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A Bayesian statistical model is proposed that combines information from a multimodel ensemble of atmosphere–ocean general circulation models (AOGCMs) and observations to determine probability distributions of future temperature change on a regional scale. The posterior distributions derived from the statistical assumptions incorporate the criteria of bias and convergence in the relative weights implicitly assigned to the ensemble members. This approach can be considered an extension and elaboration of the reliability ensemble averaging method. For illustration, the authors consider the output of mean surface temperature from nine AOGCMs, run under the A2 emission scenario from the Synthesis Report on Emission Scenarios (SRES), for boreal winter and summer, aggregated over 22 land regions and into two 30-yr averages representative of current and future climate conditions. The shapes of the final probability density functions of temperature change vary widely, from unimodal curves for regions where model results agree (or outlying projections are discounted) to multimodal curves where models that cannot be discounted on the basis of bias give diverging projections. Besides the basic statistical model, the authors consider including correlation between present and future temperature responses, and test alternative forms of probability distributions for the model error terms. It is suggested that a probabilistic approach, particularly in the form of a Bayesian model, is a useful platform from which to synthesize the information from an ensemble of simulations. The probability distributions of temperature change reveal features such as multimodality and long tails that could not otherwise be easily discerned. Furthermore, the Bayesian model can serve as an interdisciplinary tool through which climate modelers, climatologists, and statisticians can work more closely. For example, climate modelers, through their expert judgment, could contribute to the formulations of prior distributions in the statistical model. [ABSTRACT FROM AUTHOR]

This article provides an overview of statistics in the atmospheric sciences. The motion and evolution of the atmosphere can be determined from a system of several nonlinear partial differential equations. These equations, derived from classical results in thermodynamics and fluid mechanics on a rotating sphere, are well accepted as the fundamental description of atmospheric flow and are referred to as the primitive equations. A focus for climate studies is the use of a general circulation model (GCM). A GCM is an adaptation of the primitive equations to a spatial grid and discrete steps in time. The need for accurate forecasts of the weather is undisputed. Equations on the statistical foundations of weather forecasts are provided. Turbulence in the atmosphere and ocean is an area with still many questions. In most cases turbulence can be readily identified, but a simple and rigorous definition of turbulent flow is still elusive. Popular views of statistics in the geophysical sciences often focus on spatial methods and time series.