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 | !! zdf_trd : diagnose the zdf velocity trends and the KE dissipation trend |
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14 | !!gm ==>>> zdf_trd currently not used |
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15 | !!---------------------------------------------------------------------- |
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16 | USE oce ! ocean dynamics and tracers variables |
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17 | USE phycst ! physical constants |
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18 | USE dom_oce ! ocean space and time domain variables |
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19 | USE sbc_oce ! surface boundary condition: ocean |
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20 | USE zdf_oce ! ocean vertical physics variables |
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21 | USE zdfdrg ! vertical physics: top/bottom drag coef. |
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22 | USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form |
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23 | USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing |
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24 | USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator |
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25 | USE trd_oce ! trends: ocean variables |
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26 | USE trddyn ! trend manager: dynamics |
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27 | ! |
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28 | USE in_out_manager ! I/O manager |
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29 | USE lib_mpp ! MPP library |
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30 | USE iom ! IOM library |
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31 | USE prtctl ! Print control |
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32 | USE timing ! Timing |
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33 | |
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34 | IMPLICIT NONE |
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35 | PRIVATE |
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36 | |
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37 | PUBLIC dyn_zdf ! routine called by step.F90 |
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38 | |
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39 | !! * Substitutions |
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40 | # include "vectopt_loop_substitute.h90" |
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41 | !!---------------------------------------------------------------------- |
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42 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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43 | !! $Id$ |
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44 | !! Software governed by the CeCILL licence (./LICENSE) |
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45 | !!---------------------------------------------------------------------- |
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46 | CONTAINS |
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47 | |
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48 | SUBROUTINE dyn_zdf( kt ) |
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49 | !!---------------------------------------------------------------------- |
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50 | !! *** ROUTINE dyn_zdf *** |
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51 | !! |
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52 | !! ** Purpose : compute the trend due to the vert. momentum diffusion |
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53 | !! together with the Leap-Frog time stepping using an |
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54 | !! implicit scheme. |
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55 | !! |
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56 | !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing |
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57 | !! ua = ub + 2*dt * ua vector form or linear free surf. |
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58 | !! ua = ( e3u_b*ub + 2*dt * e3u_n*ua ) / e3u_a otherwise |
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59 | !! - update the after velocity with the implicit vertical mixing. |
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60 | !! This requires to solver the following system: |
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61 | !! ua = ua + 1/e3u_a dk+1[ mi(avm) / e3uw_a dk[ua] ] |
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62 | !! with the following surface/top/bottom boundary condition: |
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63 | !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) |
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64 | !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) |
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65 | !! |
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66 | !! ** Action : (ua,va) after velocity |
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67 | !!--------------------------------------------------------------------- |
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68 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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69 | ! |
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70 | INTEGER :: ji, jj, jk ! dummy loop indices |
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71 | INTEGER :: iku, ikv ! local integers |
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72 | REAL(wp) :: zzwi, zDt_2 ! local scalars |
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73 | REAL(wp) :: zzws ! - - |
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74 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace |
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75 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - |
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76 | REAL(wp) :: ze3uw_A , ze3uw_Ap1 ! local real |
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77 | REAL(wp) :: ze3vw_A , ze3vw_Ap1 ! local real |
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78 | REAL(wp), DIMENSION(jpi,jpj) :: zsshu_hA, zsshv_hA ! 2D workspace |
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79 | !!--------------------------------------------------------------------- |
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80 | ! |
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81 | IF( ln_timing ) CALL timing_start('dyn_zdf') |
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82 | ! |
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83 | IF( kt == nit000 ) THEN !* initialization |
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84 | IF(lwp) WRITE(numout,*) |
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85 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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86 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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87 | ENDIF |
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88 | ! |
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89 | zDt_2 = rDt * 0.5_wp !* =rn_Dt except in 1st Euler time step where it is equal to rn_Dt/2 |
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90 | ! |
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91 | ! |
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92 | ! !* explicit top/bottom drag case |
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93 | IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, ub, vb, ua, va ) ! add top/bottom friction trend to (ua,va) |
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94 | ! |
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95 | ! |
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96 | IF( l_trddyn ) THEN !* temporary save of ta and sa trends |
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97 | ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) |
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98 | ztrdu(:,:,:) = ua(:,:,:) |
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99 | ztrdv(:,:,:) = va(:,:,:) |
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100 | ENDIF |
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101 | ! |
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102 | ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in ua,va) |
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103 | ! |
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104 | ! ! time stepping except vertical diffusion |
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105 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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106 | DO jk = 1, jpkm1 |
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107 | ua(:,:,jk) = ( ub(:,:,jk) + rDt * ua(:,:,jk) ) * umask(:,:,jk) |
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108 | va(:,:,jk) = ( vb(:,:,jk) + rDt * va(:,:,jk) ) * vmask(:,:,jk) |
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109 | END DO |
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110 | ELSE ! applied on thickness weighted velocity |
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111 | DO jk = 1, jpkm1 |
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112 | ua(:,:,jk) = ( e3u_b(:,:,jk)*ub(:,:,jk) + rDt * e3u_n(:,:,jk)*ua(:,:,jk) ) / e3u_a(:,:,jk) * umask(:,:,jk) |
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113 | va(:,:,jk) = ( e3v_b(:,:,jk)*vb(:,:,jk) + rDt * e3v_n(:,:,jk)*va(:,:,jk) ) / e3v_a(:,:,jk) * vmask(:,:,jk) |
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114 | END DO |
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115 | ENDIF |
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116 | ! ! add top/bottom friction |
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117 | ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. |
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118 | ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does |
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119 | ! not lead to the effective stress seen over the whole barotropic loop. |
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120 | ! G. Madec : in linear free surface, e3u_a = e3u_n = e3u_0, so systematic use of e3u_a |
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121 | IF( ln_drgimp .AND. ln_dynspg_ts ) THEN |
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122 | DO jk = 1, jpkm1 ! remove barotropic velocities |
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123 | ua(:,:,jk) = ( ua(:,:,jk) - ua_b(:,:) ) * umask(:,:,jk) |
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124 | va(:,:,jk) = ( va(:,:,jk) - va_b(:,:) ) * vmask(:,:,jk) |
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125 | END DO |
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126 | DO jj = 2, jpjm1 ! Add bottom/top stress due to barotropic component only |
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127 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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128 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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129 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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130 | ua(ji,jj,iku) = ua(ji,jj,iku) + zDt_2 * ( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * ua_b(ji,jj) / e3u_a(ji,jj,iku) |
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131 | va(ji,jj,ikv) = va(ji,jj,ikv) + zDt_2 * ( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * va_b(ji,jj) / e3v_a(ji,jj,ikv) |
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132 | END DO |
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133 | END DO |
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134 | IF( ln_isfcav ) THEN ! Ocean cavities (ISF) |
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135 | DO jj = 2, jpjm1 |
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136 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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137 | iku = miku(ji,jj) ! top ocean level at u- and v-points |
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138 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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139 | ua(ji,jj,iku) = ua(ji,jj,iku) + zDt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * ua_b(ji,jj) / e3u_a(ji,jj,iku) |
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140 | va(ji,jj,ikv) = va(ji,jj,ikv) + zDt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * va_b(ji,jj) / e3v_a(ji,jj,ikv) |
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141 | END DO |
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142 | END DO |
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143 | END IF |
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144 | ENDIF |
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145 | ! |
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146 | ! !== Vertical diffusion on u ==! |
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147 | ! |
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148 | ! !* multiplicative factors on e3uw(Naa) and e3vw(Naa) |
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149 | ! |
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150 | IF( ln_linssh ) THEN !-- linear ssh case |
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151 | DO jj = 1, jpjm1 |
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152 | DO ji = 1, jpim1 |
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153 | zsshu_hA(ji,jj) = 0._wp ! no time variation in e3 |
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154 | zsshv_hA(ji,jj) = 0._wp |
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155 | END DO |
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156 | END DO |
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157 | ELSE !-- Non linear ssh case |
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158 | DO jj = 1, jpjm1 |
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159 | DO ji = 1, jpim1 |
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160 | zsshu_hA(ji,jj) = 0.5_wp * ( ssh(ji,jj,Naa) + ssh(ji+1,jj ,Naa) ) * r1_hu_0(ji,jj) * ssumask(ji,jj) |
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161 | zsshv_hA(ji,jj) = 0.5_wp * ( ssh(ji,jj,Naa) + ssh(ji ,jj+1,Naa) ) * r1_hv_0(ji,jj) * ssvmask(ji,jj) |
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162 | END DO |
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163 | END DO |
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164 | ENDIF |
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165 | |
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166 | |
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167 | |
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168 | |
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169 | |
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170 | SELECT CASE( nldf_dyn ) !* Matrix construction |
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171 | ! |
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172 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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173 | DO jk = 1, jpkm1 |
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174 | DO jj = 2, jpjm1 |
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175 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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176 | !!gm Note that below, since ze3uw_A is used in a expression masked by wumask, |
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177 | !! one can remove wumask from its expression (same for ze3uw_Ap1 |
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178 | ze3uw_A = e3uw_0(ji,jj,jk ) * ( 1._wp + zsshu_hA(ji,jj) * wumask(ji,jj,jk ) ) |
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179 | ze3uw_Ap1 = e3uw_0(ji,jj,jk+1) * ( 1._wp + zsshu_hA(ji,jj) * wumask(ji,jj,jk+1) ) |
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180 | ! |
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181 | zzwi = - rDt * ( 0.5 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) + akzu(ji,jj,jk ) ) & |
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182 | & / ( e3u_a(ji ,jj,jk ) * ze3uw_A ) * wumask(ji,jj,jk ) |
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183 | zzws = - rDt * ( 0.5 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) + akzu(ji,jj,jk+1) ) & |
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184 | & / ( e3u_a(ji ,jj,jk ) * ze3uw_Ap1 ) * wumask(ji,jj,jk+1) |
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185 | zwi(ji,jj,jk) = zzwi |
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186 | zws(ji,jj,jk) = zzws |
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187 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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188 | END DO |
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189 | END DO |
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190 | END DO |
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191 | CASE DEFAULT ! iso-level lateral mixing |
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192 | DO jk = 1, jpkm1 |
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193 | DO jj = 2, jpjm1 |
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194 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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195 | !!gm Note that below, since ze3uw_A is used in a expression masked by wumask, |
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196 | !! one can remove wumask from its expression (same for ze3uw_Ap1 |
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197 | ze3uw_A = e3uw_0(ji,jj,jk ) * ( 1._wp + zsshu_hA(ji,jj) * wumask(ji,jj,jk ) ) |
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198 | ze3uw_Ap1 = e3uw_0(ji,jj,jk+1) * ( 1._wp + zsshu_hA(ji,jj) * wumask(ji,jj,jk+1) ) |
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199 | ! |
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200 | zzwi = - zDt_2 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( e3u_a(ji,jj,jk) * ze3uw_A ) * wumask(ji,jj,jk ) |
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201 | zzws = - zDt_2 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( e3u_a(ji,jj,jk) * ze3uw_Ap1 ) * wumask(ji,jj,jk+1) |
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202 | zwi(ji,jj,jk) = zzwi |
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203 | zws(ji,jj,jk) = zzws |
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204 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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205 | END DO |
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206 | END DO |
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207 | END DO |
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208 | END SELECT |
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209 | ! |
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210 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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211 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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212 | zwi(ji,jj,1) = 0._wp |
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213 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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214 | END DO |
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215 | END DO |
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216 | ! |
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217 | ! !== Apply semi-implicit bottom friction ==! |
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218 | ! |
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219 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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220 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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221 | ! column vector of the tri-diagonal matrix equation |
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222 | ! |
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223 | IF ( ln_drgimp ) THEN ! implicit bottom friction |
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224 | DO jj = 2, jpjm1 |
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225 | DO ji = 2, jpim1 |
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226 | iku = mbku(ji,jj) ! ocean bottom level at u- and v-points |
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227 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - zDt_2 * ( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / e3u_a(ji,jj,iku) |
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228 | END DO |
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229 | END DO |
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230 | IF ( ln_isfcav ) THEN ! top friction (always implicit) |
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231 | DO jj = 2, jpjm1 |
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232 | DO ji = 2, jpim1 |
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233 | !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed |
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234 | iku = miku(ji,jj) ! ocean top level at u- and v-points |
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235 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - zDt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / e3u_a(ji,jj,iku) |
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236 | END DO |
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237 | END DO |
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238 | END IF |
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239 | ENDIF |
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240 | ! |
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241 | ! Matrix inversion starting from the first level |
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242 | !----------------------------------------------------------------------- |
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243 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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244 | ! |
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245 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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246 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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247 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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248 | ! ( ... )( ... ) ( ... ) |
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249 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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250 | ! |
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251 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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252 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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253 | ! The solution (the after velocity) is in ua |
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254 | !----------------------------------------------------------------------- |
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255 | ! |
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256 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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257 | DO jj = 2, jpjm1 |
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258 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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259 | 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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260 | END DO |
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261 | END DO |
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262 | END DO |
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263 | ! |
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264 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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265 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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266 | ua(ji,jj,1) = ua(ji,jj,1) + zDt_2 * ( utau_b(ji,jj) + utau(ji,jj) ) / ( e3u_a(ji,jj,1) * rho0 ) * umask(ji,jj,1) |
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267 | END DO |
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268 | END DO |
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269 | DO jk = 2, jpkm1 |
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270 | DO jj = 2, jpjm1 |
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271 | DO ji = fs_2, fs_jpim1 |
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272 | ua(ji,jj,jk) = ua(ji,jj,jk) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) |
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273 | END DO |
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274 | END DO |
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275 | END DO |
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276 | ! |
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277 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==! |
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278 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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279 | ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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280 | END DO |
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281 | END DO |
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282 | DO jk = jpk-2, 1, -1 |
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283 | DO jj = 2, jpjm1 |
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284 | DO ji = fs_2, fs_jpim1 |
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285 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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286 | END DO |
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287 | END DO |
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288 | END DO |
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289 | ! |
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290 | ! !== Vertical diffusion on v ==! |
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291 | ! |
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292 | ! |
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293 | SELECT CASE( nldf_dyn ) !* Matrix construction |
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294 | CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) |
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295 | DO jk = 1, jpkm1 |
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296 | DO jj = 2, jpjm1 |
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297 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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298 | ze3vw_A = e3vw_0(ji,jj,jk ) * ( 1._wp + zsshv_hA(ji,jj) * wvmask(ji,jj,jk ) ) |
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299 | ze3vw_Ap1 = e3vw_0(ji,jj,jk+1) * ( 1._wp + zsshv_hA(ji,jj) * wvmask(ji,jj,jk+1) ) |
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300 | ! |
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301 | zzwi = - rDt * ( 0.5 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) + akzv(ji,jj,jk ) ) & |
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302 | & / ( e3v_a(ji,jj ,jk ) * ze3vw_A ) * wvmask(ji,jj,jk ) |
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303 | zzws = - rDt * ( 0.5 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) + akzv(ji,jj,jk+1) ) & |
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304 | & / ( e3v_a(ji,jj ,jk ) * ze3vw_Ap1 ) * wvmask(ji,jj,jk+1) |
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305 | zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk ) |
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306 | zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1) |
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307 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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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 | CASE DEFAULT ! iso-level lateral mixing |
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312 | DO jk = 1, jpkm1 |
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313 | DO jj = 2, jpjm1 |
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314 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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315 | ze3vw_A = e3vw_0(ji,jj,jk ) * ( 1._wp + zsshv_hA(ji,jj) * wvmask(ji,jj,jk ) ) |
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316 | ze3vw_Ap1 = e3vw_0(ji,jj,jk+1) * ( 1._wp + zsshv_hA(ji,jj) * wvmask(ji,jj,jk+1) ) |
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317 | ! |
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318 | zzwi = - zDt_2 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( e3v_a(ji,jj,jk) * ze3vw_A ) * wvmask(ji,jj,jk ) |
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319 | zzws = - zDt_2 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( e3v_a(ji,jj,jk) * ze3vw_Ap1 ) * wvmask(ji,jj,jk+1) |
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320 | zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk ) |
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321 | zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1) |
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322 | zwd(ji,jj,jk) = 1._wp - zzwi - zzws |
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323 | END DO |
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324 | END DO |
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325 | END DO |
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326 | END SELECT |
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327 | ! |
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328 | DO jj = 2, jpjm1 !* Surface boundary conditions |
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329 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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330 | zwi(ji,jj,1) = 0._wp |
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331 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
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332 | END DO |
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333 | END DO |
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334 | ! !== Apply semi-implicit top/bottom friction ==! |
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335 | ! |
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336 | ! Only needed for semi-implicit bottom friction setup. The explicit |
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337 | ! bottom friction has been included in "u(v)a" which act as the R.H.S |
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338 | ! column vector of the tri-diagonal matrix equation |
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339 | ! |
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340 | IF( ln_drgimp ) THEN |
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341 | DO jj = 2, jpjm1 |
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342 | DO ji = 2, jpim1 |
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343 | ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) |
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344 | zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - zDt_2 * ( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / e3v_a(ji,jj,ikv) |
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345 | END DO |
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346 | END DO |
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347 | IF ( ln_isfcav ) THEN |
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348 | DO jj = 2, jpjm1 |
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349 | DO ji = 2, jpim1 |
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350 | ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) |
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351 | zwd(ji,jj,iku) = zwd(ji,jj,iku) - zDt_2 * ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / e3v_a(ji,jj,ikv) |
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352 | END DO |
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353 | END DO |
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354 | ENDIF |
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355 | ENDIF |
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356 | |
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357 | ! Matrix inversion |
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358 | !----------------------------------------------------------------------- |
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359 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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360 | ! |
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361 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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362 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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363 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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364 | ! ( ... )( ... ) ( ... ) |
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365 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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366 | ! |
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367 | ! m is decomposed in the product of an upper and lower triangular matrix |
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368 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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369 | ! The solution (after velocity) is in 2d array va |
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370 | !----------------------------------------------------------------------- |
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371 | ! |
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372 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
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373 | DO jj = 2, jpjm1 |
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374 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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375 | 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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376 | END DO |
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377 | END DO |
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378 | END DO |
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379 | ! |
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380 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! |
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381 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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382 | va(ji,jj,1) = va(ji,jj,1) + zDt_2 * ( vtau_b(ji,jj) + vtau(ji,jj) ) / ( e3v_a(ji,jj,1) * rho0 ) * vmask(ji,jj,1) |
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383 | END DO |
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384 | END DO |
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385 | DO jk = 2, jpkm1 |
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386 | DO jj = 2, jpjm1 |
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387 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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388 | va(ji,jj,jk) = va(ji,jj,jk) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) |
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389 | END DO |
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390 | END DO |
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391 | END DO |
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392 | ! |
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393 | DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==! |
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394 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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395 | va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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396 | END DO |
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397 | END DO |
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398 | DO jk = jpk-2, 1, -1 |
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399 | DO jj = 2, jpjm1 |
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400 | DO ji = fs_2, fs_jpim1 |
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401 | va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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402 | END DO |
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403 | END DO |
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404 | END DO |
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405 | ! |
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406 | IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics |
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407 | IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity |
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408 | ztrdu(:,:,:) = ( ua(:,:,:) - ub(:,:,:) ) * r1_Dt - ztrdu(:,:,:) |
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409 | ztrdv(:,:,:) = ( va(:,:,:) - vb(:,:,:) ) * r1_Dt - ztrdv(:,:,:) |
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410 | ELSE ! applied on thickness weighted velocity |
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411 | ztrdu(:,:,:) = ( e3u_a(:,:,:)*ua(:,:,:) - e3u_b(:,:,:)*ub(:,:,:) ) / e3u_n(:,:,:) * r1_Dt - ztrdu(:,:,:) |
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412 | ztrdv(:,:,:) = ( e3v_a(:,:,:)*va(:,:,:) - e3v_b(:,:,:)*vb(:,:,:) ) / e3v_n(:,:,:) * r1_Dt - ztrdv(:,:,:) |
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413 | ENDIF |
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414 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt ) |
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415 | DEALLOCATE( ztrdu, ztrdv ) |
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416 | ENDIF |
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417 | ! ! print mean trends (used for debugging) |
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418 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' zdf - Ua: ', mask1=umask, & |
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419 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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420 | ! |
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421 | IF( ln_timing ) CALL timing_stop('dyn_zdf') |
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422 | ! |
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423 | END SUBROUTINE dyn_zdf |
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424 | |
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425 | !!============================================================================== |
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426 | END MODULE dynzdf |
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