Bayesian Estimation of Stochastic Parameterizations in a Numerical Weather Forecasting Model

Abstract

Abstract Parameterizations in numerical models account for unresolved processes. These parameterizations are inherently difficult to construct and as such typically have notable imperfections. One approach to account for this uncertainty is through stochastic parameterizations. This paper describes a methodological approach whereby existing parameterizations provide the basis for a simple stochastic approach. More importantly, this paper describes systematically how one can “train” such parameterizations with observations. In particular, a stochastic trigger function has been implemented for convective initiation in the Kain–Fritsch (KF) convective parameterization scheme within the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model (MM5). In this approach, convective initiation within MM5 is modeled by a binary random process. The probability of initiation is then modeled through a transformation in terms of the standard KF trigger variables, but with random parameters. The distribution of these random parameters is obtained through a Bayesian Monte Carlo procedure informed by radar reflectivities. Estimates of these distributions are then incorporated into the KF trigger function, giving a meaningful stochastic (distributional) parameterization. The approach is applied to cases from the International H2O project (IHOP). The results suggest the stochastic parameterization/Bayesian learning approach has potential to improve forecasts of convective precipitation in mesoscale models.