3D Estimates of Analysis and Short-Range Forecast Error Variances

Jie Feng

ESRL

Noon Feb 10 in Room 2155

Noon Feb 10 in Room 2155

Accurate estimates of analysis and short-range 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 produced 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) fitting variances between different lead-time forecasts valid at the same time as additional constraints of cost function, (b) using a suitable minimization algorithm, the L-BFGS (Byrd et al. 1995), and by (c) deriving 3-dimensional gridpoint-based error variance estimates via the L-BFGS algorithm. The 3-dimensional error variance estimates were examined in a simulated forecast environment with a quasi-geostrophic model where the analyses were generated using the Ensemble Kalman Filter (EnKF) scheme. It is found that the method can reproduce the area-average true analysis and forecast error within confidence intervals. Moreover, the estimated analysis errors at the gridpoint level has a high correlation with the distribution of the true analysis errors. The estimations were more accurate than those obtained from the EnKF ensemble spread. Based on these encouraging results, our next step is to apply this enhanced method to the Global Forecast System (GFS) and to compare with the error variances generated in operations