A novel approach for direct estimation of fresh groundwater discharge to an estuary

Abstract

1] Coastal groundwater discharge is an important source of freshwater and nutrients to coastal and estuarine systems. Directly quantifying the spatially integrated discharge of fresh groundwater over a coastline is difficult due to spatial variability and limited observational methods. In this study, I applied a novel approach to estimate net freshwater discharge from a groundwater‐fed tidal creek over a spring‐neap cycle, with high temporal resolution. Acoustic velocity instruments measured tidal water fluxes while other sensors measured vertical and lateral salinity to estimate cross‐sectionally aver-aged salinity. These measurements were used in a time‐ dependent version of Knudsen's salt balance calculation to estimate the fresh groundwater contribution to the tidal creek. The time‐series of fresh groundwater discharge shows the dependence of fresh groundwater discharge on tidal pump-ing, and the large difference between monthly mean dis-charge and instantaneous discharge over shorter timescales. The approach developed here can be implemented over time-scales from days to years, in any size estuary with dominant groundwater inputs and well‐defined cross‐sections. The approach also directly links delivery of groundwater from the watershed with fluxes to the coastal environment. Citation: Ganju, N. K. (2011), A novel approach for direct estima-tion of fresh groundwater discharge to an estuary, Geophys. Res. Lett., 38, L11402, doi:10.1029/2011GL047718.

Full text

A novel approach for direct estimation of fresh groundwater
discharge to an estuary
Neil K. Ganju
1
Received 8 April 2011; revised 26 April 2011; accepted 27 April 2011; published 4 June 2011.
[1] Coastal groundwater discharge is an important source of
freshwater and nutrients to coastal and estuarine systems.
Directly quantifying the spatially integrated discharge of
fresh groundwater over a coastline is difficult due to spatial
variability and limited observational methods. In this study, I
applied a novel approach to estimate net freshwater discharge
from a groundwater‐fed tidal creek over a spring‐neap cycle,
with high temporal resolution. Acoustic velocity instruments
measured tidal water fluxes while other sensors measured
vertical and lateral salinity to estimate cross‐sectionally aver-
aged salinity. These measurements were used in a time‐
dependent version of Knudsen’s salt balance calculation to
estimate the fresh groundwater contribution to the tidal creek.
The time‐series of fresh groundwater discharge shows the
dependence of fresh groundwater discharge on tidal pump-
ing, and the large difference between monthly mean dis-
charge and instantaneous discharge over shorter timescales.
The approach developed here can be implemented over time-
scales from days to years, in any size estuary with dominant
groundwater inputs and well‐defined cross‐sections. The
approach also directly links delivery of groundwater from
the watershed with fluxes to the coastal environment.
Citation: Ganju, N. K. (2011), A novel approach for direct estima-
tion of fresh groundwater discharge to an estuary, Geophys. Res.
Lett.,38, L11402, doi:10.1029/2011GL047718.
1. Introduction
[2] Quantifying fresh groundwater discharge to the coastal
margin is confounded by spatial and temporal variability
and the inherent difficulty of observing the discharge. While
many eutrophic estuaries receive the majority of their fresh-
water and nutrient loads from rivers, the effects of coastal
groundwater discharge can also be large depending on bio-
geochemistry and the transformation of nutrients during
transit time in the aquifer. Valiela et al. [1990] highlighted
the importance of coastal groundwater discharge as a large
overlooked source of nutrients to coastal ecosystems and
addressed the potential biogeochemical significance. Slomp
and Van Cappellen [2004], highlighting the higher nitro-
gen/phosphorus ratio in groundwater, explored possible
shifts in nutrient limitation and primary productivity as the
ratio of groundwater to riverine water is changed. There are
instances in which the riverine freshwater and nutrient load
is rivaled or exceeded by the coastal groundwater portion.
In Tampa Bay, Kroeger et al. [2007] found that submarine
groundwater discharge accounted for up to 33% of the fresh-
water discharge, and 50% of nutrient loads. Valiela et al.
[1990] estimated that over 70% of the nitrogen load to eight
New England bays resulted from direct coastal groundwater
discharge.
[3] Several methods to measure fresh coastal groundwater
discharge have been used with varying success dependent
on the system and the assumptions. Radiochemical tracer
methods [e.g., Moore, 1996; Cable et al., 1996] which sample
estuarine water for constituents such as radon and radium,
trace total groundwater discharge (i.e. fresh and saline) rather
than specifically freshwater discharge. Seepage meters [Lee,
1977] can be used to estimate flows but spatial variability
in groundwater seepage confounds extrapolation of those
measurements to entire basins. Advanced techniques such as
the eddy‐correlation method [Crusius et al., 2008] avoid
some complications of seepage meters and cover somewhat
larger footprints. Remote sensing methods can identify
spatial variability [Portnoy et al., 1998], but cannot readily
resolve the total mass transport. Watershed water‐balance
methods [Kroeger et al., 2006] yield whole system estimates
of fresh groundwater discharge over longer time‐periods (e.g.
annual to decadal), but cannot resolve the temporal variability
that may be caused by tidal fluctuations, discrete rainfall
events, or enhanced evapotranspiration. Lee and Kim [2007]
used intensive salinity sampling to estimate freshwater bud-
gets and the submarine groundwater discharge in a coastal
system where the oceanic end member was relatively con-
stant. There is a clear need for independent measurements of
fresh groundwater discharge, separate from saline discharge,
as only the fresh discharge carries new land‐derived materials
including nutrient loads.
[4] In contrast to the difficulty in measuring groundwater
discharge, quantifying tidal water fluxes through estuarine
cross‐sections is relatively straightforward. Simpson and
Bland [2000] first detailed the use of shipboard ADCPs
to calculate tidally varying discharge in estuarine channels;
Ruhl and Simpson [2005] further described methods to gen-
erate continuous time‐series of tidal flows in tidally affected
channels. While these methods are accurate (±5%) for
instantaneous tidal flows, extracting the mean (residual flow
due to freshwater) can be difficult due to the small ratio
of freshwater flow to instantaneous tidal flow. Ganju and
Schoellhamer [2006] found that a tidal velocity bias of
0.01 m/s was enough to reduce net freshwater flow estimates
by 50% through a large channel in San Francisco Bay. Quan-
tifying net freshwater discharge with flow measurements can
be improved by measurement of mean salinity in the channel:
as a conservative constituent, the flux of salt through the
cross‐section must balance. This article presents direct esti-
mates of fresh groundwater discharge to a groundwater‐fed
tidal creek and seaward estuary using acoustic measurements
of velocity, spatially intensive salinity measurements, and salt
1
Woods Hole Coastal and Marine Science Center, U.S. Geological
Survey, Woods Hole, Massachusetts, USA.
This paper is not subject to U.S. copyright.
Published in 2011 by the American Geophysical Union.
GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L11402, doi:10.1029/2011GL047718, 2011
L11402 1of6

balance calculations. The mechanisms and implications of the
temporal variability are discussed as well as the sensitivity of
the salt balance calculation.
2. Methods
2.1. Site Description
[5] Mashapaquit Creek (Figure 1) is a small tidal creek
(∼1.5 m deep at mean sea level) that drains into West
Falmouth Harbor, Massachusetts, located on Upper Cape
Cod. The creek is bordered by marsh and residential areas.
Groundwater is the largest source of freshwater to coastal
margins on Cape Cod [Valiela et al., 1992]; the largest lens of
the aquifer is centered 15 km northeast of West Falmouth
Harbor. Prior estimates of freshwater loading to Mashapaquit
Creek by Kroeger et al. [2006] used a mass‐balance approach
over delineated water table contours (Figure 1), using average
annual hydrological conditions. In that study the ground-
water discharge to Mashapaquit Creek was estimated to be
0.019 m
3
/s. During the summer of 2010 a suite of instruments
was deployed in Mashapaquit Creek, with the goal of mea-
suring tidal water fluxes, cross‐sectionally averaged salinity,
and fresh groundwater discharge over a spring‐neap cycle.
2.2. Tidal Water Fluxes
[6] Computing water fluxes in tidally affected channels
requires a continuous record of index velocity (v
i
) and
water level (h) and a less‐frequent record of channel‐average
velocity (v
ca
) and channel area (A) over some representative
period [Ruhl and Simpson, 2005]. A complete record of v
ca
is computed using the correlation between v
i
and v
ca
, and a
complete record of Ais computed using hand the channel
geometry. The product of v
ca
and Afrom the complete record
yields a continuous record of tidal water fluxes (Q). A Nortek
Aquadopp ADCP and Seabird 39 pressure/temperature (PT)
sensor were deployed approximately 0.1 m above the bed
to measure v
i
and hrespectively from 22 July 2010 to
9 September 2010. The package was deployed in the center of
the channel just landward of the outlet to West Falmouth
Harbor (Figure 1), approximately 400 m seaward of the ter-
mination of the creek. Measurements of v
ca
and Awere col-
lected on 11 August 2010 using a 1200 kHz RD Instruments
Rio Grande ADCP operated from an OceanSciences River
Surveyor catamaran with radio modems and a tagline secured
from bank‐to‐bank (Figure 1). At all sites U.S. Geological
Survey protocols [Mueller and Wagner, 2009] were followed
for ADCP settings, compass calibration, and edge estimates
(due to the inability to measure near banks). The survey was
performed on a spring tide (11 August 2010) when the largest
range of conditions was expected. The index velocity method
relies on the assumption that the relationship between the
index measurement and cross‐sectionally averaged value
during the tidal‐cycle survey is steady over the entire period.
This is true for the index salinity method described below.
2.3. Cross‐Sectionally Averaged Salinity
[7] Generating a continuous record of cross‐sectionally
averaged salinity (s
ca
) requires an index salinity (s
i
) mea-
surement and a less‐frequent record of cross‐sectionally
averaged salinity over some representative time period;
the correlation between the two can be used to estimate con-
tinuous cross‐sectionally averaged salinity. A YSI 6‐series
multi‐parameter sonde was deployed from a floating dock
(depth approximately 1.25 m at mean high water), with the
measurement volume approximately 0.1 m below the water
surface. The instrument was deployed in this fashion due
to prior observations of strong vertical stratification in the
shallow, groundwater‐fed creek. Vertical stratification was
Figure 1. Mashapaquit Creek and the landward portion of West Falmouth Harbor, Massachusetts. Dashed lines indicate
watershed delineation reported by Kroeger et al. [2006], and arrows denote general direction of groundwater flow.
GANJU: ESTIMATION OF GROUNDWATER DISCHARGE L11402L11402
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accounted for by deploying a vertical array of three Seabird
Microcat conductivity/temperature (CT) sensors adjacent to
the dock at 0.33, 0.55, and 0.77 mab. The dock is located
approximately 30 m landward of the ADCP/PT package
(Figure 1). The multi‐parameter sonde was downloaded
and serviced weekly following the guidelines of Wagner
et al. [2006]. The vertical salinity profiles obtained from
the floating dock and vertical array were interpolated to a
uniform depth coordinate (due to variable locations in the
water column relative to each other) and averaged to yield
a depth‐averaged salinity at the edge of the creek. Cross‐
sectionally averaged salinity was estimated by vertical pro-
filing with a multi‐parameter sonde at five equally spaced
locations in the cross‐section. The sonde sampled at 1 Hz,
and downcast data were interpolated to a uniform vertical
coordinate, weighted by total depth of the profile, and aver-
aged. Profiles along a transect (Figure 1) were collected from
a canoe secured to the tagline, intermittently during the ADCP
surveys on 11 August 2010.
2.4. Time‐Dependent Salt Balance and Freshwater
Discharge Calculation
[8]MacCready and Geyer [2010] describe the steady salt
balance of Knudsen [1900] as
Qout ¼sin
DsQRand Qin ¼sout
DsQRð1Þ
where Q
out
is the net water flux on ebb tides, s
out
is the cross‐
sectionally averaged salinity on ebb tides, Q
in
is the net
water flux on flood tides, s
in
is the cross‐sectionally averaged
salinity on flood tides, Dsis the difference between s
in
and
s
out
, and Q
R
is the total freshwater discharge to the estuary.
Equation (1) is typically applied as a spatially varying
description of tidally averaged quantities; MacCready [2011]
derived the analogous time‐dependent version of equation (1)
Qout tðÞ¼sin tðÞ
DsQRtðÞþ 1
DsVds
dt and
Qin tðÞ¼sout tðÞ
DsQRtðÞþ 1
DsVds
dt
ð2Þ
where the last term on the right hand sides accounts for
storage of salt or freshwater within an estuary of volume V.
Rearranging the first relationship to solve for the freshwater
discharge gives
QRtðÞ¼ Ds
sin tðÞ
Qout tðÞ 1
sin tðÞ
Vds
dt ð3Þ
Assuming zero net salt flux eliminates the last term in
equation (3) and allows for the calculation of Q
R
using
instantaneous tidal water flux and cross‐sectionally averaged
salinity data. The tidal water flux and salinity merely need
to be separated based on whether the water and salt flux are
landward or seaward.
3. Results
3.1. Tidal Water Fluxes
[9] An index velocity relationship between v
i
and v
ca
was successfully developed with the continuous and cross‐
sectional ADCP data (Figure S1 of the auxiliary material); the
stage‐area relationship was constructed with a high‐water
channel geometry cross‐section and the continuous water
level data (Figure S2 of the auxiliary material and Figure 2).
1
Figure 2. Time‐series measurements of water level, tidal water flux, cross‐sectionally averaged salinity, and calculated fresh
groundwater discharge (over varying averaging windows). Negative freshwater fluxes may arise from error or more landward
transport of fresh groundwater from other areas of the harbor.
1
Auxiliary materials are available in the HTML. doi:10.1029/
2011GL047718.
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The computed tidal water flux (Figure 2) shows a maximum
tidal water flux of 5 m
3
/s, with a pronounced spring‐neap
signal. Maximum neap tidal water flux was about half the
spring tide magnitude. The time‐mean of this tidal water flux
is 0.2 m
3
/s (in the seaward direction), which equates to a
representative water velocity of 0.007 m/s (using the average
channel area) and is approximately the same as the error of the
index velocity relationship. The average tidal excursion at
the site was approximately 1 km, larger than the distance to
the creek terminus.
3.2. Cross‐Sectionally Averaged Salinity
[10] The continuous vertical profile data showed that
the creek was strongly stratified on ebb tides, with vertical
salinity gradients exceeding 25 m
−1
on neap tides. Stratifi-
cation was less on spring tides, due to greater tidal energy
and mixing. The relationship between the creek‐edge,
depth‐averaged salinity and the cross‐sectionally aver-
aged salinity during the 11 August 2010 survey was linear
(Figure S3 of the auxiliary material).The time‐series of
computed continuous cross‐sectionally averaged salinity
(Figure 2) shows the largest fluctuations in tidal‐timescale
salinity occur during the spring tide (8 August 2010 –
15 August 2010), when the salinity difference between flood
and ebb tide is maximized.
3.3. Freshwater Discharge Calculation
[11] The tidal water flux and cross‐sectionally averaged
salinity data were used in equation (3) by separating the data
depending on whether the current was flooding or ebbing
(to separate Q
in
from Q
out
, and s
in
from s
out
). This separation
was first performed over the entire time‐series resulting in a
groundwater flux of 0.02 m
3
/s; separation was then applied in
moving windows of 30 and 120 h, to evaluate the temporal
variation of groundwater discharge over varying timescales
(Figure 2). With the shortest 30‐h averaging window (which
essentially represents a “tidally averaged”window), the peak
fresh groundwater discharge was 0.85 m
3
/s during the spring
tide, which is an order of magnitude larger than the period
mean. During neap tides groundwater flux was closer to the
period mean. Rainfall during this period was minimal (http://
www.emc.ncep.noaa.gov) and cannot account for the large
variations in freshwater discharge. Small negative values may
be due to error or landward transport of fresh groundwater
from elsewhere in the harbor.
4. Discussion
4.1. Sensitivity of Salt Balance
[12] The salt balance calculation is most sensitive to sys-
tematic bias in tidal water flux measurements (Table 1), and
is largely insensitive to random errors and biases in salinity
measurement. The sensitivity to tidal water flux bias is due to
the tight coupling between near‐slack tide (i.e. zero tidal
water flux) and maximum fresh groundwater input to the
creek. Synthetically biasing the tidal water flux measure-
ments with a sensitivity analysis essentially shifts the phasing
between slack tide and minimum salinity such that ebb tide
carries fresher water seaward, thus resulting in larger calcu-
lated fresh groundwater discharge. However, identifying slack
tide with acoustic velocity measurements is relatively reliable
in a small channel. Biases in salinity are less critical due to
the Dsterm in equation (3) which is unaffected by bias.
Random errors are minor as they do not shift the phasing of
tidal water flux and salinity, nor alter the net water transport
on flood and ebb tides.
4.2. Fresh Groundwater Discharge and Tidal Pumping
[13] The temporal variability in fresh groundwater discharge
is highly correlated with tidal range (Figure 3). Correlations
were tested between the fresh groundwater discharge and
tidal range (r
2
= 0.79), low‐tide level (r
2
= 0.51), and time
below a range of arbitrary tide levels (r
2
< 0.4). The 120‐h
mean fresh groundwater discharge was used to reduce scatter
in the relationship and highlight the lower frequency varia-
tion with tidal range. The stronger correlation with tidal range
as opposed to low tide level supports the “tidal pumping”
mechanism elucidated by others [Nielsen, 1990; Moore,
1999] whereby increased tidal action extracts more ground-
Table 1. Sensitivity Analyses for Salt Balance Calculation
a
Perturbed Variable Time‐mean Q
R
(m
3
/s) Error Max Q
R
(m
3
/s) Error
Q
in,out
+ 5% random error 0.020 0% 0.85 0%
Q
in,out
+ 5% seaward bias 0.045 125% 0.90 6%
s
in,out
+ 5% random error 0.020 0% 0.84 1%
s
in,out
+ 5% fresh bias 0.021 5% 0.89 5%
Q
in,out
,s
in,out
+ 5% random error 0.021 5% 0.85 0%
Q
in,out
,s
in,out
+ 5% seaward/fresh bias 0.047 135% 0.95 12%
a
Original value of Q
R
was 0.02 m
3
/s, maximum Q
R
was 0.85 m
3
/s.
Figure 3. Relationship between daily tidal range and
mean fresh groundwater discharge over a full spring‐neap
cycle.
GANJU: ESTIMATION OF GROUNDWATER DISCHARGE L11402L11402
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water from the aquifer. Those studies apply to the total sub-
marine groundwater discharge (i.e. fresh and recirculated
saline groundwater); the results of this study show that the
mechanism applies for the fresh groundwater component
alone as well. The large temporal variability over spring‐neap
timescales (from virtually no net discharge to peak discharge
in a few days) has major implications for ecosystems. The
delivery of “new”nutrients in fresh groundwater fluctuates
over short timescales and may confound ecological observa-
tions (e.g. primary production estimates) that are not as tem-
porally resolved.
4.3. Steady Salt Balance Assumption
[14] The steady salt balance assumption which simplifies
equation (3) is supported by two calculations. Firstly, the salt
storage term in equation (3) can be calculated using repre-
sentative values of estuarine volume landward of the cross‐
section (V), the variation in subtidal salinity (ds/dt), and flood
tide salinity (s
in
) for comparison with Q
R
.Vis calculated as
6.25 × 10
4
m
3
assuming an area that includes the channel and
adjacent marsh plain (1.25 × 10
5
m
2
) and an average depth
of 0.5 m; over the neap‐to‐spring transition from 4 August
2010 to 11 August 2010 ds/dt is approximately 1 d
−1
, and s
in
is approximately 20, giving a value of 3.125 × 10
3
m
3
/d or
0.036 m
3
/s. This is an order of magnitude less than the cal-
culated peak Q
R
using either the 30‐h or 120‐h averaging
windows. Secondly, the increased fresh groundwater dis-
charge on spring tides is not caused by storage of freshwater
during neap tide periods (when flushing is reduced) and
subsequent export on spring tides with greater flushing
ability. The total volume of exported freshwater between
6 August 2010 and 17 August 2010 was 1.4 × 10
5
m
3
; over
the area of Mashapaquit Creek’s channel and marsh plain
(∼1.25 × 10
5
m
2
) this would require a subtidal water level
increase of 1 m which is not supported by the data (Figure 2).
In systems with larger embayments, however, storage of
freshwater on neap tides could be an important mechanism
controlling the temporal variability of freshwater export at
the estuary mouth. In this case the data support storage within
the coastal aquifer on neap tides, and enhanced extraction on
spring tides.
5. Conclusion
[15] This study presents a new robust approach to quan-
tifying the fresh portion of coastal groundwater discharge
to estuarine systems. The methods require careful acoustic
velocity and salinity surveys, but rely on a simple time‐
dependent salt balance which can be applied over multiple
timescales. The approach was implemented in a groundwater‐
fed tidal creek and quantified the large temporal variability
in fresh groundwater discharge over the spring‐neap time-
scale. The variability was highly correlated with tidal range,
supporting the tidal pumping mechanism for sequentially
increasing and decreasing pressure gradients within the coastal
aquifer leading to increased discharge of fresh groundwater.
The method is most sensitive to the phasing of tidal water
flux and salinity, though this sensitivity ultimately depends
on the nature of the tidal wave (i.e. standing vs. progressive)
at the estuarine cross‐section. This approach can be used
to complement other methods (gas tracer, high‐resolution
models) by quantifying specifically the fresh portion of
coastal groundwater discharge. The approach can be applied
in any estuarine cross‐section where groundwater is the
dominant source of freshwater, and provides a foundation
for estimating loads of watershed‐derived constituents to
coastal margins.
[16]Acknowledgments. Funding was provided by the USGS Coastal
and Marine Geology Program. Access to Mashapaquit Creek was allowed
by Alan Rottenberg and Michael Jackson. Patrick Dickhudt designed and
fabricated the vertical CTD array. Jon Borden, Jennifer Thomas, Lane Boyer,
and Alex Nunez performed tidal‐cycle surveys with support from Marinna
Martini and Christine Sabens. Christopher Sherwood retrieved precipitation
data and provided motivation for the study. Kevin Kroeger, David Ralston,
and John Warner provided indispensable feedback on this study and manu-
script. Finally, Rocky Geyer provided the critical guidance needed to apply
the methods in a robust manner and was extremely generous with his time.
Any use of trade, product, or firm names is for descriptive purposes only
and does not imply endorsement by the U.S. Government.
[17]The Editor thanks John Largier and an anonymous reviewer.
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