Drainage of sloping lands with variable recharge: Analytical formulas and model development

Semianalytical transient equations for shallow subsurface transverse draina ge systems installed in sloping lands are developed. They provide a general relationship between drain flow rates, water table elevations, and recharg e rates. This relationship demonstrates that, depending on the recharge int ensity, several drain flow rates can be observed at a given water table ele vation. The recharge contribution is shown to depend on a water table shape factor and to decrease when the water table is low or the slope is steep. For very steep slopes, the recharge intensity no longer influences the drai n flow rate. These equations can be used to confirm previous results obtain ed in steady-state conditions and to determine precisely under which condit ions slope needs to be considered in drainage design. They have been incorp orated into the field drainage model SIDRA, which simulates hourly values o f water table elevations and drain flow rates. The model predictions are co mpared with the predictions of a steady-state equation and a numerical mode l, which solves the Boussinesq equation (SLOP model).