On the Physical and Mathematical Modeling of the Coupling of Rivers and Aquifers as Sustainable Water Supply Systems

On the Physical and Mathematical Modeling of the Coupling of Rivers and Aquifers as Sustainable Water Supply Systems

J.D. Martínez-Nájera C. Cruickshank-Villanueva M. Berezowsky-Verduzco 

Comisión Federal de Electricidad, GEIC, Subgerencia de Estudios Hidrográficos, México

Universidad Nacional Autónoma de México, Instituto de Ingeniería, México

22 May 2013
| Citation



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


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