Analytical Solution for Transient Water Table Heights and Outflows from Inclined Ditch-Drained Terrains

Abstract

This paper presents two analytical solutions of the linearized Boussinesq equation for an inclined aquifer, drained by ditches, subjected to a constant recharge rate. These solutions are based on different initial conditions. First, the transient solution is obtained for an initially fully saturated aquifer. Then, an analytical expression is derived for the steady state solution by allowing time to approach infinity. As this solution represents the groundwater table shape more realistically, this water table profile is used as an initial condition in the derivation of the second analytical solution for the groundwater table height, and the in- and outflow into the ditches. The solutions allow the calculation of the transient behavior of the groundwater table, and its ouflow, due to changing percolation rates or water level heights in both ditches.