Sensitivity of a lumped and semi-distributed hydrological model to several methods of rainfall interpolation on a large basin in West Africa

Abstract

This paper examines the sensitivity of a hydrological model to several methods of spatial interpolation of rainfall data. The question is investigated in a context of scarcity of data over a large West African catchment (100,000 km2) subject to a drastic trend of rain deficit since the 1970s. Thirteen widely scattered rainfall stations and their daily time series were used to interpolate gridded rainfall surfaces over the 1950-1992 period via various methods: Thiessen polygons, inverse distance weighted (IDW) method, thin smooth plate splines (spline), and ordinary kriging. The accuracy of these interpolated datasets was evaluated using two complementary approaches. First, a point-by-point assessment was conducted, involving comparison of the interpolated values by reference to observed point data. Second, a conceptual rainfall-runoff model (Hydrostrahler) was used in order to assess whether and to what extent the alternative sets of interpolated rainfall impacted on the hydrological simulations. A lumped modelling exercise over a long period (1952-1992) and a semi-distributed exercise over a short period (1971-1976) were performed, using calibrations aimed at optimizing a Nash-Sutcliffe criterion. The results were evaluated for each interpolated forcing dataset using statistical analysis and visual inspection of the simulated and observed hydrographs and the parameters obtained from calibration. Assessment of the interpolation methods by reference to point data indicates that interpolations using the IDW and kriging methods are more efficient than the simple Thiessen technique, and, to a lesser extent, than spline. The use of these data in a daily lumped modelling application shows a different ranking of the various interpolation methods with regard to various hydrological assessments. The model is particularly sensitive to the differences in the rainfall input volume produced by each interpolation method: the IDW dataset yields the highest hydrological efficiency while the spline dataset gets the poorest results. Although the calibration procedure makes it possible to partly compensate for the differences (or errors) between rain input datasets, the semi-distributed hydrological model remains sensitive to volumetric and spatial differences. Then, assessment of these combined differences through the sensitivity of the semi-distributed model provides us with more complete discrimination between the interpolated data inputs. The output results at the basin outlet do not decrease between the lumped and semi-distributed modelling exercises with the IDW and kriging datasets, in contrast to the Thiessen and spline datasets, which tends to indicate the superiority of the former two interpolated inputs. In this hydrological application, the IDW dataset is still shown to provide the most realistic results. Moreover, despite the scarcity of rainfall data, coherent semi-distributed values of the model parameters are obtained by calibration over a large gradient of climate conditions. Finally, it is observed that although the model reproduced the rainfall-runoff relationship before 1970 very well, regardless of which interpolated datasets were used, it was not able to satisfactorily simulate the basin behaviour after the change in rainfall regime. This inability needs further investigation and is the subject of ongoing research. © 2008 Elsevier B.V. All rights reserved.