Bayesian Hierarchical Modeling for Post-processing of Data from Numerical Weather Prediction Systems

An important forecasting application of numerical weather prediction is to use its results to improve planning and response to weather-sensitive decision making. However, the output from such models is often not directly suitable for such purposes because it does not include information about the impact of weather. Post-processing of the output from a physical weather model is required to link it with real observations and to enable the modeling of the weather impact. Since the relevant data and applications are inherently temporal and spatial, we use a Bayesian hierarchical model to “post-process” the multivariate data produced by the weather model. We recognize that different types of weather impact models would lead to different post-processing requirements. Hence, we will illustrate an application of this idea to the problem of modeling outages in the overhead electric power infrastructure of a major utility company in the northeastern United States caused by severe weather. In the electric power outage forecasting modeling, we are interested in several weather parameters, including hourly maximum gust speed, daily rainfall and daily minimum pressure for each of the eleven substation areas of the utility company's service territory.

To begin this effort we build upon our earlier work in the implementation and applications of an operational meso-scale numerical weather prediction and visualization system dubbed "Deep Thunder". We utilized output from 24-hour model runs, typically generated thrice daily (initialized at 06, 12 and 18 UTC) with triply nested, two-way-coupled grids at sixteen, four and one km resolution from September 2008 to August 2009. Explicit, bulk cloud microphysics were included in the model predictions to enable forecasts of potentially severe weather. Since the utility company's service territory straddled portions of the one and four km nests, we use data from the two innermost nests. The surface and near-surface data from each model run were interpolated to the centroids of the eleven aforementioned substation areas. For the same period, we used weather observations from a local, relatively dense mesonet operated by AWS Convergence Technologies, which included a dozen weather stations located in the utility company's service territory. The AWS weather observations provided gust measurement which cannot be produced directly from the weather model. Therefore, we developed a statistical dynamic model to estimate hourly gust speed based on the current wind speed forecasted from the weather model and previous time-unit gust speed measured from AWS weather stations. To postprocess the minimum pressure, we utilized the correlation of wind speed and pressure to improve the estimation of pressure. In the Bayesian hierarchical model, we incorporated AWS weather measurement errors, spatial interpolation errors and the physical model systematic errors to provide uncertainty analysis of the estimation. We divide the entire dataset into training and testing parts. The estimation results are tested using the testing dataset. The post-processed weather outputs are used as inputs for the electric power outage forecasting model.