Stream Depletion in Alluvial Valleys Using the SDF Semianalytical Model

Abstract

A semianalytical method commonly used for quantifying stream depletion caused by ground water pumping was reviewed for applicability in narrow alluvial aquifers. This stream depletion factor (SDF) method is based on the analytic Glover model, but uses a numerical model-derived input parameter, called the SDF, to partly account for mathematically nonideal conditions such as variable transmissivity and nearby aquifer boundaries. Using the SDF can improve and simplify depletion estimates. However, the method's approximations introduce error that increases with proximity to the impermeable aquifer boundary. This article reviews the history of the method and its assumptions. New stream depletion response curves are presented as functions of well position within bounded aquifers. A simple modification to modeled SDF values is proposed that allows the impermeable boundary to be accounted for with image wells, but without overaccounting for boundary effects that are already reflected in modeled SDFs. It is shown that SDFs for locations closer to the river than to the aquifer boundary do not reflect impermeable-boundary effects, and thus need no modification, and boundary effects in the other portion of the aquifer follow a predictable removable pattern. This method is verified by comparing response curves using modified SDFs with response curves from an extensively calibrated numerical model of a managed ground water recharge site. The modification improves SDF-based stream depletion estimates in bounded aquifers while still benefiting from the additional information contained in SDF maps and retaining their value as standardized references for water rights administration.

Recent advances in modeling of well hydraulics

“…In addition, the image-well method can also be applied to the case of triangle aquifers [16] and rectangle aquifers [226,227]. Other applications of image-well method can be found, such as for flow to a drain near a leaky layer [228], pumping in sloping fault zone aquifers [229], tunnel water inflow or flow toward drains [230], pumping near a constant-head linear boundary [231], quantifying stream depletion in narrow alluvial aquifers [232], the drawdown in aquifers with irregularly shaped boundaries [233], and the drawdown for pumping at a finite-diameter well in a wedge-shaped aquifer [234].…”

Stream depletion rate and volume from groundwater pumping in wedge-shape aquifers

“…A number of analytical models have been developed for leaky aquifers (e.g., Zlotnik, 2004;Butler et al, 2007;Zlotnik and Tartakovsky, 2008). And lately, Miller et al (2007) described a modified Jenkins method to assess the effect of lateral impermeable aquifer boundaries.…”

Estimating stream filtration from a meandering stream under the Robin condition

“…A no-flow boundary parallel to a stream for narrow aquifers can significantly affect the temporal SDR distribution at a late period of pumping time [Miller et al, 2007;Huang et al, 2014]. The aquifer boundary is considered under the condition that @s=@x50 at x52L 1 and L 2 (5a)…”