An efficient conceptual model to simulate surface water body-aquifer interaction in conjunctive use management models

1 In conjunctive use management models, the surface and subsurface components must be simultaneously simulated because of the hydraulic interactions and to the combined operating rules inherent to such schemes. When many management alternatives have to be simulated over long time horizon or when optimizing complex large-scale systems, an efficient tool for surface water body-aquifer interaction simulation is needed. In this paper, we present a parsimonious conceptual model as an alternative approach to simulate aquifer storage and surface water body-aquifer interaction for linear aquifers (linear response of head to stresses). The formulation is deduced from a finite difference model preserving its approach of the geometry, boundary conditions, hydrodynamic parameters (heterogeneity), and spatial distribution of the stresses. It does not require any additional assumption. The solution, obtained using eigenvalue techniques, is formulated with an explicit state equation that is a function of time and does not need to be calculated in a sequential way (that is, time is not discretized). The structure of the solution finally deduced allows a simple conceptual interpretation of surface water body-aquifer interaction phenomenon as the drainage of a number of independent linear reservoirs. The parameters and initial conditions of each linear reservoir are mathematically defined in a univocal way from the original calibrated finite difference model preserving its characteristics. In most practical cases, an accurate solution can be obtained with a reduced number of linear reservoirs. Therefore this multireservoir conceptual definition enables an important reduction in the dimension of the model matrices and provides a straightforward means of incorporating the accuracy of more complex calibrated distributed-parameter numerical models for simulating surface water body-aquifer interaction within conjunctive use management models and with a minimum computational cost. Several case studies (synthetic and real world cases) are used to illustrate the applicability of the methodology.