Local Predictability of the Performance of an Ensemble Forecast System

The main goal of the present study is to lay the theoretical foundation of a practical approach to predict the spatio-temporal changes in the performance of an ensemble prediction system. The motivation to develop such an approach is the recognition that the performance of an ensemble prediction system is inherently flow dependent. Linear diagnostics applied to the ensemble perturbations in a small local neighborhood of each model grid point are used to explore the spatio-temporally changing predictive qualities of the ensemble. In particular, a local state vector and the associated local covariance matrix is defined to represent the state and the uncertainty in the state estimate at each grid point. A set of local diagnostics based on the eigen-solution of the local covariance matrix is introduced. Numerical experiments are carried out with an implementation of the Local Ensemble Transform Kalman Filter (LETKF) data assimilation system on a reduced resolution (T62L28) version of the National Centers of Environmental Prediction (NCEP) Global Forecast System (GFS). It is found that the ensemble dimension (E-dimension) diagnostic is a good predictor of the ensemble performance, in the sense that a low value of the E-dimension indicates that the ensemble efficiently captures the uncertain forecast features. The significance of this result is that the location of large forecast errors in the 1-5 days are also the locations of low E-dimension.

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