Material and Methods Optimization of the Acid Catalyst Concentration for Synthesis of Anti‐Cancer Agent Gamavuton‐0 by Using Mathematical and Statistical Software
73
Figure 2. Elevation Data in the Sungai Mariam Mahakam Estuary
The averaged monthly river discharge data of the Mahakam river –
8 obtained from the Research and Development rrigation Ministry Public Work, Republic
of ndonesia are shown in Fig.
Figure 3. The average monthly river discharge data of the Mahakam river
2.2. Hydrodynamics
Model Estuary and Coastal Ocean Model with Sediment Transport ECOMSED is a three‐
dimensional hydrodynamic and sediment transport model. The hydrodynamic module solves the conservation of mass and momentum equations with a . ‐level turbulent
closure scheme on a curvilinear orthogonal grid in horizontal plane and ‐coordinate in the vertical direction. Water circulation, salinity, and temperature are obtained from the
hydrodynamic module. The sediment transport module computes the sediment settling and resuspension processes for both cohesive and noncohesive sediments under the
impact of waves and currents. The governing equations of the hydrodynamic component in ECOMSED are the
continuity equation, Reynold’s equations, heat and salinity transport equations. The basic equations for the three-dim ensional m ode are:
The continuity equations:
z W
y V
x U
,
74 where U,V,W are the eastward z , northward y , and upward z components of
the current. A dynamic boundary condition evaluated at the sea surface z = will indicate the relation between sea surface elevation and vertical velocity at the sea
surface W
as,
W
V y
U x
t
,
The vertical velocity at the sea surface W
can be obtained by integrating from
the bottom z = ‐H to the sea surface z = . The m om en tum equation s usin g the Boussin esq approxim ation s an d the
assum ption of vertical hydrostatic equilibrium in Cartesian coordin ates are given below.
, 2
1
x V
y U
A y
x U
A x
z U
A z
x P
fV z
U W
y U
V x
U U
t U
M M
V
3
, 2
1
y V
A y
x V
y U
A x
z V
A z
y P
fU z
V W
y V
V x
V U
t V
M M
V
4
z
dz B
g P
, g
B
, an d, the equation s of tem perature an d salin ity,
,
y T
H A
y x
T H
A x
z T
V K
z z
T W
y T
V x
T U
t T
,
y S
A y
x S
A x
z S
K z
z S
W y
S V
x S
U t
S
H H
V
8
where T denotes the temperature, S the salinity, f the Coriolis parameter = sin ; = . x
‐
s
‐
and is the latitude , ρ the density, ρ the reference density =
. 8 kg m
‐
, g the acceleration of gravity = .8 m s
‐
, P the pressure, B the buoyancy, A
V
and K
V
the vertical eddy viscosity and vertical diffusion coefficient, A
M
the horizontal eddy viscosity, A
H
the horizontal diffusion coefficient. The horizontal eddy viscosity and diffusivity coefficient is given on the basis of
Smagorinsky formula where they increase proportionally to the grid spacing and the velocity shear.
, 2
2 1
2 2
2
y
V y
U y
V x
U y
x A
A
H M
where α is a constant = . and x and y are horizontal mesh size x = y =
m . The vertical eddy diffusivity coefficients of momentum, temperature, salinity, and
suspended sediment concentration are obtained through the . level turbulence closure scheme developed by Mellor and Yamada
8 .
7 The development of three‐dimensional ‐D hydrodynamic models started in the
late s. Three‐dimensional hydrodynamic models are numerical code solving generally the Boussinesq equations. The availability of equations based on physical laws of classic
mechanics, know from 8th century, is one of the main differences between hydrodynamic and biogeochemistry models, because equations for biogeochemical
phenomena are generally not universally accepted and in most cases empirical or semi‐ empirical.
2.3. Ecosystem
Model The biological model cycles concentrations of organic carbon and nitrogen
through microplankton and detrital compartments with associated changes in dissolved concentrations of nitrate, ammonium and oxygen. The concentrations are updated in
time by solving a transport equation for each state variable where by the biological interactions are included as source and sink terms and which takes account of vertical
sinking and the physical transport by advection and diffusion. As an exception, chlorophyll is derived algebraically from microplankton carbon and nitrogen
concentrations. The sediment model determines the time evolution and transport of inorganic particulate material. Exchanges between the water column and the seabed are
modelled through a fluff” layer in the microplankton and detritus compartments and in the sediment model.
The nutrient N
N
and N
P
N
N
; Dissolved norganic Nitrogen and N
P
; Phosphate , phytoplankton P, zooplankton Z and detritus D are included in this numerical ecosystem
model Yanagi, ; Anukul et al.,
8 . The concentration of dissolved oxygen O is calculate at the same time. The state variables obey the following equations which
include advection, diffusion and biochemical processes :
, 3
2 1
Z A
P A
P A
z P
V K
z x
P H
K x
z P
p S
z P
W y
P V
x P
U t
P
, 6
5 4
3 Z
A Z
A Z
A Z
A z
P V
K z
x P
H K
x z
Z W
y Z
V x
Z U
t Z
, 7
6 1
Z A
Z A
Z A
z P
V K
z x
P H
K x
z N
N W
y N
N V
x N
N U
t N
N
, 7
6 1
D A
P A
P A
z P
N V
K z
x P
N H
K x
z P
N W
x P
N U
t P
N
, 7
5 4
2 D
A D
A P
A P
A z
D V
K z
x D
H K
x z
D D
S z
D W
x D
U t
D
7 .
4 3
2 1
2 2
2 2
2 P
B P
B P
B P
B z
O V
K z
x O
H K
x z
O W
x O
U t
O
The origin of the Cartesian coordinate system is set at the sea surface of the estuary head with the x ‐ axis directed toward the estuary mouth and the z‐axis upward.
U and W denote the velocity in the x and z directions, respectively. Sp denotes the sinking speed of phytoplankton and SD that of detritus. K
H
and K
V
denote the horizontal and vertical diffusivities, which depend on the tidal current Amplitude and the
Richardson number. The computational domain, grid spacing and time steps were the same as those of
ECOMSED the same as those of temperature and salinity with fixed values at all grid locations along the boundary plane throughout model operation. The loads of major
rivers were taken into consideration, while non‐point source nutrients along coastlines were ignored due to a lack of reliable data. nitial values of ecosystem parameters,
derived from the overall average of measured data, were set to be identical in all experiments – . mg m– , . µM‐N l – and . µM‐P l– for chl‐a, DN and DP,
respectively. Zooplankton and detritus were assigned as 8. of chl‐a and equal to chl‐a concentrations, respectively, similar to the lateral boundary setting.
The model operation was tested and a steady state of all simulated parameters was attained after days of computation. Calculated results were collected and
averaged from days to in the same way as those of circulation model. Simulated chl‐a distributions in the same months of observational cruises are presented and
discussed.