A numerical model based on coupled one‐dimensional Richards and Boussinesq equations

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Abstract
An approximate numerical method to solve transient two‐dimensional unsaturated‐saturated subsurface flow problems is presented. Several one‐dimensional vertical unsaturated column models are linked to a one‐dimensional saturated flow model. The Dupuit‐Forchheimer assumptions are used for the saturated flow, and the unsaturated flow is assumed to be strictly vertical. The systems are linked because solutions of the equation governing unsaturated flow determine recharge and storage information used to solve the equation governing saturated flow. In addition, the position of the water table locates the lower boundaries of the unsaturated models. The solution of a test problem using a linked model is compared with results from a rigorous two‐dimensional model. The comparison is good at early times when recharge to the water table is small but poor at later times when recharge increases. Applications are then made to field‐size problems. Results compare closely with an actual groundwater hydrograph. In addition, a linked model is used to show that in a specific humid climate watershed the type of vegetation does not significantly affect the groundwater regimen, whereas in a given arid climate watershed the type of vegetation would determine whether groundwater recharge occurred. For field‐size problems where water table movement is relatively small, where the Dupuit‐Forchheimer assumptions are valid, and where lateral unsaturated flow is not important, the linked model offers an efficient approximate way to solve unsaturated‐saturated flow problems.