Effective groundwater–surface water exchange at watershed scales

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Coupled groundwater–surface water (GW–SW) models are capable of simulating complex hydrological systems when used at fine resolutions. However, properly characterizing bulk GW–SW fluxes for either coarsely resolved integrated models or basin-discretized surface water models remains a challenge. Loss of subgrid detail, while beneficially decreasing computational cost, leads to a decrease in model accuracy as scale effects become important. Ideally, coarse low-resolution models should be informed by expected subgrid behaviour, reducing the impact of scale effects. Determining how to best represent these fine-scale details in lower-resolution models is important for improving the accuracy and appropriateness of these models. To investigate some of these scale effects, we here explore the relationships between area-averaged hydraulic head and bulk GW–SW exchange fluxes (e.g. evapotranspiration and discharge), all of which are presumed to be controlled predominantly by subgrid topographic effects. These relationships may be useful for simply upscaling models without the complete loss of crucial fine-resolution subgrid details. Using finely resolved simulation output from Modflow for a fine-resolution simulation and post-processed results generated to represent coarser resolutions, upscaled flux relationships (UFRs) are generated for multiple terrains; these UFRs define the relationships that exist between average hydraulic head and average fluxes in unconfined aquifer systems. It is found that, for steady-flow regimes, similar one-to-one power law relationships consistently exist between area-averaged hydraulic heads, exchange fluxes and saturated area for a variety of terrains. Additionally, when the averaged values are properly normalized, the generated steady-state UFRs for a single terrain are independent of hydraulic conductivity and potential evapotranspiration rates and apparently insensitive to the presence of mild heterogeneity. While some hysteresis is apparent in the relationships under transient conditions, transient artefacts are shown to be minor under some circumstances, indicating that UFRs may be applied to both steady-state and transient scenarios. Simpler tests performed under saturated and variably saturated conditions in a cross-sectional model show similar trends, suggesting that the UFR representation is extendable to systems where the vadose zone plays a significant role. It is suggested that relatively simple UFRs such as these may find use as an alternative to direct point upscaling or multi-resolution models for estimating GW–SW exchange fluxes in coarse-scale models. They also appear to justify the functional form of some classical models of baseflow and evapotranspiration used in conceptual surface water models. Copyright © 2015 John Wiley & Sons, Ltd.

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