| Transient storage has a major influence on solute transport in streams, on biogeochemical
cycling, water quality and on the functioning of aquatic ecosystems. The first part of the
research reported here focuses on surface transient storage (STS) zones between groins along
small streams. Such groins are used to protect banks, but also to increase habitat diversity and
are, thus, not restricted to large rivers. Repeated tracer dilution experiments on the
Mödlingbach, a small stream in Austria some 30 km south of Vienna, have been analyzed to
determine the solute residence time between groins and to characterize the exchange
processes between dead zones and main stream.
Pairs of related breakthrough curves were measured in main stream and storage zones,
resp., and used subsequently to estimate the solute residence time in the surface dead zones
under study. Following previous work (Weitbrecht et al., 2008; Jackson et al., 2012) these
residence times were, in turn, expressed as
T = -W–.hD-
k -
u hE
(1)
with W denoting groin length, u main stream flow velocity, hD mean water depth between the
groins and hE depth at the interface dead zone - main stream. Coefficient k, finally, is
thought to depend on a type of hydraulic radius, RD = W.L/(W+L), with L denoting
the distance between the groins, measured in main flow direction. Using both the
Mödlingbach STS zone data and the results of the aforementioned study (Weitbrecht et al.,
2008) the following regression equation was derived (hS denotes main stream water
depth):
k = 0.00282-
RD + 0.00802
hS
(2)
The second part of this research focuses on the dependency of solute residence time on flow
rate, which is important for an improved understanding of longitudinal solute transport in
streams and for the application of mathematical models. The scaling law proposed here is
based on a physics-related theory combined with extensive data sets available form a decade
of stream tracer experiments on the Mödlingbach stream supplemented with data from
Torrente Lura near Milan, Italy. Extensive analysis of tracer dilution experiments from the
above-mentioned streams revealed the storage zone residence time to be the parameter
with the least scatter and to show a well-defined functional dependency on the flow
rate.
Wörman and Wachniew (2007) developed a physics-based expression of residence time
in hyporheic transient storage (HTS) zones depending on surface roughness wavelength,
hydraulic conductivity, water-depth and flow velocity. Here, that expression has been
further developed into a relationship between residence time T and flow rate Q to
yield:
T = a-
Q -b
(3)
with coefficient a denoting a constant of proportionality and b an exponent, for HTS zones
theoretically amounting to 23/40 = 0.575. Simplified analysis of the exchange with STS
zones between groins showed that the general form of the law (3) still holds, but a lower
exponent b - 0.40 is to be expected.
Collapsing the Mödlingbach and Torrente Lura residence time data into a single
functional relationship of the above form yielded:
- 0.50
T = a-
Q
(4)
with a - 48 and b between the theoretical values for HTS and STS zones.
References
Jackson, T.R., Haggerty, R., Apte, S.V., Coleman, A., Drost, K.J. (2012). Defining and
measuring the mean residence time of lateral surface transient storage zones in
small streams". Water Resources Res. 48, W10501, doi 10.1029/2012WR012096,
1-20.
Weitbrecht, V, Socolofsky, S.A., Jirka, G.H. (2008). "Experiments on mass
exchange between groin fields and main stream in rivers". J. of Hydraul. Eng. 134 (2),
173-183.
Wörman, A. and Wachniew, P. (2007): "Reach scale and evaluation methods as
limitations for transient storage properties in streams and rivers" Water Resources Res. 43,
W10405, doi: 10.1029/2006WR005808. |