Ie. Amin et Me. Campana, A GENERAL LUMPED-PARAMETER MODEL FOR THE INTERPRETATION OF TRACER DATA AND TRANSIT-TIME CALCULATION IN HYDROLOGIC SYSTEMS, Journal of hydrology, 179(1-4), 1996, pp. 1-21
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.