Deterministic Ensemble Forecasts Using Gene-Expression Programming

A method called gene-expression programming (GEP), which uses symbolic regression to form a nonlinear combination of ensemble NWP forecasts, is introduced. From a population of competing and evolving algorithms (each of which can create a different combination of NWP ensemble members), GEP uses computational natural selection to find the algorithm that maximizes a weather verification fitness function. The resulting best algorithm yields a deterministic ensemble forecast (DEF) that could serve as an alternative to the traditional ensemble average. Motivated by the difficulty in forecasting montane precipitation, the ability of GEP to produce bias-corrected short-range 24-h-accumulated precipitation DEFs is tested at 24 weather stations in mountainous southwestern Canada. As input to GEP are 11 limited-area ensemble members from three different NWP models at four horizontal grid spacings. The data consist of 198 quality controlled observation-forecast date pairs during the two fall-spring rainy seasons of October 2003-March 2005. Comparing the verification scores of GEP DEF versus an equally weighted ensemble-average DEF, the GEP DEFs were found to be better for about half of the mountain weather stations tested, while ensemble-average DEFs were better for the remaining stations. Regarding the multimodel multigrid-size "ensemble space'' spanned by the ensemble members, a sparse sampling of this space with several carefully chosen ensemble members is found to create a DEF that is almost as good as a DEF using the full 11-member ensemble. The best GEP algorithms are nonunique and irreproducible, yet give consistent results that can be used to good advantage at selected weather stations.