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A Robin type boundary condition (BC), commonly adopted at stream-aquifer interface, excludes a term associated with streambed accounting for the effects of streambed storage and width. This study presents two new analytical models for describing confined flow induced by pumping in a stream-aquifer system. One model considers a single-zone aquifer and treats the streambed as a lagging Robin BC with a time lag parameter related to the effects. The other considers a two-zone aquifer consisting of aquifer and streambed zones. A Dirichlet BC for stream water level is specified at the edge of the streambed. The time-domain solutions of both models are developed to describe spatiotemporal drawdown and temporal stream filtration/depletion rate (SDR). The finite element solutions (FESs) of both models are also built. Results suggest the lag time equals the half of the squared streambed width divided by the streambed hydraulic diffusivity. The effects of streambed width and storage on SDR should be considered when their lumped parameter exceeds 0.1. Neglecting their effects causes 25% difference in SDR when the lumped parameter equals 10. Based on the FESs, the use of the lagging Robin BC takes nearly a tenth of computing time of obtaining accurate steady-state SDR for the simulation of the two-zone aquifer. In addition, the present solutions agree to a field SDR experiment conducted by Hunt et al. (2001Hunt et al. ( , https://doi.org/10.1111Hunt et al. ( /j.1745Hunt et al. ( -6584.2001. To conclude, this study presents two new models for describing groundwater flow in a stream-aquifer system and explores the joint effect of streambed width and storage on SDR.

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This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant‐rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual‐porosity model. The Laplace‐domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time‐domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.