Multi‐model fusion and error parameter estimation

Abstract

SUMMARYA robust and practical methodology for multi-model ocean forecast fusion has been sought. Present regional ocean forecasting systems adapt and evolve in response to modelled processes. This makes it imperative that a forecast combination methodology be adaptive and capable to operate with a small sample of past validating events. To this end, we consider an extension of maximum-likelihood error parameter estimation to multi-model predictive systems, and utilize the resulting methodology for adaptive Bayesian model fusion. The methodology consists of the following three general steps: (a) parametrization of forecast uncertainties through either a suitable parametric family (e.g. covariance models) or through a low-rank approximation (e.g. flow-dependent error subspaces); (b) update of uncertainty parameters via maximum likelihood; and (c) combining model forecasts based on their uncertainty parameters via maximum likelihood. In order to implement step (b), we have extended the maximum-likelihood error parameter estimation methodology to multi-model forecasting systems using the expectation-maximization technique, with the true state-space vector at observation locations treated as missing data. With only one forecasting model, the procedure reduces to the standard maximum-likelihood error parameter estimation. The proposed multi-model fusion methodology neglects cross-model error correlations in order to gain the capability to work with a small sample of past events. We illustrate the methodology with a twomodel forecasting example (HOPS, ROMS) within the framework of the real-time forecasting experiment held in Monterey Bay during 2003.

Enhanced ocean temperature forecast skills through 3‐D super‐ensemble multi‐model fusion

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