An efficient and guaranteed stable numerical method for continuous modeling of infiltration and redistribution with a shallow dynamic water table

Abstract

We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call ''GARTO'' can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a nearsurface water table.

Earthworms and tree roots: A model study of the effect of preferential flow paths on runoff generation and groundwater recharge in steep, saprolitic, tropical lowland catchments

“…Water infiltration occurs in both the VPFPs and the soil matrix but water in the VPFPs reaches the sub‐layer bottom very quickly and goes below the preferential flow layer to become groundwater recharge. In the matrix domain, downward water movement was simulated using the GARTO method [ Lai et al ., ]. Water from the VPFP domain was assumed to not interact with the matrix, and LPFPs and VPFPs were treated as disconnected.…”

“…This structure assumed that Darcian matrix flow is the only type of flow in the unsaturated zone. We used the GARTO scheme [ Lai et al ., ] to simulate soil matrix flow. The GARTO scheme agrees closely with the numerical solution of Richards' equation [ Richards , ] but is much more computationally efficient with guaranteed convergence and mass conservation.…”

Land Use‐Dependent Preferential Flow Paths Affect Hydrological Response of Steep Tropical Lowland Catchments With Saprolitic Soils

“…The sublayer was further divided into two domains, a matrix infiltration domain and a vertical PFP domain. In the matrix infiltration domain, downward water movement was simulated using the Green‐Ampt infiltration with redistribution (GAR) model with features from the Talbot‐Ogden (T‐O) infiltration and redistribution method (Lai et al, ), which is a simplified version of the finite moisture content solution of the Soil Moisture Velocity Equation (Ogden et al, , ). Macropores in the vertical PFP domain were assumed to fully penetrate the preferential flow layer and were referred to as “effective percolating vertical PFPs.” Water movement through these effective percolating vertical macropores was explicitly simulated using a laminar pipe flow equation.…”

A new general 1‐D vadose zone flow solution method

“…For instance, Lai et al [2015] found that only 10 groundwater bins allowed accurate simulation of the effects of water table dynamics on a Green and Ampt redistribution (GAR) scheme [Ogden and Saghafian, 1997].…”