1. Project Report
on
Hydrodynamics and pollutant transport off Mumbai
coastal region
submitted by
Prabhas Ranjan Gupta
Indian Institute of Technology Guwahati
under the guidance of
Dr. P. Vethamony
Scientist-G
Physical Oceanography Division
National Institute of Oceanography, Goa
India
28th
May to 28th
July 2010
2. 1
Acknowledgements
I would first like to thank Dr. P. Vethamony for giving me an opportunity to learn and work under his
expert guidance. I am grateful to him for giving me much of his precious time and patiently
discussing the progress of the project at every stage. This small but important work would have
been impossible but for his continuous support, guidance and encouragement.
I would also like to express my sincere thanks to Dr. S.R. Shetye, Director, NIO, for providing me all
the facilities needed for the successful completion of this project work.
Special thanks are due to Mr. Vinodkumar for helping me learn the specifics of MIKE 21. I would like
to thank Mr. V.M. Aboobacker for carefully revising the draft of this report and giving me his time
and insightful feedbacks during the project. I am also grateful to Mr. V.R. Renjith, Mr. K. Sudheesh,
Ms. Betty John and others in the POD lab for extending their generous help whenever I was in
need. Lastly, I would like to give a special thanks to Mr. Saheed P.P. for giving me his valuable
advice and inputs from day one and for maintaining a cheerful atmosphere in the lab.
3. 2
Contents
Page
Acknowledgements 1
List of figures 4
List of tables 5
List of abbreviations 6
List of symbols 8
Chapter 1 Introduction 9
1.1 Coastal waters and marine outfalls 9
1.2 Study area: Mumbai coastal region 10
1.3 Review of water quality modelling studies 12
1.4 Objectives of the present study 13
Chapter 2 Simulation of off-shore hydrodynamics 14
2.1 Hydrodynamical modeling 14
2.1 MIKE 21 flow model 15
2.3 Model setup 16
2.3.1 Model domain and grid size 16
2.3.2 Time step and length of simulation 16
2.3.3 Bathymetry 17
2.3.4 Bed roughness coefficients 18
2.3.5 Momentum dispersion coefficients 19
2.3.6 Wind data and wind friction factor 20
2.3.7 Initial and boundary conditions 22
2.4 Model calibration, validation and simulation 23
2.4.1 Model calibration 23
2.4.2 Model validation 23
4. 3
2.4.3 Final simulations 25
Chapter 3 BOD-DO modeling of wastewater outfalls 26
3.1 The importance of dissolved oxygen 26
3.2 Effluent dispersal processes 26
3.3 Processes affecting DO levels 29
3.3.1 Reaeration 29
3.3.2 Photosynthesis and respiration 29
3.3.3 BOD exertion 30
3.3.4 SOD exertion 31
3.4 Model setup 31
3.4.1 ECO Lab 31
3.4.2 Wastewater disposal scenario and outfall parameter values 32
3.4.3 Description of chosen template and process rate estimates 33
3.5 Final simulations 35
Chapter 4 Results and discussion 37
4.1 Southwest monsoon season 37
4.2 Northeast monsoon season 40
Chapter 5 Summary and conclusion 43
References 44
5. 4
List of figures
Title Page
Fig. 1 A marine outfall: shown above is the Boston outfall, which discharges into
Massachusetts bay
9
Fig. 2 Bandra and Worli outfalls and Mumbai‟s drainage zones 10
Fig. 3 DO levels along Mumbai‟s west coast 11
Fig. 4 Interpolated bathymetry for the model domain 18
Fig. 5 Wind rose diagram for Worli during 1 Aug to 31 Aug, 2009 (SW monsoon period) 21
Fig. 6 Wind rose diagram for Worli during 22 Oct to 22 Nov, 2009 (NE monsoon period) 21
Fig. 7 Plot of initial surface elevation 22
Fig. 8 Comparison between measured and simulated water levels at Worli 24
Fig. 9 Comparison between measured and simulated u-component of currents off Worli 24
Fig. 10 Comparison between measured and simulated v-component of currents off Worli 24
Fig. 11 BOD exertion curve (schematic) 30
Fig. 12 Variation of (a) BOD and (b) DO at the outfall location during the SW monsoon 37
Fig. 13 BOD distribution after 72 hours of discharge for (a) case 1 (b) case 2 39
Fig. 14 Relative magnitudes of processes 39
Fig. 15 Tidal variations in plume pattern: (a) flood tide (b) ebb tide 40
Fig. 16 Comparison between (a) BOD and (b) DO levels at the outfall during the two
study periods, viz. SW monsoon (Aug) and NE monsoon (Oct-Nov) seasons
41
6. 5
List of tables
Title Page
Table 1 Basic and hydrodynamical parameter values used for final simulations 25
Table 2 Outfall parameters 32
Table 3 ECO Lab process constants 35
Table 4 BOD maximum and DO minimum at outfall location during SW monsoon 38
Table 5 BOD maximum and DO minimum at outfall location during NE monsoon 42
7. 6
List of abbreviations
AOML Atlantic Oceanographic and Meteorological Laboratory
AD Advection-Dispersion
ADI Alternating Direction Implicit
BOD Biochemical Oxygen Demand
CBOD Carbonaceous Biochemical Oxygen Demand
CFL Courant-Friedrichs-Lewy
CPU Central Processing Unit
DHI Danish Hydraulic Institute
DO Dissolved Oxygen
DS Double Sweep
ECMWF European Center for Medium-range Weather Forecast
FC Fecal Coliform
GODAE Global Ocean Data Assimilation Experiment
HD Hydrodynamic
IRS Indian Remote-Sensing Satellite
LAT Lowest Astronomical Tide
MISST Multi-sensor Improved Sea Surface Temperatures
MLD Million Litres per Day
MSL Mean Sea Level
MWF Mean Wind Field
MT Mud Transport
NBOD Nitrogenous Biochemical Oxygen Demand
NEERI National Environmental Engineering Research Institute, India
NHO Naval Hydrographic Office, Dehradun, India
NS Navier-Stokes
OTPS OSU Tidal Prediction Software
PA Particle tracking
9. 8
List of symbols
C Chezy number
Cd Drag coefficient (bed resistance)
CD Drag coefficient (wind friction)
CR Courant number
d Time-varying water depth
E Eddy viscosity coefficient
f Wind friction factor
g Acceleration due to gravity
h Water depth
H Henry‟s law constant
M Manning number
NE Northeast
p, q Flow fluxes in x and y directions, respectively
Six, Siy Source impulses in x and y directions, respectively
SW Southwest
t Time, temperature
u, v Current velocities in x and y directions, respectively
x, y Cartesian space coordinates
∆x, ∆y Grid spacing in x and y directions, respectively
∆t Time step for numerical simulations
Ω Coriolis parameter
ρa, ρair Density of air
ρw Density of water
η Surface elevation
𝜏 Effective shear stress
θ Arrhenius temperature coefficient
10. 9
1. Introduction
1.1 Coastal waters and marine outfalls
Coastal waters provide for society‟s critical needs: they have, since mankind‟s early days, been an
easily accessible resource of food and are also likely to serve as the major source of drinking water
in the near future as inland freshwater resources become increasingly scarce. Coastal industries
are now withdrawing sea water for their coolant plants as this need cannot be met entirely by
groundwater. Moreover, coastal waters are also among the world‟s most ecologically important
domains. They support a rich biodiversity of marine lifeforms and form an integral component of the
Earth‟s overall ecosystem.
At the same time, coastal waters are also seen as an almost infinite sink for anthropogenic wastes
due to their high dilution and dispersion characteristics. They are now being increasingly used for
this purpose, with coastal cities in several developing countries considering the construction of
marine outfalls (Figure 1) to dispose off their municipal sewage and industrial effluents. Developed
countries have already been using this method of waste disposal since several decades (Gupta et
al., 2006).
Figure 1: A marine outfall: shown above is the Boston outfall, which discharges into Massachusetts
bay (from Hunt et al., 2010)
11. 10
Marine pollution occurs when wastewater discharges from such outfalls get concentrated in a
limited area instead of being dispersed over large areas and at longer distances away from the
coast. The resulting degradation in marine water quality is a matter of serious concern because of
its potential impacts on human and aquatic ecosystem health (Gupta et al., 2009). This gives rise to
the need for an accurate prediction of effluent dispersal patterns and water quality around existing
and proposed marine outfalls.
1.2 Study area: Mumbai coastal region
Figure 2: Bandra and Worli outfalls and Mumbai‟s drainage zones (from Kumar et al., 2000)
12. 11
The first scheme for the marine disposal of wastewater from the entire Bombay municipal area
through outfalls at Bandra and Worli was envisaged in 1970 (NEERI, 1995a). The city of Mumbai,
with a population of over 18 million (Sawant et al., 2007), generates more than 2700 million litres
per day (MLD) of sewage from seven drainage zones (Vyas and Vyas, 2007). Five of these,
discharge their sewage into the Arabian Sea waters off the west coast. Sewage disposal at Bandra
and Worli is being done through two 3.4 km long outfalls with a diffuser system at their end. Primary
pre-treatment, comprising of screening and degritting procedures, is given to the sewage before it is
disposed off into the sea (Gupta et al., 2006).
Figure 3: DO levels along Mumbai‟s west coast (from Kumar et. al., 2000)
13. 12
Regions such as Malad and Mahim, which receive about 50% of the wastewater discharge from the
city, have been reported as highly polluted, going by the Dissolved Oxygen (DO) levels of their off-
shore waters (Kumar et al., 2000). Other stretches of the Mumbai coast are affected by moderate
DO depletion (Figure 3). Biochemical Oxygen Demand (BOD) and nutrients have been reported low
in most of the regions. Fecal Coliform (FC) levels, considered to be the best pollution indicator for
coastal waters, have been reported high in 75% of areas with values ranging from 103
-104
counts
per 100mL.
1.3 Review of water quality modelling studies
Coastal systems are extremely complicated and include many variables and processes which
exhibit highly non-linear interactions. However, due to recent advances in computing power,
physical and ecological models have emerged as one of the most potent tools for predicting
pollutant dispersal and water quality variations (James, 2002). As a result, several outfall modeling
studies have been conducted in the past for different regions along Mumbai‟s coast. Some of these
are discussed below.
A project feasibility and environmental impact assessment study was undertaken by NEERI in the
1990‟s, wherein it was concluded that construction of outfalls at Bandra and Worli would eliminate
the DO depletion problem near the coast and considerably improve the ecological health of the
near-shore waters in the region (NEERI, 1995b). DO and BOD levels near the diffusers were
reported as expected to be above 4mg/L and below 3mg/L respectively during most of the tidal
cycle. Although high BOD levels near the diffuser (>20mg/L) were also predicted, their probability of
occurrence was reported to be very low (less than 0.01). In a later study, Kumar et al. (2000)
predicted Fecal Coliform concentrations for several hypothetical outfall discharge scenarios at
Bandra and Worli. Considerable reductions in waste field sizes were reported for secondary pre-
treatment schemes and outfall lengths greater than 8 km.
A comparison of far-field dilutions was undertaken by Gupta et al. (2006), in which values obtained
through dye experiments were compared with the predictions of empirical and numerical models.
Sasamal et al. (2007) carried out an analysis of sewage and industrial pollution distribution in Thane
Creek, Mumbai using Indian Remote-Sensing Satellite (IRS) data, in which pollutant plumes were
identified and spread areas were approximately estimated. Vyas and Vyas (2007) simulated the
spread of Fecal Coliform (FC) patches around sewage outfalls at Worli, Bandra, Versova and Malad
during the monsoon season, for different lengths of outfalls and various levels of land pre-treatment.
More recently, Vijay et al. (2010) carried out hydrodynamic and water quality simulations for Malad
creek and evaluated various wastewater discharge scenarios, including a proposed 3.4 km long
outfall at Erangal, using the MIKE 21 flow model. The study concluded that diverting effluents from
14. 13
wastewater treatment facilities to the proposed ocean outfall would significantly improve the water
quality of Malad creek.
1.4 Objectives of the present study
Keeping in mind the above developments and the available time frame, the following objectives
have been defined for this study:
Simulating hydrodynamics off the Mumbai coastal region.
Simulating Biochemical Oxygen Demand (BOD) and Dissolved Oxygen (DO) concentrations
around an existing outfall at Worli, Mumbai.
Comparing water quality around the outfall for periods with contrasting met-ocean
conditions, namely, the southwest monsoon and the northeast monsoon seasons.
Comparing water quality around the outfall for atleast two discharge cases.
15. 14
2. Simulation of off-shore hydrodynamics
2.1 Hydrodynamical modeling
In coastal systems, it is the physical system that is more fundamental and which “sets the stage” for
the chemical and biological systems (James, 2002). Physical conditions, which include currents,
tides, waves, turbulence, light, temperature, salinity, bed materials and suspended particles,
determine the transport and dispersion of all suspended and dissolved material in the sea, including
contaminants and nutrients, and affect all biological activity from the transport of larvae and bacteria
and the growth of phytoplankton to the behaviour of fish. Therefore, a necessary condition for
modeling any estuary or coastal region is that the physics be properly represented. Hydrodynamical
modeling is thus considered to be a prerequisite for ecological investigations (Babu et al., 2005).
The oceans are forced by a variety of mechanisms. In addition to the periodic gravitational forces of
the moon and sun that generate the tides, the ocean surface is subject to wind stress that drives
most ocean currents. Local differences between air and sea temperatures generate heat fluxes,
evaporation, and precipitation, which in turn act as thermodynamical forcings capable of modifying
the wind-driven currents or of producing additional currents (Cushman-Roisin, 2010).
Hydrodynamical modeling of the ocean system involves solving the well-known Navier-Stokes (NS)
equations for fluid flow after incorporating additional terms that include the effects of the Earth‟s
rotation. In case of near-shore waters, as the horizontal dimensions of the ocean are much larger
compared to its depth, the flow system is treated as two-dimensional, and stratification and density
variations are neglected (Boussinesq approximation). This assumption is implemented by depth-
integrating the Navier-Stokes equations, which results in the so called „shallow water equations‟
(Haidvogel and Beckmann, 1998).
The model used for hydrodynamical simulations in this study is the MIKE 21 Flow Model. The form
of the continuity equation and the depth-averaged momentum equations in the x and y directions
used in this model is as follows (DHI, 2009b):
Continuity equation (mass conservation):
𝜕𝜂
𝜕𝑡
+
𝜕𝑝
𝜕𝑥
+
𝜕𝑞
𝜕𝑦
=
𝜕𝑑
𝜕𝑡
(1)
x-momentum equation:
𝜕𝑝
𝜕𝑡
+
𝜕
𝑝2
𝜕𝑥
+
𝜕
𝑝𝑞
𝜕𝑦
+ 𝑔
𝜕𝜂
𝜕𝑥
+
𝑔𝑝 𝑝2+𝑞2
𝐶2 2
−
1
𝜌 𝑤
𝜕 𝜏 𝑥𝑥
𝜕𝑥
+
𝜕 𝜏 𝑥𝑦
𝜕𝑦
− 𝛺𝑞 − 𝑓𝑉𝑉𝑥 +
𝜌 𝑤
𝜕𝑝 𝑎
𝜕𝑥
= 𝑆𝑖𝑥 (2)
16. 15
y-momentum equation:
𝜕𝑞
𝜕𝑡
+
𝜕
𝑞2
𝜕𝑦
+
𝜕
𝑝𝑞
𝜕𝑥
+ 𝑔
𝜕𝜂
𝜕𝑦
+
𝑔𝑞 𝑝2+𝑞2
𝐶2 2
−
1
𝜌 𝑤
𝜕 𝜏 𝑦𝑦
𝜕𝑦
+
𝜕 𝜏 𝑥𝑦
𝜕𝑥
− 𝛺𝑝 − 𝑓𝑉𝑉𝑦 +
𝜌 𝑤
𝜕𝑝 𝑎
𝜕𝑦
= 𝑆𝑖𝑦 (3)
where, p and q are the fluxes in the x and y directions respectively, h is the water depth, d is the
time-varying water depth, t is time, g is acceleration due to gravity, η is surface elevation, ρw is the
density of water, Ω is the latitude-dependent coriolis parameter, pa is the atmospheric pressure, f is
the wind friction factor, C is Chezy‟s bed resistance coefficient, 𝜏 𝑥𝑥 , 𝜏 𝑥𝑦 , 𝜏 𝑦𝑦 are the components of
effective shear stress, and Six and Siy are the source impulses in the x and y directions.
The following sections describe details of hydrodynamical simulations using the MIKE 21 flow
modeling system.
2.2 MIKE 21 flow model
MIKE 21 Flow Model is a modeling system for 2-D free surface flows developed by the Danish
Hydraulic Institute (DHI), Denmark. It is capable of simulating hydraulic and environmental
phenomena in lakes, estuaries, bays and coastal waters. It is usually used for systems, where
stratification can be neglected (DHI, 2009a).
The hydrodynamic module (MIKE 21 HD) is the basic module in the MIKE 21 Flow Model. It
simulates water level variations and flows in response to a variety of forcing functions such as tides
and winds. The HD Module can be applied to a wide range of hydraulic and related phenomena,
which include:
modelling of tidal hydraulics
wind and wave generated currents
storm surges
MIKE 21 HD is a very general hydraulic model and can be easily set up to describe specific
hydraulic phenomena. The module outputs current speed and direction, that has vital importance in
applications such as dispersion of substances, water quality management, oil spill analysis,
sediment transport, etc. Hence this module is the basis for using the other MIKE 21 Flow Model
modules, such as the Advection-Dispersion module (AD), the Sediment transport module (ST), the
Mud transport module (MT), the Particle tracking module (PA) and the Environment module (ECO
Lab).
17. 16
The numerical scheme of the HD module makes use of the Alternating Direction Implicit (ADI)
technique to integrate the equations for mass and momentum conservation in the space-time
domain. The equation matrices that result for each direction and each individual grid line are
resolved by a Double Sweep (DS) algorithm (DHI, 2009b).
2.3 Model setup
MIKE 21 HD requires the following input data for hydrodynamic simulations (DHI, 2009a).
Model domain and grid size
Time step and length of simulation
Bathymetry
Bed roughness coefficients
Momentum dispersion coefficients
Wind data and wind friction factor
Initial and Boundary conditions
2.3.1 Model domain and grid size
The MIKE 21 Flow Model is a finite difference model with constant grid spacing in the x and y
directions, i.e. a uniform rectangular or square grid is used to solve the shallow water equations.
Grids must be large enough to avoid perturbations along the boundary and small enough to allow
accurate description of the complex features like reef and channel systems.
In the areas where the flow is very complex due to the complexity in the bathymetry, high resolution
grids need to be used for a better representation of flow. The model domain should be selected in
such a way that the region of interest and the measurement locations for calibration and validation
are away from the boundaries (Vinodkumar, 2010).
The model domain extends from 70° 50‟E to 73° 03‟E and from 18° 15‟N to 19°
57‟N. The model
domain was selected in such a way that the region of interest (Mumbai coastal region) and the
measurement location for calibration and validation (Worli) are away from the boundaries. The grid
size was chosen as 500m (in both x and y directions) based on earlier works using model grids of
similar size (Sharif, 2009). The number of grid points in the x and y-directions were taken as 460
and 360, respectively. The model domain thus covers an area of about 41,400 km2
, in which the
land area is about 3900 km2
.
2.3.2 Time step and length of simulation
Time step refers to the time step used in the numerical solution of the model equations. Although
better results can be obtained reducing the time step, this often leads to large CPU running times.
Thus, a compromise between the numerical accuracy of solution and CPU running time has to be
18. 17
worked out. Another consideration is the Courant–Friedrichs–Lewy (CFL) stability criterion, which
defines the Courant number CR as:
𝐶 𝑅 = (𝑐 × ∆𝑡)/∆𝑥 (4)
where, 𝑐 = 𝑔 is the wave celerity. Here, h is the water depth at a given grid point, and g is
acceleration due to gravity.
∆t is the time step for the computation, and
∆x is the grid spacing
As the information (about water levels and fluxes) in the computational grid travels at a speed
corresponding to the celerity, the Courant number expresses how many grid points the information
moves in one time step. Normally, this measure should be close to 1. However, a Courant number
of upto 5 is usually allowable. Higher Courant numbers may be allowed for model domains in which
the bathymetry is very smooth (DHI, 2009a).
For the hydrodynamic simulations in this study, a time step of 30 seconds was eventually selected
after several trials. This corresponds to a Courant number of 1.93. These values were considered to
provide a good balance between the numerical stability, accuracy and running time of the
simulation. It should be kept in mind that the in-built criterion check uses the maximum depth in the
bathymetry to calculate the Courant number. Thus, the value of CR at other grid points is always
less than the value displayed.
It was decided to simulate hydrodynamics and study effluent dispersal patterns during periods of
contrasting met-ocean conditions. Two periods, viz. 1st
August to 31st
August, 2009 and 22nd
October to 22nd
November, 2009, were chosen for this purpose. While the former is representative
of the southwest monsoon season, the latter heralds the onset of the northeast monsoon.
2.3.3 Bathymetry
Bathymetry refers to the depth of the sea bed referred to a chosen datum. It is usually provided in
nautical charts as depth values at distinct points. These charts use the Lowest Astronomical Tide
(LAT) level as their datum, which is usually established from a long time series of water level
observations. This datum is employed because such charts are used for navigational purposes, and
knowing the minimum water depth at any point helps mariners to navigate vessels safely (DHI,
2009a). However, for hydrodynamic modeling purposes, referencing the bathymetry to Mean Sea
Level (MSL) is more useful since other input data, such as boundary tidal levels, is referenced to
Mean Sea Level. MSL is defined as the average of hourly water level measurements taken over a
time period of 18.6 years. This accounts for variability due to all possible factors. However, the
definition of MSL makes it a local datum, different for each tidal station.
19. 18
Figure 4: Interpolated bathymetry for the model domain
The bathymetry used for model simulations is presented in figure 4. Bathymetry data for the model
domain was sourced from nautical chart no. INT 7334 published by the Naval Hydrographic Office
(NHO), Dehradun. The depth values were digitised using the bathymetry editor in MIKE ZERO and
interpolated onto the model grid points using bilinear interpolation (DHI, 2009d). The Universal
Transverse Mercator (UTM) map projection for UTM Zone 43 was used for this purpose. The
bathymetry thus obtained was relative to LAT level. To reference the bathymetry to MSL, the
average of differences between LAT and MSL for the model domain was added to all grid points.
The maximum depth in the bathymetry is around 105 m and occurs in the southwest corner of the
domain, at a distance of roughly 225 km from the coast.
2.3.4 Bed roughness coefficients
The sea bed sediment is usually mobile and its roughness may impact the flow and therefore act as
a feedback between the sea floor and overlying flows. Sea bed roughness depends upon the shape
and size characteristics of sediment particles. Friction from the sea bed gains importance in shallow
waters where it can act significantly to retard the flow. In MIKE 21, the shear due to bed resistance
is implemented as (Lambkin, 2010):
𝜏 𝑏 = 𝜌𝐶𝑑 𝑈2
(5)
where, ρ is the density of water, U is the depth-averaged velocity and Cd is a drag coefficient.
20. 19
The drag coefficient Cd is specified as:
𝐶𝑑 = 𝑔/𝐶2
(6)
where, g is the acceleration due to gravity and C is the Chezy number.
Bed roughness is considered as a primary calibration variable within the HD module. The bed
roughness can be specified using either the Chezy number or Manning number. However, Manning
numbers, if specified, are converted to Chezy numbers for use in the above equation (DHI, 2009a):
𝐶 = 𝑀 ×
1
6 (7)
where, h is the water depth.
Thus, the running time of the simulation increases when Manning numbers are specified. The
Manning number as used in MIKE 21 is the reciprocal of the Manning number as understood in
hydraulics. Hence, in MIKE 21, smaller values of M (or C) imply larger bed resistance for the same
flow velocity and water depth, and vice-versa. For this study, the default value of Manning number,
M=32, was applied over the whole model domain.
2.3.5 Momentum dispersion coefficients
The finite spatial and temporal resolutions used for the numerical solution of flow dynamics result in
finer scales of motion being left unaccounted for. Examples include molecular motion and fluid
motion due to turbulence. Also, the depth-integrated Navier-Stokes equations necessarily imply
neglecting vertical velocity gradients in the case of shear flows. Since these non-resolved scales
also contribute to momentum transfer, it becomes necessary to account for them in some way to
correctly model the flow. The effective shear stresses ( 𝜏 𝑥𝑥 , 𝜏 𝑥𝑦 , 𝜏 𝑦𝑦 ) in the momentum equations
(Eqns. 2 and 3) incorporate the momentum fluxes due to turbulence, vertical integration and sub-
grid scale fluctuations. In MIKE 21 HD, these stresses are calculated using the eddy viscosity
concept (DHI, 2009a).
The eddy viscosity coefficient E can be taken as constant or can be defined using the Smagorinsky
scheme, which expresses E as a time-varying function of local gradients of depth-averaged velocity:
𝐸 = 𝐶𝑠
2
∆2 𝜕𝑢
𝜕𝑥
2
+
1
2
𝜕𝑢
𝜕𝑦
+
𝜕𝑣
𝜕𝑥
2
+
𝜕𝑣
𝜕𝑦
2
(8)
where, u and v are depth-averaged velocity components in the x and y directions respectively, ∆ is
the grid spacing and Cs, the Smagorinsky factor, is a constant to be chosen in the interval of 0.25 to
1 (DHI, 2009a). Note that E has dimensions of L2
T-1
. To avoid stability problems, the Eddy viscosity
coefficient must satisfy the following criterion:
21. 20
𝐸. ∆𝑡/∆𝑥2
≤ 1
2 (9)
In the present study, the velocity-based Smagorinsky scheme has been employed and a constant
value of Cs = 0.4 has been applied over the domain for all simulations.
2.3.6 Wind data and wind friction factor
Winds blowing over the ocean surface transfer momentum to the waters below, generating wind-
driven currents. Winds can also induce flows indirectly, by causing vertical motions of the ocean
boundary layer, a phenomenon known as Ekman pumping, which leads to vertical displacements in
the thermocline that eventually produce geostrophic currents.
Momentum transfer from the atmosphere to the ocean takes place through wind stress, which is the
horizontal force of the wind on the sea surface. Wind stress T is calculated from:
𝑇 = 𝜌 𝑎𝑖𝑟 𝐶 𝐷 𝑈10
2
(10)
where, ρ represents density, U10 is the wind speed at 10 m above the sea surface and CD is the drag
coefficient (Stewart, 2008).
The drag coefficient CD is estimated from measurements and generally increases with increasing
wind speed. However, it has been reported that values of CD stabilize and even decrease as wind
speeds approach hurricane speeds (Powell et al., 2003; Donelan et al., 2004; Moon et al., 2004).
From these studies it can be concluded that CD values upto 2.6 × 10−3
may be used for strong and
moderate ocean winds.
Zonal (u) and meridional (v) wind speeds over the domain for the periods of study were obtained
from the CERSAT database maintained by IFREMER, France (Bentamy and Croizé-Fillon, 2006).
The Blended Mean Wind Fields (MWF Blended) product was used, which is a combination of wind
fields derived from scatterometer data and ECMWF wind analyses (CERSAT, 2010). The spatial
and temporal resolutions of the gridded data are 0.25° and 6 h, respectively. The data was
subsequently interpolated onto the model grid points to generate input wind fields for the HD
module. The wind rose diagrams at Worli (72°
43‟ 35.1”E 19°
03‟ 31.6”N), which is the measurement
location used for model calibration, are presented in figures 5 and 6. Winds speeds shown are in
m/s.
From these diagrams, it can easily be seen that the predominant wind direction in the months of
August and October-November is south-westerly and north-easterly respectively, which is expected,
as these periods correspond to the SW and NE monsoon seasons.
22. 21
Figure 5: Wind rose diagram for Worli during 1 Aug to 31 Aug, 2009 (SW monsoon period)
Figure 6: Wind rose diagram for Worli during 22 Oct to 22 Nov, 2009 (NE monsoon period)
23. 22
2.3.7 Initial and boundary conditions
As the depth-integrated shallow water equations are partial differential equations, they require
specification of initial and boundary conditions for their solution. Boundary conditions specify the
values of dependant variable or its derivatives at the boundaries of the mathematical model domain.
Since MIKE 21 HD solves for surface elevations and the flux densities in x and y directions, either
water levels or fluxes have to be specified at all open boundaries. Land boundaries do not require
such specifications since no flow occurs through them. Further, since water levels near the shore
are mainly influenced by tides, these can be obtained using global or regional tidal models.
Accuracy of boundary conditions is important to ensure a consistent specification of flow properties
at the interface between the interior and the exterior of the model domain.
The boundary conditions at the north and south boundaries were specified as water levels, which
were predicted using the OSU Tidal Prediction Software (OTPS). For the points on the western
boundary, which is located far away from the shore, fluxes were calculated using geostrophic
currents obtained from AOML (Atlantic Oceanographic and Meteorological Laboratory) databases.
Specification of initial conditions requires providing the elevation of the water surface at the zeroth
time step. If differences in initial boundary surface elevations are not too large, an average value
can be computed and applied as a constant over the whole model domain. However, significant
variations in boundary levels were observed in this case and hence the initial surface elevations
were directly generated using the OTPS tidal model.
Figure 7: Plot of initial surface elevation
24. 23
Figure 7 shows the water surface elevation at the start of the simulation. Note that the northern
coastal regions in the model domain are experiencing high tide, while the southern ones are
experiencing low tide.
2.4 Model calibration, validation and simulation
2.4.1 Model calibration
Model calibration is defined as the fine tuning of model parameters until model results and field
measurements are within an acceptable tolerance. Calibration is necessary to ensure that the
model correctly reproduces actual flow conditions. Calibration is accomplished by modifying the
boundary conditions, improving the hydrometeorological forcing input and by adjusting the
calibration parameters, viz. bed resistance, wind friction factor and eddy viscosity. The relative
importance of a parameter to the calibration process depends upon the model output‟s sensitivity to
that parameter. Usually, the model output is calibrated using data on water levels and currents, as
these are easier to measure compared to other quantities like fluxes. Simulated values are
compared to measured values in order to get a good agreement between the two.
In this study, model calibration was done using measured water levels and currents off Worli (72°
43‟ 35.1” E 19° 03‟ 31.6” N). Data was available for the period from 22nd
October to 22nd
November,
2009. After evaluating several combinations of calibration parameters, it was found that a Manning
number of 32 and a wind friction factor equal to 0.0026 gave the best results. The model output was
not very sensitive to changes in eddy viscosity, and a value of 0.4 has been used in the final
simulations.
2.4.2 Model validation
Calibration is followed by a process called validation, wherein model output is compared with
measured parameter values at several locations within the domain. This provides an indication of
the model‟s sensitivity and gives confidence that the results produced fall within the desired range of
accuracy and are applicable over the model domain.
Comparison between measured and simulated water levels off Worli is presented in figure 8. It can
be seen that simulated water levels match very well with measured water levels. Figures 9 and 10
show the comparison between simulated and measured values for zonal (u) and meridional (v)
components of currents off Worli.
The simulated currents yield a good match, in general, with the measured values. The
discrepancies may be because currents measured at a specific depth do not truly represent the
depth-averaged currents which the model simulates. The significant amplitude difference in the
case of meridional current may be due to lack of information on flow directions. The model assumes
25. 24
that the flow is perpendicular or nearly perpendicular to the boundary, a condition which might not
hold true for this particular model domain.
Figure 8: Comparison between measured and simulated water levels at Worli
Figure 9: Comparison between measured and simulated u-component of currents off Worli
Figure 10: Comparison between measured and simulated v-component of currents off Worli
26. 25
2.4.3 Final simulations
The final HD simulations for the months of August and October-November were carried out using
the values of input parameters given in Table 1.
Table 1. Basic and hydrodynamical parameter values used for final simulations
Basic parameters Selection
Simulation period (SW monsoon) 1-8-2009 (00:00 h) to 31-8-2009 (00:00 h)
Simulation period (NE monsoon) 22-10-2009 (00:00 h) to 22-11-2009 (18:00 h)
Time step and Max. Courant No. 30 s, 1.93
Bathymetry Digitized from NHO Nautical Chart INT 7334
Coriolis forcing option Applied, as domain lies away from the equator
Flooding and Drying depths 0.1m and 0.2m, respectively
Hydrodynamic parameters Selection
Water levels OSU Tidal Prediction Software
Fluxes (geostrophic currents) AOML Databases
Bed Resistance 32 (Manning number)
Eddy Viscosity 0.4
Wind Used ECMWF Blended MWF
Wind friction factor 0.0026
27. 26
3 . BOD-DO modeling of wastewater outfalls
3.1 Importance of dissolved oxygen
Dissolved oxygen refers to molecular oxygen present in the dissolved state in water. The
concentration of dissolved oxygen is a critical attribute of aquatic ecosystems, as it determines the
suitability of natural waters for many types of organisms. Dissolved oxygen is vital, because it is
required for respiration and cellular metabolism. Sufficient DO levels in natural water bodies are
thus necessary for sustenance of aquatic and marine communities and for preserving the health of
the ecological system.
The principal inputs affecting the DO levels of aquatic systems are municipal sewage and certain
industrial waste discharges. Dissolved oxygen depletion basically begins with the input of oxygen
demanding wastes into a water body. If oxygen is consumed at a rate that exceeds the
replenishment rate of DO from the atmosphere or from photosynthesis, the DO concentration can
decrease to less than a few mg per litre, leading to anaerobic conditions. Fish mortality, unpleasant
odours and other aesthetic nuisances are the common symptoms of low DO concentrations
(Thomann, 1987). Another important aspect of sewage disposal in natural waters is the
phenomenon of Eutrophication. Municipal sewage contains a high amount of nutrients which can
lead to excess growth of algae, which would in turn further deplete the DO levels in the water body.
Therefore, reducing the severity of oxygen depletion in the vicinity of pollutant discharge points,
such as sewage outfalls, is a major concern.
For modeling the dissolved oxygen in an natural system, the quantity and strength (in terms of
BOD) of discharged effluents has to be considered. In addition, internal sinks of DO, which
continuously remove a part of the dissolved oxygen, must also be included. These comprise of the
oxygen demand due to respiration processes and the benthic oxygen demand which originates from
the sediment bed (the benthic zone). One also has to take into account oxygen replenishment,
which takes place concurrently through the processes of reaeration and photosynthesis. Further, in
case of highly dynamic flow systems like the oceans, advection and dispersion processes play a
major role in reducing the impact of sewage on dissolved oxygen, by ensuring the effective
dispersal of discharged effluents. All these processes are now discussed in greater detail in the
following sections.
3.2 Effluent dispersal processes
Effluent dispersal occurs due to advection and dispersion. Advection refers to the transport of a
dissolved or suspended substance due to the bulk motion of the fluid medium. Dispersion is a
general term which refers to the scattering of fluid particles due to both random processes like
28. 27
molecular and turbulent diffusion, and due to the effects of velocity gradients. Advection is the main
phenomenon responsible for spreading of pollutant in rivers and coastal waters. In a given amount
of time, the distances over which mass is carried by dispersive transport are usually not as great as
those covered by advection (Hemond and Fechner-Levy, 1999).
In advection, the chemical is transported at the same velocity as the fluid, by which it is meant that
the center of mass of the chemical moves by advection at the average fluid velocity. Flux density
due to advection (Ja) is equal to the product of a chemical‟s concentration in the fluid (C) and the
velocity (V) of the fluid:
𝐽𝑎 = 𝐶𝑉 (11)
Flux density is the mass of chemical transported across an imaginary surface of unit area per unit of
time.
Turbulent fluid motions contain constantly changing swirls of fluid, known as eddies, of many
different sizes. Turbulent diffusion arises from the random mixing of the air or water by these
eddies. This type of motion neither augments nor impedes the advective motion of a chemical
(Hemond and Fechner-Levy, 1999). Turbulent diffusion has the net effect of carrying mass in the
direction of decreasing chemical concentration. Fick‟s first law is typically used to describe the flux
density of mass transport by turbulent diffusion (Jt):
𝐽𝑡 = −𝐷(𝑑𝐶/𝑑𝑥) (12)
for one dimension. Here, D is called the turbulent (or eddy) diffusion coefficient. Its value varies
greatly, depending upon the intensity of fluid turbulence. D can not only be anisotropic, but may also
vary with time and location.
Even if a fluid is entirely stationary and without obstructions, chemicals will still move from regions of
higher concentration to regions of lower concentration, due to the ceaseless random movement of
molecules. Mixing resulting due to this process is called molecular diffusion. Flux density due to
molecular diffusion is also described by Fick‟s first law and D in this case is called the molecular
diffusion coefficient. Unlike the turbulent diffusion coefficient, molecular diffusion coefficients can be
estimated without reference to a particular situation, because they depend primarily on the size of
the molecules that are diffusing. At environmental temperatures, molecular diffusion coefficients in
water for most chemicals are of the order of 10-9
m2
/s (Hemond and Fechner-Levy, 1999). Molecular
diffusion increases in magnitude at higher temperatures and for chemicals with smaller size
molecules or particles.
Dispersion also includes the spreading caused by velocity shear which arises due to velocity
gradients within the flow. This phenomenon is known as the shear effect and flows with velocity
29. 28
gradients are often referred to as shear flows. When approximating three-dimensional flows as two-
dimensional, the depth integration filters out the vertical velocity profiles which are responsible for
additional spreading in the direction of flow. This effect is accounted for by including a „shear
viscosity‟ coefficient in the overall dispersion coefficient. For the large scales usually considered in
surface water quality modeling, molecular and turbulent mixing effects are practically negligible in
comparison to mixing due to the shear effect (DHI, 2009c).
At this point, it is important to note that diffusion and other processes are actually advective
transport processes at their own length scales. However, since the spatial resolution of the model
grid is much greater than these length scales, such advective processes are not resolved by the
model. It is because of this that their contribution to chemical mixing has to be accounted for using
Fick‟s law. Continuing further, it follows that as the grid size is increased, higher and higher length
scales would count as non-resolved and would thus require inclusion in the dispersion coefficients.
Thus, as ∆x increases, the dispersion coefficients should also increase. It thus becomes natural to
relate them in some way to ∆x and ∆t, the spatial and temporal resolutions of the flow model. This
can be done using several possible forms, such as k.(∆x2
/t), k.(∆x.u) and k.(∆t.u2
), where u is the
depth-integrated current velocity and k is a dimensionless constant. However, the scale above
which such relationships can be assumed to hold true must first be known. It has been found that
this lower limit occurs when ∆x is approximately equal to h. At this scale, the largest non-resolved
motions are due to the shear effect (DHI, 2009c).
The advection-dispersion equation used by the AD module in MIKE 21 is described below. This is
the equation for advective-dispersive transport of dissolved or suspended substances in two
dimensions.
𝜕
𝜕𝑡
(𝑐) +
𝜕
𝜕𝑥
(𝑢𝑐) +
𝜕
𝜕𝑦
(𝑣𝑐) =
𝜕
𝜕𝑥
𝐷𝑥
𝜕𝑐
𝜕𝑥
+
𝜕
𝜕𝑦
𝐷𝑦
𝜕𝑐
𝜕𝑦
− 𝐹. . 𝑐 + 𝑆 13)
Here, h is the water depth, u and v are current velocities in the x and y directions, respectively, c is
concentration of the substance under investigation, Dx and Dy are the dispersion coefficients in the x
and y directions, respectively, F is a linear decay coefficient for non-conservative substances, and S
is given by:
𝑆 = 𝑄𝑠 × 𝑐𝑠 − 𝑐 (14)
where, Qs and cs are the source(sink) discharge rate and chemical concentration, respectively.
30. 29
3.3 Processes affecting DO levels
3.3.1 Reaeration
Reaeration is the process describing the exchange of oxygen between the water and the
atmosphere. The concentration of oxygen (or any gas or volatile substance) in surface water that is
equilibrium with the atmosphere above it, is given by Henry‟s law as:
𝐶𝑒𝑞 = 𝐶𝑎𝑖𝑟 /𝐻 (15)
where, Cair is the concentration of oxygen in air (usually expressed as a partial pressure), and H is
the Henry‟s law constant of oxygen. If the concentration in water (Cw) differs from Ceq, exchange of
oxygen between air and water takes place. The flux density of this exchange is directly proportional
to the difference between Cw and Ceq:
𝐽 = −𝑘 𝑤 𝐶 𝑤 − 𝐶𝑒𝑞 (16)
where, J is the flux density and kw is the gas exchange coefficient or reaeration rate. kw depends
upon the nature of the water flow and air movement above the water. Ceq is also known as the
saturation concentration and it depends upon the salinity and temperature of water.
3.3.2 Photosynthesis and respiration
All aquatic plant forms including attached and floating aquatic weeds, algae and phytoplankton
generate oxygen through photosynthesis. Photosynthesis can result in the supersaturation of water
with oxygen, and DO levels as high as 150 to 200% are not uncommon (Thomann, 1987). The
photosynthesis reaction can be represented as:
6CO2 + 6H2O → C6H12O6 + 6O2 (17)
Because photosynthesis is dependent on sunlight, the production of DO through photosynthesis
occurs only during daylight. DO levels in natural waters show a diurnal variation, with minima at pre-
dawn and maxima at afternoon. Apart from solar intensity, the rate of photosynthesis depends upon
the depth at which photosynthesis takes place and on the availability of nutrients. Photosynthetic
rates can be estimated through several methods, one of which involves relating primary productivity
to observed chlorophyll-a levels (Benrenfeld and Falkowski, 1997).
Concurrently with photosynthetic DO production, aquatic plants and other aquatic life forms also
consume oxygen during respiration. Net O2 production is equivalent to the gross O2 production
minus the oxygen consumed by autotrophic and heterotrophic respiration (Dickson et al., 2001).
31. 30
3.3.3 BOD exertion
The oxygen demand exerted by effluents is generally classified according to the nature of the
compounds that give rise to such demand. Biochemical oxygen demand or BOD is a measure of the
amount of oxygen required to completely oxidize all dissolved and suspended organic matter
present in a volume of water. BOD is thus an indirect measure of the organic content of water. BOD
is further differentiated as Carbonaceous BOD (CBOD) and Nitrogenous BOD (NBOD), based on
whether it originates from the presence of carbonaceous matter or nitrogenous matter (Thomann,
1987). CBOD is exerted by heterotrophic organisms capable of deriving energy by oxidizing organic
carbon substrates to CO2 and H2O. As an example, the aerobic oxidation of glucose (C6H12O6) is
presented below:
C6H1206 + 6O2 → 6CO2 + 6H2O (18)
NBOD exertion results from the oxidation of ammonia present in water to nitrite and then to nitrate
nitrogen. Nitrifying bacteria break down proteins, amino acids, urea and other nitrogenous
compounds present in sewage into simpler compounds like ammonia. This process, known as
deamination, is followed by nitrification, in which ammonia is oxidized to nitrate.
NH4 + 1.5 O2 → 2H+
+ H2O + NO2
−
(19)
NO2
−
+ 0.5 O2 → NO3
−
(20)
The BOD exertion phenomenon shows a lag phase, followed by a rising curve terminating in a
plateau, yielding an ultimate carbonaceous BOD (Swamee and Ojha, 1991). For substrates rich in
nitrogenous compounds, there is a further increase in the curve, which saturates at the second
stage ultimate BOD value (Figure 11). Nitrogenous BOD has not been considered in this study.
Figure 11: BOD exertion curve (schematic)
32. 31
In simplistic models of BOD exertion, like the Streeter-Phelps model (Metcalf and Eddy, 1991), BOD
is assumed to decay at a first order rate:
𝑑
𝑑𝑡
𝐵𝑂𝐷 = −𝑘 𝐵𝑂𝐷 × 𝐵𝑂𝐷 (21)
kBOD is typically of the order of 0.2/day (Hemond and Fechner-Levy, 1999), and depends upon
temperature and the concentration of dissolved oxygen remaining in the water.
3.3.4 SOD exertion
Sediment oxygen demand (SOD) or Benthic oxygen demand arises due to sediment organic
material which requires oxygen for stabilization. Dead rooted aquatic plants and settled
phytoplankton may constitute such benthic organic matter. SOD may also be due to settled sludge
banks below a waste outfall. These deposits may build up over time and remove oxygen from the
overlying water. The oxygen utilization therefore depends on the extent of organic material and the
nature of the benthic community. Estimates of SOD range from 0.07 gO2/m2
/day for mineral soils to
10 gO2/m2
/day for municipal sewage sludge in the vicinity of an outfall (Thomann, 1987). The rate
of SOD exertion depends upon temperature, DO levels in water, and the depth of the deposit in the
case of sewage sludge deposition.
3.4 Model setup
3.4.1 ECO lab
BOD-DO modeling has been carried out using the ECO Lab module in the MIKE 21 Flow Model.
ECO Lab is a numerical lab for ecological modelling. It is an open and generic tool for customizing
aquatic ecosystem models to describe water quality, eutrophication, heavy metals and ecology
(DHI, 2009e). The module can describe chemical, biological, ecological processes and interactions
between state variables, and physical processes, such as the sedimentation of various components.
Apart from BOD and DO, other variables which ECO Lab can model include ammonia, nitrite,
nitrate, phosphorus, fecal and total coliforms, and one or more user-defined pollutants. As ECO Lab
is integrated with the Advection-Dispersion (AD) module in MIKE 21, the physical transport of state
variables due to advection-dispersion processes can be described, based on the hydrodynamics of
the system being modelled (DHI, 2009f).
In ECO Lab, one can choose from several pre-defined templates, which contain mathematical
descriptions of various ecosystems. These can be modified to suit user requirements. It is also
possible to develop custom templates using in-built constants and functions (DHI, 2009e).
Apart from the data required to run the HD module, ECO lab requires additional data in order to
correctly simulate the processes in the template used. Initial and boundary conditions for the state
33. 32
variables being modelled have to be provided. Also needed are estimates of the values of the
coefficients governing various process rates. As the AD module is integrated with ECO Lab,
dispersion coefficients for each modelled component have to be specified. Additional forcings such
as salinity and temperature have to be specified over the model domain. Finally, if any sources and
sinks are included, component concentrations for these have to be specified.
3.4.2 Wastewater disposal scenario and outfall parameter values
As mentioned before, a single outfall at Worli has been considered for this study. Outfall parameters
relevant to model input have been taken from NEERI, 1995. Discharge rates vary widely, ranging
from 4m3
/s in the dry season to 24 m3
/s during rainy seasons. Outfall parameters are summarized in
Table 2 below.
Table 2. Outfall parameters
Outfall location and position in model domain Worli (406, 163)
Length of outfall 3.5 kms
Alignment (direction of discharge) 290o
(clockwise from North)
Discharge rates 10 m3
/s, 15 m3
/s
Discharge velocity 1 m/s
The outfall is located 3.5 km away from Worli at a point where the water depth is 8.5 m. Through
this outfall, BOD is introduced into the model continuously, starting from the first time step.
Simulation of BOD and DO has been carried out for two different discharge cases:
Case 1: Effluent BOD is 40 mg/L and the outfall discharge rate is 10 m3
/s.
Case 2: Effluent BOD is 50 mg/L and the outfall discharge rate is 15 m3
/s.
The BOD throughout the model domain has been initialized to a very small value (10-6
mg/L). This
has been done to separate BOD dispersal patterns around the outfall from the decreasing trend in
background BOD (found in trial runs that high background BOD values decayed rapidly to zero). To
distinguish water from land, the initial BOD value was kept positive, since the model takes BOD on
land points to be equal to zero.
Dissolved Oxygen was initialized to a value of 6 mg/L throughout the model domain. This value was
chosen within the range of saturation oxygen concentrations, considering the variations in surface
temperature and salinity of water.
Temperature forcing was given as a time-varying input. Data on sea-surface temperature (SST) for
both periods of study was obtained from the Multi-sensor Improved Sea Surface Temperatures
34. 33
(MISST) for the Global Ocean Data Assimilation Experiment (GODAE) database (MISST, 2010).
The original SST data with a resolution of 0.088° was interpolated to the model grid following the
same procedure as for the wind data. Salinity was taken to be constant over the whole domain, with
a value equal to 35.2 psu (practical salinity unit).
Dispersion coefficients for the AD module were chosen following the guidelines given in the
scientific documentation for the MIKE 21 AD Module (DHI, 2009c). As the grid spacing (∆x = ∆y =
500m) in this case is much greater than the range of depth values observed in the model domain
(10 to 100 m), it was decided to specify the dispersion coefficients as k∆xu, where k is a constant in
the range 0.01-0.2 and u is the current velocity (DHI, 2009c). Since data for calibrating these
coefficients was unavailable, the value of k has been taken as 0.1.
3.4.3 Description of chosen template and process rate estimates
The ECO Lab template „WQsimple‟ has been chosen for the purposes of this study. This allows
modeling of Biochemical oxygen demand (BOD) and Dissolved Oxygen (DO) in natural waters.
Three sinks, namely BOD, SOD and respiration, and two sources, namely photosynthesis and
reaeration, of dissolved oxygen are included in this template. The following expressions describe
the rate of change of BOD and DO, due to the combined action of included sinks and sources:
d
dt
(BOD) = −bodd (22)
d
dt
(DO) = reaera + phtsyn − respT − bodd − sod (23)
The mathematical formulations of the processes included in these equations, as given in the
WQsimple template, are described below:
Reaeration
reaera =
k2 Cs − DO ; for DO > 0
k2Cs ; for DO < 0
(24)
Here, Cs represents the saturation concentration of oxygen at the given temperature and salinity,
DO represents dissolved oxygen variable and k2 is the reaearation constant. An expression for k2 is
included, which is as follows:
k2 = 3.93Vsp
0.5
/dz0.5
+ 0.728Wsp
0.5
− 0.371Wsp + 0.0372Wsp
2
/dz (25)
Here, Wsp represents the wind speed, Vsp the current speed, and dz the depth of the layer, which in
this case is equal to the water depth, as there is only one vertical layer in the model.
35. 34
Photosynthesis
The photosynthetic oxygen production is described by:
phtsyn =
Lambert_Beer1 Pmax ., dz, 2.3
SD ×
suninp
depth ; if SD > 0
0 ; if SD < 0
(26)
Here, SD refers to Secchi disk depth, depth refers to water depth, Pmax refers to maximum primary
production at noon. „Lambert_Beer1‟ and „suninp‟ are functions which are defined below.
Lambert_Beer1 Pmax , dz, 2.3
SD = Pmax × e−dz× 2.3
SD (27)
The above function returns the light intensity at the top of a layer, given the light intensity at the top
of the overlying layer. Secchi disk depth has been taken as a constant, with a value equal to 10m
(Suresh et al., 2006).
suninp =
cos
2πt
24
α
0 ; during night
; during day (28)
where, t is relative daytime in hours. „suninp‟ varies the light intensity returned by „Lambert_Beer1‟
according to the hour of the day. The primary productivity value for the Arabian sea has been taken
as 1.7 gO2/m2
/day (Babu et al., 2006). Dickson et al. (2001) have reported remarkable similarity in
production rates in the Arabian sea during the southwest and northeast monsoon seasons.
Respiration
respT = resp × θ t−20
×
DO
DO+mdo
×
1
depth
(29)
Here, resp is the respiration rate of plants, t is temperature in degree Celsius and θ is the Arrhenius
temperature coefficient for respiration rate. „mdo‟ is the half-saturation concentration of oxygen for
respiration. It is the DO level at which the respiration rate becomes equal to half its maximum value.
The respiration rate, „resp‟, has been assumed to be 25% of the primary productivity value (Babu et
al., 2006).
36. 35
BOD decay
bodd = k3 × θ t−20
× BOD ×
DO
DO +hdobod
(30)
Here, k3 is the BOD decay rate, t is temperature in degrees Celsius, θ is the Arrhenius temperature
coefficient which describes the temperature dependency of k3, and hdobod is the half-saturation
oxygen concentration for BOD. It is the DO level at which the BOD exertion rate becomes equal to
half its maximum value. k3 has been taken equal to 1/day, based on values given the literature for
the Mumbai coastal region (Gupta et al., 2006).
Sediment Oxygen Demand (SOD)
The rate of oxygen consumption due to sediment oxygen demand is given by:
sod = B1sed × θ t−20
×
DO
DO +mdosed
× 1/dz (31)
Here, B1sed is the Sediment oxygen demand, t is temperature in degrees Celsius, θ is the
Arrhenius temperature coefficient, dz is the water depth and mdosed is the half-saturation oxygen
concentration for SOD. It is the DO level at which the SOD exertion rate becomes equal to half its
maximum value. B1sed has been taken equal to the default value of 0.5g/m2
/day.
3.5 Final simulations
For the final simulations, the HD time step was doubled to 60 s to reduce the total computational
time of the simulations. This gave a maximum Courant number of 3.86, well within the guideline
value (CR=5) prescribed by the HD reference manual (DHI, 2009a). The update frequency for the
ECO lab module was chosen equal to 5 AD time steps. Results were written to the output file every
360 time steps, i.e. BOD and DO outputs were obtained at 6-hourly intervals. The period of
simulations was reduced to 15 days, from the originally planned 30 days, in order to further reduce
the total computational time of the simulations.
Table 3 summarizes the values of ECO lab process constants used for the final simulations.
Table 3. ECO lab process constants
Parameter Value Units
ECO Lab template WQsimple.ecolab -
First order decay rate for BOD 1 day-1
Temperature coeff. for BOD decay 1.07 Dimensionless
Half-saturation O2 conc. for BOD 2 mg/L
37. 36
Max. O2 production at noon 1.7 gO2/m2
/day
Secchi disk depth 10 M
Time correction for noon 0 Hours
Respiration rate for plants 0.425 gO2/m2
/day
Temperature coeff. for respiration rate 1.08 Dimensionless
Half-saturation O2 conc. for respiration 2 mg/L
Sediment oxygen demand 0.5 gO2/m2
/day
Temperature coeff. for SOD exertion 1.07 Dimensionless
Half-saturation O2 conc. for SOD 2 mg/L
38. 37
4. Results and discussion
4.1 Southwest monsoon season
As mentioned before, model runs were carried out for two discharge cases. BOD maximum and DO
minimum obtained at the outfall for both the cases are given in Table 4. Figures 12a and b show
the variation of BOD and DO at the outfall location in both discharge cases.
(a)
(b)
Figure 12: Variation of (a) BOD and (b) DO at the outfall location during the SW monsoon
39. 38
Table 4. BOD maximum and DO minimum at outfall location during SW monsoon
BOD maximum (mg/L)
(initial BOD ≈ 0 (10-6
mg/L))
DO minimum (mg/L)
(initial DO = 6 mg/L)
Discharge case 1 0.43 5.55
Discharge case 2 0.81 5.38
It can be seen that BOD and DO values oscillate in phase with the tidal variations. For an outfall
discharge rate of 10 m3
/s and effluent BOD of 40 mg/l (Case 1), BOD at the outfall increases upto
0.43 mg/L from the initial level of 10-6
mg/L. When BOD loading is increased to 50mg/L, at a
discharge rate of 15 m3
/s (Case 2), BOD levels at the outfall also show a corresponding increase,
reaching upto 0.81 mg/L. The drop in DO level is also more for the second case (0.62 mg/L) when
compared to that for the first case (0.45 mg/L).
The spread and concentration of BOD around the outfall for both cases after 72 hrs of discharge are
shown in Figures 13a and b. A plume of higher BOD value is seen to develop along the southwest-
northeast direction, parallel to the coast.
For case 1, approximately 50 km2
area around the outfall has a BOD value greater than 0.05 mg/L.
For case 2, the same area increases to more than 120 km2
. Higher values of BOD near the outfall
for case 2 can also be clearly seen from these figures.
(a)
40. 39
(b)
Figure 13: BOD distribution after 72 hours of discharge for (a) case 1 (b) case 2
Plume pattern is found to vary in phase with tidal variations. Figures 15a and b show the BOD
plume (for the case 2 scenario) during typical flood and ebb tides in the SW monsoon, along with
the corresponding current patterns. During flood tide, the currents are alongshore and moving
northwards, whereas during ebb tide they are seen to be moving southwards. One can see a clear
change in the shape and direction of the plume during the two phases of the tide.
Figure 14 shows the relative magnitudes of the physical and ecological processes contributing to
the dissolved oxygen balance in water that have been considered by the model. Degradation of
Figure 14: Relative magnitudes of processes
41. 40
(a) (b)
Figure 15: Tidal variations in plume pattern: (a) flood tide (b) ebb tide
BOD from the sewage outfall consumes dissolved oxygen at the fastest rate, followed by aquatic
respiration and benthic (sediment) oxygen demand. The curve for BOD degradation mirrors the
curve for BOD (Figure 12a) since the rate of BOD decay is directly proportional to the amount of
biochemical oxygen demand present (Eqns. 21, 22 and 30). Replenishment of dissolved oxygen
takes place mostly through phytoplankton photosynthesis, as reaeration contributes little to this side
of the DO balance. Photosynthesis however, occurs only during daytime, and moreover, peaks only
at noon (12:00 h), as can be made out from the curve for photosynthesis rate. This explains why DO
values at the outfall exhibit a continuous decrease (Figure 12b) even though two inputs of DO are
present.
4.2 Northeast monsoon season
Figures 16a and b show the comparison between BOD and DO levels at the outfall location during
the two study periods under consideration. The curves are based on the results for discharge case
2 (effluent BOD load=50mg/L and outfall discharge rate=15 m3
/s). The x-axis represents the time
elapsed in days since the starting of the simulation and outfall BOD loading. The BOD level appears
to be higher for the October-November NE monsoon period, but this difference may be attributed to
42. 41
the difference in tidal phase between the starting points of the two periods. Dissolved oxygen levels
though, do show a significant difference, with DO at the outfall being considerably higher for many
(a)
(b)
Figure 16: Comparison between (a) BOD and (b) DO levels at the outfall during the two study
periods, viz. SW monsoon (Aug) and NE monsoon (Oct-Nov) seasons
days in case of the SW monsoon period. However, outfall DO levels become almost equal after 14
days of continuous discharge in both periods, and thereafter DO level during the SW monsoon is
seen to fall below that for the NE monsoon period.
0.00E+00
1.00E-01
2.00E-01
3.00E-01
4.00E-01
5.00E-01
6.00E-01
7.00E-01
8.00E-01
9.00E-01
0 2 4 6 8 10 12 14 16
BOD(mg/L)
Days elapsed since t=0
Aug_BOD
Oct_BOD
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
0 2 4 6 8 10 12 14 16
DO(mg/L)
Days elapsed since t=0
Aug_DO
Oct_DO
43. 42
Table 5 presents the maximum BOD and minimum DO obtained at the outfall during the NE
monsoon period, for both discharge cases. It can again be seen that increasing the effluent BOD
load and outfall discharge rate increases the BOD level and decreases the DO level at the outfall. A
comparison with corresponding values for the SW monsoon (Table 4) yields no significant
difference in values. BOD maximum and DO minimum values are nearly equal in both the seasons.
Table 5. BOD maximum and DO minimum at outfall location during NE monsoon
BOD maximum
(initial BOD ≈ 0 (10-6
mg/L))
DO minimum
(Initial DO=6 mg/L)
Discharge case 1 0.43 5.55
Discharge case 2 0.80 5.39
This lack of variability can be explained by the fact that the currents along the west coast of India
are primarily tide-driven during the northeast monsoon season (Tomczak and Godfrey, 1994).
Winds have a negligible impact upon the flow dynamics off the Mumbai coast during this period
(Vinodkumar, 2010). Tidal forcings play a major role and the hydrodynamics of the study region is
influenced mainly by them.
44. 43
5. Summary and conclusion
This study examines the water quality around an existing marine outfall located off the Mumbai
coast near Worli, Mumbai. The hydrodynamics of the Mumbai coastal region is simulated first, since
this is a prerequisite to the water quality investigation. Results obtained using the Hydrodynamic
(HD) module of the MIKE 21 Flow Model matched very well with measurements. Hence, the MIKE
21 model was further used along with its in-built ECO Lab module, for simulating Biochemical
Oxygen Demand (BOD) and Dissolved Oxygen (DO) concentrations around the above mentioned
outfall. Simulations were carried out for two periods, viz. the southwest monsoon season and the
northeast monsoon season, as these are known to display contrasting met-ocean conditions.
Further, two outfall discharge cases were considered, with a higher BOD loading and outfall
discharge rate being provided in the second case.
The study found no significant difference in maximum BOD values and minimum DO values at the
outfall during the two periods under investigation. However, as expected, values of these statistics
were seen to increase appreciably in discharge case 2, i.e. upon increasing the BOD input to the
coastal waters. A plume of higher BOD was found to develop in a direction parallel to the coast at
Worli. The plume pattern showed a periodic directional change, which was in phase with the tidal
reversal of off-shore currents.
This study has provided a rough estimate of the level of BOD increase and DO depletion that can
be expected to occur in ocean waters off the Mumbai coast during the operation of a single outfall. It
has also helped in visualizing and understanding the formation of the effluent plume pattern, and its
shifting with tidal reversals in coastal currents. This work can now be taken further to develop an
understanding of near-shore water quality for actual field conditions, where usually several
wastewater outfalls, with different effluent loadings and discharge rates, operate simultaneously.
45. 44
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