Locally Calibrated Probabilistic Temperature Forecasting Using Geostatistical Model Averaging and Local Bayesian Model Averaging

William Kleiber 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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Jeffrey Baars Department of Atmospheric Sciences, University of Washington, Seattle, Washington

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Tilmann Gneiting Institute of Applied Mathematics, University of Heidelberg, Heidelberg, Germany

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Clifford F. Mass Department of Atmospheric Sciences, University of Washington, Seattle, Washington

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Eric Grimit 3Tier Environmental Forecast Group, Seattle, Washington

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Abstract

The authors introduce two ways to produce locally calibrated grid-based probabilistic forecasts of temperature. Both start from the Global Bayesian model averaging (Global BMA) statistical postprocessing method, which has constant predictive bias and variance across the domain, and modify it to make it local. The first local method, geostatistical model averaging (GMA), computes the predictive bias and variance at observation stations and interpolates them using a geostatistical model. The second approach, Local BMA, estimates the parameters of BMA at a grid point from stations that are close to the grid point and similar to it in elevation and land use. The results of these two methods applied to the eight-member University of Washington Mesoscale Ensemble (UWME) are given for the 2006 calendar year. GMA was calibrated and sharper than Global BMA, with prediction intervals that were 8% narrower than Global BMA on average. Examples using sparse and dense training networks of stations are shown. The sparse network experiment illustrates the ability of GMA to draw information from the entire training network. The performance of Local BMA was not statistically different from Global BMA in the dense network experiment, and was superior to both GMA and Global BMA in areas with sufficient nearby training data.

Current affiliation: Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, Colorado.

Corresponding author address: William Kleiber, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. E-mail: wkleiber@ucar.edu

Abstract

The authors introduce two ways to produce locally calibrated grid-based probabilistic forecasts of temperature. Both start from the Global Bayesian model averaging (Global BMA) statistical postprocessing method, which has constant predictive bias and variance across the domain, and modify it to make it local. The first local method, geostatistical model averaging (GMA), computes the predictive bias and variance at observation stations and interpolates them using a geostatistical model. The second approach, Local BMA, estimates the parameters of BMA at a grid point from stations that are close to the grid point and similar to it in elevation and land use. The results of these two methods applied to the eight-member University of Washington Mesoscale Ensemble (UWME) are given for the 2006 calendar year. GMA was calibrated and sharper than Global BMA, with prediction intervals that were 8% narrower than Global BMA on average. Examples using sparse and dense training networks of stations are shown. The sparse network experiment illustrates the ability of GMA to draw information from the entire training network. The performance of Local BMA was not statistically different from Global BMA in the dense network experiment, and was superior to both GMA and Global BMA in areas with sufficient nearby training data.

Current affiliation: Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, Colorado.

Corresponding author address: William Kleiber, Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322. E-mail: wkleiber@ucar.edu
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