1 | MODULE trazdf_imp_tam |
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2 | #ifdef key_tam |
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3 | !!============================================================================== |
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4 | !! *** MODULE trazdf_imp_tam *** |
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5 | !! Ocean active tracers: vertical component of the tracer mixing trend |
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6 | !! Tangent and Adjoint Module |
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7 | !!============================================================================== |
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8 | !! History of the direct module: |
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9 | !! OPA ! 1990-10 (B. Blanke) Original code |
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10 | !! 7.0 ! 1991-11 (G. Madec) |
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11 | !! ! 1992-06 (M. Imbard) correction on tracer trend loops |
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12 | !! ! 1996-01 (G. Madec) statement function for e3 |
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13 | !! ! 1997-05 (G. Madec) vertical component of isopycnal |
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14 | !! ! 1997-07 (G. Madec) geopotential diffusion in s-coord |
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15 | !! ! 2000-08 (G. Madec) double diffusive mixing |
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16 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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17 | !! 2.0 ! 2006-11 (G. Madec) New step reorganisation |
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18 | !! 3.2 ! 2009-03 (G. Madec) heat and salt content trends |
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19 | |
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20 | !! History of the T&A module: |
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21 | !! ! 09-01 (A. Vidard) tam of the 06-11 version |
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22 | !!---------------------------------------------------------------------- |
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23 | !! tra_zdf_imp_tan : Update the tracer trend with the diagonal vertical |
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24 | !! part of the mixing tensor (tangent). |
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25 | !! tra_zdf_imp_adj : Update the tracer trend with the diagonal vertical |
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26 | !! part of the mixing tensor (adjoint). |
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27 | !!---------------------------------------------------------------------- |
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28 | !! * Modules used |
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29 | USE par_kind |
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30 | USE par_oce |
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31 | USE oce_tam |
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32 | USE dom_oce |
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33 | USE oce |
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34 | USE zdf_oce |
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35 | USE ldftra_oce |
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36 | USE zdfddm |
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37 | USE traldf_tam |
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38 | USE in_out_manager |
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39 | USE gridrandom |
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40 | USE dotprodfld |
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41 | USE tstool_tam |
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42 | USE trc_oce |
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43 | USE trc_oce_tam |
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44 | USE ldftra |
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45 | USE lib_mpp |
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46 | USE wrk_nemo |
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47 | USE timing |
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48 | USE ldfslp |
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49 | USE paresp |
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50 | |
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51 | IMPLICIT NONE |
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52 | PRIVATE |
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53 | |
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54 | !! * Routine accessibility |
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55 | PUBLIC tra_zdf_imp_tan ! routine called by tra_zdf_tan.F90 |
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56 | PUBLIC tra_zdf_imp_adj ! routine called by tra_zdf_adj.F90 |
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57 | PUBLIC tra_zdf_imp_adj_tst ! routine called by tst.F90 |
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58 | #if defined key_tst_tlm |
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59 | PUBLIC tra_zdf_imp_tlm_tst ! routine called by tamtst.F90 |
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60 | #endif |
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61 | |
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62 | !! * Substitutions |
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63 | # include "domzgr_substitute.h90" |
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64 | # include "ldftra_substitute.h90" |
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65 | # include "zdfddm_substitute.h90" |
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66 | # include "vectopt_loop_substitute.h90" |
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67 | !!---------------------------------------------------------------------- |
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68 | !!---------------------------------------------------------------------- |
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69 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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70 | !! $Id: trazdf_imp.F90 1156 2008-06-26 16:06:45Z rblod $ |
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71 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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72 | !!---------------------------------------------------------------------- |
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73 | CONTAINS |
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74 | |
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75 | SUBROUTINE tra_zdf_imp_tan( kt, kit000, cdtype, p2dt, ptb_tl, pta_tl, kjpt ) |
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76 | !!---------------------------------------------------------------------- |
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77 | !! *** ROUTINE tra_zdf_imp_tan *** |
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78 | !! |
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79 | !! ** Purpose of the direct routine: |
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80 | !! Compute the trend due to the vertical tracer diffusion |
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81 | !! including the vertical component of lateral mixing (only for 2nd |
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82 | !! order operator, for fourth order it is already computed and add |
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83 | !! to the general trend in traldf.F) and add it to the general trend |
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84 | !! of the tracer equations. |
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85 | !! |
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86 | !! ** Method of the direct routine : |
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87 | !! The vertical component of the lateral diffusive trends |
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88 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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89 | !! potential surfaces to which an eddy induced advection can be |
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90 | !! added. It is computed using before fields (forward in time) and |
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91 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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92 | !! |
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93 | !! Second part: vertical trend associated with the vertical physics |
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94 | !! =========== (including the vertical flux proportional to dk[t] |
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95 | !! associated with the lateral mixing, through the |
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96 | !! update of avt) |
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97 | !! The vertical diffusion of tracers (t & s) is given by: |
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98 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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99 | !! It is computed using a backward time scheme (t=ta). |
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100 | !! Surface and bottom boundary conditions: no diffusive flux on |
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101 | !! both tracers (bottom, applied through the masked field avt). |
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102 | !! Add this trend to the general trend ta,sa : |
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103 | !! ta = ta + dz( avt dz(t) ) |
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104 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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105 | !! |
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106 | !! Third part: recover avt resulting from the vertical physics |
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107 | !! ========== alone, for further diagnostics (for example to |
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108 | !! compute the turbocline depth in zdfmxl.F90). |
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109 | !! avt = zavt |
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110 | !! (avs = zavs if lk_zdfddm=T ) |
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111 | !! |
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112 | !! ** Remarks on the tangent routine : - key_vvl is not available in tangent yet. |
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113 | !! Once it will be this routine wil need to be rewritten |
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114 | !! - simplified version, slopes (wslp[ij]) |
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115 | !! assumed to be constant (read from the trajectory). same for av[ts] |
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116 | !! |
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117 | !!--------------------------------------------------------------------- |
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118 | !! |
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119 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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120 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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121 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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122 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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123 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
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124 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb_tl ! before and now tracer fields |
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125 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta_tl ! tracer trend |
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126 | !! * Local declarations |
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127 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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128 | REAL(wp) :: zavi, zrhstl, znvvl, & ! temporary scalars |
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129 | ze3tb, ze3tn, ze3ta, zvsfvvl ! variable vertical scale factors |
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130 | REAL(wp), POINTER, DIMENSION(:,:,:) :: & |
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131 | zwi, zwt, zwd, zws ! workspace arrays |
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132 | !!--------------------------------------------------------------------- |
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133 | ! |
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134 | IF( nn_timing == 1 ) CALL timing_start('tra_zdf_imp_tan') |
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135 | ! |
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136 | CALL wrk_alloc( jpi, jpj, jpk, zwi, zwt, zwd, zws ) |
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137 | ! |
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138 | IF( kt == kit000 ) THEN |
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139 | IF(lwp)WRITE(numout,*) |
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140 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp_tan : implicit vertical mixing on ', cdtype |
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141 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' |
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142 | ENDIF |
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143 | |
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144 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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145 | ! ------------------- |
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146 | ! ... not available in tangent yet |
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147 | ! II. Vertical trend associated with the vertical physics |
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148 | ! ======================================================= |
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149 | ! (including the vertical flux proportional to dk[t] associated |
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150 | ! with the lateral mixing, through the avt update) |
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151 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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152 | DO jn = 1, kjpt ! tracer loop ! |
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153 | ! ! ============= ! |
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154 | ! |
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155 | ! Matrix construction |
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156 | ! -------------------- |
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157 | ! Build matrix if temperature or salinity (only in double diffusion case) or first passive tracer |
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158 | ! |
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159 | IF( ( cdtype == 'TRA' .AND. ( jn == jp_tem .OR. ( jn == jp_sal .AND. lk_zdfddm ) ) ) .OR. & |
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160 | & ( cdtype == 'TRC' .AND. jn == 1 ) ) THEN |
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161 | ! |
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162 | ! vertical mixing coef.: avt for temperature, avs for salinity and passive tracers |
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163 | IF( cdtype == 'TRA' .AND. jn == jp_tem ) THEN ; zwt(:,:,2:jpk) = avt (:,:,2:jpk) |
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164 | ELSE ; zwt(:,:,2:jpk) = fsavs(:,:,2:jpk) |
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165 | ENDIF |
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166 | zwt(:,:,1) = 0._wp |
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167 | ! |
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168 | ! II.0 Matrix construction |
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169 | ! ------------------------ |
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170 | #if defined key_ldfslp |
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171 | ! update and save of avt (and avs if double diffusive mixing) |
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172 | IF ( ln_traldf_grif ) THEN |
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173 | IF ( lwp ) WRITE(numout, *) 'Griffies operator for lateral tracer diffusion not avaible in TAM yet' |
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174 | CALL abort |
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175 | ELSE IF( l_traldf_rot ) THEN |
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176 | DO jk = 2, jpkm1 |
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177 | DO jj = 2, jpjm1 |
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178 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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179 | zwt(ji,jj,jk) = zwt(ji,jj,jk) + fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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180 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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181 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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182 | END DO |
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183 | END DO |
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184 | END DO |
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185 | ENDIF |
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186 | #endif |
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187 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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188 | DO jk = 1, jpkm1 |
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189 | DO jj = 2, jpjm1 |
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190 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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191 | ze3ta = 1._wp ! after scale factor at T-point |
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192 | ze3tn = fse3t(ji,jj,jk) ! now scale factor at T-point |
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193 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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194 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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195 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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196 | END DO |
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197 | END DO |
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198 | END DO |
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199 | ! |
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200 | ! II.1. Vertical diffusion on t |
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201 | ! --------------------------- |
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202 | ! |
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203 | !! Matrix inversion from the first level |
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204 | !!---------------------------------------------------------------------- |
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205 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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206 | ! |
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207 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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208 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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209 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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210 | ! ( ... )( ... ) ( ... ) |
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211 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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212 | ! |
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213 | ! m is decomposed in the product of an upper and lower triangular matrix |
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214 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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215 | ! The second member is in 2d array zwy |
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216 | ! The solution is in 2d array zwx |
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217 | ! The 3d arry zwt is a work space array |
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218 | ! zwy is used and then used as a work space array : its value is modified! |
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219 | |
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220 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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221 | DO jj = 2, jpjm1 |
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222 | DO ji = fs_2, fs_jpim1 |
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223 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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224 | END DO |
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225 | END DO |
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226 | DO jk = 2, jpkm1 |
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227 | DO jj = 2, jpjm1 |
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228 | DO ji = fs_2, fs_jpim1 |
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229 | 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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230 | END DO |
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231 | END DO |
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232 | END DO |
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233 | END IF |
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234 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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235 | DO jj = 2, jpjm1 |
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236 | DO ji = fs_2, fs_jpim1 |
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237 | ze3tb = 1._wp |
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238 | ze3tn = 1._wp |
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239 | pta_tl(ji,jj,1,jn) = ze3tb * ptb_tl(ji,jj,1,jn) + p2dt(1) * ze3tn * pta_tl(ji,jj,1,jn) |
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240 | END DO |
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241 | END DO |
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242 | |
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243 | DO jk = 2, jpkm1 |
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244 | DO jj = 2, jpjm1 |
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245 | DO ji = fs_2, fs_jpim1 |
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246 | ze3tb = 1._wp |
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247 | ze3tn = 1._wp |
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248 | zrhstl = ze3tb * ptb_tl(ji,jj,jk,jn) + p2dt(jk) * ze3tn * pta_tl(ji,jj,jk,jn) ! zrhs=right hand side |
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249 | pta_tl(ji,jj,jk,jn) = zrhstl - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * pta_tl(ji,jj,jk-1,jn) |
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250 | END DO |
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251 | END DO |
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252 | END DO |
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253 | |
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254 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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255 | ! Save the masked temperature after in ta |
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256 | ! (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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257 | DO jj = 2, jpjm1 |
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258 | DO ji = fs_2, fs_jpim1 |
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259 | pta_tl(ji,jj,jpkm1,jn) = pta_tl(ji,jj,jpkm1,jn) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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260 | END DO |
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261 | END DO |
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262 | DO jk = jpk-2, 1, -1 |
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263 | DO jj = 2, jpjm1 |
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264 | DO ji = fs_2, fs_jpim1 |
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265 | pta_tl(ji,jj,jk,jn) = ( pta_tl(ji,jj,jk,jn) - zws(ji,jj,jk) * pta_tl(ji,jj,jk+1,jn) ) & |
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266 | & / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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267 | END DO |
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268 | END DO |
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269 | END DO |
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270 | ! ! ================= ! |
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271 | END DO ! end tracer loop ! |
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272 | ! ! ================= ! |
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273 | ! |
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274 | CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwt, zwd, zws ) |
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275 | ! |
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276 | IF( nn_timing == 1 ) CALL timing_stop('tra_zdf_imp_tan') |
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277 | ! |
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278 | END SUBROUTINE tra_zdf_imp_tan |
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279 | SUBROUTINE tra_zdf_imp_adj( kt, kit000, cdtype, p2dt, ptb_ad, pta_ad, kjpt ) |
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280 | !!---------------------------------------------------------------------- |
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281 | !! *** ROUTINE tra_zdf_imp_adj *** |
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282 | !! |
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283 | !! ** Purpose of the direct routine: |
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284 | !! Compute the trend due to the vertical tracer diffusion |
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285 | !! including the vertical component of lateral mixing (only for 2nd |
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286 | !! order operator, for fourth order it is already computed and add |
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287 | !! to the general trend in traldf.F) and add it to the general trend |
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288 | !! of the tracer equations. |
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289 | !! |
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290 | !! ** Method of the direct routine : |
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291 | !! The vertical component of the lateral diffusive trends |
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292 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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293 | !! potential surfaces to which an eddy induced advection can be |
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294 | !! added. It is computed using before fields (forward in time) and |
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295 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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296 | !! |
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297 | !! Second part: vertical trend associated with the vertical physics |
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298 | !! =========== (including the vertical flux proportional to dk[t] |
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299 | !! associated with the lateral mixing, through the |
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300 | !! update of avt) |
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301 | !! The vertical diffusion of tracers (t & s) is given by: |
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302 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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303 | !! It is computed using a backward time scheme (t=ta). |
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304 | !! Surface and bottom boundary conditions: no diffusive flux on |
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305 | !! both tracers (bottom, applied through the masked field avt). |
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306 | !! Add this trend to the general trend ta,sa : |
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307 | !! ta = ta + dz( avt dz(t) ) |
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308 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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309 | !! |
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310 | !! Third part: recover avt resulting from the vertical physics |
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311 | !! ========== alone, for further diagnostics (for example to |
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312 | !! compute the turbocline depth in zdfmxl.F90). |
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313 | !! avt = zavt |
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314 | !! (avs = zavs if lk_zdfddm=T ) |
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315 | !! |
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316 | !! ** Remarks on the adjoint routine : - key_vvl is not available in adjoint yet. |
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317 | !! Once it will be this routine wil need to be rewritten |
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318 | !! - simplified version, slopes (wslp[ij]) |
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319 | !! assumed to be constant (read from the trajectory). same for av[ts] |
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320 | !! |
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321 | !!--------------------------------------------------------------------- |
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322 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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323 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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324 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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325 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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326 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
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327 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: ptb_ad ! before and now tracer fields |
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328 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta_ad ! tracer trend |
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329 | !! * Local declarations |
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330 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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331 | REAL(wp) :: zavi, zrhsad, znvvl, & ! temporary scalars |
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332 | ze3tb, ze3tn, ze3ta, zvsfvvl ! variable vertical scale factors |
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333 | REAL(wp), POINTER, DIMENSION(:,:,:) :: & |
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334 | zwi, zwt, zws, zwd ! workspace arrays |
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335 | !!--------------------------------------------------------------------- |
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336 | ! |
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337 | IF( nn_timing == 1 ) CALL timing_start('tra_zdf_imp_adj') |
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338 | ! |
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339 | CALL wrk_alloc( jpi, jpj, jpk, zwi, zwt, zws, zwd ) |
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340 | ! |
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341 | IF( kt == nitend ) THEN |
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342 | IF(lwp)WRITE(numout,*) |
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343 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp_adj : implicit vertical mixing on', cdtype |
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344 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~~~~~ ' |
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345 | ENDIF |
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346 | |
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347 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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348 | ! ------------------- |
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349 | ! ... not available in tangent yet |
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350 | ! II. Vertical trend associated with the vertical physics |
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351 | ! ======================================================= |
---|
352 | ! (including the vertical flux proportional to dk[t] associated |
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353 | ! with the lateral mixing, through the avt update) |
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354 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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355 | DO jn = 1, kjpt ! tracer loop ! |
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356 | ! ! ============= ! |
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357 | ! |
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358 | ! Matrix construction |
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359 | ! -------------------- |
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360 | ! Build matrix if temperature or salinity (only in double diffusion case) or first passive tracer |
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361 | ! |
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362 | IF( ( cdtype == 'TRA' .AND. ( jn == jp_tem .OR. ( jn == jp_sal .AND. lk_zdfddm ) ) ) .OR. & |
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363 | & ( cdtype == 'TRC' .AND. jn == 1 ) ) THEN |
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364 | ! |
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365 | ! vertical mixing coef.: avt for temperature, avs for salinity and passive tracers |
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366 | IF( cdtype == 'TRA' .AND. jn == jp_tem ) THEN ; zwt(:,:,2:jpk) = avt (:,:,2:jpk) |
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367 | ELSE ; zwt(:,:,2:jpk) = fsavs(:,:,2:jpk) |
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368 | ENDIF |
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369 | zwt(:,:,1) = 0._wp |
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370 | |
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371 | #if defined key_ldfslp |
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372 | ! update and save of avt (and avs if double diffusive mixing) |
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373 | IF ( ln_traldf_grif ) THEN |
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374 | IF ( lwp ) WRITE(numout, *) 'Griffies operator for lateral tracer diffusion not avaible in TAM yet' |
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375 | CALL abort |
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376 | ELSE IF( l_traldf_rot ) THEN |
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377 | DO jk = 2, jpkm1 |
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378 | DO jj = 2, jpjm1 |
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379 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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380 | zwt(ji,jj,jk) = zwt(ji,jj,jk) + fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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381 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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382 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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383 | END DO |
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384 | END DO |
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385 | END DO |
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386 | ENDIF |
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387 | #endif |
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388 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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389 | DO jk = 1, jpkm1 |
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390 | DO jj = 2, jpjm1 |
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391 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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392 | ze3ta = 1._wp ! after scale factor at T-point |
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393 | ze3tn = fse3t(ji,jj,jk) ! now scale factor at T-point |
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394 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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395 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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396 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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397 | END DO |
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398 | END DO |
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399 | END DO |
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400 | |
---|
401 | !! Matrix inversion from the first level |
---|
402 | !!---------------------------------------------------------------------- |
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403 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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404 | ! |
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405 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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406 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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407 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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408 | ! ( ... )( ... ) ( ... ) |
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409 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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410 | ! |
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411 | ! m is decomposed in the product of an upper and lower triangular matrix |
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412 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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413 | ! The second member is in 2d array zwy |
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414 | ! The solution is in 2d array zwx |
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415 | ! The 3d arry zwt is a work space array |
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416 | ! zwy is used and then used as a work space array : its value is modified! |
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417 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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418 | DO jj = 2, jpjm1 |
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419 | DO ji = fs_2, fs_jpim1 |
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420 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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421 | END DO |
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422 | END DO |
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423 | DO jk = 2, jpkm1 |
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424 | DO jj = 2, jpjm1 |
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425 | DO ji = fs_2, fs_jpim1 |
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426 | 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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427 | END DO |
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428 | END DO |
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429 | END DO |
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430 | END IF |
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431 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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432 | ! Save the masked temperature after in ta |
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433 | ! (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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434 | DO jk = 1, jpk-2 |
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435 | DO jj = 2, jpjm1 |
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436 | DO ji = fs_2, fs_jpim1 |
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437 | pta_ad(ji,jj,jk+1,jn) = pta_ad(ji,jj,jk+1,jn) - zws(ji,jj,jk) * pta_ad(ji,jj,jk,jn) & |
---|
438 | & / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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439 | pta_ad(ji,jj,jk,jn) = pta_ad(ji,jj,jk,jn) / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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440 | END DO |
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441 | END DO |
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442 | END DO |
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443 | DO jj = 2, jpjm1 |
---|
444 | DO ji = fs_2, fs_jpim1 |
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445 | pta_ad(ji,jj,jpkm1,jn) = pta_ad(ji,jj,jpkm1,jn) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
---|
446 | END DO |
---|
447 | END DO |
---|
448 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
---|
449 | DO jk = jpkm1, 2, -1 |
---|
450 | DO jj = 2, jpjm1 |
---|
451 | DO ji = fs_2, fs_jpim1 |
---|
452 | ze3tb = 1._wp |
---|
453 | ze3tn = 1._wp |
---|
454 | zrhsad = zrhsad + pta_ad(ji,jj,jk,jn) |
---|
455 | pta_ad(ji,jj,jk-1,jn) = pta_ad(ji,jj,jk-1,jn) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * pta_ad(ji,jj,jk,jn) |
---|
456 | pta_ad(ji,jj,jk,jn) = 0.0_wp |
---|
457 | ptb_ad(ji,jj,jk,jn) = ptb_ad(ji,jj,jk,jn) + ze3tb * zrhsad |
---|
458 | pta_ad(ji,jj,jk,jn) = pta_ad(ji,jj,jk,jn) + p2dt(jk) * ze3tn * zrhsad |
---|
459 | zrhsad = 0.0_wp |
---|
460 | END DO |
---|
461 | END DO |
---|
462 | END DO |
---|
463 | DO jj = 2, jpjm1 |
---|
464 | DO ji = fs_2, fs_jpim1 |
---|
465 | ze3tb = 1._wp |
---|
466 | ze3tn = 1._wp |
---|
467 | ptb_ad(ji,jj,1,jn) = ptb_ad(ji,jj,1,jn) + ze3tb * pta_ad(ji,jj,1,jn) |
---|
468 | pta_ad(ji,jj,1,jn) = pta_ad(ji,jj,1,jn) * p2dt(1) * ze3tn |
---|
469 | END DO |
---|
470 | END DO |
---|
471 | END DO |
---|
472 | ! |
---|
473 | CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwt, zws, zwd ) |
---|
474 | ! |
---|
475 | IF( nn_timing == 1 ) CALL timing_stop('tra_zdf_imp_adj') |
---|
476 | ! |
---|
477 | END SUBROUTINE tra_zdf_imp_adj |
---|
478 | SUBROUTINE tra_zdf_imp_adj_tst( kumadt ) |
---|
479 | !!----------------------------------------------------------------------- |
---|
480 | !! |
---|
481 | !! *** ROUTINE tra_zdf_imp_adj_tst *** |
---|
482 | !! |
---|
483 | !! ** Purpose : Test the adjoint routine. |
---|
484 | !! |
---|
485 | !! ** Method : Verify the scalar product |
---|
486 | !! |
---|
487 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
488 | !! |
---|
489 | !! where L = tangent routine |
---|
490 | !! L^T = adjoint routine |
---|
491 | !! W = diagonal matrix of scale factors |
---|
492 | !! dx = input perturbation (random field) |
---|
493 | !! dy = L dx |
---|
494 | !! |
---|
495 | !! |
---|
496 | !! History : |
---|
497 | !! ! 08-08 (A. Vidard) |
---|
498 | !!----------------------------------------------------------------------- |
---|
499 | !! * Modules used |
---|
500 | |
---|
501 | !! * Arguments |
---|
502 | INTEGER, INTENT(IN) :: & |
---|
503 | & kumadt ! Output unit |
---|
504 | |
---|
505 | !! * Local declarations |
---|
506 | INTEGER :: & |
---|
507 | & istp, & |
---|
508 | & jstp, & |
---|
509 | & ji, & ! dummy loop indices |
---|
510 | & jj, & |
---|
511 | & jk |
---|
512 | REAL(KIND=wp) :: & |
---|
513 | & zsp1, & ! scalar product involving the tangent routine |
---|
514 | & zsp2 ! scalar product involving the adjoint routine |
---|
515 | REAL(KIND=wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
516 | & zta_tlin , & ! Tangent input |
---|
517 | & ztb_tlin , & ! Tangent input |
---|
518 | & zsa_tlin , & ! Tangent input |
---|
519 | & zsb_tlin , & ! Tangent input |
---|
520 | & zta_tlout, & ! Tangent output |
---|
521 | & zsa_tlout, & ! Tangent output |
---|
522 | & zta_adin , & ! Adjoint input |
---|
523 | & zsa_adin , & ! Adjoint input |
---|
524 | & zta_adout, & ! Adjoint output |
---|
525 | & ztb_adout, & ! Adjoint output |
---|
526 | & zsa_adout, & ! Adjoint output |
---|
527 | & zsb_adout, & ! Adjoint output |
---|
528 | & zr ! 3D random field |
---|
529 | CHARACTER(LEN=14) :: cl_name |
---|
530 | ! Allocate memory |
---|
531 | |
---|
532 | ALLOCATE( & |
---|
533 | & zta_tlin( jpi,jpj,jpk), & |
---|
534 | & zsa_tlin( jpi,jpj,jpk), & |
---|
535 | & ztb_tlin( jpi,jpj,jpk), & |
---|
536 | & zsb_tlin( jpi,jpj,jpk), & |
---|
537 | & zta_tlout(jpi,jpj,jpk), & |
---|
538 | & zsa_tlout(jpi,jpj,jpk), & |
---|
539 | & zta_adin( jpi,jpj,jpk), & |
---|
540 | & zsa_adin( jpi,jpj,jpk), & |
---|
541 | & zta_adout(jpi,jpj,jpk), & |
---|
542 | & zsa_adout(jpi,jpj,jpk), & |
---|
543 | & ztb_adout(jpi,jpj,jpk), & |
---|
544 | & zsb_adout(jpi,jpj,jpk), & |
---|
545 | & zr( jpi,jpj,jpk) & |
---|
546 | & ) |
---|
547 | !================================================================== |
---|
548 | ! 1) dx = ( un_tl, vn_tl, hdivn_tl ) and |
---|
549 | ! dy = ( hdivb_tl, hdivn_tl ) |
---|
550 | !================================================================== |
---|
551 | |
---|
552 | ! initialization (normally done in traldf) |
---|
553 | l_traldf_rot = .TRUE. |
---|
554 | |
---|
555 | ! Test for time steps nit000 and nit000 + 1 (the matrix changes) |
---|
556 | |
---|
557 | DO jstp = nit000, nit000 + 2 |
---|
558 | istp = jstp |
---|
559 | IF ( jstp == nit000+2 ) istp = nitend |
---|
560 | |
---|
561 | !-------------------------------------------------------------------- |
---|
562 | ! Reset the tangent and adjoint variables |
---|
563 | !-------------------------------------------------------------------- |
---|
564 | zta_tlin( :,:,:) = 0.0_wp |
---|
565 | ztb_tlin( :,:,:) = 0.0_wp |
---|
566 | zsa_tlin( :,:,:) = 0.0_wp |
---|
567 | zsb_tlin( :,:,:) = 0.0_wp |
---|
568 | zta_tlout(:,:,:) = 0.0_wp |
---|
569 | zsa_tlout(:,:,:) = 0.0_wp |
---|
570 | zta_adin( :,:,:) = 0.0_wp |
---|
571 | zsa_adin( :,:,:) = 0.0_wp |
---|
572 | zta_adout(:,:,:) = 0.0_wp |
---|
573 | zsa_adout(:,:,:) = 0.0_wp |
---|
574 | ztb_adout(:,:,:) = 0.0_wp |
---|
575 | zsb_adout(:,:,:) = 0.0_wp |
---|
576 | zr( :,:,:) = 0.0_wp |
---|
577 | tsb_ad(:,:,:,:) = 0.0_wp |
---|
578 | tsb_ad(:,:,:,:) = 0.0_wp |
---|
579 | !-------------------------------------------------------------------- |
---|
580 | ! Initialize the tangent input with random noise: dx |
---|
581 | !-------------------------------------------------------------------- |
---|
582 | |
---|
583 | CALL grid_random( zr, 'T', 0.0_wp, stdt ) |
---|
584 | DO jk = 1, jpk |
---|
585 | DO jj = nldj, nlej |
---|
586 | DO ji = nldi, nlei |
---|
587 | zta_tlin(ji,jj,jk) = zr(ji,jj,jk) |
---|
588 | END DO |
---|
589 | END DO |
---|
590 | END DO |
---|
591 | CALL grid_random( zr, 'T', 0.0_wp, stdt ) |
---|
592 | DO jk = 1, jpk |
---|
593 | DO jj = nldj, nlej |
---|
594 | DO ji = nldi, nlei |
---|
595 | ztb_tlin(ji,jj,jk) = zr(ji,jj,jk) |
---|
596 | END DO |
---|
597 | END DO |
---|
598 | END DO |
---|
599 | CALL grid_random( zr, 'T', 0.0_wp, stds ) |
---|
600 | DO jk = 1, jpk |
---|
601 | DO jj = nldj, nlej |
---|
602 | DO ji = nldi, nlei |
---|
603 | zsa_tlin(ji,jj,jk) = zr(ji,jj,jk) |
---|
604 | END DO |
---|
605 | END DO |
---|
606 | END DO |
---|
607 | CALL grid_random( zr, 'T', 0.0_wp, stds ) |
---|
608 | DO jk = 1, jpk |
---|
609 | DO jj = nldj, nlej |
---|
610 | DO ji = nldi, nlei |
---|
611 | zsb_tlin(ji,jj,jk) = zr(ji,jj,jk) |
---|
612 | END DO |
---|
613 | END DO |
---|
614 | END DO |
---|
615 | |
---|
616 | |
---|
617 | tsa_tl(:,:,:,jp_tem) = zta_tlin(:,:,:) |
---|
618 | tsa_tl(:,:,:,jp_sal) = zsa_tlin(:,:,:) |
---|
619 | tsb_tl(:,:,:,jp_tem) = ztb_tlin(:,:,:) |
---|
620 | tsb_tl(:,:,:,jp_sal) = zsb_tlin(:,:,:) |
---|
621 | CALL tra_zdf_imp_tan ( istp, nit000, 'TRA', r2dtra, tsb_tl, tsa_tl, jpts ) |
---|
622 | zta_tlout(:,:,:) = tsa_tl(:,:,:,jp_tem) |
---|
623 | zsa_tlout(:,:,:) = tsa_tl(:,:,:,jp_sal) |
---|
624 | |
---|
625 | !-------------------------------------------------------------------- |
---|
626 | ! Initialize the adjoint variables: dy^* = W dy |
---|
627 | !-------------------------------------------------------------------- |
---|
628 | |
---|
629 | DO jk = 1, jpk |
---|
630 | DO jj = nldj, nlej |
---|
631 | DO ji = nldi, nlei |
---|
632 | zta_adin(ji,jj,jk) = zta_tlout(ji,jj,jk) & |
---|
633 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) & |
---|
634 | & * tmask(ji,jj,jk) * wesp_t(jk) |
---|
635 | zsa_adin(ji,jj,jk) = zsa_tlout(ji,jj,jk) & |
---|
636 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) & |
---|
637 | & * tmask(ji,jj,jk) * wesp_s(jk) |
---|
638 | END DO |
---|
639 | END DO |
---|
640 | END DO |
---|
641 | !-------------------------------------------------------------------- |
---|
642 | ! Compute the scalar product: ( L dx )^T W dy |
---|
643 | !-------------------------------------------------------------------- |
---|
644 | |
---|
645 | zsp1 = DOT_PRODUCT( zta_tlout, zta_adin ) & |
---|
646 | & + DOT_PRODUCT( zsa_tlout, zsa_adin ) |
---|
647 | |
---|
648 | !-------------------------------------------------------------------- |
---|
649 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
650 | !-------------------------------------------------------------------- |
---|
651 | |
---|
652 | tsa_ad(:,:,:,jp_tem) = zta_adin(:,:,:) |
---|
653 | tsa_ad(:,:,:,jp_sal) = zsa_adin(:,:,:) |
---|
654 | |
---|
655 | CALL tra_zdf_imp_adj ( istp, nit000, 'TRA', r2dtra, tsb_ad, tsa_ad, jpts ) |
---|
656 | |
---|
657 | zta_adout(:,:,:) = tsa_ad(:,:,:,jp_tem) |
---|
658 | zsa_adout(:,:,:) = tsa_ad(:,:,:,jp_sal) |
---|
659 | ztb_adout(:,:,:) = tsb_ad(:,:,:,jp_tem) |
---|
660 | zsb_adout(:,:,:) = tsb_ad(:,:,:,jp_sal) |
---|
661 | zsp2 = DOT_PRODUCT( zta_tlin, zta_adout ) & |
---|
662 | & + DOT_PRODUCT( zsa_tlin, zsa_adout ) & |
---|
663 | & + DOT_PRODUCT( ztb_tlin, ztb_adout ) & |
---|
664 | & + DOT_PRODUCT( zsb_tlin, zsb_adout ) |
---|
665 | |
---|
666 | ! 14 char:'12345678901234' |
---|
667 | IF ( istp == nit000 ) THEN |
---|
668 | cl_name = 'trazdfimpadjT1' |
---|
669 | ELSEIF ( istp == nit000 +1 ) THEN |
---|
670 | cl_name = 'trazdfimpadjT2' |
---|
671 | ELSEIF ( istp == nitend ) THEN |
---|
672 | cl_name = 'trazdfimpadjT3' |
---|
673 | END IF |
---|
674 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
675 | |
---|
676 | END DO |
---|
677 | |
---|
678 | DEALLOCATE( & |
---|
679 | & zta_tlin, & |
---|
680 | & ztb_tlin, & |
---|
681 | & zsa_tlin, & |
---|
682 | & zsb_tlin, & |
---|
683 | & zta_tlout, & |
---|
684 | & zsa_tlout, & |
---|
685 | & zta_adin, & |
---|
686 | & zsa_adin, & |
---|
687 | & zta_adout, & |
---|
688 | & ztb_adout, & |
---|
689 | & zsa_adout, & |
---|
690 | & zsb_adout, & |
---|
691 | & zr & |
---|
692 | & ) |
---|
693 | |
---|
694 | |
---|
695 | |
---|
696 | END SUBROUTINE tra_zdf_imp_adj_tst |
---|
697 | #endif |
---|
698 | END MODULE trazdf_imp_tam |
---|