The forecasting error statistics for convective-scale prediction: the impact of correlated errors in radar observations

The McGill radar data assimilation system has been used to study the forecasting error covariance matrix at convective scale by means of an ensemble approach. By perturbing radar data we have simulated the effect of errors of observations, and these perturbed observations have been assimilated to obtain an ensemble of analyses. The special characteristic of these perturbations is the organized structure of the errors introduced by specifying an error correlation length of observations of reflectivity and Doppler velocity as well as space-correlated errors in the background term..

After integrating the model forward in time, we have investigated the impact of using correlated errors as perturbations on the spread of the ensemble of forecasts (as a manner to quantify the forecasting error variance), the auto correlation functions of the errors in model variables and on the cross-correlation between the errors in different variables. In addition, the distribution of forecast errors at different lead-times is compared for different correlation lengths of the errors. We demonstrate in this manner the critical importance of spatial correlation of errors in generating the spread of the ensembles.