1 | MODULE trcldf_bilap |
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2 | !!============================================================================== |
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3 | !! *** MODULE trcldf_bilap *** |
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4 | !! Ocean passive tracers: horizontal component of the lateral tracer mixing trend |
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5 | !!============================================================================== |
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6 | #if defined key_passivetrc |
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7 | !!---------------------------------------------------------------------- |
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8 | !! trc_ldf_bilap : update the tracer trend with the horizontal diffusion |
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9 | !! using a iso-level biharmonic operator |
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10 | !!---------------------------------------------------------------------- |
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11 | !! * Modules used |
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12 | USE oce_trc ! ocean dynamics and active tracers variables |
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13 | USE trc ! ocean passive tracers variables |
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14 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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15 | USE prtctl_trc ! Print control for debbuging |
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16 | |
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17 | IMPLICIT NONE |
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18 | PRIVATE |
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19 | |
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20 | !! * Routine accessibility |
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21 | PUBLIC trc_ldf_bilap ! routine called by step.F90 |
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22 | |
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23 | !! * Substitutions |
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24 | # include "passivetrc_substitute.h90" |
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25 | !!---------------------------------------------------------------------- |
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26 | !! OPA 9.0 , LODYC-IPSL (2003) |
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27 | !!---------------------------------------------------------------------- |
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28 | |
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29 | CONTAINS |
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30 | |
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31 | SUBROUTINE trc_ldf_bilap( kt ) |
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32 | !!---------------------------------------------------------------------- |
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33 | !! *** ROUTINE trc_ldf_bilap *** |
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34 | !! |
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35 | !! ** Purpose : Compute the before horizontal tracer tra diffusive |
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36 | !! trend and add it to the general trend of tracer equation. |
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37 | !! |
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38 | !! ** Method : 4th order diffusive operator along model level surfaces |
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39 | !! evaluated using before fields (forward time scheme). The hor. |
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40 | !! diffusive trends of passive tracer is given by: |
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41 | !! * s-coordinate ('key_s_coord' defined), the vertical scale |
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42 | !! factors e3. are inside the derivatives: |
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43 | !! Laplacian of trb: |
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44 | !! zlt = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(trb) ] |
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45 | !! + dj-1[ e1v*e3v/e2v dj(trb) ] } |
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46 | !! Multiply by the eddy diffusivity coef. and insure lateral bc: |
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47 | !! zlt = ahtt * zlt |
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48 | !! call to lbc_lnk |
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49 | !! Bilaplacian (laplacian of zlt): |
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50 | !! difft = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(zlt) ] |
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51 | !! + dj-1[ e1v*e3v/e2v dj(zlt) ] } |
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52 | !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: |
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53 | !! Laplacian of trb: |
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54 | !! zlt = 1/(e1t*e2t) { di-1[ e2u/e1u di(trb) ] |
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55 | !! + dj-1[ e1v/e2v dj(trb) ] } |
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56 | !! Multiply by the eddy diffusivity coef. and insure lateral bc: |
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57 | !! zlt = ahtt * zlt |
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58 | !! call to lbc_lnk |
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59 | !! Bilaplacian (laplacian of zlt): |
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60 | !! difft = 1/(e1t*e2t) { di-1[ e2u/e1u di(zlt) ] |
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61 | !! + dj-1[ e1v/e2v dj(zlt) ] } |
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62 | !! |
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63 | !! Add this trend to the general trend tra : |
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64 | !! tra = tra + difft |
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65 | !! |
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66 | !! ** Action : - Update tra arrays with the before iso-level |
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67 | !! biharmonic mixing trend. |
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68 | !! - Save the trends in trtrd ('key_trc_diatrd') |
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69 | !! |
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70 | !! History : |
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71 | !! ! 91-11 (G. Madec) Original code |
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72 | !! ! 93-03 (M. Guyon) symetrical conditions |
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73 | !! ! 95-11 (G. Madec) suppress volumetric scale factors |
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74 | !! ! 96-01 (G. Madec) statement function for e3 |
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75 | !! ! 96-01 (M. Imbard) mpp exchange |
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76 | !! ! 97-07 (G. Madec) optimization, and ahtt |
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77 | !! ! 00-05 (MA Foujols) add lbc for tracer trends |
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78 | !! ! 00-10 (MA Foujols E. Kestenare) use passive tracer coefficient |
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79 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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80 | !! 9.0 ! 04-03 (C. Ethe ) F90: Free form and module |
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81 | !!---------------------------------------------------------------------- |
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82 | !! * Arguments |
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83 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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84 | |
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85 | !! * Local declarations |
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86 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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87 | #if defined key_partial_steps |
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88 | INTEGER :: iku, ikv ! temporary integers |
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89 | #endif |
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90 | REAL(wp) :: ztra ! temporary scalars |
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91 | |
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92 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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93 | zeeu, zeev, zbtr, zlt ! workspace |
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94 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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95 | ztu, ztv ! workspace |
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96 | CHARACTER (len=22) :: charout |
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97 | !!---------------------------------------------------------------------- |
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98 | |
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99 | IF( kt == nittrc000 ) THEN |
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100 | IF(lwp) WRITE(numout,*) |
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101 | IF(lwp) WRITE(numout,*) 'trc_ldf_bilap : iso-level biharmonic operator' |
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102 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' |
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103 | ENDIF |
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104 | ! |
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105 | |
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106 | DO jn = 1, jptra |
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107 | ! =============== |
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108 | DO jk = 1, jpkm1 ! Horizontal slab |
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109 | ! ! =============== |
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110 | |
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111 | ! 0. Initialization of metric arrays (for z- or s-coordinates) |
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112 | ! ---------------------------------- |
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113 | |
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114 | DO jj = 1, jpjm1 |
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115 | DO ji = 1, fs_jpim1 ! vector opt. |
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116 | #if defined key_s_coord || defined key_partial_steps |
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117 | ! s-coordinates, vertical scale factor are used |
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118 | zbtr(ji,jj) = 1. / ( e1t(ji,jj)*e2t(ji,jj)*fse3t(ji,jj,jk) ) |
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119 | zeeu(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) |
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120 | zeev(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) |
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121 | #else |
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122 | ! z-coordinates, no vertical scale factors |
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123 | zbtr(ji,jj) = 1. / ( e1t(ji,jj)*e2t(ji,jj) ) |
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124 | zeeu(ji,jj) = e2u(ji,jj) / e1u(ji,jj) * umask(ji,jj,jk) |
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125 | zeev(ji,jj) = e1v(ji,jj) / e2v(ji,jj) * vmask(ji,jj,jk) |
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126 | #endif |
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127 | END DO |
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128 | END DO |
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129 | |
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130 | |
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131 | ! 1. Laplacian |
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132 | ! ------------ |
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133 | |
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134 | ! First derivative (gradient) |
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135 | DO jj = 1, jpjm1 |
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136 | DO ji = 1, fs_jpim1 ! vector opt. |
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137 | ztu(ji,jj,jk) = zeeu(ji,jj) * ( trb(ji+1,jj ,jk,jn) - trb(ji,jj,jk,jn) ) |
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138 | ztv(ji,jj,jk) = zeev(ji,jj) * ( trb(ji ,jj+1,jk,jn) - trb(ji,jj,jk,jn) ) |
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139 | END DO |
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140 | END DO |
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141 | #if defined key_partial_steps |
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142 | |
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143 | DO jj = 1, jpj-1 |
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144 | DO ji = 1, jpi-1 |
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145 | ! last level |
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146 | iku = MIN ( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1 |
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147 | ikv = MIN ( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1 |
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148 | IF( iku == jk ) THEN |
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149 | ztu(ji,jj,jk) = zeeu(ji,jj) * gtu(ji,jj) |
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150 | ENDIF |
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151 | IF( ikv == jk ) THEN |
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152 | ztv(ji,jj,jk) = zeev(ji,jj) * gtv(ji,jj) |
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153 | ENDIF |
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154 | END DO |
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155 | END DO |
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156 | #endif |
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157 | |
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158 | ! Second derivative (divergence) |
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159 | DO jj = 2, jpjm1 |
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160 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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161 | zlt(ji,jj) = zbtr(ji,jj) * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) |
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162 | END DO |
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163 | END DO |
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164 | |
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165 | ! Multiply by the eddy diffusivity coefficient |
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166 | DO jj = 2, jpjm1 |
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167 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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168 | zlt(ji,jj) = fsahtrt(ji,jj,jk) * zlt(ji,jj) |
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169 | END DO |
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170 | END DO |
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171 | |
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172 | ! Lateral boundary conditions on the laplacian zlt (unchanged sgn) |
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173 | CALL lbc_lnk( zlt, 'T', 1. ) |
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174 | |
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175 | ! 2. Bilaplacian |
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176 | ! -------------- |
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177 | |
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178 | ! third derivative (gradient) |
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179 | DO jj = 1, jpjm1 |
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180 | DO ji = 1, fs_jpim1 ! vector opt. |
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181 | ztu(ji,jj,jk) = zeeu(ji,jj) * ( zlt(ji+1,jj ) - zlt(ji,jj) ) |
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182 | ztv(ji,jj,jk) = zeev(ji,jj) * ( zlt(ji ,jj+1) - zlt(ji,jj) ) |
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183 | END DO |
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184 | END DO |
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185 | |
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186 | ! fourth derivative (divergence) and add to the general tracer trend |
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187 | DO jj = 2, jpjm1 |
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188 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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189 | ! horizontal diffusive trends |
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190 | ztra = zbtr(ji,jj) * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) |
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191 | ! add it to the general tracer trends |
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192 | tra(ji,jj,jk,jn) = tra(ji,jj,jk,jn) + ztra |
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193 | #if defined key_trc_diatrd |
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194 | ! save the horizontal diffusive trends |
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195 | trtrd(ji,jj,jk,jn,4) = ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zbtr(ji,jj) |
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196 | trtrd(ji,jj,jk,jn,5) = ( ztv(ji,jj,jk) - ztv(ji-1,jj,jk) ) * zbtr(ji,jj) |
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197 | #endif |
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198 | END DO |
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199 | END DO |
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200 | ! ! =============== |
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201 | END DO ! Horizontal slab |
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202 | ! ! =============== |
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203 | #if defined key_trc_diatrd |
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204 | ! Lateral boundary conditions on the laplacian zlt (unchanged sgn) |
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205 | CALL lbc_lnk( trtrd(:,:,:,jn,5), 'T', 1. ) |
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206 | #endif |
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207 | END DO |
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208 | |
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209 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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210 | WRITE(charout, FMT="('ldf - bilap')") |
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211 | CALL prt_ctl_trc_info(charout) |
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212 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm,clinfo2='trd') |
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213 | ENDIF |
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214 | |
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215 | END SUBROUTINE trc_ldf_bilap |
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216 | |
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217 | #else |
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218 | !!---------------------------------------------------------------------- |
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219 | !! Default option Empty module |
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220 | !!---------------------------------------------------------------------- |
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221 | CONTAINS |
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222 | SUBROUTINE trc_ldf_bilap( kt ) |
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223 | INTEGER, INTENT(in) :: kt |
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224 | WRITE(*,*) 'trc_ldf_bilap: You should not have seen this print! error?', kt |
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225 | END SUBROUTINE trc_ldf_bilap |
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226 | #endif |
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227 | !!============================================================================== |
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228 | END MODULE trcldf_bilap |
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