Users’ Guide for the T63L30 OGCM_1.0
Zhou Tianjun, Jin Xiangze and Zhang Xuehong
LASG, Institute of Atmospheric Physics (IAP) of the Chinese
Academy of Science (CAS)
May 20th , 2000
ⅠModel use
(I) Run the model
1. Code
There are three subdirectories in the directory of T63L30:
⑴FILE：to place the source codes，including 24 “.f” FORTRAN programs、6 “.h” files which
define parameters and dimensions，and makefile。
⑵FORT22：to put the field of December 31st of each year for restarting the model. The file names
are “fort.22.????Dec”，in which “????” indicates the model year.
⑶OMMEAN：to save the model results.
2. Description for model run
In UNIX system，in the subdirectory FILE, the special subdirectory for the ocean model,
run “make”, by virtue of “makefile” compiling the source codes, producing the executable file
L30T63_OGCM, then return the father directory of FILE, run the model.
After the model run, there are information outputs to the screen for monitoring the model
run, including parameters and energy balance. These outputs can be saved to a file for analysis
need.
In addition, there is a text file “modeltime”, which may be modified by model output for
monitoring the current model date.
(II) Input parameters
Three aspects are included: the model integration time (month), the time interval (year) of
output results and the start state (1 indicates the initial run and 0 indicates the continue run). These
parameters are defined in the file “ccinput”.
In addition, sea surface forcing fields also need in the model run. The data of sea surface
forcing are saved in the file “MODEL.FRC”, which can be read from file channel No. 90 by the
subroutine program “rdriver.f”, no more interfere by users.
(III) Model output
The output variables are sea surface height, sea ice area, sea ice thickness, convection
frequency (the numbers of convection), temperature, salt, zonal and meridinal current speed. The
process is controlled by the subroutine “SSAVE.f”.
It is noticed that the ocean model output data is very large, so in order to save space these
three dimension variables , such as temperature, salt, zonal and meridinal current speed, just are
saved for the upper 5 levels in the first 11 month each year; they are saved for the all 30 levels in
the last month (December). The saving uses unformatted manner. If all 30 level results need, the
“KLV” should be defined as 30 in the file “SSAVE.f”.
II Model structure
1. Model principal
Refer to the technical guide to ML20 in attachment.
2. The structure of the subroutine
File name
Function
Included
param.h
Subroutine
files
grid parameters: IMT=194, JMT=92, KM=30
tracer numbers: NTRA=2
IMM=193, JMM=91, KMP1=31, KMM1=29
comblk.h
16 common blocks for all the model’s variables
dncoef.h
Normalized  , S, and the coefficients of a 3rd-order
polynomials for sea water state equation of Bryan and Cox
(1972)
isopyc.h
common block for isopycnal diffusion variables
pconst.h
common blocks for land/sea mask
1-d grid-, time-, and physical parameters
pmix.h
common block for calculating Richardson number in order to
computing vertical mixing coefficients based on Pacanowski &
Philander (1981).
Main program
main.f
main program
Subroutines
accumy.f accumulate prognostic variables for monthly mean output use ACCUMM
addps.f
compensating the loss of gross mass
ADDPS
barotr.f
solve the barotropic mode of momentum equations
BAROTR
bclinic.f
solve the baroclinic mode of momentum equations
BCLINIC
comqd.f
const.f
calculate Haney’s Q and D
COMQD
set physical constants, B-C state equation coefficients, time CONST
steps, calendar constants, and mixing-controllor ISOP (not
finished)
convadj.f
GFDL's full convective adjustment
CONVADJ
density.f
calculate density in terms of the 3rd-order polynomials of B-C DENSITY
formula
energy.f
Calculate the total kinetic energy,total available potential ENERGY
energy,total avaiable surface potential energy,and total mass .
filter.f
perform 1-D zonal fouriour filtering
FILTER
grids.f
produce all the grid parameters
GRIDS
Sea ice model
ICESNOW
inirun.f
Initialize the model
INIRUN
intfor.f
Interpolates monthly mean fields
INTFOR
ice.f
isopycmix.f isopycnal mixing scheme of Gent_McWilliams (1990)
ISOPYI
ISOPYC
ISOADV
ISOPLUX
readyc.f
calculate the advective and viscous terms in the barotropic and READYC
baroclinic modes of momentum equations
readyt.f
calculate the buyancy, pressure-gradient, and other terms READYT
related to  -coordinates in the barotropic and baroclinic
modes of momentum equations
rdriver.f
smth.f
Read in climatological forcing fields
RDRIVER
Perform nine-points smoothing for 2-D variables or 3-D SMOOTH
variables;
Perform 1-D zonal smoothing
SMOOT3
SMT
ssave.f
output some prescribed monthly mean variables at the end of SSAVE
each month,and yearly mean variables at the end of each year.
tracer.f
solve tracer equations (isopycnal mixing not finished)
TRACER,
INVTRI
upwell.f
calculate vertical velocity
UPWELL
vinteg.f
Perform vertical integration
VINTEG
3. The management of hard disk and save directories
The outputs are saved in the subdirectories “OMMEAN”. They are the fields of monthly
mean, and the file names are MMEAN????Jan 、 MMEAN????Feb 、 MMEAN????Mar 、
MMEAN????Apr、MMEAN????May、MMEAN????Jun、MMEAN????Jul、MMEAN????Aug、
MMEAN????Sep、MMEAN????Oct、MMEAN????Nov、MMEAN????Dec，in which the “????”
indicate the current model year.
4. The step for the model run
When the model starts, there are two state for the initial field:
(1) If the ocean state is immobile, the initial temperature and salt fields (annual mean state of
observation) need to be read. The data are saved in the unformatted file “TSinitial”, which can be
read from the file channel No. 81.
(2) If the ocean is integrated from a middle state, the ocean state data (including sea surface
height, temperature, salt, current speed, sea ice area and sea ice thickness) in the start model year
need to be copied from the directory FORT22 to fort.22 in the current directory, that is the
FORT22/fort.22????Dec need to be copied to fort.22, in which, the “????” indicates the current
model year, such as 2220.
It is noticed that the choice for weather the ocean is immobile need to be defined in the file
“ccinput”. In generally, a ocean model need for a long time (thousands years) to turn to the
equilibrium state, so experiments should run after the spinup process. In another word, when
experiments are used for research, the start state should select the latter choice.
III Model variables and parameters
Table 3.1 The prediction variables（in COMMON /NVAR1/）
variables
Account
Unit
UB (IMT,JMT)
Barotropic velocity in zonal direction
ms-1
VB (IMT,JMT)
Barotropic velocity in meridional direction
ms-1
H0 (IMT,JMT)
Sea surface elevation
m
UBP(IMT,JMT)
Same as UB(i,j) but for previous step
ms-1
VBP(IMT,JMT)
Same as VB(i,j) but for previous step
ms-1
H0P(IMT,JMT)
H0(i,j) at previous step
m
U (IMT,JMT,KM)
Total zonal velocity, positive for eastward
ms-1
V (IMT,JMT,KM)
Total meridional velocity, positive for southward
ms-1
Vertical velocity in η-coordinate
sec-1
UP(IMT,JMT,KM)
Same as U(i,j,k) but for previous step
ms-1
VP(IMT,JMT,KM)
Same as V(i,j,k) but for previous step
ms-1
WS(IMT,JMT,KMP1)
AT(IMT,JMT,KM,NTRA)
ATB(IMT,JMT,KM,NTRA)
Table 3.2 Two-dimension prediction variables（in COMMON /NVAR2/）
Variables
Account
Unit
H0L(IMT,JMT)
Sea surface elevations deduced from H0(i,j)
m
H0F(IMT,JMT)
Sea surface elevations deduced from H0(i,j)
m
H0BL(IMT,JMT)
Sea surface elevations deduced from H0(i,j)
m
H0BF(IMT,JMT)
Sea surface elevations deduced from H0(i,j)
m
UTL(IMT,JMT,KM)
Zonal velocity deduced from U(i,j,k)
ms-1
UTF(IMT,JMT,KM)
Zonal velocity deduced from U(i,j,k)
ms-1
VTL(IMT,JMT,KM)
Meridional velocity deduced from V(i,j,k)
ms-1
VTF(IMT,JMT,KM)
Meridional velocity deduced from V(i,j,k)
ms-1
Table 3.3
Sea ice prediction variables（in COMMON /NSICE/）
Variables
Account
ITICE(IMT,JMT)
Index field of sea ice(=1 for ice and 0 for water)
ALEAD(IMT,JMT)
Percentage of area covered by ice
TLEAD(IMT,JMT)
The increase of SST in the leads
HI(IMT,JMT)
Unit
Thickness of sea ice
Table 3.4
K
Meter
Sea surface forcing fields（in COMMON /NCYC/）
Variables
Account
SU3(I2,J1,12) Climatological monthly mean zonal wind stress at sea surface
Unit
10-3Nm-2
for the m-th month
SV3(I2,J1,12) Climatological monthly mean meridional wind stress at sea
10-3Nm-2
surface for the m-th month
PSA3(I2,J1,12) Climatological monthly mean sea surface air pressure for the
hPa
m-th month
TSA3(I2,J1,12)
Climatological monthly mean sea level air temperature for
℃
the m-th month
SSS3(I2,J1,12) Climatological monthly mean sea surface salinity for the m-th
psu
month
SWV3(I2,J1,12)
Climatological monthly mean solar radiation absorbed by the
Wm-2
surface for the m-th month
UVA3(I2,J1,12)
Climatological monthly mean sea surface wind speed for the
ms-1
m-th month
QAR3(I2,J1,12)
Climatological monthly mean surface air mixing ratio for the
-
m-th month
CLD3(I2,J1,12)
Observed monthly mean cloud fraction for the m-th month
percentage
Table 3.5 Model output variables（in COMMON /NMMN/）
Variables
Account
Z0MON(I2,J1) Monthly mean sea surface elevation
WSMON(I2,J1,K0) Monthly mean vertical velocity in z-coordinate
TSMON(I2,J1,K0) Monthly mean temperature
Unit
m
ms-1
℃
SSMON(I2,J1,K0) Monthly mean salinity
psu
USMON(I2,J1,K0) Monthly mean zonal velocity
ms-1
VSMON(I2,J1,K0) Monthly mean meridional velocity
ms-1
HIMON(I2,J1) Monthly mean sea-ice thickness
m
HDMON(IMT,JMT)
Monthly mean average thickness of sea ice in one grid
ICMON(IMT,JMT,2)
Frequency of convection within a month
m
unitless
Table 3.6 Parameters I（in COMMON /NMIX/）
Parameters
Value
Account
AM
0.5 105 m2  s1 for 50°N-60°S,
Lateral eddy viscosity coefficient
2.0 105 m2  s1 for the other region
AMV
1.0 104 m2  s1
Vertical viscosity coefficient
AH
2.0 103 m2  s1
Lateral diffusion coefficient
AHV(KM)
0.3 104 m2  s1
Vertical diffusion coefficient
AHICE
= AHV ( 0)
Diffusivity between ice &
water
Table 3.7 Parameters II（in COMMON /NCN1/）
Parameters
Value
Account
D0
1029.0 kg  m3
CP
3901.0 J  kg 1  K 1
Reference density of sea water,  o
specific heat of sea water at constant pressure,
cp
9.806 m  s2
Acceleration of gravity, g
C0
2.6  103
bottom friction coefficient
TBICE
-1.8  C
frozen point of sea water
G
 1
OD0
0
SAG
sin  g
 g = 10 (bias angle of bottom friction)
CAG
cos  g
 g = 10 (bias angle of bottom friction)
OD0CP
 C 
RSD
0
1
p
 AMV 0 1
total area of the model’s surface layer
ASEA
AFB1
0.025
AFB2
1  2  B
AFC1
0.43
AFC2
1  2  C
AFT1
0.43
AFT2
1  2  T
Asselin Filter coefficient,  B
Asselin Filter coefficient,  C
Asselin Filter coefficient,  T
Table 3.8 Parameters for integration and time control（in COMMON /NCMN/）
Parameters
Value
Account
DTB
t B =FLOAT(IDTB)
IDTB=120 seconds
DTC
tC =FLOAT(IDTC)*60.0
IDTC=240 minutes
DTS
tT =FLOAT(IDTS)*3600.0
IDTS= 8 hrs
DTB2
2 t B
DTC2
2 tC
NBB
N B  tC / t B
Barotropic steps within one baroclinic
step
NCC
N C  tT / tC
Baroclinic steps within one thermohaline
step
NSS
24/IDTS
ONBB
 N B  11
ONBC
 N C  N B  11
ONCC
 N C  11
ISB
0 for Euler-forward scheme
steps for thermohaline process per day
switch on Euler-forward or leap-frog
scheme for barotropic mode
ISC
0 for Euler-forward scheme
switch on Euler-forward or leap-frog
scheme for baroclinic mode
IST
0 for Euler-forward scheme
switch on Euler-forward or leap-frog
scheme for thermohaline process
NMONTH /31, 28, 31, 30, 31, 30, 31, 31, 30,
(12)
31, 30, 31/
MSTART /16, 14, 16, 15, 16, 15, 16, 16, 15,
(12)
the day of mid-month
16, 15, 16/
ABMON / 'Jan', 'Feb', 'Mar',' Apr', 'May',
(12)
day number of each calendar month
Character string for naming the monthly
'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', mean outputs
'Dec' /
Attachment:
Technical Guide to ML20 (the previous edition of
T63L30_OGCM)
A2.1 INTRODUCTION
The component OGCM of the GOALS/IAP model is the ML20-1, of which the main features can
be summarized as follows (see Jin et al., 1999, Chapter 5 in this book for details):
 The model is a fully primitive equation model with a free surface instead of using rigid-lid
approximation.
 The zonal mean standard stratifications of temperature and salinity, as well as density and
pressure are introduced into the model’s governing equations. Thus, all the thermodynamic variables in
this model are replaced by their departures from the standard stratifications. The climatological zonal
mean thermohaline structure is used as the model’s initial conditions, which may be helpful in
accelerating the convergence of the model’s thermohaline structure.
 The  -coordinate system (Mesinger et al., 1985; Yu, 1989) is adopted to describe both the free
surface and the complex bottom topography.
 A method for separating and coupling external and internal modes in ocean models with a free
surface, combined with the Asselin time-filter (Asselin, 1971) , is used in the model’s time integration.
Thus, the time step of the internal-mode integration is free from the critical limitation related to surface
gravitational waves. Within the internal mode, the thermohaline process is further separated from the
momentum process.
 A simple thermodynamic sea-ice model is incorporated into the ocean model.
 The model domain covers the global scope except the North Pole with the horizontal resolution
of 45 in the colatitude-longitude coordinates. Arakawa's B-grid (Betteen et al., 1981) is used in the
model. There are twenty layers in vertical direction covering the maximum depth of 5000m. The
model’s topography and geometry is generated based on 1 1 data of Gates and Nelson (1975).
The sea surface forcing fields for driving the model include:
 Sea level air pressure (Esbensen and Kushnir, 1981)
 Sea level air temperature (Esbensen and Kushnir (1981) combined with the ECMWF ten-year
averaged analysis data in high latitudes)
 Sea surface wind stress (Hellerman and Rosenstein, 1983)
 Snowfall (set to zero here)
 Sea surface salinity (Levitus, 1982)
 Solar radiation arrived at the surface (Esbensen and Kushnir, 1981)
 Sea surface wind speed (Esbensen and Kushnir, 1981)
 Surface air mixing ratio (Esbensen and Kushnir, 1981)
 Cloud fraction (Esbensen and Kushnir, 1981)
All of these data are packed into a file, fort.90.
Before running the model, three control parameters listed in a file ccinput should be prescribed.
 NUMBER = the integration length in month.
 NSTART = the switch for setting the initial conditions. If set to 1 the model is integrated from
a motionless state, otherwise from a restarted condition given by a file fort.22.
 MFOPUT = the time interval for outputting monthly mean results.
In addition, a parameter NUP is defined in the program MAIN for choosing the diffusion scheme.
The traditionally diffusion scheme is applied if NUP is set to 1; otherwise, it is replaced by an
“upwind” finite-difference scheme where the explicit diffusion term in temperature and salinity
equations is discarded. The NUP is defaulted at 1 in the model.
A2.2 NUMERICAL SCHEME
A2.2.1 Grid Arrangement
The horizontal grid system is a rectangular Arakawa staggered B grid, with i (1 i 74) and j (1 j
 46) representing the discretized coordinates in - and - directions, respectively. The vertical layers
are numbered by k (1 k  20) in the order from top to bottom (see Table 5.2). According to the
definition of B-grid, two kinds of cells, i.e. "T-cells" and "V-cells" are defined. Temperature, salinity
and density are defined at the center of each T-cell (T-point). Similarly, the zonal and meridional
velocity components are defined at the center of each V-cell (V-point). It should be kept in mind that
the southward meridional velocity component is defined as positive due to using the colatitude-latitude
coordinate system. In addition, pressure and vertical velocity (positive in upward direction) are defined
at the center of the bottom faces of T-cells, and sea surface height is defined at the center of the surface
of the uppermost T-cells. The T-cell with i=1 and j=1 is located at the point (90N, 0), and the V-cell
with i=1 and j=1 is located at the point (88 N, 2.5W). The cells with i=73 and 74 are overlapped with
the cells with i=1 and 2, respectively.
There are two integer three-dimensional arrays, i.e. IT(74,46,20) and IV(74,46,20), giving the
land-sea marks on the T-cells and V-cells, respectively. These two three-dimensional index arrays are
saved in the files, fort.71 and fort.72, respectively.
A2.2.2 Time Integration
The “Leap-frog” time integration scheme is used for barotropic mode, baroclinic mode and
thermohaline mode with different time steps. An “Euler-forward” scheme is applied at the first step of
each month to prevent the separation of the solutions at odd and even time steps due to the use of
“leap-frog” method.
In order to enlarge the time steps and to ensure the computational stability, the Asselin time-filter
(Asselin, 1971) is adapted at each time step as follows,
Fs  (1  )F n 
 n 1
(F  F n 1 )
2
(A2.1)
where Fs is the smoothed solution while F may be the barotropic velocities, sea surface height,
baroclinic velocities, temperature and salinity. In the code, ( 1  ) and  / 2 are defined as AFB1 and
AFB2 (=0.025) for barotropic mode, AFC1 and AFC2 (=0.86) for baroclinic mode, and AFT1 and
AFT2 (=0.86) for thermohaline mode.
A2.2.3 External-Internal Mode Interaction
The model integration is separated into three parts. The external (barotropic) mode is calculated in
the subroutine BAROTR, predicting the sea surface height and the brotropic velocities, u and v .
The internal (baroclinic) mode is calculated in the subroutine BCLINC, predicting the total velocities, u
and v. The thermohaline mode is calculated in the subroutine THERMO, predicting the perturbed
temperature, T , and salinity, S . At first, the external mode is integrated N B times with a time step
t B to match a baroclinic step. Then the internal mode is integrated once with a time step
tC  N B  tB , while the thermohaline process remains unchanged during this step. Since the internal
and external modes have different truncation errors, so that the vertical integrals of the (u, v) may
depart slightly from ( u , v ) during the course of a long integration. We therefore adjust (u, v) at the end
of each baroclinic step by replacing the vertical averages of (u, v) with the updated ( u , v ). Based on
the updated baroclinic velocities, the diagnostic vertical velocity is calculated in terms of the continuity
equation. Finally, after N C baroclinic steps, the thermohaline mode is integrated with a time step of
tTS  N C  tC .
A2.3 LIST OF MODEL PROGRAMS
The model programs are listed in the followings with brief descriptions about what they do.
A2.3.1 Program MAIN
Program MAIN contains the program-flow control, and the input of model’s control parameters
(NUMBER, NSTART and MFOPUT) and index fields (fort.71 and fort.72). It becomes a subroutine in
the programs of the GOALS model.
A2.3.2 Subroutine ADDPS
This subroutine is used for compensating the loss of the total volume of model’s ocean by having
the global averaged sea surface height equal to zero. Theoretically the finite-difference scheme of the
continuity equation has been designed to keep the total volume conservation, but the conservation may
be destroyed by the round-off error of computer.
A2.3.3 Subroutine ADJUST
This subroutine contains an explicit convection scheme, which may totally remove all
gravitational instability in the water column. The potential density of seawater is calculated in terms of
the polynomial formula given by Bryan and Cox (1972) with the reference level at the sea surface.
A2.3.4 Subroutine BAROTR
This subroutine is used to solve the vertically integrated velocity components, u and v , and the sea
surface height, zo. The equations for u and v can be derived by vertically integrating Eqs.(5.20) and
(5.21). The vertical integrals of the advection and viscosity terms (DLUB and DLVB, see Table A2.1)
are calculated in the subroutine READYC in advance. Additional barotropic viscosity terms are
introduced into the equations following the method of Killworth (1991). This method actually provides
some horizontal smoothing in the barotropic equations and it is beneficial to the stability of the model.
In addition, a semi-implicit scheme is used for the Coriolis terms both for barotropic mode in this
subroutine and for baroclinic mode in subroutine BCLINC.
A2.3.5 Subroutine BCLINC
This subroutine is used to solve the momentum equations to obtain baroclinic velocities. The
advection and viscosity terms (including surface wind stress and bottom friction) are calculated in the
subroutine READYC. The coupling between the barotropic and baroclinic mode is performed after u
and v updated. Finally, the vertical velocity is calculated by subroutine UPWELL.
A2.3.6 Subroutine COMQD
This subroutine is used to calculate two coefficients D and Q in the Eq.(5.32), a generalized form
of the Haney-type surface heat flux formula (Haney, 1971):
D  4  0.985  (0.39  0.05 e A )(1.0  0.6n c2 )  TA3

 0.622 
e (T ) 
  2353  ln 10  s 2A 
  A C D VA c p  L  

TA 
 ps 

(A2.2)
Q  (1   g )SA  0.985  (0.39  0.05 e A )(1.0  0.6n c2 )  TA4
 0.622 

qA 
  e s (TA )  1.0 

  A C D VA L  


q s (TA ) 
 ps 

(A2.3)
where the external forcing fields include the sea surface air temperature (T A), pressure (p A) , humidity
(qA), wind speed (VA), total cloudiness (nc), and incoming solar radiation at the surface (SA). These
variables are daily updated.
A2.3.7 Subroutine CONST and CONSJK
These two subroutines produce most of constants used in the model, such as time integration steps,
depth of each layer, Asselin low pass filter coefficients, parameters of physical processes, and
finite-difference coefficients related to the grid parameters etc.
A2.3.8 Subroutine ENERGY
This subroutine calculates of the total kinetic energy (EK), total available potential energy (EA),
total available surface potential energy (EAS) and total mass perturbation of free surface (TM). All of
these variables are used to monitor the integration process of the model.
EK  
1
 0 (u 2  v 2 )a 2 sin dddz
2
EA   
EAS  
(  ~
) 2 2
a sin dddz
d
2g
dz
1
 0 g(z 0 ) 2 a 2 sin dd
2
TM   0 z 0a 2 sin dd
(A2.4)
(A2.5)
(A2.6)
(A2.7)
A2.3.9 Subroutine FFORCE
This subroutine is used to calculate the perturbed sea surface air pressure and its gradient, and to
prepare some intermediate variables or coefficients for solving temperature and salinity equations.
A2.3.10 Subroutine ICESNOW
This subroutine contains a simple thermodynamic sea ice model described in the section 5.2.2.
The initial thickness of sea ice is set to 5 cm. There will be no snow remained if sea ice is totally
melted.
A2.3.11 Subroutine INIRUN
This subroutine is used to initialize the model. If NSTART=1, the model will be integrated from
the first month (MONTH=1) of the model. The initial perturbed temperature and salinity, velocity, as
well as the sea surface height are set to zero. If NSTART=0, the model will be integrated from a
restarted data set contained in a file, fort.22. If the model is not restarted from Jan. 1, another data file
fort.21 is required for obtaining correct annual mean output. The initial barotropic velocities are
obtained by vertical integrations of the baroclinic velocities, and the initial vertical velocity is
calculated by subroutine UPWELL.
A2.3.12 Subroutine MSO AND ZLEVI
These two subroutines cast the observed zonal mean temperature and salinity of Levitus (1982) on
model’s grid system, calculate the zonal mean meridional pressure gradient, and calculate global mean
density (see Eq.(A2.8-11)) and its vertical gradient which is required for calculating total available
potential energy in subroutine ENERGY.
A2.3.13 Subroutine RDRIVER
This subroutine reads in ten climatological monthly mean forcing fields for driving the model.
They are the zonal and meridional components of sea surface wind stresses, sea level pressure, sea
level air temperature, sea surface salinity, snowfall, solar radiation at sea surface, sea surface wind
speed, sea surface air mixing ratio and cloud fraction. The annual mean forcing fields are calculated in
this subroutine, which will be used to drive the model if the switch (NA) is set to 1 in the program
MAIN. In order to parameterize the brine rejection effect in the freezing process, the observed sea
surface salinity is enhanced artificially in a region around the Antarctic. This artificial
salinity-enhancement should be replaced by using a parameterization of brine rejection in sea ice model
in the future.
A2.3.14 Subroutine READYC
This subroutine is used to calculate the horizontal/vertical advections and viscosities in the
momentum equations, and their vertical integrations. The surface wind stress and the bottom friction
stress are used in surface and bottom boundary conditions.
A2.3.15 Subroutine READYT
This subroutine calculates the perturbed density, buoyancy, perturbed pressure and its zonal and
meridional gradients, as well as some variables related to the transformation from z-coordinate to
 -coordinate.
The density is calculated based on the formula of Eckart (1958):
  103 
P  b1
b 2  0.689(P  b1 )
P  P(z)  1 
z
10.13
(A2.8)
(A2.9)
b1  b1 (T, S)  5890  38T  0.375T 2  3S
(A2.10)
b 2  b 2 (T, S)  1779.5  11.25T  0.0745T 2  (3.8  0.01T)S
(A2.11)
The units for T, S and  are ºC, psu and kg  m 3 , respectively.
A2.3.16 Subroutine SFIELD
This subroutine computes some intermediate quantities, which are kept unchanged during the
model’s integration.
A2.3.17 Subroutine SSAVE
This subroutine is used to produce the restart file fort.22 and fort.21. These two files are updated
automatically every month. In addition, the file fort.22 produced at the end of each year will be saved
automatically every ten years in a separated file, e.g., fort.22.1100Dec (which represents the restart data
at the end of the December of the 100th model year).
To output z- vertical velocity, the following equation

z
w   H m  o

s

 

 

  1  
s
 

 z o



 t  v   1  
s


 
z o 
 
 
(A2.12)
can be used.
A2.3.18 Subroutine THERMO
This subroutine contains the solver of temperature and salinity equations.
A2.3.19 Subroutine UPWELL
This subroutine calculates the vertical velocity in  -coordinate based on the continuity equation.
A2.3.20 Subroutine VITVU
This subroutine generates several index fields based on IT and IV, which are used in
finite-difference calculations.
A2.3.21 Utility Subroutines
Three major utility subroutines are ICSSCU (Spline smoother), ICSIVU (Spline interpolation),
DCSEVU (Spline derivation). All these subroutines are copied from IMSL (International Mathematical
and Statistical Library) and can be easily understood by reading the explanation lines in the code.
A2.4 FORTRAN DICTIONARY
Included in Table A2.1 are the FORTRAN symbols of the model program code, which are listed
alphabetically with a brief description. The subscripts, i (1 i 74) and j (1 j 46), represent the
discretized coordinates in - and - directions, respectively, k (1 k  20) for vertical layers from top to
bottom and m (1 m 12) for month. All of these symbols are defined in the common block file,
comblk.h. The other temporal and local variables are not listed here.
Table A2.1. FORTRAN Dictionary (A-C)
Symbol
A
Subroutine
CONST, CONSJK,
Description
radius of Earth, a, (6,371,000 m)
MSO
ABMON(m)
SSAVE
Character*3, (Jan, Feb, . . . Dec)
AFB1, AFB2
CONST，BAROTR
Asselin filter coefficients for barotropic mode, see Eq.(A2.1)
AFC1, AFC2
CONST，BCLINC
Asselin filter coefficients for baroclinic mode, see Eq.(A2.1)
AFT1, AFT2
CONST,
Asselin filter coefficients for thermohaline mode, see Eq.(A2.1)
AM
CONST, BAROTR
horizontal viscosity, AMH, (8.0105 m2s-1), see Eq.(5.7)
ASEA
SFIELD，ADDPS
non-dimensional total surface area of model’s ocean
AT1, AT2, AT3,
CONST，ADJUST
coefficients for calculation of potential density (Bryan and Cox,
THERMO
ATS, AT2S,
1972)
AS1, AS3, AS2T
BKI
CONST，ICESNOW
ice conductivity, I, (2.04 Wm-1K-1), see Eq.(5.39)
BKS
CONST，ICESNOW
snow conductivity S, (0.31 Wm-1K-1), see Eq.(5.38)
BKW
ICESNOW
o  cp  AHV(0)
C0
CONST，READYC
bottom frictional coefficient, C0, (2.610-3), see Eq.(5.36)
CAG
CONST，READYC
cosine of the Ekman deflection angle, , see Eq.(5.36)
CLD3(i,j,m)
INTFOR，RDRIVER
monthly mean cloudiness, nc, see Eq.(A2.2) and (A2.3)
CP
CONST，FFORCE， specific heat of sea water, cp, (3901.0 J kg-1 K-1)
COMQD


CV1(j)
CONSJK，BAROTR
a 2 1  ctg2 j1/ 2 , see Eq.(5.7)
CV2(j)
CONSJK，BAROTR
a 2 ctg j1/ 2  sin  j1/ 2


1
, see Eq.(5.7)
Table A2.1 (Continued) (D)
Name
D0
Subroutine
CONST, ENERGY
Description
reference sea water density, 0, (1029.0 kg m-3)
READYC, READYT
DB00(k)
MSO
globally averaged density,  z  in kg m-3
DBB(j,k)
MSO, ENERGY,
(, z) in kg m-3, see Eq.(5.9)
standard zonal mean density, ~
READYC
DBDZ(k)
MSO, ENERGY
DDD(i,j)
FFORCE,

for calculation of the total available potential energy
z
heat flux coefficient, D in Wm-2 K-1, see Eq.(5.32)
ICESNOW
DHI(i,j)
ICESNOW
freezing rate of sea ice in ms-1, see Eq.(5.45)
DLU(i,j,k)
READYC, BCLINC
 L(u )  H m2

u 
 
1  ctg 2 
2ctg  v 
 A MV
  A MH  u 
u 2
2

 
 
a
a sin   

see Eqs.(5.21)
DLV(i,j,k)
READYC, BCLINC
 L( v)  H m2

 
v 
1  ctg 2 
2ctg u 
 A MV
  A MH  v 
v 2
2

 
 
a
a sin   

see Eqs.(5.20)
DLUB(i,j)
BAROTR
1 0
 DLU d , see A2.3.4
S S
DLVB(i,j)
BAROTR
1 0
 DLV d , see A2.3.4
S S
DTB
CONST, BAROTR
time step for barotropic mode, tB in sec
DTB2
CONST, BAROTR
2tB
DTC
CONST, BCLINC
time step for baroclinic mode, tC in sec
DTC2
CONST, BCLINC
2tC
DTS
CONST, THERMO
time step for thermohaline process, tTS in sec
DTS2
CONST, THERMO
2tTS
DX
CONSJK
longitudinal width of cell , =/36 (5)
DY(j)
CONSJK
latitudinal width of cell, =/45 (4)
DZAB(i,j,k)
SFIELD, READYC
k  Hm (Hb)-1 at T-point
DZABU(i,j,k)
SFIELD, VINTEG
k  Hm (Hb)-1 at V-point
DZP(k)
CONSJK, SFIELD,
-thickness of the k-th layer, k, see Eq.(5.14)
ENERGY, UPWELL
DZPH(i,j)
SFIELD, BAROTR
total -thickness, s, at T-point, see Eq.(5.14)
Table A2.1 (Continued) (E-G)
Name
Subroutine
Description
EA0
INIRUN, ENERGY
total available potential energy, see Eq.(A2.5)
EAS0
INIRUN, ENERGY
total available surface potential energy, see Eq.(A2.6)
EBEA(j), EBEB(j)
CONSJK, BAROTR
parameters used in Coriolis adjustment process at Euler forward
step in barotropic mode
EBLA(j), EBLB(j)
CONSJK, BAROTR
parameters used in Coriolis adjustment process at leap-frog step
in barotropic mode
EK0
INIRUN, ENERGY
total kinetic energy, see Eq.(A2.4)
EPEA(j),EPEB(j)
CONSJK, BCLINC
same as EBEA and EBEB except for baroclinic mode
EPLA(j),EPLB(j)
CONSJK, BCLINC
same as EBLA and EBLB except for baroclinic mode
G
CONST, MSO,
gravitational acceleration of Earth, g, (9.81 ms-2)
READYT, BAROTR,
BCLINC, ENERGY

g in ms-2, see Eq.(5.26)
0
GG(i,j,k)
READYT
buoyancy at T point, g  
GGU(i,j,k)
READYT, BCLINC
g' at V point
GPY(j,k)
READYT, BCLINC
~
p
, see Eq.(5.20)
a
GPYB(i,j)
SFIELD, BAROTR
vertically averaged GPY
GSY(j,k)
MSO, THERMO
~
S
, used in Eq.(5.19)
a
GSYY(j,k)
MSO, THERMO
GSZ(j,k)
MSO, THERMO
GSZ0(j)
MSO, FFORCE
 ~

 S  , used in Eq.(5.31)
 z 
  z 0
GSZZ(j,k)
MSO, THERMO
~
 
S 
, used in Eq.(5.19)
A HV
z 
z 
GTY(j,k)
MSO, THERMO
GTYY(j,k)
MSO, THERMO
GTZ(j,k)
MSO, THERMO
GTZ0(j)
MSO, FFORCE
GTZZ(j,k)
MSO, THERMO
~
A HH  
S 
, used in Eq.(5.19)
sin

a 
a 2 sin   
~
S
, used in Eq.(5.19)
z
~
T
, used in Eq.(5.18)
a
~
A HH  
T 
sin

, used in Eq.(5.18)
a 
a 2 sin   
~
T
, used in Eq.(5.18)
z
~
 T

 , used in Eq.(5.30)
 z 

 z 0
~
 
T 
A
, used in Eq.(5.18)
HV
z 
z 
(Continued)
Name
H0(i,j)
Subroutine
INIRUN, READYC,
Description
sea surface height, zo in m, see Eq.(5.22)
READYT, BAROTR,
BCLINC, THERMO,
ADDPS, SSAVE
H0BT(i,j)
INIRUN, READYC,
(H0BF, H0BL)
BCLINC
H0F(i,j)
INIRUN, READYT, ,
(H0L, H0T)
THERMO
time-weighted average of zo in baroclinic mode
time-weighted average of zo in thermohaline mode
H0P(i,j)
INIRUN, BAROTR,
zo at the previous step
SSAVE
HB(i,j)
SFIELD, READYT
model ocean's depth at T-point, Hb in m, see Eq.(5.14)
HBX(i,j)
SFIELD, READYT
H b
, implicitly included in Eq.(5.21)
a sin 
HBY(i,j)
SFIELD, READYT
H b
, implicitly included in Eq.(5.20)
a
HHS(i,j)
INIRUN, ICESNOW,
thickness of snow over sea ice, hS in m, see Eq.(5.38)
SSAVE
HI(i,j)
INIRUN, READYC,
thickness of sea ice, hI in m, see Eq.(5.39)
THERMO, SSAVE
HIM(i,j)
SSAVE
annual mean hI
HIMON(i,j)
SSAVE
monthly mean hI, which would be set to 0 if more than half of a
month are ice free.
HM
SFIELD, UPWELL,
maximum depth of model’s ocean, Hm, (5000 m), see Eq.(5.14)
ENERGY, SSAVE
HMDZP(k)
CONSJK, READYT,
k  Hm
BCLINC
HMOB(i,j)
SFIELD, THERMO
Hm  (Hb)-1
ICVM(i,j,k)
INIRUN,
frequency of convective adjustment within a year
ADJUST,
SSAVE
ICVMON(i,j,k)
ADJUST, SSAVE
frequency of convective adjustment within a month
IDTB
CONST
integer data of tB in sec
IDTC
CONST
integer data of tC in min
IDTS
CONST
integer data of tTS in hr
ISB
MAIN, BAROTR
Switch for Euler forward scheme used in barotropic mode
ISB=1: Euler forward, ISB=0: leap-frog
ISC
MAIN, BCLINC
same as ISB but for baroclinic mode
IST
MAIN, THERMO
same as ISB but for thermohaline mode
IT(i,j,k)
VITVU et al.
integer index field for T-cells
0: land; -1: inner ocean; 1-8: near-boundary cells
ITICE(i,j)
ITSNOW(i,j)
IV(i,j,k)
INIRUN, READYC,
index field of sea ice:
THERMO, SSAVE
1 for ice; 0 for water
INIRUN,
index field of snow over ice:
COMQD,
ICESNOW, SSAVE
1 for snow-covered ice; 0 for bare ice or water
VITVU et al.
integer index field for V-cells:
0 for land cell; nonzero for ocean cell
(Continued)
Name
Subroutine
Description
MEND
MAIN
the end month of the current run
MFOPUT
MAIN, SSAVE
interval for output monthly mean results (in month), see
MONTH
MAIN, INIRUN,
time counter in month
SSAVE
MSTART(m)
CONST, INTFOR,
the mid-day of each month
SSAVE
NBB
CONST, BAROTR,
number of barotropic steps within one baroclinic step, NB
BCLINC
NCC
MAIN, CONST,
number of baroclinic steps within one tracers step, NC
THERMO
NMONTH(m)
MAIN, CONST,
number of days of each month
INTFOR, SSAVE
NSS
MAIN, CONST
number of thermohaline steps in one day
NTA(i,j)
MAIN, VITVU,
number of layers at T-point
ADJUST
NVA(i,j)
VITVU
number of layers at V-point
O
CONST, CONSJK
angular frequency of Earth,  (0.7292 sec-1)
OD0
CONST, FFORCE,
(o)-1
READYT, BAROTR,
BCLINC
ODDD(i,j)
FFORCE
o  cp  D-1
ODZT(k)
CONSJK, THERMO
(k+1/2)-1
OHB(i,j)
SFIELD, UPWELL
(Hb)-1 at T-cell
OHBU(i,j)
SFIELD, BAROTR,
(Hb)-1 at V-cell
UPWELL
ONBB
CONST, BCLINC
( NB +1)-1
ONBC
CONST, THERMO
(NB  NC +1) -1
ONCC
CONST, THERMO
( NC +1)-1
OTX2(j)
CONSJK, BAROTR,
(2asinj)-1
UPWELL, THERMO
OTX4(j)
CONSJK, THERMO
(4asinj)-1
OUX2(j)
CONSJK, READYC,
(2asinj+1/2)-1
FFORCE, BAROTR,
BCLINC
OY1
CONSJK
(a)-1
OY2
CONSJK, FFORCE,
(2a)-1
READYT, BAROTR,
BCLINC, THERMO
OY4
CONSJK, BCLINC
(4a)-1
OZ1(k)
CONSJK, THERMO
(k)-1
OZ2(k)
CONSJK, READYC,
(2k)-1
THERMO
OZ4(k)
CONSJK
(4k)-1
(Continued)
Name
Subroutine
Description
PAX(i,j)
FFORCE, BAROTR

pA
1
, see Eqs.(5.21) and (5.28)
0 a sin 
PAY(i,j)
FFORCE, BAROTR

1 pA
, see Eq.(5.20) and (5.28)
0 a
PSA(i,j)
RDRIVER, COMQD
daily sea level pressure, pA, interpolated from PSA3
FFORCE, INTFOR
PSA3(i,j,m)
MAIN, RDRIVER,
monthly mean pA in hPa
INTFOR
PSAL(j)
MSO, RDRIVER,
annual mean and zonal averaged pA
INTFOR
PXB(i,j)
READYT, BAROTR
1 0  1
 p 
d
  
S S  0 a sin  
PYB(i,j)
READYT, BAROTR
1 0  1  p 
d
 
S S  0 a 
QAR3(i,j,m)
MAIN, RDRIVER,
monthly mean sea level air mixing ratio, qA, see Eq.(A2.2)
INTFOR
QII
CONST, ICESNOW
heat fusion of ice, QI (302.0 MJm-3), see Eq.(5.45)
QQQ(i,j)
FFORCE, COMQD,
surface heat flux parameter, Q (in Wm-2) , see Eq.(5.32)
ICESNOW
QSS
CONST, ICESNOW
heat fusion of snow, QS (110.0 MJm-3) , see Eq.(5.33)
(Continued)
Name
Subroutine
Description
R104(j)
CONSJK, READYC
sinj+1/(4asinj+1/2)
R11(j)
CONSJK, THERMO
sinj+1/2/(asinj)
R12(j)
CONSJK, BAROTR,
sinj+1/2/(2asinj)
UPWELL, THERMO
R14(j)
CONSJK, THERMO
sinj+1/2/(4asinj)
R11Y(j)
CONSJK, THERMO
sinj+1/2/(a22sinj)
R204(j)
CONSJK, READYC
sinj/(4asinj+1/2)
R21(j)
CONSJK, THERMO
sinj-1/2/(asinj)
R22(j)
CONSJK, BAROTR,
sinj-1/2/(2asinj)
UPWELL, THERMO
R24(j)
CONSJK, THERMO
sinj-1/2/(4asinj)
R21Y(j)
CONSJK, THERMO
sinj-1/2/(a22sinj)
RAZ1(k)
CONSJK
zk/(zk+zk+1)
RAZ2(k)
CONSJK
zk+1/(zk+zk+1)
RKH2V
SFIELD, READYC
AMV  (Hm)-2
RKT(k)
MSO, THERMO
vertical diffusion coefficient, AHV(z), see Eqs.(5.18) and (5.19)
RKT0
CONST, FFORCE
AHV (0) (0.310-4 m2s-1)
RKV
CONST
vertical viscosity, AMV (1.010-4 m2s-1), see Eqs.(5.20) and (5.21)
RMU
CONST, FFORCE,
inverse of the restoring time scale for salinity,  ((20 day)-1), see
THERMO
Eq.(5.31)
RMUHM
CONST, THERMO
50    (Hm)-1
RMUT
CONST, FFORCE
50  
RSD
CONST, READYC
Hm  (o  AMV)-1
RU10(j)
CONSJK, READYC,
sinj+1/(a22sinj+1/2)
BAROTR
RU20(j)
CONSJK, READYC,
sinj/(a22sinj+1/2)
BAROTR
(Continued)
Name
SBB(j,k)
Subroutine
MSO, CONSJK,
THERMO
Description
~
zonally averaged standard salinity, S(, z) in psu, see Eq.(5.9)
SINT(j)
CONSJK, ENERGY
sin  j
SINU(j)
CONSJK, ENERGY
sin  j1/ 2
SNF(i,j)
RDRIVER, INTFOR,
daily snowfall, interpolated from SNF3
ICESNOW
SNF3(i,j,m)
RDRIVER, INTFOR
monthly mean snowfall (here it is set to zero)
SOTX(j)
CONSJK, THERMO
1 /(a sin  j ) 2
SOUX(j)
CONSJK, READYC,
1 /(a sin  j1 2 ) 2
BAROTR
SS(i,j,k)
READYT, SSAVE,
S' in psu, see Eq.(5.9)
THERMO
SSC(i,j)
FFORCE, THERMO
~
S * S(,0) , see Eq.(5.31)
SSM(i,j,k)
SSAVE
annual mean salinity, S
SSMON(i,j,k)
SSAVE
monthly mean salinity, S
SSP(i,j,k)
THERMO
S' at the previous step
SSS(i,j)
RDRIVER
daily S*, interpolated from SSS3
SSS3(i,j,m)
RDRIVER
observed monthly mean surface salinity, S* in psu
SWV3(i,j,m)
RDRIVER, INTFOR
monthly mean incoming solar radiation, SA in Wm-2
SU(i,j)
INTFOR, READYC
daily , interpolated from SU3
SU3(i,j,m)
RDRIVER
monthly mean zonal wind stress,  in 10-3 Nm-2
SV(i,j)
INTFOR, READYC
daily , interpolated from SV3
SV3(i,j,m)
RDRIVER
monthly mean meridional wind stress,  in 10-3 Nm-2
(Continued)
Name
TBB(j,k)
TBICE
Subroutine
Description
MSO, THERMO,
~
zonally averaged standard temperature, T(, z)
SSAVE
Eq.(5.9)
CONST, THERMO,
ice base temperature, TB (271.2 K)
in ºC, see
ICESNOW
TEA0
MAIN, INIRUN,
total available energy
ENERGY
TIB(j)
MSO, THERMO,
~
T(, z) + 273.0 (in K), see Eq.(5.39)
ICESNOW
TM0
INIRUN, ENERGY
total mass perturbation of free surface in kg, see Eq.(A2.7)
TSA(i,j)
FFORCE, INTFOR
daily TA, interpolated from TSA3, see Eq.(5.32)
TSA3(i,j,m)
RDRIVER, INTFOR
monthly mean sea surface air temperature, TA in ºC
TSAICE(i,j)
FFORCE,ICESNOW
same as TSA but used over sea ice
TSC(i,j)
FFORCE, THERMO
~
TA  D 1Q  T(,0)
TSM(i,j,k)
INIRUN, SSAVE
annual mean TA
TSMON(i,j,k)
SSAVE
monthly TA
TT(i,j,k)
INIRUN, THERMO,
T in ºC, see Eq.(5.9)
ICESNOW, SSAVE
TTP(i,j,k)
THERMO
T at the previous step
(Continued)
Name
U(i,j,k)
Subroutine
Description
INIRUN, BCLINC,
zonal component of velocity, u in ms-1, positive for eastward, see
ENERGY, UPWELL,
Eq.(5.21)
SSAVE
UB(i,j)
INIRUN, BAROTR,
barotropic u-component, u , see subsection A2.3.4
SSAVE
UBP(i,j)
INIRUN, BAROTR,
u at the previous step
SSAVE
UIT1/2/3/4/5(i,j,k)
THERMO
VIT-based index fields used in calculation of diffusions
UP(i,j,k)
READYC, BCLINC
u at the previous step
USM(i,j,k)
INIRUN, SSAVE
annual mean u
USMON(i,j,k)
SSAVE
monthly mean u
UTL(i,j,k),
INIRUN, READYT,
time-weighted averages of u
UTF(i,j,k)
BCLINC, THERMO,
SSAVE
UVA3(i,j,m)
RDRIVER, INTFOR
monthly mean sea surface wind speed, VA in ms-1, see Eq.(5.33)
V(i,j,k)
INIRUN, BCLINC,
meridional component of velocity, v in ms-1, positive southward,
ENERGY, UPWELL,
see Eq.(5.20)
SSAVE
VB(i,j)
VBP(i,j)
INIRUN, BAROTR,
barotropic v-component, v barotropic u-component, u , see
SSAVE
subsection A2.3.4
INIRUN, BAROTR,
v at the previous step
SSAVE
VIT(i,j,k)
many places
T-cell index field, 1.0: ocean; 0.0: land
VIV(i,j,k)
many places
V-cell index field, 1.0: ocean; 0.0: land or boundary
VP(i,j,k)
READYC, BCLINC
v at the previous step
VSM(i,j,k)
INIRUN, SSAVE
annual mean v
VSMON(i,j,k)
SSAVE
monthly mean v
VTL(i,j,k),
INIRUN, READYT,
time-weighted averages of v
VTF(i,j,k)
BCLINC, THERMO,
SSAVE
(Continued)
Name
Subroutine
WGP(i,j)
READYT, BAROTR
WHX(i,j)
READYT, BAROTR
Description
g g
, used in vertically integrated Eqs.(5.20) and (5.21)

g gs
g
S2 a sin 
WHY(i,j)
READYT, BAROTR
WS(i,j,k)
INIRUN, READYC,
 s
, used in vertically integrated Eq.(5.21)

g  s
, used in vertically integrated Eq.(5.20)
S2 a 
-vertical velocity,  in s-1
SSAVE
WSM(i,j,k)
SSAVE
annual mean vertical velocity, w in mday -1
WSMON(i,j,k)
SSAVE
monthly mean w
Z0M(i,j)
SSAVE
annual mean zo
Z0MON(i,j)
SSAVE
monthly mean zo
ZK0(k)
CONSJK
z at the surface of k-th layer, zk-1/2 (for a flat-surface ocean)
ZKP(k)
CONSJK
 at the surface of k-th layer, k-1/2
ZKT(k)
CONSJK
 at mid-level of k-th layer, k
ZMID(k)
MSO, ICESNOW,
depth at the mid-level of the k-th layer, z k 1/ 2
READYT, ENERGY
Acknowledgements We would like to thank Keming Chen for his great effort in drafting the User's Guide for
the original version of the ocean model (ML20-0). The materials were much helpful in writing this Appendix.
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