Quantifying Uncertainty in Projections of Regional Climate Change: A Bayesian Approach to the Analysis of Multimodel Ensembles

Abstract

A Bayesian statistical model is proposed that combines information from a multi-model ensemble of atmosphere-ocean general circulation models 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, we consider output of mean surface temperature from 9 AOGCMs, run under the A2 SRES scenario, for Boreal winter and summer, aggregated over 22 land regions. 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 due to bias, to multimodal curves where models that cannot be discounted on the basis of bias give diverging projections. Besides the basic statistical model, we consider including correlation between present and future temperature responses, and test alternative forms of probability distributions for the model error terms. We suggest 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, at regional scales. The probability distributions of temperature change reveal features such as multi-modality 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.

Linking climate change modelling to impacts studies: recent advances in downscaling techniques for hydrological modelling

“…Stott, 2003;Tebaldi et al, 2004bTebaldi et al, , 2005Dessai et al, 2005;Greene et al, 2006;Räisänen and Ruokolainen, 2006;Stott et al, 2006), with some studies aimed directly at the production of regional change pdfs for climate change impact assessment of hydrological systems (e.g. Ekström et al, 2007;Hingray et al, 2007a).…”

“…However, the alternative multi-model methods are predicated on the fundamental belief that no model is the true model, and there is value in synthesizing projections from an ensemble, even when the individual models seem to disagree with one another. The two published statistical methods (Tebaldi et al, 2004b(Tebaldi et al, , 2005Greene et al, 2006) use a Bayesian approach to estimate the probability distribution of future climate, using information from past observed climate and the corresponding GCM simulated climatologies. The Greene et al method combines the ensemble of models by calibrating their past trends at regional scales to the observed trends, and using the calibration coefficients (and their estimated uncertainty ranges) to derive probabilistic projections of future trends.…”

A framework for testing the ability of models to project climate change and its impacts

“…Assignment of weights to the ensemble members may be a plausible way of incorporating model accuracy and credibility in the ensemble projection, but it may be difficult to apply in practice. Since model performance cannot be directly assessed for future conditions, additional assumptions are needed, such as assuming time invariant model bias or using a pseudo reality for assessing future model performance (such as the ensemble mean projection used by Tebaldi et al (2005)). An additional practical problem is that models perform differently with respect to different performance measures (Christensen et al 2010).…”

Skill of ECMWF system‐4 ensemble seasonal climate forecasts for East Africa

“…Probabilistic approaches overcome these limitations through ensemble prediction (Kalnay et al, 2006) using multiple realizations for a single forecast time and location to sample forecast uncertainty. Ensemble generation is achieved by either perturbations of initial conditions, perturbations introduced at each model integration (stochastic physics) or use of multi-model ensembles (Graham et al, 2000;Tebaldi et al, 2004;Thomson et al, 2006;Shutts et al, 2011;Weisheimer et al, 2011;Doblas-Reyes et al, 2013;Weisheimer and Palmer, 2014).…”