| We introduce a flexible parametric family of matrix-valued covariance functions for multivariate spatial random fields, where each constituent component is a Matern process The model parameters are interpretable in terms of process variance, smoothness, correlation length, and co-located correlation coefficients, which can be positive or negative. Both the marginal and the cross-covariance functions are of the Matern type. In a data example on error fields for numerical predictions of surface pressure and temperature over the Pacific Northwest, we compare the bivariate Matern model to the traditional linear model of coregionalization.;Accurate weather forecasts benefit society in crucial functions, including agriculture, transportation, recreation, and basic human and infrastructural safety. Over the past two decades, ensembles of numerical weather prediction models have been developed, in which multiple estimates of the current state of the atmosphere are used to generate probabilistic forecasts for future weather events. However, ensemble systems are uncalibrated and biased, and thus need to be statistically postprocessed. Bayesian model averaging (BMA) is a preferred way of doing this Particularly for surface temperature and quantitative precipitation, biases and calibration errors depend critically on local terrain features. We introduce a geostatistical approach to modeling locally varying BMA parameters, as opposed to the extant method that holds parameters constant across the forecast domain. For precipitation, degeneracies caused by enduring dry periods are overcome by Bayesian regularization and Laplace approximations. The new approach, called geostatistical model averaging (GMA), was applied to 48-hour ahead forecasts of daily precipitation accumulation and surface temperature over the North American Pacific Northwest, using the eight-member University of Washington Mesoscale Ensemble. GMA had better aggregate and local calibration than the extant technique, and was sharper on average. |
