Temperature and TOA Forcing

Guest Post by Willis Eschenbach

I’ve been thinking about temperature and top-of-atmosphere (TOA) forcing. TOA forcing is the imbalance between the TOA upwelling and downwelling radiation. The CERES satellite dataset contains observations of the TOA radiation imbalance on a gridcell-by-gridcell basis. It is calculated as the downwelling solar radiation for that month by gridcell, minus upwelling reflected solar radiation, minus upwelling longwave radiation. Figure 1 shows the distribution of the TOA radiation imbalance around the planet.

Figure 1. Average top-of-atmosphere (TOA) imbalance. 

Some areas in Figure 1, such as those around the tropics, absorb more radiation than they emit (positive values). The extra-tropics and the poles, on the other hand, emit more radiation than they are absorbing (negative values). The balance is maintained by the constant transfer of heat between the tropics and the poles by means of the ocean and atmosphere .

We can also take a look at the amazing stability of the net TOA radiation over time. Figure 2 shows the month-by-month changes in the global net TOA radiation.

Figure 2. Decomposition of the net TOA radiation into the seasonal and residual components. Top panel shows the raw data, the observed monthly changes in the net TOA radiation. The middle panel shows the seasonal component, i.e. the average values which repeat every year. The bottom panel shows the observed data minus the seasonal component. Blue line shows the gaussian smooth of the raw data. Dotted horizontal gold lines show the standard deviation of the residuals.

The annual swings in the net TOA radiation are the result of the earth moving nearer to and further from the sun. As one might expect in a responsive system, the change in net TOA radiation is considerably smaller than the change in the solar radiation. When the downwelling solar radiation varies, the variation is partially counteracted by changes in the upwelling longwave and shortwave.

As mentioned, the net TOA radiation is also remarkable for its stability (bottom panel, Figure 2). The standard deviation of the global imbalance in net TOA radiation is about six-tenths of a watt per square metre (dotted horizontal gold lines). Note also that over the fourteen-year period there is no trend in the net TOA radiation.

With all of that as prologue, let me move on to my latest peregrinations through the CERES satellite dataset. I decided to take a look, on a gridcell by gridcell basis, at the relationship between the net TOA radiation imbalance and the surface temperature. It is often useful to look separately at the land and the ocean. Figure 3 is a scatterplot of the net TOA radiation versus the surface temperature, by gridcell, looking at just the ocean data.

Figure 3. Annual averages, ocean temperature versus net TOA radiation imbalance, ocean only. Blue dots show individual ocean gridcells. Red line shows a loess smooth of the data. Areas below freezing are ice-covered ocean. Dotted black horizontal line shows 30°C, which is the approximate maximum open ocean average temperature. A positive net TOA value shows that incoming solar is greater than outgoing solar + longwave.

As one might expect, there is indeed a relationship between the sustained TOA imbalance and the temperature. And as one might also expect, increasing net TOA radiation is associated with increasing temperature. However, the relationship is far from linear. Instead, it varies with the temperature.

Temperature response to forcing is largest at temperatures below freezing (steeply increasing red line at left of Figure 3). Above freezing the temperature response is roughly linear up to about 20°C or so. Above about 20°C, the temperature becomes less and less responsive to increasing radiation (leveling off of red line at top right of Figure 3).

Note that in fact, we should expect this pattern. This is in part because for any heat engine, in general parasitic losses go up as some increasing function of input energy. A car is a good example. If you double the amount of gas it’s getting, you don’t get twice the speed. Similarly, we’d expect a decreasing temperature response as the input energy continues to increase. I’ve previously shown that parasitic losses (sensible and latent heat losses from the surface) increase with temperature in a post entitled Marginal Parasitic Loss Rates.

As I mentioned above, the relationship between TOA radiation imbalance and surface temperature over the ocean is far from linear. But that non-linearity pales compared to the situation over the land. Figure 4 shows that situation.

Figure 4. As in Figure 3, but for land only. 

That’s about as non-linear as I can imagine. Note how there seems to be some kind of upper limit on land temperatures regardless of the TOA imbalance. Now, some of the non-linearity comes from altitude, since the higher you go the colder it gets. The very cold data at the bottom of Figure 4, for example, comes from the high plateaus of Antarctica. However, adjusting for altitude at a nominal rate of 1°C per hundred metres of elevation only solves part of the problem. Figure 5 shows the same data used in Figure 4 after adding one degree per hundred metres of elevation.

Figure 5. As in Figure 4, but with the temperatures adjusted for elevation by adding one degree C for every hundred metres of altitude. Note the different scale from Figure 4.

As you can see, although this is a crude adjustment method, it brings Antarctica much more into line. However, it doesn’t change what’s happening up at around 30°C. Just as in the ocean, at the top end the land temperature is pretty much decoupled from the radiation imbalance.

Conclusions? I don’t have a whole lot of them. This is all part of my continuing effort to understand this marvelous and mysterious climate system. The one solid conclusion is that the relationship between forcing and temperature is both non-linear and temperature dependent, with the temperature response generally diminishing with increasing temperature. My other conclusion is that given the significant lack of linearity, any average value for the relationship between TOA radiation and temperature is bound to be both misleading and meaningless.

Best regards to all,

w.

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