Solution of non-linearities in the eigenvalue method application for the simulation of complex conjunctive use systems. Extension to unconfined aquifers

To evaluate water resources management alternatives in conjunctive use systems mathematical models that simulate simultaneously surface and groundwater components and their interaction are required. If the system is complex and scenarios are defined over long accumulated time periods to take into account the stochastic behaviour of surface hydrology, efficient aquifer models are required. In order to keep the computational time small, the groundwater flow equation ought to be solved using explicit techniques such as influence functions or the eigenvalue technique. These methods are strictly applicable only to confined aquifers, which are modelled with a linear groundwater flow equation. The eigenvalue technique provides an explicit and continuous in time solution of the confined groundwater flow equation using a state equation. Through this solution the hydraulic heads and the stream aquifer flow exchange can be efficiently computed. It represents an important computational advantage in conjunctive use simulations. However, many commonly exploited aquifers connected with the surface system are unconfined, and should be modelled using the non-linear Boussinesq equation. A solution of the groundwater flow problem in unconfined aquifers is presented. It is based on a new approach to linearize the Boussinesq equation. Using a change of variable, it is possible to define an equation with a structure similar to the linear groundwater flow equation. The only difference is found in a term that depends on the solution, and makes the equation non linear. Approaching this term by means of a fictitious stress constant in each stress period, a linear equation analogous to the confined groundwater flow one is obtained. The most usual boundary conditions employed to model aquifer flow can also be formulated as a function of the new variable with linear expressions. Therefore the groundwater flow problem defined can be solved applying the superposition principle, and it is possible to define a solution with a reduced computational cost using the eigenvalue technique. This is a solution that permits the integration of unconfined groundwater flow in conjunctive use models.