# Fun with Trends

Brief Note by Kip Hansen – 17 August 2022

I have been doing research for other people’s book projects (I do not write books).  One of the topics I looked at recently was the USCRN — U.S. Surface Climate Observing Reference Networks (noaa.gov);  Self-described as “The U.S. Climate Reference Network (USCRN) is a systematic and sustained network of climate monitoring stations with sites across the conterminous U.S., Alaska, and Hawaii. These stations use high-quality instruments to measure temperature, precipitation, wind speed, soil conditions, and more.”

A main temperature data product produced by USCRN is Average Temperature Anomaly for the entire network over its full length of about 17 years.  It is shown up-to-date here at WUWT in the Reference Pages section as “Surface Temperature, US. Climate Reference Network, 2005 to present” where it looks like this:

Now, a lot of people would like to jump in and start figuring out trend lines and telling us that the US Average Temperature Anomaly is either “going up” or “going down” and how quickly it is doing so.

I suggest the following:

1.  What is the range over the time period presented (2005-2022)?

Highest to lowest, the range is about 11 °F or 6 °C.  This range represents not a rise or fall of the metric but rather the variability (natural or forced).  Look at the difference between the high in late 2005 and the low in early 2021.  If this graph had been unlabeled, I would have identified it as semi-chaotic.

2.  Is the anomaly visually going up or down?

Well, for me, it was hard to say.  Oddly, the anomaly seems to run a bit above “0” – which tells us that the base period for the anomaly must be from some other time period.   And it is, USCRN uses a 1981-2010 base period for “0” when figuring these anomalies, the base period is not inside the time range of this particular time-series data set.

We can, however, ask Excel to tell us mathematically, what the trend is over the whole time period.

There, now you know.  Or do you?  MS Excel says that USCRN Average Temperature Anomaly is trending up, quite a bit, about 1 °F (0.6 ° C) over 17 years

~ ~ ~

Now comes the FUN!

I’ve arbitrarily picked five-year time increments as they are about 1/3 of the whole period.  Three five-year trends (the last one, slightly longer) which are all down-trending, add up to one up-trending graph when placed end to end in date order.

Lessons We Might Learn:

a.  Don’t use short time periods when determining trends in a time series.  Trends are always sensitive to start and end dates.

b.  This phenomena is somewhat akin to Simpson’s Paradox: “is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined.”

“In his 2022 book Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy and Everything Else, Jordan Ellenberg argues that Simpson’s paradox is misnamed:”

“Paradox” isn’t the right name for it, really, because there’s no constriction involved, just two different ways to think about the same data. … The lesson of Simpson’s paradox isn’t really to tell us which viewpoint to take but to insist that we keep both the parts and the whole in mind at once.”  [ source ]

c.  It does bring to mind other data sets that change trend (or even trend sign) when looked at in differing time lengths  — sea level rise comes to mind, with the short satellite record claiming to be double the century-long tide-gauge SLR rate.

d.  Why look at trends that are obviously not reliable over different time scales?   This is a philosophical question.  Can a longer trend be real if all the shorter components of the trend have the opposite sign?  Can three shorter down-trends add up to a longer up-trend that has applicability in the Real World?  Or is it just an artifact of the time scale chosen?  Or is the opposite true?  Are three shorter down-trends real if they add up to an up-trend? (When I say “real” I do not mean just mathematically correct – but physically correct.)

e.  Are we dealing with a Simpson’s-like aberration here?  Is there something important to learn from this?  Both views are valid but seem improbable.

f.  Or, is what we see here just a matter of attempting to force a short highly variable data set to have a real world trend?   Are we fooling ourselves with the interpretation of the USCRN Average Temperature Anomaly as having an upward trend – when the physical reality is that this rather short data set is better described as simply “highly variable”?

# # # # #

Author’s Comment:

I hope some reader’s will find this Brief Note interesting and that it might lead to some deeper thought than “the average and its trend have to be correct – they are simply maths”.

Many metrics of CliSci are viewed at an artificially assigned time scale of  “since the beginning of the modern Industrial Era” usually interpreted as the late 19th century,  roughly 1860 to 1890.  Judith Curry, in her recent interview at Mind and Matter suggests that this is literally “short sighted” and that for many metrics, a much longer time period should be considered.

# # # # #

Article Rating
Inline Feedbacks
M Courtney
August 17, 2022 6:06 am

It seems fair to include all data in the trend unless there is a discussed reason not to.
The only graph that matters, if any do, is all of the data.
We can always find other things to discuss if we ignore some data for some unstated reason. But we shouldn’t do that.

kzb
August 17, 2022 7:35 am

The start date is not really arbitrary. It is supposedly the start of significant fossil fuel use, the idea being to correlate (previously buried) CO2 emissions with temperature. So there is a good reason why the start date is where it is.

MarkW
August 17, 2022 7:51 am

Except that start date is also during the coldest period of the last 10,000 years.
Of course the world has warmed up since then, and most, perhaps all of that warming would have occurred even if man hadn’t burned any fossil fuels.
Heck, the world still hasn’t returned to the average temperature for the last 10,000 years.

Joao Martins
August 17, 2022 10:09 am

Can you tell us about anything LESS ARBITRARY than the statement of (my stress) “significant fossil fuel use”? … and that statement implying that CO2 emissions are the sole cause of temperature changes?

Retired_Engineer_Jim
August 17, 2022 10:23 am

According to some sources, the Industrial Revolution began in 1760.

MarkW
August 17, 2022 10:25 am

Fossil fuel use in 1860 was not “significant”.
It didn’t become “significant” until sometime after 1950.

John B
August 18, 2022 1:53 am

In SE Australia, most rural temperature readings show a cooling from about 1900 (the Federation drought) to the late 1970s than a warming tend. Sydney shows a warming from 1950, but I put that down to the immigration growth in the cities after WWII, and the associated UHI effect. All capital cities attracted migrants after WWII and this would explain a lot of the warming in the cities). The cool PDO (~1944-1978) may have had an effect on the cooling in the 1970s. The recent La Nina most likely affected last year’s Summer, which dropped up to 3 degrees C from the year before. I also think from the 50s in the country, weather stations were moved to the airports, also contributing to an increasing trend. Also, as an exercise, I graphed the temperatures (mean max summer-JJA) of 3 central England stations (CET (comp) , Sheffield & Oxford) and compared them to 3 remote Scotland stations (Lerwick, Stornoway & Tiree), also the mean Max Summer temp. The 3 mean England stations temperature trended at 1.1C per century, whereas, the Scotland temperature trended at only 0.2C per century. From what I have seen through my research is that the UHI effect is not adequately accounted for in any adjustment.

John B
August 18, 2022 1:56 am

Make of it what you will.

Carlo, Monte
August 18, 2022 5:48 am

Very interesting to see.

Clyde Spencer
August 17, 2022 11:04 am

No matter how well justified rationalized, one has to be concerned about spurious correlations. Correlations may have predictive value, but they may have little or no value for establishing causation, particularly when time is the independent variable.

Tim Gorman
August 17, 2022 3:57 pm

They may also have *no* predictive value. In a time series, giving equal weight to past history as you give to current history is a recipe for forecasting disaster. Unless you can define a functional causal relationship for the values of the time series you really don’t have an idea of what is going to happen in the future.

Ask anyone that has tried to forecast where a new telephone central office should be located or where a new grocery store should be located. If you just use population growth data over time with no weighting as a predictor your prediction is quite likely to be wrong. Your long term trend may indicate growth while the more recent data indicates movement away from the long term trend (e.g. conversion from landlines to cell phones, population movement away from from high density areas).

Focusing solely on CO2 as the main driver for the functional relationship of temperature and time is missing the forest for the trees!

Clyde Spencer
August 17, 2022 4:59 pm

Yes, implicit in the typical auto-correlation in time-series, the correlation tends to break down the farther one goes back in time. Note that I said, “may have predictive value.”

Redge
August 17, 2022 11:33 pm

The start date is not really arbitrary.

Of course, the start date is arbitrary.

Why not start with the MWP, the Roman Warm Period or the Minoan Warm Period?

Or would using the Holocene Climate Optimum as the starting point show the current warming period is nothing new?

Ron Long
August 17, 2022 8:23 am

Thanks for this posting and reply. As a geologist that specializes in detecting gold deposit trends, I am certain that not only should all data be studied, but that the investigator must update the trend interpretation every time new and relevant data appears. However, after studying all data not all needs to be included in updated thinking, some data needs to be set aside (but not destroyed).

Gary Pearse
August 17, 2022 8:28 am

Kip: as a geologist, it is ingrained to consider larger time frames. A favorite one in the climate sphere concerns a single dead rooted tree at Tuktuyaktuk on the NW Canada Arctic coast that was dated at 5000 yrs ago:

This a white spruce, currently about 100km north of the modern tree line but, another couple of hundred km north of today’s living white spruce (Yes! the very same species) of this size where the average temperature would be some 6 to 8°C warmer than Tuk. Reckoning Arctic amplification at double the Global avg T at the time, suggests it was 3 to 4°C warmer globally 5000yrs ago and no runaway anything or Crisis at all. It would have been a nice quiet forest with pleasant bird noises and occasional soughing wind through the treetops.

MarkW
August 17, 2022 7:49 am

The problem with that is that the end points could contain anomalies.

Clyde Spencer
August 17, 2022 11:09 am

And, the presented slope(s) should always be presented with uncertainties and statistical significance, which is a rarity in climatology.

Tim Gorman
August 17, 2022 4:00 pm

You just nailed the problem with *all* temperature data graphs. No uncertainties presented – meaning you don’t know if the data lies within the uncertainty interval or not, thus you simply don’t know what the true trend is.

All temperatures should be given as “stated value +/- uncertainty” and then the uncertainty should be propagated into the results using standard procedures.

Richard M
August 17, 2022 7:59 am

I disagree. Sometime you already know “all the data” will be influenced by a known factor. All you will see is the effect of that factor. Hence, it would be much more informative to try and eliminate the influence of that factor.

In this case we know the PDO went negative in 2006 and turned positive in 2014. Hence, we would expect a positive trend based only on the influence of the PDO. In this case the only really meaningful data is what happened prior to and after the PDO switch. We were shown the 2015-2022 data. It’s a start. The 2006-2014 data would also be informative.

Truthbknown
August 17, 2022 9:21 am

That is the “science” part of it! They manipulate the data to brainwash idiots!

ferdberple
August 17, 2022 4:52 pm

If changing the endpoints changes the trend, then what you have is not a trend.

What you have is a curve fit of degree 1 with no predictive power..

Scissor
August 17, 2022 6:07 am

From one month to the next, global T commonly jumps by a third of a degree. A handful more jumps up than down over a decade or even more so over a century is probably insignificant from a statistical point of view.

Scissor
August 17, 2022 10:17 am

Yes, that’s a key question.

I know at least one physicist having the opinion that a number of contributors to the global climate system behave as nonlinear chaotic subsystems, which are difficult to model.

Scissor
August 17, 2022 2:31 pm

There you go.

Jeff Alberts
August 17, 2022 3:27 pm

Haven’t they re-defined that already? To fit their agenda, like everything else?

bdgwx
August 17, 2022 8:02 pm

Jeff Alberts said: “Haven’t they re-defined that already? To fit their agenda, like everything else?”

No. They’ve always maintained that predictions of exact states (meaning exact properties at exact times at exact locations) is nearly impossible in the long range. In fact, the data suggests that useful skill of predictions of exact states will always be limited to about 15 days regardless of the advancements in modeling. After that predictions tend to focus on the movement of the attractors of the chaotic system and so only the average state (meaning average of the properties over large spatial and temporal domains) is possible.

Jim Gorman
August 18, 2022 12:30 pm

This is from a book Confessions of a climate scientist by Mototaka Nakamura.

That is, the selection of the parameter values is a poor engineering process to “make the model appear to work” rather than a scientific process. The models are “tuned” by tinkering around with values of various parameters until the best compromise is obtained. I used to do it myself. It is a necessary and unavoidable procedure and is not a problem so long as the user is aware of its ramifications and is honest about them. But it is a serious and fatal flaw if it is used for climate forecasting/prediction purposes.”

This from a researcher who worked with and did research using GCM’s.

Joe Born
August 17, 2022 6:12 am

There are endless ways to have fun–or maybe it’s make mischief–with trends. One that I always point out is the way in which climate-textbook author Raymond Pierrehumbert used sea-level trends to accuse Unsettled author Steven Koonin of cherry picking.

GuyFromBerlin
August 17, 2022 6:26 am

Looks like very improperly done low-passing to me! There are so much better algorithms to do this kind of thing – one might look into A/V processing techniques. If you’d mutilate an audio or video signal (which in its digital form is just the same thing as any other timeseries of values, it doesn’t matter if what you sample are sea levels, temperatures, movements of a microphone diaphragm, or brightnesses of a row of pixels) in the way I regularly see done to climate-related “signals”, your eyes and ears would tell you in no time that THIS DOESN’T WORK, because the resulting sound and image would be distorted beyond recognition. Lowpassing without ringing, rippling and phase/time-distortion isn’t easy and certainly not doable with sophomore mathematics like fitting trend lines or trailing averages. No wonder that people see everything and nothing in the resulting graphs (just like you might, with enough imagination, hear anything from Beethoven to the noise of Niagara Falls in audio “processed” in such crude ways….)

Joe Born
August 17, 2022 8:40 am

Dr. Pierrehumbert based his argument on trends, so in this case plotting trend values was the appropriate approach.

Yes, I often use Gaussian or binomial filters when I’m looking at temperature time series, but temperature series aren’t audio signals, and, esthetics aside, I haven’t been able to come up with a satisfactory argument for the proposition that in the case of temperature series such filters are necessarily superior to, say, rectangular filters.

Editor
August 17, 2022 10:12 am

Joe, the problem with using rectangular filters is exemplified by this graph from my post “Sunny Spots Along The Parana River“.

It shows the normalized sunspot anomaly, along with the 11-year rectangular “boxcar” filter of the same data. The correlation is horrible, R^2 is 0.01, and many peaks are converted into troughs and vice versa.

So yes, almost ANY filter would be preferable to a boxcar filter in this case.

w.

Joe Born
August 17, 2022 11:01 am

Yes, I understand that the filtered signal doesn’t look like the original signal. But preferable implies some criterion; what do you want the filtered signal to tell you? If the question were what the eleven-year average is, then the rectangular filter would be precisely what you want.

True, such a filter is usually undesirable in signal processing because it leaves what the guys I’ve dealt with seem to call “side lobes” in the resultant spectrum. I’m told that this is bad for, e.g. frequency-division multiplexing.

But I’m also told that the zeroes in such a filter’s Fourier transform (a sinc function) may enable you to suppress unwanted periodicity in the original signal.

Hey, you probably see something I’m missing; I don’t profess to be a filter expert. I made my living as a lawyer, not an engineer. But different horses for different courses is the impression I took from guys who seemed to know this stuff.

August 17, 2022 11:49 am

The only useful information conveyed by the analysis is that the sunspot cycle is approximately 11 years long, so you get an extreme moire effect through the filter. Think of filming a propellor at a frame rate that is almost an exact multiple of its rotation frequency.

Jim Gorman
August 17, 2022 10:53 am

The use of filters is primarily used to eliminate real “noise”. What is the noise you are hoping to eliminate and what is the signal you are hoping to isolate?

Is there something other than temperature you are hoping to see?

Jim Gorman
August 17, 2022 9:27 am

OMG, how appropriate. Someone who knows more than simple averaging. Looking for a “signal” in data that IS THE SIGNAL is confirmation bias of the worst kind.

Bellman
August 17, 2022 8:36 am

As I keep pointing out to thoise who think Monckton’s pauses and rapid cooling periods are relevant. Even Monckton points out that short term trends are bogus.

But just because some trend are cherry-picked to make a point, doesn’t mean that all trends are meaningless, and there are ways of determining one from another. Is it significant, does it represent a significant change, does the short term trend meet up with the end of the previous change or does it create an unrealistic discontinuity.

Doonman
August 17, 2022 9:06 am

The trend is not bogus, the value of the trend is. But as you say Monckton points that out meaning that you agree with him. But then you keep arguing with him about showing the trend, which can only mean you dislike Monckton and not the trend.

Jim Gorman
August 17, 2022 10:56 am

The trend Monckton is using is to show that CO2 does not control temperature. That is all. The longer the pause the less likely that growing CO2 is even a factor!

Bellman
August 17, 2022 4:24 pm

Could you point to a single example where Monckton says that?

bdgwx
August 17, 2022 7:18 pm

I don’t know that Monckton is saying that. But I find it ironic that several of us on here who have actually attempted to model the UAH temperature using CO2 as a parameter expect the pause to continue for several more months.

Clyde Spencer
August 17, 2022 11:36 am

The alarmist thesis is that CO2 is the dominant driver of temperature; therefore, one would expect that there would be a high correlation between the measured CO2 increase and the temperature. “Monckton’s Pauses” clearly demonstrate the ineffectiveness of monotonic annual increases of CO2 and that it is easily over-powered by other factors.

During the July 1991 total solar eclipse that I observed at Cabo San Lucas (Baja), during the 6+ minutes of totality, I measured a drop in air temperature of about 1 deg F per minute. Obviously, there are things that affect global temperature (such as clouds and aerosols) that have more influence than CO2.

bdgwx
August 17, 2022 12:09 pm

The Monckton Pause appears to be inline with expectations to me.

Derg
August 17, 2022 1:55 pm

We just need one more model and then the science will be completely settled.

Meanwhile China doesn’t give 2 runny sh1ts and uses fossil fuels like their lives depend on it.

Hashbang
August 18, 2022 1:34 am

Which it does and so do ours.

Jim Gorman
August 17, 2022 2:04 pm

So you think CO2 is THE CONTROL KNOB along with whoever wrote the model? Look at the model difference with wo/CO2 and w/CO2!

Looks like tuning to me. How does the projection from 5years ago from this compare to what it shows now? What did they change to show cooling?

bdgwx
August 17, 2022 2:27 pm

No. I don’t think CO2 is THE control knob. The data is not consistent with that hypothesis. However, the data is consistent with it being A control knob.

Derg
August 17, 2022 3:39 pm

A control knob 😉

That was funny

Tim Gorman
August 17, 2022 4:09 pm

How do you know it isn’t an “effect” from other control knobs?

bdgwx
August 17, 2022 6:43 pm

That model does not tell if you if CO2 is driven by other control knobs. What the model does is show that increasing CO2 is not inconsistent with the Monckton Pause.

Derg
August 18, 2022 6:05 am

It shows that the models are wrong.

Carlo, Monte
August 18, 2022 6:23 am

bgwxyz has a big audio soundboard of control knobs…

bdgwx
August 18, 2022 6:56 am

Can you post the objective criteria by which you claim the model I posted above is wrong?

Clyde Spencer
August 17, 2022 5:16 pm

Like playing an electronic synthesizer.

If CO2 isn’t THE control knob, why is there so much effort and money being spent on controlling it?

Clyde Spencer
August 17, 2022 5:05 pm

Note that CO2 is just one of 4 explicit parameters. The other parameters are composites of several different physical measurements, chief among them being temperature.

The divergence supposedly due to CO2 doesn’t show up until about 1994. Mauna Loa measurements have been taken since 1958, and supposedly have been impacting temperature since the late 18th century. It is weak support of your claim.

bdgwx
August 17, 2022 6:39 pm

My claim is that the Monckton Pause is not inconsistent with CO2 being a control knob. It is certainly inconsistent with CO2 being the control knob though.

Sorry, I don’t engage in policy discussions. I’m only interested in the science.

Derg
August 18, 2022 6:06 am

Lol the science 😉

Kinda like the gene therapy shot science?

Clyde Spencer
August 18, 2022 11:25 am

I didn’t bring up any issues of policy. It looks like an attempt at deflection on your part instead of responding to the facts of science I pointed out that you had wrong.

bdgwx
August 18, 2022 12:43 pm

CS said: I didn’t bring up any issues of policy.

You askedIf CO2 isn’t THE control knob, why is there so much effort and money being spent on controlling it?” That is a question that directly relates to public policy. I don’t participate in those kinds of discussions.

Bellman
August 17, 2022 4:29 pm

The alarmist thesis is that CO2 is the dominant driver of temperature; therefore, one would expect that there would be a high correlation between the measured CO2 increase and the temperature

If true, it’s the dominant driver of temperature on the scale of the next century or so. That doesn’t mean over a few years other factors, such as ENSO don’t have a bigger effect.

The correlation between CO2 and temperature has not changed other this “pause”. If anything it’s gotten stronger.

Obviously, there are things that affect global temperature (such as clouds and aerosols) that have more influence than CO2.

We’ll yes, turning off the sun will have a big effect than CO2. But what happened after the eclipse. Did temperatures remain 6°F lower or did they eventually return to equilibrium?

Clyde Spencer
August 17, 2022 5:21 pm

After the roosters quit crowing, the sun decided to grant their plea, and returned the air temperature to what it had been.

The point of the story is how quickly air temperatures respond to insolation. It doesn’t take 7 years to restore a perturbation.

TheLastDemocrat
August 17, 2022 4:46 pm

This statement from CS is very important:
“the ineffectiveness of monotonic annual increases of CO2 and that it is easily over-powered by other factors.”

We are trying to see if one thing co-varies with another. If one data set has a monotonic function, you cannot theoretically carry out a covariance analysis (“covariance” with a small “c”).

We are trying to examine whether “planet temp” covaries with “co2.” A more complete way to say this is: if co2 goes up, does planet temp go up, and if co2 goes down, does planet temp go down?”

We can ask that. But to answer it, we have to have both ups and down in “planet temp,” and also in “co2.” –This is an “assumption” that must be met.

For our examinations of “does planet temp go up or down as co2 goes up or down,” we NEVER have co2 going down!

So, these time-based analyses of the relation between co2 and planet temp are not valid.

Mauna Loa goes back to 1960. Has been monotonic the whole time.

If we trust ice core estimates of co2 back to the last Ice Age, then we have a chance at data to suit the analysis. And, (proxy-based) temps and co2 trends do not really co-vary at all. So, the temp-co2 relation hypothesis is dead before it starts. co2 influence upon planet temp is so modest, if it exists, it cannot be discerned out of the other much greater influences – not even with PCA as was done in MBH98.

https://gml.noaa.gov/ccgg/trends/

Tim Gorman
August 17, 2022 5:17 pm

+100

Clyde Spencer
August 17, 2022 5:42 pm

we NEVER have co2 going down!

Actually, we do every Summer and Fall. It did during 2020, with the April decline being -18% of anthro’ emissions compared to 2019. However, the 2020 seasonal variations in CO2 were indistinguishable from 2019 and 2021. All of those years include the “Monckton Pause.”

One can unequivocally say that a decline in CO2 does not result in the immediate response seen with either an eclipse, thick clouds passing overhead, or the sometime effect of dense contrails.

https://wattsupwiththat.com/2021/06/11/contribution-of-anthropogenic-co2-emissions-to-changes-in-atmospheric-concentrations/

https://wattsupwiththat.com/2022/03/22/anthropogenic-co2-and-the-expected-results-from-eliminating-it/

Derg
August 17, 2022 1:53 pm

No kidding, we had the 4th coldest April ever.

AGW is Not Science
August 17, 2022 11:46 am

I often think of the “pre industrial” start point for the ‘climate’ nonsense as the ultimate cherry pick, one which allows continual “trend” obfuscation.

Just think of a roller coaster rising vs. falling measured relative to its start point. As it descends the first hill, at any point one could argue that the “long term trend” is “still up,” even as the coaster is going down.

This will be the climate fascist playbook until the inevitable decline of “average temperature,” as meaningless as that is, can no longer be hidden by “adjustments.”

August 17, 2022 11:56 am

A trend is a trend, is a trend, but the question is, will it bend? Will it alter its course, through some unforeseen force and come to a premature end?

~Sir Alec Carincross, economist

August 17, 2022 6:24 am

Trends have only 2 ways to go – up or down. They might be totally flat, but the chances for this are infinitely small with any random walk. Predicting the climate should be warming because fo CO2, has naturally a 50% chance of materializing. It is not the most compelling evidence.

And then you have this largely ignored issue. We have something that explains the 5 decadal warming trend, and it is NOT CO2. Moreover, if we take a closer look on the CO2 hypothesis, it is easy to see it is not even working, as overlaps were not considered in climate sensitivity estimates. Including overlaps, ECS simply collapses and turns negligible. Something even modtran shows..

I can only recommend to pay more attention to the contrail issue..

https://greenhousedefect.com/contrails-a-forcing-to-be-reckoned-with

Sandwood
August 17, 2022 6:28 am

Applying linear trend lines to cyclical data only works if the start and end points are at the same point in the cycle. When the system has multiple or irregular cycles, as in this case, or unknown cycles, an applied linear trend line can never be correct.

Jim Gorman
August 17, 2022 6:55 am

This is my big gripe. The parts are pretty much cyclical. From orbital, sun, currents, precession, etc. They all combine into a complex of what is called climate.

Trying to do a linear regression on a cyclical phenomena leads to HUGE uncertainty levels.

Clyde Spencer
August 17, 2022 11:40 am

And, with multiple cyclical drivers with different periods and phases, one ends up with constructive and destructive interference, meaning that only by Fourier decomposition can anything be deduced about long-term trends.

Jim Gorman
August 17, 2022 5:01 pm

It is not real. From the other thread on averaging intensive variables, the global average temperature just doesn’t relate well when you look at enthalpy. I’ve seen too many projections from people I trust for places like Iceland, Greenland, Japan, U.S., South Africa where individual stations show no warming. If CO2 is well mixed then everywhere should be warming at least at a constant rate, even if the rates differ.

For every place like the image I took from another thread, there must be another place that has a lot of warming. Why do none of the CAGW folks here never post any local graphs that show really high warming? The would need one, isolated from UHI, with what, at least 3 degrees of warming? Where does that exist using raw station data?

Clyde Spencer
August 17, 2022 5:47 pm

You typed an “r” for an “f” again. 🙂

Ten-percent is a relatively small change, but can be measured and be meaningful with high precision data. The problem is that it is not uncommon to observe an uncertainty of +/-50% in climatology measurements — when they even bother to cite the uncertainty.

Lit
August 17, 2022 6:28 am

Just do average temperature in Kelvin plotted for 100 years. You won´t even see a trend.

Jim Gorman
August 17, 2022 6:58 am

Go back and read what his purpose is. When you find a deterministic functional relationship for CO2 vs temp, post it.

Macha
August 17, 2022 7:34 am

Like this SST one?

Carlo, Monte
August 17, 2022 7:51 am

Substitute U.S. Postal rates for sea surface temperature…

TheLastDemocrat
August 17, 2022 4:53 pm

Macha – the vertical axis is not CO2; it is “time.”
Prove me wrong.

Plotting this way does not get rid of the confounder of time.

Plot Mauna Loa x time. Same graph.

As Del Monte Carlo says: you can also substitute postal rate.

There is no up-and-down in time; time just goes up and up. Also, no up-and-down in postal rate; it just goes up, and pretty monotonically.

TheFinalNail
August 17, 2022 6:38 am

a. Don’t use short time periods when determining trends in a time series. Trends are always sensitive to start and end dates.

Lord Monckton, take note!

TheFinalNail
August 17, 2022 7:21 am

Are you referring to his “The Pause is now X year long”?

Actually, he has it down to the month, at the moment. A trend is still a trend, whether you count backwards or forwards from or to a particular point. So your advice still applies to Lord M’s monthly UAH ‘pause’ updates: too short a period and highly dependant on start and end dates.

Geoff Sherrington
August 17, 2022 7:44 am

TFN,
I use this method because it helps detect a change in trend.
Like, Australia UAH LT shows no linear least squares fit warming for the last 10 years.
If we are in a transition from warming to cooling, we would expect this.
It indicates when the transition started, so we can examine what causative variables might have changed then.
There is no suggestion that coming temperatures will rise, fall or stay flat – the data are incapable of predicting the future, they merely observe the past. Geoff S

Clyde Spencer
August 17, 2022 11:48 am

Time-series are often auto-correlated, so at least short-term predictions are more reliable than random guesses.

Joe Born
August 17, 2022 8:59 am

Quite right. I have had no reluctance to criticize Lord Monckton’s ravings on other subjects, but his pauses are what they are, and he (largely) leaves us to make of them what we will.

To me they militate against the proposition that natural variation is minor.

Derg
August 17, 2022 1:58 pm

He uses their math to show the follly of their theory.

Bellman
August 17, 2022 9:08 am

No, really, a PAUSE is a temporary phenomena — thus it must have a start and end (even it is ‘to-date’) and is expressly only the part of some greater whole (in time).

Except he still keeps talking about the old pause, and that ended sometime after the new one began.

His claim is only that rise in temperature (UAH) has temporarily ceased rising since such-and-such a date.

UAH warming rate from 1979 to the start of pause was 0.11°C / decade.

UAH warming rate from 1979 to current date is 0.13°C / decade.

I’m not sure what the evidence is that warming has temporarily ceased.

mkelly
August 17, 2022 10:39 am

WE were told that if a pause occurred and lasted over 15 years then all the models were wrong. Because models never predicted a pause that long.

When the pause lasted longer than required we got excuses. The models were still claimed to be valid even after alarmists said they should not be.

Clyde Spencer
August 17, 2022 11:54 am

Except he still keeps talking about the old pause, …

If your car engine has suddenly stopped on more than one occasion, would you conclude that there was some problem that needed to be discovered and fixed to increase the reliability?

The hiatus is an indicator that because there is not a close coupling between CO2 and temperature, the models are defective and are unreliable for periods of several years running.

bdgwx
August 17, 2022 2:22 pm

Several months ago I tested the hypothesis that models do not predict long pause like the current one.

Using the CMIP5 model data from the KNMI Explorer and the Monckton method the data suggests that about 21% of the months should be included in a pause lasting at least 90 months. The UAH observations showed 26%. That’s not a bad prediction.

Using my trivial 3 component model above and the Monckton method the data suggests that about 26% of the months to be included in a pause lasting at least 90 months. Again, the observation is 26%. The model is in excellent agreement with the observations.

Tim Gorman
August 17, 2022 4:18 pm

The problem is that the models turn into y = mx + b equations after a few years. Run’em for 100 years, 200 years, or 10000 years – the models will predict that the earth *will* turn into a cinder, no more ice ages. No pauses, no bending of the projection, no nothing. *That* is not a good model

TheLastDemocrat
August 17, 2022 4:59 pm

This is true, and at least partly because relations between “forcings” have to include geometric functions – tipping points. Water heats and heats and heats – and then turns into steam.

If you do not model at least one “tipping point” correctly, one influence is going to be exaggerated, and it is only a matter of time until it runs crazy.

So, you add bounds to at least one of the relations. Well, then you either run off the chart another way, or are limited to an upper and lower bound forever, always to be hit and never exceeded.

Good luck.

bdgwx
August 17, 2022 6:47 pm

Which one of the CMIP5 members shows Earth turning into a cinder in 100, 200, or 10000 years? Can you post a link to the data you are looking at so that I can download and verify it?

Tim Gorman
August 18, 2022 6:18 am

Do you see any bending in the 8.5 or 6.0 scenario’s? Even the 4.5 scenario shows continual growth although it does show the slope changing in the out years. The only one that shows growth stopping is the 2.5 scenario, the one no one believes will ever happen (see India and China for examples)

Carlo, Monte
August 18, 2022 6:27 am

He lives in De Nile.

bdgwx
August 18, 2022 7:29 am

None of those show the Earth turning into a cinder.

bdgwx
August 19, 2022 10:40 am

I don’t really have much choice at this point to dismiss the claim that CMIP5 shows the Earth turning into a cinder.

Tim Gorman
August 19, 2022 11:15 am

When they continue going up with no bound then the only conclusion is that the earth *WILL* turn into a cinder. That’s what the “consensus” climate scientists are predicting. We will soon reach the tipping point where we can’t stop the warming and it will kill us all! Just ask John Kerry!

bdgwx
August 19, 2022 12:40 pm

TG said: “When they continue going up with no bound then the only conclusion is that the earth *WILL* turn into a cinder.”

Where do you see that any of the CMIP5 models show the global average temperature continuing to go up indefinitely to the point that Earth turns into a cinder? All I’m asking for is a link or some kind of reference here. I’ll you one last chance here. After that I don’t have any other option but to dismiss the claim.

BTW…how would even be able to assess whether the Earth turns into a cinder using the global average temperature anyway? According to Essex et al. it does not actually exist.

Tim Gorman
August 20, 2022 1:23 pm

I gave you a graph. In the out years both RCP 8.5 and 4.5 are nothing more than y = mx +b linear trends. The termination of the runs are generated by computing limits more than by the trend ending.

After that I don’t have any other option but to dismiss the claim.”

That’s one of your main tactics. Argument by Dismissal, an argumentative fallacy. You simply can’t show where the 8.5 and 4.5 runs bend down in any way, shape, or form. So you just dismiss any argument that says the trend lines from the models will continue indefinitely until the oceans boil!

“BTW…how would even be able to assess whether the Earth turns into a cinder using the global average temperature anyway? According to Essex et al. it does not actually exist.”

It doesn’t exist. That doesn’t keep the climate models from saying it does and using it to forecast the end of the world.

Clyde Spencer
August 17, 2022 5:59 pm

Using my trivial 3 component model above …

I count 4 variables plus a constant.

Not knowing the details of how you did your analysis, I can’t provide an informed comment.

bdgwx
August 17, 2022 6:34 pm

Yes. Typo. 4.

I performed the analysis using the Monckton method.

Tim Gorman
August 17, 2022 4:15 pm

+100!

Jeff Alberts
August 17, 2022 5:47 pm

At those rates, in ten decades, you still wouldn’t notice a change in temperature.

Richard M
August 17, 2022 8:11 am

The pauses continue to be a big problem for the climate cult. It’s now pretty obvious the breakpoint was due to the PDO phase change in 2014. When you look before and after that obvious warming influence you seeing nothing. The only possible conclusion is we’ve gone 25 years with no evidence for man made warming.

https://woodfortrees.org/plot/uah6/from:1997.5/to/plot/uah6/from:1997.5/to:2014.5/trend/plot/uah6/from:2015.5/to/trend/plot/uah6/from:2014.5/to:2015.5/trend

TheFinalNail
August 17, 2022 8:47 am

You mean if we leave out the periods of natural warming but keep in the periods of natural cooling we can get a cooler temperature series? Never thought of that.

Jim Gorman
August 17, 2022 8:43 am

Why don’t you post the reason for examining this short trend so everyone can see you are in error!

CO2 is not a control knob for temperature if temps don’t increase along with increasing CO2.

Bellman
August 17, 2022 9:10 am

Why do you always want to ignore the uncertainty in these trend lines?

Clyde Spencer
August 17, 2022 11:56 am

Funny that you would accuse Jim of that! The uncertainty is taken into account when determining the statistical significance.

Carlo, Monte
August 17, 2022 3:04 pm

No kidding, this is a troll comment if there ever was one.

Bellman
August 17, 2022 3:20 pm

Yes, ironic. Jim, Tim and Carlo have spent years trying to claim that UAH data is completely unreliable because uncertainty increases the more observations you make, that it’s impossible to know what any trend is , and now wonlt even accept that it’s possible to average temperature.

Yet will then insist that a carefully selected flat trend line covering a few years of highly variable data, is somehow so certain you can use it to prove anything you want. Last discussion I was being told that there is zero uncertainty in the trend, whilst at the same time being told the true trend over the 7 year period could be at least ±3°C / decade.

Carlo, Monte
August 17, 2022 3:42 pm

Last discussion I was being told that there is zero uncertainty in the trend

You’re insane.

Tim Gorman
August 17, 2022 4:27 pm

Yep!

Tim Gorman
August 17, 2022 4:26 pm

In other words you get pissed when someone else uses the data you look at as religious dogma in order to disprove the CAGW theory!

ROFL!!

Bellman
August 17, 2022 5:31 pm

I don’t know how many times I have to tell you this before it penetrates your understanding, but I do not regard UAH data as perfect. I don’t regard any data as perfect but UAH least of all. The only reason I go along with UAH data here is because up to recently it was the only data set regarded as acceptable.

Just because I don’t accept the ±1.5°C uncertainty you want to pluck out of the air, does not mean I regard Dr Spencer’s work as religious dogma.

Tim Gorman
August 18, 2022 5:56 am

Just because I don’t accept the ±1.5°C uncertainty you want to pluck out of the air, does not mean I regard Dr Spencer’s work as religious dogma.”

The only data I accept as minimally usable is degree-day data for cooling and heating. That data is actually in use by professionals to size HVAC systems and by agricultural scientists to advise farmers. The users of those HVAC systems and of the ag advice would quickly abandon the professionals and the ag scientists is they are continuously wrong. Climate scientists have no real users except governments who don’t care if the climate scientists are wrong as long as their predictions lead to increased power in the hands of the politicians.

Even HDD/CDD has problems. It doesn’t tell you the enthalpy. It’s why you could have the same HDD/CDD values in Phoenix and Miami on the same day. Humidity and pressure aren’t considered. Until the climate scientists are forced to use actual physical attributes that can be compared I will remain doubtful of their conclusions. That doesn’t mean I won’t use their own data against them.

bdgwx
August 18, 2022 6:55 am

TG said: “The only data I accept as minimally usable is degree-day data for cooling and heating.”

Back in Kip’s previous article you said the average temperature is meaningless and useless and even advocated for the position of them being non-existent. Yet you find HDD and CDD usable despite them being dependent on a meaningless, useless, and non-existent metric?

Bellman
August 18, 2022 11:53 am

The only data I accept as minimally usable is degree-day data for cooling and heating.

But they are based on the same temperature readings as any of the land based global sets. Do you use CDDs and HDDs as a global average or just for specific locations?

Tim Gorman
August 19, 2022 5:33 am

“But they are based on the same temperature readings as any of the land based global sets. Do you use CDDs and HDDs as a global average or just for specific locations?”

HDD and CDD are degree-days, not degrees. Still, I do *NOT* add them up to use them as a global average. Have you *EVER* seen me do that? Be honest!

What I do is to use them to evaluate if HDD/CDD is going up or down at a location. I can then assign them a cooling/warming metric for both minimum and maximum temps and can compare those metrics over a region. I try to use stations that are not located at an airport or in the middle of an urban heat complex.

If I find a region (e.g. central Peru) that shows mostly cooling/heating then I can ask “where is the offsetting region that would cause global warming?”. If I find a 0.5C cooling slope then there needs to be a 1.0C warming slope somewhere to offset it if we are to believe in “global” warming.

There is absolutely no reason why climate scientists could not do exactly the same. More complicated? Sure! So what? More believable result? Sure!

Doing minimums (HDD) and maximums (CDD) gives FAR more knowledge than the hokey, unphysical, global temperature mid-range average value. I suspect that is one reason why climate science refuses to do abandon their current method. It would make it easier to hold their feet to the fire over predictions of the future!

Carlo, Monte
August 19, 2022 6:47 am

Can you imagine trying to make a model to spit out these numbers instead of a single global average?

Tim Gorman
August 19, 2022 2:20 pm

Can you imagine trying to make a model to spit out these numbers instead of a single global average?”

Actually I can. But it wouldn’t fit the agenda!

bdgwx
August 19, 2022 9:11 am

TG said: “What I do is to use them to evaluate if HDD/CDD is going up or down at a location.”

According to you HDD/CDD are dependent on a useless and meaningless quantity. So how exactly are finding meaning and use out of them?

Carlo, Monte
August 19, 2022 10:27 am

According to you HDD/CDD are dependent on a useless and meaningless quantity.

A lie disguising a strawman.

bdgwx
August 19, 2022 11:50 am

CM said: “A lie disguising a strawman.”

If I’m mistaken then so be it. I assure you it is not intentional. My statement is based on the comments in Kip’s previous article in which TG advocated for the position that the average of temperature observations is meaningless and useless. Is that not TG’s position?

TG, what say you? Is your position that the average of temperature observations is meaningless and useless or not?

Tim Gorman
August 19, 2022 2:24 pm

TG, what say you? Is your position that the average of temperature observations is meaningless and useless or not?”

You don’t even know what the dimensions of HDD and CDD are, do you?

They are *NOT* averages. They are integration of the temperature curve – i.e. they are the area between the temperature curve and a base set line. They are an AREA, not a “degree”.

bdgwx
August 19, 2022 7:39 pm

TG said: “They are *NOT* averages.”

I never said they were averages. I said they depend on temperature averages. Specifically the formula is HDD = 65 F – (Tmin + Tmax) / 2 or CDD = (Tmin + Tmax) / 2 – 65 F. [1]

Carlo, Monte
August 19, 2022 9:12 pm

bgwxyz throws another wad at the wall, hoping it will stick.

Carlo, Monte
August 19, 2022 2:35 pm

You think if you can find just a single example of averaging temperatures then the entire Essex paper must be wrong, so you go around throwing up nonsense like this hoping it will stick.

Tim Gorman
August 19, 2022 2:22 pm

Yep.

Tim Gorman
August 19, 2022 2:22 pm

According to you HDD/CDD are dependent on a useless and meaningless quantity. So how exactly are finding meaning and use out of them?”

You *still* haven’t learned what an HDD/CDD is, have you? You *really* need to go learn about them. If they were meaningless then HVAC professionals would be using them to size installations.

bdgwx
August 19, 2022 7:36 pm

TG said: “You *still* haven’t learned what an HDD/CDD is, have you?”

I learned about degrees days long ago. According to the National Weather Service degree days are “the difference between the daily temperature mean, (high temperature plus low temperature divided by two) and 65°F.”
﻿

Tim Gorman
August 21, 2022 4:50 am

According to the National Weather Service degree days are “the difference between the daily temperature mean, (high temperature plus low temperature divided by two) and 65°F.””

That is the *old* way of doing it — and it is wrong, wrong, wrong. I’m not surprised to see the government still using an old, wrong definition.

(Tmax + Tmin)/2 is *NOT* the daily temperature mean. It never has been. It’s just a convenient relationship to use with no regard to its physical accuracy.

The mean of the daytime temp is .63Tmax. The mean of the nighttime temp is ln(2)/k where k is the decay factor. So what is the actual mean of the daily temperature profile? It is *NOT* (Tmax – Tmin)/2!

The process used today is to integrate the temperature curve since most useful measurement stations record in minutes if not more often. This finds the actual area under the temperature curve in degree-days.

That is where the .63 factor comes from for the day and the ln(2)/k comes from for the night.

If you don’t have a quasi-smooth curve for either the day or night you can still do a numeric integration.

In essence you are using the argumentative fallacy of Appeal to Tradition. Stop it.

bdgwx
August 21, 2022 12:57 pm

Can you post a link to the literature 1) showing the new method and 2) showing that NWS retrospectively analyzed the data and replaced the old values with the new values in the official reporting? I’m very interested in review the materials you can provide.

Tim Gorman
August 21, 2022 6:23 pm

Some other sources (particularly generalist weather-data providers for whom degree days are not a focus) are still using outdated approximation methods that either simplistically pretend that within-day temperature variations don’t matter, or they try to estimate them from daily average/maximum/minimum temperatures. We discuss these approximation methods in more detail further below, but, in a nutshell: the Integration Method is best because it uses detailed within-day temperature readings to account for within-day temperature variations accurately.”

Like I told you, the government still uses the old method of finding the mid-range temps (Tmax+Tmin)/2 and comparing that with the set point temperature. I don’t know of any reputable engineer that still does that.

go here (this site only offers the integration method): https://energy-data.io/energy-tools/degree-day-calculator-free/

I shouldn’t have to do this research for you. Having to do so only indicates to me that all you are interested in on this subject is being a troll.

bdgwx
August 22, 2022 5:17 am

TG said: “go here: https://www.degreedays.net/calculation

Yep. That’s what I thought you were going to reference.

The integration technique still uses average temperatures.

Calculate the average number of degrees by which the temperature was below the base temperature over the calculated time period (1). In this simple example this is always the base temperature minus the average of the two recorded temperatures.

Nevermind that each temperature observation is itself an average over a 5 minute period. See the ASOS User Guide for details. In other words, all methods use an average temperature in some way shape or form whether you understood that or not.

Carlo, Monte
August 22, 2022 6:25 am

So why did you not just come right out and say what you found on the internet, and instead tried to lay what you think is a trap, mr. disingenuous?

WOOHOO! bgwxyz takes another vicollly lap!

As usual, you are about as genuine as a three-dollar bill.

And your “nevermind”? This is averaging data from ONE instrument at ONE location. Does your hallowed ASOS guide tell you how to propagate the measurement uncertainty in this procedure?

Try again to Keep the Rise Alive.

bdgwx
August 22, 2022 8:00 am

The point is this. I don’t think you, Jim, Tim, and Kip are as convicted regarding the proclamation that averaging temperatures is meaningless and useless as you let on. Afterall, we’re being told that HDD/CDD are meaningful and useful despite them being dependent on averaging temperatures. And it’s not just HDD/CDD. We’re being told that the particular soil moisture product used in the comments here is meaningful and useful enough to determine droughts despite it being dependent on averaging temperatures. It is a contradictory position. I’ll even argue that it is a hypocritical position since we are all being told that we shouldn’t do it yet the contrarians here not only do it themselves but defend their use vigorously.

Carlo, Monte
August 22, 2022 8:23 am

You label anything you please “averaging”! Go lecture someone else.

bdgwx
August 22, 2022 8:44 am

CM said: “You label anything you please “averaging”! Go lecture someone else.”

Not at all. I only label the operation Σ[x_i, 1, n] / n as “averaging” and nothing more.

On the contrary, it is Essex et al. that were discussing how there are an infinite number of ways to average a set of values only one of which fits the canonical formula above. So you tell me…who’s labeling anything they please as “averaging”?

Carlo, Monte
August 22, 2022 9:38 am

Not at all. I only label the operation Σ[x_i, 1, n] / n as “averaging” and nothing more.

Liar, go read the GUM H3 again. YOU!

bdgwx
August 22, 2022 10:11 am

bdgwx said: “I only label the operation Σ[x_i, 1, n] / n as “averaging” and nothing more.”

CM said: “Liar, go read the GUM H3 again. YOU!”

I did as you requested. It still says t_bar =  Σ[t_k, 1, n] / n which is the same as the last time I read it and the time before that.

Carlo, Monte
August 22, 2022 10:28 am

Went to see the captain, strangest I could find
Laid my proposition down, laid it on the line
I won’t slave for beggar’s pay, likewise gold and jewels
But I would slave to learn the way to sink your ship of fools

Ship of fools sail away from me
It was later than I thought when I first believed you
But now I cannot share your laughter, ship of fools

The bottles stand as empty now, as they were filled before
Time there was and plenty, but from that cup no more
Though I could not caution all, I still might warn a few
Don’t lend your hand to raise no flag atop no ship of fools

Ship of fools sail away from me
It was later than I thought when I first believed you
But now I cannot share your laughter, ship of fools

Jim Gorman
August 22, 2022 10:50 am

Here is the deal. Many of us have been calling GAT meaningless for a long, long time. Do you think we made this decision out of clear blue sky? Most of us have scientific educations and have dealt with applying these in our careers to solve problems. We don’t just jump when someone pontificates without having some mathematics to back up their assertions.

My first recognition was when no one was ever quoting a standard deviation to go along with the distributions they were using to calculate a mean. Why? Still don’t have an answer, not even from you! Why? I would never have passed statistics if I had done that!

My second recognition was that only temperatures were being averaged. Temperatures NEVER tell you about the amount of heat in a substance, i.e., enthalpy. The amount of HEAT tells you the energy held by a substance. Mechanical and electrical engineers spend many hours in class learning about this. How do you think a steam boiler in a power plant or a heating plant is evaluated to determine how much energy can be extracted when turning a turbine or driving a process? Trial and error? Guess and by golly? Dude, this is all calculated before physical design is started. These are not a joke. Very, very high temperatures and pressures are involved. Personal and equipment safety is paramount.

My third recognition was that unreasonable uncertainties we’re being quoted based upon measurements that were AT BEST taken to an uncertainty of ±0.5 degrees. The predominate figure quoted was actually the SEM divided by √N. This computation is not defined in statistics. What is divided by the √N is the POPULATION standard deviation and not the standard deviation of the sample mean.

My fourth was sampling theory was not being applied correctly. Review the requirements of the different sampling theories and see if they are being meant.

Wise up and take some calculus based physics and thermodynamic classes and follow up with metrology classes.

Tim Gorman
August 22, 2022 1:06 pm

Afterall, we’re being told that HDD/CDD are meaningful and useful despite them being dependent on averaging temperatures.”

That is the OLD method, called the Mean Temperature Method, not the new method called the Integration method. If you had bothered to read the entire link I gave you rather than trying to cherry pick the first thing you came across you would realize that!

The Integration Method DOES NOT AVERAGE ANYTHING. I don’t know why you and bellman are so intent on defining integration as averaging. IT IS NOT!

“droughts despite it being dependent on averaging temperatures.”

Droughts are dependent on temperature? Droughts are typically defined by the amount of water in the soil (an extensive property) at specified depths plus the amount of surface water in lakes, ponds, streams, rivers, etc, again an extensive property, as well as precipitation, i..e the volume of rain, again an extensive property.

Do you and bellman live in the land beyond the looking glass?

yet the contrarians here not only do it themselves but defend their use vigorously.”

You are looking through a fun house mirror! You can’t even define reality (e.g. droughts) correctly!

Tim Gorman
August 22, 2022 12:59 pm

You nailed it!

Carlo, Monte
August 22, 2022 1:33 pm

I cannot for the life of me understand how they can willy-nilly ignore non-trivial details and context. This is the domain of religion and pseudoscience, not science and engineering.

Jim Gorman
August 22, 2022 8:48 am

You do realize that “at a distance” is vastly different than “an average over 5 minutes at the same place and with the same device”, right.

Go find an actual physics or thermodynamic reference for averaging intensive measurements of different objects at a distance to obtain a real physical measurement.

The GUM does not deal with this separation of physical quantities and qualities. It was never intended to. It was written for people trying to convey uncertainty in MEASUREMENTS, not for what appropriate measurements are and how they should be combined.

I know you are trying to destroy the belief that intensive values can not generally be averaged to obtain a real physical quantity. To do so you need to deal with physics, chemistry, and thermodynamic subjects to find references that deal with these issues. Uncertainty in MEASUREMENTS is not the appropriate choice of subject matter.

Carlo, Monte
August 22, 2022 9:39 am

bdgwx
August 22, 2022 10:59 am

JG said: “Go find an actual physics or thermodynamic reference for averaging intensive measurements of different objects at a distance to obtain a real physical measurement.”

I did as you suggested. I pulled out my Mesoscale Meterology book by Markowski and Richardson and Dynamic Meteorology by Holton and Hakim. Both refer to average temperature and averages of various other intensive properties. It’s been awhile since I’ve opened these up. I hadn’t realized just how prolifically average temperatures are used in them until now. BTW…these are great references if you want to learn more about the kinematic and thermodynamic nature of the atmosphere.

Tim Gorman
August 22, 2022 1:24 pm

My guess is that those books speak to the averaging the temperature in a single object that is in equilibrium. E.g. in a wall between the inside and outside. They are finding the average value of the gradient between two points.

This was part of an entire piece of Essex. Averaging two different, independent objects to find a value for a third independent object. I.e. the average of the gradient in one of your house walls, the gradient in one of your neighbor’s house walls, and the surface temperature of the asphalt on your nearest street!

None of those temperatures can act at a distance to determine either of the other two. So the average of the three is meaningless.

Yet you, for some reason, want to keep claiming that such an average *is* meaningful while never actually trying to explain what it is useful for! You can’t explain it because the average you find doesn’t exist!

Carlo, Monte
August 22, 2022 1:38 pm

Or a triple-point bath inside a laboratory controlled to less than ±0.1°C.

Without these meaningless global air temperature averages, they are totally and completely bankrupt.

bdgwx
August 22, 2022 2:03 pm

TG said: “My guess is that those books speak to the averaging the temperature in a single object that is in equilibrium.”

They are in reference to volumes of the atmosphere. And I’m sure you already know that no volume of the atmosphere is ever in equilibrium which is why we have weather. And it’s not just temperature these books are referring to. Average vorticity, average density, average pressure, average divergence, and various other intensive properties are used throughout.

Tim Gorman
August 22, 2022 3:05 pm

I’ll give you just one instance. Vorticity is a calculated value based on the mean angular displacement and center of mass. In other words it is *exactly* what you continue to do – conflate a calculated intensive value derived from extensive properties with a measured intensive property!

In none of the examples you give do you measure the intensive value and then average it. You measure extensive values and then calculate an intensive property. Density requires averaging mass and volume. two extensive values that can be measured! You don’t measure density and then average the values! What kind of probe would you use to measure density anyway!

Jim Gorman
August 23, 2022 9:39 am

You are just stomping on his belief that a GAT has some meaning. Temperature is not the appropriate measure to be using for determining the energy contained in the atmosphere. It only measures translational energy and totally ignores latent energy.

bdgwx
August 23, 2022 11:49 am

JG said: “Temperature is not the appropriate measure to be using for determining the energy contained in the atmosphere.”

Deflection and diversion. The claim is that averages of intensive properties regardless of context is meaningless and useless up to and including the claim that it doesn’t even exist and whether trends based on those values has meaning and usefulness as well. Nobody is challenging the idea that temperature only provides limited insights into the energy content of a body or even discussing the relation between temperature and heat/energy at all.

Jim Gorman
August 23, 2022 7:52 am

Do you think meteorology texts have good thought out math justifications for averaging temps at a distance? Do your books talk about averaging Sacramento and Rochester temps for a purpose.

I did reference physics and chemistry and thermodynamics on purpose. These subjects have detailed math justification for what is stated.

You are basically trying to justify averaging temps for something like an average temp at a location or small region. It is OK to average temps if all you are trying to find is average temperature. However, it is NOT OK to use that average temp as a proxy for the amount of heat (enthalpy) in two different locations or objects! If you are dealing with the sun’s ENERGY, you must use enthalpy to track the total energy in the system.

Have you had any calculus based science like physics, chemistry, or thermodynamics?

bdgwx
August 23, 2022 2:02 pm

JG said: “Do you think meteorology texts have good thought out math justifications for averaging temps at a distance?”

Yes. They have good thought out math justification for averaging other intensive properties as well.

Jim Gorman
August 23, 2022 4:31 pm

Show us the math. You can surely scan the pages that have the mathematical derivations of how temperature averages can determine the enthalpy in the atmosphere.

Tim Gorman
August 22, 2022 12:24 pm

The integration technique still uses average temperatures.”

You are as bad as bellman! Integration is not AVERAGING!

In this simple example this is always the base temperature minus the average of the two recorded temperatures.”

This is *NOT* the integration method. It is the older method known as the Mean Temperature Method, not the Integration Method!

If you would read on down the page it shows using the integration method.

As usual with you and bellman, you are cherry picking something you think will prove a point you have made but you fail to understand the entire context of what you are cherry picking from!

Nevermind that each temperature observation is itself an average over a 5 minute period.”

Not from my weather station. Nor does it need to be from any newer, digital weather station. You are still trying to use the Argument to Tradition fallacy.

“Once each minute the ACU calculates the 5-minute average ambient temperature and dew point temperature from the 1-minute average observations (provided at least 4 valid 1-minute averages are available). These 5-minute averages are rounded to the nearest degree Fahrenheit, converted to the nearest 0.1 degree Celsius, and reported once each minute as the 5-minute average ambient and dew point temperatures” (bolding mine, tg)

Please note that the readings are rounded to the nearest Fahrenheit degree and then converted to the nearest 0.1C. That’s truly a violation of stating values! 1F is about 0.5C not 0.1C. This algorithm severely overstates the precision of the data!

In other words, all methods use an average temperature in some way shape or form whether you understood that or not.”

I would also note what the uncertainty of the measurements are. For the range of -58F to +122F the uncertainty is +-/ 1.8F (+/- 1.0C)

With that kind of an uncertainty any error from averaging will be totally masked by the measurement uncertainty itself.

The one-minute average is obtained from 10 sec measurements (6 per minute). Each measurement is from approximately the same measurand. This simply isn’t like trying to find an average between two different locations. While not perfect, this is about 30 measurements per 5 minute average. This is as close to 30 measurements of the same measurand as one cat get.

Stop trying to cherry pick things without getting the full context. You only lower further your already low credibility!

bdgwx
August 22, 2022 1:58 pm

TG said: “You are as bad as bellman! Integration is not AVERAGING!”

I didn’t say it was. I said their integration technique uses temperature averages. BTW…don’t conflate their integration technique with proper calculus integrals.

TG said: “This is *NOT* the integration method.”

That is what they call the “Integration Method”. It is documented under the heading How do you calculate degree days using the Integration Method? It definitely involves averaging temperatures. Note that it is different from what they call the Mean Temperature Method which also involves averaging temperatures.

TG said: “While not perfect, this is about 30 measurements per 5 minute average. This is as close to 30 measurements of the same measurand as one cat get.”

It’s still an average.

Tim Gorman
August 22, 2022 3:19 pm

BTW…don’t conflate their integration technique with proper calculus integrals.”

Your knowledge of calculus is just as bad as bellman’s. You’ve never heard of numerical integration I guess. I’m not surprised!

“That is what they call the “Integration Method”. It is documented under the heading How do you calculate degree days using the Integration Method?”

You STILL haven’t bothered to read the link I gave you! The link has another link to a page that explains how they calculate their degree-day value. It is *NOT* an average!

———————————————————–
Although the Integration Method is the most accurate degree-day-calculation method, and the one that we use, many other sources (especially non-specialist sources) calculate degree days using an approximation method based on daily summary data (some or all of daily average, maximum, and minimum temperatures).

There are three popular methods for approximating degree days from daily temperature data:
The first two are both known as the “Mean Temperature Method”. They approximate the degree days for each day using the average temperature for the day. For HDD they subtract the average temperature from the base temperature (taking zero if the average temperature is greater than the base temperature on that day). For CDD they subtract the base temperature from the average temperature (taking zero if the base temperature is greater than the average temperature).
This sounds like one method, but it’s actually two because there are two commonly-used ways to calculate the average temperature for each day, both of which give slightly different results:

1. The average temperature is taken to be half way between the maximum and the minimum temperatures on each day.
2. The average temperature is calculated from detailed readings taken throughout each day (this method gives a more accurate average temperature).

The third is the Met Office Method – a set of equations that aim to approximate the Integration Method using daily max/min temperatures only. They work on the assumption that temperatures follow a partial sine-curve pattern between their daily maximum and minimum values.
Another approximation method deserves mentioning: The Enhanced Met Office Method. This is based on the original Met Office Method, but, whilst the original Met Office Method approximates the daily average temperature by taking the midpoint between the daily maximum and minimum temperatures, the Enhanced Met Office Method uses the real daily average temperature (calculated from temperature readings taken throughout the day). The daily maximum and minimum temperatures also play a role in approximating within-day temperature variations, as they do for the Met Office Method.
————————————————————

It’s still an average.”

OF THE SAME MEASURAND, or at least as close as you can get!

Carlo, Monte
August 22, 2022 3:33 pm

Your knowledge of calculus is just as bad as bellman’s. You’ve never heard of numerical integration I guess. I’m not surprised!

They just pile the lies higher and higher.

Jim Gorman
August 23, 2022 2:52 pm

You’ll notice that the question about what calculus based physics, chemistry, and thermodynamic classes they have goes unanswered.

Carlo, Monte
August 23, 2022 4:34 pm

Oh yes, this is quite telling. Might as well be a physical geography background, which back in the day counted toward arts and humanities credits.

Just like how he avoids the issue of how a laboratory triple-point bath can be identical to averaging Timbuktu and Kalamazoo air temperatures.

bdgwx
August 22, 2022 5:16 pm

TG said: “You STILL haven’t bothered to read the link I gave you!”

Yes I read it. That’s how I know their method uses an average temperature. They state it explicitly and even give examples. They not only use an average once or even twice but three separate times! First, they rely on the observations from the automated stations which are themselves averages. Second, they take those detailed observations and group them into “consecutive pairs” and take the average of all the pairs. Third, they multiple difference of that average and the reference by the time representing the pairs which as Bellman astutely recognized is effectively averaging; just a slightly different order than the canonical formula.

What follows here is the alternative methods to their “Integration Method”. You did not post their method.

Tim Gorman
August 24, 2022 3:42 am

The link to their method appears on the link I gave you. This is just proof that you did not *READ* the link. You just cherry picked something with a glance and, as usual, it was wrong.

Tim Gorman
August 24, 2022 6:17 am

First, they rely on the observations from the automated stations which are themselves averages.”

Multiple observations of the SAME THING, or at least as close as you can get! I’ve given you the answer on this after you referred to NWS standards. Of course you blew that off!

“Second, they take those detailed observations and group them into “consecutive pairs” and take the average of all the pairs.”

They actually INTERPOLATE a middle value. And, as I pointed out in another message, when doing interpolation/averaging between points when doing numerical integration, you get the *MOST ACCURATE” calculation of the area under the curve. And I am positive you have no clue as to why that is!

“Third, they multiple difference of that average and the reference by the time representing the pairs which as Bellman astutely recognized is effectively averaging; just a slightly different order than the canonical formula.”

It is *NOT* averaging! Neither you nor he understands calculus at all! Averaging gives you degrees/time, not degree-time! You can’t even do simple dimensional analysis that 8th graders can do! You split the time period into intervals, be they minute, hours, seconds, or whatever.

∫sin(x) dx

sin(x) in degrees multiplied by dx in hours, minutes, seconds, etc.

This way you wind up with degree-time units. If your period is 24 hours then your intervals could be in hours, or minutes, or seconds. NOT 1/24hours. Again, that would give you degree/hour!

You and bellman like to portray yourselves as very good mathematicians. You are nothing of the sort! Nor do either of you have any relationship to the real world! Neither of you understand that when calibrating a thermometer in a thermal bath that you don’t average the water temp across a number of thermal baths to determine the average temperature to be used as the calibration temperature of the thermal bath you are using in the calibration routine. You take multiple measurements of the SAME thermal bath and use the average of those!

Bellman
August 22, 2022 2:29 pm

You are as bad as bellman! Integration is not AVERAGING!

Have you still not understood that taking 24 temperature readings through the day, multiplying them each by 1/24 of a day, and adding them together is no different to adding the 24 values and then dividing them by 24?

Tim Gorman
August 23, 2022 6:19 am

Have you still not understood that taking 24 temperature readings through the day, multiplying them each by 1/24 of a day, and adding them together is no different to adding the 24 values and then dividing them by 24?”

This is *NOT* how you do integration!

Sampling the temperatures is to create a temperature signal, just like sampling in a software defined radio (SDR) does for radio signals or a digital signal generator does for creating a sine wave.

That curve is then integrated. The intervals are *NOT* 1/24. Each interval is an interval of 1. You have 24 samples, that’s all. You are trying to build the averaging into the calculation. By doing so you wind up with a dimension of degree instead of degree-day or degree-hour (or whatever) for the final value! Learn some basic dimensional analysis for what you try to do. If the dimensions don’t match then you have done something wrong!

Interval 1 (of size 1/24) is a width of one. Interval 2 is a width of 1. Interval 3 is a width of one. Etc. The height of Interval 1 is sin(π/24). The height of Interval 2 is sin(2π/24). Etc.

That’s for numerical integration. If the temperature profile is at least quasi-sinusoidal then just do the standard integration:

2∫Asin(x)dx from 0 to π/2 => 2A where A is the peak value of the sine wave.

Please note carefully that is *NOT* the same as the sum of the values of the sine wave over an interval of pi.

2Σsin(x) from 0 to π/2 = 3.5. Divide that by the interval of π and you get 0.56, much different than the value of .637 you get when dividing the area under the curve by the π.

The dimensions don’t even match with the two. The sum gives you a dimension of “degree”. Divide that by radians and you get degree/rad. The integration gives you degree-rad and when you divide by radians you get a dimension of degree. Degree/rad is not the same thing as degree!

I keep telling you that you *need* to take a first year engineering calculus course. But for some reason you just want to continue down the path of trying to prove something that is wrong.

Bellman
August 23, 2022 6:52 am

This is *NOT* how you do integration!

Correct. To do integration you have to take the sample width to the limit of zero. But it’s an approximation, and it is what your preferred source calls the “integration method”. I think they add a few bells and whistles which don;t make much difference.

Learn some basic dimensional analysis for what you try to do. If the dimensions don’t match then you have done something wrong!

And what happens to your dimensional analysis when you take your sum of degree days and divide by days?

Interval 1 (of size 1/24) is a width of one.

One what?

The height of Interval 1 is sin(π/24). The height of Interval 2 is sin(2π/24). Etc.

You need to take the proverbial remedial class in basic trigonometry.

That’s for numerical integration. If the temperature profile is at least quasi-sinusoidal then just do the standard integration

We keep going through this. You complain that multiple samples can never be exactly correct, but then are happy to approximate values based on just two readings and an assumption of a sine wave.

Which you then screw up because you still cannot see why daily temperatures are not defined just by the maximum temperature, and daily temperatures do not have a mid-point of zero.

2Σsin(x) from 0 to π/2 = 3.5.

What do you mean by sum here? What are you summing?

The dimensions don’t even match with the two. The sum gives you a dimension of “degree”. Divide that by radians and you get degree/rad.”

If you are just adding temperatures then you are not going to divide by radians. You are just dividing by a dimensionless count. If you are doing an approximate integral you are not just adding degrees, you are adding degree * whatever the x axis is, in this case you are adding degree*radians. Then you divide by radians to get degrees.

I keep telling you that you *need* to take a first year engineering calculus course. But for some reason you just want to continue down the path of trying to prove something that is wrong.

Sorry, but if your understanding is what comes from “engineering calculus” I think I’ll stick to my degree courses in analysis.

Tim Gorman
August 24, 2022 3:56 am

Correct. To do integration you have to take the sample width to the limit of zero. But it’s an approximation, and it is what your preferred source calls the “integration method”. I think they add a few bells and whistles which don;t make much difference.”

Just like bdgwx you have not *READ* the link I gave you. You glanced at it and left with no actual understanding of what they do.

Just like bdgwx, you have not heard of numerical integration either. Let alone doing piecewise numerical integration.

And what happens to your dimensional analysis when you take your sum of degree days and divide by days?”

You get degrees. So what? Degrees is not what you are looking for!

One what?”

One INTERVAL. Just what I said in my post!

“We keep going through this. You complain that multiple samples can never be exactly correct, but then are happy to approximate values based on just two readings and an assumption of a sine wave.”

We’ve been through this! You propagate the uncertainty through to the result. I tutored you earlier this year on how to calculate the uncertainty of a sine wave. The method is right there in Taylor’s book and examples. But you *STILL* have not actually studied Taylor or done the examples. You just keep on trying to cherry pick pieces without understanding what you are cherry picking.

Do we need to go over how to calculate the uncertainty associated with a sine wave again?

Bellman
August 24, 2022 2:43 pm

What link? What bit do you want me to read? Why do you think I don;t understand integration, yet you do?

The uncertainty of a sine wave depend on the assumption that what you are measuring is a sine wave.

Tim Gorman
August 24, 2022 3:03 pm

What link? What bit do you want me to read? Why do you think I don;t understand integration, yet you do?”

The link to degreeday.net. But you won’t go read it for meaning. I know you won’t.

“The uncertainty of a sine wave depend on the assumption that what you are measuring is a sine wave.”

What is sin(x) = sin(L)sin(ð) + cos(L)cos(ð)cos(h)

That *is* the path the sun follows across the sky. It *is* a sine wave. It is the first order driver of daytime temperature. There are numerous secondary drivers which I have shown as ⱷ(a,b,….). Many of these secondary drivers are functions themselves. Some may modulate the maximum temperature in a day (e.g. overcast skys) and some may modulate the temperature in other ways (e.g. a low pressure cold front moving through). But none of these changes can’t be accounted for by moving to numerical integration if needed.

The temperatures still have to be measured and that implies uncertainty. My guess is that you STILL haven’t worked out the examples in Taylor’s book on how to do this for functions. You never will. Knowledge just isn’t important enough to you for you to actually learn anything.

Bellman
August 24, 2022 3:22 pm

That *is* the path the sun follows across the sky.

But unless you live in a vacuum it is not a measure of temperature.

My guess is that you STILL haven’t worked out the examples in Taylor’s book on how to do this for functions.

That’s a book about error. UNCERTAINTY IS NOT ERROR.

Tim Gorman
August 25, 2022 5:59 am

But unless you live in a vacuum it is not a measure of temperature.”

NO KIDDING! It *is* the first order driver of temperature! Everything else is a secondary driver.

You simply can’t admit that using sin(x + ⱷ) *is* a direct, and meaningful simplification for daytime temperature, can you?

Like usual, you are going to throw all kinds of crap against the wall hoping something will stick in order to try and refute it.

That’s a book about error. UNCERTAINTY IS NOT ERROR.”

I’m going to offer you up a link in the faint, faint hope you will read it for meaning. I know you won’t but hope springs eternal.

https://sepmetrologie.com/en/2021/08/02/what-is-the-difference-between-error-and-uncertainty/

Unlike errors, measurement uncertainty is the quantification of the doubt, which is obtained from the result of a measurement. The uncertainty value has the list of components coming from systematic and random effects on previous measurements, due to elements that are calculated by a series of statistical distributions, of the measurement values.”

Bellman
August 25, 2022 6:56 am

You simply can’t admit that using sin(x + ⱷ) *is* a direct, and meaningful simplification for daytime temperature, can you?

Not if I want to keep my sanity I can’t.

I’m sure we must be talking at cross purposes, and what you are saying means something to you, but you are just very bad at explaining it, and refuse to admit you might possibly have made a simple mistake.

Maybe if you could draw a diagram to show what you think sin(x + ⱷ) looks like for a given value of , it would be clearer.

Tim Gorman
August 25, 2022 10:28 am

Not if I want to keep my sanity I can’t.”

==> Not if I want to keep my insanity I can’t.

There, I fixed it for you!

“I’m sure we must be talking at cross purposes, and what you are saying means something to you, but you are just very bad at explaining it, and refuse to admit you might possibly have made a simple mistake.”

I can’t do any more than

1. give you equation for the height of the sun in the sky
2. tell you that the height of the sun in the sky is the primary driver of temperature on the Earth during the day.
3. The factors determining the height of the sun are not time delays but are describing the orbital relationships between the sun and the earth.

I can’t make you believe this no matter what I give you.

There are multiple other secondary drivers of the temperature that modulate the result of the primary driver.

Maybe if you could draw a diagram to show what you think sin(x + ⱷ) looks like for a given value of , it would be clearer.”

I’ll attach one but you won’t believe it or understand it. You’ll just deny it also. It will be a waste of time.

Bellman
August 25, 2022 2:04 pm

Not if I want to keep my insanity I can’t.

Slow hand clap.

1. give you equation for the height of the sun in the sky
2. tell you that the height of the sun in the sky is the primary driver of temperature on the Earth during the day.
3. The factors determining the height of the sun are not time delays but are describing the orbital relationships between the sun and the earth.

The problem is even your claim that the height of the sun is the primary driver of temperature is wrong. The effects of the sun are cumulative. During the day, temperatures are not generally hottest at noon, but several hour afterwards. During the year the summer solstice does not mark the warmest part of summer. Despite the sun getting lower each day, temperatures keep building.

Then there’s the length of the day. Days are longer in summer and that has a bigger effect than the sun beinbg a bit higher in the sky.

Just knowing how high the sun is at any point, is not going to tell you how hot it is, even on average.

And then there are all those other pesky factors such as different air masses, direction of wind, cloud cover etc.

I can’t make you believe this no matter what I give you.

You can’t make me believe that 2 + 2 = 5. It doesn’t mean I‘m insane.

I’ll attach one but you won’t believe it or understand it. You’ll just deny it also. It will be a waste of time.

What is x in that diagram, what is ⱷ?

Tim Gorman
August 26, 2022 7:13 am

The problem is even your claim that the height of the sun is the primary driver of temperature is wrong. The effects of the sun are cumulative. During the day, temperatures are not generally hottest at noon, but several hour afterwards. During the year the summer solstice does not mark the warmest part of summer. Despite the sun getting lower each day, temperatures keep building.”

You are describing thermal inertia! That’s why it’s hottest in the afternoon!

So what? That doesn’t change the fact that the daytime temp is a sinusoid!

Have you *ever* taken a calculus based physics or thermodynamic course? Does the phrase “normal to the plane” mean *anything* to you? The sun dumps the largest amount of heat into the earth when its rays are perpendicular (normal) to the plane. That occurs when the sun is directly overhead. That heat doesn’t immediately appear as temperature. But the temperature will rise to a max and then decrease based on the sine of the angle of the sun dumping heat into the earth.

It doesn’t keep the temperature from being a sine wave related to the path of the sun. It’s just one more factor that has to be considered in the functions “x” and “ⱷ” in sin(x + ⱷ).

Then there’s the length of the day. Days are longer in summer and that has a bigger effect than the sun beinbg a bit higher in the sky.”

Of course it does impact the length of the day! What does that have to do with the path of the sun being a sinusoid? You’ve never actually read the site you linked to for the height of the sun and understood the equations there, have you? As usual, you just cherry picked a site with the operative equation and threw it out hoping people would believe you actually understood what was in it!

Just knowing how high the sun is at any point, is not going to tell you how hot it is, even on average.”

Who ever said it would? That’s why “x” and “ⱷ” are functions and not numbers!

And then there are all those other pesky factors such as different air masses, direction of wind, cloud cover etc.”

Which, if you will go back, I listed as factors in the function “ⱷ”

And you left out terrain, geography, elevation, and atmospheric pressure, all of which I have already listed out! Terrain is itself a function of land use, surface water, sub-soil moisture, vegetation, etc. Clouds are a function of humidity, pressure, wind, aerosols, etc. Did you think you were coming up with something original?

What is x in that diagram, what is ⱷ?”

You are kidding me, right? In the formula for the height of the sun you can’t tell from the equation
sin(x) = sin(L)sin(ð) + cos(L)cos(ð)cos(h)
what “x” is and what “ⱷ” is?

It’s useless trying to teach you anything!

Bellman
August 26, 2022 7:13 pm

Ah ha. I think I’ve finally figured out what you are trying to say. Your x in sin(x), which you were originally calling t, is the height of the sun. That makes more sense.

Sorry if I missed any explanation of that amidst all your yelling and insults.

Tim Gorman
August 27, 2022 5:35 am

Ah ha. I think I’ve finally figured out what you are trying to say. Your x in sin(x), which you were originally calling t, is the height of the sun. That makes more sense.”

No! As I’ve told you multiple times “x” is a function all of its own. Sun height is only a part of it! Height, in radians/degrees or whatever, is not temperature. There has to be other factors involved to come up with temperature. Again, the sun is the primary driver of daytime temps, it’s path is a sinusoid and that is why daytime temps typically look like a sinusoid. I’m not sure how to quantify all the factors in “x” ==> f_x(a,b,c,…) but solar insolation would be the start. Not being able to quantify the factors doesn’t keep one from using the function f_x(a,b,c,…) in sin(x), or if you like sin[f_x(a,b,c,…)]. sin(x) is just far easier to write or type.

Bellman
August 28, 2022 3:32 pm

That’s a relief. I was worried I’d misjudged you.

Tim Gorman
August 24, 2022 4:01 am

What do you mean by sum here? What are you summing?”

You keep want to call integration “averaging”. An average is a sum divided by the number of components. So here is the sum of the values of a normalized sine wave!

If you are just adding temperatures then you are not going to divide by radians. You are just dividing by a dimensionless count. “

Really? And you couldn’t figure out the intervals? Using an interval of 1/24hrs gives you a dimension of 1/hrs. Now you are saying the intervals should be dimensionless? It’s no wonder you can’t figure out what is going on!

Sorry, but if your understanding is what comes from “engineering calculus” I think I’ll stick to my degree courses in analysis.”

There was *NEVER* any doubt you were going to stay in your little box of understanding. You just never learn anything!

bdgwx
August 23, 2022 6:57 am

TG said: “This is *NOT* how you do integration!”

Then you need to have that discussion with them. Because that’s exactly how they say they are doing their “Integration Method”. I also don’t understand why you referred us to them if you disapprove of their method.
﻿
TG said: “The intervals are *NOT* 1/24”

That is literally their first example.

Calculate the time (in days) over which the temperature was below the base temperature. In this simple example this is always an hour (1/24 days).

They are using average temperature whether you realized it or not.

I can say the same thing about the GUM JCGM 6:2020 document you wanted me to look at as well. It not only averages temperatures, but says it can be done to “abate the extent of the uncertainty.”

Let me summarize where we are at this point.

Kip’s article and defense of it tells us that averaging intensive properties like temperature is meaningless, useless, and non existent.

We are told that a particular soil moisture product can be used to assess drought even though it depends on averaging temperature.

We are told that HDD/CDD are useful even though they depend on averaging temperature.

Furthermore, we are told that we must use the GUM to assess uncertainty even though it says averaging temperature is appropriate if you want to “abate the extent of the uncertainty”.

Tim Gorman
August 24, 2022 4:42 am

Then you need to have that discussion with them. Because that’s exactly how they say they are doing their “Integration Method”. I also don’t understand why you referred us to them if you disapprove of their method.”

You *still* have not bothered to actually read the link! Their integration method is *NOT* the Mean Temperature Method. You are as bad as bellman in just scanning something to find something to cherry pick.

“That is literally their first example.”

You don’t understand integration any more than bellman! Do I need to draw you a picture of how you do numerical integration?

From the link: “If your integrand cannot be evaluated at the midpoints of your intervals, you can modify rectangular integration to use the function’s value at either the left boundary or right boundary as the rectangle’s height. These 2 values can be taken directly from the function values, but the resulting approximation is not as good as using the midpoint rule. “(bolding mine, tg)

Can you tell us why the mid-point rule is more accurate? I doubt it!

They are using average temperature whether you realized it or not.”

No, they aren’t!

“I can say the same thing about the GUM JCGM 6:2020 document you wanted me to look at as well. It not only averages temperatures, but says it can be done to “abate the extent of the uncertainty.”

This is averaging multiple measurements of a measurand (singlular). It is not integrating and it is *NOT* averaging measurements of different measurands!

Kip’s article and defense of it tells us that averaging intensive properties like temperature is meaningless, useless, and non existent.”

You keep missing the details. You can’t average properties that are not additive or which can’t be divided as well as those which don’t act at a distance. You have to read for UNDERSTADING, not to just cherry pick pieces!

Averaging extensive properties in order to calculate an intensive value is *NOT* averaging intensive values!

“We are told that a particular soil moisture product can be used to assess drought even though it depends on averaging temperature.”

Again, give us the functional relationship between soil moisture and temperature. I can’t find one. Most measurements are volume/volume, i..e volume of water per volume of material. Nothing about temperature.

We are told that HDD/CDD are useful even though they depend on averaging temperature.”

The integration method of finding HDD/CDD does *NOT* depend on averaging temperature. Again, you don’t understand calculus at all! You especially don’t understand how to do numerical integration. You are a perfect example of a climate scientist!

“”Furthermore, we are told that we must use the GUM to assess uncertainty even though it says averaging temperature is appropriate if you want to “abate the extent of the uncertainty”.

For at least the fifth time – when you have multiple measurements of the SAME THING which generate a normal distribution around a true value (assuming insignificant systemic uncertainty) you can average the measurements in order to find the true value.

STUDY TAYLOR FOR UNDERSTANDING!

Don’t just use Taylor for cherry picking. Do the examples!

Carlo, Monte
August 23, 2022 12:56 pm

This is *NOT* how you do integration!

Absolutely incredible, almost impossible to believe anyone could be this far out.

bdgwx
August 23, 2022 1:26 pm

CM said: “Absolutely incredible, almost impossible to believe anyone could be this far out.”

And yet it seems like Tim isn’t understanding that the degreedays.net “Integration Method” isn’t using proper calculus integration. All they’re doing is grouping temperature observations into pairs, averaging them, multiplying the averages by the amount of time represented by the pairs, and summing the result. Let me repeat that. They are averaging temperature observations and found enough meaning in that to then use the value in further steps. Nevermind, that each individual temperature observation they are using is itself an average of more fine grained temperature observations.

Carlo, Monte
August 23, 2022 2:16 pm

Bellman
August 19, 2022 11:59 am

But this whole debate is whether it makes sense to look at trends of US or global temperature if you don’t think the average temperatures have any physical meaning. If you can’t average degree-days across the US or globe, then the question is still why you think the pause is a reality.

Tim Gorman
August 19, 2022 2:26 pm

But this whole debate is whether it makes sense to look at trends of US or global temperature if you don’t think the average temperatures have any physical meaning. “

INTEGRALS ARE NOT AVERAGES!

“f you can’t average degree-days across the US or globe, then the question is still why you think the pause is a reality.”

Integrals are *NOT* averages. And where did I talk about averaging degree-days?

Like I keep telling you, go take a remedial calculus course! Take bdgwx with you!

Bellman
August 19, 2022 2:57 pm

I’m asking how you can use CDDs or whatever to get an indication of what is happening either globally or in the US without averaging them.

This thread all starts with me saying it’s ironic that you et al, want to accept the idea of a pause. despite it being based on data you say is meaningless both because it’s an average temperature which is impossible, or because satellite data is so uncertain you can’t even tell if it’s warming or not.

Your response to to say the only temperature data you accept is CDDs based on surface thermometer data. And all I’m trying to understand is how you could use that data to confirm the pause, without averaging them.

Tim Gorman
August 19, 2022 3:10 pm

You didn’t?

bellman “If you can’t average degree-days across the US or globe, then the question is still why you think the pause is a reality.”

“I’m asking how you can use CDDs or whatever to get an indication of what is happening either globally or in the US without averaging them.”

I’ve given you this twice. Learn to read.

This thread all starts with me saying it’s ironic that you et al, want to accept the idea of a pause. despite it being based on data you say is meaningless both because it’s an average temperature which is impossible, or because satellite data is so uncertain you can’t even tell if it’s warming or not.”

As I’ve told you multiple times, I don’t trust *any* temperature data set that is based on averages. That doesn’t mean I can’t point out what those data set show when others are using them.

﻿

Jim Gorman
August 17, 2022 4:30 pm

You do understand that UAH uses an entirely different method to judge temperatures don’t you. My problem with UAH uncertainty is that there are things in the atmosphere that can bias the readings used in different directions increasing the stated uncertainty.

Don’t try to lecture me on uncertainty. I have experience in making precision measurements and know how hard it is to achieve truly accurate ones with little uncertainty. You certainly can’t get it making one reading on different things.

Bellman
August 17, 2022 5:13 pm

Yet it’s the UAH data, and the zero uncertainty pause trend you use to claim “CO2 is not a control knob for temperature if temps don’t increase along with increasing CO2.”

bdgwx
August 17, 2022 7:13 pm

I’m trying to figure out why uncertainty and trends in the UAH data matter to you so much if you don’t even think the global average temperature even exists. How can a non existent metric have an uncertainty or trend anyway? And so there is no confusion let it be known that I’m asking the question from the devil’s advocate point of here.

Carlo, Monte
August 17, 2022 8:56 pm

How can a non existent metric have an uncertainty or trend anyway?

Silly question—air temperatures are MEASUREMENTS (except the fraudulent made-up data of course).

bdgwx
August 18, 2022 4:10 am

So the global average temperature is a measurement that does not exist?

Carlo, Monte
August 18, 2022 5:49 am

That you continue to deny the reality of propagation of measurement uncertainty is no surprise.

Jim Gorman
August 18, 2022 6:39 am

Go read the other thread again about averaging intensive measurements. Dose the fact that temperature misses heat in the atmosphere and its location bother you?

Tim Gorman
August 18, 2022 4:20 pm

Where can one go to measure the global average temperature?

Jim Gorman
August 18, 2022 5:34 am

Do you understand the difference in thermometer readings vs what UAH measures?

Just one example is the spatial coverage.

Bellman
August 18, 2022 5:42 am

The claim is that you cannot average temperatures because they are an intensive property – no buts. This has nothing to do with the way you measure temperatures or in the spatial coverage.

Carlo, Monte
August 18, 2022 5:53 am

You can add up a column of numbers and divide by N, just like you can divide standard deviation by root-N.

Just because it is possible doesn’t indicate they have any basis in reality.

But you must fulfill your mission in life to Keep the Rise Alive, at any cost.

The ends justify any means, the watermelon credo.

Tim Gorman
August 18, 2022 4:23 pm

Temperature is determined by the micro-climate at a point. It is not determined by the temperature at a distant point. In that micro-climates are *NOT* the same everywhere an “average” temperature is meaningless. The temperature in Phoenix and the temperature in Miami can’t be averaged to find an “average” temp somewhere in between. It doesn’t work for the north/south side of the Kansas River valley. It doesn’t work for *anywhere*.

Tim Gorman
August 18, 2022 4:19 pm

I’m trying to figure out why uncertainty and trends in the UAH data matter”

Guess you don’t understand the role of a sceptic. Use their own data as an argument against their conclusions!

How can a non existent metric have an uncertainty or trend anyway?”

The uncertainty is part of the measurement. There is nothing that keeps a temperature measurement from having an uncertainty interval associated with it. It is the uncertainty that propagates into the uncertainty of the temperature trend.

bdgwx
August 18, 2022 6:16 pm

So you believe an average temperature does not exist while simultaneously believing that its uncertainty can be assessed?

Jim Gorman
August 19, 2022 6:28 am

Actually, the uncertainty of a measurement is neither intensive or extensive. It is a description of the measurement itself. Ask yourself this, is the measurement itself used in uncertainty calculations or just the possible variance of the measurement? I think you will find uncertainty doesn’t originate with what you are measuring, only with the instrument doing the measuring.

Carlo, Monte
August 19, 2022 6:48 am

They still think uncertainty drops out by subtracting the baseline, so they don’t care.

bdgwx
August 19, 2022 9:07 am

Yeah, so it sounds like to me you believe we can assess the uncertainty of non-existent quantities? Correct?

Tim Gorman
August 19, 2022 10:13 am

If it doesn’t exist then how can you measure it?

Where do you go to measure the “global average temperature”?

bdgwx
August 19, 2022 11:44 am

It’s a good question. There are others that are similar in a nature. Where do you go to measure the temperature of the CMB? Where do you go to measure the mass of Earth? Where do you go to measure the volume of the ocean? Where do you go to measure the total solar irradiance? Where do you go to measure countless other quantities of a similar nature?

I don’t think you necessarily need to “go” anywhere to measure something. Nor do I think you need to probe every single atom of the body to “measure” it. One of the great things about science is that we can estimate quantities of bodies with incomplete information and from an observational perspective that is far away in many cases.

Anyway, let me play the devil’s advocate here and assume some quantities (like an average of intrinsic property) do not exist. How do you assess the uncertainty of these quantities if they do not even exist?

Tim Gorman
August 19, 2022 1:39 pm

Where do you go to measure the temperature of the CMB?”

You don’t go anywhere. You use a radio telescope to measure the EM radiation which is pretty much uniform as far as teh background is concerned. You then calculate the temperature of that signal, you don’t measure it!

Where do you go to measure the mass of Earth?”

You don’t. You estimate it based on its impacts on the other planets and their influence on the earth. Mass creates a distortion in the space-time continuum known as gravity. You can estimate mass from the effects of that gravity. It’s also why there is always an uncertainty quoted with the mass!

Where do you go to measure the total solar irradiance?”

You don’t go measure it. You measure the solar irradiance at a point and then calculate the total.

“Where do you go to measure countless other quantities of a similar nature?”

You don’t. You measure what you can measure and then use functional relationships to calculate them. It’s why you can’t measure temperature at a point and calculate the temperature of the earth. No functional relationship exists to do that!

I don’t think you necessarily need to “go” anywhere to measure something.”

Really? Observations are what validate or invalidate theories. If you don’t go somewhere to make observations then you really aren’t doing validation or invalidation of anything.

“Nor do I think you need to probe every single atom of the body to “measure” it.”

Who is claiming that you have to?

One of the great things about science is that we can estimate quantities of bodies with incomplete information and from an observational perspective that is far away in many cases.”

Estimates imply uncertainty. Why do we never see measurement uncertainties propagated forward from temperature measurements?

Incomplete data means you are guessing. Estimates require calculating from known values even if you aren’t quite sure what the functional relationship is. We used to teach Boy Scouts how to estimate the height of a tree – but it required a measurement of something, even it was units of “thumb” or “steps”.

How do you assess the uncertainty of these quantities if they do not even exist?”

Ah! Another trick question! If the quantity doesn’t exist then how does it have an uncertainty? Having an uncertainty implies that it *does* exist! How would a non-existing global average temperature have an uncertainty?

The issue here is that a skeptic trying to question the applicability of something must work with that something. If that something is a global average temperature then trying to show how the uncertainties associated with it would mask any differential being looked for is certainty an acceptable path to take.

bdgwx
August 19, 2022 2:22 pm

TG said: “Why do we never see measurement uncertainties propagated forward from temperature measurements?”

I have seen it done. I’ve even posted several publications doing just that.

TG said: “Really?”

Yes. We’ve learned a lot about countless objects without going to them.

TG said: “If the quantity doesn’t exist then how does it have an uncertainty?”

That’s my question.

TG said: “Having an uncertainty implies that it *does* exist!”

That’s what I was thinking.

TG said: “How would a non-existing global average temperature have an uncertainty?”

That’s my question.

Tim Gorman
August 20, 2022 6:10 am

I have seen it done. I’ve even posted several publications doing just that.”

No, you haven’t. Everything I’ve seem from you is focused on the standard deviation of the sample means. That is *NOT* propagating measurement uncertainty. Standard deviation of the sample means simply tells you nothing about the accuracy of the sample means.

“Yes. We’ve learned a lot about countless objects without going to them.”

Not from direct measurements of intensive attributes!

That’s my question.”

A non-existent value has no uncertainty. You are trying to conflate an average temperature which doesn’t exist with a direct measurement of temperature at a location between two points.

That direct measurement *can* have a measurement uncertainty.

That’s what I was thinking.”

The average temp doesn’t exist. It doesn’t have a measurement uncertainty since it can’t be measured. The temp at an intermediate point can be measured and will have a measurement uncertainty.

You are still trying to conflate the two.

That’s my question.”

Since it doesn’t exist it can’t have a measurement uncertainty. Insofar as it is an average of measurements the individual measurement uncertainties should be propagated into the average value that is calculated. That uncertainty will, sooner or later with enough measurement stations, overwhelm the average thus showing that it is impossible to actually calculate it.

You can run but you can’t hide. The global average temperature is meaningless and useless.

bdgwx
August 20, 2022 6:43 am

TG said: “Since it doesn’t exist it can’t have a measurement uncertainty.”

That was my thinking too. Perhaps the next time someone who believes the global average temperature does not exist and yet still posts an uncertainty estimate for it can be informed of the mistake?

Tim Gorman
August 20, 2022 1:47 pm

It would be far better to educate them in how to propagate the measurement uncertainty forward from the measurements. Then they could see that the average makes no sense even if you *could* average it.

Carlo, Monte
August 19, 2022 11:07 am

It sounds to me like you don’t understand ANYTHING about uncertainty.

bdgwx
August 19, 2022 12:36 pm

I’m not foolish enough to claim I understand EVERYTHING about uncertainty, but I do think I think I claim I know SOMETHING about it. For example, I know you can propagate the uncertainty of individual measurements that have gone through a combining function using GUM equation 10.

Carlo, Monte
August 19, 2022 2:44 pm

The ONLY reason you do is because of your false belief that you can use it to average uncertainties away.

As Jim has tried to tell you countless times, Eq. 10 is for a functional relationship between an output quantity and the input quantities needed to calculate it. A mindless average operation doesn’t qualify!

This is the entire extent of your uncertainty knowledge, and it is 1000% wrong.

Tim Gorman
August 19, 2022 3:04 pm

For example, I know you can propagate the uncertainty of individual measurements that have gone through a combining function using GUM equation 10.”

That is *ONLY* useful for where you have multiple measurements of the SAME thing that generate something like a Gaussian distribution!

From the GUM:

The standard uncertainty of y, where y is the estimate of the measurand Y”

Please note carefully (this has been pointed out to you MULTIPLE times over the past year) the word “measurand“.

It doesn’t say measurands.

If you look at Fig 1 it says: “Figure 1 — Graphical illustration of evaluating the standard uncertainty of an input quantity from repeated observations ”

“AN INPUT QUANTITY”. Not input quantities!

I’ve attached a screenshot of Figure 1. Please note that it lays out a GAUSSIAN distribution!

The odds of getting a Gaussian distribution from 1000’s of temperature measurements stations is so low as to be zero!

bdgwx
August 19, 2022 7:26 pm

TG said: “That is *ONLY* useful for where you have multiple measurements of the SAME thing that generate something like a Gaussian distribution!”

And yet the GUM provides examples of the individual measurements being of different things. In fact, the measurements in their examples don’t even have the same units in many cases. If you believe they have made a mistake perhaps you can contact them and lobby to have the GUM changed. When you get it changed let me know and I’ll change my position on this matter.

Carlo, Monte
August 19, 2022 9:08 pm

Idiot, you just dig the hole you are in deeper and deeper with nonsense like this.

Unskilled and Unaware

Tim Gorman
August 20, 2022 1:18 pm

He never looks up to see how deep the hole is!

Tim Gorman
August 20, 2022 6:24 am

And yet the GUM provides examples of the individual measurements being of different things.”

I can’t find it associated with Eq. 10. If you can then please post a quote or at least a link to it!

“In fact, the measurements in their examples don’t even have the same units in many cases.”

As C,M has pointed out, that is for when you are trying to calculate a functional relationship. The dimensions always finally work out to the dimension of the quantity you are trying to find the uncertainty of. Each of those component values must have their uncertainty propagated from the measurements of those component values into the functional relationship.

E.g. finding current in an electrical circuit. You can measure voltage and resistance, each with a valid set of measurements of the same thing, and calculate the current along with its associated propagated uncertainty. The dimensions of voltage and resistance work out to amperes!

“If you believe they have made a mistake perhaps you can contact them and lobby to have the GUM changed. “

They haven’t made a mistake. *YOU* just don’t understand what they are saying!

Jim Gorman
August 20, 2022 5:06 pm

You have a penchant for understatement.

bdgwx
August 21, 2022 3:35 pm

TG said: “I can’t find it associated with Eq. 10. If you can then please post a quote or at least a link to it!”

According to the verbiage on pg. 19 for equation 10 f is the function given in equation 1 and described on pg. 8 as Y = f(X_1, X_2, …, X_n). There is no requirement stated that the X inputs must be of the same thing. And, in fact, the example given on pg. 9 is of X’s of different things. The verbiage also indicates that the X’s can themselves be dependent on other quantiles.

Jim Gorman
August 21, 2022 4:51 pm

function given in equation 1 and described on pg. 8 as Y = f(X_1, X_2, …, X_n). There is no requirement stated that the X inputs must be of the same thing. “

There is no requirement that the input variables be need be the same thing is true. However, the dimensional analysis of the inputs must provide the correct output value.

Functional relationships require exact descriptions of the physical units needed. You can’t just throw some things in a pot and come up with a functional relationship. If you’ve never done dimensional analysis, you have never taken a physical science course.

Tim Gorman
August 21, 2022 7:54 pm

According to the verbiage on pg. 19 for equation 10 f is the function given in equation 1 and described on pg. 8 as Y = f(X_1, X_2, …, X_n). There is no requirement stated that the X inputs must be of the same thing. And, in fact, the example given on pg. 9 is of X’s of different things. The verbiage also indicates that the X’s can themselves be dependent on other”

You are as bad as bellman at cherry picking stuff you simply don’t understand hoping it will bolster your argumeent.

From the wording around equation 1:

“Many measurements are modelled by a real functional relationship f between N real valued input quantities X1 , . . . , XN and a single real-valued output quantity (or measurand) Y in the form

Y = f (X1 , . . . , XN ).”

The term measurand is singlular! It is not multiple. The X quantities are associated with ONE MEASURAND!

You are trying to turn the equation into a multivariate one and the same page says: “The measurement model can be multivariate where there is more than one measurand, denoted by Y1 , . . . , Ym;”

I would also point you to

———————————————–
3.8 multivariate measurement model multivariate model measurement model in which there is any number of output quantities NOTE 1 The general form of a multivariate measurement model is the equations
h1(Y1, . . . , Ym, X1, . . . , XN ) = 0, . . . , hm(Y1, . . . , Ym, X1, . . . , XN ) = 0,
where Y1, . . . , Ym, the output quantities, m in number, in the multivariate measurement model, constitute the measurand, the quantity values of which are to be inferred from information about input quantities X1, . . . , XN in the multivariate measurement model.

—————————————————

Stop trying to cherry pick from the GUM so you can say that it handles multiple measurements of different things the same way it handles multiple measurements of the same thing. The first has multiple measurands, the second has one measurand and that is what the GUM addresses!

bdgwx
August 22, 2022 5:40 am

TG said: “The term measurand is singlular! It is not multiple. The X quantities are associated with ONE MEASURAND!”

First, the function f accepts multiple measurands X_1 through X_N. That is plural as in many. And the example given on pg. 9 is of measurands (plural) of different things.

Second, section 4.1.2 states “The input quantities X_1, X_2, …, X_N upon which the output quantity Y depends may themselves be viewed as measurands and may themselves depend on other quantities, including corrections and correction factors for systematic effects, thereby leading to a complicated functional relationship f that may never be written down explicitly.”

Third, the term “measurand” is defined exactly as “particular quantity subject to measurement where “measurement” is defined exactly as “set of operations having the object of determining a value of a quantity”

Fourth, most of the examples given in the GUM are of functions that accept inputs of different things. One notable exception is that of H.3 which…wait for it…not only sums temperatures but averages them to. Clearly the GUM thinks averaging temperatures is meaningful and useful.

Carlo, Monte
August 22, 2022 6:41 am

Fourth, most of the examples given in the GUM are of functions that accept inputs of different things. One notable exception is that of H.3 which…wait for it…not only sums temperatures but averages them to. Clearly the GUM thinks averaging temperatures is meaningful and useful.

mr. disingenuous counts another coup!

Clearly you did not understand what you were reading, while engrossed in your headlong desperate search for any example you think vindicates your nonsense.

Opening the GUM, going to example H3; the TITLE says:

“H.3 Calibration of a thermometer”

Did it ever dawn inside your trendologist brain that this might be a leeeeeetle different? This is for a calibration in a lab!

Continuing:

“This example illustrates the use of the method of least squares to obtain a linear calibration curve and how the parameters of the fit, the intercept and slope, and their estimated variances and covariance, are used to obtain from the curve the value and standard uncertainty of a predicted correction. “

“H.3.1 The measurement problem

“A thermometer is calibrated by comparing n = 11 temperature readings t_k of the thermometer, each having negligible uncertainty, with corresponding known reference temperatures t_R, k in the temperature range 21 °C to 27 °C to obtain the corrections b_k = t_R, k − t_k to the readings. The measured corrections b_k and measured temperatures t_k are the input quantities of the evaluation. A linear calibration curve

“b(t) = y_1 + y_2(t – T_0) H.12

“is fitted to the measured corrections and temperatures by the method of least squares. The parameters y_1 and y_2, which are respectively the intercept and slope of the calibration curve, are the two measurands or output quantities to be determined.”

Absolutely NOTHING in here about any kind of averaging; this is a comparison of the output of an thermometer being calibrated against a calibration reference. Completely UNLIKE air temperature averaging in the context of global warming.

Try again, mr. disingenuous, another fail. Your paragraph quoted above is a LIE.

bdgwx
August 22, 2022 7:48 am

CM said: “Your paragraph quoted above is a LIE.”

I stand by what I said. They not only do they sum temperatures but they average temperatures as well and use it (see H.16a). Just because you didn’t notice or ignored it doesn’t make it any less true. Clearly they think averaging temperatures is meaningful and useful.

Carlo, Monte
August 22, 2022 8:02 am

A characteristic of hardened liars is that when confronted with their falsehoods, they double-down and deny with additional lies: “It’s not me in that video!”

The text prior to H.16a says NOTHING about averaging! It is about removing correlation between the slope and the intercept.

I repeat:

Completely UNLIKE air temperature averaging in the context of global warming.

Are there ANY mathematical operations that you DON’T label as “averaging”?

bdgwx