A new kinematic wave model that describes lateral subsurface flow and percolation in hillslopes

Abstract

Kinematic wave (KW) models are commonly used for flood forecasting in large river basins, but have limitations in their ability to simulate percolation effects. Here, we suggest an extended KW model wherein the vertical pressure head is under non-hydrostatic conditions. The proposed model uses the Brooks Corey and Mualem models to estimate the water retention curve and unsaturated hydraulic conductivity and adopts the pressure head gradient as a new variable to calculate runoff based on changing water content distributions over time due to percolation. The increase in the pressure head gradient with rainfall infiltration is determined from the relationship between water storage and pressure head distribution, while the decrease in pressure head gradient due to percolation is modeled as exponential decay with time. A comparison of the proposed KW model and a numerical solution of the Richards equation shows that the proposed KW model can reproduce the storage effect caused by percolation, delaying runoff and reducing peak discharge. The agreement between the proposed KW model and the Richards equation is high for soils with high water retention. Conversely, the agreement becomes lower for soil with low water retention or deep soil layer thickness, where the complexity of water content distribution requires further refinement. The proposed model can easily be incorporated into distributed models while low computational cost with keeping the important percolation effects.