&EPA
United States
Environmental Protection
Aqencv
Quantifying Seepage Flux
using Sediment Temperatures
Office of Research and Development
Land Remediation and Pollution Control Division
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EPA/600/R-15/454
December 2014
Quantifying Seepage Flux using
Sediment Temperatures
by
Bob K. Lien
U.S. EPA/National Risk Management Research Laboratory/Land
Remediation and Pollution Control Division, Cincinnati, OH 45268
Robert G. Ford
U.S. EPA/National Risk Management Research Laboratory/Land
Remediation and Pollution Control Division, Cincinnati, OH 45268
Land Remediation and Pollution Control Division
National Risk Management Research Laboratory
Cincinnati, Ohio, 45268
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Notice
The U.S. Environmental Protection Agency, through its Office of Research and Development, funded and
conducted the research described herein under an approved Quality Assurance Project Plan (Quality
Assurance Identification Number L18757-RT-1-0). It has been subjected to the Agency's peer and
administrative review and has been approved for publication as an EPA document. Mention of trade names
or commercial products does not constitute endorsement or recommendation for use.
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Abstract
This report provides a demonstration of different modeling approaches that use sediment temperatures to
estimate the magnitude and direction of water flux across the groundwater-surface water transition zone.
Analytical models based on steady-state or transient temperature solutions are reviewed and demonstrated.
Case study applications of these modeling approaches are illustrated for two different field settings with
quiescent and flowing surface water systems. For the quiescent system, application of two different
steady-state models to evaluate temperature records from three depths is illustrated for estimating
groundwater seepage into a pond. For the flowing water system, application of two different transient
models is illustrated for estimating water exchange across a granular cap placed on top of sediments in a
small river. The transient models use amplitude ratio or phase shift of diurnal temperature records from
two depths to estimate seepage flux. These models require isolation of a diurnal signal component from
the raw temperature time-series. Two diurnal signal extraction techniques of harmonic regression and
bandpass filtering were implemented and compared. The results indicate that average calculated fluxes
were indistinguishable for both signal isolation techniques. However, it was demonstrated that the
harmonic regression technique provided greater detail in the temporal fluctuations in calculated seepage.
Application of forward modeling using IDTempPro with the VS2DH flow and heat-transport model to
assess the reliability of calculated seepage from steady-state and transient models is also demonstrated.
This report covers a period from 31 July 2011 to 31 July 2012 and work was completed as of 3 August
2012.
in
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Foreword
The U.S. Environmental Protection Agency (US EPA) is charged by Congress with protecting the Nation's
land, air, and water resources. Under a mandate of national environmental laws, the Agency strives to
formulate and implement actions leading to a compatible balance between human activities and the ability
of natural systems to support and nurture life. To meet this mandate, US EPA's research program is
providing data and technical support for solving environmental problems today and building a science
knowledge base necessary to manage our ecological resources wisely, understand how pollutants affect
our health, and prevent or reduce environmental risks in the future.
The National Risk Management Research Laboratory (NRMRL) within the Office of Research and
Development (ORD) is the Agency's center for investigation of technological and management
approaches for preventing and reducing risks from pollution that threaten human health and the
environment. The focus of the Laboratory's research program is on methods and their cost-effectiveness
for prevention and control of pollution to air, land, water, and subsurface resources; protection of water
quality in public water systems; remediation of contaminated sites, sediments and groundwater;
prevention and control of indoor air pollution; and restoration of ecosystems. NRMRL collaborates with
both public and private sector partners to foster technologies that reduce the cost of compliance and to
anticipate emerging problems. NRMRL's research provides solutions to environmental problems by:
developing and promoting technologies that protect and improve the environment; advancing scientific
and engineering information to support regulatory and policy decisions; and providing the technical
support and information transfer to ensure implementation of environmental regulations and strategies at
the national, state, and community levels.
Determination of the magnitude and variability of water flow between groundwater and surface water,
or seepage flux, is critical for evaluating potential impacts to the aquatic environment and for design of
restoration efforts. Use of measured sediment temperatures provides a flexible and cost-effective tool to
locate areas of groundwater discharge and calculate the magnitude and direction of seepage flux.
Provided in this report is a review of the theoretical basis for calculating seepage flux, the requirements
for design of the temperature monitoring network, and examples of data processing and calculations of
seepage flux for standing and moving surface water systems. This publication has been produced as part
of the Laboratory's strategic long-term research plan. It is published and made available by US EPA's
Office of Research and Development to assist the user community and to link researchers with their
clients.
Cynthia Sonich-Mullin, Director
National Risk Management Research Laboratory
IV
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Table of Contents
Notice
Abstract iii
Acknowledgments x
Forward iv
Table of Contents v
Figures vi
Tables vii i
Acknowledgments ix
1.0 Introduction 1
2.0 Temperature Method 2
2.1 Steady-State Methods 3
2.2 Transient Methods 5
2.2.1 Diurnal Signal Extraction 9
3.0 Illustrations of Method Application 11
3.1 Steady-State Method Example 12
3.2 Transient Method Example 18
4.0 Forward Modeling with IDTempPro and VS2DH 26
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5.0 Summary and Research Needs 31
6.0 References 34
VI
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Figures
Figure 1. The conceptual boundary conditions applicable to the Bredehoeft model. 4
Figure 2. The conceptual boundary conditions applicable to the Schmidt model. 5
Figure 3. The conceptual boundary conditions applicable to both Hatch and Keery models. 7
Figure 4. Example of type curves for the Hatch and Keery models as a function of thermal
conductivity and thermal dispersivity. 9
Figure 5. Percent difference in seepage flux estimation of Keery model relative to Hatch model
as a function of thermal conductivity and thermal dispersivity. 10
Figure 6. Design schematic of iButton® installation device constructed using readily-available
plumbing materials. 14
Figure 7. General physiography of SITE1 with nine locations for temperature profiling
installations. 15
Figure 8. Schematic of iButton® installation at SITE1 and example of temperature signal
collected at each depth for each profile location. 16
Figure 9. Spatial distribution of averaged seepage flux at SITE1 during the period of August 1,
2011 to September 13, 2011. 17
Figure 10. Correlation of Schmidt and Bredehoeft models for seepage flux estimation at
SITE1. 18
Figure 11. A hypothetical example showing percent increase in seepage flux estimation as a
function of percentage increase in the reference groundwater temperature used in the Schmidt
model. 19
Figure 12. Seepage flux investigation locations at SITE2. 20
Figure 13. Schematic of iButton® installation at SITE2 and example of typical corresponding
temperature profile at SITE2 location. 21
VII
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Figure 14. Raw temperature data, 4th-order harmonic regression fit and diurnal (first harmonic)
components of the temperature time-series signals from location WT1 at SITE2. 22
Figure 15. Spatial and temporal distribution of seepage flux at the SITE2 transect. 24
Figure 16. Diurnal components of temperature time-series data isolated by bandpass filter for
location WT1 at SITE2 and comparison of signal amplitude ratio for each 24-hour period
calculated using the bandpass filter or harmonic regression. 25
Figure 17. Comparison of seepage flux of the SITE2 transect derived from the two different
diurnal signal extraction techniques. 26
Figure 18. Comparative plot of average seepage flux at the transect locations derived from the
two different diurnal signal isolation techniques. 27
Figure 19. Comparative plot of VS2DH predicted temperature trend using the average
calculated seepage flux from the Schmidt and Bredehoeft models at 30-cm depth for location
STBatSITEl 29
Figure 20. Comparative plot of VS2DH predicted temperature trend using the average
calculated seepage flux from the Schmidt and Bredehoeft models at 30-cm depth for location
4TBatSITE1. 30
Figure 21. Comparative plot of VS2DH predicted temperature trend using the average
calculated seepage flux from the Keery and Bredehoeft models at 10-cm depth for location
WT1 at SITE2. 32
Figure 22. Comparative plot of VS2DH predicted temperature trend using the average
calculated seepage flux from the Keery and Bredehoeft models at 10-cm depth for location
WT5 at SITE2. 32
VIII
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Tables
Table 1. Parameters used in SITE2 seepage flux calculation 23
Table 2. RMSE of VS2DH model prediction based on seepage flux estimated by the
corresponding method 31
IX
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Acknowledgments
The following individuals are acknowledged for their technical reviews of an earlier draft of this report:
Greg Davis (Brown and Caldwell), Donald Rosenberry (U.S. Geological Survey) and Randall Ross
(U.S. EPA ORD). Patrick Clark (U.S. EPA ORD) assisted with field technical support.
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1.0 Introduction
Seepage flux is the rate of water exchange across the sediment-water interface. Hillel (1982) defined flux
as the volume of water flowing through a unit cross-sectional area per unit time (L3/L2T). Equivalent to
Darcy velocity, the net unit of seepage flux is length per time (L/T). Terms such as specific discharge,
groundwater discharge, and groundwater seepage are commonly used interchangeably to depict seepage
flux. Seepage flux is a quantity vector and is bidirectional in nature. In the following discussion, positive
values of seepage flux represent upward groundwater discharge, while negative values of seepage flux
represent downward groundwater recharge to the aquifer. The magnitude and direction of seepage flux is
largely dependent on natural and anthropogenic processes locally and regionally (Hatch et al., 2006).
For sites where contaminant exchange across the groundwater-surf ace water transition zone occurs, it is
important to assess the relative contribution of groundwater seepage to contaminant exposure and to
consider this exposure route in the evaluation of potential risk management procedures (USEPA, 2005;
USEPA, 2008). The interactions of groundwater and surface water and its importance have been
thoroughly documented (Sophocleous, 2002; Winter et al., 1998). In spite of the numerous techniques
available for the measurement of flow exchanges (Kalbus et al., 2006; Rosenberry and LaBaugh, 2008),
quantifying seepage flux continues to be challenging. Hatch et al. (2006) described applicable spatial and
temporal scales, assumptions, uncertainties, cost, and limitations of numerous methods for estimating
seepage flux. Although heat-flow theory has been influential in the development of the theory of
groundwater flow, interest in using temperature measurements themselves in groundwater investigations
has been sporadic (Anderson, 2005). Sediment temperature is relatively easy and inexpensive to measure.
With the advancements of temperature sensor technologies that enable remote and continuous
measurements and improved analytical techniques and computational capabilities, the renewed interest in
sediment temperature method could potentially make quantitative estimation of groundwater seepage
simple and cost effective.
The purpose of this review is to provide an overview of the prevailing analytical models that have been
developed to use temperature measurements to estimate seepage flux in hydrologic settings where steady-
state or transient conditions may be encountered within the monitored groundwater-surface water
transition zone. Using temperature data acquired from two case study locations, application of the
different modeling approaches is illustrated, along with assessment of some issues concerning data
acquisition, data pre-processing and model selection. The measurement and analysis methods employed
in this review represent one of many options available to characterize seepage flux using sediment
temperature measurements. Where appropriate, alternative approaches to data acquisition and analysis
are noted by reference to examples in the peer-reviewed literature.
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2.0 Temperature Method
It has long been recognized that the flow of groundwater can affect the subsurface thermal distribution
(Stallman, 1963; Suzuki, 1960). It is feasible to use heat flux as a natural tracer to characterize groundwater
and surface water interactions (Anibas et al., 2011; Baskaran et al., 2009; Cartwrig, 1970; Conant, 2004;
Constantz, 2008; Gamble et al., 2003; Jensen and Engesgaard, 2011; Lowry et al., 2007; Schmidt et al.,
2006; Silliman and Booth, 1993). Over the years, following on the theory of interaction between heat
conduction processes and advection of water, researchers have developed methods utilizing sediment
temperatures to inversely quantify seepage fluxes (Bredehoeft and Papadopulos, 1965; Hatch et al., 2006;
Keery et al., 2007; McCallum et al., 2012; Schmidt et al, 2007; Stallman, 1965; Suzuki, 1960).
Specifically, there are four commonly used derivations of the general equation for the simultaneous, one-
dimensional (ID) transport of heat and water through saturated sediments: (1) Bredehoeft model
(Bredehoeft and Papadopoulos, 1965), (2) Schmidt model (Schmidt et al., 2007), (3) Hatch model (Hatch
et al., 2006), and (4) Keery model (Keery et al., 2007). The Bredehoeft and Schmidt models are based on
the assumption of steady-state temperature conditions, whereas the Hatch and Keery models are based on
the assumption of transient-state temperature conditions. None of these inverse methods requires model
calibration. The uncertainty in the flux estimation originates from the combination of uncertainties in the
value of input parameters and the potential disparity between the boundary conditions imposed by the
models and the actual physical conditions of the site (Shanafield et al., 2011).
The underlying theory of using sediment temperatures to quantify seepage flux evolves from the
assumptions that the sediment is thermally and hydraulically homogeneous, the direction of flow is
predominantly vertical within the physical boundaries of the monitored area, and that sediment
temperature profiles are subjected to influences of diurnal and seasonal oscillations in the temperature of
surface water. The zone of oscillation, or depth of penetration of a diurnal temperature signal into the
sediment, depends largely on the magnitude and direction of the seepage flux (Conant, 2004; Schmidt et
al., 2007). For upward groundwater seepage (discharge), the zone of diurnal oscillation generally
decreases in depth as flux increases. But for downward seepage (recharge), the effect is reversed such that
the depth of penetration of the diurnal temperature signature increases as flux increases (e.g., Stonestrom
and Constantz, 2003). Below the transient zone of diurnal oscillation is the zone of quasi-steady-state
conditions where temperature variation is less pronounced with increasing depth. This depth zone
coincides with the zone of seasonal variation (Lapham, 1989; Stonestrom and Constantz, 2003). Seasonal
temperature variations can penetrate deeper into sediments, but this occurs over a longer time frame than
is typically evaluated when monitoring diurnal temperature signal propogation into sediment. Although
in reality the vertical sediment temperature profile will most likely include data both influenced by
transient-state and quasi-steady-state conditions, Anibas et al. (2009) suggested there will likely be periods
throughout the year where transient influences on the temperature signal will be negligible such that the
data can be approximated to be at quasi-steady-state. These periods exist when changes in the average air
temperature are not large during the monitoring period, which occur during the maximum and minimum
of sinusoidal temperature oscillations occurring during weekly, monthly or seasonal cycles.
Stallman (1963) defined the general differential equation for anisothermal flow of an incompressible fluid
through isotropic, homogeneous porous medium as
d2T
dy2 dz2
B(qyT)
dx dy dz
dT
kfs dt
(1)
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where
T = Temperature at any point at time t (°C),
pfCf = Volumetric heat capacity of the fluid (J m^K"1),
pfsCfs = Volumetric heat capacity of the saturated porous medium (J m^K"1),
kfs = Thermal conductivity of the saturated porous medium (J s^m^K"1),
x,y,z = Distance along a Cartesian coordinates (m),
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Since diurnal as well as seasonal fluctuations of temperature are anticipated for time-series measurements,
a true steady-state condition may not exist. As shown by Anibas et al. (2009), one may minimize the
influence of non-steady-state conditions by selecting periods of record during which temperature
oscillations in surface water (or sediment surface) are near a maximum or minimum. Alternatively, a
steady-state condition may be emulated by calculating a 24-hour, moving average for the data as proposed
by Schmidt et al. (2007). With this approach, the calculated seepage flux becomes more representative of
the average flux over the period of record and deviates from an instantaneous value for a given date.
Application of the Bredehoeft method can be found in (Anibas et al., 2011; Arriaga and Leap, 2006;
Cartwrig, 1970; Hyun et al., 2011; Jensen and Engesgaard, 2011; Kalbus et al., 2007; Land and Paull,
2001; Schmidt et al., 2006; Schornberg et al., 2010; Sebok et al., 2013; Sorey, 1971; Swanson and
Cardenas, 2011; Taniguchi et al., 2003).
Figure 1. The conceptual boundary conditions applicable to the Bredehoeft model. The Bredehoeft
method is a steady-state model and it applies to bidirectional flow over a finite depth.
Schmidt et al. (2007) derived a one-dimensional, steady-state model for an assumed condition of upward
vertical flux through an infinite aquifer thickness. Two observation points, in addition to a constant
groundwater reservoir temperature, are required for this model (Figure 2). Depending on the depth interval
of interest, the location for temperature T0 may be at or below the sediment surface. The method uses the
analytical solution of Equation (3) by Turcotte and Schubert (1982) to quantify the rate of groundwater
discharge. For a uniform reservoir temperature Tr, where dT/dz^-0 and T7—»• Tr as z^-co, the analytical
solution is given as
T —T I
s r I
= exp —q,
71,, - T. \ k
(5)
with To as the sediment temperature at the sediment surface, Tz as the sediment temperature at depth z,
and Tr as the uniform groundwater temperature at z—>co. Schmidt et al. (2007) modified the original
solution from Turcotte and Schubert (1982), so that upward flow is positive in Equation (5). The Schmidt
model is sensitive to kfs, and the degree of sensitivity is a function of the magnitude of the flux. In addition,
the model is more sensitive to Tr than T0, so the accuracy of the monitored temperature for deeper
groundwater is important (Schmidt et al., 2007). Implementation of the Schmidt method can be found in
4
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(Brookfield and Sudicky, 2013; Kikuchi et al., 2012; Swanson and Cardenas, 2011).
Figure 2. The conceptual boundary conditions applicable to the Schmidt model. The Schmidt method is a
steady-state model, and it only applies to upward vertical flow through an infinite aquifer thickness.
2.2 Transient Methods
Two derivations of analytical solutions for the general heat and water transfer equation that assume
adherence to transient-state conditions are considered in this report. Stallman (1965) developed an
analytical solution to simultaneously describe heat transport by conduction and heat transport by advection
of fluid flow. For a semi-infinite half space where the temperature of the upper surface is varying
sinusoidally, the temperature at any depth and time is expressed as
T(z,t} = A-exp
Vz
ZD~
cos
\
I
(6)
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where A is amplitude, P is period, Fis thermal front velocity, De is effective thermal diffusivity, and z is
depth (Goto et al., 2005; Hatch et al., 2006; Stallman, 1965). The above equation is subject to the
assumptions (McCallum et al., 2012; Stallman, 1965) that (1) fluid flow is in the vertical direction only
(Cuthbert and Mackay, 2013; Roshan et al., 2012), (2) fluid flow is at steady state (Anibas et al., 2009),
(3) fluid and solid properties are constant in both space and time (Ferguson and Bense, 2011), and (4)
fluid and solid temperatures at any particular point in space are equal at all times (Roshan et al., 2014).
For each of these assumptions, the reader is referred to published evaluations (cited in parentheses) in
which the impact of the various assumption violations has been examined. In general, studies comparing
temperature-based methods to alternative characterization methods (direct and indirect) for determining
seepage flux show that the departures from ideal conditions are quantitatively acceptable (e.g., Briggs et
al., 2014;Huntetal., 1996).
Hatch et al. (2006) solved Equation (6) for the thermal front velocity as a function of amplitude ratio Ar
and phase shift A0 relations:
(7)
PAz
(8)
where Az is the spacing between two observation points and De is the effective thermal diffusivity.
McCallum et al. (2012) pointed out some confusion in Hatch et al. (2006) concerning the inconsistent
representation of Darcy velocity and its relationship to thermal front velocity and thermal diffusivity. To
set out the terms, which deviates from Hatch et al. (2006), the effective thermal diffusivity De is herein
defined as a function of thermal dispersivity P and thermal front velocity V based on (de Marsily, 1986;
Ferguson, 2007; Rau et al., 2012):
Pfscfs Pfscfs
Since the solution of both Equation (7) and (8) is implicit, thermal front velocity V must be solved
iteratively. Once Fis solved, qz can be calculated by
>! (10)
The conceptual boundary conditions pertinent to the Hatch model are shown in Figure 3. Two temperature
observation points in the diurnal oscillation zone with at least one full diurnal period are required to apply
the Hatch method. The concepts of amplitude ratio and phase shift, determined from the diurnal
components of the temperature time-series at two different depths, are illustrated in Figure 3. Seepage
flux is estimated by solving Equation (7) or Equation (8) after amplitude ratio and phase shift are
determined. McCallum et al. (2012) modified the original solution from (Hatch et al., 2006) so that upward
flow is positive in Equation (7). Hatch et al. (2006) stated that temperature sensor spacing, streambed
thermal parameters, and the absolute magnitude of measured temperature variations all influence
6
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applicability of the method. Application of the Hatch method can be found in (Briggs et al., 2012a; Gordon
et al., 2012; Hatch et al., 2010; Jensen and Engesgaard, 2011; Kikuchi et al., 2012; Lautz and Ribaudo,
2012; Lautz, 2010; Lautz, 2012; Shanafield et al., 2011; Swanson and Cardenas, 2011).
Surface
water
v T,
Sediments
Time
Figure 3. The conceptual boundary conditions applicable to both Hatch and Keery models (left). These
methods are time-series models which apply to bidirectional flow over a finite boundary between two
observation points in a zone of diurnal oscillation. The concept of amplitude ratio (Ar) and phase shift
(A®) of diurnal components from different depths is illustrated (right).
Similar to the concept of the Hatch method, Keery et al. (2007) rearranged the solution of Stallman (1965)
to compute vertical seepage flux in terms of amplitude ratio (Ar~) or the phase shift (A®) of two diurnal
temperature signals at different depths,
ln4Ar
Az*
= 0
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thermal dispersivity, which is often an indefinite value for the site of interest, was not included in the
Keery model. Keery et al. (2007) concluded that the effect of neglecting thermal dispersivity in their
analysis is insignificant. The premise by Keery et al. (2007) is not unique. Schmidt et al. (2007) set thermal
dispersivity to zero in their model simulation, stating that thermal dispersion is negligible compared to
thermal conduction, as suggested by Hopmans et al. (2002). Luce et al. (2013) also neglected thermal
dispersivity in developing an explicit solution for the diurnal forced advection-diffusion equation, citing
issues of identifiability between the effects of dispersion and diffusion observed by Anderson (2005).
Figure 4 shows an example of the similarity between the Keery and Hatch solutions as the two type curves
overlay when the value of thermal dispersivity is small. The type curves begin to deviate further as the
value of thermal dispersivity increases. However, as suggested by Rau et al. (2012), it is apparent that the
divergence induced by thermal dispersivity is insignificant in the low seepage flux range. Portions of the
type curves overlay, regardless of the thermal dispersivity value, when the seepage flux is low. Eventually
the seepage flux attains a value above which the influence of thermal dispersivity becomes significant and
the type curves diverge.
<
o
4->
tu
Cd
"o.
E
kfs = 0,84 J s^nv'K!
Keery
- -Hatch ((3=0.001)
Hatch (p=0.01)
Hatch ((3=0.02)
kfs = 2.5 J s^m^K-1
Keery
- -Hatch (3=0-001)
Hatch (P=0.01)
Hatch (P=0.02)
-300 -250 -200 -150 -100 -50
50 100 150 200 250 300
Seepage Flux (cm/day)
Figure 4. Example of changes in Hatch type curves, as a function of thermal conductivity (kfs) and thermal
dispersivity (/J), relative to the Keery type curve where the thermal dispersivity is neglected.
The effect of omitting thermal dispersivity on the estimated seepage flux is illustrated in Figure 5. The
amplitude ratio reflects the relative magnitude and direction of the flow, where Ar —» 1 indicates rapid
downward flow and Ar —» 0 indicates rapid upward flow (Hatch et al., 2006). The difference between the
two calculation approaches is generally less than 10% within the flow range of ±50 cm/day. The difference
escalates as flow rate increases and is most significant for the upward seepage flux direction. As ft becomes
larger, the seepage flux at which divergence between the two modeling approaches begins becomes
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smaller and the rate of divergence increases. The result of this comparison is an indication that caution
should be taken when applying the Keery method in settings where seepage flux may exceed ±50 cm/day.
This theoretical analysis points to the importance of revisiting whether site conditions reasonably adhere
to the assumptions underlying a particular model and consideration of using alternative model(s) that
better align with site conditions. For additional perspective, the application of the Keery method can be
found in (Gordon et al., 2012; Munz et al., 2011; Swanson and Cardenas, 2011).
100%
90% -
80% -
70%
—p=0.001
—p=0.01
i = 2.5 J s^
—0=0,001
—p=0.01
p=0,02
0.20
0.40 0.60 0.80
Amplitude Ratio
i.oo
Figure 5. Percent difference in seepage flux estimation of Keery model relative to Hatch model as a
function of thermal conductivity and thermal dispersivity. The amplitude ratio Ar —» 1 indicates rapid
downward flow; Ar —» 0 indicates rapid upward flow.
2.2.1 Diurnal Signal Extraction
Both the Hatch and Keery methods are transient models which use the amplitude ratio Ar or the phase
shift AO of two diurnal temperature time-series to derive seepage flux. Since the analysis is based on the
assumption that the daily temperature cycle in surface water is the source of the diurnal variations, the
model solution requires a full 24-hour period of sinusoidal temperature data for the analysis. The
observed raw temperature signal is composed of a longer-term trend, a sinusoidal component that may
consist of several harmonics, and irregular white-noise components (Gordon et al., 2012). In order to
extract the diurnal sinusoidal signal from the raw temperature observations, a harmonic regression
9
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model (Gordon et al., 2012; Vogt et al., 2010), similar to a Fourier series approximation, is used to best-
fit each full cycle of temperature measurements using Equation (13),
Ar
yt = Tt+^\aicas(tt>it) + bi.
(13)
where yt is the observed time-series, Tt is a trend, t is time, /' is the harmonic number and a, b and co are
the respective cosine, sine coefficients and frequency. The amplitude A, and phase angle fa of the
respective harmonic can be calculated by (Davis, 1967)
(14)
tan"1
Because the observed diurnal cycle is defined by the observed data points, it is apparent that the amplitude
and phase angle of a time-series are inherently affected by the sampling interval. A practical corollary
would suggest a finer sampling interval should yield better chances for adequately defining these two
properties of the sinusoidal signal. As suggested later, an hourly sampling frequency is desired in order
to properly define the phase shift between temperature signals.
The first harmonic, or the diurnal frequency component, of the harmonic regression is the signal of interest
for the seepage flux computation. After the amplitude and phase angle of the first harmonic are determined
for each observation point, the amplitude ratio Ar and the phase shift A0 can be calculated using Equation
(16) and Equation (17), respectively (Gordon et al., 2012), or determined graphically from the temperature
maxima or minima of the diurnal sinusoidal cycle. The seepage flux qz can then be solved using the Hatch
or the Keery model. It is important to note that seepage flux calculated with phase shift only yields the
magnitude of the flux, but not its direction.
Ar =
A7
-^
AT° (16)
P
— (
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sampling step. Thus, if the temperature sampling interval was one every 4 hours (0.17 day), the range of
the frequency-domain data to transform would be that falling within a period of 0.83-1.17 day. One
limitation of the bandpass filter approach is that accuracy of the transformed signal at the ends of the total
data period is corrupted as an outcome of the mathematical transformations that are implemented (e.g.,
see Figure 12 in Hatch et al., 2006). This distortion of data can be controlled through use of modifying
mathematical functions that control data record endpoint distortion (e.g., Hatch et al., 2006) and/or by
artificially extending the data record period by adding replicated portions of the beginning and end of the
original record to extend the total time period of the record (e.g., Munz et al., 2011). The need to take
these steps is necessitated by the mathematical requirement of an infinite period of record to avoid
endpoint distortions (Christiano et al., 1999). Ideally, application of the bandpass filter may be most suited
to long periods of data record where potential loss of several days of data at the beginning and end of the
data record is not detrimental to the system analysis.
It should be noted that the quantitative estimation of seepage flux based on these one-dimensional inverse
models may not adequately reflect flow for systems where there is a significant horizontal component to
the net flow vector. This situation may be encountered in flowing systems where hyporheic flow exchange
occurs as a result of overlying surface water passing through a portion of the sediment bed (Bencala, 2006;
Cranswick et al., 2014; Cuthbert and Mackay, 2013; Lautz et al., 2010). This may also occur within
quiescent systems where the horizontal component of the flow field may be more pronounced near the
shoreline of the surface water body (Roshan et al., 2012). Lautz (2010) stated that under the scenario
where horizontal flow contributes to the total seepage flux, the estimated flux from the one-dimensional
inverse, analytical models is generally higher than the true vertical flux. The error could be quite
significant and is attributed to the additional transport of heat into the sediments in directions oblique to
the sediment bed interface. Lautz (2010) explored the effects of non-vertical flow by applying analytical
methods to synthetic temperature data and suggested that the percent error of flux estimation could be
40% or greater when the horizontal flux was more than twice the vertical flux. Relative to application of
the one-dimensional inverse models discussed herein, there currently are not verified analysis procedures
within the analytical modeling protocols to assess the relative importance of a two-dimensional flow
regime.
3.0 Illustrations of Method Application
In the discussion that follows, implementation of the data analysis approaches described in prior sections
will be demonstrated to give context for the process of applying this site characterization approach. Two
case study examples will be addressed to illustrate the types of considerations for planning, implementing
and analyzing sediment temperature data to estimate seepage flux. The instrumentation for data
acquisition discussed in this report provide one option for the measurement of temperature signals in space
and time. The main objective is to collect a vertical profile of temperature signals to provide the input
data needed to solve the one-dimensional analytical solutions presented in previous sections. For the
steady-state models, the vertical temperature profile could be measured manually to provide a snap-shot
in time (e.g. Anibas et al., 2009), or automated temperature sensors could be used to measure the vertical
temperature profile over an extended period of time (e.g., Briggs et al., 2012a; Johnson et al., 2005;
Molinero et al., 2013; Lautz and Ribaudo, 2012; Lautz, 2010; Rau et al., 2010). Use of automated
temperature sensors with the ability to log a temperature signal over time is a requirement for use of the
transient models. Since one typically does not know in advance whether a steady-state or transient model
will be applicable for a given setting, it is advisable to plan for use of automated temperature sensors. In
11
-------
addition, the solution of the different analytical models is implemented within this report using the Excel®
spreadsheet program as the mathematical platform. Alternative approaches have been developed based
on other software platforms with varying degrees of automation and sophistication (e.g., Rau et al., 2014).
The tools and approaches employed in this work represent a balance between cost, ease of implementation
and maintenance, and functionality.
3.1 Steady-State Method Example
As part of the pre-remedial site characterization effort, quantification of seepage flux in a quiescent surface
water system was undertaken at a location where a contaminated groundwater plume discharged into a
pond (referred to as SITE1 herein). The objective was to determine the distribution and magnitudes of
groundwater discharge using the temperature method. Temperature measurements included surface water
temperature, aquifer groundwater temperature, and sediment temperature profile. For this study, the
Maxim DS1922L iButton® temperature logger was used since, according to the manufacture's
specification, this model has an accuracy of ± 0.5 °C and a resolution of 0.0625 °C. It stores up to 2048
high resolution (or 4096 low resolution) readings in the measurement range of-40 to 85 °C. In water, the
response time constant of the DS1922L model installed inside the protective capsule (NexSens DS9010K)
is approximately 130 seconds. The temperature loggers were calibrated by the manufacturer, and the stated
performance characteristics were verified prior to depolyment by reference to a thermometer certified by
the National Institute of Standards and Technology.
Prior to installation, all temperature loggers were synchronized for time and sampling interval, and they
were programmed to begin data logging at the same date and time with a 4-hour sampling interval. The
NexSens micro-T software and a USB adapter were used to communicate with the iButton® to setup
deployment options and to download data. Each iButton® has a unique identification number inscribed
on the metal casing and programmed into the built-in memory of the unit by the manufacturer. The
identification number and its corresponding, user-supplied deployment identification code were recorded
prior to the installation.
Figure 6 shows the schematic of an installation device used to drive each encapsulated iButton® to desired
depth below the sediment surface. The iButton® temperature logger was securely seated inside the
capsule. Nine locations in SITE1 were targeted for seepage flux investigation (Figure 7). A vertical
profile of temperature loggers was installed at each location as illustrated in Figure 8 (left). A temperature
logger was also placed at the bottom of a 7-m deep neighboring piezometer to log the local groundwater
temperature. All deployed temperature loggers were tethered to a steel pipe driven into the sediments
using braided, stainless steel wire attached to the protective capsule. Each temperature logger was offset
approximately 5-cm in horizontal placement to facilitate collapse of the sediment and ensure thermal
isolation from preferential flow paths. The deployent period of the seepage flux investigation at SITE1
was August 1 - September 13, 2011. At the conclusion of field deployment, all temperature loggers were
retrieved for data download. The raw data were extracted from each individual iButton® into a NexSens
micro-T database, then exported and saved in a Microsoft Excel® file format. The resultant data matrix
included sampling date and time, iButton® identification number, deployment depth, deployment
identification code, and raw temperature data.
12
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Inner 1/2" PVC pipe
(used to anchor iButton
during drive rod retrieval)
Drive rod - 3/4" steel pipe
Drive shoe-modified l"x
3/4" reducingcoupling with
1/4" groove for cable
iButton capsule with
stain less steel cable
Figure 6. Design schematic of iButton® installation device constructed using readily-available plumbing
materials.
13
-------
Grassland
71
Waste
Management
Unit
Grassland-Soil Cover
Over Geomembrane
71
\
Groundwater A
Piezometer
Patchy
Grassland
Figure 7. General physiography of SITE1 with nine locations for temperature profiling installations.
Locations of reference groundwater piezometer is shown with open triangle.
Figure 8 (right) is an example of a typical temperature profile at the investigated locations. While the
effect of diurnal and longer-term fluctuations of temperature was evident in the surface water, diurnal
oscillations in temperature signals were absent at locations in contact with sediment. The absence of
diurnal oscillation in the sediment temperatures, even at the sediment surface, ruled out the use of transient
methods for analysis. Steady-state methods of Bredehoeft and Schmidt were deemed more approprate for
analysis of data from this system. In order to apply the steady-state methods, it may be necessary to pre-
process the temperature data using a 24-hour, moving average in order to emulate a quasi-steady state
condition (Schmidt et al., 2007). Comparison of calculated seepage flux based on the raw and pre-
processed data for a subset of our temperature data indicated this step did not significantly alter the
calculated value for seepage flux. However, for the purpose of this demonstration, all data were pre-
processed using a 24-hour, moving average. An important aspect is that the steady-state methods utilize
the strong contrast between surface water temperature and the ambient groundwater temperature normally
during summer and winter. The temperature contrast could gradually diminish during fall and spring and
render the analysis unreliable. The sediment temperatures should be in the order that T0 > Tz > TL for the
warm season or T0
-------
process. Otherwise, the flux calculation using Equation (4) or Equation (5) would be in error.
iButton
Surface water
Sediments
26
24
22
m
18
10
3TB
ive sediment
(J
0
-------
interval. Figure 9 (left) shows the spatial distribution of averaged seepage flux for the period from August
1 to September 13, 2011. Spatial variation existed among the investigated locations. Temporal fluctuation
of seepage at each location was considered minor as suggested by standard deviation values that ranged
within 10-36% of the absolute average for the 9 locations. The Bredehoeft method calculated seepage flux
using Equation (5), which required the Excel® Solver add-in for an iterative solution. With a simple
Excel® Macro, repeat iteration of seepage flux calculation for each 4-hour interval could be performed
automatically. Figure 9 (right) shows the spatial distribution of averaged seepage flux estimated by the
Bredehoeft method. The results again revealed that spatial variation existed among the investigated
locations. The Bredehoeft method also exhibited considerable temporal fluctuation of seepage at some
locations, as indicated by large standard deviation values for the 9 locations. At location 4TB, estimated
seepage flux measurements indicated the occurrence of a flow reversal at this location with an average
downward flux (negative) for the period of observation. Correspondingly, the Schmidt method also
yielded the lowest seepage flux at the 4TB location. Although the Schmidt and Bredehoeft methods
produced dissimilar results to a certain degree, a significant correlation (0.72 correlation coefficient) was
noted between the estimated average seepage flux for the two methods (Figure 10). The divergence may
come from different inherent assumptions and boundary conditions of the two methods.
1.38 ± 0.27
SITE1 shoreline
Figure 9. Spatial distribution of averaged seepage flux (cm/day) at SITE1 during the period of August 1,
2011 to September 13, 2011.
For the Schmidt model it was assumed that the origin of the upward flow was from a deep groundwater
reservoir (e.g., 5-10 m) that will normally have a low temperature for the period of observation. The use
of a lower boundary temperature value will yield a lower calculated seepage flux value. In reality, the
origin of flow may come from much shallower depth with warmer temperature. For example, since
horizontal gradients tend to exceed vertical gradients within the upgradient groundwater flow field, the
contribution of discharging groundwater will likely derive from depths more shallow than is generally
assumed for the Schmidt model. Figure 11 shows the sensitivity of groundwater reservoir temperature Tr
on the seepage flux estimation, using sediment temperature data for location 3TB. If the location of Tr
measurement was moved from the original deep well to a shallow well where Tr was approximately 10%
16
-------
higher, the average calculated seepage flux would increase 85% nonlinearly from 7.01 to 12.99 cm/day.
Keep in mind the Schmidt model is based on the assumption that Tr is from an infinite depth where
dT/dz—>0. To satisfy the required boundary condition, seepage flux estimation using the Schmidt method
may skew toward lower values.
25 -1
-Q 2° -
^
u
M~
a)
DC
g. 10-
01
a>
i/i
Bredehoeft
O U1
1 1
i iii
/ SITEl^'
1TB i /
T /
"§ / ,'
1
1 '
^ J '
-^ / 1 LJ i /
"t J L J^V
U 1 ^ -fj- *
ll t ^
STB ^ x X
1-9TB
" * Calculated Flux Data
T 4TB Correlation (Calculated)
Correlation (Ideal)
1
i ill
-50 5 10 15 20 25
Schmidt - Seepage Flux (cm/day)
Figure 10. Correlation of Schmidt and Bredehoeft models for seepage flux estimation at SITE1. The
coefficient of correlation was 0.72. Error bar represents ± 1 standard deviation of the average flux.
17
-------
c
o
E
+3
140%
120%
100% -
80%
c 60% -
0)
in
S 40% -
20% -
0% v
0%
2%
4%
6%
8%
10% 12%
% increase in Tr
Figure 11. A hypothetical example on the STB location showing percent increase in seepage flux
estimation as a function of percentage increase in the reference groundwater temperature (Tr) used in the
Schmidt model.
3.2 Transient Method Example
As part of the post remedial site characterization effort, a seepage flux investigation was carried out at a
flowing river site (referred to as SITE2 herein). At the time of the investigation, the river had been restored
by dredging and subsequently protected by a cap cover consisting dominantly of sandy material, but
inclusive of materials ranging in texture from silty to gravelly. The objective of this evaluation was to
determine the spatial and temporal variation of the magnitude and direction of the seepage flux along a
transect perpendicular to the river flow. Five equally spaced locations along the targeted transect were
investigated (Figure 12). The entire river channel shown in this figure had been dredged and capped. The
temperature method was chosen as an indirect approach for the seepage flux study. The deployment of
iButton® as the temperature logger was similar to the approach described for SITE1. Figure 13 (left)
illustrates the schematic of iButton® installations at SITE2. In order to avoid penetration through the
protective cap and risk compromising its integrity, the installation was limited to the top 20 cm of the cap.
Prior to the installation, all temperature loggers were synchronized for time and sampling interval and
were programmed to begin data logging at the same date and time with a 4-hour sampling interval. All
deployed temperature loggers were tethered to a plastic-coated, braided wire cable stretched across the
river channel and anchored to each shoreline. As at SITE1, the tether consisted of braided, stainless steel
wire attached to the protective capsule. The deployment period of the seepage flux investigation at SITE2
was June 24 - July 29,2012. At the conclusion of field deployment, all temperature loggers were retrieved
for data download. The raw data were extracted from each individual iButton® into a NexSens micro-T
database, then exported and saved in a Microsoft Excel® file format.
18
-------
Figure 22. Seepage flux investigation locations at SITE2. The entire reach of the river shown in this view
was dredged and subsequently capped.
Figure 13 (right) is an example of a typical sediment temperature profile at the investigated locations. The
seasonal and diurnal effect on temperature fluctuation was evident at all three observation depths. The
display of diurnal oscillation in the sediment temperatures suggested that the use of transient method for
seepage flux estimation was more desirable than the steady-state method. The analysis of the transient
time-series method was not as straightforward as the steady-state method. First, each cycle of the raw
temperature time-series was best-fit to Equation (13) with four harmonic components to ensure a
creditable fit. Fuggle (1971) suggested that 98% of the variation in temperature is related to the first two
harmonics of the series. The sum of four harmonic components was considered adequate to depict the raw
temperature signals observed at SITE2. Secondly, the 1st harmonic component of the regression fit was
extracted to determine the amplitude and phase angle of each diurnal cycle using Equation (14) and
Equation (15), or determined graphically from the temperature maxima or minima of the diurnal sinusoidal
cycle. Thirdly, matched amplitude pairs from the time-series signal were used to calculate amplitude ratios
and phase shifts using Equation (16) and Equation (17). And finally, the Keery and/or Hatch models were
used to estimate daily seepage flux value using the amplitude ratio or phase shift. Unlike the steady-state
methods where seepage flux can be determined for each 4-hour sampling interval, the time-series methods
only yield one flux value per diurnal cycle (24 hour period). The underlying assumption is that although
seepage fluxes in many natural systems will vary continuously and slowly over days to weeks or more
(Hatch et al., 2006), the seepage flux is assumed constant throughout the period of a diurnal cycle when
using the time-series method. Hatch et al. (2006) concluded that the time-series method is sensitive to
abrupt changes in seepage rates and directions, and the significance of this limitation depends on the
magnitude and frequency of seepage flux variations.
19
-------
iButton
V
Surface water
Sand Cap
Sediments
WT1
Sand cap surface
U
o
OJ
1_
U
4-J
-------
u
o
(U
Q.
E
28
27
26
25
24
23 -
22
1.5
1.0
0.5
0.0
-0.5
-1.0 -
• Sand cap surface
• 10 cm below sand cap
•—Harmonic Regression
Harmonic Regression
Sand cap surface
10 cm below sand cap
-1.5
06/24/12
07/04/12
07/14/12
Date
07/24/12
08/03/12
Figure 44. (Top) Raw temperature time-series data at WT1 SITE2 are shown using points and the 4th-
order harmonic regression fit is shown as solid lines. (Bottom) Diurnal (first harmonic) components of the
temperature time-series signals extracted from raw data by harmonic regression. Extracted signal for
whole period consists of individual fits to each 24-hour period.
As shown in Figure 14, temperature time-series from the cap surface and 10 cm below the cap were used
as the signal pair to derive amplitude ratio and phase shift. Only the derived amplitude ratio was to
calculate flux based on work that has demonstrated greater reliability of this approach over a larger range
of seepage flux magnitude (Briggs et al., 2014). Table 1 lists the parameters used for the Keery and Hatch
model calculations of seepage flux. A value of thermal conductivity (kfs) = 1.50 J s"1rn"1K"1 was assumed
appropriate for the SITE2 sand cap material in which the temperature loggers were embedded. Selection
of appropriate value of thermal dispersivity is of importance for accurate seepage flux calculation using
the Hatch method, and the inaccuracy especially becomes important at higher flow rates (Hatch et al.,
2006). Assuming that thermal dispersivities are similar in magnitude to chemical dispersivities, Hatch et
al. (2006) suggested that P ~ 0.001-m is an adequate value to use in most situations.
Table
21
-------
Table 1 — Parameters used in SITE2 seepage JIux calculation.
Parameter
Volumetric heat capacity of the fluid pfcf
Volumetric heat capacity of the solid pscss
Volumetric heat capacity of the saturated medium, pf
Unit
JmP^
£:f J m-3K-!
Thermal conductivity of the saturated porous medium. ksd J s4m4K
Porosity, T]
Period, P
Sensor spacing, Az
Thermal dispersivity, p*
^from (Schmidt et al., 2007)
c pfecfe = t](pfcf)+(l- T|){ psCs) from (Silliman et al
A from the range of values suggested by (Arriaga
5 from (Hatch et al., 2006)
-
day
m
m
, 1995)
and Leap, 2006:
Keery Model
4. 19x1 0s
2. OOxl 0s
2. 66x1 0s
:•* i .so
0.30
1
0.1
-
Schmidt etal., 200
Hatch Model
4.19xlOs
2.00xl05
2.66xlOs
1.50
0.30
1
0.1
0.001
»
The Keery method used Equation (11) to solve for Darcy flow velocity. To solve the 3rd order polynomial
equation, an Excel® Polynomials add-in was used to obtain the roots. In all of our cases, only one of the
three roots was a real number, and the other two were a conjugate complex pair. Hence the single real root
was accepted as the representative value. The Hatch method solved Equation (7) for thermal front velocity,
and subsequently used Equation (9) and Equation (10) to solve for Darcy velocity. Because the Hatch
model is implicit, thermal front velocity was solved iteratively using the Excel® Solver. With simple
Excel® Macros, the repetitive computation of seepage flux values was performed automatically. Figure
15 shows the spatial and temporal distributions of seepage flux at the SITE2 transect. At any given location
on the ordinate and any given time on the abscissa, the magnitude and direction of the seepage is indicated
by the color scale on the right. The blue color spectrum represents upward flow in the range of 0 to +55
cm/day, and the red color spectrum represents downward flow in the range of 0 to -45 cm/day. There were
minor differences between the results of Hatch (top) and Keery (bottom), which was expected based on
the illustration of Figure 4 that the two type curves overlaid each other when the value of thermal
dispersivity was 0.001 m. For this data set, the rate of exceeding the ±50 cm/day threshold ranged between
3-15% (average 9%) across the five locations. Of these locations, WT2 had the greatest exceedance rate
of approximately 15%, as reflected in Figure 15 by the highest calculated upward seepage flux.
Note that the Keery and Hatch models are identical when thermal dispersivity is omitted. Since solving
the Keery model is a computationally simpler process, it is suggested that the Hatch model be used only
when significant thermal dispersion is suspected. An alternative way to avoid this parameter is to analyze
data using the analytical solution derived by McCallum et al. (2012), in which the thermal front velocity
is derived as a function of both amplitude ratio and phase shift. The resultant analytical solution is
independent of thermal dispersivity. Unfortunately, due to the coarse sampling interval of our data, the
phase shift could not be adequately defined, preventing analysis using the analytical solution derived by
McCallum et al. (2012). Figure 15 demonstrates that seepage fluxes at the SITE2 transect exhibited
significant spatial variation as well as temporal variation. From a spatial perspective, estimated seepage
flux on the south end of the WT transect seemingly displayed higher magnitude of upwelling than toward
the north end. Considerable downward estimated seepage flux was observed near the WT5 location. From
a temporal perspective, the estimated seepage flux varied continuously with occasional abrupt changes.
22
-------
WT5
Hatch
WTZ
WT1
Seepage Flux
(cm/day)
I
55
50
45
40
35
30
25
20
15
10
5
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
06/26/2012
07/06/2012
07/16/2012
07/26/2012
Figure 55. Spatial and temporal distribution of seepage flux at the SITE2 transect. At any given location
on the Y-axis and any given time on the X-axis, the magnitude and direction of seepage flux was indicated
by the color scale. Blue color spectrum represented upwelling flow; red color spectrum represented
downward flow. Seepage fluxes calculated by Keery and Hatch (P=0.001 m) methods exhibited subtle
differences.
23
-------
1.0
Sand Cap surface
10 cm below sand cap
-1.0
0.7
"ro
01
CD
"O
Q.
<
0.6 -
0.5 -
0.4 -
0.3 -
0.2 -
0.1
Bandpass
Harmonic Regression
0.0
06/24/12
07/04/12
07/14/12
Date
07/24/12
08/03/12
Figure 66. (Top) Diurnal components of temperature time-series isolated by bandpass filter from data at
WT1 SITE2. (Bottom) Amplitude ratio for each 24-hour period calculated using diurnal data extracted by
bandpass filter or harmonic regression.
To evaluate an alternative of extracting diurnal components using bandpass filter, an Excel® bandpass
filter add-in based on the default ideal bandpass filter described in Christiano and Fitzgerald (1999) was
applied to the same raw temperature time-series of SITE2 with the bandpass period range in the frequency-
domain of 0.83 day to 1.17 day. The bandpass filter add-in used in this analysis (BP-Filter Add-In) was
developed by Annen (2004) and is available as a freeware download at www.web-reg.de. Figure 16 (top)
shows an example of diurnal components of the raw temperature time-series (time unit = days) isolated
by bandpass filter using analysis constraints of drift = 0, minimum oscillation period (pi) = 0.83, and
maximum oscillation period (pu) = 1.17. By comparison of the diurnal signal components from Figure 16
and Figure 14, it can be seen that the bandpass filter technique smoothed out the diurnal signal variation
whereas harmonic regression emerged as less manipulative and stayed true to the raw temperature series.
After amplitude ratios were derived from the bandpass diurnal components, the Keery model was used to
calculate seepage flux at the five locations. Comparison of the amplitude ratio obtained from the two
diurnal signal extraction techniques is shown in the bottom panel of Figure 16. The bandpass filter
dampened the amplitude ratio variation relative to that observed using harmonic regression.
A comparison of the spatial and temporal variations in seepage flux estimated using the Keery model
based on bandpass filter and harmonic regression signal extraction is shown in Figure 17. There is general
correspondence in the calculated spatial and temporal variations for the transect, regardless of diurnal
temperature signal extraction technique. In response to the dampening of the amplitude ratio magnitude
and time-dependent variability, the bandpass filter approach consequently dampened the magnitude of
24
-------
spatial and temporal fluctuations in the estimated seepage flux. Nevertheless, the observation of higher
upward flow on the south end gradually transitioning toward downward flow on the north end of the
transect was in agreement between the two signal extraction techniques. Despite the apparent spatial and
temporal differences shown in Figure 17, the average estimated seepage flux derived from the two
different diurnal signal extractions approaches were indistinguishable (Figure 18), based on statistical t-
test at a 95% confidence level. It was also obvious that the harmonic regression approach yielded higher
standard deviation as a consequence of staying true to the temperature fluctuations of the raw data.
WT5
Bandpass Filter
Seepage Flux
(cm/day)
WTl
06/26/2012
07/06/2012
07/16/2012
07/26/2012
Figure 77. Comparison of seepage flux of the SITE2 transect derived from the two different diurnal signal
extraction techniques. Although bandpass filter smoothed out the crest and trough of the seepage
fluctuations, the distribution of higher upward flow at the south end gradually trending toward downward
flow at the north end was in agreement between the two approaches.
As previously noted, it may be possible to approximate a quasi-steady state condition for a system that
presents temperature signals with a diurnal oscillatory component. However, caution should be taken if
attempting to apply the steady-state method to analysis of data displaying this transient characteristic. To
illustrate this issue, the SITE2 data set was subjected to a 24-hour, moving average pre-processing step
and analyzed using the steady-state Bredehoeft model using data from depths of 0-cm, 10-cm and 20-cm
and assuming sediment thermal properties listed in Table 1. For this site, the steady-state model yielded
consistently higher magnitude for the average seepage flux as compared to the transient models, although
there is overlap in the total range of calculated flux across the three models. In addition, the presence of
periods of downward flux at location WT5 was not observed. The average seepage flux calculated by the
Bredehoeft solution was 34.6±8.9, 71.0±10.9, 33.8±11.2, 39.6±8.1, and 10.5±7.2 cm/day for WTl, WT2,
WT3, WT4, and WT5, respectively. It was observed that the magnitude of average seepage flux was more
than twofold at some locations in relation to the transient method approach. The average flow direction
also changed at WT5. This is not to suggest that the steady-state method is not applicable for data showing
25
-------
an oscillatory characteristic, since the general trend in the magnitude of calculate seepage flux for the five
monitored locations was preserved for the transient and steady-state methods. As long as the pre-processed
data could emulate a quasi-steady-state condition, the steady-state method may very well be suitable for
seepage flux estimation. However, to avoid uncertain results with questionable model application, it is
strongly recommended that the signal characteristics of the raw temperature data be mindfully evaluated
before selection of an analytical model.
WT5
Bredehoeft
Bandpass, 0.83
-------
observed temperature signal at different locations and time period provides a means to make a qualitative
and semi-quantitative assessment of the degree of accuracy of estimated seepage flux derived from
application of the inverse, one-dimensional heat and fluid transport models.
The U.S. Geological Survey computer code entitled Variably Saturated 2-Dimensional Heat Transport
(VS2DH) numerically simulates fluid flow and heat-transport in saturated porous media. VS2DH is useful
in modeling the near-surface transport of water and heat in porous sediments for cases in which transport
in the vapor phase and density variations are negligible (Healy and Ronan, 1996). While quantifying
seepage flux from sediment temperatures is an inverse process that derives the magnitude and direction
of seepage from the measured temperatures, modeling with VS2DH is a forward process that predicts the
temporal pattern of sediment temperatures from the given hydraulic and thermal properties. By comparing
the forward-model prediction to the measured temperature, forward modeling can be used as a tool to
evaluate the appropriateness of the seepage flux estimated using the inverse model.
Forward modeling in one dimension with VS2DH was carried out using a graphical user interface
program, IDTempPro (Version 1.0.1.2; Voytek et al., 2013), for the simulation of vertical one-
dimensional temperature profiles under saturated flow conditions. At both SITE1 and SITE2, sediment
temperature were measured at three different depths (Figure 8, Figure 13). For application of these
verification checks, temperature time-series from the shallowest and deepest monitored depths were used
as input boundary conditions within IDTempPro with internal calculation, using VS2DH, of the
temperature at the intermediate monitored depth. The same sediment thermal parameters as used for the
one-dimensional inverse models were used for calculations by VS2DH. Average seepage flux at each
location was calculated from the seepage flux time-series estimated by the inverse method (presented in
Figure 9 and Figure 15), and entered as one of the IDTempPro input parameters. (Note that this approach
does not address the reliability of the temporal distribution of estimated seepage flux derived from the
inverse modeling approaches.) The VS2DH model generated a predicted temperature time-series for the
intermediate depth, and a calculated root mean square error (RMSE) as a measure of the difference
between predicted and measured temperatures. The accuracy of the inverse-method seepage flux estimate
increases with decreasing value of the forward model RMSE, as previously illustrated by Rau et al. (2010).
As suggested by Briggs et al. (2013), the minimum value of RMSE will be limited by the resolution of
the temperature datalogger.
The degree of divergence between the VS2DH model predictions and the measured temperature at
intermediate depth at the SITE1 3TB monitoring location is shown in Figure 19. The temperature signal
generated from the one-dimensional VS2DH model based on average calculated seepage flux from the
Schmidt model yields both a larger RMSE and a larger difference from the measured temperature than
results from the Bredehoeft model. However, both forward model predictions of higher temperature
compared to the measured temperature suggests that the flux value was underestimated by both Schmidt
and Bredehoeft models. Shown in Figure 20 is another example of the differences between the one-
dimensional VS2DH model prediction and the measured temperature at the SITE1 4TB monitoring
location, where the average seepage flux was positive (upward flow) versus negative (downward flow)
when estimated by the Schmidt and Bredehoeft models, respectively. Despite the similar RMSE values,
the one-dimensional VS2DH model produced dissimilar predictions of temperature time-series based on
the average estimated seepage flux from the Schmidt and Bredehoeft models. The results suggest that
for the 4TB location, the Schmidt model generally overestimated seepage flux (indicated by model
temperature lower than measured) and the Bredehoeft model generally underestimated seepage flux
(indicated by model temperature higher than measured). However, there were periods of time for both
inverse methods for which each of the predicted time-series was more reflective of the measured
temperatures. As indicated by the similar RMSE values, both inverse models appeared to provide results
27
-------
of indistinguishable value relative to the apparent "true" seepage flux at monitoring location 4TB.
Values of RMSE for the one-dimensional VS2DH model predictions based on average seepage flux
estimated using the Schmidt and Bredehoeft models at other SITE1 locations are listed in Table 2. Based
on the generally lower RMSE values for all of the monitoring locations, the Bredehoeft model appeared
to provide more representative estimates of seepage flux for SITE1.
u
o
CD
L_
=3
4->
ra
CD
Q_
E
£
i —
J. J.U
14.5 -
14.0 -
13.5 -
13.0
12.5 -
12.0 -
11.5 -
11.0 -
10.5
10.0 -
Measured (@ -0.3 m)
VS2DH model (Schmidt)
VS2DH model (Bredehoeft)
RMSE = 0.676 °C
i
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^^^.
^ .^
N^-
-i: =
RMSE = 0.167 °C
1 1 1
7/31/11 8/10/11 8/20/11 8/30/11
1
9/9/11
Figure 19. Comparative plot of VS2DH predicted temperature trend using the average calculated
seepage flux from the Schmidt and Bredehoeft models at SITE1 STB 30-cm below sediment.
21.5
QJ
TO
21.0
20.5
20.0
19.5
19.0
18.5
18.0
17.5
17.0
. Measured (@-0.3 m)
VS2DH model (Schmidt)
VS2DH model (Bredehoeft)
RMSE = 0.306 °C
RMSE = 0.318 °C
7/31/11
8/10/11
8/20/11
8/30/11
9/9/11
Figure 20. Comparative plot of VS2DH predicted temperature trend using the average calculated seepage
flux from the Schmidt and Bredehoeft models at SITE1 4TB 30-cm below sediment.
28
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The degree of divergence between the VS2DH model predictions and the measured temperature at
intermediate depth at the SITE2 WT1 monitoring location is shown in Figure 21. The model temperature
derived using the average seepage flux from the Keery and Hatch models were practically identical, and
convincingly matched the measured temperature. Values of RMSE for VS2DH model predictions based
on average seepage flux estimated using the Keery and Hatch models at other SITE2 locations are listed
in Table 2. In general, both transient methods appeared to provide reliable estimates of average seepage
flux that yielded small RMSE in forward modeling verification. Omission of thermal dispersivity in the
Keery model did not affect the outcome of the VS2DH evaluation. Forward modeling was also used to
evaluate the influence of a change in the value of thermal conductivity on calculated seepage flux. The
Keery model was run again using a value of kfs = 0.61 J s^m^K"1, which resulted in calculated flux values
of 0.3±9.5, 3.0±9.7, 0.4±9.3, -2.4±8.9, and -14.1±9.1 cm/day for locations WT1, WT2, WT3, WT4 and
WT5, respectively. The factor-of-three reduction in the value of thermal conductivity resulted in an
approximate three-order-of-magnitude reduction in calculated seepage flux. However, the new average
calculated seepage flux values for locations WT1 and WT5 were re-evaluated by forward modeling with
VS2DH in combination with a value of kfs = 0.61 J s^m^K"1. The outcome of this test showed a
degradation in the resultant temperature trend prediction with new goodness-of-fit values for RMSE of
0.209°C and 0.250°C for WT1 and WT5, respectively. In both cases, the new average seepage flux values
and kfs resulted in a predicted temperature trend with values higher than the measured temperature, which
is consistent with an underestimate of the seepage flux at both locations. This analysis demonstrates the
importance of selecting a reasonable value for thermal conductivity, and the utility of using forward
modeling with VS2DH to assess reliability for this parameter.
To examine the appropriateness of applying a steady-state model on transient characteristic data of SITE2,
the average seepage flux derived from the Bredehoeft method was also evaluated at each monitoring
location by application of the one-dimensional VS2DH model via IDTempPro. Figure 22 is a comparative
plot of one-dimensional VS2DH predictions, using the Keery and Bredehoeft method estimated average
fluxes, versus the measured temperature at 10-cm below the sand cap for the WT5 monitoring location.
Both IDTempPro model predictions matched the measured temperature data reasonably well in terms of
magnitude and oscillation. The RMSE results indicate a slight improvement based on average seepage
flux derived from the transient, Keery method. Values of RMSE from the one-dimensional VS2DH model
prediction based on average seepage flux derived from the steady-state, Bredehoeft method for other
SITE2 locations are also listed in Table 2. Examination of the value of RMSE calculated for a period of
record during which the average temperature at the intermediate depth was more stable (i.e., July 20-30),
resulted in the same trend in apparent goodness-of-fit for the transient and steady-state model shown in
Table 2. With an approximate order-of-magnitude difference in the average calculated seepage flux from
these two models for location WT5, the results shown in Table 2 indicate that the calculations
implemented within IDTempPro (Version 1.0.1.2) are relatively insensitive to this input parameter or are
potentially limited by the resolution of the temperature loggers used in this study (resolution
approximately 0.06°C). Based on the fit results presented in Table 2, one would be hard-pressed to suggest
that the steady-state method of Bredehoeft is not suitable for the SITE2 data. However, a conclusive
verdict on the appropriateness of applying steady-state model(s) on transient characteristic data would
require further evaluation from more data sets collected under a wider variety of physical settings.
29
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Table 2 - RMSE of VS2DH model prediction based on
method.
VS2DH RMSE (°C)
SITE1 Schmidt1 Bredehoeftb
1TB 0.103 0.023
2TB 0.031 0.015
3TB 0.676 0.167
4TB 0.318 0.306
5TB 1.000 0.452
6TB 0.480 0.102
7TB 1.108 0.129
8'TB 0.213 0.068
9TB 0.232 0.103
*:b VS2DH input parameter: TJ = 0.35=
c VS2DH input parameter: TJ = 0.30=
c VS2DH input parameter: r[ = 0.30=
a VS2DH input parameter: n = 0.30=
seepage jlwc estimated by the corresponding
YS2DH RMSE (°C)
SITE2 Keeryc
WIT. 0.053
WT2 0.102
WT3 0.059
WT4 0.085
WT5 0.088
fca= 0.84 ™n4C
kft=1.5wm-1Cr
k&=1.5wm-1C-
Hatch2
0.053
0.102
0.059
0.085
0.088
Bredehoeft-
0.043
0.061
0.047
0.062
0.108
. p = 0 m. pjCs— 2e+6 Jm C .
[= p = 0 m= pscs = 2e+6 Jm^C'1.
l= p = 0.001 m, pfcCs= 2e+6 Jm-3CJ.
l= p = 0 m, pici = 2e+6 Jm^C'1.
27.0
26.5 -
26.0 -
25.5 -
OJ 25.0 -
L_
•^ 245 -
nj e-^—>
i_
OJ
Q. 24.0 -
E
!<" 23.5 -
23.0 -
22.5 -
22.0
Measured (@ -10 cm)
VS2DH Model (Keery)
VS2DH Model (Hatch)
RMSE = 0.053 °C
6/24/12
7/4/12
7/14/12
7/24/12
8/3/12
Figure 21. Comparative plot of VS2DH predicted temperature trend using the average calculated seepage
flux from the Keery and Bredehoeft models at SITE2 WT1 10-cm below sand cap. Calculated RMSE
was identical for both inverse models.
30
-------
26.5
26.0 -
25.5 -
U 25.0 H
o
24.0 -
23.5
23.0 -
22.5 -
22.0
Measured (<5> -10 on)
VS2DH Model (Keery), RMSE =0.088
VS2DH Model (Bredehoeft), RMSE=0.108
6/24/12
7/4/12
7/14/12
7/24/12
8/3/12
Figure 22. Comparative plot of VS2DH predicted temperature trend using the average calculated seepage
flux from the Keery and Bredehoeft models at SITE2 WT5 10-cm below sand cap.
5.0 Summary and Research Needs
The results from these case study examples, in combination with published studies referenced herein,
indicate that the temperature method provides a flexible and relatively simple alternative to the traditional
techniques of seepage flux quantification. With the availability of a range of autonomous temperature
logging devices, it is feasible to acquire data over extended periods of time. This capability facilitates a
more complete knowledge of the temporal dynamics of water movement across the groundwater-surface
water transition zone, and it helps insure the acquisition of temperature data for time periods that meet the
requirements of the analytical models used to calculate seepage flux. The computational requirements for
processing raw temperature data and solving the analytical equations for both the steady-state and transient
models reviewed in this report can be achieved with readily available spreadsheet programs such as
Excel®. The design of the monitoring network to acquire temperature data will be governed by the types
of questions that need to be addressed through the site characterization effort. For situations where the
technical need is to provide a screening analysis of the relative distribution and magnitude of potential
groundwater discharge zones, a manual survey to establish vertical temperature profiles within the area of
interest may be sufficient. The snap-shot of temperature profile data can be evaluated with a steady-state
model to map out the relative distribution of discharge (or recharge) zones within the surface water body.
For situations where more detailed knowledge is needed concerning the temporal variation of discharge-
recharge patterns, then deployment of temperature loggers over extended periods of time will be required.
The resulting time-series data can then be analyzed using either steady-state or transient models,
depending on the characteristics of the data signals.
31
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Results from application of the different model approaches in this report highlight several issues to
consider prior to design of the monitoring network and the implementation of a ID inverse model.
Relative to monitoring system design, issues to consider include:
• Implementation of an inverse steady-state model requires at least three temperature signals from
different depths.
• Implementation of an inverse transient model requires at least two temperature signals from
different depths.
• Implementation of forward modeling with VS2DH as a screening assessment of the reliability of
the estimated seepage flux derived from the inverse models requires at least three temperature
signals from different depths.
Relative to selection and implementation of the inverse models reviewed in this report:
• Raw temperature signals should be examined for the presence of a sinusoidal pattern to determine
if a transient model can be used.
• Steady-state models can be used with data containing a sinusoidal pattern, although pre-processing
the data to emulate quasi-steady state conditions may be required.
• For the steady-state models, the analytical solution will be undefined if the intermediate depth
temperature does not lie within the range of temperatures of the upper and lower boundary
temperatures.
• Extraction of the diurnal temperature signal for application of transient models can be
accomplished using different techniques (e.g., harmonic regression, bandpass filtering). While the
type of data extraction technique may not significantly influence the magnitude of the average
estimated seepage flux, it may influence the magnitude and phase of the seepage flux variability
in space and time.
• For application of the transient models using phase shift, the temperature sampling interval needs
to be shorter than the lag time between extracted sinusoidal signals.
• The implementation of data pre-processing and the analytical solutions for the steady-state and
transient models can be accomplished efficiently within Excel® (or comparable programs) with
available add-ins and macro programming features.
While the use of inverse, one-dimensional analytical models reviewed in this report provides a useful tool
for qualitative and quantitative assessments of water exchange across the ground water-surf ace water
transition zone, there are known and uncertain limitations to their reliability for a given site. One clear
technical limitation is the application of these models to provide quantitative estimates of vertical seepage
flux in zones where water flow is not purely vertical. In some cases the level of error in ID model
projections may be acceptable relative to the site characterization questions that are to be addressed.
However, there remains a need to provide users of these analysis approaches with physical and analytical
tools that can be used to assess the relative magnitude of error or bias within the ID model projections.
In addition, there also needs to be additional work to more reliably benchmark the results of the inverse
temperature methods to alternative direct and indirect methods of quantifying seepage flux at varying
scales. The following provides some potential targets to be addressed with future work:
32
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• Development and validation of screening approaches, through indirect field measurements or data
analysis procedures within the analytical model framework, to assess whether horizontal flow
components may impede use of ID, inverse models.
• Synthesis of studies with independent measures of seepage flux to support statistical evaluation of
the accuracy of temperature-based measurements across a range of site conditions.
• A critical survey of direct measurements of sediment properties that are model inputs in order to
help constrain the process of model input parameter value selection.
• Studies to provide better context for the importance of assessing temporal and spatial variability
of seepage flux. It would be useful to have a decision framework that links desired use of seepage
flux determinations to the types of data acquisition approaches that are needed.
While not an all-inclusive list of research needs, they are intended to focus future work towards facilitating
the appropriate use of temperature monitoring to characterize and assess the importance of water flow
across the groundwater-surface water transition zone in support of site restoration activities and watershed
revitalization and protection decisions.
33
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&EPA
United States
Environmental Protection
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PRESORTED STANDARD
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