Modélisation des échanges surface/subsurface à l'échelle de la parcelle par une approche darcéenne multidomaine

Cette etude s’inscrit dans le cadre de la modelisation distribuee a base physique des interactions entre processus de surface et de subsurface. Une nouvelle approche de modelisation, dite darceenne multidomaine , est presentee. Les equations de Richards et de l’onde diffusive sont respectivement utilisees pour decrire le processus d’infiltration et de ruissellement. L’equation de l’onde diffusive est transformee en une equation de diffusion non lineaire similaire a l’equation de Richards. L’ecoulement d’eau a la surface du sol est alors assimile a un ecoulement dans un milieu poreux aux proprietes particulieres. Une couche de milieu poreux, appelee couche de ruissellement, est introduite dans le domaine de calcul. L’ensemble de la dynamique surface/subsurface est alors decrite dans un continuum darceen par une seule equation de Darcy non lineaire avec des parametres domaine-dependants. Cela permet notamment d’imposer une continuite hydraulique entre l’eau de surface et l’eau de subsurface. Un modele de transport permettant de s’attaquer a la problematique de la separation d’hydrogramme est egalement implemente. Le modele developpe est evalue a partir de cas tests classique de la litterature. Une analyse de sensibilite ainsi qu’une etude detaillee du ruissellement hortonien sont ensuite presentee. Enfin, l’experience realisee par l’IRD sur la parcelle de Thies au Senegal est reproduite. Les resultats sont encourageants et laisse penser que l’approche de modelisation developpee permet de reproduire correctement a petite echelle la dynamique fortement couplee des systemes hydrologiques de type parcelle ou versants.

[1]  T. Dunne,et al.  Effects of Rainfall, Vegetation, and Microtopography on Infiltration and Runoff , 1991 .

[2]  D. Zimmer,et al.  Steady state analysis of unsaturated flow above a shallow water-table aquifer drained by ditches , 2001 .

[3]  C. Michel,et al.  Un modèle pluie-débit journalier à trois paramètres , 1989 .

[4]  David Favis-Mortlock,et al.  Emergence and erosion: a model for rill initiation and development , 2000 .

[5]  I. Ginzburg,et al.  A seepage face model for the interaction of shallow water tables with the ground surface: Application of the obstacle-type method , 2006 .

[6]  Rao S. Govindaraju,et al.  Dynamics of Moving Boundary Overland Flows Over Infiltrating Surfaces at Hillslopes , 1991 .

[7]  Numerical analysis of ponded rainfall infiltration , 2009 .

[8]  François Lehmann,et al.  Comparison of Equivalent Conductivities for Numerical Simulation of One‐Dimensional Unsaturated Flow , 2005 .

[9]  L. Rosenhead Conduction of Heat in Solids , 1947, Nature.

[10]  J. Rubin,et al.  Soil Water Relations During Rain Infiltration: I. Theory1, 2 , 1963 .

[11]  G. Gottardi,et al.  A control-volume finite-element model for two-dimensional overland flow , 1993 .

[12]  T. Cundy,et al.  Modeling of two‐dimensional overland flow , 1989 .

[13]  Mario Putti,et al.  A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems , 1994 .

[14]  J. Hewlett,et al.  Moisture and energy conditions within a sloping soil mass during drainage , 1963 .

[15]  Roger E. Smith,et al.  The infiltration envelope: Results from a theoretical infiltrometer , 1972 .

[16]  F. Henderson Open channel flow , 1966 .

[17]  John Wainwright,et al.  Measurement and modelling of high resolution flow-velocity data under simulated rainfall on a low-slope sandy soil , 2008 .

[18]  M. Th. van Genuchten,et al.  Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions , 2000 .

[19]  M. Celia,et al.  A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation , 1990 .

[20]  Jeffrey J. McDonnell,et al.  Quantifying the relative contributions of riparian and hillslope zones to catchment runoff , 2003 .

[21]  P. E. O'connell,et al.  An introduction to the European Hydrological System — Systeme Hydrologique Europeen, “SHE”, 2: Structure of a physically-based, distributed modelling system , 1986 .

[22]  P. E. O'connell,et al.  An introduction to the European Hydrological System — Systeme Hydrologique Europeen, “SHE”, 1: History and philosophy of a physically-based, distributed modelling system , 1986 .

[23]  P. Huyakorn,et al.  A three‐dimensional finite‐element model for simulating water flow in variably saturated porous media , 1986 .

[24]  Alain Millard,et al.  A Modern Approach of Large Computer Codes for Structural Analysis , 1989 .

[25]  Axel Bronstert,et al.  Modelling of runoff generation and soil moisture dynamics for hillslopes and micro-catchments , 1997 .

[26]  R. Horton The Rôle of infiltration in the hydrologic cycle , 1933 .

[27]  Zoubir Makhlouf Complements sur le modele pluie-debit gr4j et essai d'estimation de ses parametres , 1994 .

[28]  S. Murty Bhallamudi,et al.  Conjunctive surface-subsurface modeling of overland flow , 1998 .

[29]  Jeffrey J. McDonnell,et al.  A rationale for old water discharge through macropores in a steep, humid catchment. , 1990 .

[30]  G. Pinder,et al.  Computational Methods in Subsurface Flow , 1983 .

[31]  R. Hawkins,et al.  FLOW PATH OF RAIN FROM THE SOIL SURFACE TO THE WATER TABLE , 1965 .

[32]  Th. Xanthopoulos,et al.  NUMERICAL SIMULATION OF A TWO DIMENSIONAL FLOOD WAVE PROPAGATION DUE TO DAM FAILURE , 1976 .

[33]  F. Melone,et al.  On the interaction between infiltration and Hortonian runoff , 1998 .

[34]  Abdul S. Abdul,et al.  Laboratory Studies of the Effects of the Capillary Fringe on Streamflow Generation , 1984 .

[35]  Christophe Le Potier,et al.  Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés , 2005 .

[36]  L. A. Richards Capillary conduction of liquids through porous mediums , 1931 .

[37]  S. P. Neuman,et al.  SATURATED-UNSATURATED SEEPAGE BY FINITE ELEMENTS , 1973 .

[38]  R. Maxwell,et al.  Integrated surface-groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model , 2006 .

[39]  A. M. Wasantha Lal,et al.  Weighted Implicit Finite-Volume Model for Overland Flow , 1998 .

[40]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[41]  E. Todini,et al.  A conservative finite elements approach to overland flow: the control volume finite element formulation , 1996 .

[42]  S. Galle,et al.  Overland flow and infiltration modelling for small plots during unsteady rain: numerical results versus observed values , 2000 .

[43]  R. D. Black,et al.  Partial Area Contributions to Storm Runoff in a Small New England Watershed , 1970 .

[44]  W. Gray,et al.  A unifying framework for watershed thermodynamics: constitutive relationships , 1999 .

[45]  Qihua Ran,et al.  Adding sediment transport to the integrated hydrology model (InHM): Development and testing , 2006 .

[46]  Jeffrey J. McDonnell,et al.  Using numerical modelling to evaluate the capillary fringe groundwater ridging hypothesis of streamflow generation , 2006 .

[47]  G. Chavent Mathematical models and finite elements for reservoir simulation , 1986 .

[48]  Christophe Le Potier,et al.  Schéma volumes finis monotone pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés , 2005 .

[49]  D. A. Woolhiser,et al.  Effects of Spatial Variability of Saturated Hydraulic Conductivity on Hortonian Overland Flow , 1996 .

[50]  G. Vachaud,et al.  Experimental and numerical study of a transient, two‐dimensional unsaturated‐saturated water table recharge problem , 1979 .

[51]  P. K. Parhi,et al.  A Modification to Kostiakov and Modified Kostiakov Infiltration Models , 2007 .

[52]  Malcolm G. Anderson,et al.  The role of topography in controlling throughflow generation , 1978 .

[53]  T. Hromadka,et al.  SOLVING THE TWO-DIMENSIONAL DIFFUSION FLOW MODEL. , 1985 .

[54]  Sang-Jin Ahn,et al.  On the Applicable Ranges of Kinematic and Diffusion Models in Open Channels , 1993 .

[55]  G. L. Guymon,et al.  A two-dimensional dam-break flood plain model , 1985 .

[56]  Norbert Silvera,et al.  Microrelief induced by tillage: measurement and modelling of Surface Storage Capacity , 2002 .

[57]  E. Sudicky,et al.  Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media , 1996 .

[58]  C. Y. Kuo,et al.  Runoff in Shallow Soils under Laboratory Conditions , 1999 .

[59]  M. Voltz,et al.  Contribution of groundwater and overland flows to storm flow generation in a cultivated Mediterranean catchment. Quantification by natural chemical tracing , 2000 .

[60]  W. Kreutz,et al.  Tracers Determine Movement of Soil Moisture and Evapotranspiration , 1966, Science.

[61]  M. H. Diskin,et al.  Ponding time and infiltration capacity variation during steady rainfall , 1996 .

[62]  Young-Jin Park,et al.  An assessment of the tracer‐based approach to quantifying groundwater contributions to streamflow , 2006 .

[63]  Michel Vauclin,et al.  Experimental and numerical analysis of two-phase infiltration in a partially saturated soil , 1986 .

[64]  Michael J. Singer,et al.  Crusting, runoff, and erosion response to soil water content and successive rainfalls , 1992 .

[65]  E. C. Childs Dynamics of fluids in Porous Media , 1973 .

[66]  David A. Woolhiser,et al.  Unsteady, one‐dimensional flow over a plane—The rising hydrograph , 1967 .

[67]  M. Esteves,et al.  PSEM_2D: A physically based model of erosion processes at the plot scale , 2005 .

[68]  J. Rubin,et al.  Soil Water Relations During Rain Infiltration: II. Moisture Content Profiles During Rains of Low Intensities1 , 1964 .

[69]  L. K. Sherman Streamflow from rainfall by the unit-graph method , 1932 .

[70]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[71]  S. Gounand,et al.  The Andra Couplex 1 Test Case: Comparisons Between Finite-Element, Mixed Hybrid Finite Element and Finite Volume Element Discretizations , 2004 .

[72]  Jeffrey J. McDonnell,et al.  Virtual experiments: a new approach for improving process conceptualization in hillslope hydrology , 2004 .

[73]  John D. Hewlett,et al.  The Varying Source Area of Streamflow from Upland Basins , 1970 .