Probabilistic Quantitative Precipitation Forecasting Using Bayesian Model Averaging

J. Mc Lean Sloughter Department of Statistics, University of Washington, Seattle, Washington

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Adrian E. Raftery Department of Statistics, University of Washington, Seattle, Washington

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Tilmann Gneiting Department of Statistics, University of Washington, Seattle, Washington

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Chris Fraley Department of Statistics, University of Washington, Seattle, Washington

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Abstract

Bayesian model averaging (BMA) is a statistical way of postprocessing forecast ensembles to create predictive probability density functions (PDFs) for weather quantities. It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are posterior probabilities of the models generating the forecasts and reflect the forecasts’ relative contributions to predictive skill over a training period. It was developed initially for quantities whose PDFs can be approximated by normal distributions, such as temperature and sea level pressure. BMA does not apply in its original form to precipitation, because the predictive PDF of precipitation is nonnormal in two major ways: it has a positive probability of being equal to zero, and it is skewed. In this study BMA is extended to probabilistic quantitative precipitation forecasting. The predictive PDF corresponding to one ensemble member is a mixture of a discrete component at zero and a gamma distribution. Unlike methods that predict the probability of exceeding a threshold, BMA gives a full probability distribution for future precipitation. The method was applied to daily 48-h forecasts of 24-h accumulated precipitation in the North American Pacific Northwest in 2003–04 using the University of Washington mesoscale ensemble. It yielded predictive distributions that were calibrated and sharp. It also gave probability of precipitation forecasts that were much better calibrated than those based on consensus voting of the ensemble members. It gave better estimates of the probability of high-precipitation events than logistic regression on the cube root of the ensemble mean.

Corresponding author address: Adrian E. Raftery, Department of Statistics, University of Washington, Box 354320, Seattle, WA 98195-4320. Email: raftery@u.washington.edu

Abstract

Bayesian model averaging (BMA) is a statistical way of postprocessing forecast ensembles to create predictive probability density functions (PDFs) for weather quantities. It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are posterior probabilities of the models generating the forecasts and reflect the forecasts’ relative contributions to predictive skill over a training period. It was developed initially for quantities whose PDFs can be approximated by normal distributions, such as temperature and sea level pressure. BMA does not apply in its original form to precipitation, because the predictive PDF of precipitation is nonnormal in two major ways: it has a positive probability of being equal to zero, and it is skewed. In this study BMA is extended to probabilistic quantitative precipitation forecasting. The predictive PDF corresponding to one ensemble member is a mixture of a discrete component at zero and a gamma distribution. Unlike methods that predict the probability of exceeding a threshold, BMA gives a full probability distribution for future precipitation. The method was applied to daily 48-h forecasts of 24-h accumulated precipitation in the North American Pacific Northwest in 2003–04 using the University of Washington mesoscale ensemble. It yielded predictive distributions that were calibrated and sharp. It also gave probability of precipitation forecasts that were much better calibrated than those based on consensus voting of the ensemble members. It gave better estimates of the probability of high-precipitation events than logistic regression on the cube root of the ensemble mean.

Corresponding author address: Adrian E. Raftery, Department of Statistics, University of Washington, Box 354320, Seattle, WA 98195-4320. Email: raftery@u.washington.edu

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