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Ein physikalisch basiertes Modellkonzept zur Transportmodellierung in gekoppelten Hydrosystemen

A physically based model concept for transport modelling in coupled hydrosystems

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Kurzfassung

Hydrosysteme sind komplexe Systeme, in denen eine Vielzahl von Prozessen gleichzeitig auf unterschiedlichen Raum- und Zeitskalen ablaufen. In diesem Artikel stellen wir ein Kompartimentkonzept zur Simulation von Stoff- und Wärmetransportprozessen in gekoppelten Hydrosystemen vor. Das Konzept beinhaltet die Kopplung von Strömungs- und Transportprozessen über die Grenzflächen der Kompartimente (oder der Prozessdomäne) unter Beibehaltung der rechentechnischen Anforderungen und Optimierungen für die numerische Lösung jedes einzelnen Prozesses. Neu ist auch die Verwendung stochastischer Partikelmethoden (random walk particle tracking – RWPT) zur Analyse von Stofftransport in gekoppelten Hydrosystemen. Wir stellen zunächst kurz die verwendete RWPT-Methode und die maßgeblichen Gleichungen für Strömung, Wärme- und Stofftransport in der gesättigten und der ungesättigten Zone sowie auf der Landoberfläche vor. Fließvorgänge werden durch (z. T. nichtlineare) Diffusionsgleichungen beschrieben (Darcy-Gleichung für Grundwasserströmung, Richards-Gleichung für Strömung in der ungesättigten Zone und diffusive Wellengleichung für Oberflächenabfluss) und über Austauschterme (Flüsse) gekoppelt. Transportprozesse werden durch Advektions-Diffusionsgleichungen beschrieben und advektiv gekoppelt. Wir stellen drei Anwendungsbeispiele für Strömungs-, Stoff- und Wärmetransportvorgänge in gekoppelten Hydrosystemen vor basierend auf Hortonschen und Dunneschen Oberflächenabflüssen sowie hyporheischen Fließvorgängen.

Abstract

Hydrosystems are very complex systems with numerous processes occuring simultaneously at different spatial and temporal scales. In this paper we present the concept of a compartment approach for the analysis of coupled hydrosystems including heat and mass transport. In this concept, flow and transport processes are coupled via their compartment (or process domain) boundaries without giving up the computational necessities and optimisations for the numerical solution of each individual process. In this new approach, random walk particle tracking (RWPT) methods are integrated into the coupled hydrosystem analysis. We briefly introduce the RWPT method and the governing equations for water flow, heat, and mass transport in aquifers, soils and on surfaces. Flow processes are described by diffusion equations (Darcy equation for groundwater flow, Richards equation for flow in the unsaturated zone, and the diffusive wave approximation for overland flow) which are coupled by exchange fluxes. Transport processes are described by advection-diffusion equations and coupled with the exchange fluxes by advection. We present three application examples concerning flow, mass and heat transport in coupled hydrosystems based on Horton- and Dunne overland flow as well as on hyporheic flows.

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Literatur

  • Abbott, M. B., Babovic, V. M., Cunge, J. A.: Towards the hydraulics of the hydroinformatics era.- J. Hydraul. Res 39(4), 339–349 (2001)

    Google Scholar 

  • Abbott, M. B., Bathurst, J. C., Cunge, J. A., O’Connell, P. E., Rasmussen, J.: An introduction to the european hydrological system – Systéme Hydrologique Européen, ‚SHE‘, 2: Structure of a physically-based, distributed modelling system.- J. Hydrol. 87(2), 61–77 (1986)

    Article  Google Scholar 

  • Abdul, A. S., Gilham, R. W.: Laboratory studies of the effects of the capillary fringe on streamflow generation.- Water Resour. Res. 20(6), 691–698 (1984)

    Article  Google Scholar 

  • Abdul, A. S., Gilham, R. W.: Field studies of the effects of the capillary fringe on streamflow generation.- J. Hydrol. 112, 1–18 (1989)

    Article  Google Scholar 

  • Akan, A. O., Yen, B. C.: Mathematical model of shallow water flow over porous media.- J. Hydr. Div. ASCE 107(4), 479–494 (1981)

    Google Scholar 

  • Anderson, M. G., Burt, P. T.: Hydrological forecasting; Wiley Publisher, Berlin (1985)

  • Arnold, J. G., Sirinivasan, R., Muttiah, R. S., Williams, J. R.: Large area hydrologic modeling and assessment, part 1 – model development.- J. Am. Water Resour. Assoc. 34(1), 73–89 (1998)

    Article  Google Scholar 

  • Bear, J.: Dynamics of fluids in porous media.- Dover Publications Inc. New York, 2. Aufl. (1988)

  • Bertoldi, G., Tamanini, D., Zanotti, F., Rigon, R.: GEOtop, A hydrological balance model, technical description and programs guide (Version 0.875). Department of Civil and Environmental Engineering, University of Trento (2004)

  • Bhallamudi, S. M., Panday, S., Huyakorn, P. S.: Sub-timing in fluid flow and transport simulations.- Adv. Water Resour. 26(5), 477–489 (2003)

    Article  Google Scholar 

  • Brunke, M., Gonser, T.: The ecological significance of exchange processes between rivers and groundwater.- Freshwater Biol. 37, 1–33 (1997)

    Article  Google Scholar 

  • Cardenas, M. B., Wilson, J. L.: Effects of current-bed form induced fluid flow on the thermal regime of sediments.- Water Resour. Res. 43, W08431, doi:10.1029/2006WR005343 (2007)

  • Chen, Q., Morales-Chaves, Y., Li, H., Mynett, A.: Hydroinformatics techniques in eco-environmental modelling and management.- J. Hydroinf. 8(4), 297–316 (2006)

    Article  Google Scholar 

  • Constantz, J., Stonestrom, D.: Heat as a tracer of water movement near streams.- In: Stonestrom, D., Constantz, J. (Hrsg.): Heat as a tool for studying the movement of ground water near streams.- USGS Survey Circular 1260 (2003)

  • Darcy, H. P. G.: Les fontaines publiques de la ville de Dijon; Victor Dalmont, Paris (1856)

  • Dawson, C.: Analysis of discontinuous finite element methods for groundwater/surface water coupling.- SIAM J. Num. Anal. 52, 63–88 (2006)

    Google Scholar 

  • Delay, F., Ackerer, P., Danquigny, C.: Simulating solute transport in porous or fractured formations using random walk particle tracking: a review.- Vadose Zone J. 4(2), 360–379 (2005)

    Article  Google Scholar 

  • Delfs, J.-O., Park, C.-H., Kolditz, O.: A sensitivity analysis of Hortonian flow.- Adv. Water Resour., doi:10.1016/j.advwatres.2009.06.005 (2009, in Druck)

  • Delfs, J.-O., Park, C.-H., Kolditz, O.: Benchmarking of flow and transport in coupled surface/subsurface hydrosystems. Helmholtz Zentrum für Umweltforschung – UFZ; Leipzig (2008)

  • Donigian, A. S., Imhoff, J.: History and evolution of watershed modelling derived from the Stanford Watershed Model. CRC Press, Boca Raton.- In: Singh, V. P., Frevert, D. (Hrsg.): Watershed Models (2006)

  • Du, Y., Kolditz, O.: Time discretization for Richards flow modelling.- Tech. Rep. 2005-50; Center of Applied Geoscience, University of Tübingen, GeoSys-Preprint (2005)

  • Forsyth, P. A., Wu, Y. S., Pruess, K.: Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media.- Adv. Water Resour. 18, 25–38 (1995)

    Article  Google Scholar 

  • Freeze, R. A., Harlan, R. L.: Blueprint for a physically based, digitally-simulated hydrological response model.- J. Hydrol. 9, 237–258 (1969)

    Article  Google Scholar 

  • Gerbeau, J.-F., Perthame, B.: Derivation of viscous Saint Venant system for laminar shallow water: Numerical validation.- Discrete Contin. Dyn. Syst. Ser. B 1(1), 89–102 (2001)

  • Govindaraju, R. S.: Modeling overland flow contamination by chemicals mixed in shallow soil horizons under variable source area hydrology.- Water Resour. Res. 32(3), 753–758 (1996)

    Article  Google Scholar 

  • Govindaraju, R. S., Kavvas, M. L.: Dynamics of moving boundary overland flows over infiltrating surfaces at hillslopes.- Water Resour. Res. 27(8), 1885–1898 (1991)

    Article  Google Scholar 

  • Green, W. A., Ampt, G. A.: Studies on soil physics I. The flow of air and water through soils.- J. of Agr. Sci. 4, 1–24 (1911)

    Article  Google Scholar 

  • Gunduz, O., Aral, M. M., 2005. River networks and groundwater flow: simultaneous solution of a coupled system.- J. Hydrol. 301(1–4), 216–234 (2005)

    Google Scholar 

  • Harbaugh, A. W., Banta, E. R., Hill, M. C., McDonald, M. G.: MODFLOW-2000, the U. S. geological survey modular ground-water model – user guide to modularization concepts and the groundwater flow process.- Tech. Rep. 00-92, U. S. Geological Survey, Open-File Report (2000)

  • Hoteit, H., Mose, R., Younes, A., Lehmann, F., Ackerer, P.: Three-dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random-walk methods.- Math. Geol. 34(4), 435–456 (2002)

    Article  Google Scholar 

  • Huyakorn, P., Pinder, G.: Computational methods in subsurface flow; Academic Press, New York (1983)

  • Ibisch, R. B., Borchardt, D., Seydell, I.: Influence of periphyton biomass dynamics on biological colmation processes in the hyporheic zone of a gravel bed river (River Lahn, Germany).- Fundam. Appl. Limnol. (2009, im Druck)

  • Julien, P. Y.: River mechanics.- Cambridge University Press; Cambridge (2002)

  • Kalbus, E., Reinstorf, F., Schirmer, M.: Measuring methods for groundwater – surface water interactions: a review.- Hydrol. Earth Syst. Sci. 10(6), 873–887 (2006)

    Google Scholar 

  • Kinzelbach, W.: Numerische Methoden zur Modellierung des Transports von Schadstoffen im Grundwasser; Oldenburg Verlag, München und Wien (1987)

  • Kolditz, O., Bauer, S.: A process-orientated approach to compute multi-field problems in porous media.- International J. Hydroinf. 6, 225–244 (2004)

    Google Scholar 

  • Kolditz, O., Delfs, J.-O., Bürger, C., Beinhorn, M., Park, C.-H.: Numerical analysis of coupled hydrosystems based on an object-oriented compartment approach.- J. Hydroinf. 10(3), 227–244 (2008)

    Article  Google Scholar 

  • Kolditz, O., Shao, H. (Hrsg.): OpenTHMC – Developer Benchmark Book based on GeoSys/RockFlow Version 4. 9. 06. Report 15, Helmholtz Centre for Environmental Reserach – UFZ Leipzig (2009)

  • Kollet, S. J., Maxwell, R. M.: Integrated surface-groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model.- Adv. Water Resour. 29(7), 945–958 (2006)

    Article  Google Scholar 

  • Lees, M.: Data-based mechanistic modelling and forecasting of hydrological systems.- J. Hydroinf. 2(1), 15–34 (2000)

    Google Scholar 

  • LeVeque, R. J.: Finite volume methods for hyperbolic problems; Cambridge University Press, Cambridge (2002)

  • Li, Q., Unger, A., Sudicky, E.: Simulating the multi-seasonal response of a large-scale watershed with a 3D physically-based hydrologic model.- J. Hydrol. 357(3–4), 317–336 (2008)

    Google Scholar 

  • Manning, R.: On the flow of water in open channels and pipes.- Trans. Inst. Civil Eng. Ireland 20, 161–207 (1891)

    Google Scholar 

  • Morita, M., Yen, B. C.: Modeling of conjunctive two-dimensional surface-three-dimensional subsurface flows.- J. Hydraul. Eng. 128(2), 184–200 (2002)

    Article  Google Scholar 

  • Park, C.-H., Beyer, C., Bauer, S., Kolditz, O.: A study of preferential flow in heterogeneous media using random walk particle tracking.- Geosci. J. 12(3), 285–297 (2008a)

    Article  Google Scholar 

  • Park, C.-H., Beyer, C., Bauer, S., Kolditz, O.: Using global node-based velocity in random walk particle tracking in variably saturated porous media: Application to contaminant leaching from road constructions.- Environ. Geol. 55, 1755–1766 (2008b)

    Article  Google Scholar 

  • Park, Y., Sudicky, E., Panday, S.: Application of implicit sub-time stepping to simulate flow and transport in fractured porous media.- Adv. Water Resour. 31(7), 995–1003 (2008c)

    Article  Google Scholar 

  • Philip, J. R.: The theory of infiltration: 3. Moisture profiles and relation to experiment.- Soil Sci. 83, 163–178 (1957)

    Article  Google Scholar 

  • Ponce, V. M., Ruh-Ming, L., Simmons, D. B.: Applicability of kinematic and diffusion models.- J. Hydr. Div. ASCE 104, 353–360 (1978)

    Google Scholar 

  • Richards, C. P., Parr, A. D.: Modified Fickian model for solute uptake by runoff.- J. Env. Engrg. 114(4), 792–809 (1988)

    Article  Google Scholar 

  • Richards, L. A.: Capillary conduction of liquids through porous mediums.- Phys. 1, 318–333 (1931)

    Article  Google Scholar 

  • Sänger, N., Zanke, U. C.: A depth – oriented view of hydraulic exchange patterns between surface water and the hyporheic zone: analysis of field experiments at the River Lahn, Germany.- Arch. Hydrobiol. (2009, in Druck)

  • Samaniego, L., Bárdossy, A.: Exploratory modelling applied to integrated water resources management. Proceedings 3rd International Symposium on Integrated Water Resources Management, Bochum, September 2006.- IAHS Publ. 317 (2007)

  • Simunek, J., Sejna, M., Genuchten, M. T. v.: The Hydrus-2D software package for simulating two-dimensional movement of water, head and multiple solutes in variably saturated media. Version 2.0, IGWMC-TPS-53. International GroundWater Modeling Center, Colorado School of Mines, Golden, Colorado (1999)

  • Singh, V., Bhallamudi, S. M.: Conjunctive surface-subsurface modeling of overland flow.- Adv. Water Resour. 21(7), 567–579 (1998)

    Article  Google Scholar 

  • Singh, V. P.: Derivation of errors of kinematic-wave and diffusion-wave approximations for space-independent flows.- Water Resour. Manage. 8, 57–82 (1994)

    Article  Google Scholar 

  • Singh, V. P., Frevert, D. K. (Hrsg.): Watershed Models; CRC, USA (2005)

  • Smith, R. E., Woolhiser, D. A.: Overland flow on an infiltrating surface.- Water Resour. Res. 7(4), 899–913 (1971)

    Article  Google Scholar 

  • Sudicky, E., Jones, J., Park, Y.: Simulating complex flow and transport dynamics in an integrated surface-subsurface modeling framework.- Geosci. J. 12(2), 107–122 (2008)

    Article  Google Scholar 

  • Sudicky, E. A., Jones, J. P., McLaren, R. G., Brunner, D. S., VanderKwaak, J. E.: A fully-coupled model of surface and subsurface water flow: Model overview and application to the Laurel Creek watershed.- In: Balkema, A. A. (Hrsg.): Computational methods in water resources Nr. 2, 1093–1099 (2000)

  • Teutsch, G.: Grundwassermodelle im Karst: Praktische Ansätze am Beispiel zweier Einzugsgebiete im Tiefen und Seichten Malmkarst der Schwäbischen Alb. Dissertation, Zentrum für Angewandte Geowissenschaften, Universität Tübingen (1988)

  • Therrien, R., McLaren, R. G., Sudicky, E. A., Panday, S.: HydroSphere: A three-dimensional numerical model describing fully-integrated subsurface and surface flow and solute transport; Université Laval and University of Waterloo (2004)

  • Thoms, R. B.: Simulating fully coupled overland and variably saturated subsurface flow using MODFLOW. Magisterarbeit, OGI School for Science and Engineering, Oregon Health & Science University, Beaverton, USA (2003)

  • van Genuchten, M. T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soil.- Soil Sci. Soc. of Am. J. 44, 892–898 (1980)

    Article  Google Scholar 

  • VanderKwaak, J. E.: Numerical simulation of flow and chemical transport in integrated surface-subsurface hydrologic systems. Dissertation, Department of Earth Sciences, University of Waterloo, Ontario, Canada (1999)

  • Vreugdenhil, C. B.: Numerical Methods for Shallow-Water Flow. Kluwer Academic Publishers, Dordrecht (1994)

  • Wallach, R., van Genuchten, T., Spencer, W.: Modelling solute transfer from soil to surface runoff: The concept of effective depth of transfer.- J. Hydrol. 109, 307–317 (1989)

    Article  Google Scholar 

  • Wang, W., Kolditz, O.: Object-oriented finite element analysis of thermo-hydro-mechanical (THM) problems in porous media.- Int. J. Numer. Methods Eng. 69(1), 162–201 (2007)

    Article  Google Scholar 

  • Warrick, J. W., 2003.- Soil water dynamics. Oxford University Press Inc., New York.

  • Wasy Software: IFMMIKE11 1.1, User manual; Wasy GmbH, Institute for Water Resources Planning and System Research (2004)

  • Watanabe, N.: Mesh design for finite element analysis of geo-hydrological systems. Magisterarbeit, Graduate School of Environmental science, Okayama University, Japan (2008)

  • Weisbach, J.: Lehrbuch der Ingenieur- und Maschinen-Mechanik.- Water & Power Press, Braunschweig (1845)

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  1. Department Umweltinformatik, Helmholtz-Zentrum für Umweltforschung – UFZ Leipzig, Permoserstr. 15, 04318, Leipzig, Deutschland

    J.-O. Delfs,  C.-H. Park &  O. Kolditz

  2. Department Hydrogeologie, Helmholtz-Zentrum für Umweltforschung – UFZ Leipzig, Permoserstr. 15, 04318, Leipzig, Deutschland

    E. Kalbus

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  1. J.-O. Delfs
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  2. C.-H. Park
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  3. O. Kolditz
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  4. E. Kalbus
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Delfs, JO., Park, CH., Kolditz, O. et al. Ein physikalisch basiertes Modellkonzept zur Transportmodellierung in gekoppelten Hydrosystemen. Grundwasser 14, 219–235 (2009). https://doi.org/10.1007/s00767-009-0114-0

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