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Rainfall stations of a certain number and spatial distribution supply sampling records of rainfall processes in a river basin. Uncertainty may be introduced when the station records are spatially interpolated for the purpose of hydrological simulations. This study adopts a bootstrap method to quantitatively estimate the uncertainty of areal rainfall estimates and its effects on hydrological simulations. The observed rainfall records are first analyzed using clustering and correlation methods and possible average basin rainfall amounts are calculated with a bootstrap method using various combinations of rainfall station subsets. Then, the uncertainty of simulated runoff, which is propagated through a hydrological model from the spatial uncertainty of rainfall estimates, is analyzed with the bootstrapped rainfall inputs. By comparing the uncertainties of rainfall and runoff, the responses of the hydrological simulation to the rainfall spatial uncertainty are discussed. Analyses are primarily performed for three rainfall events in the upstream of the Qingjian River basin, a sub-basin of the middle Yellow River; moreover, one rainfall event in the Longxi River basin is selected for the analysis of the areal representation of rainfall stations. Using the Digital Yellow River Integrated Model, the results show that the uncertainty of rainfall estimates derived from rainfall station network has a direct influence on model simulation, which can be conducive to better understand of rainfall spatial characteristic. The proposed method can be a guide to quantify an approximate range of simulated error caused by the spatial uncertainty of rainfall input and the quantified relationship between rainfall input and simulation performance can provide useful information about rainfall station network management in river basins.

Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method