1 | MODULE trcadv_cen2 |
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2 | !!============================================================================== |
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3 | !! *** MODULE trcadv_cen2 *** |
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4 | !! Ocean passive tracers: horizontal & vertical advective tracer trend |
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5 | !!============================================================================== |
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6 | #if defined key_passivetrc |
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7 | !!---------------------------------------------------------------------- |
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8 | !! trc_adv_cen2 : update the tracer trend with the horizontal |
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9 | !! and vertical advection trends using a 2nd order |
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10 | !! centered finite difference scheme |
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11 | !!---------------------------------------------------------------------- |
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12 | !! * Modules used |
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13 | USE oce_trc ! ocean dynamics and active tracers variables |
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14 | USE trc ! ocean passive tracers variables |
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15 | USE trcbbl ! advective passive tracers in the BBL |
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16 | USE prtctl_trc |
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17 | |
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18 | IMPLICIT NONE |
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19 | PRIVATE |
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20 | |
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21 | !! * Accessibility |
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22 | PUBLIC trc_adv_cen2 ! routine called by trcstp.F90 |
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23 | |
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24 | !! * Substitutions |
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25 | # include "passivetrc_substitute.h90" |
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26 | !!---------------------------------------------------------------------- |
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27 | !! OPA 9.0 , LODYC-IPSL (2003) |
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28 | !!---------------------------------------------------------------------- |
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29 | |
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30 | CONTAINS |
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31 | |
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32 | !!---------------------------------------------------------------------- |
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33 | !! Default option : 2nd order centered scheme (k-j-i loop) |
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34 | !!---------------------------------------------------------------------- |
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35 | |
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36 | SUBROUTINE trc_adv_cen2( kt ) |
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37 | !!---------------------------------------------------------------------- |
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38 | !! *** ROUTINE trc_adv_cen2 *** |
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39 | !! |
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40 | !! ** Purpose : Compute the now trend due to the advection of tracers |
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41 | !! and add it to the general trend of passive tracer equations. |
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42 | !! |
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43 | !! ** Method : The advection is evaluated by a second order centered |
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44 | !! scheme using now fields (leap-frog scheme). In specific areas |
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45 | !! (vicinity of major river mouths, some straits, or where tn is |
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46 | !! is approaching the freezing point) it is mixed with an upstream |
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47 | !! scheme for stability reasons. |
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48 | !! Part 0 : compute the upstream / centered flag |
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49 | !! (3D array, zind, defined at T-point (0<zind<1)) |
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50 | !! Part I : horizontal advection |
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51 | !! * centered flux: |
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52 | !! * s-coordinate (lk_sco=T) or |
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53 | !! * z-coordinate with partial steps (lk_zps=T), |
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54 | !! the vertical scale factors e3. are inside the derivatives: |
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55 | !! zcenu = e2u*e3u un mi(tn) |
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56 | !! zcenv = e1v*e3v vn mj(tn) |
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57 | !! * z-coordinate (default key), e3t=e3u=e3v: |
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58 | !! zcenu = e2u un mi(tn) |
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59 | !! zcenv = e1v vn mj(tn) |
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60 | !! * horizontal advective trend (divergence of the fluxes) |
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61 | !! * s-coordinate (lk_sco=T) or |
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62 | !! * z-coordinate with partial steps (lk_zps=T) |
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63 | !! ztra = 1/(e1t*e2t*e3t) { di-1[zwx] + dj-1[zwy] } |
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64 | !! * z-coordinate (default key), e3t=e3u=e3v: |
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65 | !! ztra = 1/(e1t*e2t) { di-1[zwx] + dj-1[zwy] } |
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66 | !! * Add this trend now to the general trend of tracer tra: |
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67 | !! tra = tra + ztra |
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68 | !! * trend diagnostic ('key_trc_diatrd'): the trend is saved |
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69 | !! for diagnostics. The trends saved is expressed as |
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70 | !! Uh.gradh(T) |
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71 | !! |
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72 | !! Part II : vertical advection |
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73 | !! For any tracer the advective trend is computed as follows : |
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74 | !! ztra = 1/e3t dk+1[ zwz ] |
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75 | !! where the vertical advective flux, zwz, is given by : |
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76 | !! zwz = zcofk * zupst + (1-zcofk) * zcent |
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77 | !! with |
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78 | !! zupsv = upstream flux = wn * (trb(k) or trb(k-1) ) [wn>0 or <0] |
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79 | !! zcenu = centered flux = wn * mk(trn) |
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80 | !! The surface boundary condition is : |
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81 | !! rigid-lid (default option) : zero advective flux |
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82 | !! free-surf ("key_fresurf_cstvol") : wn(:,:,1) * trn(:,:,1) |
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83 | !! Add this trend now to the general trend of tracer tra : |
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84 | !! tra = tra + ztra |
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85 | !! Trend diagnostic ('key_trc_diatrd'): the trend is saved for |
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86 | !! diagnostics. The trends saved is expressed as : |
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87 | !! save trend = w.gradz(T) = ztra - trn divn. |
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88 | !! |
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89 | !! ** Action : - update tra with the now advective tracer trends |
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90 | !! - save the trends in trtrd ('key_trc_diatrd') |
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91 | !! |
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92 | !! History : |
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93 | !! 8.2 ! 01-08 (M-A Filiberti, and M.Levy) trahad+trazad = traadv |
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94 | !! 8.5 ! 02-06 (G. Madec, C. Ethe) F90: Free form and module |
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95 | !!---------------------------------------------------------------------- |
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96 | !! * Modules used |
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97 | USE oce_trc , zwx => ua, & ! use ua as workspace |
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98 | & zwy => va ! use va as workspace |
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99 | #if defined key_trcbbl_adv |
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100 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & ! temporary arrays |
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101 | & zun, zvn, zwn |
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102 | #else |
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103 | USE oce_trc , zun => un, & ! When no bbl, zun == un |
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104 | & zvn => vn, & ! When no bbl, zvn == vn |
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105 | & zwn => wn ! When no bbl, zwn == wn |
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106 | #endif |
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107 | |
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108 | |
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109 | !! * Arguments |
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110 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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111 | |
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112 | !! * Local save |
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113 | REAL(wp), DIMENSION(jpi,jpj), SAVE :: & |
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114 | zbtr2 |
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115 | |
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116 | !! * Local declarations |
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117 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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118 | REAL(wp) :: & |
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119 | zbtr, ztra, zfui, zfvj, & ! temporary scalars |
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120 | zhw, ze3tr, zcofi, zcofj, & ! " " |
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121 | zupsut, zupsvt, & ! " " |
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122 | zfp_ui, zfp_vj, zfm_ui, zfm_vj, & ! " " |
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123 | zcofk, zupst, zcent, & ! " " |
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124 | zfp_w, zfm_w, & ! " " |
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125 | zcenut, zcenvt ! |
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126 | |
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127 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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128 | zind ! temporary workspace arrays |
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129 | #if defined key_trc_diatrd |
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130 | REAL(wp) :: & |
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131 | ztai, ztaj, & ! temporary scalars |
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132 | zfui1, zfvj1 ! " " |
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133 | #endif |
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134 | CHARACTER (len=22) :: charout |
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135 | !!---------------------------------------------------------------------- |
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136 | |
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137 | IF( kt == nittrc000 ) THEN |
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138 | IF(lwp) WRITE(numout,*) |
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139 | IF(lwp) WRITE(numout,*) 'trc_adv_cen2 : 2nd order centered advection scheme' |
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140 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~ Vector optimization case' |
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141 | IF(lwp) WRITE(numout,*) |
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142 | |
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143 | zbtr2(:,:) = 1. / ( e1t(:,:) * e2t(:,:) ) |
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144 | ENDIF |
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145 | |
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146 | #if defined key_trcbbl_adv |
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147 | |
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148 | ! Advective bottom boundary layer |
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149 | ! ------------------------------- |
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150 | zun(:,:,:) = un(:,:,:) - u_trc_bbl(:,:,:) |
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151 | zvn(:,:,:) = vn(:,:,:) - v_trc_bbl(:,:,:) |
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152 | zwn(:,:,:) = wn(:,:,:) + w_trc_bbl(:,:,:) |
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153 | #endif |
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154 | |
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155 | |
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156 | ! Upstream / centered scheme indicator |
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157 | ! ------------------------------------ |
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158 | |
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159 | DO jk = 1, jpk |
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160 | DO jj = 1, jpj |
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161 | DO ji = 1, jpi |
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162 | zind(ji,jj,jk) = MAX ( upsrnfh(ji,jj) * upsrnfz(jk), & ! changing advection scheme near runoff |
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163 | & upsadv(ji,jj) & ! in the vicinity of some straits |
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164 | #if defined key_ice_lim |
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165 | & , tmask(ji,jj,jk) & ! half upstream tracer fluxes |
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166 | & * MAX( 0., SIGN( 1., fzptn(ji,jj) & ! if tn < ("freezing"+0.1 ) |
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167 | & +0.1-tn(ji,jj,jk) ) ) & |
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168 | #endif |
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169 | & ) |
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170 | END DO |
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171 | END DO |
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172 | END DO |
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173 | |
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174 | |
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175 | DO jn = 1, jptra |
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176 | ! I. Horizontal advective fluxes |
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177 | ! ------------------------------ |
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178 | |
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179 | ! Second order centered tracer flux at u and v-points |
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180 | |
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181 | ! ! =============== |
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182 | DO jk = 1, jpkm1 ! Horizontal slab |
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183 | ! ! =============== |
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184 | DO jj = 1, jpjm1 |
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185 | DO ji = 1, fs_jpim1 ! vector opt. |
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186 | ! upstream indicator |
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187 | zcofi = MAX( zind(ji+1,jj,jk), zind(ji,jj,jk) ) |
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188 | zcofj = MAX( zind(ji,jj+1,jk), zind(ji,jj,jk) ) |
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189 | ! volume fluxes * 1/2 |
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190 | #if defined key_s_coord || defined key_partial_steps |
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191 | zfui = 0.5 * e2u(ji,jj) * fse3u(ji,jj,jk) * zun(ji,jj,jk) |
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192 | zfvj = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * zvn(ji,jj,jk) |
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193 | #else |
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194 | zfui = 0.5 * e2u(ji,jj) * zun(ji,jj,jk) |
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195 | zfvj = 0.5 * e1v(ji,jj) * zvn(ji,jj,jk) |
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196 | #endif |
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197 | ! upstream scheme |
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198 | zfp_ui = zfui + ABS( zfui ) |
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199 | zfp_vj = zfvj + ABS( zfvj ) |
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200 | zfm_ui = zfui - ABS( zfui ) |
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201 | zfm_vj = zfvj - ABS( zfvj ) |
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202 | zupsut = zfp_ui * trb(ji,jj,jk,jn) + zfm_ui * trb(ji+1,jj ,jk,jn) |
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203 | zupsvt = zfp_vj * trb(ji,jj,jk,jn) + zfm_vj * trb(ji ,jj+1,jk,jn) |
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204 | ! centered scheme |
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205 | zcenut = zfui * ( trn(ji,jj,jk,jn) + trn(ji+1,jj ,jk,jn) ) |
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206 | zcenvt = zfvj * ( trn(ji,jj,jk,jn) + trn(ji ,jj+1,jk,jn) ) |
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207 | ! mixed centered / upstream scheme |
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208 | zwx(ji,jj,jk) = zcofi * zupsut + (1.-zcofi) * zcenut |
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209 | zwy(ji,jj,jk) = zcofj * zupsvt + (1.-zcofj) * zcenvt |
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210 | END DO |
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211 | END DO |
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212 | |
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213 | |
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214 | ! 2. Tracer flux divergence at t-point added to the general trend |
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215 | ! ------------------------- |
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216 | |
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217 | DO jj = 2, jpjm1 |
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218 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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219 | #if defined key_s_coord || defined key_partial_steps |
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220 | zbtr = zbtr2(ji,jj) / fse3t(ji,jj,jk) |
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221 | #else |
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222 | zbtr = zbtr2(ji,jj) |
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223 | #endif |
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224 | ! horizontal advective trends |
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225 | ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) & |
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226 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) ) |
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227 | |
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228 | ! add it to the general tracer trends |
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229 | tra(ji,jj,jk,jn) = tra(ji,jj,jk,jn) + ztra |
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230 | |
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231 | #if defined key_trc_diatrd |
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232 | ! recompute the trends in i- and j-direction as Uh gradh(T) |
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233 | # if defined key_s_coord || defined key_partial_steps |
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234 | zfui = 0.5 * e2u(ji ,jj) * fse3u(ji, jj,jk) * zun(ji, jj,jk) |
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235 | zfui1= 0.5 * e2u(ji-1,jj) * fse3u(ji-1,jj,jk) * zun(ji-1,jj,jk) |
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236 | zfvj = 0.5 * e1v(ji,jj ) * fse3v(ji,jj ,jk) * zvn(ji,jj ,jk) |
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237 | zfvj1= 0.5 * e1v(ji,jj-1) * fse3v(ji,jj-1,jk) * zvn(ji,jj-1,jk) |
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238 | # else |
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239 | zfui = 0.5 * e2u(ji ,jj) * zun(ji, jj,jk) |
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240 | zfui1= 0.5 * e2u(ji-1,jj) * zun(ji-1,jj,jk) |
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241 | zfvj = 0.5 * e1v(ji,jj ) * zvn(ji,jj ,jk) |
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242 | zfvj1= 0.5 * e1v(ji,jj-1) * zvn(ji,jj-1,jk) |
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243 | # endif |
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244 | ztai = - zbtr * ( zfui * ( trn(ji+1,jj ,jk,jn) - trn(ji, jj,jk,jn) ) & |
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245 | & + zfui1 * ( trn(ji, jj, jk,jn) - trn(ji-1,jj,jk,jn) ) ) |
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246 | ztaj = - zbtr * ( zfvj * ( trn(ji ,jj+1,jk,jn) - trn(ji,jj ,jk,jn) ) & |
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247 | & + zfvj1 * ( trn(ji ,jj ,jk,jn) - trn(ji,jj-1,jk,jn) ) ) |
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248 | ! save i- and j- advective trends computed as Uh gradh(T) |
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249 | trtrd(ji,jj,jk,jn,1) = ztai |
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250 | trtrd(ji,jj,jk,jn,2) = ztaj |
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251 | #endif |
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252 | END DO |
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253 | END DO |
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254 | ! ! =============== |
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255 | END DO ! End of slab |
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256 | ! ! =============== |
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257 | ENDDO |
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258 | |
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259 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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260 | WRITE(charout, FMT="('centered2 - had')") |
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261 | CALL prt_ctl_trc_info(charout) |
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262 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm,clinfo2='trd') |
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263 | ENDIF |
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264 | |
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265 | ! II. Vertical advection |
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266 | ! ---------------------- |
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267 | DO jn = 1, jptra |
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268 | |
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269 | ! Bottom value : flux set to zero |
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270 | zwx(:,:,jpk) = 0.e0 |
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271 | |
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272 | ! Surface value |
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273 | IF( lk_dynspg_fsc ) THEN ! free surface-constant volume |
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274 | zwx(:,:, 1 ) = zwn(:,:,1) * trn(:,:,1,jn) |
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275 | ELSE ! rigid lid : flux set to zero |
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276 | zwx(:,:, 1 ) = 0.e0 |
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277 | ENDIF |
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278 | |
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279 | ! 1. Vertical advective fluxes |
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280 | ! ---------------------------- |
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281 | |
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282 | ! Second order centered tracer flux at w-point |
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283 | |
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284 | DO jk = 2, jpk |
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285 | DO jj = 2, jpjm1 |
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286 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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287 | ! upstream indicator |
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288 | zcofk = MAX( zind(ji,jj,jk-1), zind(ji,jj,jk) ) |
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289 | ! velocity * 1/2 |
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290 | zhw = 0.5 * zwn(ji,jj,jk) |
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291 | ! upstream scheme |
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292 | zfp_w = zhw + ABS( zhw ) |
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293 | zfm_w = zhw - ABS( zhw ) |
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294 | zupst = zfp_w * trb(ji,jj,jk,jn) + zfm_w * trb(ji,jj,jk-1,jn) |
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295 | ! centered scheme |
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296 | zcent = zhw * ( trn(ji,jj,jk,jn) + trn(ji,jj,jk-1,jn) ) |
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297 | ! centered scheme |
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298 | zwx(ji,jj,jk) = zcofk * zupst + (1.-zcofk) * zcent |
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299 | END DO |
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300 | END DO |
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301 | END DO |
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302 | |
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303 | |
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304 | ! 2. Tracer flux divergence at t-point added to the general trend |
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305 | ! ------------------------- |
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306 | |
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307 | DO jk = 1, jpkm1 |
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308 | DO jj = 2, jpjm1 |
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309 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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310 | ze3tr = 1. / fse3t(ji,jj,jk) |
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311 | ! vertical advective trends |
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312 | ztra = - ze3tr * ( zwx(ji,jj,jk) - zwx(ji,jj,jk+1) ) |
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313 | ! add it to the general tracer trends |
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314 | tra(ji,jj,jk,jn) = tra(ji,jj,jk,jn) + ztra |
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315 | #if defined key_trc_diatrd |
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316 | ! save the vertical advective trends computed as w gradz(T) |
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317 | trtrd(ji,jj,jk,jn,3) = ztra - trn(ji,jj,jk,jn) * hdivn(ji,jj,jk) |
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318 | #endif |
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319 | END DO |
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320 | END DO |
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321 | END DO |
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322 | |
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323 | END DO |
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324 | |
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325 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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326 | WRITE(charout, FMT="('centered - zad')") |
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327 | CALL prt_ctl_trc_info(charout) |
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328 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm,clinfo2='trd') |
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329 | ENDIF |
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330 | |
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331 | END SUBROUTINE trc_adv_cen2 |
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332 | #else |
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333 | |
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334 | !!---------------------------------------------------------------------- |
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335 | !! Default option Empty module |
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336 | !!---------------------------------------------------------------------- |
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337 | CONTAINS |
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338 | SUBROUTINE trc_adv_cen2( kt ) |
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339 | INTEGER, INTENT(in) :: kt |
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340 | WRITE(*,*) 'trc_adv_cen2: You should not have seen this print! error?', kt |
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341 | END SUBROUTINE trc_adv_cen2 |
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342 | #endif |
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343 | !!====================================================================== |
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344 | END MODULE trcadv_cen2 |
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