Guest Post by Willis Eschenbach
I have the world’s best science gig. I can research whatever I want, whenever I want, for as long as I want, and I don’t get paid a dime no matter how hard I work. What’s not to like?
In any case, I got to wondering about how many temperature stations we’d need to get an accurate idea of the average temperature of the earth. Being a data guy rather than a theory guy, I figured I could use the CERES dataset to take a first cut at the question.
Let me preface this by explaining the temperature dataset I use in my analyses. The CERES radiation datasets don’t contain a surface temperature dataset. However, they have an upwelling surface upwelling longwave (thermal) radiation dataset. Because many of my analyses use the CERES dataset, I used the CERES surface radiation dataset to create a surface temperature dataset. I did the calculation using the Stefan-Boltzmann equation and utilizing the gridded surface emissivity from here.
How good is the resulting CERES calculated temperature dataset? Here’s a comparison with the Berkeley Earth, HadCRUT, and Japanese Meteorological Agency datasets. Seasonal variations have been removed from all datasets.
As you can see, the calculated CERES surface temperature agrees with the other three as well as they agree with each other. Turns out it also agrees better than either the HadCRUT or the JMA dataset with the Berkeley Earth dataset… so I use the CERES data in this and my other analyses. However, as indicated by the graph above, it makes no practical difference which dataset is used. Doing the following analysis on the Berkeley Earth gridded temperature dataset gives essentially the same results as using the CERES dataset.
With that as prologue, my scheme was to randomly pick a subset of the 64,800 1° latitude by 1° longitude gridcells that make up the earth’s surface, and see what that subset gave me as an average temperature.
The most interesting results were when I used just one percent of the gridcells (n = 648). Here’s an example of one of the random selections of 1% of the gridcells.
As you might imagine, running the random example many times gave very different average temperatures from different random subsets of 1% of the gridcells. Here’s a histogram of the average temperatures of a typical run of 100 trials using only 1% of the gridcells.
The average temperatures range from 13.5 to 16.5 degrees, so there is little agreement between subsets. No surprise, as I said.
But my next graph was a surprise. I decided to plot the monthly data for some of the individual runs. Here’s an example of ten runs, including the linear trend lines. I’ve removed the seasonal variations from each dataset.
Two things were surprising about this. One was that the trends were all pretty much identical. I expected much greater differences using only 1% of the data.
The other was that the actual monthly results were all so similar, having the same overall shape with just a different average temperature.
To investigate further, I plotted up the anomalies for each of the runs. I created the anomalies by subtracting the average of each run from the values of that run. Here are those results.
Fascinating. Although we can’t get much clarity on the absolute global average temperature from 1% of the data, we can use that same 1% of the data to get a pretty good idea regarding the overall trend and the monthly variations in the global average data. None of the individual 1% runs vary much at all from the global average, and their trends are tightly clustered. I didn’t expect that at all.
Next, I got to thinking about the oft-repeated claims that the Little Ice Age back in the 1600’s – 1700’s was just a Northern Hemisphere phenomenon, or that it’s only based on land records, or both. So, I thought I’d take a look at just the NH land data, to see how random subsets of just the northern hemisphere land matched up with the global data. Of course, since the NH land is much smaller than the globe and it’s land rather than ocean, the temperature swings in the average NH land temperature will be larger than the swings in the entire global average. So in order to compare them, I’ve adjusted for that in the following graph.
Again, most interesting. With knowledge of the temperature in around a hundred twenty randomly selected gridcells out of the 64,800 total gridcells, with the known gridcells located only on land and covering less than a quarter of one percent of the earth’s surface, we can closely approximate both the global temperature anomaly and the global temperature trend.
Any given run may or may not be all that exact a match to the entire globe, but none of them are much different, and their trends only vary slightly … which makes me misdoubt the idea that the Little Ice Age was a local phenomenon.
Seems like a validation of what I modestly call “Willis’s First Rule Of Climate“, which states:
“In climate, everything is related to everything else, which in turn is related to everything else … except when it isn’t.”
Best of life to everyone,
w.
As Always: I ask that when you comment you quote the exact words you are referring to. I can defend my words. I can’t defend your idea of what my words say.
Was this idea played in reverse a while ago ..?
If the global average is on a trend, we should see this (trend) reflected in any long term temperature set.
The longest IIRC is the records for Central England ?
Or in a chart of population increase, or in a chart of urban growth, or…
Willis wrote: “Being a data guy rather than a theory guy”
That is certainly true. Which brings up the thought: wouldn’t a smart person spend a bit of time learning theory, before spending years and years looking at data that he doesn’t understand in the slightest? And then posting thousands of words of nonsense based on a total lack of theoretical understanding? I won’t go so far as to ask you to stop denigrating those of us who have learned it; that’s a proposal for another time. However, I daresay that this is what The Captain would suggest – before you make any more of a mess of his previously good family name. Fortunately, there’s still plenty of time to redeem yourself.
Let’s start here: we’ve already established that a Watt is defined as a Joule per second, so what do you think a Joule is? (Hint: there are two correct answers, but neither of them is “power”.) Next, why would you think that radiant energy should be measured in Watts? No physicist or physics textbook would say that (because it’s not how physics works). But definitely consult both if you think I am mistaken. You have all the time in the world, after all! And these days, you can do it all online from the comfort of your living room…
And before you say yet again “just because the ‘climate scientists’ said so”, please keep in mind this handy debating pyramid that I found floating around somewhere. Note that logical fallacies, such as this Argument from Authority that you are so fond of, are so far from actual debating, that they don’t even show up here. (It obviously never occurred to Paul Graham that anyone would be so intellectually impoverished that they thought a Logical Fallacy could be seriously presented in place of an actual argument. I think I’ll have to make a new pyramid with Logical Fallacies inserted between Contradiction and Responding to Tone.) In any case, try to stick to the top three rows, please:
Once again, Steve can find nothing wrong with my post, so he attacks me instead.
In any case, Steve, you invite me to present a scientific claim that radiant energy is measured in watts, viz:
Glad to oblige. What I study is generally not “radiant energy”, however. It is the rate of flow of radiant energy, the “radiant flux”. For example, the sun provides a constant flow of radiant energy to the earth in the form of an electromagnetic wave, which is on the order of 340 watts per square meter. Here’s a quote from NASA regarding why that measurement is in watts.
However, I fail to see what that has to do with this post … other than to provide a place for you to stand on tiptoes while unsuccessfully trying to bite my ankles.
Look, I understand your frustration. I’d be frustrated too if all I had to whine about was terminology. So how about you try to find something actually wrong with my analysis before you start up again with your endless, meaningless complaints?
w.
Thanks, Willis. Finally an answer to my question. Whew. That was more painful than pulling teeth. So now that we have established that “radiant energy (SI unit: joule, J)” is measured in Joules, not Watts, contrary to what you wrote earlier (viz., “Radiant energy (measured in W/m^2)”, a mistake which we can now write off as simple sloppiness on your part), we can ask the next logical question, which is: what controls “the rate of flow of radiant energy”, and in what direction does it “flow”?
(Your other previous statement that “The “radiant” part means it’s flowing” is also false, by the way, and likely to confuse you, so stop thinking that – nothing in the quote from the Global Monitoring Laboratory above would imply that “radiant” implies “flowing” implies “power”, and indeed they are very careful to distinguish between radiant energy and radiant power, which are not the same thing at all)
I doubt that glaciologists in general ever took the hockey stick seriously. From Jean Grove (1988) to Brenda Hall ( https://phys.org/news/2023-02-elephant-antarctic-sea-warmer-mid-to-late.html ), the consensus of earth scientists has been that the LIA was global. –AGF
Willis, as always, it is good. But what grinds my teeth is that “temperature anomaly” crap. Anomaly from what specific temperature? Why do they never, ever share that value?
Huh? The baseline period used for calculating the anomaly is almost always specifically stated. Typically it’s a 30-year period. For many years the period was 1951-1980. Recently some studies are using 1981-2010. The choice is totally arbitrary.
I used the entire period of each gridcell record (Mar 2000 – Feb – 2022) as the baseline.
w.
Interesting take on it Willis.
However, I think you should take into account that the gridcells closer to the poles are smaller than the ones nearer to Equator.
The small polar gridcells should therefore not count as much as the large equatorial ones.
To do that you must multiply each gridcell with cosine of the latitude.
/Jan
Jan, good to hear from you as always.
All of the calculations for all of the graphics and values in the head post were area-weighted, for the reason you explain above.
Best to you,
w.
A 1 degree grid is going to over represent the polar regions.
A 100km by 100km grid is very close to a 1 degree grid at the equator and doesn’t distort at the poles
Alternatively one can correct for 1 degree distortion by oversampling based on lattitude.
Ferd, had the same comment just above yours.
You can correct for this by giving the grid cells a weight equal to cosine of latitude. Willis has done that.
The Central Limit Theorem is why random sampling as Willis has done is likely to outperform gridding.
While gridding is a form of sampling, it is not random.
Random sampling could be improved by sampling the underlying ceres data before it was gridded by ceres. Using an equal area filter to remove sampling bias.
The problem with grids is the assumption that the grids are unbiased is wrong because the grids are not homogeneous with respect to altitude or surface material. Averaging locks in this bias even at the 1 degree level.
The problem with gridding is simple to see. Say you have a biased grid square among n grid squares.
Your true error is then proportional to 1/n and the grid square in question cannot be isolated using averaging.
Now random sample. Some samples will have the grid square, some will not. The error will now be isolated and the variance will increase, increasing your standard error.
The increase in the error is a good thing because it tells you there is a biased square while the climate science approach buries the error. It is there, but hidden, giving a false estimate of the error when averaging instead of sampling.
Data that does the unexpected is the best way of ascertaining what’s going on.
I wonder what the set of enclosed water bodies with cities/large towns on their banks would yield, Red Sea, Baikal, Tanganyika, Superior, North Sea. Marmora…
JF
Willis,
Seeking your approval to use the CERES graph of CERES data monthly trends 10 runs in a nearly-complete article for WUWT,
I seek to compare the Ceres patterns with a land temperture set to show differences.
Cheers Geoff S
Absolutely. Rock on.
w.
Many thanks, Willis.
Geoff