Specific yield for a two-dimensional flow

We investigate the systematic secular spatial variation of specific yield. As a vehicle for this analysis we consider a canonical unconfined aquifer consisting of a porous zone whose cross section is a simple long rectangle. The hydraulic conductivity in the unsaturated zone is modeled by the quasi-linear approximation. We find that locally the specific yield may be strongly influenced by the water table depth and mildly dependent on the recharge rate if that rate is high. For the simple geometry considered, a lateral component of flow has been found to have an insignificant effect on the local specific yield and that a model that assumes locally purely vertical flow to the given phreatic surface provides a more-than-adequate estimate of the specific yield. For the overall yield of an aquifer we find that the simplest model, wherein the flow through the soil is neglected, i.e., the model with static water and horizontal phreatic surface, provides a reasonable indication of the actual specific yield for most infiltration rates and aquifer dimensions. However, if the infiltration rate is high or the aquifer is particularly long, then the yield obtained from an assumed purely vertical flow, presupposing that the phreatic depth is accurately known, gives an excellent estimate of the actual specific yield.