The influence of spatial variability in rainfall on the catchment response
A new stochastic rainfall field model is described which employs the Turning Bands Method (TBM) to transform a unidimensional Gaussian process, generated by the fractional differencing process along a line, into a multidimensional space-time Gaussian process with a specified space-time correlation structure. Transformations are applied to give the rainfall process a non-Gaussian and non-stationary structure. A correction factor is introduced into the model to take account of the effect of topography on rainfall. The model has been applied to the small upland Wye catchment in mid Wales (area 10.55 km2) and shown to reproduce satisfactorily the statistics and correlation structure of observed hourly point rainfall.
As an extension to the rainfall field model, a new technique of conditional simulation has been used to generate the rainfall fields. The conditionally simulated rainfall fields reproduce exactly the observed point rainfalls at measurement points and likely realizations of rainfall fields between points.
Rainfall fields generated by the above mentioned rainfall field model and the conditional simulation technique are fed directly into the Systeme Hydrologique European (SHE) model and the sensitivity of runoff prediction errors to (i) level of space-time correlation (ii) sampling of rainfall with different schemes in space and (iii) antecedent conditions are explored. It is found that in case of Wye catchment the errors deriving from sampling procedure used are generally small when rainfall fields were based on observed correlation structure. Sensitivity of errors to different correlation levels give the impression that errors increase with a decrease in correlation level. Further it is noticed that this trend of errors is more pronounced in `dry' catchment conditions as compared to `wet' catchment conditions. Overall the results for the small Wye catchment illustrate that the catchment acts as a smoother of the spatially distributed rainfall input at this spatial scale and for the rainfall regime in question. However, the results imply that for the typical raingauge densities encountered for larger catchments, significant errors may occur.