water
ArticleSimulating the Effects of Lake Wind Waves on Waterand Solute Exchange across the Lakeshore
Using Hydrus-2D
Yong Li 1,2, *, Jirka Šimůnek 3 , Shuang Wang 2 , Weiwei Zhang 2 and Jiahui Yuan 2
1
2
3

*

Ministry of Education Key Laboratory of Integrated Regulation and Resource Development on Shallow
Lakes, Hohai University, Nanjing 210098, China
College of Environment, Hohai University, Nanjing 210098, China; sswwhhu@163.com (S.W.);
zwwhhu@163.com (W.Z.); jhyhhu@163.com (J.Y.)
Department of Environmental Sciences, University of California, Riverside, CA 92521, USA;jsimunek@ucr.edu
Correspondence: liyonghh@hhu.edu.cn; Tel.: +86-025-83787145

Received: 28 March 2017; Accepted: 26 July 2017; Published: 30 July 2017

Abstract: Wind waves, which frequently occur on large surface water bodies such as lakes, may
temporarily alter flow patterns in a subsurface zone and the corresponding water and nutrientinteractions between surface waters and shallow groundwaters. To better understand these processes,
soil flume experiments were carried out to investigate wind wave-driven water and chloride
interactions across the lake–groundwater interface, and the Hydrus-2D model was used to analyze
and evaluate the observed experimental results. Two interaction cases between the lake andgroundwater systems were considered: groundwater discharging into a lake (the GDL case), and lakewater recharging groundwater (the LRG case). For comparison, no-wave conditions for both the GDLand LRG cases were also analyzed. The results revealed that, similarly to no-wave conditions, waterand chloride exchange fluxes between the lake and groundwater systems under wave conditions
occurred mainly within narrow bands near the intersection of the water level in the lake and theinterface in both the GDL and LRG cases, and then exponentially decreased along the interface.
Most water and chloride that infiltrated into the subsurface zone through the upper part of theinterface during a wave crest returned to the lake through the lower part during a wave trough inboth the GDL and LRG cases, creating local recirculation zones in the subsurface near the interface.
Such recirculation produced a more frequent exchange of water and solute across the interface
compared with those under no-wave conditions. During a one-day period after wind waves started,
the total exchange fluxes of water and chloride to the lake decreased by 36.2% and 71.9%, respectively,
compared to the no-wave conditions in the GDL case. In the LRG case, the total exchange water fluxes
to the subsurface increased by 89.7%, while the total exchange chloride fluxes increased only slightly(4.5%) compared to the no-wave conditions due to the difference in chloride concentrations between
the upper and lower parts of the interface. The sensitivity analysis revealed that the hydraulicconductivity of the lakeshore zone and the characteristics of the waves were important factors
influencing water and chloride exchange between the lake and groundwater systems. The simulated
results helped us to better understand water and solute interactions in the lake–groundwater system
during windy periods.
Keywords: lake; groundwater; wind wave; flow pattern; solute exchange; Hydrus-2D

1. Introduction
The exchange of water and nutrients between groundwater and surface water bodies, such as lakes,
occurs everywhere where aquifers are hydraulically connected to surface water bodies [1]. Interactions
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between lake and groundwater systems have become major concerns during recent decades [2–5],
since they may exert an important control on lake ecology [6,7] and on the nearshore water quality [8]in multiple ways. An understanding of the distribution and rate of seepage to and from lakes istherefore needed for environmental management and the restoration of lake ecosystems [8–10].
Studies evaluating water and solute exchange between surface waters and groundwater havebeen frequently reported for coastal regions, especially with respect to tide (or wave)-driven waterlevel fluctuations [5,11,12]. For example, Harvey et al. [13] used a one-dimensional numerical model
to explore the effects of tidal amplitudes and mean water levels on the groundwater flow of a Virginia
salt marsh (USA). They found that an increase in the elevation of the mean water level relative to the
top of the marsh platform caused a significant decrease in the total volume of groundwater exchangeover a tidal cycle. A two-dimensional numerical model developed by Wilson and Gardner [14]showed that, for the same tidal amplitude, the groundwater exchange in a simulated marsh was
higher when the marsh was inundated by the tide than when it was not. Waves create steep hydraulicgradients near the interface between the surface and groundwater and local water circulations inthe subsurface zone, which largely accelerates water exchange [15–18]. Xin et al. [19] reported thatwave-induced circulations increased both water flows in the nearshore zone and the exchange between
the subterranean estuary and ocean, contributing 61% of the total submarine groundwater discharge
for simulated conditions.
Furthermore, tide (or wave)-driven groundwater table fluctuations in coastal regions were also
shown to impact solute exchange across the sediment–surface water interface [19–22]. Chen and
Pinder [1] reported that tidal fluctuations decrease the average concentrations of groundwatercontaminants discharging into coastal waters. Wilson and Morris [23] reported that tidal fluctuations
are the most important driver for groundwater exchange in coastal areas. Small increases in the meanwater level associated with sea level rise could significantly increase nutrient export into marshes
with elevations that are equilibrated with mean water levels; on the other hand, the rising sea level
could decrease the export of nutrients into estuaries adjacent to these marshes. Anwar et al. [24]demonstrated, using a numerical investigation, that tides and waves modify the subsurface discharge
pathways of land-derived nutrients by changing the nearshore groundwater flow dynamics.
As discussed above, many studies focused on the sea–groundwater interactions in subsurface
beach zones, which are substantially influenced by waves and tides, and are subject todensity-dependent flow patterns [22,25–27]. Additionally, the effects of fluctuating water levels
due to waves are much more significant than the effects of variations in water densities as reported by
Rimmer et al. [28]. They produce a change in the local direction and velocity of subsurface flow bytemporarily uplifting the groundwater table near the interface during windy days, depending on the
duration and characteristics of the waves. A hypothesis was proposed that, similar to the effects of
tidal waves in coastal areas, in lakes subjected to wind waves, fluctuating water levels alter subsurface
flow patterns and corresponding water and solute exchange between the lakes and the surrounding
groundwater. Wind waves particularly occur on large and shallow lakes in plain regions during windy
seasons, where the groundwater table surrounding these lakes is generally shallow and approaches
the mean water level in the lake [29]. Once wind waves occur, the original subsurface flow direction
and velocity near the shoreline may be changed, and consequently the nutrient exchange [18] andnearshore water quality [16,18,24,30,31] are affected.
To verify the hypothesis mentioned above, this study therefore is to evaluate the subsurface flow
patterns and solute exchange between a lake and groundwater due to wind waves. We first evaluate
subsurface flow patterns and chloride distributions in a subsurface zone at no-wave conditions for thecases of groundwater discharging into a lake (the GDL case) and lake water recharging groundwater(the LRG case). Then, we compare the results of the water and solute exchange flux and distribution
for these two no-wave conditions with the results for conditions with wind waves. The effects ofwind waves in a lake on the water and solute exchanges with groundwater are discussed. Finally,a sensitivity analysis evaluating the effects of the hydraulic conductivity of the lakeshore zone andWater 2017, 9, 566

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effectsof wind waves in a lake on the water and solute exchanges with groundwater are discussed.
Finally, a sensitivity analysis evaluating the effects of the hydraulic conductivity of the lakeshorezone
wave characteristics
on waterandexchange
chloride exchange
is carriedout. Hydrus-2D
waveandcharacteristics
on water andchlorideis carried out.
Hydrus-2Dmodeling modelingis used to
is
used
to
betterunderstand
water
and
soluteexchange
between
the
lake
and
groundwater
systems
better understand water and solute exchange between the lake and groundwater systems driven
bydrivenbywindwaves.
The
simulated
resultsarecomparedwithexperimental
data
obtainedduringwind waves. The simulated results are compared with experimental data obtained during experiments
experimentsa large soil flume.
conducted inconducteda large soilinflume.

2.
2. Materials
Materials andand Methods
Methods

2.1. Soil
Soil Flume
Flume Experiments
Experiments
2.1.
2.1.1. Experimental
Experimental Set
Set UpUp andand Design
Design2.1.1.
A largelarge flume
filledwitha loamysandsoil soil
to represent
a lakeshorezone
A
flume ininaalaboratory,laboratory,partiallypartially
filledwitha loamysand
to represent
a lakeshore(Figure1), wasto observe
flowflowpatterns
andandsolutetransport
in ainsubsurface
zone
subjected
tozone(Figure1), used
was used
to observe
patterns
solutetransport
a subsurface
zone
subjected
wind
waves
in
a
lake.
The
loamy
sand
soil
(with
87.4%
sand,
10.2%
silt,
0.18%
organic
matter,andto wind waves in a lake. The loamy sand soil (with 87.4% sand, 10.2% silt, 0.18% organic matter, and−3 bulk density) was filled into the flume and compacted layer by layer. The lakeshore slope
1.43 g
g cm
cm−3
1.43
bulk density) was filled into the flume and compacted layer by layer. The lakeshore slope
(α)
was
set
at about
about 35°.
35◦ . A
A hydraulically
hydraulically driven
driven piston-type
piston-type wave
wave maker
maker was
was installed
installed 15
15 m
m awayaway(α) was set at
from
point
O
(Figure
1a).
Two
types
of
interactions
betweenalake
andsurrounding
groundwaterfrom point O (Figure 1a). Two types of interactions between a lake and surrounding groundwater
were considered
consideredininthis
thisstudy:
study:(1)(1)
GDL
case,
(2) LRGat eitherno-waveor
werethethe
GDL
case,andand(2) LRG
cases,cases,
each eachat eitherno-waveor wavewave
conditions.
Ahypotheticalpollution
sourcewassetup
outsideofthelakeshoretorepresentconditions. A hypothetical pollution source was set up outside of the lakeshore to represent aa
fishpond/paddyfield,which
whichusuallyusuallylocateslocatesaroundaroundlakes
lakesininplainplainregions,regions, fromfrom which
which pollutants
pollutants at
at
fishpond/paddyfield,
relatively highhigh concentrations
concentrations leachedleached into
into thethe shallow
shallow groundwater.
groundwater.
relatively

(a)

(b)
FigureFigure 1.
1. Schematic
Schematic view
view ofof thethe experimental
experimental set
set upup andand positions
positions ofof observation
observation points.
points. All
All units
units are
are
in
cm.
(GWT,
groundwater
table;
WT,awave
troughheight(point
A),
30.0
cm;
ML,
a
mean
lake
in cm. (GWT, ground water table; WT, a wave trough height (point A), 30.0 cm; ML, a mean lake level
level
heightheight (point(point B),
B), 38.5
38.5 cm;
cm; WC,WC, aa wave
wave crest
crest heightheight (point(point C),
C), 4747 cm,
cm, andand RU,RU, aa run-up
run-up heightheight (point(pointD),
50
cm,
respectively;
point
W,
a
hypotheticalpollution
sourcerepresentingafishpond/paddyfield).
D), 50 cm, respectively; point W, a hypothetical pollution source representing a fishpond/paddyfield).
(a)
Side
view
of of
thethelakeshorezone(observation
pointsfor(a) Plan
Plan view
viewofofthe
theexperimental
experimentalset-up;
set-up;(b)(b)
Side
view
lakeshorezone(observation
points
● : S1–S3 and S5–S7) and groundwater table (GWT, ■ : G1–G5)). GDL,
soluteconcentrations(
for solute concentrations ( : S1 –S3 and S5 –S7 ) and groundwater table (GWT, : G1 –G5 )). GDL,
groundwater
recharging groundwater.
groundwater.
groundwater discharging
discharging into
into aa lake;
lake; LRG,
LRG, lake
lake water
water recharging

First, steady-state flow conditions in the subsurface zone were established by maintaining aFirst, steady-state flow conditions in the subsurface zone were established by maintaining a
constant groundwater table (60 cm for GDL and 20 cm for LRG) and a constant lake water level (38.5
constant groundwater table (60 cm for GDL and 20 cm for LRG) and a constant lake water levelcm) (Table 1, Figure 1b). Next, for the GDL case with wind waves, the groundwater table (at the IP(38.5 cm) (Table 1, Figure 1b). Next, for the GDL case with wind waves, the groundwater table (at theboundary in Figure 1b) was still kept constant at 60 cm, but the lake water level (on the OF boundary
IP boundary in Figure 1b) was still kept constant at 60 cm, but the lake water level (on the OF boundary
in Figure 1b) was varied following a sinusoidal function with a mean level of 38.5 cm, an amplitudein Figure 1b) was varied following a sinusoidal function with a mean level of 38.5 cm, an amplitudeof 8.5 cm, and a time period of 3 s. An observed mean run-up height (RU) of lake water driven byof 8.5 cm, and a time period of 3 s. An observed mean run-up height (RU) of lake water driven byWater 2017, 9, 566

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wind waves was about 3.0 cm, i.e., the maximum height of the lake water level on the lakeshore slope
reached about 50 cm. For the LRG case with wind waves, the groundwater table at the IP boundary
was maintained at a constant depth of 20 cm as during steady-state conditions, while the lake waterlevel followed the same sine function as for the GDL cases. Each of the two experiments for both the
GDL and LRG cases with wind waves lasted one day (24 h). In all of the experiments, a hypotheticalpollution source representing a fishpond/paddyfield was set up on the land surface 95 cm away fromthe IP boundary (Figure 1b) with a constant flux of 10 cm day−1 controlled by a micro pump.
The GDL experiment at steady-state condition was conducted first, and continued for one month.
The chloride concentrations in the upstream reservoir (the IP boundary, Figure 1b) and in the lake wereabout 0.5–1.6 mg L−1 (tap water). Next, the chloride concentrations in the lake were set at 80 mg L−1 ,and the experiment with wind waves was conducted for one day. After the GDL experiments wereconcluded, the soil flume was slowly flushed for one month until the chloride concentrations at allobservation points stabilized. The LRG steady-state experiment was carried out next, and it also
continued for one month after the chloride concentration in the lake water was again initially set at
80 mg L−1 . Finally, the LRG experiment with wind waves was carried out during one day, and thechloride concentration in lake water was still set at 80 mg L−1 . In all of the experiments, the chloride
concentration in the fishpond/paddyfield at point W (Figure 1) was constant and equal to 160 mg L−1(Table 1).
Table 1. Water flow and solute transport conditions for experiments in the soil flume andin HYDRUS-2D simulations (GDL, groundwater discharge into a lake; LRG, a lake recharging
groundwater, IP Boundary, a groundwater boundary in the lakeshore zone; OF Boundary, thelake–groundwater interface).
Case

Condition

IP Boundary

Pollution
SourceOF Boundary

Running Time

GDL

Steady-stateNo-wave *Wave *

60 cm,
0 mg L−1

10 cm day−1 ,160 mg L−1

Constant head of 38.5 cm, zero gradient **Constant head of 38.5 cm, zero gradient **Variable head (waves), 80 mg L−1

30 days
1 day
1 day

LRG

Steady-stateNo-wave *Wave *

20 cm, zero
gradient **10 cm day−1 ,160 mg L−1

Constant head of 38.5 cm, 80 mg L−1
Constant head of 38.5 cm, 80 mg L−1
Variable head (waves) , 80 mg L−1

30 days
1 day
1 day

* All experiments and simulations under no-wave and wave conditions use the final results of steady-state
conditions (a preliminary run for 30 days) as initial conditions; ** The solute concentration was set as a zero
gradient boundary condition.

2.1.2. Measurements and Analyses
In the 30-day preliminary experiments, water fluxes across the IP boundary, pressure heads,
and chloride concentrations in the subsurface zone (Figure 1b) were measured once every threedays. After wind waves started, the inflow/outflow fluxes across the IP boundary and from afishpond/paddyfield (Figure 1b) were recorded once every three hours using flow meters. Pressure
heads in the subsurface zone were observed once every three hours using automatic pressuretransducers (PT, Model no. 1151AP, Fisher, a detection limit of 0.1 cm), which were installed beneaththe groundwater table at 100, 200, 290, 420, and 465 cm away from the IP boundary. Three micropressure transducers (5 kPa, 13.5 mm in diameter and 9.5 mm in height, a detection limit of 0.01 kPa)
were set at point C (Figure 1b) to measure the pressure heads at wave crest stages. The height oflake levels on the lakeshore slope was observed using an automatic electronic gauge (WG, Model no.
LV5900, Omega Engineering, a detection limit of 0.1 cm). In addition, soil solutions were collectedonce every three hours after wind waves started, using porous ceramic suction cups at observation
points S1 –S3 and S5 –S7 (Figure 1b). The chloride concentration was analyzed using a continuous flow
auto-analyzer (FIA-6000, Skalar, Breda, The Netherlands).

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2.2. Hydrus-2D Model Simulations
2.2.1. Model Description
To improve our understanding of subsurface flow patterns and solute exchange between a lakeand groundwater driven by wind waves, the Hydrus-2D software [32,33] was used to reproduce
the results of the soil flume experiments. The two-dimensional, isothermal, Darcian water flow
and solute transport in a variably-saturated, rigid porous medium, assuming that the air phase
plays an insignificant role in the liquid flow process, can be described using the Richards andconvection-dispersion equations, respectively. Both governing equations are numerically solvedin Hydrus-2D using the method of finite elements. An appropriate spatial discretization is crucial to
avoid numerical oscillations and to achieve acceptable mass balance errors [32]. In all simulations,the total number of triangular finite elements (FE) was 18,167. At the slope surface and near the
fishpond/paddyfield (areas with large pressure head gradients), the size of the FE was approximately
1 cm, while in other parts of the transport domain it was approximately 1–6 cm. Time steps wereautomatically controlled by the Hydrus-2D model within the initially specified range of 0.001 and
0.1 s. As suggested in the manual of the Hydrus-2D model for minimizing or eliminating numericaloscillations, the Peclet (Pe) and Courant (Cr) numbers were controlled by a stability condition“Pe × Cr ≤ 2” [34].
2.2.2. Input Parameters
Soil hydraulic and solute transport parameters are required to characterize the water flow
and chloride transport in soils using the Hydrus-2D model. The van Genuchten soil hydraulicparameters [35], which include the residual water content θ r (0.055 cm−3 cm−3 ), the saturated watercontent θ S (0.40 cm−3 cm−3 ), shape parameters α (0.121 cm−1 ) and n (2.16), and the saturated hydraulicconductivity Ks (338.9 cm day−1 ), were directly adopted from our previous study using the same
experimental set up [36]. The pore connectivity parameter (l) was assumed to be equal to an averagevalue of 0.5 [35]. The solute transport parameters were considered using the following values: themolecular diffusion coefficient in free water (Dw ) for Cl− was 1.64 cm2 day−1 , and the longitudinal
dispersivity (αL ) and transverse dispersivity (αT ) were 7.0 cm and 0.5 cm, respectively [36].
2.2.3. Initial and Boundary Conditions
The steady-state water flow and chloride transport for the GDL and LRG cases were establishedfirst during a 30-day period. The final results were then used as initial conditions in simulations during
a one-day period under no-wave and wave conditions (Table 1).
For the GDL and LRG cases, the groundwater tables at the IP boundary were assumed to be
60 and 20 cm above the bottom of the soil flume, respectively (Figure 1b and Table 1). The mean
lake level (ML) was set as 38.5 cm at steady-state conditions in both the GDL and LRG cases andfor both no-wave and wave conditions. The boundary (line OF) exposed to lake water was assigned
a linearly increasing pressure head. A dynamic seepage boundary condition was prescribed at theupper part of the OF line (above the wave trough, Figure 1b) with an option to allow the developmentof a seepage zone [14,37]. When wind waves started, the lake level at the OF boundary followed asine function, with a wave period of 3 s and an amplitude of 8.5 cm. The wave run up section of the
OF boundary (above the wave crest) was simply assigned a linearly increasing pressure head basedon the measured pressure heads at point C (Figure 1b). In all simulations, a constant flux boundary
condition (10 cm day−1 ) was assigned to the boundary representing a fishpond/paddyfield at point W(Figure 1). Evaporation was neglected in this study due to relatively its low effect on the water andsolute exchanges.
At steady-state conditions, the constant relative chloride concentrations were set at C/C0 = 0.0 on
the IP boundary in the GDL case and at C/C0 = 0.5 (about 80.0 mg L−1 , Table 1) on the OF boundary in
the LRG case, respectively. When wind waves started, the OF boundary in both the GDL and LRG cases

Water 2017, 9, 566

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was set to be equal to a constant relative chloride concentration of C/C0 = 0.5 (about 80.0 mg L−1 ); theIP boundary condition remained the same as at steady-state conditions. The chloride concentrations in
the fishpond/paddyfield in both the GDL and LRG cases were set at C/C0 = 1.0 (about 160.0 mg L−1 )in all simulations.
2.3. Model Evaluation
The simulated values of the pressure heads, total water fluxes, and chloride concentrations inthe soil were compared with the corresponding values recorded during the soil flume experiments.
The correspondence between the simulated and observed data was evaluated using the coefficientof determination (R2 ) and the root mean square error (RMSE). The coefficient of determination was
calculated as:
SSerr
R2 = 1 −(1)
SStot
where SSerr is the sum of squared differences between modeled and observed values, and SStot is thesum of squared differences between observed values and the mean of observed values.
The RMSE was calculated as:
s
1 n
(2)
RMSE =( S i − Mi ) 2n∑1
where Si and Mi are simulated and measured values, respectively, and n is the number ofcompared values.
3. Results
3.1. Groundwater TableThe simulated pressure heads in the subsurface zone at both steady-state conditions andconditions with wind waves (Figure 2) show good agreement with the observed data at G1 –G5 ,with RMSE = 0.62 cm (n = 55, R2 = 0.96, note that the range of pressure head values during thesimulation was about 130 cm) in the GDL cases and with RMSE = 0.45 cm (n = 55, R2 = 0.97) inthe LRG cases. It is clear that the pressure heads in the subsurface zone near the interface (OF line,
Figure 1b) quickly varied when wind waves occurred. The pressure heads at G1 –G5 in both the GDLand LRG cases with wind waves clearly increased from their initial values, which were the averagepressure heads at their respective steady-state conditions. In the GDL case, the average pressure headat G1 increased slightly (0.6 cm) during a one-day period after the wind waves started compared tosteady-state conditions, but increased much more at G2 , G3 , G4 , and G5 by 1.4, 2.2, 3.5, and 2.4 cm,
respectively (Figure 2a). In the LRG case with waves, the average pressure heads at G1 , G2 , G3 , G4 , andG5 increased 1.2, 2.1, 3.1, 4.2, and 2.7 cm, respectively, compared to steady-state conditions (Figure 2b).
Furthermore, in the GDL case, wind waves produced quick fluctuations of the pressure heads
at both G4 and G5 with amplitudes of 1.1–1.9 cm and 5.1–7.4 cm, respectively, but only had a small
effect on G3 (0.05 cm) and G2 (0.004 cm), and almost no effect on G1 (Figure 2a). In the LRG case,while the pressure heads at G4 and G5 fluctuated with amplitudes of about 0.9-1.6 cm and 5.0–7.3 cm,
respectively, they displayed little fluctuations in G1 , G2 , and G3 (Figure 2b). The variations of hydraulicheads in the subsurface zone due to wind waves are smaller than the variations of the lake water level(8.5 cm). As the distance of the observation points from the shoreline increased, the effect of wind
waves on the pressure heads decreased

Water 2017, 9, 566
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Water 2017, 9, 566

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Figure(lines) andobserved (points) pressure heads during a one-day
period after wind
Figure 2.
2. Simulated
Simulated
one-day(a)(lines)
GDL and observed (points) pressure heads during a (b)LRG period after wind
waves
started
in
the
GDL
(a)
and
LRG
(b)
cases.
All
observation
points
were
at
the
same
heightof 20
waves started in the GDL (a) and LRG (b) cases. All observation points were at thesameheightofFigure2. Simulated(lines)and observed(points)pressureheads
duringa one-dayperiodafter windcm
(Figure1b).
Exceptfortime
between12.000and
12.002h,
onlyvalues
when
the
lake
water
20 cm (Figure 1b). Except for time between 12.000 and 12.002 h, only values when the lake water level
level
waves
startedin the GDLare(a)shown.
and LRG (b) cases. All observation points were at the same height of 20
waswas atat itsits meanmean position
position are shown.
cm (Figure 1b). Except for time between 12.000 and 12.002 h, only values when the lake water level
was atits meanposition
are shown.
The
wind
waves
also greatly
influenced the pressure head distributions along the OF line (Figure.
1b). At no-wave conditions, the pressure heads linearly increased along the OF line, ranging fromThe
windwaveswaves also
greatly
influenced pressure
the pressure
distributions
along
line
wind
greatly
headtohead
distributions
along
the
OF thelineOF(Figure−83.6The
to 38.5cm in thealso
GDL
case influenced(Figure 3a)theand from −95.8
38.5 cm in the
LRG
case(Figure3b).
(Figure1b). At no-wave
conditions,the pressure linearly
heads linearly increased
along
OFrangingline, ranging
1b).
Atwindno-waveconditions,
OF=the
line,
Once
waves
occurred,thethepressurepressureheads
heads below increased
a point ofalong
aboutthed/L
0.6 (The
ratiofrom
d/L
from
−
83.6
to
38.5
cm
in
the
GDL
case
(Figure
3a)
and
from
−
95.8
to
38.5
cm
in
the
LRG case−83.6 to 38.5
cm in theGDL case−95.8point
to 38.5
the LRG
case above(Figure3b).
represents
a relative
distanceof a (Figure
point on3a)
theandOFfromline fromO cm
or ainrelative
heightpoint(Figurewind3b). Oncewaves occurred,
the pressure
headsabelow
aof
point
of about= d/L
0.6 (Theratio
Once
waveswindoccurred,pressure
heads
point
about
0.6 =(The
ratio
d/L
O,
and L represents
the lengththeor heightof theOF belowline) weredifferent
fromd/Ltheir respective
steadyd/L
representsarelative
distance
of
a
point
on
the
OF
line
from
point
O
or
a
relativeheightabove
represents
a relative
distanceof a pointon theOF linefrom pointthe
O ora relative
height
above
point
state
conditions
in boththe GDLand LRG
cases.
Furthermore,pressure
heads
below
point
D
point
O,
and
L represents
the lengthor heightof theOFline)were different
fromtheir respectiveO,andL
represents
thelengthorheight
of
the
OF
line)
were
different
from
their
respective
steadydiffered depending on the stage of a wave cycle. At the mean lake level (ML) stage for both risingsteady-state
conditions
both
the andGDLLRG
and LRG
Furthermore,
the pressure
heads
below point
state
conditions
bothinthe
GDL
cases.cases.
Furthermore,thepressure
heads
below
D
and
falling
waterinlevels,thepressure
heads between
points B and C
wereapproximately
zero,point
similarD
differeddepending
on
the
stage
of
a
wave
cycle.
At
the
mean
lake
level
(ML)
stage
for
both
risingdiffereddependingthe stageof a Awave
Atwavethe meanlake
level(ML)Thestage
for bothrisingtothe pressure
headsonbetween
pointsand cycle.
C at thetrough(WT)stage.
pressureheads
inand falling
falling water
water levels,
levels, thethe pressurepressure heads
heads between
between points
points B
B and
and C
C werewere approximately
approximately zero,
zero, similar
similarandthe LRG case at each stage of a wave cycle were similarly distributed as they were in the GDL case.
to thethe pressurepressure heads
heads between
between points
points A
A and
and C
C at
at thethe wave
wave troughtrough (WT)
(WT) stage.
stage. The
The pressurepressure heads
heads in
in
to
the
LRG
case
at
each
stage
of
a
wave
cycle
were
similarly
distributed
as
they
were
in
the
GDL
case.
the LRG case at each stage of a wave cycle were similarly distributed as they were in the GDL case.

(a) GDL(b) LRG

Figure 3. Pressure head distributions on the lakeshore (the OF line, Figure 1) during no-wave(a) GDL(b) LRG
conditions and at different stages of a wave cycle for the GDL (a) and LRG (b) cases. See Figure 1 for
Figure3.ofPressureon lakeshore
the lakeshore
(the
OF
line,
1)
duringno-wavelocationspoints headA,headB, distributions
C, distributions
D, F, and O.
solid
represent
relative
distancesofconditions
pointsA,
Figure 3.
Pressure
onHorizontal
the(thelines
OF
line,
Figure1)Figureduringno-waveconditions
andatdifferent
stages
of
a
wave
cycle
for
the
GDL
(a)
and
LRG
(b)
cases.
See
Figure
1
for
B,
C,
and
D
from
point
O.
The
gray
horizontal
line
representsazeropressure
head.
The
ratio
d/L
and at different stages of a wave cycle for the GDL (a) and LRG (b) cases. See Figure 1 for locations oflocations
A,and
B, C,
F,
O. Horizontal
linespoint
represent
relative
distancesof pointsA,
represents
relative
distanceof anda point
on thelines
OF solid
line fromO ora relative
height A,
above
points A,of
B,apoints
C,
D, F,
O.D,Horizontal
solid
represent
relative
distancesofpointsB, C,point
andB,
C,represents
andD frompoint
grayofline
horizontal
linearepresentsa zeropressurehead.
ratio d/LaOlengthorTheheighttherepresents
OF line).
D (L
from
point
O.the
The
grayO.horizontal
zero pressurehead.
The ratio
d/LTherepresents
representsarelative
distance
of
a
point
on
the
OF
line
from
point
O
or
a
relativeheightabove
point
relative distance of a point on the OF line from point O or a relative height above point O (L representsO(L
represents
thelengthorheightoftheOFline).
3.2. Subsurface
Flow
Patterns
the length or height of the OF line).

The subsurface flow patterns near the OF line (Figure 1b), including flow directions and flux
3.2. Subsurface Flow Patterns
distributions, changed after wind waves started and depended on wave stages (Figure 4). At no-wave
The subsurface
flow
near thedischarge
OF line (Figure1b), including
directions
andconditionsin the GDL
case,patterns
the subsurface(to the lake)
peaked at flow
a maximum
value
offlux
113
distributions, changed after wind waves started and depended on wave stages (Figure 4). At no-wave
conditions in the GDL case, the subsurface discharge (to the lake) peaked at a maximum value of 113

Water 2017, 9, 566

8 of 18

3.2. Subsurface Flow Patterns
The subsurface flow patterns near the OF line (Figure 1b), including flow directions and flux
distributions, changed after wind waves started and depended on wave stages (Figure 4). At no-wave
conditions in the GDL case, the subsurface discharge (to the lake) peaked at a maximum valueof 113 cm day−1 at point B (Figure 5a), while in the LRG case, the maximum infiltration flux of−53 cm day−1 also occurred at point B (Figure 5b). Below point B, fluxes declined rapidly along
the OF line and reached zero at point O. After wind waves started, the discharge velocities of thesubsurface flow near the OF line at the ML stage (rising) of a wave cycle in the GDL (Figure 4a) andLRG (Figure 4e) cases peaked at point B (Figure 5), with maximum discharge velocities of 210 and
164 cm day−1 , respectively. The subsurface flow above point B was directed downwards along theinterface and vertically upward (into the lake) below point B. At the RU stage of both the GDL and
LRG cases (Figure 4b,f), the subsurface flow had much higher fluxes than at the ML stage (Figure 4a,e).
The water exchange flux at the RU stage occurred mainly within a narrow band near point D, with the
maximum fluxes at point D of 1800 cm day−1 in the GDL case and 5080 cm day−1 in the LRG case
(Figure 5).
When the lake level declined between the RU and ML (falling) stages in both the GDL and LRG
cases, the groundwater table near the OF line also dropped rapidly (Figure 4c,g). The maximum
fluxes of 240 cm day−1 in the GDL case (Figures 4c and 5a) and 199 cm day−1 in the LRG case
(Figures 4g and 5b) occurred at point B. During this stage in both the GDL and LRG cases, thesubsurface flow discharge into the lake was mainly concentrated near point B (Figure 4c,g).
Above point B, most subsurface flow was directed downwards along the interface. Finally, at thewave trough stage (WT), the subsurface flow near the interface was directed downwards to point
A, where water was discharged into the lake with the maximum fluxes of 178 cm day−1 in the GDLcase (Figures 4d and 5a) and 170 cm day−1 in the LRG case (Figures 4h and 5b). Overall, during anentire wave cycle in both the GDL and LRG cases, lake water infiltrated into the subsurface zone withrelatively high fluxes during the wave crest, while subsurface flow discharged into the lake duringother stages. Wind waves thus produced the formation of water circulations in the subsurface zone
near the interface (Figure 4).
Additionally, lake waves produce rapid changes in the extent of the seepage face along theinterface. At the rising ML stage of a wave cycle in the GDL case, a short seepage face (3.1 cm long
along the interface, 1.8 cm in height) developed above point B (Figure 4a), and no seepage face wasobserved at this stage in the LRG case (Figure 4e). No seepage face occurred at the RU stage in boththe GDL and LRG cases (Figure 4b,f). While the flow patterns near the interface at the falling ML
stage were similar to those at the rising ML stage, the seepage faces above point B were longer, 5.0 cm(2.9 cm in height) in the GDL case and 4.1 cm (2.4 cm in height) in the LRG case (Figure 4c,g). Finally,
the longest seepage faces above point A developed at the WT stage in both the GDL and LRG cases,
with lengths of 14.4 cm (8.3 cm in height) and 11.5 cm (6.7 cm in height), respectively. The locationand length of the seepage face along the interface responded to the fluctuations of the lake water level
driven by waves. Seepage face lengths due to wind waves increased when the lake level was rapidly
falling, but decreased when it was rapidly rising in both the GDL and LRG cases (Figures 4 and 5).

Water 2017, 9, 566
Water 2017, 9, 566

9 of 18
9 of 18

Figure
Local
water
flow
patterns
nearlake-groundwaterinterfacedifferent
stagesa waveFigure
4. 4.
Local
water
flow
patterns
nearthethelake-groundwaterinterface
at atdifferent
stagesof ofa wavecycle(indicateda point
a sinewave)
GDL(a,b,c,d,
left)
and
LRG
(e,f,g,h,right)
cases.
cycle(indicatedbyby
a pointonon
a sinewave)
inin
thetheGDL(a,b,c,d,
left)
and
LRG
(e,f,g,h,right)
cases.
Black
solid
lines
and
green
dashedarrow
lines
represent
thegroundwater
table
(zero
pressure
heads)
Black solid lines and green dashed arrow lines represent the groundwater table (zero pressure heads)
andflow
directions
a corresponding
stage,
respectively.
ML,
RU,
and
WT
represent
mean
lake
and
flow
directionsat ata corresponding
stage,
respectively.
ML,
RU,
and
WT
represent
thethe
mean
lake
level
(38.5
cm),
run-upheight
cm),
and
wave
troughcm),
respectively.
level
(38.5
cm),
thetherun-upheight(50(50cm),
andthethewave
trough(30(30cm),
respectively.

Water 2017, 9, 566

10 of 18

Water 2017, 9, 566

10 of 18(a) GDL(b) LRG

Figure 5. Distributions of water fluxes along the lake–groundwater interface (OF) for no-wave
Figure 5. Distributions of water fluxes along the lake–groundwater interface (OF) for no-wave
conditions and at different stages of a wave cycle for the GDL (a) and LRG (b) cases. (ML, RU, andconditions and at different stages of a wave cycle for the GDL (a) and LRG (b) cases. (ML, RU,
WT represent the mean lake level (38.5 cm), the run-up height (50 cm), and the wave trough (30 cm),and WT represent the mean lake level (38.5 cm), the run-up height (50 cm), and the wave troughrespectively;
positive fluxes
are into
the subsurface
and negative
into thefluxeslake). into
See Figure(30 cm), respectively;
positive
fluxesare into thezone
subsurface
zone fluxes
and negative
the lake).
1 forpointsA, B, ofC,points
D, F, andO.C,Horizontal
lines represent
distancesof
Seelocations
Figure 1offor
locations
A, B,
D, F, and solid
O. Horizontal
solid relativelines represent
relative
points
A,
B,
C,
and
D
from
point
O.
The
gray
horizontal
line
represents
zero
water
flux.
Noticethe
distances of points A, B, C, and D from point O. The gray horizontal line represents zero water flux.
breakin theaxis.
Noticetheverticalbreak inthe vertical axis.

3.3. Water Exchange
3.3. Water Exchange−1) agreed well with the observed
The simulated cumulative water fluxes (412.8–820.8 cm2 day
The simulated cumulative water fluxes (412.8–820.8 cm2 day−1 ) agreed well with the observed
data during a one-day period, including inflow and outflow fluxes across the IP boundary (Figure
data during a one-day period, including inflow and outflow fluxes across the IP boundary (Figure 1b),
2 day−1 (n = 8, and R2 = 0.95) in the GDL case and RMSE = 15.7 cm2 day−1 (n1b), with RMSE = 18.3 cm
with RMSE = 18.3 cm2 day−1 (n = 8, and R2 = 0.95) in the GDL case and RMSE = 15.7 cm2 day−1 (n = 8,
= 8, and R22 = 0.96) in the LRG case. Changes in the pressure head and flow patterns in the subsurface
and R = 0.96) in the LRG case. Changes in the pressure head and flow patterns in the subsurface
zone due to wind waves caused changes in the exchange water fluxes across the interface (Figure 5).
zone due to wind waves caused changes in the exchange water fluxes across the interface (Figure 5).
The exchange water fluxes varied in phase with wind waves. The distributions of water fluxes on the
The exchange water fluxes varied in phase with wind waves. The distributions of water fluxes on theinterface were significantly different for no-wave conditions and for conditions with wind waves atinterface were significantly different for no-wave conditions and for conditions with wind waves atdifferent stages of a wave cycle.
different stages of a wave cycle.
For no-wave conditions in the GDL case, discharging water fluxes (into the lake) peaked at point
For no-wave conditions in the GDL case, discharging water fluxes (into the lake) peaked at point
B (Figure 5a), and 50% of the flux occurred within a narrow band (6.2 cm in length on the interface)
B (Figure 5a), and 50% of the flux occurred within a narrow band (6.2 cm in length on the interface)
below point B. For conditions with wind waves, discharging water fluxes at the ML stages (bothbelow point B. For conditions with wind waves, discharging water fluxes at the ML stages (both risingrising and falling) still peaked at point B. However, both fluxes were relatively higher, and 50% of
and falling) still peaked at point B. However, both fluxes were relatively higher, and 50% of their
their volume was concentrated within narrow bands (7.1 cm for the rising stage and 8.0 cm for thevolume was concentrated within narrow bands (7.1 cm for the rising stage and 8.0 cm for the falling
falling stages) below point B. At the RU stage, the infiltration fluxes peaked at point D. At the WT
stages) below point B. At the RU stage, the infiltration fluxes peaked at point D. At the WT stage, thestage, the discharging fluxes were mainly distributed near point A where they peaked. The exchange
discharging fluxes were mainly distributed near point A where they peaked. The exchange water
water fluxes at each stage of a wave cycle in the LRG case (Figure 5b) had similar distributions tofluxes at each stage of a wave cycle in the LRG case (Figure 5b) had similar distributions to those in
those in the GDL case (Figure 5a), except for different values of flux peaks and reverse directions at
the GDL case (Figure 5a), except for different values of flux peaks and reverse directions at no-wave
no-wave conditions. After wind waves started, lake water infiltrated into the subsurface zone through theconditions. After wind waves started, lake water infiltrated into the subsurface zone through theupper part of the interface near the run-up height (at point D), and exfiltrated through its lower part (atupper part of the interface near the run-up height (at point D), and exfiltrated through its lower part
point A) in both the GDL (Figure 4a–d) and LRG (Figure 4e–h) cases.
(at point A) in both the GDL (Figure 4a–d) and LRG (Figure 4e–h) cases.
Cumulative exchange water fluxes (CEWFs) during a one-day period with wind waves were
Cumulative exchange water fluxes (CEWFs) during a one-day period with wind waves weredifferent than those at no-wave conditions (Table 2). At no-wave conditions in the GDL case, thedifferent than those at no-wave
conditions (Table 2). At no-wave conditions in the GDL case, the CEWF
−1 (negative values represent groundwater discharging into lake), andCEWF was about −826 2cm2 day
was about −826 cm day−1 (negative values represent groundwater discharging into lake), and thethe part of the lakeshore above the mean lake level accounted for about 9.5% of the total flux. On thepart of the lakeshore above the mean lake level accounted for about 9.5% of the total−1flux. On theother hand, at no-wave conditions in the LRG case, the CEWF was about 412 cm2 day(positive
other hand, at no-wave conditions in the LRG case, the CEWF was about 412 cm2 day−1 (positive
values represent groundwater receiving lake water), and the part of the lakeshore above the meanvalues represent groundwater receiving lake water), and the part of the lakeshore above the mean lake
lake level accounted for about 8.8% of the total flux. The simulated results also showed that inflow
level accounted for about 8.8% of the total flux. The simulated results also showed that inflow andand outflow between the lake and groundwater coexisted when wind waves were present in bothoutflow between the lake and groundwater coexisted when wind
waves were present in both the GDL
the GDL and LRG cases. However, although the CEWF (−527
cm2 day−1) during a one-day period withand LRG cases. However, although the CEWF (−527 cm2 day−1 ) during a one-day period with wind
wind waves in the GDL case was lower than for the no-wave conditions, the overall flow was still
directed into the lake. In the LRG case with wind waves, the CEWF (832 cm2 day−1) was higher thanthat for the no-wave conditions, but was still directed into the subsurface zone.

Water 2017, 9, 566

11 of 18

waves in the GDL case was lower than for the no-wave conditions, the overall flow was still directed
into the lake. In the LRG case with wind waves, the CEWF (832 cm2 day−1 ) was higher than that for
the no-wave conditions, but was still directed into the subsurface zone.
Table 2. Cumulative exchange water and chloride fluxes during a one-day period and sensitivity
analysis due to the aquifer hydraulic conductivity (Ks ), the wave cycle period (P), and amplitude (A).
Case

BC at Line OF *Ks (cm day−1 )P (s)A (cm)

CEWF *** (cm2 day−1 )CECF *** (mg cm−1 day−1 )AML **BML **Total

AML **BML **

Total

GDL

No-waveWave
No-waveWave
No-wave
Wave
Wave
Wave

338.9
338.9
677.8
677.8
169.5
169.5
338.9
338.9

3
3
3
3
3
3
6
3

8.5
8.5
8.5
8.5
8.5
8.5
8.5
17.0

−79
1063
−165
2043
−26
369
1073
1656

−747
−1590
−1557
−3261
−244
−475
−1589
−2032

−826
−527
−1722
−1218
−270
−105
−516
−376

−26
427
−29
826
−16
176
496
667

−101
−463
−108
−935
−63
−121
−456
−625

−128
−36
−137
−110
−79
55
39
42

LRG

No-waveWave
No-waveWave
No-wave
Wave
Wave
Wave

338.9
338.9
677.8
677.8
169.5
169.5
338.9
338.9

3
3
3
3
3
3
6
3

8.5
8.5
8.5
8.5
8.5
8.5
8.5
17.0

36
1742
73
3270
11
597
1783
2489

376
−960
759
−1836
116
−280
−959
−1496

412
832
412
1434
128
317
824
993

26
736
53
1512
8
279
769
992

206
−493
416
−951
64
−145
−496
−763

232
243
469
561
72
133
272
229

* BC: boundary condition; line OF: lake–groundwater interface, see Figure 1b; ** AML: above the mean lake level(namely above 38.5 cm); BML: below the mean lake level; *** CEWF: a cumulative exchange water flux during a
one-day period (negative into the lake); CECF: a cumulative exchange chloride flux during a one-day period.

3.4. Solute Concentrations
The simulated chloride concentrations (0.0–80.0 mg L−1 ) agreed well with the observed data at
S1 –S3 and S5 –S7 , with an average RMSE value of 0.13 mg L−1 (n = 59, and R2 = 0.95) in both the GDLand LRG cases. At no-wave conditions in both the GDL and LRG cases, the chloride concentrations
at all observation points remained constant (not shown) and the same as the initial concentration
values for conditions with wind waves (Figure 6). In the GDL case with one-day wind waves, thechloride concentrations increased at S1 and S2 , and remained almost constant at other observation
points (Figure 6a). The chloride concentrations at S2 quickly increased and stabilized at C/C0 = 0.5(the chloride concentration in lake water) after wind waves started, while those at S1 increased more
gradually. Th chloride concentrations at S3 , S5 , S6 , and S7 were dominated by the transport of chloride
from the upstream pollutions source at point W (Figure 1). However, in the LRG case, the presenceof wind waves did not lead to any changes in chloride concentrations at the six observation points(Figure 6b) that were dominated by chloride concentration in the lake water.
The chloride concentrations in the subsurface zone at no-wave and wave conditions are shownin Figure 7. These concentration distributions can more clearly explain the changes of chloride
concentrations at the observation points. In the GDL case at no-wave condition, water and solute flow
into the lake and the subsurface concentration profiles are not affected by concentrations in the lake
(Figure 7a). After wind waves started, lake water and its solutes gradually infiltrated (mainly during
the wave crest stage) into the subsurface zone through the interface between points A and D, and thearea affected by lake water gradually extended into the subsurface zone (Figure 7a). This affected area
gradually increased with time until an equilibrium distribution on the vertical profile was reached.
On the other hand, in the LRG case with wind waves, no apparent changes of the chloride distribution
were observed compared to no-wave conditions (Figure 7b). Chloride distribution in the subsurface
zone in the LRG case was always determined by chloride concentrations in lake water.

points (Figure 6a). The chloride concentrations at S2 quickly increased and stabilized at C/C0 = 0.5 (thechloride concentration in lake water) after wind waves started, while those at S1 increased more
gradually. Th chloride concentrations at S3, S5, S6, and S7 were dominated by the transport of chloride
from the upstream pollutions source at point W (Figure 1). However, in the LRG case, the presenceof windpointsWater
2017,waves
9, 566 did not lead to any changes in chloride concentrations at the six observation 12
of 18(Figure 6b) that were dominated by chloride concentration in the lake water.
Obs. Sim.

C/C0 of Chloride

0.8
0.6
Water 2017, 9, 566
0.4

1.0

Obs. Sim.
S1
S2
S3

S5
S6
S7

0.8
C/C0 of Chloride

1.0

0.6

Obs. Sim.

Obs. Sim.
S1
S2
S3

S5
S6
S7

12 of 18

0.4

The chloride concentrations in the subsurface zone at no-wave and wave conditions are shownin Figure7. These concentration distributions can more
0.2
0.2 clearly explain the changes of chloride
concentrations at the observation points. In the GDL case at no-wave condition, water and solute flow
0.0 lake and the subsurface concentration profiles 0.0
into theare not affected by concentrations in the lake
0
3
6
9
12
15
18
21
24
0
3
6
9
12
15
18
21
24
(Figure 7a). After windTime
waves
started, lake water and its solutes graduallyTime
infiltrated(mainly during(hour)(hour)
the wave crest stage) into
the subsurface zone through the interface between
points A and D, and the(a) GDL(b) LRG
area affected by lake water gradually extended into the subsurface zone (Figure 7a). This affected
Figure 6.6.Simulated
Simulatedandandobserved
chloride concentrations
nearlake–groundwater
the lake–groundwaterobserved
chlorideneardistribution
theinterfaceinterface
during wasarea Figure
gradually increased
with
time
until concentrations
an equilibriumon the verticalprofileduringaone-day
period
after
wind
waves
started
in
the
GDL
(a)
and
LRG
(b)
cases.
(lines:simulateda one-dayperiodwind
startedthe wind
GDL (a)and LRG(b) cases. changes(lines: simulatedbyreached.
On theotherafter
hand,
in waves
the LRG
caseinwithwaves,
no apparentof the chloride
by Hydrus-2D;
symbols:
observed
duringthe soilflume experiments).
Cchloride
0: the input chloride
Hydrus-2D;
symbols:
observed
during
the
soil
flume
experiments).
C
:
the
input
concentration
0
distribution were observed compared to no-wave conditions (Figure 7b). Chloride distribution in theconcentrationfrom the fishpond/paddyfield.
fromthefishpond/paddyfield.
subsurface
zone
in the LRG case was always determined by chloride concentrations in lake water.

Figure 7.
7. Chloride
Chloride concentration
concentration profiles
Figureprofiles inin thethe subsurface
subsurface zone
zone at
at no-wave
no-wave (top)(top) andand wave
wave (bottom)(bottom)conditions
in
the
GDL
(a)
and
LRG
(b)
cases.
Distributionsofchlorideinboth
no-waveandwave
conditions in the GDL (a) and LRG (b) cases. Distributions of chloride in both no-wave and wave
conditions
are
the
final
resultsofone-day
simulations
starting
fromrespective
initialconditions
conditions are the final results of one-day simulations starting from respective initial conditions(steady-state). Red
Red points
points represent
represent thethe locations
locations ofof observation
observation points
points forfor chloride
chloride concentration.
concentration.
(steady-state).

Furthermore, while in the GDL case chloride distributions on the interface were greatly
Furthermore, while in the GDL case chloride distributions on the interface were greatly influenced
influenced by the occurrence of wind waves, there were almost no changes in chloride distributions
by the occurrence of wind waves, there were almost no changes in chloride distributions at theat the interface in the LRG cases with and without waves (Figure 8). In the GDL case with windinterface in the LRG cases with and without waves (Figure 8). In the GDL case with wind waves,waves, chloride concentrations between points A and D were about equal to the chloride
chloride concentrations between points A and D were about equal to the chloride concentration
concentration in lake water (C/C0 = 0.5), and declined rapidly above point D and below point A
in lake water (C/C0 = 0.5), and declined rapidly above point D and below point A (Figure 8a).
(Figure 8a). Chloride concentrations below point A, and even near point O, changed compared to noChloride concentrations below point A, and even near point O, changed compared to no-wave
wave conditions, apparently as a result of water circulation due to wind waves. Chloride
conditions, apparently as a result of water circulation due to wind waves. Chloride concentrations
concentrations above a point of d/L = 0.45 were not influenced by wind waves. In the LRG cases,
above a point of d/L = 0.45 were not influenced by wind waves. In the LRG cases, chloride
chloride concentrations below a point of d/L = 0.5 were equal to the chloride concentration in the lake
concentrations below a point of d/L = 0.5 were equal to the chloride concentration in the lake water
water (C/C0 = 0.5), and declined rapidly to zero above this point (Figure 8b). In both the GDL and(C/C0 = 0.5), and declined rapidly to zero above this point (Figure 8b). In both the GDL and LRG
LRG cases, chloride concentrations above a point of about d/L = 0.75 approached zero at both nocases, chloride concentrations above a point of about d/L = 0.75 approached zero at both no-wave andwave and wave conditions.
wave conditions.

Water 2017, 9, 566

13 of 18

Water 2017, 9, 566

13 of 18(a) GDL(b) LRG

Figureof ofchlorideconcentrations
along
the thelake–groundwaterinterface(OF)(OF)at noFigure8.8.Distributions
Distributions
chlorideconcentrations
alonglake–groundwaterinterfaceatwave
conditions
in
the
GDL
(a)
and
LRG
(b)
cases
and
one
day
after
wind
waves
started.
See
Figureno-wave conditions in the GDL (a) and LRG (b) cases and one day after wind waves started. See
1Figurefor the1locationsof points ofA, points
B, C, D,A,
F, B,
and
lines represent
relative
distancesoffor the locations
C,O.
D,Horizontal
F, and O. solid
Horizontal
solid lines
represent
relative
pointsA, B,ofC,points
and D from
O. C
the input
chloridefrom thefishpond/paddyfield.
distancesA, B,point
C, andD0: from
point
O. C0 :concentration
the input chloride
concentrationfrom the0 = 0.5 represents the relative chloride concentration in lakeThegrayhorizontal
dashedline
atC/C
fishpond/paddyfield. The gray horizontal dashed line at C/C0 = 0.5 represents the relative chloride
water.
concentration in lake water.

3.5. Solute Exchange
3.5. Solute Exchange
Overall, the chloride exchange fluxes across the interface (Table 2) corresponded with their
Overall, the chloride exchange fluxes across the interface (Table 2) corresponded with theirrespective water exchange fluxes. At no-wave conditions in the GDL case, the cumulative exchange
respective water exchange fluxes. At no-wave conditions in the GDL case, the cumulative exchange−1 day−1chloride flux (CECF) across the whole interface during a one-day period was −128 mg cm
chloride flux (CECF) across the whole interface during a one-day period was −128 mg cm−1 day−1(negative values indicate fluxes into the lake). The solute flux through the upper part of the interface(negative values indicate fluxes into the lake). The solute flux through the upper part of the interface
above the mean lake level (ML) accounted for about 20.7% of the total solute flux. After wind waves
above the mean lake level (ML) accounted for about 20.7% of the total solute flux. After wind waves
occurred, the CECF across the whole interface declined by about 72%. Wind waves resulted in aoccurred, the CECF across the whole interface declined by about 72%. Wind waves resulted in asimultaneous increase in the CECFs across both the upper (above ML) and lower (below ML) parts
simultaneous increase in the CECFs across both the upper (above ML) and lower (below ML) parts ofof the interface, although in opposite directions.
the interface, although in opposite directions.
At no-wave conditions in the LRG case (Table 2), the CECF across the upper part of the boundary
At no-wave conditions in the LRG case (Table 2), the CECF across the upper part of the boundary
was 26 mg cm−1−1day−1−(intothe subsurface) and accounted for about 11.3% of the total solute flux of
was 26 mg cm day 1 (into the subsurface) and accounted for about 11.3% of the total solute flux of
232 mg cm−1−1day−1−. Afterwind
waves occurred, while the overall CECF remained about the same, it
232 mg cm day 1 . After wind waves occurred, while the overall CECF remained about the same, it
greatly increased across the upper part of the boundary to 736 cm−−11 day−1−,1as well as across the lower
greatly increased across the upper part of the boundary to 736 cm day , as well as across the lower−1.
part of the boundary (in the opposite direction) to −493 mg cm−1−daypart of the boundary (in the opposite direction) to −493 mg cm 1 day−1 .
3.6.
3.6.Sensitivity
SensitivityAnalysis
AnalysisThe
analysiswas
wascarried
carriedin thisto evaluate
the ofeffectsof thehydraulicaquifer
The sensitivity
sensitivity analysis
outoutin thisstudystudy
to evaluate
the effects
the aquifer
hydraulicconductivity(Ks) and wind wave characteristics (a wave period, P, and a wave amplitude,
conductivity (Ks ) and wind wave characteristics (a wave period, P, and a wave amplitude, A) both onA)
onandthesolute
water exchange
and soluteexchange
and theandsubsurface,andon the inflow
thebothwater
betweenthe between
lake and thethe lakesubsurface,on the flow
patterns
thepatterns
inthesubsurface
zone.
Asensitivity
analysisofthesolutetransport
parameters
has
not
been
subsurface zone. A sensitivity analysis of the solute transport parameters has not been evaluated in
evaluated
this study.in this study.
Simulations
Simulationswere
werecarried
carriedout
outusing
usingthetheHydrus-2D
Hydrus-2Dmodel
modelforforthethesamesameconditions
conditionsas
asforforwhich
which
the
model
was
calibrated(i.e.,
a
loamy
sand
soil,
waves
with
a
period
P
of
3
s
and
an
amplitude
the model was calibrated (i.e., a loamy sand soil, waves with a period P of 3 s and an amplitudeAAofof−11s being either half or double the original value (338.9 cm day−8.5
cm),
except
for
K
)
in
the
original
8.5 cm), except for Ks being either half or double the original value (338.9 cm day ) in the original
simulations
simulations(Table(Table 2).
2). When
Whenthe
theKKs svalue
valueofofthe
theaquifer
aquiferdecreased
decreasedby
by50%,
50%, thethe CEWFs
CEWFs acrossacross thetheinterfaceduringaone-day
perioddeclined
by
about
67.3%
in
the
GDL
case
and
69.1%
in
interface during a one-day period declined by about 67.3% in the GDL case and 69.1% inthe
theLRG
LRG
case
caseatattheir
theirno-wave
no-waveconditions,conditions,butbutdeclined
declinedby
byabout
about80.1%
80.1%andand59.5%
59.5%in
inthe
theGDL
GDLandandLRG
LRGcases
cases
with
wind
waves,
respectively.
Similarly,
the
CECFs
declined
by
about
38.4%
in
the
GDL
with wind waves, respectively. Similarly, the CECFs declined by about 38.4% in the GDLcase
caseandand−1−1day69.0%
butchangedfrom−36−tocm−1cmday(in −a1
69.0%in
inthe
theLRG
LRGcasecaseatattheir
theirno-wave
no-waveconditions,conditions,butchanged
from
3655
to mg
55 mg
reversed
direction)and declined
by about
45.0%
in the
GDL
and
LRG
cases
(in a reversed
direction)and declined
by about
45.0%
in the
GDL
andLRG
caseswithwithwindwindwaves,waves,
respectively. On the other hand, when the Ks value increased by 100%, the CEWFs during a one-day
period increased by about 108.5% in the GDL case and 101.9% in the LRG case at their no-wave
conditions, and increased by about 131.1% and 83.3% in the GDL and LRG cases with wind waves,Water 2017, 9, 566

14 of 18

respectively. On the other hand, when the Ks value increased by 100%, the CEWFs during a one-day
period increased by about 108.5% in the GDL case and 101.9% in the LRG case at their no-wave
conditions, and increased by about 131.1% and 83.3% in the GDL and LRG cases with wind waves,respectively. Concurrently, the CECFs increased by about 7.2% in the GDL case and 101.9% in the LRG
case at their no-wave conditions, but increased by about 205.3% and 131.4% in the GDL and LRG caseswith wind waves, respectively. The Ks value of the aquifer thus greatly influences the water and soluteexchange fluxes between the lake and groundwater.
The characteristics of wind waves, including the cycle period and wave amplitude, also influencelake–groundwater interactions. When the cycle period increased from 3 to 6 s, the CEWFs slightly
decreased (by about 2.1%) in the GDL case and slightly increased (by 5.7%) in the LRG case (Table 2).
However, the CECFs in the GDL case reversed their direction (from −36 to 39 mg cm−1 day−1 ) and in
the LRG case, increased by about 12.3% (from 243 to 272 mg cm−1 day−1 ). Consequently, increasing
a wave period (from 3 to 6 s) apparently increased the water and solute exchange fluxes in the LRG
cases, but decreased the water exchange flux and reversed the solute exchange direction in the GDLcase. On the other hand, the simulations showed that an increase in the wind amplitude from 8.5 to
17.0 cm (Table 2) produces a decrease in the CEWFs of about 45.2% in the GDL case and an increase ofabout 41.8% in the LRG case, compared to the original simulations. Similar to the effects of increasing
a wave period, the CECFs reversed their direction (from 87 cm2 day−1 to −36 cm2 day−1 ) in the GDLcase and increased by about 13.3% in the LRG case.
4. Discussion
The groundwater table and water flow in the subsurface zone were substantially influenced bywind waves in the lake. The groundwater table was locally uplifted near point D in the subsurface
zone in both the GDL and LRG cases (Figure 2). It is interesting that the largest increases of pressure
heads after wind waves started appeared at G4 but not at G5 in both the GDL and LRG cases due tohigh-frequency wind waves. Wave run-up further elevated the groundwater tables in the vicinity ofthe shoreline, similarly as observed in other studies [22,25,31]. Furthermore, wave run-up caused a
relatively rapid infiltration of water near point D to the subsurface zone (Figure 4b,f), which resulted
in a local uplift of the groundwater table at G4 and a relatively slow subsurface flow. The temporarily
uplifted groundwater table at G5 (near the interface) caused by wave run-up then quickly declined due
to downwards flow and seepage during other stages of the wave cycle (Figure 4a,c–e,g,h). An averageincrease of the groundwater table at G5 remained relatively lower than at G4 . Additionally, in both the
GDL and LRG cases, after wind waves occurred, zero pressure head regions were formed between
points A and C at the WT stage and between points B and C at the ML stage, which markedly differedwith those for no-wave conditions (Figure 3). Boufadel et al. [38] reported that water and solute canmove in both directions at locations where the pressure head is zero.
Many studies, including modeling and field investigations of groundwater–lake systems, reported
that seepage inflow to lakes is generally highest near the lakeshore and decreases with the distancefrom the shore, and the seepage of lake water to ground water does not occur near the shore of lakes
that are bounded by water-table mounds [2,39–41]. In this study, when wind waves occurred, seepageof lake water to groundwater increased near the shore of the lakes in the LRG case, and decreased
with the distance from the shore (Figure 5) even though water-table mounds existed (Figure 4).
In general, similarly as in other studies [2,5,10,36,39,40,42], seepage fluxes at steady-state conditions
were concentrated within a narrow band on the surface–groundwater interface, and the dischargethen exponentially decreased with the distance offshore. Our simulation results additionally showed
that, in the presence of wind waves, the exchange water fluxes were also concentrated within a narrow
band near the intersection point of the lakeshore with the lake level (Figure 5), and that this band
moved up and down along the interface with the lake water level. Gardner [43] and Gardner andWilson [44] reported for a creek–groundwater system that groundwater flow occurred primarily inthe creek bank, even when the marsh platform was inundated at high tide; at all stages of the tide theWater 2017, 9, 566

15 of 18

largest flow velocities developed just below the intersection of the tide at the creek bank, and mostflow developed within 15 m of the creek.
Wind waves in the lake increased the recharging flux from the lake into the subsurface zone
in the LRG case, but decreased the discharging flux from the subsurface zone into the lake in the
GDL case. The temporary uplift of the groundwater table (mounding) due to waves was created by
the asymmetry in the instantaneous recharging-discharging (Figure 5), with high-volume infiltration
occurring during the wave crest, followed by lower volume exfiltration during the wave trough.
This groundwater surface uplift was sufficient to temporarily reverse the direction of the waterexchange flux, as also reported in other studies [18,22,45]. Compared to the no-wave conditions, waves
modified the groundwater flow pattern and substantially increased the magnitude of the groundwaterflow velocity near the interface, suggesting that waves would induce large infiltration and exfiltration
across the interface. The waves created a steep hydraulic gradient in the subsurface zone near thelakeshore face, which substantially slowed the discharging flux into the lake in the GDL case andaccelerated the recharging flux into the subsurface zone in the LRG case (Table 2). Similar to the CEWFs
across the interface, wind waves resulted in both a more proportional chloride exchange across theupper part of the interface and a simultaneous increase in both the recharge and discharge of chloride
across the upper and lower parts of the interface, respectively. These increases were mainly ascribedto local water circulations driven by wind waves (Figure 4). Rosenberry et al. [46] reported for theGreat Salt Lake (USA) that there may be infiltration/exfiltration reversals due to waves, as well as
reversals in the flow direction across the sediment–water interface. Similarly, Longuet-Higgins [47],Lenkopane et al. [48], Wilson and Gardner [14], and Gibbes et al. [49] reported that the mean onshorepressure gradient due to wave run up drives a groundwater circulation within the beach zone. Suchcirculations substantially enhanced the local water and solute exchanges between lake water andgroundwater in both the GDL and LRG cases.
Wind waves could temporarily slow down groundwater discharge (in the GDL case) or
accelerate infiltration from the lake (in the LRG case), and the resulting local water cycles could
substantially promote the exchange of water and nutrients in the lake–groundwater system. For some
non-conservative solutes, such as nitrogen species, waves correspondingly increased the residence
time in the subsurface zone from a fishpond/paddyfield to the lake in the GDL case and consequently
changed their concentrations on the interface. As Boufadel et al. [16] and Geng et al. [22] reported,
wind waves also created additional pathways for the transport of solutes to the interface and shifted
the solute exchange zone in comparison with no-wave conditions. Had the solute concentrations in
the lake in the GDL case been lower than those in the subsurface zone, the solute concentrations near
the interface would have decreased once wind waves occurred. This diluted solute in the subsurface
zone near the interface would then be discharged into the lake by the local water circulation orwhen wind waves ceased. Several studies [1,50] have reported a decrease in solute concentrations
in downstream reservoirs driven by tidally fluctuating water levels, while solute concentrations
in groundwater were higher than those in the downstream reservoirs. As Lewandowski et al. [8]reported, the biogeochemical turnover of nitrogen is common at the reactive aquifer–lake interface,in particular when driven by local water circulations. Furthermore, local water cycles driven bywind waves activated water and solute exchange between two water bodies at the lakeshore bottom(Figures 4d,h and 8), which were previously commonly considered to be stagnant zones [51,52].
The sensitivity analysis showed that, after wind waves started, the hydraulic conductivity of
the lakeshore zone was a key factor influencing water and solute exchange between the lake andgroundwater systems, while the amplitude and period of the waves were less important. Many
studies have shown that Ks of the aquifer is a key factor influencing the subsurface flow patterns
and the exchange of water and solutes between the surface and groundwater [22]. It is interestingthat when Ks changed, in both the GDL and LRG cases, the CECFs during a one-day period did notproportionally change with the corresponding CEWFs. This could be related to the differences inchloride concentrations and in CECFs between the upper and lower parts of the interface as discussed

Water 2017, 9, 566

16 of 18

earlier (Figures 7a and 8a). Additional parameters (e.g., solute transport parameters) and scenarios(e.g., waves with different characteristics) should be considered when evaluating the effects of waves
on the interaction between a lake and the surrounding shallow groundwater.
5. Conclusions
Wind waves frequently occur on large lakes during windy seasons, producing oscillations in
the lake level and corresponding changes in the water and solute interactions between lakes andgroundwater. Our results indicate that wind waves may substantially change the subsurface flow
patterns (such as temporarily uplifting the groundwater table, increasing subsurface flow velocity, andchanging the flow direction) near the lake–groundwater interface compared to steady-state conditions.
Local water circulations were produced in the subsurface zone due to wind waves, resulting in mostwater and solutes that infiltrated from the lake into the groundwater during the wave crest being
discharged back into the lake through the lower interface during the remainder of a wave cycle.
Such water circulations driven by wind waves accelerate water and solute exchange between lakeand groundwater systems, and activate a relatively stagnant zone at the lakeshore bottom. Overall,wind waves may decrease the cumulative water and solute exchange fluxes between the lake and thesurrounding groundwater, redistribute solute concentrations on the interface in the GDL cases, andincrease them in the LRG cases, as compared to their respective no-wave conditions.
The results of the sensitivity analysis carried out using the Hydrus-2D simulations show thatthe hydraulic conductivity of the subsurface zone plays a relatively more important role in waterand solute exchange than the characteristics of the waves. The simulated results provide detailed
information both about the water and solute source/sink interactions between groundwater andnearshore lake areas, and their redistributions along the lakeshore slope during windy seasons.
Acknowledgments: The work described in this publication was supported by the National Natural Science
Foundation of China (Nos: 51579074 and 51079048), the Fundamental Research Funds for the Central Universities(No: 2009B16914), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD),
and the China Scholarship Council. The authors would like to thank two anonymous reviewers for providing
thoughtful comments that helped us to significantly improve the manuscript and the editors for their careful andresponsible work.
Author Contributions: Yong Li conceived and designed the experiments; Shuang Wang, Weiwei Zhang, andJiahui Yuan performed the experiments; Shuang Wang, Weiwei Zhang, and Jiahui Yuan analyzed the data; Yong Li
and Jirka Šimůnek contributed reagents/materials/analysis tools; Yong Li and Jirka Šimůnek wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.

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