Application of fiducial method for streamflow prediction under small sample cases in Xiangxihe watershed, China

Abstract Hydrological prediction in basins with few data remains an important task for hydrologists given the practical relevance of hydrological prediction for water management and infrastructure design. In this article, fiducial method is applied for hydrological prediction to deal with small sample cases. Fiducial inference can be viewed as a procedure that obtains a measure on a parameter space while assuming less than Bayesian inference does (no prior); it can also be viewed, as a procedure that in a routine algorithmic way finds approximate pivots for parameters of interest, which is one of the main goals of frequential inference. In addition, fiducial methods require only the information from samples (streamflow data). Such that fiducial methods can account for valid information of streamflow observation and avoid model uncertainties. Three goodness-of-fit performance measures in terms of width of prediction interval (PI), accuracy and comprehensive measure will be examined to demonstrate the feasibility of fiducial method in hydrological prediction. Soil and water assessment tool (SWAT) based on Bayesian inference is used for comparison. Results show that (a) the performance of sharpness for the two methods is basically same under small nominal coverage; (b) fiducial PI can captures more observations with the similar width; (c) prediction performance of fiducial method is more satisfactory than SWAT based on Bayesian inference under small sample cases according to interval skill score; (d) fiducial method for hydrological prediction is much more time-saving than SWAT based on Bayesian inference. In summary, fiducial method has significant implications in increasing the performance and efficiency for hydrological prediction under small sample cases.