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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.

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