Deterministic Ensemble Forecasts Using Gene-Expression Programming*

Abstract

Abstract 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.