Is the groundwater reservoir linear? A mathematical analysis of two limiting cases

Abstract

Storage-discharge relationships of the groundwater reservoirs of several catchments in a temperate-humid climate were reported in the literature to be seemingly non-linear. Once recharge was adequately accounted for during model calibration they turned out to be linear. The question was posed if this linearity was a fundamental property of 5 groundwater reservoirs in general. A mathematical analysis based on analytical solutions for several cases involving parallel flow in horizontal aquifers shows that this is not the case when the surface water level is close to the aquifer bottom. When the aquifer is of constant thickness, linear-reservoir behaviour arises when the forcings remain constant for a sufficiently long time. This can range from a few weeks for aquifers with 10 a dense drainage network of streams or ditches to years or centuries for large aquifers drained by rivers many kilometers apart. The characteristic time of the groundwater reservoir depends on whether or not the aquifer is leaky and recharge is non-zero. It is concluded that groundwater reservoirs can only be linear if their thickness can be assumed independent of the hydraulic head, and if they have a dense drainage network. 15