1 | CCC $Header$ |
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2 | CDIR$ LIST |
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3 | SUBROUTINE h3clys |
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4 | #if defined key_passivetrc && defined key_trc_hamocc3 |
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5 | CCC--------------------------------------------------------------------- |
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6 | CCC |
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7 | CCC ROUTINE h3clys |
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8 | CCC ****************** |
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9 | CCC |
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10 | CCC |
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11 | CCC PURPOSE. |
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12 | CCC -------- |
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13 | CCC *H3CLYS* CALCULATES DEGREE OF CACO3 SATURATION IN THE WATER |
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14 | CCC COLUMN, DISSOLUTION/PRECIPITATION OF CACO3 AND LOSS |
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15 | CCC OF CACO3 TO THE CACO3 SEDIMENT POOL. |
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16 | CCC |
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17 | CC |
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18 | CC METHOD. |
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19 | CC ------- |
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20 | CC [H+] AND [CO3--] FOR THE ACTUAL TIME STEP ARE CALCULATED |
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21 | CC BY NEWTON-RAPHSON ITERATION (E.G. SCARBOROUGH, 1958). |
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22 | CC |
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23 | CC EXTERNALS. |
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24 | CC ---------- |
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25 | CC NONE. |
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26 | CC |
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27 | CC REFERENCE. |
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28 | CC ---------- |
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29 | CC |
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30 | CC SCARBOROUGH, J. (1958) NUMERICAL MATHEMATICAL ANALYSIS. |
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31 | CC OXFORD UNIVERSITY PRESS, LONDON, 4TH ED., 576 PP.. |
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32 | CC |
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33 | CC* VARIABLE TYPE PURPOSE. |
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34 | CC -------- ---- -------- |
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35 | CC |
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36 | CC *NYEAR* INTEGER COUNTS TIMESTEPS (YEARS) OF INTEGRATION |
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37 | CC (INTEGER, INPUT) |
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38 | CC *CONVEG* REAL CHECK FOR CONVERGENCE OF NEWTON-RAPHSON |
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39 | CC METHOD |
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40 | CC *KITTER* INTEGER SETS UPPER LIMIT FOR NUMBER OF ITERATIONS |
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41 | CC TO DETERMINE [CO3--] AND [H+] |
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42 | CC *AKW* REAL APPROXIMATE VALUE OF IONIC PRODUCT OF |
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43 | CC WATER |
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44 | CC *H* REAL [H+], DUMMY VARIABLE |
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45 | CC *R* REAL [CO3--] [MOLE/L], DUMMY VARIABLE |
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46 | CC *ALKA* REAL GIVEN ALKALINITY [EQV/L], DUMMY VARIABLE |
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47 | CC *C* REAL GIVEN [SUM(12C)O2] [MOLE/L], DUMMY VARIABLE |
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48 | CC *A* REAL ALKALINITY [EQV/L] AS FUNCTION OF [CO3--] |
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49 | CC AND [H+], DUMMY VARIABLE |
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50 | CC *DELCO3* REAL DEVIATION OF ACTUAL CACO3 CONCENTRATION FROM |
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51 | CC SATURATION VALUE |
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52 | CC *UNDSAT* REAL UNDERSATURATION OF CACO3 (E.G. 3.=THREEFOLD) |
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53 | CC *EXCESS* REAL EXCESS OF CACO3 (E.G. 3.=THREEFOLD) |
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54 | CC *DISPOT* REAL FRACTION CACO3 (12C) THAT IS DISSOLVED |
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55 | CC *EXCE14* REAL SUPERSATURATION IN CA(14C)O3 (E.G. 3.= |
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56 | CC THREEFOLD) |
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57 | CC *DISP14* REAL FRACTION CACO3 (14C) THAT IS DISSOLVED |
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58 | CC *EXCE13* REAL SUPERSATURATION IN CA(13C)O3 (E.G. 3.= |
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59 | CC THREEFOLD) |
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60 | CC *DISP13* REAL FRACTION CACO3 (13C) THAT IS DISSOLVED |
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61 | CC *SEDLOS* REAL FRACTION OF CACO3 IN THE BOTTOM WATER LAYER |
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62 | CC LOST TO THE CACO3 SEDIMENT POOL |
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63 | CC *SEDLOI* REAL FRACTION OF CACO3 IN THE BOTTOM WATER LAYER |
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64 | CC WHICH REMAINS IN THE WATER COLUMN |
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65 | CC |
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66 | CC MODIFICATIONS: |
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67 | CC -------------- |
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68 | CC original : 1988-07 E. MAIER-REIMER MPI HAMBURG |
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69 | CC additions : 1998 O. Aumont |
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70 | CC modifications : 1999 C. Le Quere |
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71 | CC --------------------------------------------------------------------------- |
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72 | CC parameters and commons |
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73 | CC ====================== |
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74 | CDIR$ NOLIST |
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75 | USE oce_trc |
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76 | USE trp_trc |
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77 | USE sms |
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78 | IMPLICIT NONE |
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79 | CDIR$ LIST |
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80 | CC---------------------------------------------------------------------- |
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81 | CC local declarations |
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82 | CC ================== |
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83 | C |
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84 | INTEGER ji, jj, jk, jn |
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85 | INTEGER kitter |
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86 | REAL bot, alka |
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87 | REAL r, a, c |
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88 | REAL delco3, excess, dispot |
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89 | REAL h,remco3,ah2 |
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90 | REAL conveg, bicarb, caralk |
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91 | C |
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92 | C ------------------------------------------------------------------ |
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93 | C |
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94 | C* 1. SET HALF PRECISION CONSTANTS |
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95 | C -------------------------------- |
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96 | C |
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97 | zero = 0. |
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98 | C |
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99 | C =========================================================== |
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100 | C* 2. ITERATION TO DETERMINE [CO3--] AND [H+] |
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101 | C (NEWTON-RAPHSON METHOD: |
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102 | C THE VALUES OF [SUM(CO2)] AND [ALK] ARE GIVEN, |
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103 | C DESIRED ROOTS OF [CO3--] AND [H+] FOR THAT PAIR |
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104 | C ARE DETERMINED BY SOLVING NUMERICALLY THE SYSTEM |
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105 | C OF THE TWO NONLINEAR EQUATIONS |
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106 | C 1) [ALK]GIVEN - [ALK]([CO3--],[H+]) = 0 (=F) |
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107 | C 2) [SUM(CO2)]GIVEN - [SUM(CO2)]([CO3--],[H+]) = 0 (=GG) |
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108 | C =========================================================== |
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109 | C |
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110 | C |
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111 | C* 2.1 SET MAX. NUMBER OF ITERATIONS |
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112 | C -------------------------------------- |
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113 | C |
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114 | kitter = 15 |
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115 | C |
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116 | C* 2.2 SET DAMPING PARAMETERS FOR CORRECTIONS OF [CO3--] |
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117 | C AND [H+] |
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118 | C ------------------------------------------------------- |
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119 | C |
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120 | C |
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121 | C 2.3 INITIALISATION OF [HI+], and [CO3--] |
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122 | C ---------------------------------------- |
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123 | C |
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124 | DO jk=1,jpkm1 |
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125 | DO jj=1,jpj |
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126 | DO ji=1,jpi |
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127 | caralk = trn(ji,jj,jk,jptal)- |
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128 | & borat(ji,jj,jk)/(1.+1E-8/akb3(ji,jj,jk)) |
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129 | co3(ji,jj,jk) = caralk-trn(ji,jj,jk,jpdic) |
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130 | & +(1.-tmask(ji,jj,jk))*.5e-3 |
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131 | bicarb = (2.*trn(ji,jj,jk,jpdic)-caralk) |
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132 | hi(ji,jj,jk) = ak23(ji,jj,jk)*bicarb/co3(ji,jj,jk) |
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133 | END DO |
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134 | END DO |
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135 | END DO |
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136 | C |
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137 | C* 2.4 BEGIN OF ITERATION |
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138 | C ------------------------ |
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139 | C |
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140 | DO jn = 1,kitter |
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141 | C |
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142 | C* 2.5 COMPUTE [CO3--] and [H+] CONCENTRATIONS |
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143 | C ------------------------------------------- |
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144 | C |
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145 | rconvs=0. |
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146 | DO jk = 1,jpkm1 |
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147 | DO jj=1,jpj |
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148 | DO ji = 1, jpi |
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149 | C |
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150 | C* 2.6 SET DUMMY VARIABLE FOR TOTAL BORATE |
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151 | C ----------------------------------------- |
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152 | C |
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153 | bot = borat(ji,jj,jk) |
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154 | C |
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155 | C* 2.7 SET DUMMY VARIABLE FOR [H+], AND [CO3--] |
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156 | C ---------------------------------------------- |
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157 | C |
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158 | h = hi(ji,jj,jk)+(1.-tmask(ji,jj,jk))*1.e-9 |
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159 | h = amax1(hi(ji,jj,jk),1.E-10) |
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160 | r = co3(ji,jj,jk)+(1.-tmask(ji,jj,jk))*.5e-3 |
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161 | C |
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162 | C* 2.8 SET DUMMY VARIABLE FOR [ALK]GIVEN AND |
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163 | C [SUM(CO2)]GIVEN |
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164 | C ------------------------------------------- |
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165 | C |
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166 | alka = trn(ji,jj,jk,jptal) |
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167 | c = trn(ji,jj,jk,jpdic) |
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168 | C |
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169 | C* 2.9 CALCULATE [ALK]([CO3--], [HCO3-]) |
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170 | C ------------------------------------ |
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171 | C |
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172 | a=alka- |
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173 | & (akw3(ji,jj,jk)/h-h+bot/(1.+h/akb3(ji,jj,jk))) |
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174 | C |
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175 | C* 2.10 CALCULATE [H+] and [CO3--] |
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176 | C ----------------------------------------- |
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177 | C |
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178 | ah2=sqrt((c-a)**2+4.*(a*ak23(ji,jj,jk)/ak13(ji,jj,jk)) |
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179 | & *(2*c-a)) |
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180 | ah2=0.5*ak13(ji,jj,jk)/a*((c-a)+ah2) |
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181 | co3(ji,jj,jk) = a/(2.+ah2/ak23(ji,jj,jk)) |
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182 | C |
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183 | C* 2.11 CONTROL VARIABLE TO CHECK CONVERGENCE |
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184 | C ------------------------------------------- |
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185 | C |
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186 | c |
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187 | conveg=((ah2-hi(ji,jj,jk))/hi(ji,jj,jk))**2 |
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188 | $ *tmask(ji,jj,jk) |
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189 | rconvs = rconvs+conveg |
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190 | hi(ji,jj,jk) = ah2 |
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191 | ENDDO |
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192 | ENDDO |
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193 | END DO |
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194 | C |
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195 | C |
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196 | C 2.12 CHECK CONVERGENCE |
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197 | C ---------------------- |
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198 | C |
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199 | IF (rconvs.LE.1.E-2) EXIT |
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200 | C |
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201 | END DO |
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202 | C |
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203 | C --------------------------------------------------------- |
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204 | C* 3. CALCULATE DEGREE OF CACO3 SATURATION AND CORRESPONDING |
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205 | C DISSOLOUTION AND PRECIPITATION OF CACO3 (BE AWARE OF |
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206 | C MGCO3) |
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207 | C --------------------------------------------------------- |
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208 | C |
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209 | DO jk = 2,jpkm1 |
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210 | DO jj = 1,jpj |
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211 | DO ji = 1, jpi |
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212 | C |
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213 | C* 3.1 DEVIATION OF [CO3--] FROM SATURATION VALUE |
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214 | C ------------------------------------------------ |
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215 | C |
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216 | delco3 = co3(ji,jj,jk)-aksp(ji,jj,jk)/calcon |
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217 | C |
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218 | C* 3.2 SET DEGREE OF UNDER-/SUPERSATURATION |
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219 | C ------------------------------------------ |
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220 | C |
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221 | excess = amax1(zero,delco3) |
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222 | C |
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223 | C* 3.3 AMOUNT CACO3 (12C) THAT RE-ENTERS SOLUTION |
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224 | C (ACCORDING TO THIS FORMULATION ALSO SOME PARTICULATE |
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225 | C CACO3 GETS DISSOLVED EVEN IN THE CASE OF OVERSATURATION) |
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226 | C -------------------------------------------------------------- |
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227 | C |
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228 | dispot = trn(ji,jj,jk,jpcal)*amin1(1., |
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229 | & (1.-delco3/(dispo0+abs(delco3))) ) |
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230 | # if defined key_off_degrad |
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231 | & *facvol(ji,jj,jk) |
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232 | # endif |
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233 | C |
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234 | C* 3.5 CHANGE OF PARTICULATE CACO3 AND TOTAL INORGANIC 14C |
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235 | C IN THE WATER COLUMN DUE TO CACO3 DISSOLUTION/PRECIP. |
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236 | C ---------------------------------------------------------- |
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237 | C |
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238 | cristl = spocri |
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239 | # if defined key_off_degrad |
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240 | & *facvol(ji,jj,jk) |
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241 | # endif |
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242 | C* 3.8 CHANGE OF [CO3--] , [ALK], PARTICULATE [CACO3], |
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243 | C AND [SUM(CO2)] DUE TO CACO3 DISSOLUTION/PRECIPITATION |
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244 | C ----------------------------------------------------------- |
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245 | C |
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246 | remco3=(dispot-excess*cristl)/rmoss |
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247 | co3(ji,jj,jk) = co3(ji,jj,jk) |
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248 | & +remco3*rfact |
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249 | tra(ji,jj,jk,jptal) = tra(ji,jj,jk,jptal)+ |
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250 | & 2.*remco3 |
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251 | tra(ji,jj,jk,jpcal) = tra(ji,jj,jk,jpcal)- |
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252 | & remco3 |
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253 | tra(ji,jj,jk,jpdic) = tra(ji,jj,jk,jpdic)+ |
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254 | & remco3 |
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255 | # if defined key_trc_biohamocc13 |
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256 | tra(ji,jj,jk,jp13c) = tra(ji,jj,jk,jp13c)+pdb* |
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257 | & remco3 |
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258 | # endif |
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259 | C |
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260 | C |
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261 | ENDDO |
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262 | ENDDO |
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263 | END DO |
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264 | C |
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265 | #endif |
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266 | RETURN |
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267 | END |
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268 | |
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