Abstract 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.

中文翻译：

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雨量计密度和分布对使用集总水文建模方法进行径流模拟的影响

摘要 大多数集总水文模型使用区域平均降水数据作为模型输入。尽管近年来提出了基于天气雷达和基于卫星的降水估计方法，但雨量计仍然是最广泛使用的降水测量工具。雨量计数量和位置的最佳选择将以最小的成本提高区域平均降水估计的准确性。在这项研究中，分析了雨量计密度和分布对不同集水区大小的集总水文建模不确定性的影响。为此，比较了集总水文模型新安江模型在不同规格密度和分布的稠密流域、湘江流域及其子流域中的性能。首先，定义了七个级别的雨量计密度。对于每个密度级别，随机选择几个不同雨量计分布的样本。然后，估计每个样本的区域平均降水量并将其用作新安江模型的输入。最后，使用混洗复杂进化（SCE-UA）算法对模型进行校准，并通过贝叶斯方法评估模型的不确定性。结果表明：1) 由稀疏且不规则的雨量计网络测量的不完善的降水输入将导致模型参数估计和洪水模拟的大量不确定性；2）通过调整模型参数，可以在一定程度上降低降水估算不完善对模型效率的影响；3）通过增加雨量计密度或优化雨量计分布模式来降低建模的不确定性；