1 | MODULE trazdf_imp |
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2 | !!====================================================================== |
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3 | !! *** MODULE trazdf_imp *** |
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4 | !! Ocean active tracers: vertical component of the tracer mixing trend |
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5 | !!====================================================================== |
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6 | !! History : OPA ! 1990-10 (B. Blanke) Original code |
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7 | !! 7.0 ! 1991-11 (G. Madec) |
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8 | !! ! 1992-06 (M. Imbard) correction on tracer trend loops |
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9 | !! ! 1996-01 (G. Madec) statement function for e3 |
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10 | !! ! 1997-05 (G. Madec) vertical component of isopycnal |
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11 | !! ! 1997-07 (G. Madec) geopotential diffusion in s-coord |
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12 | !! ! 2000-08 (G. Madec) double diffusive mixing |
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13 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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14 | !! 2.0 ! 2006-11 (G. Madec) New step reorganisation |
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15 | !! 3.2 ! 2009-03 (G. Madec) heat and salt content trends |
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16 | !!---------------------------------------------------------------------- |
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17 | |
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18 | !!---------------------------------------------------------------------- |
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19 | !! tra_zdf_imp : Update the tracer trend with the diagonal vertical |
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20 | !! part of the mixing tensor. |
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21 | !!---------------------------------------------------------------------- |
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22 | USE oce ! ocean dynamics and tracers variables |
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23 | USE dom_oce ! ocean space and time domain variables |
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24 | USE zdf_oce ! ocean vertical physics variables |
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25 | USE ldftra_oce ! ocean active tracers: lateral physics |
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26 | USE ldfslp ! lateral physics: slope of diffusion |
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27 | USE trdmod ! ocean active tracers trends |
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28 | USE trdmod_oce ! ocean variables trends |
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29 | USE zdfddm ! ocean vertical physics: double diffusion |
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30 | USE in_out_manager ! I/O manager |
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31 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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32 | USE prtctl ! Print control |
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33 | USE domvvl ! variable volume |
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34 | USE ldftra ! lateral mixing type |
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35 | |
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36 | IMPLICIT NONE |
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37 | PRIVATE |
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38 | |
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39 | PUBLIC tra_zdf_imp ! routine called by step.F90 |
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40 | |
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41 | !! * Substitutions |
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42 | # include "domzgr_substitute.h90" |
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43 | # include "ldftra_substitute.h90" |
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44 | # include "zdfddm_substitute.h90" |
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45 | # include "vectopt_loop_substitute.h90" |
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46 | !!---------------------------------------------------------------------- |
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47 | !! NEMO/OPA 3.2 , LOCEAN-IPSL (2009) |
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48 | !! $Id$ |
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49 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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50 | !!---------------------------------------------------------------------- |
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51 | CONTAINS |
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52 | |
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53 | SUBROUTINE tra_zdf_imp( kt, p2dt ) |
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54 | !!---------------------------------------------------------------------- |
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55 | !! *** ROUTINE tra_zdf_imp *** |
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56 | !! |
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57 | !! ** Purpose : Compute the trend due to the vertical tracer diffusion |
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58 | !! including the vertical component of lateral mixing (only for 2nd |
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59 | !! order operator, for fourth order it is already computed and add |
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60 | !! to the general trend in traldf.F) and add it to the general trend |
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61 | !! of the tracer equations. |
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62 | !! |
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63 | !! ** Method : The vertical component of the lateral diffusive trends |
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64 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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65 | !! potential surfaces to which an eddy induced advection can be |
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66 | !! added. It is computed using before fields (forward in time) and |
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67 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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68 | !! |
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69 | !! Second part: vertical trend associated with the vertical physics |
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70 | !! =========== (including the vertical flux proportional to dk[t] |
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71 | !! associated with the lateral mixing, through the |
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72 | !! update of avt) |
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73 | !! The vertical diffusion of tracers (t & s) is given by: |
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74 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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75 | !! It is computed using a backward time scheme (t=ta). |
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76 | !! Surface and bottom boundary conditions: no diffusive flux on |
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77 | !! both tracers (bottom, applied through the masked field avt). |
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78 | !! Add this trend to the general trend ta,sa : |
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79 | !! ta = ta + dz( avt dz(t) ) |
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80 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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81 | !! |
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82 | !! Third part: recover avt resulting from the vertical physics |
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83 | !! ========== alone, for further diagnostics (for example to |
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84 | !! compute the turbocline depth in zdfmxl.F90). |
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85 | !! avt = zavt |
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86 | !! (avs = zavs if lk_zdfddm=T ) |
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87 | !! |
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88 | !! ** Action : - Update (ta,sa) with before vertical diffusion trend |
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89 | !! |
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90 | !!--------------------------------------------------------------------- |
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91 | USE oce , ONLY : zwd => ua ! ua used as workspace |
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92 | USE oce , ONLY : zws => va ! va - - |
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93 | !! |
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94 | INTEGER , INTENT(in) :: kt ! ocean time-step index |
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95 | REAL(wp), DIMENSION(jpk), INTENT(in) :: p2dt ! vertical profile of tracer time-step |
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96 | !! |
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97 | INTEGER :: ji, jj, jk ! dummy loop indices |
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98 | REAL(wp) :: zavi, zrhs, znvvl ! temporary scalars |
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99 | REAL(wp) :: ze3tb, ze3tn, ze3ta ! variable vertical scale factors |
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100 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwt, zavsi ! workspace arrays |
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101 | !!--------------------------------------------------------------------- |
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102 | |
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103 | IF( kt == nit000 ) THEN |
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104 | IF(lwp)WRITE(numout,*) |
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105 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp : implicit vertical mixing' |
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106 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' |
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107 | zavi = 0.e0 ! avoid warning at compilation phase when lk_ldfslp=F |
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108 | ENDIF |
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109 | |
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110 | ! I. Local initialization |
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111 | ! ----------------------- |
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112 | zwd (1,:, : ) = 0.e0 ; zwd (jpi,:,:) = 0.e0 |
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113 | zws (1,:, : ) = 0.e0 ; zws (jpi,:,:) = 0.e0 |
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114 | zwi (1,:, : ) = 0.e0 ; zwi (jpi,:,:) = 0.e0 |
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115 | zwt (1,:, : ) = 0.e0 ; zwt (jpi,:,:) = 0.e0 |
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116 | zavsi(1,:, : ) = 0.e0 ; zavsi(jpi,:,:) = 0.e0 |
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117 | zwt (:,:,jpk) = 0.e0 ; zwt ( : ,:,1) = 0.e0 |
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118 | zavsi(:,:,jpk) = 0.e0 ; zavsi( : ,:,1) = 0.e0 |
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119 | |
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120 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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121 | ! ------------------- |
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122 | IF( lk_vvl ) THEN ; znvvl = 1. |
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123 | ELSE ; znvvl = 0.e0 |
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124 | ENDIF |
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125 | |
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126 | ! II. Vertical trend associated with the vertical physics |
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127 | ! ======================================================= |
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128 | ! (including the vertical flux proportional to dk[t] associated |
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129 | ! with the lateral mixing, through the avt update) |
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130 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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131 | |
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132 | |
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133 | ! II.0 Matrix construction |
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134 | ! ------------------------ |
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135 | |
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136 | #if defined key_ldfslp |
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137 | ! update and save of avt (and avs if double diffusive mixing) |
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138 | IF ( ln_traldf_grif ) THEN |
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139 | DO jk = 2, jpkm1 |
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140 | DO jj = 2, jpjm1 |
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141 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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142 | zavi = fsahtw(ji,jj,jk) * wslp2(ji,jj,jk) ! vertical mixing coef. due to lateral mixing |
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143 | zwt(ji,jj,jk) = avt(ji,jj,jk) + zavi ! zwt=avt+zavi (total vertical mixing coef. on temperature) |
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144 | # if defined key_zdfddm |
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145 | zavsi(ji,jj,jk) = fsavs(ji,jj,jk) + zavi ! dd mixing: zavsi = total vertical mixing coef. on salinity |
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146 | # endif |
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147 | END DO |
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148 | END DO |
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149 | END DO |
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150 | ELSE IF (l_traldf_rot ) THEN |
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151 | DO jk = 2, jpkm1 |
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152 | DO jj = 2, jpjm1 |
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153 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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154 | zavi = fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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155 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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156 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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157 | zwt(ji,jj,jk) = avt(ji,jj,jk) + zavi ! zwt=avt+zavi (total vertical mixing coef. on temperature) |
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158 | # if defined key_zdfddm |
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159 | zavsi(ji,jj,jk) = fsavs(ji,jj,jk) + zavi ! dd mixing: zavsi = total vertical mixing coef. on salinity |
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160 | # endif |
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161 | END DO |
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162 | END DO |
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163 | END DO |
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164 | ELSE ! no rotation but key_ldfslp defined |
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165 | zwt (:,:,:) = avt(:,:,:) |
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166 | # if defined key_zdfddm |
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167 | zavsi(:,:,:) = avs(:,:,:) ! avs /= avt (double diffusion mixing) |
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168 | # endif |
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169 | ENDIF |
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170 | #else |
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171 | ! No isopycnal diffusion |
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172 | zwt(:,:,:) = avt(:,:,:) |
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173 | # if defined key_zdfddm |
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174 | zavsi(:,:,:) = avs(:,:,:) |
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175 | # endif |
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176 | |
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177 | #endif |
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178 | |
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179 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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180 | DO jk = 1, jpkm1 |
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181 | DO jj = 2, jpjm1 |
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182 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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183 | ze3ta = ( 1. - znvvl ) & ! after scale factor at T-point |
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184 | & + znvvl * fse3t_a(ji,jj,jk) |
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185 | ze3tn = znvvl & ! now scale factor at T-point |
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186 | & + ( 1. - znvvl ) * fse3t_n(ji,jj,jk) |
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187 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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188 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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189 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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190 | END DO |
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191 | END DO |
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192 | END DO |
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193 | |
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194 | ! Surface boudary conditions |
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195 | DO jj = 2, jpjm1 |
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196 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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197 | ze3ta = ( 1. - znvvl ) & ! after scale factor at T-point |
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198 | & + znvvl * fse3t_a(ji,jj,1) |
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199 | zwi(ji,jj,1) = 0.e0 |
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200 | zwd(ji,jj,1) = ze3ta - zws(ji,jj,1) |
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201 | END DO |
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202 | END DO |
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203 | |
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204 | |
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205 | ! II.1. Vertical diffusion on t |
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206 | ! --------------------------- |
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207 | |
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208 | !! Matrix inversion from the first level |
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209 | !!---------------------------------------------------------------------- |
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210 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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211 | ! |
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212 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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213 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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214 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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215 | ! ( ... )( ... ) ( ... ) |
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216 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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217 | ! |
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218 | ! m is decomposed in the product of an upper and lower triangular matrix |
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219 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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220 | ! The second member is in 2d array zwy |
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221 | ! The solution is in 2d array zwx |
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222 | ! The 3d arry zwt is a work space array |
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223 | ! zwy is used and then used as a work space array : its value is modified! |
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224 | |
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225 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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226 | DO jj = 2, jpjm1 |
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227 | DO ji = fs_2, fs_jpim1 |
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228 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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229 | END DO |
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230 | END DO |
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231 | DO jk = 2, jpkm1 |
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232 | DO jj = 2, jpjm1 |
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233 | DO ji = fs_2, fs_jpim1 |
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234 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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235 | END DO |
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236 | END DO |
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237 | END DO |
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238 | |
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239 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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240 | DO jj = 2, jpjm1 |
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241 | DO ji = fs_2, fs_jpim1 |
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242 | ze3tb = ( 1. - znvvl ) + znvvl * fse3t_b(ji,jj,1) |
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243 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t(ji,jj,1) |
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244 | ta(ji,jj,1) = ze3tb * tb(ji,jj,1) + p2dt(1) * ze3tn * ta(ji,jj,1) |
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245 | END DO |
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246 | END DO |
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247 | DO jk = 2, jpkm1 |
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248 | DO jj = 2, jpjm1 |
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249 | DO ji = fs_2, fs_jpim1 |
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250 | ze3tb = ( 1. - znvvl ) + znvvl * fse3t_b(ji,jj,jk) |
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251 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t (ji,jj,jk) |
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252 | zrhs = ze3tb * tb(ji,jj,jk) + p2dt(jk) * ze3tn * ta(ji,jj,jk) ! zrhs=right hand side |
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253 | ta(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * ta(ji,jj,jk-1) |
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254 | END DO |
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255 | END DO |
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256 | END DO |
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257 | |
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258 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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259 | ! Save the masked temperature after in ta |
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260 | ! (c a u t i o n: temperature not its trend, Leap-frog scheme done it will not be done in tranxt) |
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261 | DO jj = 2, jpjm1 |
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262 | DO ji = fs_2, fs_jpim1 |
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263 | ta(ji,jj,jpkm1) = ta(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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264 | END DO |
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265 | END DO |
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266 | DO jk = jpk-2, 1, -1 |
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267 | DO jj = 2, jpjm1 |
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268 | DO ji = fs_2, fs_jpim1 |
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269 | ta(ji,jj,jk) = ( ta(ji,jj,jk) - zws(ji,jj,jk) * ta(ji,jj,jk+1) ) / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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270 | END DO |
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271 | END DO |
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272 | END DO |
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273 | |
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274 | ! II.2 Vertical diffusion on salinity |
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275 | ! ----------------------------------- |
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276 | |
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277 | #if defined key_zdfddm |
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278 | ! Rebuild the Matrix as avt /= avs |
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279 | |
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280 | ! Diagonal, inferior, superior (including the bottom boundary condition via avs masked) |
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281 | DO jk = 1, jpkm1 |
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282 | DO jj = 2, jpjm1 |
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283 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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284 | ze3ta = ( 1. - znvvl ) & ! after scale factor at T-point |
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285 | & + znvvl * fse3t_a(ji,jj,jk) |
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286 | ze3tn = znvvl & ! now scale factor at T-point |
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287 | & + ( 1. - znvvl ) * fse3t_n(ji,jj,jk) |
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288 | zwi(ji,jj,jk) = - p2dt(jk) * zavsi(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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289 | zws(ji,jj,jk) = - p2dt(jk) * zavsi(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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290 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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291 | END DO |
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292 | END DO |
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293 | END DO |
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294 | |
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295 | ! Surface boundary conditions |
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296 | DO jj = 2, jpjm1 |
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297 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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298 | ze3ta = ( 1. - znvvl ) + znvvl * fse3t_a(ji,jj,1) |
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299 | zwi(ji,jj,1) = 0.e0 |
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300 | zwd(ji,jj,1) = ze3ta - zws(ji,jj,1) |
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301 | END DO |
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302 | END DO |
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303 | #endif |
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304 | |
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305 | |
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306 | !! Matrix inversion from the first level |
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307 | !!---------------------------------------------------------------------- |
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308 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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309 | ! |
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310 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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311 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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312 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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313 | ! ( ... )( ... ) ( ... ) |
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314 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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315 | ! |
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316 | ! m is decomposed in the product of an upper and lower triangular |
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317 | ! matrix |
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318 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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319 | ! The second member is in 2d array zwy |
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320 | ! The solution is in 2d array zwx |
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321 | ! The 3d arry zwt is a work space array |
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322 | ! zwy is used and then used as a work space array : its value is modified! |
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323 | |
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324 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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325 | DO jj = 2, jpjm1 |
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326 | DO ji = fs_2, fs_jpim1 |
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327 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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328 | END DO |
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329 | END DO |
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330 | DO jk = 2, jpkm1 |
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331 | DO jj = 2, jpjm1 |
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332 | DO ji = fs_2, fs_jpim1 |
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333 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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334 | END DO |
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335 | END DO |
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336 | END DO |
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337 | |
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338 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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339 | DO jj = 2, jpjm1 |
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340 | DO ji = fs_2, fs_jpim1 |
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341 | ze3tb = ( 1. - znvvl ) & ! before scale factor at T-point |
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342 | & + znvvl * fse3t_b(ji,jj,1) |
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343 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t (ji,jj,1) ! now scale factor at T-point |
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344 | sa(ji,jj,1) = ze3tb * sb(ji,jj,1) + p2dt(1) * ze3tn * sa(ji,jj,1) |
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345 | END DO |
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346 | END DO |
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347 | DO jk = 2, jpkm1 |
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348 | DO jj = 2, jpjm1 |
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349 | DO ji = fs_2, fs_jpim1 |
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350 | ze3tb = ( 1. - znvvl ) & ! before scale factor at T-point |
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351 | & + znvvl * fse3t_b(ji,jj,jk) |
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352 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t (ji,jj,jk) ! now scale factor at T-point |
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353 | zrhs = ze3tb * sb(ji,jj,jk) + p2dt(jk) * ze3tn * sa(ji,jj,jk) ! zrhs=right hand side |
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354 | sa(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *sa(ji,jj,jk-1) |
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355 | END DO |
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356 | END DO |
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357 | END DO |
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358 | |
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359 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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360 | ! Save the masked temperature after in ta |
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361 | ! (c a u t i o n: temperature not its trend, Leap-frog scheme done it will not be done in tranxt) |
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362 | DO jj = 2, jpjm1 |
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363 | DO ji = fs_2, fs_jpim1 |
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364 | sa(ji,jj,jpkm1) = sa(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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365 | END DO |
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366 | END DO |
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367 | DO jk = jpk-2, 1, -1 |
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368 | DO jj = 2, jpjm1 |
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369 | DO ji = fs_2, fs_jpim1 |
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370 | sa(ji,jj,jk) = ( sa(ji,jj,jk) - zws(ji,jj,jk) * sa(ji,jj,jk+1) ) / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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371 | END DO |
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372 | END DO |
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373 | END DO |
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374 | ! |
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375 | END SUBROUTINE tra_zdf_imp |
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376 | |
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377 | !!============================================================================== |
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378 | END MODULE trazdf_imp |
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