Minimax filtering for sequential aggregation: Application to ensemble forecast of ozone analyses
Résumé
This paper presents a new algorithm for sequential aggregation of an ensemble of forecasts. At any forecasting step, the aggregation consists of (1) computing new weights for the ensemble members represented by different numerical models and (2) forecasting with a weighted linear combination of the ensemble members. We assume that the time evolution of the weights is described by a linear equation with uncertain parameters and apply a minimax filter (and also Kalman filter, for comparison) in order to estimate the vector of weights given "observations". The "observation" equation for the filter compares the aggregated forecast with the analysis determined in a data assimilation cycle together with its variance. The minimax approach allows one to work with flexible uncertainty description: deterministic bounding sets for uncertain parameters in weight's equation, and error covariance matrices for the "observational" errors. Our key contribution is an uncertainty estimate of the aggregated forecast, for which we introduce an evaluation test. The performance of the method is assessed for the forecast of ground-level ozone daily peaks over Europe, for the year 2001. Compared to forecasts generated by classical data assimilation, the root mean square error is decreased by 16% for prediction of the analyses and by 20% for prediction of the observations.