Editorial Type:
Article
Article Type:
Research Article

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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Print Publication:
01 Jan 2014
DOI:
https://doi.org/10.1175/MWR-D-13-00271.1
Page(s):
448–456
Restricted access

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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  • Ben Bouallègue, Z., 2013: Calibrated short-range ensemble precipitation forecasts using extended logistic regression with interaction terms. Wea. Forecasting, 28, 515–524.

    • Search Google Scholar
    • Export Citation

  • Bröcker, J., and L. A. Smith, 2007: Increasing the reliability of reliability diagrams. Wea. Forecasting, 22, 651–661.

  • Epstein, E. S., 1969: A scoring system for probability forecasts of ranked categories. J. Appl. Meteor., 8, 985–987.

  • Glahn, H., and D. Lowry, 1972: The use of model output statistics (MOS) in objective weather forecasting. J. Appl. Meteor., 11, 1203–1211.

    • Search Google Scholar
    • Export Citation

  • Gneiting, T., A. E. Raftery, A. H. Westveld, and T. Goldman, 2005: Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Mon. Wea. Rev., 133, 1098–1118.

    • Search Google Scholar
    • Export Citation

  • Hamill, T. M., 2012: Verification of TIGGE multimodel and ECMWF reforecast-calibrated probabilistic precipitation forecasts over the contiguous United States. Mon. Wea. Rev., 140, 2232–2252.

    • Search Google Scholar
    • Export Citation

  • Hamill, T. M., C. Snyder, and J. S. Whitaker, 2003: Ensemble forecasts and the properties of flow-dependent analysis-error covariance singular vectors. Mon. Wea. Rev., 131, 1741–1758.

    • Search Google Scholar
    • Export Citation

  • Hamill, T. M., J. S. Whitaker, and X. Wei, 2004: Ensemble reforecasting: Improving medium-range forecast skill using retrospective forecasts. Mon. Wea. Rev., 132, 1434–1447.

    • Search Google Scholar
    • Export Citation

  • Johnson, N. L., S. Kotz, and N. Balakrishnan, 1995: Continuous Univariate Distributions. Vol. 2. Wiley, 752 pp.

  • Lorenz, E., 1996: Predictability: A problem partly solved. Proc. ECMWF Seminar on Predictability, Reading, United Kingdom, ECMWF, 1–18.

  • Messner, J. W., and A. Zeileis, cited 2013: crch: Censored Regression with Conditional Heteroscedasticity. R package version 0.1-0. [Available online at http://CRAN.R-project.org/package=crch.]

  • Molteni, F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc., 122, 73–119.

    • Search Google Scholar
    • Export Citation

  • Nelder, J., and R. Wedderburn, 1972: Generalized linear models. J. Roy. Stat. Soc., 135A, 370–384.

  • Raftery, A. E., T. Gneiting, F. Balabdaoui, and M. Polakowski, 2005: Using Bayesian model averaging to calibrate forecast ensembles. Mon. Wea. Rev., 133, 1155–1174.

    • Search Google Scholar
    • Export Citation

  • R Core Team, cited 2012: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. [Available online at http://www.R-project.org/.]

  • Roulin, E., and S. Vannitsem, 2012: Postprocessing of ensemble precipitation predictions with extended logistic regression based on hindcasts. Mon. Wea. Rev., 140, 874–888.

    • Search Google Scholar
    • Export Citation

  • Roulston, M. S., and L. A. Smith, 2003: Combining dynamical and statistical ensembles. Tellus, 55A, 16–30.

  • Ruiz, J. J., and C. Saulo, 2012: How sensitive are probabilistic precipitation forecasts to the choice of calibration algorithms and the ensemble generation method? Part I: Sensitivity to calibration methods. Meteor. Appl., 19, 302–313.

    • Search Google Scholar
    • Export Citation

  • Schefzik, R., T. Thorarinsdottir, and T. Gneiting, 2013: Uncertainty quantification in complex simulation models using ensemble copula coupling. Stat. Sci., in press.

    • Search Google Scholar
    • Export Citation

  • Scheuerer, M., 2013: Probabilistic quantitative precipitation forecasting using ensemble model output statistics. Quart. J. Roy. Meteor. Soc., in press.

    • Search Google Scholar
    • Export Citation

  • Schmeits, M. J., and K. J. Kok, 2010: A comparison between raw ensemble output, (modified) Bayesian model averaging, and extended logistic regression using ECMWF ensemble precipitation reforecasts. Mon. Wea. Rev., 138, 4199–4211.

    • Search Google Scholar
    • Export Citation

  • Wang, X., and C. H. Bishop, 2003: A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes. J. Atmos. Sci., 60, 1140–1158.

    • Search Google Scholar
    • Export Citation

  • Wilks, D. S., 2006a: Comparison of ensemble-MOS methods in the Lorenz ’96 setting. Meteor. Appl., 13, 243–256.

  • Wilks, D. S., 2006b: Statistical Methods in the Atmospheric Sciences. 2nd ed. Academic Press, 627 pp.

  • Wilks, D. S., 2009: Extending logistic regression to provide full-probability-distribution MOS forecasts. Meteor. Appl., 368, 361–368.

    • Search Google Scholar
    • Export Citation

  • Wilks, D. S., and T. M. Hamill, 2007: Comparison of ensemble-MOS methods using GFS reforecasts. Mon. Wea. Rev., 135, 2379–2390.

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