From Untitled (call me Stephen)
How accurate are our historical temperature records?
In 2021 Bugatti released their Chiron Super Sport 300+. The “300+” is because it is the first road-legal car that has reached speeds above 300mph, although production models are electronically limited to 271mph.
This car can accelerate to its top speed of 490km/h in around 40 seconds and can come to a complete stop from that speed in less than 15 seconds.
The Dublin Port tunnel was opened on 20th December 2006. Technically there are two 4.5km long tunnels, one for each direction of traffic.
The walls of the tunnel are hard, unlike surface level motorways which have flexible safety barriers. Crashing into the walls at high speeds would be not only fatal for those involved in the crash but could also potentially damage the tunnel’s structural integrity.
To encourage people to respect the 80km/h speed limit, average speed cameras have been installed. An average speed camera system consists of at least two cameras (but ideally more) distributed over the region where the speed limit is being enforced.
The cheap option would be two cameras on each tunnel, one at the start and one at the end. If the timestamp of your car passing the second camera is less than 202.5 seconds after you passed the first camera then you have travelled the 4.5km at an average speed faster than 80km/h and a speeding ticket and penalty points for your license will follow.
The better option is to have more than two cameras distributed along the tunnel to prevent any reckless and idiotic Chiron Super Sport 300+ driver from attempting the following…
- Enter the tunnel at a rolling 80km/h start
- Put your foot down and reach the top speed of 490km/h after about 33.5s
- Hold top speed for about 1.5s
- Break hard to 30km/h over 3.5s
- Keep to 30km/h for the remaining 164s of the journey
Because that takes exactly 202.5 seconds, if the Dublin Port tunnel only has two cameras installed per tunnel, the average speed is 80km/h even though the car’s speed varied between 30km/h and 490hm/h!
“Stephen, what exactly have the Bugatti Chiron Super Sport 300+ and the Dublin Port tunnel got to do with comparing past and present temperatures” I hear you ask. Please stick with me. I hope that it will make sense by the time you reach the end.
The thermometer is a relatively recent invention. While Galileo was messing about with thermoscopes as early as 1603, it would take until 1724 when Daniel Gabriel Fahrenheit proposed his thermometer scale before the idea of standardized temperature scales would take off. That René-Antoine Ferchault de Réaumur and Anders Celsius proposed different and competing standards in 1732 and 1742 should be unsurprising to anyone familiar with how standards work.
Unfortunately for Réaumur, his choice of 80 degrees between freezing and boiling points of water didn’t catch on.
Most of the world now uses the Celsius scale, though with the 0°C and 100°C points reversed from Anders’ original proposal, with only the United States, the Bahamas, the Cayman Islands, Palau, the Federated States of Micronesia and the Marshall Islands using Fahrenheit.
Our earliest actual temperature measurements, especially those from before 1732, rely on people either having later cross-calibrated the thermometers they originally used with other ones, or having documented their own choice of reference.
It also took a while for people to figure out how to measure the temperature. Most of the early measurements are actually indoor measurements from unheated rooms recorded once a day. Eventually it was figured out that measuring the outdoor temperature required the thermometer to actually be outside and shaded from the sun.
It would be 1864 before Thomas Stevenson would propose a standardised instrument shelter and after comparing with other shelters his final Stevenson screen design was published in 1884.
While we may laugh now at people who measured the outdoor temperature with a thermometer located in an indoor unheated room, because the room has a large heat capacity, that is it takes a while to both heat up and cool down, taking one indoor measurement a day is actually not that bad a way to measure the average outdoor temperature.
When you move your thermometer to a well-ventilated outdoor shelter such as a Stevenson screen, the thermometer will change much more rapidly. If you want to measure the average temperature you will need to take multiple readings throughout the day and night.
In 1780, James Six invented a thermometer that keeps track of the maximum and minimum temperature since it was reset, though as it relied on mercury to move the markers, it can have issues in cold temperatures. By 1790 Daniel Rutherford had developed designs for separate minimum and maximum thermometers that used alcohol and mercury respectively and allowed for greater accuracy of both readings.
It would take until the 1870’s before minimum and maximum thermometers would be widely used to track the variability of temperature. For example the Central England Temperature history, the longest temperature record, is based on observations for a variety of hours prior to 1877 with daily minimum and maximum temperatures used thereafter.
Meteorologists use the daily minimum and maximum temperatures to estimate the daily average temperature by just averaging the minimum and maximum. This is called Taxn and the formula is: Taxn=(Tmax+Tmin)/2.
Do not get me wrong, if all you have is the daily minimum and maximum temperatures, averaging the two is the best guess you can make, but it is not the average daily temperature called Tavg which you get from measuring the temperature ideally more than 20 times evenly spaced throughout the 24 hour period and averaging all of those results.
Here’s where the Bugatti Chiron Super Sport 300+ and the Dublin Port tunnel come back in. If I told you the top speed of the Bugatti in the tunnel was 490km/h and it never went slower than 30km/h, if we used the Meteorologists’ algorithm we would conclude that it was travelling on average at (490+30)/2=260km/h. Yet we know from earlier that it is possible for those two limits to result in an average speed of 80km/h.
If you work it out, keeping the minimum and maximum speeds in the tunnel at 30km/h and 490km/h it is possible to get an average speed anywhere between 71km/h and 332km/h. While the Meteorologists’ 260km/h average speed is in that range, the range is quite wide.
To give another example of how the Meteorologists’ method can give an estimate that is quite a bit off, according to the Irish Central Statistics Office, in 2022 the top 1% of workers earned at least €3,867 per week. In contrast the bottom 1% of workers earned at most €92 per week. The mean weekly earnings were €856 per week and only 27% of workers earned at least that with the median weekly earnings being €671.
If we take the average of €3,867 and €92 that’s €1,980 per week. Less than 6% of earners received at least €1,980 per week which puts the Meteorologists’ average quite a bit off for estimating earnings or the average speed of a Bugatti through the port tunnel.
In the 1970’s, with the advent of cheap computers, it became possible to automate temperature measurement. A computer has no choice, if we tell it to measure the temperature every hour or every 5 minutes, rain or shine, sleet or snow, the measurement will be recorded. As most of the weather stations transitioned to automated measurement, mostly in the period 1990-2010, we are now able to measure the true average temperature, Tavg.
Valentia Observatory is 1km west of Cahirciveen, Co Kerry and a weather station has been operated in the area, with some temperature records for 1850-51 and continuous daily min-max records since mid-January 1872. The historical data sets have been carefully transcribed and are available from Met Éireann, 1850-1920 and 1921-1943. In 1944 Met Éireann did something a bit unusual, they started measuring the temperature every hour. Rain or shine, sleet or snow, the diligent staff of Met Éireann would go out to the weather station and record the temperature. Between January 1944 and April 2012 when the station was replaced with an automated station only 2 hours were missed. The data set from 1944 onwards is available from the Irish Government website: daily summary (includes minimum and maximum temperature) and hourly measurements.
Because we have an overlap of measurements from minimum and maximum thermometers and the 24 hourly measurements for Valentia, this means we can check just what the difference is between Tavg and Taxn to see how accurate the Meteorologists’ method of estimating average temperature from Tmin and Tmax is.
This first graph shows the difference Tavg-Taxn for every day since 14th January 1944 plotted as blue points. Overlaid is the 1 year rolling average as a red line. If you are interested in the statistics, Tavg is greater than Taxn in Valentia on average by 0.17ºC (std deviation 0.53, N=29339, min=-2.20, max=3.20).
If we just look at the rolling average, you can see that the relationship is not constant, for example in the 1970’s the average temperature was on average 0.35ºC warmer than the Meteorological estimate, while in the late 1940’s, 1990’s and 2000’s there were occasions where the Meteorological estimate was slightly higher that the actual average daily temperature.
It’s important to highlight that this multi-year variability is both unexpected and intriguing, particularly for those examining temperature anomalies. However, putting aside the multi-year variability, by squeezing nearly 30,000 data points onto the x-axis we may have hidden a potential explanation why the blue points typically show a spread of about ±1ºC… Is ±1°C spread seasonal variability?
The shortest day of the year in Valentia is December 21st when the day lasts for approximately 7h55m. The longest day of the year is June 21st when the day lasts for 16h57m. On the shortest day of the year there is little time for the sun to heat up and most of the time it is dark and we expect heat to be lost. So we expect the average temperature to be closer to the minimum temperature during the winter than during the summer.
We can check the seasonal effects in the difference between Tavg and Taxn by looking at a time dependent correlation. As not everyone will be familiar with this kind of analysis, I will start by showing you the time dependent correlation of Tavg with itself:
The x-axis is how many days there are between measurements and the y-axis is the Pearson correlation coefficient, known as r, which measures how similar measurements are averages across all the data. A Pearson correlation coefficient of +1 means that the changes in one are exactly matched by changes in the other, a coefficient of -1 means that the changes are exactly opposite and a correlation coefficient of 0 means that the two variables have no relationship to each other.
The first point on the x-axis is for 1 day separation between the average temperature measurements.
The laziest weather forecast is the following:
“Tomorrow’s weather will be basically the same as today’s”
The r value of +0.91 for 1 day separation is an illustration of the accuracy of the laziest weather forecast and suggests that for average temperature it is approximately 82% accurate.
If we move out to half a year separation, we get an r value of -0.64 which says that 6 months from now, 41% of the average daily temperature can be explained as the opposite of today’s.
At a year separation the r value of 0.67 days that 44% of today’s average temperature can be explained as seasonal for this time of year. What this means is that actually the laziest weather forecast is only explaining 38% better than the seasonal forecast
You see very similar graphs if you look at the time-dependent correlation of the Tmax, Tmin or indeed the Taxn, with the 1 day r values being 0.90, 0.81 and 0.90 respectively and the seasonal swing being approximately -0.6 to +0.6 for 6 months and 1 year.
The above graph basically tells us what to expect when something is strongly seasonal.
What happens when we plot the time-dependent correlation of Tavg-Taxn? Well you get this:
The 1 day correlation is 0.19, this tells us that approximately 4% of today’s correction factor between Tavg and Taxn can be predicted if we know yesterday’s correction factor. The seasonality is even worse, the 6 month correlation coefficient is -0.02 and the 1 year correlation coefficient is +0.07.
This answers our earlier question… The ±1°C spread is not seasonal variability.
What this means is that if we only know Taxn then Tavg could be anywhere ±1°C.
Here is another graph to illustrate this. The x-axis is Tavg and the y-axis is Taxn. Now obviously when the average daily temperature is higher, the average of the minimum and maximum temperatures is also higher and so we get a straight line of slope 1, but the thickness of the line represents the uncertainty of the relationship, so if we know Taxn is say 15°C then from this graph we can say that Tavg is probably between 13.5°C and 16.5°C.
Now because most weather stations were not recording hourly until recently, most of our historical temperature data is the Taxn form and not the Tavg. That means that if Valentia is representative then the past temperature records are only good to ±1°C. If somebody tells you that the average temperature in Valentia on the 31st of May 1872 was 11.7°C, the reality is that we just do not know. It’s 95% likely to have been somewhere between 10.6ºC and 12.7ºC and we have no way of knowing just like knowing what the maximum and minimum speeds of the Bugatti through the port tunnel doesn’t really tell us much about its average speed.
In this last graph the blue points show the average Taxn of each year at Valentia since 1873 with vertical error bars showing the 95% confidence interval. The red points show the average Tavg for each year starting from 1944 with error bars showing the annual variation. The blue poking out from under the red shows the difference, even on the scale of a yearly average between the Meteorologist’s estimate of average temperature and the actual average temperature.
Valentia Observatory is one of the best weather stations globally. With the switch to automated stations in the 1990s, we can now get precise average temperatures.
Thanks to the meticulous efforts of past and present staff of Valentia Observatory and Met Éireann, we have 80 years of data which allows comparison of the old estimation methods with actual averages.
The takeaway?
Our historical temperature records are far less accurate than we once believed.
Subscribe to Untitled (call me Stephen)
I have known this for 30 years now because the equipment, upkeep and record keeping were never consistent and stable.
And I have known this for about the same amount of time because the people who consistently wish to immiserate us insist that the equipment, (it’s) upkeep and record keeping have always been consistent and stable.
I wonder how often it was just people being careless- or tired, or had a few drinks- making mistakes.
I think this post says the readings were pretty.good. The graph of difference between Tavg and Taxn shows a maximum range of 0.35C, and since 1990 a range of 0.2C. That is with different intruments differently read. Even if they were reading the same thing, that is pretty good. But as the author says, they are not quite the same, and yet there is that level of agreement.
You still don’t understand uncertainty do you? The stated values may be within a given range, but the uncertainty still remains, that is, ±1.
In addition, even with a range of 0.2°C, how do you justify quoting an accurate anomaly of 0.01°C. That would work out to 0.01 ±0.2°C. Even more ridiculous is 0.01 ±1°C
However, it is a strong argument that claims of “record” or “unprecedented” temperatures based on an assumed precision of +/-0.005 deg C are not valid.
“Our historical temperature records are far less accurate than we once believed.”
That is why climate science uses anomalies. It doesn’t really matter what the exact temperature in that white box is, because we want to use it as a sample of changes in the air temperature around. Tavg and Taxn may differ in absolute value, but what counts is what happens when you subtract the respective means, a process which removes most of this difference.
Here is a plot of Boulder, Colo hourly readings, with Tavg as above, and calculated Taxn based on observed hourly min and max. Taxn actually depends a lot on when you read the min/max, so I have shown a range of possibilities. The plot is actually a running annual mean, to remove seasonality:
The Tavg just behaves like one of the Taxn curves; thee is a fairly constant offset, which disappears once ypu take anomalies. The differences between times of observartion of min/max also disappear, as long as they are consistent. If TOBS changes, an adjustment is needed, and it is pretty obvious from this kind of plot what it should be.
We have no idea what the actual temperatures were, but if we use the magical anomaly, we can still pretend that we have measured the temperature to 1 hundredths of a degree.
Speaking of anomalies I’m afraid Nick simply isn’t where it’s at with the doomsters nowadays what with his unwoke chromosomes-
Sky News host mocks Canadian MP getting emotional over ‘climate emergency’ (msn.com)
They keep banging on about saving the planet but you haven’t got a clue which one they’re on.
That’s HILARIOUS.
No-one in Canda is facing a climate emergency of any sort whatsoever.
If there is one country in the world that could definitely do with a degree or two of warming, it is Canada 🙂
Yes, dearie.. you are hysterical, and very, very stupid. !!
Correct. A few months ago we were supposed to be heading into the worst fire season evah here in BC. Now we have a cold wet spring.
I was wondering what was happening with the wildfires that started in April. I have seen nothing about them on the news and was considering doing an online search for the status.
Yes. I’m south of you on Whidbey Island, WA. Usually about now the rains have stopped for a couple weeks, and the grass is starting to turn brown.
Instead we’ve had rain most days in May, and so far in June. It’s having trouble getting out of the 60sF.
And use that as a basis for a “boiling earth”, and to manically spend $trillions/year to reduce the ever-increasing CO2, that will impoverish us peons, but not the elites.
CO2 has been proven to play no harmful role, but only a life-sustaining role for all flora and fauna.
The lapdog Media and bought-and-paid-for academia have been enlisted to spread the true-and-approved, privately owned “science”
MarkW,
You beat me to saying just that. Thank you.
Geoff S
The anomaly is climate ‘science’ itself. The ‘science’ was comprehensibly captured both politically and ideologically decades ago by the anti-humanist, de-growth green fear mongering CAGW globalist elites.
The made up ‘science’ and modelling is simply a weapon in the arsenal in the war on carbon dioxide, fossil fuels and human flourishing.
You still don’t understand uncertainty. Anomalies DO NOT reduce uncertainty. Uncertainties are additive. Even 1st year statistical students are taught that variances add when adding or subtracting the means of random variables.
Consequently, when subtracting a monthly mean and a baseline mean, their variances (uncertainties) are added. If the uncertainties (variance) are equal to “1”, you get √(1² + 1²) = ±1.4. That means a small anomaly of 0.01°C has an uncertainty of ±1.4°C. That is not a very certain answer. And remember, that is not even using an expanded value of uncertainty which would make it larger.
Anomalies are a ΔT, that is a change. They are not a temperature as everyone likes to think of them. That change occurs at a baseline. The baseline is important to know in order to judge the impact. Let’s assume a 1.5°C ΔT over a century. And let’s assume that the start is 14°C.
That means we have gone from 14°C (57°F) to 15.5°C (60°F). From cold to slightly less cold!
We are in an Ice Age, and in an interglacial. Of course it is cold. Even warmer yet would be better.
Uncertainties are additive. Yes.
Purple Entity, below, sums up in layman’s terms why that is. I’m going to spell it out at length though, purely for pedagogical purposes.
What is the anomaly an ‘anomaly’ to?
Why, it must be the measured temperature (±1°) less the average temperature (also ±1°).
How do we know that the sign of the uncertainty in the measured temperature is the same sign of the uncertainty as in the average temperature?
We don’t.
So the uncertainties do not cancel out. They add up.
That is a pretty good explanation.
Technically, the standard deviations are a ± interval. Variance is the square of the standard deviation.
It is the variances that add.
“1” is kinda a unique value when squaring and finding the square root.
The reason for RSS is that there may be some cancelation.
I fully agree. And you are right, there may be some cancelation.
There probably is.
But, near certainly, not all cancelling out.
And stating the worst case assumption would be to state that the uncertainties do not cancel at all.
The very worst case is obviously an extreme and very unlikely.
I didn’t say anomalies reduced the uncertainty of temperatures at that station. They don’t.
What they do is make possible the calculation of an average over stations, and specifically a spatial average. The reason is that they are much more homogeneous. Temperatures vary greatly with latitude, altitude etc, and to get a meaningful average you have to sample very carefully (and you don’t have much choice). Anomalies do not have that variation.
You keep using the term average. But you never, ever mention the other statistical parameters that go along with an average of a distribution of data.
Tell us how a monthly average can have an uncertainty of ±2 and the baseline average have an uncertainty of ±1, yet the anomaly has no uncertainty that you can quote.
Lots of enquiring minds wish to know just exactly what calculations are done such that uncertainty goes away.
Homogeneous does not decrease the uncertainty of the anomalies. When you average two anomalies, the uncertainty grows, even if they have exactly the same mean value.
Agreed.
I respectfully disagree. They are entirely dependant on the original measurements. And the cancelling does not occur.
It only looks like they are more homogenous because they have lost (up to) twice the information. They are vaguer, not more accurate.
That may look more useful, and it may well be easier to handle, but it’s not actually better data.
My analogy would be to make the Mona Lisa easier to copy by photographing it with a gauze over the lens and then copying the fuzzy image, It’s a lot quicker to replicate if you ignore the smile and background details,
Great answer.
Anomalies only have small variance because they are small numbers. But calculating the variance of those small numbers only, means the variance inherited from the actual measurements has been tossed in the waste can. As a result, the apparent variance is 2 orders of magnitude too small.
Thank you. I was proud of my analogy too.
But,,,
I would say the apparent variance is up to 2 orders of magnitude too small.
(I do enjoy pedantry)
Pedantry would make me say “at least 2 orders of magnitude too small”!
LOL
“I respectfully disagree.”
Well, you shouldn’t. It’s obvious. In the US, eg, temperatures will vary by up to 50C. Anomalies will vary by less than 5C, because latitude and altitude effects have been removed. You didn’t want to know about latitude and altitude effects. They don’t change. It is the anomaly that includes the changes due to weather and climate.
You keep ignoring the fact that anomalies ARE NOT standalone numbers with no uncertainty. Anomalies inherit the uncertainty of the random variables used to calculate them.
What that means is if a monthly average has an uncertainty of ±2.0, then the anomaly inherits that uncertainty. Homogenizing uncertain data just spreads the uncertainty even further.
You are making an assumption that the anomalies aren’t affected by such things as a microclimate. If a station that is missing a value is near the ocean or a large lake, the variance in temperature can be expected to be smaller than a station in the Outback. Using anomalies can force a station near a moderating body of water to inherit the variance of a station that doesn’t have the moderating influence. Using anomalies may be a convenience for spatial averaging — if one isn’t concerned about accuracy.
“Using anomalies can force a station near a moderating body of water to inherit the variance of a station that doesn’t have the moderating influence.”
It does nothing like that.
It really does. It has to, if you think about your example of geography being constant.
It isn’t constant over short periods of time.
Because the response of one microclimate to a weather front will be different to another. A shiny lake and a dark, coniferous forest will respond differently to a sunny spell.
In the end, the fact remains, throwing out information makes data easier to handle, not more representative.
Because I said so! That is an argument fallacy called ipse dixit – because I said so!
It certainly can occur if the differences of pairwise is being done. You need to provide evidence that false positives never occur.
Do min/max thermometers also record the time of day that the min and max temperatures were measured, or do they simply present the max and min temperatures since the thermometer was reset?
No. Observers usually have a prescribed time they are supposed to record the temperature. Usually they record the current temperature too, which is something of a check.
All you’re doing is propagating the prior flaws of those absolute temperatures into the anomalies.
It is a pity that you didn’t provide the full available data set for what I assume is USCRN Boulder 14 W and only show days 200 to 900.
It would also have been good to plot the difference.
Note: in the attached graph Taxn is using 0600 as the synoptic time in the above and following graphs
Statistics for Tavg – Taxn:
Min: -5.3885416666666615
Max: 8.429513888888888
Average: 0.2430135335905587
Standard Deviation: 1.2697404070433427
Count: 6720
Percentiles:
1.0%: -2.219950367647059
5.0%: -1.4917708333333333
25.0%: -0.5903645833333332
50.0%: 0.0465277777777775
75.0%: 0.9072048611111112
95.0%: 2.604184027777778
99.0%: 4.089920138888885
So the 95%CI for Boulder Co is actually ±2.5ºC which is larger than for Valentia
The rolling average for Boulder CO also shows some big swings… like I found for Valentia
That you have quite a significant swing on the yearly average suggests there may be implications for those using temperature anomalies and relying on historical, pre-digital instrumentation, data which was only Taxn
The time dependent correlation for the difference is also exceedingly weak, suggesting that the difference is not seasonal and closer to random…
I think you missed the point of my article, namely that the pre-digital instrumentation records are all mostly Taxn and there is an unknown and unknowable correction factor on any given day and can be, for a 95% CI, ±1ºC for Valentia or seemingly ±2.5ºC for Boulder
Sorry for the multiple posts… I kept getting “your post is too long”… should have gone with my initial idea of posting the full reply on twitter and then just a link here
Thank you for posting here. I don’t ‘do’ twitter.
Me neither, by personal choice. Drags everyone down to untalented teenage levels of understanding and experience . Little to be gained, precious time to be lost on trivia. Geoff S
I do but it takes time to do multiple posts to get a scientific thought across. Then you have to hope people follow the posts in the proper order.
It a lot like the school yard yel, na, na, na, na, ya.
“I think you missed the point of my article, namely that the pre-digital instrumentation records are all mostly Taxn and there is an unknown and unknowable correction factor “
The basic fallacy here is that Tavg is right and Taxn is wrong. They are both temperature indices. The mean from 6am to 6am would be another index. There is no reason to expect climate to take notice of what we define to be a calendar day.
There is a case for preferring Tavg, but there is a big one for preferring Taxn. It is the one we have historic data for.
Details of the Boulder analysis are in a post here.
Ahhh! Tevye from Fiddler on the Roof would be proud of you. Tradition, Tradition.
No one is saying to do away with the old data. We are saying it should be treated properly. The need for traditional Taxn is so that “long” records can be claimed. This is no different than Mann appending a measurement sequence to a proxy sequence. The uncertainties in each should be shown and the effects should be discussed.
The uncertainty of data is ignored in climate science, whether you admit it or not. You never, ever go through how measurement uncertainty is derived nor how it is propagated all the way through to a global average ΔT. That fact is illuminating as to your attitude to the physical science of measurement.
Ok so:
I am not saying Taxn is wrong and Tavg is right. I am saying that Taxn is less accurate an estimator of the average temperature of the geo-grid that the weather station is being used as a proxy for.
If we take GHCNv4 that works out as something like a 75km x 75km average grid square per station (with the US being significantly more dense and Africa and the Southern Hemisphere being significantly less dense.
We use one single reading as an estimate of the average air temperature of that whole 75km x 75km grid… there can be a 5ºC difference between the shade at the back of my house and the sunny back garden 5ft further behind… yet we pretend the single weather station’s Tavg or Taxn is accurate for the whole! Reality is that it is only accurate for the temperature inside the Stevenson screen… there is lots and lots of uncertainty and Taxn is just adding even more into the mix
Exactly. Microclimates are different. It introduces an environmental uncertainty that would normally be considered in an accurate uncertainty budget.
Nice.
But you know that you are goring several people’s oxen with this. Expect some vitriol in return.
For sure I expect it, but if they’re going to try and post a counter-example, they should at least try and find one that is actually counter to what I observed with Valentia and not do 10% of the work and appear to selectively display even at that… though perhaps Nick just didn’t understand the point I was making about how anomalies rely on the offset being constant in order to have any historical validity that is narrower than the variability in the offset
Nick almost certainly understands. He is a bright, well-educated guy. Unfortunately, he also has a reputation for having a talent for sophistry to argue his position.
Clyde,
There is a place for the anomaly method in this type of weather and climate research, but it’s value is limited to those few cases in which its use does not distort understanding. One has to accept that each step away from the original, measured value involves more uncertainty, as many others have shown with specific examples like correct compounding of variances of both original and reference periods. The uncertainty increases. But then, despite the efforts of Pat Frank to estimate real errors and include their effects in overall uncertainty, people stubbornly fail to understand uncertainty. I have given up on Nick because his mind is closed. Geoff S
They, including Nick, refuse to acknowledge or understand that error is not uncertainty. And the IPCC has its own esoteric definitions for “uncertainty”.
Mr. S: You recently described a CO2-in-the-atmosphere analogy using a 10-meter string and showing 4 mm. I liked that, and wanted to describe my own. I reference those “ball-pit” playroom for kids that contained lots of colored plastic balls. It’s hard to picture a million, but like your string, 10,000 is easier to see, and in my example there are exactly 10,000 balls in the room- all white, representing the non-CO2 content of the atmosphere. Replace 3 white balls with 3 black “CO2” balls, and pause to consider the heat of those three balls. Replace one more ball, and imagine how much extra heat happens.
Up to that point, I’m confident, here’s where I may need help- the next step is to consider water vapor. Do I add 2000 “water” balls (to make 12,000) or replace 2,000 white balls; then ask to imagine the heat effect of that one additional black ball. Even Mr. Stokes can input on this, even Mr. J. Might force them to consider whether their pet theory includes water vapor. I know, I know, they say it does, but a credible source is preferred.
Condensing molecules must be considered as extra because they can come and go without subtracting from non-condensing molecules.
Mr. Gorman: Thanks, you are a preferred source.
Not me.
But I guess that’s what a good training in physical chemistry does to somebody. Has them focusing on pesky details like the actual absorption spectra.
Mr. Connolly: Not you, then I’d use “Mr. C.”. Mr Geoff made that string analogy. I did read your fine article, it brought out Mr. Stokes and his magic anomoly approach, which carries over all the error but gives the result that CliScis require.
“Anomalies” based on flawed (or tampered with) records?
Why not just admit, “We don’t really know.” rather than spend trillions to “solve” a problem that no one can measure or separate Man’s impact from Ma’ Nature’s”?
Rising sea levels show that the planet is warming, satellites show that the planet is warming, melting glaciers and retreating Arctic sea ice show that the planet is warming, ocean heat content shows that the planet is warming, sea surface temperature measurements show that the planet is warming, thermometer measurements show that the planet is warming. This is not an area about which there is any credible doubt.
There is doubt. You can not just dismiss the fact that there are many stations with little to no warming. Are those stations inept or badly in error? Before talking about the globe warming, those exceptions must be dealt with.
This whole thread puts past temperature data into doubt with a large uncertainty. That can not be ignored.
Measurement uncertainty has not been routinely calculated with proper propagation. A ±1 or 2 degree uncertainty places the whole warming from pre-industrial times in doubt.
You would do better to investigate these and determine how the global average temperature has dealt with them, rather than just dismissing them as “denier” propaganda.
NIST TN 1900 should give you a good start. That has a minimum value of uncertainty for an actual station for a month. You can do that for a local station and then for a baseline at that station. Show us what the anomaly uncertainty calculation has for a value.
I think that the fact that sea level is rising and the maps for planting dates and the dates for first and last killing frost are changing in a manner to suggest warming, it is pretty hard to argue that there is no warming. The problem is that those don’t provide a numerical estimate of the rate or integrated total warming. More importantly, those lines of evidence don’t establish cause and effect.
SSTs are increasing (as is ocean heat content). 70% of the planet’s surface is covered in water. The issues described in this post, even if valid (and they are not, see Nick’s comment above), do not apply to SSTs. So there is no possible room for doubt about the magnitude of the ongoing warming trend.
“70% of the planet’s surface is covered in water.”
Actual covered in water is closer to 79%. Yes the extra 9 percent is that hard white stuff that you don’t have to be Jesus to walk on, but it is still water.
The Antarctic Ice Sheet covers 8.3% of the Earth’s land surface.
The Greenland Ice Sheet has a sea level equivalent ice volume of 7.42 m, and covers 1.2% of the global land surface
These are May ΔT’s for Topeka, KS. Forbes Air Base. May is a traditional planting time. Tmax shows little change. One might tease out a small Tmin increase since 1999. However, the entire trend for both is not statistically significant as all variations are within the uncertainty interval.
I should point out that the uncertainty is the expanded standard deviation of the mean as shown in NIST TN 1900.
Using the standard deviation is the better indication of the dispersion of the data around the stated value of the measurand, but would generate arguments beyond what is important. Since the shown uncertainty interval obviously includes 95% of the measured values, that is sufficient.
Liar.
Other than the rise has not accelerated for a long, long time. Accelerated warming should result in accelerated rise.
And effects of land rising or sinking are just ignored.
Mr. J: Each of your examples of global warming you cite is a local measure that your science friends extrapolate to “global”. When rooted tree stumps emerge from under glaciers in the arctic, it’s just local or limited to regional. Not global you say. Frankly, you guys give cause for credible doubt with each post.
When rooted trees and other buried artifacts appear from under glaciers on different continent’s, it is difficult to say it wasn’t warmer globally.
Mr. Gorman: For some, it’s all too easy to say, Mr. J will be along any moment to say just that. But that type must remember what they said before. For those who value truth, it’s…more difficult.
Your graph makes it look like the temperatures are known exactly. They aren’t! There is an uncertainty associated with every measurement, which is simply ignored. Subtracting one big number from another big number usually results in a difference with fewer significant figures. Therefore, the uncertainty becomes a larger percentage of the difference, the so-called anomaly. Indeed, if the actual uncertainty of the original measurement is about 1 degree, then it is about the same magnitude as the nominal values of the anomalies. Yet, you still ignore it, even though the uncertainty may be pushing 100%.
You lost me after 3 paragraphs, but much appreciated for your willingness to explain it.
Go back to grade school
According to NASA GISTEMP the NH annual mean temperature has increased by ~1.2C since 1940-5 whereas the Valentia Observatory on Valentia I off the SW coast of Ireland has recorded (eyeballing) virtually no net warming during the same time period although has warmed since ~1980.
What local factors can be preventing SW Ireland and other locations from enjoying a balmier climate like the rest of us, the claimed warming being entirely and totally due to well-mixed human GHG emissions according to NASA and the IPCC⸮
My hunch is that the global annual mean temperature record would have looked more like that for Valentia I if extraneous factors like UHI affected sites had been excluded and other data had not been tortured unmercifully.
You are exactly correct. That has been noticed on X also for this exact same station. Other stations around the globe also have little to no increase in temperature.
The global average as calculated has real problems with combining winter and summer temperatures into a single value. Both have different variances and a simple average just covers that up.
What you end up with is an anomaly at milli-kelvin with integer uncertainty. Not a good look.
“What local factors can be preventing SW Ireland and other locations from enjoying a balmier climate like the rest of us”
It lies on the SW coast of Ireland.
Prevailing winds for Ireland and the UK are SW’ly.
Ergo the temperature there is moderated by sea temps.
(akin to what a coastal sea breeze does)
Let’s see,
Ergo, the ocean must not be warming!
Hmmm, is only interior land warming?
Hmmm, is sea ice affected by something other than warming ocean?
No, sea temps have risen:
Data recorded at Valentia Observatory since 1976 has shown average annual rainfall and mean temperatures have risen significantly over the last 40 years.
Average annual rainfall (based on data available online from Met Éireann) was just under 1,400 millimetres per year in 1976, but has risen consistently since then. The average is now just under 1,600 millimetres.
Annual mean temperatures have also climbed. The average in Valentia is currently 11 degrees Celsius, a rise of well over half a degree since 1986.
https://www.independent.ie/regionals/kerry/news/hi%20storic-year-for-valentia-weather/35358060.html
Woo hoo! 1/2 degree in almost 40 years and just a touch higher what the 1930/1940’s were.
It would be nice to see the uncertainty range for all those. Like this.
Actually:
“a rise of well over half a degree since 1986.”
”Ergo, the ocean must not be warming!”
Yes, well done – you figured out the obvious.
It’s like averaging the pressures in your 4 tires –
you get an answer of 45 psi, which conforms to the manufacturer’s recommendation, but in fact your 4 readings were 20, 60, 30, 70 psi.
There’s a 50% chance you’ll be going in circles if you take your hands off the wheel.
And the average human has a penis & a womb …
Therefore, is a hermaphrodite !!
Technically that is only true if you average between one male and one female, back to the two camera speed average. However less than 50% of the population is male, and not all of the female population have wombs.
Let’s correct that.
And the average human has half a penis & half a womb
With today’s crowd, that is probably the left side of both.
The average human has less than two legs.
Which is another mean thing to say.
“Fewer” than two legs.
(I love the smell of pedantry in the morning.
Smells like – NickPick)
🙂
You are correct.
I concede the point,
(A reply to all of the above fun little side.)
Statically, all humans have one brain.
But that doesn’t mean they can’t be of two minds …
Or even no mind.
And after accounting for traumatic brain injury in war and vehicle accidents, brain cells killed from alcohol and recreational drug use, the average IQ of adults is less than 100.
But are current temperature records any better?
From memory some where on this site there was query re maximum temperature when temperature could be caused by some non-weather event, e.g. hot exhaust blowing on the reading site for 5+ minutes hence causing a phoney high reading.
The other small problem I have with daily, usually by the hour, published temperature is how much is “homogenised”.
Raw data is seldom really published. Here I look at such sites in Australia as The BoM and Weather Zone.
The concept of homogenising really relates to mining for ore reserves and underground water table holdings. It seems to only recently been taken buy various weather reporting bureaucratises, e.g. BoMs, to make thing suite and agenda.
I have taken my grandfather’s approach, he was old time farmer, to the weather and temperature.
Look at the sky, feel the temperature today, check sky at night. Clear sky day time depending on time of year, warm,(winter), or hot,(summer), clear sky at night, freezing, (winter) or cool sort of, (summer).
The only thing I look at from the OZ BoM is their synoptic charts. At best they are only good for 6 hours anyway.
If you really need local temperatures, max, min, etc., set up your own weather station and record the data.
Whatever could have made you think the recordings are for you or me?
nhasys,
As a mineral geochemist, I cannot understand your reference to homogenisation and mining for ore reserves. For sure we use statistical tools such as geostatistics and interpolation of ore grades to create, for example, blocks of roch that can be classed as ore or waste to handle as excavation proceeds. But the estimates of grade and hence value of ore is strictly traced to original chemical analysis (assay) using numbers that have not been homogenised. Unless something changed recently. Geoff S
Geostatistics as used in minerals deals with deposits that don’t change chaotically by large amounts on a continuous basis.
Global portends a change that occurs everywhere. Extraordinary claims need extraordinary evidence that is beyond approach. That means manipulating data in an acceptable manner with correct statistical parameters.
Jim G, “deposits that don’t change chaotically by large amounts on a continuous basis.”
They do before we are finished with them. Look at these beauties changed continuopusly over 30-40 years of digging. These are aerial shots of several that I assisted in discovery and/or development. They are large by world standards, but not the largest by a long way. Geoff S
I didn’t mean to imply that they do not change over time. What I was trying to emphasize is that they don’t change hour by hour and day by day. Nor are the changes controlled by chaos, changes are pretty linear.
The use of temperature anomalies introduces another bias into climate studies.
Clive Best provides this animation of recent monthly temperature anomalies which demonstrates how most variability in anomalies occur over northern continents.
https://rclutz.com/2017/01/28/temperature-misunderstandings/
What I take from this is how does the “heat” from CO2 move around so much? For a global figure, you would expect a much more stable location of hot spots. Especially since so many headlines from around the world trumpet how each location is warming faster than the global average.
And all the children are above average.
Jim, alarmists term this effect “Arctic Amplification” for scary purposes. The higher temps at higher latitudes is a combination of the bias included in anomalies plus meridional transport. In Sum:
Arctic Amplification is an artifact of Temperature AnomaliesArctic Surface Stations Records Show Ordinary WarmingArctic Warmth Comes from Meridional Heat Transport, not CO2https://rclutz.com/2023/08/19/arctic-amplication-not-what-you-think/
You miss my point. If a point has truly warmed, then it should stay warmed. A point with a positive anomaly and then a negative anomaly is not really warming is it? Nor is it under control of CO2.
Greater fluctuation can leave no mean warming but would still be climate change.
OK, this argument rules out the feedbacks that are fundamental to newsworthy climate change.
But it doesn’t rule out any anthropogenic climate change.
Good article. The only criticism is that you use the word accuracy throughout and that is not the proper use. What you really are describing is the uncertainty of the readings. Accuracy is defined as to how well a stated value represents the accepted value.
In this case, you are evaluating just one component of uncertainty. That would be the reproducibility uncertainty. There is also a component of repeatability uncertainty. The only way to obtain repeatability uncertainty is to have multiple calibrated thermometers in order to have multiple readings of the exact same thing.
I do want to commend you on recognizing and developing a good view of how badly Tₐₓₙ actually represents an average daily temperature. The variance of two readings at different times of different waveforms is so large as to make the arithmetic average highly uncertain as to an actual daily average as you have shown.
You should know that HVAC people are moving to using an actual integral of the finest temperature readings available. In some cases ASOS has six second readings but I think most are 5 minute averages. That provides a very accurate degree·day value.
Thank you for your feedback. I think you use accuracy where I would use precision. My use of accuracy is distinct from precision and is more the antonym of uncertainty
If you haven’t studied the GUM (JCGM 100:2008) carefully, and no reason you should, that is what I use. It really doesn’t have a definition at the current time for precision. From other documents there is a pretty standard definition. In my words precision is the ability of a measuring device to repeatedly provide the exact same value each time a repeated measurement of the same measurand is taken. That very much sounds like the repeatability uncertainty defined in the GUM.
Accuracy is defined in the GUM as:
Atmospheric temperature measurement doesn’t have a good way to achieve repeatability uncertainty, especially when using a single instrument with hysteresis.
I can have a min-max thermometer that is calibrated to 0.01°C and is read by a D/A converter such that this precision is retained. Thus we can have a very precise reading for the min and the max, but we are only sure that at the exact location where the thermometer was, those precise readings were obtained… as a proxy for the rest of the surroundings it may or may not be accurate at the same level of precision.
I can then take these two very precise min and max readings, and average them to get Taxn… this is again a very precise reading, but it is not an accurate estimate of Tavg unless we are exceedingly lucky.
I can take the precise thermometer and take 24 hourly readings, that again will give me a precise average (though there is at least from averaging a standard deviation in the observations… but I can work that out very precisely). That 24h average is a more accurate estimate of the true average temperature. A more accurate estimate is from 288 5 minute readings… this may have in fact the same (or very similar) standard deviation (because the std deviation in that case arises from the spread from min to max and the histogram)
When I am talking about the accuracy of Taxn as a measurement of Tavg… that seems to align exactly with the GUM definition you cite.
I think my use of accuracy aligns with the GUM definition you provide.
We do not know the true value of the average air temperature in Valentia on 1st of June 1873. We have an estimate from Taxn, but it is only accurate to within ±1ºC based on the historical accuracy of Taxn at estimating Tavg at that location.
P.S. see elsewhere in the comments for the even more shocking ±2.5ºC accuracy of Taxn as an estimate of Tavg at Boulder CO 14W USCRN station!!!
I agree with most of what you have said. Just two points.
Repeatability as defined by the GUM is basically, measuring the same thing, multiple times, by the same observer, with the same device, over a short period of time. See GUM B.2.15 defines these as repeatability conditions. In essence, it is a gauge of how precise a measurement is.
It is not a measure of accuracy. There are a number of influence quantities that can affect the width of the uncertainty interval surrounding a stated value (the mean of the measurements).
Each measurement of Taxn has an uncertainty interval. Since we do not have multiple measurements, a Type B uncertainty must be allocated.
Then we approach the reproducibility uncertainty as defined in GUM B.2.16. These are what occurs under non-ideal conditions. Measuring the same thing under changed conditions. Reproducibility uncertainty requires multiple measurements and is gauged by the mean and variance.
Taxn then has two uncertainties at this point. Repeatability (Type B) and reproducibility (Type A). These two uncertainties will be pretty large. There a multitude of other influence quantities that should be considered in an uncertainty budget.
Tavg measurement uncertainty would be the result of multiple measurements of different things. Each measurement would have a repeatability uncertainty (Type B again) and a reproducibility uncertainty derived from the mean and variance of the distribution throughout the day.
Then one moves to monthly averages. These suffer from measurement uncertainty in each daily value and reproducibility uncertainty over the months time.
Let me reiterate, I am very interested in your work. It seems to validate work I have done in determining the uncertainty in daily and monthly temperature measands, especially with LIG thermometers.
Something that needs to be taken into account is how finely the measurement can be resolved. That is commonly addressed with the number of significant figures. Accuracy means whether or not the measurement is correct, precision means how finely the measurement is resolved, and uncertainty addresses the repeatability of the measurement.
I like this article. It helps get to the very difficult task of answering the question of what temperature measurements are and are not. Most people won’t try to grasp the task of trying to know temperature in a meaningful way. I once was involved in temperature mapping for autoclave validation. In short, I learned that even under extremely well controlled geometry, density, and time, temperature prediction is only constrained to ranges of variability. It is never, and will never, be exact. In my idle moments I allowed myself to contemplate what the statistically supportable temperature measurement in my back yard might look like. I didn’t belabor the thought as the problems are stupendously complex. When I hear that the globe is warmed by carbon dioxide, and carbon dioxide alone, mind you, I cannot take it seriously. However, unless you have genuinely tried to manage a meaningful measurement of anything, you don’t grasp the problem. And that is why the public can be fooled by this nonsense.
Not clear why we are forced to scan through two pages of “Bugatti Chiron Super Sport 300+… ” and “distribution of weekly earnings in euros ” before coming to discussion on temperatures. Sorry, maybe I missed the point, I have several other important things occupying my time right now. OK.
Danley, my approach is to “skim” articles for points of interest to me.
Saves wading through every sentence written.
See, “skimming” is not just something that Democrat Rep Maxine Waters does with campaign funds.
https://www.foxnews.com/politics/maxine-waters-paid-daughter-192000-campaign-funds-2022-cycle-filings-show
You missed the entire point. Taking two values as an average can mislead as to what actually occured between those two values. Just like the car can go like hell for a period then slow down to make the average come out, temperature can do the same.
Tₐₓₙ as an average does not tell you what temperature did in between the two values.
I am sorry that you were held at gunpoint and forced to read this article. When my brother said “WUWT would like to put your post on their site” I didn’t realise that this would be followed with your life being threatened if you didn’t read my post.
in future when writing a post for a non-WUWT audience I will remind myself that it may still get picked up by WUWT and some of the readers on WUWT are forced to read the content even if it includes content to make technical points more accessible to a non technical audience
my sincerest apologies. Nod slowly two times if the man with the gun is still in the room
You make this understandable to the great unwashed, but you have not approached the problems with historical temperature records.
So, reading LIG thermometers from a shorter person vs a taller person?
What time was the observation taken?
Did the station move?
When did the observations become higher-resolution?
And how many times a day?
You chose to write this, tell us the error bars from each year.
The records are not fit to determine whether the so-called Global Average Temperature has changed AT ALL.
Moon
Not to mention that the stations have all been moved to the hottest UHI locations available. Twain said it best, “There are lies, damned lies, and statistics.” To whom does it feel hotter?
The media and the University Presidents have chosen to Defend The Earth by attacking all forms of Mining, upon which our modern prosperity is dependent. This too shall pass….
If I add 2 more characters to that post then substack refuses to send it my email to my subscribers.
it is already quite unwieldy with nearly 2500 words a d some quite complex graphs. Sure I could remove the Bugatti reference, which – if I had been targeting a more technical audience i probably would – would cut some fluff but at the side effect of leaving a general audience alienated.
the post was not written for here but for Twitter and my substack subscribers (all free tier)
I am currently trying to see if I can find interesting ways to make more of the issues with accuracy accessible to the general public.
Stephen,
Thank you for this careful work with its large volume of T data that appear to have fewer extraneous factors affecting them than do most weather stations.
I thank you for a style of confirmation. Since year 2000 or so, I have often written that historic daily temperatures such as these, in reality as opposed to mathematical theory, can be anywhere within +/- 1 deg C of the estimate. More often I have used +/- 0.7 deg C. These are for 2 sigma if classical terms apply, though distributions seldom resemble a normal shape.
My comments apply to Australian data. My conclusions come from several different lines of investigation. One of the most compelling lines harnesses the expertise of our Bureau of Meteorology which has produced 4 different homogenised series of temperature/time series in an effort to correct what their experts believe is the most credible pattern. Their spread of daily results for their 100+ selected stations is typically above +/- 1 deg C.
(My web hosting is down; reliance on memory here, apologies if wrong).
Besides, I spent years in analytical chemistry where uncertainty, error, accuracy and precision are performed to higher standards than used in climate temperature research.
Several past WUWT articles can be searched with “Sherrington Uncertainty”. Geoff S
You mean you can’t tell a client’s gold nugget is 99.9876 grams when weighing it to the nearest gram 1000 times?
Analytical and physical chemists of the world unite!
Stephen,
I question the validity of the term Taxn, the math average of Tmax and Tmin on a day. You should not average these temperatures for statistical work because they are not samples of one population of numbers. There are at least 2 parent populations, one for Tmax and one for Tmin. The events that trigger their capture are different. Mostly, T max is triggered by the passing of maximum daily insolation, as complicated by factors such as cloud, rain, wind, original humidity etc. The Tmin capture is often soon before sunrise as heat shedding is slowing to low values, again with complications. Because the Tmax and Tmin captures have different causes, they are from different master populations for formal stats work. There is a variable day-to-day time difference between Tmax and Tmin capture that to date is unpredictable. Geoff S
Taxn also can have a similar value for quite different values. The variance then becomes even more important to describe range of the values. In other words it smears too much together.
It only makes statistical sense to do nothing more than treat Tmax and Tmin entirely separate.
Sadly the value and how it is calculated is not my doing.
it gets given many different names, the most common being “mean daily temperature” and can even be written as $T_{mean}$
because for a large period of time this is the best *available* estimate of the average temperature, that’s all we’ve got.
the point I am making is just that we should be aware of how it is different.
technically it is the Average of the maXimum and miNimum so to distinguish it from an actual average in the meaning most people understand I wrote it as Taxn which is also a name I have seen used by others, but it is not a universal term.
the 1992 or something like that paper detailing the Central England Temperature record refers to it as $T_d$
Stephen,
Yes, I know that about common practice. My objection is a statistical one, that the calculation of Taxn should not be done because it violates classical statistical rules.
I agree with Jim G that Tmax and T min should be used alone, not in any combination.
People schooled in statistics must know that you cannot combine samples of different populations this way, yet they fail to display professionalism by not only refusing to do the incorrect procedure, but also educatind those entering statistics as to what is the right thing.
Too mucg formal math and science has been corrupted recently by not-so-wise people essentially adopting “I know the text books say otherwise, but I like my home-made version better so I will push it and simply be silent about whether it is valid.” That is not how good science progresses.
(I’m not accusing you of anything bad – quite the opposite, I welcome the rather important contribution that you have presented here and I hope that it helps lead to better quality all round. It should.).
Geoff S
Ah, ok I see the point you are making.
yes it would be good if people used actual observations directly rather than trying to apply multiple layers of “corrections” to come up with an imaginary temperature for each day that may or may not have been representative of the weather of the whole 75km x 75km average grid of surface air temperature that the station is being stretched to apply to.
sadly, this is not what happens, the homogenisation process making things even further from reality (but finding a way to explain that to lay people is tricky)
I will point out, however, that because temperature is a continuous variable, Taxn does have one property: there was at least one time during the day that the temperature inside the Stevenson screen was half way between the minimum and maximum temperatures recorded on that day.
we do not know when or for how long the temperature was at, min, max or axn… but we know it was at all three… now ok axn has two measurement errors combined (because you read two scaled to get it)
Someone, somewhere, in the past decided averaging the two temperatures was the thing to do and the term “average” kinda stuck. It is NOT and average, it is a mid-range temperature, half-way between the high and low temperatures.
As you say, it provides no information as to the actual temperature distribution throughout the 24 hour period. Temperatures could have been around the max for six hours and around the minimum for 1 hour and you’ll never know. You can get the same “average” for a desert with no humidity as a tropical location “average” with 100% humidity.
As Geoff points out, combining a single sample from two distributions is not even correct from a statistical standpoint let alone a physical one. Your analysis provides an excellent view of why the errors compound when this is done.
Keep up the good work.
For anyone who is interested, I got the terms Taxn and Tavg from the NOAA readme file that you can find here: https://www.ncei.noaa.gov/pub/data/ghcn/daily/readme.txt
TAXN = Average daily temperature computed as (TMAX+TMIN)/2.0 (tenths of degrees C) TAVG = Average daily temperature (tenths of degrees C) [Note that TAVG from source 'S' corresponds to an average of hourly readings for the period ending at 2400 UTC rather than local midnight or other Local Standard Time according to a specific Met Service's protocol] [For sources other than 'S' TAVG is computed in a variety of ways including traditional fixed hours of the day whereas TAXN is solely computed as (TMAX+TMIN)/2.0]There is another variable not accounted for. Temperature measurements all have an error and those errors are in the higher temperature direction. Most of those errors are caused by poorly located thermometers. There are many sources of heat, AC, asphalt, buildings, etc. And there are essentially no sources of lower temperature measurements.
You are not wrong. I have found that when writing an article for the general public, as I was in this case, it is best to try to stick to one point and one point only.
Yes my post is long, but in my opinion necessarily long. People see these graphs of historical temperature (anomalies) that always have the x-axis starting in the 1970’s and the graphs look like it is very obvious that temperature has risen… and by using anomalies which they describe as the change since a reference time, you get a number like +0.5ºC or whatever… and that seems to the general public like “oooh look”
When they present longer x-axis data, it is always the output from homogenisation algorithms that effectively take the numerical majority of urban stations and their urban warming and apply it to the numerical minority of rural stations. This is despite the fact that rural stations are used to represent the surface area majority. The side effect of that is to suppress the rural warm periods in the 1940’s (and 1870’s if the data goes back that far)… though apart from Valentia’s 1944 data I, the absolute value of the maximum in the 1870’s is unclear because that’s all Taxn… and I suspect almost all weather stations besides Valencia are Taxn even for the 1940’s local maximum.
If we want to restore trust in science in the public, we have to treat them as intelligent beings who have the capacity to understand (but were not given the right stimuli)
There was a local maximum in the 1940’s which, apart from Valentia from 1944 onwards, is mostly shown in Taxn records and thus subject to possibly significant uncertainty of the absolute position. If we take Valentia as a reference, it says ±1ºC. If we take Boulder CO, that says ±2.5ºC. So we could shift that local maximum up or down by let’s say conservatively 0.3ºC… on one extreme that suggests current temperatures are the same as that local maximum and there is nothing to be alarmed… on the other extreme that suggests that the local maximum is rising in line with the CO₂ levels (yes doomers, Taxn uncertainty allows for the possibility that you are correct… while simultaneously allowing for the possibility that you are completely wrong… be careful with this double edged sword)
We have a lot less data, but the data we do have suggests there may also have been a local maximum in the 1870’s (some claim there is a 60-70 year climate cycle… but we don’t have enough data to say that with certainty… need another 140 years at least!!!) that local maximum presents a major challenge to the CO₂ doomers as even with the Taxn uncertainty it contradicts the CO₂ hypothesis… to dismiss that one you need to bring in the early instrumentation errors etc… though I find that hard to buy when you read the inspection reports of Valentia observatory… there could certainly be issues around siting of weather stations… and then things like measurement methodology changes (it is very convenient that CET only starts using Taxn after 1877… Valentia’s data suggests that a possible warm tail had vanished from 1872 to 1877… a methodology change could erase or depress an 1870s local maximum… or the Taxn uncertainty could say that there was no local maximum)
The reality is that we don’t even know the current temperatures… but try fitting that into less than 2500 words and making it something that the general population is capable of understanding if we give them credit for their ability to understand and stop treating them like babies… a quart into a pint pot would be easier
Your article while long is very appropriate. You’ll notice it took me awhile to post. It does take time to go back and forth to assure understanding.
Good job!
A bit late to the party, but better late than never.
I found it difficult to get past the stuff about cars, tunnels and wages in Ireland and find out what this post is about. It seems to be a mix of things, in particular the use of (Tmax + Tmin)/2 to calculate daily mean temperature, and indices based on more frequent readings averaged through the day. (in Australia it was commonplace to observe wet and dry bulb temperatures every three hours, but use the accepted (Tmax + Tmin)/2 method to describe the daily average. As that practice has been the norm since before Federation, it should not change.
Daily temperatures are independent observations and therefore errors do not propagate from day to day. While distributional statistics may be calculated, they reflect the measurements – variation in the medium being measured, not the instrument. The standard deviation of Tmax or Tmin for instance, or daily rainfall, reflects variation in the climate not the instrument. It is a fallacious argument to confound issues such as accuracy, precision and instrument uncertainty into discussions about T-measurement. It can be shown for example, that as the frequency of measurements and accuracy/precision of instruments increase, ‘noise’, which is variance, increases also. Sorting out the ‘signal’ from the noise then becomes a challenge.
It is also obvious that the practical difference between (Tmax + Tmin)/2 method and other methods of calculating averages, is at best a distraction. The graph of the difference shows no material bias high or low. The data table (https://wattsupwiththat.com/2024/06/01/comparing-temperatures-past-and-present/#comment-3919663) shows data are warm-tailed, the mean being factors higher than the median while the distribution >1% vs >99% is obviously lop-sided. So, data are distinctly non-normal in their distribution. The purpose of calculating anomalies, which often stirs passionate debate is to levelise the effect of site differences when comparing different datasets.
Whether data are homogeneous or not can be resolved using a range of statistical tests corroborated by independent sources such as aerial photographs, metadata etc, and should not be taken for granted.
All the best,
Dr Bill Johnston
http://www.bomwatch.com.au
Daily temperatures are independent, that is , yesterday’s reading does not have an effect on today’s reading.
However, when the measurand is declared to be Tmax_monthly_average there are two uncertainties that need to be propagated. Tmax repeatability. That is uncalculatable because there is only a single reading per day (GUM B.2.15). Therefore a Type B uncertainty must be used and propagated into the Tmax-montly_average. The reproducibility uncertainty arises from the daily influence quantities changing so that the distribution reflects changing conditions (GUM B.2.16).
This is predominantly affected by the definition of the measurand. In this case there is only one measurand, Tmax-montly_average and the value of this measurand is determined from the daily readings.
You are wrong Tim and it was not so long ago that you were arguing that error WAS propagated between successive observations. You also said here somewhere, that the variance is calculated from the SD, where in fact the SD is calculated from variance. Why did you not criticize some of the graphs in this post. Surely you would know that Pearsons coefficient of linear correlation is not valid when used on cycling data – all the correlation is due to the cycle, not variation in the data.
Also, how was average Taxn of each year at Valentia since 1873 with vertical error bars showing the 95% confidence interval calculated? What are the error bars? Are they 2-sigma for each year’s daily or monthly data. If they are CIs (2*SEM) on what basis were they calculated (daily, monthly); were data de-seasoned or do the bars include the annual cycle? If so why so?
Your reasoning in the second paragraph is also a fallacy. Forget the GUM, toss it out the window and work with data. The only uncertainty in a T-observation is instrument uncertainty/error, which as it is expressed as +/- half the instrument interval, cancels-out. Furthermore, if you are talking about temperature, talk about degC or DegF, not the fluffy, woke measurand term which is actually a concept not an instrument or interval scale.
You say:
“Therefore a Type B uncertainty must be used and propagated into the Tmax-montly_average. The reproducibility uncertainty arises from the daily influence quantities changing so that the distribution reflects changing conditions (GUM B.2.16).
Show us your wizardry by calculating Type B uncertainty for a bunch of observations. You can’t. You think the GUM is all so important, but beyond the lab, it is nonsense. Anyway, you have never undertaken standard met observations, so what would you know? You are simply leading people astray.
Yours sincerely,
Dr Bill Johnston
http://www.bomwatch.com.au