A stochastic model for the spatial‐temporal simulation of nonhomogeneous rainfall occurrence and amounts

[1] The nonhomogeneous spatial activation of raincells (NSAR) model is presented which provides a continuous spatial-temporal stochastic simulation of rainfall exhibiting spatial nonstationarity in both amounts and occurrence. Spatial nonstationarity of simulated rainfall is important for hydrological modeling of mountainous catchments where orographic effects on precipitation are strong. Such simulated rainfall fields support the current trend toward distributed hydrological modeling. The NSAR model extends the Spatial Temporal Neyman-Scott Rectangular Pulses (STNSRP) model, which has a homogeneous occurrence process, by generating raincells with a spatially nonhomogeneous Poisson process. An algorithm to simulate nonhomogeneous raincell occurrence is devised. This utilizes a new efficient and accurate algorithm to simulate raincells from an infinite 2-D Poisson process, in which only raincells relevant to the application are simulated. A 4009 km2 Pyrenean catchment exhibiting extreme orographic effects provides a suitable case study comprising seven daily rain gauge records with hourly properties estimated using regional downscaling relationships. Both the NSAR and the STNSRP models are fitted to five calibration rain gauges. Simulated hourly fields are validated using the remaining two rain gauges providing the first validation of time series sampled from STNSRP or NSAR processes at locations not used in model fitting. The NSAR model exhibits considerable improvement over the STNSRP model particularly with respect to nonhomogeneous rainfall occurrence at both daily and hourly resolutions. Further, the NSAR simulation provides an excellent match to the spatially nonhomogeneous observed daily mean, proportion dry, variance, coefficient of variation, autocorrelation, skewness coefficient, cross correlation and extremes, and to the hourly proportion dry and variance properties.