1 | MODULE dynvor_tam |
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2 | #if defined key_tam |
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3 | !!====================================================================== |
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4 | !! *** MODULE dynvor_tam *** |
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5 | !! Ocean dynamics: Update the momentum trend with the relative and |
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6 | !! planetary vorticity trends |
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7 | !! Tangent and Adjoint Module |
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8 | !!====================================================================== |
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9 | !! History of the drect module: |
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10 | !! History : OPA ! 1989-12 (P. Andrich) vor_ens: Original code |
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11 | !! 5.0 ! 1991-11 (G. Madec) vor_ene, vor_mix: Original code |
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12 | !! 6.0 ! 1996-01 (G. Madec) s-coord, suppress work arrays |
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13 | !! 8.5 ! 2002-08 (G. Madec) F90: Free form and module |
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14 | !! NEMO 1.0 ! 2004-02 (G. Madec) vor_een: Original code |
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15 | !! - ! 2003-08 (G. Madec) add vor_ctl |
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16 | !! - ! 2005-11 (G. Madec) add dyn_vor (new step architecture) |
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17 | !! 2.0 ! 2006-11 (G. Madec) flux form advection: add metric term |
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18 | !! 3.2 ! 2009-04 (R. Benshila) vvl: correction of een scheme |
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19 | !! History of the TAM module: |
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20 | !! 9.0 ! 2008-06 (A. Vidard) Skeleton |
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21 | !! 9.0 ! 2009-01 (A. Vidard) TAM of the 06-11 version |
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22 | !! 9.0 ! 2010-01 (F. Vigilant) Add een TAM option |
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23 | !! NEMO 3.2 ! 2010-04 (F. Vigilant) 3.2 version |
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24 | !! NEMO 3.4 ! 2012-07 (P.-A. Bouttier) 3.4 version |
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25 | !!---------------------------------------------------------------------- |
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26 | |
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27 | !!---------------------------------------------------------------------- |
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28 | !! dyn_vor : Update the momentum trend with the vorticity trend |
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29 | !! vor_ens : enstrophy conserving scheme (ln_dynvor_ens=T) |
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30 | !! vor_ene : energy conserving scheme (ln_dynvor_ene=T) |
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31 | !! vor_mix : mixed enstrophy/energy conserving (ln_dynvor_mix=T) |
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32 | !! vor_een : energy and enstrophy conserving (ln_dynvor_een=T) |
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33 | !! vor_ctl : set and control of the different vorticity option |
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34 | !!---------------------------------------------------------------------- |
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35 | USE par_oce |
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36 | USE oce |
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37 | USE oce_tam |
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38 | USE divcur |
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39 | USE divcur_tam |
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40 | USE dom_oce |
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41 | USE dynadv |
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42 | USE lbclnk |
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43 | USE lbclnk_tam |
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44 | USE in_out_manager |
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45 | USE gridrandom |
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46 | USE dotprodfld |
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47 | USE tstool_tam |
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48 | USE dommsk |
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49 | USE lib_mpp |
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50 | USE wrk_nemo |
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51 | USE timing |
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52 | |
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53 | IMPLICIT NONE |
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54 | PRIVATE |
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55 | |
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56 | PUBLIC dyn_vor_init_tam |
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57 | PUBLIC dyn_vor_tan ! routine called by step_tam.F90 |
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58 | PUBLIC dyn_vor_adj ! routine called by step_tam.F90 |
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59 | PUBLIC dyn_vor_adj_tst ! routine called by the tst.F90 |
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60 | |
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61 | |
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62 | !!* Namelist nam_dynvor: vorticity term |
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63 | LOGICAL, PUBLIC :: ln_dynvor_ene = .FALSE. !: energy conserving scheme |
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64 | LOGICAL, PUBLIC :: ln_dynvor_ens = .TRUE. !: enstrophy conserving scheme |
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65 | LOGICAL, PUBLIC :: ln_dynvor_mix = .FALSE. !: mixed scheme |
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66 | LOGICAL, PUBLIC :: ln_dynvor_een = .FALSE. !: energy and enstrophy conserving scheme |
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67 | |
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68 | INTEGER :: nvor = 0 ! type of vorticity trend used |
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69 | INTEGER :: ncor = 1 ! coriolis |
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70 | INTEGER :: nrvm = 2 ! =2 relative vorticity ; =3 metric term |
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71 | INTEGER :: ntot = 4 ! =4 total vorticity (relative + planetary) ; =5 coriolis + metric term |
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72 | |
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73 | !! * Substitutions |
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74 | # include "domzgr_substitute.h90" |
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75 | # include "vectopt_loop_substitute.h90" |
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76 | |
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77 | CONTAINS |
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78 | |
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79 | SUBROUTINE dyn_vor_tan( kt ) |
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80 | !!---------------------------------------------------------------------- |
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81 | !! |
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82 | !! ** Purpose of the direct routine: |
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83 | !! compute the lateral ocean tracer physics. |
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84 | !! |
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85 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
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86 | !! - save the trends in (ztrdu,ztrdv) in 2 parts (relative |
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87 | !! and planetary vorticity trends) ('key_trddyn') |
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88 | !!---------------------------------------------------------------------- |
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89 | !! |
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90 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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91 | !!---------------------------------------------------------------------- |
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92 | ! |
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93 | IF( nn_timing == 1 ) CALL timing_start('dyn_vor_tan') |
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94 | ! |
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95 | !! ! vorticity term |
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96 | SELECT CASE ( nvor ) ! compute the vorticity trend and add it to the general trend |
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97 | ! |
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98 | CASE ( -1 ) ! esopa: test all possibility with control print |
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99 | CALL vor_ene_tan( kt, ntot, ua_tl, va_tl ) |
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100 | CALL vor_ens_tan( kt, ntot, ua_tl, va_tl ) |
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101 | CALL vor_mix_tan( kt ) |
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102 | CALL vor_een_tan( kt, ntot, ua_tl, va_tl ) |
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103 | ! |
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104 | CASE ( 0 ) ! energy conserving scheme |
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105 | CALL vor_ene_tan( kt, ntot, ua_tl, va_tl ) ! total vorticity |
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106 | ! |
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107 | CASE ( 1 ) ! enstrophy conserving scheme |
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108 | CALL vor_ens_tan( kt, ntot, ua_tl, va_tl ) ! total vorticity |
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109 | ! |
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110 | CASE ( 2 ) ! mixed ene-ens scheme |
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111 | CALL vor_mix_tan( kt ) ! total vorticity (mix=ens-ene) |
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112 | ! |
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113 | CASE ( 3 ) ! energy and enstrophy conserving scheme |
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114 | CALL vor_een_tan( kt, ntot, ua_tl, va_tl ) ! total vorticity |
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115 | ! |
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116 | END SELECT |
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117 | ! |
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118 | IF( nn_timing == 1 ) CALL timing_stop('dyn_vor_tan') |
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119 | ! |
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120 | END SUBROUTINE dyn_vor_tan |
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121 | SUBROUTINE vor_ene_tan( kt, kvor, pua_tl, pva_tl ) |
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122 | !!---------------------------------------------------------------------- |
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123 | !! *** ROUTINE vor_ene *** |
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124 | !! |
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125 | !! ** Purpose : Compute the now total vorticity trend and add it to |
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126 | !! the general trend of the momentum equation. |
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127 | !! |
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128 | !! ** Method : Trend evaluated using now fields (centered in time) |
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129 | !! and the Sadourny (1975) flux form formulation : conserves the |
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130 | !! horizontal kinetic energy. |
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131 | !! The trend of the vorticity term is given by: |
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132 | !! * s-coordinate (ln_sco=T), the e3. are inside the derivatives: |
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133 | !! voru = 1/e1u mj-1[ (rotn+f)/e3f mi(e1v*e3v vn) ] |
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134 | !! vorv = 1/e2v mi-1[ (rotn+f)/e3f mj(e2u*e3u un) ] |
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135 | !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: |
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136 | !! voru = 1/e1u mj-1[ (rotn+f) mi(e1v vn) ] |
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137 | !! vorv = 1/e2v mi-1[ (rotn+f) mj(e2u un) ] |
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138 | !! Add this trend to the general momentum trend (ua,va): |
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139 | !! (ua,va) = (ua,va) + ( voru , vorv ) |
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140 | !! |
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141 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
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142 | !! - save the trends in (ztrdu,ztrdv) in 2 parts (relative |
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143 | !! and planetary vorticity trends) ('key_trddyn') |
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144 | !! |
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145 | !! References : Sadourny, r., 1975, j. atmos. sciences, 32, 680-689. |
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146 | !!---------------------------------------------------------------------- |
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147 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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148 | INTEGER , INTENT(in ) :: kvor ! =ncor (planetary) ; =ntot (total) ; |
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149 | ! ! =nrvm (relative vorticity or metric) |
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150 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pua_tl ! total u-trend |
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151 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pva_tl ! total v-trend |
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152 | !! |
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153 | INTEGER :: ji, jj, jk ! dummy loop indices |
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154 | REAL(wp) :: zx1, zy1, zfact2 ! temporary scalars |
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155 | REAL(wp) :: zx1tl, zy1tl ! temporary scalars |
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156 | REAL(wp) :: zx2, zy2 ! " " |
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157 | REAL(wp) :: zx2tl, zy2tl ! " " |
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158 | REAL(wp), POINTER, DIMENSION(:,:) :: zwx, zwy, zwz ! temporary 2D workspace |
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159 | REAL(wp), POINTER, DIMENSION(:,:) :: zwxtl, zwytl, zwztl ! temporary 2D workspace |
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160 | !!---------------------------------------------------------------------- |
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161 | ! |
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162 | IF( nn_timing == 1 ) CALL timing_start('vor_ene_tan') |
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163 | ! |
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164 | CALL wrk_alloc( jpi, jpj, zwx, zwy, zwz ) |
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165 | CALL wrk_alloc( jpi, jpj, zwxtl, zwytl, zwztl ) |
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166 | ! |
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167 | IF( kt == nit000 ) THEN |
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168 | IF(lwp) WRITE(numout,*) |
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169 | IF(lwp) WRITE(numout,*) 'dyn:vor_ene_tan : vorticity term: energy conserving scheme' |
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170 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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171 | ENDIF |
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172 | |
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173 | zfact2 = 0.5 * 0.5 ! Local constant initialization |
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174 | |
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175 | !CDIR PARALLEL DO PRIVATE( zwx, zwy, zwz ) |
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176 | ! ! =============== |
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177 | DO jk = 1, jpkm1 ! Horizontal slab |
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178 | ! ! =============== |
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179 | ! |
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180 | ! Potential vorticity and horizontal fluxes |
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181 | ! ----------------------------------------- |
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182 | SELECT CASE( kvor ) ! vorticity considered |
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183 | CASE ( 1 ) ; zwz(:,:) = ff(:,:) ; zwztl(:,:) = 0. |
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184 | CASE ( 2 ) ; zwz(:,:) = rotn(:,:,jk) ; zwztl(:,:) = rotn_tl(:,:,jk) ! relative vorticity |
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185 | CASE ( 3 ) ! metric term |
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186 | DO jj = 1, jpjm1 |
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187 | DO ji = 1, fs_jpim1 ! vector opt. |
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188 | zwz(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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189 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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190 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
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191 | zwztl(ji,jj) = ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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192 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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193 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
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194 | END DO |
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195 | END DO |
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196 | CASE ( 4 ) ; zwz(:,:) = ( rotn(:,:,jk) + ff(:,:) ) ; zwztl(:,:) = rotn_tl(:,:,jk) ! total (relative + planetary vorticity) |
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197 | CASE ( 5 ) ! total (coriolis + metric) |
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198 | DO jj = 1, jpjm1 |
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199 | DO ji = 1, fs_jpim1 ! vector opt. |
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200 | zwz(ji,jj) = ( ff (ji,jj) & |
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201 | & + ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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202 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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203 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) & |
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204 | & ) |
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205 | zwztl(ji,jj) = ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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206 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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207 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
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208 | END DO |
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209 | END DO |
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210 | END SELECT |
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211 | |
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212 | IF( ln_sco ) THEN |
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213 | zwz(:,:) = zwz(:,:) / fse3f(:,:,jk) |
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214 | zwx(:,:) = e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
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215 | zwy(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
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216 | zwztl(:,:) = zwztl(:,:) / fse3f(:,:,jk) |
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217 | zwxtl(:,:) = e2u(:,:) * fse3u(:,:,jk) * un_tl(:,:,jk) |
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218 | zwytl(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn_tl(:,:,jk) |
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219 | ELSE |
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220 | zwx(:,:) = e2u(:,:) * un(:,:,jk) |
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221 | zwy(:,:) = e1v(:,:) * vn(:,:,jk) |
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222 | zwxtl(:,:) = e2u(:,:) * un_tl(:,:,jk) |
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223 | zwytl(:,:) = e1v(:,:) * vn_tl(:,:,jk) |
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224 | ENDIF |
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225 | |
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226 | ! Compute and add the vorticity term trend |
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227 | ! ---------------------------------------- |
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228 | DO jj = 2, jpjm1 |
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229 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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230 | zy1 = zwy(ji,jj-1) + zwy(ji+1,jj-1) |
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231 | zy2 = zwy(ji,jj ) + zwy(ji+1,jj ) |
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232 | zx1 = zwx(ji-1,jj) + zwx(ji-1,jj+1) |
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233 | zx2 = zwx(ji ,jj) + zwx(ji ,jj+1) |
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234 | zy1tl = zwytl(ji,jj-1) + zwytl(ji+1,jj-1) |
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235 | zy2tl = zwytl(ji,jj ) + zwytl(ji+1,jj ) |
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236 | zx1tl = zwxtl(ji-1,jj) + zwxtl(ji-1,jj+1) |
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237 | zx2tl = zwxtl(ji ,jj) + zwxtl(ji ,jj+1) |
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238 | pua_tl(ji,jj,jk) = pua_tl(ji,jj,jk) + zfact2 / e1u(ji,jj) * ( zwztl(ji ,jj-1) * zy1 + zwztl(ji,jj) * zy2 ) & |
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239 | & + zfact2 / e1u(ji,jj) * ( zwz(ji ,jj-1) * zy1tl + zwz(ji,jj) * zy2tl ) |
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240 | pva_tl(ji,jj,jk) = pva_tl(ji,jj,jk) - zfact2 / e2v(ji,jj) * ( zwztl(ji-1,jj ) * zx1 + zwztl(ji,jj) * zx2 ) & |
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241 | & - zfact2 / e2v(ji,jj) * ( zwz(ji-1,jj ) * zx1tl + zwz(ji,jj) * zx2tl ) |
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242 | END DO |
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243 | END DO |
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244 | ! ! =============== |
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245 | END DO ! End of slab |
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246 | ! ! =============== |
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247 | CALL wrk_dealloc( jpi, jpj, zwx, zwy, zwz ) |
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248 | CALL wrk_dealloc( jpi, jpj, zwxtl, zwytl, zwztl ) |
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249 | ! |
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250 | IF( nn_timing == 1 ) CALL timing_stop('vor_ene_tan') |
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251 | ! |
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252 | END SUBROUTINE vor_ene_tan |
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253 | |
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254 | |
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255 | SUBROUTINE vor_mix_tan( kt ) |
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256 | !!---------------------------------------------------------------------- |
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257 | !! *** ROUTINE vor_mix *** |
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258 | !! |
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259 | !! ** Purpose : Compute the now total vorticity trend and add it to |
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260 | !! the general trend of the momentum equation. |
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261 | !! |
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262 | !! ** Method : Trend evaluated using now fields (centered in time) |
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263 | !! Mixte formulation : conserves the potential enstrophy of a hori- |
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264 | !! zontally non-divergent flow for (rotzu x uh), the relative vor- |
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265 | !! ticity term and the horizontal kinetic energy for (f x uh), the |
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266 | !! coriolis term. the now trend of the vorticity term is given by: |
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267 | !! * s-coordinate (ln_sco=T), the e3. are inside the derivatives: |
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268 | !! voru = 1/e1u mj-1(rotn/e3f) mj-1[ mi(e1v*e3v vn) ] |
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269 | !! +1/e1u mj-1[ f/e3f mi(e1v*e3v vn) ] |
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270 | !! vorv = 1/e2v mi-1(rotn/e3f) mi-1[ mj(e2u*e3u un) ] |
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271 | !! +1/e2v mi-1[ f/e3f mj(e2u*e3u un) ] |
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272 | !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: |
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273 | !! voru = 1/e1u mj-1(rotn) mj-1[ mi(e1v vn) ] |
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274 | !! +1/e1u mj-1[ f mi(e1v vn) ] |
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275 | !! vorv = 1/e2v mi-1(rotn) mi-1[ mj(e2u un) ] |
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276 | !! +1/e2v mi-1[ f mj(e2u un) ] |
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277 | !! Add this now trend to the general momentum trend (ua,va): |
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278 | !! (ua,va) = (ua,va) + ( voru , vorv ) |
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279 | !! |
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280 | !! ** Action : - Update (ua,va) arrays with the now vorticity term trend |
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281 | !! - Save the trends in (ztrdu,ztrdv) in 2 parts (relative |
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282 | !! and planetary vorticity trends) ('key_trddyn') |
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283 | !! |
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284 | !! References : Sadourny, r., 1975, j. atmos. sciences, 32, 680-689. |
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285 | !!---------------------------------------------------------------------- |
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286 | INTEGER, INTENT(in) :: kt ! ocean timestep index |
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287 | !! |
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288 | INTEGER :: ji, jj, jk ! dummy loop indices |
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289 | REAL(wp) :: zfact1, zua, zcua, zx1, zy1 ! temporary scalars |
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290 | REAL(wp) :: zfact2, zva, zcva, zx2, zy2 ! " " |
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291 | REAL(wp) :: zuatl, zcuatl, zx1tl, zy1tl ! temporary scalars |
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292 | REAL(wp) :: zvatl, zcvatl, zx2tl, zy2tl ! " " |
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293 | REAL(wp), POINTER, DIMENSION(:,:) :: zwxtl, zwytl, zwztl, zwwtl ! temporary 3D workspace |
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294 | REAL(wp), POINTER, DIMENSION(:,:) :: zwx, zwy, zwz, zww ! temporary 3D workspace |
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295 | !!---------------------------------------------------------------------- |
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296 | ! |
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297 | IF( nn_timing == 1 ) CALL timing_start('vor_mix_tan') |
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298 | ! |
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299 | CALL wrk_alloc( jpi, jpj, zwx, zwy, zwz, zww ) |
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300 | CALL wrk_alloc( jpi, jpj, zwxtl, zwytl, zwztl, zwwtl ) |
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301 | ! |
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302 | IF( kt == nit000 ) THEN |
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303 | IF(lwp) WRITE(numout,*) |
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304 | IF(lwp) WRITE(numout,*) 'dyn:vor_mix : vorticity term: mixed energy/enstrophy conserving scheme' |
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305 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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306 | ENDIF |
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307 | |
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308 | zfact1 = 0.5 * 0.25 ! Local constant initialization |
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309 | zfact2 = 0.5 * 0.5 |
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310 | |
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311 | !CDIR PARALLEL DO PRIVATE( zwx, zwy, zwz, zww ) |
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312 | ! ! =============== |
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313 | DO jk = 1, jpkm1 ! Horizontal slab |
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314 | ! ! =============== |
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315 | ! |
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316 | ! Relative and planetary potential vorticity and horizontal fluxes |
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317 | ! ---------------------------------------------------------------- |
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318 | IF( ln_sco ) THEN |
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319 | IF( ln_dynadv_vec ) THEN |
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320 | zww(:,:) = rotn(:,:,jk) / fse3f(:,:,jk) |
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321 | zwwtl(:,:) = rotn_tl(:,:,jk) / fse3f(:,:,jk) |
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322 | ELSE |
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323 | DO jj = 1, jpjm1 |
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324 | DO ji = 1, fs_jpim1 ! vector opt. |
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325 | zww(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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326 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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327 | & * 0.5 / ( e1f(ji,jj) * e2f (ji,jj) * fse3f(ji,jj,jk) ) |
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328 | zwwtl(ji,jj) = ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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329 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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330 | & * 0.5 / ( e1f(ji,jj) * e2f (ji,jj) * fse3f(ji,jj,jk) ) |
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331 | END DO |
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332 | END DO |
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333 | ENDIF |
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334 | zwz(:,:) = ff (:,:) / fse3f(:,:,jk) |
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335 | zwx(:,:) = e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
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336 | zwy(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
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337 | zwztl(:,:) = 0._wp |
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338 | zwxtl(:,:) = e2u(:,:) * fse3u(:,:,jk) * un_tl(:,:,jk) |
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339 | zwytl(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn_tl(:,:,jk) |
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340 | ELSE |
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341 | IF( ln_dynadv_vec ) THEN |
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342 | zww(:,:) = rotn(:,:,jk) |
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343 | zwwtl(:,:) = rotn_tl(:,:,jk) |
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344 | ELSE |
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345 | DO jj = 1, jpjm1 |
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346 | DO ji = 1, fs_jpim1 ! vector opt. |
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347 | zww(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
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348 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
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349 | & * 0.5 / ( e1f(ji,jj) * e2f (ji,jj) ) |
---|
350 | zwwtl(ji,jj) = ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
351 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
352 | & * 0.5 / ( e1f(ji,jj) * e2f (ji,jj) ) |
---|
353 | END DO |
---|
354 | END DO |
---|
355 | ENDIF |
---|
356 | zwz(:,:) = ff (:,:) |
---|
357 | zwx(:,:) = e2u(:,:) * un(:,:,jk) |
---|
358 | zwy(:,:) = e1v(:,:) * vn(:,:,jk) |
---|
359 | zwztl(:,:) = 0.0_wp |
---|
360 | zwxtl(:,:) = e2u(:,:) * un_tl(:,:,jk) |
---|
361 | zwytl(:,:) = e1v(:,:) * vn_tl(:,:,jk) |
---|
362 | ENDIF |
---|
363 | |
---|
364 | ! Compute and add the vorticity term trend |
---|
365 | ! ---------------------------------------- |
---|
366 | DO jj = 2, jpjm1 |
---|
367 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
368 | zy1 = ( zwy(ji,jj-1) + zwy(ji+1,jj-1) ) / e1u(ji,jj) |
---|
369 | zy2 = ( zwy(ji,jj ) + zwy(ji+1,jj ) ) / e1u(ji,jj) |
---|
370 | zx1 = ( zwx(ji-1,jj) + zwx(ji-1,jj+1) ) / e2v(ji,jj) |
---|
371 | zx2 = ( zwx(ji ,jj) + zwx(ji ,jj+1) ) / e2v(ji,jj) |
---|
372 | zy1tl = ( zwytl(ji,jj-1) + zwytl(ji+1,jj-1) ) / e1u(ji,jj) |
---|
373 | zy2tl = ( zwytl(ji,jj ) + zwytl(ji+1,jj ) ) / e1u(ji,jj) |
---|
374 | zx1tl = ( zwxtl(ji-1,jj) + zwxtl(ji-1,jj+1) ) / e2v(ji,jj) |
---|
375 | zx2tl = ( zwxtl(ji ,jj) + zwxtl(ji ,jj+1) ) / e2v(ji,jj) |
---|
376 | ! enstrophy conserving formulation for relative vorticity term |
---|
377 | zua = zfact1 * ( zww(ji ,jj-1) + zww(ji,jj) ) * ( zy1 + zy2 ) |
---|
378 | zva =-zfact1 * ( zww(ji-1,jj ) + zww(ji,jj) ) * ( zx1 + zx2 ) |
---|
379 | zuatl = zfact1 * ( zwwtl(ji ,jj-1) + zwwtl(ji,jj) ) * ( zy1 + zy2 ) & |
---|
380 | & + zfact1 * ( zww(ji ,jj-1) + zww(ji,jj) ) * ( zy1tl + zy2tl ) |
---|
381 | zvatl =-zfact1 * ( zwwtl(ji-1,jj ) + zwwtl(ji,jj) ) * ( zx1 + zx2 ) & |
---|
382 | & - zfact1 * ( zww(ji-1,jj ) + zww(ji,jj) ) * ( zx1tl + zx2tl ) |
---|
383 | ! energy conserving formulation for planetary vorticity term |
---|
384 | zcua = zfact2 * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 ) |
---|
385 | zcva =-zfact2 * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 ) |
---|
386 | zcuatl = zfact2 * ( zwztl(ji ,jj-1) * zy1 + zwztl(ji,jj) * zy2 ) & |
---|
387 | & + zfact2 * ( zwz(ji ,jj-1) * zy1tl + zwz(ji,jj) * zy2tl ) |
---|
388 | zcvatl =-zfact2 * ( zwztl(ji-1,jj ) * zx1 + zwztl(ji,jj) * zx2 ) & |
---|
389 | & -zfact2 * ( zwz(ji-1,jj ) * zx1tl + zwz(ji,jj) * zx2tl ) |
---|
390 | ! mixed vorticity trend added to the momentum trends |
---|
391 | ua_tl(ji,jj,jk) = ua_tl(ji,jj,jk) + zcuatl + zuatl |
---|
392 | va_tl(ji,jj,jk) = va_tl(ji,jj,jk) + zcvatl + zvatl |
---|
393 | END DO |
---|
394 | END DO |
---|
395 | ! ! =============== |
---|
396 | END DO ! End of slab |
---|
397 | ! ! =============== |
---|
398 | CALL wrk_dealloc( jpi, jpj, zwx, zwy, zwz, zww ) |
---|
399 | CALL wrk_dealloc( jpi, jpj, zwxtl, zwytl, zwztl, zwwtl ) |
---|
400 | ! |
---|
401 | IF( nn_timing == 1 ) CALL timing_stop('vor_mix_tan') |
---|
402 | ! |
---|
403 | END SUBROUTINE vor_mix_tan |
---|
404 | SUBROUTINE vor_ens_tan( kt, kvor, pua_tl, pva_tl ) |
---|
405 | !!---------------------------------------------------------------------- |
---|
406 | !! *** ROUTINE vor_ens_tan *** |
---|
407 | !! |
---|
408 | !! ** Purpose of the direct routine: |
---|
409 | !! Compute the now total vorticity trend and add it to |
---|
410 | !! the general trend of the momentum equation. |
---|
411 | !! |
---|
412 | !! ** Method of the direct routine: |
---|
413 | !! Trend evaluated using now fields (centered in time) |
---|
414 | !! and the Sadourny (1975) flux FORM formulation : conserves the |
---|
415 | !! potential enstrophy of a horizontally non-divergent flow. the |
---|
416 | !! trend of the vorticity term is given by: |
---|
417 | !! * s-coordinate (ln_sco=T), the e3. are inside the derivative: |
---|
418 | !! voru = 1/e1u mj-1[ (rotn+f)/e3f ] mj-1[ mi(e1v*e3v vn) ] |
---|
419 | !! vorv = 1/e2v mi-1[ (rotn+f)/e3f ] mi-1[ mj(e2u*e3u un) ] |
---|
420 | !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: |
---|
421 | !! voru = 1/e1u mj-1[ rotn+f ] mj-1[ mi(e1v vn) ] |
---|
422 | !! vorv = 1/e2v mi-1[ rotn+f ] mi-1[ mj(e2u un) ] |
---|
423 | !! Add this trend to the general momentum trend (ua,va): |
---|
424 | !! (ua,va) = (ua,va) + ( voru , vorv ) |
---|
425 | !! |
---|
426 | !! ** Action : - Update (ua,va) arrays with the now vorticity term trend |
---|
427 | !! - Save the trends in (ztrdu,ztrdv) in 2 parts (relative |
---|
428 | !! and planetary vorticity trends) ('key_trddyn') |
---|
429 | !! |
---|
430 | !! References : Sadourny, r., 1975, j. atmos. sciences, 32, 680-689. |
---|
431 | !!---------------------------------------------------------------------- |
---|
432 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
433 | INTEGER , INTENT(in ) :: kvor ! =ncor (planetary) ; =ntot (total) ; |
---|
434 | ! ! =nrvm (relative vorticity or metric) |
---|
435 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pua_tl ! total u-trend |
---|
436 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pva_tl ! total v-trend |
---|
437 | !! |
---|
438 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
439 | REAL(wp) :: zfact1, zuav, zvau ! temporary scalars |
---|
440 | REAL(wp), POINTER, DIMENSION(:,:) :: zwx, zwy, zwz ! temporary 3D workspace |
---|
441 | REAL(wp) :: zuavtl, zvautl ! temporary scalars |
---|
442 | REAL(wp), POINTER, DIMENSION(:,:) :: zwxtl, zwytl, zwztl ! temporary 3D workspace |
---|
443 | !!---------------------------------------------------------------------- |
---|
444 | ! |
---|
445 | IF( nn_timing == 1 ) CALL timing_start('vor_ens_tan') |
---|
446 | ! |
---|
447 | CALL wrk_alloc( jpi, jpj, zwx, zwy, zwz ) |
---|
448 | CALL wrk_alloc( jpi, jpj, zwxtl, zwytl, zwztl ) |
---|
449 | ! |
---|
450 | IF( kt == nit000 ) THEN |
---|
451 | IF(lwp) WRITE(numout,*) |
---|
452 | IF(lwp) WRITE(numout,*) 'dyn_vor_ens_tan : vorticity term: enstrophy conserving scheme' |
---|
453 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~' |
---|
454 | ENDIF |
---|
455 | ! Local constant initialization |
---|
456 | zfact1 = 0.5 * 0.25 |
---|
457 | |
---|
458 | !CDIR PARALLEL DO PRIVATE( zwx, zwy, zwz zwxtl, zwytl, zwztl) |
---|
459 | ! ! =============== |
---|
460 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
461 | ! ! =============== |
---|
462 | ! Potential vorticity and horizontal fluxes |
---|
463 | ! ----------------------------------------- |
---|
464 | SELECT CASE( kvor ) ! vorticity considered |
---|
465 | CASE ( 1 ) ; zwz(:,:) = ff(:,:) ! planetary vorticity (Coriolis) |
---|
466 | CASE ( 2 ) ; zwz(:,:) = rotn(:,:,jk) ! relative vorticity |
---|
467 | CASE ( 3 ) ! metric term |
---|
468 | DO jj = 1, jpjm1 |
---|
469 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
470 | zwz(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
471 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
472 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
473 | END DO |
---|
474 | END DO |
---|
475 | CASE ( 4 ) ; zwz(:,:) = ( rotn(:,:,jk) + ff(:,:) ) ! total (relative + planetary vorticity) |
---|
476 | CASE ( 5 ) ! total (coriolis + metric) |
---|
477 | DO jj = 1, jpjm1 |
---|
478 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
479 | zwz(ji,jj) = ( ff (ji,jj) & |
---|
480 | & + ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
481 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
482 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) & |
---|
483 | & ) |
---|
484 | END DO |
---|
485 | END DO |
---|
486 | END SELECT |
---|
487 | |
---|
488 | IF( ln_sco ) THEN |
---|
489 | DO jj = 1, jpj ! caution: don't use (:,:) for this loop |
---|
490 | DO ji = 1, jpi ! it causes optimization problems on NEC in auto-tasking |
---|
491 | zwz(ji,jj) = zwz(ji,jj) / fse3f(ji,jj,jk) |
---|
492 | zwx(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) * un(ji,jj,jk) |
---|
493 | zwy(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) * vn(ji,jj,jk) |
---|
494 | END DO |
---|
495 | END DO |
---|
496 | ELSE |
---|
497 | DO jj = 1, jpj ! caution: don't use (:,:) for this loop |
---|
498 | DO ji = 1, jpi ! it causes optimization problems on NEC in auto-tasking |
---|
499 | zwx(ji,jj) = e2u(ji,jj) * un(ji,jj,jk) |
---|
500 | zwy(ji,jj) = e1v(ji,jj) * vn(ji,jj,jk) |
---|
501 | END DO |
---|
502 | END DO |
---|
503 | ENDIF |
---|
504 | |
---|
505 | ! =================== |
---|
506 | ! Tangent counterpart |
---|
507 | ! =================== |
---|
508 | ! Potential vorticity and horizontal fluxes |
---|
509 | ! ----------------------------------------- |
---|
510 | SELECT CASE( kvor ) ! vorticity considered |
---|
511 | CASE ( 1 ) ; zwztl(:,:) = 0.0_wp ! planetary vorticity (Coriolis) |
---|
512 | CASE ( 2 ,4) ; zwztl(:,:) = rotn_tl(:,:,jk) ! relative vorticity |
---|
513 | CASE ( 3 ,5 ) ! metric term |
---|
514 | DO jj = 1, jpjm1 |
---|
515 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
516 | zwztl(ji,jj) = ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) & |
---|
517 | & * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
518 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) & |
---|
519 | & * ( e1u(ji ,jj+1) - e1u(ji,jj) ) & |
---|
520 | & ) * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
521 | END DO |
---|
522 | END DO |
---|
523 | END SELECT |
---|
524 | |
---|
525 | IF( ln_sco ) THEN |
---|
526 | DO jj = 1, jpj ! caution: don't use (:,:) for this loop |
---|
527 | DO ji = 1, jpi ! it causes optimization problems on NEC in auto-tasking |
---|
528 | zwztl(ji,jj) = zwztl(ji,jj) / fse3f(ji,jj,jk) |
---|
529 | zwxtl(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) * un_tl(ji,jj,jk) |
---|
530 | zwytl(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) * vn_tl(ji,jj,jk) |
---|
531 | END DO |
---|
532 | END DO |
---|
533 | ELSE |
---|
534 | DO jj = 1, jpj ! caution: don't use (:,:) for this loop |
---|
535 | DO ji = 1, jpi ! it causes optimization problems on NEC in auto-tasking |
---|
536 | zwxtl(ji,jj) = e2u(ji,jj) * un_tl(ji,jj,jk) |
---|
537 | zwytl(ji,jj) = e1v(ji,jj) * vn_tl(ji,jj,jk) |
---|
538 | END DO |
---|
539 | END DO |
---|
540 | ENDIF |
---|
541 | |
---|
542 | ! Compute and add the vorticity term trend |
---|
543 | ! ---------------------------------------- |
---|
544 | DO jj = 2, jpjm1 |
---|
545 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
546 | zuav = zfact1 / e1u(ji,jj) * ( zwy( ji ,jj-1) + zwy( ji+1,jj-1) & |
---|
547 | & + zwy( ji ,jj ) + zwy( ji+1,jj ) ) |
---|
548 | zvau =-zfact1 / e2v(ji,jj) * ( zwx( ji-1,jj ) + zwx( ji-1,jj+1) & |
---|
549 | & + zwx( ji ,jj ) + zwx( ji ,jj+1) ) |
---|
550 | zuavtl = zfact1 / e1u(ji,jj) * ( zwytl(ji ,jj-1) + zwytl(ji+1,jj-1) & |
---|
551 | & + zwytl(ji ,jj ) + zwytl(ji+1,jj ) ) |
---|
552 | zvautl =-zfact1 / e2v(ji,jj) * ( zwxtl(ji-1,jj ) + zwxtl(ji-1,jj+1) & |
---|
553 | & + zwxtl(ji ,jj ) + zwxtl(ji ,jj+1) ) |
---|
554 | pua_tl(ji,jj,jk) = pua_tl(ji,jj,jk) & |
---|
555 | & + zuavtl * ( zwz( ji,jj-1) + zwz( ji,jj) ) & |
---|
556 | & + zuav * ( zwztl(ji,jj-1) + zwztl(ji,jj) ) |
---|
557 | pva_tl(ji,jj,jk) = pva_tl(ji,jj,jk) & |
---|
558 | & + zvautl * ( zwz( ji-1,jj) + zwz( ji,jj) ) & |
---|
559 | & + zvau * ( zwztl(ji-1,jj) + zwztl(ji,jj) ) |
---|
560 | END DO |
---|
561 | END DO |
---|
562 | ! ! =============== |
---|
563 | END DO ! End of slab |
---|
564 | ! ! =============== |
---|
565 | CALL wrk_dealloc( jpi, jpj, zwx, zwy, zwz ) |
---|
566 | CALL wrk_dealloc( jpi, jpj, zwxtl, zwytl, zwztl ) |
---|
567 | ! |
---|
568 | IF( nn_timing == 1 ) CALL timing_stop('vor_ens_tan') |
---|
569 | ! |
---|
570 | END SUBROUTINE vor_ens_tan |
---|
571 | |
---|
572 | SUBROUTINE vor_een_tan( kt, kvor, pua_tl, pva_tl ) |
---|
573 | !!---------------------------------------------------------------------- |
---|
574 | !! *** ROUTINE vor_een_tan *** |
---|
575 | !! |
---|
576 | !! ** Purpose : Compute the now total vorticity trend and add it to |
---|
577 | !! the general trend of the momentum equation. |
---|
578 | !! |
---|
579 | !! ** Method : Trend evaluated using now fields (centered in time) |
---|
580 | !! and the Arakawa and Lamb (1980) flux form formulation : conserves |
---|
581 | !! both the horizontal kinetic energy and the potential enstrophy |
---|
582 | !! when horizontal divergence is zero (see the NEMO documentation) |
---|
583 | !! Add this trend to the general momentum trend (ua,va). |
---|
584 | !! |
---|
585 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
---|
586 | !! - save the trends in (ztrdu,ztrdv) in 2 parts (relative |
---|
587 | !! and planetary vorticity trends) ('key_trddyn') |
---|
588 | !! |
---|
589 | !! References : Arakawa and Lamb 1980, Mon. Wea. Rev., 109, 18-36 |
---|
590 | !!---------------------------------------------------------------------- |
---|
591 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
592 | INTEGER , INTENT(in ) :: kvor ! =ncor (planetary) ; =ntot (total) ; |
---|
593 | ! ! =nrvm (relative vorticity or metric) |
---|
594 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pua_tl ! total u-trend |
---|
595 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pva_tl ! total v-trend |
---|
596 | !! |
---|
597 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
598 | INTEGER :: ierr |
---|
599 | REAL(wp) :: zfac12, zua, zva ! temporary scalars |
---|
600 | REAL(wp) :: zuatl, zvatl ! temporary scalars |
---|
601 | REAL(wp), POINTER, DIMENSION(:,:) :: zwx, zwy, zwz ! temporary 2D workspace |
---|
602 | REAL(wp), POINTER, DIMENSION(:,:) :: ztnw, ztne, ztsw, ztse ! temporary 3D workspace |
---|
603 | REAL(wp), POINTER, DIMENSION(:,:) :: zwxtl, zwytl, zwztl ! temporary 2D workspace |
---|
604 | REAL(wp), POINTER, DIMENSION(:,:) :: ztnwtl, ztnetl, ztswtl, ztsetl ! temporary 3D workspace |
---|
605 | #if defined key_vvl |
---|
606 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ze3f_tl |
---|
607 | #else |
---|
608 | REAL(wp), POINTER, DIMENSION(:,:,:), SAVE :: ze3f_tl |
---|
609 | #endif |
---|
610 | !!---------------------------------------------------------------------- |
---|
611 | IF( nn_timing == 1 ) CALL timing_start('vor_een_tan') |
---|
612 | ! |
---|
613 | CALL wrk_alloc( jpi, jpj, zwx , zwy , zwz ) |
---|
614 | CALL wrk_alloc( jpi, jpj, ztnw, ztne, ztsw, ztse ) |
---|
615 | CALL wrk_alloc( jpi, jpj, zwxtl , zwytl , zwztl ) |
---|
616 | CALL wrk_alloc( jpi, jpj, ztnwtl, ztnetl, ztswtl, ztsetl ) |
---|
617 | zuatl = 0.0_wp ; zvatl = 0.0_wp |
---|
618 | zwx (:,:) = 0.0_wp ; zwy (:,:) = 0.0_wp ; zwz (:,:) = 0.0_wp |
---|
619 | ztnw(:,:) = 0.0_wp ; ztne(:,:) = 0.0_wp ; ztsw(:,:) = 0.0_wp ; ztse(:,:) = 0.0_wp |
---|
620 | zwxtl (:,:) = 0.0_wp ; zwytl (:,:) = 0.0_wp ; zwztl (:,:) = 0.0_wp |
---|
621 | ztnwtl(:,:) = 0.0_wp ; ztnetl(:,:) = 0.0_wp ; ztswtl(:,:) = 0.0_wp ; ztsetl(:,:) = 0.0_wp |
---|
622 | #if defined key_vvl |
---|
623 | CALL wrk_alloc( jpi, jpj, jpk, ze3f_tl ) |
---|
624 | #endif |
---|
625 | IF( kt == nit000 ) THEN |
---|
626 | IF(lwp) WRITE(numout,*) |
---|
627 | IF(lwp) WRITE(numout,*) 'dyn:vor_een_tam : vorticity term: energy and enstrophy conserving scheme' |
---|
628 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
629 | IF( .NOT.lk_vvl ) THEN |
---|
630 | ALLOCATE( ze3f_tl(jpi,jpj,jpk) , STAT=ierr ) |
---|
631 | IF( lk_mpp ) CALL mpp_sum ( ierr ) |
---|
632 | IF( ierr /= 0 ) CALL ctl_stop( 'STOP', 'dyn:vor_een : unable to allocate arrays' ) |
---|
633 | ze3f_tl = 0._wp |
---|
634 | ENDIF |
---|
635 | ENDIF |
---|
636 | |
---|
637 | IF( kt == nit000 .OR. lk_vvl ) THEN ! reciprocal of e3 at F-point (masked averaging of e3t) |
---|
638 | DO jk = 1, jpk |
---|
639 | DO jj = 1, jpjm1 |
---|
640 | DO ji = 1, jpim1 |
---|
641 | ze3f_tl(ji,jj,jk) = ( fse3t(ji,jj+1,jk)*tmask(ji,jj+1,jk) + fse3t(ji+1,jj+1,jk)*tmask(ji+1,jj+1,jk) & |
---|
642 | & + fse3t(ji,jj ,jk)*tmask(ji,jj ,jk) + fse3t(ji+1,jj ,jk)*tmask(ji+1,jj ,jk) ) * 0.25_wp |
---|
643 | IF( ze3f_tl(ji,jj,jk) /= 0.0_wp ) ze3f_tl(ji,jj,jk) = 1.0_wp / ze3f_tl(ji,jj,jk) |
---|
644 | END DO |
---|
645 | END DO |
---|
646 | END DO |
---|
647 | CALL lbc_lnk( ze3f_tl, 'F', 1._wp ) |
---|
648 | ENDIF |
---|
649 | |
---|
650 | zfac12 = 1.0_wp / 12.0_wp ! Local constant initialization |
---|
651 | |
---|
652 | |
---|
653 | !CDIR PARALLEL DO PRIVATE( zwx, zwy, zwz, ztnw, ztne, ztsw, ztse ) |
---|
654 | ! ! =============== |
---|
655 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
656 | ! ! =============== |
---|
657 | |
---|
658 | ! Potential vorticity and horizontal fluxes |
---|
659 | ! ----------------------------------------- |
---|
660 | SELECT CASE( kvor ) ! vorticity considered |
---|
661 | CASE ( 1 ) |
---|
662 | zwz(:,:) = ff(:,:) * ze3f_tl(:,:,jk) ! planetary vorticity (Coriolis) |
---|
663 | zwztl(:,:) = 0.0_wp |
---|
664 | CASE ( 2 ) |
---|
665 | zwz(:,:) = rotn(:,:,jk) * ze3f_tl(:,:,jk) ! relative vorticity |
---|
666 | zwztl(:,:) = rotn_tl(:,:,jk) * ze3f_tl(:,:,jk) |
---|
667 | CASE ( 3 ) ! metric term |
---|
668 | DO jj = 1, jpjm1 |
---|
669 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
670 | zwz(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
671 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
672 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) * ze3f_tl(ji,jj,jk) |
---|
673 | END DO |
---|
674 | END DO |
---|
675 | CALL lbc_lnk( zwz, 'F', 1._wp ) |
---|
676 | DO jj = 1, jpjm1 |
---|
677 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
678 | zwztl(ji,jj) = ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
679 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
680 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) * ze3f_tl(ji,jj,jk) |
---|
681 | END DO |
---|
682 | END DO |
---|
683 | CALL lbc_lnk( zwztl, 'F', 1._wp ) |
---|
684 | CASE ( 4 ) |
---|
685 | zwz(:,:) = ( rotn(:,:,jk) + ff(:,:) ) * ze3f_tl(:,:,jk) ! total (relative + planetary vorticity) |
---|
686 | zwztl(:,:) = ( rotn_tl(:,:,jk) ) * ze3f_tl(:,:,jk) |
---|
687 | CASE ( 5 ) ! total (coriolis + metric) |
---|
688 | DO jj = 1, jpjm1 |
---|
689 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
690 | zwz(ji,jj) = ( ff (ji,jj) & |
---|
691 | & + ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
692 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
693 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) & |
---|
694 | & ) * ze3f_tl(ji,jj,jk) |
---|
695 | END DO |
---|
696 | END DO |
---|
697 | CALL lbc_lnk( zwz, 'F', 1._wp ) |
---|
698 | DO jj = 1, jpjm1 |
---|
699 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
700 | zwztl(ji,jj) = ( ( ( vn_tl(ji+1,jj ,jk) + vn_tl (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
701 | & - ( un_tl(ji ,jj+1,jk) + un_tl (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
702 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) & |
---|
703 | & ) * ze3f_tl(ji,jj,jk) |
---|
704 | END DO |
---|
705 | END DO |
---|
706 | CALL lbc_lnk( zwztl, 'F', 1._wp ) |
---|
707 | END SELECT |
---|
708 | |
---|
709 | zwx(:,:) = e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
---|
710 | zwy(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
---|
711 | |
---|
712 | zwxtl(:,:) = e2u(:,:) * fse3u(:,:,jk) * un_tl(:,:,jk) |
---|
713 | zwytl(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn_tl(:,:,jk) |
---|
714 | |
---|
715 | ! Compute and add the vorticity term trend |
---|
716 | ! ---------------------------------------- |
---|
717 | jj=2 |
---|
718 | ztne(1,:) = 0.0_wp ; ztnw(1,:) = 0.0_wp ; ztse(1,:) = 0.0_wp ; ztsw(1,:) = 0.0_wp |
---|
719 | ztnetl(1,:) = 0.0_wp ; ztnwtl(1,:) = 0.0_wp ; ztsetl(1,:) = 0.0_wp ; ztswtl(1,:) = 0.0_wp |
---|
720 | DO ji = 2, jpi |
---|
721 | ztne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1) |
---|
722 | ztnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj ) |
---|
723 | ztse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1) |
---|
724 | ztsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj ) |
---|
725 | |
---|
726 | ztnetl(ji,jj) = zwztl(ji-1,jj ) + zwztl(ji ,jj ) + zwztl(ji ,jj-1) |
---|
727 | ztnwtl(ji,jj) = zwztl(ji-1,jj-1) + zwztl(ji-1,jj ) + zwztl(ji ,jj ) |
---|
728 | ztsetl(ji,jj) = zwztl(ji ,jj ) + zwztl(ji ,jj-1) + zwztl(ji-1,jj-1) |
---|
729 | ztswtl(ji,jj) = zwztl(ji ,jj-1) + zwztl(ji-1,jj-1) + zwztl(ji-1,jj ) |
---|
730 | END DO |
---|
731 | DO jj = 3, jpj |
---|
732 | DO ji = fs_2, jpi ! vector opt. |
---|
733 | ztne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1) |
---|
734 | ztnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj ) |
---|
735 | ztse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1) |
---|
736 | ztsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj ) |
---|
737 | |
---|
738 | ztnetl(ji,jj) = zwztl(ji-1,jj ) + zwztl(ji ,jj ) + zwztl(ji ,jj-1) |
---|
739 | ztnwtl(ji,jj) = zwztl(ji-1,jj-1) + zwztl(ji-1,jj ) + zwztl(ji ,jj ) |
---|
740 | ztsetl(ji,jj) = zwztl(ji ,jj ) + zwztl(ji ,jj-1) + zwztl(ji-1,jj-1) |
---|
741 | ztswtl(ji,jj) = zwztl(ji ,jj-1) + zwztl(ji-1,jj-1) + zwztl(ji-1,jj ) |
---|
742 | END DO |
---|
743 | END DO |
---|
744 | DO jj = 2, jpjm1 |
---|
745 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
746 | zuatl = + zfac12 / e1u(ji,jj) * ( ztnetl(ji,jj ) * zwy(ji ,jj ) + ztne(ji,jj ) * zwytl(ji ,jj ) & |
---|
747 | & + ztnwtl(ji+1,jj) * zwy(ji+1,jj ) + ztnw(ji+1,jj) * zwytl(ji+1,jj ) & |
---|
748 | & + ztsetl(ji,jj ) * zwy(ji ,jj-1) + ztse(ji,jj ) * zwytl(ji ,jj-1) & |
---|
749 | & + ztswtl(ji+1,jj) * zwy(ji+1,jj-1) + ztsw(ji+1,jj) * zwytl(ji+1,jj-1)) |
---|
750 | |
---|
751 | zvatl = - zfac12 / e2v(ji,jj) * ( ztswtl(ji,jj+1) * zwx(ji-1,jj+1) + ztsw(ji,jj+1) * zwxtl(ji-1,jj+1) & |
---|
752 | & + ztsetl(ji,jj+1) * zwx(ji ,jj+1) + ztse(ji,jj+1) * zwxtl(ji ,jj+1) & |
---|
753 | & + ztnwtl(ji,jj ) * zwx(ji-1,jj ) + ztnw(ji,jj ) * zwxtl(ji-1,jj ) & |
---|
754 | & + ztnetl(ji,jj ) * zwx(ji ,jj ) + ztne(ji,jj ) * zwxtl(ji ,jj ) ) |
---|
755 | pua_tl(ji,jj,jk) = pua_tl(ji,jj,jk) + zuatl |
---|
756 | pva_tl(ji,jj,jk) = pva_tl(ji,jj,jk) + zvatl |
---|
757 | END DO |
---|
758 | END DO |
---|
759 | ! ! =============== |
---|
760 | END DO ! End of slab |
---|
761 | ! ! =============== |
---|
762 | CALL wrk_dealloc( jpi, jpj, zwx , zwy , zwz ) |
---|
763 | CALL wrk_dealloc( jpi, jpj, ztnw, ztne, ztsw, ztse ) |
---|
764 | CALL wrk_dealloc( jpi, jpj, zwxtl , zwytl , zwztl ) |
---|
765 | CALL wrk_dealloc( jpi, jpj, ztnwtl, ztnetl, ztswtl, ztsetl ) |
---|
766 | #if defined key_vvl |
---|
767 | CALL wrk_dealloc( jpi, jpj, jpk, ze3f_tl ) |
---|
768 | #endif |
---|
769 | ! |
---|
770 | IF( nn_timing == 1 ) CALL timing_stop('vor_een_tan') |
---|
771 | ! |
---|
772 | END SUBROUTINE vor_een_tan |
---|
773 | |
---|
774 | |
---|
775 | SUBROUTINE dyn_vor_adj( kt ) |
---|
776 | !!---------------------------------------------------------------------- |
---|
777 | !! |
---|
778 | !! ** Purpose of the direct routine: |
---|
779 | !! compute the lateral ocean tracer physics. |
---|
780 | !! |
---|
781 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
---|
782 | !! - save the trends in (ztrdu,ztrdv) in 2 parts (relative |
---|
783 | !! and planetary vorticity trends) ('key_trddyn') |
---|
784 | !!---------------------------------------------------------------------- |
---|
785 | !! |
---|
786 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
---|
787 | !!---------------------------------------------------------------------- |
---|
788 | ! |
---|
789 | IF( nn_timing == 1 ) CALL timing_start('dyn_vor_adj') |
---|
790 | ! |
---|
791 | ! ! vorticity term |
---|
792 | SELECT CASE ( nvor ) ! compute the vorticity trend and add it to the general trend |
---|
793 | ! |
---|
794 | CASE ( -1 ) ! esopa: test all possibility with control print |
---|
795 | CALL vor_een_adj( kt, ntot, ua_ad, va_ad ) |
---|
796 | ! CALL vor_mix_adj( kt ) |
---|
797 | CALL vor_ens_adj( kt, ntot, ua_ad, va_ad ) |
---|
798 | ! CALL vor_ene_adj( kt, ntot, ua_ad, va_ad ) |
---|
799 | ! |
---|
800 | CASE ( 0 ) ! energy conserving scheme |
---|
801 | CALL ctl_stop ('vor_ene_adj not available yet') |
---|
802 | ! CALL vor_ene_adj( kt, ntot, ua_ad, va_ad ) ! total vorticity |
---|
803 | ! |
---|
804 | CASE ( 1 ) ! enstrophy conserving scheme |
---|
805 | CALL vor_ens_adj( kt, ntot, ua_ad, va_ad ) ! total vorticity |
---|
806 | ! |
---|
807 | CASE ( 2 ) ! mixed ene-ens scheme |
---|
808 | CALL ctl_stop ('vor_mix_adj not available yet') |
---|
809 | ! CALL vor_mix_adj( kt ) ! total vorticity (mix=ens-ene) |
---|
810 | ! |
---|
811 | CASE ( 3 ) ! energy and enstrophy conserving scheme |
---|
812 | CALL vor_een_adj( kt, ntot, ua_ad, va_ad ) ! total vorticity |
---|
813 | ! |
---|
814 | END SELECT |
---|
815 | ! |
---|
816 | IF( nn_timing == 1 ) CALL timing_stop('dyn_vor_adj') |
---|
817 | ! |
---|
818 | END SUBROUTINE dyn_vor_adj |
---|
819 | SUBROUTINE vor_ens_adj( kt, kvor, pua_ad, pva_ad ) |
---|
820 | !!---------------------------------------------------------------------- |
---|
821 | !! *** ROUTINE vor_ens_adj *** |
---|
822 | !! |
---|
823 | !! ** Purpose of the direct routine: |
---|
824 | !! Compute the now total vorticity trend and add it to |
---|
825 | !! the general trend of the momentum equation. |
---|
826 | !! |
---|
827 | !! ** Method of the direct routine: |
---|
828 | !! Trend evaluated using now fields (centered in time) |
---|
829 | !! and the Sadourny (1975) flux FORM formulation : conserves the |
---|
830 | !! potential enstrophy of a horizontally non-divergent flow. the |
---|
831 | !! trend of the vorticity term is given by: |
---|
832 | !! * s-coordinate (ln_sco=T), the e3. are inside the derivative: |
---|
833 | !! voru = 1/e1u mj-1[ (rotn+f)/e3f ] mj-1[ mi(e1v*e3v vn) ] |
---|
834 | !! vorv = 1/e2v mi-1[ (rotn+f)/e3f ] mi-1[ mj(e2u*e3u un) ] |
---|
835 | !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: |
---|
836 | !! voru = 1/e1u mj-1[ rotn+f ] mj-1[ mi(e1v vn) ] |
---|
837 | !! vorv = 1/e2v mi-1[ rotn+f ] mi-1[ mj(e2u un) ] |
---|
838 | !! Add this trend to the general momentum trend (ua,va): |
---|
839 | !! (ua,va) = (ua,va) + ( voru , vorv ) |
---|
840 | !! |
---|
841 | !! ** Action : - Update (ua,va) arrays with the now vorticity term trend |
---|
842 | !! - Save the trends in (ztrdu,ztrdv) in 2 parts (relative |
---|
843 | !! and planetary vorticity trends) ('key_trddyn') |
---|
844 | !! |
---|
845 | !! References : Sadourny, r., 1975, j. atmos. sciences, 32, 680-689. |
---|
846 | !!---------------------------------------------------------------------- |
---|
847 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
848 | INTEGER , INTENT(in ) :: kvor ! =ncor (planetary) ; =ntot (total) ; |
---|
849 | ! ! =nrvm (relative vorticity or metric) |
---|
850 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pua_ad ! total u-trend |
---|
851 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pva_ad ! total v-trend |
---|
852 | !! |
---|
853 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
854 | REAL(wp) :: zfact1 ! temporary scalars |
---|
855 | REAL(wp), POINTER, DIMENSION(:,:) :: zwx, zwy, zwz ! temporary 3D workspace |
---|
856 | REAL(wp) :: zuav, zvau ! temporary scalars |
---|
857 | REAL(wp) :: zuavad, zvauad ! temporary scalars |
---|
858 | REAL(wp), POINTER, DIMENSION(:,:) :: zwxad, zwyad, zwzad ! temporary 3D workspace |
---|
859 | !!---------------------------------------------------------------------- |
---|
860 | ! |
---|
861 | IF( nn_timing == 1 ) CALL timing_start('vor_ens_adj') |
---|
862 | ! |
---|
863 | CALL wrk_alloc( jpi, jpj, zwx, zwy, zwz ) |
---|
864 | CALL wrk_alloc( jpi, jpj, zwxad, zwyad, zwzad ) |
---|
865 | ! |
---|
866 | IF( kt == nitend ) THEN |
---|
867 | IF(lwp) WRITE(numout,*) |
---|
868 | IF(lwp) WRITE(numout,*) 'dyn_vor_ens_adj : vorticity term: enstrophy conserving scheme' |
---|
869 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~' |
---|
870 | ENDIF |
---|
871 | |
---|
872 | ! Local constant initialization |
---|
873 | zfact1 = 0.5 * 0.25 |
---|
874 | |
---|
875 | !CDIR PARALLEL DO PRIVATE( zwx, zwy, zwz, zwxad, zwyad, zwzad ) |
---|
876 | ! ! =============== |
---|
877 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
878 | ! ! =============== |
---|
879 | ! Potential vorticity and horizontal fluxes |
---|
880 | ! ----------------------------------------- |
---|
881 | SELECT CASE( kvor ) ! vorticity considered |
---|
882 | CASE ( 1 ) ; zwz(:,:) = ff(:,:) ! planetary vorticity (Coriolis) |
---|
883 | CASE ( 2 ) ; zwz(:,:) = rotn(:,:,jk) ! relative vorticity |
---|
884 | CASE ( 3 ) ! metric term |
---|
885 | DO jj = 1, jpjm1 |
---|
886 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
887 | zwz(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
888 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) )& |
---|
889 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
890 | END DO |
---|
891 | END DO |
---|
892 | CASE ( 4 ) ; zwz(:,:) = ( rotn(:,:,jk) + ff(:,:) ) ! total (relative + planetary vorticity) |
---|
893 | CASE ( 5 ) ! total (coriolis + metric) |
---|
894 | DO jj = 1, jpjm1 |
---|
895 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
896 | zwz(ji,jj) = ( ff (ji,jj) & |
---|
897 | & + ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
898 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
899 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) & |
---|
900 | & ) |
---|
901 | END DO |
---|
902 | END DO |
---|
903 | END SELECT |
---|
904 | |
---|
905 | IF( ln_sco ) THEN |
---|
906 | DO jj = 1, jpj ! caution: don't use (:,:) for this loop |
---|
907 | DO ji = 1, jpi ! it causes optimization problems on NEC in auto-tasking |
---|
908 | zwz(ji,jj) = zwz(ji,jj) / fse3f(ji,jj,jk) |
---|
909 | zwx(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) * un(ji,jj,jk) |
---|
910 | zwy(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) * vn(ji,jj,jk) |
---|
911 | END DO |
---|
912 | END DO |
---|
913 | ELSE |
---|
914 | DO jj = 1, jpj ! caution: don't use (:,:) for this loop |
---|
915 | DO ji = 1, jpi ! it causes optimization problems on NEC in auto-tasking |
---|
916 | zwx(ji,jj) = e2u(ji,jj) * un(ji,jj,jk) |
---|
917 | zwy(ji,jj) = e1v(ji,jj) * vn(ji,jj,jk) |
---|
918 | END DO |
---|
919 | END DO |
---|
920 | ENDIF |
---|
921 | ! =================== |
---|
922 | ! Adjoint counterpart |
---|
923 | ! =================== |
---|
924 | zuavad = 0.0_wp |
---|
925 | zvauad = 0.0_wp |
---|
926 | zwxad(:,:) = 0.0_wp |
---|
927 | zwyad(:,:) = 0.0_wp |
---|
928 | zwzad(:,:) = 0.0_wp |
---|
929 | ! Compute and add the vorticity term trend |
---|
930 | ! ---------------------------------------- |
---|
931 | DO jj = jpjm1, 2, -1 |
---|
932 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
---|
933 | ! Compute and add the vorticity term trend |
---|
934 | ! ---------------------------------------- |
---|
935 | !- Direct counterpart |
---|
936 | zuav = zfact1 / e1u(ji,jj) * ( zwy(ji ,jj-1) + zwy(ji+1,jj-1) & |
---|
937 | & + zwy(ji ,jj ) + zwy(ji+1,jj ) ) |
---|
938 | zvau =-zfact1 / e2v(ji,jj) * ( zwx(ji-1,jj ) + zwx(ji-1,jj+1) & |
---|
939 | & + zwx(ji ,jj ) + zwx(ji ,jj+1) ) |
---|
940 | !- |
---|
941 | zvauad = zvauad + pva_ad(ji,jj,jk) * ( zwz(ji-1,jj) + zwz(ji,jj) ) |
---|
942 | zwzad(ji-1,jj) = zwzad(ji-1,jj) + pva_ad(ji,jj,jk) * zvau |
---|
943 | zwzad(ji ,jj) = zwzad(ji ,jj) + pva_ad(ji,jj,jk) * zvau |
---|
944 | |
---|
945 | zuavad = zuavad + pua_ad(ji,jj,jk) * ( zwz(ji,jj-1) + zwz(ji,jj) ) |
---|
946 | zwzad(ji,jj-1) = zwzad(ji,jj-1) + pua_ad(ji,jj,jk) * zuav |
---|
947 | zwzad(ji,jj ) = zwzad(ji,jj ) + pua_ad(ji,jj,jk) * zuav |
---|
948 | |
---|
949 | zwxad(ji-1,jj ) = zwxad(ji-1,jj ) - zvauad * zfact1 / e2v(ji,jj) |
---|
950 | zwxad(ji-1,jj+1) = zwxad(ji-1,jj+1) - zvauad * zfact1 / e2v(ji,jj) |
---|
951 | zwxad(ji ,jj ) = zwxad(ji ,jj ) - zvauad * zfact1 / e2v(ji,jj) |
---|
952 | zwxad(ji ,jj+1) = zwxad(ji ,jj+1) - zvauad * zfact1 / e2v(ji,jj) |
---|
953 | zvauad = 0.0_wp |
---|
954 | |
---|
955 | zwyad(ji ,jj-1) = zwyad(ji ,jj-1) + zuavad * zfact1 / e1u(ji,jj) |
---|
956 | zwyad(ji+1,jj-1) = zwyad(ji+1,jj-1) + zuavad * zfact1 / e1u(ji,jj) |
---|
957 | zwyad(ji ,jj ) = zwyad(ji ,jj ) + zuavad * zfact1 / e1u(ji,jj) |
---|
958 | zwyad(ji+1,jj ) = zwyad(ji+1,jj ) + zuavad * zfact1 / e1u(ji,jj) |
---|
959 | zuavad = 0.0_wp |
---|
960 | END DO |
---|
961 | END DO |
---|
962 | IF( ln_sco ) THEN |
---|
963 | DO jj = jpj, 1, -1 ! caution: don't use (:,:) for this loop |
---|
964 | DO ji = jpi, 1, -1 ! it causes optimization problems on NEC in auto-tasking |
---|
965 | zwzad(ji,jj) = zwzad(ji,jj) / fse3f(ji,jj,jk) |
---|
966 | un_ad(ji,jj,jk) = un_ad(ji,jj,jk) + zwxad(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) |
---|
967 | vn_ad(ji,jj,jk) = vn_ad(ji,jj,jk) + zwyad(ji,jj) * e1v(ji,jj) * fse3v(ji,jj,jk) |
---|
968 | zwxad(ji,jj) = 0.0_wp |
---|
969 | zwyad(ji,jj) = 0.0_wp |
---|
970 | END DO |
---|
971 | END DO |
---|
972 | ELSE |
---|
973 | DO jj = jpj, 1, -1 ! caution: don't use (:,:) for this loop |
---|
974 | DO ji = jpi, 1, -1 ! it causes optimization problems on NEC in auto-tasking |
---|
975 | un_ad(ji,jj,jk) = un_ad(ji,jj,jk) + e2u(ji,jj) * zwxad(ji,jj) |
---|
976 | vn_ad(ji,jj,jk) = vn_ad(ji,jj,jk) + e1v(ji,jj) * zwyad(ji,jj) |
---|
977 | zwxad(ji,jj) = 0.0_wp |
---|
978 | zwyad(ji,jj) = 0.0_wp |
---|
979 | END DO |
---|
980 | END DO |
---|
981 | ENDIF |
---|
982 | ! Potential vorticity and horizontal fluxes |
---|
983 | ! ----------------------------------------- |
---|
984 | SELECT CASE( kvor ) ! vorticity considered |
---|
985 | CASE ( 1 ) ! planetary vorticity (Coriolis) |
---|
986 | zwzad(:,:) = 0.0_wp |
---|
987 | CASE ( 2 ,4) ! relative vorticity |
---|
988 | rotn_ad(:,:,jk) = rotn_ad(:,:,jk) + zwzad(:,:) |
---|
989 | zwzad(:,:) = 0.0_wp |
---|
990 | CASE ( 3 ,5 ) ! metric term |
---|
991 | DO jj = jpjm1, 1, -1 |
---|
992 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
993 | vn_ad(ji+1,jj,jk) = vn_ad(ji+1,jj,jk) & |
---|
994 | & + zwzad(ji,jj) * ( e2v(ji+1,jj) - e2v(ji,jj) ) & |
---|
995 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
996 | vn_ad(ji ,jj,jk) = vn_ad(ji ,jj,jk) & |
---|
997 | & + zwzad(ji,jj) * ( e2v(ji+1,jj) - e2v(ji,jj) ) & |
---|
998 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
999 | un_ad(ji,jj+1,jk) = un_ad(ji,jj+1,jk) & |
---|
1000 | & - zwzad(ji,jj) * ( e1u(ji,jj+1) - e1u(ji,jj) ) & |
---|
1001 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
1002 | un_ad(ji,jj ,jk) = un_ad(ji,jj ,jk) & |
---|
1003 | & - zwzad(ji,jj) * ( e1u(ji,jj+1) - e1u(ji,jj) ) & |
---|
1004 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) |
---|
1005 | zwzad(ji,jj) = 0.0_wp |
---|
1006 | END DO |
---|
1007 | END DO |
---|
1008 | END SELECT |
---|
1009 | ! ! =============== |
---|
1010 | END DO ! End of slab |
---|
1011 | ! ! =============== |
---|
1012 | CALL wrk_dealloc( jpi, jpj, zwx, zwy, zwz ) |
---|
1013 | CALL wrk_dealloc( jpi, jpj, zwxad, zwyad, zwzad ) |
---|
1014 | ! |
---|
1015 | IF( nn_timing == 1 ) CALL timing_stop('vor_ens_adj') |
---|
1016 | ! |
---|
1017 | END SUBROUTINE vor_ens_adj |
---|
1018 | |
---|
1019 | |
---|
1020 | SUBROUTINE vor_een_adj( kt, kvor, pua_ad, pva_ad ) |
---|
1021 | !!---------------------------------------------------------------------- |
---|
1022 | !! *** ROUTINE vor_een_adj *** |
---|
1023 | !! |
---|
1024 | !! ** Purpose : Compute the now total vorticity trend and add it to |
---|
1025 | !! the general trend of the momentum equation. |
---|
1026 | !! |
---|
1027 | !! ** Method : Trend evaluated using now fields (centered in time) |
---|
1028 | !! and the Arakawa and Lamb (19XX) flux form formulation : conserves |
---|
1029 | !! both the horizontal kinetic energy and the potential enstrophy |
---|
1030 | !! when horizontal divergence is zero. |
---|
1031 | !! The trend of the vorticity term is given by: |
---|
1032 | !! * s-coordinate (ln_sco=T), the e3. are inside the derivatives: |
---|
1033 | !! * z-coordinate (default key), e3t=e3u=e3v, the trend becomes: |
---|
1034 | !! Add this trend to the general momentum trend (ua,va): |
---|
1035 | !! (ua,va) = (ua,va) + ( voru , vorv ) |
---|
1036 | !! |
---|
1037 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
---|
1038 | !! - save the trends in (ztrdu,ztrdv) in 2 parts (relative |
---|
1039 | !! and planetary vorticity trends) ('key_trddyn') |
---|
1040 | !! |
---|
1041 | !! References : Arakawa and Lamb 1980, Mon. Wea. Rev., 109, 18-36 |
---|
1042 | !!---------------------------------------------------------------------- |
---|
1043 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
1044 | INTEGER , INTENT(in ) :: kvor ! =ncor (planetary) ; =ntot (total) ; |
---|
1045 | ! ! =nrvm (relative vorticity or metric) |
---|
1046 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pua_ad ! total u-trend |
---|
1047 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pva_ad ! total v-trend |
---|
1048 | !! |
---|
1049 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1050 | REAL(wp) :: zfac12 ! temporary scalars |
---|
1051 | REAL(wp) :: zuaad, zvaad ! temporary scalars |
---|
1052 | REAL(wp), POINTER, DIMENSION(:,:) :: zwx, zwy, zwz ! temporary 2D workspace |
---|
1053 | REAL(wp), POINTER, DIMENSION(:,:) :: ztnw, ztne, ztsw, ztse ! temporary 3D workspace |
---|
1054 | REAL(wp), POINTER, DIMENSION(:,:) :: zwxad, zwyad, zwzad ! temporary 2D workspace |
---|
1055 | REAL(wp), POINTER, DIMENSION(:,:) :: ztnwad, ztnead, ztswad, ztsead ! temporary 3D workspace |
---|
1056 | REAL(wp), POINTER, DIMENSION(:,:,:), SAVE :: ze3f_ad |
---|
1057 | !!---------------------------------------------------------------------- |
---|
1058 | ! |
---|
1059 | IF( nn_timing == 1 ) CALL timing_start('vor_een_adj') |
---|
1060 | ! |
---|
1061 | CALL wrk_alloc( jpi, jpj, zwx , zwy , zwz ) |
---|
1062 | CALL wrk_alloc( jpi, jpj, ztnw, ztne, ztsw, ztse ) |
---|
1063 | CALL wrk_alloc( jpi, jpj, zwxad , zwyad , zwzad ) |
---|
1064 | CALL wrk_alloc( jpi, jpj, ztnwad, ztnead, ztswad, ztsead ) |
---|
1065 | CALL wrk_alloc( jpi, jpj, jpk, ze3f_ad ) |
---|
1066 | ! local adjoint initailization |
---|
1067 | zuaad = 0.0_wp ; zvaad = 0.0_wp |
---|
1068 | zwx (:,:) = 0.0_wp ; zwy (:,:) = 0.0_wp ; zwz (:,:) = 0.0_wp |
---|
1069 | ztnw(:,:) = 0.0_wp ; ztne(:,:) = 0.0_wp ; ztsw(:,:) = 0.0_wp ; ztse(:,:) = 0.0_wp |
---|
1070 | zwxad (:,:) = 0.0_wp ; zwyad (:,:) = 0.0_wp ; zwzad (:,:) = 0.0_wp |
---|
1071 | ztnwad(:,:) = 0.0_wp ; ztnead(:,:) = 0.0_wp ; ztswad(:,:) = 0.0_wp ; ztsead(:,:) = 0.0_wp |
---|
1072 | ze3f_ad = 0._wp |
---|
1073 | |
---|
1074 | IF( kt == nitend ) THEN |
---|
1075 | IF(lwp) WRITE(numout,*) |
---|
1076 | IF(lwp) WRITE(numout,*) 'dyn:vor_een_adj : vorticity term: energy and enstrophy conserving scheme' |
---|
1077 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
1078 | ENDIF |
---|
1079 | |
---|
1080 | IF( kt == nit000 ) THEN ! reciprocal of e3 at F-point (masked averaging of e3t) |
---|
1081 | DO jk = 1, jpk |
---|
1082 | DO jj = 1, jpjm1 |
---|
1083 | DO ji = 1, jpim1 |
---|
1084 | ze3f_ad(ji,jj,jk) = ( fse3t(ji,jj+1,jk)*tmask(ji,jj+1,jk) + fse3t(ji+1,jj+1,jk)*tmask(ji+1,jj+1,jk) & |
---|
1085 | & + fse3t(ji,jj ,jk)*tmask(ji,jj ,jk) + fse3t(ji+1,jj ,jk)*tmask(ji+1,jj ,jk) ) * 0.25_wp |
---|
1086 | IF( ze3f_ad(ji,jj,jk) /= 0.0_wp ) ze3f_ad(ji,jj,jk) = 1.0_wp / ze3f_ad(ji,jj,jk) |
---|
1087 | END DO |
---|
1088 | END DO |
---|
1089 | END DO |
---|
1090 | CALL lbc_lnk( ze3f_ad, 'F', 1._wp ) |
---|
1091 | ENDIF |
---|
1092 | |
---|
1093 | ! Local constant initialization |
---|
1094 | zfac12 = 1.0_wp / 12.0_wp |
---|
1095 | |
---|
1096 | !CDIR PARALLEL DO PRIVATE( zwx, zwy, zwz, ztnw, ztne, ztsw, ztse ) |
---|
1097 | ! ! =============== |
---|
1098 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
1099 | ! ! =============== |
---|
1100 | |
---|
1101 | ! Potential vorticity and horizontal fluxes (Direct local variables init) |
---|
1102 | ! ----------------------------------------- |
---|
1103 | SELECT CASE( kvor ) ! vorticity considered |
---|
1104 | CASE ( 1 ) |
---|
1105 | zwz(:,:) = ff(:,:) * ze3f_ad(:,:,jk) ! planetary vorticity (Coriolis) |
---|
1106 | CASE ( 2 ) ; zwz(:,:) = rotn(:,:,jk) * ze3f_ad(:,:,jk) ! relative vorticity |
---|
1107 | CASE ( 3 ) ! metric term |
---|
1108 | DO jj = 1, jpjm1 |
---|
1109 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1110 | zwz(ji,jj) = ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
1111 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) )& |
---|
1112 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) * ze3f_ad(ji,jj,jk) |
---|
1113 | END DO |
---|
1114 | END DO |
---|
1115 | CALL lbc_lnk( zwz, 'F', 1._wp ) |
---|
1116 | CASE ( 4 ) ; zwz(:,:) = ( rotn(:,:,jk) + ff(:,:) ) * ze3f_ad(:,:,jk) ! total (relative + planetary vorticity) |
---|
1117 | CASE ( 5 ) ! total (coriolis + metric) |
---|
1118 | DO jj = 1, jpjm1 |
---|
1119 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1120 | zwz(ji,jj) = ( ff (ji,jj) & |
---|
1121 | & + ( ( vn(ji+1,jj ,jk) + vn (ji,jj,jk) ) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) & |
---|
1122 | & - ( un(ji ,jj+1,jk) + un (ji,jj,jk) ) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) ) & |
---|
1123 | & * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) & |
---|
1124 | & ) * ze3f_ad(ji,jj,jk) |
---|
1125 | END DO |
---|
1126 | END DO |
---|
1127 | CALL lbc_lnk( zwz, 'F', 1._wp ) |
---|
1128 | END SELECT |
---|
1129 | |
---|
1130 | zwx(:,:) = e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) |
---|
1131 | zwy(:,:) = e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) |
---|
1132 | |
---|
1133 | ! Compute and add the vorticity term trend |
---|
1134 | ! ---------------------------------------- |
---|
1135 | jj=2 |
---|
1136 | ztne(1,:) = 0.0_wp ; ztnw(1,:) = 0.0_wp ; ztse(1,:) = 0.0_wp ; ztsw(1,:) = 0.0_wp |
---|
1137 | DO ji = 2, jpi |
---|
1138 | ztne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1) |
---|
1139 | ztnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj ) |
---|
1140 | ztse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1) |
---|
1141 | ztsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj ) |
---|
1142 | END DO |
---|
1143 | DO jj = 3, jpj |
---|
1144 | DO ji = fs_2, jpi ! vector opt. |
---|
1145 | ztne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1) |
---|
1146 | ztnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj ) |
---|
1147 | ztse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1) |
---|
1148 | ztsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj ) |
---|
1149 | END DO |
---|
1150 | END DO |
---|
1151 | |
---|
1152 | ! =================== |
---|
1153 | ! Adjoint counterpart |
---|
1154 | ! =================== |
---|
1155 | |
---|
1156 | DO jj = jpjm1, 2, -1 |
---|
1157 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
---|
1158 | zuaad = zuaad + pua_ad(ji,jj,jk) |
---|
1159 | zvaad = zvaad + pva_ad(ji,jj,jk) |
---|
1160 | |
---|
1161 | zvaad = - zvaad * zfac12 / e2v(ji,jj) |
---|
1162 | ztswad(ji ,jj+1) = ztswad(ji ,jj+1) + zvaad * zwx (ji-1,jj+1) |
---|
1163 | zwxad (ji-1,jj+1) = zwxad (ji-1,jj+1) + zvaad * ztsw(ji ,jj+1) |
---|
1164 | ztsead(ji ,jj+1) = ztsead(ji ,jj+1) + zvaad * zwx (ji ,jj+1) |
---|
1165 | zwxad (ji ,jj+1) = zwxad (ji ,jj+1) + zvaad * ztse(ji ,jj+1) |
---|
1166 | ztnwad(ji ,jj ) = ztnwad(ji ,jj ) + zvaad * zwx (ji-1,jj ) |
---|
1167 | zwxad (ji-1,jj ) = zwxad (ji-1,jj ) + zvaad * ztnw(ji ,jj ) |
---|
1168 | ztnead(ji ,jj ) = ztnead(ji ,jj ) + zvaad * zwx (ji ,jj ) |
---|
1169 | zwxad (ji ,jj ) = zwxad (ji ,jj ) + zvaad * ztne(ji ,jj ) |
---|
1170 | zvaad = 0.0_wp |
---|
1171 | |
---|
1172 | zuaad = zuaad * zfac12 / e1u(ji,jj) |
---|
1173 | ztnead(ji ,jj ) = ztnead(ji ,jj ) + zuaad * zwy (ji ,jj ) |
---|
1174 | zwyad (ji ,jj ) = zwyad (ji ,jj ) + zuaad * ztne(ji ,jj ) |
---|
1175 | ztnwad(ji+1,jj ) = ztnwad(ji+1,jj ) + zuaad * zwy (ji+1,jj ) |
---|
1176 | zwyad (ji+1,jj ) = zwyad (ji+1,jj ) + zuaad * ztnw(ji+1,jj ) |
---|
1177 | ztsead(ji ,jj ) = ztsead(ji ,jj ) + zuaad * zwy (ji ,jj-1) |
---|
1178 | zwyad (ji ,jj-1) = zwyad (ji ,jj-1) + zuaad * ztse(ji ,jj ) |
---|
1179 | ztswad(ji+1,jj ) = ztswad(ji+1,jj ) + zuaad * zwy (ji+1,jj-1) |
---|
1180 | zwyad (ji+1,jj-1) = zwyad (ji+1,jj-1) + zuaad * ztsw(ji+1,jj ) |
---|
1181 | zuaad = 0.0_wp |
---|
1182 | END DO |
---|
1183 | END DO |
---|
1184 | DO jj = jpj, 3, -1 |
---|
1185 | DO ji = jpi, fs_2, -1 ! vector opt. |
---|
1186 | zwzad (ji ,jj-1) = zwzad(ji ,jj-1) + ztswad(ji,jj) |
---|
1187 | zwzad (ji-1,jj-1) = zwzad(ji-1,jj-1) + ztswad(ji,jj) |
---|
1188 | zwzad (ji-1,jj ) = zwzad(ji-1,jj ) + ztswad(ji,jj) |
---|
1189 | ztswad(ji ,jj ) = 0.0_wp |
---|
1190 | zwzad (ji ,jj ) = zwzad(ji ,jj ) + ztsead(ji,jj) |
---|
1191 | zwzad (ji ,jj-1) = zwzad(ji ,jj-1) + ztsead(ji,jj) |
---|
1192 | zwzad (ji-1,jj-1) = zwzad(ji-1,jj-1) + ztsead(ji,jj) |
---|
1193 | ztsead(ji,jj) = 0.0_wp |
---|
1194 | zwzad (ji-1,jj-1) = zwzad(ji-1,jj-1) + ztnwad(ji,jj) |
---|
1195 | zwzad (ji-1,jj ) = zwzad(ji-1,jj ) + ztnwad(ji,jj) |
---|
1196 | zwzad (ji ,jj ) = zwzad(ji ,jj ) + ztnwad(ji,jj) |
---|
1197 | ztnwad(ji ,jj ) = 0.0_wp |
---|
1198 | zwzad (ji-1,jj ) = zwzad(ji-1,jj ) + ztnead(ji,jj) |
---|
1199 | zwzad (ji ,jj ) = zwzad(ji ,jj ) + ztnead(ji,jj) |
---|
1200 | zwzad (ji ,jj-1) = zwzad(ji ,jj-1) + ztnead(ji,jj) |
---|
1201 | ztnead(ji,jj) = 0.0_wp |
---|
1202 | END DO |
---|
1203 | END DO |
---|
1204 | jj=2 |
---|
1205 | DO ji = jpi, 2, -1 |
---|
1206 | zwzad (ji ,jj-1) = zwzad(ji ,jj-1) + ztswad(ji,jj) |
---|
1207 | zwzad (ji-1,jj-1) = zwzad(ji-1,jj-1) + ztswad(ji,jj) |
---|
1208 | zwzad (ji-1,jj ) = zwzad(ji-1,jj ) + ztswad(ji,jj) |
---|
1209 | ztswad(ji,jj) = 0.0_wp |
---|
1210 | zwzad (ji ,jj ) = zwzad(ji ,jj ) + ztsead(ji,jj) |
---|
1211 | zwzad (ji ,jj-1) = zwzad(ji ,jj-1) + ztsead(ji,jj) |
---|
1212 | zwzad (ji-1,jj-1) = zwzad(ji-1,jj-1) + ztsead(ji,jj) |
---|
1213 | ztsead(ji ,jj ) = 0.0_wp |
---|
1214 | zwzad (ji-1,jj-1) = zwzad(ji-1,jj-1) + ztnwad(ji,jj) |
---|
1215 | zwzad (ji-1,jj ) = zwzad(ji-1,jj ) + ztnwad(ji,jj) |
---|
1216 | zwzad (ji ,jj ) = zwzad(ji ,jj ) + ztnwad(ji,jj) |
---|
1217 | ztnwad(ji ,jj ) = 0.0_wp |
---|
1218 | zwzad (ji-1,jj ) = zwzad(ji-1,jj ) + ztnead(ji,jj) |
---|
1219 | zwzad (ji ,jj ) = zwzad(ji ,jj ) + ztnead(ji,jj) |
---|
1220 | zwzad (ji ,jj-1) = zwzad(ji ,jj-1) + ztnead(ji,jj) |
---|
1221 | ztnead(ji ,jj ) = 0.0_wp |
---|
1222 | END DO |
---|
1223 | ztnead(1,:) = 0.0_wp ; ztnwad(1,:) = 0.0_wp |
---|
1224 | ztsead(1,:) = 0.0_wp ; ztswad(1,:) = 0.0_wp |
---|
1225 | |
---|
1226 | vn_ad(:,:,jk) = vn_ad(:,:,jk) + zwyad(:,:) * e1v(:,:) * fse3v(:,:,jk) |
---|
1227 | un_ad(:,:,jk) = un_ad(:,:,jk) + zwxad(:,:) * e2u(:,:) * fse3u(:,:,jk) |
---|
1228 | zwyad(:,:) = 0.0_wp |
---|
1229 | zwxad(:,:) = 0.0_wp |
---|
1230 | |
---|
1231 | ! Potential vorticity and horizontal fluxes |
---|
1232 | ! ----------------------------------------- |
---|
1233 | SELECT CASE( kvor ) ! vorticity considered |
---|
1234 | CASE ( 1 ) |
---|
1235 | zwzad(:,:) = 0.0_wp |
---|
1236 | CASE ( 2 ) |
---|
1237 | rotn_ad(:,:,jk) = rotn_ad(:,:,jk) + zwzad(:,:) * ze3f_ad(:,:,jk) |
---|
1238 | zwzad(:,:) = 0.0_wp |
---|
1239 | CASE ( 3 ) |
---|
1240 | CALL lbc_lnk_adj( zwzad, 'F', 1._wp ) ! metric term |
---|
1241 | DO jj = jpjm1, 1, -1 |
---|
1242 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
1243 | zwzad(ji ,jj ) = zwzad(ji,jj) * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) * ze3f_ad(ji,jj,jk) |
---|
1244 | vn_ad(ji+1,jj ,jk) = vn_ad(ji+1,jj ,jk) + zwzad(ji,jj) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) |
---|
1245 | vn_ad(ji ,jj ,jk) = vn_ad(ji ,jj ,jk) + zwzad(ji,jj) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) |
---|
1246 | un_ad(ji ,jj+1,jk) = un_ad(ji ,jj+1,jk) - zwzad(ji,jj) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) |
---|
1247 | un_ad(ji ,jj ,jk) = un_ad(ji ,jj ,jk) - zwzad(ji,jj) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) |
---|
1248 | zwzad(ji ,jj ) = 0.0_wp |
---|
1249 | END DO |
---|
1250 | END DO |
---|
1251 | CASE ( 4 ) |
---|
1252 | rotn_ad(:,:,jk) = rotn_ad(:,:,jk) + zwzad(:,:) * ze3f_ad(:,:,jk) |
---|
1253 | zwzad(:,:) = 0.0_wp |
---|
1254 | CASE ( 5 ) |
---|
1255 | CALL lbc_lnk_adj( zwzad, 'F', 1._wp ) ! total (coriolis + metric) |
---|
1256 | DO jj = jpjm1, 1, -1 |
---|
1257 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
1258 | zwzad(ji ,jj ) = zwzad(ji,jj) * 0.5 / ( e1f(ji,jj) * e2f(ji,jj) ) * ze3f_ad(ji,jj,jk) |
---|
1259 | vn_ad(ji+1,jj ,jk) = vn_ad(ji+1,jj ,jk) + zwzad(ji,jj) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) |
---|
1260 | vn_tl(ji ,jj ,jk) = vn_tl(ji ,jj ,jk) + zwzad(ji,jj) * ( e2v(ji+1,jj ) - e2v(ji,jj) ) |
---|
1261 | un_ad(ji ,jj+1,jk) = un_ad(ji ,jj+1,jk) - zwzad(ji,jj) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) |
---|
1262 | un_ad(ji ,jj ,jk) = un_ad(ji ,jj ,jk) - zwzad(ji,jj) * ( e1u(ji ,jj+1) - e1u(ji,jj) ) |
---|
1263 | zwzad(ji ,jj ) = 0.0_wp |
---|
1264 | END DO |
---|
1265 | END DO |
---|
1266 | END SELECT |
---|
1267 | ! ! =============== |
---|
1268 | END DO ! End of slab |
---|
1269 | ! ! =============== |
---|
1270 | CALL wrk_dealloc( jpi, jpj, zwx , zwy , zwz ) |
---|
1271 | CALL wrk_dealloc( jpi, jpj, ztnw, ztne, ztsw, ztse ) |
---|
1272 | CALL wrk_dealloc( jpi, jpj, zwxad , zwyad , zwzad ) |
---|
1273 | CALL wrk_dealloc( jpi, jpj, ztnwad, ztnead, ztswad, ztsead ) |
---|
1274 | CALL wrk_dealloc( jpi, jpj, jpk, ze3f_ad) |
---|
1275 | ! |
---|
1276 | IF( nn_timing == 1 ) CALL timing_stop('vor_een_adj') |
---|
1277 | ! |
---|
1278 | END SUBROUTINE vor_een_adj |
---|
1279 | |
---|
1280 | SUBROUTINE dyn_vor_init_tam |
---|
1281 | !!--------------------------------------------------------------------- |
---|
1282 | !! *** ROUTINE vor_ctl_tam *** |
---|
1283 | !! |
---|
1284 | !! ** Purpose : Control the consistency between cpp options for |
---|
1285 | !! tracer advection schemes |
---|
1286 | !!---------------------------------------------------------------------- |
---|
1287 | INTEGER :: ioptio ! temporary integer |
---|
1288 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1289 | NAMELIST/namdyn_vor/ ln_dynvor_ens, ln_dynvor_ene, ln_dynvor_mix, ln_dynvor_een |
---|
1290 | !!---------------------------------------------------------------------- |
---|
1291 | |
---|
1292 | REWIND ( numnam ) ! Read Namelist namdyn_vor : Vorticity scheme options |
---|
1293 | READ ( numnam, namdyn_vor ) |
---|
1294 | |
---|
1295 | IF(lwp) THEN ! Namelist print |
---|
1296 | WRITE(numout,*) |
---|
1297 | WRITE(numout,*) 'dyn:vor_init_tam : vorticity term : read namelist and control the consistency' |
---|
1298 | WRITE(numout,*) '~~~~~~~~~~~~~~~' |
---|
1299 | WRITE(numout,*) ' Namelist namdyn_vor : choice of the vorticity term scheme' |
---|
1300 | WRITE(numout,*) ' energy conserving scheme ln_dynvor_ene = ', ln_dynvor_ene |
---|
1301 | WRITE(numout,*) ' enstrophy conserving scheme ln_dynvor_ens = ', ln_dynvor_ens |
---|
1302 | WRITE(numout,*) ' mixed enstrophy/energy conserving scheme ln_dynvor_mix = ', ln_dynvor_mix |
---|
1303 | WRITE(numout,*) ' enstrophy and energy conserving scheme ln_dynvor_een = ', ln_dynvor_een |
---|
1304 | ENDIF |
---|
1305 | ! If energy, enstrophy or mixed advection of momentum in vector form change the value for masks |
---|
1306 | ! at angles with three ocean points and one land point |
---|
1307 | IF( ln_vorlat .AND. ( ln_dynvor_ene .OR. ln_dynvor_ens .OR. ln_dynvor_mix ) ) THEN |
---|
1308 | DO jk = 1, jpk |
---|
1309 | DO jj = 2, jpjm1 |
---|
1310 | DO ji = 2, jpim1 |
---|
1311 | IF( tmask(ji,jj,jk)+tmask(ji+1,jj,jk)+tmask(ji,jj+1,jk)+tmask(ji+1,jj+1,jk) == 3._wp ) & |
---|
1312 | fmask(ji,jj,jk) = 1._wp |
---|
1313 | END DO |
---|
1314 | END DO |
---|
1315 | END DO |
---|
1316 | ! |
---|
1317 | CALL lbc_lnk( fmask, 'F', 1._wp ) ! Lateral boundary conditions on fmask |
---|
1318 | ! |
---|
1319 | ENDIF |
---|
1320 | ! |
---|
1321 | ioptio = 0 ! Control of vorticity scheme options |
---|
1322 | IF( ln_dynvor_ene ) ioptio = ioptio + 1 |
---|
1323 | IF( ln_dynvor_ens ) ioptio = ioptio + 1 |
---|
1324 | IF( ln_dynvor_mix ) ioptio = ioptio + 1 |
---|
1325 | IF( ln_dynvor_een ) ioptio = ioptio + 1 |
---|
1326 | IF( lk_esopa ) ioptio = 1 |
---|
1327 | |
---|
1328 | IF( ioptio /= 1 ) CALL ctl_stop( ' use ONE and ONLY one vorticity scheme' ) |
---|
1329 | |
---|
1330 | ! ! Set nvor (type of scheme for vorticity) |
---|
1331 | IF( ln_dynvor_ene ) nvor = 0 |
---|
1332 | IF( ln_dynvor_ens ) nvor = 1 |
---|
1333 | IF( ln_dynvor_mix ) nvor = 2 |
---|
1334 | IF( ln_dynvor_een ) nvor = 3 |
---|
1335 | IF( lk_esopa ) nvor = -1 |
---|
1336 | |
---|
1337 | ! ! Set ncor, nrvm, ntot (type of vorticity) |
---|
1338 | IF(lwp) WRITE(numout,*) |
---|
1339 | ncor = 1 |
---|
1340 | IF( ln_dynadv_vec ) THEN |
---|
1341 | IF(lwp) WRITE(numout,*) ' Vector form advection : vorticity = Coriolis + relative vorticity' |
---|
1342 | nrvm = 2 |
---|
1343 | ntot = 4 |
---|
1344 | ELSE |
---|
1345 | IF(lwp) WRITE(numout,*) ' Flux form advection : vorticity = Coriolis + metric term' |
---|
1346 | nrvm = 3 |
---|
1347 | ntot = 5 |
---|
1348 | ENDIF |
---|
1349 | |
---|
1350 | IF(lwp) THEN ! Print the choice |
---|
1351 | WRITE(numout,*) |
---|
1352 | IF( nvor == 0 ) WRITE(numout,*) ' vorticity scheme : energy conserving scheme' |
---|
1353 | IF( nvor == 1 ) WRITE(numout,*) ' vorticity scheme : enstrophy conserving scheme' |
---|
1354 | IF( nvor == 2 ) WRITE(numout,*) ' vorticity scheme : mixed enstrophy/energy conserving scheme' |
---|
1355 | IF( nvor == 3 ) WRITE(numout,*) ' vorticity scheme : energy and enstrophy conserving scheme' |
---|
1356 | IF( nvor == -1 ) WRITE(numout,*) ' esopa test: use all lateral physics options' |
---|
1357 | ENDIF |
---|
1358 | ! |
---|
1359 | END SUBROUTINE dyn_vor_init_tam |
---|
1360 | |
---|
1361 | SUBROUTINE dyn_vor_adj_tst( kumadt ) |
---|
1362 | !!----------------------------------------------------------------------- |
---|
1363 | !! |
---|
1364 | !! *** ROUTINE dyn_adv_adj_tst *** |
---|
1365 | !! |
---|
1366 | !! ** Purpose : Test the adjoint routine. |
---|
1367 | !! |
---|
1368 | !! ** Method : Verify the scalar product |
---|
1369 | !! |
---|
1370 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
1371 | !! |
---|
1372 | !! where L = tangent routine |
---|
1373 | !! L^T = adjoint routine |
---|
1374 | !! W = diagonal matrix of scale factors |
---|
1375 | !! dx = input perturbation (random field) |
---|
1376 | !! dy = L dx |
---|
1377 | !! |
---|
1378 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
1379 | !! |
---|
1380 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
1381 | !! |
---|
1382 | !! History : |
---|
1383 | !! ! 08-08 (A. Vidard) |
---|
1384 | !!----------------------------------------------------------------------- |
---|
1385 | !! * Modules used |
---|
1386 | |
---|
1387 | !! * Arguments |
---|
1388 | INTEGER, INTENT(IN) :: & |
---|
1389 | & kumadt ! Output unit |
---|
1390 | |
---|
1391 | INTEGER :: & |
---|
1392 | & ji, & ! dummy loop indices |
---|
1393 | & jj, & |
---|
1394 | & jk, & |
---|
1395 | & jt |
---|
1396 | INTEGER, DIMENSION(jpi,jpj) :: & |
---|
1397 | & iseed_2d ! 2D seed for the random number generator |
---|
1398 | |
---|
1399 | !! * Local declarations |
---|
1400 | REAL(KIND=wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
1401 | & zun_tlin, & ! Tangent input: now u-velocity |
---|
1402 | & zvn_tlin, & ! Tangent input: now v-velocity |
---|
1403 | & zrotn_tlin, & ! Tangent input: now rot |
---|
1404 | & zun_adout, & ! Adjoint output: now u-velocity |
---|
1405 | & zvn_adout, & ! Adjoint output: now v-velocity |
---|
1406 | & zrotn_adout, & ! Adjoint output: now rot |
---|
1407 | & zua_adout, & ! Tangent output: after u-velocity |
---|
1408 | & zva_adout, & ! Tangent output: after v-velocity |
---|
1409 | & zua_tlin, & ! Tangent output: after u-velocity |
---|
1410 | & zva_tlin, & ! Tangent output: after v-velocity |
---|
1411 | & zua_tlout, & ! Tangent output: after u-velocity |
---|
1412 | & zva_tlout, & ! Tangent output: after v-velocity |
---|
1413 | & zua_adin, & ! Tangent output: after u-velocity |
---|
1414 | & zva_adin, & ! Tangent output: after v-velocity |
---|
1415 | & zau, & ! 3D random field for rotn |
---|
1416 | & zav, & ! 3D random field for rotn |
---|
1417 | & znu, & ! 3D random field for u |
---|
1418 | & znv ! 3D random field for v |
---|
1419 | REAL(KIND=wp) :: & |
---|
1420 | & zsp1, & ! scalar product involving the tangent routine |
---|
1421 | & zsp1_1, & ! scalar product components |
---|
1422 | & zsp1_2, & |
---|
1423 | & zsp2, & ! scalar product involving the adjoint routine |
---|
1424 | & zsp2_1, & ! scalar product components |
---|
1425 | & zsp2_2, & |
---|
1426 | & zsp2_3, & |
---|
1427 | & zsp2_4, & |
---|
1428 | & zsp2_5 |
---|
1429 | CHARACTER(LEN=14) :: cl_name |
---|
1430 | |
---|
1431 | ! Allocate memory |
---|
1432 | |
---|
1433 | ALLOCATE( & |
---|
1434 | & zun_tlin(jpi,jpj,jpk), & |
---|
1435 | & zvn_tlin(jpi,jpj,jpk), & |
---|
1436 | & zrotn_tlin(jpi,jpj,jpk), & |
---|
1437 | & zun_adout(jpi,jpj,jpk), & |
---|
1438 | & zvn_adout(jpi,jpj,jpk), & |
---|
1439 | & zrotn_adout(jpi,jpj,jpk), & |
---|
1440 | & zua_adout(jpi,jpj,jpk), & |
---|
1441 | & zva_adout(jpi,jpj,jpk), & |
---|
1442 | & zua_tlin(jpi,jpj,jpk), & |
---|
1443 | & zva_tlin(jpi,jpj,jpk), & |
---|
1444 | & zua_tlout(jpi,jpj,jpk), & |
---|
1445 | & zva_tlout(jpi,jpj,jpk), & |
---|
1446 | & zua_adin(jpi,jpj,jpk), & |
---|
1447 | & zva_adin(jpi,jpj,jpk), & |
---|
1448 | & zau(jpi,jpj,jpk), & |
---|
1449 | & zav(jpi,jpj,jpk), & |
---|
1450 | & znu(jpi,jpj,jpk), & |
---|
1451 | & znv(jpi,jpj,jpk) & |
---|
1452 | & ) |
---|
1453 | |
---|
1454 | ! init ntot parameter |
---|
1455 | CALL dyn_vor_init_tam ! initialisation & control of options |
---|
1456 | |
---|
1457 | DO jt = 1, 2 |
---|
1458 | IF (jt == 1) nvor=1 ! enstrophy conserving scheme |
---|
1459 | IF (jt == 2) nvor=3 ! energy and enstrophy conserving scheme |
---|
1460 | |
---|
1461 | ! Initialize rotn |
---|
1462 | !AV: it calls cla_init the tries to reallocate already allocated arrays...nasty |
---|
1463 | !AV CALL div_cur ( nit000 ) |
---|
1464 | |
---|
1465 | !================================================================== |
---|
1466 | ! 1) dx = ( un_tl, vn_tl, hdivn_tl ) and |
---|
1467 | ! dy = ( hdivb_tl, hdivn_tl ) |
---|
1468 | !================================================================== |
---|
1469 | |
---|
1470 | !-------------------------------------------------------------------- |
---|
1471 | ! Reset the tangent and adjoint variables |
---|
1472 | !-------------------------------------------------------------------- |
---|
1473 | |
---|
1474 | zun_tlin(:,:,:) = 0.0_wp |
---|
1475 | zvn_tlin(:,:,:) = 0.0_wp |
---|
1476 | zrotn_tlin(:,:,:) = 0.0_wp |
---|
1477 | zun_adout(:,:,:) = 0.0_wp |
---|
1478 | zvn_adout(:,:,:) = 0.0_wp |
---|
1479 | zrotn_adout(:,:,:) = 0.0_wp |
---|
1480 | zua_tlout(:,:,:) = 0.0_wp |
---|
1481 | zva_tlout(:,:,:) = 0.0_wp |
---|
1482 | zua_adin(:,:,:) = 0.0_wp |
---|
1483 | zva_adin(:,:,:) = 0.0_wp |
---|
1484 | zua_adout(:,:,:) = 0.0_wp |
---|
1485 | zva_adout(:,:,:) = 0.0_wp |
---|
1486 | zua_tlin(:,:,:) = 0.0_wp |
---|
1487 | zva_tlin(:,:,:) = 0.0_wp |
---|
1488 | znu(:,:,:) = 0.0_wp |
---|
1489 | znv(:,:,:) = 0.0_wp |
---|
1490 | zau(:,:,:) = 0.0_wp |
---|
1491 | zav(:,:,:) = 0.0_wp |
---|
1492 | |
---|
1493 | |
---|
1494 | un_tl(:,:,:) = 0.0_wp |
---|
1495 | vn_tl(:,:,:) = 0.0_wp |
---|
1496 | ua_tl(:,:,:) = 0.0_wp |
---|
1497 | va_tl(:,:,:) = 0.0_wp |
---|
1498 | un_ad(:,:,:) = 0.0_wp |
---|
1499 | vn_ad(:,:,:) = 0.0_wp |
---|
1500 | ua_ad(:,:,:) = 0.0_wp |
---|
1501 | va_ad(:,:,:) = 0.0_wp |
---|
1502 | rotn_tl(:,:,:) = 0.0_wp |
---|
1503 | rotn_ad(:,:,:) = 0.0_wp |
---|
1504 | |
---|
1505 | !-------------------------------------------------------------------- |
---|
1506 | ! Initialize the tangent input with random noise: dx |
---|
1507 | !-------------------------------------------------------------------- |
---|
1508 | |
---|
1509 | CALL grid_random( znu, 'U', 0.0_wp, stdu ) |
---|
1510 | CALL grid_random( znv, 'V', 0.0_wp, stdv ) |
---|
1511 | CALL grid_random( zau, 'U', 0.0_wp, stdu ) |
---|
1512 | CALL grid_random( zav, 'V', 0.0_wp, stdv ) |
---|
1513 | |
---|
1514 | DO jk = 1, jpk |
---|
1515 | DO jj = nldj, nlej |
---|
1516 | DO ji = nldi, nlei |
---|
1517 | zun_tlin(ji,jj,jk) = znu(ji,jj,jk) |
---|
1518 | zvn_tlin(ji,jj,jk) = znv(ji,jj,jk) |
---|
1519 | zua_tlin(ji,jj,jk) = zau(ji,jj,jk) |
---|
1520 | zva_tlin(ji,jj,jk) = zav(ji,jj,jk) |
---|
1521 | END DO |
---|
1522 | END DO |
---|
1523 | END DO |
---|
1524 | un_tl(:,:,:) = zun_tlin(:,:,:) |
---|
1525 | vn_tl(:,:,:) = zvn_tlin(:,:,:) |
---|
1526 | ua_tl(:,:,:) = zua_tlin(:,:,:) |
---|
1527 | va_tl(:,:,:) = zva_tlin(:,:,:) |
---|
1528 | |
---|
1529 | ! initialize rotn_tl with noise |
---|
1530 | CALL div_cur_tan ( nit000 ) |
---|
1531 | |
---|
1532 | DO jk = 1, jpk |
---|
1533 | DO jj = nldj, nlej |
---|
1534 | DO ji = nldi, nlei |
---|
1535 | zrotn_tlin(ji,jj,jk) = rotn_tl(ji,jj,jk) |
---|
1536 | END DO |
---|
1537 | END DO |
---|
1538 | END DO |
---|
1539 | rotn_tl(:,:,:) = zrotn_tlin(:,:,:) |
---|
1540 | |
---|
1541 | |
---|
1542 | IF (nvor == 1 ) CALL vor_ens_tan( nit000, ntot, ua_tl, va_tl ) |
---|
1543 | IF (nvor == 3 ) CALL vor_een_tan( nit000, ntot, ua_tl, va_tl ) |
---|
1544 | zua_tlout(:,:,:) = ua_tl(:,:,:) |
---|
1545 | zva_tlout(:,:,:) = va_tl(:,:,:) |
---|
1546 | |
---|
1547 | !-------------------------------------------------------------------- |
---|
1548 | ! Initialize the adjoint variables: dy^* = W dy |
---|
1549 | !-------------------------------------------------------------------- |
---|
1550 | |
---|
1551 | DO jk = 1, jpk |
---|
1552 | DO jj = nldj, nlej |
---|
1553 | DO ji = nldi, nlei |
---|
1554 | zua_adin(ji,jj,jk) = zua_tlout(ji,jj,jk) & |
---|
1555 | & * e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) & |
---|
1556 | & * umask(ji,jj,jk) |
---|
1557 | zva_adin(ji,jj,jk) = zva_tlout(ji,jj,jk) & |
---|
1558 | & * e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) & |
---|
1559 | & * vmask(ji,jj,jk) |
---|
1560 | END DO |
---|
1561 | END DO |
---|
1562 | END DO |
---|
1563 | !-------------------------------------------------------------------- |
---|
1564 | ! Compute the scalar product: ( L dx )^T W dy |
---|
1565 | !-------------------------------------------------------------------- |
---|
1566 | |
---|
1567 | zsp1_1 = DOT_PRODUCT( zua_tlout, zua_adin ) |
---|
1568 | zsp1_2 = DOT_PRODUCT( zva_tlout, zva_adin ) |
---|
1569 | zsp1 = zsp1_1 + zsp1_2 |
---|
1570 | |
---|
1571 | !-------------------------------------------------------------------- |
---|
1572 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
1573 | !-------------------------------------------------------------------- |
---|
1574 | |
---|
1575 | ua_ad(:,:,:) = zua_adin(:,:,:) |
---|
1576 | va_ad(:,:,:) = zva_adin(:,:,:) |
---|
1577 | |
---|
1578 | |
---|
1579 | IF (nvor == 1 ) CALL vor_ens_adj( nitend, ntot, ua_ad, va_ad ) |
---|
1580 | IF (nvor == 3 ) CALL vor_een_adj( nitend, ntot, ua_ad, va_ad ) |
---|
1581 | zun_adout(:,:,:) = un_ad(:,:,:) |
---|
1582 | zvn_adout(:,:,:) = vn_ad(:,:,:) |
---|
1583 | zrotn_adout(:,:,:) = rotn_ad(:,:,:) |
---|
1584 | zua_adout(:,:,:) = ua_ad(:,:,:) |
---|
1585 | zva_adout(:,:,:) = va_ad(:,:,:) |
---|
1586 | |
---|
1587 | zsp2_1 = DOT_PRODUCT( zun_tlin, zun_adout ) |
---|
1588 | zsp2_2 = DOT_PRODUCT( zvn_tlin, zvn_adout ) |
---|
1589 | zsp2_3 = DOT_PRODUCT( zrotn_tlin, zrotn_adout ) |
---|
1590 | zsp2_4 = DOT_PRODUCT( zua_tlin, zua_adout ) |
---|
1591 | zsp2_5 = DOT_PRODUCT( zva_tlin, zva_adout ) |
---|
1592 | zsp2 = zsp2_1 + zsp2_2 + zsp2_3 + zsp2_4 + zsp2_5 |
---|
1593 | |
---|
1594 | ! Compare the scalar products |
---|
1595 | |
---|
1596 | ! 14 char:'12345678901234' |
---|
1597 | IF (nvor == 1 ) cl_name = 'dynvor_adj ens' |
---|
1598 | IF (nvor == 3 ) cl_name = 'dynvor_adj een' |
---|
1599 | |
---|
1600 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
1601 | END DO |
---|
1602 | |
---|
1603 | DEALLOCATE( & |
---|
1604 | & zun_tlin, & |
---|
1605 | & zvn_tlin, & |
---|
1606 | & zrotn_tlin, & |
---|
1607 | & zun_adout, & |
---|
1608 | & zvn_adout, & |
---|
1609 | & zrotn_adout, & |
---|
1610 | & zua_adout, & |
---|
1611 | & zva_adout, & |
---|
1612 | & zua_tlin, & |
---|
1613 | & zva_tlin, & |
---|
1614 | & zua_tlout, & |
---|
1615 | & zva_tlout, & |
---|
1616 | & zua_adin, & |
---|
1617 | & zva_adin, & |
---|
1618 | & zau, & |
---|
1619 | & zav, & |
---|
1620 | & znu, & |
---|
1621 | & znv & |
---|
1622 | & ) |
---|
1623 | END SUBROUTINE dyn_vor_adj_tst |
---|
1624 | !!============================================================================= |
---|
1625 | #endif |
---|
1626 | END MODULE dynvor_tam |
---|