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Mathematical models for stream depletion with stream stage decline or drawdown are developed to overcome the deficiency in existing models that typically use the constant-head (Dirichlet) or general (Robin) boundary condition and source terms at the stream-aquifer interface. Existing approaches assume a fixed stream stage during pumping, implies that the stream is an infinite water source, with depletion defined as a decrease in stream discharge. We refer to this depletion without drawdown as the ``stream depletion paradox.'' It is a glaring model limitation, ignoring the most observable adverse effect of long-term groundwater abstraction near a stream, namely stage declines that eventually lead to dry streambeds. Field data are presented to demonstrate that stream stage responds to pumping near the stream, motivating the development of an alternative theory predicts transient stream drawdown based on the concepts of finite stream storage and mass continuity at the stream-aquifer interface. Based on this alternative theory, models are developed for the cases of a non- and a fully-penetrating stream. The proposed model reduces to the fixed-stage model in the limit as stream storage becomes infinitely large and to the limiting case of confined aquifer flow with a no-flow boundary at the streambed when the stream storage vanishes. The model is applied to field observations of both aquifer and stream drawdown from tests conducted in a confined aquifer over which a shallow stream flows. Model fits and parameter estimates are obtained both aquifer and stream drawdown data. Model predicted and observed transient drawdown behavior indicate that fixed-stage models (a) underestimate late-time aquifer drawdown and (b) overestimate the available recharge from streams to pumping wells. This has significant implications for the sustainable management of water resources in hydraulically connected stream-aquifer systems with heavy groundwater abstraction.

The results reported in this work are based in part on measurements of sap flow in a few select trees on a representative riparian forest plot coupled with a forest-wide randomized sampling of tree sapwood area in a watershed located along the Pacific coast in Santa Cruz County, California. These measurements were upscaled to estimate evapotranspiration (ET) across the forest and to quantify groundwater usage by dominant phreatophyte vegetation. Canopy cover in the study area is dominated by red alder (Alnus rubra) and arroyo willow (Salix lasiolepis), deciduous phreatophyte trees from which a small sample was selected for instrumentation with sap flow sensors on a single forest plot. These localized sap flow measurements were then upscaled to the entire riparian forest to estimate forest ET using data from a survey of sapwood area on six plots scattered randomly across the entire forest. The estimated canopy-scale ET was compared to reference ET and NDVI based estimates. The results show positive correlation between sap flow based estimates and those of the other two methods, though over the winter months, sap flow-based ET values were found to significantly underestimate ET as predicted by the other two methods. The results illustrate the importance of ground-based measurements of sap flow for calibrating satellite based methods and for providing site-specific estimates and to better characterize the ET forcing in groundwater flow models.