A Second Look At Radiation Versus Temperature

Reblogged from Watts Up With That:

Guest Post by Willis Eschenbach [See Update at end]

I kept going back and looking at the graphic from my previous post on radiation and temperature. It kept niggling at me. It shows the change in surface temperature compared to the contemporaneous change in how much energy the surface is absorbing. Here’s that graphic again:

Figure 1. From my previous post. It is a scatterplot showing the dependence of temperature on the total downwelling radiation (longwave plus shortwave) absorbed by the surface.

What I found botheracious were the outliers at the top of the diagram. I knew what they were from, which was the El Nino/La Nina of 2015-2016.

After thinking about that, I realized I’d left one factor out of the calculations above. What the El Nino phenomenon does is to periodically pump billions of cubic meters of the warmest Pacific equatorial water towards the poles. And I’d left that advected energy transfer out of the equation in Figure 1. (Horizontal transfer of energy from one place on earth to another is called “advection”).

And it’s not just advection of energy caused by El Nino. In general, heat is advected from the tropics towards the poles by the action of the ocean and the atmosphere. Figure 2 shows the average amount of energy exported (plus) or imported (minus) around the globe.

Figure 2. Net energy exported or imported by each 1° latitude by 1° longitude gridcell. The amount of the imbalance is calculated as the top of atmosphere (TOA) energy imbalance (downwelling solar minus upwelling longwave and reflected solar)

If there is no advection of energy, which occurs at the white line in Figure 2, then solar entering the system equals energy leaving to space. Figure 2 shows how the tropics absorbs much more than it is radiating. The difference is the energy transferred polewards.

As you can see above, the strongest energy export is from the tropical Pacific. And on the other hand, the most energy is imported into the Arctic. The Arctic receives more than the Antarctic because the entire Arctic Ocean is getting advected energy in the form of warm water moved up from the tropics. Antarctica, on the other hand, is only strongly warmed along the edges, with the interior receiving less energy.

Now, having that advection data allows me to make a better calculation of the relationship between surface energy absorption and temperature change. To do that, I simply adjusted the energy received by each gridcell in the prior calculation (Figure 1) according to the amount of energy that that gridcell either imported or exported. Figure 3 shows that result.

Figure 3. Scatterplot of surface temperature versus the sum of surface downwelling longwave and shortwave energy, plus or minus the amount of energy advected.

This is an interesting result. Note that the outliers from the El Nino phenomenon seen in Figure 1 are now much closer to the trend line. And the same is true for the outliers at the bottom left of Figure 1. (Statistically, this is reflected in an improvement in the R^2 value from 0.72 in Figure 1, to 0.78 after adjusting for advected energy as shown in Figure 3 .)

I note also that the trend in Figure 3 (0.39°C per 3.7 W/m2) is virtually identical to the 0.38 trend seen in Figure 1. Since the amount of energy exported is equal to the amount of energy imported, we’d expect the errors from ignoring advection to be symmetrical. I take the lack of change in the trend as support for the idea that some amount of the errors in Figure 1 were indeed due to ignoring advection.

[UPDATE] As in my previous post, I’ve compared the results to those we get using the HadCRUT temperature dataset in place of the CERES dataset. First, here is the previous comparison:

Figure 4. As in Figure 1 above, showing results without advected energy, but using the HadCRUT surface temperature dataset.

Note that as with the CERES dataset, the high values are from the El Nino phenomenon. Now, compare Figure 4 to Figure 5 below, which includes the advected energy.

Figure 5. As in Figure 4, but including the advected energy.

In a very similar manner to the CERES data, including the advected energy brings the El Nino data much closer to the trend line. In addition, as with CERES data, the trend is unchanged by the advected energy.

Incremental improvements …

Me, I’m working at finishing out the interior of a friend’s house on the Kenai River in Alaska, so my response time to the comments may be longer.

Best to all and sundry … and if “all” is really all, then what is “sundry”?

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