Offline parameter estimation using EnKF and maximum likelihood error covariance estimates: Application to a subgrid-scale orography parametrization

Recent work has shown that the parameters controlling parametrizations of the physical processes in climate models can be estimated from observations using filtering techniques. In this article, we propose an offline parameter estimation approach, without estimating the state of the climate model. It is based on the Ensemble Kalman Filter (EnKF) and an iterative estimation of the error covariance matrices and of the background state using a maximum likelihood algorithm. The technique is implemented in a subgrid-scale orography (SSO) parametrization scheme which works in a single vertical column. First, the parameter estimation technique is evaluated using twin experiments. Then, the technique is used with synthetic observations to estimate how the parameters of the SSO scheme should change when the resolution of the input orography dataset of a general circulation model is increased. Our analysis reveals that, when the resolution of the orography dataset increases, the scheme should take into account the dynamical sheltering that can occur at low levels between mountain peaks located within the same gridbox area.