A LOW-DIMENSIONAL MODEL FOR CONCENTRATION-DISCHARGE DYNAMICS IN GROUNDWATER STREAM SYSTEMS

In this paper we investigate the physical basis and validity of a dyna mical model for environmental tracer response for a groundwater-domina ted stream reach or small catchments. The dynamical model is formed by volume averaging of the local equations of saturated flow and solute transport. The approach interprets the empirical concentration-dischar ge C-Q as a pair of integrated state variables from an underlying stat e space (or phase space) for the hillslope or catchment response. The inputs represent episodic, seasonal, and random recharge rate and conc entration time series. A closed form solution is found for constant in puts. Results are compared:vith numerical solutions of the governing p artial differential equations, and agreement is found for a full range of initial states and levels of forcing. For pulse-type or piecewise constant recharge events, the phase plane trajectories for C-Q are sho wn to exhibit looping behavior, without the need for an assumption of hysteresis in the model. The orientation and looping direction of thes e solutions are shown to be controlled by the dimensionless ratio of s olute residence time to hydraulic relaxation time and the relative pha se lag between recharge and recharge concentration. The closed form so lution is extended to the case of piecewise constant, random, input se quences resulting in a ''random map'' for C-Q. An application is prese nted for seasonal storage and flushing of SO-4 in runoff for a small c atchment in central Pennsylvania.