Multimodel Combination by a Bayesian Hierarchical Model: Assessment of Ice Accumulation over the Oceanic Arctic Region

Malaak Kallache CLIMPACT and LSCE-IPSL, Paris, France

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Elena Maksimovich LOCEAN-IPSL, Paris, France

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Paul-Antoine Michelangeli CLIMPACT, Paris, France

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Philippe Naveau LSCE-IPSL, Gif-sur-Yvette, France

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Abstract

The performance of general circulation models (GCMs) varies across regions and periods. When projecting into the future, it is therefore not obvious whether to reject or to prefer a certain GCM. Combining the outputs of several GCMs may enhance results. This paper presents a method to combine multimodel GCM projections by means of a Bayesian model combination (BMC). Here the influence of each GCM is weighted according to its performance in a training period, with regard to observations, as outcome BMC predictive distributions for yet unobserved observations are obtained. Technically, GCM outputs and observations are assumed to vary randomly around common means, which are interpreted as the actual target values under consideration. Posterior parameter distributions of the authors’ Bayesian hierarchical model are obtained by a Markov chain Monte Carlo (MCMC) method. Advantageously, all parameters—such as bias and precision of the GCM models—are estimated together. Potential time dependence is accounted for by integrating a Kalman filter. The significance of trend slopes of the common means is evaluated by analyzing the posterior distribution of the parameters. The method is applied to assess the evolution of ice accumulation over the oceanic Arctic region in cold seasons. The observed ice index is created out of NCEP reanalysis data. Outputs of seven GCMs are combined by using the training period 1962–99 and prediction periods 2046–65 and 2082–99 with Special Report on Emissions Scenarios (SRES) A2 and B1. A continuing decrease of ice accumulation is visible for the A2 scenario, whereas the index stabilizes for the B1 scenario in the second prediction period.

Corresponding author address: Malaak Kallache, CLIMPACT, 79 rue du Faubourg Poissonnière, 75009 Paris, France. Email: mk@climpact.com

Abstract

The performance of general circulation models (GCMs) varies across regions and periods. When projecting into the future, it is therefore not obvious whether to reject or to prefer a certain GCM. Combining the outputs of several GCMs may enhance results. This paper presents a method to combine multimodel GCM projections by means of a Bayesian model combination (BMC). Here the influence of each GCM is weighted according to its performance in a training period, with regard to observations, as outcome BMC predictive distributions for yet unobserved observations are obtained. Technically, GCM outputs and observations are assumed to vary randomly around common means, which are interpreted as the actual target values under consideration. Posterior parameter distributions of the authors’ Bayesian hierarchical model are obtained by a Markov chain Monte Carlo (MCMC) method. Advantageously, all parameters—such as bias and precision of the GCM models—are estimated together. Potential time dependence is accounted for by integrating a Kalman filter. The significance of trend slopes of the common means is evaluated by analyzing the posterior distribution of the parameters. The method is applied to assess the evolution of ice accumulation over the oceanic Arctic region in cold seasons. The observed ice index is created out of NCEP reanalysis data. Outputs of seven GCMs are combined by using the training period 1962–99 and prediction periods 2046–65 and 2082–99 with Special Report on Emissions Scenarios (SRES) A2 and B1. A continuing decrease of ice accumulation is visible for the A2 scenario, whereas the index stabilizes for the B1 scenario in the second prediction period.

Corresponding author address: Malaak Kallache, CLIMPACT, 79 rue du Faubourg Poissonnière, 75009 Paris, France. Email: mk@climpact.com

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