A low‐dimensional hillslope‐based catchment model for layered groundwater flow

Abstract

Abstract:Despite the strong interaction between surface and subsurface waters, groundwater flow representation is often oversimplified in hydrological models. For instance, the interplay between local or shallow aquifers and deeper regional-scale aquifers is typically neglected. In this work, a novel hillslope-based catchment model for the simulation of combined shallow and deep groundwater flow is presented. The model consists of the hillslope-storage Boussinesq (hsB) model representing shallow groundwater flow and an analytic element (AE) model representing deep regional groundwater flow. The component models are iteratively coupled via a leakage term based on Darcy's law, representing delayed recharge to the regional aquifer through a low conductivity layer. Simulations on synthetic single hillslopes and on a two-hillslope open-book catchment are presented, and the results are compared against a benchmark three-dimensional Richards equation model. The impact of hydraulic conductivity, hillslope plan geometry (uniform, convergent, divergent), and hillslope inclination (0.2%, 5%, and 30%) under drainage and recharge conditions are examined. On the single hillslopes, good matches for heads, hydrographs, and exchange fluxes are generally obtained, with the most significant differences in outflows and heads observed for the 30% slope and for hillslopes with convergent geometry. On the open-book catchment, cumulative outflows are overestimated by 1-4%. Heads in the confined and unconfined aquifers are adequately reproduced throughout the catchment, whereas exchange fluxes are found to be very sensitive to the hillslope drainable porosity. The new model is highly efficient computationally compared to the benchmark model. The coupled hsB/AE model represents an alternative to commonly used groundwater flow representations in hydrological models, of particular appeal when surface-subsurface exchanges, local aquifer-regional aquifer interactions, and low flows play a key role in a watershed's dynamics.

The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange

“…Broda et al . [] couple the hsB model to an equally parsimonious and computationally efficient analytic element model of deep regional groundwater flow. Iterative updating of the hydraulic head levels in the shallow subsurface and deep aquifers is used to determine the exchange flux (leakage across a hypothetical aquitard) between the hillslope and regional groundwater units.…”

“…They find that a higher level of partitioning (discretization of the catchment into more hillslope units), by enhancing the ability of the model to represent hydrogeologic heterogeneity, improves the model performance. Broda et al [2012] couple the hsB model to an equally parsimonious and computationally efficient analytic element model of deep regional groundwater flow. Iterative updating of the hydraulic head levels in the shallow subsurface and deep aquifers is used to determine the exchange flux (leakage across a hypothetical aquitard) between the hillslope and regional groundwater units.…”

Drainage from the Critical Zone: Lithologic Controls on the Persistence and Spatial Extent of Wetted Channels during the Summer Dry Season

“…During base flow, headwater streams act as surficial expressions of groundwater conditions, providing observable spatiotemporal information of groundwater storage within catchments (e.g., Bencala et al, 2011;Biswal & Nagesh Kumar, 2013;Godsey & Kirchner, 2014;Kirchner, 2009;Shaw et al, 2017;Whiting & Godsey, 2016). In rain-dominated climates, all stream flow during these dry periods must come from water stored belowground, typically in the form of slowly draining groundwater that is locally sourced from adjacent hillslopes or is derived from regional groundwater systems that may cross local hillslopes or topographic watershed divides (e.g., Broda et al, 2012Broda et al, , 2014Clark et al, 2009;Frisbee et al, 2016;Gleeson & Manning, 2008;McNamara et al, 2011;Payn et al, 2012;Sheets et al, 2015;Tague & Grant, 2004;T oth, 1963;Troch et al, 2003;Welch & Allen, 2012). The hydraulic conductivity, geometry, and volume of this storage source should impact both the persistence and distribution of wetted channels in the dry season.…”

A hybrid‐3D hillslope hydrological model for use in Earth system models

“…However, recently this work was extended to account for the interactions between the saturated and unsaturated zones [ Paniconi et al ., ; Weiler and McDonnell , ; Hilberts et al ., ; Tromp‐van Meerveld and Weiler , ; Carrillo et al ., ]. Since the focus of this work lies in developing an efficient hillslope hydrological model for continental and global scale applications, computational constraints make it currently impossible to explicitly account for small‐scale 3‐D heterogeneity (i.e., plan form and soil properties) [e.g., Paniconi and Wood , ; Paniconi et al ., ; Weiler and McDonnell , ; Broda et al ., ]. Therefore, this study presents a hybrid 3‐D model, which couples a vertical 1‐D soil column model with a lateral pseudo‐2D saturated zone [ Troch et al ., ] and overland flow model, while specifically accounting for the 2‐D plan shape of the hillslope.…”