The effect of rain gauge density and distribution on runoff simulation using a lumped hydrological modelling approach

Most lumped hydrological models use areal average precipitation data as model input. Though weather-radar-based and satellite-based precipitation estimation methods have been proposed in recent years, the rain gauge is still the most widely used precipitation-measuring tool. Optimal selection of rain gauge number and location will improve the accuracy of areal average precipitation estimations with minimum cost. In this study, the impacts of rain gauge density and distribution on lumped hydrological modelling uncertainty with different catchment sizes are analysed. To this end, the performances of a lumped hydrological model, the Xinanjiang model, in a densely gauged river basin, the Xiangjiang River basin, and its sub-basins under different gauge density and distribution are compared. First, seven levels of rain gauge density are defined. For each density level, several samples of different rain gauge distributions are randomly selected. Then, the areal average precipitation of each sample is estimated and used as input to the Xinanjiang model. Finally, the model is calibrated using the shuffled complex evolution (SCE-UA) algorithm, and model uncertainty is evaluated via the Bayesian method. The results show that 1) imperfect precipitation inputs measured by a sparse and irregular rain gauge network will lead to substantial uncertainty in model parameter estimation and flood simulation; 2) the impacts of imperfect precipitation estimates on model efficiency can be reduced to some extent through the adjustment of model parameters; 3) modelling uncertainty is reduced by increasing the rain gauge density or optimizing the rain gauge distribution pattern; and 4) the improvement in lumped model efficiency is no longer significant when the rain gauge density exceeds a certain threshold, but a further increase in rain gauge density will reduce model parameter uncertainty and the width of the runoff confidence interval.