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. Peña 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.
Highlights
Due to the chaotic nature of the atmosphere and to the presence of initial state and model related errors, despite continual improvements in Numerical Weather Prediction (NWP) techniques numerical forecasts will never be perfect (Lorenz, 1963; Kalnay, 2002; Li and Ding, 2011)
Using ensemble variances from the same 1–5 days lead-time range that is used in the error estimation, we ensure that the spatiotemporal behaviour of ensemble perturbation variances will well capture that of the true analysis – forecast errors manifested in Statistical Analysis and Forecast Error (SAFE)
To confirm that ensemble perturbation variance is a good predictor for the spatiotemporal evolution of true analysis – forecast error variance, analogous to Fig. 4, in Fig. 5 we show the evolution of the global distribution of the SAFE estimate of true analysis error variance, along with the actual AFEV
Summary
Due to the chaotic nature of the atmosphere and to the presence of initial state and model related errors, despite continual improvements in NWP techniques numerical forecasts will never be perfect (Lorenz, 1963; Kalnay, 2002; Li and Ding, 2011). Most often the quality of numerical forecasts is assessed using either verifying observations or analyses as a reference for truth (Houtekamer et al, 2005; Whitaker et al, 2008) Such comparisons will be affected by errors present in either data source, especially at shorter lead times where the observational or analysis errors may have a magnitude comparable to that of the forecast errors. (2) SAFE is applied and evaluated in a Simulated, Nature, Observing, Data Assimilation, and Prediction (SNODAP) environment with a numerical model of intermediate complexity instead of the Lorenz toy model Such an environment where the AFEV are exactly known offers an ideal setting for a rigorous assessment of SAFE estimates.
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