Global Warming and Statistics
One of the potential problems/complaints with the Anthropogenic Global Warming (AGW) issue is how the data is often presented for public consumption. Frequently one will see graphs such as these two,
Clearly the trend line (the white lines in the two graphs) are statistically significant. But is anybody out willing to say that these trends are “real”?
If you answered “No,” then you pass. The problem with first one is that it is genereted via a random walk,
The problem with the second graph is that it was generated by an autoregressive process of order 1 (AR1),
where b is greater than zero and less than one in absolute value, and in both equations e is the error term that is normally distributed. In short, the trends are spurious. Further, in both of the specific cases above if one were to extend the data set to N = 1,000 the sign of the coefficient for the trend variable would reverse itself Now, at the same time just because this potential problem exists it does not mean that it is indeed a problem with the data.
This brings us to studies of attribution. That is the study where the causes of global warming are disentangled. How much of global warming is due to man, changes in solar irradiance, etc. These are things that are not discernable from a simple linear trend model. Take for example the second model. The coefficient on the trend variable is .00898. If this were temperature data that might be 100 years worth of temperature data and the coefficient would represent the increase in temperature per year (about 1 degree per century). However, even if this trend is legitimate it might still be the case that the anthropogenic portion of that warming is say 20%, that is about .2 degrees for the last century. This is important because it gets to the heart of the mitigation issue. If the anthropogenic portion is not large then mitigation efforts might do very little and we’d be essentially wasting money.
Further, there are problems with the data that is used for this. The data has a short history. The data has both anthropogenic and natural influences that are not related to global warming (the urban heat island effect for example). There is also paleoclimate reconstructions, but in looking at the IPCC reports on this a limited number of studies are referenced virtually all of these are in some way connected to Mann et. al. 1998 which is the cause for a great deal of controversy.
For all of these reasons, I find the portrayal of global warming via simple linear trends dubious at best and quite possible outright misleading. Having a good understanding of the underlying process is essential to good modelling. Personally, I’m not convinced, based on what I’ve read, that the understanding is all the good. In any event I wish the use of simple linear trends were not used. Granted it makes communicating the results more difficult, but I think it would be more informative.