Comparison of the multiple imputation approaches for imputing rainfall data series and their applications to watershed models

Abstract Rainfall data scarcity has caused enormous problems in hydrologic and non-point pollution (H/NPS) predictions, as rainfall data represent the key input to watershed models. In this study, the effects of different imputation methods such as the data augmentation (DA) and the expectation maximization with bootstrap (EMB) algorithms on rainfall data scarcity were compared. The effects of different data scarcity rates and periods on model performance and prediction uncertainty were then quantified. Finally, the effects of different imputed data sets on H/NPS results were evaluated with the soil and water assessment tool (SWAT). A real case study in the Daning River watershed, Three Gorges Reservoir Region, China, was evaluated. The results indicated that rainfall data scarcity during low flow periods would result in poorer model performance and larger prediction uncertainty, especially to some minimum values, and the time when the maximum values are more susceptible is the rainfall data scarcity during high flow periods. The repair of rainfall data and the H/NPS model performance obtained by the EMB algorithm are superior to the traditional DA and weather generator performances. This advantage of the EMB algorithm would be more definitive if a specific threshold of data scarcity is reached. It is noted that even if the best algorithm is used, the imputed value is always lower than the peak observed value. This paper reports important implications for the choice of imputation methods and the use of H/NPS models for solving data scarcity problems for watershed studies.