A GENERAL LUMPED-PARAMETER MODEL FOR THE INTERPRETATION OF TRACER DATA AND TRANSIT-TIME CALCULATION IN HYDROLOGIC SYSTEMS

We present a general lumped parameter mathematical model for hydrologi c tracer data interpretation and mean transit time calculation in hydr ologic systems. The model takes the form of the three-parameter gamma distribution and accounts for different mixing types: perfect mixing; no mixing (piston flow); partial mixing (dispersive mixing, or the typ e between perfect mixing and no mixing); and various combinations of t he above types. In these combinations, the different mixing types simu lated by the model conceptually represent reservoirs in series. We int roduce the mixing efficiency to characterize the extent or degree of n atural mixing in hydrologic systems. This parameter equals zero for pi ston flow (no mixing), unity for perfect mixing, and a value in betwee n these two extremes for partial mixing. The general model simulates t he combination of perfect mixing, partial mixing, and piston flow. Six other models that simulate one or two of these mixing types can be ob tained as special cases from the general model. Therefore, seven model s are introduced in this effort. Of these, four (including the general model) are new, and three are currently existing in the held of trace r hydrology. The three existing models are the perfect mixing model, p iston flow model, and the perfect-piston flow model which simulates th e combination of perfect mixing and piston flow. The new models are th e perfect-partial-piston flow model (the general model), perfect-parti al mixing model, partial-piston flow model, and partial mixing model. Modeled mean transit times for three case studies agree with previous estimates: 21 and 2.4 years for two springs (sites 2 and 45, respectiv ely) on Cheju Island, Republic of Korea; and 3.0 years for the Ottawa River basin, Canada.