Guest Post by Willis Eschenbach
Well, after my brief digression to some other topics, I’ve finally been able to get back to the reason that I got the CERES albedo and radiation data in the first place. This was to look at the relationship between the top of atmosphere (TOA) radiation imbalance and the surface temperature. Recall that the IPCC says that a change in the TOA radiation of 3.7 W/m2 from a doubling of CO2 will lead to a 3°C ± 1.5°C temperature increase. This 3°C per doubling is called the “climate sensitivity”, and its value is an open question.
Figure 1, on the other hand, shows my results regarding the same question of the climate sensitivity. These reveal nothing like a 3°C temperature rise from a doubling of CO2:
Figure 1. Gridcell-by-gridcell linear trends of the change in surface temperature (∆T) given the change in TOA radiation (∆F). Note that the surface temperature data is gridded on a 5°x5° gridcell, while the CERES TOA radiation data is on a 1°x1° gridcell basis. Graph includes a two-month lag between change in forcing and the change in temperature.
There are a variety of interesting aspects to this particular graph. Let me start by describing how I constructed it.
I began by taking the gridded HadCRUT3 temperature data for the period of the CERES study, Jan 2001 to Oct 2005. The HadCRUT data is on a 5°x5° gridcell, so I first expanded that to 1°x1° gridcells. Then I took the first differences (∆T) by subtracting each month from the succeeding month, to get the monthly change in temperature (∆T) in each gridcell.
Then I compared that ∆T dataset to the change in TOA radiation (∆F), which was constructed from the CERES TOA data. For each gridcell, I took the linear trend of the temperature changes ∆T with respect to ∆F.
Of course, the climate sensitivity results from this procedure are in units of temperature change per forcing change, which is °C per watt/square metre. To convert it to change in temperature per doubling of CO2, I multiplied the results by 3.7 W/m2 per doubling of CO2.
Finally, I needed to adjust for the lag in the system. I did this in two ways. First, I selected the lag which gave the largest temperature change, which was a two month lag. These are the results shown in Figure 1. However, this is a cyclical record of the annual fluctuations, so the equilibrium sensitivity will be underestimated. Per the insights gained from my last analysis, “Time Lags in the Climate System“, the time lag is related to the size of the reduction in temperature swing. A 1-2 month lag in the system indicates a reduction in fluctuation of about 50%. So for my final adjustment, I doubled the indicated climate sensitivity. The results of this are the values shown in Figure 1.
Now, I have long argued, solely from first principles, that climate sensitivity is a non-linear function of temperature. I have said that the sensitivity was greater when it is colder, and that it is smaller when it is warmer. I have held that this relationship was non-linear, with a kink at the temperature range for tropical thunderstorm formation. Finally, I have also argued that in some places in the tropics the climate sensitivity is actually negative, due to the action of tropical clouds and thunderstorms.
To test these claims, I plotted the sensitivity for each gridcell shown in Figure 1 against the annual average temperature for that same gridcell. The results are shown in Figure 2. As far as I know, this is the first observational evidence that shows the actual relationship between climate sensitivity and temperature, and it supports all of my contentions about that relationship.
Figure 2. Scatterplot of gridcell climate sensitivity versus gridcell temperature. Colors indicate the latitude, with red at the tropics, yellow in the temperate zones, and blue at the poles. Gray dashed line shows the linear trend, indicating that the climate sensitivity varies generally as -0.009 * temperature + 0.32 (p-value < 1e-16).
There are some important things about this plot. First, it strongly supports my claim that the climate sensitivity varies inversely with the temperature. Next, it shows that a number of areas of the tropics actually do have negative climate sensitivity. Finally, it shows that the relationship is non-linear with a kink at around the temperature for the formation of tropical thunderstorms. This is important corroborative evidence for my hypothesis that the tropical clouds and thunderstorms act as governors of the tropical temperature and are the source of the negative climate sensitivity.
Let me close by railing a bit against the pernicious nature of averages. Consider Figure 2. Normally, far too many climate scientists would take an average of that data, and come up with some number as the average climate sensitivity. But that number is meaningless, and worse, it gives the impression that the sensitivity is a fixed number. It is nothing of the sort. Not only is it not fixed, it is far, far from linear, and it goes negative at times. It is a dynamic response to changing conditions, not some fixed value.
As a result, when we average it, we come away with entirely the wrong impression of what is happening in that most complex of phenomena, the climate system. While averaging is often useful, it conceals as much as it reveals, and it can lead one to badly erroneous conclusions. That is why so many of my graphs and charts show thousands of individual points, as in Figure 2. Only by seeing the whole picture can we hope to understand the system.
My best to all,