Section: New Results

Ensemble forecasting with sequential aggregation

The aggregation of an ensemble of forecasts is an approach where the members of an ensemble are given a weight before every forecast time, and where the corresponding weighted linear combination of the forecasts provides an improved forecast. A robust aggregation can be carried out so as to guarantee that the aggregated forecast performs better, in the long run, than any linear combination of the ensemble members with time-independent weights. The approaches are then based on machine learning. The aggregation algorithms can be applied to forecast analyses (generated from a data assimilation system), so that the aggregated forecasts are naturally multivariate fields.

Application of sequential aggregation to meteorology

Participants : Paul Baudin, Vivien Mallet, Gilles Stoltz [CNRS] , Laurent Descamps [Météo France] .

Nowadays, it is standard procedure to generate an ensemble of simulations for a meteorological forecast. Usually, meteorological centers produce a single forecast, out of the ensemble forecasts, computing the ensemble mean (where every model receives an equal weight). It is however possible to apply aggregation methods. When new observations are available, the meteorological centers also compute analyses. Therefore, we can apply the ensemble forecast of analyses. Ensembles of forecasts for wind velocity and mean sea level pressure, from Météo France, were aggregated. Preliminary results show significant improvements for mean sea level pressure.

Sequential aggregation with uncertainty estimation

Participants : Vivien Mallet, Sergiy Zhuk [IBM research, Ireland] , Paul Baudin, Gilles Stoltz [CNRS] .

An important issue is the estimation of the uncertainties associated with the aggregated forecasts. One investigated direction relies on the framework of machine learning, with the aggregation of an ensemble of probability density functions instead of the point forecasts of the ensemble.

Another direction is to reformulate the aggregation problem in a filtering problem for the weights. The weights are supposed to satisfy some dynamics with unknown model error, which defines the state equation of a filter. An observation equation compares the aggregated forecast with the observations (or analyses) with known observational error variance. The filter finally computes estimates for the weights and quantifies their uncertainties. We applied a Kalman filter and a minimax filter for air quality forecasting. We also introduced a criterion that the filter results should satisfy if they are representative of the uncertainties [17] .