A novel semi-numerical infiltration model combining conceptual and physically based approaches

Abstract

Hydrological models use methods of varying complexity to compute vertical infiltration described by Richards equation, which lacks an analytical solution, and is often solved using time-consuming, iterative numerical models. For continuous hydrological simulations these models are often replaced by simpler, yet less accurate models for greater computational efficiency. Seeking a compromise between accuracy and efficiency, a new semi-numerical infiltration model, combining conceptual and physically based approaches is developed and presented in this paper. The model assumes dividing the computational domain into computational cells that retain a differential form of the mass balance equation. After linearizing the input and output flux in each cell, an analytical solution of the mass balance equation is obtained. The solution is similar to a “linear reservoir” function, and it is valid only for a discrete time interval. By combining such solutions for each computational cell, a tridiagonal system of linear equations is obtained and solved directly without iterations. This non-iterative approach to solving Richards equation is reminiscent of the Ross model, with a key difference in the “linear reservoir” exponential term, contributing to the accuracy and stability of the presented semi-numerical model. Comparison between this model and the Ross model on four numerical examples shows that, except in strictly unsaturated conditions when the soil is exposed to low-intensity precipitation, the semi-numerical model achieves more stable results with considerably smaller number of computational steps and reduced mass balance errors. This indicates a clear potential for effective application of the proposed approach in distributed hydrological models.