Multi‐model fusion and error parameter estimation

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Abstract
A 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 two‐model forecasting example (HOPS, ROMS) within the framework of the real‐time forecasting experiment held in Monterey Bay during 2003. Copyright © 2005 Royal Meteorological Society