The need for an appropriate representation of rapidly varying processes

RODRÍGUEZ LB; VIONNET CA; MADDOCK T

Exeter, UK

Conferencia; 1st British Hydrological Society International Conference on Hydrology in a Changing Environment; 1998

BHS - British Hydrological Society

Whereas the temporal variations typical of surface flows in riparian areas are in the order of hours or days, ground-water time response occurs in weeks or even months. When the time scales are so disparate, one could think about dropping the fast time scale and solve only for the slow time scale which, in turn, will provide the long term behaviour of the system. However, in presence of non-linearities, the fast time scale effects may gather up to produce cumulative effects that can influence the slow scale solution. Many stream-aquifer studies neglect the fast time scale process while others focus only on the routing of a single wave. Previous experience has shown that in streamflow dominated riparian corridors, neglecting the surface component can deprive the system from an important amount of water that could otherwise satisfy evapotranspiration losses. This paper describes the flood routing component, simulated by means of the kinematic wave approximation, the saturated flow component simulated by the well known vertically averaged ground-water flow equation, and their link, represented by a boundary integral that shows up naturally from the numerical finite element approximation of the two governing equations. Using simple scaling arguments, the fast time scale characteristic of surface water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the stream discharge, and a Biot number that relates the conductance of the river-aquifer interface to the aquifer conductance. It follows that for high Peclet numbers, the ground-water flow is indeed decoupled from the surface flows. Numerically, the problem is solved by the finite element method with a Bubnov-Galerkin approximation for the parabolic ground-water flow equation and a Petrov-Galerkin approximation for the hyperbolic kinematic wave equation. The implementation of the model on the Bill Williams River Basin, Arizona, U.S.A. incorporating multiple time steps yielded results that reproduced observed streamflow patterns and ground-water flow patterns adequately well.