Continental Shelf Research 76 (2014) 36–52

Contents lists available at ScienceDirect

Continental Shelf Research
journal homepage: www.elsevier.com/locate/csr

Research papers

Wastewater efﬂuent dispersal in Southern California Bays
Yusuke Uchiyama a,n, Eileen Y. Idica b, James C. McWilliams c, Keith D. Stolzenbach daDepartment of Civil Engineering, Kobe University, Kobe, Japan
Trussell Technologies, Inc., San Diego, CA 92075, USA
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095-1565, USAd
Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095-1593, USAbcart ic l e i nf o

a b s t r a c t

Article history:
Received 18 March 2013
Received in revised form
1 October 2013
Accepted 2 January 2014
Available online 18 January 2014

The dispersal and dilution of urban wastewater efﬂuents from offshore, subsurface outfalls is simulatedwith a comprehensive circulation model with downscaling in nested grid conﬁgurations for San Pedro
and Santa Monica Bays in Southern California during Fall of 2006. The circulation is comprised of mean
persistent currents, mesoscale and submesoscale eddies, and tides. Efﬂuent volume inﬂow rates at
Huntington Beach and Hyperion are speciﬁed, and both their present outfall locations and alternativenearshore diversion sites are assessed. The efﬂuent tracer concentration ﬁelds are highly intermittent
mainly due to eddy currents, and their probability distribution functions have long tails of highconcentration. The dilution rate is controlled by submesoscale stirring and straining in tracer ﬁlaments.
The dominant dispersal pattern is alongshore in both directions, approximately along isobaths, overdistances of more than 10 km before dilution takes over. The current outfall locations mostly keep the
efﬂuent below the surface and away from the shore, as intended, but the nearshore diversions do not.
& 2014 Elsevier Ltd. All rights reserved.

Keywords:
Regional ocean modelingSewage dispersal
Submesoscale stirring
Urban wastewater

1. Introduction
Coastal oceans are discharge sites for agricultural, industrial,and urban pollution around the world; they are also places with
dense human and wildlife populations and ﬁsheries. Pollution
management of offshore efﬂuent is necessary and relies ontreatment in reducing toxicity, and dispersal and dilution by ocean
currents to reduce local concentration levels.
Urban treated wastewater (sewage) from greater Los Angeles
has three major efﬂuent discharge pipes, two of which areconsidered here. One is near Huntington Beach in San Pedro Bay(SPB, extending south from Palos Verdes Peninsula past Newport
Beach) and is run by the Orange County Sanitation District (OCSD),
while the other is near the Hyperion Treatment Plant (HTP) in
Santa Monica Bay (SMB, extending between Point Dume and Palos
Verdes Peninsula) and is run by the City of Los Angeles Bureau of
Sanitation. Both have offshore outfalls below the surface within
embayments and inshore of the strongest currents.
In this paper we simulate efﬂuent dispersal and dilution using acirculation model that has multiply nested grids from a regional
conﬁguration for the U.S. West Coast with mesoscale horizontal
grid resolution (dx¼ 5 km) down to the SPB and SMB subdomains
with submesoscale grid resolution (dx¼75 m). The nesting
approach is necessary to represent the inﬂuence of larger scalenCorresponding author.
E-mail addresses: uchiyama@harbor.kobe-u.ac.jp (Y. Uchiyama),
eileen.idica@trusselltech.com (E.Y. Idica), jcm@atmos.ucla.edu (J.C. McWilliams),
stolzenb@ucla.edu (K.D. Stolzenbach).
0278-4343/$ - see front matter & 2014 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.csr.2014.01.002

currents on the local ones by which the dispersal occurs. We
choose the particular period of Fall 2006 to obtain a representative
range of dispersal behaviors. Model forcing is by synoptic meteorological surface ﬁelds (themselves were generated in a nested
meteorological model) and by lateral open boundary conditions
constructed from the output of a global oceanic model with data
assimilation and from an empirical tidal analysis. This conﬁguration is intended as comprehensive for all relevant types of currents
within this class of model formulation.
A regional coastal model with a nested-grid hierarchy can serve
many purposes. We use the Regional Oceanic Modeling System(ROMS) whose principal algorithms are described in Shchepetkin
and McWilliams (2005, 2008) and nesting techniques in Penven
et al. (2006) and Mason et al. (2010). Using ROMS conﬁgurations
similar to the one used here (Section 2.1), the simulation andempirical validation of the regional circulation and eddy characteristics are made for the U.S. West Coast in Marchesiello et al.
(2003) and Capet et al. (2008a) and for the Southern California
Bight (containing SPB and SMB) in Dong et al. (2009). Particular
process studies are made for island wakes (Dong and McWilliams,
2007); upwelling events (Capet et al., 2004; Dong et al., 2011);
mesoscale eddy distribution (Kurian et al., 2011) and buoyancy
ﬂux (Colas et al., 2013); California Undercurrent separationand its submesoscale instability (Molemaker et al., 2014); tidal
currents (Wang et al., 2009; Buijsmann et al., 2012); sedimenttransport (Blaas et al., 2007); nearshore particle dispersion(Romero et al., 2013); plankton productivity (Gruber et al., 2006,2012); and larval dispersal and connectivity (Carr et al., 2008;
Mitarai et al., 2009).

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

Besides including the efﬂuent sources (Section 2.2), the present
circulation and associated dispersal study is novel by incorporatingsmaller scale features and analyzing them closer to shore.1 Compared to the persistent currents and mesoscale eddies that dominate the ﬂow in deeper water offshore, the important local agentsof wastewater efﬂuent transport are the currents over the continental slope and shoaling shelf. They are comprised of mesoscaleand submesoscale eddies (including poleward-propagating coastally trapped waves), and both barotropic and internal tides (Hickey,
1992; Kim et al., 2010). Some coastal waves are generated by windﬂuctuations that are located equatorward of the model domain andhave a smaller scale than is resolved in the open boundary
condition ﬁelds; these are absent in our simulations, although
regionally generated coastal waves are present. Submesoscalecurrents arise from frontogenesis and baroclinic instability processes in the surface layer (Capet et al., 2008b) and topographic andcoastline shear wakes (Dong et al., 2009; Molemaker et al., 2014).
Our conﬁguration lacks surface gravity wave effects, so littoral
currents in the surf zone are absent, hence this ﬁnal step of efﬂuent
transport to the shoreline is missing. (We hope to address thislater.) The focus here is not as much on these different types ofcurrents and their dynamical processes but rather on the resulting
efﬂuent distributions they cause.
In Southern California discharge of wastewater efﬂuent into
the ocean was historically implemented as a way to safely disposeof minimally treated (e.g., screening only) sewage with the understanding that dilution within the ocean would render the harmful
constituents safe via biological and chemical reactions andphysical transport. However, environmental concerns grew, andthe municipalities began implementing increased treatment(e.g., primary sedimentation, secondary biological treatment) on
land as well as placing outfalls further offshore and at greater
depth (SCCWRP, 1973; Anderson et al., 1993; Sklar, 2008). Outfall
design also often included diffusers consisting of a pipe with
discharge jets under pressure through multiple ports over a length
approximately 10 times the discharge depth. This design enabled
greater immediate mixing through the individual jets, followed byincreased nearﬁeld mixing and dilution of the turbulent buoyant
plume, as compared to a single pipe outlet (Fischer et al., 1979).
Both OCSD and HTP have primary outfalls that follow this design
rationale, with outfalls that terminate approximately 5 miles offshore with multi-port, bottom-mounted diffusers at depths of
h¼ 60 m and 57 m, respectively (CRWQCB, 2010, 2012). Eachcurrently discharged secondary-treated wastewater efﬂuent,which typically has elevated levels of nitrogen (as ammonia and/or nitrate), organic matter, and pathogens relative to the receiving
ocean waters. Both efﬂuent and receiving waters are monitored forthese conventional pollutants and for numerous other contaminants (inorganic, volatile and non-volatile organics, carcinogens,etc.) that might affect human and environmental health.
The efﬂuent plumes of both the OCSD and HTP outfalls havebeen found to remain primarily subsurface below depths of
15–20 m during typical density-stratiﬁed conditions, as detectedby a variety of parameters (salinity, colored dissolved organic
matter, bacteria, ammonia) during routine monitoring (OCSD,
2012; City of Los Angeles, 2007). The routine monitoring stations
used by the agencies extend about 10 km perpendicular fromshore, and thus are not ideal for tracking the horizontal extents ofthe plumes. Jones et al. (2001) detected the OCSD efﬂuent plumeat least 12.5 km from the outfall in either alongshore direction
during two sampling periods using salinity, ammonium, and fecal
coliform bacteria as indicators. Boehm et al. (2002) investigatedcross-shelf transport of the OCSD efﬂuent plume towards theshore and found the plume within approximately 2 km of theshore (5 km from the outfall), as indicated by E. coli. Jones (2004)
found consistent results in plume sampling for cross-shelf transport
using salinity, fecal indicator bacteria, and ammonium as evidenceof plume presence. In general, studies of the OCSD efﬂuent plume
have shown mainly alongshore transport either up or downcoastfrom the outfall, over subsurface depths ranging from 15 to 70 m,
and with considerable heterogeneity in plume patterns (Jones et al.,
2001; Boehm et al., 2002; Jones, 2004; Todd et al., 2009). Efﬂuent
plume surfacing appears rare, although evidence of the HTP efﬂuent
plume on the surface has been captured by synthetic aperture radar(SAR) imagery during one winter event in 1997, with the plume
covering an area of approximately 16 km2 above the diffuser
location (Di Giacomo et al., 2004).
The current OCSD and HTP outfalls have been in continuous
operation for 40–50 years. To perform any major repairs orinternal inspection of the structures, the efﬂuent needs to be
diverted to another location. For both facilities, older, deactivatedoutfalls are permitted for use as temporary or emergency discharge locations; both discharge approximately 1 mile offshore,with the OCSD nearshore outfall at 20 m depth and the HTP outfall
at 15 m depth (CRWQCB, 2010, 2012). Use of the nearshore outfalls
for discharge diversion has been rare and recently limited to one
event during 2006 when HTP performed an internal inspection ofits standard pipe and one during 2012 when OCSD repaired its
standard pipe. Additional diversions are possible in the future.

2. Model conﬁguration
2.1. The ROMS model
The oceanic circulation model ROMS is used to simulate thecirculation and tracer efﬂuent dispersal in the coastal zone ofSouthern California. It includes K-Proﬁle Parameterization (KPP;
Large et al., 1994; Durski et al., 2004), a non-local turbulent closure
model for vertical momentum and tracer mixing in the surface
and bottom planetary boundary layers and in the interior of the
ﬂuid. In addition it has a numerical hyperdiffusion associated withhorizontal advection with an effective diffusivity coefﬁcient that
decreases with the grid scale. The present ROMS conﬁgurationconsists of quadruply nested model domains (Fig. 1) with an offline, one-way nesting technique that downscales from dx ¼5 km
horizontal resolution of the U.S. West Coast (L0), to 1 km resolution for the Southern California Bight (L1), to 250 m resolution for
the interior shallow area of the Bight with a multiple of large
islands and deep basins (L2), and then to 75 m resolution for two
separate subdomains encompassing Santa Monica Bay (L3a) and
San Pedro Bay (L3b). Each domain has 40 (L0, L1, and L2) or 32 (L3aand L3b) topography-following levels vertically stretched suchthat grid cell reﬁnement occurs most strongly near the surface
and the bottom. The model topographies are from the 30 arcsec
global bathymetry (SRTM30; Becker et al., 2009) overall, with
reﬁnement using the 3 s (dx ¼90 m) NOAA-NGDC coastal relief
dataset2 for the nearshore regions depending on data availability.
The outer L0 domain is forced by the monthly averaged data fromSODA version 2.0.4, an assimilated global oceanic dataset (Carton and
Giese, 2008) in the lateral boundary conditions; the monthly average
AVHRR Pathﬁnder satellite sea surface temperature3 (SST), and the
COADS climatological dataset for sea surface salinity4 (SSS). On the L0
grid the monthly climatology of runoff from major rivers (Dai and21

Buijsmann et al. (2012) use these same simulations to analyze the internal
tide in the Southern California Bight.

37

http://www.ngdc.noaa.gov/mgg/coastal/crm.html
http://podaac.jpl.nasa.gov/DATA_PRODUCT/SST/index.html
4
http://www.ncdc.noaa.gov/oa/climate/coads/
3

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

momentum, heat, freshwater (evaporation minus precipitation), andradiation ﬂuxes for all the ROMS models are given by an hourly
atmospheric forcing by a double-nested Weather Research andForecast model (WRF; Michalakes et al., 1998) with dx¼ 18 and
6 km horizontal grids embedded in NCEP0 s North American Regional

Trenberth, 2002) is included by addition to the surface freshwater
ﬂux. The intermediate L1 and L2 and the inner L3a and L3b grids arethen driven by the corresponding parent ROMS model solutions withdaily (L0 to L1) and 2-hourly (L1 to L2, L2 to L3a and L2 to L3b) lateralboundary updates. All the other surface boundary conditions such as

48°N

L0

6000

Seattle

2000

34.6

h (m)

5000

42°N

Santa Barbara

3000

100

34.2

2000

Santa
MonicaSt. Rosa

1000

34

San Francisco 0

S. MiguelSt. Cruz

1600

L1

L2

34.4

4000

h (m)

38

400

33.8

36°N

33.6

L2

San Pedro Bay
400

L1

0

Palos Verdes
Huntington
BeachSanta Monica Bay

Los Angeles

800

Los Angeles

L3aAnacapa

1200

33.4

30°N

St. Barbara

S. Nicolas

250
0

33
24°N

L3b
St. Catalina

33.2

32.8
S. Clemente

32.6

144°W

138°W

132°W

126°W

120°W

-121

114°W

-120.5-120-119.5-119-118.5-118-117.5

Fig. 1. The quadruply nested ROMS model domains and bathymetry [m] (gray scale). Left: three nested grids along the North American West Coast. The outer boundaries ofthe dx¼ 5 km grid (L0), 1 km grid (L1), and 250 m grid (L2) are represented by the white dashed, white solid, and black solid lines. Right: Southern California Bight where theperimeters of the dx¼1 km grid (L1), 250 m grid (L2), 75 m Santa Monica Bay grid (L3a), and 75 m San Pedro Bay grid (L3b) are represented by the thin dash-dot, thin solid,
thick dashed, and thick solid rectangles, respectively. The 100, 400, and 2500 m isobaths are plotted with black solid, black dotted and white solid contours to indicate
mainland/island shelves and continental shelf breaks.

o

SST ( C)
19.5

SPB 10/01/2006 5 h

SST (oC)
20.5

SMB 09/12/2006 7 h
30

40
25
19

y (km)

30

20

20
15

20

18.5
19.5

10
10
18
0

5
0

19

ζ / f (z > -hbl)

ζ / f (z > -hbl)
30

40

2

2
25

1

y (km)

30

0

20

-1

1

20

0

15
10

-1

10
5
-2
0

-2
0

0

10

20

30
x (km)

40

50

60

0

10

20

30

40

x (km)

Fig. 2. Instantaneous ﬁelds of surface temperature (SST; top row) [C] and vertical vorticity ζ averaged over the surface boundary layer and normalized by the Coriolis
frequency f ¼ 0:8  10  4 s  1 (bottom). The left column is SPB on October 1, 2006, and the right column is SMB on September 12, 2006. The locations of the outfall pipes areindicated by the black lines.

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

2 2(m /s )

SPB

30

39

2 2

(m /s )

SMB

40
25
-2

y (km)

-2

10

30

10

20
15

20

10
10

-3

-3

10

10

5

0

0
0

10

20

30
x (km)

40

50

60

0

10

20

30

40

x (km)

Fig. 3. Surface, subseasonal eddy kinetic energy [m2 s  2] in SPB (left column) and SMB (right). Magenta circles are the areas with a diameter of 10 km for the spatial
averaging used for Table 1 (Section 3). (For interpretation of the references to color in this ﬁgure caption, the reader is referred to the web version of this paper.)

SPB Mean

SMB Mean
0

24

24

24

0

z (m)

-20

-20

-40

-40
25

25

-60

-60
T (o C)T (o C)

-80

-80
12

14

16

18

12

-100

14

16

-100
0

5

10

15

20

0

5

SPB Mean

15

20

SMB Mean
0

24

24

10

24

0
-20

z (m)

18

-20

-40

-40
25

25

-60

-60
S (psu)S (psu)-80-80
33.4 33.5 33.6 33.7 33.8

33.4 33.5 33.6 33.7 33.8

-100

-100
0

5
10
15
cross-shore distance (km)

20

0

5
10
15
cross-shore distance (km)20

Fig. 4. Time-mean Tðx; zÞ [C] and Sðx; zÞ [PSU] along sections parallel to the outfall pipes in SPB (left column) and SMB (right column) (see Fig. 8). Black contours and labelsshow s, the density excess over 103 kg m  3. These ﬁelds are for the simulations with standard outfalls. Black triangles indicate the approximate locations of the outfall
diffusers.

Reanalysis with a 32 km horizontal grid.5 The 18 km WRF solution isused to force the ROMS L0 model, while the 6 km solution is used for
the L1, L2, L3a and L3b models with a one-way coupling approach.
The full nested sequence from L0 down to L3 is run for the primary
simulation period of August 1–November 30, 2006. Prior to this theL0 model is spun up for many years with climatological surface

5

http://www.emc.ncep.noaa.gov/mmb/rreanl/

forcing, and then a synoptic spin up run is made forL0 with QuikSCAT-ECMWF blended winds6 for 2004–2006, withshorter nested spin up periods for L1 (8 months) and L2 (1 month).
At each stage the ﬁner-grid ﬁelds are initialized with the coarser-gridﬁelds.

6
http://cersat.ifremer.fr/Data/Discovery/By-product-type/Gridded-products/
MWF-Blended

40

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

The L1 domain is forced at its lateral boundaries with waterlevel and barotropic current amplitudes, and phases for ten tidal
constituents (i.e., M2, S2, N2, K2, K1, O1, P1, Q1, Mf, and Mm). The
amplitudes and phases are synthesized with the corresponding
tidal constituents from the TPXO 7.1 global tidal prediction model(Egbert et al., 1994). At every baroclinic time step, the tidal waterlevel and velocities are superposed on the daily-averaged boundary conditions from the L0 run. The full three-dimensionalvariability in L1 is projected onto the L2 boundaries by an update
every 2 h, and the same approach is taken from L2 to L3a and L3b.
An extensive model-data comparison has been made in a nontidal conﬁguration similar to L1 by Dong et al. (2009), andBuijsmann et al. (2012) assessed barotropic and baroclinic tides
in the Bight in the L2 and L3 solutions; both of these validationassessments show fair quantitative agreement.
2.2. Efﬂuent tracer source
Given an input pollutant concentration in the outfall pipe
Cp [kg/m3] with volume ﬂux Qp ðtÞ [m3/s], we force a nondimensional tracer concentration equation by an equivalent source P [1/s]∂c¼  ∇  F þ P;
∂t

ð1Þ

with
Pðx; y; z; tÞ ¼ P s ðtÞAðx; yÞHðzÞ;ð2Þ

here c is pollutant concentration normalized by Cp (unlike salinity,
which is a mass fraction of seawater), and F ¼ uc þ Fsgs is theadvection-mixing ﬂux associated with the resolved ﬂow and thesubgrid-scale (sgs) parameterizations (Section 2.1). A and H are thespeciﬁed spatial functions mimicking the outcome of unresolved
nearﬁeld mixing above the outfall diffusers; their values are nondimensional and close to one in the source region and zero outside
it. They have integrals equal to the effective source area and depthZ∬ A dx dy ¼ As ;H dz ¼ H s ;ð3Þ
Table 1
Velocity vector magnitude [10  2 m s  1] in temporal–spatial bands: the time mean
speed and the ﬂuctuation RMS for mesoscale (period P¼ 30 h–90 days; horizontal
wavelength L 4 20 km), submesoscale (P¼ 30 h–90 days; L o 20 km), diurnal(P ¼18–30 h), and semidiurnal (P¼ 8–18 h) bands. Averages are made within acircle of diameter 10 km centered 2 km inshore from the outfall. Separate averages
are made for two depth intervals: surface ðz Z  hbl Þ and subsurface
 min½h; 75 m r z o  hbl Þ.
San Pedro Bay
component

Surface

Subsurface

Surface

Subsurface

Mean
Mesoscale
Submesoscale
DiurnalSemidiurnal

3.37
7.80
4.55
2.75
2.84

5.72
4.80
3.41
1.37
2.11

1.32
5.06
5.10
2.87
2.56

0.12
3.18
3.53
1.35
1.59

z (m)

SPB alongshore

SMB alongshore

0

0

-20

-20

-40

-40

-60

-60
contour intervals: 0.02 (m/s)
rms (m/s)
0 0.04 0.08 0.12 0.16-80contour intervals: 0.01 (m/s)
rms (m/s)
0 0.03 0.06 0.09 0.12

-80

-100

-100
0

5

10

15

20

0

SPB cross-shore

z (m)Santa Monica Bay

5

10

15

20

5
10
15
cross-shore distance (km)20

SMB cross-shore

0

0

-20

-20

-40

-40

-60

-60
contour intervals: 0.01 (m/s)
rms (m/s)
0 0.03 0.06 0.09 0.12-80contour intervals: 0.01 (m/s)
rms (m/s)
0 0.03 0.06 0.09 0.12

-80

-100

-100
0

5
10
15
cross-shore distance (km)200Fig. 5. Cross-shore sections of velocity mean (contours) and subseasonal ﬂuctuation root-mean-square (RMS; colors) [m s  1]. The sections parallel the outfall pipes in SPB(left column) and SMB (right column). The velocity vector is decomposed into its poleward alongshore component (top row) and shoreward cross-shore component (bottomrow). The heavy solid line is the zero contour, and the thin red and blue solid lines are, respectively, positive and negative contours with the indicated intervals (0.01 or
0.02 m/s). Black triangles indicate the approximate locations of the outfall diffusers. (For interpretation of the references to color in this ﬁgure caption, the reader is referredto the web version of this paper.)Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

41

c (no unit)

OCSD

-1

10

0
z (m)

-2

10

-20

-3

10

-4

-40

10

-5

S (psu)

33.6

0
z (m)

10

-20

33.4

-40
33.2

C (m)

0.3
0.2
0.1
0
08/11

08/31

9/20

10/10

10/30

11/19

Day of 2006

2

PDF[C]

10

mean=0.081 m
rms=0.036 m
Ku=3.872 m
dC=0.0050 m

1

10

0

10

0

0.05

0.1

0.15

0.2

0.25

C (m)
Fig. 6. Time series of the normalized tracer concentration cðz; tÞ, salinity Sðz; tÞ, vertically integrated normalized tracer concentration C(t), and the probability density function
P½C for the average of the Ns ¼23 model grid points used as the standard outfall efﬂuent source region of OCSD. c and S plots also show the surface turbulent boundary layer
depth, z ¼  hbl (white line). In the bottom panel the bin size for P½C is dC ¼ 0.005 m, with normalization ∑i P½C i  dC ¼ 1. The mean of C(t) is demarcated by the blue verticalline and its value is listed along with the root-mean square (RMS) and kurtosis (Ku) for C ﬂuctuations relative to the mean. S plots show mid-depth salinity minima that havebeen frequently observed in the area (e.g., Todd et al., 2009, Fig. 10), augmented by the efﬂuent freshness. (For interpretation of the references to color in this ﬁgure caption,
the reader is referred to the web version of this paper.)with As the horizontal area, Hs the vertical size, and V s ¼ As H s thevolume. P s is determined from integrated tracer equivalence
between the model source and the pipe inﬂow by the relation,
P s ¼ Qp =V s . For our simulations we use outfall data for Qp ðtÞ. To
translate from our c ﬁelds for any particular pollutant species (e.g.,CDOM), we could multiply by its inﬂow concentration value Cp .
Because the vertical structure of c is relatively simple compared toits ðx; y; tÞ structure, we deﬁne the vertically integrated, normalized
tracer by
Z
C¼

c dz;

ð4Þ

its unit is m. There is an analogous forcing source in the model0 ssalinity S equation, R ¼ Rs AH, by the freshwater ﬂow out of thepipe, where integral balance implies that Rs ¼  So Qp =V s withSo ¼35 PSU, the mean oceanic salinity.
The wastewater efﬂuents are speciﬁed as monthly-averaged
freshwater volume ﬂuxes of Qp ¼ 5:4–6:2 m3 =s smoothly interpolated in time for OCSD and a constant 15.3 m3/s for HTP; thesevalues are not precisely accurate for Fall 2006, but are representative of the discharges.7 Daily-averaged discharge of the three local
rivers (Los Angeles River, San Gabriel River, and Santa Ana River) are
included as freshwater volume ﬂuxes at the corresponding mouth
locations, although the model indicates that their inﬂuence is minor
in Fall 2006, and they will not be discussed here. The nearﬁeld
7
The efﬂuent concentrations linearly scale with Qp , apart from the additional
dynamical forcing by R, which has modest nonlinear effects in our simulations.

vertical mixing of the buoyant efﬂuent occurs on a scale smaller
than our grid resolution, and, as a hydrostatic model, ROMS is
ill-suited for the large local vertical velocities associated withthe freshwater discharge from the bottom-mounted pipes. Therefore,
we specify the outcome of the nearﬁeld initial mixing and dilution by
imposing the prescribed spatial distributions of A and H in (2).
A ¼ 1 in the horizontal grid cells that tile the diffuser pipe
2
segment, and it is zero elsewhere. So As ¼ N s dx , where Ns is the2number of tiling cells and dx ¼ 5:6  103 m2 is the cell area. For
OCSD Ns ¼23 for the 5-mile outfall pipe, and Ns ¼12 for the 1-mile
2pipe; for HTP Ns ¼32 for the 5-mile pipe, and As  dx for the
1-mile pipe (which lacks a diffuser). We ﬁt a Gaussian shapefunction to H with parameters guided by nearﬁeld buoyant plume
solutions obtained by OCSD using the model of Roberts et al.
(1989) with measured currents near the outfall:2HðzÞ ¼ expf  ðz  zs Þ2 =ds g:

ð5Þ

zs is the plume center height and ds is its vertical scale. A halfpﬃﬃﬃﬃ
space integral of this HðzÞ is 0.5 π ds . For the 5-mile outfalls, wechoose zs ¼  h þ 20 m (with h being the bathymetric depth) andpﬃﬃﬃﬃ
ds ¼7.1 m, hence H s ¼ π ds ¼ 12:5 m (neglecting top and bottom
boundary limits to the integral). This HðzÞ does not reach thesurface due to density stratiﬁcation in the pycnoline. For the
1-mile outfalls, the plume penetrates the stratiﬁcation and rises
up to the surface: zs ¼ 0. We further choose ds ¼10 m, hence
Hs ¼8.9 m neglecting the bottom boundary limit.
A feasible future generalization of this nearly steady efﬂuent
source is to use monitored Qp ðtÞ and run the nearﬁeld buoyant
plume model with modeled local currents. This would contribute42

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

additional source variability to the efﬂuent distributions seen in
the present solutions (Sections 4 and 5), and it would moreconsistently determine the nearﬁeld plume dilution rates in
response to local ambient conditions. However, we have speciﬁedRthe model source with a ﬁxed mixing volume,
AH dx, torepresent the nearﬁeld plume dilution, whereas in nature
the mixing volume may vary; this bias is difﬁcult to remedy

in a ﬁxed-grid model even with the very ﬁne dx employed
here. Furthermore, there is an issue whether the assumed
scale separation between the calculated variable circulation andconcentration and the parameterized nearﬁeld plume mixing isvalid; for ﬁne enough model resolution this assumption will fail,and the turbulence of the plume must be calculated explicitly (e.g.,
as in Weil et al., 2012, for an atmospheric convective regime).

OCSD 09/22/2006 5 h

HTP 08/25/2006 17 h
30

40
25

y (km)

30

20
15

20

10
10

5
0

0
OCSD 10/01/2006 5 h

HTP 09/12/2006 7 h
30

40
25

y (km)

30

20
15

20

10
10
5
0

0
OCSD 11/02/2006 1 h

HTP 10/30/2006 23 h
30

40
25

y (km)

30

20
15

20

10
10

5
0

0
0

10

-4

10

20

10

30
x (km)

-3

40

60

0

-1

-4

10

20

30

40

x (km)
10

C (m)

50

-2

10

10

10

-3

10

-2

10

-1

10

0

C (m)

Fig. 7. Snapshots of representative patterns of Cðx; yÞ for OCSD (left column) and for HTP (right). Thick white lines indicate standard outfall pipes, and light white lines are
the 100 and 500 m isobaths. Axis distances are in km. The middle-row times are the same as in Fig. 2.

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

OCSD Mean43

HTP Mean30

40
25

y (km)

30

20
15

20

10
10
5
0

0
OCSD RMSHTP RMS3040
25y (km)

30

20
15

20

10
10
5
0

0
0
-4

10

10

20

30
x (km)

-3

40

60

0

10

20

30

40

x (km)
-2

10

50

10

-1

10

C (m)

-4

10

-3

-2

10

10

-1

10

C (m)

Fig. 8. Mean and RMS of Cðx; y; tÞ for OCSD (left column) and HTP (right). White lines are outfall pipes, and black lines indicate the cross-sections in Fig. 9.

3. Currents and stratiﬁcation
The primary circulation pattern in the Bight is the surface
southward ﬂow of the California Current offshore and the poleward
California Undercurrent adjacent to the continental slope (Donget al., 2009). Within SPB and SMB the transient ﬂow is dominatedby eddies and tides. Illustrative patterns for surface temperature(SST) and vertical vorticity ζ are in Fig. 2. The horizontal scale in SST
is larger than in ζ. We interpret the former as more indicative of
mesoscale eddies with a size of tens of km or more, whereas ζshows submesoscale vortices and ﬁlaments with a size of a few km.
These mesoscale and submesoscale structures are ubiquitous in SPB
and SMB according to the satellite and radar observations (e.g., Di
Giacomo and Holt, 2001; Bassin et al., 2005), known as “spiraleddies”. The observed submesoscale eddies are 4–15 km in diameter and typically persist for several days. SPB typically has
warmer water supplied from the south, while SMB has cooler water
partly supplied from the north. Both bays exhibit a narrow coastal
strip (o 5 km wide) of warmer water, as a result of local heating.
We deﬁne the eddy kinetic energy, u02 =2, using the horizontal
velocity u0 extracted with a high-pass temporal ﬁlter retaining
ﬂuctuation periods P o90 days (i.e., including all subseasonal timescales). Its spatial distribution (Fig. 3) shows a systematic decrease
from the offshore region outside the bays to the coastal strip that isroughly coincident with the warm SST. Eddies are weaker within thebays due to both headland sheltering and enhanced dissipation bybottom drag in shallow nearshore water. The outfalls are in the middleof the continental shelves in an intermediate energy zone. SPB has anarrow shelf on its southeast side, and its outfall site is exposed togreater eddy activity than in SMB. This is the ﬁrst of several indications
that efﬂuent dispersal is more efﬁcient for OCSD than for HTP.
The water in the bays is well stratiﬁed in both T and S (Fig. 4). T
is the dominant inﬂuence on density s. The thermocline is shallow
and thin, spanning the depth range from the bottom of the surface
boundary layer at z ¼  hbl (determined as part of the KPP verticalmixing scheme) down to about 70 m. Thus, the standard outfalls
are in the lower thermocline, while the nearshore diversion pipes
are in very weakly stratiﬁed water (even without the destabilization by the buoyant efﬂuent plume). S has a mid-depth minimumin the thermocline. It exhibits fresh anomalies just above thestandard outfalls due to the efﬂuent plumes. The S anomaly ismuch larger in SMB ð 4 0:1 PSUÞ than SPB, due to both its higher
inﬂow rate Qp (Section 2.2) and its less efﬁcient dispersal.
Fig. 5 is the time-mean velocity and root-mean-square (RMS)
subseasonal variability in cross-shore sections parallel to theoutfall pipes. The mean ﬂow in SPB is a strong, poleward
alongshore California Undercurrent with a peak speed of
0.3 m s  1 located over the continental slope about 5 km offshore

44

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

z (m)OCSD Mean

HTP Mean

0

0

-20

-20

-40

-40

-60

-60
c (no unit)

-80

-5

10

-4

-3

10

10

c (no unit)

-80

-2

-5

10

10

-100

-4

-3

10

10

-100
0

5

10

15

20

0

5

10

15

20

5
10
15
cross-shore distance (km)20

OCSD RMS

z (m)

-2

10

HTP RMS

0

0

-20

-20

-40

-40

-60

-60
c (no unit)

-80

-5

10

-4

10

-3

10

c (no unit)

-80

-2

-5

10

10

-100

-4

10

-3

10

-2

10

-100
0

5
10
15
cross-shore distance (km)200Fig. 9. Mean and RMS of cðz; x; tÞ for OCSD (left column) and HTP (right) in the vertical cross-sections indicated by the black lines in Fig. 8. Black triangles indicate theapproximate locations of the outfall diffusers.

from the outfall.8 In contrast, the alongshore mean ﬂow in SMB is
quite weak, and its Undercurrent is much farther offshore. The crossshore mean ﬂows are weak in both bays. The alongshore and crossshore variability levels are similar offshore of both baysð  0:1 m s  1 Þ. They both decrease approaching the shoreline, much
more rapidly in the cross-shore component. There is also a moderatedecrease with depth in both components in both bays. Therefore, we
expect efﬂuent dispersal to be primarily alongshore, with an appreciable mean displacement to the northwest in SPB.
A low-pass frequency Butterworth ﬁlter is adapted to decompose
the velocity ﬁeld into seasonal (the period band P Z 90 days, simply
called time-mean) and subseasonal (P o90 days) currents (Fig. 3).
The latter is further decomposed into eddy ð30 h oP r 90 daysÞ, two
tidal (diurnal band: 18 ho P r 30 h, and semi-diurnal band:
8 h o P r 18 h), and turbulent ðP r 8 hÞ components. Then we makeuse of a Gaussian spatial ﬁlter to the eddy component to extract
mesoscale (the wavelength L 4 20 km) and submesoscaleðL o 20 kmÞ ﬂuctuations. Finally, we separate the currents into asurface layer average over the boundary layer, and subsurface
average over the interval below the boundary layer down to theshallower of either the bottom depth or the thermocline base(75 m). (The subsurface layer contains the bulk of the near-ﬁeld

8This poleward mean ﬂow on the San Pedro slope is roughly consistent with thevelocity measurements in Noble et al. (2009a; Figs. 4 and 5) and with the modeledmean subsurface ﬂow pattern in Dong et al. (2009; Fig. 6). However, the measurements also show that there can be considerable variation among currents averaged
over a single season, as here; Hamilton et al. (2006, Fig. 5) shows a relatively stronger
equatorward surface ﬂow on the shelf during summer, 2001, than that in Fig. 5.

plume from the standard outfalls.) Statistical averages are made intime (August 15–November 30, 2006) and over a circular area with a
10 km diameter containing the standard outfalls (magenta circles inFig. 3). The resultant velocity magnitudes are summarized in Table 1.
It is remarkable how all the ﬂow components contribute similarly inmagnitude. The mean (in SPB) and eddies
pﬃﬃﬃ do dominate the tides.
Tidal parcel displacements, ℓmax ¼ PU rms = 2π , are typically less than
1 km for both bands, which means that they are inefﬁcient as
dispersal agents. The mesoscale eddies have slightly stronger RMS
velocity magnitude than the submesoscale eddies in SPB, but thereverse is true in SMB. Their displacements are much larger becauseof their longer persistence (especially mesoscale).
With the same time and area averaging procedure, we determine the RMS vertical vorticity ζ to be 0.72f and 0.75f for SPB
surface and subsurface layers and 0.82f and 0.57f for SMB surface
and subsurface layers, respectively. This quantity is dominated by
the submesoscale eddies (evident in Fig. 2, right), and they also
dominate the process of increasing tracer gradient through straining deformation. Vertical vorticity ζ and the horizontal strain rate
α have equal RMS values in a non-divergent ﬂow in a homogeneous domain,9 so we can estimate α by RMS ζ. Advection by a

9
For a non-divergent horizontal ﬂow, u ¼  ∂y ψ ; v ¼ ∂x ψ with ψ the streamfunction,
ζ ¼ ∂x v  ∂y u ¼ ∂xx ψ þ ∂yy ψ ,andα2 ¼ ð∂x u ∂y vÞ2 þ ð∂y u þ ∂x vÞ2 ¼
ð∂xx ψ  ∂yy ψ Þ2 þ 4ð∂xy ψ Þ2 is the squared magnitude of the two independent com2
ponents of the strain rate tensor. The variance difference ζ  α2 ¼4ð∂xx ψ ∂yy ψ  ð∂xy ψ Þ2 Þ vanishes in an area integral, as seen by integration by partsin x and y assuming no boundary integral contributions by the homogeneity
assumption (e.g., equivalent to spatial periodicity).

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

OCSD CDOM Mean ( μg QSE / L)

45

OCSD CDOM RMS (μg QSE / L)
4.5

0

-20

4

-20

-40

3.5

-40

-60

3

-60

-80

2.5

-80

2

-100

z (m)

0

1.5

1

0.5

-100
6

8
10
12
14
cross-shore distance (km)

16

0
6

8
10
12
14
cross-shore distance (km)161Fig. 10. Mean and RMS of CDOM in μg QSE lin SPB measured by a glider along a transect about 2 km east of the transect in Fig. 8. QSE stands for quinone sulcate
equivalents. The glider measurement was conducted repeatedly from March 3, 2010 till June 17, 2010. (Courtesy of Burton Jones of University of Southern California.)

C 10500500By (km)

30
A

50
100
500

20

D

500

10

500
0

50 0
10

0

20

30

40

50

60

C(t)/mean[C] (m)40

C(t)/mean[C] (m)OCSD

C(t)/mean[C] (m)x (km)

HTP
B

25
A

50

15

D

5
0

0

10

20
x (km)

30

50

0

10

100

0
100
50

C

100

50

y (km)

20

40

C(t)/mean[C] (m)3020
A (mean=0.014)
B (mean=0.002)

15
10
5
0
40

C (mean=0.003)
D (mean=0.001)

30
20
10
0

08/11

08/31

9/20
10/10
Day of 2006

10/30

11/19

20
A (mean=0.024)
B (mean=0.003)

15
10
5
0
20

C (mean=0.002)
D (mean=0.007)

15
10
5
0

08/11

08/31

9/20

10/10

10/30

11/19

Day of 2006
Fig. 11. Point time series of C(t) [m] in OCSD (upper panels) and HTP (lower panels). Point locations are indicated on the maps in the left columns, along with the outfall
pipes and the 50, 100, and 500 m isobaths. The time series are normalized by the local time mean, listed in the panel.

pure strain ﬂow acts to decrease the horizontal scale of a tracer
ﬁeld exponentially quickly, i.e., ℓ  ℓ0 exp½  αt. Hence, we estimate a typical dilution time for a tracer patch of size ℓ0 to reachthe grid scale dx where model diffusion acts by log ½ℓ0 =dx=α,which has an approximate value of 1 day near the outfalls.

Mesoscale velocities are comparable to the submesoscale ones
(Table 1), but their strain rates are larger because their horizontal
scale is larger; thus, mesoscale dilution rates are slower thansubmesocale ones. We see the effects of both in the tracer efﬂuent
patterns in the next section.

46

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

4. Efﬂuent distribution: standard outfalls
The modeled response in the source region above the OCSD
outfall diffuser pipe is shown in Fig. 6. The concentration cðz; tÞ islargest in the depth range of HðzÞ, and the vertical structure is nothighly variable except for episodic intrusions into the surface layer(e.g., during the stormy period in late November when theboundary layer rapidly deepens). Both c and C vary much morein time than does Qp . This is due to large variations in F associatedwith local current ﬂuctuations u. The peak value of nearﬁeld cðz; tÞ
is 0.021, which is consistent with the assessment in the OCSD
(2012) report. (The corresponding peak nearﬁeld value for HTP is0.022, consistent with the assessment in City of Los Angeles,
2007.) The integrated content C(t) varies by about a factor of ten
in its extremes, and it shows time scales that are mesoscale(weeks), submesoscale (days), and tidal (semidiurnal and diurnal).

OCSD

3

10

1

10

2

0
-1

-1

5

10

15

20

0

Pt B

3

10

1

10

10

Pt B

2

10

20

mean=0.003 m
rms=0.004 m
Ku=4.214 m
dC=0.0010 m

10

0

15

3

PDF

2

5

10

mean=0.002 m
rms=0.002 m
Ku=4.216 m
dC=0.0005 m

10
PDF

0

10
0

1

10

0

10

-1

-1

10

10
0

5

10

15

20

0

Pt C

3

10

1

10

10

Pt C

2

10

20

mean=0.002 m
rms=0.003 m
Ku=8.020 m
dC=0.0010 m

10

0

15

3

PDF

2

5

10

mean=0.003 m
rms=0.007 m
Ku=14.341 m
dC=0.0050 m

10
PDF

1

10
10

10

1

10

0

10

-1

-1

10

10
0

5

10

15

20

0

Pt D

3

10

1

10

10

mean=0.007 m
rms=0.015 m
Ku=15.113 m
dC=0.0050 m

2

0

20
Pt D

10

10

15

3

PDF

2

5

10

mean=0.001 m
rms=0.003 m
Ku=37.300 m
dC=0.0020 m

10
PDF

Pt A
mean=0.024 m
rms=0.027 m
Ku=7.684 m
dC=0.0050 m

10

10

1

10

0

10

-1

10

HTP

3

10

PDF

2

PDF

Pt A
mean=0.013 m
rms=0.012 m
Ku=3.496 m
dC=0.0050 m

10

The tidally induced ﬂuctuations are small compared to the eddy
ones. The mean value of C is larger here than the RMS of the
ﬂuctuations around it. The probability density function (PDF) for C,
P½C, has a broad distribution with an approximately exponential
shape to the tail, P  exp½  γ C for some constant γ; this indicatesintermittent occurrence of relatively high concentration compared
to a normal distribution, although the kurtosis value (Ku½C ¼ 3:9,
the normalized fourth moment of ﬂuctuations about the mean ofC) is only moderately large at the outfall because of the nearly
constant inﬂow. The source-region salinity proﬁle Sðz; tÞ shows afresh anomaly that largely mirrors the cðz; tÞ variations.
We estimate an approximate value for the source region~ p and a typicalconcentration c~ s assuming a source inﬂow Q
advection velocity u~ s . A volume integral over the source regionand quasi-steady balance in the tracer Eq. (1) is a balance between~ p , and the advective ﬂux through a side
the total source, P s V s ¼ Q

-1

0

10

20
C(t)/mean[C] (m)

30

40

10

0

5

10

15

20

C(t)/mean[C] (m)Fig. 12. PDFs P½C for the average of the nine model grid points around the point locations indicated in Fig. 11: OCSD (left column) and HTP (right). The bin size for each P[C] islisted, and the mean of C(t) is plotted with a blue line ( ¼ 1 on the normalized abscissa) and is listed along with the RMS and Ku values for C ﬂuctuations about the mean.

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

OCSD Surface RMS

47

HTP Surface RMS
30

40
25

y (km)

30

20
15

20

10
10
5
0

0
OCSD Subsurface RMS

HTP Subsurface RMS
30

40
25

y (km)

30

20
15

20

10
10
5
0

0
0
-4

10

10

20

30
x (km)

-3

40

60

0

10

20

30

40

x (km)
-2

10

50

10

-1

10

-4

10

-3

-2

10

10

-1

10

C (m)

C (m)

Fig. 13. RMS of C(x,y,t) vertically integrated over the surface layer, deﬁned as between the water surface and the bottom of the surface boundary layer (upper row), and overthe subsurface layer, deﬁned as between the bottom of the boundary layer and the shallower of either the bottom depth or 75 m (lower): OCSD (left column) and HTP (right).

section, u~ s H s Ls c~ s , with Ls a typical section width in the near ﬁeld,
assuming that there is no inﬂux from the upstream sidec~ s ¼~p
Q:
H s Ls u~ sð6ÞThis is only a rough interpretive relation because even the meanof F is not just uniform advection. Nevertheless, for the OCSD values~ p  5 m3 s  1 , H s  10 m, Ls  500 m, and u~ s  0:1 m=s (cf.,of Q
Section 2.2, Table 1 for RMS subsurface velocity, and Fig. 7 for
initial plume width), we obtain c~ s  10  2 and C~ s ¼ c~ s H s  0:1 m,
which are consistent with the top and bottom panels in Fig. 6.
Instantaneous efﬂuent patterns are highly variable (Fig. 7). At
times the lateral plume moving away from the source is coherent
over tens of km, but other times it folds back on itself due to eddy
current reversals. Tracer movement is usually more alongshore
than cross-shore. Mostly the tracer stays on the continental shelf,and excursions beyond the continental slope are rare. Hence C issmall in the open sea. Dilution is evidently occurring because thepatterns of previously emitted efﬂuents are erased approximately
on a mesoscale length as large as the width of the bays and a timescale of about a week (Fig. 6). Dilution of individual realizations of
the efﬂuent distribution occurs rapidly at the pattern edges mostly
due to submesoscale ( km) shredding of the mesoscale (  tens ofkm) patterns with a straining time scale of 1=α  1 day (Section 3).
Time animations10 exhibit tidal wobbling in the patterns, but notmuch associated pattern shredding.

Horizontal maps of the time mean and RMS variability of C
(Fig. 8) conﬁrm the strong bathymetric conﬁnement to the shelfand slope. In both bays a mean tongue of C extends past thewestern bounding headland (Palos Verdes in SPB and Point Dumein SMB), consistent with a westward mean ﬂow during Fall 2006.
However, tracers also extend alongshore to the east against thismean ﬂow. The modeled lateral dispersal pattern is qualitatively
consistent with a wastewater plume-tracking conducted in May
2000 (Boehm et al., 2002). These facts strongly suggest that thedominant dispersal occurs alongshore in both directions, approximately along isobaths, apparently driven by the prevailing alongshore velocity ﬂuctuations (Fig. 5) associated with reversals of
tidal and eddying currents, not by simply following the mean ﬂow.
In particular, the importance of mesoscale and submesoscaleeddies in dispersion is also evident in Table 1 and in the ﬂow
visualization in Figs. 2 and 7. The simplest explanation for thecontour-following barotropic ﬂow is that it conserves its potential
vorticity, hence is a quasi-stationary, favored dynamical state.
Overall the RMS variability is at least as large as the mean except
very near the source, and it becomes relatively even larger towardboth the coastline and the open sea. At the coast C is not as large asover the middle of the shelf, which indicates an inhibition of cross-10
Movies of the full simulations can be seen in the Supplemental Materials at
http://www2.kobe-u.ac.jp/  uchiyama/sewage/.

48

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

shore transport into very shallow water even in the presence ofeddies and tides with cross-shelf ﬂow (Noble et al., 2009b). C also
decreases toward deeper water by some combination of a weakcross-shore advection and a high dilution rate further offshore
where the eddy currents are stronger.
The tracer concentrations are higher for HTP than OCSD. Partly thisis a consequence of the three times larger source strength Qp (Section2.2), but this does not fully account for the even larger difference in C.
Furthermore, the HTP patterns more completely ﬁll SMB than OCSD
does in SPB. We conclude that SMB is a more sheltered embayment
with less effective dispersal and dilution; this is consistent withprevious ﬁndings that SMB has a much longer tracer residence time
(Oram, 2004) than does SPB (Idica, 2010). Also notice the relatively
low C values in the northwest corner of SPB that have no counterpart
in SMB. Because this corner is not a region of high eddy activity(Fig. 3), hence not a high dilution rate, it must be due to a weak
shoreward penetration from the main C tongue over the bathymetricslope contours in the western part of SPB.
Cross-sectional maps of mean and RMS c distributions (Fig. 9)
show peaks at the source region and depth zc and mostly lateral
spreading in the injection depth range of HðzÞ. The spatial maximum of temporal mean ½cðx; zÞ is 0.0021 for OCSD (ten times
smaller than the peak value of cðz; tÞ in Fig. 6, top panel) and
0.0057 for HTP (four times smaller than its peak value). The OCSDHTP difference in peak mean ½c is consistent with the difference insource strength Qp , which implies that the dispersal differences
between the bays are not very large on average in the nearﬁeld
region above the offshore outfalls. On the other hand, the smaller
ratio of peak to mean for SMB indicates that its events with thehighest rate is smaller than those in SPB.
Offshore the tracer extends seaward well beyond the shelf
without much downward transport. Towards the shore there is aweak tendency for the c distribution to climb the shoaling bottom; an0analogous descent occurs down the upper slope. Above the source
location, c is elevated all the way to the surface, more so in RMS thanin mean. This is consistent with episodic entrainment of the nearﬁeld
plume by deeper boundary layer mixing. The monitored CDOM datanear the transects shown by black lines in Fig. 8 demonstrates thatthe peak of the mean and RMS of CDOM is centered atz   38 7 5 m in SMB (City of Los Angeles, 2007; Figs. 3-8 and3-9) and at z  46 7 5 m in SPB (Fig. 10; courtesy of B. Jones of USC,
personal communication). The latter is closely related to the modeled
tracer distribution (Fig. 9) with the upslope transport to the shore. The
RSB initial dilution model (Roberts et al., 1989) for the OCSD outfall
diffusers also conﬁrms that the middle of the plume corresponding to
the depth of the minimum dilution is at z ¼ 36:7 7 2:90 m in 1999
and z ¼ 38:9 7 3:31 m in 2001 (USGS, 2004; Tables 4-2). These all
support a ﬁrst order accuracy of the simpliﬁed near ﬁeld buoyant
stage model employed in the present study.
Local time series and PDFs of C (Figs. 11 and 12) are noticeably
different at different sites within the bays, not only in the overall C
level (Fig. 8) but also in the character of the temporally intermittent
high concentration events associated with eddy transport; these are
identiﬁed by spikes in C(t) and long tails in P½C. Away from theoutfall, the RMS[C] values are at least as large as the mean, and theirratio increases with distance outside the mean-C tongue.
For OCSD along the mean-C tongue (point A with Ku ¼3.5),
there is much less intermittency than in the opposite alongshore
direction (point C with Ku ¼ 14.3). The low-C northwest corner(point B with Ku ¼4.2) does not have prominent spikes, suggestiveof a diffusive leakage process more than direct tracer ﬁlament
penetration, although its P½C also has a long tail to larger C.
Offshore (point D with Ku ¼37.3) the spikes are almost the whole
signal. Both points C and D show a much larger ratio between the
maximum and mean C values than either along the mean-C
tongue or near the source (Fig. 7). For HTP there are similarc (no unit)

OCSD

-1

10

z (m)

-2

10

-5

-3

10

-10

-4

10

-5

-15

10
S (psu)

33.6

z (m)

0
-5

33.4
-10
-15

33.2

C (m)

0.2
0.1
0
08/11

08/31

9/20

10/10

10/30

11/19

Day of 2006

2

PDF[C]

10

mean=0.100 m
rms=0.029 m
Ku=3.620 m
dC=0.0050 m

1

10

0

10

0

0.05

0.1

0.15

0.2

C (m)
Fig. 14. Source region tracer and salinity for the OCSD nearshore outfall. The format is the same as Fig. 6.

0.25

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

OCSD Mean49

HTP Mean30

40
25

y (km)

30

20
15

20

10
10
5
0

0
OCSD RMSHTP RMS3040
25y (km)

30

20
15

20

10
10
5
0

0
0
-4

10

10

20

30
x (km)

-3

40

60

0

10

20

30

40

x (km)
-2

10

50

10

-1

10

C (m)

-4

10

-3

-2

10

10

-1

10

C (m)

Fig. 15. Mean and RMS of Cðx; y; tÞ for OCSD (left column) and HTP (right) for the nearshore outfalls; cf., Fig. 8 for the offshore outfall. The black lines indicate the verticalsections in Fig. 16.

behaviors. The point B is well within the main mean-C pool andhas moderate intermittency (Ku ¼ 4.2), but the intermittency
increases with distance from the source, both along the mean-C
tongue (point A with Ku ¼7.7), near the coast in the opposite
direction (point C with Ku ¼8.0), and offshore (point D with
Ku ¼ 15.1).
For the standard outfall locations, the surface layer has smaller
C values than the subsurface layer, both in the mean (not shown)
and RMS ﬁelds (Fig. 13). The spatial patterns are broadly similar
between these two layers, although the spatial extent of thepatterns is less in the surface layer, indicative of its greater dilution
rate in association with its stronger currents (Section 3). Fig. 6
shows that the tracer enters the surface layer during particular
events with deeper boundary layer mixing (notice late November).
These events will be more frequent in the winter season withsurface cooling, weaker stratiﬁcation, and stormy winds. Hence,the surface pollution levels will probably be higher throughout the
winter, but our present simulations do not extend long enough toshow this.

penetrates to the surface (Section 2.2), and the tracer is more
conﬁned to the inner shelf adjacent to the shore.
The source region tracer concentration cðz; tÞ for OCSD isstrongly trapped at the surface with somewhat larger values thanfor the offshore outfalls, and the boundary layer depth is madevery shallow because of the buoyant freshwater anomaly in Sðz; tÞ(Fig. 14). The peak value of nearﬁeld cðz; tÞ is 0.059, about 3 times
larger than the peak value for the offshore OCSD outfall (Fig. 6).
(The analogous nearshore outfall value for HTP is 0.129, about
6 times larger than its offshore outfall value.) The mean verticallyintegrated concentration C is only slightly larger than for theoffshore outfall (Fig. 6), indicating that nearﬁeld vertical dispersal
is less efﬁcient with nearshore outfalls, consistent with the smaller
vertical extent of the source function H (Section 2.2). The variability and intermittency in C(t) and P½C are somewhat less near
the outfall here than for the offshore outfall, but their statisticalcharacteristics (not shown) are similar at the same sites as inFigs. 11 and 12.
The horizontal distributions of the mean and RMS of C (Fig. 15)
can reach to the coast11 in the shoreline sector near the outfall

5. Efﬂuent distribution: nearshore outfalls
With nearshore outfall pipes, there are two major differences inthe efﬂuent dispersal behavior: the nearﬁeld buoyant plume11
We reiterate a caution about the limitation of the dx ¼75 m grid resolution invery shallow water ðh o 10 mÞ and the absence of wave-driven littoral currents inthe present model conﬁguration.

50

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

z (m)OCSD Mean

HTP Mean

0

0

-20

-20

-40

-40

-60

-60
c (no unit)

-80

-5

10

-4

-3

10

10

c (no unit)

-80

-2

-5

10

10

-100

-4

-3

10

10

-100
0

5

10

15

20

0

5

10

15

20

5
10
15
cross-shore distance (km)20

OCSD RMS

z (m)

-2

10

HTP RMS

0

0

-20

-20

-40

-40

-60

-60
c (no unit)

-80

-5

10

-4

-3

10

10

c (no unit)

-80

-2

-5

10

10

-100

-4

10

-3

10

-2

10

-100
0

5
10
15
cross-shore distance (km)200Fig. 16. Mean and RMS of cðx; z; tÞ for OCSD (left column) and HTP (right) for the nearshore outfalls along the black lines in Fig. 15; cf., Fig. 9 for the offshore outfall. Black
triangles indicate the approximate locations of the outfall diffusers.

pipe. They do not extend offshore much beyond the inner shelfwhere hr 100 m, but they do extend alongshore over tens of km,comparable to the extent for the offshore outfall (Fig. 8). The RMS
variability exceeds the mean C except near the source, and thetemporal intermittency (not shown) increases with distance fromthe source. Both of these characteristics are true as well for theoffshore outfalls but to a lesser degree with the nearshore outfalls.
Vertical sections of cðx; z; tÞ in Fig. 16 clearly show the surface
and shoreline conﬁnement, strikingly different from the offshore
outfalls (Fig. 9). The spatial maximum of temporal mean ½cðx; zÞ is0.0048 for OCSD (twice the offshore outfall mean value in Fig. 9)
and 0.051 for HTP (about nine times larger than its offshore outfall
mean value). The latter ratio indicates that nearshore dispersal isespecially inefﬁcient in SMB. In summary, the nearshore outfalls
undergo less dispersion and reduced dilution, consistent withweaker ﬂows close to the coast (Section 3).

6. Summary and discussion
Our simulations of efﬂuent dispersal in two Southern California
bays are improved in their inclusion of circulation processes. They
cover a broader spatial area than has been common in the waterquality monitoring surveys. They provide insight into whichcurrents are most effective in tracer dispersion and dilution, andthey demonstrate the potential for full spatial and temporalcharacterization of pollutants in the environment. The predictedtracer distributions are at least qualitatively consistent withprevious measurements (Section 1), and a more quantitative

comparison will be made in a companion paper comparing withhydrographic proﬁle and glider measurements. We envision thatsimilar simulations could be adduced for other sites and different
emission protocols as a powerful tool for planning and assessment.
After the initial dilution and vertical proﬁles caused by thenearﬁeld buoyant plumes, subsequent tracer transport is mostly
lateral and is dominated by eddy ﬂows, rather than tides or meancurrents. The local concentration c(t) in the source region is highlyvariable due to transport ﬂuctuations, even with little variation in
the outfall ﬂux Qp . The vertical structure of c(z) stays relatively
simple and close to the proﬁles established near the source. For
the normal outfall locations, surface-layer concentrations are
relatively small, but episodic ventilation events occur, especiallywhen the boundary layer deepens. The lateral transport is highly
anisotropic, with alongshore excursions much greater than crossshore; this is consistent with a statistical analysis of particle-pairdispersion in coastal zone in the Southern California Bight using
some of the same simulations (Romero et al., 2013). The peakRvalues of the temporal mean and RMS of Cðx; yÞ ¼ c dz occur overthe middle of the continental shelf and upper part of thecontinental slope. Shoreward transport is inhibited in shallow
water, and offshore concentrations are low because of increased
dilution in larger, stronger eddies there. The poleward mean ﬂow
gives an up-coast bias to the tracer distribution, but large concentrations are found down-coast as well, spilling over into
adjacent regions outside the bays in both directions. Local C(t)values are highly intermittent, with PDFs P½C showing long tails
for large C, and the intermittency increases with distance from thesource. Lateral patterns in Cðx; yÞ show stirring by mesoscale

Y. Uchiyama et al. / Continental Shelf Research 76 (2014) 36–52

meandering tongues and dilution by submesoscale shredding of
the tongues. Tidal currents cause primarily oscillatory displacements and do not effect signiﬁcant far-ﬁeld dilution. Peak C values
decrease only slowly away from the source region in individual
realizations of tracer patterns (Fig. 7), although on longer timescales and distances mesoscale ﬂow reversals do erase previously
emitted efﬂuent patterns. That is, dilution is relatively inefﬁcient
over several days and the tens of km size of the bays (20–40 km;
Figs. 7 and 8). At the pattern edges dilution occurs by submesoscale straining on a time scale of about a day. Dispersal and dilution
are relatively more efﬁcient in SPB than in SMB because the former
is exposed to stronger mean and eddy ﬂows. From both bays the
efﬂuent pattern is advected past Palos Verdes peninsula to add tothe contamination in the adjacent bay.
With the nearshore diversion outfalls, the shoreline is much
more exposed to the efﬂuent tracers than with the standard
offshore outfalls. This occurs by a combination of surface penetration of the nearﬁeld buoyant plumes and weaker eddy currents
and weaker dilution over the inner shelf, especially in the crossshore direction.

Acknowledgments
We thank our colleagues Florian Lemarie, Jeroen Molemaker,
and Alexander Shchepetkin for their help in preparing the meteorological ﬁelds and developing the modeling capabilities. We also
thank Burt Jones (USC, KAUST) and George Robertson (OCSD) for
guidance on efﬂuent plumes. We appreciate support from theOfﬁce of Naval Research (N00014-12-1-0939), the Orange County
Sanitation District, the National Oceanic and Atmospheric Administration (A11NOS0120029) through the Southern California
Coastal Ocean Observing System, and the Grant-in-Aid for Scientiﬁc Research (24560622).
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