3D Estimates of Analysis and ShortRange Forecast Error Variances

Accurate estimates of analysis and shortrange forecast error variances are critical for successful data assimilation and ensemble forecasting applications. Pena and Toth (2014, PT14) introduced a statistical minimization algorithm for the unbiased estimation of the variance between “truth” interpolated to a Numerical Weather Prediction (NWP) model grid and the NWP analysis or forecast (i.e., “true” errors). The method uses variances between NWP forecasts and analyses (i.e., “perceived” forecast errors) and assumptions about the growth and correlation of errors. After demonstrating in simple model experiments that the method produces unbiased error variance estimates, PT14 estimated the mean of true analysis and forecast error variances for NWP systems over large domains.

The present study expands on PT14 by (a) introducing a more suitable minimization algorithm, and by (b) deriving 3dimensional gridpointbased error variance estimates via a global minimization. Preliminary 3D error variance estimates will be presented for (a) controlled analysis forecast experiments with a quasigeostrophic model, and (b) the NCEP operational Global Forecast System (GFS). Potential use of the 3D error variance estimates include the specification of (a) background error variances in data assimilation (DA) independent of the DA schemes themselves and (b) initial ensemble perturbation variance.