Probabilistic Wind Vector Forecasting Using Ensembles and Bayesian Model Averaging

J. McLean Sloughter Seattle University, Seattle, Washington

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Tilmann Gneiting Heidelberg University, Heidelberg, Germany

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Adrian E. Raftery University of Washington, Seattle, Washington

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Abstract

Probabilistic forecasts of wind vectors are becoming critical as interest grows in wind as a clean and renewable source of energy, in addition to a wide range of other uses, from aviation to recreational boating. Unlike other common forecasting problems, which deal with univariate quantities, statistical approaches to wind vector forecasting must be based on bivariate distributions. The prevailing paradigm in weather forecasting is to issue deterministic forecasts based on numerical weather prediction models. Uncertainty can then be assessed through ensemble forecasts, where multiple estimates of the current state of the atmosphere are used to generate a collection of deterministic predictions. Ensemble forecasts are often uncalibrated, however, and Bayesian model averaging (BMA) is a statistical way of postprocessing these forecast ensembles to create calibrated predictive probability density functions (PDFs). It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights reflect the forecasts’ relative contributions to predictive skill over a training period. In this paper the authors extend the BMA methodology to use bivariate distributions, enabling them to provide probabilistic forecasts of wind vectors. The BMA method is applied to 48-h-ahead forecasts of wind vectors over the North American Pacific Northwest in 2003 using the University of Washington mesoscale ensemble and is shown to provide better-calibrated probabilistic forecasts than the raw ensemble, which are also sharper than probabilistic forecasts derived from climatology.

Corresponding author address: J. McLean Sloughter, Department of Mathematics, Seattle University, 901 12th Ave., P.O. Box 222000, Seattle, WA 98122. E-mail: sloughtj@seattleu.edu

Abstract

Probabilistic forecasts of wind vectors are becoming critical as interest grows in wind as a clean and renewable source of energy, in addition to a wide range of other uses, from aviation to recreational boating. Unlike other common forecasting problems, which deal with univariate quantities, statistical approaches to wind vector forecasting must be based on bivariate distributions. The prevailing paradigm in weather forecasting is to issue deterministic forecasts based on numerical weather prediction models. Uncertainty can then be assessed through ensemble forecasts, where multiple estimates of the current state of the atmosphere are used to generate a collection of deterministic predictions. Ensemble forecasts are often uncalibrated, however, and Bayesian model averaging (BMA) is a statistical way of postprocessing these forecast ensembles to create calibrated predictive probability density functions (PDFs). It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights reflect the forecasts’ relative contributions to predictive skill over a training period. In this paper the authors extend the BMA methodology to use bivariate distributions, enabling them to provide probabilistic forecasts of wind vectors. The BMA method is applied to 48-h-ahead forecasts of wind vectors over the North American Pacific Northwest in 2003 using the University of Washington mesoscale ensemble and is shown to provide better-calibrated probabilistic forecasts than the raw ensemble, which are also sharper than probabilistic forecasts derived from climatology.

Corresponding author address: J. McLean Sloughter, Department of Mathematics, Seattle University, 901 12th Ave., P.O. Box 222000, Seattle, WA 98122. E-mail: sloughtj@seattleu.edu
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