Modelling the effects of spatial variability in rainfall on catchment response. 1. Formulation and calibration of a stochastic rainfall field model

Abstract

The relationship between the spatial variability of rainfall and catchment response is investigated by conducting experiments with a stochastic rainfall field model and a physically based distributed modelling system, the Système Hydrologique Européen (SHE), both of which are calibrated for a small upland catchment. The development and calibration of the rainfall field model is described in Part 1 of this paper, and the experiments with simulated rainfall fields and the SHE catchment model are described in Part 2. The rainfall field model is based on the use of the Turning Bands Method (TBM) incorporating a fractionally differenced line process to generate Gaussian random fields with a specified space-time correlation structure which can be isotropic or anisotropic. A transformation is then applied to the Gaussian field to reproduce the non-stationary temporal structure and skewed marginal distribution of observed rainfall. The transformed field is then propagated in space with the required velocity. The model is calibrated using hourly data for ten storms observed at three sites in the upper Wye catchment (area 10.55 km2) at Plynlimon, Wales. As rainfall over the catchment exhibits significant variation with altitude (and other factors), an altitude correction factor is applied to the simulated rainfall fields. Comparisons of the means, variances, skewnesses, cross- and auto-correlation functions of observed and simulated storms at the sampling points show good agreement, and realistic spatial patterns are observed in the simulated fields. A procedure is developed and applied for generating conditional simulations whereby the historical storm rainfall at the sampling points can be reproduced exactly in simulated fields, thus allowing several realizations of the unobserved spatial variability of rainfall at all other points in the catchment to be generated for any historical storm. © 1996 - Elsevier Science B.V. All rights reserved.