Cette partie a fait l’objet d’une publication dans la revue Hydrological Processes actuellement sous presse qui a été reproduite ici avec l’accord de l’éditeur Elsevier.
Résumé
Cet article présente un modèle verticalement intégré pour l'étude des échanges d'eau et de solutés entre une grande rivière et un aquifère alluvial peu profond à travers la zone hyporhéique. Le modèle hydraulique couple les équations de Saint Venant en 2D horizontale pour les écoulements dans la rivière et l'équation de Darcy-Dupuit en 2D pour les écoulements dans l'aquifère. Le couplage entre rivière et aquifère est obtenu en imposant la continuité des flux et des hauteurs d'eau entre les deux domaines. Les équations sont regroupées en une seule matrice et résolues simultanément afin d'assurer la continuité entre le cours d'eau et l'aquifère et pour bien modéliser les échanges couplés entre les deux domaines. Le modèle est appliqué à un tronçon (environ 38 km²) de la Garonne (sud-ouest de la France) et de sa plaine d'inondation, incluant un site instrumenté (environ 13 km²) au niveau d'un méandre. Les niveaux d'eau simulés dans la zone hyporhéique et l'aquifère sont comparés aux mesures dans plusieurs piézomètres. Afin de vérifier que le modèle peut reproduire les échanges dynamiques à travers la zone hyporhéique, tant du point de vue spatial que temporel, 2 jeux de données ont été confrontés aux simulations. Le premier inclut les niveaux d'eau mesurés pour une date (le 30 mars 2000) sur 27 piézomètres ; le second inclut les niveaux d'eau mesurés en continu pendant 5 mois (du 1er janvier au 1er juin 2000) dans 5 piézomètres répartis sur le site.Le modèle confirme l'existence de connections hydrauliques fortes entre eau de surface et eau souterraine, qui sont confirmées par les variations de niveau simultanées entre la rivière et les piézomètres situés près des berges. Les simulations confirment également que le modèle est capable de reproduire les changements de direction des écoulements souterrains lors d'épisodes de crue.
La partie hydraulique a ensuite été couplée à un modèle de transport, basé sur les équations d'advection-dispersion, afin de suivre la dynamique théorique d'un traceur conservatif pendant 5 ans sur le secteur de Garonne modélisé. Les résultats montrent que les méandres favorisent les échanges entre surface et subsurface et que le traceur, bien que dilué dans le cours d'eau, contamine tout le secteur en aval des sites d'injection.
"A coupled vertically integrated model to describe lateral
exchanges between surface and subsurface in large alluvial
floodplains with a fully penetrating river"
D. Peyrard(1), S. Sauvage(1), P. Vervier(1), J.M. Sanchez-Pérez(1), M. Quintard(2)
(1)
Laboratoire d’Ecologie Fonctionnelle (EcoLab), UMR 5245 CNRS-INP/ENSAT-Univ. Toulouse III
Ecole Nationale Supérieure Agronomique de Toulouse (ENSAT), Avenue de l'Agrobiopole BP 32607 Auzeville Tolosane 31326 CASTANET TOLOSAN Cedex, France.
(2)
Institut de Mécanique des Fluides de Toulouse (IMFT), UMR 5502 CNRS-INP-UPS 1 Allée du Professeur Camille Soula, 31400 Toulouse, France.
ABSTRACT
This paper presents a vertically averaged model for studying water and solute exchanges between a large river and its adjacent alluvial aquifer. The hydraulic model couples horizontal 2D Saint Venant equations for river flow and a 2D Dupuit equation for aquifer flow. The dynamic coupling between river and aquifer is provided by continuity of fluxes and water level elevation between the two domains. Equations are solved simultaneously by linking the two hydrological system matrices in a single global matrix in order to ensure the continuity conditions between river and aquifer and to accurately model two-way coupling between these two domains.
The model is applied to a large reach (about 38 km²) of the Garonne River (south-western France) and its floodplain, including an instrumented site in a meander. Simulated hydraulic heads are compared with experimental measurements on the Garonne River and aquifer in the floodplain. Model verification includes comparisons for one point sampling date (27 piezometers, 30 March 2000) and for hydraulic heads variations measured continuously over 5 months (5 piezometers, 1 January - 1 June 2000). The model accurately reproduces the strong hydraulic connections between the Garonne River and its aquifer, which are confirmed by the simultaneous variation of the water level in the river and in piezometers located near the river bank. The simulations also confirmed that the model is able to reproduce groundwater flow dynamics during flood events.
Given these results, the hydraulic model was coupled with a solute-transport component, based on advection-dispersion equations, to investigate the theoretical dynamics of a conservative tracer over 5 years throughout the 38 km² reach studied. Meanders were shown to favour exchanges between river and aquifer, and although the tracer was diluted in the river, the contamination moved downstream from the injection plots and affected both river banks.
Keywords : Ecohydrology, river-aquifer interactions, transport, coupled model, Garonne River, 2D Saint Venant, 2D Dupuit.
AI. Introduction
River-aquifer systems are composed of dynamic spatial mosaics connected by fluxes of water, matter and organisms (Jones and Mulholland, 2000 ; Sophocleous, 2002). Hydrological connections between the main river channel and the adjacent aquifer in the floodplain are considered to be essential for the operation and integrity of fluvial hydrosystems (Thoms, 2003). These connections can facilitate the exchange of carbon and nutrients between the river channel and the aquifer. They take place in a subsurface zone composed of riverbed sediments called the hyporheic zone (Triska et al., 1989 ; Findlay, 1995 ; Bencala, 2000). Research over the past two decades has established that this zone has a great impact on the productivity of the entire river system (see reviews in Jones and Holmes, 1996 ; Brunke and Gonser, 1997 ; Boulton et al., 1998 ; Sophocleous, 2002). The impact of the hyporheic zone on stream ecosystem operation is determined by biogeochemical processes and by the proportion of water fluxes exchanged between river and aquifer. In large rivers, the hydrological regime influences the degree of interaction among soils, groundwater and surface water. At low flow, rivers are primarily influenced by aquifer discharge, and surface water penetration into the floodplain is limited (Baker and Vervier, 2004). During high flow, river water penetrates far into the floodplain, the aquifer table rises and areas hydrologically connected to the river channel may extend laterally for up to several kilometres in alluvial floodplains (Stanford and Ward, 1993 ; Wroblicky et al., 1998). In the broad floodplains of large rivers, underflow is expected to be dominated by advected channel water (White, 1993) and the resulting hyporheic zone might be primarily lateral on a scale of hundreds of metres (Ward, 1989 ; Stanford and Ward, 1993).
As they allow complex geometry and boundary conditions to be reproduced, numerical models such as finite-element or finite-difference techniques are frequently used to study river-aquifer interactions. This is a complex, multi-scale and inter-disciplinary problem, and a number of modelling methods have been proposed (see reviews by Packman and Bencala, 2000 ; Runkel et al., 2003 ; Cardenas et al., 2004 ; Boano et al., 2006). One of the principal current focuses of this field of research is the method of coupling between river and aquifer equations (Kollet and Maxwell, 2006). Indeed, despite the fact that aquifer and surface water are hydraulically interconnected, they are often modelled as two separate systems and are analysed independently (Liang et al., 2007). It is now well recognised that fully coupled models for river and aquifer flows are necessary to obtain a better understanding of the hydrological pathways in hydrosystems (Panday and Huyakorn, 2004 ; Gunduz and Aral, 2005). Fairbanks et al. (2001) demonstrated that the ‘fully implicit’ approach, in which both systems of equations are solved in a single global matrix, is the most numerically stable method to couple surface and subsurface models. Gunduz and Aral (2003) tested this solution by coupling a one-dimensional channel flow model based on the dynamic wave form of the Saint Venant equations with a two-dimensional vertically averaged saturated groundwater flow model. They concluded that this approach provides an efficient solution for the coupled flow problem formulated for both systems. Liang et al. (2007) used a similar approach to build a two-dimensional numerical model for predicting flood flows. The solution proposed by Gunduz and Aral (2003) can be particularly efficient for studying two-way interactions between rivers and aquifers, but examples of such applications are still rare (Langevin et al., 2005). Many coupled models of variable complexity have been developed to simulate the
the spatial extent of the interactions between groundwater and surface water is assumed to be constant, or spatially and temporally transient changes in processes are considered in a rudimentary manner (Krause and Bronstert, 2007). In addition, the full three-dimensional (3D) numerical solution encounters limitations in mesoscale applications because of the high computation time required (Krause and Bronstert, 2007). Gunduz and Aral (2003) also concluded that the coupled models tend to be increasingly complex and their solution can suffer from numerical complications. It appears that the complexity of the model should thus depend on the objectives of each case.
In this context, our main objective was to propose a coupled and simultaneous solved model to quantify fluxes of water and solutes between a large river and its shallow aquifer at mesoscale (see Malard et al., 2002 ; Krause and Bronstert, 2007). Our aim was to propose a clear model at the interface between hydrology and ecology, with an interdisciplinary and integrated approach (see Gurnell et al., 2000 ; Tetzlaff et al., 2007), which could be easier to apply than 3D solvers previously developed. The model includes the hydraulic model presented by Liang et al. (2007) but has been extended to compute solute transport. It requires input data that are relatively easy to obtain (stream and floodplain geometry in two dimensions, averaged impermeable bedrock elevation, mean hydraulic conductivity and porosity). It can be relevant to consider such vertically integrated two-dimensional (2D) models when lateral exchange is a dominant process between river and aquifer, or when the geomorphology of the studied site allows integration over the z direction. This model might thus be useful when complex models are not fully necessary, for example when the objective is to have an averaged quantification of the hydrology of a site in order to integrate biogeochemistry.
Our model, called 2SWEM (for Surface-Subsurface Water Exchange Model) consists of an hydraulic component that describes the main hydrological characteristics of surface water and groundwater, coupled with a solute-transport component to follow the dynamics of nutrients. The hydraulic model is based on the equations system of Liang et al. (2007) : the flow equations in the river and in the aquifer are integrated over the z direction to produce a coupled two-dimensional model in both domains.
In this paper, 2SWEM was tested by applying it to a large sector (about 38 km²) of the Garonne River, the third largest river in France and the largest river in south-west France. In its middle course, it fully penetrates the alluvial aquifer, leading to significant lateral interactions (Weng et al., 2003 ; Baker and Vervier, 2004) that increase the surface and length of contact between streamwater solutes and active biological zones in floodplain sediments. The 2SWEM simulation results were compared with hydraulic heads measured (i) on one sampling date (30 March 2000) in the floodplain using 27 piezometers and (ii) daily over 5 months (from January to June 2000) using 5 piezometers. After model verification, we added the solute-transport component in order to simulate the injection of a conservative tracer at some locations in the alluvial aquifer and to follow its theoretical transport.