1 | MODULE traadv_fct_lf |
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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-lf : 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 - loop fusion version |
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12 | !! nonosc_lf : compute monotonic tracer fluxes by a non-oscillatory algorithm - loop fusion version |
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13 | !!---------------------------------------------------------------------- |
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14 | USE oce ! ocean dynamics and active tracers |
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15 | USE dom_oce ! ocean space and time domain |
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16 | USE trc_oce ! share passive tracers/Ocean variables |
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17 | USE trd_oce ! trends: ocean variables |
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18 | USE trdtra ! tracers trends |
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19 | USE diaptr ! poleward transport diagnostics |
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20 | USE diaar5 ! AR5 diagnostics |
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21 | USE phycst , ONLY : rho0_rcp |
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22 | USE zdf_oce , ONLY : ln_zad_Aimp |
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23 | ! |
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24 | USE in_out_manager ! I/O manager |
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25 | USE iom ! |
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26 | USE lib_mpp ! MPP library |
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27 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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28 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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29 | USE traadv_fct |
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30 | |
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31 | IMPLICIT NONE |
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32 | PRIVATE |
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33 | |
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34 | PUBLIC tra_adv_fct_lf ! called by traadv.F90 |
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35 | |
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36 | LOGICAL :: l_trd ! flag to compute trends |
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37 | LOGICAL :: l_ptr ! flag to compute poleward transport |
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38 | LOGICAL :: l_hst ! flag to compute heat/salt transport |
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39 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
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40 | |
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41 | ! ! tridiag solver associated indices: |
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42 | INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition |
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43 | INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition |
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44 | |
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45 | !! * Substitutions |
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46 | # include "do_loop_substitute.h90" |
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47 | # include "domzgr_substitute.h90" |
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48 | |
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49 | #define tracer_flux_i(out,zfp,zfm,ji,jj,jk) \ |
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50 | zfp = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) ) ; \ |
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51 | zfm = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) ) ; \ |
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52 | out = 0.5 * ( zfp * pt(ji,jj,jk,jn,Kbb) + zfm * pt(ji+1,jj,jk,jn,Kbb) ) |
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53 | |
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54 | #define tracer_flux_j(out,zfp,zfm,ji,jj,jk) \ |
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55 | zfp = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) ) ; \ |
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56 | zfm = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) ) ; \ |
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57 | out = 0.5 * ( zfp * pt(ji,jj,jk,jn,Kbb) + zfm * pt(ji,jj+1,jk,jn,Kbb) ) |
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58 | |
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59 | #define search_in_neighbour(out,OP,vec,ji,jj,jk) \ |
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60 | out = OP(vec(ji,jj,jk),vec(ji-1,jj,jk),vec(ji+1,jj,jk), \ |
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61 | vec(ji,jj-1,jk),vec(ji,jj+1,jk),vec(ji,jj,MAX(jk-1,1)),vec(ji,jj,jk+1)) |
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62 | |
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63 | #define pos_part_of_flux(ji,jj,jk,out) \ |
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64 | out = MAX(0.,paa_in(ji-1,jj,jk)) - MIN(0.,paa_in(ji,jj,jk)) \ |
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65 | + MAX(0.,pbb_in(ji,jj-1,jk)) - MIN(0.,pbb_in(ji,jj,jk)) \ |
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66 | + MAX(0.,pcc_in(ji,jj,jk+1)) - MIN(0.,pcc_in(ji,jj,jk)) |
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67 | |
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68 | #define neg_part_of_flux(ji,jj,jk,out) \ |
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69 | out = MAX( 0.,paa_in(ji,jj,jk) ) - MIN( 0., paa_in(ji-1,jj,jk)) \ |
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70 | + MAX( 0.,pbb_in(ji,jj,jk) ) - MIN( 0., pbb_in(ji,jj-1,jk)) \ |
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71 | + MAX( 0.,pcc_in(ji,jj,jk) ) - MIN( 0., pcc_in(ji,jj,jk+1)) |
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72 | |
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73 | #define beta_terms(bt,betup,betdo,up,pos,do,neg,ji,jj,jk) \ |
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74 | bt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt ; \ |
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75 | betup = ( up - paft(ji,jj,jk) ) / ( pos + zrtrn ) * bt ; \ |
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76 | betdo = ( paft(ji,jj,jk) - do ) / ( neg + zrtrn ) * bt |
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77 | |
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78 | #define monotonic_flux(a,b,c,betup_p1,betdo_p1,vec,vec_in,jk) \ |
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79 | a = MIN( 1._wp, zbetdo(ji,jj), betup_p1 ) ; \ |
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80 | b = MIN( 1._wp, zbetup(ji,jj), betdo_p1 ) ; \ |
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81 | c = ( 0.5_wp + SIGN( 0.5_wp , vec_in(ji,jj,jk) ) ) ; \ |
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82 | vec(ji,jj,jk) = vec_in(ji,jj,jk) * ( c * a + ( 1._wp - c) * b ) |
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83 | |
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84 | #define monotonic_flux_k(a,b,c,betup,betdo,vec,vec_in,jk) \ |
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85 | a = MIN( 1._wp, betdo, zbetup_ptr(ji,jj) ) ; \ |
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86 | b = MIN( 1._wp, betup, zbetdo_ptr(ji,jj) ) ; \ |
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87 | c = ( 0.5 + SIGN( 0.5_wp , vec_in(ji,jj,jk) ) ) ; \ |
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88 | vec(ji,jj,jk) = vec_in(ji,jj,jk) * ( c * a + ( 1._wp - c) * b ) |
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89 | |
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90 | !!---------------------------------------------------------------------- |
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91 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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92 | !! $Id: traadv_fct.F90 13660 2020-10-22 10:47:32Z francesca $ |
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93 | !! Software governed by the CeCILL license (see ./LICENSE) |
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94 | !!---------------------------------------------------------------------- |
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95 | CONTAINS |
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96 | |
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97 | SUBROUTINE tra_adv_fct_lf( kt, kit000, cdtype, p2dt, pU, pV, pW, & |
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98 | & Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v ) |
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99 | !!---------------------------------------------------------------------- |
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100 | !! *** ROUTINE tra_adv_fct *** |
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101 | !! |
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102 | !! ** Purpose : Compute the now trend due to total advection of tracers |
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103 | !! and add it to the general trend of tracer equations |
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104 | !! |
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105 | !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction |
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106 | !! (choice through the value of kn_fct) |
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107 | !! - on the vertical the 4th order is a compact scheme |
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108 | !! - corrected flux (monotonic correction) |
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109 | !! |
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110 | !! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends |
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111 | !! - send trends to trdtra module for further diagnostics (l_trdtra=T) |
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112 | !! - poleward advective heat and salt transport (ln_diaptr=T) |
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113 | !!---------------------------------------------------------------------- |
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114 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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115 | INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices |
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116 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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117 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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118 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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119 | INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) |
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120 | INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) |
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121 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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122 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(inout) :: pU, pV, pW ! 3 ocean volume flux components |
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123 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation |
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124 | ! |
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125 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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126 | REAL(wp) :: ztra ! local scalar |
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127 | REAL(wp) :: zwx_im1, zfp_ui, zfp_ui_m1, zfp_vj, zfp_vj_m1, zfp_wk, zC2t_u, zC4t_u ! - - |
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128 | REAL(wp) :: zwy_jm1, zfm_ui, zfm_ui_m1, zfm_vj, zfm_vj_m1, zfm_wk, zC2t_v, zC4t_v ! - - |
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129 | REAL(wp) :: ztu_im1, ztu_ip1, ztv_jm1, ztv_jp1 |
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130 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx_3d, zwy_3d, zwz, ztw, zltu_3d, zltv_3d, ztu, ztv |
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131 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry |
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132 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup |
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133 | LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection |
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134 | !!---------------------------------------------------------------------- |
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135 | ! |
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136 | IF( kt == kit000 ) THEN |
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137 | IF(lwp) WRITE(numout,*) |
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138 | IF(lwp) WRITE(numout,*) 'tra_adv_fct_lf : FCT advection scheme on ', cdtype |
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139 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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140 | ENDIF |
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141 | !! -- init to 0 |
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142 | zwx_3d(:,:,:) = 0._wp |
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143 | zwy_3d(:,:,:) = 0._wp |
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144 | zwz(:,:,:) = 0._wp |
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145 | zwi(:,:,:) = 0._wp |
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146 | ! |
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147 | l_trd = .FALSE. ! set local switches |
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148 | l_hst = .FALSE. |
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149 | l_ptr = .FALSE. |
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150 | ll_zAimp = .FALSE. |
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151 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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152 | IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE. |
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153 | IF( cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. & |
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154 | & iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE. |
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155 | ! |
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156 | IF( l_trd .OR. l_hst ) THEN |
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157 | ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) ) |
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158 | ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp |
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159 | ENDIF |
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160 | ! |
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161 | IF( l_ptr ) THEN |
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162 | ALLOCATE( zptry(jpi,jpj,jpk) ) |
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163 | zptry(:,:,:) = 0._wp |
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164 | ENDIF |
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165 | ! |
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166 | ! If adaptive vertical advection, check if it is needed on this PE at this time |
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167 | IF( ln_zad_Aimp ) THEN |
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168 | IF( MAXVAL( ABS( wi(:,:,:) ) ) > 0._wp ) ll_zAimp = .TRUE. |
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169 | END IF |
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170 | ! If active adaptive vertical advection, build tridiagonal matrix |
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171 | IF( ll_zAimp ) THEN |
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172 | ALLOCATE(zwdia(jpi,jpj,jpk), zwinf(jpi,jpj,jpk),zwsup(jpi,jpj,jpk)) |
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173 | DO_3D( 1, 1, 1, 1, 1, jpkm1 ) |
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174 | 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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175 | & / e3t(ji,jj,jk,Krhs) |
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176 | zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs) |
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177 | zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs) |
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178 | END_3D |
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179 | END IF |
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180 | ! |
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181 | DO jn = 1, kjpt !== loop over the tracers ==! |
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182 | ! |
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183 | ! !== upstream advection with initial mass fluxes & intermediate update ==! |
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184 | ! !* upstream tracer flux in the k direction *! |
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185 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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186 | zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) ) |
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187 | zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) ) |
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188 | 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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189 | END_3D |
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190 | IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) |
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191 | IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface |
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192 | DO_2D( 1, 1, 1, 1 ) |
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193 | 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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194 | END_2D |
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195 | ELSE ! no cavities: only at the ocean surface |
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196 | DO_2D( 1, 1, 1, 1 ) |
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197 | zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb) |
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198 | END_2D |
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199 | ENDIF |
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200 | ENDIF |
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201 | ! |
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202 | ! !* upstream tracer flux in the i and j direction |
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203 | DO jk = 1, jpkm1 |
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204 | DO jj = 1, jpj-1 |
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205 | tracer_flux_i(zwx_3d(1,jj,jk),zfp_ui,zfm_ui,1,jj,jk) |
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206 | tracer_flux_j(zwy_3d(1,jj,jk),zfp_vj,zfm_vj,1,jj,jk) |
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207 | END DO |
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208 | DO ji = 1, jpi-1 |
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209 | tracer_flux_i(zwx_3d(ji,1,jk),zfp_ui,zfm_ui,ji,1,jk) |
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210 | tracer_flux_j(zwy_3d(ji,1,jk),zfp_vj,zfm_vj,ji,1,jk) |
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211 | END DO |
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212 | DO_2D( 1, 1, 1, 1 ) |
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213 | tracer_flux_i(zwx_3d(ji,jj,jk),zfp_ui,zfm_ui,ji,jj,jk) |
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214 | tracer_flux_i(zwx_im1,zfp_ui_m1,zfm_ui_m1,ji-1,jj,jk) |
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215 | tracer_flux_j(zwy_3d(ji,jj,jk),zfp_vj,zfm_vj,ji,jj,jk) |
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216 | tracer_flux_j(zwy_jm1,zfp_vj_m1,zfm_vj_m1,ji,jj-1,jk) |
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217 | ztra = - ( zwx_3d(ji,jj,jk) - zwx_im1 + zwy_3d(ji,jj,jk) - zwy_jm1 + zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) * r1_e1e2t(ji,jj) |
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218 | ! ! update and guess with monotonic sheme |
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219 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra & |
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220 | & / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk) |
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221 | zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) & |
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222 | & / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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223 | END_2D |
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224 | END DO |
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225 | |
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226 | IF ( ll_zAimp ) THEN |
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227 | CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 ) |
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228 | ! |
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229 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ; |
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230 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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231 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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232 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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233 | 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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234 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes |
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235 | END_3D |
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236 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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237 | 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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238 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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239 | END_3D |
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240 | ! |
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241 | END IF |
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242 | ! |
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243 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes) |
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244 | ztrdx(:,:,:) = zwx_3d(:,:,:) ; ztrdy(:,:,:) = zwy_3d(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) |
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245 | END IF |
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246 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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247 | IF( l_ptr ) zptry(:,:,:) = zwy_3d(:,:,:) |
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248 | ! |
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249 | ! !== anti-diffusive flux : high order minus low order ==! |
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250 | ! |
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251 | SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes |
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252 | ! |
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253 | CASE( 2 ) !- 2nd order centered |
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254 | DO_3D( 2, 1, 2, 1, 1, jpkm1 ) |
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255 | zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj,jk,jn,Kmm) ) - zwx_3d(ji,jj,jk) |
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256 | zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj+1,jk,jn,Kmm) ) - zwy_3d(ji,jj,jk) |
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257 | END_3D |
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258 | ! |
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259 | CASE( 4 ) !- 4th order centered |
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260 | zltu_3d(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
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261 | zltv_3d(:,:,jpk) = 0._wp |
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262 | DO jk = 1, jpkm1 ! Laplacian |
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263 | DO_2D( 1, 0, 1, 0 ) ! 1st derivative (gradient) |
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264 | 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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265 | 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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266 | END_2D |
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267 | DO_2D( 0, 0, 0, 0 ) ! 2nd derivative * 1/ 6 |
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268 | zltu_3d(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 |
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269 | zltv_3d(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 |
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270 | END_2D |
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271 | END DO |
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272 | CALL lbc_lnk_multi( 'traadv_fct', zltu_3d, 'T', 1.0_wp , zltv_3d, 'T', 1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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273 | ! ! |
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274 | DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 ) |
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275 | 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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276 | zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm) |
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277 | ! ! C4 minus upstream advective fluxes |
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278 | zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( zC2t_u + zltu_3d(ji,jj,jk) - zltu_3d(ji+1,jj,jk) ) - zwx_3d(ji,jj,jk) |
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279 | zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( zC2t_v + zltv_3d(ji,jj,jk) - zltv_3d(ji,jj+1,jk) ) - zwy_3d(ji,jj,jk) |
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280 | END_3D |
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281 | ! |
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282 | CALL lbc_lnk_multi( 'traadv_fct', zwx_3d, 'U', -1.0_wp , zwy_3d, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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283 | CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested |
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284 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Horizontal advective fluxes |
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285 | ztu_im1 = ( pt(ji ,jj ,jk,jn,Kmm) - pt(ji-1,jj,jk,jn,Kmm) ) * umask(ji-1,jj,jk) |
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286 | ztu_ip1 = ( pt(ji+2,jj ,jk,jn,Kmm) - pt(ji+1,jj,jk,jn,Kmm) ) * umask(ji+1,jj,jk) |
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287 | |
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288 | ztv_jm1 = ( pt(ji,jj ,jk,jn,Kmm) - pt(ji,jj-1,jk,jn,Kmm) ) * vmask(ji,jj-1,jk) |
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289 | ztv_jp1 = ( pt(ji,jj+2,jk,jn,Kmm) - pt(ji,jj+1,jk,jn,Kmm) ) * vmask(ji,jj+1,jk) |
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290 | |
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291 | 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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292 | zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm) |
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293 | ! ! C4 interpolation of T at u- & v-points (x2) |
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294 | zC4t_u = zC2t_u + r1_6 * ( ztu_im1 - ztu_ip1 ) |
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295 | zC4t_v = zC2t_v + r1_6 * ( ztv_jm1 - ztv_jp1 ) |
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296 | ! ! C4 minus upstream advective fluxes |
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297 | zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx_3d(ji,jj,jk) |
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298 | zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy_3d(ji,jj,jk) |
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299 | END_3D |
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300 | CALL lbc_lnk_multi( 'traadv_fct', zwx_3d, 'U', -1.0_wp , zwy_3d, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn) |
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301 | ! |
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302 | END SELECT |
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303 | ! |
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304 | SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values) |
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305 | ! |
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306 | CASE( 2 ) !- 2nd order centered |
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307 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) |
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308 | 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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309 | & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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310 | END_3D |
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311 | ! |
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312 | CASE( 4 ) !- 4th order COMPACT |
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313 | CALL interp_4th_cpt( pt(:,:,:,jn,Kmm) , ztw ) ! zwt = COMPACT interpolation of T at w-point |
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314 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) |
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315 | zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
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316 | END_3D |
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317 | ! |
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318 | END SELECT |
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319 | IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0 |
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320 | zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked |
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321 | ENDIF |
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322 | ! |
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323 | CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp) |
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324 | ! |
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325 | IF ( ll_zAimp ) THEN |
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326 | DO_3D( 1, 1, 1, 1, 1, jpkm1 ) !* trend and after field with monotonic scheme |
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327 | ! ! total intermediate advective trends |
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328 | ztra = - ( zwx_3d(ji,jj,jk) - zwx_3d(ji-1,jj ,jk ) & |
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329 | & + zwy_3d(ji,jj,jk) - zwy_3d(ji ,jj-1,jk ) & |
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330 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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331 | ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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332 | END_3D |
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333 | ! |
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334 | CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 ) |
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335 | ! |
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336 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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337 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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338 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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339 | 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) |
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340 | END_3D |
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341 | END IF |
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342 | ! |
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343 | ! !== monotonicity algorithm ==! |
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344 | ! |
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345 | #if defined key_agrif |
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346 | CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt ) |
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347 | #else |
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348 | CALL nonosc_lf( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt ) |
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349 | #endif |
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350 | ! |
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351 | ! !== final trend with corrected fluxes ==! |
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352 | ! |
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353 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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354 | ztra = - ( zwx_3d(ji,jj,jk) - zwx_3d(ji-1,jj ,jk ) & |
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355 | & + zwy_3d(ji,jj,jk) - zwy_3d(ji ,jj-1,jk ) & |
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356 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
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357 | pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm) |
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358 | zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk) |
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359 | END_3D |
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360 | ! |
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361 | IF ( ll_zAimp ) THEN |
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362 | ! |
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363 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp |
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364 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask) |
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365 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
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366 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
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367 | 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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368 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic |
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369 | END_3D |
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370 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
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371 | 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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372 | & * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm) |
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373 | END_3D |
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374 | END IF |
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375 | ! NOT TESTED - NEED l_trd OR l_hst TRUE |
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376 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport |
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377 | ztrdx(:,:,:) = ztrdx(:,:,:) + zwx_3d(:,:,:) ! <<< add anti-diffusive fluxes |
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378 | ztrdy(:,:,:) = ztrdy(:,:,:) + zwy_3d(:,:,:) ! to upstream fluxes |
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379 | ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! |
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380 | ! |
---|
381 | IF( l_trd ) THEN ! trend diagnostics |
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382 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) ) |
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383 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) ) |
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384 | CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) ) |
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385 | ENDIF |
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386 | ! ! heat/salt transport |
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387 | IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) ) |
---|
388 | ! |
---|
389 | ENDIF |
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390 | ! NOT TESTED - NEED l_ptr TRUE |
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391 | IF( l_ptr ) THEN ! "Poleward" transports |
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392 | zptry(:,:,:) = zptry(:,:,:) + zwy_3d(:,:,:) ! <<< add anti-diffusive fluxes |
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393 | CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) ) |
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394 | ENDIF |
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395 | ! |
---|
396 | END DO ! end of tracer loop |
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397 | ! |
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398 | IF ( ll_zAimp ) THEN |
---|
399 | DEALLOCATE( zwdia, zwinf, zwsup ) |
---|
400 | ENDIF |
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401 | IF( l_trd .OR. l_hst ) THEN |
---|
402 | DEALLOCATE( ztrdx, ztrdy, ztrdz ) |
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403 | ENDIF |
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404 | IF( l_ptr ) THEN |
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405 | DEALLOCATE( zptry ) |
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406 | ENDIF |
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407 | ! |
---|
408 | END SUBROUTINE tra_adv_fct_lf |
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409 | |
---|
410 | SUBROUTINE nonosc_lf( Kmm, pbef, paa, pbb, pcc, paft, p2dt ) |
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411 | !!--------------------------------------------------------------------- |
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412 | !! *** ROUTINE nonosc *** |
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413 | !! |
---|
414 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
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415 | !! scheme and the before field by a nonoscillatory algorithm |
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416 | !! |
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417 | !! ** Method : ... ??? |
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418 | !! warning : pbef and paft must be masked, but the boundaries |
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419 | !! conditions on the fluxes are not necessary zalezak (1979) |
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420 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
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421 | !! in-space based differencing for fluid |
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422 | !!---------------------------------------------------------------------- |
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423 | INTEGER , INTENT(in ) :: Kmm ! time level index |
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424 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
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425 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field |
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426 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions |
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427 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: paa_in, pbb_in, pcc_in ! monotonic fluxes in the 3 directions |
---|
428 | ! |
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429 | REAL(dp), DIMENSION (jpi,jpj,jpk) :: zbup, zbdo |
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430 | ! |
---|
431 | INTEGER :: ji, jj, jk ! dummy loop indices |
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432 | REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars |
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433 | REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
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434 | REAL(dp) :: zbt_ip1, zpos_ip1, zneg_ip1, zup_ip1, zdo_ip1, zbetup_ip1, zbetdo_ip1 |
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435 | REAL(dp) :: zbt_jp1, zpos_jp1, zneg_jp1, zup_jp1, zdo_jp1, zbetup_jp1, zbetdo_jp1 |
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436 | REAL(dp), TARGET, DIMENSION(jpi,jpj) :: zbetup_buf, zbetdo_buf, zbetup_ptr_buf, zbetdo_ptr_buf |
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437 | REAL(dp), POINTER, DIMENSION(:,:) :: tmp, zbetup, zbetdo, zbetup_ptr, zbetdo_ptr |
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438 | !!---------------------------------------------------------------------- |
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439 | ! |
---|
440 | zbig = 1.e+40_dp |
---|
441 | zrtrn = 1.e-15_dp |
---|
442 | |
---|
443 | paa_in(:,:,:) = paa(:,:,:) |
---|
444 | pbb_in(:,:,:) = pbb(:,:,:) |
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445 | pcc_in(:,:,:) = pcc(:,:,:) |
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446 | ! Search local extrema |
---|
447 | ! -------------------- |
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448 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
449 | zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & |
---|
450 | & paft * tmask - zbig * ( 1._wp - tmask ) ) |
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451 | zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & |
---|
452 | & paft * tmask + zbig * ( 1._wp - tmask ) ) |
---|
453 | |
---|
454 | zbetup => zbetup_buf |
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455 | zbetdo => zbetdo_buf |
---|
456 | zbetup_ptr => zbetup_ptr_buf |
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457 | zbetdo_ptr => zbetdo_ptr_buf |
---|
458 | |
---|
459 | DO_2D( 1, 0, 1, 0 ) |
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460 | |
---|
461 | ! search maximum in neighbourhood |
---|
462 | search_in_neighbour(zup,MAX,zbup,ji,jj,1) |
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463 | search_in_neighbour(zup_ip1,MAX,zbup,ji+1,jj,1) |
---|
464 | search_in_neighbour(zup_jp1,MAX,zbup,ji,jj+1,1) |
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465 | |
---|
466 | ! search minimum in neighbourhood |
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467 | search_in_neighbour(zdo,MIN,zbdo,ji,jj,1) |
---|
468 | search_in_neighbour(zdo_ip1,MIN,zbdo,ji+1,jj,1) |
---|
469 | search_in_neighbour(zdo_jp1,MIN,zbdo,ji,jj+1,1) |
---|
470 | |
---|
471 | ! positive part of the flux |
---|
472 | pos_part_of_flux(ji,jj,1,zpos) |
---|
473 | pos_part_of_flux(ji+1,jj,1,zpos_ip1) |
---|
474 | pos_part_of_flux(ji,jj+1,1,zpos_jp1) |
---|
475 | |
---|
476 | ! negative part of the flux |
---|
477 | neg_part_of_flux(ji,jj,1,zneg) |
---|
478 | neg_part_of_flux(ji+1,jj,1,zneg_ip1) |
---|
479 | neg_part_of_flux(ji,jj+1,1,zneg_jp1) |
---|
480 | |
---|
481 | ! up & down beta terms |
---|
482 | beta_terms(zbt,zbetup(ji,jj),zbetdo(ji,jj),zup,zpos,zdo,zneg,ji,jj,1) |
---|
483 | beta_terms(zbt_ip1,zbetup_ip1,zbetdo_ip1,zup_ip1,zpos_ip1,zdo_ip1,zneg_ip1,ji+1,jj,1) |
---|
484 | beta_terms(zbt_jp1,zbetup_jp1,zbetdo_jp1,zup_jp1,zpos_jp1,zdo_jp1,zneg_jp1,ji,jj+1,1) |
---|
485 | |
---|
486 | ! 3. monotonic flux in the i & j (paa & pbb) |
---|
487 | ! ---------------------------------------- |
---|
488 | monotonic_flux(zau,zbu,zcu,zbetup_ip1,zbetdo_ip1,paa,paa_in,1) |
---|
489 | monotonic_flux(zav,zbv,zcv,zbetup_jp1,zbetdo_jp1,pbb,pbb_in,1) |
---|
490 | |
---|
491 | END_2D |
---|
492 | tmp => zbetup_ptr |
---|
493 | zbetup_ptr => zbetup |
---|
494 | zbetup => tmp |
---|
495 | |
---|
496 | tmp => zbetdo_ptr |
---|
497 | zbetdo_ptr => zbetdo |
---|
498 | zbetdo => tmp |
---|
499 | |
---|
500 | DO jk = 2, jpk-1 |
---|
501 | DO_2D( 1, 0, 1, 0 ) |
---|
502 | |
---|
503 | ! search maximum in neighbourhood |
---|
504 | search_in_neighbour(zup,MAX,zbup,ji,jj,jk) |
---|
505 | search_in_neighbour(zup_ip1,MAX,zbup,ji+1,jj,jk) |
---|
506 | search_in_neighbour(zup_jp1,MAX,zbup,ji,jj+1,jk) |
---|
507 | |
---|
508 | ! search minimum in neighbourhood |
---|
509 | search_in_neighbour(zdo,MIN,zbdo,ji,jj,jk) |
---|
510 | search_in_neighbour(zdo_ip1,MIN,zbdo,ji+1,jj,jk) |
---|
511 | search_in_neighbour(zdo_jp1,MIN,zbdo,ji,jj+1,jk) |
---|
512 | |
---|
513 | ! positive part of the flux |
---|
514 | pos_part_of_flux(ji,jj,jk,zpos) |
---|
515 | pos_part_of_flux(ji+1,jj,jk,zpos_ip1) |
---|
516 | pos_part_of_flux(ji,jj+1,jk,zpos_jp1) |
---|
517 | |
---|
518 | ! negative part of the flux |
---|
519 | neg_part_of_flux(ji,jj,jk,zneg) |
---|
520 | neg_part_of_flux(ji+1,jj,jk,zneg_ip1) |
---|
521 | neg_part_of_flux(ji,jj+1,jk,zneg_jp1) |
---|
522 | |
---|
523 | ! up & down beta terms |
---|
524 | beta_terms(zbt,zbetup(ji,jj),zbetdo(ji,jj),zup,zpos,zdo,zneg,ji,jj,jk) |
---|
525 | beta_terms(zbt_ip1,zbetup_ip1,zbetdo_ip1,zup_ip1,zpos_ip1,zdo_ip1,zneg_ip1,ji+1,jj,jk) |
---|
526 | beta_terms(zbt_jp1,zbetup_jp1,zbetdo_jp1,zup_jp1,zpos_jp1,zdo_jp1,zneg_jp1,ji,jj+1,jk) |
---|
527 | |
---|
528 | ! 3. monotonic flux in the i & j (paa & pbb) |
---|
529 | ! ---------------------------------------- |
---|
530 | monotonic_flux(zau,zbu,zcu,zbetup_ip1,zbetdo_ip1,paa,paa_in,jk) |
---|
531 | monotonic_flux(zav,zbv,zcv,zbetup_jp1,zbetdo_jp1,pbb,pbb_in,jk) |
---|
532 | |
---|
533 | ! monotonic flux in the k direction, i.e. pcc |
---|
534 | ! ------------------------------------------- |
---|
535 | monotonic_flux_k(za,zb,zc,zbetup(ji,jj),zbetdo(ji,jj),pcc,pcc_in,jk) |
---|
536 | END_2D |
---|
537 | tmp => zbetup_ptr |
---|
538 | zbetup_ptr => zbetup |
---|
539 | zbetup => tmp |
---|
540 | |
---|
541 | tmp => zbetdo_ptr |
---|
542 | zbetdo_ptr => zbetdo |
---|
543 | zbetdo => tmp |
---|
544 | END DO |
---|
545 | ! |
---|
546 | DO_2D( 1, 0, 1, 0 ) |
---|
547 | ! monotonic flux in the k direction, i.e. pcc |
---|
548 | ! ------------------------------------------- |
---|
549 | monotonic_flux_k(za,zb,zc,0._dp,0._dp,pcc,pcc_in,jpk) |
---|
550 | END_2D |
---|
551 | END SUBROUTINE nonosc_lf |
---|
552 | |
---|
553 | END MODULE traadv_fct_lf |
---|