1 | subroutine moldiff(ngrid,nlayer,nq, |
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2 | & pplay,pplev,pt,pdt,pq,pdq,ptimestep, |
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3 | & zzlay,pdteuv,pdtconduc,pdqdiff) |
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4 | |
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5 | use tracer_mod, only: igcm_co2, igcm_co, igcm_o, igcm_o1d, |
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6 | & igcm_o2, igcm_o3, igcm_h, igcm_h2, igcm_oh, |
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7 | & igcm_ho2, igcm_h2o2, igcm_n2, igcm_ar, |
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8 | & igcm_h2o_vap, mmol |
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9 | use conc_mod, only: rnew, mmean |
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10 | USE comcstfi_h |
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11 | implicit none |
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12 | |
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13 | c |
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14 | c Input/Output |
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15 | c |
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16 | integer,intent(in) :: ngrid ! number of atmospheric columns |
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17 | integer,intent(in) :: nlayer ! number of atmospheric layers |
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18 | integer,intent(in) :: nq ! number of advected tracers |
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19 | real ptimestep |
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20 | real pplay(ngrid,nlayer) |
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21 | real zzlay(ngrid,nlayer) |
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22 | real pplev(ngrid,nlayer+1) |
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23 | real pq(ngrid,nlayer,nq) |
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24 | real pdq(ngrid,nlayer,nq) |
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25 | real pt(ngrid,nlayer) |
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26 | real pdt(ngrid,nlayer) |
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27 | real pdteuv(ngrid,nlayer) |
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28 | real pdtconduc(ngrid,nlayer) |
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29 | real pdqdiff(ngrid,nlayer,nq) |
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30 | c |
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31 | c Local |
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32 | c |
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33 | |
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34 | integer,parameter :: ncompmoldiff = 14 |
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35 | real hco2(ncompmoldiff),ho |
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36 | |
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37 | integer ig,nz,l,n,nn,iq |
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38 | real del1,del2, tmean ,dalfinvdz, d |
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39 | real hh,dcoef,dcoef1,ptfac, ntot, dens, dens2, dens3 |
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40 | real hp(nlayer) |
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41 | real tt(nlayer) |
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42 | real qq(nlayer,ncompmoldiff) |
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43 | real dmmeandz(nlayer) |
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44 | real qnew(nlayer,ncompmoldiff) |
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45 | real zlocal(nlayer) |
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46 | real alf(ncompmoldiff-1,ncompmoldiff-1) |
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47 | real alfinv(nlayer,ncompmoldiff-1,ncompmoldiff-1) |
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48 | real indx(ncompmoldiff-1) |
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49 | real b(nlayer,ncompmoldiff-1) |
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50 | real y(ncompmoldiff-1,ncompmoldiff-1) |
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51 | real aa(nlayer,ncompmoldiff-1,ncompmoldiff-1) |
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52 | real bb(nlayer,ncompmoldiff-1,ncompmoldiff-1) |
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53 | real cc(nlayer,ncompmoldiff-1,ncompmoldiff-1) |
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54 | real atri(nlayer-2) |
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55 | real btri(nlayer-2) |
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56 | real ctri(nlayer-2) |
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57 | real rtri(nlayer-2) |
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58 | real qtri(nlayer-2) |
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59 | real alfdiag(ncompmoldiff-1) |
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60 | real wi(ncompmoldiff), flux(ncompmoldiff), pote |
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61 | |
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62 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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63 | c tracer numbering in the molecular diffusion |
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64 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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65 | c Atomic oxygen must always be the LAST species of the list as |
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66 | c it is the dominant species at high altitudes. |
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67 | integer,parameter :: i_co = 1 |
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68 | integer,parameter :: i_n2 = 2 |
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69 | integer,parameter :: i_o2 = 3 |
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70 | integer,parameter :: i_co2 = 4 |
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71 | integer,parameter :: i_h2 = 5 |
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72 | integer,parameter :: i_h = 6 |
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73 | integer,parameter :: i_oh = 7 |
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74 | integer,parameter :: i_ho2 = 8 |
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75 | integer,parameter :: i_h2o = 9 |
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76 | integer,parameter :: i_h2o2 = 10 |
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77 | integer,parameter :: i_o1d = 11 |
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78 | integer,parameter :: i_o3 = 12 |
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79 | integer,parameter :: i_ar = 13 |
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80 | integer,parameter :: i_o = 14 |
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81 | |
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82 | ! Tracer indexes in the GCM: |
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83 | integer,save :: g_co2=0 |
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84 | integer,save :: g_co=0 |
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85 | integer,save :: g_o=0 |
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86 | integer,save :: g_o1d=0 |
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87 | integer,save :: g_o2=0 |
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88 | integer,save :: g_o3=0 |
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89 | integer,save :: g_h=0 |
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90 | integer,save :: g_h2=0 |
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91 | integer,save :: g_oh=0 |
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92 | integer,save :: g_ho2=0 |
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93 | integer,save :: g_h2o2=0 |
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94 | integer,save :: g_n2=0 |
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95 | integer,save :: g_ar=0 |
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96 | integer,save :: g_h2o=0 |
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97 | |
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98 | integer,save :: gcmind(ncompmoldiff) ! array of GCM indexes |
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99 | integer ierr |
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100 | |
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101 | logical,save :: firstcall=.true. |
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102 | real abfac(ncompmoldiff) |
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103 | real,save :: dij(ncompmoldiff,ncompmoldiff) |
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104 | |
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105 | ! Initializations at first call |
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106 | if (firstcall) then |
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107 | call moldiffcoeff(dij) |
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108 | print*,'MOLDIFF EXO' |
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109 | |
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110 | ! identify the indexes of the tracers we'll need |
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111 | g_co2=igcm_co2 |
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112 | if (g_co2.eq.0) then |
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113 | write(*,*) "moldiff: Error; no CO2 tracer !!!" |
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114 | stop |
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115 | endif |
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116 | g_co=igcm_co |
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117 | if (g_co.eq.0) then |
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118 | write(*,*) "moldiff: Error; no CO tracer !!!" |
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119 | stop |
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120 | endif |
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121 | g_o=igcm_o |
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122 | if (g_o.eq.0) then |
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123 | write(*,*) "moldiff: Error; no O tracer !!!" |
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124 | stop |
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125 | endif |
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126 | g_o1d=igcm_o1d |
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127 | if (g_o1d.eq.0) then |
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128 | write(*,*) "moldiff: Error; no O1D tracer !!!" |
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129 | stop |
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130 | endif |
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131 | g_o2=igcm_o2 |
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132 | if (g_o2.eq.0) then |
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133 | write(*,*) "moldiff: Error; no O2 tracer !!!" |
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134 | stop |
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135 | endif |
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136 | g_o3=igcm_o3 |
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137 | if (g_o3.eq.0) then |
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138 | write(*,*) "moldiff: Error; no O3 tracer !!!" |
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139 | stop |
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140 | endif |
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141 | g_h=igcm_h |
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142 | if (g_h.eq.0) then |
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143 | write(*,*) "moldiff: Error; no H tracer !!!" |
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144 | stop |
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145 | endif |
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146 | g_h2=igcm_h2 |
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147 | if (g_h2.eq.0) then |
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148 | write(*,*) "moldiff: Error; no H2 tracer !!!" |
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149 | stop |
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150 | endif |
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151 | g_oh=igcm_oh |
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152 | if (g_oh.eq.0) then |
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153 | write(*,*) "moldiff: Error; no OH tracer !!!" |
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154 | stop |
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155 | endif |
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156 | g_ho2=igcm_ho2 |
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157 | if (g_ho2.eq.0) then |
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158 | write(*,*) "moldiff: Error; no HO2 tracer !!!" |
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159 | stop |
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160 | endif |
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161 | g_h2o2=igcm_h2o2 |
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162 | if (g_h2o2.eq.0) then |
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163 | write(*,*) "moldiff: Error; no H2O2 tracer !!!" |
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164 | stop |
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165 | endif |
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166 | g_n2=igcm_n2 |
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167 | if (g_n2.eq.0) then |
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168 | write(*,*) "moldiff: Error; no N2 tracer !!!" |
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169 | stop |
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170 | endif |
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171 | g_ar=igcm_ar |
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172 | if (g_ar.eq.0) then |
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173 | write(*,*) "moldiff: Error; no AR tracer !!!" |
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174 | stop |
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175 | endif |
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176 | g_h2o=igcm_h2o_vap |
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177 | if (g_h2o.eq.0) then |
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178 | write(*,*) "moldiff: Error; no water vapor tracer !!!" |
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179 | stop |
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180 | endif |
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181 | |
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182 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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183 | c fill array to relate local indexes to gcm indexes |
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184 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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185 | |
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186 | gcmind(i_co) = g_co |
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187 | gcmind(i_n2) = g_n2 |
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188 | gcmind(i_o2) = g_o2 |
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189 | gcmind(i_co2) = g_co2 |
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190 | gcmind(i_h2) = g_h2 |
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191 | gcmind(i_h) = g_h |
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192 | gcmind(i_oh) = g_oh |
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193 | gcmind(i_ho2) = g_ho2 |
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194 | gcmind(i_h2o) = g_h2o |
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195 | gcmind(i_h2o2) = g_h2o2 |
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196 | gcmind(i_o1d) = g_o1d |
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197 | gcmind(i_o3) = g_o3 |
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198 | gcmind(i_o) = g_o |
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199 | gcmind(i_ar) = g_ar |
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200 | |
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201 | firstcall= .false. |
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202 | endif ! of if (firstcall) |
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203 | |
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204 | |
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205 | |
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206 | c |
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207 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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208 | |
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209 | nz=nlayer |
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210 | |
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211 | do ig=1,ngrid |
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212 | |
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213 | do l=2,nz-1 |
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214 | tt(l)=pt(ig,l)+pdt(ig,l)*ptimestep |
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215 | & +pdteuv(ig,l)*ptimestep |
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216 | & +pdtconduc(ig,l)*ptimestep |
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217 | |
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218 | do nn=1,ncompmoldiff |
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219 | qq(l,nn)=pq(ig,l,gcmind(nn))+pdq(ig,l,gcmind(nn))*ptimestep |
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220 | qq(l,nn)=max(qq(l,nn),1.e-30) |
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221 | enddo |
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222 | hp(l)=-log(pplay(ig,l+1)/pplay(ig,l-1)) |
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223 | dmmeandz(l)=(mmean(ig,l+1)-mmean(ig,l-1))/hp(l) |
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224 | enddo |
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225 | |
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226 | tt(1)=pt(ig,1) +pdt(ig,1)*ptimestep |
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227 | & +pdteuv(ig,1)*ptimestep |
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228 | & +pdtconduc(ig,1)*ptimestep |
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229 | tt(nz)=pt(ig,nz)+pdt(ig,nz)*ptimestep |
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230 | & +pdteuv(ig,nz)*ptimestep |
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231 | & +pdtconduc(ig,nz)*ptimestep |
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232 | |
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233 | do nn=1,ncompmoldiff |
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234 | qq(1,nn)=pq(ig,1,gcmind(nn))+pdq(ig,1,gcmind(nn))*ptimestep |
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235 | qq(nz,nn)=pq(ig,nz,gcmind(nn))+pdq(ig,nz,gcmind(nn))*ptimestep |
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236 | qq(1,nn)=max(qq(1,nn),1.e-30) |
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237 | qq(nz,nn)=max(qq(nz,nn),1.e-30) |
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238 | enddo |
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239 | hp(1)=-log(pplay(ig,2)/pplay(ig,1)) |
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240 | dmmeandz(1)=(-3.*mmean(ig,1)+4.*mmean(ig,2) |
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241 | & -mmean(ig,3))/(2.*hp(1)) |
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242 | hp(nz)=-log(pplay(ig,nz)/pplay(ig,nz-1)) |
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243 | dmmeandz(nz)=(3.*mmean(ig,nz)-4.*mmean(ig,nz-1) |
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244 | & +mmean(ig,nz-2))/(2.*hp(nz)) |
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245 | c |
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246 | c Setting-up matrix of alfa coefficients from Dickinson and Ridley 1972 |
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247 | c |
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248 | do l=1,nz |
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249 | if(abs(dmmeandz(l)) .lt. 1.e-5) dmmeandz(l)=0.0 |
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250 | hh=rnew(ig,l)*tt(l)/g |
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251 | ptfac=(1.e5/pplay(ig,l))*(tt(l)/273)**1.75 |
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252 | ntot=pplay(ig,l)/(1.381e-23*tt(l)) ! in #/m3 |
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253 | |
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254 | do nn=1,ncompmoldiff-1 ! rows |
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255 | alfdiag(nn)=0. |
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256 | dcoef1=dij(nn,i_o)*ptfac |
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257 | do n=1,ncompmoldiff-1 ! columns |
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258 | y(nn,n)=0. |
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259 | dcoef=dij(nn,n)*ptfac |
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260 | alf(nn,n)=qq(l,nn)/ntot/1.66e-27 |
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261 | & *(1./(mmol(gcmind(n))*dcoef)-1./(mmol(g_o)*dcoef1)) |
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262 | alfdiag(nn)=alfdiag(nn) |
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263 | & +(1./(mmol(gcmind(n))*dcoef)-1./(mmol(g_o)*dcoef1)) |
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264 | & *qq(l,n) |
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265 | enddo |
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266 | dcoef=dij(nn,nn)*ptfac |
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267 | alfdiag(nn)=alfdiag(nn) |
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268 | & -(1./(mmol(gcmind(nn))*dcoef)-1./(mmol(g_o)*dcoef1)) |
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269 | & *qq(l,nn) |
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270 | alf(nn,nn)=-(alfdiag(nn) |
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271 | & +1./(mmol(g_o)*dcoef1))/ntot/1.66e-27 |
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272 | y(nn,nn)=1. |
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273 | b(l,nn)=-(dmmeandz(l)/mmean(ig,l) |
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274 | & +mmol(gcmind(nn))/mmean(ig,l)-1.) |
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275 | enddo |
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276 | |
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277 | c |
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278 | c Inverting the alfa matrix |
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279 | c |
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280 | call ludcmp_sp(alf,ncompmoldiff-1,ncompmoldiff-1,indx,d,ierr) |
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281 | |
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282 | c TEMPORAIRE ***************************** |
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283 | if (ierr.ne.0) then |
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284 | write(*,*)'In moldiff: Problem in LUDCMP_SP with matrix alf' |
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285 | write(*,*) 'Singular matrix ?' |
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286 | c write(*,*) 'Matrix alf = ', alf |
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287 | write(*,*) 'ig, l=',ig, l |
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288 | write(*,*) 'No molecular diffusion this time !' |
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289 | pdqdiff(1:ngrid,1:nlayer,1:nq)=0 |
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290 | return |
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291 | c stop |
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292 | end if |
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293 | c ******************************************* |
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294 | do n=1,ncompmoldiff-1 |
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295 | call lubksb_sp(alf,ncompmoldiff-1,ncompmoldiff-1,indx,y(1,n)) |
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296 | do nn=1,ncompmoldiff-1 |
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297 | alfinv(l,nn,n)=y(nn,n)/hh |
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298 | enddo |
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299 | enddo |
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300 | enddo |
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301 | |
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302 | c |
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303 | c Calculating coefficients of the system |
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304 | c |
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305 | |
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306 | c zlocal(1)=-log(pplay(ig,1)/pplev(ig,1))* Rnew(ig,1)*tt(1)/g |
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307 | zlocal(1)=zzlay(ig,1) |
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308 | |
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309 | do l=2,nz-1 |
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310 | del1=hp(l)*pplay(ig,l)/(g*ptimestep) |
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311 | del2=(hp(l)/2)**2*pplay(ig,l)/(g*ptimestep) |
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312 | do nn=1,ncompmoldiff-1 |
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313 | do n=1,ncompmoldiff-1 |
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314 | dalfinvdz=(alfinv(l+1,nn,n)-alfinv(l-1,nn,n))/hp(l) |
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315 | aa(l,nn,n)=-dalfinvdz/del1+alfinv(l,nn,n)/del2 |
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316 | & +alfinv(l-1,nn,n)*b(l-1,n)/del1 |
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317 | bb(l,nn,n)=-2.*alfinv(l,nn,n)/del2 |
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318 | cc(l,nn,n)=dalfinvdz/del1+alfinv(l,nn,n)/del2 |
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319 | & -alfinv(l+1,nn,n)*b(l+1,n)/del1 |
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320 | enddo |
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321 | enddo |
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322 | |
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323 | c tmean=tt(l) |
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324 | c if(tt(l).ne.tt(l-1)) |
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325 | c & tmean=(tt(l)-tt(l-1))/log(tt(l)/tt(l-1)) |
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326 | c zlocal(l)= zlocal(l-1) |
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327 | c & -log(pplay(ig,l)/pplay(ig,l-1))*rnew(ig,l)*tmean/g |
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328 | zlocal(l)=zzlay(ig,l) |
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329 | enddo |
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330 | |
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331 | c zlocal(nz)= zlocal(nz-1) |
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332 | c & -log(pplay(ig,nz)/pplay(ig,nz-1))*rnew(ig,nz)*tmean/g |
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333 | zlocal(nz)=zzlay(ig,nz) |
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334 | |
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335 | ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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336 | c Escape velocity from Jeans equation for the flux of H and H2 |
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337 | c (Hunten 1973, eq. 5) |
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338 | |
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339 | do n=1,ncompmoldiff |
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340 | wi(n)=1. |
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341 | flux(n)=0. |
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342 | abfac(n)=1. |
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343 | enddo |
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344 | |
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345 | dens=pplay(ig,nz)/(rnew(ig,nz)*tt(nz)) |
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346 | c |
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347 | c For H: |
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348 | c |
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349 | pote=(3398000.+zlocal(nz))/ |
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350 | & (1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h)*g)) |
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351 | wi(i_h)=sqrt(2.*1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h))) |
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352 | & /(2.*sqrt(3.1415))*(1.+pote)*exp(-pote) |
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353 | flux(i_h)=qq(nz,i_h)*dens/(1.6605e-27*mmol(g_h))*wi(i_h) |
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354 | flux(i_h)=flux(i_h)*1.6606e-27 |
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355 | abfac(i_h)=0. |
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356 | c |
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357 | c For H2: |
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358 | c |
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359 | pote=(3398000.+zlocal(nz))/ |
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360 | & (1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h2)*g)) |
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361 | wi(i_h2)=sqrt(2.*1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h2))) |
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362 | & /(2.*sqrt(3.1415))*(1.+pote)*exp(-pote) |
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363 | flux(i_h2)=qq(nz,i_h2)*dens/(1.6605e-27*mmol(g_h2))*wi(i_h2) |
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364 | flux(i_h2)=flux(i_h2)*1.6606e-27 |
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365 | abfac(i_h2)=0. |
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366 | |
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367 | c ********* TEMPORAIRE : no escape for h and h2 |
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368 | c do n=1,ncomptot |
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369 | c wi(n)=1. |
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370 | c flux(n)=0. |
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371 | c abfac(n)=1. |
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372 | c enddo |
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373 | c ******************************************** |
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374 | |
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375 | |
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376 | ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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377 | |
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378 | c |
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379 | c Setting coefficients for tridiagonal matrix and solving the system |
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380 | c |
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381 | |
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382 | do nn=1,ncompmoldiff-1 |
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383 | do l=2,nz-1 |
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384 | atri(l-1)=aa(l,nn,nn) |
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385 | btri(l-1)=bb(l,nn,nn)+1. |
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386 | ctri(l-1)=cc(l,nn,nn) |
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387 | rtri(l-1)=qq(l,nn) |
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388 | do n=1,ncompmoldiff-1 |
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389 | rtri(l-1)=rtri(l-1)-(aa(l,nn,n)*qq(l-1,n) |
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390 | & +bb(l,nn,n)*qq(l,n) |
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391 | & +cc(l,nn,n)*qq(l+1,n)) |
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392 | enddo |
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393 | rtri(l-1)=rtri(l-1)+(aa(l,nn,nn)*qq(l-1,nn) |
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394 | & +bb(l,nn,nn)*qq(l,nn) |
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395 | & +cc(l,nn,nn)*qq(l+1,nn)) |
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396 | enddo |
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397 | |
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398 | c |
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399 | c Boundary conditions: |
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400 | c Escape flux for H and H2 at top |
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401 | c Diffusive equilibrium for the other species at top |
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402 | c Perfect mixing for all at bottom |
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403 | c |
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404 | |
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405 | rtri(nz-2)=rtri(nz-2) |
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406 | & -ctri(nz-2)*flux(nn)*mmol(gcmind(nn))/(dens*wi(nn)) |
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407 | |
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408 | atri(nz-2)=atri(nz-2) |
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409 | & -abfac(nn)*ctri(nz-2)/(3.-2.*hp(nz)*b(nz,nn)) |
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410 | btri(nz-2)=btri(nz-2) |
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411 | & +abfac(nn)*4.*ctri(nz-2)/(3.-2.*hp(nz)*b(nz,nn)) |
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412 | |
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413 | c rtri(1)=rtri(1)-atri(1)*qq(1,nn) |
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414 | btri(1)=btri(1)+atri(1) |
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415 | |
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416 | call tridag_sp(atri,btri,ctri,rtri,qtri,nz-2) |
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417 | |
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418 | do l=2,nz-1 |
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419 | c qnew(l,nn)=qtri(l-1) |
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420 | qnew(l,nn)=max(qtri(l-1),1.e-30) |
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421 | enddo |
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422 | |
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423 | qnew(nz,nn)=flux(nn)*mmol(gcmind(nn))/(dens*wi(nn)) |
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424 | & +abfac(nn)*(4.*qnew(nz-1,nn)-qnew(nz-2,nn)) |
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425 | & /(3.-2.*hp(nz)*b(nz,nn)) |
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426 | c qnew(1,nn)=qq(1,nn) |
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427 | qnew(1,nn)=qnew(2,nn) |
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428 | |
---|
429 | qnew(nz,nn)=max(qnew(nz,nn),1.e-30) |
---|
430 | qnew(1,nn)=max(qnew(1,nn),1.e-30) |
---|
431 | |
---|
432 | enddo ! loop on species |
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433 | |
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434 | DO l=1,nz |
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435 | if(zlocal(l).gt.65000.)then |
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436 | pdqdiff(ig,l,g_o)=0. |
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437 | do n=1,ncompmoldiff-1 |
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438 | pdqdiff(ig,l,gcmind(n))=(qnew(l,n)-qq(l,n)) |
---|
439 | pdqdiff(ig,l,g_o)=pdqdiff(ig,l,g_o)-(qnew(l,n)-qq(l,n)) |
---|
440 | pdqdiff(ig,l,gcmind(n))=pdqdiff(ig,l,gcmind(n))/ptimestep |
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441 | enddo |
---|
442 | pdqdiff(ig,l,g_o)=pdqdiff(ig,l,g_o)/ptimestep |
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443 | endif |
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444 | ENDDO |
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445 | |
---|
446 | c do l=2,nz |
---|
447 | c do n=1,ncomptot-1 |
---|
448 | c hco2(n)=qnew(l,n)*pplay(ig,l)/(rnew(ig,l)*tt(l)) / |
---|
449 | c & (qnew(l-1,n)*pplay(ig,l-1)/(rnew(ig,l-1)*tt(l-1))) |
---|
450 | c hco2(n)=-(zlocal(l)-zlocal(l-1))/log(hco2(n))/1000. |
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451 | c enddo |
---|
452 | c write(225,*),l,pt(1,l),(hco2(n),n=1,6) |
---|
453 | c write(226,*),l,pt(1,l),(hco2(n),n=7,12) |
---|
454 | c enddo |
---|
455 | |
---|
456 | enddo ! ig loop |
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457 | |
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458 | return |
---|
459 | end |
---|
460 | |
---|
461 | c ******************************************************************** |
---|
462 | c ******************************************************************** |
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463 | c ******************************************************************** |
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464 | |
---|
465 | subroutine tridag_sp(a,b,c,r,u,n) |
---|
466 | c parameter (nmax=100) |
---|
467 | c dimension gam(nmax),a(n),b(n),c(n),r(n),u(n) |
---|
468 | real gam(n),a(n),b(n),c(n),r(n),u(n) |
---|
469 | if(b(1).eq.0.)then |
---|
470 | stop 'tridag_sp: error: b(1)=0 !!! ' |
---|
471 | endif |
---|
472 | bet=b(1) |
---|
473 | u(1)=r(1)/bet |
---|
474 | do 11 j=2,n |
---|
475 | gam(j)=c(j-1)/bet |
---|
476 | bet=b(j)-a(j)*gam(j) |
---|
477 | if(bet.eq.0.) then |
---|
478 | stop 'tridag_sp: error: bet=0 !!! ' |
---|
479 | endif |
---|
480 | u(j)=(r(j)-a(j)*u(j-1))/bet |
---|
481 | 11 continue |
---|
482 | do 12 j=n-1,1,-1 |
---|
483 | u(j)=u(j)-gam(j+1)*u(j+1) |
---|
484 | 12 continue |
---|
485 | return |
---|
486 | end |
---|
487 | |
---|
488 | c ******************************************************************** |
---|
489 | c ******************************************************************** |
---|
490 | c ******************************************************************** |
---|
491 | |
---|
492 | SUBROUTINE LUBKSB_SP(A,N,NP,INDX,B) |
---|
493 | |
---|
494 | implicit none |
---|
495 | |
---|
496 | integer i,j,n,np,ii,ll |
---|
497 | real sum |
---|
498 | real a(np,np),indx(np),b(np) |
---|
499 | |
---|
500 | c DIMENSION A(NP,NP),INDX(N),B(N) |
---|
501 | II=0 |
---|
502 | DO 12 I=1,N |
---|
503 | LL=INDX(I) |
---|
504 | SUM=B(LL) |
---|
505 | B(LL)=B(I) |
---|
506 | IF (II.NE.0)THEN |
---|
507 | DO 11 J=II,I-1 |
---|
508 | SUM=SUM-A(I,J)*B(J) |
---|
509 | 11 CONTINUE |
---|
510 | ELSE IF (SUM.NE.0.) THEN |
---|
511 | II=I |
---|
512 | ENDIF |
---|
513 | B(I)=SUM |
---|
514 | 12 CONTINUE |
---|
515 | DO 14 I=N,1,-1 |
---|
516 | SUM=B(I) |
---|
517 | IF(I.LT.N)THEN |
---|
518 | DO 13 J=I+1,N |
---|
519 | SUM=SUM-A(I,J)*B(J) |
---|
520 | 13 CONTINUE |
---|
521 | ENDIF |
---|
522 | B(I)=SUM/A(I,I) |
---|
523 | 14 CONTINUE |
---|
524 | RETURN |
---|
525 | END |
---|
526 | |
---|
527 | c ******************************************************************** |
---|
528 | c ******************************************************************** |
---|
529 | c ******************************************************************** |
---|
530 | |
---|
531 | SUBROUTINE LUDCMP_SP(A,N,NP,INDX,D,ierr) |
---|
532 | |
---|
533 | implicit none |
---|
534 | |
---|
535 | integer n,np,nmax,i,j,k,imax |
---|
536 | real d,tiny,aamax |
---|
537 | real a(np,np),indx(np) |
---|
538 | integer ierr ! error =0 if OK, =1 if problem |
---|
539 | |
---|
540 | PARAMETER (NMAX=100,TINY=1.0E-20) |
---|
541 | c DIMENSION A(NP,NP),INDX(N),VV(NMAX) |
---|
542 | real sum,vv(nmax),dum |
---|
543 | |
---|
544 | D=1. |
---|
545 | DO 12 I=1,N |
---|
546 | AAMAX=0. |
---|
547 | DO 11 J=1,N |
---|
548 | IF (ABS(A(I,J)).GT.AAMAX) AAMAX=ABS(A(I,J)) |
---|
549 | 11 CONTINUE |
---|
550 | IF (AAMAX.EQ.0.) then |
---|
551 | write(*,*) 'In moldiff: Problem in LUDCMP_SP with matrix A' |
---|
552 | write(*,*) 'Singular matrix ?' |
---|
553 | c write(*,*) 'Matrix A = ', A |
---|
554 | c TO DEBUG : |
---|
555 | ierr =1 |
---|
556 | return |
---|
557 | c stop |
---|
558 | END IF |
---|
559 | |
---|
560 | VV(I)=1./AAMAX |
---|
561 | 12 CONTINUE |
---|
562 | DO 19 J=1,N |
---|
563 | IF (J.GT.1) THEN |
---|
564 | DO 14 I=1,J-1 |
---|
565 | SUM=A(I,J) |
---|
566 | IF (I.GT.1)THEN |
---|
567 | DO 13 K=1,I-1 |
---|
568 | SUM=SUM-A(I,K)*A(K,J) |
---|
569 | 13 CONTINUE |
---|
570 | A(I,J)=SUM |
---|
571 | ENDIF |
---|
572 | 14 CONTINUE |
---|
573 | ENDIF |
---|
574 | AAMAX=0. |
---|
575 | DO 16 I=J,N |
---|
576 | SUM=A(I,J) |
---|
577 | IF (J.GT.1)THEN |
---|
578 | DO 15 K=1,J-1 |
---|
579 | SUM=SUM-A(I,K)*A(K,J) |
---|
580 | 15 CONTINUE |
---|
581 | A(I,J)=SUM |
---|
582 | ENDIF |
---|
583 | DUM=VV(I)*ABS(SUM) |
---|
584 | IF (DUM.GE.AAMAX) THEN |
---|
585 | IMAX=I |
---|
586 | AAMAX=DUM |
---|
587 | ENDIF |
---|
588 | 16 CONTINUE |
---|
589 | IF (J.NE.IMAX)THEN |
---|
590 | DO 17 K=1,N |
---|
591 | DUM=A(IMAX,K) |
---|
592 | A(IMAX,K)=A(J,K) |
---|
593 | A(J,K)=DUM |
---|
594 | 17 CONTINUE |
---|
595 | D=-D |
---|
596 | VV(IMAX)=VV(J) |
---|
597 | ENDIF |
---|
598 | INDX(J)=IMAX |
---|
599 | IF(J.NE.N)THEN |
---|
600 | IF(A(J,J).EQ.0.)A(J,J)=TINY |
---|
601 | DUM=1./A(J,J) |
---|
602 | DO 18 I=J+1,N |
---|
603 | A(I,J)=A(I,J)*DUM |
---|
604 | 18 CONTINUE |
---|
605 | ENDIF |
---|
606 | 19 CONTINUE |
---|
607 | IF(A(N,N).EQ.0.)A(N,N)=TINY |
---|
608 | ierr =0 |
---|
609 | RETURN |
---|
610 | END |
---|
611 | |
---|