Post-processing Multiensemble Temperature and Precipitation Forecasts Through an Exchangeable Normal-Gamma Model and Its Tobit Extension

Meteorological ensemble members are a collection of scenarios for future weather issued by a meteorological center. Such ensembles nowadays form the main source of valuable information for probabilistic forecasting which aims at producing a predictive probability distribution of the quantity of interest instead of a single best guess point-wise estimate. Unfortunately, ensemble members cannot generally be considered as a sample from such a predictive probability distribution without a preliminary post-processing treatment to re-calibrate the ensemble. Two main families of post-processing methods, either competing such as the BMA or collaborative such as the EMOS, can be found in the literature. This paper proposes a mixed-effect model belonging to the collaborative family. The structure of the model is formally justified by Bruno de Finetti’s representation theorem which shows how to construct operational statistical models of ensemble based on judgments of invariance under the relabeling of the members. Its interesting specificities are as follows: (1) exchangeability contributes to parsimony, with an interpretation of the latent pivot of the ensemble in terms of a statistical synthesis of the essential meteorological features of the ensemble members, (2) a multiensemble implementation is straightforward, allowing to take advantage of various information so as to increase the sharpness of the forecasting procedure. Focus is cast onto normal statistical structures, first with a direct application for temperatures, then with its very convenient Tobit extension for precipitation. Inference is performed by expectation maximization (EM) algorithms with both steps leading to explicit analytic expressions in the Gaussian temperature case, and recourse is made to stochastic conditional simulations in the zero-inflated precipitation case. After checking its good behavior on artificial data, the proposed post-processing technique is applied to temperature and precipitation ensemble forecasts produced for lead times from 1 to 9 days over five river basins managed by Hydro-Québec, which ranks among the world’s largest electric companies. These ensemble forecasts, provided by three meteorological global forecast centers (Canadian, USA and European), were extracted from the THORPEX Interactive Grand Global Ensemble (TIGGE) database. The results indicate that post-processed ensembles are calibrated and generally sharper than the raw ensembles for the five watersheds under study. Supplementary materials accompanying this paper appear on-line.