On-line diagnosis and optimization of ensemble forecasts

We present a technique for on-line evaluation and optimization of ensemble forecasts that are produced by considering uncertainties either in initial conditions or different model versions, or both. The technique is based on the explicit evaluation of probabilities that are associated with the Gaussian stochastic representation of the weather analysis and forecast. It combines an ensemble technique for estimating the analysis error covariance and the standard procedures for computing probabilities from a known Gaussian distribution either by Monte-Carlo sampling or analytical expression, depending on the size of the problem. The technique allows evaluation of the skill of individual ensemble members in wide variety of fields and improvements in the consensus forecasts gained by optimal weighting of the ensemble members based on time-varying, prior-probabilistic skill measures. The technique was first demonstrated in a tutorial manner on two relatively simple examples to illustrate impact of ensemble characteristics including ensemble size, various observation strategies, and configurations including different model versions and varying initial conditions. The technique was then applied to high resolution regional forecasts with WRF-ARW model to examine value of precursors (derived diagnostic variables) and their employment in the optimization of the ensemble precipitation forecasting. For this purpose, simulations of two events associated with “atmospheric rivers” affecting the California coast and Sierra Foothills were performed. The two events were represented by seven 12-hour long forecast periods. The ensemble consisted of 20 members including various physical parameterizations and initial conditions.

The results indicated that precursors such as low-level moisture flux and precipitable water (which are naturally well correlated with the precipitation in both observed and forecast data) were not well suited for the diagnoses and optimization of the precipitation forecast with the current ensemble configuration. The errors in the precursors were not strongly correlated with the errors in the precipitation forecast by the current ensemble representation of the forecast errors. In terms of weighting of the ensemble members for the purpose of reducing ensemble forecast mean error in precipitations, the results show that this error could be notably reduced when the weights are based on short-term prior probabilistic error measure of the precipitation itself and when there is a consistency in the precipitation trend in the forecast relative to the observations. Overall, the results show that the ensemble forecast optimization by the probabilistic short-term prior variable weighting approach has a strong potential, but also indicate that an improved representation of the forecast errors is required for the optimal performance.