Abstract
Abstract. Capturing the spatial distribution of high-intensity rainfall over short-time intervals is critical for accurately assessing the efficacy of urban stormwater drainage systems. In a stochastic simulation framework, one method of generating realistic rainfall fields is by multiplicative random cascade (MRC) models. Estimation of MRC model parameters has typically relied on radar imagery or, less frequently, rainfall fields interpolated from dense rain gauge networks. However, such data are not always available. Furthermore, the literature is lacking estimation procedures for spatially incomplete datasets. Therefore, we proposed a simple method of calibrating an MRC model when only data from a moderately dense network of rain gauges is available, rather than from the full rainfall field. The number of gauges needs only be sufficient to adequately estimate the variance in the ratio of the rain rate at the rain gauges to the areal average rain rate across the entire spatial domain. In our example for Warsaw, Poland, we used 25 gauges over an area of approximately 1600 km2. MRC models calibrated using the proposed method were used to downscale 15-min rainfall rates from a 20 by 20 km area to the scale of the rain gauge capture area. Frequency distributions of observed and simulated 15-min rainfall at the gauge scale were very similar. Moreover, the spatial covariance structure of rainfall rates, as characterized by the semivariogram, was reproduced after allowing the probability density function of the random cascade generator to vary with spatial scale.
Highlights
Urban catchments, due to their diminished damping properties relative to rural and natural catchments, are responsive to bursts of local, high intensity rainfall
Advantages of using long time series are that they allow for a statistical analysis of system performance and they eliminate the problem of defining the appropriate initial catchment water storage for a design storm (Hingray and Ben Haha, 2005)
We focus on multifractal cascade models because, as noted by Veneziano et al (2006), multifractal models are simpler and have fewer parameters, and though we do not consider these properties in this study, one can deduce the frequency distribution of rainfall intensities and rainfall extremes from their multi-fractal structure
Summary
Due to their diminished damping properties relative to rural and natural catchments, are responsive to bursts of local, high intensity rainfall This makes characterization of the spatial distribution of rainfall at small time scales critical to evaluating the efficacy of urban stormwater drainage systems. Parameter estimation has mostly been done using radar-derived rainfall fields, though in a small number of cases rainfall fields were generated by interpolating rain gauge data (Svensson et al, 1996; Jothityangkoon et al, 2000; Sharma et al, 2007). When the gauge density is coarse relative to the final spatial resolution of interest, the interpolation methods will fail because they smooth out the fine-scale variability It is common for large metropolitan areas to have in excess of twenty rain gauges installed, whereas reliable fine scale radar-rainfall is less common (e.g., Thames Water, 2010). Parameterization of a space-time model will be a topic of a subsequent paper
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