Optimal Detection of Regional Trends Using Global Data

A complete accounting of model uncertainty in the optimal detection of climate signals requires normalization of the signals produced by climate models; however, there is not yet a well-defined rule for the normalization. This study seeks to discover such a rule. The authors find that, to arrive at the equations of optimal detection from a general application of Bayesian statistics to the problem of climate change, it is necessary to assume that 1) the prior probability density function (PDF) for climate change is separable into independent PDFs for sensitivity and the signals' spatiotemporal patterns; 2) postfit residuals are due to internal variability and are normally distributed; 3) the prior PDF for sensitivity is uninformative; and 4) a continuum of climate models used to estimate model uncertainty gives a normally distributed PDF for the spatiotemporal patterns for the climate signals. This study also finds that the rule for normalization of the signals' patterns is a simple division of model-simulated climate change in any observable quantity or set of quantities by a change in a single quantity of interest such as regionally averaged temperature or precipitation. With this normalization, optimal detection yields the most probable estimates of the underlying changes in the region of interest due to external forcings. Data outside the region of interest add information that effectively suppresses the interannual fluctuations associated with internal climate variability.