Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Abstract

Abstract. The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection–diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection–diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs) in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space – between the two reaches located in the unsaturated zone (R1), and in the zone that is both unsaturated and saturated (R2) – as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions) and localized infiltration in the secondary conduit network (tributaries) in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit–matrix exchanges, inducing a complex water mixing effect in the saturated zone. From our results we build the functional scheme of the karst system. It demonstrates the impact of the saturated zone on matrix–conduit exchanges in this shallow phreatic aquifer and highlights the important role of the unsaturated zone on storage and transfer functions of the system.

Stream Centric Methods for Determining Groundwater Contributions in Karst Mountain Watersheds

“…At the reach scale (Figure a), net gains are significant during spring runoff (R1 and R2) and constant during base flow (R1). However, similar to the variability of gains and losses found by Cholet et al (), these longer reaches can alternate between gaining and losing conditions (e.g., R2). Such findings highlight the need to understand karst aquifer exchanges over shorter reaches to inform resource management and policy (Rugel et al, ).…”

Quantifying peakflow attenuation/amplification in a karst river using the diffusive wave model with lateral flow

“…Globally, this sensitivity analysis shows that various lateral hydrographs are simulated for different couples of C and D parameters, due to equifinality in the modelling approach. As observed in previous studies (Charlier, Moussa, Cattan, Cabidoche, & Voltz, ; Cholet et al, ; Moussa & Bocquillon, ; Yu, Sombatpanit, Rose, Ciesiolka, & Coughlan, ), C is more sensitive than D , as a variation of C by 4 in our test case generated a same range of lateral peakflow variations as a variation of D by 10,000.…”

“…The solution of the inverse problem proposed is part of the hydrological MHYDAS model (Distributed Hydrological Modelling of AgroSystems; Moussa, Voltz, & Andrieux, ). Using this inverse problem for the DWE, we can simulate the global dynamics of lateral flow during floods, which provides information on the hydrological processes involved, such as tracking loss and gain reaches in rivers (Charlier, Moussa, et al, ) or characterizing matrix/conduit relationships through the underground network of a karst aquifer (Cholet, Charlier, Moussa, Steinmann, & Denimal, ); both these publications showed promises in the ability of such models to quantify lateral flow in a karst basin.…”

A novel platform to evaluate the dampening of water and solute transport in an experimental channel under unsteady flow conditions

“…Both water and solute models were incorporated into the hydrological models ModSpa (Moussa, ; Moussa, Chahinian, & Bocquillon, ) and MHYDAS (Charlier et al, ; Cholet et al, ; Moussa et al, ).…”

“…In order to characterize water and solute dampening, we first calculate dampening ratios based on peak coordinates of time flow curves and time mass curves and that express the decrease of peak amplitude ( RP ) and the increase of peak occurrence time ( RT ) between the input and output curves. Then, in order to simulate the experimental data, we use a solute transport model coupling the diffusive wave equation (DWE) with lateral flow for water transfer and the advection–diffusion equation (ADE) for solute transport, both developed in the ModSpa and MHYDAS models (Moussa, ; Moussa, Voltz, & Andrieux, ; Moussa, Chahinian, & Bocquillon, ; Cholet, Charlier, Moussa, Steinmann, & Denimal, ; Moussa & Majdalani, ).…”