Guest Post by Willis Eschenbach
I’ve been mulling over a comment made by Steven Mosher. I don’t have the exact quote, so he’s welcome to correct any errors. As I understood it, he said that much of the variation in temperatures around the planet can be explained by a combination of elevation and latitude. He described this as a “temperature field”, because at any given latitude and elevation it has a corresponding estimated temperature value.
Intrigued by this idea, I decided to use the CERES dataset. However, rather than using latitude, I decided to take a look at how well a combination of the sunlight and the elevation can predict the average temperature. Let’s start with the average surface temperature. It’s shown below in Figure 1.
To estimate the temperature, what I did was to make a simple linear function of solar energy and elevation (see end notes for details). This gave me the following estimate of gridcell temperatures.
Now, that’s a pretty good facsimile of the actual temperatures shown in Figure 1. Indeed, the “R-squared” (R^2) of the temperature field and the observations is 0.95, meaning that the temperature field explains 95% of the variation in the observed temperature.
That’s not the interesting part, however. The fun questions are, where is the temperature NOT as expected, and why? Where is the greatest departure from the estimated temperature, and why is it there? To investigate those, I next looked at the difference between observations and the estimated temperature field. Figures 3 and 4 show two views of the observations minus the temperature field.
Figure 3. Observed temperatures minus the estimated temperature field, centered on Greenwich. Gray line shows the boundary between positive and negative values. Positive values (yellow to red) mean that the observations are warmer than expected.
I found this most fascinating, as it shows the great oceanic heat transport systems that move the energy from the tropics, where there is an excess, to the poles where it is radiated to space. I was surprised to see that the warmest location compared to expectations is the area above Scandinavia. This has to be a result of the Gulf Stream current which is also quite visible along the edge of the East Coast of North America.
I note that as we’d expect, the deserts and arid areas of the world like the Sahara, the Namib, and the Australian deserts are warmer than would be otherwise expected.
You can see another view showing the overall results of the El Nino/La Nina heat pump below in Figure 4. This is the same data as in Figure 3, but centered on the Pacific.
Figure 4. Observed temperatures minus the estimated temperature field, centered on the International Dateline. Gray line shows the boundary between positive and negative values. Positive values mean that the observations are warmer than expected.
Here we can see the area off of Peru that runs cool because the El Nino/La Nina pump pushes warm surface water across the Pacific. This exposes underlying cooler waters. When the warm water hits the Asia/Indonesia/Australia landmasses, the warm water splits north and south and moves polewards. As with the area above Scandinavia, the heat seems to pile up at the polar extremities of the heat transport system. In the case of the Pacific, the northern branch ends up in the Gulf of Alaska. The southern branch ends up where it is blocked by the shallow narrows between the Antarctic Peninsula and the tip of South America.
In any case, that’s what I learned from my wanderings. The beauty of climate is that there are always more puzzles to be solved and oddities to be pondered. For example, why are the western parts of the northern hemisphere continents warmer than the eastern parts?
My best to each of you,
As I’ve Mentioned: If you disagree with someone, please quote the exact words you disagree with so we can all understand your objections.
The Math: I used the form:
Estimated Temperature = a * sunlight + b * elevation + c * sunlight * elevation + m
where a, b, c, and m are fitted constants. The results were as follows:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.052e+01 7.122e-02 -568.9 <2e-16 ***
sunvec 1.675e-01 2.033e-04 823.8 <2e-16 ***
elvec -1.918e-02 7.723e-05 -248.4 <2e-16 ***
sunvec:elvec 4.354e-05 2.485e-07 175.2 <2e-16 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2557 on 64796 degrees of freedom
Multiple R-squared: 0.9479, Adjusted R-squared: 0.9479
F-statistic: 3.933e+05 on 3 and 64796 DF, p-value: < 2.2e-16
where “sunvec” is average gridcell solar energy in W/m2, and elvec is the average gridcell elevation in meters.