A simple approach for stochastic generation of spatial rainfall patterns

Rainfall scenarios are of considerable interest for design flood and flood risk analysis. To this end, the stochastic generation of continuous rainfall sequences is often coupled with the continuous hydrological modelling. In this context, the spatial and the temporal rainfall variability represents a significant issue, especially for basins in which the rainfall field cannot be approximated through the use of a single station. Therefore, methodologies for the spatially and temporally correlated rainfall generation are welcome. An example of such a methodology is the well-established Spatial-Temporal Neyman-Scott Rectangular Pulse (STNSRP), a modification of the single-site Neyman-Scott Rectangular Pulse (NSRP) approach, designed to incorporate specific features to reproduce the rainfall spatial cross-correlation. In order to provide a simple alternative to the STNSRP, a new method of generating synthetic rainfall time series with pre-set spatial-temporal correlation is proposed herein. This approach relies on the single- site NSRP model, which is used to generate synthetic hourly independent rainfall time series at each rain gauge station with the required temporal autocorrelation (and several other appropriately selected statistics). The rank correlation method of Iman and Conover (IC) is then applied to these synthetic rainfall time series in order to introduce the same spatial cross-correlation that exists between the observed time series. This combination of the NSRP model with the IC method consents the reproduction of the observed spatial-temporal variability of a rainfall field. In order to verify the proposed procedure, four sub-basins of the Upper Tiber River basin are investigated whose basin areas range from 165 km² to 2040 km². Results show that the procedure is able to preserve both the rainfall temporal autocorrelation at single site and the rainfall spatial cross-correlation at basin scale, and its performance is comparable with that of the STNSRP model for rainfall field generation. Given its simple formal structure (based on well established methods: i.e. NSRP and IC), we believe that the proposed approach can be conveniently utilized to generate spatially and temporally correlated rainfall scenarios.