Dynamically Stratified Monte Carlo Forecasting

Abstract

A new method for performing Monte Carlo forecasts is introduced. The method, called dynamic stratification, selects initial perturbations based on a stratification of the error distribution. A simple implementation is presented in which the error distribution used for the stratification is estimated from a linear model derived from a large ensemble of 12-h forecasts with the full dynamical model. The stratification thus obtained is used to choose a small subsample of initial states with which to perform the dynamical Monte Carlo forecasts. Several test cases are studied using a simple two-level general circulation model (GCM) with uncertain initial conditions. It is found that the method provides substantial reductions in the sampling error of the forecast mean and variance when compared to the more traditional approach of choosing the initial perturbations at random. The degree of improvement, however, is sensitive to the nature of the initial error distribution and to the base state. In practice the method may be viable only if the computational burden involved in obtaining an adequate estimate of the error distribution is shared with the data-assimilation procedure.