Hydrology and Earth Systems Sciences | Zhang et al. 
Rainfall stations with 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 analysed 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 analysed with the bootstrapped rainfall inputs. By comparing the uncertainties of rainfall and runoff, the responses of the hydrological simulation to the spatial uncertainty of rainfall are discussed. Analyses are performed for three rainfall events in the upstream of the Qingjian River basin, a sub-basin of the Yellow River. 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 simulated runoff processes. This quantified relationship between rainfall input and simulation performance can provide useful information on managing rainfall station density in river basins. The proposed method could be a guide to quantify an approximate range of simulated error caused by the spatial uncertainty of rainfall input.
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