1 | MODULE dynzdf |
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2 | !!============================================================================== |
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3 | !! *** MODULE dynzdf *** |
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4 | !! Ocean dynamics : vertical component of the momentum mixing trend |
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5 | !!============================================================================== |
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6 | !! History : 1.0 ! 2005-11 (G. Madec) Original code |
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7 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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8 | !! 4.0 ! 2017-06 (G. Madec) remove the explicit time-stepping option + avm at t-point |
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9 | !!---------------------------------------------------------------------- |
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10 | |
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11 | !!---------------------------------------------------------------------- |
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12 | !! dyn_zdf : compute the after velocity through implicit calculation of vertical mixing |
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13 | !!---------------------------------------------------------------------- |
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14 | USE oce ! ocean dynamics and tracers variables |
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15 | USE phycst ! physical constants |
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16 | USE dom_oce ! ocean space and time domain variables |
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17 | USE sbc_oce ! surface boundary condition: ocean |
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18 | USE zdf_oce ! ocean vertical physics variables |
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19 | USE zdfdrg ! vertical physics: top/bottom drag coef. |
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20 | USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form |
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21 | USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing |
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22 | USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator |
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23 | USE trd_oce ! trends: ocean variables |
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24 | USE trddyn ! trend manager: dynamics |
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25 | ! |
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26 | USE in_out_manager ! I/O manager |
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27 | USE lib_mpp ! MPP library |
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28 | USE prtctl ! Print control |
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29 | USE timing ! Timing |
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30 | |
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31 | IMPLICIT NONE |
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32 | PRIVATE |
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33 | |
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34 | PUBLIC dyn_zdf ! routine called by step.F90 |
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35 | |
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36 | REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise |
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37 | |
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38 | !! * Substitutions |
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39 | # include "vectopt_loop_substitute.h90" |
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40 | !!---------------------------------------------------------------------- |
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41 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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42 | !! $Id$ |
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43 | !! Software governed by the CeCILL license (see ./LICENSE) |
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44 | !!---------------------------------------------------------------------- |
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45 | CONTAINS |
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46 | |
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47 | SUBROUTINE dyn_zdf( kt, Kbb, Kmm, Krhs, puu, pvv, Kaa ) |
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48 | !!---------------------------------------------------------------------- |
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49 | !! *** ROUTINE dyn_zdf *** |
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50 | !! |
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51 | !! ** Purpose : compute the trend due to the vert. momentum diffusion |
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52 | !! together with the Leap-Frog time stepping using an |
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53 | !! implicit scheme. |
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54 | !! |
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55 | !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing |
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56 | !! u(after) = u(before) + 2*dt * u(rhs) vector form or linear free surf. |
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57 | !! u(after) = ( e3u_b*u(before) + 2*dt * e3u_n*u(rhs) ) / e3u(after) otherwise |
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58 | !! - update the after velocity with the implicit vertical mixing. |
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59 | !! This requires to solver the following system: |
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60 | !! u(after) = u(after) + 1/e3u(after) dk+1[ mi(avm) / e3uw(after) dk[ua] ] |
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61 | !! with the following surface/top/bottom boundary condition: |
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62 | !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) |
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63 | !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) |
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64 | !! |
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65 | !! ** Action : (puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) after velocity |
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66 | !!--------------------------------------------------------------------- |
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67 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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68 | INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices |
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69 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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70 | ! |
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71 | INTEGER :: ji, jj, jk ! dummy loop indices |
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72 | INTEGER :: iku, ikv ! local integers |
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73 | REAL(wp) :: zzwi, ze3ua, zdt ! local scalars |
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74 | REAL(wp) :: zzws, ze3va ! - - |
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75 | REAL(wp) :: z1_e3ua, z1_e3va ! - - |
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76 | REAL(wp) :: zWu , zWv ! - - |
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77 | REAL(wp) :: zWui, zWvi ! - - |
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78 | REAL(wp) :: zWus, zWvs ! - - |
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79 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace |
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80 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - |
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81 | !!--------------------------------------------------------------------- |
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82 | ! |
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83 | IF( ln_timing ) CALL timing_start('dyn_zdf') |
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84 | ! |
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85 | IF( kt == nit000 ) THEN !* initialization |
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86 | IF(lwp) WRITE(numout,*) |
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87 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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88 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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89 | ! |
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90 | If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator |
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91 | ELSE ; r_vvl = 1._wp |
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92 | ENDIF |
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93 | ENDIF |
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94 | ! !* set time step |
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95 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; r2dt = rdt ! = rdt (restart with Euler time stepping) |
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96 | ELSEIF( kt <= nit000 + 1 ) THEN ; r2dt = 2. * rdt ! = 2 rdt (leapfrog) |
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97 | ENDIF |
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98 | ! |
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99 | ! !* explicit top/bottom drag case |
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100 | IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, Kmm, puu(:,:,:,Kbb), pvv(:,:,:,Kbb), puu(:,:,:,Krhs), pvv(:,:,:,Krhs) ) ! add top/bottom friction trend to (puu(Kaa),pvv(Kaa)) |
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101 | ! |
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102 | ! |
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103 | IF( l_trddyn ) THEN !* temporary save of ta and sa trends |
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104 | ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) |
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105 | ztrdu(:,:,:) = puu(:,:,:,Krhs) |
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106 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) |
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107 | ENDIF |
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108 | ! |
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109 | ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) |
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110 | ! |
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111 | ! ! time stepping except vertical diffusion |
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112 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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113 | DO jk = 1, jpkm1 |
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114 | puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kbb) + r2dt * puu(:,:,jk,Krhs) ) * umask(:,:,jk) |
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115 | pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kbb) + r2dt * pvv(:,:,jk,Krhs) ) * vmask(:,:,jk) |
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116 | END DO |
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117 | ELSE ! applied on thickness weighted velocity |
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118 | DO jk = 1, jpkm1 |
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119 | puu(:,:,jk,Kaa) = ( e3u(:,:,jk,Kbb) * puu(:,:,jk,Kbb) & |
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120 | & + r2dt * e3u(:,:,jk,Kmm) * puu(:,:,jk,Krhs) ) / e3u(:,:,jk,Kaa) * umask(:,:,jk) |
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121 | pvv(:,:,jk,Kaa) = ( e3v(:,:,jk,Kbb) * pvv(:,:,jk,Kbb) & |
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122 | & + r2dt * e3v(:,:,jk,Kmm) * pvv(:,:,jk,Krhs) ) / e3v(:,:,jk,Kaa) * vmask(:,:,jk) |
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123 | END DO |
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124 | ENDIF |
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125 | ! ! add top/bottom friction |
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126 | ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. |
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127 | ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does |
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128 | ! not lead to the effective stress seen over the whole barotropic loop. |
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129 | ! G. Madec : in linear free surface, e3u(:,:,:,Kaa) = e3u(:,:,:,Kmm) = e3u_0, so systematic use of e3u(:,:,:,Kaa) |
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130 | IF( ln_drgimp .AND. ln_dynspg_ts ) THEN |
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131 | DO jk = 1, jpkm1 ! remove barotropic velocities |
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132 | puu(:,:,jk,Kaa) = ( puu(:,:,jk,Kaa) - uu_b(:,:,Kaa) ) * umask(:,:,jk) |
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133 | pvv(:,:,jk,Kaa) = ( pvv(:,:,jk,Kaa) - vv_b(:,:,Kaa) ) * vmask(:,:,jk) |
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134 | END DO |
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135 | DO jj = 2, jpjm1 ! Add bottom/top stress due to barotropic component only |
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136 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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137 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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138 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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139 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) |
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140 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) |
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141 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua |
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142 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va |
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143 | END DO |
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144 | END DO |
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145 | IF( ln_isfcav ) THEN ! Ocean cavities (ISF) |
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146 | DO jj = 2, jpjm1 |
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147 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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148 | iku = miku(ji,jj) ! top ocean level at u- and v-points |
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149 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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150 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) |
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151 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) |
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152 | puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * uu_b(ji,jj,Kaa) / ze3ua |
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153 | pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * vv_b(ji,jj,Kaa) / ze3va |
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154 | END DO |
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155 | END DO |
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156 | END IF |
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157 | ENDIF |
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158 | ! |
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159 | ! !== Vertical diffusion on u ==! |
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160 | ! |
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161 | ! !* Matrix construction |
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162 | zdt = r2dt * 0.5 |
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163 | IF( ln_zad_Aimp ) THEN !! |
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164 | SELECT CASE( nldf_dyn ) |
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165 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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166 | DO jk = 1, jpkm1 |
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167 | DO jj = 2, jpjm1 |
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168 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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169 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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170 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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171 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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172 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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173 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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174 | zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua |
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175 | zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua |
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176 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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177 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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178 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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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 | CASE DEFAULT ! iso-level lateral mixing |
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183 | DO jk = 1, jpkm1 |
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184 | DO jj = 2, jpjm1 |
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185 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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186 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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187 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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188 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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189 | zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua |
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190 | zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua |
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191 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) |
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192 | zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) |
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193 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) |
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194 | END DO |
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195 | END DO |
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196 | END DO |
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197 | END SELECT |
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198 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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199 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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200 | zwi(ji,jj,1) = 0._wp |
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201 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) |
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202 | zzws = - zdt * ( avm(ji+1,jj,2) + avm(ji ,jj,2) ) / ( ze3ua * e3uw(ji,jj,2,Kmm) ) * wumask(ji,jj,2) |
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203 | zWus = ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) / ze3ua |
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204 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWus, 0._wp ) |
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205 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWus, 0._wp ) ) |
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206 | END DO |
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207 | END DO |
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208 | ELSE |
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209 | SELECT CASE( nldf_dyn ) |
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210 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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211 | DO jk = 1, jpkm1 |
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212 | DO jj = 2, jpjm1 |
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213 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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214 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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215 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & |
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216 | & / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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217 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & |
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218 | & / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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219 | zwi(ji,jj,jk) = zzwi |
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220 | zws(ji,jj,jk) = zzws |
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221 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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222 | END DO |
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223 | END DO |
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224 | END DO |
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225 | CASE DEFAULT ! iso-level lateral mixing |
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226 | DO jk = 1, jpkm1 |
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227 | DO jj = 2, jpjm1 |
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228 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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229 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point |
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230 | zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk ) |
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231 | zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1) |
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232 | zwi(ji,jj,jk) = zzwi |
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233 | zws(ji,jj,jk) = zzws |
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234 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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235 | END DO |
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236 | END DO |
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237 | END DO |
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238 | END SELECT |
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239 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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240 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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241 | zwi(ji,jj,1) = 0._wp |
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242 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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243 | END DO |
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244 | END DO |
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245 | ENDIF |
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246 | ! |
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247 | ! |
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248 | ! !== Apply semi-implicit bottom friction ==! |
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249 | ! |
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250 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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251 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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252 | ! column vector of the tri-diagonal matrix equation |
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253 | ! |
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254 | IF ( ln_drgimp ) THEN ! implicit bottom friction |
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255 | DO jj = 2, jpjm1 |
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256 | DO ji = 2, jpim1 |
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257 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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258 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point |
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259 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua |
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260 | END DO |
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261 | END DO |
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262 | IF ( ln_isfcav ) THEN ! top friction (always implicit) |
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263 | DO jj = 2, jpjm1 |
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264 | DO ji = 2, jpim1 |
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265 | !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed |
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266 | iku = miku(ji,jj) ! ocean top level at u- and v-points |
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267 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point |
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268 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua |
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269 | END DO |
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270 | END DO |
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271 | END IF |
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272 | ENDIF |
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273 | ! |
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274 | ! Matrix inversion starting from the first level |
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275 | !----------------------------------------------------------------------- |
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276 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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277 | ! |
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278 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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279 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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280 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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281 | ! ( ... )( ... ) ( ... ) |
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282 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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283 | ! |
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284 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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285 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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286 | ! The solution (the after velocity) is in puu(:,:,:,Kaa) |
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287 | !----------------------------------------------------------------------- |
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288 | ! |
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289 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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290 | DO jj = 2, jpjm1 |
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291 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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292 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
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293 | END DO |
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294 | END DO |
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295 | END DO |
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296 | ! |
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297 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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298 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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299 | ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) + r_vvl * e3u(ji,jj,1,Kaa) |
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300 | puu(ji,jj,1,Kaa) = puu(ji,jj,1,Kaa) + r2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & |
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301 | & / ( ze3ua * rau0 ) * umask(ji,jj,1) |
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302 | END DO |
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303 | END DO |
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304 | DO jk = 2, jpkm1 |
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305 | DO jj = 2, jpjm1 |
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306 | DO ji = fs_2, fs_jpim1 |
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307 | puu(ji,jj,jk,Kaa) = puu(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * puu(ji,jj,jk-1,Kaa) |
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308 | END DO |
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309 | END DO |
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310 | END DO |
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311 | ! |
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312 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==! |
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313 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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314 | puu(ji,jj,jpkm1,Kaa) = puu(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
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315 | END DO |
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316 | END DO |
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317 | DO jk = jpk-2, 1, -1 |
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318 | DO jj = 2, jpjm1 |
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319 | DO ji = fs_2, fs_jpim1 |
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320 | puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - zws(ji,jj,jk) * puu(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
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321 | END DO |
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322 | END DO |
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323 | END DO |
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324 | ! |
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325 | ! !== Vertical diffusion on v ==! |
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326 | ! |
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327 | ! !* Matrix construction |
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328 | zdt = r2dt * 0.5 |
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329 | IF( ln_zad_Aimp ) THEN !! |
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330 | SELECT CASE( nldf_dyn ) |
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331 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv) |
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332 | DO jk = 1, jpkm1 |
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333 | DO jj = 2, jpjm1 |
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334 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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335 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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336 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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337 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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338 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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339 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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340 | zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va |
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341 | zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va |
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342 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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343 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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344 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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345 | END DO |
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346 | END DO |
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347 | END DO |
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348 | CASE DEFAULT ! iso-level lateral mixing |
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349 | DO jk = 1, jpkm1 |
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350 | DO jj = 2, jpjm1 |
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351 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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352 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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353 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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354 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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355 | zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va |
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356 | zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va |
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357 | zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) |
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358 | zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) |
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359 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) |
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360 | END DO |
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361 | END DO |
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362 | END DO |
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363 | END SELECT |
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364 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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365 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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366 | zwi(ji,jj,1) = 0._wp |
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367 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) |
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368 | zzws = - zdt * ( avm(ji,jj+1,2) + avm(ji,jj,2) ) / ( ze3va * e3vw(ji,jj,2,Kmm) ) * wvmask(ji,jj,2) |
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369 | zWvs = ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) / ze3va |
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370 | zws(ji,jj,1 ) = zzws - zdt * MAX( zWvs, 0._wp ) |
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371 | zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWvs, 0._wp ) ) |
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372 | END DO |
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373 | END DO |
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374 | ELSE |
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375 | SELECT CASE( nldf_dyn ) |
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376 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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377 | DO jk = 1, jpkm1 |
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378 | DO jj = 2, jpjm1 |
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379 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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380 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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381 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & |
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382 | & / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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383 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & |
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384 | & / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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385 | zwi(ji,jj,jk) = zzwi |
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386 | zws(ji,jj,jk) = zzws |
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387 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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388 | END DO |
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389 | END DO |
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390 | END DO |
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391 | CASE DEFAULT ! iso-level lateral mixing |
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392 | DO jk = 1, jpkm1 |
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393 | DO jj = 2, jpjm1 |
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394 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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395 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point |
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396 | zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk ) |
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397 | zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1) |
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398 | zwi(ji,jj,jk) = zzwi |
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399 | zws(ji,jj,jk) = zzws |
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400 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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401 | END DO |
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402 | END DO |
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403 | END DO |
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404 | END SELECT |
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405 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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406 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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407 | zwi(ji,jj,1) = 0._wp |
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408 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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409 | END DO |
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410 | END DO |
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411 | ENDIF |
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412 | ! |
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413 | ! !== Apply semi-implicit top/bottom friction ==! |
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414 | ! |
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415 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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416 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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417 | ! column vector of the tri-diagonal matrix equation |
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418 | ! |
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419 | IF( ln_drgimp ) THEN |
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420 | DO jj = 2, jpjm1 |
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421 | DO ji = 2, jpim1 |
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422 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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423 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point |
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424 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va |
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425 | END DO |
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426 | END DO |
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427 | IF ( ln_isfcav ) THEN |
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428 | DO jj = 2, jpjm1 |
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429 | DO ji = 2, jpim1 |
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430 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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431 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point |
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432 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) / ze3va |
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433 | END DO |
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434 | END DO |
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435 | ENDIF |
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436 | ENDIF |
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437 | |
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438 | ! Matrix inversion |
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439 | !----------------------------------------------------------------------- |
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440 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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441 | ! |
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442 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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443 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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444 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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445 | ! ( ... )( ... ) ( ... ) |
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446 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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447 | ! |
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448 | ! m is decomposed in the product of an upper and lower triangular matrix |
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449 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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450 | ! The solution (after velocity) is in 2d array va |
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451 | !----------------------------------------------------------------------- |
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452 | ! |
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453 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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454 | DO jj = 2, jpjm1 |
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455 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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456 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
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457 | END DO |
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458 | END DO |
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459 | END DO |
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460 | ! |
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461 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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462 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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463 | ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) + r_vvl * e3v(ji,jj,1,Kaa) |
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464 | pvv(ji,jj,1,Kaa) = pvv(ji,jj,1,Kaa) + r2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & |
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465 | & / ( ze3va * rau0 ) * vmask(ji,jj,1) |
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466 | END DO |
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467 | END DO |
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468 | DO jk = 2, jpkm1 |
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469 | DO jj = 2, jpjm1 |
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470 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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471 | pvv(ji,jj,jk,Kaa) = pvv(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * pvv(ji,jj,jk-1,Kaa) |
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472 | END DO |
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473 | END DO |
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474 | END DO |
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475 | ! |
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476 | DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==! |
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477 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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478 | pvv(ji,jj,jpkm1,Kaa) = pvv(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1) |
---|
479 | END DO |
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480 | END DO |
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481 | DO jk = jpk-2, 1, -1 |
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482 | DO jj = 2, jpjm1 |
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483 | DO ji = fs_2, fs_jpim1 |
---|
484 | pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - zws(ji,jj,jk) * pvv(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk) |
---|
485 | END DO |
---|
486 | END DO |
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487 | END DO |
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488 | ! |
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489 | IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics |
---|
490 | ztrdu(:,:,:) = ( puu(:,:,:,Kaa) - puu(:,:,:,Kbb) ) / r2dt - ztrdu(:,:,:) |
---|
491 | ztrdv(:,:,:) = ( pvv(:,:,:,Kaa) - pvv(:,:,:,Kbb) ) / r2dt - ztrdv(:,:,:) |
---|
492 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt, Kmm ) |
---|
493 | DEALLOCATE( ztrdu, ztrdv ) |
---|
494 | ENDIF |
---|
495 | ! ! print mean trends (used for debugging) |
---|
496 | IF(ln_ctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Kaa), clinfo1=' zdf - Ua: ', mask1=umask, & |
---|
497 | & tab3d_2=pvv(:,:,:,Kaa), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
---|
498 | ! |
---|
499 | IF( ln_timing ) CALL timing_stop('dyn_zdf') |
---|
500 | ! |
---|
501 | END SUBROUTINE dyn_zdf |
---|
502 | |
---|
503 | !!============================================================================== |
---|
504 | END MODULE dynzdf |
---|