| Several tracers for dating groundwater (18O/2H, 3H, CFCs, SF6, 85Kr) need lumped
parameter modeling (LPM) to convert measured values into numbers with unit time. Other
tracers (T/3He, 39Ar, 14C, 81Kr) allow the computation of apparent ages with a
mathematical formula using radioactive decay without defining the age mixture
that any groundwater sample represents. Also interpretation of the latter profits
significantly from LPM tools that allow forward modeling of input time series to
measurable output values assuming different age distributions and mixtures in the
sample.
This talk presents a Lumped Parameter Modeling code, Lumpy, combining up to two
LPMs in parallel. The code is standalone and freeware. It is based on MS Access and Access
Basic (AB) and allows using any number of measurements for both input time series and
output measurements, with any, not necessarily constant, time resolution. Several tracers, also
comprising very different timescales like e.g. the combination of 18O, CFCs and 14C, can be
modeled, displayed and fitted simultaneously. Lumpy allows for each of the two
parallel models the choice of the following age distributions: Exponential Piston flow
Model (EPM), Linear Piston flow Model (LPM), Dispersion Model (DM), Piston
flow Model (PM) and Gamma Model (GM). Concerning input functions, Lumpy
allows delaying (passage through the unsaturated zone) shifting by a constant value
(converting 18O data from a GNIP station to a different altitude), multiplying by a
constant value (geochemical reduction of initial 14C) and the definition of a constant
input value prior to the input time series (pre-bomb tritium). Lumpy also allows
underground tracer production (4He or 39Ar) and the computation of a daughter
product (tritiugenic 3He) as well as partial loss of the daughter product (partial
re-equilibration of 3He). These additional parameters and the input functions can be defined
independently for the two sub-LPMs to represent two different recharge areas. For a
user defined choice of up to five parameters (mean residence times and dispersion
parameters of the two sub-LPM plus the mixing ratios of the two models) the best fit can
be determined. Fits can be assessed using different methods for the Goodness Of
Fit.
Input and output data are send to MS Excel for interactive display of modeling result and
comparison with measurements. Excel only serves as data display; computations are
performed in AB throughout. Lumpy allows display of time series and any combination of
tracer vs. tracer plot. In the latter, the possible output data space assessable by the input
variables can be displayed, to check if any of the model combinations under consideration is
able to explain the measured data. Comparison and fit to measurements is possible after each
of the two sub-models and after mixing these two. The talk will demonstrate the usefulness of
this approach with examples from the Croatian Karst (Babinka 2007), the Fischa tracer test
(Stolp et al., 2010) and the 30 years monthly tritium time series of the Danube (Aggarwal et
al., 2010).
References:
Aggarwal, P.K., Araguas-Araguas, L., Gröning, M., Newman, B., Kurttas, T., Papesch,
W., Rank, D., Suckow, A., Vitvar, T. 2010. Long-term tritium monitoring to study
river basin dynamics: case of the Danube River basin. EGU General Assembly 12
EGU2010-11775.
Babinka, S. 2007. Multi-Tracer Study of Karst Waters and Lake Sediments in Croatia and
Bosnia-Herzegovina: Plitvice Lakes National Park and Bihac Area. PhD thesis, Universität
Bonn.
Stolp, B. J., Solomon, D. K., Suckow, A., Vitvar, T., Rank, D., Aggarwal, P. K., Han, L.-F.
2010. Age dating base flow at springs and gaining streams using helium-3 and tritium:
Fischa-Dagnitz system, southern Vienna Basin, Austria. Water Resources Research 46, DOI:
10.1029/2009WR008006. |