ABSTRACT: A new method is proposed for exploring the amplification of the atmosphere with respect to the surface. The method, which I call “temporal evolution”, is shown to reveal the change in amplification with time. In addition, the method shows which of the atmospheric datasets are similar and which are dissimilar. The method is used to highlight the differences between the HadAT2 balloon, UAH MSU satellite, RSS MSU satellite, and CGCM3.1 model datasets.
“Amplification” is the term used for the general observation that the atmospheric temperatures tend to vary more than the surface temperature. If surface and atmospheric temperatures varied by exactly the same amount, the amplification would be 1.0. If the atmosphere varies more than the surface, the amplification will be greater than one, and vice versa.
Recently there has been much discussion of the Douglass et al. and the Santer et al. papers on tropical tropospheric amplification. The issue involved is posed by Santer et al. in their abstract, viz:
The month-to-month variability of tropical temperatures
is larger in the troposphere than at the Earth’s surface.
This amplification behavior is similar in a range of
observations and climate model simulations, and is
consistent with basic theory. On multi-decadal timescales,
tropospheric amplification of surface warming is a robust
feature of model simulations, but occurs in only one
observational dataset [the RSS dataset]. Other observations show weak or
even negative amplification. These results suggest that
either different physical mechanisms control
amplification processes on monthly and decadal
timescales, and models fail to capture such behavior, or
(more plausibly) that residual errors in several
observational datasets used here affect their
representation of long-term trends.
I asked a number of people who were promoting some version of the Santer et al. claim that “the amplification behaviour is similar in a range of observations and climate model simulations”, just what studies had shown these results? I was never given any answer to my questions, so I decided to look into it myself.
To investigate whether the tropical amplification is “robust” at various timescales, I calculated the tropical and global amplification at all time scales between one month and 340 months for a variety of datasets. I used both the UAH and the RSS versions of the satellite record. The results are shown in Figure 1 below. To create the graphs, for every time interval (e.g. 5 months) I calculated the amplification of all contiguous 5-month periods in the entire dataset. I took the average of the results for each time interval, and calculated the 95% confidence interval (CI). Details of the method are given in Appendices 2 and 3.
I plotted the results as a curve which shows the average amplification for the various time periods.

Figure 1. Change of amplification with time periods. T2 and TMT are middle troposphere measurements. T2LT and TLT are lower troposphere. Typical 95% CIs are shown on two of the curves. Starting date is January 1979. Shortest period shown is three months. Effective weighted altitudes are about 4 km (~600 hPa) for the lower altitude measurements, UAH T2LT and RSS TLT. They are about 6 km (~500 hPa) for the higher measurements, UAH T2 and RSS TMT.
I love surprises, and climate science holds many … despite the oft repeated claims that the “science is settled”. And there are several surprises in these results, which is great.
1. In both the global and tropical cases, the higher altitude data shows less amplification than the lower altitude. This is the opposite of the expected result. In the UAH data, T2LT, the lower layer, has more amplification than T2, the higher layer. The same is true for the RSS data regarding TLT and TMT. Decreasing amplification with altitude seems a bit odd …
2. In both the global and tropical cases, amplification starts small. Then it rises to about double its starting value over about ten years. It then gradually decays over the rest of the record. The RSS and the UAH datasets differ mainly in the rate of this decay.
3. The 1998 El Nino is visible in every record at about 240 months from the starting date (January 1979).
In an effort to get a better handle on the issues, I examined the HadAt2 balloon record. Here, finally, I see crystal clear evidence of tropical tropospheric amplification.
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