Developing a vertical quasi-two-dimensional surface-subsurface flow model using an approximation for hydraulic gradient

Abstract

Various models have been developed to predict rainfall-runoff. However, practical models often simplify the actual phenomena and do not always provide sufficient accuracy for field-observed parameter values, such as soil water retention and permeability. Other models based on Richards’ equation can directly account for these factors but are not practical because of their huge computational cost. In this study, we developed a vertical quasi-two-dimensional surface-subsurface flow model (quasi-2D model) based on Richards’ equation, in which the hydraulic gradient in the downward direction was approximated by the slope gradient. This method makes it possible to consider soil moisture distribution perpendicular to the slope and simplify the modeling of the runoff process. Rainfall-runoff simulations were conducted on a single slope using the quasi-2D model and compared with the results computed under the same conditions using a detailed model solving the two-dimensional Richards’ equation (2D model). For both subsurface and surface flows, the quasi-2D model reproduced the results of the 2D model well (NSE > 0.99), and performed particularly well on steeper slopes. The computation time of the quasi-2D model was reduced to less than 1/10 of that of the 2D model, confirming the usefulness of the quasi-2D model.