Estimation of the functional form of subgrid-scale schemes using ensemble-based data assimilation: a simple model experiment

Abstract

Oceanic and atmospheric global numerical models represent explicitly the large‐scale dynamics while the smaller‐scale processes are not resolved, so that their effects in the large‐scale dynamics are included through subgrid‐scale parametrizations. These parametrizations represent small‐scale effects as a function of the resolved variables. In this work, data assimilation principles are used not only to estimate the parameters of subgrid‐scale parametrizations but also to uncover the functional dependencies of subgrid‐scale processes as a function of large‐scale variables. Two data assimilation methods based on the ensemble transform Kalman filter (ETKF) are evaluated in the two‐scale Lorenz '96 system scenario. The first method is an online estimation which uses the ETKF with an augmented space state composed of the model large‐scale variables and a set of unknown global parameters from the parametrization. The second method is an offline estimation which uses the ETKF to estimate an augmented space state composed of the large‐scale variables and by a space‐dependent model error term. Then a polynomial regression is used to fit the estimated model error as a function of the large‐scale model variables in order to develop a parametrization of small‐scale dynamics. The online estimation shows a good performance when the parameter‐state relationship is assumed to be a quadratic polynomial function. The offline estimation captures better some of the highly nonlinear functional dependencies found in the subgrid‐scale processes. The nonlinear and non‐local dependence found in an experiment with shear‐generated small‐scale dynamics is also recovered by the offline estimation method. Therefore, the combination of these two methods could be a useful tool for the estimation of the functional form of subgrid‐scale parametrizations.