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\begin{document}
\title{Seasonal variation of infiltration rates through pond bed in a managed
aquifer recharge system in St-Andr\selectlanguage{ngerman}é, Belgium\selectlanguage{english}}
\author[1]{Sayantan Samanta}%
\author[2]{Zhuping Sheng}%
\author[3]{Clyde Munster}%
\author[4]{Emmanuel Houtte}%
\affil[1]{Texas A\&M University College Station}%
\affil[2]{Texas Agrilife Research}%
\affil[3]{Texas A\&M University}%
\affil[4]{Intermunicipal Water Company of the Veurne Region (IWVA)}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
In Belgium, IWVA uses Managed Aquifer Recharge (MAR) to recharge the
aquifer with treated wastewater generated from the communities to
sustain the potable water supply on the Belgian coast. This MAR facility
is faced with a challenge of reduced infiltration rates during the
winter season when pond water temperatures near 4 \selectlanguage{ngerman}°C. This study
involves the identification of the predominant factor influencing the
rate of infiltration through the pond bed. Several factors including
pumping rates, natural recharge, tidal influences of the North Sea and
pond-water temperature were identified as potential causes for variation
of the recharge rate. Correlation statistics and linear regression
analysis were used to determine the sensitivity of the infiltration rate
to the aforementioned factors. Two groundwater flow models were
developed in visual MODFLOW to simulate the water movement under the
pond bed and to obtain the differences in flux to track the effects of
variation of hydraulic conductivity during the two seasons. A 32 \%
reduction in vertical hydraulic gradient in the top portion of the
aquifer was observed in winter causing the recharge rates to fluctuate.
Results showed that water temperature caused a 30 \% increase in
hydraulic conductivity in summer as compared to winter and has the
maximum impact on infiltration rate. Cyclic variations in water
viscosity, occurring because of seasonal temperature changes, influence
the saturated hydraulic conductivity of the pond bed. Results from the
models confirm the impact on infiltration rate by temperature influenced
hydraulic conductivity.%
\end{abstract}\selectlanguage{ngerman}%
\sloppy
\textbf{1. Introduction}
Managed Aquifer Recharge (MAR) is a relatively new method to increase
potable water supplies in Belgium. MAR provides a sustainable solution
to increasing water supply, without compromising the water quality, and
often uses treated wastewater, agricultural return flows or excess water
from streams (Massmann et al., 2008). The main objective of the St-Andr\selectlanguage{ngerman}é
MAR facility is to meet the water demands of the surrounding area,
replenish the overexploited aquifer and restore the groundwater table in
the unconfined dune aquifer (Vandenbohede, Van Houtte, \& Lebbe, 2008a).
Infiltration rate (IR) is the most important parameter controlling
recharge capacity in the St-André Managed Aquifer Recharge facility. A
higher infiltration rate through the pond bed signifies better recharge
capacity and in turn increase groundwater availability (Sheng \& Zhao,
2015). However, data collected from this facility reveals that the
infiltration rate is lower in the winter and higher in the summer
(Vandenbohede \& Houtte, 2012), indicating that the total volumes of
water recharged by the MAR system are lower during the winter.
The variation of the vertical flow velocity of groundwater may occur as
a result of changes in aquifer properties such as lower hydraulic
gradient, reduced hydraulic conductivity of aquifer media and reduced
leakance through pond bed occurring as a result of reduced conductivity
of the bed during the winter. Suzuki (1960) and Stallman (1965) started
the development of computation of infiltration rates from observed
temperatures near the land surface with the idea that low temperatures
are effective at reducing hydraulic conductivity of the soil media.
Constantz, Thomas, \& Zellweger (1994) studied the influence of diurnal
variations in stream temperature on streamflow loss and groundwater
recharge. They observed a trend of diurnal variation of stream
temperature and seepage and hypothesized that the two are related and
that regardless of timescale, a significant change in stream temperature
can cause a measurable response in seepage loss in a reach. Their study
yielded to the conclusion that a fluctuation in stream temperature
changes the hydraulic conductivity of the underlying sediments in a
losing stream. The temperature of streambed layer is controlled by the
temperature of the stream and is dependent on factors such as depth,
thickness, degree of saturation and rate of flow of water through it.
For both reaches, the predicted influence of stream temperature on
hydraulic conductivity of bed accounted for all the variation in the
seepage loss. Similar behavior was reported again by Constantz and
Thomas (1997), Constantz (1998), and Heilweil and Watt (2011).
Lin, Greenwald, \& Banin (2003) stated that infiltration rates (IR) in a
large-scale effluent recharge facility can be affected by factors such
as physical clogging, biological clogging, temperature variations,
entrapped air, dispersion and the swelling of clay. With the assumption
that all factors controlling IR are constant and only temperature is the
variable property, they studied the impact of temperature in the
variation of infiltration rate through a natural porous media. Based on
the hypothesis that relative infiltration rate is driven by temperature
or temperature-controlled properties such as density and viscosity, the
study could generate expression of IR in terms of viscosity at a given
temperature with reference to 25°C. However, the entire variability of
IR could not be accounted for with just viscosity and changes in
entrapped air content was stated as an alternate explanation to the
variation of IR. Similar study has been published by Braga, Horst, \&
Traver (2007) on the effect of temperature on the infiltration rate
through an infiltration basin BMP (best management practice) to develop
a methodology to simulate varying infiltration rates. The study has been
done though a model that uses Green-Ampt equation for infiltration,
assuming that all precipitation inputs the system and the only outflow
from the system is infiltration. Also, it is assumed that there is no
infiltration through the sidewalls of the BMP. The modified Green-Ampt
equation used in this paper assumes that there is no ponding at the
surface such that the infiltration rate is always the infiltration
capacity. Braga et al. (2007) shows a strong relationship between
hydraulic conductivity and mean bed temperature. They found that during
warmer period the infiltration rate increases by as much as 56\%.
Racz, Fisher, Schmidt, Lockwood, \& Huertos (2012) studied the spatial
and temporal infiltration dynamics during managed aquifer recharge (MAR)
and noticed a seasonal trend in hydraulic conductivity variation. The
study reported that the daily temperature of water reduced in amplitude
and shifted in phase as depth from surface increased. However, Racz et
al. (2012) did not consider any possible relation between temperature
and hydraulic conductivity variation and was more interested in the
various possibilities that could generate spatial and temporal
variations in the MAR system. This study suggested that variable source
area concept can be extended to infiltration as a framework for
describing spatial and temporal variability.
(Loizeau et al., 2017) have studied the combined involvement of water
temperature and air entrapment on infiltration rate variations at a
scale of infiltration basins. They employed both experimental design and
modelling work to address the issue. The key assumption made for this
study was that when one component or an ensemble of components are
analyzed for their impact on hydraulic conductivity, all other factors
are treated as constants. Their primary hypothesis was that the basin
response to infiltration is dependent on temperature contrast between
surface and groundwater and on air entrapped in the porous media. The
study involved three infiltration experiments for injection of warm and
cold surface water at an initial dry basin and injection of temperate
surface water in an initially wet basin. Unsaturated and saturated flow
models were developed using the 2D Richards equation. The experiments
and model simulations verified that temperature-contrast and air
entrapment could significantly impact infiltration rates and the effects
are similar in magnitude. Loizeau et al. (2017) showed a very critical
understanding of variation of infiltration rates from a management point
of view by stating that all temporary reduction in rates should not be
attributed to clogging. There are multiple ways of misinterpretation of
infiltration rates and the measurements must be made for a long enough
time to show some trends in variation.
Vandenbohede and Houtte (2012) studied the influence of temperature
variation of infiltration water in the managed aquifer recharge facility
in Belgium and stated that temperature variations have a number of
consequences on the operation and management of the MAR system. They
made a few hypotheses justifying the variation of infiltration rates
such as temperature variations causes change in hydraulic conductivity
since pore water density and viscosity are temperature dependent;
temperature can be used to study residence time of infiltrated water,
which was causing fluctuation in infiltration rates; and that recharge
water had in most cases a different composition than the pore water
triggering a number of reactions which are influenced by temperature.
The paper employed a hypothetical 2D groundwater flow and heat transport
model to test 5 alternating scenarios which would represent different
temperature conditions and inflow/extraction rate in the system.
MOCDENS3D in combination with SEAWAT was used to simulate the conditions
of St-André MAR system. Results of the flow and transport model were
compared to time series of hydraulic head in observation wells, of
chloride concentration in the extraction wells and of temperature
observations in observation wells. It was found that placing the
extraction wells deeper or lowering the extraction to infiltration ratio
for a given system, increased the temperature influence outside the well
battery but remained limited to the immediate vicinity of the MAR
system. Heat conduction smoothened the temperature variations in the
aquifer. Close to the pond and in the shallow part of the aquifer,
short-term temperature variations of the infiltration water persisted.
Temperature variations influence hydraulic conductivity, and this
resulted in a larger infiltration capacity in summer than in winter by
1.7 times.
The motive of this paper was to provide a process-based understanding of
the variation of infiltration rates and indicate the factors that
influence this variation by using statistical and numerical models for
different seasonal scenarios. The objectives were to (a) identify
possible factors that influence the variation in infiltration capacity
in this site, (b) develop a relationship between the predominant factor
and the infiltration rate, and (c) develop MODFLOW models to simulate
water movements below the ponds and assess hypothetical scenarios for
summer and winter to verify flux and flow velocity during the two
seasons. Finally, a quantitative evaluation was provided to account for
the variations in the recharge rates.
\textbf{2. Material and Methods}
In this study, changes in hydraulic gradient due to natural recharge,
and changes in hydraulic conductivity of pond bed due to
temperature-induced water viscosity were quantified. Two groundwater
flow models were developed to identify variations in the average linear
vertical flow velocities of water with variations in hydraulic
conductivity of pond bed occurring over time. This study used observed
data from St-André, Belgium to understand the water movement below the
infiltration basin and the seasonal variation of hydraulic conductivity
under different seasonal conditions. Additionally, it was assumed that
the infiltration ponds are connected to the groundwater, therefore there
is no unsaturated zone between the ponds and the groundwater table.
2.1 Study Area
The MAR facility is located on the west coast of Belgium, close to the
French-Belgium border (Fig. 1). The recharge pond is located on the
dunes of the western Belgian coastal plain. The dune extends inland by 2
km to 2.5 km and has a surface elevation ranging from 6 mTAW to 35 mTAW
(mTAW is the reference level corresponding to the mean low tide level,
calculated as 2.36 m below mean sea level; mTAW is a standard Belgian
reference). The mean thickness of the Quaternary phreatic aquifer under
the entire region is 30m. The confining layer of this aquifer is a 100m
thick clay layer, which is of the Eocene age and is considered
impermeable in this study. The upper part of the aquifer consists of
yellow Aeolian dune sands having considerable amounts of organic matter
in it. A larger part of the aquifer is comprised of fine medium sand
with occasional presence of silty and fine clayey sand lenses. The lower
part of the aquifer consists of medium to coarse-medium sand pertaining
to Eemian age (Vandenbohede, Van Houtte, \& Lebbe, 2008b).
The WPC Torreele produces infiltration water from the effluent of the
Wastewater Treatment plant of Wulpen (operated by Aquafin). This
infiltration water is pumped to the St-André MAR facility through a 2.5
km long pipeline (Van Houtte \& Verbauwhede, 2012) where it supplies an
artificial infiltration pond (recharge method) with a surface area of
18,200 m2. The infiltration pond recharges an unconfined sandy dune
aquifer (storage space) and water is then recovered from this aquifer
using 137 wells (recovery facilities) which surround the pond. The
recovered water is then used for municipal water supplies (end use)
after aeration step, rapid sand filtration and UV disinfection
(post-treatment) (Van Houtte \& Verbauwhede, 2012). The schematic
diagram of the processes involved in the St-André MAR facility are shown
in fig. 2.
\textbf{Fig. 1} Location of Wulpen wastewater treatment plant (WWTP),
and St-André Managed Aquifer Recharge Facility
\textbf{Fig. 2} Process of St-André Managed Aquifer Recharge Facility
2.2 Observed data at St. Andre MAR facility
Temperature and groundwater elevation data were obtained from the
monitoring wells using the transducers. The monitoring wells are
represented as WP, which is the abbreviation of Dutch words ``Waarneming
Putten'', meaning observation wells. The convention used for numbering
the wells are shown in fig. 3. All monitoring wells have a series of 4
levels of well with screen openings at different depths. The level 1
wells have screens at -20 mTAW, which are the deepest wells and level 4
wells are the shallowest wells having screens at 3.55 mTAW. Level 2
wells are located at a depth of -5 mTAW and level 3 wells are at 0.55
mTAW. The negative mTAWs indicate that they are below the standard
reference of low tide sea level and the positive mTAWs are above the
reference elevation. The ground elevation around the pond is 7.1 mTAW
and the pond bed elevation is 6.2 mTAW. However, the obtained data had
periods of missing information. To combat this problem, Genetic
Programming (GP) was employed. GP is a form of evolutionary algorithm,
which is a component of machine learning. GP is a powerful tool, which
employs non-linear regression to develop a relationship between
variables with very little domain knowledge (Koza, 1994). The
statistical indices used for evaluating the efficiency of the model are
coefficient of determination (R2) and Nash-Sutcliffe Efficiency (NSE).
Temperature data of water in the infiltration ponds are available from
January 2014 to June 2015 and from April to June 2016. For the missing
period, Genetic Programming (GP) was employed to develop a non-linear
relationship between minimum and maximum air temperatures with water
temperature in the infiltration ponds. Fig 4 shows the equation tree
consisting of numeric operators and 2 variables, X1 and X2. X1 is the
minimum air temperature, X2 is the maximum air temperature and Y is pond
water temperature.
\textbf{Fig. 3} Schematic reference of well screen depths at St-André
MAR site
\textbf{Fig. 4} Genetic Programming equation tree for prediction of pond
water temperature. X1 is the minimum air temperature, X2 is the maximum
air temperature and Y is pond water temperature
2.3 Hydraulic gradient analysis
Contours of groundwater elevations have been developed using data
obtained from monitoring wells around the pond at elevations -5 mTAW and
-20 mTAW. Four days have been selected to monitor the contours, two
representing winter conditions (01/19/2015 and 01/11/2016) and two
representing summer conditions (07/13/2015 and 07/19/2016). The contours
help in visualizing the groundwater elevations as well as the direction
of water flow. The flow of groundwater occurs in two distinct
directions, i.e. radially outwards from the infiltration ponds to the
pumping wells and radially inwards from the area outside the pumping
wells towards the pumping wells.
Vertical hydraulic gradients are calculated using heads at elevations
3.55 mTAW (approximately 3 m below the surface), 0.55 mTAW (approx. 6 m
below the surface) and -5 mTAW (approx. 11.5 m below the surface) at
well series WP 21, 22, 23 and 24 surrounding the infiltration ponds.
Analysis has been done on the average heads for the summer months (JJA)
and the winter months (DJF) for 2015 and 2016. The variation of
hydraulic heads with different seasons is also reflected on the vertical
hydraulic gradient. WP 6.2 is assumed to reflect the conditions exactly
underneath the ponds as it is located centrally between the two ponds.
Vertical hydraulic gradient has been calculated between WP 6.2 and the
pond bed to observe the variation of vertical gradient between summer
and winter
2.4 Statistical analysis methods
Infiltration rate through pond bed was calculated by eq. 1, derived from
water budget.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ \textbf{~}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
\(q=\frac{Q}{A}+\frac{\text{dH}}{\text{dt}}-E+P\)~ ~ ~ (\textbf{1)}\tabularnewline
\bottomrule
\end{longtable}
Where, \emph{q} is the infiltration rate (m/day), \emph{Q} is the
measured inflow to the pond (m3 day-1), \emph{A} is the surface area of
the pond (m2), \emph{H} is the ponding depth (m), \emph{t} is time
(day), \emph{E} is evapotranspiration (m day-1) and \emph{P} is
precipitation (m day-1). Evaporation from the ponds has been calculated
as evapotranspiration using Hargreaves method (Hargreaves \& Samani
1985). Linear regression analysis has been used to analyze the
sensitivities of (1) Natural recharge, (2) Tidal effect of North Sea,
(3) Pumping rate and (4) Pond water temperature on infiltration rate.
Natural recharge varies seasonally as it is influenced primarily by
precipitation and has been hence considered in the study. Tidal effect
is suspected to have some impact on the groundwater levels since the
site is very close to the North Sea. The shifting of saltwater --
freshwater boundary may cause variation in daily groundwater levels in
the area. Pumping rate is the main driving force in the movement of
water in this system and has high potential to influence groundwater
levels and infiltration rates. Temperature of water controls the
fluidity of water and might have an impact on the hydraulic conductivity
of the soil.
Natural recharge has been calculated by the SCS curve number method
(Mockus, 2004). The area adjacent to the pond is a grassland with little
vegetation and has dune soil. According to the hydrologic soil group
(HSG) classification, the soil in this area represents group A which
signifies lower runoff (Mockus, 2004). The curve number for this soil
type and land use is 39 (NRCS, 1986). Calculation of natural recharge
requires the potential of maximum retention and initial abstraction to
obtain the contribution of rainfall to runoff and infiltration.
Tidal effects are evaluated by using daily sea level information
obtained from sea level station monitoring facility at Oostende, which
is 21 km away from the St-Andr\selectlanguage{ngerman}é MAR facility, along the coast of North
Sea. Pumping rates and water temperature have been measured on site by
the IWVA (Intercommunal Water Company of Veurne-Ambacht), who manages
this site. Viscosity and density are two factors that are directly
influenced by temperature. Dynamic viscosity of water is calculated
using the International Association for the Properties of Water and
Steam 1997 (IAPWS 97) and density of water is calculated using the
equation given by Maidment (1993).
The aforementioned parameters were analyzed using single variable linear
regression to develop a relationship between two variables by fitting a
linear equation individually to each observed parameter. Coefficient of
determination (R2) has been used as a statistical measure to judge the
sensitivity of infiltration rates to the parameters. A second method of
multivariate regression was used to verify the findings, where the
sensitivities of parameters are assessed in combination. For this
method, p- value has been used as the statistical measure, such that the
variable with the lowest p-value is the most sensitive. A p-value of
0.05 indicates a 95\% probability of the variable to have some effect on
the parameter it is being compared to (Abbaspour, 2007).
2.5 Visual MODFLOW Model description of MAR System
Visual MODFLOW was used in this study to develop a groundwater flow
model representing the area close to the infiltration ponds for the
period of January 2015 to March 2016 to verify the variation of
infiltration rates. Two models were developed to represent the
conditions for summer and winter seasons. Constant pumping and
infiltration rates were used in each model to observe the impact of
leakance through pond bed. The primary objective is to observe the
modelled heads at the location of the monitoring wells and verify how
closely they match the observed heads under controlled circumstances.
The model area is 1100 m long, 630 m wide and is centered on the
infiltration ponds. The model has been slightly rotated to match the
north boundary to the coast of North Sea (fig. 5). It is divided into
110 columns and 63 rows each cell having a 1 m x 1 m area. The aquifer
thickness is 31 m and is divided into 32 layers. All layers are of 1 m
depth except for between 3 and 4 mTAW where they are of 0.5 m depth. The
sources of water in this model are recharge through the pond beds and
natural recharge in the area. There are 137 extraction wells surrounding
the ponds, which act as the sinks.
\textbf{Fig. 5} Layout of St-André MAR MODFLOW model
The hydraulic conductivity and specific yield of the layers have been
set based on borehole measurements obtained at the location of WP6 and
from the parameters used in previously developed models for the area
(Vandenbohede \& Houtte, 2012). A low permeable zone was introduced in
the model just under the bed of both ponds to match the effect of
vertical gradient in the area. Vandenbohede et al. (2008b) also
mentioned the presence of a low permeable layer under the west pond.
Fig. 6 shows a two-dimensional vertical cross-section of the model with
the various hydraulic conductivity zones with hydraulic conductivity
values as shown in Table 1. Boundary conditions have been set based on
groundwater flow models developed previously for St-André MAR facility
(Vandenbohede \& Houtte, 2012) and from the groundwater flow analysis
from this study.
MODFLOW Lake package (LAK3) has been used to model the infiltration
ponds in both models. The lake bottom is at 6.24 mTAW. The average
precipitation is 345 mm/year and the evaporation are 450 mm/year in both
the models. Heads have been simulated at monitoring wells WP 6.2, WP
22.2 and WP 42.2. Both the models have been calibrated to match the
heads in the aforementioned monitoring wells. The variations of
hydraulic conductivity of the pond bed has been implemented in the
models by changing the leakance parameter. Pond bed leakance is
expressed as (eq. 2),
\par\null
\(L=\frac{K_{z}}{b}\)~ ~ ~\textbf{(2)}
Where, \emph{L} is leakance (day -1), \(K_{z}\) is vertical
hydraulic conductivity and b is the thickness of pond bed.
\textbf{Fig. 6} Zones of hydraulic conductivity in the model
\textbf{Table 1} Hydraulic conductivity zones used in the models
2.5.1 Groundwater flow conceptual model representing summer conditions
The first MODFLOW model developed for the summer months
(June-July-August) using conditions from summer (JJA) of 2015 uses a
North-South constant head boundary of 3.5 mTAW based on the analysis of
heads in section 3.2.1. The East-West boundary is defined as a general
head boundary in reference to the mean lake stage during this period. A
constant pumping rate of 8,400 m3day-1 and an inflow rate of 6,080
m3day-1 has been used for this model, which represents the mean pumping
rate and inflow rate during this period. The mean observed lake stage is
6.9 mTAW. Leakance through pond bed is set as 0.39 day-1, which is 30 \%
higher than the leakance of pond bed in winter corresponding to the
findings of impact of fluidity on hydraulic conductivity of the pond
bed.
2.5.2 Groundwater flow conceptual model representing summer conditions
A second MODFLOW model has been developed for the winter months
(December-January-February) using conditions from winter (DJF) of
2015-2016. It uses a constant head North-South boundary of 4 mTAW and
the East-West boundary is a general head boundary which follows the mean
lake stage during this period. The pumping rate is set at 7,000 m3day-1
and the inflow rate to the lake is 4,310 m3day-1. The mean observed lake
stage is 6.97 mTAW and pond bed leakance is 0.30 day-1.
\textbf{3. Results and Discussion}
3.1 Groundwater flow analysis
The infiltration ponds are the primary source of water in the area
between the ponds and pumping wells. The pumping wells adjacent to the
ponds create a barrier to the flow of water around the ponds.
Groundwater level contours have been developed at a depth of -5 mTAW
(level 2 wells), focusing only on the area between the ponds and the
pumping wells. The flow in this region is outwards from the ponds
towards the pumping wells. Fig. 7 shows the variation of groundwater
elevations between summer and winter months. The contours have higher
values in winter 2015 and 2016 (fig. 7.a and 7.c). Groundwater heads are
lower during summer 2015 and 2016 (fig. 7.b and 7.d) indicating a higher
vertical gradient between the pond and the aquifer, thereby increasing
the flow rate. The direction of flow does not change much over time.
However, the horizontal gradient is observed to increase in summer in
the northern parts of the infiltration ponds. This hints towards a
higher flow rate in summer.
\textbf{Fig. 7} Contour of hydraulic head near the infiltration ponds at
-5 mTAW (Level 2 monitoring wells) during: i) Winter 2015 (01/09/2015),
ii) Summer 2015 (07/13/2015), iii) Winter 2016 (01/11/2016) and, iv)
Summer 2016 (07/19/2016)
Groundwater level contours at a depth of -5 mTAW (Level 2 monitoring
wells) are shown in fig. 8 and the same at -20 mTAW (Level 1 monitoring
wells) is shown in fig. 9 for a larger area near the ponds. It can be
observed from the contours that the hydraulic heads around the pumping
wells are higher during the winters (fig. 8.a, 8.c, 9.a and 9.c) and
lower during the summers (fig. 8.b, 8.d, 9.b and 9.d). Similar effect
can be observed in groundwater elevations at Level 1 monitoring wells
located at -20 mTAW elevation. The groundwater flow is radially inwards
towards the location of the pumping wells. The average horizontal
gradient in winter is 7.21E-03 whereas that in summer is 8.90E-03 for
the level 2 wells and in level 1 wells, the average horizontal gradient
in winter is 1.19E-03 whereas that in summer is 1.40E-03 (fig. 10). Both
the well levels indicate higher flows from the dunes or areas outside
the boundary of pumping wells towards the pumping wells in summer than
those in winter.
\textbf{Fig. 8} Contour of hydraulic head at -5 mTAW (Level 2 monitoring
wells) around the pumping wells during: i) Winter 2015 (01/09/2015), ii)
Summer 2015 (07/13/2015), iii) Winter 2016 (01/11/2016) and, iv) Summer
2016 (07/19/2016)
\textbf{Fig. 9} Contour of hydraulic head at -20 mTAW (Level 1
monitoring wells) around the pumping wells during: i) Winter 2015
(01/09/2015), ii) Summer 2015 (07/13/2015), iii) Winter 2016
(01/11/2016) and, iv) Summer 2016 (07/19/2016)
\textbf{Fig. 10} Horizontal gradients between dunes and pumping wells
Between 3.55 mTAW and 0.55 mTAW elevation, the hydraulic gradient is
higher in summer than that in winter for the WP 21, 23 and 24 monitoring
wells (fig 11). However, at WP 22, the winter of 2016 showed a higher
gradient than the summer gradients. This may be attributed to a less
permeable soil lens present in the area. WP 21 shows very high hydraulic
gradients in both summer and winter, suggesting the presence of a less
permeable lens in the area between 3.55 and 0.55 mTAW in the northern
side of the west pond. The occurrence of a shallow low-permeable layer
under the western pond is also mentioned by Vandenbohede et al. (2008a)
between 3.55 and 0.55 mTAW, even though the lateral extent of the layer
in unknown.
\textbf{Fig. 11:} Vertical hydraulic gradient in Well series 21, 22, 23
and 24 for 2015-2016 period between Level 4 (3.55 mTAW) and Level 3
(0.55 mTAW) wells
\textbf{Fig. 12} Vertical hydraulic gradient in Well series 21, 22, 23
and 24 for 2015-2016 period between Level 3 (0.55 mTAW) and Level 2 (-5
mTAW) wells
Between 0.55 mTAW and -5 mTAW elevation, there is not much variation in
gradients (fig 12). The lower part of the aquifer has lower hydraulic
conductivity (Vandenbohede et al., 2008b). From the regional groundwater
model and the existing local groundwater model (Vandenbohede \& Houtte,
2012), it is inferred that the hydraulic conductivity is approximately
20 m day-1 at the top of the aquifer and 1 m day-1 at the bottom. In WP
23, the summer gradients are higher than the winter gradients. This
occurrence is due to the high anisotropy in the region.
WP 6.2 is assumed to reflect the conditions exactly underneath the ponds
as it is located centrally between two ponds. Vertical hydraulic
gradient has been calculated between WP 6.2 and the pond bed to observe
the variation of vertical gradient between summer and winter. Fig. 13
shows that the gradients are higher for summer of 2015 and 2016 in
comparison to the winter of 2015 and 2016. This also suggests that the
rate of infiltration through pond bed is higher in summer as compared to
that in winter.
\textbf{Fig. 13} Vertical hydraulic gradient between WP 6.2 and pond bed
Assuming hydraulic conductivity does not change over time, the rate of
vertical flow is directly proportional to the change in vertical
hydraulic gradient (eq. 2).
\(q\propto i\)~ ~ ~\textbf{(2)}
During the summer season, a lowering in hydraulic head is observed
followed by an increase in vertical gradient. As a result, the vertical
flow velocity is expected to be higher in summer. During the winter, the
reverse phenomenon is observed. As the hydraulic head rises, the
vertical gradient lowers and flow velocity reduces. It is seen from the
vertical hydraulic gradients at WP 6.2 that the hydraulic gradient
reduces considerable in winter as compared to that in summer.
The average reduction in regional vertical hydraulic gradient in winter
as compared to summer is 32 \% from 3.55 to 0.55 mTAW depth and 4 \%
from 0.55 to -5 mTAW. However, Vandenbohede \& Houtte (2012) reports
that the reduction of infiltration capacity in winter ranges from 33 -
50 \%. Thus, the variation in vertical hydraulic gradient alone does not
contribute to the overall fluctuation of infiltration rates. Hence, the
assumption that hydraulic conductivity is constant over time does not
stand valid and it is essential to take into account the variability of
hydraulic conductivity as well.
3.2 Factors influencing infiltration rate
Four factors namely, natural recharge, tidal effects of North Sea,
pumping rate of the MAR facility and pondwater temperature have been
analyzed using single regression analysis and multivariate regression
analysis. Coefficient of determination (R2) indicated the role of each
parameter in the variation of infiltration rates in the single variable
simple regression approach and for multivariate regression approach,
p-value provided the sensitivities of the parameters. From the single
linear regression analysis, it is observed that natural recharge and
tidal effect of the North Sea do not significantly affect the
infiltration rate (figures 14.a and 14.b). However, daily pumping volume
and water temperature show a positive correlation (figures 14.c, 14.d)
with infiltration rate. Temperature shows the highest correlation of
0.42 with infiltration rate whereas pumping rates have a correlation
coefficient of 0.23. From this test, it is inferred that temperature is
the most influencing factor in the seasonal variation of infiltration
rate through the pond bed.
\textbf{Fig. 14} Linear regression plot for i) natural recharge vs
infiltration rate, ii) daily sea level vs infiltration rate, iii) daily
pumping rate vs infiltration rate, and iv) daily pondwater temperature
vs infiltration rate
On performing a multivariate analysis of the 4 factors, the following
relation (eq. 3) has been obtained:
\(y=0.1094+0.0035\ x_{1}+0.0255x_{2}+{5.41\times 10^{-6}x}_{3}+0.0053x_{4}\)~ ~\textbf{(3)}
Where \emph{y} is predicted infiltration rate, \emph{x1} is natural
recharge, \emph{x2} is daily sea level in the North Sea, \emph{x3} is
daily pumping rate and \emph{x4} is mean daily pond water temperature.
Table 2 shows the statistics of the multivariate regression analysis and
it is observed that the pond water temperature (variable x4) shows the
least p-value of \textless{} 2E-16 and the highest coefficient among all
other parameters. From fig. 15, it can be seen that the observed and
predicted infiltration rate shows a fairly good match with a coefficient
of determination of 0.4382. However, there are a few outliers in the
observed infiltration rates, which may be attributed to human errors
involved in the process of data collection for the parameters required
for calculation of infiltration rates. Also, the outliers might have
originated at the time of scheduled maintenance and cleaning of the
infiltration ponds. It is conclusive from the tests that temperature is
a dominant factor in influencing the infiltration rate across the pond
bed.
\textbf{Table 2.} Components of multivariate linear regression to obtain
infiltration rate
\textbf{FIg. 15} Observed vs Predicted infiltration rate obtained after
multivariate regression analysis
It was found that temperature has the most influence in the variation of
infiltration rates across the pond bed. This can also be visually
verified from fig 16. Temperature follows a sinusoidal pattern
(Vandenbohede \& Houtte, 2012) and infiltration rate is also seen to
follow a cyclic pattern where the highest rates are observed in summer
and lowest in winter. The R2 between temperature and infiltration rate
is 0.424.
Viscosity and density of water are the two derivate properties of
temperature. Sensitivities of density and viscosity on infiltration rate
are checked by using linear regression. It is necessary to know which
component of temperature is responsible for temperature to be the
dominant factor controlling the variation of infiltration rate. From
figures 17.a and 17.b and 18, it is seen that with an increase of both
viscosity and density of pond water, the rate of infiltration through
pond bed decreases. However, the R2 between viscosity and infiltration
rate is higher than that of density and infiltration rate.
~
\textbf{Fig.} \textbf{16} Comparison of mean daily pond water
temperature and infiltration rate through pond bed
~
\textbf{Fig. 17} Regression analysis for density of water vs
infiltration rate through pond bed
~
~~~~~~~~~~~ Following Muskat's~ relation between hydraulic conductivity
and intrinsic permeability (Muskat, 1937), hydraulic conductivity can be
expressed as a function of temperature of water (eq, 4), assuming
intrinsic permeability of the pond bed to be constant over time.
\par\null
\(K\left(T\right)=K_{\text{ref}}\times\ \frac{f\left(T\right)}{f\left(T_{\text{ref}}\right)}\)~\textbf{(4)}
\textbf{}
where, \emph{K(T)} is the hydraulic conductivity at a
temperature\emph{T}°C,\(K_{\text{ref}}\) is the hydraulic conductivity
at a reference temperature ( \(T_{\text{ref}}\)) and f is the kinematic
fluidity of water which is also a function of temperature.
The mean temperature of infiltration water is 15 °C. The upper quartile
(3rd quartile) of pond water temperature provides the reference for the
average hydraulic conductivities in summer and the lower quartile (1st
quartile) provides reference for the winter conductivities. The upper
quartile of pond water temperature is at 9.3 °C and the lower quartile
is at 21 °C. After fitting these values to equation 8, it is observed
that the hydraulic conductivity increases by 15 \% in summer and
decreases by 14.7 \% in winter. In other words, there is a 30\% increase
in hydraulic conductivity of the pond bed in summer as compared to that
in winter. The change in hydraulic conductivity is not constant through
the entire soil profile since the temperature variation with depth is
not uniform. According to (Vandenbohede \& Houtte, 2012), the
temperature of water changes as it moves down, which is influenced by
the existing groundwater residing in the aquifer. Temperature becomes
constant after a depth of 25 m below the ground surface. Hence, the
influence of temperature is predominant only close to the ground
surface.
3.3 Groundwater flow model of the MAR System
WP 6, WP 22 and WP 42 are the monitoring wells located within the
pumping well barrier and have been used to observe the impact of
variation infiltration rates for summer and winter. Figures 18.a and
18.b show the comparison between simulated heads with summer conditions,
heads with winter conditions and observed heads. A satisfactory fit is
obtained between the observed and simulated heads in summer months for
the summer model as well as in the winter months for the winter model in
all the wells (table 3). The maximum Darcy velocity through the recharge
ponds in winter is 0.22 m day-1 whereas in summer the maximum Darcy
velocity is 0.31 m day-1.
\textbf{Table 3} Statistical indices showing goodness of fit of the two
groundwater flow models at different monitoring wells
\par\null
\textbf{Fig. 18} Observed vs simulated heads from MODFLOW model at
Torreele MAR facility. a) Results from summer model during summer months
(JJA); b) Results from winter model for winter months (DJF)
The models have been developed with constant pumping and infiltration
rates to match the respective seasons. The target of these two models is
to depict the impact of leakance on the recharge rate and the flow
velocity. Leakance is proportional to the hydraulic conductivity of the
pond bed. The summer model uses a leakance value which is 30\% higher
than the leakance value of winter corresponding to the 30\% rise in
hydraulic conductivity of the pond bed during the summer months. The
results obtained from the two models at the respective time zones show a
good match. The combined RMSE is 0.74 for WP 22.2, 0.66 m for WP 42.2
and 0.39 for WP 6.2. The variation in accuracy is caused due to the
spatial variation of hydraulic parameters in soil. WP 42.2 and WP 22.2
show a higher RMSE as the model assumes a single value for the hydraulic
parameters for a single layer. However, WP 6.2 shows a fairly good match
as it is located very close to the ponds and it reflects the vertical
flux well.
The residence time of water is responsible for the high RMSE in the
models. The response of the heads in WP 6.2 to the change in temperature
conditions is faster than the other two. The heads in WP 6.2 in December
fairly relates to the simulated heads in the winter model. However, in
WP 22.2 and WP 42.2 the heads in December are very low and they
correspond to the heads in summer scenario. This may be attributed to
the distance travelled by the water before it reaches the pumping wells.
The variation in residence time occurs due to the presence of a low
permeable soil layer on the north side of the west pond. The overall
deviation in observed and simulated heads from the models are due to the
fact that hydraulic conductivity is constantly varying with time as
temperature changes. However, in the models, the conductivity values
have been kept constant all throughout each season.
It is observed from the hypothetical scenarios that the mean Darcy
velocity through the pond bed during summer is 0.31 m day-1 and that
during the winter is 0.22 m day-1 which is at par with the observed
recharge rates as calculated. This velocity can also be accounted as the
seepage rate or recharge rate. The reduction in winter recharge rate is
hence reduced by about 27 \%. This suggests that the variation in
observed heads is partly influenced by leakance, which is proportional
to the hydraulic conductivity of the pond bed.
\textbf{4. Conclusion}
The overall objective of this study was to identify the primary factor
responsible for the seasonal variation of recharge rate from the
infiltration ponds at the St-André MAR facility in Belgium. Infiltration
rates across the pond bed have been studied for a period of 2 years and
lower infiltration rates have been noticed in the winter months. Two
major factors impacting the variability of infiltration rates are the
alterations in vertical hydraulic gradient and hydraulic conductivity of
pond bed.
Observed heads at the monitoring wells are mostly found to be higher in
winters and lower in summers, creating a higher gradient in summers. A
32 \% reduction in vertical hydraulic gradient observed in the top
portion of the aquifer directly influenced the recharge rates. Regarding
the variation of hydraulic conductivity, temperature has been identified
as the dominant factor influencing this process. Results show that there
is a strong correlation between temperature and infiltration rate on a
daily scale. The temporal variation of temperature causes variation in
kinematic viscosity. With increase in viscosity of recharge water,
higher resistance is imparted by the pond bed to the flow of water.
In addition, the temperature of water influences the hydraulic
conductivity of the soil. With the data obtained from the St-André MAR
site, it is theoretically found that there is a 30 \% increase in
hydraulic conductivity in summer as compared to that in the winter.
Lowering of temperature causes a reduction in hydraulic conductivity,
thereby providing additional resistance to the flow of water through the
pond bed. MODFLOW models have been used to simulate different conditions
for summer and winter and it is found that with a lower leakance of the
pond bed in the winter months, the recharge rate decreases by about 27
\%.
Temperature of recharge water changes as it moves into the subsurface
and it is highly influenced by the previously residing water.
Temperature at different depths in the aquifer creates a definite
response in the hydraulic conductivity of the media. Lack of temperature
data at multiple depths hindered the study of the impact of groundwater
temperature on the soil properties. This can be a scope of future study
and would greatly enhance the understanding of the water flow and
availability in the area.
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