1 | MODULE traadv_ubs |
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2 | !!============================================================================== |
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3 | !! *** MODULE traadv_ubs *** |
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4 | !! Ocean active tracers: horizontal & vertical advective trend |
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5 | !!============================================================================== |
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6 | !! History : 1.0 ! 2006-08 (L. Debreu, R. Benshila) Original code |
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7 | !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport |
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8 | !!---------------------------------------------------------------------- |
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9 | |
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10 | !!---------------------------------------------------------------------- |
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11 | !! tra_adv_ubs : update the tracer trend with the horizontal |
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12 | !! advection trends using a third order biaised scheme |
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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 ! trends manager: tracers |
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19 | USE dynspg_oce ! choice/control of key cpp for surface pressure gradient |
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20 | USE diaptr ! poleward transport diagnostics |
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21 | ! |
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22 | USE lib_mpp ! I/O library |
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23 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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24 | USE in_out_manager ! I/O manager |
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25 | USE wrk_nemo ! Memory Allocation |
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26 | USE timing ! Timing |
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27 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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28 | |
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29 | IMPLICIT NONE |
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30 | PRIVATE |
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31 | |
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32 | PUBLIC tra_adv_ubs ! routine called by traadv module |
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33 | |
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34 | LOGICAL :: l_trd ! flag to compute trends or not |
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35 | |
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36 | !! * Substitutions |
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37 | # include "domzgr_substitute.h90" |
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38 | # include "vectopt_loop_substitute.h90" |
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39 | !!---------------------------------------------------------------------- |
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40 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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41 | !! $Id$ |
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42 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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43 | !!---------------------------------------------------------------------- |
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44 | CONTAINS |
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45 | |
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46 | SUBROUTINE tra_adv_ubs ( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & |
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47 | & ptb, ptn, pta, kjpt ) |
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48 | !!---------------------------------------------------------------------- |
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49 | !! *** ROUTINE tra_adv_ubs *** |
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50 | !! |
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51 | !! ** Purpose : Compute the now trend due to the advection of tracers |
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52 | !! and add it to the general trend of passive tracer equations. |
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53 | !! |
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54 | !! ** Method : The upstream biased scheme (UBS) is based on a 3rd order |
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55 | !! upstream-biased parabolic interpolation (Shchepetkin and McWilliams 2005) |
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56 | !! It is only used in the horizontal direction. |
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57 | !! For example the i-component of the advective fluxes are given by : |
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58 | !! ! e2u e3u un ( mi(Tn) - zltu(i ) ) if un(i) >= 0 |
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59 | !! ztu = ! or |
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60 | !! ! e2u e3u un ( mi(Tn) - zltu(i+1) ) if un(i) < 0 |
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61 | !! where zltu is the second derivative of the before temperature field: |
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62 | !! zltu = 1/e3t di[ e2u e3u / e1u di[Tb] ] |
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63 | !! This results in a dissipatively dominant (i.e. hyper-diffusive) |
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64 | !! truncation error. The overall performance of the advection scheme |
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65 | !! is similar to that reported in (Farrow and Stevens, 1995). |
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66 | !! For stability reasons, the first term of the fluxes which corresponds |
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67 | !! to a second order centered scheme is evaluated using the now velocity |
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68 | !! (centered in time) while the second term which is the diffusive part |
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69 | !! of the scheme, is evaluated using the before velocity (forward in time). |
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70 | !! Note that UBS is not positive. Do not use it on passive tracers. |
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71 | !! On the vertical, the advection is evaluated using a TVD scheme, |
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72 | !! as the UBS have been found to be too diffusive. |
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73 | !! |
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74 | !! ** Action : - update (pta) with the now advective tracer trends |
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75 | !! |
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76 | !! Reference : Shchepetkin, A. F., J. C. McWilliams, 2005, Ocean Modelling, 9, 347-404. |
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77 | !! Farrow, D.E., Stevens, D.P., 1995, J. Phys. Ocean. 25, 1731Ð1741. |
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78 | !!---------------------------------------------------------------------- |
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79 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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80 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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81 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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82 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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83 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
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84 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean transport components |
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85 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields |
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86 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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87 | ! |
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88 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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89 | REAL(wp) :: ztra, zbtr, zcoef, z2dtt ! local scalars |
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90 | REAL(wp) :: zfp_ui, zfm_ui, zcenut, ztak, zfp_wk, zfm_wk ! - - |
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91 | REAL(wp) :: zfp_vj, zfm_vj, zcenvt, zeeu, zeev, z_hdivn ! - - |
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92 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztu, ztv, zltu, zltv, zti, ztw |
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93 | !!---------------------------------------------------------------------- |
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94 | ! |
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95 | IF( nn_timing == 1 ) CALL timing_start('tra_adv_ubs') |
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96 | ! |
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97 | CALL wrk_alloc( jpi, jpj, jpk, ztu, ztv, zltu, zltv, zti, ztw ) |
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98 | ! |
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99 | IF( kt == kit000 ) THEN |
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100 | IF(lwp) WRITE(numout,*) |
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101 | IF(lwp) WRITE(numout,*) 'tra_adv_ubs : horizontal UBS advection scheme on ', cdtype |
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102 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~' |
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103 | ENDIF |
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104 | ! |
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105 | l_trd = .FALSE. |
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106 | IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
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107 | ! |
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108 | ! ! =========== |
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109 | DO jn = 1, kjpt ! tracer loop |
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110 | ! ! =========== |
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111 | ! 1. Bottom value : flux set to zero |
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112 | ! ---------------------------------- |
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113 | zltu(:,:,jpk) = 0.e0 ; zltv(:,:,jpk) = 0.e0 |
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114 | ! |
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115 | DO jk = 1, jpkm1 ! Horizontal slab |
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116 | ! |
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117 | ! Laplacian |
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118 | DO jj = 1, jpjm1 ! First derivative (gradient) |
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119 | DO ji = 1, fs_jpim1 ! vector opt. |
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120 | zeeu = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) |
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121 | zeev = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) |
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122 | ztu(ji,jj,jk) = zeeu * ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) ) |
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123 | ztv(ji,jj,jk) = zeev * ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) |
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124 | END DO |
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125 | END DO |
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126 | DO jj = 2, jpjm1 ! Second derivative (divergence) |
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127 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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128 | zcoef = 1. / ( 6. * fse3t(ji,jj,jk) ) |
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129 | zltu(ji,jj,jk) = ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zcoef |
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130 | zltv(ji,jj,jk) = ( ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) * zcoef |
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131 | END DO |
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132 | END DO |
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133 | ! |
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134 | END DO ! End of slab |
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135 | CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) |
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136 | |
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137 | ! |
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138 | ! Horizontal advective fluxes |
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139 | DO jk = 1, jpkm1 ! Horizontal slab |
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140 | DO jj = 1, jpjm1 |
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141 | DO ji = 1, fs_jpim1 ! vector opt. |
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142 | ! upstream transport (x2) |
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143 | zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) |
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144 | zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) |
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145 | zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) |
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146 | zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) |
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147 | ! 2nd order centered advective fluxes (x2) |
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148 | zcenut = pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ) |
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149 | zcenvt = pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) ) |
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150 | ! UBS advective fluxes |
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151 | ztu(ji,jj,jk) = 0.5 * ( zcenut - zfp_ui * zltu(ji,jj,jk) - zfm_ui * zltu(ji+1,jj,jk) ) |
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152 | ztv(ji,jj,jk) = 0.5 * ( zcenvt - zfp_vj * zltv(ji,jj,jk) - zfm_vj * zltv(ji,jj+1,jk) ) |
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153 | END DO |
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154 | END DO |
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155 | END DO ! End of slab |
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156 | |
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157 | zltu(:,:,:) = pta(:,:,:,jn) ! store pta trends |
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158 | |
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159 | DO jk = 1, jpkm1 ! Horizontal advective trends |
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160 | DO jj = 2, jpjm1 |
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161 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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162 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) & |
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163 | & - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk) & |
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164 | & + ztv(ji,jj,jk) - ztv(ji ,jj-1,jk) ) / ( e1e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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165 | END DO |
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166 | END DO |
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167 | ! |
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168 | END DO ! End of slab |
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169 | |
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170 | ! Horizontal trend used in tra_adv_ztvd subroutine |
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171 | zltu(:,:,:) = pta(:,:,:,jn) - zltu(:,:,:) |
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172 | |
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173 | ! |
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174 | IF( l_trd ) THEN ! trend diagnostics |
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175 | CALL trd_tra( kt, cdtype, jn, jptra_xad, ztu, pun, ptn(:,:,:,jn) ) |
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176 | CALL trd_tra( kt, cdtype, jn, jptra_yad, ztv, pvn, ptn(:,:,:,jn) ) |
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177 | END IF |
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178 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
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179 | IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN |
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180 | IF( jn == jp_tem ) htr_adv(:) = ptr_sj( ztv(:,:,:) ) |
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181 | IF( jn == jp_sal ) str_adv(:) = ptr_sj( ztv(:,:,:) ) |
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182 | ENDIF |
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183 | |
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184 | ! TVD scheme for the vertical direction |
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185 | ! ---------------------- |
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186 | IF( l_trd ) zltv(:,:,:) = pta(:,:,:,jn) ! store pta if trend diag. |
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187 | |
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188 | ! Bottom value : flux set to zero |
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189 | ztw(:,:,jpk) = 0.e0 ; zti(:,:,jpk) = 0.e0 |
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190 | |
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191 | ! Surface value |
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192 | IF( lk_vvl ) THEN ; ztw(:,:,1) = 0.e0 ! variable volume : flux set to zero |
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193 | ELSE ; ztw(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ! free constant surface |
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194 | ENDIF |
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195 | ! upstream advection with initial mass fluxes & intermediate update |
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196 | ! ------------------------------------------------------------------- |
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197 | ! Interior value |
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198 | DO jk = 2, jpkm1 |
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199 | DO jj = 1, jpj |
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200 | DO ji = 1, jpi |
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201 | zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) |
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202 | zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) |
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203 | ztw(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) |
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204 | END DO |
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205 | END DO |
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206 | END DO |
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207 | ! update and guess with monotonic sheme |
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208 | DO jk = 1, jpkm1 |
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209 | z2dtt = p2dt(jk) |
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210 | DO jj = 2, jpjm1 |
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211 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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212 | zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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213 | ztak = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr |
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214 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztak |
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215 | zti(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ( ztak + zltu(ji,jj,jk) ) ) * tmask(ji,jj,jk) |
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216 | END DO |
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217 | END DO |
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218 | END DO |
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219 | ! |
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220 | CALL lbc_lnk( zti, 'T', 1. ) ! Lateral boundary conditions on zti, zsi (unchanged sign) |
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221 | |
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222 | ! antidiffusive flux : high order minus low order |
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223 | ztw(:,:,1) = 0.e0 ! Surface value |
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224 | DO jk = 2, jpkm1 ! Interior value |
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225 | DO jj = 1, jpj |
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226 | DO ji = 1, jpi |
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227 | ztw(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) - ztw(ji,jj,jk) |
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228 | END DO |
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229 | END DO |
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230 | END DO |
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231 | ! |
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232 | CALL nonosc_z( ptb(:,:,:,jn), ztw, zti, p2dt ) ! monotonicity algorithm |
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233 | |
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234 | ! final trend with corrected fluxes |
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235 | DO jk = 1, jpkm1 |
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236 | DO jj = 2, jpjm1 |
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237 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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238 | zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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239 | ! k- vertical advective trends |
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240 | ztra = - zbtr * ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) |
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241 | ! added to the general tracer trends |
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242 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra |
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243 | END DO |
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244 | END DO |
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245 | END DO |
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246 | |
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247 | ! Save the final vertical advective trends |
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248 | IF( l_trd ) THEN ! vertical advective trend diagnostics |
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249 | DO jk = 1, jpkm1 ! (compute -w.dk[ptn]= -dk[w.ptn] + ptn.dk[w]) |
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250 | DO jj = 2, jpjm1 |
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251 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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252 | zbtr = 1.e0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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253 | z_hdivn = ( pwn(ji,jj,jk) - pwn(ji,jj,jk+1) ) * zbtr |
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254 | zltv(ji,jj,jk) = pta(ji,jj,jk,jn) - zltv(ji,jj,jk) + ptn(ji,jj,jk,jn) * z_hdivn |
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255 | END DO |
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256 | END DO |
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257 | END DO |
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258 | CALL trd_tra( kt, cdtype, jn, jptra_zad, zltv ) |
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259 | ENDIF |
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260 | ! |
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261 | END DO |
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262 | ! |
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263 | CALL wrk_dealloc( jpi, jpj, jpk, ztu, ztv, zltu, zltv, zti, ztw ) |
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264 | ! |
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265 | IF( nn_timing == 1 ) CALL timing_stop('tra_adv_ubs') |
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266 | ! |
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267 | END SUBROUTINE tra_adv_ubs |
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268 | |
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269 | |
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270 | SUBROUTINE nonosc_z( pbef, pcc, paft, p2dt ) |
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271 | !!--------------------------------------------------------------------- |
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272 | !! *** ROUTINE nonosc_z *** |
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273 | !! |
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274 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
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275 | !! scheme and the before field by a nonoscillatory algorithm |
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276 | !! |
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277 | !! ** Method : ... ??? |
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278 | !! warning : pbef and paft must be masked, but the boundaries |
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279 | !! conditions on the fluxes are not necessary zalezak (1979) |
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280 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
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281 | !! in-space based differencing for fluid |
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282 | !!---------------------------------------------------------------------- |
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283 | REAL(wp), INTENT(in ), DIMENSION(jpk) :: p2dt ! vertical profile of tracer time-step |
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284 | REAL(wp), DIMENSION (jpi,jpj,jpk) :: pbef ! before field |
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285 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: paft ! after field |
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286 | REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pcc ! monotonic flux in the k direction |
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287 | ! |
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288 | INTEGER :: ji, jj, jk ! dummy loop indices |
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289 | INTEGER :: ikm1 ! local integer |
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290 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt ! local scalars |
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291 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zbetup, zbetdo |
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292 | !!---------------------------------------------------------------------- |
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293 | ! |
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294 | IF( nn_timing == 1 ) CALL timing_start('nonosc_z') |
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295 | ! |
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296 | CALL wrk_alloc( jpi, jpj, jpk, zbetup, zbetdo ) |
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297 | ! |
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298 | zbig = 1.e+40_wp |
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299 | zrtrn = 1.e-15_wp |
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300 | zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp |
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301 | |
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302 | ! Search local extrema |
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303 | ! -------------------- |
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304 | ! large negative value (-zbig) inside land |
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305 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) |
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306 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) |
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307 | ! search maximum in neighbourhood |
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308 | DO jk = 1, jpkm1 |
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309 | ikm1 = MAX(jk-1,1) |
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310 | DO jj = 2, jpjm1 |
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311 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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312 | zbetup(ji,jj,jk) = MAX( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & |
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313 | & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & |
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314 | & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) |
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315 | END DO |
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316 | END DO |
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317 | END DO |
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318 | ! large positive value (+zbig) inside land |
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319 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) |
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320 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) |
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321 | ! search minimum in neighbourhood |
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322 | DO jk = 1, jpkm1 |
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323 | ikm1 = MAX(jk-1,1) |
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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 | zbetdo(ji,jj,jk) = MIN( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & |
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327 | & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & |
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328 | & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) |
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329 | END DO |
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330 | END DO |
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331 | END DO |
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332 | |
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333 | ! restore masked values to zero |
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334 | pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) |
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335 | paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) |
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336 | |
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337 | |
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338 | ! 2. Positive and negative part of fluxes and beta terms |
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339 | ! ------------------------------------------------------ |
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340 | |
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341 | DO jk = 1, jpkm1 |
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342 | z2dtt = p2dt(jk) |
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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 | ! positive & negative part of the flux |
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346 | zpos = MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
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347 | zneg = MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
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348 | ! up & down beta terms |
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349 | zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) / z2dtt |
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350 | zbetup(ji,jj,jk) = ( zbetup(ji,jj,jk) - paft(ji,jj,jk) ) / (zpos+zrtrn) * zbt |
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351 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zbetdo(ji,jj,jk) ) / (zneg+zrtrn) * zbt |
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352 | END DO |
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353 | END DO |
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354 | END DO |
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355 | ! monotonic flux in the k direction, i.e. pcc |
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356 | ! ------------------------------------------- |
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357 | DO jk = 2, jpkm1 |
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358 | DO jj = 2, jpjm1 |
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359 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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360 | za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj,jk-1) ) |
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361 | zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj,jk-1) ) |
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362 | zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pcc(ji,jj,jk) ) ) |
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363 | pcc(ji,jj,jk) = pcc(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) |
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364 | END DO |
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365 | END DO |
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366 | END DO |
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367 | ! |
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368 | CALL wrk_dealloc( jpi, jpj, jpk, zbetup, zbetdo ) |
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369 | ! |
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370 | IF( nn_timing == 1 ) CALL timing_stop('nonosc_z') |
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371 | ! |
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372 | END SUBROUTINE nonosc_z |
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373 | |
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374 | !!====================================================================== |
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375 | END MODULE traadv_ubs |
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