Multiplicative cascade models for fine spatial downscaling of rainfall: parameterization with rain gauge data

摘要

Capturing the spatial distribution of high-intensity rainfall overshort-time intervals is critical for accurately assessing the efficacy ofurban stormwater drainage systems. In a stochastic simulation framework, onemethod of generating realistic rainfall fields is by multiplicative randomcascade (MRC) models. Estimation of MRC model parameters has typicallyrelied on radar imagery or, less frequently, rainfall fields interpolatedfrom dense rain gauge networks. However, such data are not always available.Furthermore, the literature is lacking estimation procedures for spatiallyincomplete datasets. Therefore, we proposed a simple method of calibratingan MRC model when only data from a moderately dense network of rain gaugesis available, rather than from the full rainfall field. The number of gaugesneeds only be sufficient to adequately estimate the variance in the ratio ofthe rain rate at the rain gauges to the areal average rain rate across theentire spatial domain. In our example for Warsaw, Poland, we used 25 gaugesover an area of approximately 1600 km2. MRC models calibrated usingthe proposed method were used to downscale 15-min rainfall rates from a20 by 20 km area to the scale of the rain gauge capture area. Frequencydistributions of observed and simulated 15-min rainfall at the gaugescale were very similar. Moreover, the spatial covariance structure ofrainfall rates, as characterized by the semivariogram, was reproduced afterallowing the probability density function of the random cascade generator tovary with spatial scale.