Impact of aquifer desaturation on steady-state river seepage

•Provided an exact expression for incipience of desaturation in a stream–aquifer hydraulic connection.•Provided explicit formulae for the seepage rate once hydraulic connection is unsaturated.•Demonstrated that head is essentially uniform at the bottom of the clogging layer (riverbed).•Demonstrated that the approximation of an average flat water table below the riverbed is legitimate•Demonstrated that the water table head varies linearly between the river bank to the “far (enough) distance”.

Flow exchange between surface and ground water is of great importance be it for beneficial allocation and use of the water resources or for the proper exercise of water rights. That exchange can take place under a saturated or unsaturated flow regime. Which regimes occur depend on conditions in the vicinity of the interactive area. Withdrawals partially sustained by seepage may not bring about desaturation but greater amounts eventually will. The problem considered in this paper deals only with the steady-state case. It is meant as a first step toward a simple, yet accurate and physically based treatment of the transient situation. The primary purpose of the article is to provide simple criteria for determination of the initiation of desaturation in an aquifer originally in saturated hydraulic connection with a river or a recharge area. The extent of the unsaturated zone in the aquifer will increase with increasing withdrawals while at the same time the seepage rate from the river increases. However the seepage increase will stop once infiltration takes place strictly by gravity in the aquifer and is no longer opposed by the capillary rise from the water table below the riverbed. Following desaturation simple criteria are derived and simple analytical formulae provided to estimate the river seepage based on the position of the water table mound below the clogging layer and at some distance away from the river bank. They fully account for the unsaturated flow phenomena, including the existence of a drainage entry pressure. Two secondary objectives were to verify that (1) the assumption of uniform vertical flow through a clogging layer and that (2) the approximation of the water table mound below the seepage area as a flat surface were both reasonably legitimate. This approach will be especially advantageous for the implementation of the methodology in large-scale applications of integrated hydrologic models used for management.