Detecting Climate Signals: Some Bayesian Aspects

A Bayesian approach to detecting forced climate signals in a dataset is presented. First, the detection algorithm derived is shown to be capable of uniquely identifying several signals optimally. Other detection techniques are shown to be limiting cases. Second, this approach naturally lends itself to rating models relatively according to their predictions. Both the accuracy of the model prediction and the precision of the prediction are accounted for in rating models. In general, complex models are less probable than simpler models. Finally, this approach to detection is used to detect a signal induced by the solar cycle in the surface temperature record over the past 100 yr. The solar cycle signal-to-noise ratio is found to be 1 but is probably not detected. Estimates of the natural variability noise are taken from model prescriptions, each of which is vastly different. The Geophysical Fluid Dynamics Laboratory models, though, best match the residual temperature fluctuations after the signals are subtracted. The Bayesian viewpoint emphasizes the need for the estimation of uncertainties associated with model predictions. Without estimates of uncertainties it is impossible to determine the predictive capabilities of models.