Inference of stochastic parametrizations for model error treatment using nested ensemble Kalman filters

Abstract

Stochastic parametrizations are increasingly used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parametrizations is the characterization of the statistical properties of the stochastic processes within their formulation. In this work, a hierarchical Bayesian approach based on two nested ensemble Kalman filters is proposed for inferring parameters associated with stochastic parametrizations. The proposed technique is based on the Rao-Blackwellization of the parameter estimation problem. It consists of an ensemble of ensemble Kalman filters, each of them using a different set of stochastic parameter values. We show the ability of the technique to infer parameters related to the covariance of stochastic representations of model error in the Lorenz-96 dynamical system. The evaluation is conducted with stochastic twin experiments and with imperfect model experiments with unresolved physics in the forecast model. The technique performs successfully under different model error covariance structures. The technique is conceived to be applied offline as part of an apriori optimization of the data assimilation system and could, in principle, be extended to the estimation of other hyperparameters of the data assimilation system.