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 | !!---------------------------------------------------------------------- |
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17 | |
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18 | !!---------------------------------------------------------------------- |
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19 | !! dyn_hpg : update the momentum trend with the now horizontal |
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20 | !! gradient of the hydrostatic pressure |
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21 | !! dyn_hpg_init : initialisation and control of options |
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22 | !! hpg_zco : z-coordinate scheme |
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23 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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24 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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25 | !! hpg_hel : s-coordinate (helsinki modification) |
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26 | !! hpg_wdj : s-coordinate (weighted density jacobian) |
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27 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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28 | !! hpg_rot : s-coordinate (ROTated axes scheme) |
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29 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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30 | !!---------------------------------------------------------------------- |
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31 | USE oce ! ocean dynamics and tracers |
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32 | USE dom_oce ! ocean space and time domain |
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33 | USE phycst ! physical constants |
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34 | USE trdmod ! ocean dynamics trends |
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35 | USE trdmod_oce ! ocean variables trends |
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36 | USE in_out_manager ! I/O manager |
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37 | USE prtctl ! Print control |
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38 | USE lbclnk ! lateral boundary condition |
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39 | USE lib_mpp ! MPP library |
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40 | |
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41 | IMPLICIT NONE |
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42 | PRIVATE |
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43 | |
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44 | PUBLIC dyn_hpg ! routine called by step module |
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45 | PUBLIC dyn_hpg_init ! routine called by opa module |
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46 | |
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47 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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48 | LOGICAL , PUBLIC :: ln_hpg_zco = .TRUE. !: z-coordinate - full steps |
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49 | LOGICAL , PUBLIC :: ln_hpg_zps = .FALSE. !: z-coordinate - partial steps (interpolation) |
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50 | LOGICAL , PUBLIC :: ln_hpg_sco = .FALSE. !: s-coordinate (standard jacobian formulation) |
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51 | LOGICAL , PUBLIC :: ln_hpg_hel = .FALSE. !: s-coordinate (helsinki modification) |
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52 | LOGICAL , PUBLIC :: ln_hpg_wdj = .FALSE. !: s-coordinate (weighted density jacobian) |
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53 | LOGICAL , PUBLIC :: ln_hpg_djc = .FALSE. !: s-coordinate (Density Jacobian with Cubic polynomial) |
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54 | LOGICAL , PUBLIC :: ln_hpg_rot = .FALSE. !: s-coordinate (ROTated axes scheme) |
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55 | LOGICAL , PUBLIC :: ln_hpg_prj = .FALSE. !: s-coordinate (Pressure Jacobian scheme) |
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56 | REAL(wp), PUBLIC :: rn_gamma = 0._wp !: weighting coefficient |
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57 | LOGICAL , PUBLIC :: ln_dynhpg_imp = .FALSE. !: semi-implicite hpg flag |
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58 | |
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59 | INTEGER :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) |
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60 | |
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61 | !! * Substitutions |
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62 | # include "domzgr_substitute.h90" |
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63 | # include "vectopt_loop_substitute.h90" |
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64 | !!---------------------------------------------------------------------- |
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65 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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66 | !! $Id$ |
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67 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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68 | !!---------------------------------------------------------------------- |
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69 | CONTAINS |
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70 | |
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71 | SUBROUTINE dyn_hpg( kt ) |
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72 | !!--------------------------------------------------------------------- |
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73 | !! *** ROUTINE dyn_hpg *** |
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74 | !! |
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75 | !! ** Method : Call the hydrostatic pressure gradient routine |
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76 | !! using the scheme defined in the namelist |
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77 | !! |
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78 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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79 | !! - Save the trend (l_trddyn=T) |
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80 | !!---------------------------------------------------------------------- |
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81 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
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82 | USE wrk_nemo, ONLY: ztrdu => wrk_3d_1 , ztrdv => wrk_3d_2 ! 3D workspace |
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83 | !! |
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84 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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85 | !!---------------------------------------------------------------------- |
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86 | ! |
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87 | IF( wrk_in_use(3, 1,2) ) THEN |
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88 | CALL ctl_stop('dyn_hpg: requested workspace arrays are unavailable') ; RETURN |
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89 | ENDIF |
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90 | ! |
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91 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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92 | ztrdu(:,:,:) = ua(:,:,:) |
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93 | ztrdv(:,:,:) = va(:,:,:) |
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94 | ENDIF |
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95 | ! |
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96 | SELECT CASE ( nhpg ) ! Hydrastatic pressure gradient computation |
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97 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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98 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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99 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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100 | CASE ( 3 ) ; CALL hpg_hel ( kt ) ! s-coordinate (helsinki modification) |
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101 | CASE ( 4 ) ; CALL hpg_wdj ( kt ) ! s-coordinate (weighted density jacobian) |
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102 | CASE ( 5 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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103 | CASE ( 6 ) ; CALL hpg_rot ( kt ) ! s-coordinate (ROTated axes scheme) |
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104 | CASE ( 7 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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105 | END SELECT |
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106 | ! |
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107 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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108 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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109 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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110 | CALL trd_mod( ztrdu, ztrdv, jpdyn_trd_hpg, 'DYN', kt ) |
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111 | ENDIF |
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112 | ! |
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113 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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114 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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115 | ! |
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116 | IF( wrk_not_released(3, 1,2) ) CALL ctl_stop('dyn_hpg: failed to release workspace arrays') |
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117 | ! |
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118 | END SUBROUTINE dyn_hpg |
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119 | |
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120 | |
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121 | SUBROUTINE dyn_hpg_init |
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122 | !!---------------------------------------------------------------------- |
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123 | !! *** ROUTINE dyn_hpg_init *** |
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124 | !! |
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125 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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126 | !! computation and consistency control |
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127 | !! |
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128 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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129 | !! with the type of vertical coordinate used (zco, zps, sco) |
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130 | !!---------------------------------------------------------------------- |
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131 | INTEGER :: ioptio = 0 ! temporary integer |
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132 | !! |
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133 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, ln_hpg_hel, & |
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134 | & ln_hpg_wdj, ln_hpg_djc, ln_hpg_rot, ln_hpg_prj, rn_gamma , ln_dynhpg_imp |
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135 | !!---------------------------------------------------------------------- |
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136 | ! |
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137 | REWIND( numnam ) ! Read Namelist namdyn_hpg |
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138 | READ ( numnam, namdyn_hpg ) |
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139 | ! |
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140 | IF(lwp) THEN ! Control print |
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141 | WRITE(numout,*) |
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142 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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143 | WRITE(numout,*) '~~~~~~~~~~~~' |
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144 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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145 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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146 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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147 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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148 | WRITE(numout,*) ' s-coord. (helsinki modification) ln_hpg_hel = ', ln_hpg_hel |
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149 | WRITE(numout,*) ' s-coord. (weighted density jacobian) ln_hpg_wdj = ', ln_hpg_wdj |
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150 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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151 | WRITE(numout,*) ' s-coord. (ROTated axes scheme) ln_hpg_rot = ', ln_hpg_rot |
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152 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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153 | WRITE(numout,*) ' weighting coeff. (wdj scheme) rn_gamma = ', rn_gamma |
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154 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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155 | ENDIF |
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156 | ! |
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157 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) & |
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158 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl require:& |
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159 | & the standard jacobian formulation hpg_sco or & |
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160 | & the pressure jacobian formulation hpg_prj') |
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161 | ! |
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162 | ! ! Set nhpg from ln_hpg_... flags |
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163 | IF( ln_hpg_zco ) nhpg = 0 |
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164 | IF( ln_hpg_zps ) nhpg = 1 |
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165 | IF( ln_hpg_sco ) nhpg = 2 |
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166 | IF( ln_hpg_hel ) nhpg = 3 |
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167 | IF( ln_hpg_wdj ) nhpg = 4 |
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168 | IF( ln_hpg_djc ) nhpg = 5 |
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169 | IF( ln_hpg_rot ) nhpg = 6 |
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170 | IF( ln_hpg_prj ) nhpg = 7 |
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171 | ! |
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172 | ! ! Consitency check |
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173 | ioptio = 0 |
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174 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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175 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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176 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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177 | IF( ln_hpg_hel ) ioptio = ioptio + 1 |
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178 | IF( ln_hpg_wdj ) ioptio = ioptio + 1 |
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179 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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180 | IF( ln_hpg_rot ) ioptio = ioptio + 1 |
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181 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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182 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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183 | ! |
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184 | END SUBROUTINE dyn_hpg_init |
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185 | |
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186 | |
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187 | SUBROUTINE hpg_zco( kt ) |
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188 | !!--------------------------------------------------------------------- |
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189 | !! *** ROUTINE hpg_zco *** |
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190 | !! |
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191 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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192 | !! The now hydrostatic pressure gradient at a given level, jk, |
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193 | !! is computed by taking the vertical integral of the in-situ |
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194 | !! density gradient along the model level from the suface to that |
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195 | !! level: zhpi = grav ..... |
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196 | !! zhpj = grav ..... |
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197 | !! add it to the general momentum trend (ua,va). |
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198 | !! ua = ua - 1/e1u * zhpi |
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199 | !! va = va - 1/e2v * zhpj |
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200 | !! |
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201 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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202 | !!---------------------------------------------------------------------- |
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203 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
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204 | !! |
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205 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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206 | !! |
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207 | INTEGER :: ji, jj, jk ! dummy loop indices |
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208 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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209 | !!---------------------------------------------------------------------- |
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210 | |
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211 | IF( kt == nit000 ) THEN |
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212 | IF(lwp) WRITE(numout,*) |
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213 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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214 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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215 | ENDIF |
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216 | |
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217 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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218 | |
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219 | ! Surface value |
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220 | DO jj = 2, jpjm1 |
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221 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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222 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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223 | ! hydrostatic pressure gradient |
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224 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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225 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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226 | ! add to the general momentum trend |
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227 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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228 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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229 | END DO |
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230 | END DO |
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231 | ! |
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232 | ! interior value (2=<jk=<jpkm1) |
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233 | DO jk = 2, jpkm1 |
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234 | DO jj = 2, jpjm1 |
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235 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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236 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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237 | ! hydrostatic pressure gradient |
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238 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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239 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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240 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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241 | |
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242 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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243 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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244 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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245 | ! add to the general momentum trend |
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246 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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247 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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248 | END DO |
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249 | END DO |
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250 | END DO |
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251 | ! |
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252 | END SUBROUTINE hpg_zco |
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253 | |
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254 | |
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255 | SUBROUTINE hpg_zps( kt ) |
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256 | !!--------------------------------------------------------------------- |
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257 | !! *** ROUTINE hpg_zps *** |
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258 | !! |
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259 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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260 | !! |
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261 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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262 | !!---------------------------------------------------------------------- |
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263 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
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264 | !! |
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265 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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266 | !! |
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267 | INTEGER :: ji, jj, jk ! dummy loop indices |
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268 | INTEGER :: iku, ikv ! temporary integers |
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269 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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270 | !!---------------------------------------------------------------------- |
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271 | |
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272 | IF( kt == nit000 ) THEN |
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273 | IF(lwp) WRITE(numout,*) |
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274 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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275 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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276 | ENDIF |
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277 | |
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278 | ! Local constant initialization |
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279 | zcoef0 = - grav * 0.5_wp |
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280 | |
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281 | ! Surface value (also valid in partial step case) |
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282 | DO jj = 2, jpjm1 |
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283 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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284 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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285 | ! hydrostatic pressure gradient |
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286 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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287 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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288 | ! add to the general momentum trend |
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289 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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290 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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291 | END DO |
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292 | END DO |
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293 | |
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294 | ! interior value (2=<jk=<jpkm1) |
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295 | DO jk = 2, jpkm1 |
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296 | DO jj = 2, jpjm1 |
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297 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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298 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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299 | ! hydrostatic pressure gradient |
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300 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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301 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
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302 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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303 | |
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304 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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305 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
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306 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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307 | ! add to the general momentum trend |
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308 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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309 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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310 | END DO |
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311 | END DO |
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312 | END DO |
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313 | |
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314 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
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315 | # if defined key_vectopt_loop |
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316 | jj = 1 |
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317 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
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318 | # else |
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319 | DO jj = 2, jpjm1 |
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320 | DO ji = 2, jpim1 |
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321 | # endif |
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322 | iku = mbku(ji,jj) |
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323 | ikv = mbkv(ji,jj) |
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324 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
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325 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
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326 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
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327 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
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328 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
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329 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
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330 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
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331 | ENDIF |
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332 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
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333 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
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334 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
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335 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
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336 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
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337 | ENDIF |
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338 | # if ! defined key_vectopt_loop |
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339 | END DO |
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340 | # endif |
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341 | END DO |
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342 | ! |
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343 | END SUBROUTINE hpg_zps |
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344 | |
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345 | |
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346 | SUBROUTINE hpg_sco( kt ) |
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347 | !!--------------------------------------------------------------------- |
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348 | !! *** ROUTINE hpg_sco *** |
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349 | !! |
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350 | !! ** Method : s-coordinate case. Jacobian scheme. |
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351 | !! The now hydrostatic pressure gradient at a given level, jk, |
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352 | !! is computed by taking the vertical integral of the in-situ |
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353 | !! density gradient along the model level from the suface to that |
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354 | !! level. s-coordinates (ln_sco): a corrective term is added |
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355 | !! to the horizontal pressure gradient : |
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356 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
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357 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
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358 | !! add it to the general momentum trend (ua,va). |
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359 | !! ua = ua - 1/e1u * zhpi |
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360 | !! va = va - 1/e2v * zhpj |
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361 | !! |
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362 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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363 | !!---------------------------------------------------------------------- |
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364 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
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365 | !! |
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366 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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367 | !! |
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368 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
369 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
370 | !!---------------------------------------------------------------------- |
---|
371 | |
---|
372 | IF( kt == nit000 ) THEN |
---|
373 | IF(lwp) WRITE(numout,*) |
---|
374 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
375 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
376 | ENDIF |
---|
377 | |
---|
378 | ! Local constant initialization |
---|
379 | zcoef0 = - grav * 0.5_wp |
---|
380 | ! To use density and not density anomaly |
---|
381 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
382 | ELSE ; znad = 0._wp ! Fixed volume |
---|
383 | ENDIF |
---|
384 | |
---|
385 | ! Surface value |
---|
386 | DO jj = 2, jpjm1 |
---|
387 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
388 | ! hydrostatic pressure gradient along s-surfaces |
---|
389 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
390 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
391 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
392 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
393 | ! s-coordinate pressure gradient correction |
---|
394 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
395 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
396 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
397 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
398 | ! add to the general momentum trend |
---|
399 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
400 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
401 | END DO |
---|
402 | END DO |
---|
403 | |
---|
404 | ! interior value (2=<jk=<jpkm1) |
---|
405 | DO jk = 2, jpkm1 |
---|
406 | DO jj = 2, jpjm1 |
---|
407 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
408 | ! hydrostatic pressure gradient along s-surfaces |
---|
409 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
410 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
411 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
412 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
413 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
414 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
415 | ! s-coordinate pressure gradient correction |
---|
416 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
417 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
418 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
419 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
420 | ! add to the general momentum trend |
---|
421 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
422 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
423 | END DO |
---|
424 | END DO |
---|
425 | END DO |
---|
426 | ! |
---|
427 | END SUBROUTINE hpg_sco |
---|
428 | |
---|
429 | |
---|
430 | SUBROUTINE hpg_hel( kt ) |
---|
431 | !!--------------------------------------------------------------------- |
---|
432 | !! *** ROUTINE hpg_hel *** |
---|
433 | !! |
---|
434 | !! ** Method : s-coordinate case. |
---|
435 | !! The now hydrostatic pressure gradient at a given level |
---|
436 | !! jk is computed by taking the vertical integral of the in-situ |
---|
437 | !! density gradient along the model level from the suface to that |
---|
438 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
439 | !! to the horizontal pressure gradient : |
---|
440 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
441 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
442 | !! add it to the general momentum trend (ua,va). |
---|
443 | !! ua = ua - 1/e1u * zhpi |
---|
444 | !! va = va - 1/e2v * zhpj |
---|
445 | !! |
---|
446 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
447 | !! - Save the trend (l_trddyn=T) |
---|
448 | !!---------------------------------------------------------------------- |
---|
449 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
450 | !! |
---|
451 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
452 | !! |
---|
453 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
454 | REAL(wp) :: zcoef0, zuap, zvap ! temporary scalars |
---|
455 | !!---------------------------------------------------------------------- |
---|
456 | |
---|
457 | IF( kt == nit000 ) THEN |
---|
458 | IF(lwp) WRITE(numout,*) |
---|
459 | IF(lwp) WRITE(numout,*) 'dyn:hpg_hel : hydrostatic pressure gradient trend' |
---|
460 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, helsinki modified scheme' |
---|
461 | ENDIF |
---|
462 | |
---|
463 | ! Local constant initialization |
---|
464 | zcoef0 = - grav * 0.5_wp |
---|
465 | |
---|
466 | ! Surface value |
---|
467 | DO jj = 2, jpjm1 |
---|
468 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
469 | ! hydrostatic pressure gradient along s-surfaces |
---|
470 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj ,1) * rhd(ji+1,jj ,1) & |
---|
471 | & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
472 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3t(ji ,jj+1,1) * rhd(ji ,jj+1,1) & |
---|
473 | & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
474 | ! s-coordinate pressure gradient correction |
---|
475 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & |
---|
476 | & * ( fsdept(ji+1,jj,1) - fsdept(ji,jj,1) ) / e1u(ji,jj) |
---|
477 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & |
---|
478 | & * ( fsdept(ji,jj+1,1) - fsdept(ji,jj,1) ) / e2v(ji,jj) |
---|
479 | ! add to the general momentum trend |
---|
480 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
481 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
482 | END DO |
---|
483 | END DO |
---|
484 | ! |
---|
485 | ! interior value (2=<jk=<jpkm1) |
---|
486 | DO jk = 2, jpkm1 |
---|
487 | DO jj = 2, jpjm1 |
---|
488 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
489 | ! hydrostatic pressure gradient along s-surfaces |
---|
490 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
491 | & + zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,jk ) * rhd(ji+1,jj,jk) & |
---|
492 | & -fse3t(ji ,jj,jk ) * rhd(ji ,jj,jk) ) & |
---|
493 | & + zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,jk-1) * rhd(ji+1,jj,jk-1) & |
---|
494 | & -fse3t(ji ,jj,jk-1) * rhd(ji ,jj,jk-1) ) |
---|
495 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
496 | & + zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,jk ) * rhd(ji,jj+1,jk) & |
---|
497 | & -fse3t(ji,jj ,jk ) * rhd(ji,jj, jk) ) & |
---|
498 | & + zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,jk-1) * rhd(ji,jj+1,jk-1) & |
---|
499 | & -fse3t(ji,jj ,jk-1) * rhd(ji,jj, jk-1) ) |
---|
500 | ! s-coordinate pressure gradient correction |
---|
501 | zuap = - zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
502 | & * ( fsdept(ji+1,jj,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj) |
---|
503 | zvap = - zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
504 | & * ( fsdept(ji,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) |
---|
505 | ! add to the general momentum trend |
---|
506 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
507 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
508 | END DO |
---|
509 | END DO |
---|
510 | END DO |
---|
511 | ! |
---|
512 | END SUBROUTINE hpg_hel |
---|
513 | |
---|
514 | |
---|
515 | SUBROUTINE hpg_wdj( kt ) |
---|
516 | !!--------------------------------------------------------------------- |
---|
517 | !! *** ROUTINE hpg_wdj *** |
---|
518 | !! |
---|
519 | !! ** Method : Weighted Density Jacobian (wdj) scheme (song 1998) |
---|
520 | !! The weighting coefficients from the namelist parameter rn_gamma |
---|
521 | !! (alpha=0.5-rn_gamma ; beta=1-alpha=0.5+rn_gamma |
---|
522 | !! |
---|
523 | !! Reference : Song, Mon. Wea. Rev., 126, 3213-3230, 1998. |
---|
524 | !!---------------------------------------------------------------------- |
---|
525 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
526 | !! |
---|
527 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
528 | !! |
---|
529 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
530 | REAL(wp) :: zcoef0, zuap, zvap ! temporary scalars |
---|
531 | REAL(wp) :: zalph , zbeta ! " " |
---|
532 | !!---------------------------------------------------------------------- |
---|
533 | |
---|
534 | IF( kt == nit000 ) THEN |
---|
535 | IF(lwp) WRITE(numout,*) |
---|
536 | IF(lwp) WRITE(numout,*) 'dyn:hpg_wdj : hydrostatic pressure gradient trend' |
---|
537 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ Weighted Density Jacobian' |
---|
538 | ENDIF |
---|
539 | |
---|
540 | ! Local constant initialization |
---|
541 | zcoef0 = - grav * 0.5_wp |
---|
542 | zalph = 0.5_wp - rn_gamma ! weighting coefficients (alpha=0.5-rn_gamma |
---|
543 | zbeta = 0.5_wp + rn_gamma ! (beta =1-alpha=0.5+rn_gamma |
---|
544 | |
---|
545 | ! Surface value (no ponderation) |
---|
546 | DO jj = 2, jpjm1 |
---|
547 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
548 | ! hydrostatic pressure gradient along s-surfaces |
---|
549 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * rhd(ji+1,jj ,1) & |
---|
550 | & - fse3w(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
551 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * rhd(ji ,jj+1,1) & |
---|
552 | & - fse3w(ji ,jj ,1) * rhd(ji, jj ,1) ) |
---|
553 | ! s-coordinate pressure gradient correction |
---|
554 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & |
---|
555 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
556 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & |
---|
557 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
558 | ! add to the general momentum trend |
---|
559 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
560 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
561 | END DO |
---|
562 | END DO |
---|
563 | |
---|
564 | ! Interior value (2=<jk=<jpkm1) (weighted with zalph & zbeta) |
---|
565 | DO jk = 2, jpkm1 |
---|
566 | DO jj = 2, jpjm1 |
---|
567 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
568 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
569 | & * ( ( fsde3w(ji+1,jj,jk ) + fsde3w(ji,jj,jk ) & |
---|
570 | & - fsde3w(ji+1,jj,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
571 | & * ( zalph * ( rhd (ji+1,jj,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
572 | & + zbeta * ( rhd (ji+1,jj,jk ) - rhd (ji,jj,jk ) ) ) & |
---|
573 | & - ( rhd (ji+1,jj,jk ) + rhd (ji,jj,jk ) & |
---|
574 | & - rhd (ji+1,jj,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
575 | & * ( zalph * ( fsde3w(ji+1,jj,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
576 | & + zbeta * ( fsde3w(ji+1,jj,jk ) - fsde3w(ji,jj,jk ) ) ) ) |
---|
577 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
578 | & * ( ( fsde3w(ji,jj+1,jk ) + fsde3w(ji,jj,jk ) & |
---|
579 | & - fsde3w(ji,jj+1,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
580 | & * ( zalph * ( rhd (ji,jj+1,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
581 | & + zbeta * ( rhd (ji,jj+1,jk ) - rhd (ji,jj,jk ) ) ) & |
---|
582 | & - ( rhd (ji,jj+1,jk ) + rhd (ji,jj,jk ) & |
---|
583 | & - rhd (ji,jj+1,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
584 | & * ( zalph * ( fsde3w(ji,jj+1,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
585 | & + zbeta * ( fsde3w(ji,jj+1,jk ) - fsde3w(ji,jj,jk ) ) ) ) |
---|
586 | ! add to the general momentum trend |
---|
587 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
588 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
589 | END DO |
---|
590 | END DO |
---|
591 | END DO |
---|
592 | ! |
---|
593 | END SUBROUTINE hpg_wdj |
---|
594 | |
---|
595 | |
---|
596 | SUBROUTINE hpg_djc( kt ) |
---|
597 | !!--------------------------------------------------------------------- |
---|
598 | !! *** ROUTINE hpg_djc *** |
---|
599 | !! |
---|
600 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
601 | !! |
---|
602 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
603 | !!---------------------------------------------------------------------- |
---|
604 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
---|
605 | USE oce , ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
606 | USE wrk_nemo, ONLY: drhox => wrk_3d_1 , dzx => wrk_3d_2 |
---|
607 | USE wrk_nemo, ONLY: drhou => wrk_3d_3 , dzu => wrk_3d_4 , rho_i => wrk_3d_5 |
---|
608 | USE wrk_nemo, ONLY: drhoy => wrk_3d_6 , dzy => wrk_3d_7 |
---|
609 | USE wrk_nemo, ONLY: drhov => wrk_3d_8 , dzv => wrk_3d_9 , rho_j => wrk_3d_10 |
---|
610 | USE wrk_nemo, ONLY: drhoz => wrk_3d_11 , dzz => wrk_3d_12 |
---|
611 | USE wrk_nemo, ONLY: drhow => wrk_3d_13 , dzw => wrk_3d_14 |
---|
612 | USE wrk_nemo, ONLY: rho_k => wrk_3d_15 |
---|
613 | !! |
---|
614 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
615 | !! |
---|
616 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
617 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
618 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
619 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
620 | !!---------------------------------------------------------------------- |
---|
621 | |
---|
622 | IF( wrk_in_use(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) THEN |
---|
623 | CALL ctl_stop('dyn:hpg_djc: requested workspace arrays unavailable') ; RETURN |
---|
624 | ENDIF |
---|
625 | |
---|
626 | IF( kt == nit000 ) THEN |
---|
627 | IF(lwp) WRITE(numout,*) |
---|
628 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
629 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
630 | ENDIF |
---|
631 | |
---|
632 | ! Local constant initialization |
---|
633 | zcoef0 = - grav * 0.5_wp |
---|
634 | z1_10 = 1._wp / 10._wp |
---|
635 | z1_12 = 1._wp / 12._wp |
---|
636 | |
---|
637 | !---------------------------------------------------------------------------------------- |
---|
638 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
639 | !---------------------------------------------------------------------------------------- |
---|
640 | |
---|
641 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
642 | |
---|
643 | DO jk = 2, jpkm1 |
---|
644 | DO jj = 2, jpjm1 |
---|
645 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
646 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
647 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
648 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
649 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
650 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
651 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
652 | END DO |
---|
653 | END DO |
---|
654 | END DO |
---|
655 | |
---|
656 | !------------------------------------------------------------------------- |
---|
657 | ! compute harmonic averages using eq. 5.18 |
---|
658 | !------------------------------------------------------------------------- |
---|
659 | zep = 1.e-15 |
---|
660 | |
---|
661 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
662 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
663 | |
---|
664 | DO jk = 2, jpkm1 |
---|
665 | DO jj = 2, jpjm1 |
---|
666 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
667 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
668 | |
---|
669 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
670 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
671 | |
---|
672 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
673 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
674 | |
---|
675 | IF( cffw > zep) THEN |
---|
676 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
677 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
678 | ELSE |
---|
679 | drhow(ji,jj,jk) = 0._wp |
---|
680 | ENDIF |
---|
681 | |
---|
682 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
683 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
684 | |
---|
685 | IF( cffu > zep ) THEN |
---|
686 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
687 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
688 | ELSE |
---|
689 | drhou(ji,jj,jk ) = 0._wp |
---|
690 | ENDIF |
---|
691 | |
---|
692 | IF( cffx > zep ) THEN |
---|
693 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
694 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
695 | ELSE |
---|
696 | dzu(ji,jj,jk) = 0._wp |
---|
697 | ENDIF |
---|
698 | |
---|
699 | IF( cffv > zep ) THEN |
---|
700 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
701 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
702 | ELSE |
---|
703 | drhov(ji,jj,jk) = 0._wp |
---|
704 | ENDIF |
---|
705 | |
---|
706 | IF( cffy > zep ) THEN |
---|
707 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
708 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
709 | ELSE |
---|
710 | dzv(ji,jj,jk) = 0._wp |
---|
711 | ENDIF |
---|
712 | |
---|
713 | END DO |
---|
714 | END DO |
---|
715 | END DO |
---|
716 | |
---|
717 | !---------------------------------------------------------------------------------- |
---|
718 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
719 | !---------------------------------------------------------------------------------- |
---|
720 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
721 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
722 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
723 | |
---|
724 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
725 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
726 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
727 | |
---|
728 | |
---|
729 | !-------------------------------------------------------------- |
---|
730 | ! Upper half of top-most grid box, compute and store |
---|
731 | !------------------------------------------------------------- |
---|
732 | |
---|
733 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
734 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
735 | |
---|
736 | DO jj = 2, jpjm1 |
---|
737 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
738 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
739 | & * ( rhd(ji,jj,1) & |
---|
740 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
741 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
742 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
743 | END DO |
---|
744 | END DO |
---|
745 | |
---|
746 | !!bug gm : here also, simplification is possible |
---|
747 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
748 | |
---|
749 | DO jk = 2, jpkm1 |
---|
750 | DO jj = 2, jpjm1 |
---|
751 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
752 | |
---|
753 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
754 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
755 | & - grav * z1_10 * ( & |
---|
756 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
757 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
758 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
759 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
760 | & ) |
---|
761 | |
---|
762 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
763 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
764 | & - grav* z1_10 * ( & |
---|
765 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
766 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
767 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
768 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
769 | & ) |
---|
770 | |
---|
771 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
772 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
773 | & - grav* z1_10 * ( & |
---|
774 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
775 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
776 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
777 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
778 | & ) |
---|
779 | |
---|
780 | END DO |
---|
781 | END DO |
---|
782 | END DO |
---|
783 | CALL lbc_lnk(rho_k,'W',1.) |
---|
784 | CALL lbc_lnk(rho_i,'U',1.) |
---|
785 | CALL lbc_lnk(rho_j,'V',1.) |
---|
786 | |
---|
787 | |
---|
788 | ! --------------- |
---|
789 | ! Surface value |
---|
790 | ! --------------- |
---|
791 | DO jj = 2, jpjm1 |
---|
792 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
793 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
794 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
795 | ! add to the general momentum trend |
---|
796 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
797 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
798 | END DO |
---|
799 | END DO |
---|
800 | |
---|
801 | ! ---------------- |
---|
802 | ! interior value (2=<jk=<jpkm1) |
---|
803 | ! ---------------- |
---|
804 | DO jk = 2, jpkm1 |
---|
805 | DO jj = 2, jpjm1 |
---|
806 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
807 | ! hydrostatic pressure gradient along s-surfaces |
---|
808 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
809 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
810 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
811 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
812 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
813 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
814 | ! add to the general momentum trend |
---|
815 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
816 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
817 | END DO |
---|
818 | END DO |
---|
819 | END DO |
---|
820 | ! |
---|
821 | IF( wrk_not_released(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) & |
---|
822 | CALL ctl_stop('dyn:hpg_djc: failed to release workspace arrays') |
---|
823 | ! |
---|
824 | END SUBROUTINE hpg_djc |
---|
825 | |
---|
826 | |
---|
827 | SUBROUTINE hpg_rot( kt ) |
---|
828 | !!--------------------------------------------------------------------- |
---|
829 | !! *** ROUTINE hpg_rot *** |
---|
830 | !! |
---|
831 | !! ** Method : rotated axes scheme (Thiem and Berntsen 2005) |
---|
832 | !! |
---|
833 | !! Reference: Thiem & Berntsen, Ocean Modelling, In press, 2005. |
---|
834 | !!---------------------------------------------------------------------- |
---|
835 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
---|
836 | USE oce , ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
837 | USE wrk_nemo, ONLY: zdistr => wrk_2d_1 , zsina => wrk_2d_2 , zcosa => wrk_2d_3 |
---|
838 | USE wrk_nemo, ONLY: zhpiorg => wrk_3d_1 , zhpirot => wrk_3d_2 |
---|
839 | USE wrk_nemo, ONLY: zhpitra => wrk_3d_3 , zhpine => wrk_3d_4 |
---|
840 | USE wrk_nemo, ONLY: zhpjorg => wrk_3d_5 , zhpjrot => wrk_3d_6 |
---|
841 | USE wrk_nemo, ONLY: zhpjtra => wrk_3d_7 , zhpjne => wrk_3d_8 |
---|
842 | !! |
---|
843 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
844 | !! |
---|
845 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
846 | REAL(wp) :: zforg, zcoef0, zuap, zmskd1, zmskd1m ! temporary scalar |
---|
847 | REAL(wp) :: zfrot , zvap, zmskd2, zmskd2m ! " " |
---|
848 | !!---------------------------------------------------------------------- |
---|
849 | |
---|
850 | IF( wrk_in_use(2, 1,2,3) .OR. & |
---|
851 | wrk_in_use(3, 1,2,3,4,5,6,7,8) ) THEN |
---|
852 | CALL ctl_stop('dyn:hpg_rot: requested workspace arrays unavailable') ; RETURN |
---|
853 | ENDIF |
---|
854 | |
---|
855 | IF( kt == nit000 ) THEN |
---|
856 | IF(lwp) WRITE(numout,*) |
---|
857 | IF(lwp) WRITE(numout,*) 'dyn:hpg_rot : hydrostatic pressure gradient trend' |
---|
858 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, rotated axes scheme used' |
---|
859 | ENDIF |
---|
860 | |
---|
861 | ! ------------------------------- |
---|
862 | ! Local constant initialization |
---|
863 | ! ------------------------------- |
---|
864 | zcoef0 = - grav * 0.5_wp |
---|
865 | zforg = 0.95_wp |
---|
866 | zfrot = 1._wp - zforg |
---|
867 | |
---|
868 | ! inverse of the distance between 2 diagonal T-points (defined at F-point) (here zcoef0/distance) |
---|
869 | zdistr(:,:) = zcoef0 / SQRT( e1f(:,:)*e1f(:,:) + e2f(:,:)*e1f(:,:) ) |
---|
870 | |
---|
871 | ! sinus and cosinus of diagonal angle at F-point |
---|
872 | zsina(:,:) = ATAN2( e2f(:,:), e1f(:,:) ) |
---|
873 | zcosa(:,:) = COS( zsina(:,:) ) |
---|
874 | zsina(:,:) = SIN( zsina(:,:) ) |
---|
875 | |
---|
876 | ! --------------- |
---|
877 | ! Surface value |
---|
878 | ! --------------- |
---|
879 | ! compute and add to the general trend the pressure gradients along the axes |
---|
880 | DO jj = 2, jpjm1 |
---|
881 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
882 | ! hydrostatic pressure gradient along s-surfaces |
---|
883 | zhpiorg(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,1) * rhd(ji+1,jj,1) & |
---|
884 | & - fse3t(ji ,jj,1) * rhd(ji ,jj,1) ) |
---|
885 | zhpjorg(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,1) * rhd(ji,jj+1,1) & |
---|
886 | & - fse3t(ji,jj ,1) * rhd(ji,jj ,1) ) |
---|
887 | ! s-coordinate pressure gradient correction |
---|
888 | zuap = -zcoef0 * ( rhd (ji+1,jj ,1) + rhd (ji,jj,1) ) & |
---|
889 | & * ( fsdept(ji+1,jj ,1) - fsdept(ji,jj,1) ) / e1u(ji,jj) |
---|
890 | zvap = -zcoef0 * ( rhd (ji ,jj+1,1) + rhd (ji,jj,1) ) & |
---|
891 | & * ( fsdept(ji ,jj+1,1) - fsdept(ji,jj,1) ) / e2v(ji,jj) |
---|
892 | ! add to the general momentum trend |
---|
893 | ua(ji,jj,1) = ua(ji,jj,1) + zforg * ( zhpiorg(ji,jj,1) + zuap ) |
---|
894 | va(ji,jj,1) = va(ji,jj,1) + zforg * ( zhpjorg(ji,jj,1) + zvap ) |
---|
895 | END DO |
---|
896 | END DO |
---|
897 | |
---|
898 | ! compute the pressure gradients in the diagonal directions |
---|
899 | DO jj = 1, jpjm1 |
---|
900 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
901 | zmskd1 = tmask(ji+1,jj+1,1) * tmask(ji ,jj,1) ! mask in the 1st diagnonal |
---|
902 | zmskd2 = tmask(ji ,jj+1,1) * tmask(ji+1,jj,1) ! mask in the 2nd diagnonal |
---|
903 | ! hydrostatic pressure gradient along s-surfaces |
---|
904 | zhpitra(ji,jj,1) = zdistr(ji,jj) * zmskd1 * ( fse3t(ji+1,jj+1,1) * rhd(ji+1,jj+1,1) & |
---|
905 | & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
906 | zhpjtra(ji,jj,1) = zdistr(ji,jj) * zmskd2 * ( fse3t(ji ,jj+1,1) * rhd(ji ,jj+1,1) & |
---|
907 | & - fse3t(ji+1,jj ,1) * rhd(ji+1,jj ,1) ) |
---|
908 | ! s-coordinate pressure gradient correction |
---|
909 | zuap = -zdistr(ji,jj) * zmskd1 * ( rhd (ji+1,jj+1,1) + rhd (ji ,jj,1) ) & |
---|
910 | & * ( fsdept(ji+1,jj+1,1) - fsdept(ji ,jj,1) ) |
---|
911 | zvap = -zdistr(ji,jj) * zmskd2 * ( rhd (ji ,jj+1,1) + rhd (ji+1,jj,1) ) & |
---|
912 | & * ( fsdept(ji ,jj+1,1) - fsdept(ji+1,jj,1) ) |
---|
913 | ! back rotation |
---|
914 | zhpine(ji,jj,1) = zcosa(ji,jj) * ( zhpitra(ji,jj,1) + zuap ) & |
---|
915 | & - zsina(ji,jj) * ( zhpjtra(ji,jj,1) + zvap ) |
---|
916 | zhpjne(ji,jj,1) = zsina(ji,jj) * ( zhpitra(ji,jj,1) + zuap ) & |
---|
917 | & + zcosa(ji,jj) * ( zhpjtra(ji,jj,1) + zvap ) |
---|
918 | END DO |
---|
919 | END DO |
---|
920 | |
---|
921 | ! interpolate and add to the general trend the diagonal gradient |
---|
922 | DO jj = 2, jpjm1 |
---|
923 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
924 | ! averaging |
---|
925 | zhpirot(ji,jj,1) = 0.5 * ( zhpine(ji,jj,1) + zhpine(ji ,jj-1,1) ) |
---|
926 | zhpjrot(ji,jj,1) = 0.5 * ( zhpjne(ji,jj,1) + zhpjne(ji-1,jj ,1) ) |
---|
927 | ! add to the general momentum trend |
---|
928 | ua(ji,jj,1) = ua(ji,jj,1) + zfrot * zhpirot(ji,jj,1) |
---|
929 | va(ji,jj,1) = va(ji,jj,1) + zfrot * zhpjrot(ji,jj,1) |
---|
930 | END DO |
---|
931 | END DO |
---|
932 | |
---|
933 | ! ----------------- |
---|
934 | ! 2. interior value (2=<jk=<jpkm1) |
---|
935 | ! ----------------- |
---|
936 | ! compute and add to the general trend the pressure gradients along the axes |
---|
937 | DO jk = 2, jpkm1 |
---|
938 | DO jj = 2, jpjm1 |
---|
939 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
940 | ! hydrostatic pressure gradient along s-surfaces |
---|
941 | zhpiorg(ji,jj,jk) = zhpiorg(ji,jj,jk-1) & |
---|
942 | & + zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,jk ) * rhd(ji+1,jj,jk ) & |
---|
943 | & - fse3t(ji ,jj,jk ) * rhd(ji ,jj,jk ) & |
---|
944 | & + fse3t(ji+1,jj,jk-1) * rhd(ji+1,jj,jk-1) & |
---|
945 | & - fse3t(ji ,jj,jk-1) * rhd(ji ,jj,jk-1) ) |
---|
946 | zhpjorg(ji,jj,jk) = zhpjorg(ji,jj,jk-1) & |
---|
947 | & + zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,jk ) * rhd(ji,jj+1,jk ) & |
---|
948 | & - fse3t(ji,jj ,jk ) * rhd(ji,jj, jk ) & |
---|
949 | & + fse3t(ji,jj+1,jk-1) * rhd(ji,jj+1,jk-1) & |
---|
950 | & - fse3t(ji,jj ,jk-1) * rhd(ji,jj, jk-1) ) |
---|
951 | ! s-coordinate pressure gradient correction |
---|
952 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) & |
---|
953 | & * ( fsdept(ji+1,jj ,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj) |
---|
954 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
955 | & * ( fsdept(ji ,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) |
---|
956 | ! add to the general momentum trend |
---|
957 | ua(ji,jj,jk) = ua(ji,jj,jk) + zforg*( zhpiorg(ji,jj,jk) + zuap ) |
---|
958 | va(ji,jj,jk) = va(ji,jj,jk) + zforg*( zhpjorg(ji,jj,jk) + zvap ) |
---|
959 | END DO |
---|
960 | END DO |
---|
961 | END DO |
---|
962 | |
---|
963 | ! compute the pressure gradients in the diagonal directions |
---|
964 | DO jk = 2, jpkm1 |
---|
965 | DO jj = 1, jpjm1 |
---|
966 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
967 | zmskd1 = tmask(ji+1,jj+1,jk ) * tmask(ji ,jj,jk ) ! level jk mask in the 1st diagnonal |
---|
968 | zmskd1m = tmask(ji+1,jj+1,jk-1) * tmask(ji ,jj,jk-1) ! level jk-1 " " |
---|
969 | zmskd2 = tmask(ji ,jj+1,jk ) * tmask(ji+1,jj,jk ) ! level jk mask in the 2nd diagnonal |
---|
970 | zmskd2m = tmask(ji ,jj+1,jk-1) * tmask(ji+1,jj,jk-1) ! level jk-1 " " |
---|
971 | ! hydrostatic pressure gradient along s-surfaces |
---|
972 | zhpitra(ji,jj,jk) = zhpitra(ji,jj,jk-1) & |
---|
973 | & + zdistr(ji,jj) * zmskd1 * ( fse3t(ji+1,jj+1,jk ) * rhd(ji+1,jj+1,jk) & |
---|
974 | & -fse3t(ji ,jj ,jk ) * rhd(ji ,jj ,jk) ) & |
---|
975 | & + zdistr(ji,jj) * zmskd1m * ( fse3t(ji+1,jj+1,jk-1) * rhd(ji+1,jj+1,jk-1) & |
---|
976 | & -fse3t(ji ,jj ,jk-1) * rhd(ji ,jj ,jk-1) ) |
---|
977 | zhpjtra(ji,jj,jk) = zhpjtra(ji,jj,jk-1) & |
---|
978 | & + zdistr(ji,jj) * zmskd2 * ( fse3t(ji ,jj+1,jk ) * rhd(ji ,jj+1,jk) & |
---|
979 | & -fse3t(ji+1,jj ,jk ) * rhd(ji+1,jj, jk) ) & |
---|
980 | & + zdistr(ji,jj) * zmskd2m * ( fse3t(ji ,jj+1,jk-1) * rhd(ji ,jj+1,jk-1) & |
---|
981 | & -fse3t(ji+1,jj ,jk-1) * rhd(ji+1,jj, jk-1) ) |
---|
982 | ! s-coordinate pressure gradient correction |
---|
983 | zuap = - zdistr(ji,jj) * zmskd1 * ( rhd (ji+1,jj+1,jk) + rhd (ji ,jj,jk) ) & |
---|
984 | & * ( fsdept(ji+1,jj+1,jk) - fsdept(ji ,jj,jk) ) |
---|
985 | zvap = - zdistr(ji,jj) * zmskd2 * ( rhd (ji ,jj+1,jk) + rhd (ji+1,jj,jk) ) & |
---|
986 | & * ( fsdept(ji ,jj+1,jk) - fsdept(ji+1,jj,jk) ) |
---|
987 | ! back rotation |
---|
988 | zhpine(ji,jj,jk) = zcosa(ji,jj) * ( zhpitra(ji,jj,jk) + zuap ) & |
---|
989 | & - zsina(ji,jj) * ( zhpjtra(ji,jj,jk) + zvap ) |
---|
990 | zhpjne(ji,jj,jk) = zsina(ji,jj) * ( zhpitra(ji,jj,jk) + zuap ) & |
---|
991 | & + zcosa(ji,jj) * ( zhpjtra(ji,jj,jk) + zvap ) |
---|
992 | END DO |
---|
993 | END DO |
---|
994 | END DO |
---|
995 | |
---|
996 | ! interpolate and add to the general trend |
---|
997 | DO jk = 2, jpkm1 |
---|
998 | DO jj = 2, jpjm1 |
---|
999 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
1000 | ! averaging |
---|
1001 | zhpirot(ji,jj,jk) = 0.5 * ( zhpine(ji,jj,jk) + zhpine(ji ,jj-1,jk) ) |
---|
1002 | zhpjrot(ji,jj,jk) = 0.5 * ( zhpjne(ji,jj,jk) + zhpjne(ji-1,jj ,jk) ) |
---|
1003 | ! add to the general momentum trend |
---|
1004 | ua(ji,jj,jk) = ua(ji,jj,jk) + zfrot * zhpirot(ji,jj,jk) |
---|
1005 | va(ji,jj,jk) = va(ji,jj,jk) + zfrot * zhpjrot(ji,jj,jk) |
---|
1006 | END DO |
---|
1007 | END DO |
---|
1008 | END DO |
---|
1009 | ! |
---|
1010 | IF( wrk_not_released(2, 1,2,3) .OR. & |
---|
1011 | wrk_not_released(3, 1,2,3,4,5,6,7,8) ) CALL ctl_stop('dyn:hpg_rot: failed to release workspace arrays') |
---|
1012 | ! |
---|
1013 | END SUBROUTINE hpg_rot |
---|
1014 | |
---|
1015 | |
---|
1016 | SUBROUTINE hpg_prj( kt ) |
---|
1017 | !!--------------------------------------------------------------------- |
---|
1018 | !! *** ROUTINE hpg_prj *** |
---|
1019 | !! |
---|
1020 | !! ** Method : s-coordinate case. |
---|
1021 | !! Reformulate the horizontal hydrostatical pressure gradient |
---|
1022 | !! term using Pressure Jacobian. A new correction term |
---|
1023 | !! is developed to eliminate the sigma-coordinate error. |
---|
1024 | !! |
---|
1025 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
1026 | !! - Save the trend (l_trddyn=T) |
---|
1027 | !! |
---|
1028 | !!---------------------------------------------------------------------- |
---|
1029 | |
---|
1030 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
---|
1031 | USE oce , ONLY: fsde3w_tmp => ta ! (ta,sa) used as 3D workspace |
---|
1032 | USE oce , ONLY: rhd_tmp => sa |
---|
1033 | USE wrk_nemo, ONLY: zhpi => wrk_3d_3 |
---|
1034 | USE wrk_nemo, ONLY: zu => wrk_3d_4 |
---|
1035 | USE wrk_nemo, ONLY: zv => wrk_3d_5 |
---|
1036 | USE wrk_nemo, ONLY: fsp => wrk_3d_6 |
---|
1037 | USE wrk_nemo, ONLY: xsp => wrk_3d_7 |
---|
1038 | USE wrk_nemo, ONLY: asp => wrk_3d_8 |
---|
1039 | USE wrk_nemo, ONLY: bsp => wrk_3d_9 |
---|
1040 | USE wrk_nemo, ONLY: csp => wrk_3d_10 |
---|
1041 | USE wrk_nemo, ONLY: dsp => wrk_3d_11 |
---|
1042 | !! |
---|
1043 | !!---------------------------------------------------------------------- |
---|
1044 | !! |
---|
1045 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
1046 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
1047 | !! |
---|
1048 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
1049 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
1050 | !! |
---|
1051 | !! The local varialbes for the correction term |
---|
1052 | INTEGER :: jke, jkw, jkn, jks, jk1 |
---|
1053 | REAL(wp) :: zze, zzw, zzn, zzs, rre, rrw, rrn, rrs |
---|
1054 | REAL(wp) :: zuijk, zvijk, pe, pw, pn, ps, dze, dzw, dzn, dzs |
---|
1055 | REAL(wp) :: rhde, rhdw, rhdn, rhds,rhdt1, rhdt2 |
---|
1056 | REAL(wp) :: dpdx1, dpdx2, dpdy1, dpdy2 |
---|
1057 | INTEGER :: bhitwe, bhitns |
---|
1058 | !!---------------------------------------------------------------------- |
---|
1059 | |
---|
1060 | IF( wrk_in_use(3, 3,4,5,6,7,8,9,10,11) ) THEN |
---|
1061 | CALL ctl_stop('dyn:hpg_prj: requested workspace arrays unavailable') ; RETURN |
---|
1062 | ENDIF |
---|
1063 | |
---|
1064 | IF( kt == nit000 ) THEN |
---|
1065 | IF(lwp) WRITE(numout,*) |
---|
1066 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
1067 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
1068 | ENDIF |
---|
1069 | |
---|
1070 | !!---------------------------------------------------------------------- |
---|
1071 | ! Local constant initialization |
---|
1072 | zcoef0 = - grav |
---|
1073 | znad = 0.0_wp |
---|
1074 | IF(lk_vvl) znad = 1._wp |
---|
1075 | |
---|
1076 | ! Save fsde3w and rhd |
---|
1077 | fsde3w_tmp(:,:,:) = fsde3w(:,:,:) |
---|
1078 | rhd_tmp(:,:,:) = rhd(:,:,:) |
---|
1079 | |
---|
1080 | ! Clean 3-D work arraies |
---|
1081 | zhpi(:,:,:) = 0. |
---|
1082 | |
---|
1083 | |
---|
1084 | !how to add vector opt.? N.B., jpi&jpi rather than jpim1&jpjm1 are needed here |
---|
1085 | |
---|
1086 | ! Preparing vertical density profile for hybrid-sco coordinate |
---|
1087 | DO jj = 1, jpj |
---|
1088 | DO ji = 1, jpi |
---|
1089 | jk = mbathy(ji,jj) |
---|
1090 | IF(jk <= 0) THEN; rhd(ji,jj,:) = 0._wp |
---|
1091 | ELSE IF(jk == 1) THEN; rhd(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
1092 | ELSE IF(jk < jpkm1) THEN |
---|
1093 | DO jkk = jk+1, jpk |
---|
1094 | rhd(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1),& |
---|
1095 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
1096 | END DO |
---|
1097 | END IF |
---|
1098 | END DO |
---|
1099 | END DO |
---|
1100 | |
---|
1101 | DO jj = 1, jpj |
---|
1102 | DO ji = 1, jpi |
---|
1103 | fsde3w(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) |
---|
1104 | fsde3w(ji,jj,1) = fsde3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
1105 | DO jk = 2, jpk |
---|
1106 | fsde3w(ji,jj,jk) = fsde3w(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
1107 | END DO |
---|
1108 | END DO |
---|
1109 | END DO |
---|
1110 | |
---|
1111 | DO jk = 1, jpkm1 |
---|
1112 | DO jj = 1, jpj |
---|
1113 | DO ji = 1, jpi |
---|
1114 | fsp(ji,jj,jk) = rhd(ji,jj,jk) |
---|
1115 | xsp(ji,jj,jk) = fsde3w(ji,jj,jk) |
---|
1116 | END DO |
---|
1117 | END DO |
---|
1118 | END DO |
---|
1119 | |
---|
1120 | ! Constrained cubic spline interpolation |
---|
1121 | |
---|
1122 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
1123 | |
---|
1124 | |
---|
1125 | |
---|
1126 | ! Calculate the pressure at T(ji,jj,1) |
---|
1127 | DO jj = 2, jpj |
---|
1128 | DO ji = 2, jpi |
---|
1129 | rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & |
---|
1130 | bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & |
---|
1131 | * 0.5_wp * fsde3w(ji,jj,1) |
---|
1132 | rhdt1 = max(rhdt1, 0.0_wp) |
---|
1133 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * rhdt1 |
---|
1134 | END DO |
---|
1135 | END DO |
---|
1136 | |
---|
1137 | |
---|
1138 | |
---|
1139 | ! print*, 'max&min fse3w=',maxval(fse3w), minval(fse3w) |
---|
1140 | ! print*, 'max&min rhd===',maxval(rhd), minval(rhd) |
---|
1141 | |
---|
1142 | ! Calculate the pressure at T(ji,jj,2:jpkm1) |
---|
1143 | DO jk = 2, jpkm1 |
---|
1144 | DO jj = 2, jpj |
---|
1145 | DO ji = 2, jpi |
---|
1146 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
1147 | integ2(fsde3w(ji,jj,jk-1),fsde3w(ji,jj,jk),& |
---|
1148 | asp(ji,jj,jk-1),bsp(ji,jj,jk-1),& |
---|
1149 | csp(ji,jj,jk-1),dsp(ji,jj,jk-1)) |
---|
1150 | END DO |
---|
1151 | END DO |
---|
1152 | END DO |
---|
1153 | |
---|
1154 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
1155 | |
---|
1156 | DO jj = 2, jpjm1 |
---|
1157 | DO ji = 2, jpim1 |
---|
1158 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshu_n(ji,jj) * znad) |
---|
1159 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshv_n(ji,jj) * znad) |
---|
1160 | END DO |
---|
1161 | END DO |
---|
1162 | |
---|
1163 | DO jk = 2, jpkm1 |
---|
1164 | DO jj = 2, jpjm1 |
---|
1165 | DO ji = 2, jpim1 |
---|
1166 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
1167 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
1168 | END DO |
---|
1169 | END DO |
---|
1170 | END DO |
---|
1171 | |
---|
1172 | DO jk = 1, jpkm1 |
---|
1173 | DO jj = 2, jpjm1 |
---|
1174 | DO ji = 2, jpim1 |
---|
1175 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
1176 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
1177 | END DO |
---|
1178 | END DO |
---|
1179 | END DO |
---|
1180 | |
---|
1181 | DO jk = 1, jpkm1 |
---|
1182 | DO jj = 2, jpjm1 |
---|
1183 | DO ji = 2, jpim1 |
---|
1184 | |
---|
1185 | pe = 0.; pw = 0.; dze = 0.; dzw = 0. |
---|
1186 | pn = 0.; ps = 0.; dzn = 0.; dzs = 0. |
---|
1187 | bhitwe = 0; bhitns = 0 |
---|
1188 | zuijk = zu(ji,jj,jk) |
---|
1189 | zvijk = zv(ji,jj,jk) |
---|
1190 | |
---|
1191 | !! for u equation |
---|
1192 | IF(-fsde3w(ji+1,jj,jk) > zuijk) THEN |
---|
1193 | DO jk1 = jk+1, mbathy(ji+1,jj) |
---|
1194 | IF(-fsde3w(ji+1,jj,jk1) > zuijk) THEN |
---|
1195 | pe = pe + & |
---|
1196 | integ2(fsde3w(ji+1,jj,jk1-1),fsde3w(ji+1,jj,jk1),& |
---|
1197 | asp(ji+1,jj,jk1-1),bsp(ji+1,jj,jk1-1),& |
---|
1198 | csp(ji+1,jj,jk1-1),dsp(ji+1,jj,jk1-1)) |
---|
1199 | IF(jk1 == mbathy(ji+1,jj)) bhitwe = 1 |
---|
1200 | ELSE |
---|
1201 | zze = -fsde3w(ji+1,jj,jk1-1) - zuijk |
---|
1202 | pe = pe + & |
---|
1203 | integ2(fsde3w(ji+1,jj,jk1-1),-zuijk,& |
---|
1204 | asp(ji+1,jj,jk1-1),bsp(ji+1,jj,jk1-1),& |
---|
1205 | csp(ji+1,jj,jk1-1),dsp(ji+1,jj,jk1-1)) |
---|
1206 | EXIT |
---|
1207 | ENDIF |
---|
1208 | END DO |
---|
1209 | |
---|
1210 | IF(jk == mbathy(ji+1,jj)) bhitwe = 1 |
---|
1211 | |
---|
1212 | IF(bhitwe == 1) zuijk = -fsde3w(ji+1,jj,mbathy(ji+1,jj)) |
---|
1213 | |
---|
1214 | DO jk1 = jk-1, 1, -1 |
---|
1215 | IF(-fsde3w(ji,jj,jk1) < zuijk) THEN |
---|
1216 | pw = pw + & |
---|
1217 | integ2(fsde3w(ji,jj,jk1),fsde3w(ji,jj,jk1+1),& |
---|
1218 | asp(ji,jj,jk1),bsp(ji,jj,jk1),& |
---|
1219 | csp(ji,jj,jk1),dsp(ji,jj,jk1)) |
---|
1220 | IF(jk1 == 1) THEN |
---|
1221 | rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & |
---|
1222 | bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & |
---|
1223 | * (zuijk + fsde3w(ji,jj,1)) |
---|
1224 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1225 | rrw = rhdt1 |
---|
1226 | zzw = zuijk + fsde3w(ji,jj,1) |
---|
1227 | pw = pw + min(0.5 * (rhd(ji,jj,1) + rrw) * zzw, zhpi(ji,jj,1)) |
---|
1228 | END IF |
---|
1229 | ELSE |
---|
1230 | zzw = zuijk + fsde3w(ji,jj,jk1+1) |
---|
1231 | pw = pw + & |
---|
1232 | integ2(-zuijk,fsde3w(ji,jj,jk1+1),& |
---|
1233 | asp(ji,jj,jk1),bsp(ji,jj,jk1),& |
---|
1234 | csp(ji,jj,jk1),dsp(ji,jj,jk1)) |
---|
1235 | EXIT |
---|
1236 | ENDIF |
---|
1237 | END DO |
---|
1238 | |
---|
1239 | IF(jk == 1) THEN |
---|
1240 | rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & |
---|
1241 | bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & |
---|
1242 | * (zuijk + fsde3w(ji,jj,1)) |
---|
1243 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1244 | rrw = rhdt1 |
---|
1245 | zzw = zuijk + fsde3w(ji,jj,1) |
---|
1246 | pw = pw + min(0.5 * (rhd(ji,jj,1) + rrw) * zzw, zhpi(ji,jj,1)) |
---|
1247 | END IF |
---|
1248 | |
---|
1249 | ELSE |
---|
1250 | |
---|
1251 | DO jk1 = jk+1, mbathy(ji,jj) |
---|
1252 | IF(-fsde3w(ji,jj,jk1) > zuijk) THEN |
---|
1253 | pw = pw - & |
---|
1254 | integ2(fsde3w(ji,jj,jk1-1),fsde3w(ji,jj,jk1),& |
---|
1255 | asp(ji,jj,jk1-1),bsp(ji,jj,jk1-1),& |
---|
1256 | csp(ji,jj,jk1-1),dsp(ji,jj,jk1-1)) |
---|
1257 | IF(jk1 == mbathy(ji,jj)) bhitwe = 1 |
---|
1258 | ELSE |
---|
1259 | zzw = -fsde3w(ji,jj,jk1-1) - zuijk |
---|
1260 | pw = pw - & |
---|
1261 | integ2(fsde3w(ji,jj,jk1-1),-zuijk,& |
---|
1262 | asp(ji,jj,jk1-1),bsp(ji,jj,jk1-1),& |
---|
1263 | csp(ji,jj,jk1-1),dsp(ji,jj,jk1-1)) |
---|
1264 | EXIT |
---|
1265 | ENDIF |
---|
1266 | END DO |
---|
1267 | |
---|
1268 | IF(jk == mbathy(ji,jj)) bhitwe = 1 |
---|
1269 | |
---|
1270 | IF(bhitwe == 1) zuijk = -fsde3w(ji,jj,mbathy(ji,jj)) |
---|
1271 | |
---|
1272 | DO jk1 = jk-1, 1, -1 |
---|
1273 | IF(-fsde3w(ji+1,jj,jk1) < zuijk) THEN |
---|
1274 | pe = pe - & |
---|
1275 | integ2(fsde3w(ji+1,jj,jk1),fsde3w(ji+1,jj,jk1+1),& |
---|
1276 | asp(ji+1,jj,jk1),bsp(ji+1,jj,jk1),& |
---|
1277 | csp(ji+1,jj,jk1),dsp(ji+1,jj,jk1)) |
---|
1278 | IF(jk1 == 1) THEN |
---|
1279 | rhdt1 = rhd(ji+1,jj,1) - interp3(fsde3w(ji+1,jj,1),asp(ji+1,jj,1), & |
---|
1280 | bsp(ji+1,jj,1),csp(ji+1,jj,1),dsp(ji+1,jj,1)) & |
---|
1281 | * (zuijk + fsde3w(ji+1,jj,1)) |
---|
1282 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1283 | rre = rhdt1 |
---|
1284 | zze = zuijk + fsde3w(ji+1,jj,1) |
---|
1285 | pe = pe - min(0.5 * (rhd(ji+1,jj,1) + rre) * zze, zhpi(ji+1,jj,1)) |
---|
1286 | END IF |
---|
1287 | ELSE |
---|
1288 | zze = zuijk + fsde3w(ji+1,jj,jk1+1) |
---|
1289 | pe = pe - & |
---|
1290 | integ2(-zuijk,fsde3w(ji+1,jj,jk1+1),& |
---|
1291 | asp(ji+1,jj,jk1),bsp(ji+1,jj,jk1),& |
---|
1292 | csp(ji+1,jj,jk1),dsp(ji+1,jj,jk1)) |
---|
1293 | EXIT |
---|
1294 | ENDIF |
---|
1295 | END DO |
---|
1296 | |
---|
1297 | IF(jk == 1) THEN |
---|
1298 | rhdt1 = rhd(ji+1,jj,1) - interp3(fsde3w(ji+1,jj,1),asp(ji+1,jj,1), & |
---|
1299 | bsp(ji+1,jj,1),csp(ji+1,jj,1),dsp(ji+1,jj,1)) & |
---|
1300 | * (zuijk + fsde3w(ji+1,jj,1)) |
---|
1301 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1302 | rre = rhdt1 |
---|
1303 | zze = zuijk + fsde3w(ji+1,jj,1) |
---|
1304 | pe = pe - min(0.5 * (rhd(ji+1,jj,1) + rre) * zze, zhpi(ji+1,jj,1)) |
---|
1305 | END IF |
---|
1306 | |
---|
1307 | ENDIF |
---|
1308 | |
---|
1309 | |
---|
1310 | dpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
1311 | IF(lk_vvl) THEN |
---|
1312 | dpdx2 = zcoef0 / e1u(ji,jj) * (pw + pe + (sshn(ji+1,jj)-sshn(ji,jj))) |
---|
1313 | ELSE |
---|
1314 | dpdx2 = zcoef0 / e1u(ji,jj) * (pw + pe) |
---|
1315 | ENDIF |
---|
1316 | |
---|
1317 | ua(ji,jj,jk) = ua(ji,jj,jk) + (dpdx1 + dpdx2)*& |
---|
1318 | & umask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji+1,jj,jk) |
---|
1319 | |
---|
1320 | !! for v equation |
---|
1321 | |
---|
1322 | IF(-fsde3w(ji,jj+1,jk) > zvijk) THEN |
---|
1323 | DO jk1 = jk+1, mbathy(ji,jj+1) |
---|
1324 | IF(-fsde3w(ji,jj+1,jk1) > zvijk) THEN |
---|
1325 | pn = pn + & |
---|
1326 | integ2(fsde3w(ji,jj+1,jk1-1),fsde3w(ji,jj+1,jk1),& |
---|
1327 | asp(ji,jj+1,jk1-1),bsp(ji,jj+1,jk1-1),& |
---|
1328 | csp(ji,jj+1,jk1-1),dsp(ji,jj+1,jk1-1)) |
---|
1329 | IF(jk1 == mbathy(ji,jj+1)) bhitns = 1 |
---|
1330 | ELSE |
---|
1331 | zzn = -fsde3w(ji,jj+1,jk1-1) - zvijk |
---|
1332 | pn = pn + & |
---|
1333 | integ2(fsde3w(ji,jj+1,jk1-1),-zvijk,& |
---|
1334 | asp(ji,jj+1,jk1-1),bsp(ji,jj+1,jk1-1),& |
---|
1335 | csp(ji,jj+1,jk1-1),dsp(ji,jj+1,jk1-1)) |
---|
1336 | EXIT |
---|
1337 | ENDIF |
---|
1338 | END DO |
---|
1339 | |
---|
1340 | IF(jk == mbathy(ji,jj+1)) bhitns = 1 |
---|
1341 | |
---|
1342 | |
---|
1343 | IF(bhitns == 1) zvijk = -fsde3w(ji,jj+1,mbathy(ji,jj+1)) |
---|
1344 | |
---|
1345 | |
---|
1346 | DO jk1 = jk-1, 1, -1 |
---|
1347 | IF(-fsde3w(ji,jj,jk1) < zvijk) THEN |
---|
1348 | ps = ps + & |
---|
1349 | integ2(fsde3w(ji,jj,jk1),fsde3w(ji,jj,jk1+1),& |
---|
1350 | asp(ji,jj,jk1),bsp(ji,jj,jk1),& |
---|
1351 | csp(ji,jj,jk1),dsp(ji,jj,jk1)) |
---|
1352 | IF(jk1 == 1) THEN |
---|
1353 | rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & |
---|
1354 | bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & |
---|
1355 | * (zvijk + fsde3w(ji,jj,1)) |
---|
1356 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1357 | rrs = rhdt1 |
---|
1358 | zzs = zvijk + fsde3w(ji,jj,1) |
---|
1359 | ps = ps + min(0.5 * (rhd(ji,jj,1) + rrs ) * zzs, zhpi(ji,jj,1)) |
---|
1360 | END IF |
---|
1361 | ELSE |
---|
1362 | zzs = zvijk + fsde3w(ji,jj,jk1+1) |
---|
1363 | ps = ps + & |
---|
1364 | integ2(-zvijk,fsde3w(ji,jj,jk1+1),& |
---|
1365 | asp(ji,jj,jk1),bsp(ji,jj,jk1),& |
---|
1366 | csp(ji,jj,jk1),dsp(ji,jj,jk1)) |
---|
1367 | EXIT |
---|
1368 | ENDIF |
---|
1369 | END DO |
---|
1370 | |
---|
1371 | IF(jk == 1) THEN |
---|
1372 | rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & |
---|
1373 | bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & |
---|
1374 | * (zvijk + fsde3w(ji,jj,1)) |
---|
1375 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1376 | rrs = rhdt1 |
---|
1377 | zzs = zvijk + fsde3w(ji,jj,1) |
---|
1378 | ps = ps + min(0.5 * (rhd(ji,jj,1) + rrs) * zzs, zhpi(ji,jj,1)) |
---|
1379 | END IF |
---|
1380 | |
---|
1381 | ELSE |
---|
1382 | |
---|
1383 | DO jk1 = jk+1, mbathy(ji,jj) |
---|
1384 | IF(-fsde3w(ji,jj,jk1) > zvijk) THEN |
---|
1385 | ps = ps - & |
---|
1386 | integ2(fsde3w(ji,jj,jk1-1),fsde3w(ji,jj,jk1),& |
---|
1387 | asp(ji,jj,jk1-1),bsp(ji,jj,jk1-1),& |
---|
1388 | csp(ji,jj,jk1-1),dsp(ji,jj,jk1-1)) |
---|
1389 | IF(jk1 == mbathy(ji,jj)) bhitns = 1 |
---|
1390 | ELSE |
---|
1391 | zzs = -fsde3w(ji,jj,jk1-1) - zvijk |
---|
1392 | ps = ps - & |
---|
1393 | integ2(fsde3w(ji,jj,jk1-1),-zvijk,& |
---|
1394 | asp(ji,jj,jk1-1),bsp(ji,jj,jk1-1),& |
---|
1395 | csp(ji,jj,jk1-1),dsp(ji,jj,jk1-1)) |
---|
1396 | EXIT |
---|
1397 | ENDIF |
---|
1398 | END DO |
---|
1399 | |
---|
1400 | IF(jk == mbathy(ji,jj)) bhitns = 1 |
---|
1401 | |
---|
1402 | |
---|
1403 | IF(bhitns == 1) zvijk = -fsde3w(ji,jj,mbathy(ji,jj)) |
---|
1404 | |
---|
1405 | DO jk1 = jk-1, 1, -1 |
---|
1406 | IF(-fsde3w(ji,jj+1,jk1) < zvijk) THEN |
---|
1407 | pn = pn - & |
---|
1408 | integ2(fsde3w(ji,jj+1,jk1),fsde3w(ji,jj+1,jk1+1),& |
---|
1409 | asp(ji,jj+1,jk1),bsp(ji,jj+1,jk1),& |
---|
1410 | csp(ji,jj+1,jk1),dsp(ji,jj+1,jk1)) |
---|
1411 | IF(jk1 == 1) THEN |
---|
1412 | rhdt1 = rhd(ji,jj+1,1) - interp3(fsde3w(ji,jj+1,1),asp(ji,jj+1,1), & |
---|
1413 | bsp(ji,jj+1,1),csp(ji,jj+1,1),dsp(ji,jj+1,1)) & |
---|
1414 | * (zvijk + fsde3w(ji,jj+1,1)) |
---|
1415 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1416 | rrn = rhdt1 |
---|
1417 | zzn = zvijk + fsde3w(ji,jj+1,1) |
---|
1418 | pn = pn - min(0.5 * (rhd(ji,jj+1,1) + rrn) * zzn, zhpi(ji,jj+1,1)) |
---|
1419 | END IF |
---|
1420 | |
---|
1421 | ELSE |
---|
1422 | zzn = zvijk + fsde3w(ji,jj+1,jk1+1) |
---|
1423 | pn = pn - & |
---|
1424 | integ2(-zvijk,fsde3w(ji,jj+1,jk1+1),& |
---|
1425 | asp(ji,jj+1,jk1),bsp(ji,jj+1,jk1),& |
---|
1426 | csp(ji,jj+1,jk1),dsp(ji,jj+1,jk1)) |
---|
1427 | EXIT |
---|
1428 | ENDIF |
---|
1429 | END DO |
---|
1430 | |
---|
1431 | IF(jk == 1) THEN |
---|
1432 | rhdt1 = rhd(ji,jj+1,1) - interp3(fsde3w(ji,jj+1,1),asp(ji,jj+1,1), & |
---|
1433 | bsp(ji,jj+1,1),csp(ji,jj+1,1),dsp(ji,jj+1,1)) & |
---|
1434 | * (zvijk + fsde3w(ji,jj+1,1)) |
---|
1435 | rhdt1 = max(rhdt1,0.0_wp) |
---|
1436 | rrn = rhdt1 |
---|
1437 | zzn = zvijk + fsde3w(ji,jj+1,1) |
---|
1438 | pn = pn - min(0.5 * (rhd(ji,jj+1,1) + rrn) * zzn, zhpi(ji,jj+1,1)) |
---|
1439 | END IF |
---|
1440 | |
---|
1441 | ENDIF |
---|
1442 | |
---|
1443 | |
---|
1444 | dpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
1445 | if(lk_vvl) then |
---|
1446 | dpdy2 = zcoef0 / e2v(ji,jj) * (ps + pn + (sshn(ji,jj+1)-sshn(ji,jj))) |
---|
1447 | else |
---|
1448 | dpdy2 = zcoef0 / e2v(ji,jj) * (ps + pn ) |
---|
1449 | end if |
---|
1450 | |
---|
1451 | va(ji,jj,jk) = va(ji,jj,jk) + (dpdy1 + dpdy2)*& |
---|
1452 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
1453 | |
---|
1454 | |
---|
1455 | END DO |
---|
1456 | END DO |
---|
1457 | END DO |
---|
1458 | |
---|
1459 | ! Restore fsde3w and rhd |
---|
1460 | |
---|
1461 | fsde3w(:,:,:) = fsde3w_tmp(:,:,:) |
---|
1462 | rhd(:,:,:) = rhd_tmp(:,:,:) |
---|
1463 | |
---|
1464 | ! |
---|
1465 | IF( wrk_not_released(3, 3,4,5,6,7,8,9,10,11) ) & |
---|
1466 | CALL ctl_stop('dyn:hpg_prj: failed to release workspace arrays') |
---|
1467 | ! |
---|
1468 | |
---|
1469 | END SUBROUTINE hpg_prj |
---|
1470 | |
---|
1471 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
1472 | !!---------------------------------------------------------------------- |
---|
1473 | !! *** ROUTINE cspline *** |
---|
1474 | !! |
---|
1475 | !! ** Purpose : constrained cubic spline interpolation |
---|
1476 | !! |
---|
1477 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
1478 | !! Reference: K.W. Brodlie, A review of mehtods for curve and function |
---|
1479 | !! drawing, 1980 |
---|
1480 | !! |
---|
1481 | !!---------------------------------------------------------------------- |
---|
1482 | IMPLICIT NONE |
---|
1483 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
1484 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
1485 | ! the interpoated function |
---|
1486 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
1487 | ! 2: Linear |
---|
1488 | |
---|
1489 | ! Local Variables |
---|
1490 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1491 | INTEGER :: jpi, jpj, jpkm1 |
---|
1492 | REAL(wp) :: df1, df2, ddf1, ddf2, tmp1, tmp2, dxtmp |
---|
1493 | REAL(wp) :: dxtmp1, dxtmp2, alpha |
---|
1494 | REAL(wp) :: df(size(fsp,3)) |
---|
1495 | !!---------------------------------------------------------------------- |
---|
1496 | |
---|
1497 | jpi = size(fsp,1) |
---|
1498 | jpj = size(fsp,2) |
---|
1499 | jpkm1 = size(fsp,3) - 1 |
---|
1500 | |
---|
1501 | ! Clean output arrays |
---|
1502 | asp = 0.0_wp |
---|
1503 | bsp = 0.0_wp |
---|
1504 | csp = 0.0_wp |
---|
1505 | dsp = 0.0_wp |
---|
1506 | |
---|
1507 | |
---|
1508 | Do ji = 1, jpi |
---|
1509 | Do jj = 1, jpj |
---|
1510 | |
---|
1511 | If (polynomial_type == 1) Then !Constrained Cubic Spline |
---|
1512 | Do jk = 2, jpkm1-1 |
---|
1513 | dxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
1514 | dxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1515 | df1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / dxtmp1 |
---|
1516 | df2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / dxtmp2 |
---|
1517 | |
---|
1518 | alpha = ( dxtmp1 + 2._wp * dxtmp2 ) / ( dxtmp1 + dxtmp2 ) / 3._wp |
---|
1519 | |
---|
1520 | If(df1 * df2 <= 0._wp) Then |
---|
1521 | df(jk) = 0._wp |
---|
1522 | Else |
---|
1523 | df(jk) = df1 * df2 / ( ( 1._wp - alpha ) * df1 + alpha * df2 ) |
---|
1524 | End If |
---|
1525 | End Do |
---|
1526 | |
---|
1527 | df(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - & |
---|
1528 | & 0.5_wp * df(2) |
---|
1529 | df(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
1530 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
1531 | & 0.5_wp * df(jpkm1 - 1) |
---|
1532 | |
---|
1533 | Do jk = 1, jpkm1 - 1 |
---|
1534 | dxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1535 | tmp1 = (df(jk+1) + 2._wp * df(jk)) / dxtmp |
---|
1536 | tmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / dxtmp / dxtmp |
---|
1537 | ddf1 = -2._wp * tmp1 + tmp2 |
---|
1538 | tmp1 = (2._wp * df(jk+1) + df(jk)) / dxtmp |
---|
1539 | ddf2 = 2._wp * tmp1 - tmp2 |
---|
1540 | |
---|
1541 | dsp(ji,jj,jk) = (ddf2 - ddf1) / 6._wp / dxtmp |
---|
1542 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * ddf1 - xsp(ji,jj,jk)*ddf2 ) / 2._wp / dxtmp |
---|
1543 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / dxtmp - & |
---|
1544 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
1545 | & dsp(ji,jj,jk) * ( xsp(ji,jj,jk+1)**2 + & |
---|
1546 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk) + & |
---|
1547 | & xsp(ji,jj,jk)**2 ) |
---|
1548 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) - & |
---|
1549 | & csp(ji,jj,jk) * xsp(ji,jj,jk)**2 - & |
---|
1550 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)**3 |
---|
1551 | End Do |
---|
1552 | |
---|
1553 | Else If (polynomial_type == 2) Then !Linear |
---|
1554 | |
---|
1555 | Do jk = 1, jpkm1-1 |
---|
1556 | dxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1557 | tmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
1558 | |
---|
1559 | dsp(ji,jj,jk) = 0._wp |
---|
1560 | csp(ji,jj,jk) = 0._wp |
---|
1561 | bsp(ji,jj,jk) = tmp1 / dxtmp |
---|
1562 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
1563 | End Do |
---|
1564 | |
---|
1565 | Else |
---|
1566 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
1567 | End If |
---|
1568 | |
---|
1569 | End Do |
---|
1570 | End Do |
---|
1571 | |
---|
1572 | End Subroutine cspline |
---|
1573 | |
---|
1574 | |
---|
1575 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
1576 | !!---------------------------------------------------------------------- |
---|
1577 | !! *** ROUTINE interp1 *** |
---|
1578 | !! |
---|
1579 | !! ** Purpose : 1-d linear interpolation |
---|
1580 | !! |
---|
1581 | !! ** Method : |
---|
1582 | !! interpolation is straigt forward |
---|
1583 | !! extrapolation is also permitted (no value limit) |
---|
1584 | !! |
---|
1585 | !! H.Liu, Jan 2009, POL |
---|
1586 | !!---------------------------------------------------------------------- |
---|
1587 | IMPLICIT NONE |
---|
1588 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
1589 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
1590 | REAL(wp) :: deltx |
---|
1591 | !!---------------------------------------------------------------------- |
---|
1592 | |
---|
1593 | deltx = xr - xl |
---|
1594 | IF(abs(deltx) <= 10._wp * EPSILON(x)) THEN |
---|
1595 | f = 0.5_wp * (fl + fr) |
---|
1596 | ELSE |
---|
1597 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / deltx |
---|
1598 | END IF |
---|
1599 | |
---|
1600 | END FUNCTION interp1 |
---|
1601 | |
---|
1602 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
1603 | !!---------------------------------------------------------------------- |
---|
1604 | !! *** ROUTINE interp1 *** |
---|
1605 | !! |
---|
1606 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
1607 | !! |
---|
1608 | !! ** Method : cubic spline interpolation |
---|
1609 | !! |
---|
1610 | !!---------------------------------------------------------------------- |
---|
1611 | IMPLICIT NONE |
---|
1612 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
1613 | REAL(wp) :: f ! value from the interpolation |
---|
1614 | !!---------------------------------------------------------------------- |
---|
1615 | |
---|
1616 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
1617 | |
---|
1618 | END FUNCTION interp2 |
---|
1619 | |
---|
1620 | |
---|
1621 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
1622 | !!---------------------------------------------------------------------- |
---|
1623 | !! *** ROUTINE interp1 *** |
---|
1624 | !! |
---|
1625 | !! ** Purpose : deriavtive of a cubic spline function |
---|
1626 | !! |
---|
1627 | !! ** Method : |
---|
1628 | !! |
---|
1629 | !!---------------------------------------------------------------------- |
---|
1630 | IMPLICIT NONE |
---|
1631 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
1632 | REAL(wp) :: f ! value from the interpolation |
---|
1633 | !!---------------------------------------------------------------------- |
---|
1634 | |
---|
1635 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
1636 | |
---|
1637 | END FUNCTION interp3 |
---|
1638 | |
---|
1639 | |
---|
1640 | FUNCTION integ2(xl, xr, a, b, c, d) RESULT(f) |
---|
1641 | !!---------------------------------------------------------------------- |
---|
1642 | !! *** ROUTINE interp1 *** |
---|
1643 | !! |
---|
1644 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
1645 | !! |
---|
1646 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
1647 | !! |
---|
1648 | !!---------------------------------------------------------------------- |
---|
1649 | IMPLICIT NONE |
---|
1650 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
1651 | REAL(wp) :: a1, a2,a3 |
---|
1652 | REAL(wp) :: f ! integration result |
---|
1653 | !!---------------------------------------------------------------------- |
---|
1654 | |
---|
1655 | a1 = 0.5_wp * b |
---|
1656 | a2 = c / 3.0_wp |
---|
1657 | a3 = 0.25_wp * d |
---|
1658 | |
---|
1659 | f = xr * ( a + xr * ( a1 + xr * ( a2 + a3 * xr ) ) ) - & |
---|
1660 | & xl * ( a + xl * ( a1 + xl * ( a2 + a3 * xl ) ) ) |
---|
1661 | |
---|
1662 | END FUNCTION integ2 |
---|
1663 | |
---|
1664 | |
---|
1665 | !!====================================================================== |
---|
1666 | END MODULE dynhpg |
---|