| The purpose of an ensemble prediction system is to account for the influence of the spatio-temporal changes in the predictability on the forecasts. The spatio-temporal changes in the structure of the uncertain forecast features make the utility of an ensemble prediction system of a finite number of ensemble members inherently flow dependent. Thus, a uniformly good performance of the ensemble forecast system over all forecast situations cannot be expected. In this talk, we describe a toolkit of simple mathematical tools to study the flow dependence of the utility of an ensemble system. These tools are based on investigating the behavior of the ensemble perturbations in a small local neighborhood of each model grid point. A local error covariance matrix is defined for each grid point and the diagnostic tools are applied to the linear space spanned by the ensemble based estimate of the local error covariance matrix. We argue, based on the results of experiments carried out with a sophisticated global circulation model of the atmosphere, that while the local linear space provides an efficient representation of the forecast uncertainties in situations where the forecast error is large, predicting the spectrum of uncertainties in the linear space is more challenging. |
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