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co3.F
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co3.F
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*
* co3.F
*
* Andreas Schmittner ([email protected])
* Jul 24 2007
*
* Returns carbonate ion concentration (CO_3^2-) of sea water
*
SUBROUTINE co3_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 carbonate ion (CO3) concentration (mol m-3) using
. OCMIP routines' )
CALL ef_set_num_args(id, 5)
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)
arg = 5
CALL ef_set_arg_name(id, arg, 'PRES')
CALL ef_set_arg_unit(id, arg, 'bar')
CALL ef_set_arg_desc(id, arg, 'pressure')
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 co3_compute(id, arg_1, arg_2, arg_3, arg_4, arg_5
.,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 arg_5(mem5lox:mem5hix, mem5loy:mem5hiy, mem5loz:mem5hiz,
. mem5lot:mem5hit, mem5loe:mem5hie, mem5lof:mem5hif)
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
INTEGER i5, j5, k5, l5, m5, n5
real pt_in,sit_in,atmpres,phlo,phhi,co2ccn
real co3, 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)
n5 = arg_lo_ss(F_AXIS,ARG5)
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)
m5 = arg_lo_ss(E_AXIS,ARG5)
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)
l5 = arg_lo_ss(T_AXIS,ARG5)
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)
k5 = arg_lo_ss(Z_AXIS,ARG5)
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)
j5 = arg_lo_ss(Y_AXIS,ARG5)
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)
i5 = arg_lo_ss(X_AXIS,ARG5)
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)) .OR.
. (arg_5(i5,j5,k5,l5,m5,n5) .EQ. bad_flag(ARG5)) ) 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
& ,arg_5(i5,j5,k5,l5,m5,n5),co3
& ,dco2star,pCO2surf,dpco2)
result(i,j,k,l,m,n) = co3
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)
i5 = i5 + arg_incr(X_AXIS,ARG5)
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)
j5 = j5 + arg_incr(Y_AXIS,ARG5)
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)
k5 = k5 + arg_incr(Z_AXIS,ARG5)
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)
l5 = l5 + arg_incr(T_AXIS,ARG5)
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)
m5 = m5 + arg_incr(E_AXIS,ARG5)
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)
n5 = n5 + arg_incr(F_AXIS,ARG5)
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,ocnpres
& ,co3,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))
dv1 = -25.5 + 0.1271*t
dk1 = -3.08e-3 + 0.0877e-3*t
R = 83.131
k1 = k1*exp((-dv1*ocnpres+0.5*dk1*ocnpress**2)/(R*tk))
k2=10**(-1*(1394.7*invtk + 4.777 -
& 0.0184*s + 0.000118*s2))
dv2 = -15.82 - 0.0219*t
dk2 = 1.13e-3 - 0.1475e-3*t
k2 = k2*exp((-dv2*ocnpres+0.5*dk2*ocnpress**2)/(R*tk))
! 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)
t2 = t*t
dvb = -29.48 + 0.1622*t + 2.608e-3*t2
dkb = -2.84e-3
kb = kb*exp((-dvb*ocnpres+0.5*dkb*ocnpress**2)/(R*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)
dvw = -25.6 + 0.2324*t - 3.6246e-3*t2
dkw = -5.13e-3 + 0.0794e-3*t
kw = kw*exp((-dvw*ocnpres+0.5*dkw*ocnpress**2)/(R*tk))
!-----------------------------------------------------------------------
! 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))
dvs = -18.03 + 0.0466*t + 0.316e-3*t2
dks = -4.53e-3 + 0.09e-3*t
ks = ks*exp((-dvs*ocnpres+0.5*dks*ocnpress**2)/(R*tk))
!-----------------------------------------------------------------------
! 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))
dvf = -9.78 - 0.009*t - 0.942e-3*t2
dkf = -3.91e-3 + 0.054e-3*t
kf = kf*exp((-dvf*ocnpres+0.5*dkf*ocnpress**2)/(R*tk))
!-----------------------------------------------------------------------
! 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)
hco3=dic/(1.+htotal/k1 + k2/htotal)
co3=dic/(1.+htotal/k2 + htotal2/(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
co3 = co3 / 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