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

Jie Feng* and Malaquias Pena, Zoltan Toth

Accurate estimates of analysis and short-range forecast error variances are critical for successful data assimilation and ensemble forecasting applications. Peña 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) fitting variances between different lead-time forecasts valid at the same time as additional constraints of cost function, (b) introducing a more suitable minimization algorithm L-BFGS (Byrd et al. 1995), and by (c) deriving 3-dimensional gridpoint-based error variance estimates via the minimization algorithm. Preliminary 3D error variance estimates were presented in a simulated forecast environment with a quasi-geostrophic model where the analyses were generated using the Ensemble Kalman Filter (EnKF) scheme. The method can reproduce the area-average true analysis and forecast error within confidence intervals. When compared to the 3D EnKF ensemble spread, the gridpoint estimates of the new method have close correlation with the distribution of true analysis errors, but have much more accurate estimation of the analysis error magnitudes. In the future, the 3D error variance estimates will be further applied to 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.

*email: jie.feng@noaa.gov
*Preference: Oral