## THE TRUE MEANING OF NUMBERS...

Gavin has already discussed John Christy’s misleading graph earlier in 2016, however, since the end of 2016, there has been a surge in interest in this graph in Norway amongst people who try to diminish the role of anthropogenic global warming...

I think this graph is warranted some extra comments in addition to Gavin’s points because it is flawed on more counts beyond those that he has already discussed. In fact, those using this graph to judge climate models reveal an elementary lack of understanding of climate data.

Fig. 1. Example of Christy’s flawed evaluation taken from Comparing models to the satellite datasets.

Different types of numbers
The upper left panel in Fig. 1 shows that Christy compared the average of 102 climate model simulations with temperature from satellite measurements (average of three different analyses) and weather balloons (average of two analyses). This is a flawed comparison because it compares a statistical parameter with a variable.

A parameter, such as the mean (also referred to as the ‘average’) and the standard deviation, describe the statistical distribution of a given variable. However, such parameters are not equivalent to the variable they describe.

The comparison between the average of model runs and observations is surprising, because it is clearly incorrect from elementary statistics (This is similar statistics-confusion as the flaw found in the Douglass et al. (2007)).

I can illustrate this with an example: Fig. 2 shows 108 different model simulations of the global mean temperature (from the CMIP5 experiment). The thick black line shows the average of all the model runs (the ‘multi-model ensemble’).

Fig. 2. Global mean temperature from ensemble simulations (CMIP5) and the NCEP/NCAR reanalysis 1 (baseline: 1961-90). (Figure source code)

None of the individual runs (coloured thin curves) match the mean (thick black curve), and if I were to use the same logic as Christy, I could incorrectly claim that the average is inconsistent with the individual runs because of their different characters. But the average is based on all these individual runs. Hence, this type of logic is obviously flawed.

To be fair, the observations shown in Cristy’s graph were also based on averages, although of a small set of analyses. This does not improve the case because all the satellite data are based on the same measurements and only differ in terms of synthesis and choices made in the analyses (they are highly correlated, as we will see later on).

By the way, one of the curves shown in Fig. 2 is observations. Can you see which? Eyeballing such curves, however, is not the proper way to compare different data, and there are numerous statistical tests to do so properly.

Different physical aspects
Christy compared temperatures estimated for the troposphere (satellites and balloons) with near-surface temperature computed by global climate models. This is a fact because the data portal where he obtained the model results was the KNMI ClimateExplorer. ClimateExplorer does not hold upper air temperature stored as 3D-fields (I checked this with Geert Jan van der Oldenborgh)(correction: ‘taz’ is zonally integrated temperature as a function of height but does not take into account the differences between land and sea. Nevertheless, this variable still does not really correspond closely with those measured from satellites)

A proper comparison between the satellite temperature and the model results needs to estimate a weighted average of the temperature over the troposphere and lower stratosphere with an appropriate altitude-dependent weighting. The difference between the near-surface and tropospheric temperature matters as the stratosphere has cooled in contrast to the warming surface.

Temperature from satellites are also model results
It is fair to compare the satellite record with model results to explore uncertainties, but the satellite data is not the ground truth and cannot be used to invalidate the models. The microwave sounding unit (MSU), the instrument used to measure the temperature, measures light in certain wavelength bands emitted by oxygen molecules.

An algorithm is then used to compute the air temperature consistent with the measured irradiance. This algorithm is a model based on the same physics as the models which predict that higher concentrations of CO2 result in higher surface temperatures.

I wonder if Christy sees the irony in his use of satellite temperatures to dispute the effect of CO2 on the global mean temperature.

It is nevertheless reassuring to see a good match between the balloon and satellite data, which suggests that the representation of the physics in both the satellite retrieval algorithm and the climate models are more or less correct.

How to compare the models with observations
The two graphs (courtesy of Gavin) below show comparisons between tropospheric mean temperatures (TMT) that are comparable to the satellite data and include confidence interval for the ensemble rather than just the ensemble mean. This type of comparisons is more consistent with standard statistical tests such as the students t-test.

The graphs also show several satellite-based analyses: the Remote Sensing Systems (RSS; different versions), University of Alabama in Huntsville (UAH; Different versions), and NOAA (STAR). All these curves are so similar (highly correlated) that taking the average doesn’t make much difference.

Fig. 3. Comparison between the evolution of the global mean tropospheric temperature (TMT). From Gavin.

According to Fig. 3, the tropospheric temperature simulated by the global climate models (from the CMIP5 experiment) increased slightly faster than the temperatures derived from the satellite measurements between 2000 and 2015, but they were not very different. The RSS temperatures gave the closest match with the global climate models.

Fig. 4. Comparison of global mean tropospheric temperature trends where the satellite estimates are shown with confidence intervals. Trends for each model run also have similar error bars (not shown), but the trend statistics for the ensemble is presented through a histogram. From Gavin.

Fig. 4 shows a trend analysis for the 1979-2016 interval where the satellite-based temperature trends are shown with appropriate error bars. The trends from the satellite analyses and the model results overlap if the confidence limits are taken into consideration.

The story behind the upper tropospheric warming
The biggest weight of the troposphere temperature trends come from the tropics because it accounts for the largest volume (half of the Earth’s surface area lies between 30°S and 30°N due to its geometric shape), and they are therefore sensitive to conditions around the equator. This is also where large-scale convection takes place that produce bands of high clouds (the Inter-Tropical Convergence Zone – ITCZ).

Cloud formation through convection and condensation is associated with release of latent heat and influences the temperatures (e.g. Vecchi et al., 2006). It is part of the hydrological cycle, and a slow change in the atmospheric overturning, moisture and circulation patterns is expected to have a bearing on the global tropospheric temperature trend estimates.

This means that the picture is complex when it comes to the global tropospheric temperature trends because many physical processes have an influence that take place on a wide range of spatial scales.

Hard evidence of misrepresentation
Despite the complicated nature of tropospheric temperatures, it is an indisputable fact that Christy’s graph presents numbers with different meanings as if they were equivalent. It is really surprising to see such a basic misrepresentation in a testimony at the U.S. House Committee on Science, Space & Technology. One of the most elementary parts of science is to know what the numbers really represent and how they should be interpreted.

## References

1. G.A. Vecchi, B.J. Soden, A.T. Wittenberg, I.M. Held, A. Leetmaa, and M.J. Harrison, "Weakening of tropical Pacific atmospheric circulation due to anthropogenic forcing", Nature, vol. 441, pp. 73-76, 2006. http://dx.doi.org/10.1038/nature04744

by: rasmus @ 2 March 2017

source: http://www.realclimate.org/

original story HERE

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