Leroy, S.S., J.A. Dykema, and J.G. Anderson, “Scalar prediction in climate using data and model,” Submitted to J. Climate (2008).
Scalar detection in climate change research, having taken the form of optimal detection/linear multi-pattern regression, has been used in the recent past to detect multiple climate signals in the presence of natural inter- annual variability and associate those signals with specific causes. It has been applied to many climate observables to show high probabilities of human influence on climatic trends. One of the sources of uncertainty and instability in this methodology concerns the degree to which one can trust the fine details of a signal's shape in using it as a fingerprint associated with forced climate change. In a recent paper by Huntingford et al.~(2006), this problem has been largely solved using multi-model ensemble simulations of signal shapes to ascertain the degree to which details of signal shapes can be trusted. We show that this method, when generalized in the context of Bayesian inference, is a powerful tool----one that carefully incorporates the scientific method----for predicting arbitrary scalar trends in the climate system that optimally considers both observed trends and ensemble model prediction of those trends. In this method, arbitrary but informative data sets with credible trends can be used in conjunction with a large ensemble of disparate climate models to forecast anything from regional trends in temperature, humidity, cloud-cover, and precipitation to global scale trends in surface air temperature or widening of the Hadley circulation. The method weights data by inter-annual variability and connects arbitrary data sets to scalar quantities of interest according to the certainty of the physics that relates the data type to the quantities. Depending on the data set and geophysical variable of interest, forecast accuracy for that variable can be improved by large factors over simple trending of past measurements of that variable. We will present a Bayesian derivation of this methodology and give several illustrative examples for its application.