Indlæg ved DVK temamøde om ’Minimumsafstrømning i vandløb’ 9-10 juni 1999 i Silkeborg
Regional variations in groundwater discharge to streams
Mette Dahl, William G. Harrar, Hans Jørgen Henriksen and Christen Knudby,
Geological Survey of Denmark and Greenland
Introduction
The interaction between groundwater and surface water is an important component of catchment scale
hydrology. Throughout Denmark groundwater flow to streams accounts for a high percentage of the
total discharge from aquifer systems. Management of regional water resources often requires finding a
delicate balance between competing interests of maximizing groundwater extraction and maintanence
of minimum streamflow. Numerical models are commonly used to evaluate the response of
groundwater / surface water systems to exploitation. Accurate representation of the spatial
distribution of the exchange of water between the groundwater and surface water systems is needed if
modeling results are to be successfully used as a management tool.
The objective of this study (Dahl et al., 1998) was to examine the importance of distributing aquifer river exchange parameters, namely stream bed leakage coefficients, in simulating the spatial
distribution of baseflow on a regional scale.
A commonly used relation expressing the exchange of water between an aquifer system and a stream
has been presented by McDonald and Harbaugh (1988):
Q = (K L W / M) (Haq - Hst)
where Q is the volumetric flow between the aquifer and the stream, K is the hydraulic conductivity of
stream bottom sediments, L is the stream length, W is the stream width, M is the stream bed thickness,
Haq is the hydraulic head in the aquifer and Hst the water level (stage) in the stream. Information on
stage and channel geometry can readily be obtained from the field. The stream bed leakage
coefficient, K / M, is difficult to estimate due largely to a lack of knowledge of the stream bed
hydraulic conductivity and thickness. The head difference, Haq - Hst, and the cross sectional area of
flow, L W, may change in time and space within one order of magnitude. The head difference may
also change sign and thereby direction of water flow. Contrary to this the stream bed leakage
coefficients can vary several orders of magnitude within short distances along streams (Calver, 1997),
and may even change as a function of discharge (van Wonderen and Wyness, 1995). The leakage
coefficient is thus the most important controlling factor in the exchange of water between the two
systems. In models best-guess estimates are typically assigned and adjusted within reasonable range
during model calibration.
Figure 1. The Isle of Funen with hydrogeologic profiles (see figure 2) and distribution of stream areas.
Methodology
This study was conducted in Denmark on the Isle of Funen (Figure 1) covering an area of
approximately 3000 km2. Quaternary deposits consist of up to 150 meters thick primarily clayey till
with lenses and alternating more or less regional layers of outwash sand (Figure 2). A conceptual
model of baseflow generation was developed based on streamflow measurements conducted during
extented dry periods, assuming that the streamflow in these periods entirely consists of groundwater
seepage. 600 synchronious streamflow measurements were corrected according to their relation to the
median minimum streamflow at gauging stations with a long record of data (Fyns Amt, 1995). For
each reach between adjacent monitoring stations the net baseflow gain per unit stream length was
calculated. The stream reaches were then combined into 50 stream areas comprising similar
magnitudes of net baseflow gain per unit stream length (Figure 1). The stream areas were classified as
low (< 1 l/s/km), medium (1-7 l/s/km) and high (> 7 l/s/km) baseflow areas. The low baseflow areas
were generally located in the till uplands, whereas the high baseflow areas were located in the valley
bottoms directly overlying regional sand aquifers (Figure 2). Medium baseflow areas were underlain
by both till and sand.
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Figure 2. Hydrogeologic profiles (see figure 1) showing model layers, major groundwater discharge
zones and streams.
The MIKE SHE model (Henriksen et al, 1997) was used to evaluate the response of baseflow
simulation to three different representations of the stream bed leakage coefficients, encompassing one
of constant value (1e-7 s-1), and two in which the leakage coefficients were varied according to the
conceptual model (Dahl et al., 1998). The values of leakage coefficients providing the best simulated
baseflow results were for low (till) and high (sand) baseflow areas estimated from the average
thickness and vertical hydraulic conductivity of the till and sand layers containing the streams,
respectively. These vertical hydraulic conductivities were equal to values applied for till and sand
layers in the groundwater model (Henriksen et al., 1997). For medium (till and sand) baseflow areas a
value between the two others was applied. The assigned values were 2e-10 s-1, 2e-8 s-1 and 2e-6 s-1 for
low, medium and high baseflow areas, respectively.
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Conclusions
The main conclusions drawn from this study are 1) The spatial distribution of water exchange
between groundwater and surface water systems obtained from numerical models can be improved by
distributing leakage coefficients of the stream bed based on geology of the layers in which the streams
are imbedded. The obtained improvements are largest in low permeable areas. 2) To achieve a good
tool for groundwater management purposes on a regional scale the model must be calibrated to both
groundwater heads, transient streamflow and distributed baseflow. Following the above procedure
ensures a more reliable distributed quantification of flow paths through the aquifer systems to the
streams within the whole area of concern. These conclusions are supported by similar findings by
Christensen et al. (1998). 3) Specifically for the Isle of Funen it was equally important to represent the
exchange of water between the groundwater and surface water systems for both low, medium and
high baseflow areas, as they each contribute approximately one third of the cumulated baseflow. The
high baseflow areas, situated where the streams have direct contact with regional aquifers, act as
groundwater seepage ’hot spots’ because of their small areal extent. 4) The last conclusion is that
there is still much to understand concerning the processes governing the interaction between aquifers
and surface water systems. Key questions in simulating the exchange are how to define and delineate
the zone controlling this interaction and how to determine the hydraulic conductivity and thickness of
this zone.
References
Christensen, S., Rasmussen, K.R., and Møller, K., 1998. Prediction of Regional Ground Water Flow to Streams.
Ground Water 36(2): 351-360.
Calver, A. 1997. Towards generalisation of channel-aquifer transfer parameters. Institute of Hydrology. Project
T0406415, Interim report. Wallingford, United Kingdom.
Dahl, M., Harrar, W.G., Henriksen, H.J. and Knudby, C., 1998. Integrated hydrological modelling af fresh water
resources in Denmark – Distribution of aquifer-river exchange parameters. Preceedings from IAH/AIH
Conference ‘Gambling with groundwater’, Las Vegas, USA.
Fyns Amt, 1995. Bestemmelse af vandføringens medianminimum i Fyns Amt [in Danish].
Henriksen, H.J., Knudby, C.J. and Rasmussen, P., 1997. National Vandressource Model. Danmarks og
Grønlands Geologiske Undersøgelse. Rapport 139 [in Danish].
McDonald, M.G. and Harbaugh, A.W., 1988. A modular three-dimensional Finite Difference Groundwater Flow
Model. US Geological Survey, Techniqes of Water Resources Investigations, Book 6, U.S. Government
Printing Office, Washington, DC.
van Wonderen, J. and Wyness, A., 1995. The validity of methods used for modelling of river-aquifer interaction.
In Younger, P.L (ed) Modelling river-aquifer interactions. Proceeding of British Hydrological Society : 101116.
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