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pco2.F
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*
* pco2.F
*
* Andreas Schmittner ([email protected])
* Jul 24, 2017
*
* Returns pCO2 (ppmv) of sea water
*
SUBROUTINE pco2_init(id)
INCLUDE 'ferret_cmn/EF_Util.cmn'
INTEGER id, arg
CALL ef_version_test(ef_version)
* **********************************************************************
* USER CONFIGURABLE PORTION |
* |
* V
CALL ef_set_desc(id,
. 'returns surface pCO2 (ppmv=uatm) using OCMIP routines' )
CALL ef_set_num_args(id, 4)
CALL ef_set_axis_inheritance_6d(id,
. IMPLIED_BY_ARGS, IMPLIED_BY_ARGS,
. IMPLIED_BY_ARGS, IMPLIED_BY_ARGS,
. IMPLIED_BY_ARGS, IMPLIED_BY_ARGS)
CALL ef_set_piecemeal_ok_6d(id, YES, YES, YES, YES, YES, YES)
arg = 1
CALL ef_set_arg_name(id, arg, 'TEMP')
CALL ef_set_arg_unit(id, arg, 'deg C')
CALL ef_set_arg_desc(id, arg, 'temperature')
CALL ef_set_axis_influence_6d(id, arg,
. YES, YES, YES, YES, YES, YES)
arg = 2
CALL ef_set_arg_name(id, arg, 'SALT')
CALL ef_set_arg_unit(id, arg, 'su')
CALL ef_set_arg_desc(id, arg, 'salinity')
CALL ef_set_axis_influence_6d(id, arg,
. YES, YES, YES, YES, YES, YES)
arg = 3
CALL ef_set_arg_name(id, arg, 'DIC')
CALL ef_set_arg_unit(id, arg, 'mol/m^3')
CALL ef_set_arg_desc(id, arg, 'dissolved inorganic carbon')
CALL ef_set_axis_influence_6d(id, arg,
. YES, YES, YES, YES, YES, YES)
arg = 4
CALL ef_set_arg_name(id, arg, 'ALK')
CALL ef_set_arg_unit(id, arg, 'mol/m^3')
CALL ef_set_arg_desc(id, arg, 'total alkalinity')
CALL ef_set_axis_influence_6d(id, arg,
. YES, YES, YES, YES, YES, YES)
* ^
* |
* USER CONFIGURABLE PORTION |
* **********************************************************************
RETURN
END
*
* In this subroutine we compute the result
*
SUBROUTINE pco2_compute(id, arg_1, arg_2, arg_3, arg_4, result)
IMPLICIT NONE
INCLUDE 'ferret_cmn/EF_Util.cmn'
INCLUDE 'ferret_cmn/EF_mem_subsc.cmn'
INTEGER id
REAL arg_1(mem1lox:mem1hix, mem1loy:mem1hiy, mem1loz:mem1hiz,
. mem1lot:mem1hit, mem1loe:mem1hie, mem1lof:mem1hif)
REAL arg_2(mem2lox:mem2hix, mem2loy:mem2hiy, mem2loz:mem2hiz,
. mem2lot:mem2hit, mem2loe:mem2hie, mem2lof:mem2hif)
REAL arg_3(mem3lox:mem3hix, mem3loy:mem3hiy, mem3loz:mem3hiz,
. mem3lot:mem3hit, mem3loe:mem3hie, mem3lof:mem3hif)
REAL arg_4(mem4lox:mem4hix, mem4loy:mem4hiy, mem4loz:mem4hiz,
. mem4lot:mem4hit, mem4loe:mem4hie, mem4lof:mem4hif)
REAL result(memreslox:memreshix, memresloy:memreshiy,
. memresloz:memreshiz, memreslot:memreshit,
. memresloe:memreshie, memreslof:memreshif)
* After initialization, the 'res_' arrays contain indexing information
* for the result axes. The 'arg_' arrays will contain the indexing
* information for each variable's axes.
INTEGER res_lo_ss(6),
. res_hi_ss(6),
. res_incr (6)
INTEGER arg_lo_ss(6,EF_MAX_ARGS),
. arg_hi_ss(6,EF_MAX_ARGS),
. arg_incr (6,EF_MAX_ARGS)
REAL bad_flag(EF_MAX_ARGS), bad_flag_result
* **********************************************************************
* USER CONFIGURABLE PORTION |
* |
* V
INTEGER i, j, k, l, m, n
INTEGER i1, j1, k1, l1, m1, n1
INTEGER i2, j2, k2, l2, m2, n2
INTEGER i3, j3, k3, l3, m3, n3
INTEGER i4, j4, k4, l4, m4, n4
real pt_in,sit_in,atmpres,phlo,phhi,co2ccn
real pco2, co2star, dco2star, dpco2, pco2surf, ph
CALL ef_get_res_subscripts_6d(id, res_lo_ss, res_hi_ss, res_incr)
CALL ef_get_arg_subscripts_6d(id, arg_lo_ss, arg_hi_ss, arg_incr)
CALL ef_get_bad_flags(id, bad_flag, bad_flag_result)
co2ccn=280.
pt_in=0.5125e-3 !mol/m^3
atmpres=1.0 !atm
sit_in=7.6875e-03 !mol/m^3
phlo=6.
phhi=9.
n1 = arg_lo_ss(F_AXIS,ARG1)
n2 = arg_lo_ss(F_AXIS,ARG2)
n3 = arg_lo_ss(F_AXIS,ARG3)
n4 = arg_lo_ss(F_AXIS,ARG4)
DO 600 n = res_lo_ss(F_AXIS), res_hi_ss(F_AXIS)
m1 = arg_lo_ss(E_AXIS,ARG1)
m2 = arg_lo_ss(E_AXIS,ARG2)
m3 = arg_lo_ss(E_AXIS,ARG3)
m4 = arg_lo_ss(E_AXIS,ARG4)
DO 500 m = res_lo_ss(E_AXIS), res_hi_ss(E_AXIS)
l1 = arg_lo_ss(T_AXIS,ARG1)
l2 = arg_lo_ss(T_AXIS,ARG2)
l3 = arg_lo_ss(T_AXIS,ARG3)
l4 = arg_lo_ss(T_AXIS,ARG4)
DO 400 l = res_lo_ss(T_AXIS), res_hi_ss(T_AXIS)
k1 = arg_lo_ss(Z_AXIS,ARG1)
k2 = arg_lo_ss(Z_AXIS,ARG2)
k3 = arg_lo_ss(Z_AXIS,ARG3)
k4 = arg_lo_ss(Z_AXIS,ARG4)
DO 300 k = res_lo_ss(Z_AXIS), res_hi_ss(Z_AXIS)
j1 = arg_lo_ss(Y_AXIS,ARG1)
j2 = arg_lo_ss(Y_AXIS,ARG2)
j3 = arg_lo_ss(Y_AXIS,ARG3)
j4 = arg_lo_ss(Y_AXIS,ARG4)
DO 200 j = res_lo_ss(Y_AXIS), res_hi_ss(Y_AXIS)
i1 = arg_lo_ss(X_AXIS,ARG1)
i2 = arg_lo_ss(X_AXIS,ARG2)
i3 = arg_lo_ss(X_AXIS,ARG3)
i4 = arg_lo_ss(X_AXIS,ARG4)
DO 100 i = res_lo_ss(X_AXIS), res_hi_ss(X_AXIS)
IF ( (arg_1(i1,j1,k1,l1,m1,n1) .EQ. bad_flag(ARG1)) .OR.
. (arg_2(i2,j2,k2,l2,m2,n2) .EQ. bad_flag(ARG2)) .OR.
. (arg_3(i3,j3,k3,l3,m3,n3) .EQ. bad_flag(ARG3)) .OR.
. (arg_4(i4,j4,k4,l4,m4,n4) .EQ. bad_flag(ARG4)) ) THEN
result(i,j,k,l,m,n) = bad_flag_result
ELSE
call co2calc(arg_1(i1,j1,k1,l1,m1,n1)
& ,arg_2(i2,j2,k2,l2,m2,n2),arg_3(i3,j3,k3,l3,m3,n3)
& ,arg_4(i4,j4,k4,l4,m4,n4),pt_in,sit_in
& ,phlo,phhi,ph,co2ccn,atmpres
& ,co2star,dco2star,pCO2surf,dpco2)
result(i,j,k,l,m,n) = pCO2surf
ENDIF
i1 = i1 + arg_incr(X_AXIS,ARG1)
i2 = i2 + arg_incr(X_AXIS,ARG2)
i3 = i3 + arg_incr(X_AXIS,ARG3)
i4 = i4 + arg_incr(X_AXIS,ARG4)
100 CONTINUE
j1 = j1 + arg_incr(Y_AXIS,ARG1)
j2 = j2 + arg_incr(Y_AXIS,ARG2)
j3 = j3 + arg_incr(Y_AXIS,ARG3)
j4 = j4 + arg_incr(Y_AXIS,ARG4)
200 CONTINUE
k1 = k1 + arg_incr(Z_AXIS,ARG1)
k2 = k2 + arg_incr(Z_AXIS,ARG2)
k3 = k3 + arg_incr(Z_AXIS,ARG3)
k4 = k4 + arg_incr(Z_AXIS,ARG4)
300 CONTINUE
l1 = l1 + arg_incr(T_AXIS,ARG1)
l2 = l2 + arg_incr(T_AXIS,ARG2)
l3 = l3 + arg_incr(T_AXIS,ARG3)
l4 = l4 + arg_incr(T_AXIS,ARG4)
400 CONTINUE
m1 = m1 + arg_incr(E_AXIS,ARG1)
m2 = m2 + arg_incr(E_AXIS,ARG2)
m3 = m3 + arg_incr(E_AXIS,ARG3)
m4 = m4 + arg_incr(E_AXIS,ARG4)
500 CONTINUE
n1 = n1 + arg_incr(F_AXIS,ARG1)
n2 = n2 + arg_incr(F_AXIS,ARG2)
n3 = n3 + arg_incr(F_AXIS,ARG3)
n4 = n4 + arg_incr(F_AXIS,ARG4)
600 CONTINUE
* ^
* |
* USER CONFIGURABLE PORTION |
* **********************************************************************
RETURN
END
subroutine co2calc(t,s,dic_in,ta_in,pt_in,sit_in
& ,phlo,phhi,ph,xco2_in,atmpres
& ,co2star,dco2star,pCO2surf,dpco2)
!-----------------------------------------------------------------------
! subroutine CO2CALC
! PURPOSE
! Calculate delta co2* from total alkalinity and total CO2 at
! temperature (t), salinity (s) and "atmpres" atmosphere total pressure.
! USAGE
! call co2calc(t,s,dic_in,ta_in,pt_in,sit_in
! & ,phlo,phhi,ph,xco2_in,atmpres
! & ,co2star,dco2star,pCO2surf,dpco2)
! INPUT
! dic_in = total inorganic carbon (mol/m^3)
! where 1 T = 1 metric ton = 1000 kg
! ta_in = total alkalinity (eq/m^3)
! pt_in = inorganic phosphate (mol/m^3)
! sit_in = inorganic silicate (mol/m^3)
! t = temperature (degrees C)
! s = salinity (PSU)
! phlo = lower limit of pH range
! phhi = upper limit of pH range
! xco2_in =atmospheric mole fraction CO2 in dry air (ppmv)
! atmpres = atmospheric pressure in atmospheres
! (1 atm==1013.25mbar)
! Note: arguments dic_in, ta_in, pt_in, sit_in, and xco2_in are
! used to initialize variables dic, ta, pt, sit, and xco2.
! * Variables dic, ta, pt, and sit are in the common block
! "species".
! * Variable xco2 is a local variable.
! * Variables with "_in" suffix have different units
! than those without.
! OUTPUT
! co2star = CO2*water (mol/m^3)
! dco2star = delta CO2 (mol/m^3)
! pco2surf = oceanic pCO2 (ppmv)
! dpco2 = Delta pCO2, i.e, pCO2ocn - pCO2atm (ppmv)
! IMPORTANT: Some words about units - (JCO, 4/4/1999)
! - Models carry tracers in mol/m^3 (on a per volume basis)
! - Conversely, this routine, which was written by observationalists
! (C. Sabine and R. Key), passes input arguments in umol/kg
! (i.e., on a per mass basis)
! - I have changed things slightly so that input arguments are in
! mol/m^3,
! - Thus, all input concentrations (dic_in, ta_in, pt_in, and st_in)
! should be given in mol/m^3; output arguments "co2star" and
! "dco2star" are likewise in mol/m^3.
! FILES and PROGRAMS NEEDED
! drtsafe
! ta_iter_1
!-----------------------------------------------------------------------
real invtk,is,is2
real k0,k1,k2,kw,kb,ks,kf,k1p,k2p,k3p,ksi
common /const/k0,k1,k2,kw,kb,ks,kf,k1p,k2p,k3p,ksi,ff,htotal
common /species/bt,st,ft,sit,pt,dic,ta
external ta_iter_1
! ----------------------------------------------------------------
! Change units from the input of mol/m^3 -> mol/kg:
! (1 mol/m^3) x (1 m^3/1024.5 kg)
! where the ocean's mean surface density is 1024.5 kg/m^3
! Note: mol/kg are actually what the body of this routine uses
! for calculations.
! ----------------------------------------------------------------
permil = 1.0 / 1024.5
! To convert input in mol/m^3 -> mol/kg
pt=pt_in*permil
sit=sit_in*permil
ta=ta_in*permil
dic=dic_in*permil
! ----------------------------------------------------------------
! Change units from uatm to atm. That is, atm is what the body of
! this routine uses for calculations.
! ----------------------------------------------------------------
permeg=1.e-6
! To convert input in uatm -> atm
xco2=xco2_in*permeg
! ----------------------------------------------------------------
!***********************************************************************
! Calculate all constants needed to convert between various measured
! carbon species. References for each equation are noted in the code.
! Once calculated, the constants are
! stored and passed in the common block "const". The original version of
! this code was based on the code by Dickson in Version 2 of "Handbook
! of Methods for the Analysis of the Various Parameters of the Carbon
! Dioxide System in Seawater", DOE, 1994 (SOP No. 3, p25-26).
! Derive simple terms used more than once
tk = 273.15 + t
tk100 = tk/100.0
tk1002=tk100*tk100
invtk=1.0/tk
dlogtk=log(tk)
is=19.924*s/(1000.-1.005*s)
is2=is*is
sqrtis=sqrt(is)
s2=s*s
sqrts=sqrt(s)
s15=s**1.5
scl=s/1.80655
! f = k0(1-pH2O)*correction term for non-ideality
! Weiss & Price (1980,Mar. Chem.,8,347-359; Eq 13 with table 6 values)
ff = exp(-162.8301 + 218.2968/tk100 +
& 90.9241*log(tk100) - 1.47696*tk1002 +
& s * (.025695 - .025225*tk100 +
& 0.0049867*tk1002))
! K0 from Weiss 1974
k0 = exp(93.4517/tk100 - 60.2409 + 23.3585 * log(tk100) +
& s * (.023517 - 0.023656 * tk100 + 0.0047036
& * tk1002))
! k1 = [H][HCO3]/[H2CO3]
! k2 = [H][CO3]/[HCO3]
! Millero p.664 (1995) using Mehrbach et al. data on seawater scale
k1=10**(-1*(3670.7*invtk - 62.008 + 9.7944*dlogtk -
& 0.0118 * s + 0.000116*s2))
k2=10**(-1*(1394.7*invtk + 4.777 -
& 0.0184*s + 0.000118*s2))
! kb = [H][BO2]/[HBO2]
! Millero p.669 (1995) using data from Dickson (1990)
kb=exp((-8966.90 - 2890.53*sqrts - 77.942*s +
& 1.728*s15 - 0.0996*s2)*invtk +
& (148.0248 + 137.1942*sqrts + 1.62142*s) +
& (-24.4344 - 25.085*sqrts - 0.2474*s) *
& dlogtk + 0.053105*sqrts*tk)
! k1p = [H][H2PO4]/[H3PO4]
! DOE(1994) eq 7.2.20 with footnote using data from Millero (1974)
k1p = exp(-4576.752*invtk + 115.525 - 18.453 * dlogtk +
& (-106.736*invtk + 0.69171) * sqrts +
& (-0.65643*invtk - 0.01844) * s)
! k2p = [H][HPO4]/[H2PO4]
! DOE(1994) eq 7.2.23 with footnote using data from Millero (1974))
k2p = exp(-8814.715*invtk + 172.0883 - 27.927 * dlogtk +
& (-160.340*invtk + 1.3566) * sqrts +
& (0.37335*invtk - 0.05778) * s)
!-----------------------------------------------------------------------
! k3p = [H][PO4]/[HPO4]
! DOE(1994) eq 7.2.26 with footnote using data from Millero (1974)
k3p = exp(-3070.75*invtk - 18.141 +
& (17.27039*invtk + 2.81197) *
& sqrts + (-44.99486*invtk - 0.09984) * s)
!-----------------------------------------------------------------------
! ksi = [H][SiO(OH)3]/[Si(OH)4]
! Millero p.671 (1995) using data from Yao and Millero (1995)
ksi = exp(-8904.2*invtk + 117.385 - 19.334 * dlogtk +
& (-458.79*invtk + 3.5913) * sqrtis +
& (188.74*invtk - 1.5998) * is +
& (-12.1652*invtk + 0.07871) * is2 +
& log(1.0-0.001005*s))
!-----------------------------------------------------------------------
! kw = [H][OH]
! Millero p.670 (1995) using composite data
kw = exp(-13847.26*invtk + 148.9652 - 23.6521 * dlogtk +
& (118.67*invtk - 5.977 + 1.0495 * dlogtk) *
& sqrts - 0.01615 * s)
!-----------------------------------------------------------------------
! ks = [H][SO4]/[HSO4]
! Dickson (1990, J. chem. Thermodynamics 22, 113)
ks=exp(-4276.1*invtk + 141.328 - 23.093*dlogtk +
& (-13856*invtk + 324.57 - 47.986*dlogtk) * sqrtis +
& (35474*invtk - 771.54 + 114.723*dlogtk) * is -
& 2698*invtk*is**1.5 + 1776*invtk*is2 +
& log(1.0 - 0.001005*s))
!-----------------------------------------------------------------------
! kf = [H][F]/[HF]
! Dickson and Riley (1979) -- change pH scale to total
kf=exp(1590.2*invtk - 12.641 + 1.525*sqrtis +
& log(1.0 - 0.001005*s) +
& log(1.0 + (0.1400/96.062)*(scl)/ks))
!-----------------------------------------------------------------------
! Calculate concentrations for borate, sulfate, and fluoride
! Uppstrom (1974)
bt = 0.000232 * scl/10.811
! Morris & Riley (1966)
st = 0.14 * scl/96.062
! Riley (1965)
ft = 0.000067 * scl/18.9984
!***********************************************************************
! Calculate [H+] total when DIC and TA are known at T, S and 1 atm.
! The solution converges to err of xacc. The solution must be within
! the range x1 to x2.
! If DIC and TA are known then either a root finding or iterative method
! must be used to calculate htotal. In this case we use the
! Newton-Raphson "safe" method taken from "Numerical Recipes" (function
! "rtsafe.f" with error trapping removed).
! As currently set, this procedure iterates about 12 times. The x1 and
! x2 values set below will accomodate ANY oceanographic values. If an
! initial guess of the pH is known, then the number of iterations can be
! reduced to about 5 by narrowing the gap between x1 and x2. It is
! recommended that the first few time steps be run with x1 and x2 set as
! below. After that, set x1 and x2 to the previous value of the pH +/-
! ~0.5. The current setting of xacc will result in co2star accurate to 3
! significant figures (xx.y). Making xacc bigger will result in faster
! convergence also, but this is not recommended (xacc of 10**-9 drops
! precision to 2 significant figures).
! Parentheses added around negative exponents (Keith Lindsay)
x1 = 10.0**(-phhi)
x2 = 10.0**(-phlo)
xacc = 1.e-10
htotal = drtsafe(ta_iter_1,x1,x2,xacc)
! Calculate [CO2*] as defined in DOE Methods Handbook 1994 Ver.2,
! ORNL/CDIAC-74, Dickson and Goyet, eds. (Ch 2 p 10, Eq A.49)
htotal2=htotal*htotal
co2star=dic*htotal2/(htotal2 + k1*htotal + k1*k2)
co2starair=xco2*ff*atmpres
dco2star=co2starair-co2star
ph=-log10(htotal)
! ---------------------------------------------------------------
!c Add two output arguments for storing pCO2surf
!c Should we be using K0 or ff for the solubility here?
! ---------------------------------------------------------------
pCO2surf = co2star / ff
dpCO2 = pCO2surf - xco2*atmpres
! Convert units of output arguments
! Note: co2star and dco2star are calculated in mol/kg within this
! routine. Thus Convert now from mol/kg -> mol/m^3
co2star = co2star / permil
dco2star = dco2star / permil
! Note: pCO2surf and dpCO2 are calculated in atm above.
! Thus convert now to uatm
pCO2surf = pCO2surf / permeg
dpCO2 = dpCO2 / permeg
return
end
!_ ---------------------------------------------------------------------
!_ RCS lines preceded by "c_ "
!_ ---------------------------------------------------------------------
!_
!_ $Source: /www/html/ipsl/OCMIP/phase2/simulations/Abiotic/Cchem/RCS/
!_ drtsafe.f,v $
!_ $Revision: 1.1 $
!_ $Date: 1999/04/03 22:00:42 $ ; $State: Exp $
!_ $Author: orr $ ; $Locker: $
!_
!_ ---------------------------------------------------------------------
!_ $Log: drtsafe.f,v $
!_ Revision 1.1 1999/04/03 22:00:42 orr
!_ Initial revision
!_
!_ ---------------------------------------------------------------------
!_
real FUNCTION DRTSAFE(FUNCD,X1,X2,XACC)
! File taken from Numerical Recipes. Modified R.M.Key 4/94
MAXIT=100
call FUNCD(X1,FL,DF)
call FUNCD(X2,FH,DF)
if (FL .lt. 0.0) then
XL=X1
XH=X2
else
XH=X1
XL=X2
SWAP=FL
FL=FH
FH=SWAP
endif
DRTSAFE=.5*(X1+X2)
DXOLD=ABS(X2-X1)
DX=DXOLD
call FUNCD(DRTSAFE,F,DF)
do 100, J=1,MAXIT
if (((DRTSAFE-XH)*DF-F)*((DRTSAFE-XL)*DF-F) .ge. 0.0 .or.
& ABS(2.0*F) .gt. ABS(DXOLD*DF)) then
DXOLD=DX
DX=0.5*(XH-XL)
DRTSAFE=XL+DX
if (XL .eq. DRTSAFE) return
else
DXOLD=DX
DX=F/DF
TEMP=DRTSAFE
DRTSAFE=DRTSAFE-DX
if (TEMP .eq. DRTSAFE) return
endif
if (ABS(DX) .lt. XACC) return
call FUNCD(DRTSAFE,F,DF)
if (F .lt. 0.0) then
XL=DRTSAFE
FL=F
else
XH=DRTSAFE
FH=F
endif
100 continue
return
end
!_ ---------------------------------------------------------------------
!_ RCS lines preceded by "c_ "
!_ ---------------------------------------------------------------------
!_
!_ $Source: /www/html/ipsl/OCMIP/phase2/simulations/Abiotic/Cchem/RCS/
!_ ta_iter_1.f,v $
!_ $Revision: 1.2 $
!_ $Date: 1999/09/01 17:55:41 $ ; $State: Exp $
!_ $Author: orr $ ; $Locker: $
!_
!_ ---------------------------------------------------------------------
!_ $Log: ta_iter_1.f,v $
!_ Revision 1.2 1999/09/01 17:55:41 orr
!_ Fixed sign error in dfn/dx following remarks of C. Voelker
!_ (10/Aug/1999)
!_
!_ Revision 1.1 1999/04/03 22:00:42 orr
!_ Initial revision
!_
!_ ---------------------------------------------------------------------
!_
subroutine ta_iter_1(x,fn,df)
real k12,k12p,k123p
real k0,k1,k2,kw,kb,ks,kf,k1p,k2p,k3p,ksi
common /const/k0,k1,k2,kw,kb,ks,kf,k1p,k2p,k3p,ksi,ff,htotal
common /species/bt,st,ft,sit,pt,dic,ta
! This routine expresses TA as a function of DIC, htotal and constants.
! It also calculates the derivative of this function with respect to
! htotal. It is used in the iterative solution for htotal. In the call
! "x" is the input value for htotal, "fn" is the calculated value for TA
! and "df" is the value for dTA/dhtotal
x2=x*x
x3=x2*x
k12 = k1*k2
k12p = k1p*k2p
k123p = k12p*k3p
c = 1.0 + st/ks
a = x3 + k1p*x2 + k12p*x + k123p
a2=a*a
da = 3.0*x2 + 2.0*k1p*x + k12p
b = x2 + k1*x + k12
b2=b*b
db = 2.0*x + k1
! fn = hco3+co3+borate+oh+hpo4+2*po4+silicate+hfree+hso4+hf+h3po4-ta
fn = k1*x*dic/b +
& 2.0*dic*k12/b +
& bt/(1.0 + x/kb) +
& kw/x +
& pt*k12p*x/a +
& 2.0*pt*k123p/a +
& sit/(1.0 + x/ksi) -
& x/c -
& st/(1.0 + ks/x/c) -
& ft/(1.0 + kf/x) -
& pt*x3/a -
& ta
! df = dfn/dx
df = ((k1*dic*b) - k1*x*dic*db)/b2 -
& 2.0*dic*k12*db/b2 -
& bt/kb/(1.0+x/kb)**2. -
& kw/x2 +
& (pt*k12p*(a - x*da))/a2 -
& 2.0*pt*k123p*da/a2 -
& sit/ksi/(1.0+x/ksi)**2. -
& 1.0/c +
& st*(1.0 + ks/x/c)**(-2.)*(ks/c/x2) +
& ft*(1.0 + kf/x)**(-2.)*kf/x2 -
& pt*x2*(3.0*a-x*da)/a2
return
end