1 | MODULE traadv_qck |
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2 | !!============================================================================== |
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3 | !! *** MODULE traadv_qck *** |
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4 | !! Ocean active tracers: horizontal & vertical advective trend |
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5 | !!============================================================================== |
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6 | |
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7 | !!---------------------------------------------------------------------- |
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8 | !! tra_adv_qck : update the tracer trend with the horizontal |
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9 | !! advection trends using a 3st order |
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10 | !! finite difference scheme |
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11 | !! The vertical advection scheme is the 2nd centered scheme |
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12 | !!---------------------------------------------------------------------- |
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13 | !! * Modules used |
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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 trdmod ! ocean active tracers trends |
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17 | USE trdmod_oce ! ocean variables trends |
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18 | USE flxrnf ! |
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19 | USE trabbl ! advective term in the BBL |
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20 | USE ocfzpt ! |
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21 | USE lib_mpp |
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22 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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23 | USE in_out_manager ! I/O manager |
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24 | USE diaptr ! poleward transport diagnostics |
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25 | USE dynspg_oce ! |
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26 | USE prtctl ! Print control |
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27 | |
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28 | IMPLICIT NONE |
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29 | PRIVATE |
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30 | |
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31 | !! * Accessibility |
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32 | PUBLIC tra_adv_qck ! routine called by step.F90 |
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33 | |
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34 | !! * Module variables |
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35 | REAL(wp), DIMENSION(jpi,jpj), SAVE :: & |
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36 | zbtr2 |
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37 | REAL(wp), DIMENSION(jpi,jpj,jpk), SAVE :: & |
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38 | sl |
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39 | REAL(wp) :: & |
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40 | cst1, cst2, dt, coef1 ! temporary scalars |
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41 | INTEGER :: & |
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42 | ji, jj, jk ! dummy loop indices |
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43 | !!---------------------------------------------------------------------- |
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44 | !! * Substitutions |
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45 | # include "domzgr_substitute.h90" |
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46 | # include "vectopt_loop_substitute.h90" |
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47 | !!---------------------------------------------------------------------- |
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48 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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49 | !! $Header$ |
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50 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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51 | !!---------------------------------------------------------------------- |
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52 | |
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53 | CONTAINS |
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54 | |
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55 | SUBROUTINE tra_adv_qck( kt, pun, pvn, pwn ) |
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56 | !!---------------------------------------------------------------------- |
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57 | !! *** ROUTINE tra_adv_qck *** |
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58 | !! |
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59 | !! ** Purpose : Compute the now trend due to the advection of tracers |
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60 | !! and add it to the general trend of passive tracer equations. |
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61 | !! |
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62 | !! ** Method : The advection is evaluated by a third order scheme |
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63 | !! For a positive velocity u : |
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64 | !! |
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65 | !! |
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66 | !! i-1 i i+1 i+2 |
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67 | !! |
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68 | !! |--FU--|--FC--|--FD--|------| |
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69 | !! u(i)>0 |
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70 | !! |
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71 | !! For a negative velocity u : |
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72 | !! |
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73 | !! |------|--FD--|--FC--|--FU--| |
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74 | !! u(i)<0 |
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75 | !! |
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76 | !! FU is the second upwind point |
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77 | !! FD is the first douwning point |
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78 | !! FC is the central point (or the first upwind point) |
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79 | !! |
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80 | !! Flux(i) = u(i) * {0.5(FC+FD) -0.5C(i)(FD-FC) -((1-C(i)å?)/6)(FU+FD-2FC)} |
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81 | !! with C(i)=|u(i)|dx(i)/dt (Courant number) |
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82 | !! |
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83 | !! dt = 2*rdtra and the scalar values are tb and sb |
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84 | !! |
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85 | !! On the vertical, the simple centered scheme used tn and sn |
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86 | !! |
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87 | !! The fluxes are bounded by the ULTIMATE limiter |
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88 | !! to guarantee the monotonicity of the solution and to |
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89 | !! prevent the appearance of spurious numerical oscillations |
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90 | !! |
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91 | !! ** Action : - update (ta,sa) with the now advective tracer trends |
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92 | !! - save the trends in (ttrdh,strdh) ('key_trdtra') |
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93 | !! |
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94 | !! ** Reference : Leonard (1979, 1991) |
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95 | !! History : |
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96 | !! 9.0 ! 06-09 (G. Reffray) Original code |
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97 | !!---------------------------------------------------------------------- |
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98 | !! * Arguments |
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99 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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100 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pun ! effective ocean velocity, u_component |
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101 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pvn ! effective ocean velocity, v_component |
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102 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pwn ! effective ocean velocity, w_component |
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103 | !! |
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104 | REAL(wp) :: z2 ! temporary scalar |
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105 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: ztrdt, ztrds ! temporary 3D workspace |
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106 | |
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107 | IF( kt == nit000 ) THEN |
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108 | IF(lwp) WRITE(numout,*) |
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109 | IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3st order quickest advection scheme' |
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110 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~ Vector optimization case' |
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111 | IF(lwp) WRITE(numout,*) |
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112 | |
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113 | zbtr2(:,:) = 1. / ( e1t(:,:) * e2t(:,:) ) |
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114 | cst1 = 1./12. |
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115 | cst2 = 2./3. |
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116 | IF (l_trdtra ) THEN |
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117 | CALL ctl_warn( ' Trends not yet implemented for PPM advection scheme ' ) |
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118 | ENDIF |
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119 | ENDIF |
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120 | |
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121 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; z2 = 1. |
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122 | ELSE ; z2 = 2. |
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123 | ENDIF |
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124 | |
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125 | ! Save ta and sa trends |
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126 | IF( l_trdtra ) THEN ! to be done |
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127 | ztrdt(:,:,:) = ta(:,:,:) |
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128 | ztrds(:,:,:) = sa(:,:,:) |
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129 | l_adv = 'qst' |
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130 | ENDIF |
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131 | |
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132 | ! I. Slope estimation at the T-point for the limiter ULTIMATE |
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133 | ! SL = Sum(1/C_out) with C_out : Courant number for the outflows |
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134 | !--------------------------------------------------------------- |
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135 | |
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136 | sl(:,:,:) = 100. |
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137 | |
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138 | ! =============== |
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139 | DO jk = 1, jpkm1 ! Horizontal slab |
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140 | ! ! =============== |
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141 | dt = z2 * rdttra(jk) |
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142 | DO jj = 2, jpjm1 |
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143 | DO ji = 2, fs_jpim1 ! vector opt. |
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144 | coef1 = 1.e-12 |
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145 | IF (pun(ji-1,jj ,jk ).LT.0.) coef1 = coef1 + ABS(pun(ji-1,jj ,jk ))*dt/e1t(ji,jj) |
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146 | IF (pun(ji ,jj ,jk ).GT.0.) coef1 = coef1 + ABS(pun(ji ,jj ,jk ))*dt/e1t(ji,jj) |
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147 | IF (pvn(ji ,jj-1,jk ).LT.0.) coef1 = coef1 + ABS(pvn(ji ,jj-1,jk ))*dt/e2t(ji,jj) |
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148 | IF (pvn(ji ,jj ,jk ).GT.0.) coef1 = coef1 + ABS(pvn(ji ,jj ,jk ))*dt/e2t(ji,jj) |
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149 | IF (pwn(ji ,jj ,jk+1).LT.0.) coef1 = coef1 + ABS(pwn(ji ,jj ,jk+1))*dt/(fse3t(ji,jj,jk)) |
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150 | IF (pwn(ji ,jj ,jk ).GT.0.) coef1 = coef1 + ABS(pwn(ji ,jj ,jk ))*dt/(fse3t(ji,jj,jk)) |
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151 | sl(ji,jj,jk) = 1./coef1 |
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152 | sl(ji,jj,jk) = MIN(100.,sl(ji,jj,jk)) |
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153 | sl(ji,jj,jk) = MAX(1. ,sl(ji,jj,jk)) |
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154 | ENDDO |
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155 | ENDDO |
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156 | ENDDO |
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157 | !--- Lateral boundary conditions on the limiter slope |
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158 | CALL lbc_lnk( sl(:,:,:), 'T', 1. ) |
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159 | |
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160 | ! II. The horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme |
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161 | !--------------------------------------------------------------------------- |
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162 | |
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163 | CALL tra_adv_qck_hor( kt , pun, pvn, tb , ta , pht_adv , z2) |
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164 | CALL tra_adv_qck_hor( kt , pun, pvn, sb , sa , pst_adv , z2) |
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165 | |
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166 | ! Save the horizontal advective trends for diagnostic |
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167 | ! --------------------------------------------------- |
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168 | ! IF( l_trdtra ) THEN ! to be done |
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169 | ! ! T/S ZONAL advection trends |
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170 | ! ENDIF |
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171 | |
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172 | IF(ln_ctl) THEN |
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173 | CALL prt_ctl(tab3d_1=ta, clinfo1=' centered2 had - Ta: ', mask1=tmask, & |
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174 | & tab3d_2=sa, clinfo2=' Sa: ', mask2=tmask, clinfo3='tra') |
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175 | ENDIF |
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176 | |
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177 | ! III. The vertical fluxes are computed with the 2nd order centered scheme |
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178 | !------------------------------------------------------------------------- |
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179 | |
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180 | CALL tra_adv_qck_ver( pwn, tn , ta, z2 ) |
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181 | CALL tra_adv_qck_ver( pwn, sn , sa, z2 ) |
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182 | |
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183 | ! Save the vertical advective trends for diagnostic |
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184 | ! ------------------------------------------------- |
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185 | ! IF( l_trdtra ) THEN ! to be done |
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186 | ! Recompute the vertical advection zta & zsa trends computed |
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187 | ! at the step 2. above in making the difference between the new |
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188 | ! trends and the previous one: ta()/sa - ztdta()/ztdsa() and substract |
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189 | ! the term tn()/sn()*hdivn() to recover the W gradz(T/S) trends |
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190 | ! ENDIF |
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191 | |
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192 | IF(ln_ctl) THEN |
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193 | CALL prt_ctl(tab3d_1=ta, clinfo1=' centered2 zad - Ta: ', mask1=tmask, & |
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194 | & tab3d_2=sa, clinfo2=' Sa: ', mask2=tmask, clinfo3='tra') |
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195 | ENDIF |
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196 | |
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197 | END SUBROUTINE tra_adv_qck |
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198 | |
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199 | SUBROUTINE tra_adv_qck_hor ( kt , pun, pvn, tra , traa , phtra_adv ,z2 ) |
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200 | !!---------------------------------------------------------------------- |
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201 | !! |
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202 | !!---------------------------------------------------------------------- |
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203 | !! * Arguments |
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204 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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205 | REAL, INTENT( in ) :: z2 |
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206 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pun, pvn ! horizontal effective velocity |
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207 | |
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208 | REAL(wp), INTENT ( out ), DIMENSION(jpj) :: & |
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209 | phtra_adv |
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210 | |
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211 | REAL(wp), INTENT ( inout ), DIMENSION(jpi,jpj,jpk) :: & |
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212 | tra, traa |
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213 | |
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214 | REAL(wp) :: & |
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215 | za, zbtr, e1, e2, c, dir, fu, fc, fd, & ! temporary scalars |
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216 | coef2, coef3, fho, mask, dx |
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217 | |
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218 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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219 | zee |
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220 | |
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221 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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222 | zmask, zlap, dwst, lim |
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223 | |
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224 | |
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225 | |
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226 | !---------------------------------------------------------------------- |
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227 | ! 0. Initialization (should ot be needed on the whole array ???) |
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228 | !---------------------------------------------------------------------- |
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229 | |
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230 | zmask = 0.0 |
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231 | zlap = 0.0 |
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232 | dwst = 0.0 |
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233 | lim = 0.0 |
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234 | |
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235 | !---------------------------------------------------------------------- |
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236 | ! I. Part 1 : x-direction |
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237 | !---------------------------------------------------------------------- |
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238 | |
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239 | ! =============== |
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240 | DO jk = 1, jpkm1 ! Horizontal slab |
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241 | ! ! =============== |
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242 | ! Initialization of metric arrays (for z- or s-coordinates) |
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243 | ! --------------------------------------------------------- |
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244 | DO jj = 1, jpjm1 |
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245 | DO ji = 1, fs_jpim1 ! vector opt. |
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246 | #if defined key_zco |
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247 | ! z-coordinates, no vertical scale factors |
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248 | zee(ji,jj) = e2u(ji,jj) / e1u(ji,jj) * umask(ji,jj,jk) |
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249 | #else |
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250 | ! vertical scale factor are used |
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251 | zee(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) |
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252 | #endif |
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253 | END DO |
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254 | END DO |
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255 | |
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256 | ! Laplacian of tracers (at before time step) |
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257 | ! ------------------------------------------ |
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258 | !--- First derivative (gradient) |
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259 | DO jj = 1, jpjm1 |
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260 | DO ji = 1, fs_jpim1 ! vector opt. |
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261 | zmask(ji,jj,jk) = zee(ji,jj) * ( tra(ji+1,jj ,jk) - tra(ji,jj,jk) ) |
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262 | END DO |
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263 | END DO |
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264 | DO jj = 2, jpjm1 |
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265 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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266 | #if defined key_zco |
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267 | zee(ji,jj) = e1t(ji,jj) / e2t(ji,jj) |
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268 | #else |
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269 | zee(ji,jj) = e1t(ji,jj) / (e2t(ji,jj) * fse3t(ji,jj,jk)) |
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270 | #endif |
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271 | zlap(ji,jj,jk) = zee(ji,jj) * ( zmask(ji,jj,jk) - zmask(ji-1,jj,jk) ) |
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272 | END DO |
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273 | END DO |
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274 | !--- Function lim=FU+SL*(FC-FU) used by the limiter |
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275 | !--- Computation of the ustream and downstream lim at the T-points |
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276 | DO jj = 2, jpjm1 |
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277 | DO ji = 2, fs_jpim1 ! vector opt. |
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278 | ! Upstream in the x-direction for the tracer |
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279 | zmask(ji,jj,jk)=tra(ji-1,jj,jk)+sl(ji,jj,jk)*(tra(ji,jj,jk)-tra(ji-1,jj,jk)) |
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280 | ! Downstream in the x-direction for the tracer |
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281 | dwst (ji,jj,jk)=tra(ji+1,jj,jk)+sl(ji,jj,jk)*(tra(ji,jj,jk)-tra(ji+1,jj,jk)) |
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282 | ENDDO |
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283 | ENDDO |
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284 | END DO |
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285 | !--- Lateral boundary conditions on the laplacian (unchanged sgn) |
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286 | CALL lbc_lnk( zlap(:,:,:), 'T', 1. ) |
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287 | !--- Lateral boundary conditions for the lim function |
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288 | CALL lbc_lnk( zmask(:,:,:), 'T', 1. ) ; CALL lbc_lnk( dwst(:,:,:), 'T', 1. ) |
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289 | ! =============== |
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290 | DO jk = 1, jpkm1 ! Horizontal slab |
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291 | ! ! =============== |
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292 | ! --- lim at the U-points in function of the direction of the flow |
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293 | ! ---------------------------------------------------------------- |
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294 | DO jj = 1, jpjm1 |
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295 | DO ji = 1, fs_jpim1 ! vector opt. |
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296 | dir = 0.5 + sign(0.5,pun(ji,jj,jk)) ! if pun>0 : diru = 1 otherwise diru = 0 |
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297 | lim(ji,jj,jk)=dir*zmask(ji,jj,jk)+(1-dir)*dwst(ji+1,jj,jk) |
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298 | ! Mask at the T-points in the x-direction (mask=0 or mask=1) |
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299 | zmask(ji,jj,jk)=tmask(ji-1,jj,jk)+tmask(ji,jj,jk)+tmask(ji+1,jj,jk)-2 |
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300 | END DO |
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301 | END DO |
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302 | END DO |
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303 | !--- Lateral boundary conditions for the mask |
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304 | CALL lbc_lnk( zmask(:,:,:), 'T', 1. ) |
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305 | |
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306 | ! Horizontal advective fluxes |
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307 | ! --------------------------- |
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308 | ! =============== |
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309 | DO jk = 1, jpkm1 ! Horizontal slab |
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310 | ! =============== |
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311 | dt = z2 * rdttra(jk) |
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312 | !--- tracer flux at u and v-points |
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313 | DO jj = 1, jpjm1 |
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314 | DO ji = 1, fs_jpim1 ! vector opt. |
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315 | #if defined key_zco |
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316 | e2 = e2u(ji,jj) |
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317 | #else |
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318 | e2 = e2u(ji,jj) * fse3u(ji,jj,jk) |
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319 | #endif |
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320 | dir = 0.5 + sign(0.5,pun(ji,jj,jk)) ! if pun>0 : diru = 1 otherwise diru = 0 |
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321 | |
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322 | dx = dir * e1t(ji,jj) + (1-dir)* e1t(ji+1,jj) |
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323 | c = ABS(pun(ji,jj,jk))*dt/dx ! (0<cx<1 : Courant number on x-direction) |
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324 | |
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325 | fu = lim(ji,jj,jk) ! FU + sl(FC-FU) in the x-direction for T |
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326 | fc = dir*tra(ji ,jj,jk)+(1-dir)*tra(ji+1,jj,jk) ! FC in the x-direction for T |
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327 | fd = dir*tra(ji+1,jj,jk)+(1-dir)*tra(ji ,jj,jk) ! FD in the x-direction for T |
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328 | |
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329 | !--- QUICKEST scheme |
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330 | ! Temperature on the x-direction |
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331 | coef1 = 0.5*(fc+fd) |
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332 | coef2 = 0.5*c*(fd-fc) |
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333 | coef3 = ((1.-(c*c))/6.)*(dir*zlap(ji,jj,jk) + (1-dir)*zlap(ji+1,jj,jk) ) |
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334 | fho = coef1-coef2-coef3 |
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335 | fho = bound(fu,fd,fc,fho) |
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336 | !--- If the second ustream point is a land point |
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337 | !--- the flux is computed by the 1st order UPWIND scheme |
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338 | mask=dir*zmask(ji,jj,jk)+(1-dir)*zmask(ji+1,jj,jk) |
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339 | fho = mask*fho + (1-mask)*fc |
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340 | dwst(ji,jj,jk)=e2*pun(ji,jj,jk)*fho |
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341 | END DO |
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342 | END DO |
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343 | |
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344 | !--- Tracer flux divergence at t-point added to the general trend |
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345 | DO jj = 2, jpjm1 |
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346 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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347 | !--- horizontal advective trends |
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348 | #if defined key_zco |
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349 | zbtr = zbtr2(ji,jj) |
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350 | #else |
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351 | zbtr = zbtr2(ji,jj) / fse3t(ji,jj,jk) |
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352 | #endif |
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353 | za = - zbtr * ( dwst(ji,jj,jk) - dwst(ji-1,jj ,jk) ) |
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354 | !--- add it to the general tracer trends |
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355 | traa(ji,jj,jk) = traa(ji,jj,jk) + za |
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356 | END DO |
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357 | END DO |
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358 | ! ! =============== |
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359 | END DO ! End of slab |
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360 | ! ! =============== |
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361 | !---------------------------------------------------------------------- |
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362 | ! I. Part 2 : y-direction |
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363 | !---------------------------------------------------------------------- |
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364 | ! ============== |
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365 | DO jk = 1, jpkm1 ! Horizontal slab |
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366 | ! ! =============== |
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367 | ! Initialization of metric arrays (for z- or s-coordinates) |
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368 | ! --------------------------------------------------------- |
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369 | DO jj = 1, jpjm1 |
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370 | DO ji = 1, fs_jpim1 ! vector opt. |
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371 | #if defined key_zco |
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372 | ! z-coordinates, no vertical scale factors |
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373 | zee(ji,jj) = e1v(ji,jj) / e2v(ji,jj) * vmask(ji,jj,jk) |
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374 | #else |
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375 | ! s-coordinates, vertical scale factor are used |
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376 | zee(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) |
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377 | #endif |
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378 | END DO |
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379 | END DO |
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380 | |
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381 | ! Laplacian of tracers (at before time step) |
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382 | ! ------------------------------------------ |
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383 | !--- First derivative (gradient) |
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384 | DO jj = 1, jpjm1 |
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385 | DO ji = 1, fs_jpim1 ! vector opt. |
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386 | zmask(ji,jj,jk) = zee(ji,jj) * ( tra(ji ,jj+1,jk) - tra(ji,jj,jk) ) |
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387 | END DO |
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388 | END DO |
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389 | !--- Second derivative (divergence) |
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390 | DO jj = 2, jpjm1 |
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391 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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392 | #if defined key_zco |
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393 | zee(ji,jj) = e2t(ji,jj) / e1t(ji,jj) |
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394 | #else |
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395 | zee(ji,jj) = e2t(ji,jj) / (e1t(ji,jj) * fse3t(ji,jj,jk)) |
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396 | #endif |
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397 | zlap(ji,jj,jk) = zee(ji,jj) * ( zmask(ji,jj,jk) - zmask(ji,jj-1,jk) ) |
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398 | END DO |
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399 | END DO |
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400 | !--- Function lim=FU+SL*(FC-FU) used by the limiter |
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401 | !--- Computation of the ustream and downstream lim at the T-points |
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402 | DO jj = 2, jpjm1 |
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403 | DO ji = 2, fs_jpim1 ! vector opt. |
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404 | ! Upstream in the y-direction for the tracer |
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405 | zmask(ji,jj,jk)=tra(ji,jj-1,jk)+sl(ji,jj,jk)*(tra(ji,jj,jk)-tra(ji,jj-1,jk)) |
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406 | ! Downstream in the y-direction for the tracer |
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407 | dwst (ji,jj,jk)=tra(ji,jj+1,jk)+sl(ji,jj,jk)*(tra(ji,jj,jk)-tra(ji,jj+1,jk)) |
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408 | ENDDO |
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409 | ENDDO |
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410 | END DO |
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411 | !--- Lateral boundary conditions on the laplacian (unchanged sgn) |
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412 | CALL lbc_lnk( zlap(:,:,:), 'T', 1. ) |
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413 | !--- Lateral boundary conditions for the lim function |
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414 | CALL lbc_lnk( zmask(:,:,:), 'T', 1. ) ; CALL lbc_lnk( dwst(:,:,:), 'T', 1. ) |
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415 | |
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416 | DO jk = 1, jpkm1 ! Horizontal slab |
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417 | ! ! =============== |
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418 | ! --- lim at the V-points in function of the direction of the flow |
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419 | ! ---------------------------------------------------------------- |
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420 | DO jj = 1, jpjm1 |
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421 | DO ji = 1, fs_jpim1 ! vector opt. |
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422 | dir = 0.5 + sign(0.5,pvn(ji,jj,jk)) ! if pvn>0 : dirv = 1 otherwise dirv = 0 |
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423 | lim(ji,jj,jk)=dir*zmask(ji,jj,jk)+(1-dir)*dwst(ji,jj+1,jk) |
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424 | ! Mask at the T-points in the y-direction (mask=0 or mask=1) |
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425 | zmask(ji,jj,jk)=tmask(ji,jj-1,jk)+tmask(ji,jj,jk)+tmask(ji,jj+1,jk)-2 |
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426 | END DO |
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427 | END DO |
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428 | END DO |
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429 | !--- Lateral boundary conditions for the mask |
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430 | CALL lbc_lnk( zmask(:,:,:), 'T', 1. ) |
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431 | |
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432 | ! Horizontal advective fluxes |
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433 | ! ------------------------------- |
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434 | ! =============== |
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435 | DO jk = 1, jpkm1 ! Horizontal slab |
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436 | ! =============== |
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437 | dt = z2 * rdttra(jk) |
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438 | !--- tracer flux at u and v-points |
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439 | DO jj = 1, jpjm1 |
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440 | DO ji = 1, fs_jpim1 ! vector opt. |
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441 | #if defined key_zco |
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442 | e1 = e1v(ji,jj) |
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443 | #else |
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444 | e1 = e1v(ji,jj) * fse3v(ji,jj,jk) |
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445 | #endif |
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446 | dir = 0.5 + sign(0.5,pvn(ji,jj,jk)) ! if pvn>0 : dirv = 1 otherwise dirv = 0 |
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447 | |
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448 | dx = dir * e2t(ji,jj) + (1-dir)* e2t(ji,jj+1) |
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449 | c = ABS(pvn(ji,jj,jk))*dt/dx ! (0<cy<1 : Courant number on y-direction) |
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450 | |
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451 | fu = lim(ji,jj,jk) ! FU + sl(FC-FU) in the y-direction for T |
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452 | fc = dir*tra(ji,jj ,jk)+(1-dir)*tra(ji,jj+1,jk) ! FC in the y-direction for T |
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453 | fd = dir*tra(ji,jj+1,jk)+(1-dir)*tra(ji,jj ,jk) ! FD in the y-direction for T |
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454 | |
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455 | !--- QUICKEST scheme |
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456 | ! Temperature on the y-direction |
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457 | coef1 = 0.5*(fc+fd) |
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458 | coef2 = 0.5*c*(fd-fc) |
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459 | coef3 = ((1.-(c*c))/6.)*(dir*zlap(ji,jj,jk) + (1-dir)*zlap(ji,jj+1,jk) ) |
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460 | fho = coef1-coef2-coef3 |
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461 | fho = bound(fu,fd,fc,fho) |
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462 | !--- If the second ustream point is a land point |
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463 | !--- the flux is computed by the 1st order UPWIND scheme |
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464 | mask=dir*zmask(ji,jj,jk)+(1-dir)*zmask(ji,jj+1,jk) |
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465 | fho = mask*fho + (1-mask)*fc |
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466 | dwst(ji,jj,jk)=e1*pvn(ji,jj,jk)*fho |
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467 | END DO |
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468 | END DO |
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469 | |
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470 | !--- Tracer flux divergence at t-point added to the general trend |
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471 | DO jj = 2, jpjm1 |
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472 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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473 | !--- horizontal advective trends |
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474 | #if defined key_zco |
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475 | zbtr = zbtr2(ji,jj) |
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476 | #else |
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477 | zbtr = zbtr2(ji,jj) / fse3t(ji,jj,jk) |
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478 | #endif |
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479 | za = - zbtr * ( dwst(ji,jj,jk) - dwst(ji ,jj-1,jk) ) |
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480 | !--- add it to the general tracer trends |
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481 | traa(ji,jj,jk) = traa(ji,jj,jk) + za |
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482 | END DO |
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483 | END DO |
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484 | ! ! =============== |
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485 | END DO ! End of slab |
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486 | ! ! =============== |
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487 | |
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488 | ! "zonal" mean advective heat and salt transport |
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489 | IF( ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN |
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490 | #if defined key_zco |
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491 | DO jk = 1, jpkm1 |
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492 | DO jj = 2, jpjm1 |
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493 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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494 | dwst(ji,jj,jk) = dwst(ji,jj,jk) * fse3v(ji,jj,jk) |
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495 | END DO |
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496 | END DO |
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497 | END DO |
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498 | phtra_adv(:) = ptr_vj( dwst(:,:,:) ) |
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499 | #else |
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500 | phtra_adv(:) = ptr_vj( dwst(:,:,:) ) |
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501 | # endif |
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502 | ENDIF |
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503 | |
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504 | END SUBROUTINE tra_adv_qck_hor |
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505 | |
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506 | SUBROUTINE tra_adv_qck_ver ( pwn, tra , traa, z2 ) |
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507 | !!---------------------------------------------------------------------- |
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508 | !! |
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509 | !!---------------------------------------------------------------------- |
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510 | !! * Arguments |
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511 | |
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512 | REAL(wp), INTENT ( in ) :: z2 |
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513 | REAL(wp), INTENT ( in ), DIMENSION(jpi,jpj,jpk) :: & |
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514 | pwn |
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515 | REAL(wp), INTENT ( inout ), DIMENSION(jpi,jpj,jpk) :: & |
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516 | tra, traa |
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517 | |
---|
518 | REAL(wp) :: & |
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519 | za, ze3tr, dt, dir, fc, fd ! temporary scalars |
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520 | |
---|
521 | ! Vertical advection |
---|
522 | ! ------------------ |
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523 | |
---|
524 | ! 1. Vertical advective fluxes |
---|
525 | ! ---------------------------- |
---|
526 | |
---|
527 | !Bottom value : flux set to zero |
---|
528 | sl(:,:,jpk) = 0.e0 |
---|
529 | |
---|
530 | ! Surface value |
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531 | IF( lk_dynspg_rl .OR. lk_vvl ) THEN |
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532 | ! rigid lid : flux set to zero |
---|
533 | sl(:,:, 1 ) = 0.e0 |
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534 | ELSE |
---|
535 | ! free surface-constant volume |
---|
536 | sl(:,:, 1 ) = pwn(:,:,1) * tra(:,:,1) |
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537 | ENDIF |
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538 | |
---|
539 | ! Second order centered tracer flux at w-point |
---|
540 | |
---|
541 | DO jk = 2, jpkm1 |
---|
542 | dt = z2 * rdttra(jk) |
---|
543 | DO jj = 2, jpjm1 |
---|
544 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
545 | dir = 0.5 + sign(0.5,pwn(ji,jj,jk)) ! if pwn>0 : dirw = 1 otherwise dirw = 0 |
---|
546 | fc = dir*tra(ji,jj,jk )*fse3t(ji,jj,jk-1)+(1-dir)*tra(ji,jj,jk-1)*fse3t(ji,jj,jk ) ! FC in the z-direction for T |
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547 | fd = dir*tra(ji,jj,jk-1)*fse3t(ji,jj,jk )+(1-dir)*tra(ji,jj,jk )*fse3t(ji,jj,jk-1) ! FD in the z-direction for T |
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548 | !--- Second order centered scheme |
---|
549 | sl(ji,jj,jk)=pwn(ji,jj,jk)*(fc+fd)/(fse3t(ji,jj,jk-1)+fse3t(ji,jj,jk)) |
---|
550 | END DO |
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551 | END DO |
---|
552 | END DO |
---|
553 | |
---|
554 | ! 2. Tracer flux divergence at t-point added to the general trend |
---|
555 | ! --------------------------------------------------------------- |
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556 | |
---|
557 | DO jk = 1, jpkm1 |
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558 | DO jj = 2, jpjm1 |
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559 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
560 | ze3tr = 1. / fse3t(ji,jj,jk) |
---|
561 | ! vertical advective trends |
---|
562 | za = - ze3tr * ( sl(ji,jj,jk) - sl(ji,jj,jk+1) ) |
---|
563 | ! add it to the general tracer trends |
---|
564 | traa(ji,jj,jk) = traa(ji,jj,jk) + za |
---|
565 | END DO |
---|
566 | END DO |
---|
567 | END DO |
---|
568 | |
---|
569 | END SUBROUTINE tra_adv_qck_ver |
---|
570 | |
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571 | REAL FUNCTION bound(fu,fd,fc,fho) |
---|
572 | real :: fu,fd,fc,fho,fref1,fref2 |
---|
573 | fref1 = fu |
---|
574 | fref2 = MAX(MIN(fc,fd),MIN(MAX(fc,fd),fref1)) |
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575 | bound = MAX(MIN(fho,fc),MIN(MAX(fho,fc),fref2)) |
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576 | END FUNCTION |
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577 | |
---|
578 | !!====================================================================== |
---|
579 | END MODULE traadv_qck |
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