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

2017 ◽  
Vol 21 (7) ◽  
pp. 3635-3653 ◽  
Author(s):  
Cybèle Cholet ◽  
Jean-Baptiste Charlier ◽  
Roger Moussa ◽  
Marc Steinmann ◽  
Sophie Denimal
Keyword(s):  
Inverse Problem ◽  
Solute Transport ◽  
Unsaturated Zone ◽  
Flood Routing ◽  
Saturated Zone ◽  
Karst System ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Karst Conduit ◽  
Conduit Network

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.

scholarly journals Framework for assessing lateral flows and fluxes during floods in a conduit-flow dominated karst system using an inverse diffusive model

2016 ◽  
Author(s):  
Cybèle Cholet ◽  
Jean-Baptiste Charlier ◽  
Roger Moussa ◽  
Marc Steinmann ◽  
Sophie Denimal
Keyword(s):  
Unsaturated Zone ◽  
Flood Routing ◽  
Saturated Zone ◽  
Karst System ◽  
Diffuse Infiltration ◽  
Hydrological Conditions ◽  
Functional Scheme ◽  
The Impact ◽  
Karst Conduit ◽  
Conduit Network

Abstract. The aim of this study is to present a framework giving new keys to characterize the spatio-temporal variability of lateral exchanges for flows and fluxes in a karst conduit network during flood events. An inverse model using an analytical solution of the diffusive wave model is applied on data from two successive gauging stations to simulate 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 of 5–10 km characterizing the network from sinkhole to cave stream, and to the spring. The model is applied after separation of the base and the flood components on discharge and total dissolved solids (TDS) in order to assess lateral flows and mass-fluxes and compare them to help identify water origin. Our results showed various lateral contributions in space – between the two reaches located in the unsaturated (R1), and in both unsaturated and saturated zone (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 mass flux 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.

Identification of a space- and time-dependent source in a variable coefficient advection-diffusion equation from Dirichlet and Neumann boundary measured outputs

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Cristiana Sebu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Variable Coefficient ◽  
Source Function ◽  
Practical Interest ◽  
Time Dependent ◽  
Input Output ◽  
Space And Time ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

AbstractThis paper considers the inverse problem of identifying an unknown space- and time-dependent source function F(x,t) in the variable coefficient advection-diffusion equationu_{t}=(D(x)u_{x})_{x}-(V(x)u)_{x}+F(x,t)from the Dirichlet \nu(t):=u(\ell,t) and Neumann f(t):=-D(0)u_{x}(0,t), t\in(0,T], boundary measured outputs. This problem was motivated by several important real-world applications in the field of contaminant hydrogeology, and the novel analysis presented here is highly relevant to problems of practical interest. The input-output operators corresponding to the Dirichlet and Neumann measured boundary data are introduced. The inverse problem is then formulated as a system of operator equations consisting of these operators and the measured outputs. The compactness and Lipschitz continuity of the input-output operators are proved in the relevant classes of admissible source functions ℱ and \mathcal{F}_{r}. These results together with the derived trace estimates allow us to show the existence of a quasi-solution of the inverse source problem as a minimum of the Tikhonov functional, under minimal regularity assumptions with respect to the source function and other inputs. An explicit gradient formula for the Fréchet gradient of the Tikhonov functional is also derived by means of an appropriate adjoint problem.

scholarly journals Inverse Problem in Space Fractional Advection Diffusion Equation

2020 ◽  
Author(s):  
Gisele Moraes Marinho ◽  
Jader Lugon Júnior ◽  
Diego Campos Knupp ◽  
Antônio J. Silva Neto ◽  
Antônio J. Silva Neto ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

scholarly journals Determination of Optimal Diffusion Coefficients in Lake Zirahuén through a Local Inverse Problem

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1695
Author(s):  
Tzitlali Gasca-Ortiz ◽  
Francisco J. Domínguez-Mota ◽  
Diego A. Pantoja
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficients ◽  
Simple Technique ◽  
Diffusion Tensor ◽  
Cross Term ◽  
Release Experiment ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Dye Release

In this study, optimal diffusion coefficients for Lake Zirahuén, Mexico, were found under particular conditions based on images taken with a drone of a dye release experiment. First, the dye patch concentration was discretized using image processing tools, and it was then approximated by an ellipse, finding the optimal major and minor axes. The inverse problem was implemented by comparing these observational data with the concentration obtained numerically from the 2D advection–diffusion equation, varying the diffusion tensor. When the tensor was isotropic, values of K11=K22≈0.003 m2/s were found; when nonequal coefficients were considered, it was found that K11≈0.005 m2/s and K22≈0.002 m2/s, and the cross-term K12 influenced the results of the orientation of the ellipse. It is important to mention that, with this simple technique, the parameter estimation had consequences of great importance as the value for the diffusion coefficient was bounded significantly under particular conditions for this site of study.

scholarly journals Reducing the ambiguity of karst aquifer models by pattern matching of flow and transport on catchment scale

2015 ◽  
Vol 19 (2) ◽  
pp. 893-912 ◽  
Author(s):  
S. Oehlmann ◽  
T. Geyer ◽  
T. Licha ◽  
M. Sauter
Keyword(s):  
Groundwater Flow ◽  
Solute Transport ◽  
Karst Aquifer ◽  
Karst Area ◽  
Hydraulic Parameters ◽  
Karst Aquifers ◽  
Flow And Transport ◽  
Model Ambiguity ◽  
Karst Conduit ◽  
Conduit Network

Abstract. Assessing the hydraulic parameters of karst aquifers is a challenge due to their high degree of heterogeneity. The unknown parameter field generally leads to a high ambiguity for flow and transport calibration in numerical models of karst aquifers. In this study, a distributed numerical model was built for the simulation of groundwater flow and solute transport in a highly heterogeneous karst aquifer in south-western Germany. Therefore, an interface for the simulation of solute transport in one-dimensional pipes was implemented into the software COMSOL Multiphysics® and coupled to the three-dimensional solute transport interface for continuum domains. For reducing model ambiguity, the simulation was matched for steady-state conditions to the hydraulic head distribution in the model area, the spring discharge of several springs and the transport velocities of two tracer tests. Furthermore, other measured parameters such as the hydraulic conductivity of the fissured matrix and the maximal karst conduit volume were available for model calibration. Parameter studies were performed for several karst conduit geometries to analyse the influence of the respective geometric and hydraulic parameters and develop a calibration approach in a large-scale heterogeneous karst system. Results show that it is possible not only to derive a consistent flow and transport model for a 150 km2 karst area but also to combine the use of groundwater flow and transport parameters thereby greatly reducing model ambiguity. The approach provides basic information about the conduit network not accessible for direct geometric measurements. The conduit network volume for the main karst spring in the study area could be narrowed down to approximately 100 000 m3.

scholarly journals Reducing the ambiguity of karst aquifer models by pattern matching of flow and transport on catchment scale

2014 ◽  
Vol 11 (8) ◽  
pp. 9281-9326
Author(s):  
S. Oehlmann ◽  
T. Geyer ◽  
T. Licha ◽  
M. Sauter
Keyword(s):  
Groundwater Flow ◽  
Solute Transport ◽  
Karst Aquifer ◽  
Karst Area ◽  
Hydraulic Parameters ◽  
Karst Aquifers ◽  
Flow And Transport ◽  
Model Ambiguity ◽  
Karst Conduit ◽  
Conduit Network

Abstract. Assessing the hydraulic parameters of karst aquifers is a challenge due to their high degree of heterogeneity. The unknown parameter field generally leads to a high ambiguity for flow and transport calibration in numerical models of karst aquifers. In this study, a distributive numerical model was built for the simulation of groundwater flow and solute transport in a highly heterogeneous karst aquifer in south western Germany. Therefore, an interface for the simulation of solute transport in one-dimensional pipes was implemented into the software Comsol Multiphysics® and coupled to the three-dimensional solute transport interface for continuum domains. For reducing model ambiguity, the simulation was matched for steady-state conditions to the hydraulic head distribution in the model area, the spring discharge of several springs and the transport velocities of two tracer tests. Furthermore, other measured parameters such as the hydraulic conductivity of the fissured matrix and the maximal karst conduit volume were available for model calibration. Parameter studies were performed for several karst conduit geometries to analyse the influence of the respective geometric and hydraulic parameters and develop a calibration approach in a large-scale heterogeneous karst system. Results show that it is not only possible to derive a consistent flow and transport model for a 150 km2 karst area, but that the combined use of groundwater flow and transport parameters greatly reduces model ambiguity. The approach provides basic information about the conduit network not accessible for direct geometric measurements. The conduit network volume for the main karst spring in the study area could be narrowed down to approximately 100 000 m3.

scholarly journals Influence of Chemical Osmosis on Solute Transport and Fluid Velocity in Clay Soils

2020 ◽  
Vol 18 (1) ◽  
pp. 232-238
Author(s):  
Zhihong Zhang ◽  
Gailei Tian ◽  
Lin Han
Keyword(s):  
Solute Transport ◽  
Transport Model ◽  
Fluid Velocity ◽  
Diffusion Mechanism ◽  
Clay Material ◽  
Chemical Osmosis ◽  
Advection Diffusion Equation ◽  
Test Study ◽  
Proposed Model ◽  
Membrane Effect

AbstractSolute transport through the clay liner is a significant process in many waste landfills or unmanaged landfills. At present, researchers mainly focus on the test study about semi-membrane property of clay material, however, the influence of chemical osmosis caused by membrane effect on solute transport and fluid velocity is insufficient. In this investigation, based on the classical advection-diffusion equation, a one-dimensional solute transport model for low-permeable clay material has been proposed, in which the coupled fluid velocity related with hydraulic gradient and concentration gradient is introduced, and the semi-membrane effect is embodied in the diffusion mechanism. The influence of chemical osmosis on fluid velocity and solute transport has been analyzed using COMSOL Multiphysics software. The simulated results show that chemical osmosis has a significant retarded action on fluid velocity and pollutant transport. The proposed model can effectively reveal the change in process of coupled fluid velocity under dual gradient and solute transport, which can provide a theoretical guidance for similar fluid movement in engineering.

scholarly journals Global heat balance and heat uptake in potential temperature coordinates

2021 ◽  
Author(s):  
Antoine Hochet ◽  
Rémi Tailleux ◽  
Till Kuhlbrodt ◽  
David Ferreira
Keyword(s):  
Global Warming ◽  
Water Mass ◽  
Potential Temperature ◽  
Effective Diffusion ◽  
Mitigation Strategies ◽  
Ocean Heat Uptake ◽  
Cold Temperatures ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Heat Uptake

AbstractThe representation of ocean heat uptake in Simple Climate Models used for policy advice on climate change mitigation strategies is often based on variants of the one-dimensional Vertical Advection/Diffusion equation (VAD) for some averaged form of potential temperature. In such models, the effective advection and turbulent diffusion are usually tuned to emulate the behaviour of a given target climate model. However, because the statistical nature of such a “behavioural” calibration usually obscures the exact dependence of the effective diffusion and advection on the actual physical processes responsible for ocean heat uptake, it is difficult to understand its limitations and how to go about improving VADs. This paper proposes a physical calibration of the VAD that aims to provide explicit traceability of effective diffusion and advection to the processes responsible for ocean heat uptake. This construction relies on the coarse-graining of the full three-dimensional advection diffusion for potential temperature using potential temperature coordinates. The main advantage of this formulation is that the temporal evolution of the reference temperature profile is entirely due to the competition between effective diffusivity that is always positive definite, and the water mass transformation taking place at the surface, as in classical water mass analyses literature. These quantities are evaluated in numerical simulations of present day climate and global warming experiments. In this framework, the heat uptake in the global warming experiment is attributed to the increase of surface heat flux at low latitudes, its decrease at high latitudes and to the redistribution of heat toward cold temperatures made by diffusive flux.

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