1 | MODULE dynadv_ubs |
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2 | !!====================================================================== |
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3 | !! *** MODULE dynadv_ubs *** |
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4 | !! Ocean dynamics: Update the momentum trend with the flux form advection |
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5 | !! trend using a 3rd order upstream biased scheme |
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6 | !!====================================================================== |
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7 | !! History : 9.0 ! 06-08 (R. Benshila, L. Debreu) Original code |
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8 | !!---------------------------------------------------------------------- |
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9 | |
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10 | !!---------------------------------------------------------------------- |
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11 | !! dyn_adv_ubs : flux form momentum advection using (ln_dynadv=T) |
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12 | !! an 3rd order Upstream Biased Scheme or Quick scheme |
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13 | !! combined with 2nd or 4th order finite differences |
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14 | !!---------------------------------------------------------------------- |
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15 | USE oce ! ocean dynamics and tracers |
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16 | USE dom_oce ! ocean space and time domain |
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17 | USE dynspg_oce ! surface pressure gradient |
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18 | USE in_out_manager ! I/O manager |
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19 | USE dynspg_rl ! I/O manager |
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20 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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21 | |
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22 | IMPLICIT NONE |
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23 | PRIVATE |
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24 | |
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25 | REAL(wp), PARAMETER :: gamma1 = 1._wp/4._wp ! =1/4 quick ; =1/3 3rd order UBS |
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26 | REAL(wp), PARAMETER :: gamma2 = 1._wp/8._wp ! =0 2nd order ; =1/8 4th order centred |
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27 | |
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28 | !! * Routine accessibility |
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29 | PUBLIC dyn_adv_ubs ! routine called by step.F90 |
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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 , LODYC-IPSL (2006) |
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36 | !! $Header$ |
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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 dyn_adv_ubs( kt ) |
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43 | !!---------------------------------------------------------------------- |
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44 | !! *** ROUTINE dyn_adv_ubs *** |
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45 | !! |
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46 | !! ** Purpose : Compute the now momentum advection trend in flux form |
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47 | !! and the general trend of the momentum equation. |
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48 | !! |
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49 | !! ** Method : The scheme is the one implemeted in ROMS. It depends |
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50 | !! on two parameter gamma1 and gamma2. The former control the |
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51 | !! upstream baised part of the scheme and the later the centred |
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52 | !! part: gamma1 = 0 pure centered (no diffusive part) |
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53 | !! = 1/4 Quick scheme |
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54 | !! = 1/3 3rd order Upstream biased scheme |
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55 | !! gamma2 = 0 2nd order finite differencing |
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56 | !! = 1/8 4th order finite differencing |
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57 | !! For stability reasons, the first term of the fluxes which cor- |
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58 | !! responds to a second order centered scheme is evaluated using |
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59 | !! the now velocity (centered in time) while the second term which |
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60 | !! is the diffusive part of the scheme, is evaluated using the |
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61 | !! before velocity (forward in time). |
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62 | !! Default value (hard coded in the begining of the module) are |
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63 | !! gamma1=1/4 and gamma2=1/8. |
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64 | !! |
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65 | !! ** Action : - update (ua,va) with the 3D advective momentum trends |
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66 | !! |
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67 | !! Reference : Shchepetkin & McWilliams, 2005, Ocean Modelling. |
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68 | !!---------------------------------------------------------------------- |
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69 | USE oce, ONLY: zfu => ta, & ! use ta as 3D workspace |
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70 | zfv => sa ! use sa as 3D workspace |
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71 | |
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72 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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73 | |
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74 | INTEGER :: ji, jj, jk ! dummy loop indices |
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75 | REAL(wp) :: zua, zva, zbu, zbv ! temporary scalars |
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76 | REAL(wp) :: zui, zvj, zfuj, zfvi, zl_u, zl_v! temporary scalars |
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77 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f ! temporary workspace |
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78 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f ! " " |
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79 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfw, zfu_uw, zfv_vw |
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80 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlu_uu, zlu_uv ! temporary workspace |
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81 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlv_vv, zlv_vu ! temporary workspace |
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82 | !!---------------------------------------------------------------------- |
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83 | |
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84 | IF( kt == nit000 ) THEN |
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85 | IF(lwp) WRITE(numout,*) |
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86 | IF(lwp) WRITE(numout,*) 'dyn_adv_ubs : UBS flux form momentum advection' |
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87 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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88 | ENDIF |
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89 | zfu_t(:,:,:) = 0.e0 |
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90 | zfv_t(:,:,:) = 0.e0 |
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91 | zfu_f(:,:,:) = 0.e0 |
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92 | zfv_f(:,:,:) = 0.e0 |
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93 | |
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94 | zlu_uu(:,:,:,:) = 0.e0 |
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95 | zlv_vv(:,:,:,:) = 0.e0 |
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96 | zlu_uv(:,:,:,:) = 0.e0 |
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97 | zlv_vu(:,:,:,:) = 0.e0 |
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98 | |
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99 | |
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100 | ! ! =============== |
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101 | DO jk = 1, jpkm1 ! Horizontal slab |
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102 | ! ! =============== |
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103 | ! Laplacian |
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104 | ! --------- |
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105 | zfu(:,:,jk) = e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
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106 | zfv(:,:,jk) = e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
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107 | |
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108 | DO jj = 2, jpjm1 |
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109 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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110 | zlu_uu(ji,jj,jk,1) = ( ub (ji+1,jj,jk)-2.*ub (ji,jj,jk)+ub (ji-1,jj,jk) ) * umask(ji,jj,jk) |
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111 | zlv_vv(ji,jj,jk,1) = ( vb (ji,jj+1,jk)-2.*vb (ji,jj,jk)+vb (ji,jj-1,jk) ) * vmask(ji,jj,jk) |
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112 | zlu_uv(ji,jj,jk,1) = ( ub (ji,jj+1,jk)-2.*ub (ji,jj,jk)+ub (ji,jj-1,jk) ) * umask(ji,jj,jk) |
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113 | zlv_vu(ji,jj,jk,1) = ( vb (ji+1,jj,jk)-2.*vb (ji,jj,jk)+vb (ji-1,jj,jk) ) * vmask(ji,jj,jk) |
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114 | |
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115 | zlu_uu(ji,jj,jk,2) = ( zfu(ji+1,jj,jk)-2.*zfu(ji,jj,jk)+zfu(ji-1,jj,jk) ) * umask(ji,jj,jk) |
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116 | zlv_vv(ji,jj,jk,2) = ( zfv(ji,jj+1,jk)-2.*zfv(ji,jj,jk)+zfv(ji,jj-1,jk) ) * vmask(ji,jj,jk) |
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117 | zlu_uv(ji,jj,jk,2) = ( zfu(ji,jj+1,jk)-2.*zfu(ji,jj,jk)+zfu(ji,jj-1,jk) ) * umask(ji,jj,jk) |
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118 | zlv_vu(ji,jj,jk,2) = ( zfv(ji+1,jj,jk)-2.*zfv(ji,jj,jk)+zfv(ji-1,jj,jk) ) * vmask(ji,jj,jk) |
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119 | END DO |
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120 | END DO |
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121 | ! ! =============== |
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122 | END DO ! End of slab |
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123 | ! ! =============== |
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124 | |
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125 | CALL lbc_lnk( zlu_uu(:,:,:,1), 'U', -1.) |
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126 | CALL lbc_lnk( zlu_uu(:,:,:,2), 'U', -1.) |
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127 | CALL lbc_lnk( zlv_vv(:,:,:,1), 'V', -1.) |
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128 | CALL lbc_lnk( zlv_vv(:,:,:,2), 'V', -1.) |
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129 | |
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130 | CALL lbc_lnk( zlu_uv(:,:,:,1), 'U', -1.) |
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131 | CALL lbc_lnk( zlu_uv(:,:,:,2), 'U', -1.) |
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132 | CALL lbc_lnk( zlv_vu(:,:,:,1), 'V', -1.) |
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133 | CALL lbc_lnk( zlv_vu(:,:,:,2), 'V', -1.) |
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134 | |
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135 | ! I. Horizontal advection |
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136 | ! ----------------------- |
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137 | ! ! =============== |
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138 | DO jk = 1, jpkm1 ! Horizontal slab |
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139 | ! ! =============== |
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140 | ! horizontal volume fluxes |
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141 | zfu(:,:,jk) = 0.25 * e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
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142 | zfv(:,:,jk) = 0.25 * e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
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143 | |
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144 | ! horizontal momentum fluxes at T- and F-point |
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145 | DO jj = 1, jpjm1 |
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146 | DO ji = 1, fs_jpim1 ! vector opt. |
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147 | zui = ( un(ji,jj,jk) + un(ji+1,jj ,jk) ) |
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148 | zvj = ( vn(ji,jj,jk) + vn(ji ,jj+1,jk) ) |
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149 | |
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150 | IF (zui > 0) THEN ; zl_u = zlu_uu(ji ,jj,jk,1) |
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151 | ELSE ; zl_u = zlu_uu(ji+1,jj,jk,1) |
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152 | ENDIF |
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153 | IF (zvj > 0) THEN ; zl_v = zlv_vv(ji,jj ,jk,1) |
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154 | ELSE ; zl_v = zlv_vv(ji,jj+1,jk,1) |
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155 | ENDIF |
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156 | |
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157 | zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) & |
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158 | & - gamma2 * ( zlu_uu(ji,jj,jk,2) + zlu_uu(ji+1,jj ,jk,2) ) ) & |
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159 | & * ( zui - gamma1 * zl_u) |
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160 | zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) & |
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161 | & - gamma2 * ( zlv_vv(ji,jj,jk,2) + zlv_vv(ji ,jj+1,jk,2) ) ) & |
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162 | & * ( zvj - gamma1 * zl_v) |
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163 | |
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164 | zfuj = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) |
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165 | zfvi = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) |
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166 | IF (zfuj > 0) THEN ; zl_v = zlv_vu( ji ,jj ,jk,1) |
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167 | ELSE ; zl_v = zlv_vu( ji+1,jj,jk,1) |
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168 | ENDIF |
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169 | IF (zfvi > 0) THEN ; zl_u = zlu_uv( ji,jj ,jk,1) |
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170 | ELSE ; zl_u = zlu_uv( ji,jj+1,jk,1) |
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171 | ENDIF |
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172 | |
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173 | zfv_f(ji ,jj ,jk) = ( zfvi - gamma2 * ( zlv_vu(ji,jj,jk,2) + zlv_vu(ji+1,jj ,jk,2) ) ) & |
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174 | & * ( un(ji,jj,jk) + un(ji ,jj+1,jk) - gamma1 * zl_u ) |
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175 | zfu_f(ji ,jj ,jk) = ( zfuj - gamma2 * ( zlu_uv(ji,jj,jk,2) + zlu_uv(ji ,jj+1,jk,2) ) ) & |
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176 | & * ( vn(ji,jj,jk) + vn(ji+1,jj ,jk) - gamma1 * zl_v ) |
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177 | END DO |
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178 | END DO |
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179 | |
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180 | ! divergence of horizontal momentum fluxes |
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181 | DO jj = 2, jpjm1 |
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182 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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183 | zbu = e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) |
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184 | zbv = e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) |
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185 | ! horizontal advective trends |
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186 | zua = - ( zfu_t(ji+1,jj ,jk) - zfu_t(ji ,jj ,jk) & |
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187 | & + zfv_f(ji ,jj ,jk) - zfv_f(ji ,jj-1,jk) ) / zbu |
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188 | zva = - ( zfu_f(ji ,jj ,jk) - zfu_f(ji-1,jj ,jk) & |
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189 | & + zfv_t(ji ,jj+1,jk) - zfv_t(ji ,jj ,jk) ) / zbv |
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190 | ! add it to the general tracer trends |
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191 | ua(ji,jj,jk) = ua(ji,jj,jk) + zua |
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192 | va(ji,jj,jk) = va(ji,jj,jk) + zva |
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193 | #if defined key_trddyn |
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194 | utrd(ji,jj,jk,1) = zua ! save the horizontal advective trend of momentum |
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195 | vtrd(ji,jj,jk,1) = zva |
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196 | #endif |
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197 | END DO |
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198 | END DO |
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199 | ! ! =============== |
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200 | END DO ! End of slab |
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201 | ! ! =============== |
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202 | |
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203 | |
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204 | ! II. Vertical advection |
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205 | ! ---------------------- |
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206 | |
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207 | ! Second order centered tracer flux at w-point |
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208 | DO jk = 1, jpkm1 |
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209 | ! Vertical volume fluxes |
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210 | zfw(:,:,jk) = 0.25 * e1t(:,:) * e2t(:,:) * wn(:,:,jk) |
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211 | ! Vertical advective fluxes |
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212 | IF( jk == 1 ) THEN |
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213 | zfu_uw(:,:,jpk) = 0.e0 ! Bottom value : flux set to zero |
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214 | zfv_vw(:,:,jpk) = 0.e0 |
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215 | ! ! Surface value |
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216 | IF( lk_dynspg_rl ) THEN ! rigid lid : flux set to zero |
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217 | zfu_uw(:,:, 1 ) = 0.e0 |
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218 | zfv_vw(:,:, 1 ) = 0.e0 |
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219 | ELSE ! free surface-constant volume |
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220 | DO jj = 2, jpjm1 |
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221 | DO ji = fs_2, fs_jpim1 |
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222 | zfu_uw(ji,jj, 1 ) = 2.e0 * ( zfw(ji,jj,1) + zfw(ji+1,jj ,1) ) * un(ji,jj,1) |
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223 | zfv_vw(ji,jj, 1 ) = 2.e0 * ( zfw(ji,jj,1) + zfw(ji ,jj+1,1) ) * vn(ji,jj,1) |
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224 | END DO |
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225 | END DO |
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226 | ENDIF |
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227 | ELSE |
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228 | ! ! interior fluxes |
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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 | zfu_uw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji+1,jj ,jk) ) * ( un(ji,jj,jk) + un(ji,jj,jk-1) ) |
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232 | zfv_vw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji ,jj+1,jk) ) * ( vn(ji,jj,jk) + vn(ji,jj,jk-1) ) |
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233 | END DO |
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234 | END DO |
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235 | ENDIF |
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236 | END DO |
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237 | |
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238 | ! momentum flux divergence at u-, v-points added to the general trend |
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239 | DO jk = 1, jpkm1 |
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240 | DO jj = 2, jpjm1 |
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241 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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242 | zua = - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) & |
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243 | & / ( e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) ) |
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244 | zva = - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) & |
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245 | & / ( e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ) |
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246 | ! add it to the general tracer trends |
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247 | ua(ji,jj,jk) = ua(ji,jj,jk) + zua |
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248 | va(ji,jj,jk) = va(ji,jj,jk) + zva |
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249 | END DO |
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250 | END DO |
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251 | END DO |
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252 | |
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253 | END SUBROUTINE dyn_adv_ubs |
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254 | |
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255 | !!============================================================================== |
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256 | END MODULE dynadv_ubs |
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