Spatially extended estimates of analysis and short-range forecast error variances

Abstract

Accurate estimates of `true' error variance between Numerical Weather Prediction (NWP) analyses and forecasts and the `reality' interpolated to a NWP model grid (Analysis and true Forecast Error Variance, hereafter AFEV) are critical for successful data assimilation and ensemble forecasting applications. Pena and Toth (2014, PT14) introduced a Statistical Analysis and Forecast Error estimation (hereafter called SAFE) algorithm for the unbiased estimation of AFEV. The method uses variances between NWP forecasts and analyses (i.e. `perceived' forecast errors) and assumptions about the time evolution of true error variances. PT14 successfully tested SAFE for the estimation of area mean error variances. In the present study, SAFE is extended by mitigating the effects of increased sampling noise and by accounting for the spatiotemporal evolution of forecast error variances, both critical for gridpoint-based applications. The enhanced method is evaluated in a Simulated Nature, Observations, Data Assimilation, and Prediction Environment using a quasi-geostrophic model and an ensemble Kalman Filter (EnKF). SAFE estimates of true analysis error variance are within 6\% of the actual values, as compared to 24-55\% deviations in EnKF estimates. The spatial correlation between estimated and actual true error variances was also found high (above 0.9) and comparable with EnKF estimates, but much higher than NMC method estimates (0.63-0.78). Estimates of the other two SAFE parameters, the growth rate and decorrelation of analysis and forecast error variances are within 3\% of the corresponding actual values.