The growing share of renewable energy in power generation increases the impact of the weather on the stability of the power grid. Especially prior to severe weather events, not only high-quality weather forecasts but also information about forecast uncertainties is needed by the transmission system operators (TSOs) to prepare stability provisions. Improving the inherent model error description is one of the goals of the research project "gridcast"' in which the German Meteorological Service (DWD) collaborates with the Fraunhofer IEE, and the German TSOs and DSOs. To this end, the DWD is enhancing its convection-permitting ensemble system COSMO-D2-EPS.
In order to accurately describe the model error, we use the following stochastic ansatz: The tendency equations for temperature, zonal and meridional winds, and relative humidity are extended by an additive tendency error approximated by a partial stochastic differential equation (SDE). This SDE consists -- similar to an Ornstein-Uhlenbeck equation -- of a damping term and a random field. However, the SDE is augmented with an additional diffusion term that ensures spatial correlations. Each of the three terms has an influence parameter that is assumed to be a function of (possibly different) flow-dependent predictor variables. Hence the relative importance of the three terms varies in space and time according to the respective weather conditions. The functional form of the parameters can be approximated from past estimates of the model error based on COSMO-D2 ensemble forecasts.
We explain the properties of the SDE and motivate its choice as representation of the model error. Furthermore, we investigate a method to empirically determine the parameters of the SDE and apply this method to the COSMO-D2-EPS at DWD for the model error of relevant forecast variables. First numerical experiments comparing this scheme to the operational model are presented.