An Information-Theoretic Framework for Improving Imperfect Dynamical Predictions Via Multi-Model Ensemble Forecasts

Abstract

This work focuses on elucidating issues related to an increasingly common technique of multi-model ensemble (MME) forecasting. The MME approach is aimed at improving the statistical accuracy of imperfect time-dependent predictions by combining information from a collection of reduced-order dynamical models. Despite some operational evidence in support of the MME strategy for mitigating the prediction error, the mathematical framework justifying this approach has been lacking. Here, this problem is considered within a probabilistic/stochastic framework which exploits tools from information theory to derive a set of criteria for improving probabilistic MME predictions relative to single-model predictions. The emphasis is on a systematic understanding of the benefits and limitations associated with the MME approach, on uncertainty quantification, and on the development of practical design principles for constructing an MME with improved predictive performance. The conditions for prediction improvement via the MME approach stem from the convexity of the relative entropy which is used here as a measure of the lack of information in the imperfect models relative to the resolved characteristics of the truth dynamics. It is also shown how practical guidelines for MME prediction improvement can be implemented in the context of forced response predictions from equilibrium with the help of the linear response theory utilizing the fluctuation–dissipation formulas at the unperturbed equilibrium. The general theoretical results are illustrated using exactly solvable stochastic non-Gaussian test models.