Estimation of the functional form of subgrid-scale parametrizations using ensemble-based data assimilation : a simplemodel 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 subgridscale 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-dependentmodel 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 performancewhen 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.