1 | MODULE traldf_bilapg |
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2 | !!============================================================================== |
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3 | !! *** MODULE traldf_bilapg *** |
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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 : 8.0 ! 1997-07 (G. Madec) Original code |
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7 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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8 | !! 3.3 ! 2010-06 (C. Ethe, G. Madec) Merge TRA-TRC |
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9 | !!============================================================================== |
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10 | #if defined key_ldfslp || defined key_esopa |
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11 | !!---------------------------------------------------------------------- |
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12 | !! 'key_ldfslp' rotation of the lateral mixing tensor |
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13 | !!---------------------------------------------------------------------- |
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14 | !! tra_ldf_bilapg : update the tracer trend with the horizontal diffusion |
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15 | !! using an horizontal biharmonic operator in s-coordinate |
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16 | !! ldfght : ??? |
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17 | !!---------------------------------------------------------------------- |
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18 | USE oce ! ocean dynamics and tracers variables |
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19 | USE dom_oce ! ocean space and time domain variables |
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20 | USE ldftra_oce ! ocean active tracers: lateral physics |
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21 | USE in_out_manager ! I/O manager |
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22 | USE ldfslp ! iso-neutral slopes available |
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23 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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24 | USE diaptr ! poleward transport diagnostics |
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25 | USE trc_oce ! share passive tracers/Ocean variables |
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26 | USE lib_mpp ! MPP library |
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27 | USE wrk_nemo ! Memory Allocation |
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28 | USE timing ! Timing |
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29 | |
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30 | IMPLICIT NONE |
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31 | PRIVATE |
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32 | |
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33 | PUBLIC tra_ldf_bilapg ! routine called by step.F90 |
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34 | |
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35 | !! * Substitutions |
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36 | # include "domzgr_substitute.h90" |
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37 | # include "ldftra_substitute.h90" |
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38 | # include "ldfeiv_substitute.h90" |
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39 | !!---------------------------------------------------------------------- |
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40 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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41 | !! $Id$ |
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42 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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43 | !!---------------------------------------------------------------------- |
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44 | CONTAINS |
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45 | |
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46 | SUBROUTINE tra_ldf_bilapg( kt, kit000, cdtype, ptb, pta, kjpt ) |
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47 | !!---------------------------------------------------------------------- |
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48 | !! *** ROUTINE tra_ldf_bilapg *** |
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49 | !! |
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50 | !! ** Purpose : Compute the before horizontal tracer diffusive |
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51 | !! trend and add it to the general trend of tracer equation. |
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52 | !! |
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53 | !! ** Method : The lateral diffusive trends is provided by a 4th order |
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54 | !! operator rotated along geopotential surfaces. It is computed |
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55 | !! using before fields (forward in time) and geopotential slopes |
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56 | !! computed in routine inildf. |
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57 | !! -1- compute the geopotential harmonic operator applied to |
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58 | !! ptb and multiply it by the eddy diffusivity coefficient |
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59 | !! (done by a call to ldfght routine, result in wk1 arrays). |
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60 | !! Applied the domain lateral boundary conditions by call to lbc_lnk |
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61 | !! -2- compute the geopotential harmonic operator applied to |
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62 | !! wk1 by a second call to ldfght routine (result in wk2) |
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63 | !! arrays). |
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64 | !! -3- Add this trend to the general trend |
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65 | !! pta = pta + wk2 |
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66 | !! |
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67 | !! ** Action : - Update pta arrays with the before geopotential |
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68 | !! biharmonic mixing trend. |
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69 | !!---------------------------------------------------------------------- |
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70 | ! |
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71 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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72 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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73 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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74 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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75 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields |
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76 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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77 | ! |
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78 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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79 | REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zwk1, zwk2 |
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80 | !!---------------------------------------------------------------------- |
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81 | ! |
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82 | IF( nn_timing == 1 ) CALL timing_start('tra_ldf_bilapg') |
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83 | ! |
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84 | CALL wrk_alloc( jpi, jpj, jpk, kjpt, zwk1, zwk2 ) |
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85 | ! |
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86 | IF( kt == kit000 ) THEN |
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87 | IF(lwp) WRITE(numout,*) |
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88 | IF(lwp) WRITE(numout,*) 'tra_ldf_bilapg : horizontal biharmonic operator in s-coordinate on ', cdtype |
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89 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~' |
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90 | ENDIF |
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91 | |
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92 | ! 1. Laplacian of ptb * aht |
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93 | ! ----------------------------- |
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94 | CALL ldfght( kt, cdtype, ptb, zwk1, kjpt, 1 ) ! rotated harmonic operator applied to ptb and multiply by aht |
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95 | ! ! output in wk1 |
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96 | ! |
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97 | DO jn = 1, kjpt |
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98 | CALL lbc_lnk( zwk1(:,:,:,jn) , 'T', 1. ) ! Lateral boundary conditions on wk1 (unchanged sign) |
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99 | END DO |
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100 | |
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101 | ! 2. Bilaplacian of ptb |
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102 | ! ------------------------- |
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103 | CALL ldfght( kt, cdtype, zwk1, zwk2, kjpt, 2 ) ! rotated harmonic operator applied to wk1 ; output in wk2 |
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104 | |
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105 | |
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106 | ! 3. Update the tracer trends (j-slab : 2, jpj-1) |
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107 | ! --------------------------- |
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108 | DO jn = 1, kjpt |
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109 | DO jj = 2, jpjm1 |
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110 | DO jk = 1, jpkm1 |
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111 | DO ji = 2, jpim1 |
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112 | ! add it to the general tracer trends |
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113 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + zwk2(ji,jj,jk,jn) |
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114 | END DO |
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115 | END DO |
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116 | END DO |
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117 | END DO |
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118 | ! |
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119 | CALL wrk_dealloc( jpi, jpj, jpk, kjpt, zwk1, zwk2 ) |
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120 | ! |
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121 | IF( nn_timing == 1 ) CALL timing_stop('tra_ldf_bilapg') |
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122 | ! |
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123 | END SUBROUTINE tra_ldf_bilapg |
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124 | |
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125 | |
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126 | SUBROUTINE ldfght ( kt, cdtype, pt, plt, kjpt, kaht ) |
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127 | !!---------------------------------------------------------------------- |
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128 | !! *** ROUTINE ldfght *** |
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129 | !! |
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130 | !! ** Purpose : Apply a geopotential harmonic operator to (pt) and |
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131 | !! multiply it by the eddy diffusivity coefficient (if kaht=1). |
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132 | !! Routine only used in s-coordinates (l_sco=T) with bilaplacian |
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133 | !! operator (ln_traldf_bilap=T) acting along geopotential surfaces |
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134 | !! (ln_traldf_hor). |
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135 | !! |
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136 | !! ** Method : The harmonic operator rotated along geopotential |
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137 | !! surfaces is applied to (pt) using the slopes of geopotential |
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138 | !! surfaces computed in inildf routine. The result is provided in |
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139 | !! (plt,pls) arrays. It is computed in 2 steps: |
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140 | !! |
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141 | !! First step: horizontal part of the operator. It is computed on |
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142 | !! ========== pt as follows (idem on ps) |
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143 | !! horizontal fluxes : |
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144 | !! zftu = e2u*e3u/e1u di[ pt ] - e2u*uslp dk[ mi(mk(pt)) ] |
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145 | !! zftv = e1v*e3v/e2v dj[ pt ] - e1v*vslp dk[ mj(mk(pt)) ] |
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146 | !! take the horizontal divergence of the fluxes (no divided by |
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147 | !! the volume element : |
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148 | !! plt = di-1[ zftu ] + dj-1[ zftv ] |
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149 | !! |
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150 | !! Second step: vertical part of the operator. It is computed on |
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151 | !! =========== pt as follows (idem on ps) |
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152 | !! vertical fluxes : |
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153 | !! zftw = e1t*e2t/e3w * (wslpi^2+wslpj^2) dk-1[ pt ] |
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154 | !! - e2t * wslpi di[ mi(mk(pt)) ] |
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155 | !! - e1t * wslpj dj[ mj(mk(pt)) ] |
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156 | !! take the vertical divergence of the fluxes add it to the hori- |
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157 | !! zontal component, divide the result by the volume element and |
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158 | !! if kaht=1, multiply by the eddy diffusivity coefficient: |
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159 | !! plt = aht / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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160 | !! else: |
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161 | !! plt = 1 / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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162 | !! |
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163 | !!---------------------------------------------------------------------- |
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164 | USE oce , ONLY: zftv => ua ! ua used as workspace |
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165 | ! |
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166 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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167 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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168 | INTEGER , INTENT(in ) :: kjpt !: dimension of |
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169 | REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,jpk,kjpt) :: pt ! tracer fields ( before for 1st call |
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170 | ! ! and laplacian of these fields for 2nd call. |
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171 | REAL(wp) , INTENT(out), DIMENSION(jpi,jpj,jpk,kjpt) :: plt !: partial harmonic operator applied to pt components except |
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172 | ! !: second order vertical derivative term |
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173 | INTEGER , INTENT(in ) :: kaht !: =1 multiply the laplacian by the eddy diffusivity coeff. |
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174 | ! !: =2 no multiplication |
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175 | !! |
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176 | INTEGER :: ji, jj, jk,jn ! dummy loop indices |
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177 | ! ! temporary scalars |
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178 | REAL(wp) :: zabe1, zabe2, zmku, zmkv |
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179 | REAL(wp) :: zbtr, ztah, ztav |
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180 | REAL(wp) :: zcof0, zcof1, zcof2, zcof3, zcof4 |
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181 | REAL(wp), POINTER, DIMENSION(:,:) :: zftu, zdkt, zdk1t |
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182 | REAL(wp), POINTER, DIMENSION(:,:) :: zftw, zdit, zdjt, zdj1t |
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183 | !!---------------------------------------------------------------------- |
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184 | ! |
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185 | IF( nn_timing == 1 ) CALL timing_start('ldfght') |
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186 | ! |
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187 | CALL wrk_alloc( jpi, jpj, zftu, zdkt, zdk1t ) |
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188 | CALL wrk_alloc( jpi, jpk, zftw, zdit, zdjt, zdj1t ) |
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189 | ! |
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190 | DO jn = 1, kjpt |
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191 | ! ! ********** ! ! =============== |
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192 | DO jk = 1, jpkm1 ! First step ! ! Horizontal slab |
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193 | ! ! ********** ! ! =============== |
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194 | |
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195 | ! I.1 Vertical gradient of pt and ps at level jk and jk+1 |
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196 | ! ------------------------------------------------------- |
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197 | ! surface boundary condition: zdkt(jk=1)=zdkt(jk=2) |
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198 | |
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199 | zdk1t(:,:) = ( pt(:,:,jk,jn) - pt(:,:,jk+1,jn) ) * tmask(:,:,jk+1) |
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200 | IF( jk == 1 ) THEN |
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201 | zdkt(:,:) = zdk1t(:,:) |
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202 | ELSE |
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203 | zdkt(:,:) = ( pt(:,:,jk-1,jn) - pt(:,:,jk,jn) ) * tmask(:,:,jk) |
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204 | ENDIF |
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205 | |
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206 | |
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207 | ! I.2 Horizontal fluxes |
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208 | ! --------------------- |
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209 | |
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210 | DO jj = 1, jpjm1 |
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211 | DO ji = 1, jpim1 |
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212 | zabe1 = re2u_e1u(ji,jj) * fse3u_n(ji,jj,jk) |
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213 | zabe2 = re1v_e2v(ji,jj) * fse3v_n(ji,jj,jk) |
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214 | |
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215 | zmku = 1./MAX( tmask(ji+1,jj,jk )+tmask(ji,jj,jk+1) & |
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216 | & +tmask(ji+1,jj,jk+1)+tmask(ji,jj,jk ),1. ) |
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217 | zmkv = 1./MAX( tmask(ji,jj+1,jk )+tmask(ji,jj,jk+1) & |
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218 | & +tmask(ji,jj+1,jk+1)+tmask(ji,jj,jk ),1. ) |
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219 | |
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220 | zcof1 = -e2u(ji,jj) * uslp(ji,jj,jk) * zmku |
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221 | zcof2 = -e1v(ji,jj) * vslp(ji,jj,jk) * zmkv |
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222 | |
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223 | zftu(ji,jj)= umask(ji,jj,jk) * & |
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224 | & ( zabe1 *( pt (ji+1,jj,jk,jn) - pt(ji,jj,jk,jn) ) & |
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225 | & + zcof1 *( zdkt (ji+1,jj) + zdk1t(ji,jj) & |
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226 | & +zdk1t(ji+1,jj) + zdkt (ji,jj) ) ) |
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227 | |
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228 | zftv(ji,jj,jk)= vmask(ji,jj,jk) * & |
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229 | & ( zabe2 *( pt(ji,jj+1,jk,jn) - pt(ji,jj,jk,jn) ) & |
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230 | & + zcof2 *( zdkt (ji,jj+1) + zdk1t(ji,jj) & |
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231 | & +zdk1t(ji,jj+1) + zdkt (ji,jj) ) ) |
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232 | END DO |
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233 | END DO |
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234 | |
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235 | |
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236 | ! I.3 Second derivative (divergence) (not divided by the volume) |
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237 | ! --------------------- |
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238 | |
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239 | DO jj = 2 , jpjm1 |
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240 | DO ji = 2 , jpim1 |
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241 | ztah = zftu(ji,jj) - zftu(ji-1,jj) + zftv(ji,jj,jk) - zftv(ji,jj-1,jk) |
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242 | plt(ji,jj,jk,jn) = ztah |
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243 | END DO |
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244 | END DO |
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245 | ! ! =============== |
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246 | END DO ! End of slab |
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247 | ! ! =============== |
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248 | ! "Poleward" diffusive heat or salt transport |
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249 | IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( kaht == 2 ) .AND. ( MOD( kt, nn_fptr ) == 0 ) ) THEN |
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250 | ! note sign is reversed to give down-gradient diffusive transports (#1043) |
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251 | IF( jn == jp_tem) htr_ldf(:) = ptr_vj( -zftv(:,:,:) ) |
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252 | IF( jn == jp_sal) str_ldf(:) = ptr_vj( -zftv(:,:,:) ) |
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253 | ENDIF |
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254 | |
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255 | ! ! ************ ! ! =============== |
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256 | DO jj = 2, jpjm1 ! Second step ! ! Horizontal slab |
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257 | ! ! ************ ! ! =============== |
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258 | |
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259 | ! II.1 horizontal tracer gradient |
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260 | ! ------------------------------- |
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261 | |
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262 | DO jk = 1, jpk |
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263 | DO ji = 1, jpim1 |
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264 | zdit (ji,jk) = ( pt(ji+1,jj ,jk,jn) - pt(ji,jj ,jk,jn) ) * umask(ji,jj ,jk) |
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265 | zdjt (ji,jk) = ( pt(ji ,jj+1,jk,jn) - pt(ji,jj ,jk,jn) ) * vmask(ji,jj ,jk) |
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266 | zdj1t(ji,jk) = ( pt(ji ,jj ,jk,jn) - pt(ji,jj-1,jk,jn) ) * vmask(ji,jj-1,jk) |
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267 | END DO |
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268 | END DO |
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269 | |
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270 | |
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271 | ! II.2 Vertical fluxes |
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272 | ! -------------------- |
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273 | |
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274 | ! Surface and bottom vertical fluxes set to zero |
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275 | zftw(:, 1 ) = 0.e0 |
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276 | zftw(:,jpk) = 0.e0 |
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277 | |
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278 | ! interior (2=<jk=<jpk-1) |
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279 | DO jk = 2, jpkm1 |
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280 | DO ji = 2, jpim1 |
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281 | zcof0 = e12t(ji,jj) / fse3w_n(ji,jj,jk) & |
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282 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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283 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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284 | |
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285 | zmku = 1./MAX( umask(ji ,jj,jk-1)+umask(ji-1,jj,jk) & |
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286 | & +umask(ji-1,jj,jk-1)+umask(ji ,jj,jk), 1. ) |
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287 | |
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288 | zmkv = 1./MAX( vmask(ji,jj ,jk-1)+vmask(ji,jj-1,jk) & |
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289 | & +vmask(ji,jj-1,jk-1)+vmask(ji,jj ,jk), 1. ) |
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290 | |
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291 | zcof3 = - e2t(ji,jj) * wslpi (ji,jj,jk) * zmku |
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292 | zcof4 = - e1t(ji,jj) * wslpj (ji,jj,jk) * zmkv |
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293 | |
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294 | zftw(ji,jk) = tmask(ji,jj,jk) * & |
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295 | & ( zcof0 * ( pt (ji,jj,jk-1,jn) - pt (ji ,jj,jk,jn) ) & |
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296 | & + zcof3 * ( zdit (ji ,jk-1 ) + zdit (ji-1,jk ) & |
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297 | & +zdit (ji-1 ,jk-1 ) + zdit (ji ,jk ) ) & |
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298 | & + zcof4 * ( zdjt (ji ,jk-1 ) + zdj1t(ji ,jk) & |
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299 | & +zdj1t(ji ,jk-1 ) + zdjt (ji ,jk ) ) ) |
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300 | END DO |
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301 | END DO |
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302 | |
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303 | |
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304 | ! II.3 Divergence of vertical fluxes added to the horizontal divergence |
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305 | ! --------------------------------------------------------------------- |
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306 | |
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307 | IF( kaht == 1 ) THEN |
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308 | ! multiply the laplacian by the eddy diffusivity coefficient |
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309 | DO jk = 1, jpkm1 |
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310 | DO ji = 2, jpim1 |
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311 | ! eddy coef. divided by the volume element |
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312 | zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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313 | ! vertical divergence |
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314 | ztav = fsahtt(ji,jj,jk) * ( zftw(ji,jk) - zftw(ji,jk+1) ) |
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315 | ! harmonic operator applied to (pt,ps) and multiply by aht |
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316 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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317 | END DO |
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318 | END DO |
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319 | ELSEIF( kaht == 2 ) THEN |
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320 | ! second call, no multiplication |
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321 | DO jk = 1, jpkm1 |
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322 | DO ji = 2, jpim1 |
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323 | ! inverse of the volume element |
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324 | zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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325 | ! vertical divergence |
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326 | ztav = zftw(ji,jk) - zftw(ji,jk+1) |
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327 | ! harmonic operator applied to (pt,ps) |
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328 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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329 | END DO |
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330 | END DO |
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331 | ELSE |
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332 | IF(lwp) WRITE(numout,*) ' ldfght: kaht= 1 or 2, here =', kaht |
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333 | IF(lwp) WRITE(numout,*) ' We stop' |
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334 | STOP 'ldfght' |
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335 | ENDIF |
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336 | ! ! =============== |
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337 | END DO ! End of slab |
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338 | ! ! =============== |
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339 | END DO |
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340 | ! |
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341 | CALL wrk_dealloc( jpi, jpj, zftu, zdkt, zdk1t ) |
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342 | CALL wrk_dealloc( jpi, jpk, zftw, zdit, zdjt, zdj1t ) |
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343 | ! |
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344 | IF( nn_timing == 1 ) CALL timing_stop('ldfght') |
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345 | ! |
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346 | END SUBROUTINE ldfght |
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347 | |
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348 | #else |
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349 | !!---------------------------------------------------------------------- |
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350 | !! Dummy module : NO rotation of the lateral mixing tensor |
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351 | !!---------------------------------------------------------------------- |
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352 | CONTAINS |
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353 | SUBROUTINE tra_ldf_bilapg( kt, kit000, cdtype, ptb, pta, kjpt ) ! Empty routine |
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354 | INTEGER :: kt, kit000 |
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355 | CHARACTER(len=3) :: cdtype |
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356 | REAL, DIMENSION(:,:,:,:) :: ptb, pta |
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357 | WRITE(*,*) 'tra_ldf_iso: You should not have seen this print! error?', & |
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358 | & kt, kit000, cdtype, ptb(1,1,1,1), pta(1,1,1,1), kjpt |
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359 | END SUBROUTINE tra_ldf_bilapg |
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360 | #endif |
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361 | |
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362 | !!============================================================================== |
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363 | END MODULE traldf_bilapg |
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