Methods for Locally Calibrated Probabilistic Forecasting

We introduce two approaches to generating locally calibrated probabilistic predictions. Both approaches rely on the statistical post-processing technique of Bayesian model averaging (BMA). Our first, geostatistical model averaging (GMA), allows the statistical parameters such as bias and predictive variance to vary by location. The second approach utilizes an interpolation scheme originally developed for correcting bias on the model grid, which we call the Mass-Baars interpolation technique. The second method, Local BMA, interpolates relevant forecast errors to the model grid according to the Mass-Baars interpolation method before forming the BMA predictive distribution.

Both methods produce predictive probability distributions that are calibrated at a single location by allowing the statistical parameters to adapt to local characteristics. We illustrate the methods on a 2-m temperature dataset in the Pacific Northwest with 48-h forecasts arising from the eight member University of Washington mesoscale ensemble. GMA retains the calibration of the global BMA model in which the statistical parameters are constant across the region, while significantly narrowing the prediction interval widths by 8% on average. Both a sparse and dense training network are considered. The sparse network illustrates the ability of GMA to draw information from the entire training network, while Local BMA succeeds in the dense training network due to the availability of nearby stations that share similar characteristics to the location of interest.