Content uploaded by Kagan Cebe
Author content
All content in this area was uploaded by Kagan Cebe on Jun 14, 2019
Content may be subject to copyright.
Applied Mathematical Modelling 40 (2016) 1887–1913
Contents lists available at ScienceDirect
Applied Mathematical Modelling
journal homepage: www.elsevier.com/locate/apm
Water quality modelling in ka ¸sbay
Ka˘
gan Cebe, Lale Balas∗
Civil Engineering Department, Engineering Faculty, Gazi University, Ankara, Turkey
article info
Article history:
Received 14 October 2014
Revised 9 June 2015
Accepted 23 September 2015
Availableonline5October2015
Keywo rds:
Water quality
Ecological model
Phytoplankton
Zooplankton
Pelagic bacteria
abstract
In this study, the physical and chemical parameters at 0.5 m and 10 m water depth (e.g. tem-
perature, salinity, density, pH, concentration of dissolved oxygen DO, nitrite NO2−,nitrate
NO3−turbidity, alkalinity and total dissolved solid TDS) have been monitored by monthly
field and laboratory measurements for 6 months in Ka¸s Bay, Eastern Mediterranean. The mea-
surements for nitrite, nitrate and dissolved oxygen concentrations were compared with the
output of the zero dimensional water quality model. The model is a sub model of HYDROTAM-
3D, which is an implicit baroclinic three dimensional model developed to simulate the wind
driven circulations, hydrodynamics and basic water quality parameters in coastal waters. The
numerical model has hydrodynamic, transport, turbulence as well as water quality compo-
nents. The water quality component is based on a marine ecological submodel, aiming to sim-
ulate marine ecosystems. By using the general conservation equations, the nitrogen, phospho-
rus and the oxygen cycles were simulated in the ecological submodel as well as the dominant
aquatic life forms, namely phytoplankton, zooplankton and the pelagic bacteria. In this paper,
the model structure and the methods used by HYDROTAM-3D to simulate water quality pa-
rameters are presented togetherwith a comparison of the model results and field observations
in Ka ¸sBay.
© 2015 Elsevier Inc. All rights reserved.
1. Introduction
The ecosystems in coastal waters, especially in enclosed or semi-enclosed waters rely upon the complex interaction between
the chemical and physical environment and the organisms that live inside this environment. These ecosystems have very com-
plicated dynamics since the presence of the spatial and seasonal variability of affecting parameters within the water body. It is
possible to define the ambient conditions by using the basic water quality parameters.
The water quality component of HYDROTAM-3D predicts the water quality parameters by using the formulations representing
physical and biochemical mechanisms that also determine the position and momentum of contaminants in a water body and
thus imitate the complex interrelations between the water quality parameters and the ecosystem.
Most of the marine ecological models aim to simulate the biological and chemical processes in marine environment to predict
water quality parameters. Since the early marine ecosystem models, ecological processes are represented as a series of formulas
driven from data assembled from field observations [2,10,12,15].
Several models are developed using a dynamic compartment modeling program for surface aquatic systems to investigate 1, 2,
and 3 dimensional systems like WASP5 [1] and QUAL2K [11].CORMIX[16] uses hydrodynamic mixing zone concept to investigate
the environmental impact of wastewater discharge from point sources. Models like Mohid use a zero-dimensional water-quality
∗Corresponding author. Tel.: +903125823217.
E-mail addresses: kcebe@nevsehir.edu.tr (K. Cebe), lalebal@gazi.edu.tr (L. Balas).
http://dx.doi.org/10.1016/j.apm.2015.09.037
S0307-904X(15)00571-5/© 2015 Elsevier Inc. All rights reserved.
1888 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
model integrated into three-dimensional water modeling system to simulate marine ecology by means of basic water quality
parameters [21].
HYDROTAM-3D, is a three-dimensional, baroclinic numerical model developed to simulate the water quality parameters as
well as the circulation and transport mechanisms in coastal waters. The model is calibrated and tested by field experiments for
over 15 years. HYDROTAM-3D has been applied successfully to Gulf of Fethiye, Gulf of ˙
Izmir, Göksu Lagoon, Gulf of Marmaris,
GulfofBodrum,GulfofÖlüdeniz,GulfofMersin,Gulfof ˙
Iskenderun, Gulf of ˙
Izmit, Gulf of Antalya, Gulf of Gökova [3,6–8,20,23].
Water quality component of HYDROTAM-3D has been developed since 2011 by a PhD research study and it has been tested and
calibrated through the field observations in Fethiye Bay and in Ka ¸s Bay along the Mediterranean coast of Turkey.
The water quality component of HYDROTAM-3D is based on fundamental biological and chemical cycles of the organic matter
and their relationships with the lower trophic levels in marine environment. In this study, the main theoretical background
will be presented and the comparison of the results of the model applied to Ka¸s Bay, Antalya will be compared with the field
measurements.
2. Method
The major forces affecting the flow mechanism in coastal waters are the gravity, the tide producing forces due to the Sun and
the Moon, the stress of the wind acting on the sea surface, the Coriolis force, the pressure gradient force and the viscous stresses.
Changes under climatic conditions influence the movement of surface waters directly by the action of wind stress exerted on
the water surface and indirectly by generating gravitational circulation induced by variations in water density resulting from
differences in temperature and salinity.
2.1. Governing equations
The numerical model has hydrodynamic, transport, turbulence and water quality components. In the hydrodynamic model
component, the Navier–Stokes equations are solved with Bussinesq approximation. In the transport model component, three-
dimensional convective diffusion equations to simulate pollutant, temperature and salinity transports in water are solved. In
the turbulence model component, k-εformulation is solved to calculate the kinetic energy of the turbulence and its rate of
dissipation which is the measure of the vertical turbulent eddy viscosity. Smagorinsky Algebraic Subgrid Scale Turbulence Model
is used to simulate the horizontal eddy viscosity. The water quality component is affected by the key environmental forces such
as currents, transport mechanism, temperature, solar radiation, wind speed and light intensity on the water surface.
The governing model equations in the three-dimensional Cartesian coordinate system are as follows [4,5]:
Continuity equation:
∂u
∂x+∂v
∂y+∂w
∂z=0.(1)
Momentum equations in horizontal directions (x–y):
∂u
∂t+u∂u
∂x+v∂u
∂y+w∂u
∂z=fv−1
ρ0
∂p
∂x+2∂
∂xvx
∂u
∂x+∂
∂yvy∂u
∂y+∂v
∂x+∂
∂zvz∂u
∂z+∂w
∂x.(2)
∂v
∂t+u∂v
∂x+v∂v
∂y+w∂v
∂z=−fu−1
ρ0
∂p
∂y+∂
∂xvx∂v
∂x+∂u
∂y+2∂
∂yvy
∂v
∂y+∂
∂zvz∂v
∂z+∂w
∂y.(3)
Momentum equation in vertical direction:
∂w
∂t+u∂w
∂x+v∂w
∂y+w∂w
∂z=− 1
ρ0
∂p
∂z+gz +∂
∂xvx∂w
∂x+∂u
∂z+∂
∂yvy∂w
∂y+∂v
∂z+2∂
∂zvz
∂w
∂z,(4)
where x,y are the horizontal coordinates; zis the vertical coordinate,tis time, u, v, w are the velocity components in x, y, z
directions at any grid locations in space, νx,νy,νzare the Eddy viscosity coefficients in x, y and zdirections respectively, fis the
Coriolis coefficient, ρ(x,y,z,t) is the in situ water density, ρois the reference density, gis the gravitational acceleration and pis
pressure.
The conservation equation for a pollutant constituent is [4,5]:
∂C
∂t+u∂C
∂x+v∂C
∂y+w∂C
∂z=∂
∂xDx
∂C
∂x+∂
∂xDy
∂C
∂y+∂
∂zDz
∂C
∂z−kpC,(5)
where Cis the pollutant concentration, kp is the decay rate of the pollutant, Dx,D
yand Dz: are the turbulent diffusion coefficient
in x,yand zdirections respectively.
In turbulence model component, k-εformulation is solved to calculate the kinetic energy of the turbulence and its rate of
dissipation which is the measure of the vertical turbulent eddy viscosity. Smagorinsky Algebraic Subgrid Scale Turbulence Model
is used to simulate the horizontal eddy viscosity.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1889
The model equations for the kinetic energy and dissipation of the kinetic energy are [4]:
∂k
∂t+u∂k
∂x+v∂k
∂y+w∂k
∂z=∂
∂zvz
σk
∂k
∂z+P+B−ε+Fk,(6)
∂ε
∂t+u∂ε
∂x+v∂ε
∂y+w∂ε
∂z=∂
∂zvz
σε
∂ε
∂z+C1ε
ε
k(P+C3εB)−C2ε
ε2
k+Fε,(7)
where kis the kinetic energy, εis the rate of dissipation of kinetic energy, νzis the vertical eddy viscosity, Fkis the horizontal
diffusion terms for the kinetic energy, Fεis the horizontal diffusion terms for the dissipation of kinetic energy, Pis the stress
production of the kinetic energy, Bis the buoyancy production of the kinetic energy.
The buoyancy production of the kinetic energy is defined by [4]:
B=g
ρ0
vz
Pr
∂ρ
∂z,(8)
where Pris the turbulent Prandtl or Schmidth number. Experiments have shown that, the turbulent Prandtl or Schmidth number,
varies slightly in a flow and from one flow to the other. Therefore, it is considered as a constant, Pr =0.7.
The horizontal diffusion terms are expressed in the following form, where qirepresents kor ε:
Fqi=∂
∂xDx
∂qi
∂x+∂
∂yDy
∂qi
∂y.(9)
The stress production of the kinetic energy is defined by [4]:
P=vh2∂u
∂x2
+2∂v
∂y2
+∂u
∂y+∂v
∂x2+vz∂u
∂z2
+∂v
∂z2,(10)
where νhis the horizontal eddy viscosity and u, v are the horizontal water particle velocities in xand ydirections respectively.
The vertical eddy viscosity is calculated by:
vz=Cμ
k2
ε(11)
The following universal empirical constants are used in diffusion equations: Cμ=0.09, σε=1.3, C1ε=1. 4 4 , C2ε=1.92, C3ε=1if
G>0 (unstable stratification) and C3ε=0.2 if G<0 (stable stratification).
To account for large scale turbulence generated by the horizontal shear, horizontal eddy viscosity can be simulated by the
Smagorinsky algebraic subgrid scale turbulence model [4]:
vh=0,01xy∂u
∂x2
+∂v
∂y2
+1
2∂u
∂y+∂v
∂y21/2
.(12)
In the case of stratified flows the influence of stratification on turbulence in the horizontal direction is negligible [4].Hence,
the horizontal eddy diffusivities are approximately equal to the horizontal eddy viscosities. On the other hand, the vertical
diffusivity, Dz, is expressed as:
Dz=
vz
Pr ,(13)
where Pris the turbulent Prandtl or Schmidth number and νzis the vertical eddy viscosity coefficient.
2.2. Boundary conditions
There are four different boundary conditions defined in the model. These are free surface, sea bed, open sea and coastal land
boundaries [4].
Free Surface Boundary Condition: The wind acting above the free surface changes water velocities just under it. The wind-
induced shear stress at the surface results in a water velocity gradient below the surface.
Sea Bed Boundary Condition: The bottom shear stress at the sea bed is determined by matching velocities with the logarithmic
law of the wall. The gradients of temperature, salinity and the pollutant are taken as zero at the sea bed. This model assumes that
there are no advective and diffusive fluxes from the sea bed to the water body.
Open Sea Boundary Condition: The open sea boundary is the lateral boundary through which mass fluxes can be occurring.
Coastal Land Boundary Condition: Shorelines in the model are defined in order to simulate the flooding and drying processes,
which can also be seen in nature depending on seasonal variations, and cause some water areas to dry out or land areas to be
flooded. At the end of each step, once the free surface and the new water velocities are computed, the total water depth and
vertical grid spacing are updated before proceeding to the next time step. The water surface slope is calculated at each time step
with the new values of water depth. If the water surface slope is positive at coastal land boundary, the water surface is extended
1890 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Fig. 1. Nitrogen Cycle in Marine Environment.
using the calculated slope until it intersects the coastal land boundary. This feature allows the model to redefine the shorelines
at each step according to the calculated water depth values.
The normal gradients of temperature, salinity and the pollutant across the shoreline are taken as zero, an assumption that
there are no advective and diffusive fluxes across the shoreline boundary.
2.3. Numerical scheme
The model is written in FORTRAN programming language and solves hydrodynamic and transport equations in a composite
finite difference and finite element scheme. Equations are solved numerically by approximating the horizontal gradient terms
using a staggered finite difference scheme. In the vertical plane, however, the Galerkin Weighted Residual Method with linear
shape functions of finite elements is utilized in order to convert the differential equation to a discrete problem. The system of
nonlinear equations is solved implicitly by the Crank Nicholson Method which has second order accuracy in time. Water depths
are divided into the same number of layers following the topography. At all nodal points, the ratio of the length (thickness) of
each element (layer) to the total depth is constant. To increase the vertical resolution wherever necessary, grid clustering can be
applied in the vertical plane. The mesh size in the horizontal plane can be variable.
2.4. Water quality component
The water quality component of HYDROTAM-3D is a zero dimensional ecological model based on the conservation equations
and formulations proposed by the United States Environmental Protection Agency in 1985 [17]. Biochemical cycles simulated in
the model are the cycles of nitrogen, phosphorus, and oxygen. Organisms simulated in the model are the low tropic levels in
aquatic environments i.e. phytoplankton, zooplankton and pelagic bacteria.
The rate of change of the water quality parameters are developed by assuming a homogenous distribution of all properties
throughout the computation cell and can be generalized as follows:
∂C
∂t+∇·(aC)=σ,(14)
where σis the sum of the internal sink and sources of the water quality parameter in mg/l/day.
For n number of neighboring computational cells, the formula can be extended as follows:
∂C
∂t=a1.∂C
∂x1
+a2∂C
∂x2
... +an
∂C
∂xn
+Si−[K]C,(15)
where Cis the concentration of the water quality parameter in mg/l, aiis the rate of exchange with neighboring computational
cell in m/day, Siis the source of pollution for cell “i” in mg/l/day, Kis the internal rate of change of the water quality parameter.
2.4.1. Nitrogen cycle
Nitrogen cycle in marine environment is one of the important phenomena since it is closely related with primary production
and eutrophication problem. In water quality model nitrogen cycle is demonstrated with basic steps of the cycle which can be
summarized in Fig. 1.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 189 1
The forms of nitrogen in marine environment demonstrated in the water quality model are ammonia (NH4−), nitrite (NO2−),
nitrate (NO3−), particulate organic nitrogen (PON), non-refractory dissolved organic nitrogen (DONnr) and refractory dissolved
organic nitrogen (DONre).
Ammonia. Main sources of ammonia in marine environment are represented in the model as follows [13]:
a. Inorganic matter from the excretion and respiration of phytoplankton.
b. Excretion of pelagic bacteria.
c. Inorganic matter from the excretion of zooplankton,
d. Inorganic matter from the respiration of zooplankton.
e. Mineralization of the refractory dissolved organic nitrogen.
Main sinks of ammonia in marine environment are represented in the model as follows [13]:
a. Uptake by phytoplankton.
b. Uptake by pelagic bacteria.
c. Nitrification of ammonia.
The rate of change in ammonia concentration can be formulized as follows:
∂CNH4
∂t=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
ff
in ·ef+rf−βf
NH4·μf·αf
N:C ·Cf
+eb−μb
NH4·αb
N:C ·Cb
+fz
in ·ez+rz·αz
N:C ·Cz
+KDONre
min ·CDONre
−KNH4
nit ·CNH4
,(16)
where ffin is the fraction of inorganic matter excreted from phytoplankton, fzin is the fraction of inorganic matter excreted from
zooplankton, βfNH4 is the ammonia preference factor in phytoplankton uptake, αfN:C is the nitrogen to carbon ratio for phyto-
plankton in mgN/mgC, αbN:C is the nitrogen to carbon ratio for bacteria in mgN/mgC, αzN:C is the nitrogen to carbon ratio for
zooplankton in mgN/mgC, KDONremin is the rate of mineralization in 1/day and KNH4nit is the nitrification rate in 1/day
Ammonia preference factor in phytoplankton uptake is formulized as a function of the concentrations of the nutrients as
follows [17]:
βf
NH4 =CNH4
Kf
N+CNH4·CNO3
Kf
N+CNO3+CNH4
CNH4+CNO3·Kf
N
Kf
N+CNO3,(17)
where KfNis the nitrogen half-saturation constant for phytoplankton uptake in mgN/l.
Mineralization and nitrification are formulized as half-saturation functions as shown below [17]:
KDONre
min =KDONre
min (Tref )·QDON re
min (T−Tref )·Cf
Kf
r+Cf,(18)
KNH4
nit =KNH4
nit (Tre f )·QNH4
nit (T−Tref )·CO
Ksat
nit +Cf,(19)
where KDONremin (Tref) is the mineralization rate for refractory dissolved organic nitrogen at reference temperature (Tref) in 1/day,
KNH4nit (Tref) is the nitrification rate for ammonia at reference temperature (Tref) in 1/day, QDONremin is the temperature constant
for mineralization of refractory dissolved organic nitrogen, Kfris the half-saturation rate for mineralization in mgC/l, QNH4nit is the
temperature constant for nitrification of ammonia, COis the concentration of oxygen in mgO2/l and Ksatnit is the half-saturation
constant for nitrification in mgO2/l.
Nitrite. The rate of change in nitrite concentration is formulated as follows:
∂CNO2
∂t=KNH4
nit ·CNH4−KNO2
nit ·CNO2,(20)
where KNO2
nit is the nitrification rate of nitrite in 1/day.
Similar to the nitrification rate for ammonia, nitrification rate for nitrite can be expressed as follows:
KNO2
nit =KNO2
nit (Tre f )·QNO2
nit (T−Tref )·CO
Ksat
nit +CO,(21)
where KNO2
nit (Tref )is the nitrification rate for nitrite at reference temperature (Tref) in 1/day, QNO2nit is the temperature coefficient
for nitrification of nitrite.
1892 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Nitrate. The rate of change in nitrite concentration is formulated as follows:
∂CNO3
∂t=−
1−βf
NH4·μf·αf
N:C ·Cf+KNO2
nit ·CNO2−Kdnit ·CNO3(22)
where Kdnit is the rate of denitrification in 1/day.
Similar to the nitrification rates, the denitrification rate is calculated as an half-saturation function as follows :
Kdnit =Kdnit(Tre f )·Qdnit (T−Tref )·Ksat
dnit
Ksat
dnit +CO(23)
where Kdnit(Tref )is the denitrification rate at reference temperature in 1/day, Qdnit is the temperature coefficient for denitrification
and Ksatdnit is the half saturation constant for denitrification in mgO2/l.
Particulate Organic Nitrogen (PON). The sources for particulate organic nitrogen in marine environment are [13]:
a. Particulate organic fraction of matter produced by excretion.
b. Respiration and mortality of the phytoplankton.
c. Particulate matter produced by mortality of the pelagic bacteria.
d. Particulate fraction of the matter that cannot be assimilated through grazing of phytoplankton and bacteria by zooplankton
and the stoichiometric losses.
e. Particulate organic fraction of matter produced by excretion, mortality and grazing of the zooplankton.
The sinks for particulate organic nitrogen can be summarized as follows [13]:
a. Uptake by pelagic bacteria.
b. Degradation to dissolved organic nitrogen.
The rate of change in particulate organic nitrogen concentration can be formulized as follows:
∂CPON
∂t=⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
1−ff
in·1−ff
orgD ·ef+rf+mf·αf
N:C·Cf
−μb
PON −mb·αb
N:C·Cb
+1−fz
in·1−fz
orgD ·ez+mz+pz·αz
N:C·Cz+δz
N+ϕz
N·Cz
−(1−forg p )·KPON
dec ·CPON
(24)
where δzNis the rate of production of the particulate fraction of the matter that cannot be assimilated by grazing of phyto-
plankton and bacteria by zooplankton in 1/day, ϕzNis the rate of the stoichiometric losses in 1/day, forgP is the fraction of the
particulate organic nitrogen available for mineralization and KPONdec is the rate of degradation of the particulate organic nitrogen
in 1/day.
The rate of production of the particulate fraction of the matter that cannot be assimilated by grazing of phytoplankton and
bacteria by zooplankton is formulated as follows [22]:
δz
N=1−Ef·αf
N:C·Cf
z+1−Eb·αb
N:C·Cb
z(25)
where Cfzis the assimilation rate of the phytoplankton by zooplankton in 1/day, Cbzis the assimilation rate of the bacteria by
zooplankton in1/day, Efis the assimilation efficiency of the phytoplankton by zooplankton and Ebis the assimilation efficiency
of the bacteria by zooplankton.
The rate of the stoichiometric losses are formulated as follow [22]:
ϕz
N=αf
N:C −αz
N:CEf·Cf
z+αb
N:C −αz
N:CEb·Cb
z,(26)
where αfN:C is the ratio of nitrogen to carbon for phytoplankton in mgN/mgC, αbN:C is the ratio of nitrogen to carbon for bacteria
in mgN/mgC and αzN:C is the ratio of nitrogen to carbon for zooplankton in mgN/mgC.
The rate of degradation of particulate organic nitrogen is defined as a temperature limiting function and formulated as
follows [17]:
KPON
dec =KPON
dec (Tre f )·Q(T−Tre f )
dec (27)
where KPONdec (Tref)is the degradation rate of PON at reference temperature (Tref) in 1/day, Qdec is the temperature constant for
degradation.
Non-refractory Dissolved Organic Nitrogen (DONnr). Sources of the non-refractory dissolved organic nitrogen (DONnr) are the
dissolved fraction of the organic matter produced by the excretion and the respiration of the phytoplankton. The sink of the
non-refractory dissolved organic nitrogen is the bacterial uptake. The rate of the change in the non-refractory dissolved organic
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1893
Fig. 2. Phosphorus Cycle in Marine Environment.
nitrogenisformulatedasfollows:
∂CDONnr
∂t=⎧
⎪
⎨
⎪
⎩
1−ff
in·ff
orgD ·(ef+rf)·αf
N:C·Cf
−μb
DONnr ·Cb
+1−fz
in·fz
orgD ·ez·αz
N:C·Cz
(28)
where μbDONnr is the uptake rat of the non-refractory dissolved organic nitrogen by bacteria 1/day.
Refractory Dissolved Organic Nitrogen (DONre). The refractory dissolved organic nitrogen (DONre) is produced by the degrada-
tion of the particulate organic nitrogen and decreases by mineralization to ammonia. The rate of change in refractory dissolved
organic nitrogen is defined as follows:
∂CDONre
∂t=(1−forgP )·KPON
dec ·CPON −KDONre
min ·CDONre (29)
where KPONdec is the rate of degradation of the particulate organic nitrogen in 1/day, KDONremin is the rate of mineralization of the
refractory dissolved organic nitrogen in 1/day.
2.4.2. Phosphorus cycle
Phosphorus cycle is demonstrated in the water quality model in basic steps of the cycle which can be summarized in Fig. 2.
The forms of phosphorus in marine environment demonstrated in the water quality model are inorganic phosphorus (IP),
particulate organic phosphorus (POP), non-refractory dissolved organic phosphorus (DOPnr), and refractory dissolved organic
phosphorus (DOPre).
Inorganic Phosphorus (IP). The sources for inorganic phosphorus are [13]:
a. Inorganic fraction of matter produced by excretion and respiration of phytoplankton.
b. Inorganic fraction of matter produced by excretion and respiration of zooplankton.
c. Mineralization of refractory and non-refractory dissolved organic phosphorus,
d. Degradation of particulate organic phosphorus.
The rate of change in concentration of the inorganic phosphorus is formulized as follows:
∂CIP
∂t=
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
ff
in ·(ef+rf)−μf·αf
P:C·Cf
+fz
in ·ez+rz·αz
P:C·Cz
+KDO Pr e
min ·CDO Pr e
+KDOPnr
min ·CDOPnr
+forgP ·KPOP
dec ·CPOP
(30)
where. ffin is the inorganic fraction of matter produced by phytoplankton, fzin is the inorganic faction of the matter produced
by zooplankton, αfP:C is the ratio of phosphorus to carbon for phytoplankton in mgP/mgC, αzP:C is the ratio of phosphorus to
carbon for zooplankton in mgP/mgC, KDOPremin is the rate of mineralization of refractory dissolved organic phosphorus in 1/day,
189 4 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
KDOPnrmin is the rate of mineralization of non-refractory dissolved organic phosphorus in 1/day, KPOPdec istherateofdegradation
of particulate organic phosphorus in 1/day.
The rate of mineralization of refractory dissolved organic phosphorus is formulized in the model as follows [17]:
KDOPre
min =KDOPre
min (Tref )·QDOP re
min (T−Tref )·Cf
Kf
r+Cf(31)
where KDOPremin (Tref)is the rate of mineralization of refractory dissolved organic phosphorus at reference temperature (Tref )
in1/day, QminDOPre is the temperature coefficient for mineralization of DOPre, Kfris the half saturation constant for in mgC/l
The rate of mineralization of non-refractory dissolved organic phosphorus is as follows [17]:
KDOPnr
min =KDOPnr
min (Tref )·QDOP nr
min (T−Tref )·Cf
Kf
r+Cf,(32)
where KDOPnrmin (Tref)is the rate of the mineralization of non-refractory dissolved organic phosphorus at reference temperature
(Tref) in 1/day, QminDOPnr is the temperature constant for mineralization of DOPnr.
The rate of degradation of the particulate organic phosphorus is formulated as follows [17]:
KPOP
dec =KPOP
dec (Tre f )·QPOP
dec (T−Tref ),(33)
where KPOPdec (Tref)is the rate of the degradation of particulate organic phosphorus at reference temperature (Tref) in 1/day,
QPOPdec is the temperature coefficient for degradation of POP.
Particulate Organic Phosphorus (POP). The sources of particulate organic phosphorus in marine environment are [13]:
a. Organic particulate fraction of the matter produced by excretion and respiration of phytoplankton
b. Mortality of phytoplankton.
c. Particulate fraction of the matter that cannot be assimilated through grazing of phytoplankton and bacteria by zooplankton
and the stoichiometric losses.
d. Organic particulate fraction of the matter produced by excretion of zooplankton.
e. Grazing and mortality of zooplankton.
POP is decreased by degradation to dissolved organic phosphorus.
The rate of change in concentration of the POP can be formulized as follows:
∂CPOP
∂t=⎧
⎨
⎩1−ff
in·1−ff
orgD ·ef+rf+mf·αf
P:C·Cf
+1−fz
in·1−fz
orgD ·ez+mz+pz·αz
P:C·Cz+δz
P+ϕz
P·Cz
−forgP ·KPOP
dec ·CPOP,
(34)
where δzPis the rate production of the matter that cannot be assimilated by zooplankton during the grazing of phytoplankton
and bacteria in 1/day, ϕzPis the rate of the stoichiometric losses in 1/day, forgP is the fraction of particulate organic phosphorus
available for mineralization.
The rate production of the matter that cannot be assimilated by zooplankton during the grazing of phytoplankton and bacteria
is defined as [22]:
δz
P=(1−Ef)·αf
P:C·Cf
z+(1−Eb)·αb
P:C·Cb
z,(35)
where Cfzis the assimilation rate of phytoplankton by zooplankton in 1/day, Cbzis the assimilation rate of bacteria by zooplankton
in 1/day, Efassimilation efficiency of phytoplankton by zooplankton, Ebis the assimilation efficiency of bacteria by zooplankton.
The rate of the stoichiometric losses for grazing of phytoplankton and bacteria by zooplankton are as follows [22]:
ϕz
P=αf
P:C−αz
P:CEf·Cf
z+αb
P:C−αz
P:CEb·Cb
z,(36)
where αfP:C is the ratio of phosphorus to carbon for phytoplankton in mgP/mgC, αbP:C is the ratio of phosphorus to carbon for
pelagic bacteria in mgP/mgC, αzP:C is the ratio of phosphorus to carbon for zooplankton in mgP/mgC.
Non-refractory Dissolved Organic Phosphorus (DOPnr). The sources of the non-refractory dissolved organic phosphorus (DONnr)
are [13]:
a. The dissolved organic faction of the matter produced by excretion and respiration of the phytoplankton.
b. The dissolved organic faction of the matter produced by excretion of zooplankton.
Non-refractory dissolved organic phosphorus decreases by mineralization to inorganic phosphorus.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1895
Fig. 3. OxygenCycleinMarineEnvironment.
The rate of change in concentration of the non-refractory dissolved organic phosphorus (DONnr) can be formulized as follows:
∂CDOPnr
∂t=⎧
⎨
⎩1−ff
in·ff
orgD ·ef+rf·αf
P:C·Cf
+1−fz
in·fz
orgD ·ez·αz
P:C·Cz
−KDOPnr
min ·CDOPnr
(37)
Refractory Dissolved Organic Phosphorus (DONre). The refractory dissolved organic phosphorus increases by the degradation of
the particulate organic phosphorus (POP) and decreases by mineralization to inorganic phosphorus.
The rate of change in the concentration of the refractory dissolved organic phosphorus is formulated as follows:
∂CDO Pr e
∂t=(1−forgP )·KPOP
dec ·CPOP −KDPO Pr e
min ·CDO Pr e(38)
2.4.3. Oxygen cycle
Oxygen cycle is demonstrated in the water quality model in basic steps of the cycle which can be summarized in Fig. 3.
Dissolved oxygen plays an important role throughout the nitrogen and phosphorus cycle as well as in the aquatic life. The
sources of the dissolved oxygen in the marine environment are [13]:
a. Photosynthesis of the phytoplankton.
b. Oxygen transfer across the water surface
c. Denitrification of the nitrate.
The sinks of the dissolved oxygen are [13]:
a. The respiration of the aquatic life forms.
b. Degradation of the particulate organic materials.
c. Mineralization of the inorganic nitrogen forms.
1896 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
The rate of change in the concentration of the dissolved oxygen can be formulated as follows:
∂CDO Pr e
∂t=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
μf·αph
O:C +1−βNH4f·μf·αNO3
O:N ·αf
N:C·Cf
+μf·αIP
O:P ·αf
P:C −rf·αf
O:C·Cf
−rz·αz
O:C ·Cz
−μb
PON +μb
DONnr ·αb
O:C ·Cb
−KDONre
min ·αmin
O:N ·CDONre
−KPOP
dec ·αmin
O:P ·C,POP −KDOPre
min ·αmin
O:P ·CDOPre −KDOPnr
min ·αmin
O:P ·CDOPnr
−KO
nit ·CNH4+KO
dnit ·CNO3
(39)
where αminO:N oxygen consumption ratio for nitrogen mineralization in mgO/mgN/day, αminO:P oxygen consumption ratio for
phosphorus mineralization in mgO/mgP/day, KOnit oxygen consumption rate in nitrification in 1/day, KOdnit oxygen consumption
rate in denitrification 1/day.
The oxygen consumption rate for nitrogen mineralization can be formulated as follows [19]:
αmin
O:N =1
αOM
N:C
·αCO2
O:C ·CO
0,5+CO(40)
Similarly, the oxygen consumption ratio for phosphorus mineralization can be formulated as follows [19]:
αmin
O:P =1
αOM
P:C
·αCO2
O:C ·CO
0,5+CO(41)
Oxygen consumption rate in nitrification can be calculated as follows [19]:
KO
nit =Knit ·αNO3
O:N ,(42)
where Knit is the rate of nitrification in 1/day.
Oxygen consumption rate in denitrification can be calculated as follows:
KO
dnit =Kdnit ·αNO3
O:N ,(43)
where Kdnit is the rate of denitrification in 1/day.
2.4.4. Phytoplankton
The change in the concentration of the phytoplankton is modelled as it is proposed by EPA [17] anddefinedasfollows:
∂Cf
∂t=μf−rf−ef−sf−mf·Cf−Gf,(44)
where Cfis the phytoplankton concentration in mgC/l, μfis the phytoplankton gross grow, rfis the respiration rate, efis the
excretion rate, sfis the settling rate, mfis the mortality rate in 1/day, Gfis the phytoplankton grazing rate in mgC/l/day.
Gross Growth Rate. The growth rate of the phytoplankton is limited by temperature, light intensity and nutrients available in
the ambient water, namely phosphorus and nitrogen. The gross growth rate of the phytoplankton is described as:
μf=μf
max(Tref )·ff(T)·ff(L)·min[,ff(P),ff(N)],(45)
where μfmax(Tref )is maximum gross growth rate at reference temperature in 1/day, Tref is the reference temperature in ºC, ff(T)is
the growth limiting function for temperature, ff(L) is the growth limiting function for light, ff(N) is the growth limiting function
for nitrogen, ff(P) is the growth limiting function for phosphorus.
The Growth Limiting Factor for Temperature. The growth limiting factor for temperature is based on the temperature-optimum
curve and temperature tolerance limits of the organism, proposed by Thornton and Lessem [30] as follows:
ff(T)=Kf
A(T)·Kf
B(T),(46)
where KAf(T) and KBf(T) are raising limb and falling limb of the temperature curve and can be formulated as follows:
Kf
A(T)=Kf
1·eγf
1·(T−Tf
min)
1+Kf
1·eγf
1·(T−Tf
min)−1,(47)
Kf
B(T)=Kf
4·eγf
2·(Tf
max−T)
1+Kf
4·eγf
2·(Tf
max−T)−1,(48)
where Kf1,Kf2,Kf3,Kf4are rate multipliers for temperature limits, Tfmin is the minimum temperature for phytoplankton, Tfmax is
the maximum temperature for phytoplankton in ºC, γf1,γf2are rate coefficients for temperature curve.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 189 7
Rate coefficients for temperature curve γ1fand γ2fare as follows:
γf
1=
ln Kf
2·1−Kf
1
Kf
11−Kf
2
Tf
opt.min −Tf
min
,(49)
γf
2=
ln Kf
3·1−Kf
4
Kf
4·1−Kf
3
Tf
max −Tf
opt.max
,(50)
where Tfopt.min is the minimum optimum temperature for phytoplankton growth and Tfopt.max is the maximum optimum temper-
ature for phytoplankton growth in ºC.
The Growth Limiting Factor for Light. The relationship between the growth of phytoplankton and the ambient light intensity is
formulated by using the growth limiting function for light as proposed by Steele [28].
ff(L)=I(z)
Iopt
·e1−I(z)
Iopt ,(51)
where Iopt is the optimum light intensity for phytoplankton growth in W/m2,I(z) is the light intensity at the depth zin W/m2.
The light intensity in the ambient water is calculated according to Beer-Lambert Law as:
I(z)=Io·e−k·z,(52)
where Iois the light intensity at the water surface in W/m2, k is the light extinction coefficient in 1/m which also varies according
to the turbidity of the ambient water.
Light extinction coefficient k can be limited as a function of chlorophyll, a concentration as Parson et al. [25] proposes:
k=0.04 +0.0088Kla +0.054Kla2/3,(53)
where Kla is the chlorophyll -a concentration in μg Kla /l. In order to calculate chlorophyll-a concentration following formula
can be used:
Kla =Cf·αKla:C·1000,(54)
where αKla:C is the chlorophyll-a to carbon rate in μgKla/μgC.
The Growth Limiting Factor for Nitrogen. The growth limiting factor for nitrogen is based on conventional Michealis and Menten
Kineticsandformulatedasfollows:
ff(N)=CNH4+CNO3
Kf
N+CNH4+CNO3
,(55)
where CNH4is the concentration of ammonium in mg N/l, CNO3is the concentration of nitrate in mg N/l, KfNis the nitrogen
half-saturation constant for phytoplankton in mg N/l.
The Growth Limiting Factor for Phosphorus. The growth limiting factor for phosphorus is similar to the growth limiting factor
for nitrogen.
ff(P)=CIP
Kf
P+CIP ,(56)
where CIP is the concentration of the inorganic phosphorus in mg P/l, KfPis the phosphorus half-saturation constant for phyto-
plankton in mg N/l.
Respiration Rate. Respiration rate of the phytoplankton can be described as proposed by Groden [18] and Park et al. [24].
rf=ref+rff,(57)
where rfeis the endogenous respiration rate, rffis the photorespiration rate in 1/day. Endogenous and photorespiration respira-
tion rate formulized as follows [17]:
ref=Kf
e·e(0,069T),(58)
rff=Kf
p·μf,(59)
where Kfeis the endogenous respiration constant, Kfpis the photorespiration constant.
Excretion Rate. Excretion rate of the phytoplankton is formulized according Collins [14] as follows:
ef=Ke·μf·(1−f(L)),(60)
where Keis the fraction of photosynthesis excreted.
189 8 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Mortality Rate. A modified Michealis-Menten type saturation function for phytoplankton mortality is used as proposed by
Rodgers and Salisbury [26].
m(Tref )=mmax (Tref )·Cf/μf
Kf
m+Cf/μf,(61)
where Kfmis the half-saturation rate for phytoplankton mortality in mg C/l.day.
Settling Rate. Phytoplankton settling rate is directly related with the density, size and physiologic condition of the cells, as
well as the density, current velocity and the turbulence of the ambient water. Scavia [27] has defined a modified Stoke law for
the settling velocity for non-spherical shaped phytoplankton cells as follows:
Vs=2
9·g·R2·(ρp−ρw)
ν·Fs
,(62)
where Vsis the settling velocity of the particle in m/day, gis the gravitational acceleration in m/day2,Ris the equivalent radius
in m, ρpis the density of the cell in kg/m3,ρwis the density of the ambient water in kg/m3,υis the kinematic viscosity, Fsis the
shape factor.
Changes in the settling velocity can be expressed according to formula below [29]:
sf=Vs(Tre f )
d·fs(T),(63)
where Vs,max(Tref )is the maximum settling velocity at reference temperature in m/day, Tref is the reference temperature and fs(T)
is the temperature adjustment function for settling velocity.
Also the temperature adjustment factor is described as follows [29]:
fs(T)=157,5
0,069 ·T2−5,3·T+177 ,6.(64)
Grazing Rate. Phytoplankton grazing is defined as a function of temperature, predator population density (i.e. zooplankton
concentration), and phytoplankton concentration as proposed by EPA [17] as follows:
Gf=pf
z·Az
max ·ff
z(A)·fz(T)·Cz.(65)
where pfzis the phytoplankton proportion in zooplankton ingestion, Azmax is the maximum ingestion rate of zooplankton in
1/day, ffz(A) is the limiting factor for prey concentration, fz(T) is the limiting factor for temperature and Czis the concentration
of zooplankton in mgC/l.
2.4.5. Pelagic bacteria
The rate of change in heterotrophic pelagic bacteria concentrations in the model is defined as it is proposed by Bernardes [9].
∂Cb
∂t=[μb−eb−mb]·Cb−Gb,(66)
where Cbis the concentration of bacteria in mgC/l, μbis the total bacterial uptake in 1/day, ebis the excretion rate in 1/day, mbis
the mortality rate in 1/day, Gbis the grazing rate of the bacteria in mgC/l/day.
Total Bacterial Uptake. Total bacterial uptake is related directly to the availability of nutrients and the temperature of the
ambient water and can be formulated as follows [22]:
μb=μb
NH4+μb
PON +μb
DONnr (67)
where μbNH4 is the ammonia uptake in 1/day, μbPON is the particulate organic nitrogen uptake in 1/day, μbDONnr is the nonre-
fractory dissolved organic nitrogen uptake in 1/day.
Similar to the phytoplankton growth, bacterial uptake function can be modified by limitation factor for temperature as follows
[22]:
μb
NH4=μb
max(Tref )·fb(T)·fb
NH4(N)
αb
N:C
(68)
μb
PON =μb
max(Tref )·fb(T)·fb
PON(N)
αb
N:C
(69)
μb
DONnr =μb
max(Tref )·fb(T)·fb
DONnr (N)
αb
N:C
(70)
where fbNH4(N), fbPON (N), fbDONnr(N) are bacterial uptake limiting functions for ammonia, particulate organic nitrogen and non-
refractory dissolved organic nitrogen, μbmax(Tref) is the maximum bacterial uptake in reference temperature in mgN/mgC/day,
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1899
fb(T) is the bacterial uptake limiting function for temperature according to Thornton and Lessem [30],αbN:C nitrogen carbon ratio
for bacteria in mgN/mgC.
Bacterial uptake limiting functions for ammonia, particulate organic nitrogen and nonrefractory dissolved organic nitrogen
are defined as Michealis-Menten Half-Saturation Function as follows:
fb
NH4(N)=⎧
⎨
⎩
CNH4
Kb
N+CNH4if,CNH4>Cb,N
min
0if,CNH4≤Cb,N
min
⎫
⎬
⎭
,(71)
fb
PON(N)=⎧
⎨
⎩
CPON
Kb
N+CPON if,CPON >Cb,N
min
0if,CPON ≤Cb,N
min
⎫
⎬
⎭
,(72)
fb
DONnr (N)=⎧
⎨
⎩
CDONnr
Kb
N+CDONnr if,CDONnr >Cb,N
min
0if,CDONnr ≤Cb,N
min
⎫
⎬
⎭
,(73)
where KbNis the half saturation rate for bacterial uptake in mgN/l, Cb,N min is the minimum concentration of nutrients for bacterial
uptake in mgN/l.
Grazing Rate. Grazing rate of heterotrophic pelagic bacteria is formulated similar to the grazing of phytoplankton by zooplank-
ton as follows:
Gb=pb
z·Az
max ·fb
z(A)·fz(T)·Cz,(74)
where pbzis the fraction of bacteria in zooplankton grazing.
Limiting factor for prey concentration can be defined also similar to the phytoplankton grazing [22]:
fb
z(A)=⎧
⎨
⎩
cb
z·Cb−Cmin,b
z
Kz
A+cb
z·Cb−Cmin,b
zif,cb
z·Cb−Cmin,b
z>0
0if,cb
z·Cb−Cmin,b
z≤0⎫
⎬
⎭
,(75)
where cbzis the assimilation efficiency of bacteria by zooplankton, Cmin,bzis the minimum concentration of zooplankton for
bacteria grazing in mgC/l, KzAis the half-saturation constant for bacteria grazing by zooplankton in mgC/l.
2.4.6. Zooplankton
The rate of change in the zooplankton concentration is defined as follows [17]:
∂Cz
∂t=[μz−rz−mz]·Cz−Gz,(76)
where Czis the concentration of zooplankton in mgC/l, μzis the gross growth rate of zooplankton in 1/day, rzis the respiration
rate in 1/day, mzmortality in 1/day, Gzis the grazing in mgC/l/day.
Gross Growth. Gross growth of zooplankton is defined as follows [17]:
μz=Cf
z·Ef+Cb
z·Eb,(77)
where Cfzis grazing rate of phytoplankton by zooplankton in 1/day, Cbzis the grazing rate of bacteria by zooplankton in 1/day, Ef
is the assimilation coefficient of phytoplankton by zooplankton, Ebis the assimilation coefficient of bacteria by zooplankton.
Grazing rates of phytoplankton and bacteria are directly related to the concentration of zooplankton and can be formulized
as follows:
Cf
z=Gf
Cz,(78)
Cb
z=Gb
Cz,(79)
where Czis the concentration of zooplankton, Gfand Gzare grazing rates of phytoplankton and bacteria.
Respiration Rate. Respiration rate of zooplankton is formulated as follows [17]:
rz=rz(Tref )·fz(T),(80)
where rz(Tref)is the respiration rate of zooplankton at reference temperature in 1/day, fz(T) is the limiting factor for zooplankton
respiration calculated similar to phytoplankton.
Mortality Rate.Mortality rate of the zooplankton is limited according to a limiting function for temperature and formulated
as follows [17]:
mz=mz(Tref )·fz(T),(81)
190 0 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Fig. 4. Location of Ka ¸s Region and Field Measurement Points (K).
where mz(Tref)is the mortality rate of zooplankton at reference temperature in 1/day and f(T) is the mortality limiting function
for temperature.
Grazing Rate. Grazing rate of zooplankton by higher trophic levels are proportional to the zooplankton concentration and
formulated as follows [17]:
Gz=pz·Cz,(82)
where pzis the zooplankton grazing rate in 1/day.
3. Study site
Ka ¸s Region is located at the Mediterranean coast of Antalya (Fig. 4). At the north of the region lies the touristic district, which
has a dense population and yacht traffic in summer season. The coast is divided into three marine subregions namely Ka ¸s, Bucak
and Limana˘
gzı Bays according to their geographical properties. Ka¸s Bay and Limana˘
gzı Bay are connected to each other with an
opening of 793 m long and 50 m deep maximum. A marina with a 472 berthing capacity has been operating since 2011 in Bucak
Bay, which is a shallow and sheltered water body. A waste water treatment facility with a capacity of 5400 m3/day is installed
in 2006, which discharges its outfall water to Ka¸s Bay. HYDROTAM-3D water quality component is adapted to Ka ¸s Region with
three interrelated computational subregions to simulate the water quality properties (Fig. 5).
3.1. Ka ¸s subregion
Ka ¸s Bay is a deep water body which is fully open to wind driven currents from the Mediterranean. The simulation area has
a 2490 m long border along the open sea through 1-1 section and 793 m long border along Limana˘
gzı bay through 2-2 section.
The cross-sectional area at 1-1 is 235,370 m2, and at 2-2, 23,520 m2. The simulated water body has a surface area of 6514,300 m2
and a water volume of 2274,00,000 m3.
The main sources that affect the water quality parameters in Ka ¸s Bay are the outfall water discharged from the waste water
treatment plant and the waste water produced by the boats berthing at Ka ¸sPort.
3.2. Limana˘
gzı subregion
Limana˘
gzı Bay is a sheltered area and connected only to Ka¸s Bay through an opening with a length of 793 m and 50 m
depth maximum. It is less subjected to open sea circulations, and there are fewer facilities discharging their waste water to the
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1901
Fig. 5. Computational Subregions of Ka ¸sRegion.
Tabl e 1
Waste water and water exchange budget for Ka¸sSubregion(m
3/day).
September 2013 October 2013 November 2013 December 2013 January 2014 February 2014
Discharge water from Ka ¸s waste water
treatment facility
2450 2450 2450 1900 1900 1900
Waste water produced by the boats
berthing at Ka ¸sPort
68 68 68 8 8 8
Water exchange with open sea through
1-1 cross section
30119.040 30119.040 64540.800 64540.800 64540.800 64540.800
Water exchange with Limana˘
gzı
Subregion through the 2-2 cross
section
2730.240 2730.240 4095.360 4095.360 4095.360 4095.360
bay without a treatment. On the other hand, the bay is visited by numerous tour boats in summer which generate considerable
pollution during tourist season. The simulated water body has a surface area of 972,910 m2and a water volume of 150,68,000 m3.
3.3. Bucak subregion
Bucak Bay has a connection to open sea through the 3-3 section with a length of 300 m and 23 m depth maximum. The main
pollution sources in Bucak Bay are the marina facility and the boats berthing there. The cross-sectional area at 3-3 is 5100 m2.
The simulated water body has a surface area of 697,800 m2and water volume of 17445,200 m3.
4. Field measurements
In order to investigate the water quality parameters, 10 measurement points are selected from the regions that can represent
the characteristics of the marine environment. The physical and chemical parameters at 0.5 m and 10 m depth (i.e. temperature,
salinity, density, pH, concentration of the dissolved oxygen DO, nitrite NO2−, nitrate NO3−, turbidity, alkalinity and total dissolved
solid TDS) are monitored monthly by field and laboratory measurements for 6 months. In order to investigate the currents and
water exchange between the computational regions the current velocities are also measured for each field measurement point.
The mean water flow through 1-1, 2-2 and 3-3 sections are calculated based on the current velocities observed for 6 months.
The mean water quality parameters of the discharged water from the treatment facility are observed to investigate the sources of
pollution. The waste water budget and the mean water exchange values used in the model are presented in the following tables
(Table 1–3):
1902 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Tabl e 2
Waste water and water exchange budget for Limana˘
gzı Subregion (m3/day).
September 2013 October 2013 November 2013 December 2013 January 2014 February 2014
Waste water produced by the boats
berthing at Limana˘
gzı Bay
68 68 68 8 8 8
Waste water produced by the facilities
located at Limana˘
gzı Bay
150 150 150 10 10 10
Water exchange with Ka ¸sSubregion
through the 2-2 cross section
2730240 2730.240 4095.360 4095.360 4095.360 4095.360
Tabl e 3
Waste water and water exchange budget for Bucak Subregion (m3/day).
September 2013 October 2013 November 2013 December 2013 January 2014 February 2014
Waste water produced by the boats
berthing at Ka ¸s Marina
2890 2890 2890 890 890 890
Water exchange with open sea through
the 2-2 cross section
1036.800 1036.800 1036.800 1036.800 1036.800 1036.800
0.008
0.012
0.016
0.02
0.024
0.028
0.032
0.036
0.04
0.044
0.048
Fig. 6. Distribution of Nitrite Concentration (mg N/l) in January 2014 at 0.5 m Depth.
4.1. Nitrite
The distribution of the nitrite concentrations for January and February 2014 at 0.5 m depth are presented in Figs. 6 and 7
respectively.
Figs. 6 and 7show the variation of nitrite concentrations measured in the labotary by analyzing the water samples taken at
0.5 m depth from the sea surface in January and February 2014. Measured values of nitrite concentration, which is one of the
parameters indicating the significance of nitrogen nutrient in water, varies between 0.008 and 0.048 mg N/l. Although the nitrite
concentrations in the region are generally below the critical values of pollution, measurements reveal higher concentration
values for Nitrite in K8 at the Marina in Bucak Bay, in K6 at the wastewater discharge and in K3 by the shore of the touristic
district, where the main pollution sources in the region are located. At the stations K1 and K10, representing offshore water
charactistics, minimum values for nitrite concentration are observed.
4.2. Nitrate
The distribution of the nitrate concentrations for January and February 2014 at 0.5 m depth are presented in Figs. 8 and 9
respectively.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1903
0.008
0.012
0.016
0.02
0.024
0.028
0.032
0.036
0.04
0.044
0.048
Fig. 7. Distribution of Nitrite Concentration (mg N/l) in February 2014 at 0.5 m Depth.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Fig. 8. Distribution of Nitrate Concentration (mg N/l) in January 2014 at 0.5 m Depth.
The nitrate concentration varies from 0 to 1.3 mg N/l for January and February 2014 as its distributions show in Figs. 8 and
9. Nitrate is another significant parameter for nitrogen nutrient in water and is only mildly toxic for the marine environment in
comparison with the other nitrogen involving pollutants. In most cases higher levels of nitrate are thought to result from human
activities since the reasons of having nitrate in water are mainly the breakdown of fertilizers, manures, plants, animals or other
organic residues by microorganisms. Similar to the distribution of the nitrite concentrations, nitrate concentrations indicate
higher levels in K8, K6, K3 as well as in K4, which are the stations near main pollution sources. Since the region is open to strong
currents from offshore water, no significant pollution level is observed at any station.
190 4 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Fig. 9. Distribution of Nitrate Concentration (mg N/l) in February 2014 at 0.5 m Depth.
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 10. Distribution of Dissolved Oxygen Concentration (mg O/l) in September 2013 at 0.5m Depth.
4.3. Dissolved oxygen
The distribution of dissolved oxygen concentrations for September, October 2013 and January, February 2014 at 0.5 m and
10m depth are presented in Figs. 10–17.
The concentration of dissolved oxygen measurements at the site varies from 5.6 to 7.6 mg O/l between September and Febru-
ary. The concentration of dissolved oxygen is inversely related to water temperature and the presence of other solutes in water. It
is clearly observed in Figs. 10–17 that the concentration increases as the ambient water temperature and salinity decreases from
September to February. The concentration values in K8 and K9 also appear to be less than in other stations because of weaker
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1905
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 11. Distribution of Dissolved Oxygen Concentration (mg O/l) in September 2013 at 10m Depth.
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 12. Distribution of Dissolved Oxygen Concentration (mg O/l) in October 2013 at 0.5m Depth.
currents inside Bucak Bay. Similar to that, due to wind and wave actions higher concentration values are observed at 0.5 m below
the surface rather than at 10 m depth, for all that the measurements are within the standart ranges of the Mediterranean.
5. Results
The measured values for nitrite, nitrate and dissolved oxygen concentrations are compared with the simulation outputs for
each computational region.
190 6 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 13. Distribution of Dissolved Oxygen Concentration (mg O/l) in October 2013 at 10m Depth.
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 14. Distribution of Dissolved Oxygen Concentration (mg O/l) in January 2014 at 0.5m Depth.
5.1. Ka ¸s subregion
Figs. 18–20 display the comparison of the mean concentration values for nitrite, nitrate and dissolved oxygene obtained
through the water quality model in comparison with the field measurements at stations K3, K4, K5, K6 and for Ka ¸s Subregion.
According to the model estimations for the Ka¸sSubregioninFig. 18, the mean nitrite concentration is around 0.035 mg N/l
in autumn and decreases to the level of approximately 0.010 mg N/l in the winter months of January and February. Comparing
the estimations with the nitrite concentrations measured in January, an overestimation of 0.001 to 0.015 mg N/l is observed. For
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1907
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 15. Distribution of Dissolved Oxygen Concentration (mg O/l) in January 2014 at 10m Depth.
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 16. Distribution of Dissolved Oxygen Concentration (mg O/l) in February 2014 at 0.5m Depth.
February, all of the field measurement values except the one at K5 show higher values than the model estimations. The deviation
varies between 0.007 and 0.016 mg N/l.
The comparison of the mean nitrate concentrations obtained through the water quality model and the field measurements
is given in Fig. 19. According to the model estimations the mean nitrate concentration, which is around 0.238 mg N/l in autumn
remains almost at the same levels during the whole period of the study. However, comparing with the the nitrate concentrations
from the field measurements, it is observed that the model underestimates the concentration values in February while result
is almost stays at the average in January. Despite that, the model estimates are found to be close to the order of the measured
values. The deviation between model results and field measurements varies between 0.12 and 0.75 mg N/l.
1908 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
5.6
5.8
6
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
Fig. 17. Distribution of Dissolved Oxygen Concentration (mg O/l) in February 2014 at 10m Depth.
Fig. 18. Nitrite Concentration Values for Ka ¸s Subregion (mg N/l).
In Fig. 20, it is observed that the estimated concentration of the mean dissolved oxygen is around 5.3 mg O/l at the end of the
summer season and it is slightly underestimated as the measured values are in between 5.7 and 6.5 mg O/l. For the following
months, with the decrease in sea water temperature, the estimations increase to the level of 7.6 mg O/l. The model estimations
for dissolved oxygen are in general quite consistent with the measurements in terms of both the level of concentrations and the
temporal variation. A slight underestimation for autumn and an underestimation for winter, however, is apparent. The deviation
between model results and field measurements varies from 0.2 to 1.2 mg O/l.
5.2. Limana˘
gzı subregion
Figs. 21–23 display the comparison of the mean concentration values for nitrite, nitrate and dissolved oxygene, obtained
through the water quality model with the field measurements at stations K2 and for Limana˘
gzı Subregion.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1909
Fig. 19. Nitrate Concentration Values for Ka ¸s Subregion (mg N/l).
Fig. 20. Dissolved Oxygen Concentration Values for Ka ¸sSubregion(mgO/l).
According to the model estimations for the Limana˘
gzı Subregion in Fig. 21, the mean nitrite concentration is increased to
0.0245 mg N/l level at the beginning of the winter and continued to increase to the levels of approximately 0.0295 mg N/l in
the winter month of February. Comparing the estimations with the nitrite concentrations measured in January, a deviation of
0.0015 mg N/l is observed. The deviation in February is more significant with a level of 0.0015 mg N/l.
In Fig. 22, the comparison of the mean nitrate concentrations obtained through the water quality model and the field mea-
surements is presented. The model estimates the mean nitrate concentration around 0.23 mg N/l through the end of autumn and
winter. The nitrate concentration in K2 station almost matches the model estimation with a slight overestimation in January. A
small deviation of 0.03 mg N/l is observed. However, in February, estimated nitrate concentrations show a large deviation from
the field measurements with a difference of approximately 0.75 mg N/l.
The comparison of the field measurements and the model results for the mean dissolved oxygen concentration in Limana˘
gzı
subregion is given in Fig. 23. At the end of summer season, the estimated concentration of the mean dissolved oxygen is around
5.9 mg O/l, and it is slightly overestimating the measured average values of 5.7 to 6.9 mg O/l. Similar to Ka¸sSubregionwith
the decrease in the sea water temperature, the estimations increase to the level of approximately 8.1 mg O/l in winter season.
1910 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Fig. 21. Nitrite Concentration Values for Limana˘
gzı Subregion (mg N/l).
Fig. 22. Nitrate Concentration Values for Limana˘
gzı Subregion (mg N/l).
The model estimations for dissolved oxygen match in general with the measurements in autumn season with a 0.3–0.5 mg O/l
deviation. However, in the measurements in winter season, especially in February, a large deviation between model estimations
and field measurements with a difference of 2.54 mg O/l is observed. The reason of this large deviation, which is also observed
in nitrite and nitrate concentration values, is thought to be the momentary regional conditions affecting the field measurement
in Limana˘
gzı Subregon, i.e. unusual discharges and excess surface runoff after rainy weather in February.
5.3. Bucak subregion
Figs. 24–26 display the comparison of the mean concentration values for nitrite, nitrate and dissolved oxygen, obtained
through the water quality model with the field measurements at stations K8 and K9 for Bucak Subregion.
The water quality model estimated the nitrite concentration above 0.05 mg N/l in autumn and 0.04 mg N/l in winter with a
gradual decrease for Bucak subregion. Although the model estimations in January is consistent to the field measurements with a
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1911
Fig. 23. Dissolved Oxygen Concentration Values for Limana˘
gzı Subregion (mg O/l).
Fig. 24. Nitrite Concentration Values for Bucak Subregion (mg N/l).
small underestimation of about 0.004 mg N/l, the estimations show respectively a large deviation from the field measurements
which is approximately 0.01–0.02 mg N/l.
The nitrate concentrations obtained through the water quality model and the field measurements for Bucak subregion are
compared in Fig. 25. The model estimation shows stable results around 0.62 mg N/l during the whole period of the study. Field
measurement results almost stay at the average in January; however, there is a significant underestimation of the model results
for Bucak subregion in February with a deviation of 0.78 mg N/l.
The comparison of the field measurements and model results for the mean dissolved oxygen concentration in Bucak sub-
region is given in Fig. 26. Similar to Figs. 20 and 23 a gradual increase in model estimations is observed as the ambient water
temperature decreases in winter. For Bucak subregion the model shows a slight overestimation in comparison to the field mea-
surements with a difference between 0.2 and 0.9 mg O/l. The deviation is more apparent in winter. Despite that the model esti-
mations for dissolved oxygen can be considered quite consistent with the measurements in general, in terms of both levels of the
concentrations.
1912 K. Cebe, L. Balas / Applied Mathematical Modelling 40 (2016) 1887–1913
Fig. 25. Nitrate Concentration Values for Bucak Subregion (mg N/l).
Fig. 26. Dissolved Oxygen Concentration Values for Bucak Subregion (mg O/l).
6. Conclusion
Except an indistinct deviation from the measured values for nitrate concentration in February 2014, the model displays almost
overlapping results for all three parameters in Ka ¸s Subregion. Measured values for nitrite concentration in Limana˘
gzı Subregion
show a similar distribution whereas the field measurements of nitrate concentration in February 2014 and of dissolved oxygen
concentration in January and February 2014 deviate distinctly from the model output. It must, however, be stressed that the
January measurements are closer to the model output than February. The Bucak Subregion measurements display a similar
graphic only with a difference of nitrate concentration in field measurement in February 2014.
These results show that the model demonstrates the changes in nitrite and dissolved oxygen concentration in a fairly real-
istic way. It can also be observed that the model displays close results to the field measurements of nitrate concentration. For
measurements where the two values derivate, the reason of the derivation is believed to depend on momentary regional condi-
tions in the field, which can be an unusual discharges, excess surface runoff after rainy weather, or any factor affecting the field
measurement in February.
In conclusion, it is proved that the water quality model with three computational subregions in Ka ¸s Region shows accurate
outputs and has tandem results with the field measurements.
K. Cebe, L. Balas /Applied Mathematical Modelling 40 (2016) 1887–1913 1913
The field measurements presented in this study provides a rich data for calibrating the water quality model of HYDROTAM
in marine environment. Future work on the water quality model will develop it according to regional dynamics. The model can
easily be extended to multiple computational zones and simulation periods, and can work coupled with the hydrodynamic and
transport models of HYDROTAM-3D interactively.
As it is demonstrated, HYDROTAM uses a comprehensive method with a 3-dimensional numerical solution scheme for hy-
drodynamics, which provides very precise predictions for the wind and tidal forced circulations in coastal waters. Besides its
precision in coastal hydrodynamics, it stands for a useful water quality tool providing a set of basic ecological simulations for
coastal waters.
Acknowledgments
This study is a part of the governmentally financed Southwestern Development Agency Support Project called “Protection,
Development and Management of Marine and Coastal Areas of Ka¸s”, which is finalized in 2014. The output of the model has been
considered in detail and the results are served to the use of coastal management in Ka ¸s Region.
References
[1] R.B. Ambrose Jr., T.A. Wool and J.L. Martin, 1993. The Water Quality Analysis Simulation Program, WASP5. U.S. Environmental Protection Agency Research
Laboratory. Athens, Georgia, U.S.
[2] R.G. Baca, R.C. Arnett, A Limniological Model for Eutrophic Lakes and Impoundments, Batelle Inc., Pacific Northwest Laboratories, Richland, Washington,
U.S., 1976.
[3] L. Balas, A. ˙
Inan, A composite finite element-finite difference model applied to turbulence modelling, in: ICCS 2007: 7th International Conference on Com-
puter Science, Lecture Notes in Computer Science, 2007, pp. 1–8.
[4] L. Balas, Three-dimensional numerical modelling of transport processes in coastal water bodies, The Graduate School of Natural and Applied Sciences,
Middle East Technical University, Ankara, Turkey, 1998 PhD thesis.
[5] L. Balas, E. Özhan, An implicit three dimensional model simulate transport processes in coastal water bodies, Int. J. Numer. Methods Fluids. 34 (2000)
307–339.
[6] L. Balas, Simulation of pollutant transport in Marmaris Bay, Chin. Ocean Eng. J. 15 (2001) 565–578.
[7] L. Balas, E. Özhan, Applications of a 3-D numerical model to circulations in coastal waters, Coast. Eng. J. 43 (2001) 99–120.
[8] L. Balas, E. Özhan, A baroclinic three dimensional numerical model applied to coastal lagoons, Lecture Notes Comput. Sci. 2658 (2003) 205–212.
[9] B.D.L. Bernardes, Hydrodynamical and Ecological Modelling of the North Sea, School of Engineering, Technical University of Lisbon, Portugal, 2007 Master
Thesis.
[10] R.J. Brandes, An Aquatic Ecologic Model for Texas Bays and Estuaries, Water Resources Engineers, Austin, Texas, U.S., 1976.
[11] L.C. Brown and T.O. Barnwell, 1987. The Enhanced Stream Water Quality Models QUAL2E and QUAL2E-UNCAS (EPA/600/3-87-007). U.S. Environmental
Protection Agency, Athens, Georgia, U.S.
[12] C.W. Chen, G.T. Orlob, Ecologic Simulation for Aquatic Environments. System Analysis and Simulation in Ecology, 3, Academic Press, New York, U.S., 1975,
pp. 476–588.
[13] B. Chubarenko, V.G. Koutitonsky, R. Neves, G. Umgiesser, Modeling Concepts, in Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use
and Development, in: I.E. Gönenç, J.P. Wolflin (Eds.), CRC Press, Florida, U.S, 2004.
[14] C.D. Collins, Formulation and validation of a mathematical model of phytoplankton growth, Ecology 61 (1980) 639–649.
[15] D.M. DiToro, R.V. Thomann, D.J. O’Connor, J.L. Mancini, Estuarine Phytoplankton Biomass Models – Verification Analyses and Preliminary Applications. The
Sea, Marine Modelling, Vol. 6, Wiley-Interscience Publications, New York, U.S., 1977.
[16] R.L. Doneker, G.H. Jirka, Expert systems for design and mixing zone analysis of aqueous pollutant discharges, J. Water Resour. Plann. Manag., ASCE 117(6)
(1991) 679–697.
[17] EPA, Rates, constants, and kinetics formulations in surface water quality modelling, 2nd ed, 1985 U.S. Environmental Protection Agency, Report EPA/600/3-
85/040.
[18] T.W. Groden, Modeling Temperature and Light Adaptation of Phytoplankton. Report No. 2, Center for Ecological Modeling, Rensselaer Polytechnic Institute,
Troy, New York, U.S., 1977.
[19] M. Gürel, A. Tanik, R.C. Russo, E. Gönenç, Biochemical Cycles, in Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development,
in: I.E. Gönenç, J.P. Wolflin (Eds.), CRC Press, Florida, U.S., 2004.
[20] A. Küçükosmano˘
glu, L. Balas, E. Özhan, Modelling of mixing and flushing in Fethiye Bay„ in: Proceedings of the Sixth International Conference on the
Mediterranean Coastal Environment, MEDCOAST 03, 7-11 October, Ravenna, Italy, 2003, pp. 2099–2107.
[21] R. Miranda, Nitrogen Biogeochemical Cycle Modeling in the North Atlantic Ocean, Technical University of Lisbon, School of Engineering, Portugal, 1999
Master Thesis.
[22] MARETEC, MOHID Water Quality Module Manual, version 1.0, Instituto Superior Técnico, Technical University of Lisbon, Portugal, Lisbon, Portugal, 2006.
[23] E. Özhan, L. Balas, Simulation of water exchange in enclosed water bodies, Lect. Notes Comput. Sci. 2658 (2003) 195–204.
[24] R.A. Park, C.D. Collins, C.I. Connoly, J.R. Albanese, B.B. MacLeod, Documentation of the Aquatic Ecosystem Model MS.CLEANER, Center for Ecological Model-
ing, Rensselaer Polytechnic Institute, Troy, New York, U.S., 1980.
[25] T.R. Parsons, M. Takahashi, B. Hargrave, Biological Oceanographic Processes, 3rd ed., Pergamon Press, Oxford, U.K., 1984.
[26] P. Rodgers, D. Salisbury, Water quality modeling of Lake Michigan and consideration of the anomalous ice cover of 1976–1977, J. Great Lakes Resour 7 (4)
(1981) 467–480.
[27] D. Scavia, An ecological model of lake Ontario, Ecol. Model. 8 (1980) 49–78.
[28] J.H. Steele, Notes on some theoretical problems in production ecology, in: C.R. Goldman (Ed.), Primary Production in Aquatic Environments, University of
California Press, Berkeley, California, U.S., 1965, pp. 393–398.
[29] Tetra Tech, Inc, Methodology for Evaluation of Multiple Power Plant Cooling SystemEffects, Volume V. Methodology Application to Prototype – Cayuga Lake,
Te tra Tec h . Inc . , Laf a ye t te, C a l ifo r nia . F or El e c tri c P ow e r Re s e arc h I nst i tut e , 19 8 0 Re p o rt E P R I EA- 1111 .
[30] K.W. Thornton, A.S. Lessem, A temperature algorithm for modifying biological rates, Trans. Am. Fish. Soc. 107 (2) (1978) 284–287.
