A comparison of stochastic models for spatial rainfall downscaling

We explore the performance of three types of stochastic models used for spatial rainfall downscaling and assess their ability to reproduce the statistics of precipitation fields observed during the GATE radar experiment. We consider a bounded multifractal cascade, an autoregressive linear process passed through a nonlinear static filter (sometimes called a meta-Gaussian model), and a model based on the presence of individual rainfall cells with power law profile. As test statistics we use the low-order moments of the amplitude distribution, the distribution of generalized fractal dimensions, the generalized scaling exponents, the slope of the power spectrum, and the properties of the spatial autocorrelation. The results of the analysis indicate that all models provide, on average, a satisfactory representation of the statistical properties of the GATE rainfall fields (including the anomalous scaling behavior), with a slightly better performance of the model based on individual rainfall cells. All models, however, display large scatter in the field-to-field comparison with the data. These results indicate that data analysis alone does not allow, at the moment, for preferring one downscaling approach over another.