Abstract
Abstract Nonhomogeneous regression models are widely used to statistically postprocess numerical ensemble weather prediction models. Such regression models are capable of forecasting full probability distributions and correcting for ensemble errors in the mean and variance. To estimate the corresponding regression coefficients, minimization of the continuous ranked probability score (CRPS) has widely been used in meteorological postprocessing studies and has often been found to yield more calibrated forecasts compared to maximum likelihood estimation. From a theoretical perspective, both estimators are consistent and should lead to similar results, provided the correct distribution assumption about empirical data. Differences between the estimated values indicate a wrong specification of the regression model. This study compares the two estimators for probabilistic temperature forecasting with nonhomogeneous regression, where results show discrepancies for the classical Gaussian assumption. The heavy-tailed logistic and Student’s t distributions can improve forecast performance in terms of sharpness and calibration, and lead to only minor differences between the estimators employed. Finally, a simulation study confirms the importance of appropriate distribution assumptions and shows that for a correctly specified model the maximum likelihood estimator is slightly more efficient than the CRPS estimator.
Highlights
Each trained model is applied on raw ensemble data of the remaining test subsample. This leads to out-of-sample forecasts not used for training, which are verified with PIW, prediction interval coverage (PIC), reliability index (RI), log score (LS), and continuous ranked probability score (CRPS)
Nonhomogeneous regression is a commonly used postprocessing strategy to statistically correct numerical weather prediction models (NWP) ensemble forecasts. This approach predicts the outcome of weather quantities of interest with full parametric forecast distributions
Log-score (LS) minimization has a long tradition in statistical modeling, whereas CRPS minimization has become popular in meteorological studies
Summary
Nonhomogeneous regression is a popular regressionbased technique to statistically correct an ensemble of numerical weather prediction models (NWP; Leith 1974). For perfect calibration the probability integral transform (PIT) should be distributed uniformly Both estimation approaches, LS and CRPS minimization, show a hump in the center bins indicating overdispersive forecasts (i.e., the forecast distribution is too wide so that observations fall overproportionally into the central range of the distribution). Both estimation approaches show only small differences and much better calibration. In this article we set out to investigate when and why results from LS and CRPS minimization will differ for symmetric distribution assumptions This is performed in terms of temperature forecasting in central Europe and with simulated data using the NGR as the benchmark approach.
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