1 | MODULE traadv_ubs |
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2 | !!============================================================================== |
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3 | !! *** MODULE traadv_ubs *** |
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4 | !! Ocean active tracers: horizontal & vertical advective trend |
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5 | !!============================================================================== |
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6 | !! History : 9.0 ! 06-08 (L. Debreu, R. Benshila) Original code |
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7 | !!---------------------------------------------------------------------- |
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8 | |
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9 | !!---------------------------------------------------------------------- |
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10 | !! tra_adv_ubs : update the tracer trend with the horizontal |
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11 | !! advection trends using a third order biaised scheme |
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12 | !!---------------------------------------------------------------------- |
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13 | USE oce ! ocean dynamics and active tracers |
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14 | USE dom_oce ! ocean space and time domain |
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15 | USE trdmod |
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16 | USE trdmod_oce |
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17 | USE lib_mpp |
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18 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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19 | USE in_out_manager ! I/O manager |
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20 | USE diaptr ! poleward transport diagnostics |
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21 | USE dynspg_oce ! choice/control of key cpp for surface pressure gradient |
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22 | USE prtctl |
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23 | |
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24 | IMPLICIT NONE |
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25 | PRIVATE |
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26 | |
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27 | PUBLIC tra_adv_ubs ! routine called by traadv module |
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28 | |
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29 | REAL(wp), DIMENSION(jpi,jpj) :: e1e2tr ! = 1/(e1t * e2t) |
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30 | |
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31 | !! * Substitutions |
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32 | # include "domzgr_substitute.h90" |
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33 | # include "vectopt_loop_substitute.h90" |
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34 | !!---------------------------------------------------------------------- |
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35 | !! OPA 9.0 , LOCEAN-IPSL (2006) |
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36 | !! $Id$ |
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37 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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38 | !!---------------------------------------------------------------------- |
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39 | |
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40 | CONTAINS |
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41 | |
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42 | SUBROUTINE tra_adv_ubs( kt, pun, pvn, pwn ) |
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43 | !!---------------------------------------------------------------------- |
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44 | !! *** ROUTINE tra_adv_ubs *** |
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45 | !! |
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46 | !! ** Purpose : Compute the now trend due to the advection of tracers |
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47 | !! and add it to the general trend of passive tracer equations. |
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48 | !! |
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49 | !! ** Method : The upstream biased third (UBS) is order scheme based |
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50 | !! on an upstream-biased parabolic interpolation (Shchepetkin and McWilliams 2005) |
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51 | !! It is only used in the horizontal direction. |
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52 | !! For example the i-component of the advective fluxes are given by : |
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53 | !! ! e1u e3u un ( mi(Tn) - zltu(i ) ) if un(i) >= 0 |
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54 | !! zwx = ! or |
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55 | !! ! e1u e3u un ( mi(Tn) - zltu(i+1) ) if un(i) < 0 |
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56 | !! where zltu is the second derivative of the before temperature field: |
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57 | !! zltu = 1/e3t di[ e2u e3u / e1u di[Tb] ] |
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58 | !! This results in a dissipatively dominant (i.e. hyper-diffusive) |
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59 | !! truncation error. The overall performance of the advection scheme |
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60 | !! is similar to that reported in (Farrow and Stevens, 1995). |
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61 | !! For stability reasons, the first term of the fluxes which corresponds |
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62 | !! to a second order centered scheme is evaluated using the now velocity |
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63 | !! (centered in time) while the second term which is the diffusive part |
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64 | !! of the scheme, is evaluated using the before velocity (forward in time). |
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65 | !! Note that UBS is not positive. Do not use it on passive tracers. |
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66 | !! On the vertical, the advection is evaluated using a TVD scheme, as |
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67 | !! the UBS have been found to be too diffusive. |
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68 | !! |
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69 | !! ** Action : - update (ta,sa) with the now advective tracer trends |
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70 | !! |
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71 | !! Reference : Shchepetkin, A. F., J. C. McWilliams, 2005, Ocean Modelling, 9, 347-404. |
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72 | !! Farrow, D.E., Stevens, D.P., 1995, J. Phys. Ocean. 25, 1731Ð1741. |
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73 | !!---------------------------------------------------------------------- |
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74 | USE oce, ONLY : zwx => ua ! use ua as workspace |
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75 | USE oce, ONLY : zwy => va ! use va as workspace |
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76 | !! |
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77 | INTEGER , INTENT(in) :: kt ! ocean time-step index |
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78 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pun ! effective ocean velocity, u_component |
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79 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pvn ! effective ocean velocity, v_component |
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80 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pwn ! effective ocean velocity, w_component |
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81 | !! |
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82 | INTEGER :: ji, jj, jk ! dummy loop indices |
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83 | REAL(wp) :: zta, zsa, zbtr, zcoef ! temporary scalars |
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84 | REAL(wp) :: zfui, zfp_ui, zfm_ui, zcenut, zcenus ! " " |
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85 | REAL(wp) :: zfvj, zfp_vj, zfm_vj, zcenvt, zcenvs ! " " |
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86 | REAL(wp) :: z_hdivn_x, z_hdivn_y, z_hdivn ! " " |
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87 | REAL(wp), DIMENSION(jpi,jpj) :: zeeu, zeev ! temporary 2D workspace |
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88 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz , zww ! temporary 3D workspace |
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89 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: ztu , ztv , zltu , zltv, ztrdt ! " " |
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90 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zsu , zsv , zlsu , zlsv, ztrds ! " " |
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91 | !!---------------------------------------------------------------------- |
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92 | |
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93 | zltu(:,:,:) = 0.e0 |
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94 | zltv(:,:,:) = 0.e0 |
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95 | zlsu(:,:,:) = 0.e0 |
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96 | zlsv(:,:,:) = 0.e0 |
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97 | |
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98 | IF( kt == nit000 ) THEN |
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99 | IF(lwp) WRITE(numout,*) |
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100 | IF(lwp) WRITE(numout,*) 'tra_adv_ubs : horizontal UBS advection scheme' |
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101 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~' |
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102 | ! |
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103 | e1e2tr(:,:) = 1. / ( e1t(:,:) * e2t(:,:) ) |
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104 | ENDIF |
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105 | |
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106 | ! Save ta and sa trends |
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107 | ztrdt(:,:,:) = ta(:,:,:) |
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108 | ztrds(:,:,:) = sa(:,:,:) |
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109 | |
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110 | zcoef = 1./6. |
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111 | ! ! =============== |
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112 | DO jk = 1, jpkm1 ! Horizontal slab |
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113 | ! ! =============== |
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114 | |
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115 | ! Initialization of metric arrays (for z- or s-coordinates) |
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116 | DO jj = 1, jpjm1 |
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117 | DO ji = 1, fs_jpim1 ! vector opt. |
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118 | #if defined key_zco |
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119 | ! z-coordinates, no vertical scale factors |
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120 | zeeu(ji,jj) = e2u(ji,jj) / e1u(ji,jj) * umask(ji,jj,jk) |
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121 | zeev(ji,jj) = e1v(ji,jj) / e2v(ji,jj) * vmask(ji,jj,jk) |
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122 | #else |
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123 | ! s-coordinates, vertical scale factor are used |
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124 | zeeu(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) |
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125 | zeev(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) / 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 | ! Laplacian |
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131 | ! First derivative (gradient) |
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132 | DO jj = 1, jpjm1 |
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133 | DO ji = 1, fs_jpim1 ! vector opt. |
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134 | ztu(ji,jj,jk) = zeeu(ji,jj) * ( tb(ji+1,jj ,jk) - tb(ji,jj,jk) ) |
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135 | zsu(ji,jj,jk) = zeeu(ji,jj) * ( sb(ji+1,jj ,jk) - sb(ji,jj,jk) ) |
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136 | ztv(ji,jj,jk) = zeev(ji,jj) * ( tb(ji ,jj+1,jk) - tb(ji,jj,jk) ) |
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137 | zsv(ji,jj,jk) = zeev(ji,jj) * ( sb(ji ,jj+1,jk) - sb(ji,jj,jk) ) |
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138 | END DO |
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139 | END DO |
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140 | ! Second derivative (divergence) |
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141 | DO jj = 2, jpjm1 |
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142 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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143 | #if ! defined key_zco |
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144 | zcoef = 1. / ( 6. * fse3t(ji,jj,jk) ) |
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145 | #endif |
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146 | zltu(ji,jj,jk) = ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zcoef |
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147 | zlsu(ji,jj,jk) = ( zsu(ji,jj,jk) - zsu(ji-1,jj,jk) ) * zcoef |
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148 | zltv(ji,jj,jk) = ( ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) * zcoef |
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149 | zlsv(ji,jj,jk) = ( zsv(ji,jj,jk) - zsv(ji,jj-1,jk) ) * zcoef |
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150 | END DO |
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151 | END DO |
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152 | ! ! ================= |
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153 | END DO ! End of slab |
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154 | ! ! ================= |
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155 | |
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156 | ! Lateral boundary conditions on the laplacian (zlt,zls) (unchanged sgn) |
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157 | CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zlsu, 'T', 1. ) |
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158 | CALL lbc_lnk( zltv, 'T', 1. ) ; CALL lbc_lnk( zlsv, 'T', 1. ) |
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159 | |
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160 | ! ! =============== |
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161 | DO jk = 1, jpkm1 ! Horizontal slab |
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162 | ! ! =============== |
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163 | ! Horizontal advective fluxes |
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164 | DO jj = 1, jpjm1 |
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165 | DO ji = 1, fs_jpim1 ! vector opt. |
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166 | ! volume fluxes * 1/2 |
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167 | #if defined key_zco |
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168 | zfui = 0.5 * e2u(ji,jj) * pun(ji,jj,jk) |
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169 | zfvj = 0.5 * e1v(ji,jj) * pvn(ji,jj,jk) |
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170 | #else |
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171 | zfui = 0.5 * e2u(ji,jj) * fse3u(ji,jj,jk) * pun(ji,jj,jk) |
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172 | zfvj = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * pvn(ji,jj,jk) |
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173 | #endif |
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174 | ! upstream scheme |
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175 | zfp_ui = zfui + ABS( zfui ) |
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176 | zfp_vj = zfvj + ABS( zfvj ) |
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177 | zfm_ui = zfui - ABS( zfui ) |
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178 | zfm_vj = zfvj - ABS( zfvj ) |
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179 | ! centered scheme |
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180 | zcenut = zfui * ( tn(ji,jj,jk) + tn(ji+1,jj ,jk) ) |
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181 | zcenvt = zfvj * ( tn(ji,jj,jk) + tn(ji ,jj+1,jk) ) |
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182 | zcenus = zfui * ( sn(ji,jj,jk) + sn(ji+1,jj ,jk) ) |
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183 | zcenvs = zfvj * ( sn(ji,jj,jk) + sn(ji ,jj+1,jk) ) |
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184 | ! mixed centered / upstream scheme |
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185 | zwx(ji,jj,jk) = zcenut - zfp_ui * zltu(ji,jj,jk) -zfm_ui * zltu(ji+1,jj,jk) |
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186 | zwy(ji,jj,jk) = zcenvt - zfp_vj * zltv(ji,jj,jk) -zfm_vj * zltv(ji,jj+1,jk) |
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187 | zww(ji,jj,jk) = zcenus - zfp_ui * zlsu(ji,jj,jk) -zfm_ui * zlsu(ji+1,jj,jk) |
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188 | zwz(ji,jj,jk) = zcenvs - zfp_vj * zlsv(ji,jj,jk) -zfm_vj * zlsv(ji,jj+1,jk) |
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189 | END DO |
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190 | END DO |
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191 | |
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192 | ! Tracer flux divergence at t-point added to the general trend |
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193 | DO jj = 2, jpjm1 |
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194 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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195 | ! horizontal advective trends |
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196 | #if defined key_zco |
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197 | zbtr = e1e2tr(ji,jj) |
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198 | #else |
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199 | zbtr = e1e2tr(ji,jj) / fse3t(ji,jj,jk) |
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200 | #endif |
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201 | zta = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) & |
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202 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) ) |
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203 | zsa = - zbtr * ( zww(ji,jj,jk) - zww(ji-1,jj ,jk) & |
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204 | & + zwz(ji,jj,jk) - zwz(ji ,jj-1,jk) ) |
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205 | ! add it to the general tracer trends |
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206 | ta(ji,jj,jk) = ta(ji,jj,jk) + zta |
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207 | sa(ji,jj,jk) = sa(ji,jj,jk) + zsa |
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208 | END DO |
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209 | END DO |
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210 | ! ! =============== |
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211 | END DO ! End of slab |
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212 | ! ! =============== |
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213 | |
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214 | ! Horizontal trend used in tra_adv_ztvd subroutine |
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215 | zltu(:,:,:) = ta(:,:,:) - ztrdt(:,:,:) |
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216 | zlsu(:,:,:) = sa(:,:,:) - ztrds(:,:,:) |
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217 | |
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218 | ! 3. Save the horizontal advective trends for diagnostic |
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219 | ! ------------------------------------------------------ |
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220 | IF( l_trdtra ) THEN |
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221 | ! Recompute the hoizontal advection zta & zsa trends computed |
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222 | ! at the step 2. above in making the difference between the new |
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223 | ! trends and the previous one ta()/sa - ztrdt()/ztrds() and add |
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224 | ! the term tn()/sn()*hdivn() to recover the Uh gradh(T/S) trends |
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225 | ztrdt(:,:,:) = 0.e0 ; ztrds(:,:,:) = 0.e0 |
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226 | ! |
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227 | ! T/S ZONAL advection trends |
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228 | DO jk = 1, jpkm1 |
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229 | DO jj = 2, jpjm1 |
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230 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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231 | !-- Compute zonal divergence by splitting hdivn (see divcur.F90) |
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232 | #if defined key_zco |
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233 | zbtr = e1e2tr(ji,jj) |
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234 | z_hdivn_x = ( e2u(ji ,jj) * pun(ji ,jj,jk) & |
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235 | & - e2u(ji-1,jj) * pun(ji-1,jj,jk) ) * zbtr |
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236 | #else |
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237 | zbtr = e1e2tr(ji,jj) / fse3t(ji,jj,jk) |
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238 | z_hdivn_x = ( e2u(ji ,jj) * fse3u(ji ,jj,jk) * pun(ji ,jj,jk) & |
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239 | & - e2u(ji-1,jj) * fse3u(ji-1,jj,jk) * pun(ji-1,jj,jk) ) * zbtr |
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240 | #endif |
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241 | ztrdt(ji,jj,jk) = - ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) ) * zbtr + tn(ji,jj,jk) * z_hdivn_x |
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242 | ztrds(ji,jj,jk) = - ( zww(ji,jj,jk) - zww(ji-1,jj,jk) ) * zbtr + sn(ji,jj,jk) * z_hdivn_x |
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243 | END DO |
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244 | END DO |
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245 | END DO |
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246 | CALL trd_mod(ztrdt, ztrds, jptra_trd_xad, 'TRA', kt) ! save the trends |
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247 | ! |
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248 | ! T/S MERIDIONAL advection trends |
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249 | DO jk = 1, jpkm1 |
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250 | DO jj = 2, jpjm1 |
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251 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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252 | !-- Compute merid. divergence by splitting hdivn (see divcur.F90) |
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253 | #if defined key_zco |
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254 | zbtr = e1e2tr(ji,jj) |
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255 | z_hdivn_y = ( e1v(ji, jj) * pvn(ji,jj ,jk) & |
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256 | & - e1v(ji,jj-1) * pvn(ji,jj-1,jk) ) * zbtr |
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257 | #else |
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258 | zbtr = e1e2tr(ji,jj) / fse3t(ji,jj,jk) |
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259 | z_hdivn_y = ( e1v(ji, jj) * fse3v(ji,jj ,jk) * pvn(ji,jj ,jk) & |
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260 | & - e1v(ji,jj-1) * fse3v(ji,jj-1,jk) * pvn(ji,jj-1,jk) ) * zbtr |
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261 | #endif |
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262 | ztrdt(ji,jj,jk) = - ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) ) * zbtr + tn(ji,jj,jk) * z_hdivn_y |
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263 | ztrds(ji,jj,jk) = - ( zwz(ji,jj,jk) - zwz(ji,jj-1,jk) ) * zbtr + sn(ji,jj,jk) * z_hdivn_y |
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264 | END DO |
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265 | END DO |
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266 | END DO |
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267 | CALL trd_mod(ztrdt, ztrds, jptra_trd_yad, 'TRA', kt) ! save the trends |
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268 | ! |
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269 | ENDIF |
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270 | |
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271 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ta, clinfo1=' ubs had - Ta: ', mask1=tmask, & |
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272 | & tab3d_2=sa, clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' ) |
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273 | |
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274 | ! "zonal" mean advective heat and salt transport |
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275 | IF( ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN |
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276 | IF( lk_zco ) THEN |
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277 | DO jk = 1, jpkm1 |
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278 | DO jj = 2, jpjm1 |
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279 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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280 | zwy(ji,jj,jk) = zwy(ji,jj,jk) * fse3v(ji,jj,jk) |
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281 | zwz(ji,jj,jk) = zwz(ji,jj,jk) * fse3v(ji,jj,jk) |
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282 | END DO |
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283 | END DO |
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284 | END DO |
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285 | ENDIF |
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286 | pht_adv(:) = ptr_vj( zwy(:,:,:) ) |
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287 | pst_adv(:) = ptr_vj( zwz(:,:,:) ) |
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288 | ENDIF |
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289 | |
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290 | ! II. Vertical advection |
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291 | ! ---------------------- |
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292 | IF( l_trdtra ) THEN ! Save ta and sa trends |
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293 | ztrdt(:,:,:) = ta(:,:,:) |
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294 | ztrds(:,:,:) = sa(:,:,:) |
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295 | ENDIF |
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296 | |
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297 | ! TVD scheme the vertical direction |
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298 | CALL tra_adv_ztvd(kt, pwn, zltu, zlsu) |
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299 | |
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300 | IF( l_trdtra ) THEN ! Save the final vertical advective trends |
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301 | DO jk = 1, jpkm1 |
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302 | DO jj = 2, jpjm1 |
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303 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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304 | #if defined key_zco |
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305 | zbtr = e1e2tr(ji,jj) |
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306 | z_hdivn_x = e2u(ji,jj)*pun(ji,jj,jk) - e2u(ji-1,jj)*pun(ji-1,jj,jk) |
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307 | z_hdivn_y = e1v(ji,jj)*pvn(ji,jj,jk) - e1v(ji,jj-1)*pvn(ji,jj-1,jk) |
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308 | #else |
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309 | zbtr = e1e2tr(ji,jj) / fse3t(ji,jj,jk) |
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310 | z_hdivn_x = e2u(ji,jj)*fse3u(ji,jj,jk)*pun(ji,jj,jk) - e2u(ji-1,jj)*fse3u(ji-1,jj,jk)*pun(ji-1,jj,jk) |
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311 | z_hdivn_y = e1v(ji,jj)*fse3v(ji,jj,jk)*pvn(ji,jj,jk) - e1v(ji,jj-1)*fse3v(ji,jj-1,jk)*pvn(ji,jj-1,jk) |
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312 | #endif |
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313 | z_hdivn = (z_hdivn_x + z_hdivn_y) * zbtr |
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314 | zbtr = e1e2tr(ji,jj) / fse3t(ji,jj,jk) |
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315 | ztrdt(ji,jj,jk) = ta(ji,jj,jk) - ztrdt(ji,jj,jk) - tn(ji,jj,jk) * z_hdivn |
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316 | ztrds(ji,jj,jk) = sa(ji,jj,jk) - ztrds(ji,jj,jk) - sn(ji,jj,jk) * z_hdivn |
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317 | END DO |
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318 | END DO |
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319 | END DO |
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320 | CALL trd_mod(ztrdt, ztrds, jptra_trd_zad, 'TRA', kt) ! <<< ADD TO PREVIOUSLY COMPUTED |
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321 | ! |
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322 | ENDIF |
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323 | |
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324 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ta, clinfo1=' ubs zad - Ta: ', mask1=tmask, & |
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325 | & tab3d_2=sa, clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra') |
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326 | ! |
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327 | END SUBROUTINE tra_adv_ubs |
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328 | |
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329 | |
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330 | SUBROUTINE tra_adv_ztvd( kt, pwn, zttrd, zstrd ) |
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331 | !!---------------------------------------------------------------------- |
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332 | !! *** ROUTINE tra_adv_ztvd *** |
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333 | !! |
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334 | !! ** Purpose : Compute the now trend due to total advection of |
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335 | !! tracers and add it to the general trend of tracer equations |
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336 | !! |
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337 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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338 | !! corrected flux (monotonic correction) |
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339 | !! note: - this advection scheme needs a leap-frog time scheme |
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340 | !! |
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341 | !! ** Action : - update (ta,sa) with the now advective tracer trends |
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342 | !! - save the trends in (ztrdt,ztrds) ('key_trdtra') |
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343 | !!---------------------------------------------------------------------- |
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344 | INTEGER , INTENT(in) :: kt ! ocean time-step |
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345 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pwn ! verical effective velocity |
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346 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: zttrd, zstrd ! lateral advective trends on T & S |
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347 | !! |
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348 | INTEGER :: ji, jj, jk ! dummy loop indices |
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349 | REAL(wp) :: z2dtt, zbtr, zew, z2 ! temporary scalar |
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350 | REAL(wp) :: ztak, zfp_wk ! " " |
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351 | REAL(wp) :: zsak, zfm_wk ! " " |
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352 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: zti, ztw ! temporary 3D workspace |
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353 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: zsi, zsw ! " " |
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354 | !!---------------------------------------------------------------------- |
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355 | |
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356 | IF( kt == nit000 .AND. lwp ) THEN |
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357 | WRITE(numout,*) |
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358 | WRITE(numout,*) 'tra_adv_ztvd : vertical TVD advection scheme' |
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359 | WRITE(numout,*) '~~~~~~~~~~~~' |
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360 | ENDIF |
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361 | |
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362 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; z2 = 1. |
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363 | ELSE ; z2 = 2. |
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364 | ENDIF |
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365 | |
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366 | ! Bottom value : flux set to zero |
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367 | ! -------------- |
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368 | ztw(:,:,jpk) = 0.e0 ; zsw(:,:,jpk) = 0.e0 |
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369 | zti (:,:,:) = 0.e0 ; zsi (:,:,:) = 0.e0 |
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370 | |
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371 | |
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372 | ! upstream advection with initial mass fluxes & intermediate update |
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373 | ! ------------------------------------------------------------------- |
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374 | ! Surface value |
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375 | IF( lk_vvl ) THEN |
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376 | ! variable volume : flux set to zero |
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377 | ztw(:,:,1) = 0.e0 |
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378 | zsw(:,:,1) = 0.e0 |
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379 | ELSE |
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380 | ! free surface-constant volume |
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381 | DO jj = 1, jpj |
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382 | DO ji = 1, jpi |
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383 | zew = e1t(ji,jj) * e2t(ji,jj) * pwn(ji,jj,1) |
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384 | ztw(ji,jj,1) = zew * tb(ji,jj,1) |
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385 | zsw(ji,jj,1) = zew * sb(ji,jj,1) |
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386 | END DO |
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387 | END DO |
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388 | ENDIF |
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389 | |
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390 | ! Interior value |
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391 | DO jk = 2, jpkm1 |
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392 | DO jj = 1, jpj |
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393 | DO ji = 1, jpi |
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394 | zew = 0.5 * e1t(ji,jj) * e2t(ji,jj) * pwn(ji,jj,jk) |
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395 | zfp_wk = zew + ABS( zew ) |
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396 | zfm_wk = zew - ABS( zew ) |
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397 | ztw(ji,jj,jk) = zfp_wk * tb(ji,jj,jk) + zfm_wk * tb(ji,jj,jk-1) |
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398 | zsw(ji,jj,jk) = zfp_wk * sb(ji,jj,jk) + zfm_wk * sb(ji,jj,jk-1) |
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399 | END DO |
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400 | END DO |
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401 | END DO |
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402 | |
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403 | ! update and guess with monotonic sheme |
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404 | DO jk = 1, jpkm1 |
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405 | z2dtt = z2 * rdttra(jk) |
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406 | DO jj = 2, jpjm1 |
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407 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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408 | zbtr = 1./ ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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409 | ztak = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr |
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410 | zsak = - ( zsw(ji,jj,jk) - zsw(ji,jj,jk+1) ) * zbtr |
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411 | ta(ji,jj,jk) = ta(ji,jj,jk) + ztak |
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412 | sa(ji,jj,jk) = sa(ji,jj,jk) + zsak |
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413 | zti (ji,jj,jk) = ( tb(ji,jj,jk) + z2dtt * ( ztak + zttrd(ji,jj,jk) ) ) * tmask(ji,jj,jk) |
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414 | zsi (ji,jj,jk) = ( sb(ji,jj,jk) + z2dtt * ( zsak + zstrd(ji,jj,jk) ) ) * tmask(ji,jj,jk) |
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415 | END DO |
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416 | END DO |
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417 | END DO |
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418 | |
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419 | ! Lateral boundary conditions on zti, zsi (unchanged sign) |
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420 | CALL lbc_lnk( zti, 'T', 1. ) |
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421 | CALL lbc_lnk( zsi, 'T', 1. ) |
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422 | |
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423 | |
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424 | ! antidiffusive flux : high order minus low order |
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425 | ! ------------------------------------------------- |
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426 | ! Surface value |
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427 | ztw(:,:,1) = 0.e0 ; zsw(:,:,1) = 0.e0 |
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428 | |
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429 | ! Interior value |
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430 | DO jk = 2, jpkm1 |
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431 | DO jj = 1, jpj |
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432 | DO ji = 1, jpi |
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433 | zew = 0.5 * e1t(ji,jj) * e2t(ji,jj) * pwn(ji,jj,jk) |
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434 | ztw(ji,jj,jk) = zew * ( tn(ji,jj,jk) + tn(ji,jj,jk-1) ) - ztw(ji,jj,jk) |
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435 | zsw(ji,jj,jk) = zew * ( sn(ji,jj,jk) + sn(ji,jj,jk-1) ) - zsw(ji,jj,jk) |
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436 | END DO |
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437 | END DO |
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438 | END DO |
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439 | |
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440 | ! monotonicity algorithm |
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441 | ! ------------------------ |
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442 | CALL nonosc_z( tb, ztw, zti, z2 ) |
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443 | CALL nonosc_z( sb, zsw, zsi, z2 ) |
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444 | |
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445 | |
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446 | ! final trend with corrected fluxes |
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447 | ! ----------------------------------- |
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448 | DO jk = 1, jpkm1 |
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449 | DO jj = 2, jpjm1 |
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450 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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451 | zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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452 | ! k- vertical advective trends |
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453 | ztak = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr |
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454 | zsak = - ( zsw(ji,jj,jk) - zsw(ji,jj,jk+1) ) * zbtr |
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455 | ! add them to the general tracer trends |
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456 | ta(ji,jj,jk) = ta(ji,jj,jk) + ztak |
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457 | sa(ji,jj,jk) = sa(ji,jj,jk) + zsak |
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458 | END DO |
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459 | END DO |
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460 | END DO |
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461 | ! |
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462 | END SUBROUTINE tra_adv_ztvd |
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463 | |
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464 | |
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465 | SUBROUTINE nonosc_z( pbef, pcc, paft, prdt ) |
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466 | !!--------------------------------------------------------------------- |
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467 | !! *** ROUTINE nonosc_z *** |
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468 | !! |
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469 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
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470 | !! scheme and the before field by a nonoscillatory algorithm |
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471 | !! |
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472 | !! ** Method : ... ??? |
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473 | !! warning : pbef and paft must be masked, but the boundaries |
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474 | !! conditions on the fluxes are not necessary zalezak (1979) |
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475 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
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476 | !! in-space based differencing for fluid |
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477 | !!---------------------------------------------------------------------- |
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478 | REAL(wp), INTENT(in ) :: prdt ! ??? |
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479 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pbef ! before field |
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480 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: paft ! after field |
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481 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pcc ! monotonic flux in the k direction |
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482 | !! |
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483 | INTEGER :: ji, jj, jk ! dummy loop indices |
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484 | INTEGER :: ikm1 |
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485 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt |
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486 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: zbetup, zbetdo |
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487 | !!---------------------------------------------------------------------- |
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488 | |
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489 | zbig = 1.e+40 |
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490 | zrtrn = 1.e-15 |
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491 | zbetup(:,:,:) = 0.e0 ; zbetdo(:,:,:) = 0.e0 |
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492 | |
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493 | ! Search local extrema |
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494 | ! -------------------- |
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495 | ! large negative value (-zbig) inside land |
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496 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) |
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497 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) |
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498 | ! search maximum in neighbourhood |
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499 | DO jk = 1, jpkm1 |
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500 | ikm1 = MAX(jk-1,1) |
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501 | DO jj = 2, jpjm1 |
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502 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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503 | zbetup(ji,jj,jk) = MAX( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & |
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504 | & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & |
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505 | & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) |
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506 | END DO |
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507 | END DO |
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508 | END DO |
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509 | ! large positive value (+zbig) inside land |
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510 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) |
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511 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) |
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512 | ! search minimum in neighbourhood |
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513 | DO jk = 1, jpkm1 |
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514 | ikm1 = MAX(jk-1,1) |
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515 | DO jj = 2, jpjm1 |
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516 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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517 | zbetdo(ji,jj,jk) = MIN( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & |
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518 | & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & |
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519 | & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) |
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520 | END DO |
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521 | END DO |
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522 | END DO |
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523 | |
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524 | ! restore masked values to zero |
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525 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) |
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526 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) |
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527 | |
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528 | |
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529 | ! 2. Positive and negative part of fluxes and beta terms |
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530 | ! ------------------------------------------------------ |
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531 | |
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532 | DO jk = 1, jpkm1 |
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533 | z2dtt = prdt * rdttra(jk) |
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534 | DO jj = 2, jpjm1 |
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535 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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536 | ! positive & negative part of the flux |
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537 | zpos = MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
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538 | zneg = MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
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539 | ! up & down beta terms |
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540 | zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) / z2dtt |
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541 | zbetup(ji,jj,jk) = ( zbetup(ji,jj,jk) - paft(ji,jj,jk) ) / (zpos+zrtrn) * zbt |
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542 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zbetdo(ji,jj,jk) ) / (zneg+zrtrn) * zbt |
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543 | END DO |
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544 | END DO |
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545 | END DO |
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546 | |
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547 | ! monotonic flux in the k direction, i.e. pcc |
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548 | ! ------------------------------------------- |
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549 | DO jk = 2, jpkm1 |
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550 | DO jj = 2, jpjm1 |
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551 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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552 | |
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553 | za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj,jk-1) ) |
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554 | zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj,jk-1) ) |
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555 | zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pcc(ji,jj,jk) ) ) |
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556 | pcc(ji,jj,jk) = pcc(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) |
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557 | END DO |
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558 | END DO |
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559 | END DO |
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560 | ! |
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561 | END SUBROUTINE nonosc_z |
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562 | |
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563 | !!====================================================================== |
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564 | END MODULE traadv_ubs |
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