An Unbiased Estimation of Analysis and Short-Range Forecast Error Variances

Accurate estimates of error variances in numerical analyses and forecasts (i.e., difference between analysis or forecast fields and nature on the resolved scales) are critical for the evaluation of forecasting systems, the tuning of data assimilation systems, and the proper initialization of ensemble forecasts. A number of issues, however, hinder related efforts, such as errors in observations and the difficulty in their estimation; the fact that estimates of analysis errors derived via data assimilation schemes are influenced by the same assumptions as those used to create the analysis fields, the quality of which we wish to evaluate; and the presumed but unknown correlation between analysis and forecast errors.

This presentation will introduce a new technique for the unbiased estimation of error variances in the initial state (i.e., analysis field) and numerical forecasts of chaotic systems. The method is independent of any assumption or tuning parameter used in DA schemes. In a simulated forecast environment, the method is demonstrated to reproduce the true analysis and forecast error within the predicted error bounds. The method is then applied to forecasts from four leading Numerical Weather Prediction centers to assess the performance of their corresponding data assimilation and modeling systems. A general relationship between the quality of shadowing (i.e., error variances in the initial and forecast states), the strength of chaotic behavior, and the effectiveness of the observing and DA systems will also be introduced and used to interpret the experimental results.