Relating Lower Tropospheric Temperature Variations to The Surface Temperature Variations: An observation based approach

When discussing climate data, it is often the case that people attempt to compare, directly, the surface and lower tropospheric temperature anomalies. This neglects the fact that the two measures are actually of different things. The satellite temperatures are measuring large parts of the atmosphere, whereas the surface data is attempting to measure temperature variations in a much shallower layer. So what, then, to make of the relationship between the two? While models generally predict that surface temperature variations will translate into basically proportional variations aloft, it is not necessarily the case that this would be so in reality. So how to see how the atmosphere actually behaves? Well, we have observational data, and I will argue that apart from potential long term biases, we can be pretty confident that both the surface and tropospheric data reflect, on an inter-annual basis the same natural climate fluctuations, from ENSO and volcanoes, which represent real signals. By comparing HadCRUT from November 1978 to May 2011, the currently available overlap with UAH, I will illustrate how these fluctuations are related between the two. To start with I will remove the OLS trends from both datasets (I will also try some other methods of removing the long term variations, like detrending using my smoothing technique) Which looks like this:

UAH residuals are in blue, HadCRUT in red. Now my first test was to see what the ratio their standard deviations  is, and it turns out to be about 1.46 (0.179/0.123) of UAH residual standard deviation and HadCRUT residual standard deviation. I expect that this overestimates the ratio of their actual co-varying behavior, due to the presence of un-related noise at from month to month. At any rate, a best fit of a regression of HadCRUT residuals on the UAH residuals yields a slope of about 1.07 and an r squared of about .54. So clearly there is a lot of noise still, but the satellite data clearly varies slightly more than the surface data in the same changes. Next, I do the same thing with twelve months smooths:

Now the ratio of standard deviations is about 1.49 (0.135/0.091) the slope is about 1.32 and the r squared about .78. At this point I think it is pretty clear that variations, at least in the short term, of surface temperatures are amplified in the troposphere. So now we come to the interesting bit (to me anyway): while this behavior is seen in the short term variations of surface and tropospheric temperatures, it is distinctly absent from the long term trends, which suggests something different is going on with the data’s long term trends than in the fluctuations: our ratios for the short term range from 1.07 to 1.49, while the trend ratio is about 0.898. Clearly there is something different going on with the long term trend.

Now personally, I think that the satellite data are pretty well supported by careful analyses done by John  Christy, so I think there are essentially three possible explanations (not necessarily mutually exclusive) of what is going on here:

1. The surface data contain a spurious warm bias due to contamination from nonclimatic effects and data quality (see for example this)

2. This a real feature of climate behavior due to different physical processes controlling the long term relationship between surface and tropospheric temperatures.

3. The surface contains additional real, climatic long term warming due to an effect which does not extend into the troposphere as a whole. This process must be pretty different from greenhouse gases, which should create warming throughout the troposphere, not isolated to the surface. Landuse seems a probable candidate.

Note that if either 2 or 3 are correct, then there is an important factor which present climate models must be missing or getting quite wrong, since they do not decouple the surface and tropospheric rates this way, but rather amplify the long term trends, too. If 1 is correct, then current models are overestimating climate sensitivity by being fit to surface temperatures with a non-climatic warming. Whatever the explanation, current mainstream interpretations of surface warming need to be re-examined, since they do not account for this feature of the data.

Oh, and I am of course going to check on how a different method detrending (my smoothing, for example) effects the numbers, but that will take a little more time. So I’ll get back to you.

UPDATE: As promised, I have tried looking at amplification with a more nonlinear detrending method, using the smoothing method I described here, (the approach that does not average all the smooths). No plots this time since you can hardly tell the difference, I think. First, for the monthly detrended, the standard deviation ratio was about 1.49, the slope about .954 and r squared of .409, the twelve month averages standard deviation ratio of about 1.56, a slope of 1.38 r squared of .781, finally comparing the relationship between the non-linear trends, it’s a slope of .928 and r squared of .919; So the final result is a range of short term amplification factors from .954 to 1.56, and long term from .898 to .919, clearly while short term fluctuations at the surface tend to be amplified in the troposphere, this is not the case over the long term.