Click
Here
WATER RESOURCES RESEARCH, VOL. 44, W09501, doi:10.1029/2007WR006782, 2008
for
Full
Article
Effects of stream-aquifer disconnection on local flow patterns
Sharon L. E. Desilets,1 Ty P. A. Ferré,1 and Peter A. Troch1
Received 20 December 2007; revised 31 May 2008; accepted 9 July 2008; published 16 September 2008.
[1] Disconnected stream-aquifer systems are becoming increasingly common because of
lowering groundwater tables. This work focuses on the pathways and rates of infiltration
and seepage as streams transition from fully connected to disconnected conditions.
HYDRUS-2D simulations show for a connected stream, water infiltrates vertically then
moves laterally below the top of the preflooding capillary fringe height, finally causing an
upward displacement of antecedent water into the vadose zone. This contradicts the
commonly held assumption that stream water moves laterally for some distance into the
stream bank, forming a wedge above the antecedent water. Even for shallow
disconnections (<1 m), there is an increase in infiltration losses from the stream,
elimination of postflooding seepage, and increased lateral and vertical mixing of stream
water and antecedent pore water.
Citation: Desilets, S. L. E., T. P. A. Ferré, and P. A. Troch (2008), Effects of stream-aquifer disconnection on local flow patterns,
Water Resour. Res., 44, W09501, doi:10.1029/2007WR006782.
1. Introduction
[2] There is growing recognition of the importance of
exchanges of water and solutes between surface water
bodies and the subsurface [Choi et al., 2000; Dahm et al.,
1998; Gooseff et al., 2002; Gooseff et al., 2007; Packman
and Mackay, 2003]. These fluxes are particularly critical in
riparian areas within water-stressed regions. For example,
recent studies have shown that lowering of water tables
due to climate change combined with sustained human
withdrawals has led to die off of long-lived riparian
species [Cooper et al., 2006; Naumburg et al., 2005;
Sarr and Hibbs, 2007]. These studies demonstrated a
correlation between water table depth and riparian vegetation morbidity.
[3] Most studies of the interaction of surface water and
groundwater in stream banks make use of one of two
limiting simplifying assumptions. Either, they assume that
the stream is connected to the groundwater system [Huth,
2003; Kondolf et al., 1987; Whitaker, 2000; Whiting and
Pomeranets, 1997], or they assume that the water table is far
below the stream [Constantz et al., 2002; Niswonger et al.,
2005; Ronan et al., 1998]. The former case is typically
conceptualized as lateral flow from the stream to the stream
bank during flooding, followed by lateral return flow to the
stream, via seepage, during recovery. The latter case is
conceptualized as predominantly vertical flow during flooding with no return flow to the stream. Analytical solutions
are available for these two end-member conditions [Hunt,
1990; Neuman, 1981; Philip, 1989; Vazquez-Suñe et al.,
2007]. We examine in more detail the changes in the rates
and patterns of water flow and solute transport that occur as
the water table elevation decreases, causing a stream to
1
Department of Hydrology and Water Resources, University of Arizona,
Tucson, Arizona, USA.
Copyright 2008 by the American Geophysical Union.
0043-1397/08/2007WR006782$09.00
transition from an initial connected condition to a state of
disconnection from the underlying aquifer.
2. Methods
[4] We use a numerical model of water flow and solute
transport [Šimůnek et al., 1999] to examine the response to a
6 h step function flooding event followed by 48 h of
recovery (Figure 1, right). We focus on the following three
features: water loss from the stream during flooding, seepage from the subsurface to the stream following flooding,
and the spatial distribution of stream water in the subsurface
following flooding and following 2 days of recovery. We
consider an initially flat lying water table and examine the
impacts of changes in the water table depth below the base
of the stream on these three behaviors.
[5] To focus on interactions between the stream bank and
seepage face, we model a vertical cross section, with the left
boundary located at the interface of the stream bank and
stream (Figure 1, left). The domain is 6 m in the vertical and
15 m in the horizontal. The datum elevation is located at the
base of the stream. The stream is represented as a vertical
line segment along the left boundary extending from 0 to
1 m (the elevation of the ground surface). The left boundary
below the stream is set to zero flux for water flow and for
solute transport to represent a symmetry boundary; as such,
the left side boundary could be considered the midpoint of
an infinitely narrow stream. The stream segment of the left
boundary is set to a constant hydraulic head of 0.4 m during
the 6 h flooding stage (Figure 1, right). Following this,
during the seepage and recovery stage, the stream boundary
segment has a seepage face condition. In HYDRUS-2D a
seepage face condition maintains zero pressure head along
the saturated portion and zero flux along the unsaturated
portion of the boundary nodes. Water that crosses the
boundary is considered to be immediately removed, as by
stream flow. The bottom (z = 5 m) and top (z = 1 m)
boundaries are zero flux for water and solute. A distant right
boundary (x = 15 m) is also zero flux.
W09501
1 of 6
DESILETS ET AL.: TECHNICAL NOTE
W09501
W09501
Figure 1. (left) Model domain and (right) schematic representation of timing of flooding and recovery.
No flow boundaries surround the domain except the area of the stream bank, which is located along the
left boundary between z = 0 and 1 m. This segment is assigned a constant head during the flood stage and
a seepage face during the recovery phase. The right boundary is far enough away that is does not
influence flow near the stream bank. The initial depth of the water table (d) is varied between 0 and 2 m.
[6] The medium is composed of an isotropic, homogeneous sand with van Genuchten [van Genuchten and
Nielsen, 1985] parameters (a = 15.5 m1, n = 2.68) and a
saturated hydraulic conductivity of Ks = 0.297 m h1. The
maximum initial water table height is z = 0 m, representing
a stream that is minimally connected to groundwater. The
initial condition above the water table is hydrostatic. We
then examine increasing stream-aquifer disconnection by
increasing the initial water table depths (d) to a maximum of
2.0 m.
[7] We use the solute transport modeling capabilities of
HYDRUS-2D to track the movement of stream water
(assigned a relative concentration of zero) and antecedent
pore water (assigned a relative concentration of one
throughout the subsurface). We assign longitudinal and
transverse dispersivities of aL = 0.5 m and aT = 0.1 m.
However, we set the diffusion coefficient to zero to avoid
unreasonably large diffusive mass fluxes due to the large
difference in relative concentrations in the stream water and
antecedent pore water.
recovery (cumulative infiltration minus cumulative seepage)
was highly nonlinear. That is, even a small disconnection
between the stream and the underlying aquifer led to a much
greater net loss of water from the stream (dashed curve in
Figure 2) throughout a flooding event.
[10] The spatial distribution of stream water following
flooding (t2 = 0 h) and 48 h after the end of the flood (t2 =
48 h) shows the subsurface zone that is affected by stream
water exchange (Figure 3, right). We show two contour
levels. Water within the 0.1 relative concentration contour
represents essentially unmixed stream water. Water outside
of the 0.9 contour represents essentially unmixed antecedent
pore water. The area between these contours represents a
zone of mixed stream water and antecedent pore water. If
the initial water table depth is located at the base of the
stream (d = 0.0 m), there is essentially no region of unmixed
stream water. The mixing zone extends horizontally 1.7 m
3. Results and Discussion
[ 8 ] Consistent with results published previously
[Niswonger et al., 2005], cumulative infiltration during
flooding is higher for disconnected streams (d > 0) than
for connected streams (solid curve in Figure 2). Our results
show that the cumulative infiltration transitions nonlinearly,
with relatively large changes occurring with the initial
disconnection of the stream and aquifer. For the flooding
scenario that we examined, if the initial water table depth is
at 0 m below the streambed, the cumulative infiltration will
be only 34% of the amount that would occur for an
infinitely deep water table (i.e., a water table that is so deep
that the infiltrating water does not reach it during the
simulated period); whereas, if the water table has dropped
to 1 m below the stream, it is 88% of that value.
[9] In all cases, infiltrated water causes the water table to
rise near the stream and extend laterally as a wedge away
from the stream (Figure 3, left). For the conditions that we
examined, water table rise near the stream led to nonzero
seepage (difference between the solid and dashed curves in
Figure 2) for an initial water table depth of 0.25 m or less.
The net water flux to the subsurface through flooding and
Figure 2. Cumulative infiltration into the stream bank (I)
after a 6 h flood (solid circles and curve), and the difference
between cumulative infiltration and cumulative seepage
from the stream bank to the stream (S) after an additional
48 h of recovery (open circles and dashed curve) as a
function of the initial water table depth (d). Cumulative
seepage for a given water table depth equals the area
between the two plotted curves.
2 of 6
W09501
DESILETS ET AL.: TECHNICAL NOTE
W09501
Figure 3. (left) Contours of water content (q = 0.4, 93% saturated) and (right) relative solute
concentration following a 6 h flood with 0.4 m stage (dashed curves) and after an additional 48 h of
recovery (solid curves). The contours show the subsurface with the stream bank located along the left
boundary between z = 0 and 1 m. Initial solute concentrations are 1.0 in the soil water and zero in the
infiltrating flood water. The 0.9 and 0.1 contours delineate a zone of essentially unmixed antecedent
water, a zone of mixing of the antecedent and infiltrated water, and a zone of essentially unmixed
infiltrated stream water. Results are shown for initial water table depths of (a) 0, (b) 0.25, and (c) 2 m
below the base of the stream.
from the stream bank and vertically to a maximum depth of
1.2 m. There is little or no change in the mixing zone during
recovery because of the significant water flow toward the
seepage face. If the initial water table depth is lowered by
0.25 m (d = 0.25 m), there is still no region of unmixed
stream water. But, the increased cumulative infiltration
extends the mixing zone horizontally 2.0 m from the
stream bank and vertically to a maximum depth of 1.6 m.
There is continued downward and rightward expansion of
the mixing zone during recovery as the water table mound
dissipates (Figure 3b). As the initial water table depth
increases to 2 m, there are significant changes in the
distributions of stream water and antecedent pore water.
Unmixed stream water extends to a lateral distance of 0.7 m
and vertically to a depth of 1.1 m. The mixing zone extends
vertically in the shallow subsurface, then laterally at and
above the initial water table depth. The lateral extent of the
mixing zone is much greater (2.1 m after flooding), partly
due to the increased cumulative infiltration. Finally, there is
significant additional lateral movement of the stream water
plume away from the stream during recovery (mixing zone
extends to 3.1 m, Figure 3c).
[11] To examine the change in distribution of the antecedent pore water following flooding and 2 days of recovery, we
calculated the change in solute mass (dM) throughout the
domain as
3 of 6
dM ¼ Cf qf Ci qi V ;
W09501
DESILETS ET AL.: TECHNICAL NOTE
Figure 4. The subsurface with the stream bank located
along the left boundary between z = 0 and 1 m. (a) Zones of
increased saturation of antecedent water for the minimally
connected case (d = 0 m). Contours are shown for dM =
0.05 where dM = (Mf – Mi)/Mi following a 6 h flood
(dashed curve) and 48 h of recovery following the end of
flooding (solid curve). (b) Velocity vectors (d = 0) show
infiltrating water moving downward, causing resident soil
water to advance upward into the previously unsaturated
stream bank. A stretching factor of 5 was used for the
vertical component of the velocity vectors. (c) Relative
change in saturation of antecedent water in the stream bank
(as represented by solute mass dMrz where subscript rz
represents root zone) for several depths following flooding
and recovery.
W09501
where C is concentration, V is the volume per unit length,
q the water content of each model element, and the
subscripts i and f indicate initial and final conditions. The
stream water has a concentration of 0.0, and the antecedent
pore water throughout the subsurface has a concentration of
1.0. Therefore, a decrease in solute mass represents a
decrease in the volume of antecedent water per unit volume
of porous medium. Similarly, an increase in solute mass
represents an increase in this ‘‘antecedent water saturation.’’
Changes in the saturation of stream water have no effect on
the solute mass unless they displace antecedent water.
[12] As expected, there is a large region of infiltrated
stream water manifested as decreased solute mass (not
shown on Figure 4a for clarity of presentation). Unexpectedly, there is a region of increased mass in the stream bank,
above the base of the stream (Figure 4a), indicating an
increase in antecedent water in this area. Examination of the
flow vectors at the onset of flooding (Figure 4b) shows that
the cause of this increase is upward flow of water from
beneath the initial water table depth in response to mounding beneath the stream. Pressure from the mounded water
propagates faster in the saturated zone than in the unsaturated zone and causes antecedent pore water to flow upward
into the previously unsaturated stream bank sediments.
Conceptually, this means that the leading edge of the wedge
of water content increase in the stream bank is composed of
antecedent water, not stream water. The stream water moves
vertically downward and mixes in higher water content
regions of the subsurface. This helps to explain why
there is no significant region of unmixed stream water
after flooding for shallow initial water table conditions
(Figures 3a and 3b, right).
[13] This circulating flow pattern is distinct from the
common assumption of lateral flow during flooding of
connected stream-aquifer systems and has several implications for solute transport. In particular, the pattern of
infiltration that we show results in limited lateral transport
of stream water during flooding. This could limit delivery of
nutrients to the riparian area from the stream and/or flushing
of nutrients from the riparian area to the stream. In addition,
water that may have moved vertically through the root zone
before a flooding event may be displaced upward, into the
root zone, in response to flooding. Finally, the dependence
of the persistence of antecedent water in the vadose zone on
the water table depth may result in geochemical changes in
the root zone as the water table depth increases.
[14] To summarize the changes in the distribution of
antecedent pore water above the base of the stream, we
calculated the change in mass of the antecedent water
compared to the mass before flooding (Figure 4c). For the
connected stream (d = 0.0), there is a significant increase in
the amount of antecedent water present immediately following flooding. However, most of this water drains out as
seepage after 2 days of recovery. If the initial water table
depth is decreased by 0.25 m, there is a similar increase in
antecedent water mass above the base of the stream.
However, under these conditions, the mass of antecedent
water continues to increase as the water table mound
redistributes laterally following flooding. Even this small
disconnection significantly limits seepage, so the antecedent
water mass that moves upward persists during recovery.
However, if the initial water table depth is 50 cm or more
4 of 6
W09501
DESILETS ET AL.: TECHNICAL NOTE
below the base of the stream, there is a net loss of
antecedent water mass due to vertical displacement by
stream water.
[ 15 ] The numerical investigation presented here is
intended to highlight some overlooked aspects of water
flow in streams that are minimally connected or disconnected
from an underlying aquifer. This study is not exhaustive,
and the findings should be tested by field investigations. In
particular, the following three factors that were not considered in this initial work could impact the rates and patterns
of water flow during flooding and recovery: anisotropy,
incomplete drainage before flooding, and the stream bank
geometry.
[16] Many streambeds exhibit anisotropy in hydraulic
conductivity, particularly as horizontal layering associated
with fluvial depositional environments. If the hydraulic
conductivities of adjacent layers contrast sharply, flow
could be guided laterally through the higher conductivity
layer. This structure could exert a primary control on both
the rate and pattern of flow. The impact of this structure will
likely depend on the preflood location of the water table
relative to the layer boundaries.
[17] We modeled a hydrostatic initial (preflood) condition. In reality, it is unlikely that the vadose zone will
achieve these conditions unless the soil is coarse and it has
been a very long time since the last flood. Incomplete
drainage, due to either frequent flooding or finer-grained
materials, could lead to a thicker zone of near-complete
water saturation above the water table. As a result, the water
table would have to fall to a lower elevation to achieve
disconnection than is reported in this study. However, even
for these conditions, water would likely flow laterally
within the saturated and near-saturated soils, as it did in
the saturated zone for the sandy soil that we examined.
Then, we expect that the same process of lateral flow in
(near) saturated soils followed by upward flow into the
vadose zone would occur. Hysteresis, which would result in
higher water contents at each depth following drainage than
would be predicted by a nonhysteretic moisture release
curve, may have a similar effect.
[18] Finally, the horizontal stream bank geometry used in
this study is greatly simplified compared to a natural stream.
Analyses of streams with stream bank angles less than 90°
from the horizontal (not shown) had infiltration rates and
mixing patterns that were very similar to those shown in this
study. However, the seepage rate decreased with decreasing
stream bank slope.
4. Conclusions
[19] We present a preliminary numerical investigation of
the changes in the response of a stream-aquifer system due
to lowering of the water table below the base of the stream
(stream disconnection). There are three primary changes
that occur when the water table elevation drops from the
base of the stream to a depth of 0.25 m below the stream.
First, there is a significant increase in cumulative infiltration
and an associated decrease in seepage return, leading to
much larger water loss from the stream over the course of
flooding and recovery. Second, there is an increase in the
lateral and vertical extents of the zone of mixing of stream
water and antecedent pore water. Furthermore, this zone
continues to expand during recovery; in contrast, this zone
W09501
shrinks or remains stable during recovery under connected
conditions. Third, there are significant changes in the
movement of antecedent pore water. The observed upward
flow pattern of antecedent water from the saturated zone to
the unsaturated zone, most prominent in the minimally
connected case (d = 0), decreases rapidly with increasing
stream disconnection. However, antecedent water that flows
upward persists in the stream bank longer in the disconnected case because of the decrease in seepage flow. As a
result, there is more net gain of antecedent water redistributed into the stream bank above the base of the stream.
[20] While the magnitudes and timings of the responses
seen in our modeling study will vary for specific site
conditions, we expect that the underlying processes will
occur to some degree in most systems. Therefore, we
recommend that researchers who are interested in processes
that rely on water and solute exchange between a stream and
the stream bank should consider the processes shown here
when designing experiments. In particular, our findings
suggest that the assumption of one-dimensional lateral flow
into the stream bank for connected and slightly disconnected
stream-aquifer systems is incorrect. Rather, infiltrating water flows predominantly downward beneath the stream. This
causes lateral flow in the saturated flow, which leads to
upward flow of antecedent water into the previously unsaturated zone. This suggests that water content (or pressure)
and solute concentration should be measured at multiple
depths in the stream bank to fully characterize streamaquifer interactions.
References
Choi, J., J. W. Harvey, and M. H. Conklin (2000), Characterizing multiple
timescales of stream and storage zone interaction that affect solute fate
and transport in streams, Water Resour. Res., 36(6), 1511 – 1518,
doi:10.1029/2000WR900051.
Constantz, J., A. E. Stewart, R. Niswonger, and L. Sarma (2002), Analysis
of temperature profiles for investigating stream losses beneath ephemeral
channels, Water Resour. Res., 38(12), 1316, doi:10.1029/
2001WR001221.
Cooper, D. J., J. Dickens, N. T. Hobbs, L. Christensen, and L. Landrum
(2006), Hydrologic, geomorphic and climatic processes controlling willow establishment in a montane ecosystem, Hydrol. Processes, 20(8),
1845 – 1864, doi:10.1002/hyp.5965.
Dahm, C. N., N. B. Grimm, P. Marmonier, H. M. Valett, and P. Vervier
(1998), Nutrient dynamics at the interface between surface waters and
groundwaters, Freshwater Biol., 40(3), 427 – 451, doi:10.1046/j.13652427.1998.00367.x.
Gooseff, M. N., D. M. McKnight, W. B. Lyons, and A. E. Blum (2002),
Weathering reactions and hyporheic exchange controls on stream water
chemistry in a glacial meltwater stream in the McMurdo Dry Valleys,
Water Resour. Res., 38(12), 1279, doi:10.1029/2001WR000834.
Gooseff, M. N., R. O. Hall, and J. L. Tank (2007), Relating transient storage
to channel complexity in streams of varying land use in Jackson Hole,
Wyoming, Water Resour. Res., 43(1), W01417, doi:10.1029/
2005WR004626.
Hunt, B. (1990), An approximation for the bank storage effect, Water
Resour. Res., 26(11), 2769 – 2775.
Huth, A. K. (2003), Geochemical and isotopic mixing models: Two case
studies in a snow-dominated and semi-arid environment, Ph.D. dissertation, Univ. of Ariz., Tucson.
Kondolf, G. M., L. M. Maloney, and J. G. Williams (1987), Effects of bank
storage and well pumping on base-flow, Carmel River, Monterey County,
California, J. Hydrol., 91(3 – 4), 351 – 369, doi:10.1016/00221694(87)90211-3.
Naumburg, E., R. Mata-Gonzalez, R. G. Hunter, T. Mclendon, and D. W.
Martin (2005), Phreatophytic vegetation and groundwater fluctuations:
A review of current research and application of ecosystem response
modeling with an emphasis on Great Basin vegetation, Environ. Manage.
N. Y., 35(6), 726 – 740, doi:10.1007/s00267-004-0194-7.
5 of 6
W09501
DESILETS ET AL.: TECHNICAL NOTE
Neuman, S. P. (1981), Delayed drainage in a stream-aquifer system, J. Irrig.
Drain. Div. Am. Soc. Civ. Eng., 107(4), 407 – 410.
Niswonger, R. G., D. E. Prudic, G. Pohll, and J. Constantz (2005), Incorporating seepage losses into the unsteady streamflow equations for simulating intermittent flow along mountain front streams, Water Resour.
Res., 41(6), W06006, doi:10.1029/2004WR003677.
Packman, A. I., and J. S. Mackay (2003), Interplay of stream-subsurface
exchange, clay particle deposition, and streambed evolution, Water Resour. Res., 39(4), 1097, doi:10.1029/2002WR001432.
Philip, J. R. (1989), Multidimensional steady infiltration to a water table,
Water Resour. Res., 25(1), 109 – 116, doi:10.1029/WR025i001p00109.
Ronan, A. D., D. E. Prudic, C. E. Thodal, and J. Constantz (1998), Field
study and simulation of diurnal temperature effects on infiltration and
variably saturated flow beneath an ephemeral stream, Water Resour. Res.,
34(9), 2137 – 2153, doi:10.1029/98WR01572.
Sarr, D. A., and D. E. Hibbs (2007), Multiscale controls on woody plant
diversity in western Oregon riparian forests, Ecol. Monogr., 77(2), 179 –
201, doi:10.1890/06-0099.
Šimůnek, J., M. Šejna, and M. T. van Genuchten (1999), The HYDRUS-2D
software package for simulating two-dimensional movement of water,
heat, and multiple solutes in variably-saturated media, version 2.0.,
W09501
IGWMC - TPS - 53, 251 pp., Int. Ground Water Modeling Cent., Colo.
Sch. of Mines, Golden, Colo.
van Genuchten, M. T., and D. R. Nielsen (1985), On describing and predicting the hydraulic-properties of unsaturated soils, Ann. Geophys., 3(5),
615 – 627.
Vazquez-Suñe, E., B. Capino, E. Abarca, and J. Carrera (2007), Estimation
of recharge from floods in disconnected stream-aquifer systems, Ground
Water, 45(5), 579 – 589, doi:10.1111/j.1745-6584.2007.00326.x.
Whitaker, M. L. P. (2000), Estimating bank storage and evapotranspiration
using soil physical and hydrological techniques in a gaining reach of the
San Pedro River, Arizona, Ph.D. dissertation, Univ. of Ariz., Tucson.
Whiting, P. J., and M. Pomeranets (1997), A numerical study of bank
storage and its contribution to streamflow, J. Hydrol., 202(1 – 4), 121 –
136, doi:10.1016/S0022-1694(97)00064-4.
S. L. E. Desilets, T. P. A. Ferré, and P. A. Troch, Department of
Hydrology and Water Resources, University of Arizona, 1133 East James E.
Rogers Way, Tucson, AZ 85721, USA. ([email protected]; seinloth@
hwr.arizona.edu; [email protected])
6 of 6