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| Titel |
Inverse Modeling of Tracer Tests in Streams Undergoing Hyporheic Exchange |
| VerfasserIn |
Zijie Liao, Olaf Arie Cirpka |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250032789
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| Zusammenfassung |
| Hyporheic exchange has been identified as a key process in solute transport, biogeochemical
cycling, and ecosystem functioning of streams. Physical solute transport through the
hyporheic zone may be characterized by the total flux of water exchange and the distribution
of hyporheic travel times. The classical method of obtaining travel-time distributions is an
artificial-tracer experiment, in which an easy to detect compound is injected into the river,
and the breakthrough curve (BTC) is measured at an observation point further downstream in
the river. This BTC is affected by in-stream transport and hyporheic exchange as expressed in
the transient storage model for linear solute transport in rivers undergoing hyporheic
exchange:
(-« )
-c+ v--c- D -2c-= q tp(Ï)c(t- Ï)exp(- λÏ)dÏ - c(t) + q (c - c(t))
-t -x -x2 he 0 in in
(1)
in which v and D are the velocity and dispersion coefficient, respectively, qhe is the
hyporheic exchange flux, Ï is the travel-time coordinate in the hyporheic zone, p(Ï) is the
probability density function of Ï, λ is a first-order rate coefficient quantifying potential decay
within the hyporheic zone, qin expresses lateral inflow, and cin is the corresponding
concentration within that inflow.
The target quantities are the exchange flux qhe and the nonnegative travel time
distribution p(Ï) in the hyporheic zone. Common transient storage models use parametric
distribution functions, such as the exponential, power-law, or log-normal distributions. By
predefining the functional form of p(Ï), however, important features such as multimodality
may remain unnoticed.
We present a nonparametric approach of obtaining p(Ï) jointly with the other transport
parameters by fitting BTCs of conservative and reactive solutes. For regularization p(Ï) is
assumed autocorrelated, and nonnegativity is enforced by the method of Lagrange
multipliers. The method extends a nonparametric deconvolution approach for the
determination of transfer functions. It requires successive linearization (Gauss-Newton
scheme), stabilized by a line-search, and forward simulation in the Laplace domain with
numerical back-transformation.
Once the hyporheic travel-time distribution p(Ï) has been identified, the transport model
can be extended to include nonlinear reactions of river-borne compound within the hyporheic
zone thus facilitating the simulation of biogeochemical cycling in streams undergoing
hyporheic exchange.
This method has been tested by virtual conservative and reactive tracer experiments
undergoing hyporheic exchange. Joint inversion of conservative and reactive tracer BTCs is
essential for distinguishing the effects of in-stream dispersion from hyporheic exchange.
Applications to field data are on the way. |
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