Heteroscedastic Extended Logistic Regression for Postprocessing of Ensemble Guidance

Jakob W. Messner Institute of Meteorology and Geophysics, University of Innsbruck, Innsbruck, Austria

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Georg J. Mayr Institute of Meteorology and Geophysics, University of Innsbruck, Innsbruck, Austria

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Achim Zeileis Department of Statistics, University of Innsbruck, Innsbruck, Austria

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Daniel S. Wilks Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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Abstract

To achieve well-calibrated probabilistic forecasts, ensemble forecasts are often statistically postprocessed. One recent ensemble-calibration method is extended logistic regression, which extends the popular logistic regression to yield full probability distribution forecasts. Although the purpose of this method is to postprocess ensemble forecasts, usually only the ensemble mean is used as the predictor variable, whereas the ensemble spread is neglected because it does not improve the forecasts. In this study it is shown that when simply used as an ordinary predictor variable in extended logistic regression, the ensemble spread affects the location but not the variance of the predictive distribution. Uncertainty information contained in the ensemble spread is therefore not utilized appropriately. To solve this drawback a new approach is proposed where the ensemble spread is directly used to predict the dispersion of the predictive distribution. With wind speed data and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) it is shown that by using this approach, the ensemble spread can be used effectively to improve forecasts from extended logistic regression.

Denotes Open Access content.

Corresponding author address: Jakob W. Messner, Institute of Meteorology and Geophysics, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria. E-mail: jakob.messner@uibk.ac.at

Abstract

To achieve well-calibrated probabilistic forecasts, ensemble forecasts are often statistically postprocessed. One recent ensemble-calibration method is extended logistic regression, which extends the popular logistic regression to yield full probability distribution forecasts. Although the purpose of this method is to postprocess ensemble forecasts, usually only the ensemble mean is used as the predictor variable, whereas the ensemble spread is neglected because it does not improve the forecasts. In this study it is shown that when simply used as an ordinary predictor variable in extended logistic regression, the ensemble spread affects the location but not the variance of the predictive distribution. Uncertainty information contained in the ensemble spread is therefore not utilized appropriately. To solve this drawback a new approach is proposed where the ensemble spread is directly used to predict the dispersion of the predictive distribution. With wind speed data and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) it is shown that by using this approach, the ensemble spread can be used effectively to improve forecasts from extended logistic regression.

Denotes Open Access content.

Corresponding author address: Jakob W. Messner, Institute of Meteorology and Geophysics, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria. E-mail: jakob.messner@uibk.ac.at
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