Two-dimensional Analytical Derivation of Incipient Desaturation Criterion in Stream-aquifer Flow Exchange

A criterion for incipient desaturation for a stream and an aquifer initially in saturated hydraulic connection is derived analytically. The riverbed acts as a clogging layer. Such a criterion cannot be derived using a one-dimensional analysis. At least a two-dimensional analysis is required. It applies for a variety of shape of cross-sections. The formulae are algebraic and show explicitly the various factors that affect the initiation of desaturation such as river width, thickness of the aquifer, thickness of the clogging layer, conductivities of the clogging layer and of the aquifer, (drainage) entry pressure of the aquifer, ponded depth over the riverbed and aquifer head at some distance from the river bank. It is shown also that neglecting the change in thickness of the capillary fringe due to flow, as opposed to its hydrostatic value, has little impact on the accuracy of the criteria for incipient desaturation.