Potential and Merits of the Eigenvalues Method to Simulate the Conjunctive Use of Groundwater and Surface Water

It is necessary predict the effect of aquifer stresses in surface water and wetlands and consider the mutual effects that are produced by the conjunctive use of surface water and groundwater. This was originally made with very simple idealized analytical methods. The next development was the application of finite differences or finite elements numerical models, but poses problems when the model has to be run many times to analyze different management alternatives. When aquifer behavior is linear, as in confined, semi-confined, or unconfined aquifers with not too large changes in its saturated thickness, it is possible to apply the superposition strategy through influence functions. That has simplified significantly modeling and improved the effectiveness of management models. However, for large models, long modeling periods and a large number of alternatives, it is needed to handle and store many influence functions and to consider and store all the previous stresses. In that case, the eigenvalue method can be a more appropriated option. This approach solves the spatially discretized flow equation explicitly and continuously in time, obtaining modal orthogonal components through very simple explicit state equations in function of time. To reduce the computational load, the simulation can be simplified with appropriate truncation using only dominant modes of the components at the expense of a small error. Efficient methods have been developed to get the modal components as well as to perform truncation with limited errors.