1 | MODULE traadv_tvd |
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2 | !!============================================================================== |
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3 | !! *** MODULE traadv_tvd *** |
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4 | !! Ocean active tracers: horizontal & vertical advective trend |
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5 | !!============================================================================== |
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6 | !! History : 7.0 ! 1995-12 (L. Mortier) Original code |
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7 | !! 8.0 ! 2000-01 (H. Loukos) adapted to ORCA |
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8 | !! - ! 2000-10 (MA Foujols E.Kestenare) include file not routine |
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9 | !! - ! 2000-12 (E. Kestenare M. Levy) fix bug in trtrd indexes |
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10 | !! - ! 2001-07 (E. Durand G. Madec) adaptation to ORCA config |
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11 | !! 8.5 ! 2002-06 (G. Madec) F90: Free form and module |
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12 | !! NEMO 1.0 ! 2004-01 (A. de Miranda, G. Madec, J.M. Molines ): advective bbl |
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13 | !! - ! 2008-04 (S. Cravatte) add the i-, j- & k- trends computation |
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14 | !! - ! 2005-11 (V. Garnier) Surface pressure gradient organization |
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15 | !! 2.4 ! 2008-01 (G. Madec) merge TRC-TRA + switch from velocity to transport |
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16 | !!---------------------------------------------------------------------- |
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17 | |
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18 | !!---------------------------------------------------------------------- |
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19 | !! tra_adv_tvd : update the tracer trend with the horizontal and |
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20 | !! vertical advection trends using a TVD scheme |
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21 | !! nonosc : compute monotonic tracer fluxes by a nonoscillatory algorithm |
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22 | !!---------------------------------------------------------------------- |
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23 | USE dom_oce ! ocean space and time domain |
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24 | USE trdmod ! ocean active tracers trends |
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25 | USE trdmod_oce ! ocean variables trends |
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26 | USE in_out_manager ! I/O manager |
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27 | USE dynspg_oce ! choice/control of key cpp for surface pressure gradient |
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28 | USE trabbl ! Advective term of BBL |
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29 | USE lib_mpp ! |
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30 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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31 | USE diaptr ! poleward transport diagnostics |
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32 | USE prtctl ! Print control |
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33 | |
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34 | IMPLICIT NONE |
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35 | PRIVATE |
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36 | |
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37 | PUBLIC tra_adv_tvd ! routine called by traadv.F90 |
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38 | |
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39 | !! * Substitutions |
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40 | # include "domzgr_substitute.h90" |
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41 | # include "vectopt_loop_substitute.h90" |
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42 | !!---------------------------------------------------------------------- |
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43 | !! NEMO/OPA 2.4 , LOCEAN-IPSL (2008) |
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44 | !! $Id$ |
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45 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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46 | !!---------------------------------------------------------------------- |
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47 | |
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48 | CONTAINS |
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49 | |
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50 | SUBROUTINE tra_adv_tvd( kt, cdtype, ktra, pun, pvn, pwn, & |
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51 | & ptb, ptn, pta ) |
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52 | !!---------------------------------------------------------------------- |
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53 | !! *** ROUTINE tra_adv_tvd *** |
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54 | !! |
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55 | !! ** Purpose : Compute the now trend due to total advection of |
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56 | !! tracers and add it to the general trend of tracer equations |
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57 | !! |
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58 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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59 | !! corrected flux (monotonic correction) |
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60 | !! note: - this advection scheme needs a leap-frog time scheme |
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61 | !! |
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62 | !! ** Action : - update pta with the now advective tracer trends |
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63 | !! - save the trends in (ztrdt,ztrds) ('key_trdtra') |
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64 | !!---------------------------------------------------------------------- |
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65 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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66 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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67 | INTEGER , INTENT(in ) :: ktra ! tracer index |
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68 | REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,jpk) :: pun, pvn, pwn ! 3 ocean velocity components |
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69 | REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk) :: ptb, ptn ! before and now tracer fields |
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70 | REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pta ! tracer trend |
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71 | !! |
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72 | INTEGER :: ji, jj, jk ! dummy loop indices |
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73 | REAL(wp) :: z2dtt, zbtr, z2, zzti ! temporary scalar |
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74 | REAL(wp) :: zfp_ui, zfp_vj, zfp_wk ! " " |
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75 | REAL(wp) :: zfm_ui, zfm_vj, zfm_wk ! " " |
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76 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: zti, ztu, ztv, ztw ! 3D workspace |
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77 | !!---------------------------------------------------------------------- |
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78 | |
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79 | zti(:,:,:) = 0.e0 |
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80 | |
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81 | IF( kt == nit000 .AND. lwp ) THEN |
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82 | WRITE(numout,*) |
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83 | WRITE(numout,*) 'tra_adv_tvd : TVD advection scheme' |
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84 | WRITE(numout,*) '~~~~~~~~~~~' |
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85 | ENDIF |
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86 | |
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87 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; z2 = 1. ! euler time-stepping |
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88 | ELSE ; z2 = 2. ! leap-frog time-stepping |
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89 | ENDIF |
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90 | |
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91 | ! 1. Bottom value : flux set to zero |
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92 | ! --------------- |
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93 | ztu(:,:,jpk) = 0.e0 ; ztv(:,:,jpk) = 0.e0 |
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94 | ztw(:,:,jpk) = 0.e0 ; zti(:,:,jpk) = 0.e0 |
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95 | |
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96 | |
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97 | ! 2. upstream advection with initial mass fluxes & intermediate update |
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98 | ! -------------------------------------------------------------------- |
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99 | ! upstream tracer flux in the i and j direction |
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100 | DO jk = 1, jpkm1 |
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101 | DO jj = 1, jpjm1 |
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102 | DO ji = 1, fs_jpim1 ! vector opt. |
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103 | zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) |
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104 | zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) |
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105 | zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) |
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106 | zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) |
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107 | ztu(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk) + zfm_ui * ptb(ji+1,jj ,jk) ) |
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108 | ztv(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk) + zfm_vj * ptb(ji ,jj+1,jk) ) |
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109 | END DO |
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110 | END DO |
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111 | END DO |
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112 | ! |
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113 | ! upstream tracer flux in the k direction |
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114 | ! ! Surface value |
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115 | IF( lk_dynspg_rl .OR. lk_vvl ) THEN ; ztw(:,:,1) = 0.e0 ! rigid lid or non-linear fs |
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116 | ELSE ; ztw(:,:,1) = pwn(:,:,1) * ptb(:,:,1) ! free surface |
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117 | ENDIF |
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118 | ! |
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119 | DO jk = 2, jpkm1 ! Interior value |
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120 | DO jj = 1, jpj |
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121 | DO ji = 1, jpi |
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122 | zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) |
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123 | zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) |
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124 | ztw(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk) + zfm_wk * ptb(ji,jj,jk-1) ) |
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125 | END DO |
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126 | END DO |
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127 | END DO |
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128 | ! |
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129 | ! upstream advective trend |
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130 | DO jk = 1, jpkm1 |
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131 | z2dtt = z2 * rdttra(jk) |
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132 | DO jj = 2, jpjm1 |
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133 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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134 | zbtr = 1./ ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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135 | ! total intermediate advective trends |
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136 | zzti = - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk ) & |
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137 | & + ztv(ji,jj,jk) - ztv(ji ,jj-1,jk ) & |
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138 | & + ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) * zbtr |
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139 | ! update and guess with monotonic sheme |
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140 | pta(ji,jj,jk) = pta(ji,jj,jk) + zzti |
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141 | zti(ji,jj,jk) = ( ptb(ji,jj,jk) + z2dtt * zzti ) * tmask(ji,jj,jk) |
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142 | END DO |
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143 | END DO |
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144 | END DO |
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145 | ! |
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146 | CALL lbc_lnk( zti, 'T', 1. ) ! Lateral boundary conditions on zti (unchanged sign) |
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147 | |
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148 | |
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149 | ! ! trend diagnostics (contribution of upstream fluxes) |
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150 | IF( l_trdtra ) THEN |
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151 | CALL trd_tra_adv( kt, ktra, jpt_trd_xad, cdtype, ztu, pun, ptn ) |
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152 | CALL trd_tra_adv( kt, ktra, jpt_trd_yad, cdtype, ztv, pvn, ptn ) |
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153 | CALL trd_tra_adv( kt, ktra, jpt_trd_zad, cdtype, ztw, pwn, ptn ) |
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154 | ENDIF |
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155 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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156 | IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN |
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157 | IF( ktra == jp_tem) pht_adv(:) = ptr_vj( ztv(:,:,:) ) |
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158 | IF( ktra == jp_sal) pst_adv(:) = ptr_vj( ztv(:,:,:) ) |
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159 | ENDIF |
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160 | |
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161 | |
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162 | ! 3. antidiffusive flux : high order minus low order |
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163 | ! -------------------------------------------------- |
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164 | ! ! anti-diffusive flux on i and j |
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165 | DO jk = 1, jpkm1 |
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166 | DO jj = 1, jpjm1 |
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167 | DO ji = 1, fs_jpim1 ! vector opt. |
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168 | ztu(ji,jj,jk) = 0.5 * pun(ji,jj,jk) * ( ptn(ji,jj,jk) + ptn(ji+1,jj,jk) ) - ztu(ji,jj,jk) |
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169 | ztv(ji,jj,jk) = 0.5 * pvn(ji,jj,jk) * ( ptn(ji,jj,jk) + ptn(ji,jj+1,jk) ) - ztv(ji,jj,jk) |
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170 | END DO |
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171 | END DO |
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172 | END DO |
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173 | ! ! antidiffusive flux on k |
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174 | ztw(:,:,1) = 0.e0 ! Surface value |
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175 | ! |
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176 | DO jk = 2, jpkm1 ! Interior value |
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177 | DO jj = 1, jpj |
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178 | DO ji = 1, jpi |
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179 | ztw(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk) + ptn(ji,jj,jk-1) ) - ztw(ji,jj,jk) |
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180 | END DO |
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181 | END DO |
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182 | END DO |
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183 | ! |
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184 | CALL lbc_lnk( ztu, 'U', -1. ) ! Lateral bondary conditions on upstream fluxes |
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185 | CALL lbc_lnk( ztv, 'V', -1. ) |
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186 | CALL lbc_lnk( ztw, 'W', 1. ) |
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187 | |
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188 | ! ! monotonicity algorithm |
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189 | CALL nonosc( ptb, ztu, ztv, ztw, zti, z2 ) |
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190 | |
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191 | |
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192 | ! 4. final trend with anti-diffusive fluxes |
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193 | ! ----------------------------------------- |
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194 | DO jk = 1, jpkm1 |
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195 | DO jj = 2, jpjm1 |
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196 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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197 | zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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198 | ! anti-diffusive trends added to the general tracer trends |
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199 | pta(ji,jj,jk) = pta(ji,jj,jk) - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk ) & |
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200 | & + ztv(ji,jj,jk) - ztv(ji ,jj-1,jk ) & |
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201 | & + ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) * zbtr |
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202 | END DO |
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203 | END DO |
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204 | END DO |
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205 | |
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206 | IF( l_trdtra ) THEN ! trend diagnostic (contribution of anti-diffusive fluxes) |
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207 | CALL trd_tra_adv( kt, ktra, jpt_trd_xad, cdtype, ztu, pun, ptn, cnbpas='bis' ) ! <<< Add to iad trend |
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208 | CALL trd_tra_adv( kt, ktra, jpt_trd_yad, cdtype, ztv, pvn, ptn, cnbpas='bis' ) ! <<< Add to jad trend |
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209 | CALL trd_tra_adv( kt, ktra, jpt_trd_zad, cdtype, ztw, pwn, ptn, cnbpas='bis' ) ! <<< Add to zad trend |
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210 | ENDIF |
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211 | ! ! "Poleward" heat and salt transports (contribution of anti-diffusive fluxes) |
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212 | IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN |
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213 | IF( ktra == jp_tem) pht_adv(:) = pht_adv(:) + ptr_vj( ztv(:,:,:) ) |
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214 | IF( ktra == jp_sal) pst_adv(:) = pst_adv(:) + ptr_vj( ztv(:,:,:) ) |
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215 | ENDIF |
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216 | ! ! control print |
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217 | IF(ln_ctl) CALL prt_ctl( tab3d_1=pta, clinfo1=' tvd - adv: ', mask1=tmask, clinfo3=cdtype ) |
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218 | ! |
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219 | END SUBROUTINE tra_adv_tvd |
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220 | |
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221 | |
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222 | SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, prdt ) |
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223 | !!--------------------------------------------------------------------- |
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224 | !! *** ROUTINE nonosc *** |
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225 | !! |
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226 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
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227 | !! scheme and the before field by a nonoscillatory algorithm |
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228 | !! |
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229 | !! ** Method : ... ??? |
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230 | !! warning : pbef and paft must be masked, but the boundaries |
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231 | !! conditions on the fluxes are not necessary zalezak (1979) |
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232 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
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233 | !! in-space based differencing for fluid |
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234 | !!---------------------------------------------------------------------- |
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235 | REAL(wp), INTENT(in ) :: prdt ! ??? |
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236 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pbef, paft ! before & after field |
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237 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: paa, pbb, pcc ! monotonic flux in the 3 directions |
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238 | !! |
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239 | INTEGER :: ji, jj, jk ! dummy loop indices |
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240 | INTEGER :: ikm1 |
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241 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: zbetup, zbetdo |
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242 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt |
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243 | !!---------------------------------------------------------------------- |
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244 | |
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245 | zbig = 1.e+40 |
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246 | zrtrn = 1.e-15 |
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247 | zbetup(:,:,:) = 0.e0 ; zbetdo(:,:,:) = 0.e0 |
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248 | |
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249 | !!gm optimisation : add the optimal version I wrote 1 year ago |
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250 | ! Search local extrema |
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251 | ! -------------------- |
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252 | ! large negative value (-zbig) inside land |
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253 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) |
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254 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) |
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255 | ! search maximum in neighbourhood |
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256 | DO jk = 1, jpkm1 |
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257 | ikm1 = MAX(jk-1,1) |
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258 | DO jj = 2, jpjm1 |
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259 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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260 | zbetup(ji,jj,jk) = MAX( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & |
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261 | & pbef(ji-1,jj ,jk ), pbef(ji+1,jj ,jk ), & |
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262 | & paft(ji-1,jj ,jk ), paft(ji+1,jj ,jk ), & |
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263 | & pbef(ji ,jj-1,jk ), pbef(ji ,jj+1,jk ), & |
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264 | & paft(ji ,jj-1,jk ), paft(ji ,jj+1,jk ), & |
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265 | & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & |
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266 | & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) |
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267 | END DO |
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268 | END DO |
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269 | END DO |
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270 | ! large positive value (+zbig) inside land |
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271 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) |
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272 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) |
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273 | ! search minimum in neighbourhood |
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274 | DO jk = 1, jpkm1 |
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275 | ikm1 = MAX(jk-1,1) |
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276 | DO jj = 2, jpjm1 |
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277 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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278 | zbetdo(ji,jj,jk) = MIN( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & |
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279 | & pbef(ji-1,jj ,jk ), pbef(ji+1,jj ,jk ), & |
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280 | & paft(ji-1,jj ,jk ), paft(ji+1,jj ,jk ), & |
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281 | & pbef(ji ,jj-1,jk ), pbef(ji ,jj+1,jk ), & |
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282 | & paft(ji ,jj-1,jk ), paft(ji ,jj+1,jk ), & |
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283 | & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & |
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284 | & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) |
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285 | END DO |
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286 | END DO |
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287 | END DO |
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288 | |
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289 | ! restore masked values to zero |
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290 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) |
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291 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) |
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292 | |
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293 | |
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294 | ! 2. Positive and negative part of fluxes and beta terms |
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295 | ! ------------------------------------------------------ |
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296 | |
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297 | DO jk = 1, jpkm1 |
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298 | z2dtt = prdt * rdttra(jk) |
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299 | DO jj = 2, jpjm1 |
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300 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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301 | ! positive & negative part of the flux |
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302 | zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) & |
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303 | & + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) & |
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304 | & + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
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305 | zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) & |
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306 | & + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) & |
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307 | & + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
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308 | ! up & down beta terms |
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309 | zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) / z2dtt |
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310 | zbetup(ji,jj,jk) = ( zbetup(ji,jj,jk) - paft(ji,jj,jk) ) / (zpos+zrtrn) * zbt |
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311 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zbetdo(ji,jj,jk) ) / (zneg+zrtrn) * zbt |
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312 | END DO |
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313 | END DO |
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314 | END DO |
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315 | |
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316 | ! lateral boundary condition on zbetup & zbetdo (unchanged sign) |
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317 | CALL lbc_lnk( zbetup, 'T', 1. ) |
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318 | CALL lbc_lnk( zbetdo, 'T', 1. ) |
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319 | |
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320 | |
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321 | ! 3. monotonic flux in the i & j direction (paa & pbb) |
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322 | ! ---------------------------------------- |
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323 | DO jk = 1, jpkm1 |
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324 | DO jj = 2, jpjm1 |
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325 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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326 | za = MIN( 1.e0, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) |
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327 | zb = MIN( 1.e0, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) |
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328 | zc = 0.5 * ( 1.e0 + SIGN( 1.e0, paa(ji,jj,jk) ) ) |
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329 | paa(ji,jj,jk) = paa(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) |
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330 | |
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331 | za = MIN( 1.e0, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) |
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332 | zb = MIN( 1.e0, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) |
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333 | zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pbb(ji,jj,jk) ) ) |
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334 | pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) |
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335 | END DO |
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336 | END DO |
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337 | END DO |
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338 | |
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339 | |
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340 | ! monotonic flux in the k direction, i.e. pcc |
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341 | ! ------------------------------------------- |
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342 | DO jk = 2, jpkm1 |
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343 | DO jj = 2, jpjm1 |
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344 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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345 | |
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346 | za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj,jk-1) ) |
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347 | zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj,jk-1) ) |
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348 | zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pcc(ji,jj,jk) ) ) |
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349 | pcc(ji,jj,jk) = pcc(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) |
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350 | END DO |
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351 | END DO |
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352 | END DO |
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353 | |
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354 | ! lateral boundary condition on paa, pbb, pcc |
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355 | CALL lbc_lnk( paa, 'U', -1. ) ! changed sign |
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356 | CALL lbc_lnk( pbb, 'V', -1. ) ! changed sign |
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357 | CALL lbc_lnk( pcc, 'W', 1. ) ! NO changed sign |
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358 | ! |
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359 | END SUBROUTINE nonosc |
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360 | |
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361 | !!====================================================================== |
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362 | END MODULE traadv_tvd |
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