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:
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.