Is the Dupuit assumption suitable for predicting the groundwater seepage area in hillslopes?

International audienceMany physically based hydrological/hydrogeological models used for predicting groundwater seepage areas, including topography-based index models such as TOPMODEL, rely on the Dupuit assumption. To ensure the sound use of these simplified models, knowledge of the conditions under which they provide a reasonable approximation is critical. In this study, a Dupuit solution for the seepage length in hillslope cross sections is tested against a full-depth solution of saturated groundwater flow. In homogeneous hillslopes with horizontal impervious base and constant-slope topography, the comparison reveals that the validity of the Dupuit solution depends not only on the ratio of depth to hillslope length d/L (as might be expected), but also on the ratio of hydraulic conductivity to recharge K/R and on the topographic slope s. The validity of the Dupuit solution is shown to be in fact a unique function of another ratio, the ratio of depth to seepage length d/LS. For d/LS0.2, it increases dramatically. In practice, this criterion can be used to test the validity of Dupuit solutions. When d/LS increases beyond that cutoff, the ratio of seepage length to hillslope length LS/L given by the full-depth solution tends toward a nonzero asymptotic value. This asymptotic value is shown to be controlled by (and in many cases equal to) the parameter R/(sK). Generalization of the findings to cases featuring heterogeneity, nonhorizontal impervious base and variable-slope topography is discussed

Topological Segmentation of 2D Vector Fields

Vector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

International audienceThis review presents the physical mechanisms generating residence time distributions (RTDs) in hydrologic systems with a focus on steady-state analytical solutions. Steady-state approximations of the RTD in hydrologic systems have seen widespread use over the last half-century because they provide a convenient, simplified modeling framework for a wide range of problems. The concept of an RTD is useful anytime that characterization of the timescales of flow and transport in hydrologic systems is important, which includes topics like water quality, water resource management, contaminant transport, and ecosystem preservation. Analytical solutions are often adopted as a model of the RTD and a broad spectrum of models from many disciplines has been applied. Although these solutions are typically reduced in dimensionality and limited in complexity, their ease of use makes them preferred tools, specifically for the interpretation of tracer data. Our review begins with the mechanistic basis for the governing equations, highlighting the physics for generating a RTD, and a catalog of analytical solutions follows. This catalog explains the geometry, boundary conditions and physical aspects of the hydrologic systems, as well as the sampling conditions, that altogether give rise to specific RTDs. The similarities between models are noted, as are the appropriate conditions for their applicability. The presentation of simple solutions is followed by a presentation of more complicated analytical models for RTDs, including serial and parallel combinations, lagged systems, and non-Fickian models. The conditions for the appropriate use of analytical solutions are discussed, and we close with some thoughts on potential applications, alternative approaches, and future directions for modeling hydrologic residence time

Using hydraulic head, chloride and electrical conductivity data to distinguish between mountain-front and mountain-block recharge to basin aquifers

This work is distributed under the Creative Commons Attribution 4.0 License.Numerous basin aquifers in arid and semi-arid regions of the world derive a significant portion of their recharge from adjacent mountains. Such recharge can effectively occur through either stream infiltration in the mountain-front zone (mountain-front recharge, MFR) or subsurface flow from the mountain (mountain-block recharge, MBR). While a thorough understanding of recharge mechanisms is critical for conceptualizing and managing groundwater systems, distinguishing between MFR and MBR is difficult. We present an approach that uses hydraulic head, chloride and electrical conductivity (EC) data to distinguish between MFR and MBR. These variables are inexpensive to measure, and may be readily available from hydrogeological databases in many cases. Hydraulic heads can provide information on groundwater flow directions and stream–aquifer interactions, while chloride concentrations and EC values can be used to distinguish between different water sources if these have a distinct signature. Such information can provide evidence for the occurrence or absence of MFR and MBR. This approach is tested through application to the Adelaide Plains basin, South Australia. The recharge mechanisms of this basin have long been debated, in part due to difficulties in understanding the hydraulic role of faults. Both hydraulic head and chloride (equivalently, EC) data consistently suggest that streams are gaining in the adjacent Mount Lofty Ranges and losing when entering the basin. Moreover, the data indicate that not only the Quaternary aquifers but also the deeper Tertiary aquifers are recharged through MFR and not MBR. It is expected that this finding will have a significant impact on the management of water resources in the region. This study demonstrates the relevance of using hydraulic head, chloride and EC data to distinguish between MFR and MBR

Partitioning a regional groundwater flow system into shallow local and deep regional flow compartments

International audienceThe distribution of groundwater fluxes in aquifers is strongly influenced by topography, and organized between hillslope and regional scales. The objective of this study is to provide new insights regarding the compartmentalization of aquifers at the regional scale and the partitioning of recharge between shallow/local and deep/regional groundwater transfers. A finite-difference flow model was implemented, and the flow structure was analyzed as a function of recharge (from 20 to 500 mm/yr), at the regional-scale (1400 km2), in three dimensions, and accounting for variable groundwater discharge zones; aspects which are usually not considered simultaneously in previous studies. The model allows visualizing 3-D circulations, as those provided by Tothian models in 2-D, and shows local and regional transfers, with 3-D effects. The probability density function of transit times clearly shows two different parts, interpreted using a two-compartment model, and related to regional groundwater transfers and local groundwater transfers. The role of recharge on the size and nature of the flow regimes, including groundwater pathways, transit time distributions, and volumes associated to the two compartments, have been investigated. Results show that topography control on the water table and groundwater compartmentalization varies with the recharge rate applied. When recharge decreases, the absolute value of flow associated to the regional compartment decreases, whereas its relative value increases. The volume associated to the regional compartment is calculated from the exponential part of the two-compartment model, and is nearly insensitive to the total recharge fluctuations

Modélisation des contrôles climatiques, topographiques, géologiques et anthropiques sur les écoulements souterrains en domaine de socle

Paru également dans la collection : Mémoire de Géosciences-Rennes n°144. ISBN : 2-914375-85-9This thesis deals with groundwater flow rate and distribution at the regional / continental scale. It addresses the partitioning between groundwater and surface water, the paths and travel times of groundwater, impact and vulnerability of pumping. The role of climatic, topographic and geologic factors is investigated. We consider these questions in the case of hard rock aquifers, which are highly heterogeneous aquifers mainly controlled by subsurface erosion and tectonic fracturing. Our work is based on the numerical modelling of free surface porous flow under the hypothesis of stationary constraints. We specially focus on the interactions of the water table with the land-surface topography. These interactions are a key point to understand groundwater flow structures. Based on an local adaptation scheme for finite volumes, we developed an efficient numerical method to solve this highly non-linear problem. We then performed a non-dimensional study of the controlling parameters of groundwater flow in an "elementary" basin representing a first-order idealized hydrogeological catchment. Results contribute to the deep understanding of fundamental controls revealing a relevant basis for the study of more complex systems. Considering more realistic configurations representative of hard rock aquifers, we identify the main processes that govern groundwater flow under recharge and pumping constraints. In particular, we present a conceptual model to deal with the impact of pumping in a fractured aquifer on natural groundwater discharge zones.L'étude des flux souterrains à l'échelle régionale / continentale englobe des problématiques majeures de l'hydrogéologie telles que le partitionnement entre nappes et rivières, les chemins et les temps de transfert des circulations souterraines, ainsi que l'impact et la vulnérabilité d'un pompage. Les flux souterrains résultent d'une combinaison complexe de facteurs climatiques, topographiques et géologiques. Dans les aquifères de socle, les structures hétérogènes d'altération de subsurface et de fracturation tectonique ont un impact particulier. Nous abordons cette thématique sous l'hypothèse de contraintes stationnaires. Notre approche repose sur la modélisation numérique des écoulements poreux à surface libre qui permet d'étudier les interactions de la nappe avec la topographie, déterminantes de l'organisation des écoulements. Basée sur un schéma d'adaptation locale de la méthode des volumes finis, une méthode numérique de résolution performante de ce problème fortement non linéaire a été développée. Dans le cadre d'un bassin "élémentaire" représentatif d'un bassin hydrogéologique de premier ordre idéalisé, une étude adimensionnelle des paramètres de contrôle des écoulements a été menée. Les résultats forment une base pertinente pour l'étude de systèmes plus complexes. Dans des configurations plus réalistes et représentatives des aquifères de socle, les principaux mécanismes régissant les écoulements souterrains sous contrainte de la recharge et d'un pompage sont mis en évidence. Ces derniers résultats ont abouti à la formulation d'un modèle conceptuel adapté à la problématique de l'influence du pompage sur les zones de décharge naturelles de l'aquifère

Topological Segmentation of 2D Vector Fields

Vector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange

Theoretical analysis of topographical, geological and climatic controls on the groundwater system

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Is the Dupuit assumption suitable for seepage area prediction?

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Capture zone delineation in hard-rock aquifers: Theoretical insights

International audienceHard-rock aquifers present a high level of complexity that makes them difficult to manage. Most of the flows are focused within a limited number of preferential paths where water can travel over large distances. It is generally admitted that the productivity of these preferential paths relies on the presence of a conductive layer, usually a more weathered zone near the ground surface, that can provide them with water. The consequences of this particular organization of flows are important for the definition of a protection perimeter around a pumping well. Because of the high complexity of this kind of medium associated to a lack of reliable characterization, building a deterministic model is neither possible nor relevant. As a consequence, a better fundamental understanding of the possible flow configurations is crucial from a management perspective. Indeed, there is a need for evaluating the possible degree of uncertainty associated with these systems, and for determining the parameters on which to focus on. We handle this problem from a theoretical point of view, in order to assess the role of permeability structures typical of hard-rock aquifers on the shape and the extension of the capture zone of a well. We explore several possible configurations in semi-regional models integrating the full dynamic of the water circulation from the recharge in the weathered zone to the deeper aquifer. We show that the recharge of the deep aquifer is especially sensitive to the distant structure of the weathered zone and its relation to the zone of intense vertical circulations. Strong connections between surface and subsurface water bodies reinforce the 3D nature of the circulations and the interactions between deep pumping and surface recharge. From this perspective, the topography also exerts a strong control on the shape of the capture zone