Probabilistic multisite precipitation downscaling by an expanded BernoulliGamma density network

A nonlinear, probabilistic synoptic downscaling algorithm for daily precipitation series at multiple sites is presented. The expanded Bernoulli–gamma density network (EBDN) represents the conditional density of multisite precipitation, conditioned on synoptic-scale climate predictors, using an artificial neural net-work (ANN) whose outputs are parameters of the Bernoulli–gamma distribution. Following the method-ology used in expanded downscaling, predicted covariances between sites are forced to match observed covariances through the addition of a constraint to the ANN cost function. The resulting model can be thought of as a regression-based downscaling model with a stochastic weather generator component. Pa-rameters of the Bernoulli–gamma distribution are downscaled from the synoptic-scale circulation, and unresolved temporal variability is generated via an autoregressive noise model. Demonstrated on a multisite precipitation dataset from coastal British Columbia, Canada, the EBDN is capable of specifying the con-ditional distribution of precipitation at each site, modeling the occurrence and the amount of precipitation simultaneously, reproducing observed spatial relationships between sites, randomly generating realistic synthetic precipitation series, and predicting precipitation amounts in excess of those in the observational record. 1