| 1 |
#include "CPP_OPTIONS.h" |
| 2 |
#include "PTRACERS_OPTIONS.h" |
| 3 |
#include "DARWIN_OPTIONS.h" |
| 4 |
|
| 5 |
#ifdef ALLOW_PTRACERS |
| 6 |
#ifdef ALLOW_DARWIN |
| 7 |
|
| 8 |
#ifdef ALLOW_CARBON |
| 9 |
|
| 10 |
CBOP |
| 11 |
C !ROUTINE: CALC_PCO2 |
| 12 |
|
| 13 |
C !INTERFACE: ========================================================== |
| 14 |
SUBROUTINE CALC_PCO2( |
| 15 |
I donewt,inewtonmax,ibrackmax, |
| 16 |
I t,s,diclocal,pt,sit,ta, |
| 17 |
I k1local,k2local, |
| 18 |
I k1plocal,k2plocal,k3plocal, |
| 19 |
I kslocal,kblocal,kwlocal, |
| 20 |
I ksilocal,kflocal, |
| 21 |
I k0local, fugflocal, |
| 22 |
I fflocal,btlocal,stlocal,ftlocal, |
| 23 |
U pHlocal,pCO2surfloc, |
| 24 |
I myThid) |
| 25 |
|
| 26 |
C !DESCRIPTION: |
| 27 |
C surface ocean inorganic carbon chemistry to OCMIP2 |
| 28 |
C regulations modified from OCMIP2 code; |
| 29 |
C Mick Follows, MIT, Oct 1999. |
| 30 |
|
| 31 |
|
| 32 |
C !USES: =============================================================== |
| 33 |
IMPLICIT NONE |
| 34 |
#include "SIZE.h" |
| 35 |
#include "DYNVARS.h" |
| 36 |
#include "EEPARAMS.h" |
| 37 |
#include "PARAMS.h" |
| 38 |
#include "GRID.h" |
| 39 |
#include "FFIELDS.h" |
| 40 |
#include "DARWIN_FLUX.h" |
| 41 |
|
| 42 |
C == Routine arguments == |
| 43 |
C diclocal = total inorganic carbon (mol/m^3) |
| 44 |
C where 1 T = 1 metric ton = 1000 kg |
| 45 |
C ta = total alkalinity (eq/m^3) |
| 46 |
C pt = inorganic phosphate (mol/^3) |
| 47 |
C sit = inorganic silicate (mol/^3) |
| 48 |
C t = temperature (degrees C) |
| 49 |
C s = salinity (PSU) |
| 50 |
INTEGER donewt |
| 51 |
INTEGER inewtonmax |
| 52 |
INTEGER ibrackmax |
| 53 |
_RL t, s, pt, sit, ta |
| 54 |
_RL pCO2surfloc, diclocal, pHlocal |
| 55 |
_RL fflocal, btlocal, stlocal, ftlocal |
| 56 |
_RL k1local, k2local |
| 57 |
_RL k1plocal, k2plocal, k3plocal |
| 58 |
_RL kslocal, kblocal, kwlocal, ksilocal, kflocal |
| 59 |
_RL k0local, fugflocal |
| 60 |
INTEGER myThid |
| 61 |
CEndOfInterface |
| 62 |
|
| 63 |
C == Local variables == |
| 64 |
C INPUT |
| 65 |
C phlo= lower limit of pH range |
| 66 |
C phhi= upper limit of pH range |
| 67 |
C atmpres = atmospheric pressure in atmospheres (1 atm==1013.25mbar) |
| 68 |
C OUTPUT |
| 69 |
C co2star = CO2*water (mol/m^3) |
| 70 |
C pco2surf = oceanic pCO2 (ppmv) |
| 71 |
C --------------------------------------------------------------------- |
| 72 |
C OCMIP NOTE: Some words about units - (JCO, 4/4/1999) |
| 73 |
C - Models carry tracers in mol/m^3 (on a per volume basis) |
| 74 |
C - Conversely, this routine, which was written by |
| 75 |
C observationalists (C. Sabine and R. Key), passes input |
| 76 |
C arguments in umol/kg (i.e., on a per mass basis) |
| 77 |
C - I have changed things slightly so that input arguments are in |
| 78 |
C mol/m^3, |
| 79 |
C - Thus, all input concentrations (diclocal, ta, pt, and st) should be |
| 80 |
C given in mol/m^3; output arguments "co2star" and "dco2star" |
| 81 |
C are likewise be in mol/m^3. |
| 82 |
C --------------------------------------------------------------------- |
| 83 |
_RL phhi |
| 84 |
_RL phlo |
| 85 |
_RL tk |
| 86 |
_RL tk100 |
| 87 |
_RL tk1002 |
| 88 |
_RL dlogtk |
| 89 |
_RL sqrtis |
| 90 |
_RL sqrts |
| 91 |
_RL s15 |
| 92 |
_RL scl |
| 93 |
_RL c |
| 94 |
_RL a |
| 95 |
_RL a2 |
| 96 |
_RL da |
| 97 |
_RL b |
| 98 |
_RL b2 |
| 99 |
_RL db |
| 100 |
_RL fn |
| 101 |
_RL df |
| 102 |
_RL deltax |
| 103 |
_RL x |
| 104 |
_RL x1 |
| 105 |
_RL x2 |
| 106 |
_RL x3 |
| 107 |
_RL xmid |
| 108 |
_RL ftest |
| 109 |
_RL htotal |
| 110 |
_RL htotal2 |
| 111 |
_RL s2 |
| 112 |
_RL xacc |
| 113 |
_RL co2star |
| 114 |
_RL co2starair |
| 115 |
_RL dco2star |
| 116 |
_RL dpCO2 |
| 117 |
_RL phguess |
| 118 |
_RL atmpres |
| 119 |
_RL fco2 |
| 120 |
INTEGER inewton |
| 121 |
INTEGER ibrack |
| 122 |
INTEGER hstep |
| 123 |
_RL fni(3) |
| 124 |
_RL xlo |
| 125 |
_RL xhi |
| 126 |
_RL xguess |
| 127 |
_RL invtk |
| 128 |
_RL is |
| 129 |
_RL is2 |
| 130 |
_RL k123p |
| 131 |
_RL k12p |
| 132 |
_RL k12 |
| 133 |
c --------------------------------------------------------------------- |
| 134 |
c import donewt flag |
| 135 |
c set donewt = 1 for newton-raphson iteration |
| 136 |
c set donewt = 0 for bracket and bisection |
| 137 |
c --------------------------------------------------------------------- |
| 138 |
C Change units from the input of mol/m^3 -> mol/kg: |
| 139 |
c (1 mol/m^3) x (1 m^3/1024.5 kg) |
| 140 |
c where the ocean's mean surface density is 1024.5 kg/m^3 |
| 141 |
c Note: mol/kg are actually what the body of this routine uses |
| 142 |
c for calculations. Units are reconverted back to mol/m^3 at the |
| 143 |
c end of this routine. |
| 144 |
c --------------------------------------------------------------------- |
| 145 |
c To convert input in mol/m^3 -> mol/kg |
| 146 |
pt=pt*permil |
| 147 |
sit=sit*permil |
| 148 |
ta=ta*permil |
| 149 |
diclocal=diclocal*permil |
| 150 |
c --------------------------------------------------------------------- |
| 151 |
c set first guess and brackets for [H+] solvers |
| 152 |
c first guess (for newton-raphson) |
| 153 |
phguess = phlocal |
| 154 |
|
| 155 |
|
| 156 |
c bracketing values (for bracket/bisection) |
| 157 |
phhi = 10.0 |
| 158 |
phlo = 5.0 |
| 159 |
c convert to [H+]... |
| 160 |
xguess = 10.0**(-phguess) |
| 161 |
xlo = 10.0**(-phhi) |
| 162 |
xhi = 10.0**(-phlo) |
| 163 |
xmid = (xlo + xhi)*0.5 |
| 164 |
|
| 165 |
|
| 166 |
c---------------------------------------------------------------- |
| 167 |
c iteratively solve for [H+] |
| 168 |
c (i) Newton-Raphson method with fixed number of iterations, |
| 169 |
c use previous [H+] as first guess |
| 170 |
|
| 171 |
c select newton-raphson, inewt=1 |
| 172 |
c else select bracket and bisection |
| 173 |
|
| 174 |
cQQQQQ |
| 175 |
if( donewt .eq. 1)then |
| 176 |
c......................................................... |
| 177 |
c NEWTON-RAPHSON METHOD |
| 178 |
c......................................................... |
| 179 |
x = xguess |
| 180 |
cdiags |
| 181 |
c WRITE(0,*)'xguess ',xguess |
| 182 |
cdiags |
| 183 |
do inewton = 1, inewtonmax |
| 184 |
c set some common combinations of parameters used in |
| 185 |
c the iterative [H+] solvers |
| 186 |
x2=x*x |
| 187 |
x3=x2*x |
| 188 |
k12 = k1local*k2local |
| 189 |
k12p = k1plocal*k2plocal |
| 190 |
k123p = k12p*k3plocal |
| 191 |
c = 1.0 + stlocal/kslocal |
| 192 |
a = x3 + k1plocal*x2 + k12p*x + k123p |
| 193 |
a2=a*a |
| 194 |
da = 3.0*x2 + 2.0*k1plocal*x + k12p |
| 195 |
b = x2 + k1local*x + k12 |
| 196 |
b2=b*b |
| 197 |
db = 2.0*x + k1local |
| 198 |
|
| 199 |
c Evaluate f([H+]) and f'([H+]) |
| 200 |
c fn = hco3+co3+borate+oh+hpo4+2*po4+silicate+hfree |
| 201 |
c +hso4+hf+h3po4-ta |
| 202 |
fn = k1local*x*diclocal/b + |
| 203 |
& 2.0*diclocal*k12/b + |
| 204 |
& btlocal/(1.0 + x/kblocal) + |
| 205 |
& kwlocal/x + |
| 206 |
& pt*k12p*x/a + |
| 207 |
& 2.0*pt*k123p/a + |
| 208 |
& sit/(1.0 + x/ksilocal) - |
| 209 |
& x/c - |
| 210 |
& stlocal/(1.0 + kslocal/x/c) - |
| 211 |
& ftlocal/(1.0 + kflocal/x) - |
| 212 |
& pt*x3/a - |
| 213 |
& ta |
| 214 |
|
| 215 |
c df = dfn/dx |
| 216 |
cdiags |
| 217 |
c WRITE(0,*)'values',b2,kblocal,x2,a2,c,x |
| 218 |
cdiags |
| 219 |
df = ((k1local*diclocal*b) - k1local*x*diclocal*db)/b2 - |
| 220 |
& 2.0*diclocal*k12*db/b2 - |
| 221 |
& btlocal/kblocal/(1.0+x/kblocal)**2. - |
| 222 |
& kwlocal/x2 + |
| 223 |
& (pt*k12p*(a - x*da))/a2 - |
| 224 |
& 2.0*pt*k123p*da/a2 - |
| 225 |
& sit/ksilocal/(1.0+x/ksilocal)**2. + |
| 226 |
& 1.0/c + |
| 227 |
& stlocal*(1.0 + kslocal/x/c)**(-2.0)*(kslocal/c/x2) + |
| 228 |
& ftlocal*(1.0 + kflocal/x)**(-2.)*kflocal/x2 - |
| 229 |
& pt*x2*(3.0*a-x*da)/a2 |
| 230 |
c evaluate increment in [H+] |
| 231 |
deltax = - fn/df |
| 232 |
c update estimate of [H+] |
| 233 |
x = x + deltax |
| 234 |
cdiags |
| 235 |
c write value of x to check convergence.... |
| 236 |
c write(0,*)'inewton, x, deltax ',inewton, x, deltax |
| 237 |
c write(6,*) |
| 238 |
cdiags |
| 239 |
|
| 240 |
end do |
| 241 |
c end of newton-raphson method |
| 242 |
c.................................................... |
| 243 |
else |
| 244 |
c.................................................... |
| 245 |
C BRACKET AND BISECTION METHOD |
| 246 |
c.................................................... |
| 247 |
c (ii) If first step use Bracket and Bisection method |
| 248 |
c with fixed, large number of iterations |
| 249 |
do ibrack = 1, ibrackmax |
| 250 |
do hstep = 1,3 |
| 251 |
if(hstep .eq. 1)x = xhi |
| 252 |
if(hstep .eq. 2)x = xlo |
| 253 |
if(hstep .eq. 3)x = xmid |
| 254 |
c set some common combinations of parameters used in |
| 255 |
c the iterative [H+] solvers |
| 256 |
|
| 257 |
|
| 258 |
x2=x*x |
| 259 |
x3=x2*x |
| 260 |
k12 = k1local*k2local |
| 261 |
k12p = k1plocal*k2plocal |
| 262 |
k123p = k12p*k3plocal |
| 263 |
c = 1.0 + stlocal/kslocal |
| 264 |
a = x3 + k1plocal*x2 + k12p*x + k123p |
| 265 |
a2=a*a |
| 266 |
da = 3.0*x2 + 2.0*k1plocal*x + k12p |
| 267 |
b = x2 + k1local*x + k12 |
| 268 |
b2=b*b |
| 269 |
db = 2.0*x + k1local |
| 270 |
c evaluate f([H+]) for bracketing and mid-value cases |
| 271 |
fn = k1local*x*diclocal/b + |
| 272 |
& 2.0*diclocal*k12/b + |
| 273 |
& btlocal/(1.0 + x/kblocal) + |
| 274 |
& kwlocal/x + |
| 275 |
& pt*k12p*x/a + |
| 276 |
& 2.0*pt*k123p/a + |
| 277 |
& sit/(1.0 + x/ksilocal) - |
| 278 |
& x/c - |
| 279 |
& stlocal/(1.0 + kslocal/x/c) - |
| 280 |
& ftlocal/(1.0 + kflocal/x) - |
| 281 |
& pt*x3/a - |
| 282 |
& ta |
| 283 |
fni(hstep) = fn |
| 284 |
end do |
| 285 |
c now bracket solution within two of three |
| 286 |
ftest = fni(1)/fni(3) |
| 287 |
if(ftest .gt. 0.0)then |
| 288 |
xhi = xmid |
| 289 |
else |
| 290 |
xlo = xmid |
| 291 |
end if |
| 292 |
xmid = (xlo + xhi)*0.5 |
| 293 |
|
| 294 |
cdiags |
| 295 |
c write value of x to check convergence.... |
| 296 |
c WRITE(0,*)'bracket-bisection iteration ',ibrack, xmid |
| 297 |
cdiags |
| 298 |
end do |
| 299 |
c last iteration gives value |
| 300 |
x = xmid |
| 301 |
c end of bracket and bisection method |
| 302 |
c.................................... |
| 303 |
end if |
| 304 |
c iterative [H+] solver finished |
| 305 |
c---------------------------------------------------------------- |
| 306 |
|
| 307 |
c now determine pCO2 etc... |
| 308 |
c htotal = [H+], hydrogen ion conc |
| 309 |
htotal = x |
| 310 |
C Calculate [CO2*] as defined in DOE Methods Handbook 1994 Ver.2, |
| 311 |
C ORNL/CDIAC-74, dickson and Goyet, eds. (Ch 2 p 10, Eq A.49) |
| 312 |
htotal2=htotal*htotal |
| 313 |
co2star=diclocal*htotal2/(htotal2 + k1local*htotal |
| 314 |
& + k1local*k2local) |
| 315 |
phlocal=-log10(htotal) |
| 316 |
|
| 317 |
c --------------------------------------------------------------- |
| 318 |
c Add two output arguments for storing pCO2surf |
| 319 |
c Should we be using K0 or ff for the solubility here? |
| 320 |
c --------------------------------------------------------------- |
| 321 |
#ifdef WATERVAP_BUG |
| 322 |
pCO2surfloc = co2star / fflocal |
| 323 |
#else |
| 324 |
c Corrected by Val Bennington (Nov 2010) |
| 325 |
fco2 = co2star / k0local |
| 326 |
pCO2surfloc = fco2/fugflocal |
| 327 |
#endif |
| 328 |
|
| 329 |
C ---------------------------------------------------------------- |
| 330 |
C Reconvert units back to original values for input arguments |
| 331 |
C no longer necessary???? |
| 332 |
C ---------------------------------------------------------------- |
| 333 |
c Reconvert from mol/kg -> mol/m^3 |
| 334 |
pt=pt/permil |
| 335 |
sit=sit/permil |
| 336 |
ta=ta/permil |
| 337 |
diclocal=diclocal/permil |
| 338 |
|
| 339 |
return |
| 340 |
end |
| 341 |
|
| 342 |
c================================================================= |
| 343 |
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC |
| 344 |
CC New efficient pCO2 solver, Mick Follows CC |
| 345 |
CC Taka Ito CC |
| 346 |
CC Stephanie Dutkiewicz CC |
| 347 |
CC 20 April 2003 CC |
| 348 |
CC ADD CO3 ESTIMATION AND PASS OUT CC |
| 349 |
CC Karsten Friis, Mick Follows CC |
| 350 |
CC 1 sep 04 CC |
| 351 |
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC |
| 352 |
#include "DARWIN_OPTIONS.h" |
| 353 |
CStartOfInterFace |
| 354 |
SUBROUTINE CALC_PCO2_APPROX_CO3( |
| 355 |
I t,s,diclocal,pt,sit,ta, |
| 356 |
I k1local,k2local, |
| 357 |
I k1plocal,k2plocal,k3plocal, |
| 358 |
I kslocal,kblocal,kwlocal, |
| 359 |
I ksilocal,kflocal, |
| 360 |
I fflocal,btlocal,stlocal,ftlocal, |
| 361 |
U pHlocal,pCO2surfloc,co3local, |
| 362 |
I myThid) |
| 363 |
C /==========================================================\ |
| 364 |
C | SUBROUTINE CALC_PCO2_APPROX_CO3 | |
| 365 |
C \==========================================================/ |
| 366 |
IMPLICIT NONE |
| 367 |
|
| 368 |
C == GLobal variables == |
| 369 |
#include "SIZE.h" |
| 370 |
#include "DYNVARS.h" |
| 371 |
#include "EEPARAMS.h" |
| 372 |
#include "PARAMS.h" |
| 373 |
#include "GRID.h" |
| 374 |
#include "FFIELDS.h" |
| 375 |
#include "DARWIN_FLUX.h" |
| 376 |
|
| 377 |
C == Routine arguments == |
| 378 |
C diclocal = total inorganic carbon (mol/m^3) |
| 379 |
C where 1 T = 1 metric ton = 1000 kg |
| 380 |
C ta = total alkalinity (eq/m^3) |
| 381 |
C pt = inorganic phosphate (mol/^3) |
| 382 |
C sit = inorganic silicate (mol/^3) |
| 383 |
C t = temperature (degrees C) |
| 384 |
C s = salinity (PSU) |
| 385 |
_RL t, s, pt, sit, ta |
| 386 |
_RL pCO2surfloc, diclocal, pHlocal |
| 387 |
_RL fflocal, btlocal, stlocal, ftlocal |
| 388 |
_RL k1local, k2local |
| 389 |
_RL k1plocal, k2plocal, k3plocal |
| 390 |
_RL kslocal, kblocal, kwlocal, ksilocal, kflocal |
| 391 |
INTEGER myThid |
| 392 |
CEndOfInterface |
| 393 |
|
| 394 |
C == Local variables == |
| 395 |
_RL phguess |
| 396 |
_RL cag |
| 397 |
_RL bohg |
| 398 |
_RL hguess |
| 399 |
_RL stuff |
| 400 |
_RL gamm |
| 401 |
_RL hnew |
| 402 |
_RL co2s |
| 403 |
_RL h3po4g, h2po4g, hpo4g, po4g |
| 404 |
_RL siooh3g |
| 405 |
c carbonate |
| 406 |
_RL co3local |
| 407 |
|
| 408 |
|
| 409 |
c --------------------------------------------------------------------- |
| 410 |
C Change units from the input of mol/m^3 -> mol/kg: |
| 411 |
c (1 mol/m^3) x (1 m^3/1024.5 kg) |
| 412 |
c where the ocean's mean surface density is 1024.5 kg/m^3 |
| 413 |
c Note: mol/kg are actually what the body of this routine uses |
| 414 |
c for calculations. Units are reconverted back to mol/m^3 at the |
| 415 |
c end of this routine. |
| 416 |
c To convert input in mol/m^3 -> mol/kg |
| 417 |
pt=pt*permil |
| 418 |
sit=sit*permil |
| 419 |
ta=ta*permil |
| 420 |
diclocal=diclocal*permil |
| 421 |
c --------------------------------------------------------------------- |
| 422 |
c set first guess and brackets for [H+] solvers |
| 423 |
c first guess (for newton-raphson) |
| 424 |
phguess = phlocal |
| 425 |
cmick - new approx method |
| 426 |
cmick - make estimate of htotal (hydrogen ion conc) using |
| 427 |
cmick appromate estimate of CA, carbonate alkalinity |
| 428 |
hguess = 10.0**(-phguess) |
| 429 |
cmick - first estimate borate contribution using guess for [H+] |
| 430 |
bohg = btlocal*kblocal/(hguess+kblocal) |
| 431 |
|
| 432 |
cmick - first estimate of contribution from phosphate |
| 433 |
cmick based on Dickson and Goyet |
| 434 |
stuff = hguess*hguess*hguess |
| 435 |
& + (k1plocal*hguess*hguess) |
| 436 |
& + (k1plocal*k2plocal*hguess) |
| 437 |
& + (k1plocal*k2plocal*k3plocal) |
| 438 |
h3po4g = (pt*hguess*hguess*hguess) / stuff |
| 439 |
h2po4g = (pt*k1plocal*hguess*hguess) / stuff |
| 440 |
hpo4g = (pt*k1plocal*k2plocal*hguess) / stuff |
| 441 |
po4g = (pt*k1plocal*k2plocal*k3plocal) / stuff |
| 442 |
|
| 443 |
cmick - estimate contribution from silicate |
| 444 |
cmick based on Dickson and Goyet |
| 445 |
siooh3g = sit*ksilocal / (ksilocal + hguess) |
| 446 |
|
| 447 |
cmick - now estimate carbonate alkalinity |
| 448 |
cag = ta - bohg - (kwlocal/hguess) + hguess |
| 449 |
& - hpo4g - 2.0*po4g + h3po4g |
| 450 |
& - siooh3g |
| 451 |
|
| 452 |
cmick - now evaluate better guess of hydrogen ion conc |
| 453 |
cmick htotal = [H+], hydrogen ion conc |
| 454 |
gamm = diclocal/cag |
| 455 |
stuff = (1.0-gamm)*(1.0-gamm)*k1local*k1local |
| 456 |
& - 4.0*k1local*k2local*(1.0-2.0*gamm) |
| 457 |
hnew = 0.5*( (gamm-1.0)*k1local + sqrt(stuff) ) |
| 458 |
cmick - now determine [CO2*] |
| 459 |
co2s = diclocal/ |
| 460 |
& (1.0 + (k1local/hnew) + (k1local*k2local/(hnew*hnew))) |
| 461 |
cmick - return update pH to main routine |
| 462 |
phlocal = -log10(hnew) |
| 463 |
|
| 464 |
c NOW EVALUATE CO32-, carbonate ion concentration |
| 465 |
c used in determination of calcite compensation depth |
| 466 |
c Karsten Friis & Mick - Sep 2004 |
| 467 |
co3local = k1local*k2local*diclocal / |
| 468 |
& (hnew*hnew + k1local*hnew + k1local*k2local) |
| 469 |
|
| 470 |
c --------------------------------------------------------------- |
| 471 |
c surface pCO2 (following Dickson and Goyet, DOE...) |
| 472 |
pCO2surfloc = co2s/fflocal |
| 473 |
|
| 474 |
C ---------------------------------------------------------------- |
| 475 |
c Reconvert from mol/kg -> mol/m^3 |
| 476 |
pt=pt/permil |
| 477 |
sit=sit/permil |
| 478 |
ta=ta/permil |
| 479 |
diclocal=diclocal/permil |
| 480 |
return |
| 481 |
end |
| 482 |
|
| 483 |
c================================================================= |
| 484 |
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC |
| 485 |
CC New efficient pCO2 solver, Mick Follows CC |
| 486 |
CC Taka Ito CC |
| 487 |
CC Stephanie Dutkiewicz CC |
| 488 |
CC 20 April 2003 CC |
| 489 |
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC |
| 490 |
C Apr 2011: fix vapour bug (following Bennington) |
| 491 |
#include "DARWIN_OPTIONS.h" |
| 492 |
CStartOfInterFace |
| 493 |
SUBROUTINE CALC_PCO2_APPROX( |
| 494 |
I t,s,diclocal,pt,sit,ta, |
| 495 |
I k1local,k2local, |
| 496 |
I k1plocal,k2plocal,k3plocal, |
| 497 |
I kslocal,kblocal,kwlocal, |
| 498 |
I ksilocal,kflocal, |
| 499 |
I k0local, fugflocal, |
| 500 |
I fflocal,btlocal,stlocal,ftlocal, |
| 501 |
U pHlocal,pCO2surfloc,co3local, |
| 502 |
I myThid) |
| 503 |
C /==========================================================\ |
| 504 |
C | SUBROUTINE CALC_PCO2_APPROX | |
| 505 |
C \==========================================================/ |
| 506 |
IMPLICIT NONE |
| 507 |
|
| 508 |
C == GLobal variables == |
| 509 |
#include "SIZE.h" |
| 510 |
#include "DYNVARS.h" |
| 511 |
#include "EEPARAMS.h" |
| 512 |
#include "PARAMS.h" |
| 513 |
#include "GRID.h" |
| 514 |
#include "FFIELDS.h" |
| 515 |
#include "DARWIN_FLUX.h" |
| 516 |
|
| 517 |
C == Routine arguments == |
| 518 |
C diclocal = total inorganic carbon (mol/m^3) |
| 519 |
C where 1 T = 1 metric ton = 1000 kg |
| 520 |
C ta = total alkalinity (eq/m^3) |
| 521 |
C pt = inorganic phosphate (mol/^3) |
| 522 |
C sit = inorganic silicate (mol/^3) |
| 523 |
C t = temperature (degrees C) |
| 524 |
C s = salinity (PSU) |
| 525 |
_RL t, s, pt, sit, ta |
| 526 |
_RL pCO2surfloc, diclocal, pHlocal |
| 527 |
_RL fflocal, btlocal, stlocal, ftlocal |
| 528 |
_RL k1local, k2local |
| 529 |
_RL k1plocal, k2plocal, k3plocal |
| 530 |
_RL kslocal, kblocal, kwlocal, ksilocal, kflocal |
| 531 |
_RL k0local, fugflocal |
| 532 |
INTEGER myThid |
| 533 |
CEndOfInterface |
| 534 |
|
| 535 |
C == Local variables == |
| 536 |
_RL phguess |
| 537 |
_RL cag |
| 538 |
_RL bohg |
| 539 |
_RL hguess |
| 540 |
_RL stuff |
| 541 |
_RL gamm |
| 542 |
_RL hnew |
| 543 |
_RL co2s |
| 544 |
_RL h3po4g, h2po4g, hpo4g, po4g |
| 545 |
_RL siooh3g |
| 546 |
_RL fco2 |
| 547 |
c carbonate |
| 548 |
_RL co3local |
| 549 |
|
| 550 |
|
| 551 |
c --------------------------------------------------------------------- |
| 552 |
C Change units from the input of mol/m^3 -> mol/kg: |
| 553 |
c (1 mol/m^3) x (1 m^3/1024.5 kg) |
| 554 |
c where the ocean's mean surface density is 1024.5 kg/m^3 |
| 555 |
c Note: mol/kg are actually what the body of this routine uses |
| 556 |
c for calculations. Units are reconverted back to mol/m^3 at the |
| 557 |
c end of this routine. |
| 558 |
c To convert input in mol/m^3 -> mol/kg |
| 559 |
pt=pt*permil |
| 560 |
sit=sit*permil |
| 561 |
ta=ta*permil |
| 562 |
diclocal=diclocal*permil |
| 563 |
c --------------------------------------------------------------------- |
| 564 |
c set first guess and brackets for [H+] solvers |
| 565 |
c first guess (for newton-raphson) |
| 566 |
phguess = phlocal |
| 567 |
cmick - new approx method |
| 568 |
cmick - make estimate of htotal (hydrogen ion conc) using |
| 569 |
cmick appromate estimate of CA, carbonate alkalinity |
| 570 |
hguess = 10.0**(-phguess) |
| 571 |
cmick - first estimate borate contribution using guess for [H+] |
| 572 |
bohg = btlocal*kblocal/(hguess+kblocal) |
| 573 |
|
| 574 |
cmick - first estimate of contribution from phosphate |
| 575 |
cmick based on Dickson and Goyet |
| 576 |
stuff = hguess*hguess*hguess |
| 577 |
& + (k1plocal*hguess*hguess) |
| 578 |
& + (k1plocal*k2plocal*hguess) |
| 579 |
& + (k1plocal*k2plocal*k3plocal) |
| 580 |
h3po4g = (pt*hguess*hguess*hguess) / stuff |
| 581 |
h2po4g = (pt*k1plocal*hguess*hguess) / stuff |
| 582 |
hpo4g = (pt*k1plocal*k2plocal*hguess) / stuff |
| 583 |
po4g = (pt*k1plocal*k2plocal*k3plocal) / stuff |
| 584 |
|
| 585 |
cmick - estimate contribution from silicate |
| 586 |
cmick based on Dickson and Goyet |
| 587 |
siooh3g = sit*ksilocal / (ksilocal + hguess) |
| 588 |
|
| 589 |
cmick - now estimate carbonate alkalinity |
| 590 |
cag = ta - bohg - (kwlocal/hguess) + hguess |
| 591 |
& - hpo4g - 2.0 _d 0*po4g + h3po4g |
| 592 |
& - siooh3g |
| 593 |
|
| 594 |
cmick - now evaluate better guess of hydrogen ion conc |
| 595 |
cmick htotal = [H+], hydrogen ion conc |
| 596 |
gamm = diclocal/cag |
| 597 |
stuff = (1.0 _d 0-gamm)*(1.0 _d 0-gamm)*k1local*k1local |
| 598 |
& - 4.0 _d 0*k1local*k2local*(1.0 _d 0-2.0 _d 0*gamm) |
| 599 |
hnew = 0.5 _d 0*( (gamm-1.0 _d 0)*k1local + sqrt(stuff) ) |
| 600 |
cmick - now determine [CO2*] |
| 601 |
co2s = diclocal/ |
| 602 |
& (1.0 _d 0 + (k1local/hnew) + (k1local*k2local/(hnew*hnew))) |
| 603 |
cmick - return update pH to main routine |
| 604 |
phlocal = -log10(hnew) |
| 605 |
|
| 606 |
c NOW EVALUATE CO32-, carbonate ion concentration |
| 607 |
c used in determination of calcite compensation depth |
| 608 |
c Karsten Friis & Mick - Sep 2004 |
| 609 |
co3local = k1local*k2local*diclocal / |
| 610 |
& (hnew*hnew + k1local*hnew + k1local*k2local) |
| 611 |
|
| 612 |
c --------------------------------------------------------------- |
| 613 |
c surface pCO2 (following Dickson and Goyet, DOE...) |
| 614 |
#ifdef WATERVAP_BUG |
| 615 |
pCO2surfloc = co2s/fflocal |
| 616 |
#else |
| 617 |
c bug fix by Bennington |
| 618 |
fco2 = co2s/k0local |
| 619 |
pco2surfloc = fco2/fugflocal |
| 620 |
#endif |
| 621 |
|
| 622 |
C ---------------------------------------------------------------- |
| 623 |
c Reconvert from mol/kg -> mol/m^3 |
| 624 |
pt=pt/permil |
| 625 |
sit=sit/permil |
| 626 |
ta=ta/permil |
| 627 |
diclocal=diclocal/permil |
| 628 |
return |
| 629 |
end |
| 630 |
|
| 631 |
c================================================================= |
| 632 |
c ******************************************************************* |
| 633 |
c================================================================= |
| 634 |
CStartOfInterFace |
| 635 |
SUBROUTINE CARBON_COEFFS( |
| 636 |
I ttemp,stemp, |
| 637 |
I bi,bj,iMin,iMax,jMin,jMax,myThid) |
| 638 |
C |
| 639 |
C /==========================================================\ |
| 640 |
C | SUBROUTINE CARBON_COEFFS | |
| 641 |
C | determine coefficients for surface carbon chemistry | |
| 642 |
C | adapted from OCMIP2: SUBROUTINE CO2CALC | |
| 643 |
C | mick follows, oct 1999 | |
| 644 |
c | minor changes to tidy, swd aug 2002 | |
| 645 |
C \==========================================================/ |
| 646 |
C INPUT |
| 647 |
C diclocal = total inorganic carbon (mol/m^3) |
| 648 |
C where 1 T = 1 metric ton = 1000 kg |
| 649 |
C ta = total alkalinity (eq/m^3) |
| 650 |
C pt = inorganic phosphate (mol/^3) |
| 651 |
C sit = inorganic silicate (mol/^3) |
| 652 |
C t = temperature (degrees C) |
| 653 |
C s = salinity (PSU) |
| 654 |
C OUTPUT |
| 655 |
C IMPORTANT: Some words about units - (JCO, 4/4/1999) |
| 656 |
c - Models carry tracers in mol/m^3 (on a per volume basis) |
| 657 |
c - Conversely, this routine, which was written by observationalists |
| 658 |
c (C. Sabine and R. Key), passes input arguments in umol/kg |
| 659 |
c (i.e., on a per mass basis) |
| 660 |
c - I have changed things slightly so that input arguments are in mol/m^3, |
| 661 |
c - Thus, all input concentrations (diclocal, ta, pt, and st) should be |
| 662 |
c given in mol/m^3; output arguments "co2star" and "dco2star" |
| 663 |
c are likewise be in mol/m^3. |
| 664 |
C |
| 665 |
C Apr 2011: fix vapour bug (following Bennington) |
| 666 |
C-------------------------------------------------------------------------- |
| 667 |
IMPLICIT NONE |
| 668 |
C == GLobal variables == |
| 669 |
#include "SIZE.h" |
| 670 |
#include "DYNVARS.h" |
| 671 |
#include "EEPARAMS.h" |
| 672 |
#include "PARAMS.h" |
| 673 |
#include "GRID.h" |
| 674 |
#include "FFIELDS.h" |
| 675 |
#include "DARWIN_FLUX.h" |
| 676 |
C == Routine arguments == |
| 677 |
C ttemp and stemp are local theta and salt arrays |
| 678 |
C dont really need to pass T and S in, could use theta, salt in |
| 679 |
C common block in DYNVARS.h, but this way keeps subroutine more |
| 680 |
C general |
| 681 |
_RL ttemp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 682 |
_RL stemp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 683 |
INTEGER bi,bj,iMin,iMax,jMin,jMax |
| 684 |
INTEGER myThid |
| 685 |
CEndOfInterface |
| 686 |
|
| 687 |
|
| 688 |
C LOCAL VARIABLES |
| 689 |
_RL t |
| 690 |
_RL s |
| 691 |
_RL ta |
| 692 |
_RL pt |
| 693 |
_RL sit |
| 694 |
_RL tk |
| 695 |
_RL tk100 |
| 696 |
_RL tk1002 |
| 697 |
_RL dlogtk |
| 698 |
_RL sqrtis |
| 699 |
_RL sqrts |
| 700 |
_RL s15 |
| 701 |
_RL scl |
| 702 |
_RL x1 |
| 703 |
_RL x2 |
| 704 |
_RL s2 |
| 705 |
_RL xacc |
| 706 |
_RL invtk |
| 707 |
_RL is |
| 708 |
_RL is2 |
| 709 |
c add Bennington |
| 710 |
_RL P1atm |
| 711 |
_RL Rgas |
| 712 |
_RL RT |
| 713 |
_RL delta |
| 714 |
_RL B1 |
| 715 |
_RL B |
| 716 |
INTEGER i |
| 717 |
INTEGER j |
| 718 |
|
| 719 |
C..................................................................... |
| 720 |
C OCMIP note: |
| 721 |
C Calculate all constants needed to convert between various measured |
| 722 |
C carbon species. References for each equation are noted in the code. |
| 723 |
C Once calculated, the constants are |
| 724 |
C stored and passed in the common block "const". The original version |
| 725 |
C of this code was based on the code by dickson in Version 2 of |
| 726 |
C "Handbook of Methods C for the Analysis of the Various Parameters of |
| 727 |
C the Carbon Dioxide System in Seawater", DOE, 1994 (SOP No. 3, p25-26). |
| 728 |
C.................................................................... |
| 729 |
|
| 730 |
do i=imin,imax |
| 731 |
do j=jmin,jmax |
| 732 |
if (hFacC(i,j,1,bi,bj).gt.0. _d 0) then |
| 733 |
t = ttemp(i,j) |
| 734 |
s = stemp(i,j) |
| 735 |
C terms used more than once |
| 736 |
tk = 273.15 _d 0 + t |
| 737 |
tk100 = tk/100. _d 0 |
| 738 |
tk1002=tk100*tk100 |
| 739 |
invtk=1.0 _d 0/tk |
| 740 |
dlogtk=log(tk) |
| 741 |
is=19.924 _d 0*s/(1000. _d 0-1.005 _d 0*s) |
| 742 |
is2=is*is |
| 743 |
sqrtis=sqrt(is) |
| 744 |
s2=s*s |
| 745 |
sqrts=sqrt(s) |
| 746 |
s15=s**1.5 _d 0 |
| 747 |
scl=s/1.80655 _d 0 |
| 748 |
C ----------------------------------------------------------------------- |
| 749 |
C added by Val Bennington Nov 2010 |
| 750 |
C Fugacity Factor needed for non-ideality in ocean |
| 751 |
C ff used for atmospheric correction for water vapor and pressure |
| 752 |
C Weiss (1974) Marine Chemistry |
| 753 |
P1atm = 1.01325 _d 0 ! bars |
| 754 |
Rgas = 83.1451 _d 0 ! bar*cm3/(mol*K) |
| 755 |
RT = Rgas*tk |
| 756 |
delta = (57.7 _d 0 - 0.118 _d 0*tk) |
| 757 |
B1 = -1636.75 _d 0 + 12.0408 _d 0*tk - 0.0327957 _d 0*tk*tk |
| 758 |
B = B1 + 3.16528 _d 0*tk*tk*tk*(0.00001 _d 0) |
| 759 |
fugf(i,j,bi,bj) = exp( (B+2. _d 0*delta) * P1atm / RT) |
| 760 |
C------------------------------------------------------------------------ |
| 761 |
C f = k0(1-pH2O)*correction term for non-ideality |
| 762 |
C Weiss & Price (1980, Mar. Chem., 8, 347-359; Eq 13 with table 6 values) |
| 763 |
ff(i,j,bi,bj) = exp(-162.8301 _d 0 + 218.2968 _d 0/tk100 + |
| 764 |
& 90.9241 _d 0*log(tk100) - 1.47696 _d 0*tk1002 + |
| 765 |
& s * (.025695 _d 0 - .025225 _d 0*tk100 + |
| 766 |
& 0.0049867 _d 0*tk1002)) |
| 767 |
C------------------------------------------------------------------------ |
| 768 |
C K0 from Weiss 1974 |
| 769 |
ak0(i,j,bi,bj) = exp(93.4517 _d 0/tk100 - 60.2409 _d 0 + |
| 770 |
& 23.3585 _d 0 * log(tk100) + |
| 771 |
& s * (0.023517 _d 0 - 0.023656 _d 0*tk100 + |
| 772 |
& 0.0047036 _d 0*tk1002)) |
| 773 |
C------------------------------------------------------------------------ |
| 774 |
C k1 = [H][HCO3]/[H2CO3] |
| 775 |
C k2 = [H][CO3]/[HCO3] |
| 776 |
C Millero p.664 (1995) using Mehrbach et al. data on seawater scale |
| 777 |
ak1(i,j,bi,bj)=10.**(-1. _d 0*(3670.7 _d 0*invtk - |
| 778 |
& 62.008 _d 0 + 9.7944 _d 0*dlogtk - |
| 779 |
& 0.0118 _d 0 * s + 0.000116 _d 0*s2)) |
| 780 |
ak2(i,j,bi,bj)=10.**(-1. _d 0*(1394.7 _d 0*invtk+ 4.777 _d 0- |
| 781 |
& 0.0184 _d 0*s + 0.000118 _d 0*s2)) |
| 782 |
C------------------------------------------------------------------------ |
| 783 |
C kb = [H][BO2]/[HBO2] |
| 784 |
C Millero p.669 (1995) using data from dickson (1990) |
| 785 |
akb(i,j,bi,bj)=exp((-8966.90 _d 0- 2890.53 _d 0*sqrts - |
| 786 |
& 77.942 _d 0*s + 1.728 _d 0*s15 - 0.0996 _d 0*s2)*invtk + |
| 787 |
& (148.0248 _d 0 + 137.1942 _d 0*sqrts + 1.62142 _d 0*s) + |
| 788 |
& (-24.4344 _d 0 - 25.085 _d 0*sqrts - 0.2474 _d 0*s) * |
| 789 |
& dlogtk + 0.053105 _d 0*sqrts*tk) |
| 790 |
C------------------------------------------------------------------------ |
| 791 |
C k1p = [H][H2PO4]/[H3PO4] |
| 792 |
C DOE(1994) eq 7.2.20 with footnote using data from Millero (1974) |
| 793 |
ak1p(i,j,bi,bj) = exp(-4576.752 _d 0*invtk + 115.525 _d 0 - |
| 794 |
& 18.453 _d 0*dlogtk + |
| 795 |
& (-106.736 _d 0*invtk + 0.69171 _d 0)*sqrts + |
| 796 |
& (-0.65643 _d 0*invtk - 0.01844 _d 0)*s) |
| 797 |
C------------------------------------------------------------------------ |
| 798 |
C k2p = [H][HPO4]/[H2PO4] |
| 799 |
C DOE(1994) eq 7.2.23 with footnote using data from Millero (1974)) |
| 800 |
ak2p(i,j,bi,bj) = exp(-8814.715 _d 0*invtk + 172.0883 _d 0 - |
| 801 |
& 27.927 _d 0*dlogtk + |
| 802 |
& (-160.340 _d 0*invtk + 1.3566 _d 0) * sqrts + |
| 803 |
& (0.37335 _d 0*invtk - 0.05778 _d 0) * s) |
| 804 |
C------------------------------------------------------------------------ |
| 805 |
C k3p = [H][PO4]/[HPO4] |
| 806 |
C DOE(1994) eq 7.2.26 with footnote using data from Millero (1974) |
| 807 |
ak3p(i,j,bi,bj) = exp(-3070.75 _d 0*invtk - 18.141 _d 0 + |
| 808 |
& (17.27039 _d 0*invtk + 2.81197 _d 0) * |
| 809 |
& sqrts + (-44.99486 _d 0*invtk - 0.09984 _d 0) * s) |
| 810 |
C------------------------------------------------------------------------ |
| 811 |
C ksi = [H][SiO(OH)3]/[Si(OH)4] |
| 812 |
C Millero p.671 (1995) using data from Yao and Millero (1995) |
| 813 |
aksi(i,j,bi,bj) = exp(-8904.2 _d 0*invtk + 117.385 _d 0 - |
| 814 |
& 19.334 _d 0*dlogtk + |
| 815 |
& (-458.79 _d 0*invtk + 3.5913 _d 0) * sqrtis + |
| 816 |
& (188.74 _d 0*invtk - 1.5998 _d 0) * is + |
| 817 |
& (-12.1652 _d 0*invtk + 0.07871 _d 0) * is2 + |
| 818 |
& log(1.0 _d 0-0.001005 _d 0*s)) |
| 819 |
C------------------------------------------------------------------------ |
| 820 |
C kw = [H][OH] |
| 821 |
C Millero p.670 (1995) using composite data |
| 822 |
akw(i,j,bi,bj) = exp(-13847.26 _d 0*invtk + 148.9652 _d 0 - |
| 823 |
& 23.6521 _d 0*dlogtk + |
| 824 |
& (118.67 _d 0*invtk - 5.977 _d 0 + 1.0495 _d 0 * dlogtk) |
| 825 |
& * sqrts - 0.01615 _d 0 * s) |
| 826 |
C------------------------------------------------------------------------ |
| 827 |
C ks = [H][SO4]/[HSO4] |
| 828 |
C dickson (1990, J. chem. Thermodynamics 22, 113) |
| 829 |
aks(i,j,bi,bj)=exp(-4276.1 _d 0*invtk + 141.328 _d 0 - |
| 830 |
& 23.093 _d 0*dlogtk + |
| 831 |
& (-13856. _d 0*invtk + 324.57 _d 0 - 47.986 _d 0*dlogtk)*sqrtis+ |
| 832 |
& (35474. _d 0*invtk - 771.54 _d 0 + 114.723 _d 0*dlogtk)*is - |
| 833 |
& 2698. _d 0*invtk*is**1.5 _d 0 + 1776. _d 0*invtk*is2 + |
| 834 |
& log(1.0 _d 0 - 0.001005 _d 0*s)) |
| 835 |
C------------------------------------------------------------------------ |
| 836 |
C kf = [H][F]/[HF] |
| 837 |
C dickson and Riley (1979) -- change pH scale to total |
| 838 |
akf(i,j,bi,bj)=exp(1590.2 _d 0*invtk - 12.641 _d 0 + |
| 839 |
& 1.525 _d 0*sqrtis + log(1.0 _d 0 - 0.001005 _d 0*s) + |
| 840 |
& log(1.0 _d 0 + (0.1400 _d 0/96.062 _d 0)*(scl)/aks(i,j,bi,bj))) |
| 841 |
C------------------------------------------------------------------------ |
| 842 |
C Calculate concentrations for borate, sulfate, and fluoride |
| 843 |
C Uppstrom (1974) |
| 844 |
bt(i,j,bi,bj) = 0.000232 _d 0 * scl/10.811 _d 0 |
| 845 |
C Morris & Riley (1966) |
| 846 |
st(i,j,bi,bj) = 0.14 _d 0 * scl/96.062 _d 0 |
| 847 |
C Riley (1965) |
| 848 |
ft(i,j,bi,bj) = 0.000067 _d 0 * scl/18.9984 _d 0 |
| 849 |
C------------------------------------------------------------------------ |
| 850 |
else |
| 851 |
c add Bennington |
| 852 |
fugf(i,j,bi,bj)=0. _d 0 |
| 853 |
ff(i,j,bi,bj)=0. _d 0 |
| 854 |
ak0(i,j,bi,bj)= 0. _d 0 |
| 855 |
ak1(i,j,bi,bj)= 0. _d 0 |
| 856 |
ak2(i,j,bi,bj)= 0. _d 0 |
| 857 |
akb(i,j,bi,bj)= 0. _d 0 |
| 858 |
ak1p(i,j,bi,bj) = 0. _d 0 |
| 859 |
ak2p(i,j,bi,bj) = 0. _d 0 |
| 860 |
ak3p(i,j,bi,bj) = 0. _d 0 |
| 861 |
aksi(i,j,bi,bj) = 0. _d 0 |
| 862 |
akw(i,j,bi,bj) = 0. _d 0 |
| 863 |
aks(i,j,bi,bj)= 0. _d 0 |
| 864 |
akf(i,j,bi,bj)= 0. _d 0 |
| 865 |
bt(i,j,bi,bj) = 0. _d 0 |
| 866 |
st(i,j,bi,bj) = 0. _d 0 |
| 867 |
ft(i,j,bi,bj) = 0. _d 0 |
| 868 |
endif |
| 869 |
end do |
| 870 |
end do |
| 871 |
|
| 872 |
return |
| 873 |
end |
| 874 |
|
| 875 |
c================================================================= |
| 876 |
c ******************************************************************* |
| 877 |
c================================================================= |
| 878 |
CStartOfInterFace |
| 879 |
SUBROUTINE CARBON_COEFFS_PRESSURE_DEP( |
| 880 |
I ttemp,stemp, |
| 881 |
I bi,bj,iMin,iMax,jMin,jMax, |
| 882 |
I Klevel,myThid) |
| 883 |
C |
| 884 |
C /==========================================================\ |
| 885 |
C | SUBROUTINE CARBON_COEFFS | |
| 886 |
C | determine coefficients for surface carbon chemistry | |
| 887 |
C | adapted from OCMIP2: SUBROUTINE CO2CALC | |
| 888 |
C | mick follows, oct 1999 | |
| 889 |
c | minor changes to tidy, swd aug 2002 | |
| 890 |
c | MODIFIED FOR PRESSURE DEPENDENCE | |
| 891 |
c | Karsten Friis and Mick Follows 2004 | |
| 892 |
C \==========================================================/ |
| 893 |
C INPUT |
| 894 |
C diclocal = total inorganic carbon (mol/m^3) |
| 895 |
C where 1 T = 1 metric ton = 1000 kg |
| 896 |
C ta = total alkalinity (eq/m^3) |
| 897 |
C pt = inorganic phosphate (mol/^3) |
| 898 |
C sit = inorganic silicate (mol/^3) |
| 899 |
C t = temperature (degrees C) |
| 900 |
C s = salinity (PSU) |
| 901 |
C OUTPUT |
| 902 |
C IMPORTANT: Some words about units - (JCO, 4/4/1999) |
| 903 |
c - Models carry tracers in mol/m^3 (on a per volume basis) |
| 904 |
c - Conversely, this routine, which was written by observationalists |
| 905 |
c (C. Sabine and R. Key), passes input arguments in umol/kg |
| 906 |
c (i.e., on a per mass basis) |
| 907 |
c - I have changed things slightly so that input arguments are in mol/m^3, |
| 908 |
c - Thus, all input concentrations (diclocal, ta, pt, and st) should be |
| 909 |
c given in mol/m^3; output arguments "co2star" and "dco2star" |
| 910 |
c are likewise be in mol/m^3. |
| 911 |
c |
| 912 |
c |
| 913 |
c NOW INCLUDES: |
| 914 |
c PRESSURE DEPENDENCE of K1, K2, solubility product of calcite |
| 915 |
c based on Takahashi, GEOSECS Atlantic Report, Vol. 1 (1981) |
| 916 |
c |
| 917 |
C-------------------------------------------------------------------------- |
| 918 |
IMPLICIT NONE |
| 919 |
C == GLobal variables == |
| 920 |
#include "SIZE.h" |
| 921 |
#include "DYNVARS.h" |
| 922 |
#include "EEPARAMS.h" |
| 923 |
#include "PARAMS.h" |
| 924 |
#include "GRID.h" |
| 925 |
#include "FFIELDS.h" |
| 926 |
#include "DARWIN_FLUX.h" |
| 927 |
C == Routine arguments == |
| 928 |
C ttemp and stemp are local theta and salt arrays |
| 929 |
C dont really need to pass T and S in, could use theta, salt in |
| 930 |
C common block in DYNVARS.h, but this way keeps subroutine more |
| 931 |
C general |
| 932 |
_RL ttemp(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
| 933 |
_RL stemp(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
| 934 |
INTEGER bi,bj,iMin,iMax,jMin,jMax |
| 935 |
c K is depth index |
| 936 |
INTEGER Klevel |
| 937 |
INTEGER myThid |
| 938 |
CEndOfInterface |
| 939 |
|
| 940 |
|
| 941 |
|
| 942 |
C LOCAL VARIABLES |
| 943 |
_RL t |
| 944 |
_RL s |
| 945 |
_RL ta |
| 946 |
_RL pt |
| 947 |
_RL sit |
| 948 |
_RL tk |
| 949 |
_RL tk100 |
| 950 |
_RL tk1002 |
| 951 |
_RL dlogtk |
| 952 |
_RL sqrtis |
| 953 |
_RL sqrts |
| 954 |
_RL s15 |
| 955 |
_RL scl |
| 956 |
_RL x1 |
| 957 |
_RL x2 |
| 958 |
_RL s2 |
| 959 |
_RL xacc |
| 960 |
_RL invtk |
| 961 |
_RL is |
| 962 |
_RL is2 |
| 963 |
INTEGER i |
| 964 |
INTEGER j |
| 965 |
INTEGER k |
| 966 |
_RL bdepth |
| 967 |
_RL cdepth |
| 968 |
_RL pressc |
| 969 |
_RL Ksp_T_Calc |
| 970 |
_RL xvalue |
| 971 |
_RL zdum |
| 972 |
_RL tmpa1 |
| 973 |
_RL tmpa2 |
| 974 |
_RL tmpa3 |
| 975 |
_RL logKspc |
| 976 |
_RL dv |
| 977 |
_RL dk |
| 978 |
_RL pfactor |
| 979 |
_RL bigR |
| 980 |
|
| 981 |
C..................................................................... |
| 982 |
C OCMIP note: |
| 983 |
C Calculate all constants needed to convert between various measured |
| 984 |
C carbon species. References for each equation are noted in the code. |
| 985 |
C Once calculated, the constants are |
| 986 |
C stored and passed in the common block "const". The original version |
| 987 |
C of this code was based on the code by dickson in Version 2 of |
| 988 |
C "Handbook of Methods C for the Analysis of the Various Parameters of |
| 989 |
C the Carbon Dioxide System in Seawater", DOE, 1994 (SOP No. 3, p25-26). |
| 990 |
C.................................................................... |
| 991 |
|
| 992 |
c determine pressure (bar) from depth |
| 993 |
c 1 BAR at z=0m (atmos pressure) |
| 994 |
c use UPPER surface of cell so top layer pressure = 0 bar |
| 995 |
c for surface exchange coeffs |
| 996 |
|
| 997 |
cmick.............................. |
| 998 |
c write(6,*)'Klevel ',klevel |
| 999 |
|
| 1000 |
bdepth = 0.0d0 |
| 1001 |
cdepth = 0.0d0 |
| 1002 |
pressc = 1.0d0 |
| 1003 |
do k = 1,Klevel |
| 1004 |
cdepth = bdepth + 0.5d0*drF(k) |
| 1005 |
bdepth = bdepth + drF(k) |
| 1006 |
pressc = 1.0d0 + 0.1d0*cdepth |
| 1007 |
end do |
| 1008 |
cmick................................................... |
| 1009 |
c write(6,*)'depth,pressc ',cdepth,pressc |
| 1010 |
cmick.................................................... |
| 1011 |
|
| 1012 |
do i=imin,imax |
| 1013 |
do j=jmin,jmax |
| 1014 |
if (hFacC(i,j,Klevel,bi,bj).gt.0.d0) then |
| 1015 |
t = ttemp(i,j,Klevel,bi,bj) |
| 1016 |
s = max(4. _d 0, stemp(i,j,Klevel,bi,bj)) |
| 1017 |
|
| 1018 |
C terms used more than once |
| 1019 |
tk = 273.15 + t |
| 1020 |
tk100 = tk/100.0 |
| 1021 |
tk1002=tk100*tk100 |
| 1022 |
invtk=1.0/tk |
| 1023 |
dlogtk=log(tk) |
| 1024 |
is=19.924*s/(1000.-1.005*s) |
| 1025 |
is2=is*is |
| 1026 |
sqrtis=sqrt(is) |
| 1027 |
s2=s*s |
| 1028 |
sqrts=sqrt(s) |
| 1029 |
s15=s**1.5 |
| 1030 |
scl=s/1.80655 |
| 1031 |
|
| 1032 |
C------------------------------------------------------------------------ |
| 1033 |
C f = k0(1-pH2O)*correction term for non-ideality |
| 1034 |
C Weiss & Price (1980, Mar. Chem., 8, 347-359; Eq 13 with table 6 values) |
| 1035 |
ff(i,j,bi,bj) = exp(-162.8301 + 218.2968/tk100 + |
| 1036 |
& 90.9241*log(tk100) - 1.47696*tk1002 + |
| 1037 |
& s * (.025695 - .025225*tk100 + |
| 1038 |
& 0.0049867*tk1002)) |
| 1039 |
C------------------------------------------------------------------------ |
| 1040 |
C K0 from Weiss 1974 |
| 1041 |
ak0(i,j,bi,bj) = exp(93.4517/tk100 - 60.2409 + |
| 1042 |
& 23.3585 * log(tk100) + |
| 1043 |
& s * (0.023517 - 0.023656*tk100 + |
| 1044 |
& 0.0047036*tk1002)) |
| 1045 |
C------------------------------------------------------------------------ |
| 1046 |
C k1 = [H][HCO3]/[H2CO3] |
| 1047 |
C k2 = [H][CO3]/[HCO3] |
| 1048 |
C Millero p.664 (1995) using Mehrbach et al. data on seawater scale |
| 1049 |
ak1(i,j,bi,bj)=10**(-1*(3670.7*invtk - |
| 1050 |
& 62.008 + 9.7944*dlogtk - |
| 1051 |
& 0.0118 * s + 0.000116*s2)) |
| 1052 |
ak2(i,j,bi,bj)=10**(-1*(1394.7*invtk + 4.777 - |
| 1053 |
& 0.0184*s + 0.000118*s2)) |
| 1054 |
C NOW PRESSURE DEPENDENCE: |
| 1055 |
c Following Takahashi (1981) GEOSECS report - quoting Culberson and |
| 1056 |
c Pytkowicz (1968) |
| 1057 |
c pressc = pressure in bars |
| 1058 |
ak1(i,j,bi,bj) = ak1(i,j,bi,bj)* |
| 1059 |
& exp( (24.2-0.085*t)*(pressc-1.0)/(83.143*tk) ) |
| 1060 |
c FIRST GO FOR K2: According to GEOSECS (1982) report |
| 1061 |
c ak2(i,j,bi,bj) = ak2(i,j,bi,bj)* |
| 1062 |
c & exp( (26.4-0.040*t)*(pressc-1.0)/(83.143*tk) ) |
| 1063 |
c SECOND GO FOR K2: corrected coeff according to CO2sys documentation |
| 1064 |
c E. Lewis and D. Wallace (1998) ORNL/CDIAC-105 |
| 1065 |
ak2(i,j,bi,bj) = ak2(i,j,bi,bj)* |
| 1066 |
& exp( (16.4-0.040*t)*(pressc-1.0)/(83.143*tk) ) |
| 1067 |
C------------------------------------------------------------------------ |
| 1068 |
C kb = [H][BO2]/[HBO2] |
| 1069 |
C Millero p.669 (1995) using data from dickson (1990) |
| 1070 |
akb(i,j,bi,bj)=exp((-8966.90 - 2890.53*sqrts - 77.942*s + |
| 1071 |
& 1.728*s15 - 0.0996*s2)*invtk + |
| 1072 |
& (148.0248 + 137.1942*sqrts + 1.62142*s) + |
| 1073 |
& (-24.4344 - 25.085*sqrts - 0.2474*s) * |
| 1074 |
& dlogtk + 0.053105*sqrts*tk) |
| 1075 |
C Mick and Karsten - Dec 04 |
| 1076 |
C ADDING pressure dependence based on Millero (1995), p675 |
| 1077 |
C with additional info from CO2sys documentation (E. Lewis and |
| 1078 |
C D. Wallace, 1998 - see endnotes for commentary on Millero, 95) |
| 1079 |
bigR = 83.145 |
| 1080 |
dv = -29.48 + 0.1622*t + 2.608d-3*t*t |
| 1081 |
dk = -2.84d-3 |
| 1082 |
pfactor = - (dv/(bigR*tk))*pressc |
| 1083 |
& + (0.5*dk/(bigR*tk))*pressc*pressc |
| 1084 |
akb(i,j,bi,bj) = akb(i,j,bi,bj)*exp(pfactor) |
| 1085 |
C------------------------------------------------------------------------ |
| 1086 |
C k1p = [H][H2PO4]/[H3PO4] |
| 1087 |
C DOE(1994) eq 7.2.20 with footnote using data from Millero (1974) |
| 1088 |
ak1p(i,j,bi,bj) = exp(-4576.752*invtk + 115.525 - |
| 1089 |
& 18.453*dlogtk + |
| 1090 |
& (-106.736*invtk + 0.69171)*sqrts + |
| 1091 |
& (-0.65643*invtk - 0.01844)*s) |
| 1092 |
C------------------------------------------------------------------------ |
| 1093 |
C k2p = [H][HPO4]/[H2PO4] |
| 1094 |
C DOE(1994) eq 7.2.23 with footnote using data from Millero (1974)) |
| 1095 |
ak2p(i,j,bi,bj) = exp(-8814.715*invtk + 172.0883 - |
| 1096 |
& 27.927*dlogtk + |
| 1097 |
& (-160.340*invtk + 1.3566) * sqrts + |
| 1098 |
& (0.37335*invtk - 0.05778) * s) |
| 1099 |
C------------------------------------------------------------------------ |
| 1100 |
C k3p = [H][PO4]/[HPO4] |
| 1101 |
C DOE(1994) eq 7.2.26 with footnote using data from Millero (1974) |
| 1102 |
ak3p(i,j,bi,bj) = exp(-3070.75*invtk - 18.141 + |
| 1103 |
& (17.27039*invtk + 2.81197) * |
| 1104 |
& sqrts + (-44.99486*invtk - 0.09984) * s) |
| 1105 |
C------------------------------------------------------------------------ |
| 1106 |
C ksi = [H][SiO(OH)3]/[Si(OH)4] |
| 1107 |
C Millero p.671 (1995) using data from Yao and Millero (1995) |
| 1108 |
aksi(i,j,bi,bj) = exp(-8904.2*invtk + 117.385 - |
| 1109 |
& 19.334*dlogtk + |
| 1110 |
& (-458.79*invtk + 3.5913) * sqrtis + |
| 1111 |
& (188.74*invtk - 1.5998) * is + |
| 1112 |
& (-12.1652*invtk + 0.07871) * is2 + |
| 1113 |
& log(1.0-0.001005*s)) |
| 1114 |
C------------------------------------------------------------------------ |
| 1115 |
C kw = [H][OH] |
| 1116 |
C Millero p.670 (1995) using composite data |
| 1117 |
akw(i,j,bi,bj) = exp(-13847.26*invtk + 148.9652 - |
| 1118 |
& 23.6521*dlogtk + |
| 1119 |
& (118.67*invtk - 5.977 + 1.0495 * dlogtk) * |
| 1120 |
& sqrts - 0.01615 * s) |
| 1121 |
C------------------------------------------------------------------------ |
| 1122 |
C ks = [H][SO4]/[HSO4] |
| 1123 |
C dickson (1990, J. chem. Thermodynamics 22, 113) |
| 1124 |
aks(i,j,bi,bj)=exp(-4276.1*invtk + 141.328 - |
| 1125 |
& 23.093*dlogtk + |
| 1126 |
& (-13856*invtk + 324.57 - 47.986*dlogtk)*sqrtis + |
| 1127 |
& (35474*invtk - 771.54 + 114.723*dlogtk)*is - |
| 1128 |
& 2698*invtk*is**1.5 + 1776*invtk*is2 + |
| 1129 |
& log(1.0 - 0.001005*s)) |
| 1130 |
C------------------------------------------------------------------------ |
| 1131 |
C kf = [H][F]/[HF] |
| 1132 |
C dickson and Riley (1979) -- change pH scale to total |
| 1133 |
akf(i,j,bi,bj)=exp(1590.2*invtk - 12.641 + 1.525*sqrtis + |
| 1134 |
& log(1.0 - 0.001005*s) + |
| 1135 |
& log(1.0 + (0.1400/96.062)*(scl)/aks(i,j,bi,bj))) |
| 1136 |
C------------------------------------------------------------------------ |
| 1137 |
C Calculate concentrations for borate, sulfate, and fluoride |
| 1138 |
C Uppstrom (1974) |
| 1139 |
bt(i,j,bi,bj) = 0.000232 * scl/10.811 |
| 1140 |
C Morris & Riley (1966) |
| 1141 |
st(i,j,bi,bj) = 0.14 * scl/96.062 |
| 1142 |
C Riley (1965) |
| 1143 |
ft(i,j,bi,bj) = 0.000067 * scl/18.9984 |
| 1144 |
C------------------------------------------------------------------------ |
| 1145 |
C solubility product for calcite |
| 1146 |
C |
| 1147 |
c Following Takahashi (1982) GEOSECS handbook |
| 1148 |
C NOT SURE THIS IS WORKING??? |
| 1149 |
C Ingle et al. (1973) |
| 1150 |
c Ksp_T_Calc = ( -34.452 - 39.866*(s**0.333333) |
| 1151 |
c & + 110.21*log(s) - 7.5752d-6 * (tk**2.0) |
| 1152 |
c & ) * 1.0d-7 |
| 1153 |
c with pressure dependence Culberson and Pytkowicz (1968) |
| 1154 |
c xvalue = (36-0.20*t)*(pressc-1.0)/(83.143*tk) |
| 1155 |
c Ksp_TP_Calc(i,j,bi,bj) = Ksp_T_Calc*exp(xvalue) |
| 1156 |
c |
| 1157 |
c |
| 1158 |
C Following Mucci (1983) - from Zeebe/Wolf-Gladrow equic.m |
| 1159 |
tmpa1 = - 171.9065 - (0.077993*tk) + (2839.319/tk) |
| 1160 |
& + (71.595*log10(tk)) |
| 1161 |
tmpa2 = +(-0.77712 + (0.0028426*tk) + (178.34/tk) )*sqrts |
| 1162 |
tmpa3 = -(0.07711*s) + (0.0041249*s15) |
| 1163 |
logKspc = tmpa1 + tmpa2 + tmpa3 |
| 1164 |
Ksp_T_Calc = 10.0**logKspc |
| 1165 |
c write(6,*)i,j,k,tmpa1,tmpa2,tmpa3,logkspc,Ksp_T_Calc |
| 1166 |
c with pressure dependence Culberson and Pytkowicz (1968) |
| 1167 |
c xvalue = (36.0-0.20*t)*(pressc-1.0)/(83.143*tk) |
| 1168 |
c Ksp_TP_Calc(i,j,bi,bj) = Ksp_T_Calc*exp(xvalue) |
| 1169 |
|
| 1170 |
c alternative pressure depdendence |
| 1171 |
c following Millero (1995) but using info from Appendix A11 of |
| 1172 |
c Zeebe and Wolf-Gladrow (2001) book |
| 1173 |
c dv = -48.6 - 0.5304*t |
| 1174 |
c dk = -11.76d-3 - 0.3692*t |
| 1175 |
c xvalue = - (dv/(bigR*tk))*pressc |
| 1176 |
c & + (0.5*dk/(bigR*tk))*pressc*pressc |
| 1177 |
c Ksp_TP_Calc(i,j,bi,bj) = Ksp_T_Calc*exp(xvalue) |
| 1178 |
|
| 1179 |
c alternative pressure dependence from Ingle (1975) |
| 1180 |
|
| 1181 |
zdum = (pressc*10.0d0 - 10.0d0)/10.0d0 |
| 1182 |
xvalue = ( (48.8d0 - 0.53d0*t)*zdum |
| 1183 |
& + (-0.00588d0 + 0.0001845d0*t)*zdum*zdum) |
| 1184 |
& / (188.93d0*(t + 273.15d0)) |
| 1185 |
|
| 1186 |
Ksp_TP_Calc(i,j,bi,bj) = Ksp_T_Calc*10**(xvalue) |
| 1187 |
|
| 1188 |
C------------------------------------------------------------------------ |
| 1189 |
else |
| 1190 |
ff(i,j,bi,bj)=0.d0 |
| 1191 |
ak0(i,j,bi,bj)= 0.d0 |
| 1192 |
ak1(i,j,bi,bj)= 0.d0 |
| 1193 |
ak2(i,j,bi,bj)= 0.d0 |
| 1194 |
akb(i,j,bi,bj)= 0.d0 |
| 1195 |
ak1p(i,j,bi,bj) = 0.d0 |
| 1196 |
ak2p(i,j,bi,bj) = 0.d0 |
| 1197 |
ak3p(i,j,bi,bj) = 0.d0 |
| 1198 |
aksi(i,j,bi,bj) = 0.d0 |
| 1199 |
akw(i,j,bi,bj) = 0.d0 |
| 1200 |
aks(i,j,bi,bj)= 0.d0 |
| 1201 |
akf(i,j,bi,bj)= 0.d0 |
| 1202 |
bt(i,j,bi,bj) = 0.d0 |
| 1203 |
st(i,j,bi,bj) = 0.d0 |
| 1204 |
ft(i,j,bi,bj) = 0.d0 |
| 1205 |
Ksp_TP_Calc(i,j,bi,bj) = 0.d0 |
| 1206 |
endif |
| 1207 |
end do |
| 1208 |
end do |
| 1209 |
|
| 1210 |
return |
| 1211 |
end |
| 1212 |
|
| 1213 |
#endif /*ALLOW_CARBON*/ |
| 1214 |
|
| 1215 |
#endif /*DARWIN*/ |
| 1216 |
#endif /*ALLOW_PTRACERS*/ |
| 1217 |
c ================================================================== |
| 1218 |
|
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