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A physical and mathematical model is presented to simulate realistic hydrological conditions and to evalu- ate coupled river and aquifer as water supply system. The approach is applied to estimate the extraction effects on the river and related aquifers under different conditions, with the purpose of determining the water supply potential and sustainability of the coupled system. The model consists of the conceptual and numerical coupling of two structures that take into account different aspects of the systems being considered. The first is a free-surface flow structure, and it carries out the balance of mass and momen- tum along the river course, whereas the second one is of hydrogeological type that performs the mass balance in combination with Darcy’s law in each aquifer of interest for evaluation purposes. The two parts of the model are coupled by their source terms with a very simple linear relationship; the numerical implementation is carried out by using MODFLOW and ISIS codes. After calibrating the models with field parameters, an iterative coupling process is given where each structure must satisfy their criteria of internal convergence. The complete model is satisfactory whenever the iterative coupling process and the hydrogeological and hydraulic models converge. The conceptual approach is applied to the real and natural system constituted by the Papagayo river and the aquifers located in the river banks locally known as Norte, Obra de Toma, and Lomas de Chapultepec, in the State of Guerrero, México to determine their sustainable water supply potential.
darcy’s law, equations of Saint-Venant, flow balance in aquifers, stream-aquifer-coupled systems
[1] Sophocleous, M. Interactions between groundwater and surface water: the state of the science. Hydrogeology Journal, 10, pp. 52–67, 2002. doi: http://dx.doi.org/10.1007/s10040-001-0170-8
[2] Nilsson, B., Dahl, M., Langhoff, J.H., Kronvang, B., Christensen, S., Andersen, H.E., Hoff- mann, C.C., Rasmussen, K.R. & Refsgaard, J.C. Groundwater/surface water interaction – A Danish typological approach. Geophysical Research Abstracts, 6, 03280, SRef-ID 1607-7962/ gra/EGU04-A-03280, European Geosciences Union, p. 2, 2004.
[3] Niazi, S. Sensitivity Analysis of time-step in Modeling River and Aquifer Interaction. Master of Science in Engineering Thesis, University of Texas at Austin, Austin, 190 pp., 2000.
[4] Swain, E.D. & Wexler, E.J. A Coupled Surface-water and Ground-water Flow Model (MODBRANCH) for Simulation of Stream-aquifer Interaction. US Geological Survey, Tech- niques of Water-Resources Investigations, Book 6, Chapter A6, Washington, D.C., p. 125, 1996.
[5] CFE 3. Subdireccion Tecnica/GEIC/SEH/ASV de MM. Reporte de avance de la modela- cion matematica del proyecto integral de abastecimiento de agua subterranea a la ciudad de Acapulco, Gro. Internal Report CFE, p. 86, 1999.
[6] Martinez-Najera, J.D., Flores-Ibarra, C. & Olvera-Coronel, M. Quantitative evaluation of river-aquifer supply systems. 2001 Annual Conference of the International Association for Mathematical Geology, Cancun: Mexico, p. 11, 2001.
[7] Schaffranek, R.W., Baltzer, R.A. & Goldberg, D.E. A model for simulation of flow in singular and interconnected channels. US Geological Survey, Techniques of Water-Resources Investi- gations, Book 7, Chapter C3, Washington, p. 110, 1981.
[8] Halcrow/ HR Wallingford. ISIS flow. User manual. Oxfordshire: UK, p. 318, 1995.
[9] Swain, E.D. Incorporating hydraulic structures in an open-channel model. Proceedings, 1992 National Hydraulic Engineering Conference, American Society of Civil Engineers, New York, NY., pp. 1118–1123, 1992.
[10] Marti, P.B. & Garrigues, R.S. Spokane river/aquifer interaction project results, May – November 1999. Washington State Department of Ecology, Publication No. 01-03-024, p. 88, 2001.
[11] Workman, S.R., Serrano, S.E. & Liberty, K. Development and application of an analytical model of stream/aquifer interaction. Journal of Hydrology, 200, pp. 149–163, 1997. doi: http:// dx.doi.org/10.1016/S0022-1694(97)00014-0
[12] Serrano, S.E. Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity. Water Resour. Res., 31(11), pp. 2733–2742, 1995. doi: http://dx.doi.org/10.1029/95WR02038
[13] Serrano, S.E. & Workman, S.R. Modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution. Journal of Hydrology, 206, pp. 245–255, 1998. doi: http://dx.doi.org/10.1016/S0022-1694(98)00111-5
[14] Adomian, G. A review of the decomposition method and some recent results for nonlinear equations. Comp. Math. Applic., 21(2), pp. 101–127, 1991. doi: http://dx.doi.org/10.1016/0898- 1221(91)90220-X
[15] Osman, Y.Z. & Bruen, M.P. Modelling stream-aquifer seepage in an alluvial aquifer: An improved loosing-stream package for MODFLOW. Journal of Hydrology, 264, pp. 69–86, 2002. doi: http://dx.doi.org/10.1016/S0022-1694(02)00067-7
[16] Bear, J., Zaslavsky, D. & Irmay, S. Physical principles of water percolation and seepage. UNESCO: Paris, p. 465, 1968.
[17] Bruen, M.P. & Osman, Y.Z. Sensitivity of stream-aquifer seepage to spatial variability of the saturated hydraulic conductivity of the aquifer. Journal of Hydrology, 293, pp. 289–302, 2004. doi: http://dx.doi.org/10.1016/j.jhydrol.2004.02.003
[18] Cruickshank-Villanueva, C. Relacion entre las aguas superficiales y las subterraneas en una cuenca. Ingenieria Hidraulica en Mexico, pp. 56–63, 1992.
[19] Bouwer, H. Theory of seepage from open channels. Advances in Hydroscience, 7, ed. Ven-Te-Chow, Mc Graw Hill: New York, pp. 121–172, 1976.
[20] Cruickshank-Villanueva, C. Personal communication, May 2004. On the infiltration formulas for rivers in the numerical simulation of aquifers.
[21] Llanusa, R.H. & Martinez-Rodriguez, J.B. Modelacion explicita de embalse y acuifero. Ing- enieria Hidraulica en Mexico, XVII(4), pp. 89–97, 2002.
[22] Fox, G. Estimating streambed and aquifer parameters from a stream/aquifer analysis test. Pro- ceedings of the 23rd Annual Geophysical Union Hydrology Days, ed. J.A. Ramirez, Colorado State University: Fort Collins, pp. 68–79, 2003.
[23] Balancing ground-water withdrawals and streamflow in the Hunt-Annaquatucket-Pettaquamscutt basin, Rhode Island. USGS Fact Sheet FS-063-01. Barlow, P.M. & Dickerman, D.C. On line. http://pubs.usgs.gov/fs/fs063-01/.
[24] Fleckenstein, J., Anderson, M., Fogg, G. & Mount, J. Managing surface water-ground water to restore fall flows in the Cosumnes River. Journal of Water Resources Planning and Management, ASCE, 130(4), pp. 301–310, 2004. doi: http://dx.doi.org/10.1061/(ASCE)0733- 9496(2004)130:4(301)
[25] Courant, R. & Lax, P. On nonlinear partial differential equations with two independent variables. Comm. Pure Appl. Math, 2(3), pp. 255–273, 1949. doi: http://dx.doi.org/10.1002/ cpa.3160020206
[26] BEAR, J. Dynamics of Fluids in Porous Media. American Elsevier: New York, p. 764, 1972.
[27] Freeze, R.A. & Cherry, J.A. Groundwater. Hemel Hempstead: Prentice-Hall, Inc., Englewood Cliffs, NJ., p. 604, 1979.
[28] McDonald, M.G. & Harbaugh, A.W. A modular three-dimensional finite-difference ground- water flow model. U.S. Geological Survey, Open-File Report: Washington, p. 568, 1988.
[29] Anderson, M.P. & Woessner, W.W. Applied Groundwater modeling. Simulation of Flow and Advective Transport. San Diego: Academic Press, p. 381, 1992.
[30] Martinez-Najera, J.D., Talamantes-Contreras, P., Sanchez-Linares, C. & Olvera-Coronel, M. Analisis del acoplamiento y modelacion matematica de sistemas embalse y acuifero. Ingenie- ria Hidraulica en Mexico, XXIV(3), pp. 91–99, 2009
[31] Martinez-Najera, J.D. & Berezowsky-Verduzco, M. Evaluacion del abastecimiento de sistemas rio-acuifero. Ingenieria Hidraulica en Mexico, XXIII(4), pp. 173–187, 2008.
[32] Preissmann, A. Propagation des intumescences dans les canaux et rivieres. 1er Congres de l’Assoc. Francaise de Calcul, Grenoble, France, pp. 433–442, 1961.
[33] Fread, D.L. An implicit dynamic wave model for mixed flows in storm sewer networks. In- ternational Symposium on Urban Hydrology, Hydraulics and Sediment Control, University of Kentucky: Lexington, Kentucky, p. 17, 1985.
[34] Chau, K.W. Application of the Preissmann scheme on flood propagation in river systems in difficult terrain. Hydrology in Mountainous Regions. I - Hydrological Measurements. The Water Cycle, Proceedings of two Lausanne Symposia, IAHS Publ. 193, pp. 535–543, 1990.
[35] CNA 1. Subdireccion General Tecnica/Gerencia de Aguas Subterraneas/Subgerencia de Exploracion y Monitoreo Geohidrologico. Informe sobre el estado actual de las principales fuentes de abastecimiento de agua potable del puerto de Acapulco, Edo. de Guerrero. Internal Report CNA, September, p. 20, 1997.
[36] CNA 2. Subdireccion General Tecnica/Gerencia de Aguas Subterraneas/Subgerencia de Exploracion y Monitoreo Geohidrologico. Comentarios preliminares acerca de la construc- cion de pozos someros en el playon de la margen derecha del rio Papagayo, en la cercania de Aguas Calientes, Edo. de Gro. Internal Report CNA, February, p. 35, 1998.
[37] CFE 1. Subdireccion Tecnica/GEIC/SEH/DGH. Avance del estudio integral de sistemas de abastecimiento de agua subterranea a la ciudad de Acapulco, Gro. (Rios Papagayo y Coyuca). Internal Report CFE, p. 50, 1998a.
[38] CFE 2. Subdireccion Tecnica/GEIC/SEH/DGH. Estudio para la caracterizacion hidrogeolog- ica sobre el rio Papagayo. Sitio Playon Norte. Internal Report CFE, p. 25, 1998b.