oEPA
             United States
             Environmental Protection
             Agency
             Office of Marine
             and Estuarine Protection
             Washington DC 20460
EPA 430/09-88-001
September 1987
             Water
A Simplified Deposition
Calculation  (DECAL) for
Organic Accumulation  Near
Marine Outfalls

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EPA Contract No. 68-01-6938
TC-3953-31
Final Report
A SIMPLIFIED DEPOSITION CALCULATION (DECAL)
FOR ORGANIC ACCUMULATION NEAR MARINE-OUTFALLS
for

Marine Operations Division
Office of Marine and Estuarine Protection
U.S. Environmental Protection Agency
Washington, DC  20460
September 1987
by

Tetra Tech, Inc.
11820 Nortfcup Way, Suite 100
Bellevue, Washington  98005

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                                  CONTENTS


                                                                        Page

LIST OF FIGURES                                                          iv

LIST OF TABLES                                                           vi

ACKNOWLEDGEMENTS                                                        vii

EXECUTIVE SUMMARY                                                      viii

  I.  INTRODUCTION                                                         1

 I!.  OVERVIEW                                                             3

           COASTAL TRANSPORT                                               3

           PARTICLE TRANSPORT AND ORGANIC CARBON CYCLES                    5

           ENVIRONMENTAL QUALITY                                           7

III.  MODEL DEVELOPMENT                                                    8

           MODELING FRAMEWORK                                              8

           MODEL FORMULATION                                             13

 IV.  MODEL RESULTS AND DISCUSSIONS                                      22

           SAMPLE CALCULATIONS                                           22

           VERIFICATION STUDIES                                          25

  V.  EXTENSION OF THE MODEL FOR PREDICTING CHEMICAL CONTAMINATION       34

           MODEL FORMULATION                                             35

           MODEL CALCULATIONS                                            37

 VI.  CONCLUSIONS                                                        45

REFERENCES                                                               47

APPENDIX A - REVIEW OF PARTICLE DEPOSITION MODELS                       A-l

-APPENDIX B - USER'S GUIDE FOR THE DECAL MODEL:  TOOL #61 ON THE
             OCEAN DATA EVALUATION SYSTEM (ODES)                        B-l

                                     ii

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APPENDIX C - MASS CONSERVATION EQUATIONS AND STEADY-STATE SOLUTIONS
             FOR PARTICLE CONCENTRATIONS IN THE LOWER WATER COLUMN      C-l

APPENDIX D - MASS CONSERVATION EQUATIONS AND STEADY-STATE SOLUTIONS
             FOR CHEMICAL CONTAMINANT CONCENTRATIONS IN THE LOWER
             WATER COLUMN                                             .  0-1
                                    iii

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                               -  FIGURES
Number                                                                  Page

   1    Simplified diagram of niunicipal~~effluent transport in coastal
        waters                                                           11

   2    Simplified diagram of particle transport and organic carbon
        cycles                                                           12
   3    Settling flux of organic carbon from the surface layer
        as a function of the phytoplankton productivity rate (Ptotal)

   4    Suspended oarticle concentration, deposition rate, and organic
        accumulation gv/en by the model as an example case               Z3

   5    Deposition rates near the Orange County outfall along the
        60-m isobath based on model predictions and field estimates      28

   6    Organic accumulation near the Orange County outfall along the
        60-m isobath based on model predictions and field estimates      29

   7    Deposition rates near the Los Angeles County outfall along the
        60-m isobath based on model predictions and field estimates      31

   8    Organic accumulation near .the Los Angeles County outfall
        along the 60-m isobath based on model predictions and field
        estimates                                                        33

   9    Chemical deposition rates near the Los Angeles County outfall
        along the 60-m isobath based on model results                    38

  10    Lead accumulation in surface sediments near the Los Angeles
        County outfall along the 60-m isobath based on model results
        and field estimates                                              41

  11    Copper accumulation in surface sediments near the Los Angeles
        County outfall along the 60-m isobath based on model results
        and field estimates                          _                   42

  12    Cadmium accumulation in surface sediments near the Los Angeles
        County outfall along the 60-m isobath based on model results
        and field estimates                                              43

  B-l   Simplified diagram of municipal effluent transport in coastal
        waters                                                          B-2
                                     iv

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B-2   Simplified diagram of particle transport  and  organic  carbon
      cycles "                                                        B-3

B-3   Record of current velocity data for currents  off  Newport
      Beach, California                                               B-7

B-4   Power spectral  density distributions of currents  off  Newport
      Beach, California         .                                      8-8

B-5   Cumulative variance distributions  of currents off Newport
      Beach, California                                               B-9

B-6   Cumulative probability curves for  nontidal  currents off
      Newport Beach,  California                                      B-ll

B-7   DECAL contour plot of total  deposition  rate of waste  particles
      for the sample  calculations                                     B-21

3-8   DECAL contour plot of waste  parncie deposition rate  for  the
      sample calculations                                            3-22

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                                   TABLES
Number               •                                                   Page

   1    Time-scale estimates for coastal  transport and particle
        dynamics                                                          9

   2    Power law relationship for coagulation/settling kinetics
        from Farley and Morel (1986)                                     14
                                    VI

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                             ACKNOWLEDGEMENTS
     This technical  document was  completed  by  Tetra Tech,  Inc. staff  for the
U.S. Environmental  Protection Agency under the 301(h)  Post-Decision Technical
Support Contract No.  68-01-6938,  Ms. Allison J. Duryee and Mr. Barry  Burgan,
Project Officers.   The  report was  authored   by  Dr.  Kevin  J.  Farley.  Drs.
W.P. Muellenhoff  and A.M.  Soldate,  Jr. provided . techni cal  editing  and
produced the final  document.

     Comments and suggestions cf  Professors Francois  M.M. Morel and ,<«=it:i C.
StoTzenbach  of  the Massachusetts  Institute  of  Technology,  Dr.  William 0.
Grant of the Woods Hole  Oceanographic Institute,  Dr.  Thomas O'Connor of the
U.S. Department of Commerce,  National  Oceanic  and  Atmospheric Administration,
and Drs. John Paul  and Donald Baumgartner of  the U.S. Environmental  Protec-
tion Agency are appreciated.   Thanks  are  also  extended  to Drs.  Tereah
Hendricks   and  Jack  Anderson  of  the   Southern  California  Coastal Water
Research Project for  providing  access  to  current  meter data and  to Tetra
Tech staff  members who participated in  this study  (particularly Mr.  Michael
Morton and Dr. Mark Clark for their work in analyzing current  meter data).
                                    VII

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                             EXECUTIVE SUMMARY
     The' deposition calculation (DECAL) presented in this report  provides  a
simple model for predicting particle deposition and accumulation  of  organic
material   in  sediments near municipal  ocean outfalls.   The  model has  been
formulated  on  the  basis  of  coastal  transport,  particle  transport,  and
organic carbon cycles, and includes the effects of  coagulation  and  settling
of effluent particles and natural  organic  material.

     inout  parameters  ror cne  model  induce  rhe discharge  flow rare,  r.ne
effluent   solids concentration,  the outfall  cliff user location and geometry,
the density  structure and  depth   of  the  water  column,  the  phytopl ankton
productivity rate,  and  a simplified description  of ocean  currents.   Three
modeling  coefficients are  required for  calculating  particle deposition  and
organic  accumulation  in surface sediments.   They  are  the  second-order
coagulation/settling  rate  coefficient,  the decomposition  rate  coefficient
for suspended organic material, and the interfacial  removal  rate coefficient
for sedimented organic material.

     Model predictions  for  particle deposition and organic  accumulation  in
sediments  near  the Orange County  and  Los  Angeles  County  outfalls  compare
well with  field estimates  at  both outfall  locations.   These results demon-
strate the applicability of the model  in predicting  deposition and accumula-
tion near relatively deep outfall  outfalls in  the  Southern California Bight.
For outfalls  in shallower waters  (where.wave-induced currents may redis-
tribute  sedimented organic  material),  model   calculations  can  be  used  to
determine initial  deposition patterns and to provide conservative estimates
for organic  accumulation  in  sediments.    Additional  verification  studies,
however,  should be performed  for deep outfalls  in  other geographic areas  and
for shallow outfall locations.
                                   vm

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     The DECAL model  has  been extended to predict  metal  and  trace organic
chemical accumulations in  sediments.  Preliminary modeling results  for metal
accumulations near  the  Los  Angeles  County outfall   compare  well  with field
estimates,  and suggest that deposited metals  are retained in sediments near
the outfall  (probably  in  the form  of  metal  sul fides) _ and are  buried  in
time.    Similar  model  calculations  for  the accumulation  of trace  organic
chemicals could be  performed  to  examine the importance  of  chemical trans-
formations  in sediments.

     DECAL  calculations   for accumulation  of  organics and  chemicals  in
sediments can  be  used  for predicting  environmental  impacts  from  ocean
outfalls regulated under Section  301(h) of the  Clean Water  Act.   The model
can also  be usea  to  heio  design monuonrg  programs,  -25:30;-sr,  -".ru.-e
monitoring   strategies,  and  analyze  field  data  for  chemical  enrichment  and
biological   impacts.    Applicability  of  the model calculations,  however,  is
dependent  upon the availability  of valid  input data  (particularly ocean
currents),  and the  assignment  of appropriate  modeling  coefficients.
Therefore,  care must  be exercised in analyzing  current  meter  records,  and
further modeling coefficient studies  may be required.   In addition, detailed
examinations of  sediment  processes  should  be  considered to  determine  the
individual  roles of microbial decomposition and  burial  in  removing organic
material from surface  sediments.   The actual removal  pathway (decomposition,
burial,  resuspension/transport, or  combination   thereof)  is  important  in
evaluating   the  long-term  environmental  impacts   of  municipal  discharges  to
coastal waters.
                                «•
     A review of several particle deposition  models is provided in Appendix
A, and Appendix B  is a users guide for  the  OECAL  model on the U.S. EPA Ocean
Data Evaluation System (ODES Tool  No. 61).
                                    IX

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                             I.  INTRODUCTION
     Assessment "of  the  fate  of discharged_wastes  is an  important  part of
determining the  impacts  of  municipal  discharges from ocean  outfalls.   For
example, these assessments are used  to:

     •    Predict environmental  effects  of  planned  improved discharges,
          especially involving outfall  relocations

     »    Evaluate  transport of  the  wastefield  relative  to special
          habitats such as kelp beds or  coral  reefs

     •    Specify monitoring  station  locations  in  areas  of  predicted
          sediment deposition.

Such  assessments  have been  limited,  however,  by  the lack  of  a generally
applicable model  that  predicts  the  farfield  fate of discharged effluent in
the marine environment.

     This report  describes a  simple model  to predict the fate of municipal
wastewaters in  the marine  environment, including  particulate  matter  and
toxic chemicals.  The model  development  involved the following tasks:

     t    Evaluate  physical/chemical  processes   affecting particle
          settling characteristics in marine  waters

     •    Develop a  simple  mathematical  formulation to  describe  the
          above relationship

     t    Construct a model  for predicting  particle  deposition, organic
          accumulation, and toxics concentrations near ocean  outfalls

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     •    Incorporate the  model  into the Ocean Data  Evaluation  System
          (ODES).
                                 _____      •
     As  a  result of  the  first  task,  this  report  provides  an overview  of
coastaj  transport, particle  transport,  and  organic carbon cycles  in  marine
waters.  A mathematical  model  is -then described to predict  particle  deposi-
tion  and organic accumulation  in  surface  sediments.   Calculations  are
provided for the Orange  County and  Los  Angeles County outfalls,  followed  by
discussions of the modeling  results.  Extension of  the model  for  predicting
metal  and  trace organic  chemical  accumulations  in  sediments  is  also  pre-
sented.

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                               II.   OVERVIEW
     Particle deposition and  organic accumulation near  ocean outfalls  are
controlled  by  coastal  transport,  particle  transport,  and  organic  carbon
cycles.  A1 summary of  these  processes  is presented,  followed  by  a  brief
discussion  of  particle deposition  and its  relationship  to  environmental
quality.

COASTAL TRANSPORT

     Outfalls extending 0-10  km  from shore  are used to  discharge municipal
wastewater to coastal environments.  Buoyancy of the wastewater  in  seawater
results in seawater entrainment and a vertical  rise of  the  wastewater  plume.
Entrainment factors of the order of 100 are common and  time  scales character-
izing the buoyancy rise are relatively  short  (minutes  to hours)  for present
designs of  outfall  diffusers.   During  stratification  periods  (Richardson
numbers  ca. 10 ), wastewater  plumes are  trapped  below the   sharp  density
gradients of the pycnocline  region.  Subsequent  transport and  dilution  of
the wastefield are controlled  by ocean currents and mixing  processes.

     Fluid  motions  in  coastal  waters  are driven  by  surface waves,  tidal
oscillations, wind-driven currents, and  large-scale mean circulation.  Wave
motions at  the surface  are characterized by orbital velocities on the order
of 1 m/sec  and periods  of  5-10 sec.   Since  wave motions conform closely  to
irrotational flow over  most of the water column, wave-induced transport  of
pollutants  is  generally of minor  importance._  Near  the surface, waves  may
play  a  significant role  in  enhancing air/sea  exchange through  surface
renewal, wave  breaking, and  sea  spray.  Exchange and  resuspension at  the
water/sediment interface  are  determined to a  large  extent by wave-induced
                                  2
shear stresses (on order 1 dyne/cm ).

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     In many coastal locations, tidal  oscillations  are a significant part  of
the  observed  currents.   Tidal  motions typically  follow elliptical  paths,
with the  major axis paralleling  the  shoreline.   Osc-i-1 lation periods  range
from 12  to 25  h  depending upon  the   relative  strength of  the main  tidal
components.   For  typical  tidal velocities  (5-15 cm/sec)  the major  axis  of
the  tidal  excursion ellipse  is  several  kilometers;  the  minor axis  vanes-
with offshore distance,  increasing  from  zero at the  coast.   Since  outfalls
are fixed in space, the effect of tidal motion is  to  distribute the diluted
                                                 7
effluent over the tidal excursion ellipse  (1-5 km ).

     Nontidal   flows  are  generally  dominated by wind-driven (or  pressure
gradient-driven)  currents.   The currents  exhibit  significant  variation,
often reversing direction in cycles of 4-8 days according to  the  passage  of
weather  systems.   Long quiescent  periods  are  also  observed.   Wind-driven
currents range in magnitude from 5 to  15 cm/sec and typically flow  parallel
to  the  coast.  Cross-shore motions,  which  show significant  variation  with
depth,  also occur  and  are associated  with  the cross-shore component of  the
wind stress and Coriolis effects.  During stratification periods, cross-shore
motions may induce upwelling or downwelling.

     Large-scale mean circulation on the  shelf is characterized  by longshore
velocities typically ranging  from  1  to 3 cm/sec.    This long-term motion  is
induced by a  sea  level slope determined by  deep oceanic  gyres  and  modified
by setup from a mean wind stress.

     Turbulent energy  production at or near  the surface and  seafloor bound-
aries is responsible for  vertical mixing in  coastal waters.   In the absence
                                                         2
of density  gradients,  vertical diffusivities of 10-50  cm /sec  are  typical.
During stratification  periods,  turbulent  fluctuations  propagating  from  the
boundaries are dampened by stabilizing density gradients.  Low diffusivities
in the  pycnocline region (0.1-1.0
of surface and lower layer waters.
                                     2
in the  pycnocline  region  (0.1-1.0 cm /sec)  can severely limit the  exchange
     Horizontal dispersion is determined  by turbulent fluctuations as well  as
by vertical variations in  horizontal velocities associated with  shear  flow.

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Dispersion  has  been  observed  to  increase  with  length  scale,  typically
expressed by a  4/3  power law (Brooks  1960;  Okubo  and Osmidov  1970;  Okubo
1971)_.  Over  length  scales" of  1-10  km,  horizontal  dTs'persion  coefficients
                      4   2
are on the order of  10  cm /sec.
PART4CLE TRANSPORT  AND  ORGANIC  CARBON CYCLES

     Mass concentrations  of  particles in coastal waters typically range from
a few tenths to a few milligrams  per liter.  The particles consist primarily
of  organic  material  derived  from phytoplankton  production  or  (for  this
                                   •
study)  discharged  from municipal  outfalls.   In  many  coastal  locations,
terrestrial  inputs  and  bottom  resuspension may also be important.

     Phytoplankton  activity  is generally confined to surface  layers  and  is
controlled  by  light,  availability of  major nutrients,  trace  metal  concen-
trations, and  temperature-dependent, metabol ic  processes.   Productivity
rates  for  total  organic  carbon  are  typically  observed  in  the  range  of
0.2-2.0 gC-m  -day    (Suess  1980; Eppley et al.  1983).   A  large portion  of
the production consists of  particles,  ranging  in  size from  a few nanometers
for  colloidal  exudates  to  a  few microns for plankton  cells.   Values  of
0.05-0.10 g POC/cm   have  been  reported  for particulate  organic  carbon/
particle volume ratios  (Eppley et al.  1977)  indicating  a high water content
for  plankton  cells and detrital  material.  The  dry weight  composition  is
primarily protein  amino  acids  and carbohydrates.   Lipid content  of  phyto-
plankton is typically less than 20 percent (Parsons et al. 1977).

     Primary losses of particles  from  surface  layers are through microbial
degradation and  coagulation/settling.    In shallow  waters,  particle removal
by  direct  contact   (coagulation)  with  the bottom  may  also  be important.
Decomposition of natural organic  particles occurs at rates  on the order  of
O.-l/day;  lipids  may degrade  more slowly.  In oligotrophic  waters,  over
90 percent  of  the  organic material may  be returned  to  the  nutrient pool  by
degradation processes.   In  highly eutrophic  waters,  a large fraction  of the
organic material  -is  transported to  lower  water layers  by coagulation/
settling.   Zooplankton  may  play  an  important role  in   both  coagulation/

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settling (through the formation of fecal  pellets)  and degradation  (by acting
as grinding  mills  to  reduce  larger  particTes  to  colloidal  or  dissolved
organic material ).

     Mass concentrations of  effluent  particles  (ca. 50-200 mg/L)  discharged
from submerged  outfalls  are  rapidly  diluted  by  plume  entrainment  and are
                                                        2
then distributed  over the tidal excursion ellipse (1-5  km ).   Primary treated
effluent consists  mostly of  biological  material with large  amounts  of
bacteria and bacterial  fragments.  Organic composition of effluent  is similar
                         %
to natural  particles; lipid  content of 20-25 percent has  been  reported (Myers
1974).   Smaller quantities  of inorganic  material  are also present  in treated
wastewater.

     During stratification  periods,  effluent  particles are typically trapped
below the  pycnocline where  they  add to  concentrations of natural particles
that have settled out of surface waters.   Decomposition  rates of the organic
material are  on  the order  of O.I/day.   Reduced  metabolic  rates  may  occur
below the  pycnocline due to  lower temperatures.  Particle deposition  rates
are often controlled by coagulation/settling  kinetics and strongly depend on
the  aggregation of  effluent  particles and  natural  particles.   Particle
removal   by contact  (coagulation)  with   sediments  is  also possible  and  is
affected by bottom boundary flow and turbulent  mixing  rates.

     Reported  estimates  of  deposition   rates  are  in  the   range of  0.25
   -2    -1
g-m  -day    (dry  wt)  for "natural"  waters  off  southern  California  (Emery
1960) to 6.0 g-nf -day   (dry wt) for municipal  effluent  particles  in the
vicinity of  the  Los  Angeles  County  outfall  (Galloway 1972).    Particles
deposited  at  the  water/sediment  interface are  generally mixed with surface
sediments  to  a depth of 1   to  10  cm by   bottom  shear  (induced  by waves and
currents)   and bioturbation.   Removal  of  organic material  from  surface
sediments  is  attributed  to  decomposition and  burial.    Interfacial turnover
rates for  the  removal of organic  material in "natural"  sediments  are in the
range of 0.01-0.025 cm/day (from field  estimates  of  Hopkinson  1985 and
references therein).  The observed turnover rates are based on steady-state"
assumptions and  include  the effects of  decomposition of  easily  degradable
                                     6

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organic material  (e.g.,  carbohydrates,  amino  acids),  decomposition of more
refractory compounds (e.g.,  complex  lipids,  humic substances), and  burial of
organic  material  as  the sediment  interface  progresses upwards  with time
(i.e., with the accumulation of  particles).   Resuspension  events  which are
typically associated with storms  may disrupt accumulated sediments.
            f
ENVIRONMENTAL  QUALITY

     Dissolved oxygen concentrations are often used as a measure of environ-
mental quality  for  coastal  waters.   In  surface  waters,  dissolved  oxygen is
usually  saturated   or  oversaturated due  to phytoplankton  production and
air/sea gas exchange.  In lower waters,  microbial  degradation of  naturally-
occurring organic material  and  effluent organic material   results  in  a net
consumption of oxygen.  During stratification periods,  oxygen resuoply from
surface waters  is limited  by  low diffusivities in  the pycnocline region.
Decreased oxygen  concentrations   in  the range  of  4-7  mg/L  are  typically
observed below  the  pycnocline;  anoxic conditions  are extremely rare  [e.g.,
New York Bight, 1976 (Gross  1983)].

     Organic  enrichment  in surface sediments  near municipal  outfalls  is
generally accompanied  by increased heterotrophic  activity  (and oxygen
consumption).   In areas  of high  organic  deposition, oxygen  demand  in surface
sediments may exceed the  rate of oxygen resupply  from  overlying waters and
result in anoxic  conditions.  Structural alterations in benthic communities
are likely and may be related to the production  of toxic hydrogen  sulfide by
anaerobic microbes (Smith and Greene 1976).  Alternatively, benthic communi-
ties may be affected by the  enrichment of metals and  trace  organic  compounds
in deposition  areas  near municipal  outfalls.   Thus, understanding particle
deposition  and  organic  accumulation in marine sediments  is  of  primary
importance  in  assessing  the  environmental  effects  of  a  coastal   municipal
discharge.

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                          III.   MODEL  DEVELOPMENT
     A simplified model for particle deposition and organic accumulation in
coastal  waters is developed in the  following  paragraphs.  Coastal transport,
phytoplankton dynamics, microbi'al  degradation,  and  coagulation/settling of
natural  particles and  effluent  particles  are considered.   Since  model
                                 •
applications are  examined  for deep  outfall  sites (ca. 60  m)  off  Southern
California,  the  model  is  presented  for  stratified  water  columns.   The
production of natural  particles  is  attributed  to carbon  fixation by phyto-
olankton  and  is  expressed  by .Tieasursd  productivity  races.  Bonn  natural
particles and effluent particles are  considered  to  be comprised of organic
material, and organic decomposition is  expressed  by a  first-order decay rate
(Stumm  and  Morgan  1981).   Details  of  coagulation/settling  kinetics  are
discussed later  in  the report.   Sediment resuspension and particle removal
by  contact  with  the  bottom are  not  expected  to  be  significant  for  deep
outfall  sites and are not  included  in  the model.

MODELING FRAMEWORK

     As a  first  step  in  constructing  a simplified model  for particle depo-
sition and organic accumulation,  coastal process time scales were examined.
For the transport and  mixing of effluent in coastal waters,  time  scales range
from a  few  minutes  for plume entrainment to  several  weeks for large-scale
mean circulation  (Table 1).  Time estimates of 8 h to 10 days are given for
water column  processes associated  with  particle "dynamics  and  organic
decomposition.   With  the   exception  of mixing in surface  sediment layers,
sediment  processes  are described  by  time  scales  of 3-100  days during
accumulation periods.

     Although time scales  for  many  processes overlap,  the following  approxi-
mations have been made to  simplify the modeling analysis.   For water column
calculations,  time  scales  of  one  to  several  days are  considered  most
                                     8

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               TABLE 1. TIME-SCALE ESTIMATES FOR COASTAL TRANSPORT
                                 AND PARTICLE DYNAMICS
                                                       TIME  SCALE (DAYS}
                                                      1.0          10          100
COASTAL  TRANSPORT
1.    Plume Entramment
2.    Tidal Oscillations
3    Wind-Driven Currents
4    Large-Scale Circulation
5.    Vertical Diffusion:
        - In surface and lower waters
        - Through the pycnocline

6.    Horizontal Dispersion

WATER COLUMN  PROCESSES
7.    Phytoplankton Productivity
8    Organic Decomposition
9.    Coagulation/Settling Kinetics

SEDIMENT  PROCESSES
10.  Mixing of Surface Sediments
11.  Decomposition of Deposited
     Organic Material
12.  Burial of Surface Sediments
13.  Frequency of Resuspension
     Events

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 important  in describing particle dynamics and organic decomposition.  Plume
 entrainment,  tidal  oscillations,  and  mixing  in the surface and lower waters
 are  characterized  by smaller time scales and are assumed instantaneous.   In
 the  model,  these processes are averaged over  the  daily  cycle.   Conversely,
 diffusion,  through  the  pycnocline  and  horizontal dispersion are characterized
.by larger  time  scales  and  are  not-considered   significant  over  travel
 distances  of 10-ZO  km.

      Based  on the  above simplifications, the vertical structure of the water
 column  is  described by a well-mixed  surface  and  lower layer,  separated by a
 pycnocline  region (Figure 1).  For   a  surfacing  waste•plume,  a single
 well-mixed  layer can be assumed.  The  daily averaged discharge of effluent is
 considered  to be  uniformly distributed  over  the  tidal  excursion  Ellipse.
 The  concept  of  uniformly distributing  a waste  over an  "extended  source"
 region  was  previously  used by  Csanady (1983).  In defining dimensions of the
 extended source, it is  convenient  to  visualize the diffuser moving through a
 stationary  water body  in the  opposite  direction  of tidal  currents  (Csanady
 1983)..   Nontidal flow by wind-driven  currents  and large-scale mean circula-
 tion are   important  in  providing  dilution  waters  to  the extended source
 region  and  in advecting effluent  from this region.

      A  schematic  of  particle  dynamics  and  organic  accumulation  (which is
 consistent  with  the daily averaging  of  transport processes)  is presented in
 Figure 2.   In  the surface  layer,  "natural" particle  concentrations  are
 controlled  by phytoplankton  production,  organic decomposition,  and coagu-
 lation/settling.   Advective transport   of  surface waters does  not  play  a
 significant role since natural concentrations  are expected to be relatively
 uniform over distances  of 10-20 km.   In  the lower  layer, discharged effluent
 particles  add to concentrations of natural  particles that have settled from
 surface waters.   Removal  mechanisms  in the  lower layer include  organic
 decomposition,   coagulation/settling,  and  advective  transport!   Removal  of
 organic material from  surface  sediments  is  attributed  to decomposition  and
 burial  and  is described by an  interfacial turnover rate.
                                     10

-------
 SIGMA-T
                  VERTICALLY
                  WELL MIXED
TIDAL MOTION
                  VERTICALLY
                  WELL MIXED
TIDAL MOTION
                                  /////////r
                             MUNICIPAL
                             EFFLUENT
                                                       NONTIDAL FLOW
                    NONTIDAL
                      FLOW
                DIFFUSER
         EXTENDED
          SOURCE
          REGION
                                              NONTIDAL
                                                FLOW
                                               TIDAL
                                               MOTION
Figure 1.   Simpiffied diagram of municipal effluent transport in coastal
           waters.
                                11

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          PHYTOPLANKTON
            PRODUCTION
 NATURAL
PARTICLES
                                '  COAGULATION/SETTLING
•>>  DECOMPOSITION
DECOMPOSITION
                                                           . DECOMPOSITION
                 COAGULATION/SETTLING
DECOMPOSITION
  AND BURIAL
^



TOTAL SOLIDS
NATURAL
PARTICLES

WASTE
PARTICLES



fe-

                            DECOMPOSITION
                              AND BURIAL
        Figure 2.  Simplified diagram of particle transport and organic carbon
                   cycles.
                                       12

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MODEL FORMULATION

     The mathematical  formulation for  calculating  particle deposition  and
organic  accumulation  presented  in  this report  is  based  on the  modeling
framework presented  in  Figures 1 and 2.  Coagulation/settling  kinetics  are
herein described  by  a simplified expression  developed  by Farley and  Morel
(1986).  Their results show that the  mass removal  rate of solids,  dC/dt,  can
be described as the sum of three power laws:


          --          2'3l'91'3
each  term  of which  corresponds  to a  oarf cuUr coacuTation  nee Nanism:
differential settling, shear, and Brownian motion.   Empirical  relationships
for  the  coefficients  Bds>  B$h,  and  Bb  are  also  provided  as  functions  of
system parameters (Table 2).

     Relationships given by Farley and Morel (1986) are expressed in terms of
floe densities and are applicable to  the wet weight  of  suspended  particles.
An  equivalent  expression for mass  removal  can be  written  in terms of  dry
weight concentrations as follows:
           dt

where  C  now represents  dry  weight concentration;  and  f is the  conversion
from dry weight to wet weight  and  is  given
fluid density, Pf, and floe porosity,  e, as:
from dry weight to wet weight and is given in terms of particle density,p ,
                     ()
     In applying Equation 2 to  coastal waters, only the differential  settling
term and the shear term are expected to be important for mass  concentrations
                                    13

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TABLE  2.   POWER  LAW  RELATIONSHIP FOR COAGULATION/SETTLING  KINETICS
                        FROM  FARLEY  AND  MOREL  (1986)
                                - 3.   C2'3 - 3   C1'9 - 3, C1'3
                                   ds         in         b
                          dt
                      .                ««          «
                   d. •  '             °e    ab         ad«    ds
                       1.33
   where C is  the aasa concentration of particles, expressed  in terms of wet  weight; Bja,
   Bsh. 3b «• th« sedimentation rate  coefficients corresponding to coagulation by dif-
   ferencial seeding, shear,  and Brownlan notion; ajs. asn, Ob  •« ehe efficiencies of
   particle collision; Kj,, K«OI Kg are dimension*!  parameters for the collision fre-
   quency functions


           ZW   3-1          C     -1          /*  \l/3  g  (0-0.)
      S"~lcmMC  1;Ksh'7l"c  ' :  K^«  'I —I	|c»'lsec'
               / 6 N 1/3  g  (Oe-0j)
   (S/h)  is  the dlaensional parameter  for Stokes settling  In a vertically homogeneous
   water  column of depth, h
                          S/h -
                                 1
                               61T2
1/3 g   (pe- Pf)
               [ca"2sec"1]
                                       3v   hP
                                               f
   k Is Che  Boltraann constant;  T Is ehe absolute temperature; u and v are  the dynamic
   and kinematic viscosities of  the fluid; G is the  shearing race of ehe  fluid; g is ehe
   gravitational acceleration; pe is Che floe density

                               pe  •  (l-«) pp + ePf

   e is che  floe porosity;  Pp and Pf are the particle  and fluid density.
                                          14

-------
greater than 0.1  mg/L  (dry wt).  Removal rates can therefore be approximated
reasonably well  by a  second-order expression:

          --  =  -BC2                                                  (4)
The coefficient,  B,  is  then  given as:
                      Bds  C     *   f-  Bsh C                    '       ,5,
where B.  and 8 .   are  given  in  Table  2;  f  is  given  by  Equation  3;  and
is an average (or  representative) dry  weight concentration.

     For  water column  concentrations  of 'particles,  the governing  mass
conservation equation  is  then  given as:

          _3C_     TRANSPORT   .  - _   . _  -2                            ,
           3t   *    FLUXES     -  S - kdC - BC                            (6)
where  3C/3t  is  the time  rate  of  change in  mass  concentration;  transport
fluxes are  associated  with  nontidal  advection  (Figure  1);  S  represents
sources  of  particles  (e.g.,  phytoplankton productivity and  municipal
effluent  in the extended  source  region); k.C is the decomposition of organic
                                    2
particles by first-order  decay and BC   is the  second-order approximation for
coagulation/settling kinetics (Equation 4).

Surface Layer

     For  "natural"  particle  concentrations  in the  surface  layer,  transport
fluxes are  not  important  (since  concentrations  are  considered  spatially
uniform)  and  particle  product.!' on__!s_expressed  by  measured  productivity
rates.  The mass conservation equation  is given as:-
                                    15

-------
                                                            -2     -1
where ptota|  represents  phytoplankton productivity in  gC-m  -day  ;  2.5  is
taken as  the  stoichiometric conversion of gC  to  g  (dry wt); and  h   is  the
surface layer depth.  Using  typical values  for coastal  waters,  the reaction
half-lime of  Equation 7  is  given as a few days  and  steady-state approxima-
tions are often reasonable.
     The  flux  of organic  carbon  settling  through  the  pycnocline can  be
expressed as:

           Psed  =  BCV2-5
                               -2    -1
whene ?   .  is  in  umco of gC-m   -day  .  Substituting  tail's  sxprgssion
the steady-state form of Equation 7. yields a simple relationship for P   .  as
a function of the productivity rate:
                                                                         (9)
                     10 B
where kdnu/B is the only adjustable parameter.
                  2
     To estimate k
-------
O.I/sec,  which  is  roughly  equivalent  to  an  energy dissipation  rate of
  -42    3
10   cm /sec .   A  collision  efficiency  of  0.3 is  assumed  for coagulation
(Farley and  Morel  1986) and  particle  concentrations are  estimated  in the
range of 0.5 mg/L (dry wt).   For  an  average  surface  layer depth of 30 m, the
calculated value  for,B equals 2-10    L-mg  -sec    (dry wt).

     Results for the  settling  flux  of  organic carbon as a  function  of the
productivity rate (Equation 9) are given by the solid curve in Figure  3 for
the values of  k.,  h  ,  and  B presented above.  The predicted curve is  shown
to compare  very  well  with  field estimates  for  stations  in   the  Southern
California Bight  and  Monterey Bay (Eppley et  al. 1983).  Field  estimates for
settling  fluxes  of organic  carbon  in  the Gulf of  Panama and  the Central
Norcn  Pacific  fail below  the  solid curve  ana  may   be  e.xplainea  oy mgner
decomposition rates (associated with higher temperatures)  or deeper surface
layers.

Lower Layer
     Calculations  for particle  concentrations  in  the  lower  layer are
developed in  similar  fashion  from Equation 6.   Here,  sources of particles
include effluent input and  the settling of natural particles  from  the  surface
layer  (Figure 2).   Transport  fluxes are  considered  in the  lower  layer  to
account for the advection  of effluent  from the  extended  source  region.

     A summary of mass conservation equations and steady-state  solutions for
suspended particle concentrations  is presented in Appendix C for background
conditions (no effluent input),  for the extended source region, and  for the
region downcurrent  of the  extended source  (see Figure 1).   Note  that  in
these  equations  the  second-order  approximation  for coagulation/settling
kinetics is assumed to be valid  for overlying  water layers,  and  is based  on
the expectation of  higher  particle concentrations  in  the lower water  laye'r
due to sewage discharge.

     Solutions presented  in  Appendix  C are dependent  on  dimensions  of the
extended source region and nontidal advection.  This information  is obtained
                                    17

-------
      10  -i
 2*
 CD
 T3
CM
 u
 2
 x
 D
 _l
 U.
 O
 UJ
 0)
10 -
10 -
       DATA FROM EPPLEY ET AL. 1983

          •   S. CALIFORNIA BIGHT

          O   S CALIFORNIA BIGHT

          Q   MONTEREY BAY

          A   CENTRAL N. PACIFIC

          O   GULF OF PANAMA
                                        EQUATION 9
                                             hu = 30m

                                             kd = 0.1/day

                                             B = 2x 10"6Lymg-sec
                   10
                     -1
                                  10V
10'
                 PRODUCTIVITY RATE (gC/m2-day)  -
   Figure 3.  Settling flux of organic carbon from the surface layer (Psed)
             as a function of the phytoplankton productivity rate (P{ .  .).
                               18

-------
 from  analysis of  current records where  harmonics  for  the  main tidal com-
 ponents  are  given  as:
u
             tidal
             tidal
                            cos
                            cos
                                   2»t
                       Zirt
                        Tj
                                 .
                                uj
rvj
                              (10)
                              (11)
 where  U-,  V.  are  amplitudes of  the  tidal  oscillations  in  the x  and y
•direction;  T.  is  the oscillation  period;  and 


-------
          Fs(t)  =  B hLC2                                              (14)

where F (t) is the sediment flux  rate  in g-m   -day   (dry wt);  and h.  is the
height of  the  lower  water layer  in meters.   For  a fixed sediment  location
(x, y), the deposition  rate  varies  throughout the tidal cycle as  overlying
waters move relative  to the  sediments.   At any instant  in  time,  the  depo-
sition rate  is  expressed  in terms  of  the water  column coordinate  system
(x1,y') using Equations 12 and 13,  where  x,y  now represent coordinates  for  a
fixed sediment  location.   Daily-averaged  deposition rates to  the  sediments
are then  computed from  flux  rates in  Equation  14  by numerically  integrating
2 ?4-h pen'!cd.

     In the  surface  sediments,  the mass  conservation  equation  for  organic
accumulation is given as:
              dCs   -  F  - K  C                                        (15)
                -      S    S  S
where C$  is  the  organic accumulation  in units  of  g/L; hg  is the mixing
depth for  surface  sediments; Fs  is the  daily-averaged  deposition rate  in
   -2     -1
g-m   -day    (dry wt);  and K   is an  apparent  interfacial  removal   rate
coefficient  for  sedimented  organic  material  and  includes  the  effects  of
decomposition and burial.  Steady-state solution for  organic  accumulation  is
given as:
          Cs(x,y)  =  Fs /Ks                                            (16)
where an approximate value for K  is given as  0.015  cm/day,  based on  steady-
state estimates of organic carbon turnover rates in  surface  sediments  (from
field studies of Hopkinson 1985 and  references therein).  The time to  reach
steady  state  is estimated  from the  mixing  depth  of  surface  sediments
(1-10 cm) and the interfacial  removal rate coefficient  for organic material
(0.01-0.025 cm/day)  and is expected to range from a month to several years.
                                    20

-------
Steady-state sediment  calculations  will   therefore  be most  applicable  to
sites where  redistribution of  sedimented material  (by  resuspension)  is not
likely to occur  at frequent  intervals.
                                    21

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                     IV.  MODEL RESULTS AND DISCUSSIONS
     Sample calculations  and' verification  studies are  presented  in  the
following sections to demonstrate the general behavior of the model  and its
predictive capabilities.

SAMPLE CALCULATIONS

     Sample calculations are presented for a 10 m /sec discharge of  primary
effluent, containing 100 mg/i_ of participate  material.  The outfall ciiffuspr
is submerged in 60 m of water,  is 1,000 m  long, and is oriented at an angle
of 30°  to  the  longshore direction.   The  water column  is  divided  into  a
surface  and  lower  layer  by a  sharp density gradient  at the mid-depth.
Phytoplankton  productivity in the surface waters is described by an  average
                -2    -1
rate of  1.0 gC-m   -day  .  Short-term oscillatory currents are described by
a semi-diurnal  tide.  The  tidal  currents in both  the  longshore and cross-
shore  direction  have  amplitudes of  0.1 m/sec  and are  30°  out  of phase.
Nontidal  flow  is  considered constant  in  time  with  a current  velocity of
0.03 m/sec in  the longshore direction.

     The  decomposition rate  of  suspended organic  material   is  taken as
O.I/day.  The  second-order rate coefficient for the coagulation/settling of
particles  is again given as  2-10    L-mg  -sec    (dry wt).   This  value is
based on previous calculations and is consistent with results from settling
column tests for  several primary effluents.  Removal  of organic material in
surface  sediments is described by  an  interfacial   rate coefficient of
0.015 cm/day.

     Model results for total suspended particle concentrations in the lower
layer, deposition rates, and organic accumulation in  sediments are shown in
Figure  4.   For suspended  concentrations,  background  values  for  "natural"
particles  are  calculated  as 0.46 mg/L  in  surface  waters and  0.25 mg/L in
                                    22

-------
   a)   SUSPENDED  PARTICLE  CONCENTRATION


                                     . 0        2.5 km
              EXTENDED SOURCE REGION
                         .63 	:— .56 -r	 .50 	r- .44
                     BACKGROUND CONCENTRATION = 0.25 mg/L
   b)   DAILY-AVERAGED  DEPOSITION  RATE
                  BACKGROUND DEPOSITION RATE - 0.35 g/m2-day
   c)   ORGANIC ACCUMULATION  IN SEDIMENTS
                 BACKGROUND ORGANIC ACCUMULATDN - 2.3 g/L
Figure 4. _ Suspended particle concentration, deposition rate, and
         organic accumulation given by the model as an example case.
                           23

-------
 lower  waters.   In the lower waters, effluent particles discharged  from  the
 outfall  are mixed  throughout  an  extended area  by  tidal  oscillations
 (Figure  4a).   in  the  "extended source" region, total  particle concentrations
 are  increased  due to  the municipal effluent.  For this calculation,  particle
 concentrations   in  the  extended  source  region  are  largely  controlled  by
 farfield  dilution (which  in  turn is  controlled  by  nontidal  currents,  the
 maximum  excursion  distance  of  the  extended  source  perpendicular to  the
 nontidal  currents, and  the height of the lower  layer).   Downcurrent of  the
 extended  source  region,  particle concentrations  decrease due  to deposition
 and  organic decomposition.

     The  background deposition rate for "natural" particles  is  calculated as
         -2     -1
 0.35 g-m   -day    (Figure 4b)  ana  is  roughly  equivalent  to   the  reported
 estimate  of Emery (1960).  In  the  vicinity of  the  outfall,  daily-averaged
 deposition  rates  are  enhanced  and are  as  much as eight times the background
 rate.  Since deposition  rates  are described by  a second-order  dependency of
 particle  concentrations,  enhancement  in deposition rates  is  more pronounced
 than increases in suspended particle concentrations.

     In  the cross-shore direction, waste particles are deposited over fairly
 large  distances  (Figure 4b).  This lateral  spreading, along  with cross-shore
 gradients  in the deposition rate, is  the  result of oscillatory tidal motion
 of the water column over the fixed sediment layer.  Tidal  effects also  occur
 in the longshore direction, as evidenced by  the deposition of waste particles
 upcurrent  of the  diffuser.  In the downcurrent direction,  nontidal  advection
 plays  the  predominant role in determining deposition  patterns.   For  the area
 mapped in  Figure 4b,  30 percent of  the  waste  particles  are  deposited  in
 sediments.   The  remainder  is  either  decomposed  in  the  water column
 (26  percent) or  advected further  downcurrent (44 percent).

     As  shown  in Figure 4c, steady-state distributions for  organic accumu-
 lations  in sediments mimic deposition  patterns.  Accumulations of organic
 material  in sediments are calculated as 2.3 g/L for  background  conditions to
-a maximum  of  18.4 g/L near the outfall.  Assuming a  sediment  water content
                                     24

-------
of 0.5  and  a particle density  for  sediments  of  2.6 g/cm ,  the results  for
organic content would range from 0.2 to 1.4  percent  on  a  dry weight  basis.
                                                          •
VERIFICATION STUDIES

     Model  veri f.ication studies are presented for the Orange County  and  Los
Angeles County outfalls  to demonstrate the  predictive  capabilities of  the
deposition  calculation.    Methods  used  to  calculate  model  parameters -are
first  described.    A  detailed  description  of modeling  the  Orange  County
outfall and  comparison of model  and  field deposition and organic  accumulation
rates  is  followed  by a  similar  description for  the  Los  Angeles  County
outfall .

     For  both  the Orange  County  and  Los  Angeles  County  outfalls,  field
estimates of  predicted model  parameters  are derived  from July  1977 data
(Word  and Mearns  1979)  and  May 1980 • data  (Swartz et  al.  1985).    Field
estimates of  inorganic deposition  rates were obtained  by assuming  that  for
steady-state conditions,  BOOs measurements for the upper 2 cm of  sediment  are
related to deposition rates as follows:
                             W         _
          Fs = BOD5 Ps - Rs (ps-^)    1.07 g02/g  dry wt  5  days          (17)
where Fs is the deposition rate in  g/mz/day; BOOs is given as mg 02  demand/kg
of dry  sediment;  Rs  is the sediment dry wtrwet wt ratio and is given as  kg
of dry sediment/kg of wet sediment; ps is the  particle  density  for  sediments
and is taken as 2.6 g/cm3; P^ is the density of seawater;  hs is the size  (or
depth)  of  the  sediment  sample  in  m; 1.07 is a  stochiometric conversion
factor; and  5  days is the  specified  time for the BODs measurement.  Fie-ld
estimates of organic  accumulation  in sediments were obtained  from COO  and
volatile solids measurements for the upper 2 cm of sediment  as  follows:

                        Rsps°w                10"3
          r        •      b 5 w
           s        Ps - Rs (ps-pw)    1.07 g02/g dry wt

                                    25

-------
or
                 A
          C  ' 10
           s           Ps - Rs ( ps-pw)
where._Cs is the organic  accumulation  in  sediment..in  g/L;  COD  is  given as  mg
Og demand/kg of dry sediment; VS is given in terms of percent  dry wt.

     For Orange County, the wasteflow rate and effluent solids concentration
are  given  as  8.2 m  /sec  and  140  mg/L, respectively,  based on  1977-1980
discharge  conditions  (Schafer  1979,  1980).   The  wastewater   is  discharged
through a 90° dogleg diffuser, having dimensions of 960 m in the  cross-shore
direction  (188°  N)  and  860  m in the  longshore  direction  (278°  N).   Water
depth  at  the  discharge  site  is  approximately 60  m.    Based on  observed
density gradients,  the  water column  is  divided into  a  surface and  lower
layer at the mid-depth.  Pnytoplankton productivity  in  the  surface  layer  is
                                       -2     -1
described by an average rate of 2.0  gC-m   -day  and is based on observations
of increased productivity near  other  large  outfalls  off  Southern California
(Thomas 1972).

     Model  parameters  for tidal  and  nontidal flow were obtained from analysis
of current meter data  (see  Ocean  Currents  in  Appendix  B for  details).  The
current meter data  were  collected  by Southern  California   Coastal  Water
Research Program (SCCWRP) personnel  from  2/2/81 to 7/21/81 at a depth of 40 m
in 55 m of water near the Orange County outfall.   These data were assumed  to
be representative  of  lower  layer flow.   A  spectral  analysis of the  data
indicates  that short-term  oscillatory  motion is  dominated  by  semidiurnal
tidal  currents.   Tidal   amplitudes  of  6.5  cm/sec in the longshore  (278°  N)
direction and  6.0  cm/sec in the cross-shore  (188° N)  direction_were  deter-
mined  by  assuming  that  all  short-term  variance  (i.e., having periods  less
than 1  day)  is associated with semidiurnal  tidal motion.   Phase shifts for
tidal  velocities in the  longshore and cross-shore directions  were  assigned
as 45° and 0°,  resulting  in  an  elliptical   tidal motion.   This motion  is
considered to  represent  average conditions  for  spreading the  sewage over  an
extended source region.
                                    26

-------
     Nontidal  flows  were- determined  from  a  24-h  running  average  of  the
current meter  record.   Nontidal  flows  in  the  cross-shore  direction were
found  to  be small  and were  considered  negligible  for  model   application.
Nontidal  flows  in the longshore direction ranged from 0 to 20 cm/sec,  often
reversing  in direction in  cycles of 4-8 days.  From a  cumulative  distribution
plot,  we  found  that  nontidal  flows  are described  by  an average  upcoast
(278° N)  velocity  of 9.0 cm/sec  occurring  67 percent of  the  time,  and an
average downcoast velocity (98° N) of 5.1 cm/sec  occurring  33 percent  of  the
time.   For model  application,  nontidal  flows were  assumed  to follow  the
local bathymetry.

     Model  predictions  for  deposition  rates near the Orange County outfall
were performed using  a  decomposition rate of  O.I/day  in  the surface  layer
and  0.05/day in  the  lower layer  (to account  for cooler water  temperatures
below  the  pycnocline).  As  in previous calculations, the  second-order rate
coefficient  for the  coagulation/settling of  particles  was  set  as  2-10
L-mg~  -sec"   (dry  wt).    Model  predictions  for  deposition rates  in  the
longshore   direction  are given by the solid  line  in  Figure 5  and  are  in
reasonable agreement  with estimates  from  field  data taken  along  the 60-m
isobath.   Note  that deposition of  effluent particles is predicted in both  the
upcoast  and  downcoast direction  due to  reversals  in the  nontidal   flow.
Results of the deposition calculation  also  indicate  that  34  percent of  the
effluent particles are deposited  within 20 km  of  the  outfall. The remainder
is either decomposed  in the water column (11  percent) or  advected from  the
study area (55 percent).

     Model  predictions  were also  performed for organic accumulation  in
surface sediments  near  the  Orange County outfall  using  a interfacial rate
coefficient of 0.015  cm/day  for  the removal of organic material in surface
sediments.  Results  are presented in Figure  6  for organic  accumulation in
the  longshore  direction and  are  in good agreement with field estimates  for
accumulation along the 60-m isobath.   Model  predictions  in Figures  5  and  6
were also  compared  to "calculated  results  for  phytoplankton  productivity
                           -2    -1
rates  of  1.0   and  2.0 gC-m  -day    (with no  effluent particles).   Results
                                     27

-------
ro
00
                      10%
                 >»  I
                 00
                 •o
                CM
E
5
UJ
z
g
H
(0
O
Q.
LU
Q
                     I
     10 -
                      10
                        o_
                         -15
                                                                                 FIELD ESTIMATES FROM BOD5
                                                                                 MEASUREMENTS (JULY 1977)
                                                                                  kd = 0 OS/day (LOWER LAYER)

                                                                                  B = 2 x 10~6 L/mg-sec
                                                           (with no effluent)
                                      LOCATION OF DIFFUSER
                                                                                        .day.
                                                                             (with no effluent)
-10
                               -5
                                                      r
                                                      5
10
15
 i
20
                                                         DISTANCE  (km)
                 Figure 5.  Deposition rates near the Orange County outfall along the 60-m isobath based on
                           model predictions and field estimates.

-------
   ZCB
   ^^^
o
       io-
O UJ
PC/)
z <

Is
       10-
                                                                •  FIELD ESTIMATES FROM COD
                                                                   MEASUREMENTS (JULY 1977)


                                                                o  FIELD ESTIMATES FROM
                                                                   VOLATILE  SOLIDS
                                                                   MEASUREMENTS (JULY 1987)
                                                                            Ks = 0015 cm/day
P'?«?!.'.20.??m  day
  (with no effluent)
                        LOCATION OF DIFFUSER
                                                   F*total = 1 OgC/ni - day (wiih no effluent)
-15
                     -10
                                 -5
i
0
  10
 i
15
20
                                          DISTANCE  (km)
 Figure 6.  Organic accumulation near the Orange County outfall along the 60-m isobath based
           on model predictions and field estimates.

-------
indicate  that  for Orange  County the  discharge of  effluent  particles  and
enhanced productivity near the outfall  are both important  in determining  the
deposition and accumulation of organic  material in  sediments.

     Similar calculations were performed for the Los  Angeles County outfall.
For Los Angeles  County,  the  wasteflow  rate and  the  effluent  solids  concen-
tration are  given  as 20 m /sec  and  165 mg/L, respectively,   based on  1977-
1980 discharge conditions (Schafer 1979,  1980).  The  effluent is  discharged
from  two  operating  diffusers.   For model  application,  the  diffusers  are
approximated by a 2,750-m continuous line source (based on endpoints of  the
                                 •
diffusers) in the longshore direction (278°  N).  Water depth at the discharge
site is approximately 60 m.   Based on  observed  density  gradients,  the  water
column  is divided  into  a surface and  lower layer at  cne  mid-aepch.  Phyto-
plankton productivity in the  surface layer  is described by an  average  rate
            -2    -1
of  2.0  gC-m  -day  , base<
the outfall  (Thomas 1972).
            -2    -1
of 2.0  gC-m  -day  ,  based on  observations  of increased productivity  near
     Model parameters for tidal  and  nontidal flow were again obtained from an
analysis of current  meter  data.  The current meter  data were collected  by
SCCWRP personnel from 4/16/79 to 9/18/79 at a  depth of 41 m in 56 m of  water
near the Los Angeles County outfall.  An analysis  of the data  indicates that
short-term oscillatory  motion  is dominated  by  semidiurnal tidal  currents,
with amplitudes of 7.0 cm/sec in both the longshore (278° N) and  cross-shore
(188° N) directions.  Phase shifts for the tidal velocities in the longshore
and  cross-shore directions  were   assigned  as  45°  and 0°,   respectively.
Nontidal  flow is  described by  an  average  upcoast (278° N)  velocity  of
5.5 cm/sec occurring 100 percent of  the time.

     For  model  application,  coefficients were  again  set at  O.I/day  and
0.05/day  for  the  decomposition  rate  in  the surface  layer and lower layer,
respectively;  at  2-10~  L-mg~  -sec"  (dry  wt)  for the  second-order coagu-
lation/settling rate; and  at  0.015  cm/day  for the removal  rate  of  organic
material  from  surface sediments.   Predictions for organic deposition  rates
near  the  Los  Angeles County  outfall  are presented in  Figure  7  and are  in
good  agreement with  field  estimates for  deposition rates along the  60-m
                                     30

-------
DEPOSITION RATE (g/m2-day
                                                              •   FIELD ESTIMATES FROM BOD5
                                                                 MEASUREMENTS (JULY 1977)

                                                              o   FIELD ESTIMATES FROM BOD-
                                                                 MEASUREMENTS (MAY 1980)
                                                                  kd = 0 05/day (LOWER LAYER)

                                                                  B = 2x 10'6 L/mg-sec
                                                 total
                                                  (with no ellluenl)
                                                       P.o.al -'OgC/taf-day

                                                         (will) no effluent)
                 LOCATION OF DIFFUSERS
-15
                    -10
-5
0
5
10
15
20
                                         DISTANCE  (km)
Figure 7.  Deposition rates near the Los Angeles County outfall along the 60-m isobath based
          on model predictions and field estimates.

-------
isobath.  Note that  the maximum  deposition  rate  near  the  Los Angeles County
outfall is  3-4  times greater  than  the predicted  deposition rate near  the
Orange County outfall.  This is primarily due to the higher effluent particle
discharge rate of 3,300 g/day  from  Los Angeles County vs.  1,150  g/day  from
Orange County.   For  Los Angeles County, results of  the deposition calcula-
tion also' indicate that 63  percent  of the  effluent particles  are deposited
within  20  km of  the outfall.    The remainder is  either  decomposed  in  the
water  column  (12  percent)  or advected out  of  the  study area  (25 percent).
(Note that the deposited material is subject to further decomposition in  the
sediments and burial).

     Model  predictions for  organic accumulation in  surface sediments near  the
Los  Angeles  County  outfall  are shown  in   Figure  8.    Again,   the results
compare quite well with field  estimates, and are 3-4  times  greater than  the
prediction  for  organic  accumulation  in 'surface  sediments  near  the  Orange
County outfall.   Calculated  results  for phytoplankton  productivity rates  of
                  -2    -1
1.0  and  2.0  gC-m -day    '(with no  effluent)  are  also given  in  Figures  7
and 8.  For Los Angeles  County, the  large  discharge of effluent particulates
plays the predominant role in determining  the deposition and accumulation  of
organic material  in  sediments near the outfall.
                                    32

-------
to
co
                -I Z

                25
                3 ?^
                  UJ
                O O
                  cc
                       103-
                       10-
-15
 I
                                 LOCATION OF DIFFUSERS
 i
-10
            .  FIELD ESTIMATES FROM COD
               MEASUREMENTS (JULY 1977)

            A  FIELD ESTIMATES FROM
               VOLATILE SOLIDS
               MEASUREMENTS (JULY 1977)

            o  FIELD ESTIMATES FROM
               VOLATILE SOLIDS
               MEASUREMENTS (MAY 1980)
                                                                                          Ks =001 5 cm/day
p,p,ai .:.20.9C/m;day..
   (with no ellluenl)


P   . =10gC/m -day (with no effluent)
                                                -5.
               10
15
 I
20
                                                        DISTANCE  (km)
                Figure 8.  Organic accumulation near the Los Angeles County outfall along the 60-m isobath
                          based on model predictions and field estimates.

-------
     V.  EXTENSION OF THE MODEL FOR PREDICTING CHEMICAL CONTAMINATION
     The accumulation of metals and trace organic chemicals in sediments is
dependent on  the partitioning  of the  chemical  between  the  dissolved and
particulate phase, particle deposition  rates,  and  removal  processes  in the
sediments.    A  model   for  predicting  particle  deposition rates  has  been
presented in the  previous sections.   In this section, the deposition  model
is extended to  include  calculations  for the deposition and accumulation of
chemical contaminants  in sediments.   Descriptions  for  the  partitioning
benavior  o-f chemicals  in tne  water  column  ana  removal   processes  in the
sediments are discussed  below.

     Several approaches  can  be  used in modeling the  partitioning behavior of
chemicals in the water column.  They  include  instantaneous (or equilibrium)
partitioning,   complete  stabilization of  the chemical in  the particulate
phase, and  kinetic release of  chemicals into solution  by desorption/dissolu-
tion  reactions.   For this model  formulation, equilibrium partition coeffi-
cients  are  used to  describe the  dissolved/particulate  interactions  in the
water column.    It   should  be   noted,  however,  that  using  the equilibrium
partitioning approach with a very high partition  coefficient  is equivalent
to assuming complete stabilization of the chemical  in  the particulate  phase
or slow kinetic release  of particle-bound  chemicals.

     Removal rates for metals  and  trace organic chemicals  from sediments may
be controlVed  by burial  of surface sediments  by  new deposits, desorption/
dissolution reactions  (possibly  related  to the  oxidation of  sulfide, the
decomposition, of  organic material, or  diffusion  across  the water/sediment
interface), or chemical transformations  (e.g., hydrolysis,  microbial
degradation).    As a  first  approximation,  the removal of  chemicals  from
surface sediments is described  in this model  by  a  first-order rate law and
an interfacial  removal  rate  coefficient.  _
                                    34

-------
MODEL FORMULATION

   .  Following the modeling approach presented  in  the  previous  sections,  the
governing mass  conservation equation  for a  trace  chemical  in the  water
column is given as:

           3C   .   TRANSPORT  _  <.   RM2_                                ,7fn
          ~3~r  +   FLUXES    "  S " BM F                                (20)

where  3C/3t  is  the time  rate of  change  of the total  concentration of  a
chemical  in the water column;  transport fluxes are associated  with  nontidal
advection   (see  Figure 1); S represents  sources  of  the  chemical  (e.g.,
                                               7
effluent in the extended source region); and  BM T  is  the deposition  rate  for
the chemical and  is  dependent  on  the second-order rate coefficient for  the
coagulation/settling of  particles  (B),  the mass  concentration  of  suspended
particles (M), and  the  particulate concentration  of  the  chemical  (r).   In
addition to deposition,  chemical transformations (e.g., hydrolysis reactions)
may occur in the water  column  and  can  be  included in the"mass  conservation
equation.

     In  solving Equation  20,  it  is necessary to specify  a  relationship  for
the total chemical concentration  and the particulate  chemical  concentration.
Here,  the  total   chemical  concentration is  given  by the  summation of  the
particulate and dissolved fractions:

          C =  TM + Cdis                                                (21)

where C  is  the total chemical  concentration in ug/L;  r is the  particulate
concentration  of  the  chemical   in  mg/g;  M  is  the  mass concentration  of
suspended particles in mg/L;  and Cdis is the dissolved chemical  concentration
in ug/L.  For  equilibrium conditions,  the particulate concentration can  be
expressed in terms of the dissolved concentration:

               r=10-6KC           •                                 (22)
                                    35

-------
where K   is  the  equilibrium  partitioning  coefficient  and  is given in units
of L/kg.  Substituting  Equations  21  and  22  into  Equation  20  yields  the
expression:
                                          _c      2             _
           3C   +  TRANSPORT      .       1Q   B KPM  C                   ,,,.
           3t       FLUXES    -     -          -6                        (23)
Mass conservation equations and steady-state solutions for chemical concen-
trations in  the  lower water column are  developed  based  on  Equation 23 and
are presented in  Appendix D  for the extended source  region and  for the region
downcurrent of the extended source (see  Figure  1).

     Chemical deposition  rates are  determined from suspended  particle
concentrations and the dissol ved/particulate distribution of  the chemical in
the overlying waters and are given as:

          Fs(t)   =  B h,_M2r                                             (24)
where F (t)  is  the deposition flux rate of  the  chemical  at any instant in
                                    -2    -1
time and  is  given in units  of  mg-m  -day   ;   and h,   is  the  height of the
lower water  layer in  meters.   Substituting Equations  21   and  22  into
Equation 24 yields a  relationship  for the deposition  rate  in terms of the
total chemical  concentration:
                         -    10~6- KC
          F.(t)  =  Bh.M*  	§	                              (25)
           5           L     1 + lO'VM

For a  fixed  sediment  location (x,y), the deposition rate varies throughout
the tidal  cycle as overlying waters move relative  to"  the  sediments.  The
deposition rate  can  be expressed  in terms  of the  water  column coordinate
system  (x',y')  using  Equations 12 and  13, where  x,y represent coordinates
for a  fixed  sediment  location.   Daily-averaged deposition  rates to  the
                                    36

-------
sediments are  then  computed  from flux  rates  in  Equation 25 by  numerically
integrating a 24-h period.

     In  the  surface  sediments,  the  mass, conservation equation  for  the
accumulation of a metal or  a  trace organic chemical  is  given  as:
          h   dCs   =  F  - K  C                                        (26)
           S  dt        s    r  s

where C   is the  accumulation  of the chemical  in  the  surface sediments  in
units of  ug/L;  h   is  the  mixing depth  for  'surface sediments;  Fs  is  the
                                          -2    -1
daily-averaged  deposition rate  in mg-m  -day  ;  and  K   is  an apparent
interfacial removal rate  coefficient  for  the  chemical  in surface  sediments
and  includes  tne effects  of  burial, desorption/aissolution reactions,  and
chemical   transformations.   Steady-state solution  for  accumulation  of  the
chemical  in the surface sediments is  given  as:

          Cs(x,y)  =  Fs /Kp                                            (27)
Appropriate values for Kp will  be discussed  in  the  following  section.

MODEL CALCULATIONS

     Sample calculations for chemical deposition rates were performed for the
Los Angeles County outfall  for  several  partition  coefficients and a 1  ug/L
effluent concentration  of a chemical  contaminant.   Calculated results  for
the  longshore  distribution of  chemical  deposition  rates  are presented  in
Figure 9.  The results clearly show that the magnitude of chemical  deposition
is significantly affected by the choice of partition  coefficient.   For  a low
partition  coefficient (<104),   a  large fraction of  the  trace chemical  is
dissolved in the water column and very  little is deposited in the  sediments.
For a high  partition  coefficient (>10^),  the discharged  chemical  is almost
entirely associated  with the particulate  phase  and ca.  25  percent of  the
chemical is deposited within 20  km of  the outfall.   (Note that this latter
case of a high partition coefficient  represents maximum deposition rates for
                                    37

-------
                               LOCATION OF DIFFUSERS
co
00
              LU
              Z
              o

              E  £
              c/>  -o

              ?~
              &•  P
              UJ  fc
              Q  O)
O
              O
                     10
                       -3
                        -15
                     -10
-5
0
10
 i

15
 i

20
                                                     DISTANCE (km)
               Figure 9.  Chemical deposition rates near the Los Angeles County outfall along the 60-m

                         isobath based on model results.

-------
the trace chemical and  is  equivalent  to assuming complete stabilization of
the chemical  in the particulate phase.)

     Values  for  partition  coefficients  are  determined by  the specific
behavior of the metal  or the  trace  organic chemical. "Coefficients  for trace
organic  chemicals are  typically  described  by  octanol/water partitioning
behavior and the  organic content of  suspended particles (Karickhoff et al.
1979).   For  metals,  partitioning behavior  is  largely  controlled  by  the
formation of organic  and inorganic  complexes in seawater,  the  precipitation/
dissolution of oxidized and  possibly  reduced  species  (if redox species are
kinetically stable over periods of  several  days), and  the  sorption  of metals
on organic and  inorganic  surfaces.   Partition coefficients  for  metals  are
difficult to assign,  but can be estimated  from laboratory data, field data,
or chemical calculations.  For example,  in this  report the relative magni-
tudes  for  the partitioning  for metals  have  been  estimated  from reported
ocean  residence   times (Balistrieri  et  al .  1981),  which  indicate  that
partition coefficients for metals can vary over several orders of  magnitude
as  follows:    lead  > copper  >»  cadmium.   This  result  is   used  below in
examining metal accumulations in sediments.

     The accumulation  of 'metals in  sediments near the  Los  Angeles County
outfall were  examined to  test  the applicability of  the  modeling approach
presented in this  report.  Model  predictions  for lead, copper, and cadmium
accumulations in surface sediments  are compared to estimates based on field
data taken  in  July 1977 (Word and Mearns  1979)  and  in May 1980 (Swartz et
al . 1985).   Field estimates were  obtained from lead,  copper,  and cadmium
measurements for the  upper  2  cm of  sediment as follows:
where  Cs  is  the  metal  accumulation  in  sediment  in  mg/L;  (Metal)  is the
observed metal concentration  in the upper 2 cm of sediment  in  mg/kg  (dry wt);
Rs is the sediment dry~wtrwet wt  ratio and  is  given  as kg  of  dry sediment/kg
of wet  sediment;  Ps is the  particle  density  for sediments and is taken as
                                    39

-------
Z.6 g/cnv3; and Pw is the density of seawater.   Values  for  (Metal)  and  Rs  are
from Word  and Mearns  (1979)  for  the  July  1977 field  estimates,  and  from
Swartz et al.  (1985) for the May 1980 field  estimates.

     The effluent lead  concentration was  taken  as  145 ug/L, based on  1977-
1980 discharge conditions (Schafer  1979, 1980), and the partition coefficient
was assumed to be greater  than  10  .  Background  concentrations  of the metal
were neglected in this examination.  The rate  coefficient  for  the  removal of
lead  from  surface  sediments,  K ,  was  adjusted  to  match the  calculated
results with  field  estimates.   Results are  presented  in  Figure 10 for  the
longshore distribution  of  lead  accumulation using a  value  of  0.007  cm/day
for Kp.

     Similar  calculations  were  performed  for copper,  using  an effluent
concentration  of  220  ug/L (Schafer 1979;  1980)  and assuming  that  the
partition coefficient  is greater than  10  .  A  good comparison of  calculated
results and field estimates was  again obtained  using  a value of  0.007  cm/day
for 
-------
                                                               FIELD ESTIMATES FROM LEAD

                                                               MEASUREMENTS (JULY 1977)
   O)
2«o
H  H
<  2
-I  UJ
O
O
   Q
   UJ
<  UJ

§<
<  u.
UJ  CE
-"  r>
   (A
       103n
        10'-
                                        o  FIELD ESTIMATES FROM LEAD

                                           MEASUREMENTS (MAY 1980)
                                                    Kf= 0007 cm/day


                                                    Kp> 107f'Ukg


                                                    Ce()| =0 145mg/L
                 LOCATION OF DIFFUSERS
          -15
-10
-5
i

5
10
15
20
                                        DISTANCE  (km)
 Figure 10.  Lead accumulation in surface sediments near the Los Angeles County outfall

            along the 60-m isobath based on model results and field estimates.

-------
                                                          •  FIELD ESTIMATES FROM COPPER
                                                            MEASUREMENTS (JULY 1977)
   0)

o
o
UJ
„ UJ
c o
£<
O
o
  DC
       10
         2_
        10'-
                                                          o FIELD ESTIMATES FROM COPPER
                                                            MEASUREMENTS (MAY 1980)
                  LOCATION OF DIFFUSERS
          -15
                  -10
 i
-5
10
                                                                     Kf = 0007 cm/day

                                                                     K > 107L/kg

                                                                          0220rrig/L
 I
15
20
                                        DISTANCE  (km)
 Figure 11.  Copper accumulation in surface sediments near the Los Angeles County outfall
            along the 60-m isobath based on model results and fluid estimates.

-------
z  P
o  S
o o
O UJ
< (/)
•5 UJ
O OC
o w
   z
        10_
                  LOCATION OF DIFFUSERS
          -15
                    -10
-5
                                                          •  FIELD ESTIMATES FROM CADMIUM
                                                            MEASUREMENTS (JULY 1977)

                                                          o  FIELD ESTIMATES FROM CADMIUM
                                                            MEASUREMENTS (MAY 1980)
10
                                        DISTANCE (km)
                                                                        K = 0 007 cm/day


                                                                        Celfl -°°27mg/L
 i
15
 i
20
 Figure 12.  Cadmium accumulation in surface sediments near the Los Angeles County outfall
            along the 60-m isobath based on model results and field estimates.

-------
copper.  A large  fraction of the cadmium  is  therefore  expected  to  remain  in
the water column  (probably  in  the  form of cadmium  complexes),  and will  be
advected away from the discharge site.

   >  Observed  distributions for  trace organic  accumulations  (e.g., PCBs,
DOT) are similar  to distributions of chemical deposition rates  in  Figure  9.
For PCBs and DDT,  both burial  and the formation  of metabolites of the  parent
compounds are expected  to  be  important removal  processes in the sediments.
Removal  rate  coefficients   should  therefore  be  greater  than  0.007  cm/day.
Further  investigations,  however, are  necessary to  determine extent  of
metabolite production in sediments  near the Los  Angeles County outfall.
                                    44

-------
                             VI.  CONCLUSIONS
     The model  presented  in  this  report provides  a simple  and  realistic
calculation for predicting  particle  deposition  and  organic accumulation in
surface sediments near  municipal  ocean  outfalls.    The  model  is formulated
based on coastal  transport,  particle  transport,  and organic carbon cycles,
and inc-ludes the  effects of  coagulation  and  settling of effluent particles
and natural organic  material.

     Input  parameters for the model  include  the cischarge flow race and the
effluent solids concentration, the outfall diffuser location  and geometry,
the  density  structure  and  depth  of the water column,  the  phytoplankton
productivity rate,  and  a  simplified  description of  ocean  currents.   Three
modeling coefficients are  required  for  calculating  particle deposition and
organic accumulation  in surface  sediments.    They  are  the  second-order
coagulation/settling rate  coefficient,  the  decomposition  rate  coefficient
for suspended  organic material,  and the  interfacial .removal rate coefficient
for sedimented organic material.  Values for the first two coefficients are
obtained from  results  of  theoretical  and laboratory  studies,  while  the
removal rate coefficient for  sedimented  organic  material  is assigned based
on field studies of  organic turnover  rates in surface sediments.

     Model  predictions  for  particle  deposition  and  organic accumulation in
sediments  near  the  Orange  County  and  Los  Angeles  County outfalls  were
performed  using  predetermined  values  for the  modeling coefficients.
Predicted  results compared well  with  field  estimates  at  both outfall
locations, demonstrating  the  applicability  of  the  model  in  predicting
deposition  and  accumulation  near deep  municipal  outfalls.    For  municipal
outfalls in shallower waters (where resuspension may play an active role in
redistributing sedimented  organic material),  model  calculations  can be used
in determining  initial  deposition patterns  and in  providing  conservative
estimates  for organic accumulation  in  sediments.   Additional  verification
                                    45

-------
studies, however, should be performed for deep outfalls in other geographic
areas and for shallow outfall  locations.

     Extension of the model for predicting metal  and trace organic chemical
accumulations in sediments has  also  been  presented.   For  chemical  calcula-
tions, -equilibrium  partition  coefficients are used  to describe dissolved/
particulate interactions in the water column.  The removal of chemicals from
surface sediments is approximated using an interfacial  removal  rate coeffi-
cient.  Preliminary  model  results  for  metal  accumulations  near  the  Los
Angeles  County  outfall  compare favorably  with  field  estimates.   These
                                      %
results suggest  that deposited metals  are  retained in sediments  near  the
outfall (probably  in the  form  of metal  sul fides) and are buried  in time.
Similar model calculations for  the  accumulation  of  trace  organic chemicals
should be performed to examine the importance  of  chemical  transformations in
sediments.

     Model  calculations for organic  accumulations  and chemical accumulations
in sediments can be  used in predicting environmental impacts  from municipal
discharges,  in  designing monitoring  programs  and establishing  future
monitoring  strategies,  and in  analyzing  field data  for chemical  enrichment
and  biological  impacts.  Applicability  of  the   model  calculations  however
will   depend  on  the  availability of  input  data   (particularly  for  ocean
currents),  and  the assignment  of  modeling  coefficients.   Future  efforts
should  therefore  be directed  at the  analysis of  long-term  current  meter
records, and  at  additional  studies  of modeling  coefficients.   In addition,
detailed examinations of sediment processes should be performed to determine,
the  individual  roles  of  microbial  decomposition  and burial  in  removing
organic material  from  surface  sediments.   The actual  removal  pathway
(decomposition vs.  burial)  will  be .-important in determining  the long-term
environmental impacts of sewage discharge.
                                    46

-------
                                REFERENCES
Balistrieri, L., P.G. Brewer, and J.W. Murray.   1981.   Scavenging  residence
times of trace metals and surface chemistry of sinking  particles  in the deep
ocean.  Deep-Sea Res. 28A:101-121.

Brandsma, M.G.,  and  T.C. Sauer, Jr.  1983.   The OOC model:   prediction  of
short  term  fate of  drilling  mud in  the  ocean.    Vot.  2:57-106.   In:   An
Evaluation of Effluent  Dispersion and  Fate Models  for OCS Platforms.   A.K.
Runchal (ed).  Prepared for U.S. Department of Interior,  Minerals Management
Service.

Brooks, N.H.  1960.  Diffusion  of sewage effluent  in an  ocean-current.   In:
Proceedings  of  the 1st  International  Conference on  Waste Disposal  in  the
Mar-ne Environment, Berkeley, CA. July  1959.   Pe^gamon  °ress,  New  York,  NY.

Chen,  C.W.,  O.J.  Smith, J.D. Jackson, and  J.D.  Hendr.ick.   1975.    Organic
sediment model for wastewater outfall.   In:   Proceedings  of the Symposium on
Modeling Tecniques, ASCE, San Francisco,  CA.

Csanady, G.T.    1983.   Dispersal by  randomly varying currents.   J.  Fluid
Mechanics 132:375-394.

CRC.  1981.   Handbook of chemistry  and  physics.   61st Edition.  CRC  Press,
Inc., Boca Raton, FL.

Emery, K.O.   1960.   The sea off southern California.  John Wiley  and  Sons,
New York, NY.

Eppley, R.W., W.G. Harrison, S.W. Chisholm,  and E.  Stewart.   1977.   Particu-
late  organic matter in surface waters  off southern  California  and  its
relationship to phytoplankton.  J. Mar.  Res.  35:671-696.

Eppley, R.W., E.H. Renger,  and  P.R. Betzer.   1983.  The  residence time  of
particulate  organic  carbon  in  the  surface  layer  of  the ocean.   Deep-Sea
Res. 30:311-323.

Farley,  K.J.,  and  F.M.M.  Morel.   1986.   The role  of  coagulation  in  the
kinetics of sedimentation.   Environ. Sci.  Technol.  20:187-195.

Farley, K.J.  1985.  A simplified deposition calculation  (DECAL)  for  organic
solids accumulation near sewage outfalls.  Draft Report.  Prepared  for U.S.
Environmental Protection Agency, Washington, DC.  Tetra Tech,  Inc.,  Bellevue,
WA.

Galloway, J.N.  1972.   Man's  alteration of the natural geochemical cycle  of
selected trace metal-s. _Ph.-D-. Dissertation.   University  of California,  San
Diego.  143 pp.

                                    47

-------
Gross,  M.G.   1983.   The  coastal  ocean:   the  regional  background.   pp.
93-128.  In:  Ocean Disposal  of Municipal  Wastewater:  Impacts on. the Coastal
Environment.  E.P. Meyers  and  E.T.  Harding  (eds).  Massachusetts  Institute
of Technology, Sea Grant College Program,  Cambridge, MA.

Hendricks,   T.J.   1974.   The  fate  of  trace metals and  particulates.   In:
Southern Cali-fornia Coastal Water Research  Project  1974  Annual  Report.  W.
Bascom (ed).  El  Segundo, CA.

Hendricks,   T.J.   1983.   Numerical  model  of sediment  quality near an  ocean
outfall.   Final   Report.   NOAA  Grant  #NA80RAD0041.    Southern   California
Coastal Water Research Project  Authority,  Long  Beach,  CA.

Hopkinson,   C.S., Jr.   1985.  Shallow-water  benthic  and pelagic  metabolism:
evidence  of  heterotrophy  in the  nearshore Georgia  Bight.   Mar.  Biol .
87:19-32.

Hunt, J.R.   1982.  Partite dynamics  in  seawater;  implications for predicting
the fate of discharged parades.  Environ.  Sci.  Technol.  16:303-309.

Karickhoff, S.W.,  D.S. Brown, and  T.A. Scott.  1979.  Sorption of  hydrophobic
pollutants  on natural  sediments.  Water  Res.  13:241-248.

Koh, R.C.Y.   1982.   Initial  sedimentation of waste particulates discharged
from ocean  outfalls.  Environ.  Sci.  Technol.  16:757-763.

Mercier,  R.S.    1984.   The  reactive  transport of suspended particles:
mechanisms   and modeling.   Ph.D. Thesis.  Massachusetts  Institute  of  Tech-
nology, Cambridge, MA.

Metcalf & Eddy,  Inc.  1972.  Wastewater  engineering:   collection, treatment,
disposal.   McGraw-Hill, Inc.  New York,  NY.   782pp.

Meyers, E.P.  1974.  The concentration  and isotopic composition of  carbon in
marine  sediments  affected by  a sewage discharge.    Ph.D.  Dissertation.
California   Institute of Technology,  Pasadena, CA.   178 pp.

Morel, F.M.M., and S.L.  Schiff.   1980.   Geochemistry  of  municipal  waste in
coastal waters.  R.M.  Parsons Laboratory Technical Report  259.  Massachusetts
Institute of Technology, Cambridge,  MA.

Oicubo, A.    1971.   Ocean diffusion diagrams.   Deep-Sea  Res. 18:789-802.

Okubo, A.,  and R.V. Osmidov.   1970.   Empirical  dependence  of the  coefficient
of horizontal turbulent diffusion in the ocean  of the  scale of phenomenon in
question.    Izd.  Acad.  of Sciences USSR,  Atmospheric and Ocean Physics:  6.

Parsons,  T.R.,  M. Takahashi,  and  B. Margrave.   1977.   Biological  ocean-
ographic processes.  2nd Edition.  Pergamon  Press,  New York, NY.  332 pp.

Runchal, A.K.  1983.  The drift model:   thoery  and development of the model.
Vol. 2:157-173.    In:   An Evaluation of  Effluent Dispersion  and  Fate Models

                                    48

-------
for OCS Platforms.  A.K. Runchal (ed).  Prepared  for U.S. Department of the
Interior, Minerals Management Service.

Schafer, H.A.   1979.    Characteristics  of  municipal  wastewater discharges,
1977.   pp. 97-102.   In:  Southern  California  Coastal  Water Research Project
1978-Annual Report. W.  Bascom (ed).   El Segundo,  CA.

Schafer, H.A.  1980.   Characteristic's  of municipal wastewater.  pp. 235-Z40.
In:  Southern  California Coastal   Water  Research Project- Biennial  Report,
1979-1980.   W.  Basconf'Ted).   Long  Beach, CA.

Seuss,  E.    1980.   Participate organic carbon  flux .in the oceans—surface
productivity and oxygen  utilization.   Nature  288:260-264.

Smith,  R.W., and  C.S. Greene.   1976.  Biological  communities near submarine
outfall.  J.  Water Pollut.  Control  Fed.  48:1894-1912.

Stull,  J.K.,  R.B. Baird,  and  T.C. Heesen.    1986.    Marine  sediment  core
profiles of  trace  constituents, offshore of a deep wastewater  outfall.   J.
Water Pollut. Control  Fed".  58:985-991.

Stumm,  W.,  and J.J. Morgan.   1981.   Aquatic  chemistry:   an  introduction
emphasizing  chemical  equilibrium  in  natural  waters.   2nd  Edition.   John
Wiley and Sons, New York, NY.  780  pp.

Suess,  E.   1980.   Participate  organic  carbon  flux  in the oceans—surface
productivity and oxygen  utilization.   Nature  288:260-264.

Swartz, R.C.,  D.W.  Schults,  G.R.  Ditsworth,  W.A.  DeBen,  and  F.A.  Cole.
1985.  Sediment toxicity, contamination, and  macrobenthic communities near a
large sewage outfall,   pp.  152-175.   In:   Validation  and Predictability of
Laboratory Methods  for  Assessing  the  Fate and Effects of  Contaminants  in
Aquatic Ecosystems.  ASTM  STP 865.   T.P.  Boyle (ed).  American Society for
Testing and Materials,  Philadelphia, PA.

Thomas, W.H.   1972.  Nutrients, chlorophyll, and  phytoplankton productivity
near  southern  California  sewage outfalls.   Univ.  of  Calif. Inst.
Mar. Res. Ref.  No. 72-19.  77 pp.
        f     +
U.S.  Environmental  Protection  Agency.    1982.   Revised  Section 301(h)
technical support document.   EPA-430/9-82-011.   Washington, DC.

Word, J.Q.,  and  A.J. Mearns.  1979.   60-meter  control  survey  off southern
California.  TM 229.   South. Calif.  Coastal  Water Res.  Proj.,  El Segundo,
CA.  58 pp.

Wu, F.,  and  T.  Lueng.   1983.  Modified Koh-Chang model,   pp.  107-126.   In:
An  Evaluation  of  Effluent  Dispersion  and Fate Models for  OCS   Platforms,
Volume  2  -  Contributed  Papers.   A.K.  Runchal  (ed).   Prepared  for  U.S.
Department'of  the Interior,  Minerals  Management Service  by  MBC  Applied
Environmental Sciences,  and Analytic and Computational  Research, Inc.
                                    49

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             APPENDIX A



REVIEW OF PARTICLE DEPOSITION MODELS

-------
                   REVIEW OF PARTICLE DEPOSITION MODELS
     Various models"  of  particle deposition  in  coastal  waters  have  been
proposed  for  examining  municipal  effluent  (and  sludge)  discharges  from
submerged  outfalls.  A comparison of  frequently cited  models  with  DECAL is
given below.
        —                                        %
CHEN ET AL.  1975

i.   Particle  deposition  rates  are  described by  a  fixed  distribution  of
    apparent settling rates for effluent particles.  Decomposition of organic
    particles in the  water  column is not considered significant.

2.   Horizontal  transport of  particles  by  ocean  currents is described  by a
    mean  flow  and a  spreading   (dispersion)  coefficient  to  account  for
    "random" components  of currents.   Vertical diffusion  is not considered
    significant.  Wastefield  height  above  the  bottom  is obtained  from
    calculations for  plume  height of rise.

3.   Solution for  the  particle transport equation  is  obtained analytically
    (using integral calculus).   Superpositioning is used in the solution for
    a continuous waste discharge.

4.   Organic decomposition  in  sediments is described by  first-order decay.
    Resuspension and redistribution of sedimented  material is  empirically
    described by a sediment diffusion mechanism.

U.S. ENVIRONMENTAL PROTECTION AGENC.Y_1982  [REVISED 301(h) TSD]

1.   Particle  deposition  rates  are  described by  a  fixed  distribution  of
    apparent settling rates for effluent particles.  Decomposition of organic
    particles in the  water  column is not considered significant.
                                   A-l

-------
2.   Horizontal  transport of particles is described by mean currents in each
    of four directions (upcoast, downcoast, onshore, offshore).  Horizontal
    dispersion and  vertical   diffusion  are not  considered  significant.
    Wastefjeld  height  above  the' bottom  is obtained  from  calculations  for
    plume height  of rise.

3.   Solution for  the particle transport  equation  is  obtained  analytically.

4.   Organic decomposition  in sediments   i's  described  by first-order decay.
    Sediment accumulation  calculations are  performed  for  steady-state or  for
    a prescribed  accumulation period  (e.g., 90 days).

KOH 1982

1.   Particle  deposition   rates  are  described by a  fixed  distribution  of
    apparent settling  rates.  Decomposition of organic particles in  the  water
    column is not considered  significant.

2.   Temporal variations in ocean currents (for periods less than 11  days)  are
    attributed  to  horizontal dispersion.   Net-flow is  not  considered.   A
    vertical diffusion coefficient  is assigned.   Wastefield height  above  the
    bottom is obtained from calculations for plume height of  rise.

3.   Solution for  the  particle  transport equation is obtained  analytically.
    Superpositioning  is used in the  solution for a  continuous waste dis-
    charge.  Steady-state  deposition  patterns  are calculated.

4.   Sediment calculations_are not performed.

HENDRICKS 1983

1.   Particle  deposition   rates  are  described by a  fixed  distribution  of
    apparent settling  rates.  Decomposition of organic particles in  the  water
    column is not considered  significant.
                                   A-2

-------
2.  Long-term drift velocities are obtained  from  progressive  vector  diagrams
    of ocean currents.   Horizontal  dispersion  and vertical  diffusion are  not
    considered significant.   Wastefield  height is assigned.

3.  Solution  for  the  particle transport equation is obtained  analytically.
    A numerical  algorithm is  used in tracking the  fate of  effluent  particles.

4.  A  second model  (submodel) is  available  to  simulate  bottom processes
    (resuspension and redistribution of  sediments, complete decomposition of
    labile material in  sediments).   The bottom processes model is empirically
    derived from observations near the Los Angeles County outfall.

OECAL MODEL

1.  Particle  deposition  rates  are determined  from coagulation  and  settling
    kinetics and are described by a second-order dependency  on  mass concen-
    tration.  Particle  interactions of  effluent- and  phytoplankton-derived
    material  are  taken  into  account.   Carbon  fixation  by  phytoplankton  is
    expressed  by  measured  productivity rates.   Decomposition of  organic
    material in the water column  is described  by  first-order  decay.

2.  Based  on  time  scale arguments,  coastal  transport  is simplified  by
    averaging over a daily  period.   Hence,  the vertical  structure of  the
    water  column  is described  by a well-mixed surface  and  lower  layer,
    separated by a pycnocline region.  In the lower layer, the daily-averaged
    discharge of  effluent is  distributed  over  an  extended area  by  tidal
    oscillations.  Nontidal flow by wind-driven currents and large-scale mean
    circulation advect diluted wastewater from the discharge  area.

3.  Solution  for  the  particle transport equation is obtained  analytically.
    A  numerical  algorithm is  used in  computing daily-averaged deposition
    rates.
                                    A-3

-------
4.  Organic decomposition  in  sediments is  described  by an apparent  first-
    order decay.   Steady-state  calculations  for  sediment  accumulation  are
    recommended.

     Previous models  for  particle  deposition^ (Chen et  al.  1975;  U.S.  Envi-
ronmental Protection Agency 1982;  Koh 1982;  Hendricks  1983)  differ primarily
in their  descriptions of  ocean  currents  (see  item  2  in model  summaries).
Other differences  also  exist  (e.g., Chen et  al.  and  Hendricks address  the
resuspension and  redeposition  of  sedimented  material  using very  different
empiricisms).

     In  the  previous  models,  particle deposition  rates are described by  a
fixed distribution  of apparent  settling rates.   (The  same Description  for
particle deposition rates is employed in the drilling  mud models  of Brandsma
and Sauer 1983; Wu and  Leung  1983;  and Runchal  1983.)   The settling  rates
are  typically  obtained  from  observations  in  laboratory  settling  columns
under quiescent conditions.  Observed  settling  rates  in laboratory  columns
however  should  not be considered  adequate  in describing the deposition  of
sewage particles in coastal waters.  Coagulation  plays  an  important  role  in
determining deposition  rates and  direct extrapolation of apparent  rates  in
laboratory columns to field conditions is  not appropriate.

     Mathematical   descriptions for  particle coagulation  are complex  and  are
not easily  incorporated  in particle deposition models  for coastal  waters.
However, simplified  descriptions  for  the  coagulation  and  settling  of
particles have been developed  from theoretical and laboratory  studies (Morel
and Schiff 1980; Hunt 1982; Farley  and Morel  1986).   In these  formulations,
particle deposition is approximately described by  a second-order  dependency
on mass concentration.

     Describing particle deposition  by a second-order rate  law represents  a
major change from  previous modeling approaches.  Modification of  an existing
model was  not  performed since  the  incorporation  of second-order  deposition
requires  new  analytical  solutions  of  the   particle  transport  equation  and
since superpositioning (used in the solutions of Chen  et al. and  Koh) is  not
                                   ' A-4

-------
valid  for  second-order  (nonlinear)  equations.  Work  in  the  301(h)  Post-
Decision study has therefore focused on the development of a new deposition
model  (see  DECAL model  summary).   In the DECAL model,  ocean  transport  is
                                                            ___      •
specified based on expected time scales  for particle deposition.

     The  new  deposition  model  (flECAL)  provides  a simple  calculation   for
organic accumulation in both "natural"  coastal  waters and  in the vicinity  of
coastal municipal outfalls.  Refinement in the present modeling approach  to
include more  detailed descriptions  of  coastal •  transport  and  parti.cle
dynamics is  possible  and would require numerical  solution  of  the particle
transport equation (e.g., see Mercier  1984).
                                    A-5

-------
                    APPENDIX B

         USER'S GUIDE  FOR THE DECAL MODEL:
TOOL #61 ON THE OCEAN  DATA EVALUATION SYSTEM (ODES)

-------
                                INTRODUCTION
     Environmental  effects  associated with  the discharge  of- effluent- in
marine water's  are often linked to  the  distribution of organic material  in
sediments.  Tool #61 on the Ocean  Data Evaluation System (ODES)  provides  the
user with a simple  model calculation  for  predicting  particle  deposition  and
organic sediment  accumulation  in  the  vicinity of municipal ocean  outfalls.
Model results can be used  in  predicting environmental  effects  from effluent
discharge, in  designing monitoring programs  and establishing future  moni-
toring strategies,  and  in  analyzing field data  for  chemical  enrichment  and
biological impacts.                                   "

MODEL DESCRIPTION

     Deposition  and  accumulation  of organic  material  in  coastal   waters  is
controlled by  fluid transport,  particle  transport,  and  organic carbon
cycles.  Modeling these processes  in detail  is extremely complex.   For  DECAL
calculations,  the modeling approach  has  been  simplified  by  assuming  that
removal of organic  material  from the water  column  primarily occurs within
the time scale of one to several  days.

     Based on the above simplification, the  fluid  transport is  approximated
by averaging  over a  daily period.  Hence, the vertical structure  of  the  water
column is described by  a well-mixed surface  and lower  layer,  separated by a
pycnocline region (Figure B-l).   (For  a  surfacing waste  plume,  a single
well-mixed layer  can  be assumed.)  In  the  lower layer, the  daily-averaged
discharge of effluent is distributed over  an  extended area  by  tidal oscilla-
tions.   Nontidal  flows by  wind-driven  (or  pressure-driven)  currents  and
large-scale mean  circulation  play  a key role in advecting diluted effluent
from the discharge area.

     Particle  dynamics  and  organic carbon  cycling are also described  by
daily-averaged rates (Figure B-2).   In the surface layer, carbon fixation by
phytoplankton is  expressed by  measured  productivity  rates  and is attributed
to production of  particulate  material  (either by formation of particles  or

                                    B-r

-------
 SIGMA-T
                                                      NONTIDAL FLOW
                 VERTICALLY
                 WELL MIXED
TIDAL MOTION
                 VERTICALLY
                 WELL MIXED
                                     TIDAL MOTION
                             MUNICIPAL
                             EFFLUENT
                    NONTIDAL
                      FLOW
                DIFFUSER
         EXTENDED
          SOURCE
          REGION
                                               TIDAL
                                              MOTION
Figure B-1.  Simplified diagram of municipal effluent transport in coastal
             waters.
                                B-2

-------
          PHYTOPLANKTON
            PRODUCTION
 NATURAL
PARTICLES
DECOMPOSITION
                                  COAGULATION/SETTLING
DECOMPOSITION
                                                            DECOMPOSITION
                 COAGULATION/SETTLING
DECOMPOSITION
  AND BURIAL




TOTAL SOLIDS
NATURAL
PARTICLES

WASTE
PARTICLES



_>.

                            DECOMPOSITION
                              AND BURIAL
       Figure B-2.  Simplified diagram of particle transport and organic carbon
                    cycles.
                                      B-3

-------
adsorption of  dissolved  organic  material  on surfaces).  Removal of  organic
material from  the surface  layer  is described by  a  first-order  decomposition
rate,  and  a second-order  approximation  for coagulation/settling  kinetics.
Effluent particles discharged in  the  lower layer  are  added  to concentrations
of  phytopl ankton-derived  material  that  has  settled  from surface  waters.
                     5-
Removal of  organic  material  from  the lower layer  is also described  by  a
first-order decomposition  rate,  and  a  second-order  approximation  for
coagulation/settling kinetics.

     Removal   of  organic  material  deposited  in the  surface  sediments  is
attributed to  decomposition and  burial,  and is  described  by  a  first-order
removal rate.   Resuspension  events  are  not considered.   Hence, the  DECAL'
model  is most  aoolicable  to  sediment accumulation periods.   The model  can
also be used  in approximating  the potential for  organic sediment accumulation
during periods when  resuspension (and possibly redistribution  of sedimented
material)  is likely,  recognizing  that the actual accumulation  is  likely  to
be less.  A  more  complete  description of the model  is  given  in the  report
"A Simplified Deposition Calculation  (DECAL)  For  Organic  Solids Accumulation
Near Marine Outfalls."

MODEL  INPUT

     Input parameters  to  DECAL  include  wasteflow characteristics,  outfall
diffuser location  and geometry,  background  oceanographic  information,  and
ocean  currents.   A  description  of   input  parameters,  including  suggested
procedures for obtaining input values, is given below:

Wasteflow Characteristics

     Values  for  the  discharge  flow   rate  and  the effluent  solids  concen-
trations are  required for  DECAL  calculations.   Depending on  the  specific
application, the user may obtain  values  for these inputs  from effluent  moni-
toring data, design  specifications for  effluent  discharge, or  NPDES  permit
linrrts.  Discharge ra4:es_for  301(h) applicants range from  0.1  to 23  m  /sec.
Average suspended solids concentrations  range from 30 to  200 mg/L.
                                   B-4

-------
Outfall Diffuser Location and Geometry

     OECAL calculations are performed for a specified study area.   The study
area  is  rectangular in  shape  and is  specified  by  its  length,  width,  and
orientation  from  true  North.   The  outfall diffuser  is  located  within  the
study area by specifying the" diffuser length,  orientation,  and  di stance "from
the study area  boundaries.  Outfall  diffusers are  typically  on the order of
100 m in length for every m^/sec of wasteflow.

Background Oceanographic Information

     Values for the total water column depth,  the height  of the lower layer,
and the  rate of  phytoplankton  production are  required  for OECAL  calcula-
tions.   For  major outfalls  in  the  Southern  California  Bight, total  water
column depths  of  60  m  are  common.   On  the  East  Coast,  municipal   ocean
outfalls are typically located in shallower waters.

     For discharged sewage that  is  trapped below the surface waters  of  the
ocean by strong density gradients, the height  of the lower  layer  is given as
the height-of-rise of the waste  plume or  the  pycnocline  height.   (Note that
the plume height of rise can be obtained from  plume model calculations; ODES
Tool  #60.)   For surfacing waste  plumes,  the  height of  the  lower  layer  is
equal  to  the  total  water column depth.  Phytoplankton production,  which is
given as  daily-averaged  productivity rates, can  be estimated  using  carbon
uptake  measurements  and is  typically observed  in the  range  of  0.2-2.0
    '"  (Suess 1980; Eppley et al . 1983).
Ocean Currents

     For OECAL model  calculations,  ocean currents are described by short-term
(tidal) oscillations and long-term  (nontidal) flows.  A  simplified  descrip-
tion for tidal and nontidal flow can be obtained from an  analysis of current
meter records.  A sample analysis is discussed for current meter measurements
                                    B-5

-------
taken' off  Newport  Beach by the  Southern  California  Coastal  Water  Research
Project (SCCWRP).

     The current meter at Newport Beach was  in  place  from  2/2/81  to 7/21/81
at a  depth of ^0 m  in 55 jn  of  water.   The data  was  transposed  by  SCCWRP
personnel   into  current velocities along the major and- minor axis  of  flow.
Monthly records  of  current velocity  data  along  the  major (longshore)  and
minor (cross-shore)  axis  of  flow are  shown  in  Figure B-3 for currents  off.
Newport Beach (6/25 to 7/27/81).   The  monthly records  were  analyzed  by first
computing  power  spectral  density  distributions.   Each  monthly  record  was
divided into four segments to increase confidence  in  the  spectral  estimates.
Results for  longshore  and  cross-shore currents  off Newport Beach are  shown
in Figure  B-4.   Both- spectra show  a significant  peak  at  approximately
2 cycles/day, indicating the dominance of  a semidiurnal  tidal oscillation.

     Cumulative  variance  distributions were  obtained by  integrating  the
spectral results and are shown in Figure B-5 for currents off Newport Beach.
For DECAL  model  applications, all  variance associated with periods  of  less
than  a  day is attributed to  the dominant  tidal  component.  Amplitudes  for
the  tidal  motion were obtained   by  comparing  variance  estimates   from  the
current velocity data  to  computed variance  for  ideal   oscillatory  motion.
For an oscillating current,  the tidal  velocity  is  given  as
                      utidal   =  Ucos

where  U  is the  amplitude  of  the  tidal  oscillation; t  is  time;  T  is  the
oscillation period; and o> is the phase shift.   The variance  for  an  arbitrary
number of tidal cycles (n)  is then given as
             variance  - -^- |"  U2cos2 f-2^- + *\   dt   -   U2/2         (B2)
j-r"
11  J(
     For the  Newport  Beach data, amplitudes  for  the tidal oscillation  are
6.5 cm/sec and  6.0  cm/sec,  respectively,  in  the  longshore and  cross-shore
direction.   Phase  shifts  for tidal  velocities  in  the longshore and  cross-

                                    B-6

-------
              Newport Beach: 6/2S to 7/27/81 •  meter/water depth = 40/56 m
   o
   0)
   V)

   £
   u
   O
   O

   UJ
   UJ
   cc
   O
   X
   
-------
              Newport Beach: 6/25 to 7/27/81 - meter/water depth =. 40/56 m
POWER SPECTRAL DENSITY
(cm/sec)2 / (cycles/day)
POWER SPECTRAL DENS
(cm/sec)2 / (cycles/day)





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„.




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•






















w— — — . —
                                      3
10
12    14
                                                               16
                         FREQUENCY  (cycles/day)
             Spectral Plot of Hendricks raw data set NB81040V.176 (Longshore)

              Newport Beach: 6/25 to 7/27/81 - meter/water depth » 40/56 m
                                      8
10    12
      14
                                                                16
                         FREQUENCY (cycles/day)
            Spectral Plot of Hendricks raw data set NB81040V.176 (Cross-shore)
Figure B-4.  Power spectral density distributions of currents off
             Newport Beach, California.
                                B-8

-------
            Newport Beach: 6/25 to 7/27/81 - meter/water depth = 40/56 m
1
CUMULATIVE VARIANCE (cm/sec)2 CUMULATIVE VARIANCE (cm/sec)2
— ^ — * M ro — * — •• ro i\> to
O Ul O (It & Ut O OU1001
1
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1
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5123456 3
PERIODS (days)
Integrated Spectral Plot of Hendricks raw data set
NB81 040V. 176 (Longshore)
Newport Beach: 6/25 to 7/27/81 - meter/water depth - 40/56 m


/
/
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i

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12345678
PERIODS (days)
Integrated Spectral Plot of Hendricks raw data set
NB81 040V. 176 (Cross-shore)
Figure B-5.  Cumulative variance distributions of currents off
             Newport Beach, California.
                               B-9

-------
shore direction are assigned  as  45°  and 0°, resulting in an elliptical tidal
motion.   This  is  motion  is considered to  represent  average  conditions  for
spreading the sewage over  the extended  source region.

     A 24.75-h  running average  of  the monthly  velocity  records  was  also
computed  and wa-s  used  in  describing nontidal  flow.  Averaging  results  for
currents  off Newport Beach are shown by the "smoothed"  lines  in Figure 8-3.
The currents range  from  0 to 20  cm/sec  and  exhibit significant variation,
often reversing direction  in  cycles  of 4-8 days according  to  the passage of
weather systems.

     Cumulative  probability (frequency)   of  occurrence is  computed using
running averages  for nontidal flows.  The  cumulative prooaoility curves  for
currents  off Newport Beach from 2/2 to 7/27/81 are given in Figure B-6.   As
shown, nontidal flows  in  the cross-shore  direction  are typically small  and
are considered  negligible  for DECAL model  applications.   Nontidal  flows in
the longshore direction are specified  by dividing the cumulative probability
curve  into  intervals  of  average  velocity  and percent  occurrence.   For
currents  off  Newport Beach,  an  average   upcoast  and average downcoast
velocity  is considered  for OECAL model  input of nontidal flows.

     Simplified descriptions  for currents  off Newport Beach (2/2 - 7/27/81)
and Palos Verdes (4/16  - 9/18/79)  are  included  in an ODES on-line dictionary
and are easily  accessible  for DECAL model  applications.   The  user  also  has
the option  of  entering  his  own  information  on  currents.   Information on
currents  should be based on long records of current meter measurements.  For
future field  studies,  we  recommend collecting current meter data  at  the
mid-depth of the lower  layer  over a  full year.

MODELING COEFFICIENTS

     Three modeling  coefficients are required for DECAL model calculations.
They  are  the  second-order  coagulation/settling  rate coefficient,  the
decomposition  rate coefficient for  suspended  organic material, and  the
interfacial  removal  rate  coefficient  for sedimented organic material.
                                    B-10

-------
       1.0
       0.9
   -;   o.a
             Newport Beach: 2/2 to 7/27/81 - meter/water depth = 40/55 m
   D
   O
   CD
   <
   m
   O
   IT
   CL

   UJ
   >
   "5.
   z>
   O
CO

CD
O
DC
0.

UJ
>   0.4
H

*5   0.3
       0.7
       0.6

       0.5
    0.2

    0.1
RUNNING AVER
— Avg. vel. = 4.31
AGE VELOCITIES
cm/sec
| Avg. pos. vel. - 9.03 cm/sec ;..-•'
"'--- ! ' : /
1 1 '
tj
\ 1 ,' '





|
I






I/I ! ! i
V '
/ i i ;
• 1 • 1
/ i
yf Avg. neg. vel. = -5.12 cm/sec :
/' 1 !
_.-^_ >
         -25   -20   -15   -10    -5
                                            10
     20   25
     1.0

     0.9

     0.8

     0.7

     0.6

     0.5

     0.4

     0.3

     0.2

     0.1
                    LONGSHORE  VELOCITY  (cm/sec)
                        Hendrick's Combined Data Sets
                        NB81040V.033 - NB81040B.176

              Newport Beach: 2/2 to 7/27/81 - meter/water depth - 40/55 m
RUN
~Avg.








NING
vel. .








AVER/
0.50 c








*GEVE
m/sec








10CIT




/
4
IES yf
/ i
/Avg. pos
/
i
i
1
;









. vel. =






/ Avg. neg. vel. - -1.87
7"





2.31 cm/sec












cm/sec
i


          -25   -20   -15   -10    -5
                                            10
15   20   25
                  CROSS-SHORE  VELOCITY  (cm/sec)
                        Hendrick's Combined Data Sets
                        NB81040V.033 - NB81040B.176
Figure B-6.  Cumulative probability curves for nontidal currents off
             Newport Beach, California.
                                B-ll

-------
Default values  for the  modeling coefficients are  given in  the prompting
sequence.   They have been obtained  as  follows:

     For the second-order coagulation/settling  rate  coefficient,  a value was
obtained  from  results of  theoretical  and  laboratory  studies  (Farley  and
Morel  1986) and the following parameters.   For  natural organic particles'and
sewage organic material, dry  density  is  estimated  to be 1.5 g/cm  based on
reported values for protein  amino  acids  and carbohydrates  (CRC  Handbook of
Chemistry  and  Physics 1981).   A floe  porosity  of 0.8  is  assumed  (Farley
and Morel   1986).   Fluid  properties  include  temperature  (T = 20°  C),
                      2                                  3
viscosity (v = 0.01 cm /sec),  and density  ( pf  = 1.025 g/cm ).  The Boltzmann
                                                            -16
constant and gravitational  acceleration are given as 1.38-10     erg/0 K and
          2
980 cm/sec  .  The  fluid  shearing rate  is  taken as O.I/sec, which is  roughly
                                                 -42    3
equivalent  to an  energy dissipation  rate  of 10    cm /sec  .   A collision
efficiency of 0.3  is  assumed  for coagulation  (Farley and Morel   1986).  The
second-order rate  coefficient is calculated as i
an estimated particle  concentration  of 1.0 mg/L.
second-order rate coefficient is calculated as 2-10   L-mg  -sec   based on
     The default value for the decomposition  rate  of organic material in the
water column is given as O.I/day.   This  value is based on  laboratory studies
for the  decomposition  of readily-degradable  fractions (e.g., carbohydrates
and amino acids)  of  effluent organic material (Metcalf & Eddy  1972).   The
interfacial  removal  rate coefficient  for  sedimented organic  material  is
given as  0.015 cm/day.  This  value  is  based on  steady-state  estimates of
organic  carbon  turnover rates in  surface  sediments (for  field  studies of
Hopkinson 1985  and  references  therein) and  is   includes the  effects  of
decomposition in surface sediments  and burial.

MODEL OUTPUT

     Output  for  the  DECAL is  given  as  sets  of  contour  plots for suspended
particle  concentrations  in  the lower water  layer, for  the  daily-averaged
deposition  rates of  organic material,  or  for organic  accumulation  in
sediments.
                                   B-12

-------
     The following is  a  sample terminal  session with ODES  Tool  #61 showing
typical  prompts and output.  User responses are underlined.
                                   B-13

-------
                              *   ODES    *


             — ODES~~Envi ronmental  Decision  Support  Tool #61 —  -


             ** SIMPLIFIED DEPOSITION  CALCULATION  (DECAL)  **

* This  tool  provides you  with a  simple  model calculation  for predicting
  particle deposition  and organic accumulation in  the vicinity  of sewage
  outfalls during sediment accumulation periods.  Processes incorporated  in
  the model  include  coastal   transport,  phytoplankton  production,   coagula-
  tion/settling  of  natural   organic material  and  sewage  particles and
  microbial degradation."  further details of the model  are discussed in the
  report "A Simplified Deposition Calculation  (DECAL)  for Organic Accumula-
  tion Near Marine Outfalls."

  — You will  first  be asked  to specify input parameters  for the DECAL
     model  which  include  wasteflow characteristics,  outfall diffuser
     location  and  geometry, background oceanographic  information,   and
     values for three modelling coefficients.

  — You will  also  be  asked  to  specify  the  types of contour plots   you
     would like to produce.

  — ODES will  then  run the model to  calculate  predicted particle deposi-
     tion and organic accumulation,  and will produce the selected plots.

> Please hit RETURN to continue or enter  B (Basic  Options)> 

* ODES will now ask you to specify two wasteflow characteristics:

  (1)'discharge  flow  rate  in cubic  meters per  second;  and   (2)  effluent
  solids concentration in  milligrams per  liter.

> Enter discharge flow rate (m3/sec)>  10

> Enter effluent solids concentration  (mg/L)>  100
                                   B-14

-------
  ODES will  now ask you to specify  the study area and diffuser location.   For
  model  calculations,  the  diffuser  is located within a rectangular grid.   You
  wi-11  be  asked  to  enter the  orientation  and  size of the  study area  by
  specifying the  clockwise rotation of  the  Y-axis  (in  degrees)  from  true
  North, and the  length (in km) of the X-axis  (XL)  and  Y-axis (YL).   You
  will also  be  asked   to'specify  the location  of  one end  of  the  diffuser
  (point A)  in  terms  of  its distance from  the origin (0,0), the  length  of
  the diffuser  (in m)  (AB),  and the orientation of  the  of  the  diffuser  in
  relation to the X-axis (angle C).  If  you  choose,  you  can  hit  RETURN after
  each prompt to .use the indicated  default value.

                     Study Area and Diffuser  Location
          km  YL +	+	+	+	+
                                    B
                 0              X	>                  XL  km

> Enter Y-axis rotation (deg from true North)  (default=0)>  0

> Enter X-axis length of study area (km)  (default=20  km)> 20

> Enter Y-axis length of study area (km)  (default=20  km)> U

> Enter X distance from origin (km) (default=10.00)>  7

> Enter Y distance from origin (km) (default=5.5)>  5.5

> Enter length of diffuser (m) (default=1000.)>  1000

> Enter orientation of diffuser (deg from X-axis)(default=0)>  30

* ODES will now ask you to specify  background oceanographic  information.   You
  must enter a value for each parameter  as no  default values are  provided.

> Enter the total water column depth (m)> 60

* You will  now  be asked to  specify the height of the lower water  layer  (in
  meters).  This value is given as the height-of-nse of the waste  plume, or
  the pycnocline height.

> Enter height of the lower  water layer  (m)> 30

> Enter phytoplankton productivity (gC/m2-day)>  1.0
                                   B-15

-------
* Ocean currents  are described  by  short-term harmonic (tidal) motions  and
  long-term advective flows.   You  can choose to enter your  own  information
  or use the information from one of several  ODES files:

          E = ENTER own information
          U = USE information from an ODES File

> Enter E (enter information) or U (use ODES  File)> U

* You will now be asked to  specify  the ODES  Current File  you want to use by
  entering its 7-character  ODES code, or you can  enter H to  look  up  valid
  codes.-

> Enter a File by its 7-character code, or H> H
                                  ODES
                     — ODES On-line Dictionary —

* The On-Line  Dictionary stores the  name  and  the 7-character  Current  File
  Code stored in the ODES Database.  You can search for a name,  or part  of a
  name, or a 7-character code.

  > SEARCH FOR>  

   CODE          CURRENT FILE NAME
   PV79041 = PALOS VERDES 4/16-9/18/79 (41/56 M)
   SAMPLE1 = SAMPLE CALCULATIONS IN DECAL REPORT
   NB81041 = NEWPORT BEACH 2/2-7/21/81 (40/55 M)

> Search for another CURRENT? (Y/N)> N

* Returning to Tool #61...

* You will now be  asked  to  specify the  ODES Current File you want to use by
  entering its 7-character  ODES code, or you can  enter  H to look  up  valid
  codes."

> Enter a File by its 7-character code,  or H> SAMPLEI
                                    B-16

-------
* If you wish, you can review a detailed description of file SAMPLE1
  before continuing.

> Do you want to review the detailed description? (Y/N)> Y_

CURRENT FILE CODE: SAMPLE1

CURRENT FILE NAME: SAMPLE CALCULATIONS IN DECAL REPORT

DESCRIPTION:

     The following description of currents was used in sampl«e calculations in
the report "A Simplified  Deposition  Calculation (DECAL) for Organic Accumula-
tion Near Marine  Outfalls."   Short-term  oscillatory  currents  are  attributed
to a  semidiurnal  tidal  component in  both  the longshore (90° N)  and  cross-
shore  (0° N)  direction.   Amplitudes of  the tidal currents  are  0.1 m/sec in
both  the  longshore  and  cross-shore  directions.    Phase  shifts  of   tidal
velocities in the  longshore and cross-shore direction  are  taken as  210° and
180°, respectively.  Long-term (nontidal) flow is considered constant  in time
with a current velocity of 0.03 m/sec in the longshore direction.
> Please press RETURN to continue > 

* Calculations can be  performed  for  steady-state  or  time-dependent  sediment
  accumulations.   You  will  now  be  asked to  specify steady-state or  time-
  dependent sediment accumulations.   If  you  select  time-dependent accumula-
  tions you will.be asked to enter the duration of the accumulation  period.

       S = Steady-state sediment accumulations
       T = Time-dependent sediment accumulations


> Enter S (Steady-state) or T (Time-dependent)> S
                                   B-17

-------
* ODES will  now ask  you  to  specify  three modelling coefficients  that  are
  required for the OECAL calculation.  You can  select the  default  val-ues by
  hitting RETURN when asked to enter a value.

* You will  be  asked  to enter  the  second  order coagulation/settling  rate
  coefficient in L/mg(dry wt)-sec.

> Enter this coefficient (default=2E-6 L/mg(dry wt)-sec)> 

* You will be asked  to  enter  the  first  order  decomposition rate coefficient
  for suspended organic material  in L/day.
       ~                                         •
> Enter this coefficient (default=0.1/day)> 

* You will be  asked  to enter the  interfacial  removal rate coefficient  for
  sedimented organic material  in cm/day.

> Enter this coefficient (default=0.015 cm/day)> 

* ODES will  now  list the values you  have  specified  for  ths  model  and  allow
  you to  change  the selections  before  the job  is submitted.   ODES  will
  display the  values on several  pages.  To  view the next page  enter C, to
  change a value enter its number, and to submit the job enter S.

* These are the values you have specified:

  WASTEFLOW CHARACTERISTICS

   1) Discharge flow rate in m3/sec:  10.
   2) Effluent solids concentration in mg/L:   100.

  STUDY AREA AND DIFFUSER LOCATION

   3) Y-axis rotation from true North, in degrees:   0.0
   4) Study area length, X-axis in km:  20.0
   5) Study area length, Y-axis in km:  11.
   6) Diffuser distance from 0, X-axis in km:   7.
   7) Diffuser distance from 0, Y-axis in km:   5.5
   8) Length of diffuser in m:  1000.
   9) Orientation of diffuser in degrees:  30:  -

  OCEANOGRAPHIC INFORMATION
  10) Total water column depth in m:  60.
  11) Water depth below pycnocline in m:  30.
  12) Phytoplankton productivity in gC/m2-day:   1.0

                                            CONTINUED...


                                    B-18

-------
> Enter a number, C to continue, or S to submit> C_

  OCEAN CURRENTS - Short-term harmonic (tidal) motion
                                  - - f
  13) Orientation of principal  axis,  in degrees:  0.000

  14) Harmonic constituents described by ODES FILE SAMPLE1
                    maj axis maj-phase  min axis  min-phase
           period  amplitude   shift    amplitude   shift
           (hours)  (m/sec)  (degrees)  (m/sec)  (degrees)

  14-1)      12.         0.1     210.0       0.1     180.0

  OCEAN CURRENTS - Long-term advective (nontidal) flows

  15) Flow conditions described by
                    direction  probability
          velocity  of flow   of occurence
           (m/sec)  (degrees)  (percent)

  15-1)       0.03      90.0      100.

  16) Sediment accumulations:  STEADY-STATE
  17) Duration' of accumulation period in days:  N/A

  MODELING COEFFICIENTS

  18) Second order coagulation/settling rate coefficient:   .000002
  19) First order organic material decomposition rate coefficient:  .1
  20) Interfacial removal rate coefficient for sedimented  organic
      material:  .015

> Enter a number, C to relist,  or S to submit> S

* You will  now  be  asked to select  the type  of  contour  plots you want  to
  produce.  Each option below produces two contour plots:

          1) Total Suspended Particles and
             Waste Suspended Particles; or

          2) Total Deposition Flux of Particles and
             Deposition Flux of Waste Particles; or

          3) Total Organic Accumulation in Sediments and
             Organic Accumulation of  Waste Particles.

> Please enter a set of contour plots by number (1, 2, or  3)> 2
                                   B-19

-------
* If you  have  a  Tektronix 4010  (or compatible)  graphics  device, you  can
  display the output from ODES Tool  61 in high-quality graphics format.

> Do you want to produce high-quality graphics? (Y/N) Y_

* ODES will  assume you  have a  Tektronix 4010 (or compatible) graphics device.

> Do you have a TEK4010? (Y/N)> Y

> Enter a 1-8 character name for your graphic) SAMPLE 1

* You may enter  a  1-40 character footnote that will  appear  on your graphic
  and accompanying back-up tables.

> Do you wish to enter a footnote? (Y/N)> N

* Thank you.

************************
JOB 5391 KVF61 SUBMITTED
************************

* Please record the above job number for subsequent retrieval.   Jobs usually
  take 5-10 min to run.
  The output plots (Figures B-7 and B-8) and summary data  from  this  job are
provided below.
                                    B-20

-------
             ODES TOOL 61:  DECAL MODEL
        Total Deposition Rate Of Waste Particles g/m**2-day



1
LLl
O
z
^
1-
C/3
Q
>





\ i •
10 -
9 -
8 -
-
6 -

5 -

4 -

3 -
2 -
1 -
0.

(
-~



/'' 	 ^""^ 	
l\\ ^"T 	 .."^ 	 ~" 	
N, *Miy ~J ^2 _^~~^ 	 •'
Xv*"- — *•• — "" 	 ^ 	 ___. 	
\vO>v_ 	 . — "^""^ 	 	 """
\*x 	 i""""


_


i i i i i i i i i
) 2 4 6 8 10 12 14 16 18 2(
                       X-DISTANCE  (km)
                       CONTOUR KEY (g/m2- day)
                                  0.3413
                         	1.0239
                         	  1.7065
                         	2.3891
                         	3.0717
                       Background Rate: 0.3413
Figure B-7.  DECAL contour plot of total deposition rate of waste particles
           for the sample calculations.
                          B-21  —

-------
            ODES TOOL 61:  DECAL MODEL
        Total Deposition-Rate Of Waste Particles g/m**2-day



E"
i
LJJ
O
Z
^
h-
52
Q
>•





1 1 •
10 -
9 -
8 -
7 -

6 -

5 -

4 -

3 -
2 -
1 -


(
- .

•


,' 	
\t f^IT"^- — ~.. 	 ~~"* 	
»<\'^^"^,1 	 , _J
'yv. — .^** — »--~ 	 "
X>N 	 . — — '"






i i i i i i i i i
) 2 4 6 8 10 12 14 16 18 2(
                     X-DISTANCE  (km)
                     CONTOUR KEY (g/m - day)

                       	0.6826

                       	1.3652

                       	2.0478
Figure B-8.  DECAL contour plot of waste particle deposition rate for the
           sample calculations.
                          B-22

-------
ODES:           OCEAN DATA EVALUATION SYSTEM
DEVELOPED BY:   AMERICAN MANAGEMENT SYSTEMS, INC. & TETRA TECH, INC.
DEVELOPED FOR:  OFFICE OF MARINE AND ESTUARINE PROTECTION, U.S. EPA
CAUTION:        DATA ARE FROM SOURCES OF VARYING QUALITY

JOB NAME:       KVF61 SUBMITTED AT 11:13:07 ON 10/03/86

    ODES TOOL 61:  A SIMPLIFIED DEPOSITION CALCULATION


    WASTEFLOW CHARACTERISTICS

    1) DISCHARGE FLOW RATE IN M3/SEC:  10.000
    2) EFFLUENT SOLIDS CONCENTRATION IN MG/L:  100.00


    STUDY AREA AND DIFFUSER LOCATION

    3) STUDY AREA ORIENTATION, YAXIS ORIENTATION
       IN DEGREES FROM TRUE NORTH:  .OOOOOE+00
    4) STUDY AREA LENGTH, X-AXIS IN KM:  20.000
    5) STUDY AREA LENGTH, Y-AXIS IN KM:  11.000
    6) DIFFUSER DISTANCE FROM 0, X-AXIS IN KM:        7.00
    7) DIFFUSER DISTANCE FROM 0, Y-AXIS IN KM:        5.50
    8) LENGTH OF DIFFUSER IN M:  1000.0
    9) ORIENTATION OF DIFFUSER IN DEGREES FROM THE X-AXIS:  30.000


    GEOGRAPHIC INFORMATION

    10) TOTAL WATER COLUMN DEPTH IN M:  60.000
    11) HEIGHT OF LOWER WATER LAYER IN M:  30.000
    12) PHYTOPLANKTON PRODUCTIVITY IN GC/M2-DAY:  1.0000
    13) PRINCIPAL AXIS FOR CURRENTS IN DEGREES
        FROM TRUE NORTH:  90.000
    14) SHORT-TERM (TIDAL) CURRENTS DESCRIBED BY:
          PERIOD  X-AMPLITUDE  X-PHASE SHIFT  Y-AMPLITUDE  Y-PHASE SHIFT
          (HOURS)   (M/SEC)      (DEGREES)      (M/SEC)      (DEGREES)
    14-1) 12.0     .10000         210.00       .10000        180.00

    15) LONG-TERM ("NON-TIDAL) CURRENTS DESCRIBED BY:
          VELOCITY       DIRECTION     PERCENT OCCURRENCE
          (M/SEC)      •  (DEGREES)
    15-1) .30000E-01     90.000              100.00

    16) STEADY-STATE SEDIMENT ACCUMULATION
    17) DURATION OF SEDIMENT ACCUMULATION PERIOD IN DAYS:  N/A
                                   B-23

-------
     MODELING COEFFICIENTS

     18) SECOND-ORDER COAGULATION/SETTLING
         RATE COEFFICIENT:                    .20000E-05 L/MG-DAY
     19) FIRST-ORDIR ORGANIC MATERIAL
         DECOMPOSITION RATE COEFFICIENT:      .10000    /DAY
     20) INTERFACIAL REMOVAL RATE COEFFICIENT
         FOR SEDIMENTED ORGANIC MATERIAL:     .15000E-01 CM/DAY
**END OF FILE**
                                    B-24

-------
                    APPENDIX C

         MASS  CONSERVATION  EQUATIONS AND
STEADY-STATE SOLUTIONS FOR PARTICLE CONCENTRATIONS
             IN THE  LOWER WATER  COLUMN

-------
          MASS CONSERVATION EQUATIONS AND STEADY-STATE  SOLUTIONS
           FOR PARTICLE  CONCENTRATIONS  IN  THE LOWER WATER COLUMN
     This appendix  provides  the  differential  conservation  equations  and
their  steady-state  solutions  used  to  determine mass  concentrations  of
suspended particles in the  lower  water column in  the  background  (i.e.,  in
the absence  of  any effluent  suspended solids particles),  in  the extended
source region,  and downcurrent  of  the  extended  source.

     Tne background mass  concentration of  suspended oarticles (CD) satisfies
the equation:
                dt
                     =  2'5 Psed/hL  -  kdCb  - BCb
which has steady-state solution:
                          28
                                  1  -
10 B
                                                         0.5

     In  the  extended source  region,  the mass  concentration of  suspended
particles (Ce) satisfies the equation:
                                                                  C. -
which has steady-state solution:
                          ZB
                                  1  -
                                                     0.5
                                    C-l

-------
                    where:    a  =  2.5 PCQj/h. +  ^a b  +  ^w w
                                         sed       ~h~A —    ~h~A —
                                                   Yes    nLAes
                              b -
                                        hLAes
     Downcurrent  of  the  extended  source region,  the  mass concentration  of

suspended particles (C
-------
   t = time
psed = the  flux of  organic carbon  settling  from  the surface  layer,
       which is a function of the productivity rate (see Equation 9-)
  kd = the decomposition rate coefficient  for suspended organic material
   B = the second-order coagulation/settling rate coefficient
  HL = the height of the lower  layer
 Aes = the area of the extended source region
  Oa = the nontidal  flow  through the extended source  region,  which is
       dependent on  the nontidal currents,  the  width  of  the  extended
       source  region  perpendicular  to  the  nontidal  currents,  and  the
       height of the lower layer
  ua = the velocity of the nontida'l  flow
  Qw - the effluent discharge flow rate
  Cw = the mass concentration of particles in the effluent
   s = the distance downcurrent of the extended source  region.
                               C-3

-------
                  APPENDIX D

        MASS CONSERVATION EQUATIONS AND
STEADY-STATE SOLUTIONS FOR CHEMICAL CONTAMINANT
   CONCENTRATIONS IN  THE  LOWER WATER COLUMN

-------
    MASS CONSERVATION EQUATIONS  AND  STEADY-STATE SOLUTIONS FOR CHEMICAL
           CONTAMINANT CONCENTRATIONS IN THE LOWER  WATER  COLUMN
     This appendix  provides  the  differential  equations  and  their  steady-
state  solutions  used  to determine  the  total  mass  concentrations  of  a
chemical  contaminant in  the lower  water  column  in  the extended source region
and downstream of  the extended  source  region.                   %

     In  the  extended source  region,  the  total  mass  concentration  of  a
chemical  contaminant (Ce)  satisfies  the  equation:
          .5
           dt
  hLAes
        IP"6  B  K
                            Ce
             10~6  K
which has steady-state solution:
                                    0  0
                                    vw vw
"L*eS
Va *
\Aes
10"6 B Kp M2
1 + l(f6 K M
1 « JLU N 1 1

            where:   M
                     e
 b
2B
1 -
                              hLAes
                                    D-l

-------
     Downcurrent of the extended source region, the total mass concentration

of a chemical contaminant (C
-------
In the above formulas:
                                   j-
  Ce = the total mass concentration of the chemical  contaminant  in  the
       extended source  region
  C,j = the total mass  concentration of the chemical  contaminant" down-
       current of the extended source  region
  Mb = the mass concentration of  background particles  in the lower layer
  Me = the mass  concentration of  suspended  particles in  the  extended
       source region
  M
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