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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]

Spatiotemporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and the large number of observation/prediction locations preclude the use of traditional covariance-based spatiotemporal statistical methods. Alternatively, we focus on conditionally specified (i.e., hierarchical) spatiotemporal models. These methods offer several advantages over traditional approaches. Primarily, physical and dynamical constraints can be easily incorporated into the conditional formulation, so that the series of relatively simple yet physically realistic conditional models leads lo a much more complicated spatiotemporal covariance structure than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, as well as multiresolution (wavelet) bases, the models can be computed with very large datasets. This modeling approach was necessitated by a scientifically meaningful problem in the geosciences. Satellite-derived wind estimates have high spatial resolution but limited global coverage. In contrast, wind fields provided by the major weather centers provide complete coverage but have low spatial resolution. The goal is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essential task to enable meteorological research, because no complete high-resolution surface wind datasets exist over the world oceans. High-resolution datasets of this type are crucial for improving our understanding of global air-sea interactions affecting climate and tropical disturbances, and for driving large-scale ocean circulation models. [ABSTRACT FROM AUTHOR]