A Bayesian decision method for climate change signal analysis

In this paper we would like to put forward another view of climate change signal analysis, namely a data based decision or selection process of specific scenarios (or hypotheses in statistical language). Given at least two scenarios (1) a control one (CTL) from unforced climate model simulations and (2) a set of climate model realizations under an identical external climate forcing, a climate change signal analysis can also be viewed as a decision or selection process of the scenario which is most probable in view of the observations. It is shown that our approach includes the classical fingerprint method. The approach is based on Bayesian decision theory. The selection of hypothesis/scenario uses the Bayes factors. It is exemplified with NCEP/NCAR reanalysis data from 1979 to 1999 as observation, a greenhouse-gas forced scenario (G) with four realizations, and a greenhouse-gas plus sulfate aerosol forced scenario (GS) with two realizations generated by the ECHAM3/LSG from 1880 to 2049. The CTL scenario is obtained from an unforced control run of ECHAM3/LSG of 1400 years length. To provide a vivid example, Northern Hemisphere extratropics area-averaged and 13-month running mean 2 m and 70 hPa temperature anomalies are selected as analysis variables. The Northern Hemisphere extratropics from 1979-1999 are considered as the most reliable area of NCEP/NCAR reanalysis data and the two dimensional setting provides valuable insight into the results. The decision test between the CTL and G scenarios shows that observations of near surface and lower stratosphere temperatures provide evidence against the CTL scenario since the late 1990s even if the prior probability for the G scenario is a third of that of the CTL scenario. The second decision experiment with a three-scenario case shows that both climate change scenarios (G and GS) have higher evidence in view of the observations of the late 1990s than the CTL scenario. A sensitivity analysis with respect to the strength of the natural variance in observations indicates that the specification of the level of the observed natural variability is a crucial factor in the Bayesian decision. In both decision experiments some of the decisions are based upon observations which have very small likelihood value given any of the scenarios, which might be due to the omission of stratospheric ozone forcing in climate change simulations or volcanic/solar forcing in the no change scenario simulation.