[3443] | 1 | MODULE sedchem |
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| 2 | |
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| 3 | !!====================================================================== |
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| 4 | !! *** Module sedchem *** |
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| 5 | !! sediment : Variable for chemistry of the CO2 cycle |
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| 6 | !!====================================================================== |
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| 7 | !! modules used |
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| 8 | USE sed ! sediment global variable |
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| 9 | USE sedarr |
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[10222] | 10 | USE eosbn2, ONLY : neos |
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| 11 | USE lib_mpp ! distribued memory computing library |
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[3443] | 12 | |
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[10222] | 13 | IMPLICIT NONE |
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| 14 | PRIVATE |
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| 15 | |
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[3443] | 16 | !! * Accessibility |
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[10222] | 17 | PUBLIC sed_chem |
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| 18 | PUBLIC ahini_for_at_sed ! |
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| 19 | PUBLIC solve_at_general_sed ! |
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[3443] | 20 | |
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[10222] | 21 | ! Maximum number of iterations for each method |
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| 22 | INTEGER, PARAMETER :: jp_maxniter_atgen = 20 |
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| 23 | REAL(wp), PARAMETER :: pp_rdel_ah_target = 1.E-4_wp |
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| 24 | |
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[3443] | 25 | !! * Module variables |
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| 26 | REAL(wp) :: & |
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| 27 | calcon = 1.03E-2 ! mean calcite concentration [Ca2+] in sea water [mole/kg solution] |
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| 28 | |
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[10222] | 29 | REAL(wp) :: rgas = 83.14472 ! universal gas constants |
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[3443] | 30 | |
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| 31 | ! coeff. for density of sea water (Millero & Poisson 1981) |
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| 32 | REAL(wp), DIMENSION(5) :: Adsw |
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| 33 | DATA Adsw/8.24493E-1, -4.0899E-3, 7.6438E-5 , -8.246E-7, 5.3875E-9 / |
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| 34 | |
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| 35 | REAL(wp), DIMENSION(3) :: Bdsw |
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| 36 | DATA Bdsw / -5.72466E-3, 1.0227E-4, -1.6546E-6 / |
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| 37 | |
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| 38 | REAL(wp) :: Cdsw = 4.8314E-4 |
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| 39 | |
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| 40 | REAL(wp), DIMENSION(6) :: Ddsw |
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| 41 | DATA Ddsw / 999.842594 , 6.793952E-2 , -9.095290E-3, 1.001685E-4, -1.120083E-6, 6.536332E-9/ |
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| 42 | |
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[10222] | 43 | REAL(wp) :: devk10 = -25.5 |
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| 44 | REAL(wp) :: devk11 = -15.82 |
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| 45 | REAL(wp) :: devk12 = -29.48 |
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| 46 | REAL(wp) :: devk13 = -20.02 |
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| 47 | REAL(wp) :: devk14 = -18.03 |
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| 48 | REAL(wp) :: devk15 = -9.78 |
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| 49 | REAL(wp) :: devk16 = -48.76 |
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| 50 | REAL(wp) :: devk17 = -14.51 |
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| 51 | REAL(wp) :: devk18 = -23.12 |
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| 52 | REAL(wp) :: devk19 = -26.57 |
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| 53 | REAL(wp) :: devk110 = -29.48 |
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[15075] | 54 | REAL(wp) :: devk120 = -14.8 |
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| 55 | REAL(wp) :: devk130 = -26.43 |
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[10222] | 56 | ! |
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| 57 | REAL(wp) :: devk20 = 0.1271 |
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| 58 | REAL(wp) :: devk21 = -0.0219 |
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| 59 | REAL(wp) :: devk22 = 0.1622 |
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| 60 | REAL(wp) :: devk23 = 0.1119 |
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| 61 | REAL(wp) :: devk24 = 0.0466 |
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| 62 | REAL(wp) :: devk25 = -0.0090 |
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| 63 | REAL(wp) :: devk26 = 0.5304 |
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| 64 | REAL(wp) :: devk27 = 0.1211 |
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| 65 | REAL(wp) :: devk28 = 0.1758 |
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| 66 | REAL(wp) :: devk29 = 0.2020 |
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| 67 | REAL(wp) :: devk210 = 0.1622 |
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[15075] | 68 | REAL(wp) :: devk220 = 0.0020 |
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| 69 | REAL(wp) :: devk230 = 0.0889 |
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[10222] | 70 | ! |
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| 71 | REAL(wp) :: devk30 = 0. |
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| 72 | REAL(wp) :: devk31 = 0. |
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| 73 | REAL(wp) :: devk32 = 2.608E-3 |
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| 74 | REAL(wp) :: devk33 = -1.409e-3 |
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| 75 | REAL(wp) :: devk34 = 0.316e-3 |
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| 76 | REAL(wp) :: devk35 = -0.942e-3 |
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| 77 | REAL(wp) :: devk36 = 0. |
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| 78 | REAL(wp) :: devk37 = -0.321e-3 |
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| 79 | REAL(wp) :: devk38 = -2.647e-3 |
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| 80 | REAL(wp) :: devk39 = -3.042e-3 |
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| 81 | REAL(wp) :: devk310 = -2.6080e-3 |
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[15075] | 82 | REAL(wp) :: devk320 = -0.4E-3 |
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| 83 | REAL(wp) :: devk330 = -0.905E-3 |
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[10222] | 84 | ! |
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| 85 | REAL(wp) :: devk40 = -3.08E-3 |
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| 86 | REAL(wp) :: devk41 = 1.13E-3 |
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| 87 | REAL(wp) :: devk42 = -2.84E-3 |
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| 88 | REAL(wp) :: devk43 = -5.13E-3 |
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| 89 | REAL(wp) :: devk44 = -4.53e-3 |
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| 90 | REAL(wp) :: devk45 = -3.91e-3 |
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| 91 | REAL(wp) :: devk46 = -11.76e-3 |
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| 92 | REAL(wp) :: devk47 = -2.67e-3 |
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| 93 | REAL(wp) :: devk48 = -5.15e-3 |
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| 94 | REAL(wp) :: devk49 = -4.08e-3 |
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| 95 | REAL(wp) :: devk410 = -2.84e-3 |
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[15075] | 96 | REAL(wp) :: devk420 = 2.89E-3 |
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| 97 | REAL(wp) :: devk430 = -5.03E-3 |
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[10222] | 98 | ! |
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| 99 | REAL(wp) :: devk50 = 0.0877E-3 |
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| 100 | REAL(wp) :: devk51 = -0.1475E-3 |
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| 101 | REAL(wp) :: devk52 = 0. |
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| 102 | REAL(wp) :: devk53 = 0.0794E-3 |
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| 103 | REAL(wp) :: devk54 = 0.09e-3 |
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| 104 | REAL(wp) :: devk55 = 0.054e-3 |
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| 105 | REAL(wp) :: devk56 = 0.3692E-3 |
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| 106 | REAL(wp) :: devk57 = 0.0427e-3 |
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| 107 | REAL(wp) :: devk58 = 0.09e-3 |
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| 108 | REAL(wp) :: devk59 = 0.0714e-3 |
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| 109 | REAL(wp) :: devk510 = 0.0 |
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[15075] | 110 | REAL(wp) :: devk520 = 0.054E-3 |
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| 111 | REAL(wp) :: devk530 = 0.0814E-3 |
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[10222] | 112 | |
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[15075] | 113 | !! * Substitutions |
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| 114 | # include "do_loop_substitute.h90" |
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| 115 | |
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[5215] | 116 | !! $Id$ |
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[3443] | 117 | CONTAINS |
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| 118 | |
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| 119 | SUBROUTINE sed_chem( kt ) |
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| 120 | !!---------------------------------------------------------------------- |
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| 121 | !! *** ROUTINE sed_chem *** |
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| 122 | !! |
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| 123 | !! ** Purpose : set chemical constants |
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| 124 | !! |
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| 125 | !! History : |
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| 126 | !! ! 04-10 (N. Emprin, M. Gehlen ) Original code |
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| 127 | !! ! 06-04 (C. Ethe) Re-organization |
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| 128 | !!---------------------------------------------------------------------- |
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| 129 | !!* Arguments |
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| 130 | INTEGER, INTENT(in) :: kt ! time step |
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| 131 | |
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| 132 | INTEGER :: ji, jj, ikt |
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[10222] | 133 | REAL(wp) :: ztc, ztc2 |
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| 134 | REAL(wp) :: zsal, zsal15 |
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[3443] | 135 | REAL(wp) :: zdens0, zaw, zbw, zcw |
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[10222] | 136 | REAL(wp), DIMENSION(jpi,jpj,15) :: zchem_data |
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[3443] | 137 | !!---------------------------------------------------------------------- |
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| 138 | |
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| 139 | |
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[10222] | 140 | IF( ln_timing ) CALL timing_start('sed_chem') |
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[3443] | 141 | |
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[10222] | 142 | IF (lwp) WRITE(numsed,*) ' Getting Chemical constants from tracer model at time kt = ', kt |
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| 143 | IF (lwp) WRITE(numsed,*) ' ' |
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[3443] | 144 | |
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| 145 | ! reading variables |
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[10222] | 146 | zchem_data(:,:,:) = rtrn |
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[3443] | 147 | |
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[10222] | 148 | IF (ln_sediment_offline) THEN |
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| 149 | CALL sed_chem_cst |
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| 150 | ELSE |
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[13295] | 151 | DO_2D( 1, 1, 1, 1 ) |
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[12377] | 152 | ikt = mbkt(ji,jj) |
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| 153 | IF ( tmask(ji,jj,ikt) == 1 ) THEN |
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| 154 | zchem_data(ji,jj,1) = ak13 (ji,jj,ikt) |
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| 155 | zchem_data(ji,jj,2) = ak23 (ji,jj,ikt) |
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| 156 | zchem_data(ji,jj,3) = akb3 (ji,jj,ikt) |
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| 157 | zchem_data(ji,jj,4) = akw3 (ji,jj,ikt) |
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| 158 | zchem_data(ji,jj,5) = aksp (ji,jj,ikt) |
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| 159 | zchem_data(ji,jj,6) = borat (ji,jj,ikt) |
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| 160 | zchem_data(ji,jj,7) = ak1p3 (ji,jj,ikt) |
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| 161 | zchem_data(ji,jj,8) = ak2p3 (ji,jj,ikt) |
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| 162 | zchem_data(ji,jj,9) = ak3p3 (ji,jj,ikt) |
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| 163 | zchem_data(ji,jj,10)= aksi3 (ji,jj,ikt) |
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| 164 | zchem_data(ji,jj,11)= sio3eq(ji,jj,ikt) |
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| 165 | zchem_data(ji,jj,12)= aks3 (ji,jj,ikt) |
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| 166 | zchem_data(ji,jj,13)= akf3 (ji,jj,ikt) |
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| 167 | zchem_data(ji,jj,14)= sulfat(ji,jj,ikt) |
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| 168 | zchem_data(ji,jj,15)= fluorid(ji,jj,ikt) |
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| 169 | ENDIF |
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| 170 | END_2D |
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[3443] | 171 | |
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[10222] | 172 | CALL pack_arr ( jpoce, ak1s (1:jpoce), zchem_data(1:jpi,1:jpj,1) , iarroce(1:jpoce) ) |
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| 173 | CALL pack_arr ( jpoce, ak2s (1:jpoce), zchem_data(1:jpi,1:jpj,2) , iarroce(1:jpoce) ) |
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| 174 | CALL pack_arr ( jpoce, akbs (1:jpoce), zchem_data(1:jpi,1:jpj,3) , iarroce(1:jpoce) ) |
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| 175 | CALL pack_arr ( jpoce, akws (1:jpoce), zchem_data(1:jpi,1:jpj,4) , iarroce(1:jpoce) ) |
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| 176 | CALL pack_arr ( jpoce, aksps (1:jpoce), zchem_data(1:jpi,1:jpj,5) , iarroce(1:jpoce) ) |
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| 177 | CALL pack_arr ( jpoce, borats(1:jpoce), zchem_data(1:jpi,1:jpj,6) , iarroce(1:jpoce) ) |
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| 178 | CALL pack_arr ( jpoce, ak1ps (1:jpoce), zchem_data(1:jpi,1:jpj,7) , iarroce(1:jpoce) ) |
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| 179 | CALL pack_arr ( jpoce, ak2ps (1:jpoce), zchem_data(1:jpi,1:jpj,8) , iarroce(1:jpoce) ) |
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| 180 | CALL pack_arr ( jpoce, ak3ps (1:jpoce), zchem_data(1:jpi,1:jpj,9) , iarroce(1:jpoce) ) |
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| 181 | CALL pack_arr ( jpoce, aksis (1:jpoce), zchem_data(1:jpi,1:jpj,10), iarroce(1:jpoce) ) |
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| 182 | CALL pack_arr ( jpoce, sieqs (1:jpoce), zchem_data(1:jpi,1:jpj,11), iarroce(1:jpoce) ) |
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| 183 | CALL pack_arr ( jpoce, aks3s (1:jpoce), zchem_data(1:jpi,1:jpj,12), iarroce(1:jpoce) ) |
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| 184 | CALL pack_arr ( jpoce, akf3s (1:jpoce), zchem_data(1:jpi,1:jpj,13), iarroce(1:jpoce) ) |
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| 185 | CALL pack_arr ( jpoce, sulfats(1:jpoce), zchem_data(1:jpi,1:jpj,14), iarroce(1:jpoce) ) |
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| 186 | CALL pack_arr ( jpoce, fluorids(1:jpoce), zchem_data(1:jpi,1:jpj,15), iarroce(1:jpoce) ) |
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| 187 | ENDIF |
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[3443] | 188 | |
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| 189 | DO ji = 1, jpoce |
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| 190 | ztc = temp(ji) |
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| 191 | ztc2 = ztc * ztc |
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| 192 | zsal = salt(ji) |
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[10222] | 193 | zsal15 = SQRT( zsal ) * zsal |
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[3443] | 194 | |
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| 195 | ! Density of Sea Water - F(temp,sal) [kg/m3] |
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| 196 | zdens0 = Ddsw(1) + Ddsw(2) * ztc + Ddsw(3) * ztc2 & |
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| 197 | + Ddsw(4) * ztc * ztc2 + Ddsw(5) * ztc2 * ztc2 & |
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| 198 | + Ddsw(6) * ztc * ztc2 * ztc2 |
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| 199 | zaw = Adsw(1) + Adsw(2) * ztc + Adsw(3)* ztc2 + Adsw(4) * ztc * ztc2 & |
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| 200 | + Adsw(5) * ztc2 * ztc2 |
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| 201 | zbw = Bdsw(1) + Bdsw(2) * ztc + Bdsw(3) * ztc2 |
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| 202 | zcw = Cdsw |
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| 203 | densSW(ji) = zdens0 + zaw * zsal + zbw * zsal15 + zcw * zsal * zsal |
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| 204 | densSW(ji) = densSW(ji) * 1E-3 ! to get dens in [kg/l] |
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| 205 | |
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[10222] | 206 | ak12s (ji) = ak1s (ji) * ak2s (ji) |
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| 207 | ak12ps (ji) = ak1ps(ji) * ak2ps(ji) |
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| 208 | ak123ps(ji) = ak1ps(ji) * ak2ps(ji) * ak3ps(ji) |
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[3443] | 209 | |
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[10222] | 210 | calcon2(ji) = 0.01028 * ( salt(ji) / 35. ) * densSW(ji) |
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| 211 | ENDDO |
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| 212 | |
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| 213 | IF( ln_timing ) CALL timing_stop('sed_chem') |
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[3443] | 214 | |
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[10222] | 215 | END SUBROUTINE sed_chem |
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[3443] | 216 | |
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[10222] | 217 | SUBROUTINE ahini_for_at_sed(p_hini) |
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| 218 | !!--------------------------------------------------------------------- |
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| 219 | !! *** ROUTINE ahini_for_at *** |
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| 220 | !! |
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| 221 | !! Subroutine returns the root for the 2nd order approximation of the |
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| 222 | !! DIC -- B_T -- A_CB equation for [H+] (reformulated as a cubic |
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| 223 | !! polynomial) around the local minimum, if it exists. |
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| 224 | !! Returns * 1E-03_wp if p_alkcb <= 0 |
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| 225 | !! * 1E-10_wp if p_alkcb >= 2*p_dictot + p_bortot |
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| 226 | !! * 1E-07_wp if 0 < p_alkcb < 2*p_dictot + p_bortot |
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| 227 | !! and the 2nd order approximation does not have |
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| 228 | !! a solution |
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| 229 | !!--------------------------------------------------------------------- |
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| 230 | REAL(wp), DIMENSION(jpoce,jpksed), INTENT(OUT) :: p_hini |
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| 231 | INTEGER :: ji, jk |
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| 232 | REAL(wp) :: zca1, zba1 |
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| 233 | REAL(wp) :: zd, zsqrtd, zhmin |
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| 234 | REAL(wp) :: za2, za1, za0 |
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| 235 | REAL(wp) :: p_dictot, p_bortot, p_alkcb |
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[3443] | 236 | |
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[10222] | 237 | IF( ln_timing ) CALL timing_start('ahini_for_at_sed') |
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| 238 | ! |
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| 239 | DO jk = 1, jpksed |
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| 240 | DO ji = 1, jpoce |
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| 241 | p_alkcb = pwcp(ji,jk,jwalk) / densSW(ji) |
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| 242 | p_dictot = pwcp(ji,jk,jwdic) / densSW(ji) |
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[15075] | 243 | p_bortot = borats(ji) |
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[10222] | 244 | IF (p_alkcb <= 0.) THEN |
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| 245 | p_hini(ji,jk) = 1.e-3 |
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| 246 | ELSEIF (p_alkcb >= (2.*p_dictot + p_bortot)) THEN |
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| 247 | p_hini(ji,jk) = 1.e-10_wp |
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| 248 | ELSE |
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| 249 | zca1 = p_dictot/( p_alkcb + rtrn ) |
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| 250 | zba1 = p_bortot/ (p_alkcb + rtrn ) |
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| 251 | ! Coefficients of the cubic polynomial |
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| 252 | za2 = aKbs(ji)*(1. - zba1) + ak1s(ji)*(1.-zca1) |
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| 253 | za1 = ak1s(ji)*akbs(ji)*(1. - zba1 - zca1) & |
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| 254 | & + ak1s(ji)*ak2s(ji)*(1. - (zca1+zca1)) |
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| 255 | za0 = ak1s(ji)*ak2s(ji)*akbs(ji)*(1. - zba1 - (zca1+zca1)) |
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| 256 | ! Taylor expansion around the minimum |
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| 257 | zd = za2*za2 - 3.*za1 ! Discriminant of the quadratic equation |
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| 258 | ! for the minimum close to the root |
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[3443] | 259 | |
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[10222] | 260 | IF(zd > 0.) THEN ! If the discriminant is positive |
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| 261 | zsqrtd = SQRT(zd) |
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| 262 | IF(za2 < 0) THEN |
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| 263 | zhmin = (-za2 + zsqrtd)/3. |
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| 264 | ELSE |
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| 265 | zhmin = -za1/(za2 + zsqrtd) |
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| 266 | ENDIF |
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| 267 | p_hini(ji,jk) = zhmin + SQRT(-(za0 + zhmin*(za1 + zhmin*(za2 + zhmin)))/zsqrtd) |
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| 268 | ELSE |
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| 269 | p_hini(ji,jk) = 1.e-7 |
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| 270 | ENDIF |
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| 271 | ! |
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| 272 | ENDIF |
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| 273 | END DO |
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| 274 | END DO |
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| 275 | ! |
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| 276 | IF( ln_timing ) CALL timing_stop('ahini_for_at_sed') |
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| 277 | ! |
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| 278 | END SUBROUTINE ahini_for_at_sed |
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[3443] | 279 | |
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[10222] | 280 | !=============================================================================== |
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| 281 | SUBROUTINE anw_infsup_sed( p_alknw_inf, p_alknw_sup ) |
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[3443] | 282 | |
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[10222] | 283 | ! Subroutine returns the lower and upper bounds of "non-water-selfionization" |
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| 284 | ! contributions to total alkalinity (the infimum and the supremum), i.e |
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| 285 | ! inf(TA - [OH-] + [H+]) and sup(TA - [OH-] + [H+]) |
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[3443] | 286 | |
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[10222] | 287 | ! Argument variables |
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| 288 | INTEGER :: jk |
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| 289 | REAL(wp), DIMENSION(jpoce,jpksed), INTENT(OUT) :: p_alknw_inf |
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| 290 | REAL(wp), DIMENSION(jpoce,jpksed), INTENT(OUT) :: p_alknw_sup |
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[3443] | 291 | |
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[10222] | 292 | DO jk = 1, jpksed |
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| 293 | p_alknw_inf(:,jk) = -pwcp(:,jk,jwpo4) / densSW(:) |
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[15075] | 294 | p_alknw_sup(:,jk) = (2. * pwcp(:,jk,jwdic) + 2. * pwcp(:,jk,jwpo4) + pwcp(:,jk,jwsil) ) & |
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| 295 | & / densSW(:) + borats(:) |
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[10222] | 296 | END DO |
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[3443] | 297 | |
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[10222] | 298 | END SUBROUTINE anw_infsup_sed |
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[3443] | 299 | |
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| 300 | |
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[10222] | 301 | SUBROUTINE solve_at_general_sed( p_hini, zhi ) |
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[3443] | 302 | |
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[10222] | 303 | ! Universal pH solver that converges from any given initial value, |
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| 304 | ! determines upper an lower bounds for the solution if required |
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[3443] | 305 | |
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[10222] | 306 | ! Argument variables |
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| 307 | !-------------------- |
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| 308 | REAL(wp), DIMENSION(jpoce,jpksed), INTENT(IN) :: p_hini |
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| 309 | REAL(wp), DIMENSION(jpoce,jpksed), INTENT(OUT) :: zhi |
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[3443] | 310 | |
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[10222] | 311 | ! Local variables |
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| 312 | !----------------- |
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| 313 | INTEGER :: ji, jk, jn |
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| 314 | REAL(wp) :: zh_ini, zh, zh_prev, zh_lnfactor |
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| 315 | REAL(wp) :: zdelta, zh_delta |
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| 316 | REAL(wp) :: zeqn, zdeqndh, zalka |
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| 317 | REAL(wp) :: aphscale |
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| 318 | REAL(wp) :: znumer_dic, zdnumer_dic, zdenom_dic, zalk_dic, zdalk_dic |
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| 319 | REAL(wp) :: znumer_bor, zdnumer_bor, zdenom_bor, zalk_bor, zdalk_bor |
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| 320 | REAL(wp) :: znumer_po4, zdnumer_po4, zdenom_po4, zalk_po4, zdalk_po4 |
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| 321 | REAL(wp) :: znumer_sil, zdnumer_sil, zdenom_sil, zalk_sil, zdalk_sil |
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| 322 | REAL(wp) :: znumer_so4, zdnumer_so4, zdenom_so4, zalk_so4, zdalk_so4 |
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| 323 | REAL(wp) :: znumer_flu, zdnumer_flu, zdenom_flu, zalk_flu, zdalk_flu |
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[15075] | 324 | REAL(wp) :: znumer_h2s, zdnumer_h2s, zdenom_h2s, zalk_h2s, zdalk_h2s |
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| 325 | REAL(wp) :: znumer_nh3, zdnumer_nh3, zdenom_nh3, zalk_nh3, zdalk_nh3 |
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[10222] | 326 | REAL(wp) :: zalk_wat, zdalk_wat |
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[15075] | 327 | REAL(wp) :: zfact, p_alktot, zdic, zbot, zpt, zst, zft, zsit, zh2s, znh3 |
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[10222] | 328 | LOGICAL :: l_exitnow |
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| 329 | REAL(wp), PARAMETER :: pz_exp_threshold = 1.0 |
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| 330 | REAL(wp), DIMENSION(jpoce,jpksed) :: zalknw_inf, zalknw_sup, rmask, zh_min, zh_max, zeqn_absmin |
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[3443] | 331 | |
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[10222] | 332 | IF( ln_timing ) CALL timing_start('solve_at_general_sed') |
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| 333 | ! Allocate temporary workspace |
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| 334 | CALL anw_infsup_sed( zalknw_inf, zalknw_sup ) |
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[3443] | 335 | |
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[10222] | 336 | rmask(:,:) = 1.0 |
---|
| 337 | zhi(:,:) = 0. |
---|
| 338 | |
---|
| 339 | ! TOTAL H+ scale: conversion factor for Htot = aphscale * Hfree |
---|
| 340 | DO jk = 1, jpksed |
---|
[3443] | 341 | DO ji = 1, jpoce |
---|
[10222] | 342 | IF (rmask(ji,jk) == 1.) THEN |
---|
| 343 | p_alktot = pwcp(ji,jk,jwalk) / densSW(ji) |
---|
| 344 | aphscale = 1. + sulfats(ji)/aks3s(ji) |
---|
| 345 | zh_ini = p_hini(ji,jk) |
---|
[3443] | 346 | |
---|
[10222] | 347 | zdelta = (p_alktot-zalknw_inf(ji,jk))**2 + 4.*akws(ji) / aphscale |
---|
[3443] | 348 | |
---|
[10222] | 349 | IF(p_alktot >= zalknw_inf(ji,jk)) THEN |
---|
| 350 | zh_min(ji,jk) = 2.*akws(ji) /( p_alktot-zalknw_inf(ji,jk) + SQRT(zdelta) ) |
---|
| 351 | ELSE |
---|
| 352 | zh_min(ji,jk) = aphscale * (-(p_alktot-zalknw_inf(ji,jk)) + SQRT(zdelta) ) / 2. |
---|
| 353 | ENDIF |
---|
[3443] | 354 | |
---|
[10222] | 355 | zdelta = (p_alktot-zalknw_sup(ji,jk))**2 + 4.*akws(ji) / aphscale |
---|
[3443] | 356 | |
---|
[10222] | 357 | IF(p_alktot <= zalknw_sup(ji,jk)) THEN |
---|
| 358 | zh_max(ji,jk) = aphscale * (-(p_alktot-zalknw_sup(ji,jk)) + SQRT(zdelta) ) / 2. |
---|
| 359 | ELSE |
---|
| 360 | zh_max(ji,jk) = 2.*akws(ji) /( p_alktot-zalknw_sup(ji,jk) + SQRT(zdelta) ) |
---|
| 361 | ENDIF |
---|
[3443] | 362 | |
---|
[10222] | 363 | zhi(ji,jk) = MAX(MIN(zh_max(ji,jk), zh_ini), zh_min(ji,jk)) |
---|
| 364 | ENDIF |
---|
| 365 | END DO |
---|
| 366 | END DO |
---|
[3443] | 367 | |
---|
[10222] | 368 | zeqn_absmin(:,:) = HUGE(1._wp) |
---|
[3443] | 369 | |
---|
[10222] | 370 | DO jn = 1, jp_maxniter_atgen |
---|
| 371 | DO jk = 1, jpksed |
---|
| 372 | DO ji = 1, jpoce |
---|
| 373 | IF (rmask(ji,jk) == 1.) THEN |
---|
[3443] | 374 | |
---|
[10222] | 375 | p_alktot = pwcp(ji,jk,jwalk) / densSW(ji) |
---|
[15075] | 376 | zdic = pwcp(ji,jk,jwdic) / densSW(ji) |
---|
| 377 | zbot = borats(ji) |
---|
| 378 | zpt = pwcp(ji,jk,jwpo4) / densSW(ji) |
---|
[10222] | 379 | zsit = pwcp(ji,jk,jwsil) / densSW(ji) |
---|
[15075] | 380 | zst = pwcp(ji,jk,jwso4) / densSW(ji) |
---|
| 381 | zft = fluorids(ji) |
---|
| 382 | zh2s = pwcp(ji,jk,jwh2s) / densSW(ji) |
---|
| 383 | znh3 = pwcp(ji,jk,jwnh4) / densSW(ji) |
---|
[10222] | 384 | aphscale = 1. + sulfats(ji)/aks3s(ji) |
---|
| 385 | zh = zhi(ji,jk) |
---|
| 386 | zh_prev = zh |
---|
[3443] | 387 | |
---|
[10222] | 388 | ! H2CO3 - HCO3 - CO3 : n=2, m=0 |
---|
| 389 | znumer_dic = 2.*ak1s(ji)*ak2s(ji) + zh*ak1s(ji) |
---|
| 390 | zdenom_dic = ak1s(ji)*ak2s(ji) + zh*(ak1s(ji) + zh) |
---|
| 391 | zalk_dic = zdic * (znumer_dic/zdenom_dic) |
---|
| 392 | zdnumer_dic = ak1s(ji)*ak1s(ji)*ak2s(ji) + zh & |
---|
| 393 | *(4.*ak1s(ji)*ak2s(ji) + zh*ak1s(ji)) |
---|
| 394 | zdalk_dic = -zdic*(zdnumer_dic/zdenom_dic**2) |
---|
[3443] | 395 | |
---|
| 396 | |
---|
[10222] | 397 | ! B(OH)3 - B(OH)4 : n=1, m=0 |
---|
[15075] | 398 | znumer_bor = akbs(ji) |
---|
| 399 | zdenom_bor = akbs(ji) + zh |
---|
| 400 | zalk_bor = zbot * (znumer_bor/zdenom_bor) |
---|
[10222] | 401 | zdnumer_bor = akbs(ji) |
---|
| 402 | zdalk_bor = -zbot*(zdnumer_bor/zdenom_bor**2) |
---|
[3443] | 403 | |
---|
| 404 | |
---|
[10222] | 405 | ! H3PO4 - H2PO4 - HPO4 - PO4 : n=3, m=1 |
---|
| 406 | znumer_po4 = 3.*ak1ps(ji)*ak2ps(ji)*ak3ps(ji) & |
---|
| 407 | & + zh*(2.*ak1ps(ji)*ak2ps(ji) + zh* ak1ps(ji)) |
---|
| 408 | zdenom_po4 = ak1ps(ji)*ak2ps(ji)*ak3ps(ji) & |
---|
| 409 | & + zh*( ak1ps(ji)*ak2ps(ji) + zh*(ak1ps(ji) + zh)) |
---|
| 410 | zalk_po4 = zpt * (znumer_po4/zdenom_po4 - 1.) ! Zero level of H3PO4 = 1 |
---|
| 411 | zdnumer_po4 = ak1ps(ji)*ak2ps(ji)*ak1ps(ji)*ak2ps(ji)*ak3ps(ji) & |
---|
| 412 | & + zh*(4.*ak1ps(ji)*ak1ps(ji)*ak2ps(ji)*ak3ps(ji) & |
---|
| 413 | & + zh*(9.*ak1ps(ji)*ak2ps(ji)*ak3ps(ji) & |
---|
| 414 | & + ak1ps(ji)*ak1ps(ji)*ak2ps(ji) & |
---|
| 415 | & + zh*(4.*ak1ps(ji)*ak2ps(ji) + zh * ak1ps(ji) ) ) ) |
---|
| 416 | zdalk_po4 = -zpt * (zdnumer_po4/zdenom_po4**2) |
---|
[3443] | 417 | |
---|
[10222] | 418 | ! H4SiO4 - H3SiO4 : n=1, m=0 |
---|
| 419 | znumer_sil = aksis(ji) |
---|
| 420 | zdenom_sil = aksis(ji) + zh |
---|
| 421 | zalk_sil = zsit * (znumer_sil/zdenom_sil) |
---|
| 422 | zdnumer_sil = aksis(ji) |
---|
| 423 | zdalk_sil = -zsit * (zdnumer_sil/zdenom_sil**2) |
---|
[3443] | 424 | |
---|
[15075] | 425 | ! H2S - HS : n=1i, m=1 |
---|
| 426 | znumer_h2s = akh2s(ji) |
---|
| 427 | zdenom_h2s = akh2s(ji) + zh |
---|
| 428 | zalk_h2s = zh2s * (znumer_h2s/zdenom_h2s) |
---|
| 429 | zdnumer_h2s = akh2s(ji) |
---|
| 430 | zdalk_h2s = -zh2s * (zdnumer_h2s/zdenom_h2s**2) |
---|
| 431 | |
---|
| 432 | ! NH4 - NH3 : n=1i, m=1 |
---|
| 433 | znumer_nh3 = aknh3(ji) |
---|
| 434 | zdenom_nh3 = aknh3(ji) + zh |
---|
| 435 | zalk_nh3 = znh3 * (znumer_nh3/zdenom_nh3) |
---|
| 436 | zdnumer_nh3 = aknh3(ji) |
---|
| 437 | zdalk_nh3 = -znh3 * (zdnumer_nh3/zdenom_nh3**2) |
---|
| 438 | |
---|
[10222] | 439 | ! HSO4 - SO4 : n=1, m=1 |
---|
| 440 | aphscale = 1.0 + zst/aks3s(ji) |
---|
| 441 | znumer_so4 = aks3s(ji) * aphscale |
---|
| 442 | zdenom_so4 = aks3s(ji) * aphscale + zh |
---|
| 443 | zalk_so4 = zst * (znumer_so4/zdenom_so4 - 1.) |
---|
| 444 | zdnumer_so4 = aks3s(ji) * aphscale |
---|
| 445 | zdalk_so4 = -zst * (zdnumer_so4/zdenom_so4**2) |
---|
[3443] | 446 | |
---|
[10222] | 447 | ! HF - F : n=1, m=1 |
---|
| 448 | znumer_flu = akf3s(ji) |
---|
| 449 | zdenom_flu = akf3s(ji) + zh |
---|
| 450 | zalk_flu = zft * (znumer_flu/zdenom_flu - 1.) |
---|
| 451 | zdnumer_flu = akf3s(ji) |
---|
| 452 | zdalk_flu = -zft * (zdnumer_flu/zdenom_flu**2) |
---|
[3443] | 453 | |
---|
[10222] | 454 | ! H2O - OH |
---|
| 455 | zalk_wat = akws(ji)/zh - zh/aphscale |
---|
| 456 | zdalk_wat = -akws(ji)/zh**2 - 1./aphscale |
---|
[3443] | 457 | |
---|
[10222] | 458 | ! CALCULATE [ALK]([CO3--], [HCO3-]) |
---|
| 459 | zeqn = zalk_dic + zalk_bor + zalk_po4 + zalk_sil & |
---|
| 460 | & + zalk_so4 + zalk_flu & |
---|
[15075] | 461 | & + zalk_wat + zalk_h2s + zalk_nh3 - p_alktot |
---|
[3443] | 462 | |
---|
[10222] | 463 | zalka = p_alktot - (zalk_bor + zalk_po4 + zalk_sil & |
---|
[15075] | 464 | & + zalk_so4 + zalk_flu + zalk_wat + zalk_h2s + zalk_nh3) |
---|
[3443] | 465 | |
---|
[10222] | 466 | zdeqndh = zdalk_dic + zdalk_bor + zdalk_po4 + zdalk_sil & |
---|
[15075] | 467 | & + zdalk_so4 + zdalk_flu + zdalk_wat + zdalk_h2s + zdalk_nh3 |
---|
[3443] | 468 | |
---|
[10222] | 469 | ! Adapt bracketing interval |
---|
| 470 | IF(zeqn > 0._wp) THEN |
---|
| 471 | zh_min(ji,jk) = zh_prev |
---|
| 472 | ELSEIF(zeqn < 0._wp) THEN |
---|
| 473 | zh_max(ji,jk) = zh_prev |
---|
| 474 | ENDIF |
---|
[3443] | 475 | |
---|
[10222] | 476 | IF(ABS(zeqn) >= 0.5_wp*zeqn_absmin(ji,jk)) THEN |
---|
| 477 | ! if the function evaluation at the current point is |
---|
| 478 | ! not decreasing faster than with a bisection step (at least linearly) |
---|
| 479 | ! in absolute value take one bisection step on [ph_min, ph_max] |
---|
| 480 | ! ph_new = (ph_min + ph_max)/2d0 |
---|
| 481 | ! |
---|
| 482 | ! In terms of [H]_new: |
---|
| 483 | ! [H]_new = 10**(-ph_new) |
---|
| 484 | ! = 10**(-(ph_min + ph_max)/2d0) |
---|
| 485 | ! = SQRT(10**(-(ph_min + phmax))) |
---|
| 486 | ! = SQRT(zh_max * zh_min) |
---|
| 487 | zh = SQRT(zh_max(ji,jk) * zh_min(ji,jk)) |
---|
| 488 | zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below |
---|
| 489 | ELSE |
---|
| 490 | ! dzeqn/dpH = dzeqn/d[H] * d[H]/dpH |
---|
| 491 | ! = -zdeqndh * LOG(10) * [H] |
---|
| 492 | ! \Delta pH = -zeqn/(zdeqndh*d[H]/dpH) = zeqn/(zdeqndh*[H]*LOG(10)) |
---|
| 493 | ! |
---|
| 494 | ! pH_new = pH_old + \deltapH |
---|
| 495 | ! |
---|
| 496 | ! [H]_new = 10**(-pH_new) |
---|
| 497 | ! = 10**(-pH_old - \Delta pH) |
---|
| 498 | ! = [H]_old * 10**(-zeqn/(zdeqndh*[H]_old*LOG(10))) |
---|
| 499 | ! = [H]_old * EXP(-LOG(10)*zeqn/(zdeqndh*[H]_old*LOG(10))) |
---|
| 500 | ! = [H]_old * EXP(-zeqn/(zdeqndh*[H]_old)) |
---|
[3443] | 501 | |
---|
[10222] | 502 | zh_lnfactor = -zeqn/(zdeqndh*zh_prev) |
---|
[3443] | 503 | |
---|
[10222] | 504 | IF(ABS(zh_lnfactor) > pz_exp_threshold) THEN |
---|
| 505 | zh = zh_prev*EXP(zh_lnfactor) |
---|
| 506 | ELSE |
---|
| 507 | zh_delta = zh_lnfactor*zh_prev |
---|
| 508 | zh = zh_prev + zh_delta |
---|
| 509 | ENDIF |
---|
[3443] | 510 | |
---|
[10222] | 511 | IF( zh < zh_min(ji,jk) ) THEN |
---|
| 512 | ! if [H]_new < [H]_min |
---|
| 513 | ! i.e., if ph_new > ph_max then |
---|
| 514 | ! take one bisection step on [ph_prev, ph_max] |
---|
| 515 | ! ph_new = (ph_prev + ph_max)/2d0 |
---|
| 516 | ! In terms of [H]_new: |
---|
| 517 | ! [H]_new = 10**(-ph_new) |
---|
| 518 | ! = 10**(-(ph_prev + ph_max)/2d0) |
---|
| 519 | ! = SQRT(10**(-(ph_prev + phmax))) |
---|
| 520 | ! = SQRT([H]_old*10**(-ph_max)) |
---|
| 521 | ! = SQRT([H]_old * zh_min) |
---|
| 522 | zh = SQRT(zh_prev * zh_min(ji,jk)) |
---|
| 523 | zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below |
---|
| 524 | ENDIF |
---|
[3443] | 525 | |
---|
[10222] | 526 | IF( zh > zh_max(ji,jk) ) THEN |
---|
| 527 | ! if [H]_new > [H]_max |
---|
| 528 | ! i.e., if ph_new < ph_min, then |
---|
| 529 | ! take one bisection step on [ph_min, ph_prev] |
---|
| 530 | ! ph_new = (ph_prev + ph_min)/2d0 |
---|
| 531 | ! In terms of [H]_new: |
---|
| 532 | ! [H]_new = 10**(-ph_new) |
---|
| 533 | ! = 10**(-(ph_prev + ph_min)/2d0) |
---|
| 534 | ! = SQRT(10**(-(ph_prev + ph_min))) |
---|
| 535 | ! = SQRT([H]_old*10**(-ph_min)) |
---|
| 536 | ! = SQRT([H]_old * zhmax) |
---|
| 537 | zh = SQRT(zh_prev * zh_max(ji,jk)) |
---|
| 538 | zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below |
---|
| 539 | ENDIF |
---|
| 540 | ENDIF |
---|
[3443] | 541 | |
---|
[10222] | 542 | zeqn_absmin(ji,jk) = MIN( ABS(zeqn), zeqn_absmin(ji,jk)) |
---|
[3443] | 543 | |
---|
[10222] | 544 | ! Stop iterations once |\delta{[H]}/[H]| < rdel |
---|
| 545 | ! <=> |(zh - zh_prev)/zh_prev| = |EXP(-zeqn/(zdeqndh*zh_prev)) -1| < rdel |
---|
| 546 | ! |EXP(-zeqn/(zdeqndh*zh_prev)) -1| ~ |zeqn/(zdeqndh*zh_prev)| |
---|
| 547 | ! Alternatively: |
---|
| 548 | ! |\Delta pH| = |zeqn/(zdeqndh*zh_prev*LOG(10))| |
---|
| 549 | ! ~ 1/LOG(10) * |\Delta [H]|/[H] |
---|
| 550 | ! < 1/LOG(10) * rdel |
---|
[3443] | 551 | |
---|
[10222] | 552 | ! Hence |zeqn/(zdeqndh*zh)| < rdel |
---|
[3443] | 553 | |
---|
[10222] | 554 | ! rdel <-- pp_rdel_ah_target |
---|
| 555 | l_exitnow = (ABS(zh_lnfactor) < pp_rdel_ah_target) |
---|
[3443] | 556 | |
---|
[10222] | 557 | IF(l_exitnow) THEN |
---|
| 558 | rmask(ji,jk) = 0. |
---|
| 559 | ENDIF |
---|
[3443] | 560 | |
---|
[10222] | 561 | zhi(ji,jk) = zh |
---|
[3443] | 562 | |
---|
[10222] | 563 | IF(jn >= jp_maxniter_atgen) THEN |
---|
| 564 | zhi(ji,jk) = -1._wp |
---|
| 565 | ENDIF |
---|
[3443] | 566 | |
---|
[10222] | 567 | ENDIF |
---|
| 568 | END DO |
---|
| 569 | END DO |
---|
| 570 | END DO |
---|
| 571 | ! |
---|
| 572 | IF( ln_timing ) CALL timing_stop('solve_at_general_sed') |
---|
[3443] | 573 | |
---|
[10222] | 574 | END SUBROUTINE solve_at_general_sed |
---|
[3443] | 575 | |
---|
[10222] | 576 | SUBROUTINE sed_chem_cst |
---|
| 577 | !!--------------------------------------------------------------------- |
---|
| 578 | !! *** ROUTINE sed_chem_cst *** |
---|
| 579 | !! |
---|
| 580 | !! ** Purpose : Sea water chemistry computed following MOCSY protocol |
---|
| 581 | !! Computation is done at the bottom of the ocean only |
---|
| 582 | !! |
---|
| 583 | !! ** Method : - ... |
---|
| 584 | !!--------------------------------------------------------------------- |
---|
| 585 | INTEGER :: ji |
---|
| 586 | REAL(wp), DIMENSION(jpoce) :: saltprac, temps |
---|
| 587 | REAL(wp) :: ztkel, ztkel1, zt , zsal , zsal2 , zbuf1 , zbuf2 |
---|
| 588 | REAL(wp) :: ztgg , ztgg2, ztgg3 , ztgg4 , ztgg5 |
---|
| 589 | REAL(wp) :: zpres, ztc , zcl , zcpexp, zoxy , zcpexp2 |
---|
| 590 | REAL(wp) :: zsqrt, ztr , zlogt , zcek1, zc1, zplat |
---|
| 591 | REAL(wp) :: zis , zis2 , zsal15, zisqrt, za1, za2 |
---|
| 592 | REAL(wp) :: zckb , zck1 , zck2 , zckw , zak1 , zak2 , zakb , zaksp0, zakw |
---|
| 593 | REAL(wp) :: zck1p, zck2p, zck3p, zcksi, zak1p, zak2p, zak3p, zaksi |
---|
[15075] | 594 | REAL(wp) :: zst , zft , zcks , zckhs, zckf , zaksp1, zcknh3 |
---|
[10222] | 595 | REAL(wp) :: total2free, free2SWS, total2SWS, SWS2total |
---|
| 596 | !!--------------------------------------------------------------------- |
---|
| 597 | ! |
---|
| 598 | IF( ln_timing ) CALL timing_start('sed_chem_cst') |
---|
| 599 | ! |
---|
| 600 | ! Computation of chemical constants require practical salinity |
---|
| 601 | ! Thus, when TEOS08 is used, absolute salinity is converted to |
---|
| 602 | ! practical salinity |
---|
| 603 | ! ------------------------------------------------------------- |
---|
| 604 | IF (neos == -1) THEN |
---|
| 605 | saltprac(:) = salt(:) * 35.0 / 35.16504 |
---|
| 606 | ELSE |
---|
[12839] | 607 | saltprac(:) = salt(:) |
---|
[10222] | 608 | ENDIF |
---|
[3443] | 609 | |
---|
[10222] | 610 | ! |
---|
| 611 | ! Computations of chemical constants require in situ temperature |
---|
| 612 | ! Here a quite simple formulation is used to convert |
---|
| 613 | ! potential temperature to in situ temperature. The errors is less than |
---|
| 614 | ! 0.04°C relative to an exact computation |
---|
| 615 | ! --------------------------------------------------------------------- |
---|
| 616 | DO ji = 1, jpoce |
---|
| 617 | zpres = zkbot(ji) / 1000. |
---|
| 618 | za1 = 0.04 * ( 1.0 + 0.185 * temp(ji) + 0.035 * (saltprac(ji) - 35.0) ) |
---|
| 619 | za2 = 0.0075 * ( 1.0 - temp(ji) / 30.0 ) |
---|
| 620 | temps(ji) = temp(ji) - za1 * zpres + za2 * zpres**2 |
---|
| 621 | END DO |
---|
[3443] | 622 | |
---|
[10222] | 623 | ! CHEMICAL CONSTANTS - DEEP OCEAN |
---|
| 624 | ! ------------------------------- |
---|
| 625 | DO ji = 1, jpoce |
---|
| 626 | ! SET PRESSION ACCORDING TO SAUNDER (1980) |
---|
| 627 | zc1 = 5.92E-3 |
---|
| 628 | zpres = ((1-zc1)-SQRT(((1-zc1)**2)-(8.84E-6*zkbot(ji)))) / 4.42E-6 |
---|
| 629 | zpres = zpres / 10.0 |
---|
[3443] | 630 | |
---|
[10222] | 631 | ! SET ABSOLUTE TEMPERATURE |
---|
| 632 | ztkel = temps(ji) + 273.15 |
---|
| 633 | zsal = saltprac(ji) |
---|
| 634 | zsqrt = SQRT( zsal ) |
---|
| 635 | zsal15 = zsqrt * zsal |
---|
| 636 | zlogt = LOG( ztkel ) |
---|
| 637 | ztr = 1. / ztkel |
---|
| 638 | zis = 19.924 * zsal / ( 1000.- 1.005 * zsal ) |
---|
| 639 | zis2 = zis * zis |
---|
| 640 | zisqrt = SQRT( zis ) |
---|
| 641 | ztc = temps(ji) |
---|
[3443] | 642 | |
---|
[10222] | 643 | ! CHLORINITY (WOOSTER ET AL., 1969) |
---|
| 644 | zcl = zsal / 1.80655 |
---|
[3443] | 645 | |
---|
[10222] | 646 | ! TOTAL SULFATE CONCENTR. [MOLES/kg soln] |
---|
| 647 | zst = 0.14 * zcl /96.062 |
---|
| 648 | |
---|
| 649 | ! TOTAL FLUORIDE CONCENTR. [MOLES/kg soln] |
---|
| 650 | zft = 0.000067 * zcl /18.9984 |
---|
| 651 | |
---|
| 652 | ! DISSOCIATION CONSTANT FOR SULFATES on free H scale (Dickson 1990) |
---|
| 653 | zcks = EXP(-4276.1 * ztr + 141.328 - 23.093 * zlogt & |
---|
| 654 | & + (-13856. * ztr + 324.57 - 47.986 * zlogt) * zisqrt & |
---|
| 655 | & + (35474. * ztr - 771.54 + 114.723 * zlogt) * zis & |
---|
| 656 | & - 2698. * ztr * zis**1.5 + 1776.* ztr * zis2 & |
---|
| 657 | & + LOG(1.0 - 0.001005 * zsal)) |
---|
| 658 | |
---|
[15075] | 659 | ! DISSOCIATION CONSTANT FOR H2S on free H scale |
---|
| 660 | zckhs = EXP(-13275.3 * ztr + 225.838 - 34.6435 * zlogt & |
---|
| 661 | & + 0.3449 * zsqrt - 0.0274 * zsal ) |
---|
| 662 | |
---|
| 663 | ! DISSOCIATION CONSTANT FOR NH3 on free H scale |
---|
| 664 | zcknh3 = EXP(-6285.33 * ztr - 0.25444 + 0.0001635 * ztkel & |
---|
| 665 | & + (0.46532 - 123.7184 * ztr) * zsqrt & |
---|
| 666 | & + (-0.01992 + 3.17556 * ztr) * zsal ) |
---|
| 667 | |
---|
[10222] | 668 | ! DISSOCIATION CONSTANT FOR FLUORIDES on free H scale (Dickson and Riley 79) |
---|
| 669 | zckf = EXP( 1590.2*ztr - 12.641 + 1.525*zisqrt & |
---|
| 670 | & + LOG(1.0d0 - 0.001005d0*zsal) & |
---|
| 671 | & + LOG(1.0d0 + zst/zcks)) |
---|
| 672 | |
---|
| 673 | ! DISSOCIATION CONSTANT FOR CARBONATE AND BORATE |
---|
| 674 | zckb= (-8966.90 - 2890.53*zsqrt - 77.942*zsal & |
---|
| 675 | & + 1.728*zsal15 - 0.0996*zsal*zsal)*ztr & |
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| 676 | & + (148.0248 + 137.1942*zsqrt + 1.62142*zsal) & |
---|
| 677 | & + (-24.4344 - 25.085*zsqrt - 0.2474*zsal) & |
---|
| 678 | & * zlogt + 0.053105*zsqrt*ztkel |
---|
| 679 | |
---|
| 680 | ! DISSOCIATION COEFFICIENT FOR CARBONATE ACCORDING TO |
---|
| 681 | ! MEHRBACH (1973) REFIT BY MILLERO (1995), seawater scale |
---|
| 682 | zck1 = -1.0*(3633.86*ztr - 61.2172 + 9.6777*zlogt & |
---|
| 683 | - 0.011555*zsal + 0.0001152*zsal*zsal) |
---|
| 684 | zck2 = -1.0*(471.78*ztr + 25.9290 - 3.16967*zlogt & |
---|
| 685 | - 0.01781*zsal + 0.0001122*zsal*zsal) |
---|
| 686 | |
---|
| 687 | ! PKW (H2O) (MILLERO, 1995) from composite data |
---|
| 688 | zckw = -13847.26 * ztr + 148.9652 - 23.6521 * zlogt + ( 118.67 * ztr & |
---|
| 689 | - 5.977 + 1.0495 * zlogt ) * zsqrt - 0.01615 * zsal |
---|
| 690 | |
---|
| 691 | ! CONSTANTS FOR PHOSPHATE (MILLERO, 1995) |
---|
| 692 | zck1p = -4576.752*ztr + 115.540 - 18.453*zlogt & |
---|
| 693 | & + (-106.736*ztr + 0.69171) * zsqrt & |
---|
| 694 | & + (-0.65643*ztr - 0.01844) * zsal |
---|
| 695 | |
---|
| 696 | zck2p = -8814.715*ztr + 172.1033 - 27.927*zlogt & |
---|
| 697 | & + (-160.340*ztr + 1.3566)*zsqrt & |
---|
| 698 | & + (0.37335*ztr - 0.05778)*zsal |
---|
| 699 | |
---|
| 700 | zck3p = -3070.75*ztr - 18.126 & |
---|
| 701 | & + (17.27039*ztr + 2.81197) * zsqrt & |
---|
| 702 | & + (-44.99486*ztr - 0.09984) * zsal |
---|
| 703 | |
---|
| 704 | ! CONSTANT FOR SILICATE, MILLERO (1995) |
---|
| 705 | zcksi = -8904.2*ztr + 117.400 - 19.334*zlogt & |
---|
| 706 | & + (-458.79*ztr + 3.5913) * zisqrt & |
---|
| 707 | & + (188.74*ztr - 1.5998) * zis & |
---|
| 708 | & + (-12.1652*ztr + 0.07871) * zis2 & |
---|
| 709 | & + LOG(1.0 - 0.001005*zsal) |
---|
| 710 | |
---|
| 711 | ! APPARENT SOLUBILITY PRODUCT K'SP OF CALCITE IN SEAWATER |
---|
| 712 | ! (S=27-43, T=2-25 DEG C) at pres =0 (atmos. pressure) (MUCCI 1983) |
---|
| 713 | zaksp0 = -171.9065 -0.077993*ztkel + 2839.319*ztr + 71.595*LOG10( ztkel ) & |
---|
| 714 | & + (-0.77712 + 0.00284263*ztkel + 178.34*ztr) * zsqrt & |
---|
| 715 | & - 0.07711*zsal + 0.0041249*zsal15 |
---|
| 716 | |
---|
[10356] | 717 | ! CONVERT FROM DIFFERENT PH SCALES |
---|
| 718 | total2free = 1.0/(1.0 + zst/zcks) |
---|
| 719 | free2SWS = 1. + zst/zcks + zft/(zckf*total2free) |
---|
| 720 | total2SWS = total2free * free2SWS |
---|
| 721 | SWS2total = 1.0 / total2SWS |
---|
| 722 | |
---|
| 723 | |
---|
[10222] | 724 | ! K1, K2 OF CARBONIC ACID, KB OF BORIC ACID, KW (H2O) (LIT.?) |
---|
| 725 | zak1 = 10**(zck1) * total2SWS |
---|
| 726 | zak2 = 10**(zck2) * total2SWS |
---|
| 727 | zakb = EXP( zckb ) * total2SWS |
---|
| 728 | zakw = EXP( zckw ) |
---|
| 729 | zaksp1 = 10**(zaksp0) |
---|
| 730 | zak1p = exp( zck1p ) |
---|
| 731 | zak2p = exp( zck2p ) |
---|
| 732 | zak3p = exp( zck3p ) |
---|
| 733 | zaksi = exp( zcksi ) |
---|
| 734 | zckf = zckf * total2SWS |
---|
| 735 | |
---|
| 736 | ! FORMULA FOR CPEXP AFTER EDMOND & GIESKES (1970) |
---|
| 737 | ! (REFERENCE TO CULBERSON & PYTKOQICZ (1968) AS MADE |
---|
| 738 | ! IN BROECKER ET AL. (1982) IS INCORRECT; HERE RGAS IS |
---|
| 739 | ! TAKEN TENFOLD TO CORRECT FOR THE NOTATION OF pres IN |
---|
| 740 | ! DBAR INSTEAD OF BAR AND THE EXPRESSION FOR CPEXP IS |
---|
| 741 | ! MULTIPLIED BY LN(10.) TO ALLOW USE OF EXP-FUNCTION |
---|
| 742 | ! WITH BASIS E IN THE FORMULA FOR AKSPP (CF. EDMOND |
---|
| 743 | ! & GIESKES (1970), P. 1285-1286 (THE SMALL |
---|
| 744 | ! FORMULA ON P. 1286 IS RIGHT AND CONSISTENT WITH THE |
---|
| 745 | ! SIGN IN PARTIAL MOLAR VOLUME CHANGE AS SHOWN ON P. 1285)) |
---|
| 746 | zcpexp = zpres / (rgas*ztkel) |
---|
| 747 | zcpexp2 = zpres * zcpexp |
---|
| 748 | |
---|
| 749 | ! KB OF BORIC ACID, K1,K2 OF CARBONIC ACID PRESSURE |
---|
| 750 | ! CORRECTION AFTER CULBERSON AND PYTKOWICZ (1968) |
---|
| 751 | ! (CF. BROECKER ET AL., 1982) |
---|
| 752 | |
---|
| 753 | zbuf1 = - ( devk10 + devk20 * ztc + devk30 * ztc * ztc ) |
---|
| 754 | zbuf2 = 0.5 * ( devk40 + devk50 * ztc ) |
---|
| 755 | ak1s(ji) = zak1 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 756 | |
---|
| 757 | zbuf1 = - ( devk11 + devk21 * ztc + devk31 * ztc * ztc ) |
---|
| 758 | zbuf2 = 0.5 * ( devk41 + devk51 * ztc ) |
---|
| 759 | ak2s(ji) = zak2 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 760 | |
---|
| 761 | zbuf1 = - ( devk12 + devk22 * ztc + devk32 * ztc * ztc ) |
---|
| 762 | zbuf2 = 0.5 * ( devk42 + devk52 * ztc ) |
---|
| 763 | akbs(ji) = zakb * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 764 | |
---|
| 765 | zbuf1 = - ( devk13 + devk23 * ztc + devk33 * ztc * ztc ) |
---|
| 766 | zbuf2 = 0.5 * ( devk43 + devk53 * ztc ) |
---|
| 767 | akws(ji) = zakw * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 768 | |
---|
| 769 | zbuf1 = - ( devk14 + devk24 * ztc + devk34 * ztc * ztc ) |
---|
| 770 | zbuf2 = 0.5 * ( devk44 + devk54 * ztc ) |
---|
| 771 | aks3s(ji) = zcks * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 772 | |
---|
| 773 | zbuf1 = - ( devk15 + devk25 * ztc + devk35 * ztc * ztc ) |
---|
| 774 | zbuf2 = 0.5 * ( devk45 + devk55 * ztc ) |
---|
| 775 | akf3s(ji) = zckf * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 776 | |
---|
| 777 | zbuf1 = - ( devk17 + devk27 * ztc + devk37 * ztc * ztc ) |
---|
| 778 | zbuf2 = 0.5 * ( devk47 + devk57 * ztc ) |
---|
| 779 | ak1ps(ji) = zak1p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 780 | |
---|
| 781 | zbuf1 = - ( devk18 + devk28 * ztc + devk38 * ztc * ztc ) |
---|
| 782 | zbuf2 = 0.5 * ( devk48 + devk58 * ztc ) |
---|
| 783 | ak2ps(ji) = zak2p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 784 | |
---|
| 785 | zbuf1 = - ( devk110 + devk210 * ztc + devk310 * ztc * ztc ) |
---|
| 786 | zbuf2 = 0.5 * ( devk410 + devk510 * ztc ) |
---|
| 787 | aksis(ji) = zaksi * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 788 | |
---|
[15075] | 789 | zbuf1 = - ( devk120 + devk220 * ztc + devk320 * ztc * ztc ) |
---|
| 790 | zbuf2 = 0.5 * ( devk420 + devk520 * ztc ) |
---|
| 791 | akh2s(ji) = zckhs * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 792 | |
---|
| 793 | zbuf1 = - ( devk130 + devk230 * ztc + devk330 * ztc * ztc ) |
---|
| 794 | zbuf2 = 0.5 * ( devk430 + devk530 * ztc ) |
---|
| 795 | aknh3(ji) = zcknh3 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 796 | |
---|
[10222] | 797 | ! Convert to total scale |
---|
| 798 | ak1s(ji) = ak1s(ji) * SWS2total |
---|
| 799 | ak2s(ji) = ak2s(ji) * SWS2total |
---|
| 800 | akbs(ji) = akbs(ji) * SWS2total |
---|
| 801 | akws(ji) = akws(ji) * SWS2total |
---|
| 802 | ak1ps(ji) = ak1ps(ji) * SWS2total |
---|
| 803 | ak2ps(ji) = ak2ps(ji) * SWS2total |
---|
| 804 | ak3ps(ji) = ak3ps(ji) * SWS2total |
---|
| 805 | aksis(ji) = aksis(ji) * SWS2total |
---|
| 806 | akf3s(ji) = akf3s(ji) / total2free |
---|
[15075] | 807 | akh2s(ji) = akh2s(ji) * SWS2total |
---|
| 808 | aknh3(ji) = aknh3(ji) * SWS2total |
---|
[10222] | 809 | |
---|
| 810 | ! APPARENT SOLUBILITY PRODUCT K'SP OF CALCITE |
---|
| 811 | ! AS FUNCTION OF PRESSURE FOLLOWING MILLERO |
---|
| 812 | ! (P. 1285) AND BERNER (1976) |
---|
| 813 | zbuf1 = - ( devk16 + devk26 * ztc + devk36 * ztc * ztc ) |
---|
| 814 | zbuf2 = 0.5 * ( devk46 + devk56 * ztc ) |
---|
| 815 | aksps(ji) = zaksp1 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 ) |
---|
| 816 | |
---|
| 817 | ! TOTAL F, S, and BORATE CONCENTR. [MOLES/L] |
---|
| 818 | borats(ji) = 0.0002414 * zcl / 10.811 |
---|
| 819 | sulfats(ji) = zst |
---|
| 820 | fluorids(ji) = zft |
---|
| 821 | |
---|
| 822 | ! Iron and SIO3 saturation concentration from ... |
---|
| 823 | sieqs(ji) = EXP( LOG( 10.) * ( 6.44 - 968. / ztkel ) ) * 1.e-6 |
---|
| 824 | END DO |
---|
| 825 | ! |
---|
| 826 | IF( ln_timing ) CALL timing_stop('sed_chem_cst') |
---|
| 827 | ! |
---|
| 828 | END SUBROUTINE sed_chem_cst |
---|
| 829 | |
---|
| 830 | |
---|
[3443] | 831 | END MODULE sedchem |
---|