Guest Post by Willis Eschenbach
I’ve been wanting to [take] another look at the relationship between net top-of-atmosphere (TOA) radiation changes on the one hand and changes in temperature on the other. As a necessary prelude, I finally have gotten round to an oft-postponed task, that of looking at the thermal lag in different areas of the planet. This is the lag between a change in TOA radiation and a corresponding change in surface temperature. Figure 1 shows my results.
As always when working with CERES data, I find that every graph brings surprises. For example, the wet land areas respond more quickly to changes in TOA radiation than do the dry land areas. Not sure I understand that. Also, you can see the quick response in the Inter-Tropical Convergence Zone (ITCZ) just above the equator in the Pacific. This suggests that the water-thunderstorm cycle transfers the energy more readily to-from the surface, with less thermal lag.
Now, I admit that there are more accurate ways of calculating the lag. However, my method gives the lag to the nearest month, so the error won’t ever be more than half a month. Here is the relationship between raw temperature and TOA radiation at a randomly chosen point in the Atlantic:
Figure 1a. Scatterplots of net TOA radiation versus surface temperature at 35°N, 10°W. Letters in the graphs are the initial letters the months, JFMAMJJASOND. All trends given are in degrees C per 3.7 W/m2 of TOA radiation change (the change expected from a doubling of CO2). Click image for larger version.
As you can see, the actual best fit for the lag is slightly more than two months, but not as large as three months. However, we won’t get much error using the 2 month lag.
In any case, having that lag data, I was able to see what the trend was between temperature and TOA radiation given the lag in each cell. Figure 2 shows that result. I have given the trend in temperature per 3.7 watts per square metre (W/m2) increase in TOA radiation. This is the change in the amount of downwelling TOA radiation that the IPCC says will result from a doubling of CO2. In other words, the graph shows the immediately change in temperature that (might) theoretically result from a doubling of CO2 IF ALL ELSE STAYED UNCHANGED. Of course, things wouldn’t stay unchanged, because change is the rule, not the exception …
… in any case, Figure 2 below shows the relationship between TOA radiation and temperature, with the trend calculated using the gridcell-by-gridcell lag:
This is the raw trend of the relationship between the net TOA radiation and the appropriately lagged temperature response.
However, we still have a problem. This is that because of the thermal lag, the surface temperature doesn’t get as high as it would if there were no lag and the thermal response were instantaneous. I discussed in Time Lags in the Climate System how we can estimate the reduction in amplitude due to the thermal lag. In general, as you might expect, the longer the thermal lag, the smaller the change in temperature.
Once I’ve adjusted the amplitudes upwards to allow for the reductions in amplitude caused by the thermal lag in each gridcell, I get the results shown in Figure 3. This is an estimate of the Transient Climate Response (TCR), which is the short-term response to an increase in net TOA forcing.
Figure 3. Best estimate, transient climate response (TCR) in degrees C per doubling of CO2 (3.7 W/m2 change in TOA radiation.) It differs from Figure 2 in that the amplitude has been increased as a function of the thermal lag.
As is expected, this adjustment increases the overall expected thermal response to the change in net TOA radiation. Note that this adjustment reduces the land/ocean difference, but without removing it entirely. I take this as support for the method being used.
So what can we learn from this? Well, first off, the transient climate response (TCR) value of 0.44°C per 3.7 W/m2 shown in Figure 3 is pretty small compared to the IPCC values. For the 18 climate models that reported results in the IPCC Fourth Assessment Report (AR4), the mean TCR is 1.8 ± 0.1 °C (std. err. of mean) per doubling of CO2. My results in Figure 3 are less than a quarter of their results.
Finally, how does the transient climate response (TCR) relate to equilibrium climate sensitivity (ECS)? The ECS is the long-term response to a change in TOA radiation after all succeeding adjustments have occurred. ECS is the sensitivity that people usually discuss.
Well, the relationship shown by the AR4 models linked above is that the ECS is about 1.82 ± 0.1 (std. err. of mean) times as large as the transient climate response (TCR). With a TCR from Figure 3 of 0.44 degrees C per doubling of CO2, that would put the equilibrium climate sensitivity at 0.8 ± 0.03 degrees C per doubling of CO2.
By comparison, the average of the 18 AR4 climate models linked to above is an equilibrium climate sensitivity of 3.2 ± 0.2 degrees C per doubling of CO2. This is about four times larger than my results.
Please note that I make no overarching claims regarding the accuracy of these measurements and estimates. They represent my best effort in my continuing quest to understand the relationship between the TOA radiation and the temperature.
Regards to all,
Usual Note: If you disagree with someone, please have the courtesy to quote the exact words you think are incorrect so that we can all understand your objection.
Math Note: Using the method in my post linked above, the multiplication factors to increase the amplitude of the temperature cycle based on the individual gridcell thermal lags are 1.0, 1.7, 2.9, and 4.8 for lags of 0, 1, 2, and 3 months respectively. In other words, amplitudes are not increased for 0 months lag; for a one month lag, all amplitudes would be multiplied by 1.7; and so forth.
I have calculated the length of the lag by using the cross-correlation function (ccf) and selecting the lag with the greatest correlation. I understand that there are likely better ways to establish the more precise value, but using the ccf was quick and did what was required.
Data Note: I’m using the CERES EBAF dataset. For the surface temperatures I’ve converted the (calculated) upwelling surface longwave radiation dataset to the corresponding blackbody temperatures. The data starts in March 2000 and ends in February 2014.