Stochastic modelling of model errors: a simulation study

In the setting with known ‘truth’, the spatio‐temporal structure of forecast‐model (tendency) errors is studied. The shallow‐water model is used as the ‘truth’ and the vorticity equation as a forecast model. It is found that state‐dependent model errors (MEs) are of primary importance. The residual state‐independent (stochastic) part of MEs can be modelled with the advection‐diffusion equation driven by the white noise. The ME effective advection velocity appears to be very different from the wind and resembles the Rossby‐wave phase velocity. Three versions of increasing complexity for the advection and diffusion operators are proposed. Ensemble‐based adequacy checks of the proposed ME model are presented. Sensitivity of the ensemble forecast‐error spatial and temporal structure to various aspects of the ME model used to create the ensemble is investigated.