Recognition of the benefits of probabilistic forecasts for users has led to increased interest in development of methods to provide probabilistic predictions of various weather and climate phenomena. This paper explores several approaches to obtain probabilistic predictions using output from the U.S. Global Forecast System (GFS) ensemble model at 18 cities in the U.S., focusing on temperature predictions, made for 12 hour intervals out until 15 days. First, dynamical model output statistics (DMOS) models are created for each site based on linear statistical models. Records used to develop the models are weighted based on recentness, ensemble spread and performance. This DMOS step produces a selection of statistical forecasts at each sample location. Second, these statistical models are combined using stacked regression. This is a, cross-validation method where the data are randomly partitioned into subsets. Withholding one of the partitions, statistical models are built, and prediction errors are estimated using the withheld data. The models are weighted using non-negative weights calculated to minimize the prediction error.

Several methods are used to combine these ensemble forecasts to produce a single probabilistic forecast: 1. the ensembles are fitted using a finite number of Gaussian distributions (as described by Wilks (2002)); 2. the mean and variance of the ensemble members are used to fit a single Gaussian distribution; and 3. the prediction error estimated using the control member of the GFS ensemble is used to fit a Gaussian distribution. This list represents a range of methods arranged in order of descending complexity. In fact, the last method does not require an ensemble forecast. Results of applying these approaches are discussed and compared using skill scores, ranked histograms and relative operating characteristic diagrams.