Water-table shapes and drain flow rates in shallow drainage systems

A relationship between drain flow rate, elevation and shape of the water-table and recharge intensity in shallow drainage systems is developed. From an analytical spatial integration of the Boussinesq equation in transient conditions, drain flow rates are shown to be the sum of three terms; the first one is proportional to the maximum water-table elevation and more generally to the steady state flow rate at the same water-table elevation; the second one is a fraction of the recharge rate of the water-table depending on the water-table shape; the third one accounts for possible changes in water storage in the water-table due to its shape changes. Drain flow rates in shallow drainage systems are shown to be fully predicted by one unique variable that is a function of a combination of the hydraulic conductivity (K), the drainable porosity (f), and the drain spacing (2L), namely σ=K/f2L2. This variable also determines the dynamics of changes in the water-table shape and in turn the respective parts of the three terms in the equation. It is shown that drainage systems with values of σ>1 m−1 h−1 respond very fast to recharge events: water-table shape changes occur very quickly so that the third component of the drain flow can be neglected; in that case, the equation results in a simplified analytical relationship. The reliability of the complete and simplified equations to predict drain flow rates in transient conditions is discussed in relation to in situ measurements.