MODULE p4zche !!====================================================================== !! *** MODULE p4zche *** !! TOP : PISCES Sea water chemistry computed following OCMIP protocol !!====================================================================== !! History : OPA ! 1988 (E. Maier-Reimer) Original code !! - ! 1998 (O. Aumont) addition !! - ! 1999 (C. Le Quere) modification !! NEMO 1.0 ! 2004 (O. Aumont) modification !! - ! 2006 (R. Gangsto) modification !! 2.0 ! 2007-12 (C. Ethe, G. Madec) F90 !! ! 2011-02 (J. Simeon, J.Orr ) update O2 solubility constants !! 3.6 ! 2016-03 (O. Aumont) Change chemistry to MOCSY standards !!---------------------------------------------------------------------- !! p4z_che : Sea water chemistry computed following OCMIP protocol !!---------------------------------------------------------------------- USE oce_trc ! shared variables between ocean and passive tracers USE trc ! passive tracers common variables USE sms_pisces ! PISCES Source Minus Sink variables USE lib_mpp ! MPP library USE eosbn2, ONLY : neos IMPLICIT NONE PRIVATE PUBLIC p4z_che ! PUBLIC p4z_che_alloc ! PUBLIC ahini_for_at ! PUBLIC solve_at_general ! REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sio3eq ! chemistry of Si REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: fekeq ! chemistry of Fe REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: chemc ! Solubilities of O2 and CO2 REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: chemo2 ! Solubilities of O2 and CO2 REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: fesol ! solubility of Fe REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: salinprac ! Practical salinity REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: tempis ! In situ temperature REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akb3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akw3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akf3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: aks3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ak1p3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ak2p3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ak3p3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: aksi3 !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: borat !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: fluorid !: ??? REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sulfat !: ??? !!* Variable for chemistry of the CO2 cycle REAL(wp), PUBLIC :: atcox = 0.20946 ! units atm REAL(wp) :: o2atm = 1. / ( 1000. * 0.20946 ) REAL(wp) :: rgas = 83.14472 ! universal gas constants REAL(wp) :: oxyco = 1. / 22.4144 ! converts from liters of an ideal gas to moles ! ! coeff. for seawater pressure correction : millero 95 ! ! AGRIF doesn't like the DATA instruction REAL(wp) :: devk10 = -25.5 REAL(wp) :: devk11 = -15.82 REAL(wp) :: devk12 = -29.48 REAL(wp) :: devk13 = -20.02 REAL(wp) :: devk14 = -18.03 REAL(wp) :: devk15 = -9.78 REAL(wp) :: devk16 = -48.76 REAL(wp) :: devk17 = -14.51 REAL(wp) :: devk18 = -23.12 REAL(wp) :: devk19 = -26.57 REAL(wp) :: devk110 = -29.48 ! REAL(wp) :: devk20 = 0.1271 REAL(wp) :: devk21 = -0.0219 REAL(wp) :: devk22 = 0.1622 REAL(wp) :: devk23 = 0.1119 REAL(wp) :: devk24 = 0.0466 REAL(wp) :: devk25 = -0.0090 REAL(wp) :: devk26 = 0.5304 REAL(wp) :: devk27 = 0.1211 REAL(wp) :: devk28 = 0.1758 REAL(wp) :: devk29 = 0.2020 REAL(wp) :: devk210 = 0.1622 ! REAL(wp) :: devk30 = 0. REAL(wp) :: devk31 = 0. REAL(wp) :: devk32 = 2.608E-3 REAL(wp) :: devk33 = -1.409e-3 REAL(wp) :: devk34 = 0.316e-3 REAL(wp) :: devk35 = -0.942e-3 REAL(wp) :: devk36 = 0. REAL(wp) :: devk37 = -0.321e-3 REAL(wp) :: devk38 = -2.647e-3 REAL(wp) :: devk39 = -3.042e-3 REAL(wp) :: devk310 = -2.6080e-3 ! REAL(wp) :: devk40 = -3.08E-3 REAL(wp) :: devk41 = 1.13E-3 REAL(wp) :: devk42 = -2.84E-3 REAL(wp) :: devk43 = -5.13E-3 REAL(wp) :: devk44 = -4.53e-3 REAL(wp) :: devk45 = -3.91e-3 REAL(wp) :: devk46 = -11.76e-3 REAL(wp) :: devk47 = -2.67e-3 REAL(wp) :: devk48 = -5.15e-3 REAL(wp) :: devk49 = -4.08e-3 REAL(wp) :: devk410 = -2.84e-3 ! REAL(wp) :: devk50 = 0.0877E-3 REAL(wp) :: devk51 = -0.1475E-3 REAL(wp) :: devk52 = 0. REAL(wp) :: devk53 = 0.0794E-3 REAL(wp) :: devk54 = 0.09e-3 REAL(wp) :: devk55 = 0.054e-3 REAL(wp) :: devk56 = 0.3692E-3 REAL(wp) :: devk57 = 0.0427e-3 REAL(wp) :: devk58 = 0.09e-3 REAL(wp) :: devk59 = 0.0714e-3 REAL(wp) :: devk510 = 0.0 ! ! General parameters REAL(wp), PARAMETER :: pp_rdel_ah_target = 1.E-4_wp REAL(wp), PARAMETER :: pp_ln10 = 2.302585092994045684018_wp ! Maximum number of iterations for each method INTEGER, PARAMETER :: jp_maxniter_atgen = 20 ! Bookkeeping variables for each method ! - SOLVE_AT_GENERAL INTEGER :: niter_atgen = jp_maxniter_atgen !!---------------------------------------------------------------------- !! NEMO/TOP 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE p4z_che !!--------------------------------------------------------------------- !! *** ROUTINE p4z_che *** !! !! ** Purpose : Sea water chemistry computed following OCMIP protocol !! !! ** Method : - ... !!--------------------------------------------------------------------- INTEGER :: ji, jj, jk REAL(wp) :: ztkel, ztkel1, zt , zsal , zsal2 , zbuf1 , zbuf2 REAL(wp) :: ztgg , ztgg2, ztgg3 , ztgg4 , ztgg5 REAL(wp) :: zpres, ztc , zcl , zcpexp, zoxy , zcpexp2 REAL(wp) :: zsqrt, ztr , zlogt , zcek1, zc1, zplat REAL(wp) :: zis , zis2 , zsal15, zisqrt, za1, za2 REAL(wp) :: zckb , zck1 , zck2 , zckw , zak1 , zak2 , zakb , zaksp0, zakw REAL(wp) :: zck1p, zck2p, zck3p, zcksi, zak1p, zak2p, zak3p, zaksi REAL(wp) :: zst , zft , zcks , zckf , zaksp1 REAL(wp) :: total2free, free2SWS, total2SWS, SWS2total !!--------------------------------------------------------------------- ! IF( ln_timing ) CALL timing_start('p4z_che') ! ! Computation of chemical constants require practical salinity ! Thus, when TEOS08 is used, absolute salinity is converted to ! practical salinity ! ------------------------------------------------------------- IF (neos == -1) THEN salinprac(:,:,:) = tsn(:,:,:,jp_sal) * 35.0 / 35.16504 ELSE salinprac(:,:,:) = tsn(:,:,:,jp_sal) ENDIF ! ! Computations of chemical constants require in situ temperature ! Here a quite simple formulation is used to convert ! potential temperature to in situ temperature. The errors is less than ! 0.04°C relative to an exact computation ! --------------------------------------------------------------------- DO jk = 1, jpk DO jj = 1, jpj DO ji = 1, jpi zpres = gdept_n(ji,jj,jk) / 1000. za1 = 0.04 * ( 1.0 + 0.185 * tsn(ji,jj,jk,jp_tem) + 0.035 * (salinprac(ji,jj,jk) - 35.0) ) za2 = 0.0075 * ( 1.0 - tsn(ji,jj,jk,jp_tem) / 30.0 ) tempis(ji,jj,jk) = tsn(ji,jj,jk,jp_tem) - za1 * zpres + za2 * zpres**2 END DO END DO END DO ! ! CHEMICAL CONSTANTS - SURFACE LAYER ! ---------------------------------- !CDIR NOVERRCHK DO jj = 1, jpj !CDIR NOVERRCHK DO ji = 1, jpi ! ! SET ABSOLUTE TEMPERATURE ztkel = tempis(ji,jj,1) + 273.15 zt = ztkel * 0.01 zsal = salinprac(ji,jj,1) + ( 1.- tmask(ji,jj,1) ) * 35. ! ! LN(K0) OF SOLUBILITY OF CO2 (EQ. 12, WEISS, 1980) ! ! AND FOR THE ATMOSPHERE FOR NON IDEAL GAS zcek1 = 9345.17/ztkel - 60.2409 + 23.3585 * LOG(zt) + zsal*(0.023517 - 0.00023656*ztkel & & + 0.0047036e-4*ztkel**2) chemc(ji,jj,1) = EXP( zcek1 ) * 1E-6 * rhop(ji,jj,1) / 1000. ! mol/(L atm) chemc(ji,jj,2) = -1636.75 + 12.0408*ztkel - 0.0327957*ztkel**2 + 0.0000316528*ztkel**3 chemc(ji,jj,3) = 57.7 - 0.118*ztkel ! END DO END DO ! OXYGEN SOLUBILITY - DEEP OCEAN ! ------------------------------- !CDIR NOVERRCHK DO jk = 1, jpk !CDIR NOVERRCHK DO jj = 1, jpj !CDIR NOVERRCHK DO ji = 1, jpi ztkel = tempis(ji,jj,jk) + 273.15 zsal = salinprac(ji,jj,jk) + ( 1.- tmask(ji,jj,jk) ) * 35. zsal2 = zsal * zsal ztgg = LOG( ( 298.15 - tempis(ji,jj,jk) ) / ztkel ) ! Set the GORDON & GARCIA scaled temperature ztgg2 = ztgg * ztgg ztgg3 = ztgg2 * ztgg ztgg4 = ztgg3 * ztgg ztgg5 = ztgg4 * ztgg zoxy = 2.00856 + 3.22400 * ztgg + 3.99063 * ztgg2 + 4.80299 * ztgg3 & & + 9.78188e-1 * ztgg4 + 1.71069 * ztgg5 + zsal * ( -6.24097e-3 & & - 6.93498e-3 * ztgg - 6.90358e-3 * ztgg2 - 4.29155e-3 * ztgg3 ) & & - 3.11680e-7 * zsal2 chemo2(ji,jj,jk) = ( EXP( zoxy ) * o2atm ) * oxyco * atcox ! mol/(L atm) END DO END DO END DO ! CHEMICAL CONSTANTS - DEEP OCEAN ! ------------------------------- !CDIR NOVERRCHK DO jk = 1, jpk !CDIR NOVERRCHK DO jj = 1, jpj !CDIR NOVERRCHK DO ji = 1, jpi ! SET PRESSION ACCORDING TO SAUNDER (1980) zplat = SIN ( ABS(gphit(ji,jj)*3.141592654/180.) ) zc1 = 5.92E-3 + zplat**2 * 5.25E-3 zpres = ((1-zc1)-SQRT(((1-zc1)**2)-(8.84E-6*gdept_n(ji,jj,jk)))) / 4.42E-6 zpres = zpres / 10.0 ! SET ABSOLUTE TEMPERATURE ztkel = tempis(ji,jj,jk) + 273.15 zsal = salinprac(ji,jj,jk) + ( 1.-tmask(ji,jj,jk) ) * 35. zsqrt = SQRT( zsal ) zsal15 = zsqrt * zsal zlogt = LOG( ztkel ) ztr = 1. / ztkel zis = 19.924 * zsal / ( 1000.- 1.005 * zsal ) zis2 = zis * zis zisqrt = SQRT( zis ) ztc = tempis(ji,jj,jk) + ( 1.- tmask(ji,jj,jk) ) * 20. ! CHLORINITY (WOOSTER ET AL., 1969) zcl = zsal / 1.80655 ! TOTAL SULFATE CONCENTR. [MOLES/kg soln] zst = 0.14 * zcl /96.062 ! TOTAL FLUORIDE CONCENTR. [MOLES/kg soln] zft = 0.000067 * zcl /18.9984 ! DISSOCIATION CONSTANT FOR SULFATES on free H scale (Dickson 1990) zcks = EXP(-4276.1 * ztr + 141.328 - 23.093 * zlogt & & + (-13856. * ztr + 324.57 - 47.986 * zlogt) * zisqrt & & + (35474. * ztr - 771.54 + 114.723 * zlogt) * zis & & - 2698. * ztr * zis**1.5 + 1776.* ztr * zis2 & & + LOG(1.0 - 0.001005 * zsal)) ! DISSOCIATION CONSTANT FOR FLUORIDES on free H scale (Dickson and Riley 79) zckf = EXP( 1590.2*ztr - 12.641 + 1.525*zisqrt & & + LOG(1.0d0 - 0.001005d0*zsal) & & + LOG(1.0d0 + zst/zcks)) ! DISSOCIATION CONSTANT FOR CARBONATE AND BORATE zckb= (-8966.90 - 2890.53*zsqrt - 77.942*zsal & & + 1.728*zsal15 - 0.0996*zsal*zsal)*ztr & & + (148.0248 + 137.1942*zsqrt + 1.62142*zsal) & & + (-24.4344 - 25.085*zsqrt - 0.2474*zsal) & & * zlogt + 0.053105*zsqrt*ztkel ! DISSOCIATION COEFFICIENT FOR CARBONATE ACCORDING TO ! MEHRBACH (1973) REFIT BY MILLERO (1995), seawater scale zck1 = -1.0*(3633.86*ztr - 61.2172 + 9.6777*zlogt & - 0.011555*zsal + 0.0001152*zsal*zsal) zck2 = -1.0*(471.78*ztr + 25.9290 - 3.16967*zlogt & - 0.01781*zsal + 0.0001122*zsal*zsal) ! PKW (H2O) (MILLERO, 1995) from composite data zckw = -13847.26 * ztr + 148.9652 - 23.6521 * zlogt + ( 118.67 * ztr & - 5.977 + 1.0495 * zlogt ) * zsqrt - 0.01615 * zsal ! CONSTANTS FOR PHOSPHATE (MILLERO, 1995) zck1p = -4576.752*ztr + 115.540 - 18.453*zlogt & & + (-106.736*ztr + 0.69171) * zsqrt & & + (-0.65643*ztr - 0.01844) * zsal zck2p = -8814.715*ztr + 172.1033 - 27.927*zlogt & & + (-160.340*ztr + 1.3566)*zsqrt & & + (0.37335*ztr - 0.05778)*zsal zck3p = -3070.75*ztr - 18.126 & & + (17.27039*ztr + 2.81197) * zsqrt & & + (-44.99486*ztr - 0.09984) * zsal ! CONSTANT FOR SILICATE, MILLERO (1995) zcksi = -8904.2*ztr + 117.400 - 19.334*zlogt & & + (-458.79*ztr + 3.5913) * zisqrt & & + (188.74*ztr - 1.5998) * zis & & + (-12.1652*ztr + 0.07871) * zis2 & & + LOG(1.0 - 0.001005*zsal) ! APPARENT SOLUBILITY PRODUCT K'SP OF CALCITE IN SEAWATER ! (S=27-43, T=2-25 DEG C) at pres =0 (atmos. pressure) (MUCCI 1983) zaksp0 = -171.9065 -0.077993*ztkel + 2839.319*ztr + 71.595*LOG10( ztkel ) & & + (-0.77712 + 0.00284263*ztkel + 178.34*ztr) * zsqrt & & - 0.07711*zsal + 0.0041249*zsal15 ! CONVERT FROM DIFFERENT PH SCALES total2free = 1.0/(1.0 + zst/zcks) free2SWS = 1. + zst/zcks + zft/(zckf*total2free) total2SWS = total2free * free2SWS SWS2total = 1.0 / total2SWS ! K1, K2 OF CARBONIC ACID, KB OF BORIC ACID, KW (H2O) (LIT.?) zak1 = 10**(zck1) * total2SWS zak2 = 10**(zck2) * total2SWS zakb = EXP( zckb ) * total2SWS zakw = EXP( zckw ) zaksp1 = 10**(zaksp0) zak1p = exp( zck1p ) zak2p = exp( zck2p ) zak3p = exp( zck3p ) zaksi = exp( zcksi ) zckf = zckf * total2SWS ! FORMULA FOR CPEXP AFTER EDMOND & GIESKES (1970) ! (REFERENCE TO CULBERSON & PYTKOQICZ (1968) AS MADE ! IN BROECKER ET AL. (1982) IS INCORRECT; HERE RGAS IS ! TAKEN TENFOLD TO CORRECT FOR THE NOTATION OF pres IN ! DBAR INSTEAD OF BAR AND THE EXPRESSION FOR CPEXP IS ! MULTIPLIED BY LN(10.) TO ALLOW USE OF EXP-FUNCTION ! WITH BASIS E IN THE FORMULA FOR AKSPP (CF. EDMOND ! & GIESKES (1970), P. 1285-1286 (THE SMALL ! FORMULA ON P. 1286 IS RIGHT AND CONSISTENT WITH THE ! SIGN IN PARTIAL MOLAR VOLUME CHANGE AS SHOWN ON P. 1285)) zcpexp = zpres / (rgas*ztkel) zcpexp2 = zpres * zcpexp ! KB OF BORIC ACID, K1,K2 OF CARBONIC ACID PRESSURE ! CORRECTION AFTER CULBERSON AND PYTKOWICZ (1968) ! (CF. BROECKER ET AL., 1982) zbuf1 = - ( devk10 + devk20 * ztc + devk30 * ztc * ztc ) zbuf2 = 0.5 * ( devk40 + devk50 * ztc ) ak13(ji,jj,jk) = zak1 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk11 + devk21 * ztc + devk31 * ztc * ztc ) zbuf2 = 0.5 * ( devk41 + devk51 * ztc ) ak23(ji,jj,jk) = zak2 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk12 + devk22 * ztc + devk32 * ztc * ztc ) zbuf2 = 0.5 * ( devk42 + devk52 * ztc ) akb3(ji,jj,jk) = zakb * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk13 + devk23 * ztc + devk33 * ztc * ztc ) zbuf2 = 0.5 * ( devk43 + devk53 * ztc ) akw3(ji,jj,jk) = zakw * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk14 + devk24 * ztc + devk34 * ztc * ztc ) zbuf2 = 0.5 * ( devk44 + devk54 * ztc ) aks3(ji,jj,jk) = zcks * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk15 + devk25 * ztc + devk35 * ztc * ztc ) zbuf2 = 0.5 * ( devk45 + devk55 * ztc ) akf3(ji,jj,jk) = zckf * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk17 + devk27 * ztc + devk37 * ztc * ztc ) zbuf2 = 0.5 * ( devk47 + devk57 * ztc ) ak1p3(ji,jj,jk) = zak1p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk18 + devk28 * ztc + devk38 * ztc * ztc ) zbuf2 = 0.5 * ( devk48 + devk58 * ztc ) ak2p3(ji,jj,jk) = zak2p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk19 + devk29 * ztc + devk39 * ztc * ztc ) zbuf2 = 0.5 * ( devk49 + devk59 * ztc ) ak3p3(ji,jj,jk) = zak3p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) zbuf1 = - ( devk110 + devk210 * ztc + devk310 * ztc * ztc ) zbuf2 = 0.5 * ( devk410 + devk510 * ztc ) aksi3(ji,jj,jk) = zaksi * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) ! CONVERT FROM DIFFERENT PH SCALES total2free = 1.0/(1.0 + zst/aks3(ji,jj,jk)) free2SWS = 1. + zst/aks3(ji,jj,jk) + zft/akf3(ji,jj,jk) total2SWS = total2free * free2SWS SWS2total = 1.0 / total2SWS ! Convert to total scale ak13(ji,jj,jk) = ak13(ji,jj,jk) * SWS2total ak23(ji,jj,jk) = ak23(ji,jj,jk) * SWS2total akb3(ji,jj,jk) = akb3(ji,jj,jk) * SWS2total akw3(ji,jj,jk) = akw3(ji,jj,jk) * SWS2total ak1p3(ji,jj,jk) = ak1p3(ji,jj,jk) * SWS2total ak2p3(ji,jj,jk) = ak2p3(ji,jj,jk) * SWS2total ak3p3(ji,jj,jk) = ak3p3(ji,jj,jk) * SWS2total aksi3(ji,jj,jk) = aksi3(ji,jj,jk) * SWS2total akf3(ji,jj,jk) = akf3(ji,jj,jk) / total2free ! APPARENT SOLUBILITY PRODUCT K'SP OF CALCITE ! AS FUNCTION OF PRESSURE FOLLOWING MILLERO ! (P. 1285) AND BERNER (1976) zbuf1 = - ( devk16 + devk26 * ztc + devk36 * ztc * ztc ) zbuf2 = 0.5 * ( devk46 + devk56 * ztc ) aksp(ji,jj,jk) = zaksp1 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) ! TOTAL F, S, and BORATE CONCENTR. [MOLES/L] borat(ji,jj,jk) = 0.0002414 * zcl / 10.811 sulfat(ji,jj,jk) = zst fluorid(ji,jj,jk) = zft ! Iron and SIO3 saturation concentration from ... sio3eq(ji,jj,jk) = EXP( LOG( 10.) * ( 6.44 - 968. / ztkel ) ) * 1.e-6 fekeq (ji,jj,jk) = 10**( 17.27 - 1565.7 / ztkel ) ! Liu and Millero (1999) only valid 5 - 50 degC ztkel1 = MAX( 5. , tempis(ji,jj,jk) ) + 273.16 fesol(ji,jj,jk,1) = 10**(-13.486 - 0.1856* zis**0.5 + 0.3073*zis + 5254.0/ztkel1) fesol(ji,jj,jk,2) = 10**(2.517 - 0.8885*zis**0.5 + 0.2139 * zis - 1320.0/ztkel1 ) fesol(ji,jj,jk,3) = 10**(0.4511 - 0.3305*zis**0.5 - 1996.0/ztkel1 ) fesol(ji,jj,jk,4) = 10**(-0.2965 - 0.7881*zis**0.5 - 4086.0/ztkel1 ) fesol(ji,jj,jk,5) = 10**(4.4466 - 0.8505*zis**0.5 - 7980.0/ztkel1 ) END DO END DO END DO ! IF( ln_timing ) CALL timing_stop('p4z_che') ! END SUBROUTINE p4z_che SUBROUTINE ahini_for_at(p_hini) !!--------------------------------------------------------------------- !! *** ROUTINE ahini_for_at *** !! !! Subroutine returns the root for the 2nd order approximation of the !! DIC -- B_T -- A_CB equation for [H+] (reformulated as a cubic !! polynomial) around the local minimum, if it exists. !! Returns * 1E-03_wp if p_alkcb <= 0 !! * 1E-10_wp if p_alkcb >= 2*p_dictot + p_bortot !! * 1E-07_wp if 0 < p_alkcb < 2*p_dictot + p_bortot !! and the 2nd order approximation does not have !! a solution !!--------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_hini INTEGER :: ji, jj, jk REAL(wp) :: zca1, zba1 REAL(wp) :: zd, zsqrtd, zhmin REAL(wp) :: za2, za1, za0 REAL(wp) :: p_dictot, p_bortot, p_alkcb !!--------------------------------------------------------------------- IF( ln_timing ) CALL timing_start('ahini_for_at') ! DO jk = 1, jpk DO jj = 1, jpj DO ji = 1, jpi p_alkcb = trb(ji,jj,jk,jptal) * 1000. / (rhop(ji,jj,jk) + rtrn) p_dictot = trb(ji,jj,jk,jpdic) * 1000. / (rhop(ji,jj,jk) + rtrn) p_bortot = borat(ji,jj,jk) IF (p_alkcb <= 0.) THEN p_hini(ji,jj,jk) = 1.e-3 ELSEIF (p_alkcb >= (2.*p_dictot + p_bortot)) THEN p_hini(ji,jj,jk) = 1.e-10_wp ELSE zca1 = p_dictot/( p_alkcb + rtrn ) zba1 = p_bortot/ (p_alkcb + rtrn ) ! Coefficients of the cubic polynomial za2 = aKb3(ji,jj,jk)*(1. - zba1) + ak13(ji,jj,jk)*(1.-zca1) za1 = ak13(ji,jj,jk)*akb3(ji,jj,jk)*(1. - zba1 - zca1) & & + ak13(ji,jj,jk)*ak23(ji,jj,jk)*(1. - (zca1+zca1)) za0 = ak13(ji,jj,jk)*ak23(ji,jj,jk)*akb3(ji,jj,jk)*(1. - zba1 - (zca1+zca1)) ! Taylor expansion around the minimum zd = za2*za2 - 3.*za1 ! Discriminant of the quadratic equation ! for the minimum close to the root IF(zd > 0.) THEN ! If the discriminant is positive zsqrtd = SQRT(zd) IF(za2 < 0) THEN zhmin = (-za2 + zsqrtd)/3. ELSE zhmin = -za1/(za2 + zsqrtd) ENDIF p_hini(ji,jj,jk) = zhmin + SQRT(-(za0 + zhmin*(za1 + zhmin*(za2 + zhmin)))/zsqrtd) ELSE p_hini(ji,jj,jk) = 1.e-7 ENDIF ! ENDIF END DO END DO END DO ! IF( ln_timing ) CALL timing_stop('ahini_for_at') ! END SUBROUTINE ahini_for_at !=============================================================================== SUBROUTINE anw_infsup( p_alknw_inf, p_alknw_sup ) ! Subroutine returns the lower and upper bounds of "non-water-selfionization" ! contributions to total alkalinity (the infimum and the supremum), i.e ! inf(TA - [OH-] + [H+]) and sup(TA - [OH-] + [H+]) ! Argument variables REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_alknw_inf REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_alknw_sup p_alknw_inf(:,:,:) = -trb(:,:,:,jppo4) * 1000. / (rhop(:,:,:) + rtrn) - sulfat(:,:,:) & & - fluorid(:,:,:) p_alknw_sup(:,:,:) = (2. * trb(:,:,:,jpdic) + 2. * trb(:,:,:,jppo4) + trb(:,:,:,jpsil) ) & & * 1000. / (rhop(:,:,:) + rtrn) + borat(:,:,:) END SUBROUTINE anw_infsup SUBROUTINE solve_at_general( p_hini, zhi ) ! Universal pH solver that converges from any given initial value, ! determines upper an lower bounds for the solution if required ! Argument variables !-------------------- REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(IN) :: p_hini REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: zhi ! Local variables !----------------- INTEGER :: ji, jj, jk, jn REAL(wp) :: zh_ini, zh, zh_prev, zh_lnfactor REAL(wp) :: zdelta, zh_delta REAL(wp) :: zeqn, zdeqndh, zalka REAL(wp) :: aphscale REAL(wp) :: znumer_dic, zdnumer_dic, zdenom_dic, zalk_dic, zdalk_dic REAL(wp) :: znumer_bor, zdnumer_bor, zdenom_bor, zalk_bor, zdalk_bor REAL(wp) :: znumer_po4, zdnumer_po4, zdenom_po4, zalk_po4, zdalk_po4 REAL(wp) :: znumer_sil, zdnumer_sil, zdenom_sil, zalk_sil, zdalk_sil REAL(wp) :: znumer_so4, zdnumer_so4, zdenom_so4, zalk_so4, zdalk_so4 REAL(wp) :: znumer_flu, zdnumer_flu, zdenom_flu, zalk_flu, zdalk_flu REAL(wp) :: zalk_wat, zdalk_wat REAL(wp) :: zfact, p_alktot, zdic, zbot, zpt, zst, zft, zsit LOGICAL :: l_exitnow REAL(wp), PARAMETER :: pz_exp_threshold = 1.0 REAL(wp), DIMENSION(jpi,jpj,jpk) :: zalknw_inf, zalknw_sup, rmask, zh_min, zh_max, zeqn_absmin IF( ln_timing ) CALL timing_start('solve_at_general') CALL anw_infsup( zalknw_inf, zalknw_sup ) rmask(:,:,:) = tmask(:,:,:) zhi(:,:,:) = 0. ! TOTAL H+ scale: conversion factor for Htot = aphscale * Hfree DO jk = 1, jpk DO jj = 1, jpj DO ji = 1, jpi IF (rmask(ji,jj,jk) == 1.) THEN p_alktot = trb(ji,jj,jk,jptal) * 1000. / (rhop(ji,jj,jk) + rtrn) aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk) zh_ini = p_hini(ji,jj,jk) zdelta = (p_alktot-zalknw_inf(ji,jj,jk))**2 + 4.*akw3(ji,jj,jk)/aphscale IF(p_alktot >= zalknw_inf(ji,jj,jk)) THEN zh_min(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_inf(ji,jj,jk) + SQRT(zdelta) ) ELSE zh_min(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_inf(ji,jj,jk)) + SQRT(zdelta) ) / 2. ENDIF zdelta = (p_alktot-zalknw_sup(ji,jj,jk))**2 + 4.*akw3(ji,jj,jk)/aphscale IF(p_alktot <= zalknw_sup(ji,jj,jk)) THEN zh_max(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_sup(ji,jj,jk)) + SQRT(zdelta) ) / 2. ELSE zh_max(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_sup(ji,jj,jk) + SQRT(zdelta) ) ENDIF zhi(ji,jj,jk) = MAX(MIN(zh_max(ji,jj,jk), zh_ini), zh_min(ji,jj,jk)) ENDIF END DO END DO END DO zeqn_absmin(:,:,:) = HUGE(1._wp) DO jn = 1, jp_maxniter_atgen DO jk = 1, jpk DO jj = 1, jpj DO ji = 1, jpi IF (rmask(ji,jj,jk) == 1.) THEN zfact = rhop(ji,jj,jk) / 1000. + rtrn p_alktot = trb(ji,jj,jk,jptal) / zfact zdic = trb(ji,jj,jk,jpdic) / zfact zbot = borat(ji,jj,jk) zpt = trb(ji,jj,jk,jppo4) / zfact * po4r zsit = trb(ji,jj,jk,jpsil) / zfact zst = sulfat (ji,jj,jk) zft = fluorid(ji,jj,jk) aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk) zh = zhi(ji,jj,jk) zh_prev = zh ! H2CO3 - HCO3 - CO3 : n=2, m=0 znumer_dic = 2.*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*ak13(ji,jj,jk) zdenom_dic = ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*(ak13(ji,jj,jk) + zh) zalk_dic = zdic * (znumer_dic/zdenom_dic) zdnumer_dic = ak13(ji,jj,jk)*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh & *(4.*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*ak13(ji,jj,jk)) zdalk_dic = -zdic*(zdnumer_dic/zdenom_dic**2) ! B(OH)3 - B(OH)4 : n=1, m=0 znumer_bor = akb3(ji,jj,jk) zdenom_bor = akb3(ji,jj,jk) + zh zalk_bor = zbot * (znumer_bor/zdenom_bor) zdnumer_bor = akb3(ji,jj,jk) zdalk_bor = -zbot*(zdnumer_bor/zdenom_bor**2) ! H3PO4 - H2PO4 - HPO4 - PO4 : n=3, m=1 znumer_po4 = 3.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & & + zh*(2.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh* ak1p3(ji,jj,jk)) zdenom_po4 = ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & & + zh*( ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh*(ak1p3(ji,jj,jk) + zh)) zalk_po4 = zpt * (znumer_po4/zdenom_po4 - 1.) ! Zero level of H3PO4 = 1 zdnumer_po4 = ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & & + zh*(4.*ak1p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & & + zh*(9.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & & + ak1p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) & & + zh*(4.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh * ak1p3(ji,jj,jk) ) ) ) zdalk_po4 = -zpt * (zdnumer_po4/zdenom_po4**2) ! H4SiO4 - H3SiO4 : n=1, m=0 znumer_sil = aksi3(ji,jj,jk) zdenom_sil = aksi3(ji,jj,jk) + zh zalk_sil = zsit * (znumer_sil/zdenom_sil) zdnumer_sil = aksi3(ji,jj,jk) zdalk_sil = -zsit * (zdnumer_sil/zdenom_sil**2) ! HSO4 - SO4 : n=1, m=1 aphscale = 1.0 + zst/aks3(ji,jj,jk) znumer_so4 = aks3(ji,jj,jk) * aphscale zdenom_so4 = aks3(ji,jj,jk) * aphscale + zh zalk_so4 = zst * (znumer_so4/zdenom_so4 - 1.) zdnumer_so4 = aks3(ji,jj,jk) zdalk_so4 = -zst * (zdnumer_so4/zdenom_so4**2) ! HF - F : n=1, m=1 znumer_flu = akf3(ji,jj,jk) zdenom_flu = akf3(ji,jj,jk) + zh zalk_flu = zft * (znumer_flu/zdenom_flu - 1.) zdnumer_flu = akf3(ji,jj,jk) zdalk_flu = -zft * (zdnumer_flu/zdenom_flu**2) ! H2O - OH aphscale = 1.0 + zst/aks3(ji,jj,jk) zalk_wat = akw3(ji,jj,jk)/zh - zh/aphscale zdalk_wat = -akw3(ji,jj,jk)/zh**2 - 1./aphscale ! CALCULATE [ALK]([CO3--], [HCO3-]) zeqn = zalk_dic + zalk_bor + zalk_po4 + zalk_sil & & + zalk_so4 + zalk_flu & & + zalk_wat - p_alktot zalka = p_alktot - (zalk_bor + zalk_po4 + zalk_sil & & + zalk_so4 + zalk_flu + zalk_wat) zdeqndh = zdalk_dic + zdalk_bor + zdalk_po4 + zdalk_sil & & + zdalk_so4 + zdalk_flu + zdalk_wat ! Adapt bracketing interval IF(zeqn > 0._wp) THEN zh_min(ji,jj,jk) = zh_prev ELSEIF(zeqn < 0._wp) THEN zh_max(ji,jj,jk) = zh_prev ENDIF IF(ABS(zeqn) >= 0.5_wp*zeqn_absmin(ji,jj,jk)) THEN ! if the function evaluation at the current point is ! not decreasing faster than with a bisection step (at least linearly) ! in absolute value take one bisection step on [ph_min, ph_max] ! ph_new = (ph_min + ph_max)/2d0 ! ! In terms of [H]_new: ! [H]_new = 10**(-ph_new) ! = 10**(-(ph_min + ph_max)/2d0) ! = SQRT(10**(-(ph_min + phmax))) ! = SQRT(zh_max * zh_min) zh = SQRT(zh_max(ji,jj,jk) * zh_min(ji,jj,jk)) zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below ELSE ! dzeqn/dpH = dzeqn/d[H] * d[H]/dpH ! = -zdeqndh * LOG(10) * [H] ! \Delta pH = -zeqn/(zdeqndh*d[H]/dpH) = zeqn/(zdeqndh*[H]*LOG(10)) ! ! pH_new = pH_old + \deltapH ! ! [H]_new = 10**(-pH_new) ! = 10**(-pH_old - \Delta pH) ! = [H]_old * 10**(-zeqn/(zdeqndh*[H]_old*LOG(10))) ! = [H]_old * EXP(-LOG(10)*zeqn/(zdeqndh*[H]_old*LOG(10))) ! = [H]_old * EXP(-zeqn/(zdeqndh*[H]_old)) zh_lnfactor = -zeqn/(zdeqndh*zh_prev) IF(ABS(zh_lnfactor) > pz_exp_threshold) THEN zh = zh_prev*EXP(zh_lnfactor) ELSE zh_delta = zh_lnfactor*zh_prev zh = zh_prev + zh_delta ENDIF IF( zh < zh_min(ji,jj,jk) ) THEN ! if [H]_new < [H]_min ! i.e., if ph_new > ph_max then ! take one bisection step on [ph_prev, ph_max] ! ph_new = (ph_prev + ph_max)/2d0 ! In terms of [H]_new: ! [H]_new = 10**(-ph_new) ! = 10**(-(ph_prev + ph_max)/2d0) ! = SQRT(10**(-(ph_prev + phmax))) ! = SQRT([H]_old*10**(-ph_max)) ! = SQRT([H]_old * zh_min) zh = SQRT(zh_prev * zh_min(ji,jj,jk)) zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below ENDIF IF( zh > zh_max(ji,jj,jk) ) THEN ! if [H]_new > [H]_max ! i.e., if ph_new < ph_min, then ! take one bisection step on [ph_min, ph_prev] ! ph_new = (ph_prev + ph_min)/2d0 ! In terms of [H]_new: ! [H]_new = 10**(-ph_new) ! = 10**(-(ph_prev + ph_min)/2d0) ! = SQRT(10**(-(ph_prev + ph_min))) ! = SQRT([H]_old*10**(-ph_min)) ! = SQRT([H]_old * zhmax) zh = SQRT(zh_prev * zh_max(ji,jj,jk)) zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below ENDIF ENDIF zeqn_absmin(ji,jj,jk) = MIN( ABS(zeqn), zeqn_absmin(ji,jj,jk)) ! Stop iterations once |\delta{[H]}/[H]| < rdel ! <=> |(zh - zh_prev)/zh_prev| = |EXP(-zeqn/(zdeqndh*zh_prev)) -1| < rdel ! |EXP(-zeqn/(zdeqndh*zh_prev)) -1| ~ |zeqn/(zdeqndh*zh_prev)| ! Alternatively: ! |\Delta pH| = |zeqn/(zdeqndh*zh_prev*LOG(10))| ! ~ 1/LOG(10) * |\Delta [H]|/[H] ! < 1/LOG(10) * rdel ! Hence |zeqn/(zdeqndh*zh)| < rdel ! rdel <-- pp_rdel_ah_target l_exitnow = (ABS(zh_lnfactor) < pp_rdel_ah_target) IF(l_exitnow) THEN rmask(ji,jj,jk) = 0. ENDIF zhi(ji,jj,jk) = zh IF(jn >= jp_maxniter_atgen) THEN zhi(ji,jj,jk) = -1._wp ENDIF ENDIF END DO END DO END DO END DO ! IF( ln_timing ) CALL timing_stop('solve_at_general') ! END SUBROUTINE solve_at_general INTEGER FUNCTION p4z_che_alloc() !!---------------------------------------------------------------------- !! *** ROUTINE p4z_che_alloc *** !!---------------------------------------------------------------------- INTEGER :: ierr(3) ! Local variables !!---------------------------------------------------------------------- ierr(:) = 0 ALLOCATE( sio3eq(jpi,jpj,jpk), fekeq(jpi,jpj,jpk), chemc(jpi,jpj,3), chemo2(jpi,jpj,jpk), STAT=ierr(1) ) ALLOCATE( akb3(jpi,jpj,jpk) , tempis(jpi, jpj, jpk), & & akw3(jpi,jpj,jpk) , borat (jpi,jpj,jpk) , & & aks3(jpi,jpj,jpk) , akf3(jpi,jpj,jpk) , & & ak1p3(jpi,jpj,jpk) , ak2p3(jpi,jpj,jpk) , & & ak3p3(jpi,jpj,jpk) , aksi3(jpi,jpj,jpk) , & & fluorid(jpi,jpj,jpk) , sulfat(jpi,jpj,jpk) , & & salinprac(jpi,jpj,jpk), STAT=ierr(2) ) ALLOCATE( fesol(jpi,jpj,jpk,5), STAT=ierr(3) ) !* Variable for chemistry of the CO2 cycle p4z_che_alloc = MAXVAL( ierr ) ! IF( p4z_che_alloc /= 0 ) CALL ctl_stop( 'STOP', 'p4z_che_alloc : failed to allocate arrays.' ) ! END FUNCTION p4z_che_alloc !!====================================================================== END MODULE p4zche