1 | MODULE tranxt |
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2 | !!====================================================================== |
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3 | !! *** MODULE tranxt *** |
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4 | !! Ocean active tracers: time stepping on temperature and salinity |
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5 | !!====================================================================== |
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6 | !! History : OPA ! 1991-11 (G. Madec) Original code |
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7 | !! 7.0 ! 1993-03 (M. Guyon) symetrical conditions |
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8 | !! 8.0 ! 1996-02 (G. Madec & M. Imbard) opa release 8.0 |
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9 | !! - ! 1996-04 (A. Weaver) Euler forward step |
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10 | !! 8.2 ! 1999-02 (G. Madec, N. Grima) semi-implicit pressure grad. |
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11 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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12 | !! - ! 2002-11 (C. Talandier, A-M Treguier) Open boundaries |
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13 | !! - ! 2005-04 (C. Deltel) Add Asselin trend in the ML budget |
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14 | !! 2.0 ! 2006-02 (L. Debreu, C. Mazauric) Agrif implementation |
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15 | !! 3.0 ! 2008-06 (G. Madec) time stepping always done in trazdf |
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16 | !! 3.1 ! 2009-02 (G. Madec, R. Benshila) re-introduce the vvl option |
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17 | !! 3.3 ! 2010-04 (M. Leclair, G. Madec) semi-implicit hpg with asselin filter + modified LF-RA |
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18 | !! - ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA |
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19 | !!---------------------------------------------------------------------- |
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20 | |
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21 | !!---------------------------------------------------------------------- |
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22 | !! tra_nxt : time stepping on tracers |
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23 | !! tra_nxt_fix : time stepping on tracers : fixed volume case |
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24 | !! tra_nxt_vvl : time stepping on tracers : variable volume case |
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25 | !!---------------------------------------------------------------------- |
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26 | USE oce ! ocean dynamics and tracers variables |
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27 | USE dom_oce ! ocean space and time domain variables |
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28 | USE sbc_oce ! surface boundary condition: ocean |
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29 | USE zdf_oce ! ??? |
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30 | USE domvvl ! variable volume |
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31 | USE dynspg_oce ! surface pressure gradient variables |
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32 | USE dynhpg ! hydrostatic pressure gradient |
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33 | USE trdmod_oce ! ocean space and time domain variables |
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34 | USE trdtra ! ocean active tracers trends |
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35 | USE phycst |
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36 | USE obc_oce |
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37 | USE obctra ! open boundary condition (obc_tra routine) |
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38 | USE bdytra ! Unstructured open boundary condition (bdy_tra routine) |
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39 | USE in_out_manager ! I/O manager |
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40 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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41 | USE prtctl ! Print control |
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42 | USE traqsr ! penetrative solar radiation (needed for nksr) |
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43 | USE traswp ! swap array |
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44 | USE obc_oce |
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45 | #if defined key_agrif |
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46 | USE agrif_opa_update |
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47 | USE agrif_opa_interp |
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48 | #endif |
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49 | |
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50 | IMPLICIT NONE |
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51 | PRIVATE |
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52 | |
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53 | PUBLIC tra_nxt ! routine called by step.F90 |
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54 | PUBLIC tra_nxt_fix ! to be used in trcnxt |
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55 | PUBLIC tra_nxt_vvl ! to be used in trcnxt |
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56 | |
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57 | REAL(wp) :: rbcp ! Brown & Campana parameters for semi-implicit hpg |
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58 | REAL(wp), DIMENSION(jpk) :: r2dt ! vertical profile time step, =2*rdttra (leapfrog) or =rdttra (Euler) |
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59 | |
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60 | !! * Substitutions |
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61 | # include "domzgr_substitute.h90" |
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62 | !!---------------------------------------------------------------------- |
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63 | !! NEMO/OPA 3.3 , LOCEAN-IPSL (2010) |
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64 | !! $Id$ |
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65 | !! Software governed by the CeCILL licence (NEMOGCM/License_CeCILL.txt) |
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66 | !!---------------------------------------------------------------------- |
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67 | |
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68 | CONTAINS |
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69 | |
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70 | SUBROUTINE tra_nxt( kt ) |
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71 | !!---------------------------------------------------------------------- |
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72 | !! *** ROUTINE tranxt *** |
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73 | !! |
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74 | !! ** Purpose : Apply the boundary condition on the after temperature |
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75 | !! and salinity fields, achieved the time stepping by adding |
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76 | !! the Asselin filter on now fields and swapping the fields. |
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77 | !! |
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78 | !! ** Method : At this stage of the computation, ta and sa are the |
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79 | !! after temperature and salinity as the time stepping has |
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80 | !! been performed in trazdf_imp or trazdf_exp module. |
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81 | !! |
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82 | !! - Apply lateral boundary conditions on (ta,sa) |
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83 | !! at the local domain boundaries through lbc_lnk call, |
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84 | !! at the radiative open boundaries (lk_obc=T), |
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85 | !! at the relaxed open boundaries (lk_bdy=T), and |
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86 | !! at the AGRIF zoom boundaries (lk_agrif=T) |
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87 | !! |
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88 | !! - Update lateral boundary conditions on AGRIF children |
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89 | !! domains (lk_agrif=T) |
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90 | !! |
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91 | !! ** Action : - (tb,sb) and (tn,sn) ready for the next time step |
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92 | !! - (ta,sa) time averaged (t,s) (ln_dynhpg_imp = T) |
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93 | !!---------------------------------------------------------------------- |
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94 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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95 | !! |
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96 | INTEGER :: jk ! dummy loop indices |
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97 | REAL(wp) :: zfact ! local scalars |
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98 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdt, ztrds |
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99 | !!---------------------------------------------------------------------- |
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100 | |
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101 | IF( kt == nit000 ) THEN |
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102 | IF(lwp) WRITE(numout,*) |
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103 | IF(lwp) WRITE(numout,*) 'tra_nxt : achieve the time stepping by Asselin filter and array swap' |
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104 | IF(lwp) WRITE(numout,*) '~~~~~~~' |
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105 | ! |
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106 | rbcp = 0.25 * (1. + atfp) * (1. + atfp) * ( 1. - atfp) ! Brown & Campana parameter for semi-implicit hpg |
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107 | ENDIF |
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108 | |
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109 | ! Update after tracer on domain lateral boundaries |
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110 | ! |
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111 | CALL lbc_lnk( tsa(:,:,:,jp_tem), 'T', 1. ) ! local domain boundaries (T-point, unchanged sign) |
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112 | CALL lbc_lnk( tsa(:,:,:,jp_sal), 'T', 1. ) |
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113 | ! |
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114 | #if defined key_obc || defined key_bdy || defined key_agrif |
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115 | CALL tra_unswap |
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116 | #endif |
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117 | |
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118 | #if defined key_obc |
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119 | IF( lk_obc ) CALL obc_tra( kt ) ! OBC open boundaries |
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120 | #endif |
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121 | #if defined key_bdy |
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122 | IF( lk_bdy ) CALL bdy_tra( kt ) ! BDY open boundaries |
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123 | #endif |
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124 | #if defined key_agrif |
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125 | CALL Agrif_tra ! AGRIF zoom boundaries |
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126 | #endif |
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127 | |
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128 | #if defined key_obc || defined key_bdy || defined key_agrif |
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129 | CALL tra_swap |
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130 | #endif |
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131 | |
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132 | ! set time step size (Euler/Leapfrog) |
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133 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; r2dt(:) = rdttra(:) ! at nit000 (Euler) |
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134 | ELSEIF( kt <= nit000 + 1 ) THEN ; r2dt(:) = 2.* rdttra(:) ! at nit000 or nit000+1 (Leapfrog) |
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135 | ENDIF |
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136 | |
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137 | ! trends computation initialisation |
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138 | IF( l_trdtra ) THEN !* store now fields before applying the Asselin filter |
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139 | ALLOCATE( ztrdt(jpi,jpj,jpk) ) ; ztrdt(:,:,:) = tsn(:,:,:,jp_tem) |
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140 | ALLOCATE( ztrds(jpi,jpj,jpk) ) ; ztrds(:,:,:) = tsn(:,:,:,jp_sal) |
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141 | ENDIF |
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142 | |
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143 | ! Leap-Frog + Asselin filter time stepping |
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144 | IF( lk_vvl ) THEN ; CALL tra_nxt_vvl( kt, 'TRA', tsb, tsn, tsa, jpts ) ! variable volume level (vvl) |
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145 | ELSE ; CALL tra_nxt_fix( kt, tsb, tsn, tsa, jpts ) ! fixed volume level |
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146 | ENDIF |
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147 | |
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148 | #if defined key_agrif |
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149 | CALL tra_unswap |
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150 | ! Update tracer at AGRIF zoom boundaries |
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151 | IF( .NOT.Agrif_Root() ) CALL Agrif_Update_Tra( kt ) ! children only |
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152 | CALL tra_swap |
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153 | #endif |
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154 | |
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155 | ! trends computation |
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156 | IF( l_trdtra ) THEN ! trend of the Asselin filter (tb filtered - tb)/dt |
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157 | DO jk = 1, jpkm1 |
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158 | zfact = 1.e0 / r2dt(jk) |
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159 | ztrdt(:,:,jk) = ( tsb(:,:,jk,jp_tem) - ztrdt(:,:,jk) ) * zfact |
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160 | ztrds(:,:,jk) = ( tsb(:,:,jk,jp_sal) - ztrds(:,:,jk) ) * zfact |
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161 | END DO |
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162 | CALL trd_tra( kt, 'TRA', jp_tem, jptra_trd_atf, ztrdt ) |
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163 | CALL trd_tra( kt, 'TRA', jp_sal, jptra_trd_atf, ztrds ) |
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164 | DEALLOCATE( ztrdt ) ; DEALLOCATE( ztrds ) |
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165 | END IF |
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166 | |
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167 | ! ! control print |
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168 | IF(ln_ctl) CALL prt_ctl( tab3d_1=tsn(:,:,:,jp_tem), clinfo1=' nxt - Tn: ', mask1=tmask, & |
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169 | & tab3d_2=tsn(:,:,:,jp_sal), clinfo2= ' Sn: ', mask2=tmask ) |
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170 | ! |
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171 | END SUBROUTINE tra_nxt |
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172 | |
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173 | |
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174 | SUBROUTINE tra_nxt_fix( kt, ptb, ptn, pta, kjpt ) |
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175 | !!---------------------------------------------------------------------- |
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176 | !! *** ROUTINE tra_nxt_fix *** |
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177 | !! |
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178 | !! ** Purpose : fixed volume: apply the Asselin time filter and |
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179 | !! swap the tracer fields. |
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180 | !! |
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181 | !! ** Method : - Apply a Asselin time filter on now fields. |
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182 | !! - save in (ta,sa) an average over the three time levels |
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183 | !! which will be used to compute rdn and thus the semi-implicit |
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184 | !! hydrostatic pressure gradient (ln_dynhpg_imp = T) |
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185 | !! - swap tracer fields to prepare the next time_step. |
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186 | !! This can be summurized for tempearture as: |
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187 | !! ztm = tn + rbcp * [ta -2 tn + tb ] ln_dynhpg_imp = T |
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188 | !! ztm = 0 otherwise |
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189 | !! with rbcp=1/4 * (1-atfp^4) / (1-atfp) |
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190 | !! tb = tn + atfp*[ tb - 2 tn + ta ] |
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191 | !! tn = ta |
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192 | !! ta = ztm (NB: reset to 0 after eos_bn2 call) |
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193 | !! |
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194 | !! ** Action : - (tb,sb) and (tn,sn) ready for the next time step |
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195 | !! - (ta,sa) time averaged (t,s) (ln_dynhpg_imp = T) |
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196 | !!---------------------------------------------------------------------- |
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197 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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198 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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199 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: ptb ! before tracer fields |
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200 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: ptn ! now tracer fields |
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201 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: pta ! tracer trend |
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202 | !! |
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203 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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204 | REAL(wp) :: ztd, ztm ! temporary scalars |
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205 | !!---------------------------------------------------------------------- |
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206 | |
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207 | IF( kt == nit000 ) THEN |
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208 | IF(lwp) WRITE(numout,*) |
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209 | IF(lwp) WRITE(numout,*) 'tra_nxt_fix : time stepping' |
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210 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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211 | ENDIF |
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212 | ! |
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213 | ! |
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214 | IF( neuler == 0 .AND. kt == nit000 ) THEN ! Euler time-stepping at first time-step |
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215 | ! ! (only swap) |
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216 | DO jn = 1, kjpt |
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217 | DO jk = 1, jpkm1 |
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218 | ptn(:,:,jk,jn) = pta(:,:,jk,jn) ! ptb <-- ptn |
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219 | END DO |
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220 | END DO |
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221 | ! |
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222 | ELSE ! general case (Leapfrog + Asselin filter |
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223 | ! |
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224 | ! ! ----------------------- ! |
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225 | IF( ln_dynhpg_imp ) THEN ! semi-implicite hpg case ! |
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226 | ! ! ----------------------- ! |
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227 | DO jn = 1, kjpt |
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228 | DO jk = 1, jpkm1 |
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229 | DO jj = 1, jpj |
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230 | DO ji = 1, jpi |
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231 | ztd = pta(ji,jj,jk,jn) - 2.* ptn(ji,jj,jk,jn) + ptb(ji,jj,jk,jn) ! time laplacian on tracers |
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232 | ztm = ptn(ji,jj,jk,jn) + rbcp * ztd ! used for both Asselin and Brown & Campana filters |
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233 | ! |
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234 | ptb(ji,jj,jk,jn) = ptn(ji,jj,jk,jn) + atfp * ztd ! ptb <-- filtered ptn |
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235 | ptn(ji,jj,jk,jn) = pta(ji,jj,jk,jn) ! ptn <-- pta |
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236 | pta(ji,jj,jk,jn) = ztm ! pta <-- Brown & Campana average |
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237 | END DO |
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238 | END DO |
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239 | END DO |
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240 | END DO |
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241 | ! ! ----------------------- ! |
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242 | ELSE ! explicit hpg case ! |
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243 | ! ! ----------------------- ! |
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244 | DO jn = 1, kjpt |
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245 | DO jk = 1, jpkm1 |
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246 | DO jj = 1, jpj |
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247 | DO ji = 1, jpi |
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248 | ztd = pta(ji,jj,jk,jn) - 2.* ptn(ji,jj,jk,jn) + ptb(ji,jj,jk,jn) ! time laplacian on tracers |
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249 | ! |
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250 | ptb(ji,jj,jk,jn) = ptn(ji,jj,jk,jn) + atfp * ztd ! ptb <-- filtered ptn |
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251 | ptn(ji,jj,jk,jn) = pta(ji,jj,jk,jn) ! ptn <-- pta |
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252 | END DO |
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253 | END DO |
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254 | END DO |
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255 | END DO |
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256 | ENDIF |
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257 | ! |
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258 | ENDIF |
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259 | ! |
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260 | END SUBROUTINE tra_nxt_fix |
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261 | |
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262 | |
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263 | SUBROUTINE tra_nxt_vvl( kt, cdtype, ptb, ptn, pta, kjpt ) |
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264 | !!---------------------------------------------------------------------- |
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265 | !! *** ROUTINE tra_nxt_vvl *** |
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266 | !! |
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267 | !! ** Purpose : Time varying volume: apply the Asselin time filter |
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268 | !! and swap the tracer fields. |
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269 | !! |
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270 | !! ** Method : - Apply a thickness weighted Asselin time filter on now fields. |
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271 | !! - save in (ta,sa) a thickness weighted average over the three |
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272 | !! time levels which will be used to compute rdn and thus the semi- |
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273 | !! implicit hydrostatic pressure gradient (ln_dynhpg_imp = T) |
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274 | !! - swap tracer fields to prepare the next time_step. |
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275 | !! This can be summurized for tempearture as: |
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276 | !! ztm = ( e3t_n*tn + rbcp*[ e3t_b*tb - 2 e3t_n*tn + e3t_a*ta ] ) ln_dynhpg_imp = T |
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277 | !! /( e3t_n + rbcp*[ e3t_b - 2 e3t_n + e3t_a ] ) |
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278 | !! ztm = 0 otherwise |
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279 | !! tb = ( e3t_n*tn + atfp*[ e3t_b*tb - 2 e3t_n*tn + e3t_a*ta ] ) |
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280 | !! /( e3t_n + atfp*[ e3t_b - 2 e3t_n + e3t_a ] ) |
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281 | !! tn = ta |
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282 | !! ta = zt (NB: reset to 0 after eos_bn2 call) |
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283 | !! |
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284 | !! ** Action : - (tb,sb) and (tn,sn) ready for the next time step |
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285 | !! - (ta,sa) time averaged (t,s) (ln_dynhpg_imp = T) |
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286 | !!---------------------------------------------------------------------- |
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287 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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288 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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289 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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290 | REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: ptb ! before tracer fields |
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291 | REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: ptn ! now tracer fields |
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292 | REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: pta ! tracer trend |
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293 | !! |
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294 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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295 | REAL(wp) :: ztc_a , ztc_n , ztc_b ! temporary scalar |
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296 | REAL(wp) :: ztc_f , ztc_d , ztc_m ! - - |
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297 | REAL(wp) :: ze3t_b, ze3t_n, ze3t_a ! - - |
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298 | REAL(wp) :: ze3t_f, ze3t_d, ze3t_m ! - - |
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299 | REAL :: zfact1, zfact2 ! - - |
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300 | !!---------------------------------------------------------------------- |
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301 | |
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302 | IF( kt == nit000 ) THEN |
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303 | IF(lwp) WRITE(numout,*) |
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304 | IF(lwp) WRITE(numout,*) 'tra_nxt_vvl : time stepping' |
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305 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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306 | ENDIF |
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307 | ! |
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308 | ! |
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309 | IF( neuler == 0 .AND. kt == nit000 ) THEN ! Euler time-stepping at first time-step |
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310 | ! ! (only swap) |
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311 | DO jn = 1, kjpt |
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312 | DO jk = 1, jpkm1 |
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313 | ptn(:,:,jk,jn) = pta(:,:,jk,jn) ! ptb <-- ptn |
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314 | END DO |
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315 | END DO |
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316 | ! |
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317 | ELSE ! general case (Leapfrog + Asselin filter) |
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318 | ! |
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319 | ! ! ----------------------- ! |
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320 | IF( ln_dynhpg_imp ) THEN ! semi-implicite hpg case ! |
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321 | ! ! ----------------------- ! |
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322 | DO jn = 1, kjpt |
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323 | DO jk = 1, jpkm1 |
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324 | DO jj = 1, jpj |
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325 | DO ji = 1, jpi |
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326 | ze3t_b = fse3t_b(ji,jj,jk) |
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327 | ze3t_n = fse3t_n(ji,jj,jk) |
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328 | ze3t_a = fse3t_a(ji,jj,jk) |
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329 | ! ! tracer content at Before, now and after |
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330 | ztc_b = ptb(ji,jj,jk,jn) * ze3t_b |
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331 | ztc_n = ptn(ji,jj,jk,jn) * ze3t_n |
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332 | ztc_a = pta(ji,jj,jk,jn) * ze3t_a |
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333 | ! ! Time laplacian on tracer contents |
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334 | ! ! used for both Asselin and Brown & Campana filters |
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335 | ze3t_d = ze3t_b - 2.* ze3t_n + ze3t_a |
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336 | ztc_d = ztc_b - 2.* ztc_n + ztc_a |
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337 | ! ! Asselin Filter on thicknesses and tracer contents |
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338 | ztc_f = ztc_n + atfp * ztc_d |
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339 | ztc_m = ztc_n + rbcp * ztc_d |
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340 | ! |
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341 | ze3t_f = 1.0 / ( ze3t_n + atfp * ze3t_d ) |
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342 | ze3t_m = 1.0 / ( ze3t_n + rbcp * ze3t_d ) |
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343 | ! ! swap of arrays |
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344 | ptb(ji,jj,jk,jn) = ztc_f * ze3t_f ! ptb <-- ptn filtered |
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345 | pta(ji,jj,jk,jn) = ztc_m * ze3t_m ! pta <-- Brown & Campana average |
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346 | ptn(ji,jj,jk,jn) = pta(ji,jj,jk,jn) ! ptn <-- pta |
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347 | END DO |
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348 | END DO |
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349 | END DO |
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350 | END DO |
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351 | ! ! ----------------------- ! |
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352 | ELSE ! explicit hpg case ! |
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353 | ! ! ----------------------- ! |
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354 | IF( cdtype == 'TRA' ) THEN |
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355 | ! |
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356 | DO jn = 1, kjpt |
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357 | DO jk = 1, jpkm1 |
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358 | zfact1 = atfp * rdttra(jk) |
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359 | zfact2 = zfact1 / rau0 |
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360 | DO jj = 1, jpj |
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361 | DO ji = 1, jpi |
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362 | ze3t_b = fse3t_b(ji,jj,jk) |
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363 | ze3t_n = fse3t_n(ji,jj,jk) |
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364 | ze3t_a = fse3t_a(ji,jj,jk) |
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365 | ! ! tracer content at Before, now and after |
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366 | ztc_b = ptb(ji,jj,jk,jn) * ze3t_b |
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367 | ztc_n = ptn(ji,jj,jk,jn) * ze3t_n |
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368 | ztc_a = pta(ji,jj,jk,jn) * ze3t_a |
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369 | ! |
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370 | ze3t_f = ze3t_n + atfp * ( ze3t_b - 2. * ze3t_n + ze3t_a ) |
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371 | ztc_f = ztc_n + atfp * ( ztc_a - 2. * ztc_n + ztc_b ) |
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372 | |
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373 | IF( jk == 1 ) THEN |
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374 | ze3t_f = ze3t_f - zfact2 * ( emp_b(ji,jj) - emp(ji,jj) ) |
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375 | IF( jn == jp_tem ) ztc_f = ztc_f - zfact1 * ( sbc_hc_n(ji,jj) - sbc_hc_b(ji,jj) ) |
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376 | IF( jn == jp_sal ) ztc_f = ztc_f - zfact1 * ( sbc_sc_n(ji,jj) - sbc_sc_b(ji,jj) ) |
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377 | ENDIF |
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378 | IF( jn == jp_tem .AND. ln_traqsr .AND. jk <= nksr ) & |
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379 | & ztc_f = ztc_f - zfact1 * ( qsr_hc_n(ji,jj,jk) - qsr_hc_b(ji,jj,jk) ) |
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380 | |
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381 | ze3t_f = 1.e0 / ze3t_f |
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382 | ptb(ji,jj,jk,jn) = ztc_f * ze3t_f ! tb <-- tn filtered |
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383 | ptn(ji,jj,jk,jn) = pta(ji,jj,jk,jn) ! tn <-- ta |
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384 | END DO |
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385 | END DO |
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386 | END DO |
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387 | END DO |
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388 | ! |
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389 | ELSE IF( cdtype == 'TRC' ) THEN |
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390 | ! |
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391 | DO jn = 1, kjpt |
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392 | DO jk = 1, jpkm1 |
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393 | DO jj = 1, jpj |
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394 | DO ji = 1, jpi |
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395 | ze3t_b = fse3t_b(ji,jj,jk) |
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396 | ze3t_n = fse3t_n(ji,jj,jk) |
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397 | ze3t_a = fse3t_a(ji,jj,jk) |
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398 | ! ! tracer content at Before, now and after |
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399 | ztc_b = ptb(ji,jj,jk,jn) * ze3t_b |
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400 | ztc_n = ptn(ji,jj,jk,jn) * ze3t_n |
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401 | ztc_a = pta(ji,jj,jk,jn) * ze3t_a |
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402 | ! |
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403 | ze3t_f = ze3t_n + atfp * ( ze3t_b - 2. * ze3t_n + ze3t_a ) |
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404 | ztc_f = ztc_n + atfp * ( ztc_a - 2. * ztc_n + ztc_b ) |
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405 | |
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406 | ze3t_f = 1.e0 / ze3t_f |
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407 | ptb(ji,jj,jk,jn) = ztc_f * ze3t_f ! tb <-- tn filtered |
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408 | ptn(ji,jj,jk,jn) = pta(ji,jj,jk,jn) ! tn <-- ta |
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409 | END DO |
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410 | END DO |
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411 | END DO |
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412 | END DO |
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413 | ! |
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414 | END IF |
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415 | ! |
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416 | ENDIF |
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417 | ! |
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418 | ENDIF |
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419 | ! |
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420 | END SUBROUTINE tra_nxt_vvl |
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421 | |
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422 | !!====================================================================== |
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423 | END MODULE tranxt |
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