In my previous post, Is There a True Average Global Temperature, I compared the mean temperature to the fourth root of the fourth moment of the temperature (the mean of T^4). Dr. Pielke was kind enough to post a comment that I misinterpreted his weblog. He says the “it is easy to show that weighting by (T+T’)**4 significantly emphasizes the lower latitudes”.

In this post, I will calculate the radiative imbalance due to the change in temperature for several years. I will briefly describe the procedure. I used the NCEP/NCAR reanalysis data as before, and calculated the mean temperature for the entire time series. I assume that each grid emits as a blackbody, and thus used the Stefan-Bolzemann Law to calculate the blackbody irradiance for both the mean temperature and the yearly mean temperature. These were then subtracted to give the “radiative imbalance” at each point for the given year.

I chose four years to apply the analysis; 1950, 1988, 1998, and 2007. These were chosen semi-randomly. I wanted last year, and a year pre-1980. The other years were because they are “interesting” years. Let’s have a look at 1950. The units of all the following figures are in W/m2.

Notice that the global average radiative imbalance is around zero - there are just as many points above zero as there are below zero. This year actually has a negative temperature anomaly compared to the mean of the entire time series. The thermodynamic temperature is regionally dependent. Areas of positive anomalies are located in eastern Asia, and negative anomalies are in the central Pacific.

1988 is interesting because this is supposed to be an El Nino year. Yet there is a negative anomaly in the central Pacific. There are large positive anomalies near Antarctica and over a large part of Asia. It is clear that this year has more positive anomalies than negative anomalies.

1998 is another El Nino year, and we can see that there is a positive anomaly in the eastern Pacific. The pattern does not look ENSO-like, but that could be because I am taking yearly averages. Similar to 1988, this year has mostly positive anomalies. The greatest anomalies tend to be located along the equator. However, there are positive anomalies in northern Canada and in Antarctica.

The final map shows the year 2007. There is an extremely large positive deviation over much of the Northern Hemisphere. The weak La Nina shows up as a negative deviation in the eastern Pacific.

I don’t want to generalize from just looking at 4 years, but it does not appear that T^4 emphasizes the lower latitudes.

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