A stochastic model of the model error to improve the ICON-D2-EPS ensemble forecasts

In this work, we aim at improving the operational regional ensemble forecast system ICON-D2-EPS at the German Meteorological Service (Deutscher Wetterdienst, DWD). To this end, we propose to describe the model error of the forecast with a random field generated by a linear stochastic partial differential equation (SPDE). The SPDE contains three terms to describe spatial and temporal correlations as well as amplitude of the model error with a coefficient for each of the terms controlling the strength of the corresponding process. To account for the weather dependence of the model error, the coefficients are flow-dependent through a dependency on the respective tendency of the perturbed variables. In order to find the coefficients, we first derive theoretical properties of the solution of the SPDE. Then we investigate historical model error fields and determine the three coefficients in such a way that the simulated perturbation fields have the same spatial and temporal correlations and amplitude as the historical model error fields. The SPDE is implemented into the ICON forecast model and an ensemble experiment for a full month has been performed. The SPDE is solved during the forecast and corrects the slow physics tendencies of the horizontal wind components and temperature in each time step with a different random field in each member. Using this approach, various ensemble verification scores such as the CRPS and spread/skill ratio both against surface synoptic observations and radiosondes measurements are improved without degrading the RMSE of the forecast.