Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes

The methodology relies on a latent Gaussian process to drive precipitation occurrence and a probability integral transformed Gaussian process for intensity. At individual locations, the model reduces to a Markov chain for precipitation occurrence and a gamma distribution for precipitation intensity, allowing statistical parameters to be included in a generalized linear model framework.

Statistical parameters are modeled as spatial Gaussian processes, which allows for interpolation to locations where there are no direct observations via kriging. One advantage of such a model for the statistical parameters is that stochastic generator parameters are immediately available at any location, with the ability to adapt to spatially varying precipitation characteristics. A second advantage is that parameter uncertainty, generally unavailable with deterministic interpolators, can be immediately quantified at all locations.