WATER RESOURCES RESEARCH, VOL. 36, NO. 6, PAGES 1467–1479, JUNE 2000

Submarine groundwater discharge into the sea and associatednutrient transport in a sandy beach
Yusuke Uchiyama,1 Kazuo Nadaoka,2 Peter Rölke,2 Kumiko Adachi,3 andHiroshi Yagi4
Abstract. Submarine groundwater discharge (SGWD) and associated nutrient fluxes at
Hasaki Beach along the Kashima coast in Japan were investigated through fieldmeasurements and numerical simulations. The field data indicate that (1) groundwater has
higher concentrations of land-derived nutrients than seawater and river water; (2)microbial activity near the shoreline is likely to induce mineralization, reduction, andoxidation of nitrogen and phosphorus; and (3) in the portion of the aquifer underlying
coastal forest, nitrate is appreciably reduced. A numerical model incorporating effects ofwater table and tidal fluctuations was developed to evaluate SGWD. Assuming that theaquifer consists of homogeneous sandy soil, the simulation results show that the nutrient
flux due to SGWD is less than that of Tone River discharge. The nutrient flux via
groundwater seepage is considered to be a minor component of primary productivity inthe surf zone.

1.

Introduction

Coastal marine ecosystems are affected by dissolved nutrient
inputs from circulating offshore water, river runoff, andgroundwater seepage. The regional nutrient budget also includes atmospheric deposition, fertilizer application, wastewater treatment plant discharge, livestock waste, and remineralization of organic matter in sediment. Among these sources theeffects of groundwater on marine environments are not as wellknown as those of river water and offshore water. Groundwater containing inorganic nutrients can have a significant influence on coastal ecosystems, especially when nutrient concentrations are high or relative contribution of submarine
groundwater discharge (SGWD) is large. Owing to nutrient
leaching from surface-applied fertilizers, groundwater usually
has a higher concentration of inorganic nutrients than does
seawater. Therefore even low rates of SGWD often need to beaccounted for in the nutrient budget for a coastal ecosystem.
Ecologists have not paid much attention to groundwater asa source of inorganic nutrients for coastal marine ecosystems.
Kohout [1964] and Kohout and Kolipinski [1967] were the firstinvestigators to study the importance of fresh groundwater
seepage into the sea. Their studies were conducted along theshore of Biscayne Bay, Florida, and showed a definite relationship between biological zonation and groundwater discharge
into the bay. Johannes [1980] pointed out that on many coasts,
groundwater discharge can provide significant amounts of nutrients. Sutcliff [1972] demonstrated a significant positive cor1
Marine Environment Division, Port and Harbour Research Institute, Nagase, Yokosuka, Japan.
2
Graduate School of Information Science and Engineering, Tokyo
Institute of Technology, O-okayama, Meguro-ku, Tokyo.
3
National Research Institute of Fisheries Engineering, Ebidai,
Hasaki, Ibaraki, Japan.
4
Department of Civil Engineering, Tokyo Institute of Technology,
O-okayama, Meguro-ku, Tokyo.

Copyright 2000 by the American Geophysical Union.
Paper number 2000WR900029.
0043-1397/00/2000WR900029$09.00

relation between the rate of nutrient discharge and commercial
fish yields. Various reports documented that groundwater
seepage has a major influence on nutrient levels on the Guamfringing reef flat [Marsh, 1977], Discovery Bay, Jamaica [D’Elia
et al., 1981], and great South Bay, New York [Capone andBautista, 1985]. More recently, McLachlan and Illenberger[1986] and Simmons [1992] presented measurements showing
quantitatively the importance of nutrient fluxes from coastal
aquifers to the marine environment.
SGWD occurs where an aquifer is connected hydraulicallywith the sea and the groundwater head is above sea level; suchconditions are very common [e.g., Emery and Foster, 1948;
Manheim, 1967]. Fresh groundwater flows out to the sea
through a narrow seepage face as shown in Figure 1 [e.g.,
Glover, 1959]. The discharged groundwater is brackish toward
the seaward edge of the aquifer because of entrainment of salt
water from the diffusion zone [Cooper, 1959]. The width of thedischarge zone (seeping face) is believed to be nearly proportional to the volume of freshwater flow [Glover, 1959]. An
underlying saltwater wedge typically intrudes beneath the
freshwater aquifer along marine coastlines. This wedge impedes the downward mixing of lighter groundwater and thus
magnifies the tendency for groundwater from unconfined aquifers to discharge close to the shore. Since the beach water tablerises and falls in response to the tides but tends to lag behind
the tides [Emery and Foster, 1948], the discharge zone may
extend above the mean seawater level at low tides. The velocity
field in a coastal aquifer appears to be complicated by the
influence of the saltwater wedge. Previous studies have nottaken into account the spatially variable flow field. Since it isextremely difficult to measure the flow in the aquifer directly,
piezometers are often used to obtain data on the head fieldfrom which the flow patterns are inferred [e.g., Neilsen andDunn, 1998]. On the other hand, the Darcy’s law and GhybenHerzberg relationships have been used to calculate the velocity
approximately [Raghunath, 1982; McLachlan and Illenberger,1986]. Previous estimates of SGWD have generally yieldedworldwide figures in the range 0.01–10% of total discharge into
the sea [e.g., Church, 1996; Johannes, 1980]. Nevertheless,

1467

1468

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

Figure 1. Conceptual illustration of groundwater flow in an
unconfined coastal aquifer.

Moore [1996] and Church [1996] inferred from 226Ra measurements in coastal waters that SGWD into the South Atlantic
Bight might amount to a flux equivalent to 40% of the total
flow entering the sea from adjacent rivers. We are unsure
whether the figure of 40% is precise; however, the uncomplicated calculations might lead to overestimates of SGWD, as
discussed by Younger [1996].
This paper reports comprehensive and spatially detailed assessment of submarine groundwater discharge, and the associated nutrient transport, at Hasaki Beach facing the Kashima
Sea in Japan. Additionally, in order to calculate the nutrient
fluxes we develop a numerical model including the effects ofwater table and tidal fluctuations to evaluate the velocity fieldin the coastal aquifer.

2.

textural variability that causes appreciable heterogeneity in the
distribution of hydraulic properties. The bedded character offluvial deposits imparts a strong anisotropy; horizontal conductivities are typically 2–10 times larger than vertical conductivities [Freeze and Cherry, 1979; Apello and Postma, 1993].
According to the survey during drilling of the observation
wells, the soil in Hasaki appears to be nearly homogeneous andhighly permeable sand. Measured sand particle diameters andthe values of the estimated hydraulic conductivity are in therange of 0.125– 0.25 mm and 10⫺3–10⫺2 cm/s, respectively. The
groundwater aquifer at Hasaki Beach is likely to be unconfined. Although no aquicludes or relatively impermeable strata
were encountered in boreholes drilled in this study, data fromother wells near the coastal area indicate that an aquiclude
exists ⬃30 – 40 m below the ground surface (Figure 3). No
information is available about deeper confined aquifers in the
study area. Here we considered that there is only the single
unconfined aquifer composed of homogeneous fine sand. This
assumption is only approximately valid over monitored section
based on drilling results.

3.

Methods

3.1.

Field Observation

Field measurements were conducted from August 7 to December 12 in 1997. A cross section showing locations of 17
observation wells installed at Hasaki Beach is indicated in
Figure 4. Three of the wells were placed near the shoreline

Study Site

Hasaki Beach, where the field measurements were conducted, is located along the Kashima coast in Japan facing the
Pacific Ocean (see Figure 2). An uninterrupted sandy beachextends 16 km from the Tone River mouth to the Kashima
port. Groundwater observation wells were installed near the
Hasaki Oceanographical Research Station (HORS), the observatory facility of the Port and Harbor Research Institute,and 12 km north of the river mouth. The Tone River is one of
the longest rivers in Japan (322 km) and has the largest drainage basin (15,760 km3).
Hasaki Beach is flanked by a 150 –500 m surf zone on theseaward side and a dune 120 m from the shoreline. The dune
is covered with sparse coastal grasses. Pine trees, which are⬃5–10 m high at present, have been planted to stabilize thearea behind the dune. Next to the pine tree strip (100 m wide),a street runs along the coast from the Tone River mouth in thesouth to the Kashima port in the north. Landward of thisstreet, a highly agricultural area begins. The agricultural area,
which is schematically indicated in Figure 2, is 4 –5 km wide,
mostly covered with paddy fields. The only unaltered area inHasaki is the narrow beach and dune strip.
The geological history of the Kanto plain, on which the study
area is located, is characterized by transgressions and regressions, often caused by tectonic and volcanic activities. Alluvial
and marine terraces generally occur in the Kanto plain. The
Hasaki area at the eastern boundary of the Kanto plain near
the Tone River mouth consists of sandy marine and alluvial
deposits, laid down in river channels or on floodplains [Kimura
et al., 1991]. These deposits are composed of unconsolidated
sand and gravel. River deposits generally have characteristic

Figure 2. Location of the field survey in the Kashima coastof Japan.

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

Figure 3. Geological columnar section. B1–B4 are 1–5 km
distant from HORS; B5 is station 6.
with datum level (DL) ⫹2.2 m (referred to as station 1) and theothers (i.e., stations 2– 6) were installed landward of station 1.
DL means the datum level of Hasaki Fishery Port and isequivalent to the low water level. High water level approximately corresponds to the ground level at station 1. A PVC
casing with a diameter of 125 mm was driven into the desired
depths of the sandy soil as well points. The deepest drilling
reached 30 m below the land surface or 22 m below thegroundwater table.
Clusters of two to five wells screened at different depths
were installed at five of the six stations (Figure 4). The screenmaterial is tetrafluoroethylene with slot size of 0.07 mm. Two

1469

different depths were considered in the upgradient area andfive different depths near the shoreline. The screen lengths
were extended in inland wells to 8 –10 m long to acquire average results for a large groundwater layer. The ground levels(GL), averaged groundwater table (GWT), and top levels of
the wells (WL) measured from DL are also displayed in Figure
4.
Samples of the groundwater in the coastal aquifer weretaken on August 7 and 22, September 5 and 25, October 9 and
31, and December 12 by using a bailer sampler [e.g., Rigg and
Hatheay, 1988; Nielsen and Yeates, 1985] made of glass with adiameter of 40.0 mm and a length of 50.0 cm. Additional
samplings at stations 1–3 were made on August 26 and December 1. These samples were stored in plastic bottles (250mL) and brought back to a laboratory for salinity measurements in a few hours. The samples were also purged withmembrane filters and stored in polyprophylene tubes (20 mL)
which were promptly frozen for preservation. Subsequently, we
analyzed the samples with a TRAACS-800 autoanalyser (Branand Ruebbe Company) to determine the concentrations of
⫺
⫺
⫹
3⫺
NO⫺
2 , NO3 ⫹ NO2 , NH4 , PO4 , and SiO2. Dissolved oxygen(DO) was measured before the sampling with a batteryoperated instrument (YSI Company) on October 31 and December 12. In addition, water samples were collected from theTone River mouth and from the beach shoreline. With thesedata we could compare the nutrient concentrations in the
groundwater, river water, and seawater. Water table elevations
were also monitored every 10 min over 5 months from August
to December in 1997 at three locations, in the observation
wells of stations 4 – 6, with pressure gages (Diver, Eijkelkamp
Company). Tide levels were observed at the tip of the observatory pier of HORS.
3.2.

Numerical Simulation

Although measurements of hydraulic head are relatively
easy to collect, it is generally difficult or impossible to measure

Figure 4. Location of the observation wells near HORS. Station 1 is located at the high water mark. DL isthe datum level of Hasaki Fishery Port, being equivalent to low water level. The ground levels (GL), averaged
groundwater table (GWT), and top levels of the wells (WL) measured from DL are also displayed.

1470

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

the velocity field in aquifers. Therefore we developed a numerical model to calculate the detailed velocity field in the coastal
aquifer. The measured tide levels and groundwater table elevations were used as boundary conditions in the model.
During the ebb tide the beach water table may become
decoupled from the ocean, resulting in the formation of aseepage face where groundwater outcrops on the intertidal
profile [e.g., Nielsen, 1990; Turner, 1993]. The groundwaterflow field in the intertidal zone is important for evaluating
material transport due to SGWD as shown in Figure 1. Since
unsaturated layers are attributed to the pressure potential distribution near the groundwater table including the intertidalzone, the numerical model should be based on the Richards
equation for saturated-unsaturated flow [Richards, 1931]. In
addition, density effects induced by intrusion of saline seawater
are not negligible in analyzing flow in a coastal aquifer.
Pinder and Cooper [1970] demonstrated the movement of
the saltwater front in confined coastal aquifers by using a
numerical model. Their model used a steady groundwater flow
equation and a time-dependent advection-dispersion equation
for salinity. Segol et al. [1975] employed this model for a computation of steady flow in unconfined aquifers. Others incorporated Richards equation for unsteady flow [e.g., Kohno et al.,1983]. Although the previous works have treated transient flow
related to surface recharge and drainage in coastal aquifers,
unsteady flow due to the fluctuating tides and waves has notbeen simulated previously using this framework. Li et al.
[1997a] recently presented a boundary element method model
solving the Laplace equation for saturated flow in an unconfined coastal aquifer. They incorporated the capillary effects
derived from the approximate solution of the one-dimensional
Richards equation [Parlange and Brutsaert, 1987] into themodel and demonstrated beach water table fluctuations due totides and waves [Li et al., 1997a, b]. In their model, however,spatial distribution of hydraulic conductivity could not be included. Additionally, they neglected the effect of densitydriven flow caused by the presence of salt water.
Assuming that the aquifer studied here is isotropic and including the variation of pressure potential due to the change ofgroundwater density, we can obtain the Darcian flow equation
as [Pinder and Cooper, 1970; Pinder and Gray, 1977]

再 冉 冊冎q ⫽ ⫺K共 ␺ 兲 grad

␺⫹

␳
z ,
␳f

(1)

where x and y are the longitudinal and transverse coordinates,
z is the vertical coordinate, q ⫽ (q x , q y , q z ) is the Darcian
velocity vector, K is the hydraulic conductivity, ␺ is the pressure potential (or matric potential in the unsaturated zone), ␳
is density of mixed fluid, and ␳ f is the density of fresh water.
Although we assume the aquifer to be homogeneous in thisstudy, K may be varied spatially and temporally in the model.
The Richards equation for saturated-unsaturated groundwater flow, which requires no special treatment of the groundwater table, is derived from (1) and mass conservation of porewater [Richards, 1931]
关C w共 ␺ 兲 ⫹ ␤ 0S兴

⭸␺
⭸
⫽
⭸t
⭸x
⫹

冉 冊
冉

⭸
⭸z

K

⭸␺
⭸x

K

⫹

⭸
⭸y

冉 冊
冊
K

␳
⭸␺
⫺ K ,
⭸ z ␳f⭸␺⭸y(2)

where C w ( ␺ ) ⬅ ⭸ ␪ /⭸ ␺ is the slope of the soil water retention
curve (or the water capacity), ␪(␺) is the volumetric watercontent, t is time, S is the specific storage, and ␤0 is a variable.
On the assumption that the porosity does not vary with fluctuations of the pressure potential, ␤0 is expressed as

␤0 ⫽

再

0

···

unsaturated

1···

saturated.

(3)

If the dispersion in the aquifer is assumed to be homogeneous, the advection-dispersion equation governing a passive
and conservative solute (e.g., salinity) is defined as (4):⭸ ␪ C ⭸共 ␪ q⬘xC兲 ⭸共 ␪ q⬘yC兲 ⭸共 ␪ q⬘zC兲
⭸
⫹
⫹
⫹
⫽
⭸t
⭸x
⭸y
⭸z
⭸x
⫹

⭸
⭸y

冉

␪ D yy

⭸C
⭸y

冊

⫹

⭸
⭸z

冉

␪ D zz冊冉␪ D xx

⭸C
⭸x

⭸C
,
⭸z

冊
(4)

where q⬘x , q⬘y , and q⬘z are the components of the pore watervelocity vector (q⬘x ⫽ q x / ␪ s , q⬘y ⫽ q y / ␪ s , q⬘z ⫽ q z / ␪ s ; ␪ s isfield-saturated volumetric water content). C is the nondimensional solute concentration (e.g., nondimensional salinity).
D xx , D yy , and D zz are components of the pore-scale dispersion
tensor. The values of ␪ D xx , ␪ D yy , and ␪ D zz are proposed by
Scheidegger [1961] and Bear [1972] as␪ D xx ⫽ ␣ L q 2x /q s ⫹ ␣ T q 2y /q s ⫹ ␣ T q z2/q s ⫹ ␪␯
␪ D yy ⫽ ␣ T q 2x /q s ⫹ ␣ L q 2y /q s ⫹ ␣ T q z2/q s ⫹ ␪␯(5)

␪ D zz ⫽ ␣ T q 2x /q s ⫹ ␣ T q 2y /q s ⫹ ␣ L q z2/q s ⫹ ␪␯ ,where q s is the velocity magnitude (⫽(q x2 ⫹ q y2 ⫹ q z2 ) 1/ 2 ), ␣ Land ␣ T are the values of the longitudinal and transversal dispersivity, and ␯ is the kinematic viscosity of water. The valuesof ␣ L and ␣ T are set to be 2.5 and 0.5 cm according to Momii
et al. [1986].
The relation between the nondimensional salinity C and thedensity of mixed fluid ␳ isC ⫽ 共 ␳ ⫺ ␳ f兲/共 ␳ s ⫺ ␳ f兲,(6)where ␳ s is the density of seawater. Nondimensional concentration C hence is 1.0 for seawater and 0.0 for fresh water.
The hydraulic conductivity K( ␺ ) in homogeneous and isotropic porous media is constant in the saturated zone; however,it varies in response to the change of the volumetric watercontent ␪(␺) in the unsaturated zone. In the present model the
relationship between K( ␺ ) and ␪(␺) proposed by Brooks andCorey [1966] is employed. Ignoring hysteresis and local anisotropy and considering the pressure head ␺ as the dependent
variable, they derived
K ⫽ K s兵共 ␪ ⫺ ␪ r兲/共 ␪ s ⫺ ␪ r兲其 m,(7)

where K s is the saturated conductivity, ␪ r is the residual watercontent, and m is a parameter which is theoretically estimatedto be 3.0 by Irmay [1954]. The values of K s and ␪ s are experimentally obtained for the sand sampled at the study site (station 4): K s ⫽ 1.331 ⫻ 10 ⫺2 cm/s, and ␪ s ⫽ 0.3759. The
value of ␪ r is set to be 1.0 ⫻ 10⫺3. While various empiricalfunctions for the retention equation exist, we chose the one
proposed by Tani [1982] to achieve computational robustness.
共 ␪ ⫺ ␪ r兲/共 ␪ s ⫺ ␪ r兲 ⫽ 共兩 ␺ / ␺ 0兩 ⫹ 1兲 exp 共兩 ␺ / ␺ 0兩兲,

(8)

where ␺0 is the matric potential that gives the maximum valueof the water capacity C w .
The backward Euler scheme was used to solve (1)–(8). It is

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

Table 1. Hydraulic and Physical Parameters of the System
Being Simulated
Parameter

Value

Specific storage S
Saturated conductivity K s , cm/s
Density of fresh water ␳ f , g/cm3
Density of seawater ␳ s , g/cm3
Field-saturated volumetric water content ␪ s
Residual water content ␪ rmLongitudinal dispersivity ␣ L , cm
Transversal dispersivity ␣ T , cm
Matric potential ␺0, cm H2O

1.0 ⫻ 10⫺3
1.33 ⫻ 10⫺2
1.0
1.025
0.37591.0 ⫻ 10⫺3
3.0
2.5
0.5
⫺100

an iterative numerical scheme employing implicit finite difference formulations. The spatial derivatives in (2) and (4) arerepresented by centered differences. A computational grid uniformly spaced in all directions was adopted, and the grid sizes
were chosen as ⌬x ⫽ ⌬y ⫽ 2.0 m and ⌬z ⫽ 0.5 m. The
successive over relaxation (SOR) method with a relaxation
parameter of ␻ ⫽ 1.2 was applied to solve the simultaneous
algebraic equations. Computational convergence was judged
with tolerances of 1.0 ⫻ 10⫺2 for (2) and of 1.0 ⫻ 10⫺4 for (4).
The hydraulic and physical parameters of the system being
simulated, which are mentioned above, are summarized inTable 1.
In the computations the x and y axes corresponded to thecross-shore and alongshore directions, respectively. Alongshore variations in ␺ and C are not considered, and therefore
the present simulations are vertically two-dimensional. Free
flux conditions were applied above the water table. Prescribed

1471

head ␺ ⫽ z 0 ␳ / ␳ f , in which z 0 is the vertical distance from thephreatic surface, and concentration (C ⫽ 0.0 at the landward
boundary, and C ⫽ 1.0 at the seaward boundary) were given
as horizontal boundary conditions. Vertical boundary conditions were no-flow and no-flux conditions. The initial values of
total potential and concentration at all nodes were set at zero;
this meant that the aquifer was filled with immobile fresh
water.

4.

Results

4.1. Nutrient Concentrations in Groundwater, Seawater,
and River Water⫺⫹
Figure 5 represents the time series of NO⫺
3 , NO2 , NH4 ,
3⫺PO4 , and SiO2 concentration in the seawater, Tone River
water, and groundwater. The groundwater was sampled atstations 6-a and 6-b and was unlikely to have been influenced
by seawater. Most values of the nutrient concentrations ingroundwater are close to or higher than those in river waterand seawater; however, river water is found to have higher
ammonium concentrations than groundwater and seawater.
⫺⫹
3⫺
Time series of NO⫺
3 , NO2 , NH4 , PO4 , and SiO2 concentration in the groundwater at stations 1-a, 1-b, and 1-c are
shown in Figure 6. These stations were situated near the shoreline where nutrient concentrations in the groundwater wereaffected by seawater. Seasonal variations in nitrite, ammonium, and phosphate concentration were clearly observed atstation 1. Such variations, however, were not seen in the inlandaquifer, e.g., at station 6. At station 1 the nutrient concentrations were remarkably high in August and September andrapidly decreased. There are several explanations for this seasonal variation that should be considered, including seasonal

Figure 5. Time series of nutrient concentration in groundwater (stations 6-a and 6-b), seawater, and riverwater.

1472

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

Figure 6. Time series of nutrient concentration in groundwater at the shoreline (stations 1-a, 1-b, and 1-c).

water temperature and water table fluctuations, timing of fertilizer application and irrigation of croplands, nearshore algal
blooms, or seasonal change in water beach profile and shoreline position, etc. Further data collections should be performed
over a full annual cycle to assess the broader context of thedata presented here.
4.2.

Verification of the Numerical Model

The numerical model was verified by comparing the computational results with experimental data obtained in a laboratory
by Tamai and Shima [1967]. The experimental formula for the
position of a salt wedge near the shoreline was proposed as
C I共l 兲 ⫽ 共q 0/␧K s兲 冑共2␧K s/q 0兲l ⫹ 0.55,(9)where l is the horizontal distance from the seaward edge of thewedge, C I is the vertical distance from the l axis to the saltwater wedge, q 0 is the volume flux of the fresh groundwater
discharge per unit width from the landward end of the aquifer,and ␧ is the normalized density difference (␧ ⫽ ( ␳ s ⫺ ␳ f )/
␳ f ⫽ 0.025). Figure 7 illustrates a definition sketch of (9), in
which the values of K s and ⌬h were set to be 0.20 cm/s and10.0 cm.
Figure 8 displays computational results of the velocity fieldand salinity distribution in the steady state. The position of theinterface calculated from (9) is also plotted in Figure 8b. The
value of q 0 was estimated to be 1.237 cm2/s by the numericalsimulator. Whereas (9) predicts the salt wedge as a sharp
interface, the simulation results showed that a thin mixing zone
separates the fresh and saline groundwater. The latter prediction is clearly more realistic. Nevertheless, we can see that thenumerical model is capable of replicating the behavior of thesalt wedge as observed in the experiments.

5.

Discussion

5.1.

Inorganic Nitrogen Compounds in Upgradient Areas

In the following discussion we investigate the spatial distribution of nutrients in groundwater during the summer, when
the nutrient concentrations near the shoreline were relatively
high as shown in Figure 6. Figure 9 indicates spatially interpo⫺⫹
lated mean distributions of NO⫺
3 , NO2 , NH4 , and DO observed from August 7 to October 9. The upper layer in theaquifer near station 6 had relatively high DO concentrations
ranging from 1.0 to 2.0 mg/L, a maximum nitrate concentration, and minima of nitrite and ammonium within the wholeobservational domain. Bacterial activity for nitrification is highin an aerobic aquifer and activates nitrification reactions of
inorganic nitrogen compounds such as those shown by (10) and(11) [e.g., Greenland and Hayes, 1981]:
NH4⫹ ⫹ 3/2 O2 7 NO3⫺ ⫹ H⫹ ⫹ H2O(10)

Figure 7. Definition sketch of the experimental formula ofTamai and Shima [1967].

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

1473

Figure 8. Computational results of (a) velocity field and (b) spatial distribution of nondimensional salinity.
The thick curve in Figure 8b indicates the position of the interface calculated with the experimental formulaof Tamai and Shima [1967].
NO2⫺ ⫹ H2O ⫹ 2 Fe3⫹ 7 NO3⫺ ⫹ 2 Fe2⫹ ⫹ 2 H⫹.

(11)

Nitrification corresponds to the oxidation reaction indicated by
dextral arrows in the above equations. In contrast, denitrifying
bacteria cause denitrification of inorganic nitrogen compounds
in an anaerobic aquifer with organic carbon, i.e., (12) [e.g.,
Freeze and Cherry, 1979]:
CH2O ⫹ 4/5 NO3⫺
3 2/5 N2 (gas) ⫹ HCO3⫺ ⫹ 1/5 H⫹ ⫹ 2/5 H2O.

(12)

Nitrification and denitrification may not be completed to thelast stage in which nitrogen compounds are entirely oxidized
into nitrate or reduced to gaseous nitrogen, respectively. In⫹
that case, NO⫺
2 , NH4 , or N2O (gas) are produced as intermediate compounds. These reactions are schematically displayedin Figure 10.
The upper groundwater layer in the upgradient area (station

6-a) was high in oxygen, and therefore appreciable nitrification
could occur there with almost no denitrification. Thus theconcentration of nitrate was high in the upper groundwaterlayer at station 6-a with little nitrite or ammonium present. On
the contrary, DO decreased markedly to nearly zero in thelower groundwater layer at station 6-b where anaerobic conditions were correlated with a downward decrease in the nitrate concentration.
The observation at station 5 showed low values of nitrite andammonium; levels roughly corresponded to those in the upper
groundwater layer of station 6 inland. Although a higher oxygen concentration (nearly 3.5 mg/L) was detected in the upper
layer at station 5, the nitrate concentration was only half of thatin the upper layer at station 6. Such a decrease in the nitrateconcentration could have been caused by microbial activity
near roots of vegetation, which consumes nitrate and releases
oxygen [Freeze and Cherry, 1979]. The pine tree vegetation is

Figure 9. Spatial distributions of nitrate, nitrite, ammonium and DO concentration.

1474

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

Figure 10. Schematic diagram of chemical reactions of inorganic nitrogen. Oxidation and reduction correspond to nitrification and denitrification, respectively.
hence considered to result in a higher utilization and removalof nitrate in the upper groundwater layers at station 5.
5.2.

Inorganic Nitrogen Compounds on Beach

Although the concentrations of NO⫺
3 in the upper layer
decreased from station 5 to 4, they increased toward station 1
near the shoreline (as shown in Figure 9) owing to nitrification
under aerobic conditions at station 1. However, the concentrations of nitrite and ammonium also increased near the shoreline in spite of the existence of oxygen. This suggests thatcomplicated biochemical reactions or mixing of deeper waterwith shallow water had occurred.
Sakamoto [1994] pointed out that dissolved organic nitrogen(DON) in seawater, which flows into and out of a coastal
aquifer by tidal pumping, is decomposed and mineralized toammonium in the aquifer and subsequently oxidized to nitrite
and nitrate by nitrifying bacteria. Reduction (i.e., denitrification) to gaseous nitrogen by denitrifying bacteria does notnormally take place in an aerobic aquifer at sandy shores.
Therefore, mineralization of DON and the uptake of dissolved
inorganic nitrogen (DIN) by bacteria determine the change inthe total amount of DIN. On the other hand, Lowrance andPionke [1989] reported that the active denitrifying bacteria
could exist in an aquifer where aerobic and anaerobic conditions alternately arise from the groundwater table fluctuations
due to tides. Moreover, a recent investigation by Sumi andUeda [1997] suggested that significant numbers of denitrifying

bacteria inhabit the aquifer near the shoreline and that denitrification can occur even in a sandy beach aquifer. The dataacquired in the present survey show that the concentrations of
nitrate, nitrite, and ammonium are high near the shoreline,
and their highest concentrations among the data collected near
the shoreline (stations 1–3) appear at station 2-b, which islocated slightly landward of station 1 and just below the upper
layer. These may suggest that in the aquifer near the shoreline,
nitrification of DIN originated in the upgradient area coincides
with mineralization of DON from seawater and that a portionof the nitrified DIN is subsequently denitrified to NO⫺
2 and
NH⫹
4 . These reactions can be caused by denitrifying and nitrification bacteria, which activate with change of chlorine ion
concentration and are the most vigorous in a brackish water[e.g., Sumi and Ueda, 1997]. Hence inorganic nitrogen is considered to experience the most notable biochemical reaction
on the interface between seawater and fresh groundwaterslightly below the seepage face near the shoreline. Detailed
investigations have to be conducted to determine which mechanism is actually responsible.
Overall, we summarize that (1) DIN near the shoreline consists of a remarkably high nitrate concentration; (2) since sufficient oxygen is found in the inland aquifer, DIN appears totend to be readily nitrified; and (3) the seaward transport of
DIN by SGWD and the mineralization of DON, which may befollowed by nitrification and denitrification, are considered tobe responsible for the distribution of the inorganic nitrogencompounds in the aquifer near the shoreline.
5.3.

Spatial Distribution of Phosphate and Silicate

The mean spatial distributions of PO3⫺
4 and SiO2 during thesummer are shown in Figure 11. Whereas relatively dilutephosphate appeared in the upgradient area, the aquifer near
the shoreline had a high concentration of phosphate. The highconcentration of phosphate near the shoreline may also havebeen caused by microbial decomposition and mineralization ofdissolved organic phosphorus (DOP) supplied by seawater[Hayashi, 1979]. With the data obtained we were not able todetermine exactly what mechanism caused the high concentration of phosphate near the shoreline. However, the data
showed that the phosphate concentration declined from thesummer to the autumn (Figure 6). Temperatures of seawaterin Hasaki are typically 22⬚–24⬚C in summer and 15⬚–17⬚C in
winter. These may support that DOP is supplied by seawater
because rate of decomposition of DOP is reduced at lower
water temperatures.
The concentration of silicate generally decreases from the

Figure 11. Spatial distributions of phosphate and silicate concentration.

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

1475

Figure 12. Time series of measured (a) tide level and (b) groundwater level at stations 4 – 6.

In order to estimate the groundwater velocity near the
shoreline, fluctuation of seawater level due to tides and waves
and groundwater table variation with precipitation should be
included in the numerical simulation. Net groundwater flow
may not be greatly influenced by waves, which require shorttime steps to simulate, and the simulation would become costly
with waves included. Therefore we incorporated only the effects of variations of the groundwater table with tide and precipitation in the simulation. The model hence has been applied
to simulate the formation of a saltwater wedge in the coastal
aquifer and to investigate the effects of the tidal water tablefluctuations.
Computations were performed for the two conditions, without (run 1) and with (run 2) the influence of the groundwatertable fluctuations. The numerical simulations for both runs
were made for 3 years; the last 3 months in run 2 corresponded
to a part of the observational period, from August 1 to October
31. The linearly interpolated groundwater table elevation at
the location 100 m inland of the shoreline (calculated frommeasured groundwater table elevations at stations 4 and 5 asshown in Figure 12) was applied to the landward boundary
conditions of pressure potential ␺. Figure 12 also shows thetime series of the tide and groundwater table data. In contrast,
mean values of groundwater table elevation and tide level ofAugust 22 at the boundaries were used in run 1; this meansthat steady salt wedge was computed in run 1.
Figures 13 and 14 show calculated results for runs 1 and 2 forvelocity fields and nondimensional salinity distributions, bothaveraged over a day representative of August 22 in 1997. It canbe seen from the velocity fields for both runs that freshwater
outflow occurs as much as 40 m offshore and that the velocities
near the seeping area are significantly higher than those of theinterior domains. Whereas the discharge appears at a single
area in run 1, the outflows in run 2 are found to occur at several
areas near the shoreline with downward velocities in the upper
layer of the aquifer beyond 40 m offshore.
The salinity distributions for runs 1 and 2 are appreciably
different. The interface between seawater and fresh water was
sharper in run 1; the dispersion width for run 2 was expanded.
The upper part of the saltwater wedge in the aquifer for run 2
was inclined toward the upgradient area as well. These results
are qualitatively consistent with the observed salinity distribution as shown in Figure 15 (note that the scales of cross-shore
coordinates are different). The inclusion of the water table

Figure 13. Computational results for run 1: spatial distribution of (a) velocity vectors and (b) nondimensional salinity.

Figure 14. Computational results for run 2: spatial distribution of (a) velocity vectors and (b) nondimensional salinity.

lower to upper groundwater layers and from the inland to theshoreline (except near station 4). Hence the primary silicate
source is considered to be from the inland rather than fromseawater.
5.4.

Tidal Effects on Formation of the Saltwater Wedge

1476

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

Figure 15. Spatial distribution of salinity measured on August 22, 1997.
fluctuations enables the model to reproduce the inclined salinity distribution near the shoreline. The water table fluctuations largely affect the flow and mass transport processes in theaquifer near the shoreline, where biochemical reaction has
significant importance and nutrient distribution appreciably
varies with depth. This effect hence must be incorporated in
the simulation as accurately as possible.
5.5.

Nutrient Fluxes Into the Sea by SGWD

To further investigate nutrient budgets in the shallow sea,
the nutrient fluxes into the sea by SGWD were examined using
the computed velocity field and the measured values of nutrient concentration in the aquifer near the shoreline. Table 2
lists the seaward nutrient fluxes caused by SGWD through thecross section at station 1 and by Tone River discharge [Ministryof Construction, 1994, 1995, 1996], both averaged over thewhole observational period. An alongshore distance L of 16.0
km was used in the calculation of SGWD, and accordingly, thegroundwater discharge ranged from 5.25 ⫻ 10⫺2 to 7.50 ⫻10⫺2 m3/s. This distance corresponds to the natural uninterrupted coastline from the Tone River mouth in the south to theartificial Kashima port in the north. For the discharge of theTone River the available data from 1993–1995 (in m3/s) wereused. In these 3 years the mean discharge was 212.2 m3/s. The⫺⫹
3⫺concentrations of NO⫺
3 , NO2 , NH4 , PO4 , and SiO2 were
measured near the Tone River mouth. It can be seen from
Table 2 that river discharge dominates nutrient supply to the
Kashima Sea; the groundwater contribution is minor. However, since not all the nutrients released from the river mouthenter the study area, the results shown in Table 2 must be
carefully interpreted. Satellite images show that the Tone
River plume drifts mostly southward, and consequently, lessdirect nutrient supply to the Kashima Sea (north of Tone Rivermouth) is expected. Even though the river outflow is a major
source of nutrients to the seawater in the Kashima Sea, its
contribution to the shallow water environment may not be as
Table 2. Nutrient Fluxes by Groundwater Seeping andTone River Discharge

NO⫺
3 -N
NO⫺
2 -N
NH⫹
4 -N
3⫺
PO4 -P
SiO2-Si

Groundwater,
ton/dTone River,
ton/d0.05480.00450.00470.00780.435122.8673
0.64853.6012
1.349611.9039high as that due to SGWD. The contribution of SGWD to thenutrient budget in the Kashima Sea thus should be discussed
from other points of reference.
The nearshore circulation cells, which were modeled by Inman et al. [1971], produce a continuous interchange of water
between the surf zone and the offshore zone. Nutrient transport processes in the nearshore shallow sea can be represented
as shown schematically in Figure 16. The cells act as distributing and dispersing mechanisms for land runoff and other materials injected into the surf zone. Nutrients from SGWD introduced into the surf zone are carried along the shore,strongly mixed with the water in the surf zone by turbulence ofwave breaking, and transported by the seaward flowing rip
currents through the cross section B-B⬘. The water subsequently spreads over the “secondary mixing zone” from the rip
heads, being transported into the surf zone by onshore masstransport due to waves. Therefore the nearshore circulation
cells horizontally mix the water of the surf zone with that of thesecondary mixing zone.
Another mixing mechanism occurs in the outer part of thesurf zone. Onshore mass transport due to wave action andoffshore return flow result in the water interchange between
the secondary mixing zone and the offshore zone at the crosssection A-A⬘. Assuming a wave period of 7.0 s and wave heightof 1.2 m representative of normal wave condition in the
Kashima Sea [e.g., Nagai et al., 1999], we estimated the onshore mass transport with second-order accuracy to be Q o ⫽Figure 16. Schematic diagram of a mixing in the surf zone
based on the model of Inman et al. [1971]. The zone between
rip currents constitutes a circulation cell. The b.p. and S in the
top indicate a breaking point and a shoreline. Q o , Q w , Q r , Q l ,and Q g are volume fluxes per unit width caused by onshore
mass transport through the cross section A-A⬘, onshore masstransport through B-B⬘, rip current through B-B⬘, alongshore
current, groundwater flow seeping near the shoreline, respectively. F g , F o , and F s are nutrient fluxes provided by groundwater at discharge zone, offshore water at A-A⬘, and water inthe secondary mixing zone at B-B⬘ over the alongshore distance L. C g , C o , and C s are nutrient concentrations ingroundwater, offshore seawater, and nearshore seawater.

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

2.24 ⫻ 10 ⫺2 (m2/s) at A-A⬘. In addition, the volume flux per
unit width caused by rip currents through the cross section
B-B⬘ is Q r ⫽ 9.43 ⫻ 10 ⫺2 (m2/s) according to Inman et al.
[1971] on the assumption that the width and the seabed slopeof the surf zone are 150 m and 1/50, respectively. The averaged
volume flux per unit width of groundwater flow was calculated
as Q g ⫽ 3.93 ⫻ 10 ⫺5 (m2/s) based on the numerical simulations.
To analyze the mixing in the surf zone and the secondary
mixing zone, we shall apply a “box” model to the water bodyconsisting of these two zones. If the flow and nutrient fields inthe alongshore direction are uniform, the budget of nutrient
fluxes in the box can be expressed as follows:
V共dC s/dt兲 ⫽ F g ⫹ F o,

(13)

where V is the volume of the box, C s is the nutrient concentration in the box, and F g and F o are the nutrient fluxes
provided by the groundwater and the offshore water over thealongshore distance L. Considering Q g ⬍⬍ Q o , F o is calculated by (14),F o ⫽ L兵Q oC o ⫺ 共Q o ⫹ Q g兲C s其 ⬵ L共Q oC o ⫺ Q oC s兲,(14)where C o is the nutrient concentration in the offshore water.
We can rewrite (13) as
V共dC s/dt兲 ⫽ F g ⫹ LQ o共C o ⫺ C s兲.

(15)

The solution for (15) is readily obtained as
Cs ⫽

冉

Fg
⫹ Co
LQ o

⫹ C s0 exp

冉

冊再
⫺

1 ⫺ exp

冊

LQ o
t ,
V

冉

⫺

LQ o
t
V

冊冎
(16)

where C s0 is the value of C s at the time t ⫽ 0. The first termon the right-hand side of (16) represents rise of concentration
due to inflow of groundwater and offshore water, and thesecond term shows decline of concentration caused by outflow
from the box to the offshore. The value of C s therefore approaches (F g /LQ o ⫹ C o ) at t 3 ⫹⬁.
The area of the cross section of the box, S, is estimated withthe seabed slope of 1/50 and a width of the secondary mixing

Table 3. Averaged Shallow Water Nutrient Concentration
C s , F g /LQ 0 Denoting the Effect of SGWD on Shallow
Water Nutrient Concentration, and the Ratio of F g /LQ 0 to
Cs

NO⫺
3 -N
NO⫺
2 -N
NH⫹
4 -N
3⫺
PO4 -P
SiO2-SiC s,
mg/L

F g /LQ 0 ,mg/L

Ratio,%

0.06530.00890.04580.0083
0.48671.77 ⫻ 10⫺3
1.45 ⫻ 10⫺4
1.52 ⫻ 10⫺42.52 ⫻ 10⫺4
1.41 ⫻ 10⫺2

2.710
1.633
0.331
3.035
2.887

zone of 270 m (1.8 times the surf zone width [cf. Inman et al.,1971]). The volume of the box, V ⫽ SL, divided by LQ o gives⬃21.9 hours, which is the residence time in the box for nutrients from the groundwater. This means that the nutrients discharged by SGWD are expected to stay in the box for almost 1
day. Figure 17 indicates the temporal variations of the concentration C s of nitrate and both the terms on the right-hand sideof (16). The offshore water concentration C o and the initialconcentration C s0 are set in the calculation of (16) to be 0.0
and 0.0653 mg/L (the measured value of the mean nitrateconcentration of the seawater). The condition of C o ⫽ 0.0
assumed here is preconceived to result in noticeable dilution.
The nitrate concentration C s actually appears to fall immediately in a few days and finally to approach F g /LQ o , 1.77 ⫻10 ⫺3 mg/L, as shown in Figure 17. The values of F g /LQ ohence are significant for estimating the contribution of SGWD
to the nutrient concentration in the nearshore water with the
influence of mixing of the seawater in the surf zone. The
averaged concentration C s of five compounds in the water near
the shoreline are listed in Table 3 with F g /LQ o and the ratios
of F g /LQ o to C s . The ratios ranging from 0.331 to 3.035%
imply that SGWD plays a minor role in the nutrient budget of
the nearshore water in the Hasaki area.
On the contrary, Tone River, which has the largest drainage
basin in Japan and a proportionally large amount of discharge,
provides enormous nutrient fluxes as shown in Table 2. In acoastal area with less river influence, nutrient inputs due to
SGWD may be more significant than that in the study area.
Although the calculations of nutrient fluxes were based on
the assumption that the aquifer consists of homogeneous sand,pipe flow through macropores is believed to affect dewateringof groundwater, as is discussed in the area of hillslope hydrology. Furthermore, outfalls, irrigation channels, and streams,
which can be seen in the field, probably introduce nutrient-richwater directly into the nearshore sea. These nutrient supplies
should be considered in analyses of nutrient budgets in future
work.

6.

Figure 17. Nutrient concentration C s as a function of timewith C o ⫽ 0.0. The circles, squares, and crosses represent C s
and second and first terms on the right-hand side of (16),respectively.

1477

Conclusion

Groundwater at Hasaki Beach, which is located in an intensively cultivated agricultural area, generally has high concentrations of inorganic nutrients compared with seawater andriver water. During summer, nitrification produces high nitrateconcentrations in the landward upper aquifer under aerobic
conditions, while nitrite and ammonium concentrations arelow. The aquifer near the shoreline is a complex chemical
environment in which denitrification and nitrification simultaneously or alternately occur. Moreover, SGWD from the up-

1478

UCHIYAMA ET AL.: SUBMARINE GROUNDWATER DISCHARGE

gradient area and decomposition and mineralization of organic
matter from the sea is considered to supply inorganic nutrientsto this part of the aquifer; those are mixed together and thentransported into the sea. The microbial activity related to biochemical processes in the aquifer near the foreshore zone
varies seasonally as evident in the seasonal changes of thenutrient concentrations.
With the effects of groundwater table and tidal fluctuations
included, a numerical model was used to estimate the nutrient
fluxes from the aquifer into the sea on the assumption that theaquifer consists of homogeneous sandy soil. The nutrient fluxes
from SGWD are found to be minor as compared with thenutrient flux from Tone River. Additionally, according to theresults of box model analysis, the nutrient fluxes due to SGWD
have little influence on the shallow water ecosystem around thesurf zone in this area.
SGWD, however, may be underestimated since pipe flow
through macropores and effects of wave run-up and setup areneglected in the computations. Therefore further investigations are needed, including a field survey and the improvementof the numerical model to clarify the importance of theseeffects.
Acknowledgments. The first author wishes to thank Y. Kuriyamaof the Port and Harbour Research Institute, Yokosuka, Japan, and
L. Li of the University of Edinburgh, Edinburgh, U.K., for their helpfulcomments on the manuscript. We are grateful to T. Nakasone(National Research Institute of Fisheries Engineering, Hasaki, Japan)
for his help with the field measurements.

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K. Nadaoka and P. Rölke, Graduate School of Information Scienceand Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama,
Meguro-ku, Tokyo 152-8552, Japan.
Y. Uchiyama, Marine Environment Division, Port and Harbour
Research Institute, 3-1-1 Nagase, Yokosuka 239-0826, Japan.
(uchiyama@ipc.phri.go.jp)
H. Yagi, Department of Civil Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan.

K. Adachi, National Research Institute of Fisheries Engineering,
Ebidai, Hasaki, Ibaraki 314-0421, Japan.

(Received February 1, 1999; revised January 24, 2000;
accepted February 7, 2000.)1480