Evaluating the effect of numerical schemes on hydrological simulations: HYMOD as A case study

Abstract

The importance of numerical schemes in hydrological models has been increasingly recognized in the hydrological community. However, the relationship between model performance and the properties of numerical schemes remains unclear. In this study, we employed two types of numerical schemes (i.e., explicit Runge-Kutta schemes with different orders of accuracy and partially implicit Euler schemes with different implicit factors) in the hydrological model (HYMOD) to simulate the flow hydrograph of the Leaf River basin from 1948 to 1988. Results computed by different numerical schemes were compared and the relationships between model performance and two scheme properties (i.e., the order of accuracy and the implicit factor) were discussed. Results showed that the more explicit schemes generally lead to the overestimation of flow hydrographs, whereas the more implicit schemes lead to underestimation. In addition, the numerical error tended to decrease with increasing orders of accuracy. As a result, the optimal parameter sets found by loworder schemes significantly deviated from those found by the analytical solution. The findings of this study can provide useful implications for designing suitable numerical schemes for hydrological models.