uncertainty from the SEM into the SD, let alone into the uncertainty of the sum.
“How do you take an average of data elements that have different variances?”
You add them up and divide by N. Someday you are going to have to explain why you have no problem taking the sum of values with different variances, but not the average.
“Are you finally waking up to what people have been trying to tell you for years when it comes to metrology?”
If you ever tried to listen to what I’ve been saying rather than the voices in your head, you might have an answer to that. I’ve been talking about mixture models ever since you were obsessed with mixing ponies and stallions.
“Are you now able to see why people say the SEM of temperature data is *not* the measurement uncertainty of the average”
If by SEM you mean SD / √N, I’ve never suggested it is. Calculating a global anomaly involves many operations all of which have uncertainty. Uncertainty analysis of the global average is complicated. I’ve just tried to point out that in general, the more measurements you have, the better (that is less uncertain) the result.
And how are Shetland ponies and Quarter-horses part of the same population? How are wooden 2″x4″ boards and steel I-beams part of the same population? How are temperatures in Las Vegas and temperatures in Miami part of the same population?
Word salad alert! Different conditions and instruments are endemic to the temperature measurement system – even at the same station!
The uncertainty represented by the SEM is SAMPLING UNCERTAINTY. The uncertainty represented by the SD is MEASUREMENT UNCERTAINTY.
They are not the same thing even though both are uncertainties.
Are you *finally* beginning to realize this?
“You add them up and divide by N”
Once again we see the statistician and climate science memes of “all measurement uncertainty is random, Gaussian, and cancels” coupled with “numbers is just numbers”.
When trying to find the best estimate of a set of measurement data the uncertainties in each data element has to be used to weight the contribution to the “average”. You only get Σx_i/n if all of the measurement uncertainties are equal. That only applies if you are measuring the same thing multiple times using the same instrument under the same conditions and even then you have to justify making the assumption that all measurement uncertainty cancels since it won’t if the measurement uncertainty is asymmetric as it will be for some instruments.
“Someday you are going to have to explain why you have no problem taking the sum of values with different variances, but not the average.”
Adding the measurement uncertainties, i.e. *propagating* the measurement uncertainties, for a sum of measurements does *NOT* involve averaging.
If the assumptions associated with the measurements are such that the standard deviation of the data is used as the uncertainty, e.g. a Gaussian distribution, then you have no weighting values to use and the best estimate is just assumed as the sum of the values divided by n.
You have *never* studied the tomes referenced to you in order to understand what assumptions are made in order to evaluate measurement uncertainty in specific situations – *NEVER*.
One of the main assumptions in Taylor and Bevington is that both the stated values are random and Gaussian and that the measurement uncertainty is random and Gaussian and cancels. This is done to make the examples simpler. Possolo even does this in TN1900, Ex2. He assumes the measurement uncertainty of each data point is 0 (zero). You can’t seem to get that into your head.
“If you ever tried to listen to what I’ve been saying rather than the voices in your head, you might have an answer to that. I’ve been talking about mixture models ever since you were obsessed with mixing ponies and stallions.”
Word salad alert! “mixture models”? You’ve asserted that the “average” of multi-modal distributions of measurements actually tells you something about the data elements in the distribution. E.g. the daily mid-range value of Tmax and Tmin represents the “average” daily temperature!
Nothing you assert has anything to do with metrology. It’s just the same two memes over and over again. “all measurement uncertainty is random, Gaussian, and cancels” and “numbers is just numbers”.
“If by SEM you mean SD / √N, I’ve never suggested it is.”
” the more measurements you have, the better (that is less uncertain) the result.”
ROFL!! You don’t even know when you are doing it. The more measurements you have the smaller SD / √N becomes. And SD / √N *IS THE SEM!
The measurement uncertainty doesn’t get better, only the SEM gets better!
What happens to the MEASUREMENT UNCERTAINTY?
He will never acknowledge this fact.
When the value of the SEM falls below the measurement resolution, it becomes worthless.
That is why the dispersion of values attributable to the measurand is the standard deviation. Not even the SD can have a resolution less than the measurement resolution if significant digits rules are properly followed.
Absolutely correct—the SD is meaningless if every measurement is 1.23, 1.23, 1.23, 1.23, 1.23, 1.23, 1.23… SPC becomes impossible.
“And how are Shetland ponies and Quarter-horses part of the same population?”
They are the population of Shetland ponies and Quarter-horses. Why you would want to treat them as a population is your own business, but if they are the only horses you are interested in than that is the population you want.
“How are wooden 2″x4″ boards and steel I-beams part of the same population?”
I see we are back to these tedious illogical arguments. Just because you can ask questions about meaningless averages does not make all averages meaningless.
“Word salad alert!”
I can;t help you with your reading comprehension if you won’t explain what part you didn’t understand.
“The uncertainty represented by the SD is MEASUREMENT UNCERTAINTY.”
It doesn’t matter how many times you say that, or how many capital letters you use – it doesn’t make it correct.
“Once again we see the statistician and climate science memes of “all measurement uncertainty is random, Gaussian, and cancels” coupled with “numbers is just numbers”.”
I’m sorry. I keep forgetting how hard you find difficult concepts like – how to calculate an average. It has nothing to do with anything being Gaussian random or cancelling – it’s simply the standard definition of a mean.
“When trying to find the best estimate of a set of measurement data the uncertainties in each data element has to be used to weight the contribution to the “average”.”
True – but that only works when you are measuring the same thing.
“Adding the measurement uncertainties, i.e. *propagating* the measurement uncertainties, for a sum of measurements does *NOT* involve averaging.”
Not the question I asked. Why would the sum of measurements each measured with a different variance be OK, but not then dividing it by N?
“Word salad alert! “mixture models”?”
https://en.wikipedia.org/wiki/Mixture_model
““all measurement uncertainty is random, Gaussian, and cancels” and “numbers is just numbers”.”
Nurse!
“The more measurements you have the smaller SD / √N becomes. And SD / √N *IS THE SEM!“
Finally he gets it. (Narrator: He hadn’t got it.)
“Different conditions and instruments are endemic to the temperature measurement system – even at the same station!”
Absolutely!
“. . . E.g. the daily mid-range value of Tmax and Tmin represents the “average” daily temperature!”
This is also correct. The “true” average (whatever that means) may be closer to Tmax or Tmin; depending on whether the temperature stays close to one limit most of the time.
The daily profile is usually quite sinusoidal. The nighttime profile is usually quite exponential decay.
That represents two entirely different distribution types. Trying to jam them together to get an “average” is far more complicated then just doing a mid-range calculation which would only be true for a Gaussian distribution.
Bully for you — but it has nothing to do with real-world metrology and measurement uncertainty, and especially not air temperature measurements.
Are you having a problem comprehending what:
this statement really means?
In each of the experiments there are N measurements and the average of each experiment is then calculated! In other words, multiple samples each with a sample size of N.
Dr. Taylor goes on to say that each experiment also has an identical x̅ and σₓ. Understand?
“Are you having a problem comprehending what…”
No. I’m having a problem comprehending why you keep omitting the word imagine
“In each of the experiments there are N measurements”
You mean “In each of the imaginary experiments…”
“In other words, multiple samples each with a sample size of N.”
In other words multiple imaginary samples each with a sample size of N.
LOL!
When one is deriving a mathematical solution, one does create imaginary assumptions. The derivation is then tested with real life measurements.
Are you claiming the derivation is incorrect? If so, show your math
“Are you claiming the derivation is incorrect? ”
No. I’m saying you are claiming you actually perform multiple experiments. You’ve been doing this for years. You just won’t accept that the reality is you get one sample and then derive estimate from that.
You don’t have a sample, you have a population. How many Tmax’s in a month? How many Tmin’s? How many Tavg’s?
If a single “sample” contains the entire population, you don’t have a sample.
“You don’t have a sample, you have a population.”
If you are talking about measuring the same thing multiple times you do not have a population. The population is the infinite number of possible measurements.
Even if you are considering a finite population, a sample is assumed to be “with replacement”. You can never sample the entire population.
If you are measuring every value in a finite population without replacement, then yes, you do not need a sample, you have the exact average (subject to measurement uncertainty). That’s the point I keep making about that TN1900 example. If you want to know the actual average of the monthly temperature and have a reading for every day, the only uncertainty is in the measurements. But TN1900 is treating the daily values as a random sample from a random probability distribution of all possible temperatures for the month.
How many Tmax temps in a month?
How many Tmin temps.in a month?
How many Tavg temps in a month?
If I count correctly, there are not an infinite number of any of those.
Why don’t you read the comment you are replying to?
If you want an exact average of daily max temperature then you can just average them, and you have that average (subject to any measurement uncertainty). Ignoring measurement uncertainty the daily max temperatures.
If on the other hand you want to do it the TN1900 way, where you are treating the daily max temperatures as coming from a probability distribution, then there are an infinite number of TMax temps in a month, of which you have taken a sample.
“ then there are an infinite number of TMax temps in a month”
No, there isn’t. If there were the climate models wouldn’t work nor would the CGM’s. They all assume the temperature is determinative, not a random value selected from a distribution of all possible values. Temperatures don’t instantaneously change just from -30C to +30C the way a random choice could cause to happen.
Why do you keep insisting on digging yourself into an ever deeper hole?
“No, there isn’t.”
There is if you use the observation model used by NIST.
Of course they assume they are samples FROM A GAUSSIAN distribution. Systematic and measurement uncertainty is negligible.
Have you heard the adage about everything in climate science is GAUSSIAN and measurment uncertainty cancel?
Show us some histograms of monthly temps. How many can you find that are Gaussian?
“Have you heard the adage about everything in climate science is GAUSSIAN and measurment uncertainty cancel?”
Could you provide one of your famous references to support such nonsense. Nobody thinks that everything is Gaussian. Nobody thinks that all measurement uncertainty cancels. And what has any of this tangent to do with what we were just talking about – apart from you realize you were wrong and need a big distraction.
“Show us some histograms of monthly temps. How many can you find that are Gaussian?”
Why would you expect them to be Gaussian?
“Nobody thinks that everything is Gaussian.”
You do. Why else would you consider the “best estimate” to be the mid-point of an interval?
” Nobody thinks that all measurement uncertainty cancels.”
You do. Why else would you consider the SEM to be the measurement uncertainty of the average?
“No, there isn’t.”
Stop lying. But then you would have no argument.
“Why else would you consider the “best estimate” to be the mid-point of an interval? ”
I don’t. I gave you an example from the IPCC were the best estimate is not the mid point. But regardless, there are many non-Gaussian distributions where the highest probability is the mid point.
“You do. ”
Stop lying.
“Why else would you consider the SEM to be the measurement uncertainty of the average?”
I don’t say it’s the “measurement” uncertainty of the mean.
What I say is the SEM can describe the uncertainty of the mean of a random sample. But that is only if the sample is truely random.
The same can be applied to to the measurement uncertainty, in as far as the measurement uncertainty is the SEM of the errors. But again only if all errors are independent.
Moreover, you keep failing to define what you mean by “all measurement uncertainty cancels”. The reason for the uncertainty decreasing in an average is not because “all the measurement uncertainty cancels” it’s because there is a tendency for some of the uncertainties to partially cancel.
And you have never shown exactly how this cancelation occurs — you just hope it happens.
I’d have thought an expert like you already understand the concept. You might not agree with it but you must have at least looked at the probabilistic basis.
All values are either underestimates or overestimates, with equal probability and enough values it becomes increasing unlikely that all will be overestimates or underestimates. Taylor explains it for adding two values with uncertainties:
“it becomes increasing unlikely that all will be overestimates or underestimates. Taylor explains it for adding two values with uncertainties:”
You don’t even understand what you are saying!
Taylor: “If x and y are measured independently and our errors are random in nature”
You don’t even understand the assumptions that go with this. It *assumes* a symmetric uncertainty distribution. And it assumes no systematic uncertainty.
Suppose you are using a metal tape whose calibration is temperature dependent. You are measuring the length of a 2″x4″ board twice. If the temperature is below the calibration temperature then the length of both measurements will come out too long (i.e. metal shrinks when it’s cold). If the temp is above the calibration on both days the lengths will come out too short.
What do you do? Add the two measurement uncertainties directly or in quadrature? If in quadrature explain how you assume that the measurement uncertainties have partial cancellation.
Clutching at straws…
He has somehow convinced himself that uncertainty analysis and evaluation is nothing but exercises in probability theory, his word salad didn’t even come close to explaining how averaging cancels uncertainty.
Back to the usual intellectual superiority put downs…
And this quote does not say how averaging cancels uncertainty.
“Back to the usual intellectual superiority put downs”
Sorry. I’ll try to be more like you and avoid any put downs.
“And this quote does not say how averaging cancels uncertainty.”
Without trying to put you down, have you tried reading up on this?Most sources on uncertainty explain how the rules work better than I can.
“I gave you an example from the IPCC were the best estimate is not the mid point.”
ROFL!! I’m sure you knew that before I showed it to you! /sarc
“ But regardless, there are many non-Gaussian distributions where the highest probability is the mid point.”
So what? How do you know when they apply to the measurement uncertainty?
“I don’t say it’s the “measurement” uncertainty of the mean.”
No sh&t! That just means you’ve been pettifogging here. In current parlance – YOU ARE A TROLL!
“The same can be applied to to the measurement uncertainty, in as far as the measurement uncertainty is the SEM of the errors. But again only if all errors are independent.”
Independence is *NOT* the only requirement. See the GUM B.2.15!
“Moreover, you keep failing to define what you mean by “all measurement uncertainty cancels”.”
Meaning you’ve never once actually bothered to STUDY Taylor, Bevington, Possolo, or the GUM for meaning. All you do is cherry pick crap to throw against the wall.
“The reason for the uncertainty decreasing in an average is not because “all the measurement uncertainty cancels” it’s because there is a tendency for some of the uncertainties to partially cancel.”
And as that “partial” cancellation approaches total cancellation? How about when that “partial” cancellation approaches zero?
This is nothing but word salad you are throwing out to cover for the fact that you’ve been on here showing how ignorant you are on this subject.
It’s the measurement uncertainties of the measurement elements that affect the total measurement uncertainty sum. What you don’t seem to understand is that you can decrease the amount of total measurement uncertainty without affecting the number of data elements, i.e. “n”, at all! Can you guess how?
So much bull crap. (X1/2) is ONE INPUT QUANTITY. (X2/2) is ONE INPUT QUANTITY. They are each unique random variables consisting of q(ₖ) observations.
From GUM 4.2.1
What is the uncertainty of X1/2? [u(X1/2)=?]
What is the uncertainty of X2/2? [u(X2/2)=?]
The propagation of uncertainty of a sum of measurements, as you say, is the RSS of the two uncertainties.
u꜀(Xᵢ) = √{ (u(X1/2))² + (u(X2/2))² }
If you know what you are doing, show us your math for the two uncertainties.
“ONE INPUT QUANTITY. (X2/2) is ONE INPUT QUANTITY.”
You can do it in that order if you want it makes no difference.
“They are each unique random variables consisting of q(ₖ) observations.”
You still don’t understand what a random variable is, do you?
“What is the uncertainty of X1/2?”
Var(X1 / 2) = Var(X1) / 4, so
SD(X1 / 2) = SD(X1) / 2
the same for X2.
It’s a simple rule that scaling a random variable by a constant C will scale the variance by C^2.
https://en.wikipedia.org/wiki/Variance#Propagation
Do I need to explain that 4 = 2^2?
“Consequently, in metrology, the measurement results cannot be expressed as an absolute number, because of the uncertainty of this result (4).”
Unless you are bellman or a climate scientist where all measurement uncertainty is random, Gaussian, and cancels along with all systematic measurement uncertainty being zero.
Thus samples taken from a population of “stated values +/- measurement uncertainty” can have the data components reduced to just “stated values” – i.e. absolute numbers. And those absolute numbers can be manipulated to produce any desired resolution for the “average” since they are not modulated in any way, shape, or form by their measurement uncertainties.
Bevington: “Removing an outlying point has a greater effect on the standard deviation than on the mean of a data sample, because the standard deviation depends on the squares of the deviations from the mean”
This also means that *adding* an outlying point has a greater effect on the standard deviation than on the mean. The odds of adding an outlying point increases with the number of observations. Sometimes the “long shot” wins! Sometimes that outlying point is just a non-statistical fluctuation, e.g a leaf temporarily blocking the air intake to an aspirated measuring station.
Yes, I thought that might have been what you were thinking about, and as so often you are doing what you accuse me of – cherry-picking something and stretching it to fit your belief. There is nothing in the comment about outliers that suggests that larger sample sizes lead to larger variance. If Bevington ever said such a thing you would have quoted him saying it.
The problem you still can’t get around is that variance is an average of all the squared differences. The larger your sample the more likely you are to have an outlier, but it will have less of an impact it will have on the variance. It’s impact will be divided by the sample size.
The main issue with outliers is there impact on a small sample.
“There is nothing in the comment about outliers that suggests that larger sample sizes lead to larger variance. “
Bevington: “It is important to realize that the standard deviation of the data does not decrease with repeated measurement, it just becomes better determined. On the other hand, the standard deviation of the mean decreases as the square root of the number of measurements”
“does not decrease”
More evidence of your lack of reading comprehension skills. If the variance doesn’t decrease when you add data then variance either stays the same or it increases. Assuming that the variance stays the same when you add data is the very same unjustified assumption that you and climate science makes that all measurement uncertainty is totally random, Gaussian, and cancels.
you: “but it will have less of an impact”
I didn’t say it would have a large impact. I said it will have an impact which you denied. The impact will be that variance of the combined measurement data *will* grow. Since variance is a metric for the accuracy, i.e. the measurement uncertainty, of the average.
This is the SEM! It is not a measurement uncertainty for the combined temperature variables. It is a metric for how precisely you have located the average of the combined data.
You simply cannot get away from the meme that the SEM is the measurement uncertainty of the average value. The SEM is *NOT* the measurement uncertainty of the average. It is a metric for how precisely you have located the population average value. It tells you nothing about the accuracy of the precisely located population average.
“does not decrease”
Does not mean it increases.
“Assuming that the variance stays the same when you add data is the very same unjustified assumption”
It’s not an assumption.
“I didn’t say it would have a large impact. I said it will have an impact which you denied.”
You are missing the point. Any increase from an outlier is temporary, and will be offset by every non outlier. On average it balencies out and the variance will tend towards the population variance as sample size increases.
“Since variance is a metric for the accuracy, i.e. the measurement uncertainty, of the average.”
Argument by repetition is so tiring. Variance tells you nothing about the accuracy of the measurements.
“This is the SEM!”
No it’s the variance. It’s literally the definition of variance, the average of the squared differences.
“It is a metric for how precisely you have located the population average value.”
Which is what most people would call the uncertainty. If you think adding the word “measurement” in front of uncertainty gives you a much larger uncertainty, then you need to define exactly what you think measurement uncertainty means, and why you think it’s a useful figure.
You seem to now be arguing that measurement uncertainty of an average is the population standard deviation, and it’s difficult to see how that has anything to do with the actual measurements.
Not a single assertion backed up by any reference whatsoever. Both Taylor and Bevington have chapters on how to decide on dropping data from out in the tails of a distribution. If the impact of data in the tails is only temporary neither would have addressed the issue with entire chapters.
And here, once again, we see the meme “all measurement uncertainty is random, Gaussian, and cancels” – even though you vehemently deny that meme is lodged in your brain and seemingly can’t be removed.
Unfreakingbelievable. Standard deviation is the square root of the variance and the standard deviation is treated in the GUM as the very definition of the accuracy of the measurements, i.e. the measurement uncertainty! In GUM, Sec 4.2.2 it is even specifically said that “The experimental variance of the observations,”
Of course that’s how you calculate variance. The *issue* is that you want to calculate the variance of the sample means as the measurement uncertainty. It is the variance of the DATA that is a metric for the measurement uncertainty – which you continue to adamantly deny!
See what I mean about you denying the variance of the DATA as the metric for measurement uncertainty? That is *NOT* what most people would call the uncertainty of the measurements! Most people go by the definition in the GUM! You seem to be speaking of most climate scientists, statisticians, and yourself. That is hardly “most people”.
How many times must you be given the definition of measurement uncertainty from the GUM before it finally sinks into your brain? I’ve quoted it twice just in this thread. Here it is again:
GUM:
It is the variance of the OBSERVATIONS that determines the measurement uncertainty, not how precisely you have located the average of the observations!
You just keep digging your hole deeper. You can’t stop yourself, can you?
“Okay, I’ll weigh in here that there are two sources of error around any temperature measurement, the first being instrument error, which presumably is a systematic bias.”
Yes, if the uncertainty is entirely due to a systematic error in the instrument, then the uncertainty in the average of multiple measurements made with the same instrument will be the same as a single measurement. This is the point I’m making against Tim Gorman continually saying things like
His argument is against me saying that when uncertainties are random and independent the uncertainty of the mean is less than the individual uncertainties – which for some reason he equates with
saying the uncertainty of the average is the same as the average uncertainty.
As to Pat Frank, I don’t think he is claiming that all the uncertainty is systematic, but is trying to argue for a definition of uncertainty which avoids probability theory in favor of interval arithmetic. Hence his comment towards the end:
That is *NOT* what I’m saying at all. Your reading comprehension skills are atrocious.
What I am saying is that the standard deviation of the sample means is not the same thing as the measurement uncertainty of the population mean.
You never define your terms specifically. You just say “uncertainty of the mean”. And then change the definition of that phrase to be whatever you need it to be in the moment – the argumentative fallacy of Equivocation.
“The 2σ = ±1.94 °C uncertainty does not indicate a range of possible temperatures but, rather, the range of ignorance over which no information is available”
You’ve never bothered to actually understand what Frank has done. Measurement uncertainty can have any form of distribution, e.g. normal. Poisson, binomial, Lorentzian, etc. YOU ALWAYS ASSUME NORMAL just like climate science. Thus when someone says that the characteristics of the uncertainty is unknown, i.e. a “range of ignorance over which no information is available”, you simply can’t comprehend it.
“That is *NOT* what I’m saying at all. Your reading comprehension skills are atrocious.”
I quoted what you said at the start:
If it’s not what you think I’m saying, whey say it at every opportunity?
“What I am saying is that the standard deviation of the sample means is not the same thing as the measurement uncertainty of the population mean.”
And nobody has ever said it was. I’ve no idea what you even mean by the “measurement uncertainty of the population mean”. I’ve told you several times that the population mean cannot have any uncertainty. But if you just mean, there’s a difference between the uncertainty of the mean caused by taking a random sample, and the uncertainty caused by measurement error, then yes. I’ve been telling you that since the start.
“the argumentative fallacy of Equivocation.”
This really shouldn’t be that hard for you to understand. “Uncertainty of the mean” means how certain we are that are estimate of the mean is close to the actual mean. This uncertainty can come from any combination of sources.
“You’ve never bothered to actually understand what Frank has done.”
I think he’s treating each daily measurement as an epistemic uncertainty, then chooses to uses interval analysis or maybe possibility theory, to justify his use of RMS. But he never states this explicitly, and I suspect he’s just choosing whatever excuse he can find to allow him to make the uncertainty as big as he can.
“Measurement uncertainty can have any form of distribution, e.g. normal. Poisson, binomial, Lorentzian, etc.”
But he’s implying it has no distribution.
“YOU ALWAYS ASSUME NORMAL”
I keep telling you, if you are just going to keep lying, try avoiding writing in all caps – it’s such a tell.
I am not assuming a normal distribution. Nothing in any of the equations requires a normal distribution.
“Thus when someone says that the characteristics of the uncertainty is unknown”
He doesn’t say the “characteristics of the uncertainty are unknown”, he says “the range of ignorance over which no information is available”.
And as I keep saying, if he doesn’t know the shape of the distribution, how can he calculate a 95% uncertainty. The fact that he gets this by multiplying σ by 1.96, only makes sense if you assume a normal distribution.
Find a statistical text that has a mathematical derivation for the use of √N to calculate the standard error of the mean and either post it or give a link.
I will repost my previous screen shot from Dr. Taylor’s book.
Read the above carefully.
See where it says, “performing a sequence of experiments, in each of which we make N measurements and compute the average”.
Then where it says, “Second, the true value for each of x1, …, xn is X; … “.
A sequence of experiments is “multiple samples” and each sample has N measurements.
Now go to NIST TN 1900 Ex. 2 and give us a numbered list of assumption that NIST uses to treat the 22 measurements as samples of size 22.
The information is there and as a statistics expert, you should be able to create a logical sequence explaining why NIST does what it does.
“Find a statistical text that has a mathematical derivation for the use of √N to calculate the standard error of the mean and either post it or give a link.”
https://en.wikipedia.org/wiki/Standard_error#Derivation
“A sequence of experiments is “multiple samples” and each sample has N measurements.”
I’ve told you enough times why this is not usually true. It’s just too time consuming and pointless, when you can calculate the SEM using the tried and tested methods. Note the operative word in Taylor’s book
“Now go to NIST TN 1900 Ex. 2 and give us a numbered list of assumption that NIST uses to treat the 22 measurements as samples of size 22.”
How many more times are you going to repeat this. I’ve given you my list several times – and you just forget it and claim I never give you the list. Here for instance:
https://wattsupwiththat.com/2024/07/14/the-hottest-june-on-record/#comment-3941335
But you keep confusing the contortions this document put itself through in order to treat this as measurement uncertainty, with the assumptions that are present the standard error of the mean equation.
In other words, you have no references to support anything you whine about.
The issue is not the time it takes to properly make measurements.
I am asking about the theoretical underpinning of the experimental procedures used to determine values.
It’s obvious you have not spent hours in a physical science lab trying to to obtain the measurements needed to replicate common standards and identify the uncertainty categories and their values. It is why analytical chemists like Dr. Frank’s have years of evaluating the vagaries of experiments.
It is why engineers are more worried about the intervals surrounding a stated value rather than how accurate the mean was calculated. In order to have detailed information about the operational variances to be expected.
‘Yes, if the uncertainty is entirely due to a systematic error in the instrument, then the uncertainty in the average of multiple measurements made with the same instrument will be the same as a single measurement.’
Sounds like we’re all on the same page with this, albeit talking past one another.
‘As to Pat Frank, I don’t think he is claiming that all the uncertainty is systematic, but is trying to argue for a definition of uncertainty which avoids probability theory in favor of interval arithmetic. Hence his comment towards the end:
If the total error (appropriately calculated in quadrature) is ‘E’, then I would think that would represent the total range of uncertainty, so would expect the interval of ignorance around our estimated average to be +/- 0.5E. However, if E represents a Gaussian distribution of the error, then the appropriate interval of ignorance becomes 2 (aka 1.96) times the standard deviation of E.
As I mentioned previously, I didn’t delve into the paper deeply enough to know which of the above treatments is most appropriate for thermometer-based temperature estimates, but agreed it should be consistent for monthly or annual averages.
I did have a question, however, on the source of the ‘0.195’ and ‘0.198’ terms in Equations 5 and 6, respectively.
That seems to be the crux of the argument(s)
Sampling uncertainties (which is where the SEM comes into it) and measurement uncertainties (which have a lower bound) are additive.
And there is the climate science meme in all its glory.
Measurements are of the form “stated value +/- measurement uncertainty”.
You can’t even accept that when you sample measurements the sample consists of measurements in the form “stated value +/- measurement uncertainty”. When you calculate the mean of that sample then it also has the form of “stated value +/- measurement uncertainty”.
When you calculate the mean and standard deviation of the sample means, known as the standard error by statisticians, that standard deviation has to be conditioned by the measurement uncertainty of the sample means. In essence the standard deviation of the stated values gets the amount of the measurement uncertainty added to it.
Statisticians and climate scientists never propagate the measurement uncertainty into the sample data or the standard error. It’s just “numbers is numbers”, i.e. the stated values, all the way down.
You can’t even get this right. You won’t even learn that measuring the same thing multiple times using the same instrument under the same conditions is different than measuring multiple things single times using different instruments each time under different conditions for each measurement.
You won’t even accept that in science assumptions HAVE TO BE JUSTIFIED! You can’t just automatically assume that even with multiple measurements of the same thing using the same instrument under the same conditions that measurement uncertainty be random, Gaussian, and cancel. That assumption has to be JUSTIFIED each and every time because it is always possible that you will not get a Gaussian distribution of measurement uncertainty. If you don’t get a Gaussian distribution of measurement uncertainty then you will *still* see the overall measurement uncertainty grow with every additional measurement.
“And there’s that familiar Gorman diversion. When in trouble just change the subject. And what do you think the point of Spencer’s paper is, if not to analyze the systematic effects of UHI, using statistical analysis.”
You can’t use statistical analysis to identify systematic measurement uncertainty. The paper is not doing measurement uncertainty analysis. it is doing an attribution study. They are different things.
Here you are again just automatically assuming that random = Gaussian. IT DOESN’T! The standard deviation of an asymmetric distribution is not a good metric for the measurement uncertainty. Nor is systematic uncertainty always a constant across multiple measurements.
I offer up this from the GUM: “F.1.1.1 Uncertainties determined from repeated observations are often contrasted with those evaluated
by other means as being “objective”, “statistically rigorous”, etc. That incorrectly implies that they can be evaluated merely by the application of statistical formulae to the observations and that their evaluation does
not require the application of some judgement.”
Pure BS. You haven’t learned a single thing over the past four years. You are *still* stuck in statistical world where everything is random and Gaussian. And even in the situation where you have random and Gaussian measurements the measurement uncertainty is *still* the standard deviation – IT IS NOT ZERO. The best “ESTIMATE* of the true value may be the mean but it is still just an ESTIMATE! The very word ESTIMATE means that there remains uncertainty in its value – and that uncertainty will never be zero.
“ the only person who claims such a thing is Pat Frank.”
You STILL haven’t figured out what Pat Frank did. The average measurement uncertainty of a set of instruments is actually a *thing”. A SINGLE thing. It is not the same as the total measurement uncertainty of a set of measurements. For instance, Simpson states the measurement uncertainty of a Simpson Model 313-3 voltmeter as 3% of the full scale value. That doesn’t mean the that the actual measurement uncertainty of a specific 313-3 is 3% of FS, that’s just a value determined from a set of evaluated 313-3 instruments. Some 313-3’s may have a better calibration and some may have a worse calibration. It’s why lab instruments are individually calibrated.
You haven’t learned *anything* about metrology. You remain willfully ignorant on its concepts and precepts. The worst kind of ignorance.
Ok. I will make some notes and some conjectures. Any criticism from you will be taken as nothing more than noise.
Ultimately, even if the measurement uncertainty was ±1.8C, the curves shown would remain and the portion ibutable to UHI would stay the same. The study was designed to analyze the portion of warming attributed to UHI, not to find an accurate value of ΔT as GAT or GMST is supposed to do.
Why don’t you post a summary of your findings from this paper? Just whining doesn’t do much to advance your arguments.
I have never said that. What I have said is that declaring MEASUREMENT VALUES without addressing uncertainty or using those values without following the significant digits rules is leaving part of the measurement unsaid. Doing this on purpose IS unscientific and is unethical.
Read this. https://pmc.ncbi.nlm.nih.gov/articles/PMC2959222/
Or this.
https://www.wmbriggs.com/post/46331/
“Any criticism from you will be taken as nothing more than noise.”
I seem to have struck a nerve.
You still don’t get that I am not complaining about the lack of measurement uncertainty in the GHCN data, or even commenting on the paper. Just pointing out your, to be polite, inconsistency when it comes to demanding uncertainty analysis.
“Ultimately, even if the measurement uncertainty was ±1.8C, the curves shown would remain and the portion ibutable to UHI would stay the same.”
Again, it’s not the uncertainty of the temperatures, it’s the uncertainty of all the correlations. Maybe you could consider your claim that individual measurements of ±1.8°C would have no effect on the curves. Is it because random errors will tend to cancel?
“Why don’t you post a summary of your findings from this paper? Just whining doesn’t do much to advance your arguments.”
I’m not “whining” about the paper – I’m pointing out your double standards.
I’m not going to go into a deep dive into the paper at this moment. May main complaint is how it’s being interpreted by the “alarmists” here as a “SHOCK CLIMATE REPORT”, and more importantly the exaggeration. I.e. claiming it shows 65% of global warming is caused by UHI, when it makes no such claims.
“What I have said is that declaring MEASUREMENT VALUES without addressing uncertainty or using those values without following the significant digits rules is leaving part of the measurement unsaid.”
Are you sure you’ve never claimed it amounts to fraud? I seem to remember you saying things to that effect, but can’t be bothered to try finding any examples at this moment. Regardless, I’m not sure why you think it’s a problem to not state measurement uncertainty, but OK to ignore all other types of uncertainty. And we spend a lot of time trying to figure out what you consider to be a “measurement” in the first place. Is the global average anomaly a measurement or a calculation? What about a linear regression?
“Read this.”
Why? Does it say anything different to the last 100 times you insisted I read it?
What part of it is relevant to anything you have just said?
You are whining! Do you think that makes you look smart? It doesn’t.
Not about measurement uncertainty. I have used fraud when speaking about temperature “adjustments” without proper justification and homogenization.
I suspect this is all confusing to you. Don’t feel bad that you’ve never had training in making measurements that have legal expectations. That is one reason engineers have special training.
“I suspect this is all confusing to you.”
I see you are down to the patronizing ad hominem stage of the argument, so we might as well leave it there.
And electrical energy generally degrades through usage to “heat” energy. Measure electrical usage for the city and it will give a measure of Entropy
addedto the UHIyes.
“Measure electrical usage for the city and it will give a measure of Entropy added to the UHI”
Great idea! ….in principle. But how could we actually do it mathematically?
It looks like a novel variant of the old apples-&-oranges problem to me: electrical usage is quantified in units of energy; UHI is quantified in units of degrees of temperature, and Entropy is quantified in units of, well, entropy.
“. . . and Entropy is quantified in units of, well, entropy.”
The usual units of entropy are joules per kelvin.
Indeed, they are, Jim, and thanks for pointing it out.
As those units imply, thermodynamic entropy is a function of two other variables, namely, thermal energy and absolute temperature. But what that function is for a complex, vaguely-defined system such as a city, heaven alone knows at the present time. Add to that the measurement problem of obtaining precise and accurate values for the two other variables at different points in time and one can get a sense of the enormous complexity of the enterprise and the amount of time and labour that would be needed to accomplish it.
I’m not meaning to suggest that it can’t be done, of course. I’m just thinking that it might be possible to simplify the whole project considerably by using an alternative metric for entropy whose calculated values are a function of the values of other variables that we can already measure relatively directly and easily, such as radiances or temperatures and their related areas of the planet’s surface for examples.
Anyway, the possibility of conceiving alternative metrics for entropy that might be more conveniently applied to cities (and perhaps the globe) was the reason for my not specifying the standard units of J/⁰K for thermodynamic entropy in my previous comment above.
It’s a nit-pick, but it’s just kelvin–not degrees kelvin.
Thanks for picking it, Jim! I’ve had that particular nit for years, not realising that the degree symbol (⁰) would be read as degrees (plural) in the context in which I was using it. But I see now that it’s how other people naturally would read it, so I am glad to get rid of it and to cease confusing or otherwise irritating folks with it.
So not knowing the units of entropy and not knowing that degrees were removed from kelvin is telling. I guess word salads is typical of your group!
“So not knowing the units of entropy and not knowing that degrees were removed from kelvin is telling.”
Those things are not true about me, Jim, and I never told them to you either. They must be things that you are telling yourself.
“I guess word salads is typical of your group!”
“Word salads”? My “group”? I don’t know what you are talking about. And those ludicrous remarks of yours make it pitifully self-evident that you don’t know what you’re talking about either!
They say when you’re in a hole–stop digging.
Enthalpy is probably a better metric to use than entropy 🙂
Oh God not the whiplash dooming too!
Power companies get a guide to making the grid withstand climate impacts
As in: no more wind turbines and solar panels?
Congratulations having run the gauntlet of orthodoxy.
You say:
We have started using a Landsat-based dataset of “impervious surfaces” to try to get at part of this issue…
I suspect that you will also need to account for the vertical surface area of urbanized land as anyone caught in the afternoon reflectance and evening re-radiation from tall buildings can attest.
[QUOTE FROM PAPER] “So, we were forced to use the raw (not homogenized) U.S. summertime GHCN daily average ([Tmax+Tmin]/2) data for the study.”
The average of the minimum and maximum temperatures for a day is a very poor indicator of the overall average temperature. It would be far more accurate to sum up hourly observations and divide by 24.
On a clear day in spring or summer (when daylight hours are longer than the nights), the atmosphere is warmed by the sun for 14 – 16 hours of the day (depending on date and latitude), and night only lasts 8 to 10 hours, meaning that the average temperature weighted by hours would be higher than (Tmin + Tmax)/2. If Tmax – Tmin = 20 F, the difference for 15 hours of daylight and 9 hours of night could be 2 to 3 degrees F.
On a clear day in autumn or winter, when the nights are longer than the days, the average temperature weighted by hours would be less than (Tmin+Tmax)/2.
This means that (Tmin+Tmax)/2 averages tend to under-estimate true daily averages in spring and summer, and over-estimate true daily averages in autumn and winter. They are only reasonably accurate near the equinoxes (March and September).
Yes. Many times here in the Northwest of the US, the mornings are cool/cold and cloudy, and the afternoons are sunny and warm. It’s clearly not a sine wave. Some days it’s cloudy and rainy all day.
Why do people make this so complicated? CO2 evenly blankets the globe, in other words it is a constant per location. The quntum mechanics of the CO2 does no vary by location or over time, so once again, CO2 is a constant in any model. What has changed over time is the concentration over time, but the concentration shows a log decay with the backradiation. It is much like painting a window black. The first coat does a lot, additional coats does very litte. In other words, beyond a certain concentration CO2 does very little. It is much like taking asprin. The first pills reduce pain, but taking too much will not help the pain, and may make you sick.
In reality all the data you need is the data for temperatures over the oceans and Antarctica to remove the UHI effect. Simply limit the data to the stations that aren’t exposed to any UHI Effect? Adding additional corrupted data sets only decreases the explainatory power of the model and increases the error. I’ve done that and when you simply select the stations with a very low BI score, you basically get no warming. If you comnbine the temperatures over the oceans with the change in cloud cover, to see that what global warming we do see id due to fewer clouds over the oceans than CO2. CO2 has absolutely nothing to do with the warming of the globe. CO2 is a trace gas of 415 ppm that termalizes 15 micron LWIR which is associated with -80C temp in the IR spectrum.
Climate Science claims to be a science. I just outlined a very simply and common sense way to control for the UHI efect and there is no need to worry about the adjusted or unadjusted data. Simply use the raw data from a station that hasn’t been impacted by the UHI efect, it is that simple. Try the unadjusted data from Alice Springs Austraila using the older version of the GISS Data before they broke up the data file.
Go to the late John Daly’s website: “Still Waiting For Greenhouse” at http://www.John-Daly.com.
From the home page, scroll down to the end and click on “Station Temperature Data”. On the
“World Map”, click on Australia and then on Alice Springs. The chart shows a plot of unadjusted temperatures obtained from the GISS and CRU data bases.
Shown in the chart (See below) is plot of annual average temperatures at Adelaide from 1859 to 1999. The plot shows a slight cooling. Note that all weather stations showed no warming especially Boda Island.
John Daly found over 200 weather stations around the world that showed no warming up to 2002. All this charts falsify the hypothesis that the increasing concentration of CO2 in the air causes an increase in surface air temperature.
If you click on the chart, it will expand and become clear. Click on the “X” to return text.
I miss John Daly.
We are consistently told that UHI is a local or at most regional issue and it’s effect is small compared to the earths surface but as Dr. Spencer notes:
“The strongest rate of warming occurs when population just starts to increase beyond wilderness conditions, and it mostly stabilizes at very high population densities”
This makes intuitive sense. The proportionate change from zero to one is greater than the change from one to two or from two to three.
I do a lot of camping and one of the biggest things I hear new campers talk about is how many stars they can see. But if you’ve ever been camping, it is quite easy to see the effect of light pollution of even small human settlements by looking at the horizon. Even a town of a few hundred people 12 miles away shows as a distinct glow against the horizon.
Below is an image showing the growth in light pollution over the last 70 or so years using the ALR scale (https://www.nps.gov/subjects/nightskies/growth.htm). This was based on 2002-2008 data collection, with a projection to 2025 so it would be interesting to see how it overlaps/interrelates with UHI trends. ArcGIS has several visualizations but I believe they are all based on a 2016 publication. What I find compelling is not the growth in intensity of urban areas, but the spread of the lower intensity pollution.
When viewing this in the context of Dr. Spencer’s observation above, 65% seems like a low estimate.
I’m not going to go looking for the paper at this time, but an explanation of data processing going into the USHCN by Tom Karl from maybe 20 years ago suggested to me blending of all the data before UHI correction. Certainly that isn’t right. I wrote a paper about it.
Moreover, think of all the increases in energy usage by the U.S. population, especially since the 1960s. Almost all that ends up as fugitive heat — a tiny amount as reconfigured mass with embedded energy.
Whenever and wherever electricity is used, heat is generated and dissipated into the immediate environment, be it a light, computer, toaster, cellphone, EV, e-bike or whatever. You can feel the warmth, irrespective of the source, be it coal, gas, nuclear, hydro, wind or solar. Most electricity is used where people live, drive and work – cities – and hence we have the heat island effect. Cities are getting warmer but the countryside? Not so much.
Not only that – all work or motion results in heat generation – which eventually vanishes to space.
A bouncing ball, rubbing your hands together, the movement of the speaker cone in your hi-fi. All generate heat.
Not widely understood by people who believe that adding CO2 to air makes it hotter.
https://wattsupwiththat.com/2024/04/16/observation-of-the-earth-shows-that-deforestation-and-urbanization-cause-three-times-more-warming-than-co2/
Today, with 11,000 “PV parks” totaling over 30,000 km2 and 5300 utility scale ‘wind farms’ now covering over 400,000 km2, rural regions and sea areas can and will play a far larger role in future warming of the planet, particularly, as these areas MUST increase by 100-fold to meet the present energy demand of the planet by 2050, and in addition, double again every 20 years to meet increased energy requirements of society.
Of course, that build-out can never happen, meaning humans will build and use fossil fueled and nuclear power plants, after wasting 10s of $trillions on wind and PV fleets.
This is the only website you need to debunk CO2 causes warming.
http://www.john-daly.com/stations/stations.htm
CO2 evenly blankets the globe; in other words, CO2 concentration is a constant per location.
The quantum mechanics of the CO2 molecule doesn’t change per location, so the backradiation of CO2 evenly blankets the globe.
What has changed over time is the concentration of CO2 over time. The scientific challenge then becomes how to design a controlled experiment that isolates the impact of CO2 on temperatures. How do you tease out the effect of the Urban Heat Island, water vapor, and other exogenous factors?
In other words how do you design this experiment : Temperature = f(CO2) and not Temperature = f(CO2, Water Vapor, UHI, and other factors)
The solution is relatively simple. One simply needs to choose locations, mostly the dry hot and cold deserts, that are shielded from large swings in H2O and impacted by the UHI. When you do that, you see that the temperature doesn’t increase with an increase in CO2. The obvious reason for that is that CO2 shows a log decay in the backradiation with an increase in concentration, and the CO2 concentration and Backradiation function forms an asymptote, and at the current concentration, the slope is approaching 0.00 quickly.
In real science, one needs to find only one example where the results don’t agree with the model to reject the null. The above link provides plenty of examples that defy the CO2 causes warming hypothesis.
Albert Einstein famously stated, “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.”
It’s amazing how multiple attempts to disprove GR have all failed.