Probabilistic Wind Speed Forecasting using Ensembles and Bayesian Model Averaging

Abstract

Probabilistic forecasts of wind speed 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. Statistical approaches to wind forecasting offer two particular challenges: the distribution of wind speeds is highly skewed, and wind observations are reported to the nearest whole knot, a much coarser discretization than is seen in other weather quantities. 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 we extend BMA to provide probabilistic forecasts of wind speed, taking account of the skewness of the predictive distributions and the discreteness of the observations. The BMA method is applied to 48-hour ahead forecasts of maximum wind speed over the North American Pacific Northwest in 2003 using the University of Washington mesoscale ensemble, and is shown to provide calibrated and sharp probabilistic forecasts. Comparisons are made between a number of formulations that account for the discretization of the observations.

Statistical downscaling of historical monthly mean winds over a coastal region of complex terrain. I. Predicting wind speed

“…Selected stations in BC were included in the downscaling studies of Sloughter et al (2010) and Thorarinsdottir and Gneiting (2010), which focused on short-range forecasting of wind speed over the Pacific Northwest. Extreme wind recurrence frequency at three stations in southern BC was analyzed in the context of larger-scale climate variability by Abeysirigunawardena et al (2009).…”

Calibrating ensemble forecasting models with sparse data in the social sciences

“…However, neither of these assumptions is strictly necessary. EBMA has been extended to handle multiple distributional forms, including a zero-inflated gamma, discrete quantitative outcomes, and binary outcomes (Montgomery et al, 2012a;Sloughter, Gneiting, & Raftery, 2010;Sloughter, Raftery, Gneiting, & Fraley, 2007). Likewise, the method allows for the estimation of distinct variance parameters, although this is not usually advantageous for limited samples in practice.…”

High resolution forecasting for wind energy applications using Bayesian model averaging

“…The model parameters are then estimated through maximum likelihood from the training data using an Estimation-Maximisation (EM) algorithm . The BMA method was further developed for parameters whose distributions do not approximate Gaussians: precipitation fitted with a mixture of a discrete component at zero and a gamma distribution (Sloughter et al, 2007), wind speed fitted with a gamma distribution (Sloughter et al, 2010) and visibility fitted with a mixture of discrete point mass and beta distribution components (Chmielecki and Raftery, 2011). Fraley et al (2010) described how the BMA method could be adapted to the case where one or more of the ensemble members are exchangeable, differing only in random perturbations.…”

“…Again, the Weibull gave a more accurate fit. The general consensus within the literature is that wind speed data are best fit by a Weibull distribution; however, Silva (2007) showed how very often the Weibull, gamma and log-normal distributions are difficult to distinguish, with Sloughter et al (2010) favouring the gamma distribution.…”

“…The parameters m and a are ensemble member specific, and as with the normal distribution can be estimated through linear regression and loglikelihood parameter estimation over the training period. The method takes into account the problems of getting the log of a wind speed value of zero and discretisation of the observations to whole numbers in knots (Sloughter et al, 2010). The parameter vector is used to construct the overall BMA forecast PDF as a weighted average of individual forecast PDFs.…”