1 | MODULE dynhpg |
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2 | !!====================================================================== |
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3 | !! *** MODULE dynhpg *** |
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4 | !! Ocean dynamics: hydrostatic pressure gradient trend |
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5 | !!====================================================================== |
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6 | !! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code |
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7 | !! 5.0 ! 1991-11 (G. Madec) |
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8 | !! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates |
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9 | !! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg |
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10 | !! 8.5 ! 2002-07 (G. Madec) F90: Free form and module |
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11 | !! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code |
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12 | !! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options |
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13 | !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot |
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14 | !! - ! 2005-11 (G. Madec) style & small optimisation |
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15 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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16 | !! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates |
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17 | !! ! (A. Coward) suppression of hel, wdj and rot options |
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18 | !! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity |
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19 | !!---------------------------------------------------------------------- |
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20 | |
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21 | !!---------------------------------------------------------------------- |
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22 | !! dyn_hpg : update the momentum trend with the now horizontal |
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23 | !! gradient of the hydrostatic pressure |
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24 | !! dyn_hpg_init : initialisation and control of options |
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25 | !! hpg_zco : z-coordinate scheme |
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26 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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27 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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28 | !! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf |
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29 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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30 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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31 | !!---------------------------------------------------------------------- |
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32 | USE oce ! ocean dynamics and tracers |
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33 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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34 | USE dom_oce ! ocean space and time domain |
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35 | USE wet_dry ! wetting and drying |
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36 | USE phycst ! physical constants |
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37 | USE trd_oce ! trends: ocean variables |
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38 | USE trddyn ! trend manager: dynamics |
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39 | !jc USE zpshde ! partial step: hor. derivative (zps_hde routine) |
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40 | ! |
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41 | USE in_out_manager ! I/O manager |
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42 | USE prtctl ! Print control |
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43 | USE lbclnk ! lateral boundary condition |
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44 | USE lib_mpp ! MPP library |
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45 | USE eosbn2 ! compute density |
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46 | USE wrk_nemo ! Memory Allocation |
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47 | USE timing ! Timing |
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48 | USE iom |
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49 | |
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50 | IMPLICIT NONE |
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51 | PRIVATE |
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52 | |
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53 | PUBLIC dyn_hpg ! routine called by step module |
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54 | PUBLIC dyn_hpg_init ! routine called by opa module |
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55 | |
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56 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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57 | LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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58 | LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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59 | LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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60 | LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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61 | LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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62 | LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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63 | |
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64 | INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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65 | |
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66 | !! * Substitutions |
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67 | # include "vectopt_loop_substitute.h90" |
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68 | !!---------------------------------------------------------------------- |
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69 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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70 | !! $Id$ |
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71 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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72 | !!---------------------------------------------------------------------- |
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73 | CONTAINS |
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74 | |
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75 | SUBROUTINE dyn_hpg( kt ) |
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76 | !!--------------------------------------------------------------------- |
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77 | !! *** ROUTINE dyn_hpg *** |
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78 | !! |
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79 | !! ** Method : Call the hydrostatic pressure gradient routine |
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80 | !! using the scheme defined in the namelist |
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81 | !! |
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82 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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83 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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84 | !!---------------------------------------------------------------------- |
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85 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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86 | INTEGER :: jk, jj, ji |
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87 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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88 | !!---------------------------------------------------------------------- |
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89 | ! |
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90 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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91 | ! |
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92 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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93 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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94 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
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95 | DO jk = 1, jpk |
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96 | DO jj = 1, jpj |
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97 | DO ji = 1, jpi |
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98 | ztrdu(ji,jj,jk) = ua(ji,jj,jk) |
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99 | ztrdv(ji,jj,jk) = va(ji,jj,jk) |
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100 | END DO |
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101 | END DO |
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102 | END DO |
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103 | ENDIF |
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104 | ! |
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105 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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106 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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107 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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108 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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109 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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110 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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111 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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112 | END SELECT |
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113 | ! |
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114 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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115 | !$OMP PARALLEL DO schedule(static) private(jk, jj, ji) |
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116 | DO jk = 1, jpk |
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117 | DO jj = 1, jpj |
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118 | DO ji = 1, jpi |
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119 | ztrdu(ji,jj,jk) = ua(ji,jj,jk) - ztrdu(ji,jj,jk) |
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120 | ztrdv(ji,jj,jk) = va(ji,jj,jk) - ztrdv(ji,jj,jk) |
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121 | END DO |
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122 | END DO |
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123 | END DO |
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124 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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125 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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126 | ENDIF |
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127 | ! |
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128 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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129 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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130 | ! |
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131 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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132 | ! |
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133 | END SUBROUTINE dyn_hpg |
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134 | |
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135 | |
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136 | SUBROUTINE dyn_hpg_init |
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137 | !!---------------------------------------------------------------------- |
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138 | !! *** ROUTINE dyn_hpg_init *** |
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139 | !! |
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140 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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141 | !! computation and consistency control |
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142 | !! |
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143 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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144 | !! with the type of vertical coordinate used (zco, zps, sco) |
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145 | !!---------------------------------------------------------------------- |
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146 | INTEGER :: ioptio = 0 ! temporary integer |
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147 | INTEGER :: ios ! Local integer output status for namelist read |
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148 | !! |
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149 | INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF |
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150 | REAL(wp) :: znad |
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151 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop, zrhd ! hypothesys on isf density |
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152 | REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF |
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153 | REAL(wp), POINTER, DIMENSION(:,:) :: ziceload ! density at bottom of ISF |
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154 | !! |
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155 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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156 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf |
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157 | !!---------------------------------------------------------------------- |
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158 | ! |
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159 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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160 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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161 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
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162 | ! |
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163 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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164 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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165 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
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166 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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167 | ! |
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168 | IF(lwp) THEN ! Control print |
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169 | WRITE(numout,*) |
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170 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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171 | WRITE(numout,*) '~~~~~~~~~~~~' |
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172 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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173 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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174 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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175 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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176 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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177 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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178 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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179 | ENDIF |
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180 | ! |
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181 | IF( ln_hpg_djc ) & |
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182 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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183 | & currently disabled (bugs under investigation). Please select & |
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184 | & either ln_hpg_sco or ln_hpg_prj instead') |
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185 | ! |
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186 | IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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187 | & CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', & |
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188 | & ' the standard jacobian formulation hpg_sco or ' , & |
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189 | & ' the pressure jacobian formulation hpg_prj' ) |
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190 | |
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191 | IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) & |
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192 | & CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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193 | IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) & |
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194 | & CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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195 | ! |
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196 | ! ! Set nhpg from ln_hpg_... flags |
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197 | IF( ln_hpg_zco ) nhpg = 0 |
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198 | IF( ln_hpg_zps ) nhpg = 1 |
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199 | IF( ln_hpg_sco ) nhpg = 2 |
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200 | IF( ln_hpg_djc ) nhpg = 3 |
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201 | IF( ln_hpg_prj ) nhpg = 4 |
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202 | IF( ln_hpg_isf ) nhpg = 5 |
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203 | ! |
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204 | ! ! Consistency check |
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205 | ioptio = 0 |
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206 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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207 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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208 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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209 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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210 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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211 | IF( ln_hpg_isf ) ioptio = ioptio + 1 |
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212 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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213 | ! |
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214 | ! initialisation of ice shelf load |
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215 | IF ( .NOT. ln_isfcav ) THEN |
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216 | !$OMP PARALLEL DO schedule(static) private(jj, ji) |
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217 | DO jj = 1, jpj |
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218 | DO ji = 1, jpi |
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219 | riceload(ji,jj)=0.0 |
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220 | END DO |
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221 | END DO |
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222 | END IF |
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223 | IF ( ln_isfcav ) THEN |
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224 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
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225 | CALL wrk_alloc( jpi,jpj,jpk, zrhd ) |
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226 | CALL wrk_alloc( jpi,jpj, zrhdtop_isf, ziceload) |
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227 | ! |
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228 | IF(lwp) WRITE(numout,*) |
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229 | IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf' |
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230 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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231 | |
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232 | ! To use density and not density anomaly |
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233 | znad=1._wp |
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234 | |
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235 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
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236 | !$OMP PARALLEL DO schedule(static) private(jj, ji) |
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237 | DO jj = 1, jpj |
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238 | DO ji = 1, jpi |
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239 | ztstop(ji,jj,1)=-1.9_wp |
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240 | ztstop(ji,jj,2)=34.4_wp |
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241 | END DO |
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242 | END DO |
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243 | |
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244 | ! compute density of the water displaced by the ice shelf |
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245 | DO jk = 1, jpk |
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246 | CALL eos(ztstop(:,:,:),gdept_n(:,:,jk),zrhd(:,:,jk)) |
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247 | END DO |
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248 | |
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249 | ! compute rhd at the ice/oce interface (ice shelf side) |
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250 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
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251 | |
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252 | ! Surface value + ice shelf gradient |
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253 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
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254 | ! divided by 2 later |
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255 | ziceload = 0._wp |
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256 | !$OMP PARALLEL |
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257 | !$OMP DO schedule(static) private(jj,ji,ikt,jk) |
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258 | DO jj = 1, jpj |
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259 | DO ji = 1, jpi |
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260 | ikt=mikt(ji,jj) |
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261 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
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262 | DO jk=2,ikt-1 |
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263 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) & |
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264 | & * (1._wp - tmask(ji,jj,jk)) |
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265 | END DO |
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266 | IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) & |
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267 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
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268 | END DO |
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269 | END DO |
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270 | !$OMP DO schedule(static) private(jj, ji) |
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271 | DO jj = 1, jpj |
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272 | DO ji = 1, jpi |
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273 | riceload(ji,jj)=ziceload(ji,jj) ! need to be saved for diaar5 |
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274 | END DO |
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275 | END DO |
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276 | !$OMP END PARALLEL |
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277 | |
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278 | CALL wrk_dealloc( jpi,jpj, 2, ztstop) |
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279 | CALL wrk_dealloc( jpi,jpj,jpk, zrhd ) |
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280 | CALL wrk_dealloc( jpi,jpj, zrhdtop_isf, ziceload) |
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281 | END IF |
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282 | ! |
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283 | END SUBROUTINE dyn_hpg_init |
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284 | |
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285 | |
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286 | SUBROUTINE hpg_zco( kt ) |
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287 | !!--------------------------------------------------------------------- |
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288 | !! *** ROUTINE hpg_zco *** |
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289 | !! |
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290 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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291 | !! The now hydrostatic pressure gradient at a given level, jk, |
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292 | !! is computed by taking the vertical integral of the in-situ |
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293 | !! density gradient along the model level from the suface to that |
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294 | !! level: zhpi = grav ..... |
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295 | !! zhpj = grav ..... |
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296 | !! add it to the general momentum trend (ua,va). |
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297 | !! ua = ua - 1/e1u * zhpi |
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298 | !! va = va - 1/e2v * zhpj |
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299 | !! |
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300 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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301 | !!---------------------------------------------------------------------- |
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302 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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303 | ! |
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304 | INTEGER :: ji, jj, jk ! dummy loop indices |
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305 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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306 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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307 | !!---------------------------------------------------------------------- |
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308 | ! |
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309 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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310 | ! |
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311 | IF( kt == nit000 ) THEN |
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312 | IF(lwp) WRITE(numout,*) |
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313 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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314 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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315 | ENDIF |
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316 | |
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317 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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318 | |
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319 | ! Surface value |
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320 | !$OMP PARALLEL |
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321 | !$OMP DO schedule(static) private(ji,jj, zcoef1) |
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322 | DO jj = 2, jpjm1 |
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323 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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324 | zcoef1 = zcoef0 * e3w_n(ji,jj,1) |
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325 | ! hydrostatic pressure gradient |
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326 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
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327 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
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328 | ! add to the general momentum trend |
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329 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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330 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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331 | END DO |
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332 | END DO |
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333 | |
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334 | ! |
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335 | ! interior value (2=<jk=<jpkm1) |
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336 | DO jk = 2, jpkm1 |
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337 | !$OMP DO schedule(static) private(ji,jj, zcoef1) |
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338 | DO jj = 2, jpjm1 |
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339 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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340 | zcoef1 = zcoef0 * e3w_n(ji,jj,jk) |
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341 | ! hydrostatic pressure gradient |
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342 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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343 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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344 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
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345 | |
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346 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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347 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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348 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
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349 | ! add to the general momentum trend |
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350 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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351 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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352 | END DO |
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353 | END DO |
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354 | !$OMP END DO NOWAIT |
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355 | END DO |
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356 | !$OMP END PARALLEL |
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357 | ! |
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358 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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359 | ! |
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360 | END SUBROUTINE hpg_zco |
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361 | |
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362 | |
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363 | SUBROUTINE hpg_zps( kt ) |
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364 | !!--------------------------------------------------------------------- |
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365 | !! *** ROUTINE hpg_zps *** |
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366 | !! |
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367 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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368 | !! |
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369 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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370 | !!---------------------------------------------------------------------- |
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371 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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372 | !! |
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373 | INTEGER :: ji, jj, jk ! dummy loop indices |
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374 | INTEGER :: iku, ikv ! temporary integers |
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375 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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376 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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377 | !!---------------------------------------------------------------------- |
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378 | ! |
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379 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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380 | ! |
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381 | IF( kt == nit000 ) THEN |
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382 | IF(lwp) WRITE(numout,*) |
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383 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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384 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
---|
385 | ENDIF |
---|
386 | |
---|
387 | ! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level |
---|
388 | !jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv ) |
---|
389 | |
---|
390 | ! Local constant initialization |
---|
391 | zcoef0 = - grav * 0.5_wp |
---|
392 | |
---|
393 | ! Surface value (also valid in partial step case) |
---|
394 | !$OMP PARALLEL |
---|
395 | !$OMP DO schedule(static) private(ji,jj,zcoef1) |
---|
396 | DO jj = 2, jpjm1 |
---|
397 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
398 | zcoef1 = zcoef0 * e3w_n(ji,jj,1) |
---|
399 | ! hydrostatic pressure gradient |
---|
400 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
401 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
402 | ! add to the general momentum trend |
---|
403 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
404 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
405 | END DO |
---|
406 | END DO |
---|
407 | |
---|
408 | ! interior value (2=<jk=<jpkm1) |
---|
409 | DO jk = 2, jpkm1 |
---|
410 | !$OMP DO schedule(static) private(ji,jj, zcoef1) |
---|
411 | DO jj = 2, jpjm1 |
---|
412 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
413 | zcoef1 = zcoef0 * e3w_n(ji,jj,jk) |
---|
414 | ! hydrostatic pressure gradient |
---|
415 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
416 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
417 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
---|
418 | |
---|
419 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
420 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
421 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
---|
422 | ! add to the general momentum trend |
---|
423 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
424 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
425 | END DO |
---|
426 | END DO |
---|
427 | END DO |
---|
428 | |
---|
429 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
---|
430 | !$OMP DO schedule(static) private(ji,jj,iku,ikv,zcoef2,zcoef3) |
---|
431 | DO jj = 2, jpjm1 |
---|
432 | DO ji = 2, jpim1 |
---|
433 | iku = mbku(ji,jj) |
---|
434 | ikv = mbkv(ji,jj) |
---|
435 | zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) ) |
---|
436 | zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) ) |
---|
437 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
438 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
439 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
440 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj) |
---|
441 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
442 | ENDIF |
---|
443 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
444 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
445 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
446 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj) |
---|
447 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
448 | ENDIF |
---|
449 | END DO |
---|
450 | END DO |
---|
451 | !$OMP END PARALLEL |
---|
452 | ! |
---|
453 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
454 | ! |
---|
455 | END SUBROUTINE hpg_zps |
---|
456 | |
---|
457 | |
---|
458 | SUBROUTINE hpg_sco( kt ) |
---|
459 | !!--------------------------------------------------------------------- |
---|
460 | !! *** ROUTINE hpg_sco *** |
---|
461 | !! |
---|
462 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
463 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
464 | !! is computed by taking the vertical integral of the in-situ |
---|
465 | !! density gradient along the model level from the suface to that |
---|
466 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
467 | !! to the horizontal pressure gradient : |
---|
468 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
469 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
470 | !! add it to the general momentum trend (ua,va). |
---|
471 | !! ua = ua - 1/e1u * zhpi |
---|
472 | !! va = va - 1/e2v * zhpj |
---|
473 | !! |
---|
474 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
475 | !!---------------------------------------------------------------------- |
---|
476 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
477 | !! |
---|
478 | INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices |
---|
479 | REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars |
---|
480 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
481 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
482 | REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter |
---|
483 | !!---------------------------------------------------------------------- |
---|
484 | ! |
---|
485 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
486 | IF( ln_wd ) CALL wrk_alloc( jpi,jpj, zcpx, zcpy ) |
---|
487 | ! |
---|
488 | IF( kt == nit000 ) THEN |
---|
489 | IF(lwp) WRITE(numout,*) |
---|
490 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
491 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
492 | ENDIF |
---|
493 | ! |
---|
494 | zcoef0 = - grav * 0.5_wp |
---|
495 | IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly |
---|
496 | ELSE ; znad = 1._wp ! Variable volume: density |
---|
497 | ENDIF |
---|
498 | ! |
---|
499 | IF( ln_wd ) THEN |
---|
500 | DO jj = 2, jpjm1 |
---|
501 | DO ji = 2, jpim1 |
---|
502 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
503 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. & |
---|
504 | & MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) & |
---|
505 | & > rn_wdmin1 + rn_wdmin2 |
---|
506 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & |
---|
507 | & MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
508 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
509 | |
---|
510 | IF(ll_tmp1) THEN |
---|
511 | zcpx(ji,jj) = 1.0_wp |
---|
512 | ELSE IF(ll_tmp2) THEN |
---|
513 | ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here |
---|
514 | zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) & |
---|
515 | & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) |
---|
516 | ELSE |
---|
517 | zcpx(ji,jj) = 0._wp |
---|
518 | END IF |
---|
519 | |
---|
520 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
521 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. & |
---|
522 | & MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) & |
---|
523 | & > rn_wdmin1 + rn_wdmin2 |
---|
524 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & |
---|
525 | & MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
526 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
527 | |
---|
528 | IF(ll_tmp1) THEN |
---|
529 | zcpy(ji,jj) = 1.0_wp |
---|
530 | ELSE IF(ll_tmp2) THEN |
---|
531 | ! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here |
---|
532 | zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) & |
---|
533 | & / (sshn(ji,jj+1) - sshn(ji,jj )) ) |
---|
534 | ELSE |
---|
535 | zcpy(ji,jj) = 0._wp |
---|
536 | END IF |
---|
537 | END DO |
---|
538 | END DO |
---|
539 | CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp ) |
---|
540 | END IF |
---|
541 | |
---|
542 | ! Surface value |
---|
543 | DO jj = 2, jpjm1 |
---|
544 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
545 | ! hydrostatic pressure gradient along s-surfaces |
---|
546 | zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
547 | & - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj) |
---|
548 | zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
549 | & - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj) |
---|
550 | ! s-coordinate pressure gradient correction |
---|
551 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
552 | & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
553 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
554 | & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
555 | |
---|
556 | |
---|
557 | IF( ln_wd ) THEN |
---|
558 | |
---|
559 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
560 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
561 | zuap = zuap * zcpx(ji,jj) |
---|
562 | zvap = zvap * zcpy(ji,jj) |
---|
563 | ENDIF |
---|
564 | |
---|
565 | ! add to the general momentum trend |
---|
566 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
567 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
568 | END DO |
---|
569 | END DO |
---|
570 | |
---|
571 | ! interior value (2=<jk=<jpkm1) |
---|
572 | DO jk = 2, jpkm1 |
---|
573 | DO jj = 2, jpjm1 |
---|
574 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
575 | ! hydrostatic pressure gradient along s-surfaces |
---|
576 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) & |
---|
577 | & * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
578 | & - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
579 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) & |
---|
580 | & * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
581 | & - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
582 | ! s-coordinate pressure gradient correction |
---|
583 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
584 | & * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj) |
---|
585 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
586 | & * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj) |
---|
587 | |
---|
588 | IF( ln_wd ) THEN |
---|
589 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
590 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
591 | zuap = zuap * zcpx(ji,jj) |
---|
592 | zvap = zvap * zcpy(ji,jj) |
---|
593 | ENDIF |
---|
594 | |
---|
595 | ! add to the general momentum trend |
---|
596 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
597 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
598 | END DO |
---|
599 | END DO |
---|
600 | END DO |
---|
601 | ! |
---|
602 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
603 | IF( ln_wd ) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy ) |
---|
604 | ! |
---|
605 | END SUBROUTINE hpg_sco |
---|
606 | |
---|
607 | |
---|
608 | SUBROUTINE hpg_isf( kt ) |
---|
609 | !!--------------------------------------------------------------------- |
---|
610 | !! *** ROUTINE hpg_isf *** |
---|
611 | !! |
---|
612 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
613 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
614 | !! is computed by taking the vertical integral of the in-situ |
---|
615 | !! density gradient along the model level from the suface to that |
---|
616 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
617 | !! to the horizontal pressure gradient : |
---|
618 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
619 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
620 | !! add it to the general momentum trend (ua,va). |
---|
621 | !! ua = ua - 1/e1u * zhpi |
---|
622 | !! va = va - 1/e2v * zhpj |
---|
623 | !! iceload is added and partial cell case are added to the top and bottom |
---|
624 | !! |
---|
625 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
626 | !!---------------------------------------------------------------------- |
---|
627 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
628 | !! |
---|
629 | INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
630 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
631 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
632 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
---|
633 | REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_oce |
---|
634 | !!---------------------------------------------------------------------- |
---|
635 | ! |
---|
636 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
---|
637 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj) |
---|
638 | CALL wrk_alloc( jpi,jpj, zrhdtop_oce ) |
---|
639 | ! |
---|
640 | ! Local constant initialization |
---|
641 | zcoef0 = - grav * 0.5_wp |
---|
642 | |
---|
643 | ! To use density and not density anomaly |
---|
644 | znad=1._wp |
---|
645 | |
---|
646 | ! iniitialised to 0. zhpi zhpi |
---|
647 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
---|
648 | |
---|
649 | ! compute rhd at the ice/oce interface (ocean side) |
---|
650 | ! usefull to reduce residual current in the test case ISOMIP with no melting |
---|
651 | DO ji=1,jpi |
---|
652 | DO jj=1,jpj |
---|
653 | ikt=mikt(ji,jj) |
---|
654 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
---|
655 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
---|
656 | END DO |
---|
657 | END DO |
---|
658 | CALL eos( ztstop, risfdep, zrhdtop_oce ) |
---|
659 | |
---|
660 | !================================================================================== |
---|
661 | !===== Compute surface value ===================================================== |
---|
662 | !================================================================================== |
---|
663 | DO jj = 2, jpjm1 |
---|
664 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
665 | ikt = mikt(ji,jj) |
---|
666 | iktp1i = mikt(ji+1,jj) |
---|
667 | iktp1j = mikt(ji,jj+1) |
---|
668 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
669 | ! we assume ISF is in isostatic equilibrium |
---|
670 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) & |
---|
671 | & * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) & |
---|
672 | & - 0.5_wp * e3w_n(ji,jj,ikt) & |
---|
673 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
674 | & + ( riceload(ji+1,jj) - riceload(ji,jj)) ) |
---|
675 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) & |
---|
676 | & * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) & |
---|
677 | & - 0.5_wp * e3w_n(ji,jj,ikt) & |
---|
678 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
679 | & + ( riceload(ji,jj+1) - riceload(ji,jj)) ) |
---|
680 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
681 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
682 | & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
683 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
684 | & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
685 | ! add to the general momentum trend |
---|
686 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
687 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
688 | END DO |
---|
689 | END DO |
---|
690 | !================================================================================== |
---|
691 | !===== Compute interior value ===================================================== |
---|
692 | !================================================================================== |
---|
693 | ! interior value (2=<jk=<jpkm1) |
---|
694 | DO jk = 2, jpkm1 |
---|
695 | DO jj = 2, jpjm1 |
---|
696 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
697 | ! hydrostatic pressure gradient along s-surfaces |
---|
698 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
699 | & * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) * wmask(ji+1,jj,jk) & |
---|
700 | & - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) * wmask(ji ,jj,jk) ) |
---|
701 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
702 | & * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) * wmask(ji,jj+1,jk) & |
---|
703 | & - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) * wmask(ji,jj ,jk) ) |
---|
704 | ! s-coordinate pressure gradient correction |
---|
705 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
706 | & * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj) |
---|
707 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
708 | & * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj) |
---|
709 | ! add to the general momentum trend |
---|
710 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
711 | va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk) |
---|
712 | END DO |
---|
713 | END DO |
---|
714 | END DO |
---|
715 | ! |
---|
716 | CALL wrk_dealloc( jpi,jpj,2 , ztstop) |
---|
717 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj) |
---|
718 | CALL wrk_dealloc( jpi,jpj , zrhdtop_oce ) |
---|
719 | ! |
---|
720 | END SUBROUTINE hpg_isf |
---|
721 | |
---|
722 | |
---|
723 | SUBROUTINE hpg_djc( kt ) |
---|
724 | !!--------------------------------------------------------------------- |
---|
725 | !! *** ROUTINE hpg_djc *** |
---|
726 | !! |
---|
727 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
728 | !! |
---|
729 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
730 | !!---------------------------------------------------------------------- |
---|
731 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
732 | !! |
---|
733 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
734 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
735 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
736 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
737 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
738 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
739 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
740 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
741 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
742 | REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter |
---|
743 | !!---------------------------------------------------------------------- |
---|
744 | ! |
---|
745 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
746 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
747 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
748 | IF( ln_wd ) CALL wrk_alloc( jpi,jpj, zcpx, zcpy ) |
---|
749 | ! |
---|
750 | ! |
---|
751 | IF( ln_wd ) THEN |
---|
752 | DO jj = 2, jpjm1 |
---|
753 | DO ji = 2, jpim1 |
---|
754 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
755 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. & |
---|
756 | & MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) & |
---|
757 | & > rn_wdmin1 + rn_wdmin2 |
---|
758 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & |
---|
759 | & MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
760 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
761 | |
---|
762 | IF(ll_tmp1) THEN |
---|
763 | zcpx(ji,jj) = 1.0_wp |
---|
764 | ELSE IF(ll_tmp2) THEN |
---|
765 | ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here |
---|
766 | zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) & |
---|
767 | & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) |
---|
768 | ELSE |
---|
769 | zcpx(ji,jj) = 0._wp |
---|
770 | END IF |
---|
771 | |
---|
772 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
773 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. & |
---|
774 | & MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) & |
---|
775 | & > rn_wdmin1 + rn_wdmin2 |
---|
776 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & |
---|
777 | & MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
778 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
779 | |
---|
780 | IF(ll_tmp1) THEN |
---|
781 | zcpy(ji,jj) = 1.0_wp |
---|
782 | ELSE IF(ll_tmp2) THEN |
---|
783 | ! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here |
---|
784 | zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) & |
---|
785 | & / (sshn(ji,jj+1) - sshn(ji,jj )) ) |
---|
786 | ELSE |
---|
787 | zcpy(ji,jj) = 0._wp |
---|
788 | END IF |
---|
789 | END DO |
---|
790 | END DO |
---|
791 | CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp ) |
---|
792 | END IF |
---|
793 | |
---|
794 | IF( kt == nit000 ) THEN |
---|
795 | IF(lwp) WRITE(numout,*) |
---|
796 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
797 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
798 | ENDIF |
---|
799 | |
---|
800 | ! Local constant initialization |
---|
801 | zcoef0 = - grav * 0.5_wp |
---|
802 | z1_10 = 1._wp / 10._wp |
---|
803 | z1_12 = 1._wp / 12._wp |
---|
804 | |
---|
805 | !---------------------------------------------------------------------------------------- |
---|
806 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
807 | !---------------------------------------------------------------------------------------- |
---|
808 | |
---|
809 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
810 | |
---|
811 | DO jk = 2, jpkm1 |
---|
812 | DO jj = 2, jpjm1 |
---|
813 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
814 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
815 | dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1) |
---|
816 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
817 | dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk ) |
---|
818 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
819 | dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk ) |
---|
820 | END DO |
---|
821 | END DO |
---|
822 | END DO |
---|
823 | |
---|
824 | !------------------------------------------------------------------------- |
---|
825 | ! compute harmonic averages using eq. 5.18 |
---|
826 | !------------------------------------------------------------------------- |
---|
827 | zep = 1.e-15 |
---|
828 | |
---|
829 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
830 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
831 | |
---|
832 | DO jk = 2, jpkm1 |
---|
833 | DO jj = 2, jpjm1 |
---|
834 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
835 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
836 | |
---|
837 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
838 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
839 | |
---|
840 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
841 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
842 | |
---|
843 | IF( cffw > zep) THEN |
---|
844 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
845 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
846 | ELSE |
---|
847 | drhow(ji,jj,jk) = 0._wp |
---|
848 | ENDIF |
---|
849 | |
---|
850 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
851 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
852 | |
---|
853 | IF( cffu > zep ) THEN |
---|
854 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
855 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
856 | ELSE |
---|
857 | drhou(ji,jj,jk ) = 0._wp |
---|
858 | ENDIF |
---|
859 | |
---|
860 | IF( cffx > zep ) THEN |
---|
861 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
862 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
863 | ELSE |
---|
864 | dzu(ji,jj,jk) = 0._wp |
---|
865 | ENDIF |
---|
866 | |
---|
867 | IF( cffv > zep ) THEN |
---|
868 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
869 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
870 | ELSE |
---|
871 | drhov(ji,jj,jk) = 0._wp |
---|
872 | ENDIF |
---|
873 | |
---|
874 | IF( cffy > zep ) THEN |
---|
875 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
876 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
877 | ELSE |
---|
878 | dzv(ji,jj,jk) = 0._wp |
---|
879 | ENDIF |
---|
880 | |
---|
881 | END DO |
---|
882 | END DO |
---|
883 | END DO |
---|
884 | |
---|
885 | !---------------------------------------------------------------------------------- |
---|
886 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
887 | !---------------------------------------------------------------------------------- |
---|
888 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
889 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
890 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
891 | |
---|
892 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
893 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
894 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
895 | |
---|
896 | |
---|
897 | !-------------------------------------------------------------- |
---|
898 | ! Upper half of top-most grid box, compute and store |
---|
899 | !------------------------------------------------------------- |
---|
900 | |
---|
901 | !!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified |
---|
902 | ! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
903 | |
---|
904 | DO jj = 2, jpjm1 |
---|
905 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
906 | rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) & |
---|
907 | & * ( rhd(ji,jj,1) & |
---|
908 | & + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) & |
---|
909 | & * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) & |
---|
910 | & / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) ) |
---|
911 | END DO |
---|
912 | END DO |
---|
913 | |
---|
914 | !!bug gm : here also, simplification is possible |
---|
915 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
916 | |
---|
917 | DO jk = 2, jpkm1 |
---|
918 | DO jj = 2, jpjm1 |
---|
919 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
920 | |
---|
921 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
922 | & * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) & |
---|
923 | & - grav * z1_10 * ( & |
---|
924 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
925 | & * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
926 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
927 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
928 | & ) |
---|
929 | |
---|
930 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
931 | & * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) & |
---|
932 | & - grav* z1_10 * ( & |
---|
933 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
934 | & * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
935 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
936 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
937 | & ) |
---|
938 | |
---|
939 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
940 | & * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) & |
---|
941 | & - grav* z1_10 * ( & |
---|
942 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
943 | & * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
944 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
945 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
946 | & ) |
---|
947 | |
---|
948 | END DO |
---|
949 | END DO |
---|
950 | END DO |
---|
951 | CALL lbc_lnk(rho_k,'W',1.) |
---|
952 | CALL lbc_lnk(rho_i,'U',1.) |
---|
953 | CALL lbc_lnk(rho_j,'V',1.) |
---|
954 | |
---|
955 | |
---|
956 | ! --------------- |
---|
957 | ! Surface value |
---|
958 | ! --------------- |
---|
959 | DO jj = 2, jpjm1 |
---|
960 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
961 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
962 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
963 | IF( ln_wd ) THEN |
---|
964 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
965 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
966 | ENDIF |
---|
967 | ! add to the general momentum trend |
---|
968 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
969 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
970 | END DO |
---|
971 | END DO |
---|
972 | |
---|
973 | ! ---------------- |
---|
974 | ! interior value (2=<jk=<jpkm1) |
---|
975 | ! ---------------- |
---|
976 | DO jk = 2, jpkm1 |
---|
977 | DO jj = 2, jpjm1 |
---|
978 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
979 | ! hydrostatic pressure gradient along s-surfaces |
---|
980 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
981 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
982 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj) |
---|
983 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
984 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
985 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj) |
---|
986 | IF( ln_wd ) THEN |
---|
987 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
988 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
989 | ENDIF |
---|
990 | ! add to the general momentum trend |
---|
991 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
992 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
993 | END DO |
---|
994 | END DO |
---|
995 | END DO |
---|
996 | ! |
---|
997 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
998 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
999 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
1000 | IF( ln_wd ) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy ) |
---|
1001 | ! |
---|
1002 | END SUBROUTINE hpg_djc |
---|
1003 | |
---|
1004 | |
---|
1005 | SUBROUTINE hpg_prj( kt ) |
---|
1006 | !!--------------------------------------------------------------------- |
---|
1007 | !! *** ROUTINE hpg_prj *** |
---|
1008 | !! |
---|
1009 | !! ** Method : s-coordinate case. |
---|
1010 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
1011 | !! based on the constrained cubic-spline interpolation for |
---|
1012 | !! all vertical coordinate systems |
---|
1013 | !! |
---|
1014 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
1015 | !!---------------------------------------------------------------------- |
---|
1016 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
1017 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
1018 | !! |
---|
1019 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
1020 | REAL(wp) :: zcoef0, znad ! local scalars |
---|
1021 | ! |
---|
1022 | !! The local variables for the correction term |
---|
1023 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
1024 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
1025 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
1026 | REAL(wp) :: zrhdt1 |
---|
1027 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
1028 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
1029 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
1030 | REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n |
---|
1031 | REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter |
---|
1032 | !!---------------------------------------------------------------------- |
---|
1033 | ! |
---|
1034 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
1035 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
1036 | CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
1037 | IF( ln_wd ) CALL wrk_alloc( jpi,jpj, zcpx, zcpy ) |
---|
1038 | ! |
---|
1039 | IF( kt == nit000 ) THEN |
---|
1040 | IF(lwp) WRITE(numout,*) |
---|
1041 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
1042 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
1043 | ENDIF |
---|
1044 | |
---|
1045 | ! Local constant initialization |
---|
1046 | zcoef0 = - grav |
---|
1047 | znad = 1._wp |
---|
1048 | IF( ln_linssh ) znad = 0._wp |
---|
1049 | |
---|
1050 | IF( ln_wd ) THEN |
---|
1051 | DO jj = 2, jpjm1 |
---|
1052 | DO ji = 2, jpim1 |
---|
1053 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
1054 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. & |
---|
1055 | & MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) & |
---|
1056 | & > rn_wdmin1 + rn_wdmin2 |
---|
1057 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & |
---|
1058 | & MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
1059 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
1060 | |
---|
1061 | IF(ll_tmp1) THEN |
---|
1062 | zcpx(ji,jj) = 1.0_wp |
---|
1063 | ELSE IF(ll_tmp2) THEN |
---|
1064 | ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here |
---|
1065 | zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) & |
---|
1066 | & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) |
---|
1067 | ELSE |
---|
1068 | zcpx(ji,jj) = 0._wp |
---|
1069 | END IF |
---|
1070 | |
---|
1071 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
1072 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. & |
---|
1073 | & MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) & |
---|
1074 | & > rn_wdmin1 + rn_wdmin2 |
---|
1075 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & |
---|
1076 | & MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
1077 | & MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
1078 | |
---|
1079 | IF(ll_tmp1) THEN |
---|
1080 | zcpy(ji,jj) = 1.0_wp |
---|
1081 | ELSE IF(ll_tmp2) THEN |
---|
1082 | ! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here |
---|
1083 | zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) & |
---|
1084 | & / (sshn(ji,jj+1) - sshn(ji,jj )) ) |
---|
1085 | ELSE |
---|
1086 | zcpy(ji,jj) = 0._wp |
---|
1087 | END IF |
---|
1088 | END DO |
---|
1089 | END DO |
---|
1090 | CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp ) |
---|
1091 | END IF |
---|
1092 | |
---|
1093 | ! Clean 3-D work arrays |
---|
1094 | zhpi(:,:,:) = 0._wp |
---|
1095 | zrhh(:,:,:) = rhd(:,:,:) |
---|
1096 | |
---|
1097 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
1098 | DO jj = 1, jpj |
---|
1099 | DO ji = 1, jpi |
---|
1100 | jk = mbkt(ji,jj)+1 |
---|
1101 | IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp |
---|
1102 | ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk) |
---|
1103 | ELSEIF( jk < jpkm1 ) THEN |
---|
1104 | DO jkk = jk+1, jpk |
---|
1105 | zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), & |
---|
1106 | & gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
1107 | END DO |
---|
1108 | ENDIF |
---|
1109 | END DO |
---|
1110 | END DO |
---|
1111 | |
---|
1112 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
1113 | DO jj = 1, jpj |
---|
1114 | DO ji = 1, jpi |
---|
1115 | zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad |
---|
1116 | END DO |
---|
1117 | END DO |
---|
1118 | |
---|
1119 | DO jk = 2, jpk |
---|
1120 | DO jj = 1, jpj |
---|
1121 | DO ji = 1, jpi |
---|
1122 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk) |
---|
1123 | END DO |
---|
1124 | END DO |
---|
1125 | END DO |
---|
1126 | |
---|
1127 | fsp(:,:,:) = zrhh (:,:,:) |
---|
1128 | xsp(:,:,:) = zdept(:,:,:) |
---|
1129 | |
---|
1130 | ! Construct the vertical density profile with the |
---|
1131 | ! constrained cubic spline interpolation |
---|
1132 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
1133 | CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
1134 | |
---|
1135 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
1136 | DO jj = 2, jpj |
---|
1137 | DO ji = 2, jpi |
---|
1138 | zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), & |
---|
1139 | & csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1) |
---|
1140 | |
---|
1141 | ! assuming linear profile across the top half surface layer |
---|
1142 | zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1 |
---|
1143 | END DO |
---|
1144 | END DO |
---|
1145 | |
---|
1146 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
1147 | DO jk = 2, jpkm1 |
---|
1148 | DO jj = 2, jpj |
---|
1149 | DO ji = 2, jpi |
---|
1150 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
1151 | & integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), & |
---|
1152 | & asp (ji,jj,jk-1), bsp (ji,jj,jk-1), & |
---|
1153 | & csp (ji,jj,jk-1), dsp (ji,jj,jk-1) ) |
---|
1154 | END DO |
---|
1155 | END DO |
---|
1156 | END DO |
---|
1157 | |
---|
1158 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
1159 | |
---|
1160 | ! Prepare zsshu_n and zsshv_n |
---|
1161 | DO jj = 2, jpjm1 |
---|
1162 | DO ji = 2, jpim1 |
---|
1163 | !!gm BUG ? if it is ssh at u- & v-point then it should be: |
---|
1164 | ! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * & |
---|
1165 | ! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
1166 | ! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * & |
---|
1167 | ! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
1168 | !!gm not this: |
---|
1169 | zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
1170 | & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
1171 | zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
1172 | & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
1173 | END DO |
---|
1174 | END DO |
---|
1175 | |
---|
1176 | CALL lbc_lnk (zsshu_n, 'U', 1.) |
---|
1177 | CALL lbc_lnk (zsshv_n, 'V', 1.) |
---|
1178 | |
---|
1179 | DO jj = 2, jpjm1 |
---|
1180 | DO ji = 2, jpim1 |
---|
1181 | zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
1182 | zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
1183 | END DO |
---|
1184 | END DO |
---|
1185 | |
---|
1186 | DO jk = 2, jpkm1 |
---|
1187 | DO jj = 2, jpjm1 |
---|
1188 | DO ji = 2, jpim1 |
---|
1189 | zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk) |
---|
1190 | zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk) |
---|
1191 | END DO |
---|
1192 | END DO |
---|
1193 | END DO |
---|
1194 | |
---|
1195 | DO jk = 1, jpkm1 |
---|
1196 | DO jj = 2, jpjm1 |
---|
1197 | DO ji = 2, jpim1 |
---|
1198 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk) |
---|
1199 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk) |
---|
1200 | END DO |
---|
1201 | END DO |
---|
1202 | END DO |
---|
1203 | |
---|
1204 | DO jk = 1, jpkm1 |
---|
1205 | DO jj = 2, jpjm1 |
---|
1206 | DO ji = 2, jpim1 |
---|
1207 | zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
1208 | zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
1209 | zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
1210 | zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
1211 | END DO |
---|
1212 | END DO |
---|
1213 | END DO |
---|
1214 | |
---|
1215 | |
---|
1216 | DO jk = 1, jpkm1 |
---|
1217 | DO jj = 2, jpjm1 |
---|
1218 | DO ji = 2, jpim1 |
---|
1219 | zpwes = 0._wp; zpwed = 0._wp |
---|
1220 | zpnss = 0._wp; zpnsd = 0._wp |
---|
1221 | zuijk = zu(ji,jj,jk) |
---|
1222 | zvijk = zv(ji,jj,jk) |
---|
1223 | |
---|
1224 | !!!!! for u equation |
---|
1225 | IF( jk <= mbku(ji,jj) ) THEN |
---|
1226 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
1227 | jis = ji + 1; jid = ji |
---|
1228 | ELSE |
---|
1229 | jis = ji; jid = ji +1 |
---|
1230 | ENDIF |
---|
1231 | |
---|
1232 | ! integrate the pressure on the shallow side |
---|
1233 | jk1 = jk |
---|
1234 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
1235 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
1236 | zuijk = -zdept(jis,jj,jk1) |
---|
1237 | EXIT |
---|
1238 | ENDIF |
---|
1239 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
1240 | zpwes = zpwes + & |
---|
1241 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
1242 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
1243 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
1244 | jk1 = jk1 + 1 |
---|
1245 | END DO |
---|
1246 | |
---|
1247 | ! integrate the pressure on the deep side |
---|
1248 | jk1 = jk |
---|
1249 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
1250 | IF( jk1 == 1 ) THEN |
---|
1251 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
1252 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
1253 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
1254 | dsp(jid,jj,1)) * zdeps |
---|
1255 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
1256 | EXIT |
---|
1257 | ENDIF |
---|
1258 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
1259 | zpwed = zpwed + & |
---|
1260 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
1261 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
1262 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
1263 | jk1 = jk1 - 1 |
---|
1264 | END DO |
---|
1265 | |
---|
1266 | ! update the momentum trends in u direction |
---|
1267 | |
---|
1268 | zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) ) |
---|
1269 | IF( .NOT.ln_linssh ) THEN |
---|
1270 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * & |
---|
1271 | & ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
1272 | ELSE |
---|
1273 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
1274 | ENDIF |
---|
1275 | IF( ln_wd ) THEN |
---|
1276 | zdpdx1 = zdpdx1 * zcpx(ji,jj) |
---|
1277 | zdpdx2 = zdpdx2 * zcpx(ji,jj) |
---|
1278 | ENDIF |
---|
1279 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk) |
---|
1280 | ENDIF |
---|
1281 | |
---|
1282 | !!!!! for v equation |
---|
1283 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
1284 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
1285 | jjs = jj + 1; jjd = jj |
---|
1286 | ELSE |
---|
1287 | jjs = jj ; jjd = jj + 1 |
---|
1288 | ENDIF |
---|
1289 | |
---|
1290 | ! integrate the pressure on the shallow side |
---|
1291 | jk1 = jk |
---|
1292 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
1293 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
1294 | zvijk = -zdept(ji,jjs,jk1) |
---|
1295 | EXIT |
---|
1296 | ENDIF |
---|
1297 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
1298 | zpnss = zpnss + & |
---|
1299 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
1300 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
1301 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
1302 | jk1 = jk1 + 1 |
---|
1303 | END DO |
---|
1304 | |
---|
1305 | ! integrate the pressure on the deep side |
---|
1306 | jk1 = jk |
---|
1307 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
1308 | IF( jk1 == 1 ) THEN |
---|
1309 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
1310 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
1311 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
1312 | dsp(ji,jjd,1) ) * zdeps |
---|
1313 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
1314 | EXIT |
---|
1315 | ENDIF |
---|
1316 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
1317 | zpnsd = zpnsd + & |
---|
1318 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
1319 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
1320 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
1321 | jk1 = jk1 - 1 |
---|
1322 | END DO |
---|
1323 | |
---|
1324 | |
---|
1325 | ! update the momentum trends in v direction |
---|
1326 | |
---|
1327 | zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) ) |
---|
1328 | IF( .NOT.ln_linssh ) THEN |
---|
1329 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * & |
---|
1330 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
1331 | ELSE |
---|
1332 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
1333 | ENDIF |
---|
1334 | IF( ln_wd ) THEN |
---|
1335 | zdpdy1 = zdpdy1 * zcpy(ji,jj) |
---|
1336 | zdpdy2 = zdpdy2 * zcpy(ji,jj) |
---|
1337 | ENDIF |
---|
1338 | |
---|
1339 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk) |
---|
1340 | ENDIF |
---|
1341 | ! |
---|
1342 | END DO |
---|
1343 | END DO |
---|
1344 | END DO |
---|
1345 | ! |
---|
1346 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
1347 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
1348 | CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
1349 | IF( ln_wd ) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy ) |
---|
1350 | ! |
---|
1351 | END SUBROUTINE hpg_prj |
---|
1352 | |
---|
1353 | |
---|
1354 | SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
1355 | !!---------------------------------------------------------------------- |
---|
1356 | !! *** ROUTINE cspline *** |
---|
1357 | !! |
---|
1358 | !! ** Purpose : constrained cubic spline interpolation |
---|
1359 | !! |
---|
1360 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
1361 | !! |
---|
1362 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
1363 | !!---------------------------------------------------------------------- |
---|
1364 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate |
---|
1365 | REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function |
---|
1366 | INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear |
---|
1367 | ! |
---|
1368 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1369 | INTEGER :: jpi, jpj, jpkm1 |
---|
1370 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
1371 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
1372 | REAL(wp) :: zdf(size(fsp,3)) |
---|
1373 | !!---------------------------------------------------------------------- |
---|
1374 | ! |
---|
1375 | !!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!! |
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1376 | jpi = size(fsp,1) |
---|
1377 | jpj = size(fsp,2) |
---|
1378 | jpkm1 = size(fsp,3) - 1 |
---|
1379 | ! |
---|
1380 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
1381 | DO ji = 1, jpi |
---|
1382 | DO jj = 1, jpj |
---|
1383 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
1384 | ! DO jk = 2, jpkm1-1 |
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1385 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
1386 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1387 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
1388 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
1389 | ! |
---|
1390 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
1391 | ! |
---|
1392 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
1393 | ! zdf(jk) = 0._wp |
---|
1394 | ! ELSE |
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1395 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
1396 | ! ENDIF |
---|
1397 | ! END DO |
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1398 | |
---|
1399 | !!Simply geometric average |
---|
1400 | DO jk = 2, jpkm1-1 |
---|
1401 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
1402 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
1403 | |
---|
1404 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
1405 | zdf(jk) = 0._wp |
---|
1406 | ELSE |
---|
1407 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
1408 | ENDIF |
---|
1409 | END DO |
---|
1410 | |
---|
1411 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
1412 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
1413 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
1414 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1) |
---|
1415 | |
---|
1416 | DO jk = 1, jpkm1 - 1 |
---|
1417 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1418 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
1419 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
1420 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
1421 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
1422 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
1423 | |
---|
1424 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
1425 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
1426 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
1427 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
1428 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
1429 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
1430 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
1431 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
1432 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
1433 | END DO |
---|
1434 | END DO |
---|
1435 | END DO |
---|
1436 | |
---|
1437 | ELSEIF ( polynomial_type == 2 ) THEN ! Linear |
---|
1438 | DO ji = 1, jpi |
---|
1439 | DO jj = 1, jpj |
---|
1440 | DO jk = 1, jpkm1-1 |
---|
1441 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1442 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
1443 | |
---|
1444 | dsp(ji,jj,jk) = 0._wp |
---|
1445 | csp(ji,jj,jk) = 0._wp |
---|
1446 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
1447 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
1448 | END DO |
---|
1449 | END DO |
---|
1450 | END DO |
---|
1451 | |
---|
1452 | ELSE |
---|
1453 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
1454 | ENDIF |
---|
1455 | |
---|
1456 | END SUBROUTINE cspline |
---|
1457 | |
---|
1458 | |
---|
1459 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
1460 | !!---------------------------------------------------------------------- |
---|
1461 | !! *** ROUTINE interp1 *** |
---|
1462 | !! |
---|
1463 | !! ** Purpose : 1-d linear interpolation |
---|
1464 | !! |
---|
1465 | !! ** Method : interpolation is straight forward |
---|
1466 | !! extrapolation is also permitted (no value limit) |
---|
1467 | !!---------------------------------------------------------------------- |
---|
1468 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
1469 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
1470 | REAL(wp) :: zdeltx |
---|
1471 | !!---------------------------------------------------------------------- |
---|
1472 | ! |
---|
1473 | zdeltx = xr - xl |
---|
1474 | IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN |
---|
1475 | f = 0.5_wp * (fl + fr) |
---|
1476 | ELSE |
---|
1477 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
1478 | ENDIF |
---|
1479 | ! |
---|
1480 | END FUNCTION interp1 |
---|
1481 | |
---|
1482 | |
---|
1483 | FUNCTION interp2( x, a, b, c, d ) RESULT(f) |
---|
1484 | !!---------------------------------------------------------------------- |
---|
1485 | !! *** ROUTINE interp1 *** |
---|
1486 | !! |
---|
1487 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
1488 | !! |
---|
1489 | !! ** Method : cubic spline interpolation |
---|
1490 | !! |
---|
1491 | !!---------------------------------------------------------------------- |
---|
1492 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
1493 | REAL(wp) :: f ! value from the interpolation |
---|
1494 | !!---------------------------------------------------------------------- |
---|
1495 | ! |
---|
1496 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
1497 | ! |
---|
1498 | END FUNCTION interp2 |
---|
1499 | |
---|
1500 | |
---|
1501 | FUNCTION interp3( x, a, b, c, d ) RESULT(f) |
---|
1502 | !!---------------------------------------------------------------------- |
---|
1503 | !! *** ROUTINE interp1 *** |
---|
1504 | !! |
---|
1505 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
1506 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
1507 | !! |
---|
1508 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
1509 | !! |
---|
1510 | !!---------------------------------------------------------------------- |
---|
1511 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
1512 | REAL(wp) :: f ! value from the interpolation |
---|
1513 | !!---------------------------------------------------------------------- |
---|
1514 | ! |
---|
1515 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
1516 | ! |
---|
1517 | END FUNCTION interp3 |
---|
1518 | |
---|
1519 | |
---|
1520 | FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f) |
---|
1521 | !!---------------------------------------------------------------------- |
---|
1522 | !! *** ROUTINE interp1 *** |
---|
1523 | !! |
---|
1524 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
1525 | !! |
---|
1526 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
1527 | !! |
---|
1528 | !!---------------------------------------------------------------------- |
---|
1529 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
1530 | REAL(wp) :: za1, za2, za3 |
---|
1531 | REAL(wp) :: f ! integration result |
---|
1532 | !!---------------------------------------------------------------------- |
---|
1533 | ! |
---|
1534 | za1 = 0.5_wp * b |
---|
1535 | za2 = c / 3.0_wp |
---|
1536 | za3 = 0.25_wp * d |
---|
1537 | ! |
---|
1538 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
1539 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
1540 | ! |
---|
1541 | END FUNCTION integ_spline |
---|
1542 | |
---|
1543 | !!====================================================================== |
---|
1544 | END MODULE dynhpg |
---|
1545 | |
---|