1 | MODULE traldf_iso |
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2 | !!====================================================================== |
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3 | !! *** MODULE traldf_iso *** |
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4 | !! Ocean tracers: horizontal component of the lateral tracer mixing trend |
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5 | !!====================================================================== |
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6 | !! History : OPA ! 1994-08 (G. Madec, M. Imbard) |
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7 | !! 8.0 ! 1997-05 (G. Madec) split into traldf and trazdf |
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8 | !! NEMO ! 2002-08 (G. Madec) Free form, F90 |
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9 | !! 1.0 ! 2005-11 (G. Madec) merge traldf and trazdf :-) |
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10 | !! 3.3 ! 2010-09 (C. Ethe, G. Madec) Merge TRA-TRC |
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11 | !!---------------------------------------------------------------------- |
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12 | #if defined key_ldfslp || defined key_esopa |
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13 | !!---------------------------------------------------------------------- |
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14 | !! 'key_ldfslp' slope of the lateral diffusive direction |
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15 | !!---------------------------------------------------------------------- |
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16 | !! tra_ldf_iso : update the tracer trend with the horizontal |
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17 | !! component of a iso-neutral laplacian operator |
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18 | !! and with the vertical part of |
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19 | !! the isopycnal or geopotential s-coord. operator |
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20 | !!---------------------------------------------------------------------- |
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21 | USE oce ! ocean dynamics and active tracers |
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22 | USE dom_oce ! ocean space and time domain |
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23 | USE trc_oce ! share passive tracers/Ocean variables |
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24 | USE zdf_oce ! ocean vertical physics |
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25 | USE ldftra_oce ! ocean active tracers: lateral physics |
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26 | USE ldfslp ! iso-neutral slopes |
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27 | USE diaptr ! poleward transport diagnostics |
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28 | USE trd_oce ! trends: ocean variables |
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29 | USE trdtra ! trends manager: tracers |
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30 | USE in_out_manager ! I/O manager |
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31 | USE iom ! I/O library |
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32 | USE phycst ! physical constants |
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33 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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34 | USE timing ! Timing |
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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_ldf_iso ! 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 "vectopt_loop_substitute.h90" |
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45 | !!---------------------------------------------------------------------- |
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46 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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47 | !! $Id$ |
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48 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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49 | !!---------------------------------------------------------------------- |
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50 | CONTAINS |
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51 | |
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52 | SUBROUTINE tra_ldf_iso( kt, kit000, cdtype, pgu, pgv, & |
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53 | & pgui, pgvi, & |
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54 | & ptb, pta, kjpt, pahtb0 ) |
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55 | !!---------------------------------------------------------------------- |
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56 | !! *** ROUTINE tra_ldf_iso *** |
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57 | !! |
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58 | !! ** Purpose : Compute the before horizontal tracer (t & s) diffusive |
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59 | !! trend for a laplacian tensor (ezxcept the dz[ dz[.] ] term) and |
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60 | !! add it to the general trend of tracer equation. |
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61 | !! |
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62 | !! ** Method : The horizontal component of the lateral diffusive trends |
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63 | !! is provided by a 2nd order operator rotated along neural or geopo- |
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64 | !! tential surfaces to which an eddy induced advection can be added |
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65 | !! It is computed using before fields (forward in time) and isopyc- |
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66 | !! nal or geopotential slopes computed in routine ldfslp. |
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67 | !! |
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68 | !! 1st part : masked horizontal derivative of T ( di[ t ] ) |
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69 | !! ======== with partial cell update if ln_zps=T. |
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70 | !! |
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71 | !! 2nd part : horizontal fluxes of the lateral mixing operator |
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72 | !! ======== |
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73 | !! zftu = (aht+ahtb0) e2u*e3u/e1u di[ tb ] |
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74 | !! - aht e2u*uslp dk[ mi(mk(tb)) ] |
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75 | !! zftv = (aht+ahtb0) e1v*e3v/e2v dj[ tb ] |
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76 | !! - aht e2u*vslp dk[ mj(mk(tb)) ] |
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77 | !! take the horizontal divergence of the fluxes: |
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78 | !! difft = 1/(e1t*e2t*e3t) { di-1[ zftu ] + dj-1[ zftv ] } |
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79 | !! Add this trend to the general trend (ta,sa): |
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80 | !! ta = ta + difft |
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81 | !! |
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82 | !! 3rd part: vertical trends of the lateral mixing operator |
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83 | !! ======== (excluding the vertical flux proportional to dk[t] ) |
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84 | !! vertical fluxes associated with the rotated lateral mixing: |
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85 | !! zftw =-aht { e2t*wslpi di[ mi(mk(tb)) ] |
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86 | !! + e1t*wslpj dj[ mj(mk(tb)) ] } |
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87 | !! take the horizontal divergence of the fluxes: |
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88 | !! difft = 1/(e1t*e2t*e3t) dk[ zftw ] |
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89 | !! Add this trend to the general trend (ta,sa): |
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90 | !! pta = pta + difft |
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91 | !! |
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92 | !! ** Action : Update pta arrays with the before rotated diffusion |
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93 | !!---------------------------------------------------------------------- |
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94 | USE oce , ONLY: zftu => ua , zftv => va ! (ua,va) used as workspace |
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95 | ! |
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96 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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97 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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98 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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99 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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100 | REAL(wp), DIMENSION(jpi,jpj ,kjpt), INTENT(in ) :: pgu , pgv ! tracer gradient at pstep levels |
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101 | REAL(wp), DIMENSION(jpi,jpj ,kjpt), INTENT(in ) :: pgui, pgvi ! tracer gradient at pstep levels |
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102 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields |
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103 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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104 | REAL(wp) , INTENT(in ) :: pahtb0 ! background diffusion coef |
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105 | ! |
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106 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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107 | INTEGER :: ikt |
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108 | REAL(wp) :: zmsku, zabe1, zcof1, zcoef3 ! local scalars |
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109 | REAL(wp) :: zmskv, zabe2, zcof2, zcoef4 ! - - |
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110 | REAL(wp) :: zcoef0, zbtr ! - - |
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111 | REAL(wp), ALLOCATABLE, DIMENSION(:,: ) :: z2d |
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112 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zdkt, zdk1t, zdit, zdjt, ztfw |
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113 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:), TARGET :: ztrax, ztray, ztraz |
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114 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:), TARGET :: ztrax_T, ztray_T, ztraz_T |
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115 | !!---------------------------------------------------------------------- |
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116 | ! |
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117 | IF( nn_timing == 1 ) CALL timing_start('tra_ldf_iso') |
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118 | ! |
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119 | ALLOCATE( z2d(1:jpi, 1:jpj)) |
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120 | ALLOCATE( zdit(1:jpi, 1:jpj, 1:jpk)) |
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121 | ALLOCATE( zdjt(1:jpi, 1:jpj, 1:jpk)) |
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122 | ALLOCATE( ztfw(1:jpi, 1:jpj, 1:jpk)) |
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123 | ALLOCATE( zdkt(1:jpi, 1:jpj, 1:jpk)) |
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124 | ALLOCATE( zdk1t(1:jpi, 1:jpj, 1:jpk)) |
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125 | ALLOCATE( ztrax(1:jpi,1:jpj,1:jpk)) |
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126 | ALLOCATE( ztray(1:jpi,1:jpj,1:jpk)) |
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127 | ALLOCATE( ztraz(1:jpi,1:jpj,1:jpk) ) |
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128 | IF( l_trdtra .and. cdtype == 'TRA' ) THEN |
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129 | ALLOCATE( ztrax_T(1:jpi,1:jpj,1:jpk)) |
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130 | ALLOCATE( ztray_T(1:jpi,1:jpj,1:jpk)) |
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131 | ALLOCATE( ztraz_T(1:jpi,1:jpj,1:jpk)) |
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132 | ENDIF |
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133 | ! |
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134 | |
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135 | IF( kt == kit000 ) THEN |
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136 | IF(lwp) WRITE(numout,*) |
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137 | IF(lwp) WRITE(numout,*) 'tra_ldf_iso : rotated laplacian diffusion operator on ', cdtype |
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138 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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139 | ENDIF |
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140 | ! |
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141 | ! ! =========== |
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142 | DO jn = 1, kjpt ! tracer loop |
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143 | ! ! =========== |
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144 | ztrax(:,:,:) = 0._wp ; ztray(:,:,:) = 0._wp ; ztraz(:,:,:) = 0._wp ; |
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145 | ! |
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146 | !!---------------------------------------------------------------------- |
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147 | !! I - masked horizontal derivative |
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148 | !!---------------------------------------------------------------------- |
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149 | !!bug ajout.... why? ( 1,jpj,:) and (jpi,1,:) should be sufficient.... |
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150 | zdit (1,:,:) = 0.e0 ; zdit (jpi,:,:) = 0.e0 |
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151 | zdjt (1,:,:) = 0.e0 ; zdjt (jpi,:,:) = 0.e0 |
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152 | !!end |
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153 | |
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154 | ! Horizontal tracer gradient |
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155 | DO jk = 1, jpkm1 |
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156 | DO jj = 1, jpjm1 |
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157 | DO ji = 1, fs_jpim1 ! vector opt. |
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158 | zdit(ji,jj,jk) = ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
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159 | zdjt(ji,jj,jk) = ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
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160 | END DO |
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161 | END DO |
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162 | END DO |
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163 | |
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164 | ! partial cell correction |
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165 | IF( ln_zps ) THEN ! partial steps correction at the last ocean level |
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166 | DO jj = 1, jpjm1 |
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167 | DO ji = 1, fs_jpim1 ! vector opt. |
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168 | ! IF useless if zpshde defines pgu everywhere |
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169 | zdit(ji,jj,mbku(ji,jj)) = pgu(ji,jj,jn) |
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170 | zdjt(ji,jj,mbkv(ji,jj)) = pgv(ji,jj,jn) |
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171 | END DO |
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172 | END DO |
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173 | ENDIF |
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174 | IF( ln_zps .AND. ln_isfcav ) THEN ! partial steps correction at the first wet level beneath a cavity |
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175 | DO jj = 1, jpjm1 |
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176 | DO ji = 1, fs_jpim1 ! vector opt. |
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177 | IF (miku(ji,jj) > 1) zdit(ji,jj,miku(ji,jj)) = pgui(ji,jj,jn) |
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178 | IF (mikv(ji,jj) > 1) zdjt(ji,jj,mikv(ji,jj)) = pgvi(ji,jj,jn) |
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179 | END DO |
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180 | END DO |
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181 | END IF |
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182 | |
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183 | !!---------------------------------------------------------------------- |
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184 | !! II - horizontal trend (full) |
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185 | !!---------------------------------------------------------------------- |
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186 | !!!!!!!!!!CDIR PARALLEL DO PRIVATE( zdk1t ) |
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187 | ! 1. Vertical tracer gradient at level jk and jk+1 |
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188 | ! ------------------------------------------------ |
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189 | ! |
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190 | ! interior value |
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191 | DO jk = 2, jpkm1 |
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192 | DO jj = 1, jpj |
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193 | DO ji = 1, jpi ! vector opt. |
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194 | zdk1t(ji,jj,jk) = ( ptb(ji,jj,jk,jn ) - ptb(ji,jj,jk+1,jn) ) * wmask(ji,jj,jk+1) |
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195 | ! |
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196 | zdkt(ji,jj,jk) = ( ptb(ji,jj,jk-1,jn) - ptb(ji,jj,jk,jn ) ) * wmask(ji,jj,jk) |
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197 | END DO |
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198 | END DO |
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199 | END DO |
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200 | ! surface boundary condition: zdkt(jk=1)=zdkt(jk=2) |
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201 | zdk1t(:,:,1) = ( ptb(:,:,1,jn ) - ptb(:,:,2,jn) ) * wmask(:,:,2) |
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202 | zdkt (:,:,1) = zdk1t(:,:,1) |
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203 | IF ( ln_isfcav ) THEN |
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204 | DO jj = 1, jpj |
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205 | DO ji = 1, jpi ! vector opt. |
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206 | ikt = mikt(ji,jj) ! surface level |
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207 | zdk1t(ji,jj,ikt) = ( ptb(ji,jj,ikt,jn ) - ptb(ji,jj,ikt+1,jn) ) * wmask(ji,jj,ikt+1) |
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208 | zdkt (ji,jj,ikt) = zdk1t(ji,jj,ikt) |
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209 | END DO |
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210 | END DO |
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211 | END IF |
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212 | |
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213 | ! 2. Horizontal fluxes |
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214 | ! -------------------- |
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215 | DO jk = 1, jpkm1 |
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216 | DO jj = 1 , jpjm1 |
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217 | DO ji = 1, fs_jpim1 ! vector opt. |
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218 | zabe1 = ( fsahtu(ji,jj,jk) + pahtb0 ) * re2u_e1u(ji,jj) * fse3u_n(ji,jj,jk) |
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219 | zabe2 = ( fsahtv(ji,jj,jk) + pahtb0 ) * re1v_e2v(ji,jj) * fse3v_n(ji,jj,jk) |
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220 | ! |
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221 | zmsku = 1. / MAX( tmask(ji+1,jj,jk ) + tmask(ji,jj,jk+1) & |
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222 | & + tmask(ji+1,jj,jk+1) + tmask(ji,jj,jk ), 1. ) |
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223 | ! |
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224 | zmskv = 1. / MAX( tmask(ji,jj+1,jk ) + tmask(ji,jj,jk+1) & |
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225 | & + tmask(ji,jj+1,jk+1) + tmask(ji,jj,jk ), 1. ) |
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226 | ! |
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227 | zcof1 = - fsahtu(ji,jj,jk) * e2u(ji,jj) * uslp(ji,jj,jk) * zmsku |
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228 | zcof2 = - fsahtv(ji,jj,jk) * e1v(ji,jj) * vslp(ji,jj,jk) * zmskv |
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229 | ! |
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230 | zftu(ji,jj,jk ) = ( zabe1 * zdit(ji,jj,jk) & |
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231 | & + zcof1 * ( zdkt (ji+1,jj,jk) + zdk1t(ji,jj,jk) & |
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232 | & + zdk1t(ji+1,jj,jk) + zdkt (ji,jj,jk) ) ) * umask(ji,jj,jk) |
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233 | zftv(ji,jj,jk) = ( zabe2 * zdjt(ji,jj,jk) & |
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234 | & + zcof2 * ( zdkt (ji,jj+1,jk) + zdk1t(ji,jj,jk) & |
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235 | & + zdk1t(ji,jj+1,jk) + zdkt (ji,jj,jk) ) ) * vmask(ji,jj,jk) |
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236 | END DO |
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237 | END DO |
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238 | |
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239 | ! II.4 Second derivative (divergence) and add to the general trend |
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240 | ! ---------------------------------------------------------------- |
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241 | DO jj = 2 , jpjm1 |
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242 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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243 | zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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244 | ztrax(ji,jj,jk) = zbtr * ( zftu(ji,jj,jk) - zftu(ji-1,jj,jk) ) |
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245 | ztray(ji,jj,jk) = zbtr * ( zftv(ji,jj,jk) - zftv(ji,jj-1,jk) ) |
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246 | END DO |
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247 | END DO |
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248 | ! ! =============== |
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249 | END DO ! End of slab |
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250 | ! ! =============== |
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251 | ! |
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252 | pta(:,:,:,jn) = pta(:,:,:,jn) + ztrax(:,:,:) + ztray(:,:,:) |
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253 | ! |
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254 | ! "Poleward" diffusive heat or salt transports (T-S case only) |
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255 | ! note sign is reversed to give down-gradient diffusive transports (#1043) |
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256 | IF( cdtype == 'TRA' .AND. ln_diaptr ) CALL dia_ptr_ohst_components( jn, 'ldf', -zftv(:,:,:) ) |
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257 | |
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258 | IF( iom_use("udiff_heattr") .OR. iom_use("vdiff_heattr") ) THEN |
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259 | ! |
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260 | IF( cdtype == 'TRA' .AND. jn == jp_tem ) THEN |
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261 | z2d(:,:) = 0._wp |
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262 | DO jk = 1, jpkm1 |
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263 | DO jj = 2, jpjm1 |
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264 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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265 | z2d(ji,jj) = z2d(ji,jj) + zftu(ji,jj,jk) |
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266 | END DO |
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267 | END DO |
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268 | END DO |
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269 | z2d(:,:) = - rau0_rcp * z2d(:,:) ! note sign is reversed to give down-gradient diffusive transports (#1043) |
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270 | CALL lbc_lnk( z2d, 'U', -1. ) |
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271 | CALL iom_put( "udiff_heattr", z2d ) ! heat transport in i-direction |
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272 | ! |
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273 | z2d(:,:) = 0._wp |
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274 | DO jk = 1, jpkm1 |
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275 | DO jj = 2, jpjm1 |
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276 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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277 | z2d(ji,jj) = z2d(ji,jj) + zftv(ji,jj,jk) |
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278 | END DO |
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279 | END DO |
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280 | END DO |
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281 | z2d(:,:) = - rau0_rcp * z2d(:,:) ! note sign is reversed to give down-gradient diffusive transports (#1043) |
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282 | CALL lbc_lnk( z2d, 'V', -1. ) |
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283 | CALL iom_put( "vdiff_heattr", z2d ) ! heat transport in i-direction |
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284 | END IF |
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285 | ! |
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286 | ENDIF |
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287 | |
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288 | !!---------------------------------------------------------------------- |
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289 | !! III - vertical trend of T & S (extra diagonal terms only) |
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290 | !!---------------------------------------------------------------------- |
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291 | |
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292 | ! Local constant initialization |
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293 | ! ----------------------------- |
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294 | ztfw(1,:,:) = 0.e0 ; ztfw(jpi,:,:) = 0.e0 |
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295 | |
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296 | ! Vertical fluxes |
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297 | ! --------------- |
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298 | |
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299 | ! Surface and bottom vertical fluxes set to zero |
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300 | ztfw(:,:, 1 ) = 0.e0 ; ztfw(:,:,jpk) = 0.e0 |
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301 | |
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302 | ! interior (2=<jk=<jpk-1) |
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303 | DO jk = 2, jpkm1 |
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304 | DO jj = 2, jpjm1 |
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305 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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306 | zcoef0 = - fsahtw(ji,jj,jk) * wmask(ji,jj,jk) |
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307 | ! |
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308 | zmsku = 1./MAX( umask(ji ,jj,jk-1) + umask(ji-1,jj,jk) & |
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309 | & + umask(ji-1,jj,jk-1) + umask(ji ,jj,jk), 1. ) |
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310 | zmskv = 1./MAX( vmask(ji,jj ,jk-1) + vmask(ji,jj-1,jk) & |
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311 | & + vmask(ji,jj-1,jk-1) + vmask(ji,jj ,jk), 1. ) |
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312 | ! |
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313 | zcoef3 = zcoef0 * e2t(ji,jj) * zmsku * wslpi (ji,jj,jk) |
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314 | zcoef4 = zcoef0 * e1t(ji,jj) * zmskv * wslpj (ji,jj,jk) |
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315 | ! |
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316 | ztfw(ji,jj,jk) = zcoef3 * ( zdit(ji ,jj ,jk-1) + zdit(ji-1,jj ,jk) & |
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317 | & + zdit(ji-1,jj ,jk-1) + zdit(ji ,jj ,jk) ) & |
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318 | & + zcoef4 * ( zdjt(ji ,jj ,jk-1) + zdjt(ji ,jj-1,jk) & |
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319 | & + zdjt(ji ,jj-1,jk-1) + zdjt(ji ,jj ,jk) ) |
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320 | END DO |
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321 | END DO |
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322 | END DO |
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323 | |
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324 | |
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325 | ! I.5 Divergence of vertical fluxes added to the general tracer trend |
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326 | ! ------------------------------------------------------------------- |
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327 | DO jk = 1, jpkm1 |
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328 | DO jj = 2, jpjm1 |
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329 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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330 | zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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331 | ztraz(ji,jj,jk) = ( ztfw(ji,jj,jk) - ztfw(ji,jj,jk+1) ) * zbtr |
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332 | END DO |
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333 | END DO |
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334 | END DO |
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335 | pta(:,:,:,jn) = pta(:,:,:,jn) + ztraz(:,:,:) |
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336 | ! |
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337 | IF( l_trdtra .AND. cdtype == "TRA" .AND. jn .eq. 1 ) THEN ! save the temperature trends |
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338 | ztrax_T(:,:,:) = ztrax(:,:,:) |
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339 | ztray_T(:,:,:) = ztray(:,:,:) |
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340 | ztraz_T(:,:,:) = ztraz(:,:,:) |
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341 | ENDIF |
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342 | IF( l_trdtrc .AND. cdtype == "TRC" ) THEN ! save the horizontal component of diffusive trends for further diagnostics |
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343 | CALL trd_tra( kt, cdtype, jn, jptra_iso_x, ztrax ) |
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344 | CALL trd_tra( kt, cdtype, jn, jptra_iso_y, ztray ) |
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345 | CALL trd_tra( kt, cdtype, jn, jptra_iso_z1, ztraz ) ! This is the first part of the vertical component. |
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346 | ENDIF |
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347 | END DO |
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348 | ! |
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349 | IF( l_trdtra .AND. cdtype == "TRA" ) THEN ! save the horizontal component of diffusive trends for further diagnostics |
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350 | CALL trd_tra( kt, cdtype, jp_tem, jptra_iso_x, ztrax_T ) |
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351 | CALL trd_tra( kt, cdtype, jp_sal, jptra_iso_x, ztrax ) |
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352 | CALL trd_tra( kt, cdtype, jp_tem, jptra_iso_y, ztray_T ) |
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353 | CALL trd_tra( kt, cdtype, jp_sal, jptra_iso_y, ztray ) |
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354 | CALL trd_tra( kt, cdtype, jp_tem, jptra_iso_z1, ztraz_T ) ! This is the first part of the vertical component |
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355 | CALL trd_tra( kt, cdtype, jp_sal, jptra_iso_z1, ztraz ) ! |
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356 | ENDIF |
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357 | ! |
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358 | DEALLOCATE( z2d ) |
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359 | DEALLOCATE( zdit) |
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360 | DEALLOCATE( zdjt) |
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361 | DEALLOCATE( ztfw) |
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362 | DEALLOCATE( zdkt ) |
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363 | DEALLOCATE( zdk1t ) |
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364 | DEALLOCATE( ztrax, ztray, ztraz ) |
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365 | IF( l_trdtra .and. cdtype == 'TRA' ) DEALLOCATE( ztrax_T, ztray_T, ztraz_T ) |
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366 | ! |
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367 | IF( nn_timing == 1 ) CALL timing_stop('tra_ldf_iso') |
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368 | ! |
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369 | END SUBROUTINE tra_ldf_iso |
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370 | |
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371 | #else |
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372 | !!---------------------------------------------------------------------- |
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373 | !! default option : Dummy code NO rotation of the diffusive tensor |
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374 | !!---------------------------------------------------------------------- |
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375 | CONTAINS |
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376 | SUBROUTINE tra_ldf_iso( kt, kit000,cdtype, pgu, pgv, pgui, pgvi, ptb, pta, kjpt, pahtb0 ) ! Empty routine |
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377 | INTEGER:: kt, kit000 |
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378 | CHARACTER(len=3) :: cdtype |
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379 | REAL, DIMENSION(:,:,:) :: pgu, pgv, pgui, pgvi ! tracer gradient at pstep levels |
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380 | REAL, DIMENSION(:,:,:,:) :: ptb, pta |
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381 | WRITE(*,*) 'tra_ldf_iso: You should not have seen this print! error?', kt, kit000, cdtype, & |
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382 | & pgu(1,1,1), pgv(1,1,1), ptb(1,1,1,1), pta(1,1,1,1), kjpt, pahtb0 |
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383 | END SUBROUTINE tra_ldf_iso |
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384 | #endif |
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385 | |
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386 | !!============================================================================== |
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387 | END MODULE traldf_iso |
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