A bootstrap method to estimate the influence of rainfall spatial uncertainty in hydrological simulations

Abstract

Abstract. 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 10 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 15 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 20 method could be a guide to quantify an approximate range of simulated error caused by the spatial uncertainty of rainfall input.

Hydraulic-based optimization algorithm for the design of stormwater drainage networks

“…The uncertainty assessment of the HBOA model is conducted using the bootstrapping technique. The bootstrapping strategy is a technique for generating a large number of random samples with replacement from a single dataset to measure uncertainty (Zhang et al 2017). In this study, this approach is utilized to create 20,000 random samples (realizations) or combinations for the storm network with various pipe diameters.…”

Bootstrap prediction intervals

“…The same situation appears in Table 2, which the original sample is from the Beta (0.7,0.7) the both methods of bootstrap have over coverage results with different sample sizes, but the smoothed bootstrap have high coverage proportions. With Beta (10,2) in Table 3 the smoothed bootstrap method has the largest value of coverage proportions, but it is over coverage in most cases. Table 4 shows prediction intervals when the original sample is from Beta (2,10).…”

“…This method developed to work with different statistical inferences, such as confidence intervals, hypothesis tests and regression, it is good technique if the sample size is small. The bootstrap method used in various fields of statistics, see [11] and [10]. Banks in [2] has developed a new version of bootstrap, which is called smoothed bootstrap method, he uses the linear interpolation histospline to smooth between the jump points of empirical distribution.…”