Putting It On The Line

Guest Post by Willis Eschenbach

Thanks to an alert commenter, half of my last post was shown to be in error. Like most folks, I really, really hate to be publicly wrong, and of course I do my utmost to avoid it. But sometimes I overlook something, or my logical staircase is missing some steps, and there I am. Wrong. In public. Again. Not pretty.

However, when I regained some semblance of detachment I realized once again that speed in finding my own errors is the most valuable part of writing for the web. Rather than spending months going down some error-lined rabbit-hole, I’m handed my head on a platter right away, so I can fix what I did wrong and move on. That’s the good part of putting it all on the line in public—my illusions don’t last long.

In this case, I’d misunderestimated the effect of the movement of heat from the tropics to the poles. Horizontal movement of heat is called “advection”. Let me start with the solar input, the only input I considered in my previous post:

Figure 1. 15-year average, solar energy input. CERES data, Mar 2000 – Feb 1015. Gray lines show the latitudes receiving the global average of 340 W/m2. All graphics show 1°x1° gridcell data.

From the tropics to the poles, there is a gradient of about 250 W/m2. However, the incoming solar is not the only energy involved. We also have the energy that is constantly being advected from the tropics to the poles. Figure 2 shows where that advected energy comes from and goes to.

Figure 2. Amount of energy either exported (red/yellow) or imported (green/blue) by each gridcell.

As you would expect, in general the areas receiving more than the average amount of solar energy export some of it, while those receiving less than the average receive some of that exported energy … but there are notable exceptions in the desert areas. You can see that the entire Sahara/Sahel/Arabian Peninsula is a net importer of energy. I ascribe this to the lack of water. Having ample water allows for the movement of latent heat, which in turn enables the entire hydrological cycle. But I digress.

Over the orange/red area the earth receives about 112 petawatts of energy. The two poles combined, on the other hand, only receive about half of that, 63 petawatts. And there are about 12 petawatts of energy constantly being moved polewards from the tropics to the two poles. By comparison, the total energy used by humans is about 12 terawatts … about a thousandth of the amount of energy exported from the tropics to the poles … but I digress.

The important issue here is that I was wrong to use just the solar input to estimate the net energy coming into each gridcell. In addition, I needed to include the advected energy shown in Figure 2.

To show the distribution of this net gridcell energy input, in Figure 3, I’ve subtracted the advected energy (Figure 2) from the solar energy (Figure 1). This give us the net energy being added to each gridcell, after advection.

Figure 3. Net amount of energy (solar ± advection) entering each gridcell.

Now, this is most interesting. I would never have guessed that the location on the planet that receives the most net energy is the North African desert. And of course including the advected energy has the effect of reducing the tropical/polar inequality. After advection the 250 W/m2 difference drops to about 200 W/m2 from the tropics to the poles.

Note also that the poles get a significant boost from advection, a difference of about a hundred more watts per square metre. However, the subtraction of the advection from the incoming solar has left one thing unchanged—the overall average. This is what we’d expect, since the system hasn’t added or subtracted any energy, just moved it around.

So I think that now we’re ready to compare Figure 3, the net gridcell energy input, with the surface temperature. In order to adjust for the effect of altitude, I have used the “potential temperature”, which is the observed gridcell temperature adjusted for the average altitude of the gridcell. Of course, for the ocean the potential temperature is equal to the observed temperature.

Figure 4 shows a scatterplot of potential temperature versus the net amount of energy entering each gridcell. As is my usual custom, one of the first things that I do is to calculate the Gaussian average to see what is happening with the data.

Figure 4. Scatterplot, net gridcell energy input (top-of-atmosphere solar plus/minus advection) versus surface potential temperature (observed temperature adjusted for altitude).

Now, I’m not much of a fan of straight-line trends. But I have to follow the data where it leads, and in this case the Gaussian average shows the underlying straight-line nature of these particular trends. So in Figure 5, I’ve added those trends.

Figure 5. Scatterplot, net gridcell energy input (top-of-atmosphere solar plus/minus advection) versus surface potential temperature (observed temperature adjusted for altitude).

I found this chart most fascinating. The area at the far left with the dark blue trendline is mostly Antarctica, where it is high, cold, and dry. It appears that the Antarctic Plateau stays cold pretty much regardless of the variations in incoming energy. This may relate to the peculiar nature of the South Polar vortex, which keeps it somewhat isolated from the rest of the climate system.

Of particular interest is the “knuckle” at ~ 342 W/m2. This value is quite close to the global average of 340 W/m2. So it appears that areas which have below-average total incoming energy warm quite a bit with increasing energy … but in areas receiving more than the average level of incoming energy, the observations show that the response to increasing incoming energy goes nearly flat.

Now, some may recall my oft-repeated description of the nature of temperature regulation by emergent phenomena. The short version is that above some thermal threshold, phenomena such as cumulus clouds and thunderstorms emerge to cool the surface. These act so effectively that they damp the temperature increase down to almost nothing.

And indeed, this is what we see in Figure 5. Below a certain threshold, we don’t get things like dust devils and thermal cumulus and tropical thunderstorms and the like, so the sun is free to warm the earth without opposition. In that section of the planet, between about three hundred and three hundred forty W/m2 of incoming energy, the temperature does indeed rise rapidly. In fact, it rises at a rate of about 3°C per doubling of CO2 (using the IPCC value of 3.7 W/m2 per doubling), which is the classic estimate of the “climate sensitivity”.

But above that threshold, we get one or more of the variety of thermoregulating phenomena that emerge to cool the surface … let me suggest that this is the reason that the so-called “climate sensitivity” has proven to be so hard to pin down—because as I have argued for over a decade now, “climate sensitivity” is not a constant. Instead the “climate sensitivity” differs in different situations, and as a result, the idea that we can push a straight-line trend through the differences is a simplistic view of a complex reality.

Anyhow … that’s what came of the most recent case of my being shown to be wrong …

w.

My Usual Request: Misunderstanding is far too common, particularly on the web, but we can minimize it by being specific about our differences. If you disagree with me or anyone, please quote the exact words you disagree with, so we can all understand the exact nature of your objections. I can defend my own words. I cannot defend someone else’s interpretation of some unidentified words of mine.

My Other Request: If you believe that e.g. I’m using the wrong method or the wrong dataset, please educate me and others by demonstrating the proper use of the right method or identifying the right dataset. While demonstrating that I’m wrong about methods or data is valuable, it doesn’t advance the discussion as much as if you can point us to the right way to do it.