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 : 2.0 ! 2006-08 (R. Benshila, L. Debreu) Original code |
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8 | !! 3.2 ! 2009-07 (R. Benshila) Suppression of rigid-lid option |
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9 | !!---------------------------------------------------------------------- |
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10 | |
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11 | !!---------------------------------------------------------------------- |
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12 | !! dyn_adv_ubs : flux form momentum advection using (ln_dynadv=T) |
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13 | !! an 3rd order Upstream Biased Scheme or Quick scheme |
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14 | !! combined with 2nd or 4th order finite differences |
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15 | !!---------------------------------------------------------------------- |
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16 | USE oce ! ocean dynamics and tracers |
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17 | USE dom_oce ! ocean space and time domain |
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18 | USE trd_oce ! trends: ocean variables |
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19 | USE trddyn ! trend manager: dynamics |
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20 | ! |
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21 | USE in_out_manager ! I/O manager |
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22 | USE prtctl ! Print control |
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23 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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24 | USE lib_mpp ! MPP library |
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25 | |
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26 | IMPLICIT NONE |
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27 | PRIVATE |
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28 | |
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29 | REAL(wp), PARAMETER :: gamma1 = 1._wp/3._wp ! =1/4 quick ; =1/3 3rd order UBS |
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30 | REAL(wp), PARAMETER :: gamma2 = 1._wp/32._wp ! =0 2nd order ; =1/32 4th order centred |
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31 | |
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32 | PUBLIC dyn_adv_ubs ! routine called by step.F90 |
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33 | |
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34 | !! * Substitutions |
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35 | # include "vectopt_loop_substitute.h90" |
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36 | !!---------------------------------------------------------------------- |
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37 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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38 | !! $Id$ |
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39 | !! Software governed by the CeCILL license (see ./LICENSE) |
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40 | !!---------------------------------------------------------------------- |
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41 | CONTAINS |
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42 | |
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43 | SUBROUTINE dyn_adv_ubs( kt, ktlev1, ktlev2, pu_rhs, pv_rhs ) |
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44 | !!---------------------------------------------------------------------- |
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45 | !! *** ROUTINE dyn_adv_ubs *** |
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46 | !! |
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47 | !! ** Purpose : Compute the now momentum advection trend in flux form |
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48 | !! and the general trend of the momentum equation. |
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49 | !! |
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50 | !! ** Method : The scheme is the one implemeted in ROMS. It depends |
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51 | !! on two parameter gamma1 and gamma2. The former control the |
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52 | !! upstream baised part of the scheme and the later the centred |
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53 | !! part: gamma1 = 0 pure centered (no diffusive part) |
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54 | !! = 1/4 Quick scheme |
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55 | !! = 1/3 3rd order Upstream biased scheme |
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56 | !! gamma2 = 0 2nd order finite differencing |
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57 | !! = 1/32 4th order finite differencing |
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58 | !! For stability reasons, the first term of the fluxes which cor- |
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59 | !! responds to a second order centered scheme is evaluated using |
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60 | !! the now velocity (centered in time) while the second term which |
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61 | !! is the diffusive part of the scheme, is evaluated using the |
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62 | !! before velocity (forward in time). |
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63 | !! Default value (hard coded in the begining of the module) are |
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64 | !! gamma1=1/3 and gamma2=1/32. |
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65 | !! |
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66 | !! ** Action : - (pu_rhs,pv_rhs) updated with the 3D advective momentum trends |
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67 | !! |
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68 | !! Reference : Shchepetkin & McWilliams, 2005, Ocean Modelling. |
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69 | !!---------------------------------------------------------------------- |
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70 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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71 | INTEGER, INTENT(in) :: ktlev1, ktlev2 ! time level indices for source terms |
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72 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pu_rhs, pv_rhs ! momentum trends |
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73 | ! |
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74 | INTEGER :: ji, jj, jk ! dummy loop indices |
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75 | REAL(wp) :: zui, zvj, zfuj, zfvi, zl_u, zl_v ! local scalars |
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76 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f, zfu_uw, zfu |
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77 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f, zfv_vw, zfv, zfw |
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78 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlu_uu, zlu_uv |
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79 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlv_vv, zlv_vu |
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80 | !!---------------------------------------------------------------------- |
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81 | ! |
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82 | IF( kt == nit000 ) THEN |
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83 | IF(lwp) WRITE(numout,*) |
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84 | IF(lwp) WRITE(numout,*) 'dyn_adv_ubs : UBS flux form momentum advection' |
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85 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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86 | ENDIF |
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87 | ! |
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88 | zfu_t(:,:,:) = 0._wp |
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89 | zfv_t(:,:,:) = 0._wp |
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90 | zfu_f(:,:,:) = 0._wp |
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91 | zfv_f(:,:,:) = 0._wp |
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92 | ! |
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93 | zlu_uu(:,:,:,:) = 0._wp |
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94 | zlv_vv(:,:,:,:) = 0._wp |
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95 | zlu_uv(:,:,:,:) = 0._wp |
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96 | zlv_vu(:,:,:,:) = 0._wp |
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97 | ! |
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98 | IF( l_trddyn ) THEN ! trends: store the input trends |
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99 | zfu_uw(:,:,:) = pu_rhs(:,:,:) |
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100 | zfv_vw(:,:,:) = pv_rhs(:,:,:) |
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101 | ENDIF |
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102 | ! ! =========================== ! |
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103 | DO jk = 1, jpkm1 ! Laplacian of the velocity ! |
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104 | ! ! =========================== ! |
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105 | ! ! horizontal volume fluxes |
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106 | zfu(:,:,jk) = e2u(:,:) * e3u(:,:,jk,ktlev2) * uu(:,:,jk,ktlev2) |
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107 | zfv(:,:,jk) = e1v(:,:) * e3v(:,:,jk,ktlev2) * vv(:,:,jk,ktlev2) |
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108 | ! |
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109 | DO jj = 2, jpjm1 ! laplacian |
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110 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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111 | zlu_uu(ji,jj,jk,1) = ( uu (ji+1,jj ,jk,ktlev1) - 2.*uu (ji,jj,jk,ktlev1) + uu (ji-1,jj ,jk,ktlev1) ) * umask(ji,jj,jk) |
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112 | zlv_vv(ji,jj,jk,1) = ( vv (ji ,jj+1,jk,ktlev1) - 2.*vv (ji,jj,jk,ktlev1) + vv (ji ,jj-1,jk,ktlev1) ) * vmask(ji,jj,jk) |
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113 | zlu_uv(ji,jj,jk,1) = ( uu (ji ,jj+1,jk,ktlev1) - uu (ji ,jj ,jk,ktlev1) ) * fmask(ji ,jj ,jk) & |
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114 | & - ( uu (ji ,jj ,jk,ktlev1) - uu (ji ,jj-1,jk,ktlev1) ) * fmask(ji ,jj-1,jk) |
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115 | zlv_vu(ji,jj,jk,1) = ( vv (ji+1,jj ,jk,ktlev1) - vv (ji ,jj ,jk,ktlev1) ) * fmask(ji ,jj ,jk) & |
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116 | & - ( vv (ji ,jj ,jk,ktlev1) - vv (ji-1,jj ,jk,ktlev1) ) * fmask(ji-1,jj ,jk) |
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117 | ! |
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118 | 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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119 | 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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120 | zlu_uv(ji,jj,jk,2) = ( zfu(ji ,jj+1,jk) - zfu(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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121 | & - ( zfu(ji ,jj ,jk) - zfu(ji ,jj-1,jk) ) * fmask(ji ,jj-1,jk) |
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122 | zlv_vu(ji,jj,jk,2) = ( zfv(ji+1,jj ,jk) - zfv(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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123 | & - ( zfv(ji ,jj ,jk) - zfv(ji-1,jj ,jk) ) * fmask(ji-1,jj ,jk) |
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124 | END DO |
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125 | END DO |
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126 | END DO |
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127 | CALL lbc_lnk_multi( 'dynadv_ubs', zlu_uu(:,:,:,1), 'U', 1. , zlu_uv(:,:,:,1), 'U', 1., & |
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128 | & zlu_uu(:,:,:,2), 'U', 1. , zlu_uv(:,:,:,2), 'U', 1., & |
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129 | & zlv_vv(:,:,:,1), 'V', 1. , zlv_vu(:,:,:,1), 'V', 1., & |
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130 | & zlv_vv(:,:,:,2), 'V', 1. , zlv_vu(:,:,:,2), 'V', 1. ) |
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131 | ! |
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132 | ! ! ====================== ! |
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133 | ! ! Horizontal advection ! |
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134 | DO jk = 1, jpkm1 ! ====================== ! |
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135 | ! ! horizontal volume fluxes |
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136 | zfu(:,:,jk) = 0.25_wp * e2u(:,:) * e3u(:,:,jk,ktlev2) * uu(:,:,jk,ktlev2) |
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137 | zfv(:,:,jk) = 0.25_wp * e1v(:,:) * e3v(:,:,jk,ktlev2) * vv(:,:,jk,ktlev2) |
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138 | ! |
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139 | DO jj = 1, jpjm1 ! horizontal momentum fluxes at T- and F-point |
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140 | DO ji = 1, fs_jpim1 ! vector opt. |
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141 | zui = ( uu(ji,jj,jk,ktlev2) + uu(ji+1,jj ,jk,ktlev2) ) |
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142 | zvj = ( vv(ji,jj,jk,ktlev2) + vv(ji ,jj+1,jk,ktlev2) ) |
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143 | ! |
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144 | IF( zui > 0 ) THEN ; zl_u = zlu_uu(ji ,jj,jk,1) |
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145 | ELSE ; zl_u = zlu_uu(ji+1,jj,jk,1) |
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146 | ENDIF |
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147 | IF( zvj > 0 ) THEN ; zl_v = zlv_vv(ji,jj ,jk,1) |
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148 | ELSE ; zl_v = zlv_vv(ji,jj+1,jk,1) |
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149 | ENDIF |
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150 | ! |
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151 | zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) & |
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152 | & - gamma2 * ( zlu_uu(ji,jj,jk,2) + zlu_uu(ji+1,jj ,jk,2) ) ) & |
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153 | & * ( zui - gamma1 * zl_u) |
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154 | zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) & |
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155 | & - gamma2 * ( zlv_vv(ji,jj,jk,2) + zlv_vv(ji ,jj+1,jk,2) ) ) & |
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156 | & * ( zvj - gamma1 * zl_v) |
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157 | ! |
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158 | zfuj = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) |
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159 | zfvi = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) |
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160 | IF( zfuj > 0 ) THEN ; zl_v = zlv_vu( ji ,jj ,jk,1) |
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161 | ELSE ; zl_v = zlv_vu( ji+1,jj,jk,1) |
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162 | ENDIF |
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163 | IF( zfvi > 0 ) THEN ; zl_u = zlu_uv( ji,jj ,jk,1) |
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164 | ELSE ; zl_u = zlu_uv( ji,jj+1,jk,1) |
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165 | ENDIF |
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166 | ! |
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167 | zfv_f(ji ,jj ,jk) = ( zfvi - gamma2 * ( zlv_vu(ji,jj,jk,2) + zlv_vu(ji+1,jj ,jk,2) ) ) & |
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168 | & * ( uu(ji,jj,jk,ktlev2) + uu(ji ,jj+1,jk,ktlev2) - gamma1 * zl_u ) |
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169 | zfu_f(ji ,jj ,jk) = ( zfuj - gamma2 * ( zlu_uv(ji,jj,jk,2) + zlu_uv(ji ,jj+1,jk,2) ) ) & |
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170 | & * ( vv(ji,jj,jk,ktlev2) + vv(ji+1,jj ,jk,ktlev2) - gamma1 * zl_v ) |
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171 | END DO |
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172 | END DO |
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173 | DO jj = 2, jpjm1 ! divergence of horizontal momentum fluxes |
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174 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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175 | pu_rhs(ji,jj,jk) = pu_rhs(ji,jj,jk) - ( zfu_t(ji+1,jj,jk) - zfu_t(ji,jj ,jk) & |
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176 | & + zfv_f(ji ,jj,jk) - zfv_f(ji,jj-1,jk) ) * r1_e1e2u(ji,jj) / e3u(ji,jj,jk,ktlev2) |
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177 | pv_rhs(ji,jj,jk) = pv_rhs(ji,jj,jk) - ( zfu_f(ji,jj ,jk) - zfu_f(ji-1,jj,jk) & |
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178 | & + zfv_t(ji,jj+1,jk) - zfv_t(ji ,jj,jk) ) * r1_e1e2v(ji,jj) / e3v(ji,jj,jk,ktlev2) |
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179 | END DO |
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180 | END DO |
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181 | END DO |
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182 | IF( l_trddyn ) THEN ! trends: send trends to trddyn for diagnostic |
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183 | zfu_uw(:,:,:) = pu_rhs(:,:,:) - zfu_uw(:,:,:) |
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184 | zfv_vw(:,:,:) = pv_rhs(:,:,:) - zfv_vw(:,:,:) |
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185 | CALL trd_dyn( zfu_uw, zfv_vw, jpdyn_keg, kt ) |
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186 | zfu_t(:,:,:) = pu_rhs(:,:,:) |
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187 | zfv_t(:,:,:) = pv_rhs(:,:,:) |
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188 | ENDIF |
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189 | ! ! ==================== ! |
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190 | ! ! Vertical advection ! |
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191 | ! ! ==================== ! |
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192 | DO jj = 2, jpjm1 ! surface/bottom advective fluxes set to zero |
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193 | DO ji = fs_2, fs_jpim1 |
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194 | zfu_uw(ji,jj,jpk) = 0._wp |
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195 | zfv_vw(ji,jj,jpk) = 0._wp |
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196 | zfu_uw(ji,jj, 1 ) = 0._wp |
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197 | zfv_vw(ji,jj, 1 ) = 0._wp |
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198 | END DO |
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199 | END DO |
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200 | IF( ln_linssh ) THEN ! constant volume : advection through the surface |
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201 | DO jj = 2, jpjm1 |
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202 | DO ji = fs_2, fs_jpim1 |
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203 | zfu_uw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * ww(ji,jj,1) + e1e2t(ji+1,jj) * ww(ji+1,jj,1) ) * uu(ji,jj,1,ktlev2) |
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204 | zfv_vw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * ww(ji,jj,1) + e1e2t(ji,jj+1) * ww(ji,jj+1,1) ) * vv(ji,jj,1,ktlev2) |
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205 | END DO |
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206 | END DO |
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207 | ENDIF |
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208 | DO jk = 2, jpkm1 ! interior fluxes |
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209 | DO jj = 2, jpj |
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210 | DO ji = 2, jpi |
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211 | zfw(ji,jj,jk) = 0.25_wp * e1e2t(ji,jj) * ww(ji,jj,jk) |
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212 | END DO |
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213 | END DO |
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214 | DO jj = 2, jpjm1 |
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215 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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216 | zfu_uw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji+1,jj,jk) ) * ( uu(ji,jj,jk,ktlev2) + uu(ji,jj,jk-1,ktlev2) ) |
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217 | zfv_vw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji,jj+1,jk) ) * ( vv(ji,jj,jk,ktlev2) + vv(ji,jj,jk-1,ktlev2) ) |
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218 | END DO |
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219 | END DO |
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220 | END DO |
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221 | DO jk = 1, jpkm1 ! divergence of vertical momentum flux divergence |
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222 | DO jj = 2, jpjm1 |
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223 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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224 | pu_rhs(ji,jj,jk) = pu_rhs(ji,jj,jk) - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) * r1_e1e2u(ji,jj) / e3u(ji,jj,jk,ktlev2) |
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225 | pv_rhs(ji,jj,jk) = pv_rhs(ji,jj,jk) - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) * r1_e1e2v(ji,jj) / e3v(ji,jj,jk,ktlev2) |
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226 | END DO |
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227 | END DO |
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228 | END DO |
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229 | ! |
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230 | IF( l_trddyn ) THEN ! save the vertical advection trend for diagnostic |
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231 | zfu_t(:,:,:) = pu_rhs(:,:,:) - zfu_t(:,:,:) |
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232 | zfv_t(:,:,:) = pv_rhs(:,:,:) - zfv_t(:,:,:) |
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233 | CALL trd_dyn( zfu_t, zfv_t, jpdyn_zad, kt ) |
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234 | ENDIF |
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235 | ! ! Control print |
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236 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' ubs2 adv - Ua: ', mask1=umask, & |
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237 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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238 | ! |
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239 | END SUBROUTINE dyn_adv_ubs |
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240 | |
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241 | !!============================================================================== |
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242 | END MODULE dynadv_ubs |
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