United States Office of Research and EPA/600/R-99/104
Environmental Protection Development September 1999
Agency Washington DC 20460
vvEPA Hydrogeologic Foundations in
Support of Ecosystem
Restoration: Base-flow
Loadings of Nitrate in
Mid-Atlantic Agricultural
Watersheds
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EPA/600/R-99/104
September 1999
Hydrogeologic Foundations in Support of
Ecosystem Restoration:
Base-flow Loadings of Nitrate in
Mid-Atlantic Agricultural Watersheds
Mohamed M. Hantush
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
Ada, OK 74820
Jerome Cruz
ManTech Environmental Research Services Corp.
Ada, OK 74820
National Risk Management Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH 45268
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Notice
The U.S. Environmental Protection Agency through its Office of Research and Devel-
opment funded the research described here through inhouse efforts. The data used in this
analysis was provided by the U.S. Geological Survey under IAG #DW14937941. This report
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.
All research projects making conclusions or recommendations based on environmen-
tally related measurements and funded by the Environmental Protection Agency are re-
quired to participate in the Agency Quality Assurance Program. This project was conducted
under an approved Quality Assurance Project Plan. The procedures specified in this plan
were used without exception. Information on the plan and documentation of the quality
assurance activities and results are available from the Principal Investigator.
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Foreword
The U.S. Environmental Protection Agency 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 these
mandates, 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 is the Agency's center for inves-
tigation of technological and management approaches for reducing risks from threats to
human health and the environment. The focus of the Laboratory's research program is on
methods for the prevention and control of pollution to air, land, water, and subsurface
resources; protection of water quality in public water systems; remediation of contaminated
sites and ground water; and prevention and control of indoor air pollution. The goal of this
research effort is to catalyze development and implementation of innovative, cost-effective
environmental technologies; develop scientific and engineering information needed by EPA
to support regulatory and policy decisions; and provide technical support and information
transfer to ensure effective implementation of environmental regulations and strategies.
This publication has been produced as part of the Laboratory's strategic long-term
ecosystem restoration research plan, and in fulfillment of the Division (SPRD) FY99 GPRA
Goals and Measures.
Clinton W. Hall, Director
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
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Abstract
Field evidence suggests that deep denitrification in the subsurface has the potential for
removal of nitrate from ground water. Two adjacent agricultural watersheds in the mid-
Atlantic coastal plain display remarkable differences in their ground-water nitrate dis-
charges. It is believed that a combination of denitrification in reducing subsurface sediments
and historical nitrogen input variations are responsible for the observed behavior. The
process of deep denitrification may be influenced by geohydrologic factors, including the
regional dip of strata in the mid-Atlantic coastal plain. A multi-scale-modeling framework is
being developed for analysis and assessment of nitrate removal by denitrification in reduc-
ing subsurface sediments in riparian zones. Analytical characteristic solutions are derived
for general transects in watersheds, and regional ground-water and nitrate transport and fate
models are being developed. Preliminary assessment based on the characteristic solutions
predicts a potential for more than 60 percent reduction of ground-water nitrate at the
discharge to Morgan Creek and 20 percent reduction at the Chesterville Branch. This may be
attributed to a shallower zone of reducing sediments (redox zone) below the former, where a
significant fraction of ground-water fluxes that enter this zone are assumed to be denitrified,
and a relatively deeper redox zone below the latter, whereby a greater portion of ground-
water flux may escape denitrification before discharging to surface water. The analysis may
have overpredicted ground-water nitrate loadings to the Chesterville Branch, possibly due
to overlooking potential denitrification in the peat-rich riparian stream-valley sediments.
Although predictions are consistent with field findings, more intensive sampling would be
required to resolve deep denitrification from potential removal within riparian stream-valley
sediments. Simple indices are derived on the basis of steady-state mass balance, which
describe the removal capacity for ground-water nitrate in agricultural watersheds. The
indices relate the reduction in nitrate base-flow loading to potential denitrification in the
subsurface in agricultural catenments and stream riparian zones. A regional ground-water
surface water flow model has been developed in order to investigate the impact of denitrifi-
cation in ground water at the watershed scale. The simulated ground-water levels and stream
discharges compared very well with quasi-steady synoptic measurements of heads in the
surficial Columbia-Aquia aquifer and the lower Hornerstown aquifer. The measured stream
flows in Morgan Creek are reproduced by the simulated values. The regional flow model is a
prelude to analysis of regional nitrate transport and fate and assessment of the potential
impact of deep denitrification on nitrate budget in the paired watersheds, including total
mass discharge to the Chester River. This report covers a period from 10/01/97 to 08/01/99
and work was completed as of 08/01/99.
IV
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Contents
Foreword iii
Abstract iv
Figures vi
Tables viii
Acknowledgments k
1. Introduction 1
2. Theoretical Foundation 3
2.1 Ground-water Flow in Unconfined Aquifer 3
2.1.1 Water Table Distribution 3
2.1.2 Ground-water Flux in Oxic and Redox Zones 5
2.2 Nitrate Transport and Fate in Ground Water 6
2.2.1 Development of Transport Equations 7
2.2.1.1 Upper Layer (Oxic Zone) 7
2.2.1.2 Lower Layer (Redox Zone) 8
2.2.2 Lagrangian Solution in the Upper Layer 8
3. Potential Nitrate Reduction by Deep Denitrification 10
3.1 Study Site Description 11
3.1.1 General 11
3.1.2 Geology of the Area 11
3.1.3 Hydrostratigraphy 12
3.1.4 Locust Grove Local Well Network and USGS-USEPA Data Sets (1997-1999) 12
3.2 Preliminary Assessment 13
3.3 Removal Capacity 19
4. Regional Ground-water Flow and Nitrate Transport and Fate Model 23
5 Summary, Conclusions, and Future Directions 28
Appendix A 30
Appendix B 33
Appendix C 36
Appendix D 39
Appendix E 40
Appendix F 41
References 44
Glossary 46
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Figures
Figure 1. Locust Grove study site with location of proposed core holes and wells
(after Bohlke and Denver, 1995) 1
Figure 2. Generalized geologic cross section through Locust Grove, MD
(after Bohlke and Denver, 1995) 2
FigureS. Conceptual model for the Morgan Creek: Unconfmed aquifer with positive inclination 3
Figure 4. Conceptual model for the Chesterville Branch: Unconfined aquifer with negative inclination 6
Figure 5. Schematic illustration of infinitesimal control volumes in the upper (oxic) and lower (redox)
layer in unconfined aquifer 7
Figure 6. Wells network in the study area. A triangle refers to a well from which the USGS synoptic
ground-water levels and quality are measured, and a solid circle refers to a core hole location 11
Figure 7(a). Overview of the location of cross section A-A' relative to the Locust Grove site
and the wells network 13
Figure 7(b). Cross section A-A' between the Morgan Creek and the Chesterville Branch with adjacent
wells labeled. The dashed line delineates the ground-water divide 14
Figure 7(c). Hydrostratigraphy along cross section A-A' illustrating the relative position of the redox zone.... 14
Figure 8(a). Measured versus estimated heads at Morgan Creek watershed 15
Figure 8(b). Measured versus estimated ground-water fluxes at Morgan Creek watershed 15
Figure 9(a). Measured versus estimated heads at Chesterville Branch watershed 17
Figure 9(b). Measured versus estimated ground-water fluxes at Chesterville Branch watershed 17
Figure 10. (a) Historical variations of NO3" concentration at the recharge (at the water table) and at
x0 = 50 m in the upper layer, (b) Mass flux of NO3~ in time at the discharge to Morgan Creek
relative to steady-state input, (c) Mass flux of NO3~ discharged from upper layer to Morgan
Creek relative to steady-state input versus time, and (d) NO3" concentration versus time 18
Figure 11. (a) Historical variations of NO3~ concentration at the recharge (water table) and at x0 = 50 m
in upper layer, and (b) Mass flux of NO3~ in time at the discharge to Chesterville Branch
relative to steady-state input, (c) Mass flux of NO3~ discharged from upper layer to Chesterville
Branch relative to steady-state input versus time, and (d) NO3" concentration versus time 20
Figure 12. Semi-log plot of the removal-capacity index IRC versus I for different values of the
dimensionless parameter e 22
Figure 13. Illustration of a riparian zone showing potential NO"3 loss pathways in organic-rich soils
and subsurface sediments and related hydrological factors 22
Figure 14. Regional ground-water conceptual model including surface-water drainage network, with the
prescribed head equal to zero (sea level) at the Sassafras River to the north and the Chester
River to the south, and no-flow boundary elsewhere 24
Figure 15. Simulated steady-state ground-water heads in the wet season (Nov.-Apr.) for the case of
prescribed heads along Mills Branch located on the eastern border of the flow domain 24
Figure 16. Simulated steady-state ground-water heads in the wet season (Nov.-Apr.) for the case of
no-flow boundary on the eastern border of the flow domain 25
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Figure 17. Ground-water flow directions simulated in the wet season (Nov.-Apr.) for a one-layer model 25
Figure 18. Simulated versus measured heads in the wet season (Nov.-Apr.) for a one-layer model:
(a) prescribed-head on the east side, and (b) no-flow boundary on the east side 26
Figure 19. Simulated versus measured heads in the dry season (May-Oct.) for a one-layer model:
(a) prescribed-head on the east side, and (b) no-flow boundary on the east side 26
Figure 20. Simulated versus measured heads at surficial aquifer (four-layer model with no-flow
boundary on the east side): (a) wet season (Nov.-Apr.), and (b) dry season (May-Oct.) 27
Figure 21. Simulated versus measured heads at Hornerstown aquifer in wet season (Nov.-Apr.)
(four-layer model with no-flow boundary on the east side) 27
Figure 22. Simulated versus measured stream-flow discharges at Morgan Creek in the wet season
(Nov.-Apr.) (no-flow boundary on the east side): (a) one-layer model, and (b) four-layer model.... 28
VII
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Tables
Table 1. Core data Submissions by USGS (as of July 1999; file sent 12/2/98) 41
Table 2. Recent Synoptic Water Table Measurements by the USGS in Locust Grove, MD 42
VIM
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Acknowledgments
This project was initiated by Dr. S. R. Kraemer, U.S. Environmental Protection Agency,
including the development of original work and quality assurance plans. Dr. D. Krantz, Dr. J.
L. Bachman, and Dr. J. K. Bohlke of the U.S. Geological Survey developed and executed the
field work plan and assisted in the interpretation of new hydrostratigraphic and geochemical
data. Dr. D. Drummond of the Maryland Geological Survey provided existing
hydrostratigraphic data for the construction of the geologic model. Mr. E. Hoque of ManTech
Environmental Research Services Corp. assisted in the regional ground-water flow modeling
effort. Ms. K. Tynsky and Ms. M. Williams of Orbiting Astronomical Observatory Corp.
provided graphical support and developed the final format of the report. We thank Dr. M.
Marino, Dr. R. Govindaraju, Dr. K. Bali, and Dr. J. Cho for their reviews and valuable
comments.
IX
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1. Introduction
Chesapeake Bay, the United States' largest and most productive estuary, faces several complex environmental issues,
including, among others, eutrophication and anoxia in the main channel and tributaries (Cronin et al,. 1999]. The
outbreak of the toxic dinoflagellate Pfiesteria piscicida is linked to nutrient enrichment in the Chesapeake Bay.
Agriculture was identified as a major contributor of nutrients to the Chesapeake Bay in the 1987 Chesapeake Bay
Agreement. Under this agreement, the states of Maryland, Pennsylvania, and Virginia, and the District of Columbia
committed to a 40 percent nutrient load reduction to the Chesapeake Bay by the year 2000 (U.S. Environmental
Protection Agency, 1992). It is imperative to estimate base flow loading since much of the nitrogen that is discharged
to the bay and its tidal tributaries is transported by ground water as base flow or direct discharge (Bachman and Phillips,
1996). Improper management of nutrients can result in losses to ground water by leaching and surface water by runoff.
Therefore, nutrient management through rate, timing, and mode of application can prevent pollution and reduce their
potential losses through runoff or leaching to ground water.
Riparian buffer zones and constructed wetlands are potential natural filters and are proposed as a nutrient management
method. In the design of riparian buffer areas, the subsurface environment, including the stream valley sediments, and
the interaction between surface and ground water are as important as the size of buffer zone and species composition.
The role of the subsurface as an integral compartment of the riparian zone needs to be emphasized and evaluated for
possible impact as a nutrient management method. Figure 1 shows paired predominantly agricultural watersheds in the
mid-Atlantic coastal plain. The area is located in Kent County, Maryland, and the two watersheds, the Morgan Creek
and the Chesterville Branch, although adjacent, show remarkably different nitrate levels in their base flows. Based on
geochemical analysis, it was reported by Bohlke and Denver (1995) that the concentrations of nitrate (NO3~) in ground-
Locust Grove Study Area
Chesterville Morgan
Branch Creek
recharge O
discharge
stream
Approximate Elevation
at the Bottom of the
Aqula Formation s.
25 MILES
-I
2*5 KILOMETERS
® PROPOSED CORE
© PROPOSED WELL
Figure 1. Locust Grove study site with location of proposed core holes and wells (after Bohlke and Denver, 1995).
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water discharge to the Morgan Creek were significantly lower than in the Chesterville Branch (Figure 2). It is believed
that a combination of deep denitrification (microbial reduction of NO3" to N2) in reducing subsurface sediments and
historical input variations is responsible for the observed behavior. The difference in the position of the redox zone
(brown-shaded in Figure 2) relative to the bottom of each streambed produced by the regional dip of the strata,
combined with the ground-water flow pattern, may be responsible for greater denitrification in ground waters
discharging to the Morgan Creek.
Nitrogen removal in riparian zones has been investigated in shallow ground waters (Yates and Sheridan, 1983;
Lowrance et at., 1984; Peter John and Cornell, 1984; Jacobs and Gilliam, 1985; and Cooper, 1990). Recently, the
impact of redox reactions (e.g., microbial denitrification) on nitrate removal in deeper ground waters has been the
subject of several studies (Trudell etal., \9$6;Postma etal., 1991; Kinzelbach et al., \99l;Korom, 1992; Bo'hlke and
Denver, 1995; and Mengis et al., 1999), which indicated the role of denitrification in ground water on the reduction of
nitrate discharge to riparian streams. While most efforts are field based and focused on mass balance of nitrogen over
an entire area of study, mechanistic models that describe transient transport and fate of nitrate in ground water (e.g.,
Kinzelbach etal., 1991) received less attention. This may be attributed to the complexity of nitrogen transformation and
uncertainty associated with the subsurface environment, which is further compounded by lack of a detailed geohydro-
logic and geochemical data base.
The current study is a consortium between the U.S. Environmental Protection Agency (National Risk Management
Research Laboratory) and the U.S. Geological Survey (Baltimore and Dover). The objectives of this study are: 1) to
develop a geohydrological database for paired agricultural watersheds shown in Figure 1; and, 2) to develop a scale-
dependent methodology for the assessment of the effectiveness of deep denitrification on the reduction of nitrate
discharge to riparian streams. The goal is to provide an adaptable framework with implication on the design of the
riparian zones and management of nitrogen in agricultural watersheds.
In the following sections the geohydrological foundation is developed for the assessment of nitrate transport and fate at
the local as well as the regional scale. At the local scale, a framework is developed which describes ground-water flow
in inclined, unconfined aquifers with implication on nitrate fate and transport in agroecosystem. The purpose of the
local-scale models is to provide a foundation, using basic physics, for understanding the impact of deep denitrification
on ground-water discharge, and to provide a viable reasoning for the observed disparity of base-flow nitrate levels at the
two watersheds. At the regional scale, the ground-water flow model is developed for the watersheds and application
results are displayed. The regional transport model, however, is not addressed in this report and is currently under
development.
Morgan Creek SW
Age (years) = altered
N03- (mg/L as N) = 2-3
Recharge
Age (years) = 3-50
N03' (mg/L as N) = 3-20
Chesterville Branch SW
Age (years) = altered
N03'(mg/L as N) = 9-10
North
South
Morgan Creek GW
Age (years) = 25-40
N03 (mg/L as N) = 0
Excess N2 (mg/L as N) = 3-4
Chesterville Branch GW
5-10 Age (years) = 30-35
2_5 N03" (mg/L as N) = 3-5
<2
relatively reduced
calcareous
glauconlttc
Figure 2. Generalized geologic cross section through Locust Grove, Maryland (after Bohlke and Denver, 1995).
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2. Theoretical Foundation
2.1 Ground-water Flow in Unconfined Aquifer
In the following sections we develop analytical solutions which describe one-dimensional and steady-state water table
elevations and ground-water fluxes in an inclined, unconfined (phreatic) aquifer subject to uniform recharge. The
solutions should enable the estimation of ground-water fluxes from the upper oxic layer to the lower anoxic layer and
ground-water discharge (base flow) to a stream. The lower anoxic layer denotes the zone of reducing sediments in the
catchment under study, in which nitrate is believed to be partially or entirely denitrified before discharging to Morgan
Creek and the Chesterville Branch. An approximate solution to the nonlinear exact solution will be obtained using
asymptotic expansions and will be used in determining transport and fate of nitrate nitrogen in the subsurface. Among
other factors, the impact of aquifer bed inclination is also considered in the solutions.
2.1.1 Water Table Distribution
Figure 3 illustrates a conceptual stream-aquifer system for Morgan Creek in which the aquifer bed is inclined with a
positive angle measured relative to a horizontal plane at a reference elevation (or datum) of the aquifer bed at the right-
hand-side boundary. Ground-water flow toward the stream occurs due to a uniform recharge of magnitude N [m/d] and
a prescribed influx Q0 [m3/d] at the right-hand-side boundary at x = 0 m (Figure 3). A water divide at x = 0, corresponds
to the special case of Q0 = 0. The steady-state flow in the unconfined aquifer may be described by the following Dupuit
equation (Bear, 1972):
dx
dx
where
h(x) =
(1)
(2)
in which h(x) is the hydraulic head at steady state [m]; r|(x) is steady-state water table elevation relative to the aquifer
bed [m]; K is the hydraulic conductivity [m/d] assumed to be constant; (3 = tan 0 is the gradient of aquifer bed; N is the
uniform recharge [m/d]; and x is the horizontal distance. Equation (1) is valid for sufficiently small (3 so that Dupuit's
k', b'
Impervious
Boundary
Figure 3. Conceptual model for the Morgan Creek: Unconfined aquifer with positive inclination.
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assumption of horizontal flow in the aquifer is applicable. We seek a solution to (1) subject to the following boundary
conditions:
—
(3a)
dx
b
(3b)
in which K' is the hydraulic conductivity of the streambed [m/d]; b is the thickness of the streambed deposits [m] (i.e.,
semipervious boundary layer); W is the stream width [m]; Hr is the streambed elevation relative to datum (m); and H
is the stream stage relative to aquifer bed at x = I. Streambed conductance K7b' = °° corresponds to the special case of
perfect hydraulic connection between the stream and the aquifer. Note that in (3b), W/2+h(/)-Hr is the ground-water
surface water discharge area per unit aquifer width, at x = I. It is based on the assumption that ground water is
intercepted entirely by the stream and that no horizontal flow occurs below the stream.
Using the linear transformation £, =
in Appendix A:
Q0, the solution to the above boundary-value problem (1-3) is shown in detail
(3
= exPi--T7
tan"
Y
Y
where
47V2
The integration of Equation (1) and the imposition of boundary condition (3b) yield
K'lb'
in which r\{ is water table elevation above the streambed at x = / [m]. Equation (4) requires that y > 0, whereas for
negative net recharge (i.e., evapotranspiration greater than infiltration), we have y < 0 and -tan'1^) in Equation (4)
should be replaced by +coth~1(*).
Note that (4) is nonlinear with respect to the dependent variable r| and can be solved using a standard iterative procedure
for solving nonlinear equations, such as the Newton Raphson method. A useful approximate but closed-form solution
to (4) can be obtained for sufficiently small (3 « 1 using a straightforward expansion in the form of a power series in
(3 (e.g., Nayfeh, 1981):
(7)
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in which (j)0(x), (j)j(x), ..etc, are to be identified. In the expansion (7) the function (j)0(x) corresponds to the case of a
horizontal bed, and (j)j(x) represents a correction due to a small inclination of the aquifer bed. It is usually sufficient to
retain the first two terms (zero- and first-order) and ignore higher order terms of O[(32] and greater. By substituting the
right-hand-side of (7) into (4) and collecting terms of equal order in (3, one can show that:
KN
i
and
(8)
,00= . , .
2<|>oOO
fm- *°w
Nx + Q0
(9)
2N
Not only do Equations (7-9) provide an approximate closed-form solution to the nonlinear head distribution in (4), but
also, as will be evident later in the analysis, they enable an analytical closed-form solution for nitrate transport in
ground water and allow for direct assessment of the impact of the denitrification in the reducing subsurface sediments
on nitrogen reduction in riparian buffer zones; i.e., potential reduction of nitrate in the discharge (base flows) to the
Morgan Creek and the Chesterville Branch.
2.1.2 Ground-water Flux in Oxic and Redox Zones
In this analysis the upper layer is referred to as oxic in order to indicate that ground waters remain oxic throughout the
upper layer and, therefore, discharge relatively unaltered to streams (Bohlke and Denver, 1995), and the lower layer is
referred to as redox to represent the reduction-oxidation process of denitrification in the reducing sediments of the
lower layer. The total ground-water flux QT(x) over a flow depth of (x) is given by the integration of Dupuit's Equation
(1) from x = 0 to x = x, which yields
Q (x) = Nx + O (10)
In Dupuit's equation, equipotential lines are assumed to be vertical and ground-water flow is essentially horizontal.
Thus, the flux in the lower (redox) layer of thickness b (Figure 3) is given by
b
IY\( V^ /
The flux in the upper oxic layer is given by
: ^(JC) £M*J (12)
Note that dQ^/cLr represents ground-water flux from the upper layer to the lower one by virtue of continuity of flow
in and out of an incremental control volume of V = b x. That is, any increase in the flow rate in the lower layer (redox
zone) must be balanced out by transfer of ground-water flow from the upper (oxic) layer. This is an important part of
the problem under consideration, because dQt(x)/dx describes the rate at which nitrate is convected to the redox zone
and, consequently, lost out of the system by denitrification in the reducing sediments before discharging to the riparian
streams.
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A direct use of (11) and (12) is not possible because of the nonlinearity of (4) with respect to r|(x), and an iterative
procedure, therefore, is needed for the flux evaluation. However, a closed-form approximate solution can be obtained
by substituting the asymptotic expansion on the right-hand-side of (7) for r| (x) in Equations (11) and (12) and collecting
and equating terms of equal order of magnitude with respect to the parameter (3,
(13)
and
Figure 4 is a mirror image to the flow scenario in the Chesterville Branch depicted in Figure 2 where the gradient of the
aquifer bed is negative and ground-water flow pathways are longer. In this case, ground-water flux is progressively
distributed over greater flow areas and a significant fraction of the ground water escapes the lower (redox) layer before
discharging to the stream. The solutions in the previous case of positive aquifer bed gradient are equally applicable to
the case of negative gradient, however, with the parameter (3 being negative. This is because the methodology above is
applicable for a general inclination angle Q, and for the Chesterville Branch, the only difference is that Q is negative
relative to the horizontal line which passes through the origin at the base of the aquifer at the water divide. In the case
of Morgan Creek, Q is positive relative to the horizontal reference level.
2.2 Nitrate Transport and Fate in Ground Water
In the following sections, the governing transport and fate equations for nitrate are developed for each layer using the
concept of conservation of mass. The resulting equation for the upper (oxic) layer is then solved analytically using a
characteristic solution in terms of the functions (|>0(x) and <|\(x)- Iftne nitrate-nitrogen is assumed to be denitrified
instantly in the lower (redox) layer (Bohlke and Denver, 1995), then base-flow loading from the upper layer is the only
source of nitrate discharged to both streams. In this case, the solution of the transport equation in the upper layer is
sufficient to describe nitrate reduction at the discharging waters, because all nitrate convected to the lower layer would
presumably be lost out of the riparian system by denitrification in the reducing sediments. If denitrification occurs at a
finite rate, rather than instantly, the solution for the transport equation in the redox layer becomes necessary since
nitrate is partially denitrified, and the discharge from the lower layer to the streams would contribute nitrate discharge
Datum
Figure 4. Conceptual model for the Chesterville Branch: Unconfined aquifer with negative inclination.
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to the stream. The solution for nitrate transport and fate in the lower layer under the condition of partial denitrification
is currently under investigation.
2.2.1 Development of Transport Equations
2.2.1.1 Upper Layer ((Me Zone)
Figure 5 shows a control volume tapping the aquifer at distance x of length Ax and height r|(x) per unit width of the
aquifer. The upper layer is of thickness r| - b and the lower layer is of thickness b. Mass balance of a contaminant
through the upper layer in the control volume requires that
Mass at time t+At = Mass at time t + Mass In during At
- Mass Out during At - Rate of Loss x At (15)
If we ignore production of nitrate within the control volume and assume convective transport (i.e., negligible dispersive
effects), then for infinitesimal Ax and At, the application of (15) to mass balance in the upper-layer portion of the
control volume (Figure 5) yields
dx
(16)
in which Cu is the concentration of nitrate in the upper layer [g/m3]; n is aquifer porosity; C"(x,t) is concentration of
nitrate at the recharge [g/ m3]; and kuis a first-order rate loss coefficient [d"1], which accounts for partial denitrification.
In Equation (16), we assumed uniform concentration throughout the depth r|-b and, therefore, convective losses of
magnitude Cu to the lower-layer portion at a rate of dQ/dr x (the fourth term on the right-hand side of (16)). Recall that
N C*(t)
Qu(x+Ax,t)Cu(x+Ax,t)
Q{(x+Ax,t)C{(x+Ax,t)
^Qu(x,t)Cu(x,t)
Oxic layer
Reducing
Sediments
Figure 5. Schematic illustration of infinitesimal control volumes in the upper (oxic) and lower (redox) layer in unconfined
aquifer.
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dQ/dx = N - dQu/dx accounts for ground-water flux transfer from the upper layer to the lower layer. After dividing both
sides of (18) by Ax At and taking the limits Ax, At —>0, the following partial differential equation is obtained
x,t) (17)
J
Equation (17) describes convective-reactive transport of nitrate-nitrogen in the upper layer of the aquifer that is subject
to a distributed source of magnitude C*(x,t), arriving at the water table at a rate equal to the recharge N. In this study,
ku is assumed zero since in oxic waters denitrification is relatively negligible. Equation (17) can be simplified further by
expanding the second term and noting that dQT/dx = d/dx (Qu+Qj) = N,
Cu =NC\x,f) (18)
2.2.1.2 Lower Layer (RedoxZone)
The application of the mass balance (15) to the lower portion of the control volume in Figure 5, for infinitesimal Ax and
At, yields
n b Ax C, ( x,t + AO - n b AxC, (x,t) = Ql (jc)C, (jc, f) M + - AxCu (x, f ) Af
dx
(19)
- Q, (x + Ax)C, (x + Ax, t)At - n b Ax k, C, (x, f) kt
in which Cj is nitrate concentration in the lower layer [g/m3], and kj is a first-order rate loss coefficient [d"1], which
accounts for denitrification in the reducing sediments. After dividing both sides of (19) by Ax At and applying the limits
Ax, At — >0 to the resulting equation, the governing convection-reaction transport equation for nitrate in the lower layer
can be obtained,
da
' ""* "' --T^u (20)
dx
Equations (18) and (20) describe convective-reactive transport of nitrate-nitrogen in the upper and adjacent lower layer
of the unconfined aquifer subject to a uniform recharge N and temporally variable nonpoint source of magnitude C*(t)
under steady-state ground-water flow conditions. As mentioned earlier, the solution of Equation (18) is sufficient to
describe nitrogen reduction at the base flow if ground waters in the lower layer are assumed to be denitrified entirely
2.2.2 Lagrangian Solution in the Upper Layer
In this section a closed-form solution to (18) is obtained by using asymptotic expansions of the form (7) and adopting
a Lagrangian framework. The solution has several advantages. First, it allows, in a rather straightforward manner, the
evaluation of the effectiveness of denitrification in riparian zones on nitrogen reduction in base-flow loading to streams.
This can be achieved without resorting to complex numerical models that require extensive data, which are either
difficult to obtain or costly. Analytical solutions can be used to verify the integrity of complex numerical models.
Secondly, the solution is not limited to a particular site; it is rather of a general use given the assumptions. Thirdly, the
characteristic Lagrangian solution allows backtracking of unknown historical records based on currently detected
pollution levels. The fact that synoptic base-flow loading to streams constitutes a mixture of fairly new and old ages of
ground waters makes the solution more suitable for nitrogen source management at the watershed scale. This is because
the solution accounts for the average travel time of pollutants originating over the entire transect length of a typical
segment in a watershed. It is the average travel time of a given historical record of nitrogen source that is reflected by
mixed discharging ground waters at the ground water-surface water interface (i.e., base flow). Therefore, the solution
-------
accounts for the integral effect of nonpoint source in a typical watershed segment (Figs. 3 and 4) on base-flow nitrate-
nitrogen loading.
A closed-form solution to (18) can be obtained by dividing both sides of the equation by Q (x) and introducing the
following Lagrangian-type relationship:
dt T\(x) - b
By recalling the definition of material derivative (convective derivative), Equation (18), after dividing by Qu(x), can be
expressed in the Lagrangian framework as (Appendix B)
N + nku(T}(x)-b) _ N *
1 -- C-,. = - L, \X.t(X))
x QH(x) " Qu(x)
in which C* is expressed as an explicit function of x. The solution of (22) is readily obtained in terms of the integration
factor,
g(x)Cu(x)=g(x0)Cu(x()) + g(^ (23)
xa ^u ( SJ
where
-b} , 1
The evaluation of the integral in (24) is not possible because r\(x) cannot be expressed explicitly in terms of x. A useful
approximation to (23), however, can be obtained for small inclination (|3«1) by expressing C (x,f) in the following
asymptotic expansion:
CttCM)=\|/o(*>0 + ViCM)P + --, P«l (25)
in which \|/0(x,t) and \|/j(x,t) are functions to be found. The substitution of (7) and (25) into (22), and expanding the
coefficients of Cu(x) and C* in (22), using Taylor series about (3 = 0, and collecting terms of equal powers in (3, yields
the following ordinary differential solutions (Appendix B):
(3°:
, , "\ N
^*r / NT
C [x,t(x)]
dx
d\\f] 1 N$0(x) , , , \ N b
-------
(28)
(29)
where
g(x) =
-b2
(30)
a =TI, +
(31)
Equation (21) is also difficult to solve since r\(x) and QU(JT) cannot be expressed explicitly in terms of x. An approximate
solution is obtained in Appendices B and C by substituting (12) for Qu(r) in (21) and expanding the right-hand side in
Taylor series about (3 = 0,
t(x) «t0 + -
a -<|>o(x)
-In
(32)
The solutions (28-32) would have been obtained by direct substitution of the asymptotic approximations (7), (14), and
(25) for (x), QU(JT), and Cu(x,/), respectively, into the partial differential equation (PDE) (18), collecting terms of equal
order of powers in (3, and then adopting the Lagrangian transformation to the resulting zero- and first-order PDEs.
In Equations (28) and (29), C*[^ , t(£)] implies C* expressed explicitly in terms of £. Thus, if the historical record of Cu
is known at spatial point XQ, Cu(x0,tQ) = f(tQ), then from (25) we deduce that \|/0(x0,t0) = f(tQ) and ^(x^t,,) =0, and (25) and
(28-32) can be applied to construct future records at any given spatial point x. Conversely, if the current record of Cu is
known at spatial point x, Cu(x,t) = f(t), then the historical record at any chosen XQ in the watershed segment can be
reproduced by switching XQ and tQ with x and t and using \|/0(x,t) = f(t). The integrals in (28), (29), and (32) can be
evaluated numerically; e.g., using the Romberg method, or using any readily available computer software (e.g.,
Mathcad, Mathematica, etc.).
It should be noted that t(x) in (32) can be interpreted as the average age of ground waters discharging at spatial point x,
which originate at time /0 between x0 and x. We note that it is not only a function of the ground-water flow rate at
upstream boundary of the ground-watershed, but also the geometric and hydraulic properties of the aquifer and the
recharge rate. Thus, Equation (28) indicates that a mixture of newly-recharged and old aged waters originating over
transect length / affects the quality of current discharges to a stream, with the impact of aquifer bed inclination
approximated by Equation (29).
3. Potential Nitrate Reduction by Deep Denitrification
In this section we demonstrate the effectiveness of denitrification in the subsurface on potential nitrogen reduction in
riparian buffer zones. The methodology is applied to paired agricultural watersheds in the mid-Atlantic coastal plain,
and the site of study is hereafter referred to as the Locust Grove (Figure 1).
10
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3.1 Study Site Description
3.1.1 General
Figure 6(a) shows the portion of the Locust Grove study site (378 km2) in Kent County, Maryland, which is targeted for
new drilling activities and measurements of water levels and stream discharges by the USGS (Baltimore and Dover).
The site is composed of two agricultural watersheds of areas that are drained by the Morgan Creek and the Chesterville
Branch (Figure 1). This site is bounded from the north by the Sassafras River. Both streams drain in to the Chester
River, which borders Kent County in the south and is located along the northeastern shore of the Chesapeake Bay.
Agriculture dominates the landscape in the study area and most of the land there is used to grow corn and soybeans in
an annual rotation with winter wheat. Riparian forested areas are marginal and restricted to strips along the two creeks
and a part of the land is used to grow ornamental trees. Soil in the study area is predominantly silt loam and to a lesser
extent ranges from loam to sandy and gravelly loam. The area is underlain by the surficial (Columbia) aquifer, which
consists of sand and gravel of fluvial origin.
Figure 10(a) shows regressed record of nitrate NO3~ (mg/L) loading from fertilizers to the water table starting in the year
1940 (adapted from Bohlke and Denver, 1995). The data are based on annual N load from fertilizers estimated from
fertilizer use records of the U.S. Department of Agriculture from 1945-1985 (Alexander and Smith, 1990) and from
records of the U.S. Environmental Protection Agency for 1985-1991. The data, however, are regionally averaged by
apportioning the annual tonnage for the state of Maryland according to the fraction of the fertilized acreage within Kent
County (1945-1985) or the fraction of the state expenditures attributed to Kent County (1985-1991). The estimate of
annual application of N in fertilizer was estimated to be around 12 g/m2/yr, and an independent estimate by Donigian
et al. (1991) indicated a value of 9 g/m2/yr for the Chester River watershed.
3.1.2 Geology of the Area
Geologic units in Locust Grove, and in Kent County, in general are chiefly composed of southeast-dipping Coastal
Plain sediments that form wedge-shaped sedimentary packages that thicken to the southeast. Truncating and blanketing
the top of these units are coarse sediments of dominantly fluvial origin (Bachman, 1984; Drummond, 1998). From
KILOMETERS 0123
Figure 6.
Wells network in the study area. A triangle refers to a well from which the USGS synoptic ground-water levels and
quality are measured, and a solid circle refers to a core hole location.
11
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youngest to oldest, the geologic formations in the Locust Grove area and their regional or correlatable equivalents are
(following Hansen, 1992): The Upper Miocene (?) to Lower Pliocene (?) Pensauken Formation (equivalent to the
Wicomico and Columbia Formations), Middle to Upper Oligocene Old Church (?) Formation, Upper Paleocene Aquia
Formation, Lower Paleocene Hornerstown Formation, Upper Cretaceous Severn Formation (part of the Monmouth
Group), Upper Cretaceous Mt. Laurel Formation (part of the Monmouth Group) and the Upper Cretaceous Matawan
Group. Lithologic descriptions that follow are based on the work by Hansen (1992) on core hole Ken Bf 180 near
Chesterville in Kent County. Some additional description is based on personal communication from Dave Krantz
(USGS-Dover, 1999) based on drilling in the Locust Grove area. A description for each formation is given in
Appendix E.
3.1.3 Hydrostratigraphy
In the Locust Grove site and adjoining areas, the Pensauken Formation, Aquia Formation, and equivalents to the
Columbia aquifer comprise the surficial unconfmed aquifer in the area. Underlying the surficial aquifer is the first
aquitard or confining unit composed of the units of the Aquia Confining Layer, although areal or regional continuity of
this unit is uncertain. Note that for regional studies, some investigators group the Aquia and the underlying
Hornerstown together to form the Aquia Formation (Clark, 1915; Overbeck and Slaughter, 1958). Drummonct'(1998)
grouped sediments including the Pensauken Formation and Kent Island Formation to form the uppermost Columbia
aquifer. He next defined, for his MODFLOW model of Kent County, a lower aquifer, the Aquia, comprised of the Old
Church, Nanjemoy, Aquia and Hornerstown Formations, as done by Hansen (1992). The latter noted that the Columbia
aquifer in Kent County (composed chiefly of the Pensauken Formation), is hydraulically connected to the subcropping
Aquia aquifer locally in Locust Grove. Regionally, the Aquia aquifer includes the lowermost Hornerstown Formation
(Overbeck and Slaughter, 1958; Hansen, 1992; Drummond, 1998), but Bohlke and Denver (1995) and Krantz (1998,
personal communication) have cited the large gamma spike at the base of the Aquia Formation, above the Hornerstown
Formation, as a confining layer locally. However, ffansen(\991) has cited the Severn Formation and basal beds of the
Hornerstown as a confining unit underlying the Aquia aquifer regionally. The finer-grained nature of the Severn
Formation is a definite factor in establishing this unit as the main, or part of the main, confining unit beneath the Aquia
aquifer.
Overbeck and'Slaughter'(1958) and Drummond(1998) classified the Monmouth aquifer as composed of the Mt. Laurel
Formation and sandy units of the Matawan Formation. Beneath the Monmouth aquifer, the Matawan is a well defined
confining unit in the area (Overbeck and Slaughter, 1958; Hansen,l992; Drummond, 1998).
Krantz (personal communication 1998, 1999) identified local hydrostratigraphic units in the Locust Grove area based
on gamma and lithologic logs from a recently established well network shown in Figure 7. From top to bottom, these
are: Pensauken Formation (which is the Columbia aquifer in Kent county), Aquia sands, redox zone, Aquia confining
layer tight (impermeable) unit, Hornerstown, Hornerstown sand (?), Hornerstown confining layer, and Severn. The
Aquia confining layer has been identified and documented as the gamma spike also observed in the report by Hansen
(1992) for KEBf 180.
For the Aquia confining units, Krantz (personal communication 1998, 1999) characterized the Aquia redox zone as a
low-permeability oxidized unit. Beneath this is a clayey unit, which gives a tight gamma spike in geophysical logs,
comprising the Aquia impermeable confining layer. Based on the averages of 8 thicknesses measured for the Aquia
redox confining layer and 10 thickness measurements for the tight Aquia confining layer, average thicknesses of 4.2
meters and 3.8 meters were calculated for the redox layer and tight (impermeable) layer, respectively.
3.1.4 Locust Grove Local Well Network and USGS-USEPA Data Sets (1997-1999)
A recent set of wells and core holes was established in the Locust Grove site based on an EPA-USGS Interagency
Agreement on Ecosystem Restoration in the Chester River watershed. Figure 6 shows wells network and core holes
locations provided by Drummond(1997) of the Maryland Geological Survey and David Krantz (1998-1999) of the
USGS-Dover. The wells network is used for measuring ground-water levels in wet and dry seasons, collecting ground-
water samples for geochemical analysis, and obtaining core samples for the description of the hydrostratigraphy. In
Appendix F, Table 1 lists core holes either recently drilled by the USGS in Locust Grove or obtained from records with
information on what geologic information was provided as of this writing. Table 2 in Appendix F provides some recent
synoptic water table measurements provided by the USGS for Locust Grove.
12
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3.2 Preliminary Assessment
Figure 7 (b) is an enlargement to the local area contained within the dashed box in Figure 7 (a). Figure 7(c) shows cross
section A-A', which is synthesized from a three-dimensional geologic model developed from the core holes (Table 2)
obtained from D.Drummond(Maryland Geological Survey) and/?. Krantz^.S. Geological Survey, Dover), and using
the GMS module (The Department of Defense Ground-water Modeling System). The cross section runs from the
northeastern branch of the Morgan Creek to the northwestern branch of the Chesterville Branch. The cross section,
which spans the surficial Columbia-Aquia aquifer, is chosen for the assessment of impacts of the geohydrology and
geochemistry on reductions of NO3~ loading to the Morgan Creek and the Chesterville Branch. In particular, we focus
on the integral effect of the zone of reducing sediments and regional dip of the stratum on the reduction of input
nitrogen that is recharging the water table. Because oxic waters dominate in the upper layer, denitrification of NO3~ is
assumed to occur exclusively in the lower layer of reducing sediments and at an instantaneous rate; i.e., kt = °° and
Cj(x,t) = 0. Thus, NO3" concentration C(x,t) is therefore given by:
(33)
where Cu (x, t) ~ \|/0 (x, t) + (3 \\fl (x, t) and Q^x) and Qu(x) are given by (10) and (14). At the base flow in the Morgan
Creek and the Chesterville Branch, we simply evaluate C(/,/), and /, recall, is the distance from the water divide to the
stream (Figures 3 and 4).
Figures 8(a) and 9(a) compare theoretical head of Equations (4) and (7) with average annual measured heads at the
Morgan Creek and Chesterville Branch sides of the Cross Section A-A' shown in Figure 7(c), respectively. The
inclination of the surficial Columbia-Aquia aquifer bed at this particular cross section was (3 = 0.0052 (0.3°), which is
obtained from the constructed geologic model. Bohlke and'Denver'(1995) reported a value of about 0.4° for the regional
dip. The fitted recharge value for the Morgan Creek side of cross section A-A' and the conductance K'/b were
76 "01 40"
75°573Q"
75°53'45"
39°2037" -
39°18'45"
-39°2037"
-39°18'45"
|-39°16'40"
76 "01 40"
© KE BE Wells ©Other Wells
75°5730"
1000 2000 m
LStream Gauge
75°53'45"
ITowns
Figure 7(a). Overview of the location of cross section A-A' relative to the Locust Grove site and the wells network.
13
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MORGAN
KE Be 156
BRANCH
62, 162, 163
E-88-0695
KEB6159 " KEB863
KE Be 211
Figure 7(b). Cross section A-A' between the Morgan Creek and the Chesterville Branch with adjacent wells labeled. The dashed
line delineates the ground-water divide.
Morgan Creek
Chesterville Branch
m u^.
-------
35
1 Divi
Divide
Morgan Creek
30 -
25 -
1 20J
co
£ 15-
10 -
5 -
Asymptotic solution
Exact solution
Aquifer bed elev.
O Measured head (m)
K'/b1 = 2.0 d
Stream
Stage
0 250 500 750 1000 1250 1500 1750 2000 2250 2500
x(m)
Figure 8(a). Measured versus estimated heads at Morgan Creek watershed.
Divide
Morgan Creek
1.2
1.0 -
0.8 -
0.6 -
0.4 -
0.2 -
0.0
Asymptotic solution (lower layer)
Exact solution (lower layer)
Asymptotic solution (upper layer)
Exact solution (upper layer)
0 500 1000 1500 2000 2500
x(m)
Figure 8(b). Measured versus estimated ground-water fluxes at Morgan Creek watershed.
15
-------
2.4 x 10~4 m/d (3.5 in/yr)and2.0 d"1, respectively, whereas at the Chesterville Branch, calibration yieldedN = 2 x 10~3m/d
(29 in/yr) and K'/b' = 2.0 d"1. However, an independent estimate of K'/b' = 0.2 d"1 (K' = 0.4 ft/d, b'= 2 ft) was obtained
by Drummond'(1998) by calibrating a regional ground-water model (MODFLOW) for Kent County. An independent
value for the hydraulic conductivity of magnitude 16.76 m/d is used. This value has been suggested by Reilly et al.
(1994) for the surficial aquifer and within the range of values reported by Drummond'(1998). The calibrated recharge
at Morgan Creek was somewhat low, however, it is consistent with the relatively poorly-drained soils at the Morgan
Creek watershed (Hydrologic Classes C and D). In general, recharge to the northern Atlantic Coastal Plain aquifer
system has been estimated to range from 10 to 25 in/yr (Meisler, 1986), and the average of the above fitted values is
about 16 in/yr, which is within range. Although the calibrated values may be valid locally (i.e., to the particular cross
section), they may not be generalized to the entire area of the paired watersheds. The exact head distribution of Equation
4 and the asymptotic approximation of Equation 7 compared very well as Figures 8(a) and 9(a) show. Figures 8(b) and
9(b) compare ground-water flux in the upper (oxic) layer and lower (anoxic) layer, in both creeks, using exact solutions
(Equations 11 and 12) and approximate expansions (Equations 13 and 14). The thickness of the lower layer of reducing
sediments (redox zone) was estimated to be 3.2 m on the basis of the three-dimensional geologic model (see,
Figure 6(c)). At Morgan Creek, about 80% of the total recharge was discharged from the redox zone (lower layer), and
the remaining 20% was discharged from the upper layer. Thus, most of the ground waters entered the reducing
sediments because of the positive inclination of aquifer bed ((3 = 0.0052) toward the Morgan Creek. At the Chesterville
Branch, however, more than 80% of the base flow was discharged from the upper layer (i.e., all discharge ground waters
escaped denitrification), because of negative inclination relative to the reference ((3 = - 0.0052 in Figure 4).
Although the exact head solution and the approximate one compared very well, that was not the case for the ground-
water fluxes in Morgan Creek as Figure 8(b) indicates. The approximate (asymptotic) solution overestimated the flux
in the upper layer, especially toward the drainage divide, by as much as 16% and, consequently, the ground-water flux
in the lower layer was underestimated by the same amount. The error, however, declines toward the discharging point
(i.e., the creek) where an almost exact estimate of the base flows is achieved by the asymptotic solution. The estimates
of ground-water fluxes in the Chesterville Branch side were almost similar between the exact and asymptotic solutions
(Figure 9(b)).
Figures 10(a-d) and ll(a-d) show the impact of the historical record (1940-1992) of the recharging nitrate levels C*(t)
in Figure 10(a) on the base-flow nitrate-nitrogen levels at Morgan Creek and Chesterville Branch, respectively. We
have assumed that the average nitrate concentrations at the recharging waters C* after year 92 remained constant at
17 mg/L. The breakthrough values in the figures are obtained from Equations (21), (28-32) and (33) and assuming
ground waters are instantly and entirely denitrified in the lower layer (redox zone or layer of reducing sediments). In the
estimations, we used XQ = 50 m, tQ = [0, 52], and Cu(xQ,t0) in Figure 10(a) was derived by assuming complete mixing of
nitrate-N in ground waters between the water divide (at x = 0) and XQ = 50 m. The assumption of complete mixing from
x = 0 to 50 m is valid, considering the distances from the water divide (Figure 7a) to both creeks (£= 1112m and 2521 m
for the Chesterville Branch and the Morgan Creek, respectively).
Figure 10(b) shows NO3~ discharged at Morgan Creek: mass flux relative to the steady-state total nitrate input over the
entire transect £= 2521 m (N L C*(°°), C*(°°) is the assumed steady value of 17 mg/L). The predicted future synoptic
corresponds to the record shown in Figure 10(a), and because of relatively low recharge of 0.00024 m/d, its impact may
not be felt at Morgan Creek before year 2092. That is, at year 2092, the mixed-discharging waters at the Creek will
consist of very old ground waters, which were recharged at year 1940, as well as newer ground waters, including those
that would be recharging at the immediate neighborhood (e.g., in riparian zones). According to the definition of t(x) in
Equation (29), the average age of ground waters that would be discharged from the upper layer at Morgan Creek at
year 2092 is 152 years, being originated as recharging waters over a distance of 2521 m between the Creek and the
water divide. In order to predict the base-flow loading pre year 2092, the input record pre year 1940 will be needed.
Equivalently, base-flow nitrate levels pre year 2092 are impacted by nitrate levels in recharging ground waters before
year 1940.
The impact of denitrification in the reducing sediments and the aquifer bed inclination is evident in Figure 10(b). For
a positive dip angle of 0.3°, there is a potential for 80% reduction of NO3~ at the base flow, provided that ground waters
entering the redox zone are entirely denitrified. A steady state concentration of NO3~ of 3.4 mg/L (0.2x17 mg/L)
compared to 17 mg/L at the source is predicted at the discharge in Morgan Creek. Because of the nature of the dip
(Figure 7 (c)), more than 80% of ground waters were predicted to discharge to the Chesterville Branch through the
upper layer (Figure 11 (a)), therefore avoiding potential denitrification in the lower layer (redox zone) and resulting in
much less reductions of NO3~ levels by 15% at a steady concentration of NO3~ of about 15 mg/L at the base flow at
16
-------
20 -
10 -
co
CD
X
Divide
K7b'= 2.0 d"
Chesterville Branch
Asymptotic solution
Exact solution
Aquifer bed elev.
O Measured head
Stream
Stage
250
500
750
1000
Figure 9(a). Measured versus estimated heads at Chesterville Branch watershed.
1.0
0.8 -
& 0.6
H
a
0.2 -
0.0
Divide
250
Chesterville Branch
Asymptotic solution (lower layer)
Exact solution (lower layer)
Asymptotic solution (upper layer)
Exact solution (upper layer)
500
x(m)
750
1000
Figure 9(b). Measured versus estimated ground-water fluxes at Chesterville Branch watershed.
17
-------
0
0.1 -
0.0
CjnH = 17 mg/L
N = 0.00024 m/d
x = 2521 m
L = 2521 m
K'/b' = 2 d"1
140
160
180
200
t(yrs)
220
240
260
O
O
a
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
16
14
K'/b1 = 2.0 d"1
N = 0.00024 m/d
L = 2521 m
ClnH=17(mg/L)
Nitrate-N Flux at x = 60 m
Nitrate-N Flux at x= 100m
Nitrate-N Flux at x= 250m
Nitrate-N Flux at x= 750m
Nitrate-N Flux at x = 1500 m
20 40 60
100 120 140 160
t(yrs)
(d)
200 220 240
6 -
4 -
2 -
K'/b1 = 2.0 d"1
N = 0.00024 m/d
L = 2521 m
CinH = 17(mg/L)
: = 1500m
reakthrough atx = 60 r
reakthrough at x = 100
reakthrough at x = 250
reakthrough at x = 750
reakthrough at x = 150
0 20 40 60 80 100 120 140 160 180 200 220 240
t(yrs)
Figure 10. (a) Historical variations of NO3~ concentration at the recharge (at the water table) and at XQ = 50 m in the
upper layer, (b) Mass flux of NO3~ in time at the discharge to Morgan Creek relative to steady-state
input, (c) Mass flux of NO3~ discharged from upper layer to Morgan Creek relative to steady-state input
versus time, and (d) NO3~ concentration versus time.
18
-------
Chesterville Branch (Figure ll(c)). The less effective capacity of the subsurface sediments to reduce NO3~ at the
Chesterville Branch is not only influenced by relative position of the redox zone (i.e., negative (3 ) but also by the
relatively higher recharge rate.
It is clear from Figure ll(c) that the impact of the historical nitrate input (Figure 11 (a)) at the recharging waters
appeared earlier at the Chesterville Branch at year 1979 because of the relatively greater recharge and smaller travel
distance from the water divide. Thus, ground waters discharging to the Chesterville Branch are relatively younger when
compared to the discharging waters at Morgan Creek and, therefore, their relatively greater NO3~ concentrations are also
the result of more recent and greater nitrate loading at the source. In order to show clearly the impact of historical input
variations (C*(t)), we considered the hypothetical case of positive inclination (0.3°, (3 = 0.0052) to be applicable to the
Chesterville Branch (i.e., the redox layer becomes increasingly shallower toward the Chesterville Branch). Figure 1 l(b)
shows that a reduction of 30% is incurred due to deep denitrification, whereas 80% reduction was predicted for the
same, but actual, scenario at Morgan Creek. This may be explained on the basis that expected reductions by
denitrification are offset by elevated levels of NO3~ in fairly younger discharging ground waters due to the historical
input variations.
Bohlke and'Denver'(1995) reported values of zero mg/L of NO3~ at the discharge at Morgan Creek and 3-5 mg/L at the
Chesterville Branch, and the location where these values were measured within close range to cross section A-A. Our
predictions, based on the theoretical framework, were 3.4 mg/L and 15 mg/L at Morgan Creek and the Chesterville
Branch, respectively. The overly predicted NO3" levels at the Chesterville Branch may be the result of ignoring the
impact of riparian woodlands as natural filters, where ground waters discharging from the oxic upper layer may be
denitrified in silty, peat-rich stream valley sediments. Recall, in the analysis we assumed that ku = 0. The case where
NO3" removal occurs in the riparian stream valley will be addressed in a future effort. The preliminary analysis is
consistent with the geochemical analysis and the results reported by Bcihlke and Denver (1995) with respect to the
behavior of nitrate-nitrogen in ground water in the paired watersheds. It appears that a combination of deep
denitrification and historical input variations seem to impact the quality of ground waters being discharged to Morgan
Creek and the Chesterville Branch. The capacity of deep denitrification to reduce NO3~ discharge to streams is
dependent on the size of the drainage area as well as the relative position of the redox zone to the surface.
3.3 Removal Capacity
A simple relationship can be developed, which measures the efficiency for nitrate reduction in ground-water sheds. The
removal capacity index I is based on the following assumptions: 1) ground-water recharge, including boundary fluxes,
is at steady state (e.g., annual average) and drained entirely by a stream; 2) steady-state nitrate concentrations in ground
water on the assumption that current agricultural practices would persist at the current steady levels of net nitrate-
nitrogen input, C*, to ground water; and 3) complete mixing in each of the modeled zones. We define the removal
capacity index as the ratio of the rate at which the constituent is lost out of the system to the rate of input, at steady state,
[ we * + QOCO ] - [QU (i)cui+Q, (*)q (i)]
I —- - /QQ\
WC*+Q0C0 (33)
where 0 . If we assume that nitrate input persists at the current level of C* and that steady and
uniform concentrations in ground water are achieved, and integrate (17) from x = 0 to x = £ after dropping the term with
partial derivative in time, we have
thus,
~~' (35)
19
-------
o
O
14 •
6 •
4 •
2
20
(a)
40
60
100
t (yrs)
O
O
o3
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
(b)
Actual (P = -0.0052)
Hypothetical (P = 0)
Chesterville Branch
= 17mg/L
N = 0.002 m/d
x= 1112m
L = 1112m
K'/b' = 2 cf1
30 40 50 60 70 80 90 100 110 120 130 140 150 160
t (yrs)
D.
c
.0
2
o
O
O
O
a
16
14 -
12 -
10 -
4 -
2 -
0 -
Chesterville Branch
K'/b1 = 2.0 cf1
N = 0.002 m/d
L = 1112m
CjnH = 17mg/L
Nitrate-N Flux at x = 60 m
Nitrate-N Flux at x = 500 m
Nitrate-N Loading at C.B.
20 40
60
100
120
140
160
t (yrs)
(d)
Chesterville Branch
K'/b1 = 2.0 d~1
N = 0.002 m/d
L = 1112 m
CinH = 17mg/L
Breakthrough atx = 60 m
Breakthrough atx = 500 m
Nitrate-N Loading at C.B.
20
40
60
100
120
140
160
t(yrs)
Figure 11. (a) Historical variations of NCy concentration at the recharge (water table) and at x0 = 50 m in upper layer, and (b)
Mass flux of NO3" in time at the discharge to Chesterville Branch relative to steady-state input, (c) Mass flux of
NO3' discharged from upper layer to Chesterville Branch relative to steady-state input versus time, and (d) NCy
concentration versus time.
20
-------
where CB =(l//)jCll(x) which upon the
substitution into (35) yields ^T~^*, „ // / ^^> ^
JVC/ + (l-(6/r|0))e0C0
(36)
in which r\Q = r|(0) is the water-table elevation relative to the aquifer bed at the inlet boundary; nu is the porosity of the
oxic layer; and as shown in Appendix D,
(37)
(3 K 2 21
In (36) we made use of (1 1) and (12). Similarly, we integrate Equation (20) from x = 0 to x = /:
(38)
The use of the third stated assumption (Q(/) = Q , C (/) = C~) and the substitution of (11) for QftS) and £?//), leads
to
, ^/^VA,7,^ ^/-^ ^(/) ^^
in which #, is the porosity of the redox layer. Finally, we obtain the following form for the removal capacity index IRC
given by (33) for the case of a water divide at x= 0; i.e., Qu(fy = Q$) = 0,
J*c = l-
in which IRC may be used as a measure for the removal efficiency of NO3~ in an agricultural catchment. If ht = b and
assuming that ground waters are instantly denitrified in the redox layer (/^—> °°), we have IRC=^\ because the aquifer
below the stream would be entirely occupied by the redox layer where all ground waters would be intercepted by the
reducing sediments before discharging to the stream. In this particular case, the redox zone acts as a potential natural
filter for the entire subwatershed, which is not uncommon to the northeastern branch of Morgan Creek where the
streambed is almost underlain by the redox zone at several locations as the constructed geologic model predicted. If k
= 0 and /^—>°°, we have IRC= bl r\r which is the case assumed in the application in the previous section where nitrate
reduction is entirely controlled by aquifer geometry at the discharging points. Figure 12 shows the variation of IRC with
£ for different values of the dimensionless parameter e = N/{(K'/b')W}. The removal capacity decreases with
transect length, £, and increases with decreasing e. This relationship shows that NO~3 removal is also influenced by the
characteristics of groundwater-surface-water interface and the recharge rate. The greater the recharge, or equivalently,
the smaller the streambed hydraulic conductance and width, the smaller the removal efficiency.
Figure 13 illustrates possible nitrate loss pathways in a riparian zone and related hydrologic and hydrogeologic factors.
In a stream riparian environment, the flux QQ at x = 0, which is equal to the total drainage from the agricultural uplands
of the watershed, may be much greater than the recharge N; i.e., N ~ 0. Also, nitrate loading is dominated by drainage
from agricultural uplands, QQ CQ, as opposed to input from riparian zones, where N C* may be relatively ignored. Thus,
Equation (33) can be used to derive an expression for the removal capacity for nitrate introduced at the upgradient
boundary of the riparian zone at x= 0, by setting N = 0 in (36) and (39), and substituting the resulting expressions into
(33):
21
-------
0.5
0.0
P = 0.0075, K2 /Kj = 1, k,= 10 d4, b = 2m, H = 15 m,
L = 2000m, Q0=0
e = 0.01
e=l
e=10
10
100 1000
/(m)
10000
Figure 12. Semi-log plot of the removal-capacity index I versus t for different values of the dimensionless parameter e.
Riparian Zone
NO3~ ^Percolation
Atmospheric
Depositions
Alluvial Stream- (Nr^^
Valley Sediments o \-_r~ ~^-
1-^ Uptake _—
_1^ by trees_ —
"*
Source: Croplands
Discharge —;
•^^
Losses (denitrification)
Figure 13. Illustration of a riparian zone showing potential NO3~ loss pathways in organic-rich soils and subsurface sediments
and related hydrological factors.
22
-------
ri,-b | b + ft^)n*-7?o- (41)
77, 77,
We emphasize that Equation (7) can be used to estimate r|0 only when N > 0. This approximation and that expressed
in (25) for Cu(x,t) are not valid when N —> 0. In fact, it was observed that the convergence of the integrals in (28) and
(29) slows down considerably as N is chosen arbitrarily smaller. The case of negligible recharge requires a separate
analysis which is currently under investigation. Equation (41) can still be applied to riparian zones whenever r|0 can be
measured at the inlet boundary. In (41), ku may account for the rate of loss by denitrification in the organic-rich stream
valley sediments and uptake by the vegetative cover (e.g., trees and shrubs) in the riparian buffer.
4. Regional Ground-water Flow and Nitrate Transport and Fate Model
A regional ground-water flow model is being developed, which covers the paired watersheds and extends from north at
the Sassafras River to south at the Chester River. The objective of the model is: 1) to estimate regional water levels and
total ground-water discharge (base flow) to Morgan Creek and the Chesterville Branch; and 2) to estimate total nitrate
base-flow discharge to the Chester River in relationship to potential deep denitrification. The model is developed using
the GMS model which implements MODFLOW, MODPATH, and MT3D modules within user friendly Graphical User
Interface (GUI). Because of the complexity of the hydrostratigraphy and drainage network in the Locust Grove site, the
effort comprised of the following major steps: 1) development of the geologic model from core data (e.g., Figure 6(c));
2) development of the conceptual model, including recharge distribution, imposition of boundary conditions, leakance
between hydrostratigraphic layers and aquifers, and delineation of the surface-water drainage network and related
hydraulic properties (Figure 14); and 3) numerical simulations and calibration. Two models are considered; a one-layer
model and a four-layer model. In the latter, the surficial (Columbia/Aquia) aquifer was separated into an upper (oxic)
and lower (redox) layer, and the lower Hornerstown and Monmouth aquifers were represented with two distinct layers.
Because the northern and southern boundaries of the ground-water flow domain coincide with the Sassafras River and
the Chester River, respectively, a prescribed-head boundary of zero is assumed on each boundary. The western
boundary (Figure 14) delineates the surface-water drainage boundary and, therefore, is assumed to approximate a
ground-water divide, and a no-flow boundary thereby is imposed there. On the east side, however, two types of
boundary conditions were considered: 1) a no-flow boundary along the surface-water drainage divide (to the east of
Mills Branch); and 2) a prescribed-head along Mills Branch, with the head equal to the surface elevation along the
Creek, and to the north of this Creek toward the Sassafras by interpolation with reported observed heads. Figures 15 and
16 show the GMS simulated heads for the wet season (November-April), which is characterized by high evapotranspi-
ration, for the two scenarios of no-flow boundary and a prescribed-head boundary on the east side of the ground-water
flow domain. The two boundary conditions produced almost similar head distribution, except that a well-defined
mound is produced between Morgan Creek, Chesterville Branch, and Mills Branch, when the latter creek is used as a
prescribed-head boundary (Figure 15). Figure 17 shows ground-water flow directions during the wet season for the one-
layer model. It is clear that ground-water flow is eventually discharged as base flow to the surface-water drainage
system.
Figures 18-21 compare simulated heads with observed seasonally-averaged water levels for the wet (November-April)
and dry (May-October) seasons, and the comparisons for the different flow scenarios mentioned above were quite
remarkable. Figure 22 compares the simulated surface-water discharge in the Morgan Creek to observed values at the
stream gauge stations (labeled with triangles in Figure 6(a)) during both seasons. Because of relative homogeneity of
the surficial aquifer, the hydraulic conductivity was assumed to be 16.76 m/d as justified in the above section. The
recharge was calibrated for a high value of 0.0016 m/d and a low value of 0.0012 m/d and the calibrated recharge values
for the dry season were one-tenth of the wet season recharge values. The close comparison between the estimated and
observed stream discharges may verify a fairly good model performance given the complexity of the actual drainage
network.
23
-------
Figure 14. Regional ground-water conceptual model including surface-water drainage network, with the prescribed head equal
to zero (sea level) at the Sassafras River to the north and the Chester River to the south, and no-flow boundary
elsewhere.
Figure 15. Simulated steady-state ground-water heads in the wet-season (Nov.-Apr.) for the case of prescribed heads along
Mills Branch located on the eastern border of the flow domain.
24
-------
Figure 16. Simulated steady-state ground-water heads in the wet season (Nov.-Apr.) for the case of no-flow boundary on the
eastern border of the flow domain.
Figure 17. Ground-water flow directions simulated in the wet season (Nov.-Apr.) for a one-layer model.
25
-------
One-Layer Model
Wet Season
(a) Fixed-Head Boundary (East Side)
25 -,
J- 20 -
•o
8 15 4
10 -
5 -
0
0 5 10 15 20
Measured head (m)
25
(b) No-Flow Boundary (East Side)
5 10 15 20
Measured head (m)
25
Figure 18. Simulated versus measured heads in the wet season (Nov.-Apr.) for a one-layer model: (a) prescribed-head on the
east side, and (b) no-flow boundary on the east side.
Dry Season
(a) Prescribed-Head Boundary (East Side)
25!
J. 20 -
| 15-
3 1
-------
Four-Layer Model
Wet-Season
No-Flow Boundary (East Side)
25 -|
J. 20 -
•o
| 15 -
| 10
1 5
5 10 15 20
Measured head (m)
25
Dry-Season
No-Flow Boundary (East Side)
25 i
5 10 15 20
Measured head (m)
25
Figure 20. Simulated versus measured heads at surficial aquifer (four-layer model with no-flow boundary on the east side): (a)
wet-season (Nov.-Apr.), and (b) dry season (May-Oct.).
Four-Layer Model
Hornerstown Aquifer
Wet Season
No-Flow Boundary (East Side)
20
•o
ro
to
£
(75
15 -
10 -
5 10 15 20
Measured head (m)
Figure 21. Simulated versus measured heads at Hornerstown aquifer in wet season (Nov.-Apr.) (four-layer model with no-flow
boundary on the east side).
27
-------
Measured Versus Estimated Discharges (mVd) at
Morgan Creek and Chesterville Branch
Wet Season
(a) One-Layer Model
(b) Four-Layer Model
20000
o
5000 10000 15000 20000
Measured Q
20000 -,
5000 10000 15000 20000
Measured Q
Figure 22. Simulated versus measured stream-flow discharges at Morgan Creek in the wet season (Nov.-Apr.) (no-flow
boundary on the east side): (a) one-layer model, and (b) four-layer model.
The integrity of the ground-water flow model will be critical in the assessment of the nitrate fate and transport in ground
water and the estimation of the capacity of the ground-watershed to reduce nitrogen loading to the Chester River by the
process of deep denitrification. Refining the model is planned in the coming year, and field measured values for the
hydraulic conductivity and transmissivities of the lower aquifers will be obtained using slug and pumping tests in order
to improve the model performance. It is worth pointing out that it is not clear if any further calibration is worthwhile in
light of the remarkably good reproduction of the observed heads and stream discharges by the numerical model.
5. Summary, Conclusions, and Future Directions
Two adjacent watersheds in the mid-Atlantic coastal plain show significant disparity in base-flow nitrate levels. It is
likely that a combination of deep denitrification (reducing subsurface sediments) and historical input variation are
mainly responsible for the disparity in observed base-flow nitrate levels. Until recently, previous studies focused on the
effects of shallow riparian zone reactions on nitrogen reduction in the discharging ground waters, and with less
emphasis on deep denitrification as an integral part of the riparian zones. In this joint effort between the USEPA and the
USGS, a well network has been established at the site for survey of synoptic water levels and nitrate concentrations in
ground water and at surface water discharge to the Morgan Creek and the Chesterville Branch. A scientific framework
has been developed based on the laws of physics and conservation of mass in order to assess potential impact of deep
denitrification on the reduction of nitrate discharge to surface waters. The framework varies from local scale to the
regional scale. The former involves the development of analytical characteristic solutions, which aim at understanding
the impact of geohydrologic factors, such as ground-water-flow pattern and geometric setup of hydrostratigraphy, on
the potential for nitrate reduction by denitrification. Also, a simple index is developed using basic physical principles,
which may be used as a measure of the removal capacity for nitrate in ground-watersheds. At a larger scale, a regional
model is being developed for the area, which aims at exploring the impact of denitrification in the subsurface on the
overall nitrate budget at the watershed scale.
Analysis based on the local-scale hydrologic and transport models indicated that the observed differences in base-flow
nitrate levels between the two watersheds may be explained on the basis of denitrification in relatively deep subsurface
reducing sediments. The models predicted a much greater capacity to reduce nitrate levels at the discharge point in
28
-------
Morgan Creek as opposed to the Chesterville Branch. The regional dip of the strata resulted in a relatively shallower
redox zone below Morgan Creek as opposed to the Chesterville Branch, and this, in combination with the ground-water
flow pattern and historical input variations, resulted in greater denitrification in the former watershed. Although these
results are consistent with the reported field findings, the observed nitrate levels in the discharging ground waters below
the Chesterville Branch were remarkably lower than theoretical predictions. This indicates that other processes may be
responsible for removal, such as denitrification in peat-rich stream valley sediments. The local-scale framework,
however, is adaptable to integrate deep denitrification and removal at the ground-water-surface water interface as an
integral element of the self-purifying nature of riparian zones. Indices were developed and proposed for the assessment
of the removal capacity of watersheds for nitrate in ground water. The indices relate nitrate reduction in stream riparian
zones to potential denitrification in subsurface reducing sediments and organic-rich stream-valley alluvium, and the
geometric and hydraulic properties of the underlying aquifer. The implication of the findings may be twofold. First,
they emphasized the possible role of deep denitrification as an integral element of riparian woodlands on nitrate
reductions. Second, the models, including the removal efficiency indices, may be used as management tools for
agricultural practices in agricultural watersheds where effective subsurface denitrification ocurrs. Although not
conclusive, the presented analysis indicates that deep denitrification has a potential for significantly reducing nitrate
loading in ground-water discharge to streams, such as the case in Morgan Creek. The analysis was based on county-
level averaged net nitrate input to ground water. The impact of the spatial variability of nitrate at the source can be
significant in the interpretation of base-flow nitrate loadings, and needs to be addressed in future studies. Additional
field work and analysis is needed to support this theory and to resolve the effectiveness of deep denitrification from
other processes responsible for nitrate removal in riparian zones, such as denitrification in organic-rich stream valley
sediments, assimilation by plants, immobilization by bacteria, or microbial nitrate ammonification. The capacity for
nitrate removal by riparian buffer zones is not completely understood, including processes occurring within soils and
streams. More intensive sampling would be required to confirm the effectiveness of deep denitrification on nitrate
removal, including sampled synoptic base-flow nitrate levels below each creek and across the peat-rich stream valley
sediments. This is planned for FY 2000 as a supplement to the current IAG project, including sampling from 33 new
wells, in addition to extensions of the theoretical framework and the development of the regional nitrate transport and
fate model. The network includes multilevel and multiport wells, which are bracketing the redox zone. Planned, also, is
the implementation of the proposed NO~3 removal capacity index IRC in GIS for the Locust Grove study area for the
purpose of delineating watersheds according to their potential removal efficiency for ground-water nitrate, and develop
maps as tools for management purposes. The research is expected to provide a scientific modeling foundation and
insights into the removal of nitrate in riparian environments, with implications on nitrogen management in agricultural
watersheds.
29
-------
Appendix A
The integration of (1) yields
*r dh Ar
Kr\ — + Nx = C (Al)
dx
in which C is a constant that can be obtained by imposing boundary condition (3a),
-P>x) + Nx = -On (A2)
dx
After multiplying (A2) by dx and using the following linear transformation
^ = Nx + Q0 (A3)
Equation (A2) can be expressed as
r\dr\ + —
N KN
Consider the transformation
Ti(x) = v(x)S(x) (A5)
which if used in (A4) yields the following ordinary differential equation
(v2+— v + - )d£ +
v N KN
The dependent and independent variables can now be separated:
After adding and subtracting the same term from the left-hand side of (A7) and completing the square in the
denominator, one obtains
J| 1 (2v + $/N)dv __ P __ dv
t 2 v2+/7Vv +
where
^2=^^7~T 2 (A9)
KN 4 N
Thus,
, | . p rfv ^Q
J 2 J 22 (A10)
30
-------
The third integral can be put in a form readily available for integration if we define the new variable u = (v + P /(27V)) / y,
then du=(\l%)dz, and
27Vy w2
(AH)
The evaluation of the integrals in (All) is straightforward:
ln£ + — Inv2 +—v +
TV KN
" -,an-
2/Vy
if y is a real number
(A12a)
In 4 +-In
,2, P
v + — v + -
1
N KN
v + -
2N,
coth l u = a,, u =
2N
if y is a complex number (A12b)
in which al is a constant of integration to be determined by imposing the boundary condition (3b). Hereafter we
consider the realistic case of y2 > 0. The solution (A12b) may be used in the case of negative recharge (e.g., when
evapotranspiration exceeds infiltration). The substitution for v and u in to (A 12) and taking the exponential of both
sides should yield
N
KN
-exp
Nj
-tan
'1
J]W_ + .P
2N
J
(A13)
in which a2 is a constant, which can be obtained by evaluating (A13) at x = /after taking the exponential of both sides
and substituting r|/for r\(/), to yield
(3
• exp
-------
N
KN
K_
N
-i
tan'1 -JKN-
-i
-tan'1 -JKN-
(A16)
Thus, by collecting terms of equal order in (3, we have the following equations for the zero-order term,
(3(0):
(A17)
and the first-order term,
(3d):
01
N
KN
tan
'1
(A18)
Equation (A17) can be solved directly to yield (8), which after the substitution into (A18) and solving for (j)j(z) results
in (9).
Equations (13) and (14) follow immediately by substituting the asymptotic expansion of (7) for r\(x) in (1 1)
Q,(x} -(Nx + Qr,}
and expanding the quotient in Taylor series about (3 = 0,
The approximation (14) for Qu(^) can be obtained directly by subtracting (A20) from QT(.r) or by the substitution of (7)
into (12) and following the same procedure above.
32
-------
Appendix B
In this section we derive the differential equations that govern the zero- and first-order concentrations. We start by
dividing Equation (18) by QU(X)
u _ N r.r .,,,
1 --- 1 -- c,. = - c \x,t(X))
u
,.
&W dt dx Qu(x) u Qu(x)
and introducing the following characteristic time relationship:
dt _ T\(x) - b
* = "~ow~
Since it is known from calculus that total derivative (or convective derivative) is given by
^Vo _ dVo , ^Vo dt
~ ~> -\
dx dx at dx
Then, (Bl) can be written in the following Lagrangian form
N * .
{B2)
u _
1 -- C,. =
"
,.
Qu(x) " Qu(x)
The coefficient of Cu and C* can be expanded in Taylor series about (3 = 0 after substituting (12) for Q (r), and (7) for
(B5)
and
N N
(B6)
Equation (B4) can be written after the use of (7), (12), (B5), and (B6) as
33
-------
...
dx dx (B?)
*
Thus, by collecting terms of equal powers in (3 , we have the following ordinary differential equations for the zero- and
first-order approximations of \|/u:
(3°:
fi\\t ^ *
f (x)\\f = f (x)C \x t(x)~] (B8]
dx
-p- + /j (x) Vi + /2 O) Vo = /4 W c* [x, t(x)] (B9)
Equation (B8) is equivalent to (26), and (27) follows immediately by inserting fory^(jr), _/£(*), and/^z) in (B9) and
arranging terms. The solutions are given in (28) and (29) by multiplying both sides of each equation by the integration
factor and integrating from tg to / and xg to x
and
JJ(¥l^)^))=ifc(^)C*[t^)]-/2(^)¥o(^)k^)4 (Bll)
x0 x0
where
The integral on the right-hand side is carried on in Appendix (C) as given by Equation (30).
A zero-order n approximation to Equation (21) can be obtained by substituting (10) and (12) for Qu(r),
dt r
Thus,
^n^W- + n/3^- (B14)
dx Q0 + Nx Q0 + Nx ( '
The integration of the zero-order term from /^to /and xgto x yields:
34
-------
This integral is evaluated in Appendix C to yield
.
In
-In
(B16)
in which a* is given by (31).
35
-------
Appendix C
Consider the transformation
1 f-r s^ \2 * 2
x + On) =a cos u
KN
Taking the derivatives of both sides yields
2
—(Nx + O0)dx = —2a cosusinudu
K
By substituting for (j) 0(x) and using the transformations (Cl) and (C2), the above integral can be written as
, sin2 u . , s
J du (C3)
JV COSM
The use of the fundamental trigonometric identity sin2u + cos2u = 1 in (C3) yields
/, = \\ du- ]cosudu> (C4)
TV [ cosw J
From Gradshteyn andRyzhik(\^^), we have
, 1 , , 1 + smw
J du = \n :— + c (C5)
cosw Vl-smw
in which c is an arbitrary constant. Thus,
1 + sinw
/, =
1 TV [""Vl-sinM
Using (Cl) and the above trigonometric identity, it can be shown that
1 , , ,
! 0 ,
In— j= — u H --
72=J +nku
J
oW (C7)
A/a
The use of (C7) in (C6) yields
36
-------
We seek the first integral since the second is evaluated above and is given by n ku
/ -1 N (
3 'Qa + Nx(^(x)-b
First, we express (C9) as the sum of two integrals,
T f N J f
73 = J dx+\-,—
Q0+Nx J(g0-
The evaluation of the first integral in (CIO) is straightforward,
N
f £^£ = |j^ | /^ _|_ ^T J£ I _(_ £
O ~i~ -/V jc
In the second integral (referred to I4) in (CIO), we introduce the transformation
, * 1 /
> -u2)(u-b)
which can be written as
in which we expressed (C14) in terms of sum of fractions,
u A, Aj A-,
_ i __ i __ £ __ i __ J
or
(C12)
J.\^ .L >
Taking the derivative of both sides yields
2udu = - — (Q0+Nx)Ndx (C13)
The use of (C12) and (C13) in the second integral in (CIO) should yield
, f u
du (C14)
^ '
_ . 1 , du 1 , du b , du .
14 = —b\ i ,— \\ ,— 1—/ ,— \\ i— 1—j 7! -f (C]^
-,(/ * t /..* .. ^l/.* . t /..* . .. /i _ A2 i/ - h\ \^LD)
(a*-u2)(u-b) Vo^-w Va*+w w~'
and the constants Ap A2, and A3, are easily obtained. Thus,
/4=-TTT \ln(V/-w)—TTT \ln(V7 + w)—^—^\n(u-b)+c (C17)
37
-------
* 7
a -b
(C18)
Finally, since
I2 = ln(Q0+N ^) + I4 + n ku I: + c (C19)
Then Equation (30) can be easily verified by substituting (C8) for I: and (C17) for I4 and taking the exponent of both
sides.
38
-------
Appendix D
The average thickness of ground water flow in the upper layer is given by:
r I7
0
and when integrated from x = 0 to x = I yields
Thus,
Finally, the substitution of (D5) into (Dl) yields the desired result in Eq. (37).
39
(Dl)
An exact expression for r|(jt) can be obtained by, first, expressing Eq. (A2) as
r|^l+Br| + — jc = -^o. (D2)
dx K K
or equivalently,
(D5)
o P| 2 K 2 ^ ^
-------
Appendix E
Pensauken Formation
The surficial Pensauken Formation consists mainly of orange and reddish brown gravelly sand composed of quartz and
feldspar (Hansen, 1992; Drummond, 1998,). It forms an erosional contact with underlying units, and paleochannel fill
may occur. Approximate thickness has been reported to be up to 145 feet (44 meters) (Drummond, 1998). It is
stratigraphically equivalent to the Wicomico Formation of Overbeck and Slaughter (\f)5'&).
Aquia Formation
The marine Aquia Formation is a calcareous, glauconitic quartz sand that coarsens upward (Hansen, 1992; Drummond,
1998); color is olive-brown to greyish-olive with a salt and pepper aspect. Bohlke and Denver (1995) noted that
between the noncalcareous, oxidized upper portion of the formation and the underlying calcareous glauconite sands is
an approximately 2 to 3 meters thick unit (referred to earlier as the redox zone) having a relatively higher gamma
signature peak corresponding to material with large amounts of interstitial clay (Figure 2). Krantz (personal
communication, 1999) has designated this as above the Aquia Confining Layer, which shows a tight gamma signal
indicating an impermeable layer underlying the redox zone.
Hornerstown Formation
The Hornerstown is a massive, fine to medium grained glauconitic sand, locally coarse. The unit is olive brown in color
in its upper section and greyish olive at lower levels, maintaining a salt and pepper aspect throughout (Hansen, 1992).
Glauconite is generally dark green, polylobate with minor alteration to limonite. A gamma ray log deflection in the
upper part of the Hornerstown near its contact with the Aquia is observed (Hansen, 1992; Bohlke and Denver 1995,
Krantz, personal communication 1998). It was likewise noted that another gamma log deflection was found near the
base of the Hornerstown, reflecting higher glauconite fractions, possibly with phosphate.
Severn Formation (upper portion ofMonmouth Group)
This formation is one of two formations comprising the Monmouth Group. The Severn is a much finer grained unit
compared to the overlying Hornerstown Formation, consisting of dark grey, glauconitic, clayey, very fine to fine sands.
It is massive with common shell fragments and a mottled texture. The Severn has a gamma ray peak near its base
[according to Hansen (1992) it may reflect the occurrence of phosphate or a high percentage of glauconite - 65%].
Glauconite grains are dark green and relatively unaltered. The formation's basal portion, consisting of quartz grains,
phosphate pebbles and shell fragments, has a sharp contact with the underlying Mt. Laurel Formation (part of the
Monmouth Group).
Mt. Laurel Formation flower part of Monmouth Group)
The Mt. Laurel Formation is the lower member of the Monmouth Group. Its lower 22 feet (6.7 meters) is composed of
medium grey, clayey glauconitic (up to 35%) very fine to fine sands. Sands are calcareous with localized pelycepod
concentrations and irregular calcite cemented zones. Its upper 56 feet (17 meters) is light olive grey, medium to fine
silty quartzose sand. Coarser beds are less glauconitic (15%). The formation ranges in thickness from 25-80 feet (7.6-
24.4 meters) in Kent County.
Matawan Group
The Matawan Group consists of a sequence of glauconitic, dark grey to olive grey silty clays and very fine to fine sands.
Bedding is massive, with some mottling and suggestion of bioturbation in the form of burrows. Beds are generally
noncalcareous below 320 feet in this core hole.
40
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Appendix F
Locust Grove Database
The data reported in Tables 1 and 2 are part of a comprehensive hydrogeological database that are collected by the US
Geological Survey under IAG #DW14937941. The comprehensive database will be detailed in a final report to be
prepared by the USGS under this agreement, including methods, procedures, quality assurance measures, and
geochemical analysis. The data will be managed by the National Risk Management Research Laboratory, U.S.
Environmental Protection Agency, in Ada, Oklahoma, and will be made available on Compact Disks (CDs) for
distribution, upon the completion of the project.
Quality of Data
The data in Table 1 and Table 2 show information on newly installed wells (wells KE Bf 74, 254, and 180, KE Be 171
are old), and synoptic measurements of water-table levels at the site (10/97-4/99). The objective of the data, including
core samples and head measurements is to: 1) develop the stratigraphic framework of the surficial (Columbia\Aquia)
unconfined aquifer, the uppermost confining layer, and the uppermost confined aquifer; 2) delineate the head
distribution and flow patterns; and 3) delineate the redox zone on top of the uppermost confining layer and assess the
geochemical processes controlling nitrogen concentration in the unconfined aquifer and in ground-water discharge to
the streams; and 4) estimate nitrogen loads to the streams from ground-water discharge.
All new wells were installed following the protocols and procedures for well installation recommended for the USGS
NAQWA program. Sampling procedures, including drilling operations, installation of wells, and measurement for
heads are documented in detail in the project Quality Assurance Plan. The data from new coreholes and existing well
log information were used to develop the stratigraphic framework by extrapolation over the entire study area, using the
GMS Model. Figure 7(c) is an illustration to the extrapolation procedure.
Table 1. Core Data Submissions by USGS (as of July 1999; file sent 12/2/98)
USGS/MGS Well Number
KEBe 185 (new)
KEBe 183 (new)
KEBe 184 (new)
KEBe 186 (new)
KEBf 180
KEBe 171
KEBe 210 (new)
KEBe 187 (new)
KEBe 188 (new)
KEBe 189 (new)
KEBe 190 (new)
KEBe 195 (new)
KEBe 196 (new)
KEBe 197 (new)
Nau Farm (new)
Locust Grove corehole (new)
KEBe 201 (new)
KE Be 202 (new)
KE Be 203 (new)
KE Be 204 (new)
KE-88-0146 (new)
KE Bf 74
KEBf 154
Utm-x
418091.9
416392.7
416770.7
419691.2
421132.6
420790.0
419129.7
415665.0
415901.1
416605.0
416700.1
417830.0
417893.7
416865.9
416959.0
418106.8
418907.5
419002.6
419154.9
419559.6
Utm-y
4353369.7
4351229.6
4350732.2
4350547.5
4348590.4
4347884.8
4351848.2
4352594.0
4352283.1
4350919.0
4350856.3
4348963.6
4348192.2
4352920.2
4352672.6
4350224.8
4351203
4348828.1
4349658.9
4349408.1
Layer information available *
Pen, AQ, ACL, TACL, Ho, HS
Pen, AQ, ACL, TACL, Ho
Pen, AQ, ACL, TACL, Ho
Pen, AQ, ACL, TACL, Ho, HS
Pen, AQ, ACL, TACL, Ho, HS and more
(see Hansen 1992)
Pen, AQ, ACL, TACL, Ho, HS, HCL
* Pen: Pensauken, AQ: Aquia, ACL: Aquia Confining Layer, TACL: ATight@ gamma peak Aquia Confining Layer, Ho: Hornerstown, HS:
Hornerstown sand (?), HCL: Hornerstown Confining Layer
41
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Table 2. Recent Synoptic Water Table Measurements by the USGS in Locust Grove, MD
Well label
KEBf 154
KEBf 155
KE-88-
0696
KEBe216
KEBf 186
Block 3-54
KEBf 184
KEBf 185
KEBe 154
KEBe213
KEBe 214
KEBe 215
Block 6-12
KE-88-
0695
KEBe 212
KEBe 211
KEBe 159
KEBe 160
KEBe 161
KEBe 63
KEBe 64
KE-94-
0144
KE-94-
0145
KE-94-
0146
KE Be 205
KE Be 203
KE Be 204
KEBe 62
KEBe 162
KEBe 163
KEBe 61
KEBe 53
KEBe 52
KEBe 59
KEBe 164
KEBe 165
KEBe 166
KEBe 167
KEBe 51
KE Be 207
KE Be 208
KEBe 50
KEBe 210
10/97
12.26
12.26
12.21
12.41
12.41
15.71
15.7
15.72
16.81
16.76
17.29
18.06
18.05
17.98
17.99
18
17.64
17.83
3/98
9.75
9.94
14.23
15.66
17.25
15.78
13.1
12.52
12.5
12.41
12.68
12.69
15.27
15.2
15.11
16.39
16.38
16.4
17.63
17.71
17.71
18.81
18.73
18.75
18.76
18.81
17.73
19.15
5/98
9.83
10
14.41
14.4
16.11
15.75
17.62
17.62
17.76
17.76
18.26
18.26
15.95
12.97
13.2
13.44
12.4
12.44
12.37
12.55
12.65
15.37
15.3
15.28
15.31
14.44
16.75
16.42
16.43
16.44
18.03
18.12
18.12
18.76
18.69
18.56
18.57
18.57
18.11
18.54
18.53
18.47
18.49
6/98
9.72
9.58
14.23
14.23
15.84
15.48
17.49
17.49
17.47
17.43
18.19
18.19
15.8
12.92
12.88
13.44
12.33
12.38
12.32
12.5
12.64
15.21
15.14
15.28
15.14
14.28
16.66
16.25
16.25
16.26
17.84
17.94
17.93
18.78
18.7
18.6
18.61
18.62
18.09
18.58
18.57
18.5
18.59
7/98
6.48
6.61
13.98
13.97
13.3
12.31
17.19
17.19
15.09
16.56
18
17.99
15.49
11.63
12.53
13.13
12.31
12.29
12.24
12.41
12.53
15.02
14.94
14.98
14.95
13.74
16.46
16.01
16
16.01
17.66
17.75
17.74
18.5
18.39
18.28
18.3
18.3
17.94
18.24
18.23
18.17
18.24
9/98
9.2
9.38
13.74
13.74
14.83
14.48
16.9
16.9
17.04
17.02
17.75
17.75
15.27
12.67
12.24
13.05
12.32
12.32
12.41
12.45
12.53
14.79
14.75
14.78
14.67
13.84
16.2
15.85
15.85
15.85
17.42
17.5
17.5
18.26
18.19
18.17
18.16
18.17
17.73
18.07
18.07
17.99
18.06
10/98
2.04
3.38
13.52
13.52
14.78
14.44
16.48
16.47
15.7
15.41
17.36
17.35
14.95
12.23
12.04
12.95
12.3
12.22
12.18
12.35
12.46
10.64
10.78
17.72
14.2
13.69
15.84
15.62
15.63
15.63
17
17.11
17.1
17.94
17.85
17.85
17.85
17.86
17.36
17.87
17.81
17.73
17.89
11/98
8.89
9.06
13.42
13.41
14.2
13.74
16.34
16.36
16.78
16.78
17.13
17.12
14.67
12.67
11.97
12.89
12.31
12.24
12.19
12.35
12.47
14.51
14.45
14.49
14.46
13.63
15.74
15.48
15.48
15.49
16.8
16.89
16.88
17.74
17.66
17.7
17.7
17.7
17.14
17.74
17.66
17.59
17.76
12/98
8.72
8.9
13.38
13.38
14.65
14.29
16.36
16.35
16.7
16.71
17.05
17.05
14.74
12.71
11.65
12.87
12.25
12.24
12.19
12.25
12.46
13.97
13.94
13.7
13.71
13.53
15.56
15.46
15.46
15.47
16.72
16.81
16.81
17.63
17.56
17.6
17.6
17.6
17.01
17.61
17.59
17.52
17.58
1/99
8.97
9.15
13.4
13.4
14.75
14.4
16.32
16.33
16.58
16.62
16.95
16.95
14.8
12.79
12.02
12.91
12.27
12.24
12.22
12.43
12.5
14.44
14.42
14.46
14.4
13.47
15.45
15.52
15.52
15.52
16.6
16.72
16.73
17.62
17.53
17.66
17.7
17.69
16.86
17.61
17.62
17.51
17.61
3/99
9.01
9.18
13.51
13.51
14.88
14.52
16.36
16.37
16.45
16.46
16.94
16.94
14.92
12.79
12.12
12.95
12.31
12.28
12.24
12.43
12.5
14.45
14.41
14.4
14.4
13.45
15.35
15.51
15.52
15.52
16.66
16.74
16.74
17.58
17.51
17.56
17.58
17.58
16.69
17.56
17.56
17.48
17.58
4/99
9.2
9.38
13.7
13.7
15.12
14.76
16.46
16.47
16.45
16.45
17.02
17.02
15.07
12.86
12.35
13.1
12.27
12.3
12.23
12.42
12.49
12.32
11.35
14.27
13.51
15.41
15.63
15.63
15.63
16.77
16.87
16.86
17.76
17.67
17.58
17.73
17.71
16.78
17.8
17.79
17.74
17.77
42
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Table 2. Continued.
KE Be 206
KEBe 198
KEBe 199
KE Be 200
KEBe 197
KEBe 187
KEBe 188
KEBe 189
KEBe 156
KEBe 157
KEBe 158
KEBe 191
KEBe 192
KEBe 193
KEBe 201
KEBe 60
KE Be 202
KEBe 195
KEBe 194
KEBe 196
KEBe 169
KEBe 170
KEBe 171
12.01
18.05
11.39
12.16
13.33
18.05
18.57
17.65
17.65
17.65
17.93
19.4
18.5
11.67
11.33
12.2
13.57
13.52
13.52
13.53
16.52
18.58
17.24
17.29
17.29
15.58
18.6
17.68
17.69
17.69
17.89
20.3
18.62
11.64
11.28
12.12
13.45
13.4
13.41
13.42
16.48
18.44
17.25
17.19
17.2
15.52
18.26
17.57
17.58
17.59
17.76
19.79
18.28
11.53
11.2
12.03
13.37
13.31
13.31
13.33
16.3
18.33
16.94
17.1
17.1
15.43
18.08
17.43
17.44
17.75
17.55
20.49
18.21
11.54
11.25
12
13.26
13.21
13.08
13.23
16
18.4
16.77
16.92
16.92
15.32
17.81
17.18
17.2
16.58
17.17
19.23
17.76
11.62
11.2
11.89
13.09
13.04
13.05
13.06
15.7
17.69
16.51
16.67
16.68
15.11
17.66
16.98
17.16
17.05
19.82
17.58
11.48
11.21
11.86
13.02
12.96
12.97
12.99
15.49
17.48
16.33
16.53
16.53
14.97
17.59
16.85
16.86
16.88
19.76
17.4
11.46
11.15
11.86
12.95
12.91
12.91
12.92
15.31
17.55
16.19
16.42
16.42
14.87
17.6
16.73
16.83
16.71
20.49
17.52
11.45
11.17
11.88
12.92
12.86
12.87
12.88
15.21
17.15
16.17
16.25
16.27
14.74
17.59
16.46
16.7
16.48
20.54
17.22
11.43
11.16
11.82
12.93
12.84
12.85
12.86
15.06
17.02
16.16
16.14
16.11
14.6
17.8
16.48
16.72
16.49
20.16
17.24
11.54
11.18
11.88
12.94
12.9
12.9
12.92
15.24
17.15
16.28
16.06
16.06
14.54
43
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45
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Glossary
Riparian zones:
Aquifer:
Unconfined aquifer:
Water table:
Hydraulic head:
Hydraulic conductivity:
Oxic zone:
Redox zone:
Denitrification:
Hydrostratigraphic unit:
Watershed:
Transect length:
are areas of vegetation (e.g., grasses, shrubs, trees, and other vegetation types) that
are adjacent to bodies of water (e.g., streams).
is a geologic formation, or a group of formations, which (i) contains water and (ii)
permits significant amounts of water to move through it under ordinary field
conditions.
is an aquifer in which the water table forms the upper boundary. Also referred to as
phreatic aquifer or water-table aquifer.
is an imaginary surface at all points of which the pressure is atmospheric (taken as
zero). Also referred to as phreatic surface.
is energy per unit weight; it is equal to the elevation at any point in the porous
medium relative to an arbitrary elevation (elevation head) plus the pressure
divided by the specific weight of the fluid (pressure head). Or it is the fluid
potential at any point in the porous medium divided by the gravitational accelera-
tion. Fluids flow in the direction of decreasing heads in porous media.
is the constant of proportionality between the specific discharge and the hydraulic
head gradient in the Darcy's law. It can also be defined as the Darcys velocity
(specific discharge) under unit hydraulic head gradient at any point in the porous
medium. It depends on properties of both the porous matrix and the fluid. Some
authors call it coefficient of permeability.
is referred to here as the zone of relatively oxidized non-calcareous portion of the
surficial Columbia\Aquia aquifer.
is referred to here as the zone of relatively reduced calcareous glauconitic
sediments, which constitutes the lower boundary of the surficial aquifer. It is the
zone of reduction-oxidation reaction (redox) where nitrate is reduced by denitrifi-
cation.
refers to the microbially mediated process whereby nitrate (NO3~) is reduced to
nitrous oxide (N2O) or nitrogen gas (N2) under anaerobic conditions.
is a geologic formation, part of a formation, or a group of formations in which
there are similar hydrologic characteristics that allow for a grouping into aquifers
and associated confining layers.
is a topographically defined area drained by a river/ stream or a system of
connecting rivers/ streams such that all outflow is discharged through a single
outlet. It can also be referred to as drainage basin.
is referred to here as the horizontal distance from the upgradient drainage divide
boundary to the downgradient stream boundary.
46
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