Calibrated Short-Range Ensemble Precipitation Forecasts Using Extended Logistic Regression with Interaction Terms

Abstract

Abstract Extended logistic regression has been shown to be a method well suited to calibrating precipitation forecasts from medium-range ensemble prediction systems. The extension of the logistic regression unifies the separate predictive equations for each threshold, introducing the predictive threshold as part of the predictors. Mutually consistent probabilities and a reduction in the total number of regression parameters to be evaluated are part of the benefits of the extended approach. However, considering the predictive threshold as the only “unification” predictor constrains the regression parameters associated with the primary predictors to be constant with the threshold. To alleviate the rigidity of the extended scheme, interaction terms are introduced in the unified predictive equation. Within the framework of the convection-permitting German-focused Consortium for Small-Scale Modeling ensemble prediction system (COSMO-DE-EPS), it is shown that extended logistic regression, applied to short-range precipitation forecasts with the ensemble mean as the primary predictor, improves the performance of the system. Interaction effects are first illustrated through the analysis of regression parameters and then the positive impact on the calibrated forecasts of the new extended logistic regression scheme, including interaction terms, is shown using quantitative and qualitative measures of reliability and sharpness.