1 | MODULE traadv_fct |
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2 | !!============================================================================== |
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3 | !! *** MODULE traadv_fct *** |
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4 | !! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method) |
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5 | !!============================================================================== |
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6 | !! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90) |
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7 | !!---------------------------------------------------------------------- |
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8 | |
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9 | !!---------------------------------------------------------------------- |
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10 | !! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme |
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11 | !! with sub-time-stepping in the vertical direction |
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12 | !! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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13 | !! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection |
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14 | !!---------------------------------------------------------------------- |
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15 | USE oce ! ocean dynamics and active tracers |
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16 | USE dom_oce ! ocean space and time domain |
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17 | ! TEMP: This change not necessary after trd_tra is tiled |
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18 | USE domain, ONLY : dom_tile |
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19 | USE trc_oce ! share passive tracers/Ocean variables |
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20 | USE trd_oce ! trends: ocean variables |
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21 | USE trdtra ! tracers trends |
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22 | USE diaptr ! poleward transport diagnostics |
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23 | USE diaar5 ! AR5 diagnostics |
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24 | USE phycst , ONLY : rho0_rcp |
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25 | USE zdf_oce , ONLY : ln_zad_Aimp |
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26 | ! |
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27 | USE in_out_manager ! I/O manager |
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28 | USE iom ! |
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29 | USE lib_mpp ! MPP library |
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30 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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31 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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32 | |
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33 | IMPLICIT NONE |
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34 | PRIVATE |
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35 | |
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36 | PUBLIC tra_adv_fct ! called by traadv.F90 |
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37 | PUBLIC interp_4th_cpt ! called by traadv_cen.F90 |
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38 | |
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39 | LOGICAL :: l_trd ! flag to compute trends |
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40 | LOGICAL :: l_ptr ! flag to compute poleward transport |
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41 | LOGICAL :: l_hst ! flag to compute heat/salt transport |
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42 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
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43 | |
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44 | ! ! tridiag solver associated indices: |
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45 | INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition |
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46 | INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition |
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47 | |
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48 | !! * Substitutions |
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49 | # include "do_loop_substitute.h90" |
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50 | # include "domzgr_substitute.h90" |
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51 | !!---------------------------------------------------------------------- |
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52 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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53 | !! $Id$ |
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54 | !! Software governed by the CeCILL license (see ./LICENSE) |
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55 | !!---------------------------------------------------------------------- |
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56 | CONTAINS |
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57 | |
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58 | SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pU, pV, pW, & |
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59 | & Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v ) |
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60 | !!---------------------------------------------------------------------- |
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61 | !! *** ROUTINE tra_adv_fct *** |
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62 | !! |
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63 | !! ** Purpose : Compute the now trend due to total advection of tracers |
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64 | !! and add it to the general trend of tracer equations |
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65 | !! |
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66 | !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction |
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67 | !! (choice through the value of kn_fct) |
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68 | !! - on the vertical the 4th order is a compact scheme |
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69 | !! - corrected flux (monotonic correction) |
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70 | !! |
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71 | !! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends |
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72 | !! - send trends to trdtra module for further diagnostics (l_trdtra=T) |
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73 | !! - poleward advective heat and salt transport (ln_diaptr=T) |
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74 | !!---------------------------------------------------------------------- |
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75 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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76 | INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices |
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77 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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78 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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79 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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80 | INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) |
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81 | INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) |
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82 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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83 | ! TEMP: This can be ST_2D(nn_hls) after trd_tra is tiled |
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84 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume flux components |
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85 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation |
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86 | ! |
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87 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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88 | ! TEMP: This change not necessary after trd_tra is tiled |
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89 | INTEGER :: itile |
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90 | REAL(wp) :: ztra ! local scalar |
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91 | REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - - |
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92 | REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - - |
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93 | REAL(wp), DIMENSION(ST_2D(nn_hls),jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw |
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94 | ! TEMP: This change not necessary after trd_tra is tiled |
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95 | REAL(wp), DIMENSION(:,:,:), SAVE, ALLOCATABLE :: ztrdx, ztrdy, ztrdz |
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96 | REAL(wp), DIMENSION(:,:,:) , ALLOCATABLE :: zptry |
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97 | REAL(wp), DIMENSION(:,:,:) , ALLOCATABLE :: zwinf, zwdia, zwsup |
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98 | LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection |
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99 | !!---------------------------------------------------------------------- |
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100 | ! TEMP: This change not necessary after trd_tra is tiled |
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101 | itile = ntile |
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102 | ! |
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103 | IF( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile |
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104 | IF( kt == kit000 ) THEN |
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105 | IF(lwp) WRITE(numout,*) |
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106 | IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype |
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107 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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108 | ENDIF |
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109 | !! -- init to 0 |
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110 | zwi(:,:,:) = 0._wp |
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111 | zwx(:,:,:) = 0._wp |
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112 | zwy(:,:,:) = 0._wp |
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113 | zwz(:,:,:) = 0._wp |
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114 | ztu(:,:,:) = 0._wp |
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115 | ztv(:,:,:) = 0._wp |
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116 | zltu(:,:,:) = 0._wp |
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117 | zltv(:,:,:) = 0._wp |
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118 | ztw(:,:,:) = 0._wp |
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119 | ! |
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120 | l_trd = .FALSE. ! set local switches |
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121 | l_hst = .FALSE. |
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122 | l_ptr = .FALSE. |
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123 | ll_zAimp = .FALSE. |
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124 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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125 | IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE. |
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126 | IF( cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. & |
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127 | & iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE. |
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128 | ! |
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129 | ! TEMP: This can be ST_2D(nn_hls) after trd_tra is tiled |
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130 | IF( kt == kit000 .AND. (l_trd .OR. l_hst) ) THEN |
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131 | ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) ) |
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132 | ENDIF |
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133 | ENDIF |
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134 | ! |
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135 | IF( l_ptr ) THEN |
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136 | ALLOCATE( zptry(ST_2D(nn_hls),jpk) ) |
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137 | zptry(:,:,:) = 0._wp |
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138 | ENDIF |
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139 | ! ! surface & bottom value : flux set to zero one for all |
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140 | zwz(:,:, 1 ) = 0._wp |
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141 | zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp |
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142 | ! |
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143 | zwi(:,:,:) = 0._wp |
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144 | ! |
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145 | ! If adaptive vertical advection, check if it is needed on this PE at this time |
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146 | IF( ln_zad_Aimp ) THEN |
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147 | IF( MAXVAL( ABS( wi(ST_2D(nn_hls),:) ) ) > 0._wp ) ll_zAimp = .TRUE. |
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148 | END IF |
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149 | ! If active adaptive vertical advection, build tridiagonal matrix |
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150 | IF( ll_zAimp ) THEN |
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151 | ALLOCATE(zwdia(ST_2D(nn_hls),jpk), zwinf(ST_2D(nn_hls),jpk), zwsup(ST_2D(nn_hls),jpk)) |
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152 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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153 | zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) & |
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154 | & / e3t(ji,jj,jk,Krhs) |
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155 | zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs) |
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156 | zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs) |
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157 | END_3D |
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158 | END IF |
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159 | ! |
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160 | DO jn = 1, kjpt !== loop over the tracers ==! |
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161 | ! |
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162 | ! !== upstream advection with initial mass fluxes & intermediate update ==! |
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163 | ! !* upstream tracer flux in the i and j direction |
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164 | DO_3D( 1, 0, 1, 0, 1, jpkm1 ) |
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165 | ! upstream scheme |
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166 | zfp_ui = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) ) |
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167 | zfm_ui = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) ) |
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168 | zfp_vj = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) ) |
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169 | zfm_vj = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) ) |
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170 | zwx(ji,jj,jk) = 0.5 * ( zfp_ui * pt(ji,jj,jk,jn,Kbb) + zfm_ui * pt(ji+1,jj ,jk,jn,Kbb) ) |
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171 | zwy(ji,jj,jk) = 0.5 * ( zfp_vj * pt(ji,jj,jk,jn,Kbb) + zfm_vj * pt(ji ,jj+1,jk,jn,Kbb) ) |
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172 | END_3D |
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173 | ! !* upstream tracer flux in the k direction *! |
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174 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) |
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175 | zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) ) |
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176 | zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) ) |
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177 | zwz(ji,jj,jk) = 0.5 * ( zfp_wk * pt(ji,jj,jk,jn,Kbb) + zfm_wk * pt(ji,jj,jk-1,jn,Kbb) ) * wmask(ji,jj,jk) |
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178 | END_3D |
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179 | IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) |
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180 | ! TODO: NOT TESTED- requires isf |
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181 | IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface |
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182 | DO_2D( 1, 1, 1, 1 ) |
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183 | zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb) ! linear free surface |
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184 | END_2D |
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185 | ELSE ! no cavities: only at the ocean surface |
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186 | DO_2D( 1, 1, 1, 1 ) |
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187 | zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb) |
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188 | END_2D |
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189 | ENDIF |
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190 | ENDIF |
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191 | ! |
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192 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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193 | ! ! total intermediate advective trends |
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194 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
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195 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
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196 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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197 | ! ! update and guess with monotonic sheme |
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198 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra & |
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199 | & / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk) |
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200 | zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) & |
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201 | & / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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202 | END_3D |
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203 | |
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204 | IF ( ll_zAimp ) THEN |
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205 | CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 ) |
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206 | ! |
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207 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ; |
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208 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
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209 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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210 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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211 | ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
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212 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes |
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213 | END_3D |
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214 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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215 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & |
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216 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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217 | END_3D |
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218 | ! |
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219 | END IF |
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220 | ! |
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221 | ! TEMP: This change not necessary after trd_tra is tiled |
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222 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes) |
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223 | DO_3D( 1, 0, 1, 0, 1, jpk ) |
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224 | ztrdx(ji,jj,jk) = zwx(ji,jj,jk) ; ztrdy(ji,jj,jk) = zwy(ji,jj,jk) ; ztrdz(ji,jj,jk) = zwz(ji,jj,jk) |
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225 | END_3D |
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226 | END IF |
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227 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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228 | IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:) |
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229 | ! |
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230 | ! !== anti-diffusive flux : high order minus low order ==! |
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231 | ! |
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232 | SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes |
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233 | ! |
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234 | CASE( 2 ) !- 2nd order centered |
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235 | DO_3D( 1, 0, 1, 0, 1, jpkm1 ) |
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236 | zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj,jk,jn,Kmm) ) - zwx(ji,jj,jk) |
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237 | zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj+1,jk,jn,Kmm) ) - zwy(ji,jj,jk) |
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238 | END_3D |
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239 | ! |
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240 | CASE( 4 ) !- 4th order centered |
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241 | zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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242 | zltv(:,:,jpk) = 0._wp |
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243 | DO jk = 1, jpkm1 ! Laplacian |
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244 | DO_2D( 1, 0, 1, 0 ) |
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245 | ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk) |
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246 | ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk) |
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247 | END_2D |
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248 | DO_2D( 0, 0, 0, 0 ) |
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249 | zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 |
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250 | zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 |
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251 | END_2D |
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252 | END DO |
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253 | CALL lbc_lnk_multi( 'traadv_fct', zltu, 'T', 1.0_wp , zltv, 'T', 1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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254 | ! |
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255 | DO_3D( 1, 0, 1, 0, 1, jpkm1 ) |
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256 | zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points |
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257 | zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm) |
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258 | ! ! C4 minus upstream advective fluxes |
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259 | zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk) |
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260 | zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk) |
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261 | END_3D |
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262 | ! |
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263 | CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested |
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264 | ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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265 | ztv(:,:,jpk) = 0._wp |
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266 | DO_3D( 1, 0, 1, 0, 1, jpkm1 ) |
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267 | ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk) |
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268 | ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk) |
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269 | END_3D |
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270 | CALL lbc_lnk_multi( 'traadv_fct', ztu, 'U', -1.0_wp , ztv, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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271 | ! |
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272 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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273 | zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points (x2) |
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274 | zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm) |
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275 | ! ! C4 interpolation of T at u- & v-points (x2) |
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276 | zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) ) |
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277 | zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) ) |
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278 | ! ! C4 minus upstream advective fluxes |
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279 | zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk) |
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280 | zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk) |
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281 | END_3D |
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282 | ! |
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283 | END SELECT |
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284 | ! |
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285 | SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values) |
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286 | ! |
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287 | CASE( 2 ) !- 2nd order centered |
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288 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
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289 | zwz(ji,jj,jk) = ( pW(ji,jj,jk) * 0.5_wp * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj,jk-1,jn,Kmm) ) & |
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290 | & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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291 | END_3D |
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292 | ! |
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293 | CASE( 4 ) !- 4th order COMPACT |
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294 | CALL interp_4th_cpt( pt(:,:,:,jn,Kmm) , ztw ) ! zwt = COMPACT interpolation of T at w-point |
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295 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
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296 | zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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297 | END_3D |
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298 | ! |
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299 | END SELECT |
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300 | IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0 |
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301 | zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked |
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302 | ENDIF |
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303 | ! |
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304 | IF ( ll_zAimp ) THEN |
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305 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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306 | ! ! total intermediate advective trends |
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307 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
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308 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
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309 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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310 | ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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311 | END_3D |
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312 | ! |
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313 | CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 ) |
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314 | ! |
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315 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
316 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
---|
317 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
---|
318 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
---|
319 | END_3D |
---|
320 | END IF |
---|
321 | ! |
---|
322 | CALL lbc_lnk_multi( 'traadv_fct', zwi, 'T', 1.0_wp, zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp, zwz, 'W', 1.0_wp ) |
---|
323 | ! |
---|
324 | ! !== monotonicity algorithm ==! |
---|
325 | ! |
---|
326 | CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx, zwy, zwz, zwi, p2dt ) |
---|
327 | ! |
---|
328 | ! !== final trend with corrected fluxes ==! |
---|
329 | ! |
---|
330 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
331 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
---|
332 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
---|
333 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
---|
334 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm) |
---|
335 | zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
---|
336 | END_3D |
---|
337 | ! |
---|
338 | IF ( ll_zAimp ) THEN |
---|
339 | ! |
---|
340 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp |
---|
341 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
342 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
---|
343 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
---|
344 | ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
---|
345 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic |
---|
346 | END_3D |
---|
347 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
348 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & |
---|
349 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
---|
350 | END_3D |
---|
351 | END IF |
---|
352 | ! |
---|
353 | ! TEMP: These changes not necessary after trd_tra is tiled |
---|
354 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport |
---|
355 | DO_3D( 1, 0, 1, 0, 1, jpk ) |
---|
356 | ztrdx(ji,jj,jk) = ztrdx(ji,jj,jk) + zwx(ji,jj,jk) ! <<< add anti-diffusive fluxes |
---|
357 | ztrdy(ji,jj,jk) = ztrdy(ji,jj,jk) + zwy(ji,jj,jk) ! to upstream fluxes |
---|
358 | ztrdz(ji,jj,jk) = ztrdz(ji,jj,jk) + zwz(ji,jj,jk) ! |
---|
359 | END_3D |
---|
360 | ! |
---|
361 | IF( ntile == 0 .OR. ntile == nijtile ) THEN ! Do only for the full domain |
---|
362 | IF( l_trd ) THEN ! trend diagnostics |
---|
363 | IF( ln_tile ) CALL dom_tile( ntsi, ntsj, ntei, ntej, ktile = 0 ) ! Use full domain |
---|
364 | |
---|
365 | ! TODO: TO BE TILED- trd_tra |
---|
366 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) ) |
---|
367 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) ) |
---|
368 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) ) |
---|
369 | |
---|
370 | IF( ln_tile ) CALL dom_tile( ntsi, ntsj, ntei, ntej, ktile = itile ) ! Revert to tile domain |
---|
371 | ENDIF |
---|
372 | ENDIF |
---|
373 | ! ! heat/salt transport |
---|
374 | IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(ST_2D(nn_hls),:), ztrdy(ST_2D(nn_hls),:) ) |
---|
375 | ! |
---|
376 | ENDIF |
---|
377 | IF( l_ptr ) THEN ! "Poleward" transports |
---|
378 | zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes |
---|
379 | CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) ) |
---|
380 | ENDIF |
---|
381 | ! |
---|
382 | END DO ! end of tracer loop |
---|
383 | ! |
---|
384 | IF ( ll_zAimp ) THEN |
---|
385 | DEALLOCATE( zwdia, zwinf, zwsup ) |
---|
386 | ENDIF |
---|
387 | ! TEMP: These changes not necessary after trd_tra is tiled |
---|
388 | ! IF( l_trd .OR. l_hst ) THEN |
---|
389 | ! DEALLOCATE( ztrdx, ztrdy, ztrdz ) |
---|
390 | ! ENDIF |
---|
391 | IF( l_ptr ) THEN |
---|
392 | DEALLOCATE( zptry ) |
---|
393 | ENDIF |
---|
394 | ! |
---|
395 | END SUBROUTINE tra_adv_fct |
---|
396 | |
---|
397 | |
---|
398 | SUBROUTINE nonosc( Kmm, pbef, paa, pbb, pcc, paft, p2dt ) |
---|
399 | !!--------------------------------------------------------------------- |
---|
400 | !! *** ROUTINE nonosc *** |
---|
401 | !! |
---|
402 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
403 | !! scheme and the before field by a nonoscillatory algorithm |
---|
404 | !! |
---|
405 | !! ** Method : ... ??? |
---|
406 | !! warning : pbef and paft must be masked, but the boundaries |
---|
407 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
408 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
409 | !! in-space based differencing for fluid |
---|
410 | !!---------------------------------------------------------------------- |
---|
411 | INTEGER , INTENT(in ) :: Kmm ! time level index |
---|
412 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
---|
413 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pbef ! before field |
---|
414 | REAL(wp), DIMENSION(ST_2D(nn_hls) ,jpk), INTENT(in ) :: paft ! after field |
---|
415 | REAL(wp), DIMENSION(ST_2D(nn_hls) ,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions |
---|
416 | ! |
---|
417 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
418 | INTEGER :: ikm1 ! local integer |
---|
419 | REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars |
---|
420 | REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
421 | REAL(dp), DIMENSION(ST_2D(nn_hls),jpk) :: zbetup, zbetdo, zbup, zbdo |
---|
422 | !!---------------------------------------------------------------------- |
---|
423 | ! |
---|
424 | zbig = 1.e+40_dp |
---|
425 | zrtrn = 1.e-15_dp |
---|
426 | zbetup(:,:,:) = 0._dp ; zbetdo(:,:,:) = 0._dp |
---|
427 | |
---|
428 | ! Search local extrema |
---|
429 | ! -------------------- |
---|
430 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
431 | DO_3D( 1, 1, 1, 1, 1, jpk ) |
---|
432 | zbup(ji,jj,jk) = MAX( pbef(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ), & |
---|
433 | & paft(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ) ) |
---|
434 | zbdo(ji,jj,jk) = MIN( pbef(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ), & |
---|
435 | & paft(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ) ) |
---|
436 | END_3D |
---|
437 | |
---|
438 | DO jk = 1, jpkm1 |
---|
439 | ikm1 = MAX(jk-1,1) |
---|
440 | DO_2D( 0, 0, 0, 0 ) |
---|
441 | |
---|
442 | ! search maximum in neighbourhood |
---|
443 | zup = MAX( zbup(ji ,jj ,jk ), & |
---|
444 | & zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), & |
---|
445 | & zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), & |
---|
446 | & zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) ) |
---|
447 | |
---|
448 | ! search minimum in neighbourhood |
---|
449 | zdo = MIN( zbdo(ji ,jj ,jk ), & |
---|
450 | & zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), & |
---|
451 | & zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), & |
---|
452 | & zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) ) |
---|
453 | |
---|
454 | ! positive part of the flux |
---|
455 | zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) & |
---|
456 | & + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) & |
---|
457 | & + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
---|
458 | |
---|
459 | ! negative part of the flux |
---|
460 | zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) & |
---|
461 | & + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) & |
---|
462 | & + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
---|
463 | |
---|
464 | ! up & down beta terms |
---|
465 | zbt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt |
---|
466 | zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt |
---|
467 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt |
---|
468 | END_2D |
---|
469 | END DO |
---|
470 | CALL lbc_lnk_multi( 'traadv_fct', zbetup, 'T', 1.0_wp , zbetdo, 'T', 1.0_wp ) ! lateral boundary cond. (unchanged sign) |
---|
471 | |
---|
472 | ! 3. monotonic flux in the i & j direction (paa & pbb) |
---|
473 | ! ---------------------------------------- |
---|
474 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
475 | zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) |
---|
476 | zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) |
---|
477 | zcu = ( 0.5 + SIGN( 0.5_wp , paa(ji,jj,jk) ) ) |
---|
478 | paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
---|
479 | |
---|
480 | zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) |
---|
481 | zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) |
---|
482 | zcv = ( 0.5 + SIGN( 0.5_wp , pbb(ji,jj,jk) ) ) |
---|
483 | pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
---|
484 | |
---|
485 | ! monotonic flux in the k direction, i.e. pcc |
---|
486 | ! ------------------------------------------- |
---|
487 | za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) ) |
---|
488 | zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) ) |
---|
489 | zc = ( 0.5 + SIGN( 0.5_wp , pcc(ji,jj,jk+1) ) ) |
---|
490 | pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb ) |
---|
491 | END_3D |
---|
492 | CALL lbc_lnk_multi( 'traadv_fct', paa, 'U', -1.0_wp , pbb, 'V', -1.0_wp ) ! lateral boundary condition (changed sign) |
---|
493 | ! |
---|
494 | END SUBROUTINE nonosc |
---|
495 | |
---|
496 | |
---|
497 | SUBROUTINE interp_4th_cpt_org( pt_in, pt_out ) |
---|
498 | !!---------------------------------------------------------------------- |
---|
499 | !! *** ROUTINE interp_4th_cpt_org *** |
---|
500 | !! |
---|
501 | !! ** Purpose : Compute the interpolation of tracer at w-point |
---|
502 | !! |
---|
503 | !! ** Method : 4th order compact interpolation |
---|
504 | !!---------------------------------------------------------------------- |
---|
505 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields |
---|
506 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts |
---|
507 | ! |
---|
508 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
509 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt |
---|
510 | !!---------------------------------------------------------------------- |
---|
511 | |
---|
512 | DO_3D( 1, 1, 1, 1, 3, jpkm1 ) |
---|
513 | zwd (ji,jj,jk) = 4._wp |
---|
514 | zwi (ji,jj,jk) = 1._wp |
---|
515 | zws (ji,jj,jk) = 1._wp |
---|
516 | zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
517 | ! |
---|
518 | IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom |
---|
519 | zwd (ji,jj,jk) = 1._wp |
---|
520 | zwi (ji,jj,jk) = 0._wp |
---|
521 | zws (ji,jj,jk) = 0._wp |
---|
522 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
523 | ENDIF |
---|
524 | END_3D |
---|
525 | ! |
---|
526 | jk = 2 ! Switch to second order centered at top |
---|
527 | DO_2D( 1, 1, 1, 1 ) |
---|
528 | zwd (ji,jj,jk) = 1._wp |
---|
529 | zwi (ji,jj,jk) = 0._wp |
---|
530 | zws (ji,jj,jk) = 0._wp |
---|
531 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
532 | END_2D |
---|
533 | ! |
---|
534 | ! !== tridiagonal solve ==! |
---|
535 | DO_2D( 1, 1, 1, 1 ) |
---|
536 | zwt(ji,jj,2) = zwd(ji,jj,2) |
---|
537 | END_2D |
---|
538 | DO_3D( 1, 1, 1, 1, 3, jpkm1 ) |
---|
539 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
540 | END_3D |
---|
541 | ! |
---|
542 | DO_2D( 1, 1, 1, 1 ) |
---|
543 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
---|
544 | END_2D |
---|
545 | DO_3D( 1, 1, 1, 1, 3, jpkm1 ) |
---|
546 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
547 | END_3D |
---|
548 | |
---|
549 | DO_2D( 1, 1, 1, 1 ) |
---|
550 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
551 | END_2D |
---|
552 | DO_3DS( 1, 1, 1, 1, jpk-2, 2, -1 ) |
---|
553 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
554 | END_3D |
---|
555 | ! |
---|
556 | END SUBROUTINE interp_4th_cpt_org |
---|
557 | |
---|
558 | |
---|
559 | SUBROUTINE interp_4th_cpt( pt_in, pt_out ) |
---|
560 | !!---------------------------------------------------------------------- |
---|
561 | !! *** ROUTINE interp_4th_cpt *** |
---|
562 | !! |
---|
563 | !! ** Purpose : Compute the interpolation of tracer at w-point |
---|
564 | !! |
---|
565 | !! ** Method : 4th order compact interpolation |
---|
566 | !!---------------------------------------------------------------------- |
---|
567 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point |
---|
568 | REAL(wp),DIMENSION(ST_2D(nn_hls) ,jpk), INTENT( out) :: pt_out ! field interpolated at w-point |
---|
569 | ! |
---|
570 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
571 | INTEGER :: ikt, ikb ! local integers |
---|
572 | REAL(wp),DIMENSION(ST_2D(nn_hls),jpk) :: zwd, zwi, zws, zwrm, zwt |
---|
573 | !!---------------------------------------------------------------------- |
---|
574 | ! |
---|
575 | ! !== build the three diagonal matrix & the RHS ==! |
---|
576 | ! |
---|
577 | DO_3D( 0, 0, 0, 0, 3, jpkm1 ) |
---|
578 | zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal |
---|
579 | zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal |
---|
580 | zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal |
---|
581 | zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS |
---|
582 | & * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) ) |
---|
583 | END_3D |
---|
584 | ! |
---|
585 | !!gm |
---|
586 | ! SELECT CASE( kbc ) !* boundary condition |
---|
587 | ! CASE( np_NH ) ! Neumann homogeneous at top & bottom |
---|
588 | ! CASE( np_CEN2 ) ! 2nd order centered at top & bottom |
---|
589 | ! END SELECT |
---|
590 | !!gm |
---|
591 | ! |
---|
592 | ! TODO: NOT TESTED- requires isf |
---|
593 | IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case |
---|
594 | zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp |
---|
595 | END IF |
---|
596 | ! |
---|
597 | DO_2D( 0, 0, 0, 0 ) |
---|
598 | ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point |
---|
599 | ikb = MAX(mbkt(ji,jj), 2) ! - above the last wet point |
---|
600 | ! |
---|
601 | zwd (ji,jj,ikt) = 1._wp ! top |
---|
602 | zwi (ji,jj,ikt) = 0._wp |
---|
603 | zws (ji,jj,ikt) = 0._wp |
---|
604 | zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) ) |
---|
605 | ! |
---|
606 | zwd (ji,jj,ikb) = 1._wp ! bottom |
---|
607 | zwi (ji,jj,ikb) = 0._wp |
---|
608 | zws (ji,jj,ikb) = 0._wp |
---|
609 | zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) ) |
---|
610 | END_2D |
---|
611 | ! |
---|
612 | ! !== tridiagonal solver ==! |
---|
613 | ! |
---|
614 | DO_2D( 0, 0, 0, 0 ) |
---|
615 | zwt(ji,jj,2) = zwd(ji,jj,2) |
---|
616 | END_2D |
---|
617 | DO_3D( 0, 0, 0, 0, 3, jpkm1 ) |
---|
618 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
619 | END_3D |
---|
620 | ! |
---|
621 | DO_2D( 0, 0, 0, 0 ) |
---|
622 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
---|
623 | END_2D |
---|
624 | DO_3D( 0, 0, 0, 0, 3, jpkm1 ) |
---|
625 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
626 | END_3D |
---|
627 | |
---|
628 | DO_2D( 0, 0, 0, 0 ) |
---|
629 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
630 | END_2D |
---|
631 | DO_3DS( 0, 0, 0, 0, jpk-2, 2, -1 ) |
---|
632 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
633 | END_3D |
---|
634 | ! |
---|
635 | END SUBROUTINE interp_4th_cpt |
---|
636 | |
---|
637 | |
---|
638 | SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev ) |
---|
639 | !!---------------------------------------------------------------------- |
---|
640 | !! *** ROUTINE tridia_solver *** |
---|
641 | !! |
---|
642 | !! ** Purpose : solve a symmetric 3diagonal system |
---|
643 | !! |
---|
644 | !! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk ) |
---|
645 | !! |
---|
646 | !! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 ) |
---|
647 | !! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 ) |
---|
648 | !! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 ) |
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649 | !! ( ... )( ... ) ( ... ) |
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650 | !! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k ) |
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651 | !! |
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652 | !! M is decomposed in the product of an upper and lower triangular matrix. |
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653 | !! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL |
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654 | !! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal). |
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655 | !! The solution is pta. |
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656 | !! The 3d array zwt is used as a work space array. |
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657 | !!---------------------------------------------------------------------- |
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658 | REAL(wp),DIMENSION(ST_2D(nn_hls),jpk), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix |
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659 | REAL(wp),DIMENSION(ST_2D(nn_hls),jpk), INTENT(in ) :: pRHS ! Right-Hand-Side |
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660 | REAL(wp),DIMENSION(ST_2D(nn_hls),jpk), INTENT( out) :: pt_out !!gm field at level=F(klev) |
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661 | INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level |
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662 | ! ! =0 pt at t-level |
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663 | INTEGER :: ji, jj, jk ! dummy loop integers |
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664 | INTEGER :: kstart ! local indices |
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665 | REAL(wp),DIMENSION(ST_2D(nn_hls),jpk) :: zwt ! 3D work array |
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666 | !!---------------------------------------------------------------------- |
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667 | ! |
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668 | kstart = 1 + klev |
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669 | ! |
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670 | DO_2D( 0, 0, 0, 0 ) |
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671 | zwt(ji,jj,kstart) = pD(ji,jj,kstart) |
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672 | END_2D |
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673 | DO_3D( 0, 0, 0, 0, kstart+1, jpkm1 ) |
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674 | zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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675 | END_3D |
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676 | ! |
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677 | DO_2D( 0, 0, 0, 0 ) |
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678 | pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart) |
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679 | END_2D |
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680 | DO_3D( 0, 0, 0, 0, kstart+1, jpkm1 ) |
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681 | pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
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682 | END_3D |
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683 | |
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684 | DO_2D( 0, 0, 0, 0 ) |
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685 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
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686 | END_2D |
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687 | DO_3DS( 0, 0, 0, 0, jpk-2, kstart, -1 ) |
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688 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
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689 | END_3D |
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690 | ! |
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691 | END SUBROUTINE tridia_solver |
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692 | |
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693 | !!====================================================================== |
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694 | END MODULE traadv_fct |
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