1 | MODULE dynhpg |
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2 | !!====================================================================== |
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3 | !! *** MODULE dynhpg *** |
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4 | !! Ocean dynamics: hydrostatic pressure gradient trend |
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5 | !!====================================================================== |
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6 | !! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code |
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7 | !! 5.0 ! 1991-11 (G. Madec) |
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8 | !! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates |
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9 | !! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg |
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10 | !! 8.5 ! 2002-07 (G. Madec) F90: Free form and module |
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11 | !! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code |
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12 | !! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options |
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13 | !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot |
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14 | !! - ! 2005-11 (G. Madec) style & small optimisation |
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15 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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16 | !! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates |
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17 | !! ! (A. Coward) suppression of hel, wdj and rot options |
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18 | !! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity |
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19 | !! 4.2 ! 2020-12 (M. Bell, A. Young) hpg_djc: revised djc scheme |
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20 | !!---------------------------------------------------------------------- |
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21 | |
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22 | !!---------------------------------------------------------------------- |
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23 | !! dyn_hpg : update the momentum trend with the now horizontal |
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24 | !! gradient of the hydrostatic pressure |
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25 | !! dyn_hpg_init : initialisation and control of options |
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26 | !! hpg_zco : z-coordinate scheme |
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27 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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28 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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29 | !! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf |
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30 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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31 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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32 | !!---------------------------------------------------------------------- |
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33 | USE oce ! ocean dynamics and tracers |
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34 | USE isf_oce , ONLY : risfload ! ice shelf (risfload variable) |
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35 | USE isfload , ONLY : isf_load ! ice shelf (isf_load routine ) |
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36 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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37 | USE dom_oce ! ocean space and time domain |
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38 | USE wet_dry ! wetting and drying |
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39 | USE phycst ! physical constants |
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40 | USE trd_oce ! trends: ocean variables |
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41 | USE trddyn ! trend manager: dynamics |
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42 | USE zpshde ! partial step: hor. derivative (zps_hde routine) |
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43 | ! |
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44 | USE in_out_manager ! I/O manager |
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45 | USE prtctl ! Print control |
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46 | USE lbclnk ! lateral boundary condition |
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47 | USE lib_mpp ! MPP library |
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48 | USE eosbn2 ! compute density |
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49 | USE timing ! Timing |
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50 | USE iom |
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51 | |
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52 | IMPLICIT NONE |
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53 | PRIVATE |
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54 | |
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55 | PUBLIC dyn_hpg ! routine called by step module |
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56 | PUBLIC dyn_hpg_init ! routine called by opa module |
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57 | |
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58 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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59 | LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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60 | LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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61 | LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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62 | LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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63 | LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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64 | LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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65 | |
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66 | ! !! Flag to control the type of hydrostatic pressure gradient |
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67 | INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion |
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68 | INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps |
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69 | INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation) |
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70 | INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation) |
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71 | INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial) |
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72 | INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme) |
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73 | INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf |
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74 | ! |
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75 | INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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76 | ! |
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77 | LOGICAL :: ln_hpg_djc_vnh, ln_hpg_djc_vnv ! flag to specify hpg_djc boundary condition type |
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78 | REAL(wp), PUBLIC :: aco_bc_hor, bco_bc_hor, aco_bc_vrt, bco_bc_vrt !: coefficients for hpg_djc hor and vert boundary conditions |
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79 | |
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80 | !! * Substitutions |
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81 | # include "do_loop_substitute.h90" |
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82 | # include "domzgr_substitute.h90" |
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83 | # include "single_precision_substitute.h90" |
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84 | |
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85 | !!---------------------------------------------------------------------- |
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86 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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87 | !! $Id$ |
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88 | !! Software governed by the CeCILL license (see ./LICENSE) |
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89 | !!---------------------------------------------------------------------- |
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90 | CONTAINS |
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91 | |
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92 | SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs ) |
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93 | !!--------------------------------------------------------------------- |
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94 | !! *** ROUTINE dyn_hpg *** |
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95 | !! |
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96 | !! ** Method : Call the hydrostatic pressure gradient routine |
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97 | !! using the scheme defined in the namelist |
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98 | !! |
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99 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
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100 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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101 | !!---------------------------------------------------------------------- |
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102 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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103 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
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104 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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105 | ! |
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106 | REAL(dp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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107 | !!---------------------------------------------------------------------- |
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108 | ! |
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109 | IF( ln_timing ) CALL timing_start('dyn_hpg') |
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110 | ! |
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111 | IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn) |
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112 | ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) ) |
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113 | ztrdu(:,:,:) = puu(:,:,:,Krhs) |
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114 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) |
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115 | ENDIF |
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116 | ! |
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117 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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118 | CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate |
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119 | CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation) |
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120 | CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation) |
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121 | CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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122 | CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme) |
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123 | CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf |
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124 | END SELECT |
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125 | ! |
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126 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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127 | ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:) |
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128 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:) |
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129 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm ) |
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130 | DEALLOCATE( ztrdu , ztrdv ) |
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131 | ENDIF |
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132 | ! |
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133 | IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=CASTWP(puu(:,:,:,Krhs)), clinfo1=' hpg - Ua: ', mask1=umask, & |
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134 | & tab3d_2=CASTWP(pvv(:,:,:,Krhs)), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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135 | ! |
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136 | IF( ln_timing ) CALL timing_stop('dyn_hpg') |
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137 | ! |
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138 | END SUBROUTINE dyn_hpg |
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139 | |
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140 | |
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141 | SUBROUTINE dyn_hpg_init( Kmm ) |
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142 | !!---------------------------------------------------------------------- |
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143 | !! *** ROUTINE dyn_hpg_init *** |
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144 | !! |
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145 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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146 | !! computation and consistency control |
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147 | !! |
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148 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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149 | !! with the type of vertical coordinate used (zco, zps, sco) |
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150 | !!---------------------------------------------------------------------- |
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151 | INTEGER, INTENT( in ) :: Kmm ! ocean time level index |
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152 | ! |
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153 | INTEGER :: ioptio = 0 ! temporary integer |
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154 | INTEGER :: ios ! Local integer output status for namelist read |
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155 | !! |
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156 | INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF |
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157 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density |
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158 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF |
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159 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF |
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160 | !! |
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161 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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162 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, & |
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163 | & ln_hpg_djc_vnh, ln_hpg_djc_vnv |
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164 | !!---------------------------------------------------------------------- |
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165 | ! |
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166 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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167 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' ) |
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168 | ! |
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169 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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170 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' ) |
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171 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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172 | ! |
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173 | IF(lwp) THEN ! Control print |
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174 | WRITE(numout,*) |
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175 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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176 | WRITE(numout,*) '~~~~~~~~~~~~' |
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177 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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178 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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179 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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180 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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181 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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182 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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183 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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184 | ENDIF |
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185 | ! |
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186 | IF( .NOT.ln_linssh .AND. (ln_hpg_zco.OR.ln_hpg_zps) ) & |
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187 | & CALL ctl_stop( 'dyn_hpg_init : non-linear free surface incompatible with hpg_zco or hpg_zps' ) |
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188 | ! |
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189 | IF( (.NOT.ln_hpg_isf .AND. ln_isfcav) .OR. (ln_hpg_isf .AND. .NOT.ln_isfcav) ) & |
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190 | & CALL ctl_stop( 'dyn_hpg_init : ln_hpg_isf=T requires ln_isfcav=T and vice versa' ) |
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191 | ! |
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192 | #if defined key_qco |
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193 | IF( ln_hpg_isf ) THEN |
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194 | CALL ctl_stop( 'dyn_hpg_init : key_qco and ln_hpg_isf not yet compatible' ) |
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195 | ENDIF |
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196 | #endif |
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197 | ! |
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198 | ! ! Set nhpg from ln_hpg_... flags & consistency check |
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199 | nhpg = np_ERROR |
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200 | ioptio = 0 |
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201 | IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF |
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202 | IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF |
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203 | IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF |
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204 | IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF |
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205 | IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF |
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206 | IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF |
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207 | ! |
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208 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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209 | ! |
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210 | IF(lwp) THEN |
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211 | WRITE(numout,*) |
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212 | SELECT CASE( nhpg ) |
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213 | CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps ' |
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214 | CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)' |
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215 | CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)' |
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216 | CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)' |
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217 | CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)' |
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218 | CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf' |
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219 | END SELECT |
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220 | WRITE(numout,*) |
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221 | ENDIF |
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222 | ! |
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223 | IF ( ln_hpg_djc ) THEN |
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224 | IF (ln_hpg_djc_vnh) THEN ! Von Neumann boundary condition |
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225 | IF(lwp) WRITE(numout,*) ' horizontal bc: von Neumann ' |
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226 | aco_bc_hor = 6.0_wp/5.0_wp |
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227 | bco_bc_hor = 7.0_wp/15.0_wp |
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228 | ELSE ! Linear extrapolation |
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229 | IF(lwp) WRITE(numout,*) ' horizontal bc: linear extrapolation' |
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230 | aco_bc_hor = 3.0_wp/2.0_wp |
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231 | bco_bc_hor = 1.0_wp/2.0_wp |
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232 | END IF |
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233 | IF (ln_hpg_djc_vnv) THEN ! Von Neumann boundary condition |
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234 | IF(lwp) WRITE(numout,*) ' vertical bc: von Neumann ' |
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235 | aco_bc_vrt = 6.0_wp/5.0_wp |
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236 | bco_bc_vrt = 7.0_wp/15.0_wp |
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237 | ELSE ! Linear extrapolation |
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238 | IF(lwp) WRITE(numout,*) ' vertical bc: linear extrapolation' |
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239 | aco_bc_vrt = 3.0_wp/2.0_wp |
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240 | bco_bc_vrt = 1.0_wp/2.0_wp |
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241 | END IF |
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242 | END IF |
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243 | ! |
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244 | END SUBROUTINE dyn_hpg_init |
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245 | |
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246 | |
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247 | SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs ) |
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248 | !!--------------------------------------------------------------------- |
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249 | !! *** ROUTINE hpg_zco *** |
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250 | !! |
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251 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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252 | !! The now hydrostatic pressure gradient at a given level, jk, |
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253 | !! is computed by taking the vertical integral of the in-situ |
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254 | !! density gradient along the model level from the suface to that |
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255 | !! level: zhpi = grav ..... |
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256 | !! zhpj = grav ..... |
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257 | !! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)). |
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258 | !! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi |
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259 | !! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj |
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260 | !! |
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261 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
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262 | !!---------------------------------------------------------------------- |
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263 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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264 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
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265 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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266 | ! |
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267 | INTEGER :: ji, jj, jk ! dummy loop indices |
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268 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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269 | REAL(wp), DIMENSION(jpi,jpj) :: zhpi, zhpj |
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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_zco : hydrostatic pressure gradient trend' |
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275 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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276 | ENDIF |
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277 | ! |
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278 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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279 | ! |
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280 | DO_2D( 0, 0, 0, 0 ) ! Surface value |
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281 | zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm) |
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282 | ! ! hydrostatic pressure gradient |
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283 | zhpi(ji,jj) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
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284 | zhpj(ji,jj) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
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285 | ! ! add to the general momentum trend |
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286 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj) |
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287 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj) |
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288 | END_2D |
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289 | ! |
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290 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1) |
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291 | zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm) |
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292 | ! ! hydrostatic pressure gradient |
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293 | zhpi(ji,jj) = zhpi(ji,jj) + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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294 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
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295 | |
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296 | zhpj(ji,jj) = zhpj(ji,jj) + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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297 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
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298 | ! ! add to the general momentum trend |
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299 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj) |
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300 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj) |
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301 | END_3D |
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302 | ! |
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303 | END SUBROUTINE hpg_zco |
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304 | |
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305 | |
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306 | SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs ) |
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307 | !!--------------------------------------------------------------------- |
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308 | !! *** ROUTINE hpg_zps *** |
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309 | !! |
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310 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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311 | !! |
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312 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
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313 | !!---------------------------------------------------------------------- |
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314 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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315 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
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316 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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317 | !! |
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318 | INTEGER :: ji, jj, jk ! dummy loop indices |
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319 | INTEGER :: iku, ikv ! temporary integers |
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320 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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321 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
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322 | REAL(wp), DIMENSION(jpi,jpj,jpts) :: zgtsu, zgtsv |
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323 | REAL(wp), DIMENSION(jpi,jpj) :: zgru, zgrv |
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324 | !!---------------------------------------------------------------------- |
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325 | ! |
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326 | IF( kt == nit000 ) THEN |
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327 | IF(lwp) WRITE(numout,*) |
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328 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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329 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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330 | ENDIF |
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331 | |
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332 | ! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level |
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333 | CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv ) |
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334 | |
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335 | ! Local constant initialization |
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336 | zcoef0 = - grav * 0.5_wp |
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337 | |
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338 | ! Surface value (also valid in partial step case) |
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339 | DO_2D( 0, 0, 0, 0 ) |
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340 | zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm) |
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341 | ! hydrostatic pressure gradient |
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342 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
343 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
344 | ! add to the general momentum trend |
---|
345 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) |
---|
346 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) |
---|
347 | END_2D |
---|
348 | |
---|
349 | ! interior value (2=<jk=<jpkm1) |
---|
350 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
351 | zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm) |
---|
352 | ! hydrostatic pressure gradient |
---|
353 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
354 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
355 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
---|
356 | |
---|
357 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
358 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
359 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
---|
360 | ! add to the general momentum trend |
---|
361 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) |
---|
362 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) |
---|
363 | END_3D |
---|
364 | |
---|
365 | ! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90) |
---|
366 | DO_2D( 0, 0, 0, 0 ) |
---|
367 | iku = mbku(ji,jj) |
---|
368 | ikv = mbkv(ji,jj) |
---|
369 | zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) ) |
---|
370 | zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) ) |
---|
371 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
372 | puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value |
---|
373 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
374 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj) |
---|
375 | puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
376 | ENDIF |
---|
377 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
378 | pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value |
---|
379 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
380 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj) |
---|
381 | pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
382 | ENDIF |
---|
383 | END_2D |
---|
384 | ! |
---|
385 | END SUBROUTINE hpg_zps |
---|
386 | |
---|
387 | |
---|
388 | SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs ) |
---|
389 | !!--------------------------------------------------------------------- |
---|
390 | !! *** ROUTINE hpg_sco *** |
---|
391 | !! |
---|
392 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
393 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
394 | !! is computed by taking the vertical integral of the in-situ |
---|
395 | !! density gradient along the model level from the suface to that |
---|
396 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
397 | !! to the horizontal pressure gradient : |
---|
398 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
399 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
400 | !! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)). |
---|
401 | !! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi |
---|
402 | !! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj |
---|
403 | !! |
---|
404 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
---|
405 | !!---------------------------------------------------------------------- |
---|
406 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
407 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
408 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
409 | !! |
---|
410 | INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices |
---|
411 | REAL(wp) :: zcoef0, zuap, zvap, ztmp ! local scalars |
---|
412 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
413 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
---|
414 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
415 | !!---------------------------------------------------------------------- |
---|
416 | ! |
---|
417 | IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj)) |
---|
418 | ! |
---|
419 | IF( kt == nit000 ) THEN |
---|
420 | IF(lwp) WRITE(numout,*) |
---|
421 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
422 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
423 | ENDIF |
---|
424 | ! |
---|
425 | zcoef0 = - grav * 0.5_wp |
---|
426 | ! |
---|
427 | IF( ln_wd_il ) THEN |
---|
428 | DO_2D( 0, 0, 0, 0 ) |
---|
429 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
430 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
431 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) & |
---|
432 | & > rn_wdmin1 + rn_wdmin2 |
---|
433 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
434 | & MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
435 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
436 | |
---|
437 | IF(ll_tmp1) THEN |
---|
438 | zcpx(ji,jj) = 1.0_wp |
---|
439 | ELSE IF(ll_tmp2) THEN |
---|
440 | ! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here |
---|
441 | zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
442 | & / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) ) |
---|
443 | ELSE |
---|
444 | zcpx(ji,jj) = 0._wp |
---|
445 | END IF |
---|
446 | |
---|
447 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
448 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
449 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) & |
---|
450 | & > rn_wdmin1 + rn_wdmin2 |
---|
451 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
452 | & MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
453 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
454 | |
---|
455 | IF(ll_tmp1) THEN |
---|
456 | zcpy(ji,jj) = 1.0_wp |
---|
457 | ELSE IF(ll_tmp2) THEN |
---|
458 | ! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here |
---|
459 | zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
460 | & / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) ) |
---|
461 | ELSE |
---|
462 | zcpy(ji,jj) = 0._wp |
---|
463 | END IF |
---|
464 | END_2D |
---|
465 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp ) |
---|
466 | END IF |
---|
467 | ! |
---|
468 | DO_2D( 0, 0, 0, 0 ) ! Surface value |
---|
469 | ! ! hydrostatic pressure gradient along s-surfaces |
---|
470 | zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) & |
---|
471 | & * ( e3w(ji+1,jj ,1,Kmm) * rhd(ji+1,jj ,1) & |
---|
472 | & - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) ) |
---|
473 | zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) & |
---|
474 | & * ( e3w(ji ,jj+1,1,Kmm) * rhd(ji ,jj+1,1) & |
---|
475 | & - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) ) |
---|
476 | ! ! s-coordinate pressure gradient correction |
---|
477 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & |
---|
478 | & * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
479 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & |
---|
480 | & * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
481 | ! |
---|
482 | IF( ln_wd_il ) THEN |
---|
483 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
484 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
485 | zuap = zuap * zcpx(ji,jj) |
---|
486 | zvap = zvap * zcpy(ji,jj) |
---|
487 | ENDIF |
---|
488 | ! ! add to the general momentum trend |
---|
489 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap |
---|
490 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap |
---|
491 | END_2D |
---|
492 | ! |
---|
493 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1) |
---|
494 | ! ! hydrostatic pressure gradient along s-surfaces |
---|
495 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) & |
---|
496 | & * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
497 | & - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) |
---|
498 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) & |
---|
499 | & * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
500 | & - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) |
---|
501 | ! ! s-coordinate pressure gradient correction |
---|
502 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) & |
---|
503 | & * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj) |
---|
504 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
505 | & * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj) |
---|
506 | ! |
---|
507 | IF( ln_wd_il ) THEN |
---|
508 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
509 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
510 | zuap = zuap * zcpx(ji,jj) |
---|
511 | zvap = zvap * zcpy(ji,jj) |
---|
512 | ENDIF |
---|
513 | ! |
---|
514 | ! add to the general momentum trend |
---|
515 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap |
---|
516 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap |
---|
517 | END_3D |
---|
518 | ! |
---|
519 | IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy ) |
---|
520 | ! |
---|
521 | END SUBROUTINE hpg_sco |
---|
522 | |
---|
523 | |
---|
524 | SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs ) |
---|
525 | !!--------------------------------------------------------------------- |
---|
526 | !! *** ROUTINE hpg_isf *** |
---|
527 | !! |
---|
528 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
529 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
530 | !! is computed by taking the vertical integral of the in-situ |
---|
531 | !! density gradient along the model level from the suface to that |
---|
532 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
533 | !! to the horizontal pressure gradient : |
---|
534 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
535 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
536 | !! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)). |
---|
537 | !! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi |
---|
538 | !! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj |
---|
539 | !! iceload is added |
---|
540 | !! |
---|
541 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
---|
542 | !!---------------------------------------------------------------------- |
---|
543 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
544 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
545 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
546 | !! |
---|
547 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
548 | INTEGER :: ikt , ikti1, iktj1 ! local integer |
---|
549 | REAL(wp) :: ze3w, ze3wi1, ze3wj1 ! local scalars |
---|
550 | REAL(wp) :: zcoef0, zuap, zvap ! - - |
---|
551 | REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj |
---|
552 | REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top |
---|
553 | REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce |
---|
554 | !!---------------------------------------------------------------------- |
---|
555 | ! |
---|
556 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
---|
557 | ! |
---|
558 | ! ! iniitialised to 0. zhpi zhpi |
---|
559 | zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp |
---|
560 | |
---|
561 | ! compute rhd at the ice/oce interface (ocean side) |
---|
562 | ! usefull to reduce residual current in the test case ISOMIP with no melting |
---|
563 | DO ji = 1, jpi |
---|
564 | DO jj = 1, jpj |
---|
565 | ikt = mikt(ji,jj) |
---|
566 | zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm) |
---|
567 | zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm) |
---|
568 | END DO |
---|
569 | END DO |
---|
570 | CALL eos( zts_top, risfdep, zrhdtop_oce ) |
---|
571 | |
---|
572 | ! !===========================! |
---|
573 | ! !===== surface value =====! |
---|
574 | ! !===========================! |
---|
575 | DO_2D( 0, 0, 0, 0 ) |
---|
576 | ikt = mikt(ji ,jj ) ; ze3w = e3w(ji ,jj ,ikt ,Kmm) |
---|
577 | ikti1 = mikt(ji+1,jj ) ; ze3wi1 = e3w(ji+1,jj ,ikti1,Kmm) |
---|
578 | iktj1 = mikt(ji ,jj+1) ; ze3wj1 = e3w(ji ,jj+1,iktj1,Kmm) |
---|
579 | ! ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
580 | ! ! we assume ISF is in isostatic equilibrium |
---|
581 | zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) * ( risfload(ji+1,jj) - risfload(ji,jj) & |
---|
582 | & + 0.5_wp * ( ze3wi1 * ( rhd(ji+1,jj,ikti1) + zrhdtop_oce(ji+1,jj) ) & |
---|
583 | & - ze3w * ( rhd(ji ,jj,ikt ) + zrhdtop_oce(ji ,jj) ) ) ) |
---|
584 | zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) * ( risfload(ji,jj+1) - risfload(ji,jj) & |
---|
585 | & + 0.5_wp * ( ze3wj1 * ( rhd(ji,jj+1,iktj1) + zrhdtop_oce(ji,jj+1) ) & |
---|
586 | & - ze3w * ( rhd(ji,jj ,ikt ) + zrhdtop_oce(ji,jj ) ) ) ) |
---|
587 | ! ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
588 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & |
---|
589 | & * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
590 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & |
---|
591 | & * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
592 | ! ! add to the general momentum trend |
---|
593 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
594 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
595 | END_2D |
---|
596 | ! |
---|
597 | ! !=============================! |
---|
598 | ! !===== interior values =====! |
---|
599 | ! !=============================! |
---|
600 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
601 | ze3w = e3w(ji ,jj ,jk,Kmm) |
---|
602 | ze3wi1 = e3w(ji+1,jj ,jk,Kmm) |
---|
603 | ze3wj1 = e3w(ji ,jj+1,jk,Kmm) |
---|
604 | ! ! hydrostatic pressure gradient along s-surfaces |
---|
605 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
606 | & * ( ze3wi1 * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) * wmask(ji+1,jj,jk) & |
---|
607 | & - ze3w * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) * wmask(ji ,jj,jk) ) |
---|
608 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
609 | & * ( ze3wj1 * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) * wmask(ji,jj+1,jk) & |
---|
610 | & - ze3w * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) * wmask(ji,jj ,jk) ) |
---|
611 | ! ! s-coordinate pressure gradient correction |
---|
612 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) & |
---|
613 | & * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
614 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
615 | & * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
616 | ! ! add to the general momentum trend |
---|
617 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
618 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk) |
---|
619 | END_3D |
---|
620 | ! |
---|
621 | END SUBROUTINE hpg_isf |
---|
622 | |
---|
623 | |
---|
624 | SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs ) |
---|
625 | !!--------------------------------------------------------------------- |
---|
626 | !! *** ROUTINE hpg_djc *** |
---|
627 | !! |
---|
628 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
629 | !! |
---|
630 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
631 | !!---------------------------------------------------------------------- |
---|
632 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
633 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
634 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
635 | !! |
---|
636 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
637 | INTEGER :: iktb, iktt ! jk indices at tracer points for top and bottom points |
---|
638 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
639 | REAL(wp) :: z_grav_10, z1_12 |
---|
640 | REAL(wp) :: cffu, cffx ! " " |
---|
641 | REAL(wp) :: cffv, cffy ! " " |
---|
642 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
643 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
---|
644 | |
---|
645 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdzx, zdzy, zdzz ! Primitive grid differences ('delta_xyz') |
---|
646 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdz_i, zdz_j, zdz_k ! Harmonic average of primitive grid differences ('d_xyz') |
---|
647 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdrhox, zdrhoy, zdrhoz ! Primitive rho differences ('delta_rho') |
---|
648 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdrho_i, zdrho_j, zdrho_k ! Harmonic average of primitive rho differences ('d_rho') |
---|
649 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rho_i, z_rho_j, z_rho_k ! Face intergrals |
---|
650 | REAL(wp), DIMENSION(jpi,jpj) :: zz_dz_i, zz_dz_j, zz_drho_i, zz_drho_j ! temporary arrays |
---|
651 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
652 | !!---------------------------------------------------------------------- |
---|
653 | ! |
---|
654 | IF( ln_wd_il ) THEN |
---|
655 | ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) ) |
---|
656 | DO_2D( 0, 0, 0, 0 ) |
---|
657 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
658 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
659 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) & |
---|
660 | & > rn_wdmin1 + rn_wdmin2 |
---|
661 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
662 | & MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
663 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
664 | IF(ll_tmp1) THEN |
---|
665 | zcpx(ji,jj) = 1.0_wp |
---|
666 | ELSE IF(ll_tmp2) THEN |
---|
667 | ! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here |
---|
668 | zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
669 | & / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) ) |
---|
670 | ELSE |
---|
671 | zcpx(ji,jj) = 0._wp |
---|
672 | END IF |
---|
673 | |
---|
674 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
675 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
676 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) & |
---|
677 | & > rn_wdmin1 + rn_wdmin2 |
---|
678 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
679 | & MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
680 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
681 | |
---|
682 | IF(ll_tmp1) THEN |
---|
683 | zcpy(ji,jj) = 1.0_wp |
---|
684 | ELSE IF(ll_tmp2) THEN |
---|
685 | ! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here |
---|
686 | zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
687 | & / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) ) |
---|
688 | ELSE |
---|
689 | zcpy(ji,jj) = 0._wp |
---|
690 | END IF |
---|
691 | END_2D |
---|
692 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp ) |
---|
693 | END IF |
---|
694 | |
---|
695 | IF( kt == nit000 ) THEN |
---|
696 | IF(lwp) WRITE(numout,*) |
---|
697 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
698 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
699 | ENDIF |
---|
700 | |
---|
701 | ! Local constant initialization |
---|
702 | zcoef0 = - grav * 0.5_wp |
---|
703 | z_grav_10 = grav / 10._wp |
---|
704 | z1_12 = 1.0_wp / 12._wp |
---|
705 | |
---|
706 | !---------------------------------------------------------------------------------------- |
---|
707 | ! 1. compute and store elementary vertical differences in provisional arrays |
---|
708 | !---------------------------------------------------------------------------------------- |
---|
709 | |
---|
710 | !!bug gm Not a true bug, but... zdzz=e3w for zdzx, zdzy verify what it is really |
---|
711 | |
---|
712 | DO_3D( 1, 1, 1, 1, 2, jpkm1 ) |
---|
713 | zdrhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
714 | zdzz (ji,jj,jk) = - gde3w(ji ,jj ,jk) + gde3w(ji,jj,jk-1) |
---|
715 | END_3D |
---|
716 | |
---|
717 | !------------------------------------------------------------------------- |
---|
718 | ! 2. compute harmonic averages for vertical differences using eq. 5.18 |
---|
719 | !------------------------------------------------------------------------- |
---|
720 | zep = 1.e-15 |
---|
721 | |
---|
722 | !! mb zdrho_k, zdz_k, zdrho_i, zdz_i, zdrho_j, zdz_j re-centred about the point (ji,jj,jk) |
---|
723 | zdrho_k(:,:,:) = 0._wp |
---|
724 | zdz_k (:,:,:) = 0._wp |
---|
725 | |
---|
726 | DO_3D( 1, 1, 1, 1, 2, jpk-2 ) |
---|
727 | cffw = 2._wp * zdrhoz(ji ,jj ,jk) * zdrhoz(ji,jj,jk+1) |
---|
728 | IF( cffw > zep) THEN |
---|
729 | zdrho_k(ji,jj,jk) = cffw / ( zdrhoz(ji,jj,jk) + zdrhoz(ji,jj,jk+1) ) |
---|
730 | ENDIF |
---|
731 | zdz_k(ji,jj,jk) = 2._wp * zdzz(ji,jj,jk) * zdzz(ji,jj,jk+1) & |
---|
732 | & / ( zdzz(ji,jj,jk) + zdzz(ji,jj,jk+1) ) |
---|
733 | END_3D |
---|
734 | |
---|
735 | !---------------------------------------------------------------------------------- |
---|
736 | ! 3. apply boundary conditions at top and bottom using 5.36-5.37 |
---|
737 | !---------------------------------------------------------------------------------- |
---|
738 | |
---|
739 | ! mb for sea-ice shelves we will need to re-write this upper boundary condition in the same form as the lower boundary condition |
---|
740 | zdrho_k(:,:,1) = aco_bc_vrt * ( rhd (:,:,2) - rhd (:,:,1) ) - bco_bc_vrt * zdrho_k(:,:,2) |
---|
741 | zdz_k (:,:,1) = aco_bc_vrt * (-gde3w(:,:,2) + gde3w(:,:,1) ) - bco_bc_vrt * zdz_k (:,:,2) |
---|
742 | |
---|
743 | DO_2D( 1, 1, 1, 1 ) |
---|
744 | IF ( mbkt(ji,jj)>1 ) THEN |
---|
745 | iktb = mbkt(ji,jj) |
---|
746 | zdrho_k(ji,jj,iktb) = aco_bc_vrt * ( rhd(ji,jj,iktb) - rhd(ji,jj,iktb-1) ) - bco_bc_vrt * zdrho_k(ji,jj,iktb-1) |
---|
747 | zdz_k (ji,jj,iktb) = aco_bc_vrt * (-gde3w(ji,jj,iktb) + gde3w(ji,jj,iktb-1) ) - bco_bc_vrt * zdz_k (ji,jj,iktb-1) |
---|
748 | END IF |
---|
749 | END_2D |
---|
750 | |
---|
751 | !-------------------------------------------------------------- |
---|
752 | ! 4. Compute side face integrals |
---|
753 | !------------------------------------------------------------- |
---|
754 | |
---|
755 | !! ssh replaces e3w_n ; gde3w is a depth; the formulae involve heights |
---|
756 | !! rho_k stores grav * FX / rho_0 |
---|
757 | |
---|
758 | !-------------------------------------------------------------- |
---|
759 | ! 4. a) Upper half of top-most grid box, compute and store |
---|
760 | !------------------------------------------------------------- |
---|
761 | ! *** AY note: ssh(ji,jj,Kmm) + gde3w(ji,jj,1) = e3w(ji,jj,1,Kmm) |
---|
762 | DO_2D( 0, 1, 0, 1) |
---|
763 | z_rho_k(ji,jj,1) = grav * ( ssh(ji,jj,Kmm) + gde3w(ji,jj,1) ) & |
---|
764 | & * ( rhd(ji,jj,1) & |
---|
765 | & + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) & |
---|
766 | & * ( ssh (ji,jj,Kmm) + gde3w(ji,jj,1) ) & |
---|
767 | & / ( - gde3w(ji,jj,2) + gde3w(ji,jj,1) ) ) |
---|
768 | END_2D |
---|
769 | |
---|
770 | !-------------------------------------------------------------- |
---|
771 | ! 4. b) Interior faces, compute and store |
---|
772 | !------------------------------------------------------------- |
---|
773 | |
---|
774 | DO_3D( 0, 1, 0, 1, 2, jpkm1 ) |
---|
775 | z_rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
776 | & * ( - gde3w(ji,jj,jk) + gde3w(ji,jj,jk-1) ) & |
---|
777 | & + z_grav_10 * ( & |
---|
778 | & ( zdrho_k (ji,jj,jk) - zdrho_k (ji,jj,jk-1) ) & |
---|
779 | & * ( - gde3w(ji,jj,jk) + gde3w(ji,jj,jk-1) - z1_12 * ( zdz_k (ji,jj,jk) + zdz_k (ji,jj,jk-1) ) ) & |
---|
780 | & - ( zdz_k (ji,jj,jk) - zdz_k (ji,jj,jk-1) ) & |
---|
781 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( zdrho_k(ji,jj,jk) + zdrho_k(ji,jj,jk-1) ) ) & |
---|
782 | & ) |
---|
783 | END_3D |
---|
784 | |
---|
785 | !---------------------------------------------------------------------------------------- |
---|
786 | ! 5. compute and store elementary horizontal differences in provisional arrays |
---|
787 | !---------------------------------------------------------------------------------------- |
---|
788 | |
---|
789 | DO_3D( 1, 0, 1, 0, 1, jpkm1 ) |
---|
790 | zdrhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
791 | zdzx (ji,jj,jk) = - gde3w(ji+1,jj ,jk) + gde3w(ji,jj,jk ) |
---|
792 | zdrhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
793 | zdzy (ji,jj,jk) = - gde3w(ji ,jj+1,jk) + gde3w(ji,jj,jk ) |
---|
794 | END_3D |
---|
795 | |
---|
796 | CALL lbc_lnk_multi( 'dynhpg', zdrhox, 'U', 1._wp, zdzx, 'U', 1._wp, zdrhoy, 'V', 1._wp, zdzy, 'V', 1._wp ) |
---|
797 | |
---|
798 | !------------------------------------------------------------------------- |
---|
799 | ! 6. compute harmonic averages using eq. 5.18 |
---|
800 | !------------------------------------------------------------------------- |
---|
801 | |
---|
802 | DO_3D( 0, 1, 0, 1, 1, jpkm1 ) |
---|
803 | cffu = 2._wp * zdrhox(ji-1,jj ,jk) * zdrhox(ji,jj,jk ) |
---|
804 | IF( cffu > zep ) THEN |
---|
805 | zdrho_i(ji,jj,jk) = cffu / ( zdrhox(ji-1,jj,jk) + zdrhox(ji,jj,jk) ) |
---|
806 | ELSE |
---|
807 | zdrho_i(ji,jj,jk ) = 0._wp |
---|
808 | ENDIF |
---|
809 | |
---|
810 | cffx = 2._wp * zdzx (ji-1,jj ,jk) * zdzx (ji,jj,jk ) |
---|
811 | IF( cffx > zep ) THEN |
---|
812 | zdz_i(ji,jj,jk) = cffx / ( zdzx(ji-1,jj,jk) + zdzx(ji,jj,jk) ) |
---|
813 | ELSE |
---|
814 | zdz_i(ji,jj,jk) = 0._wp |
---|
815 | ENDIF |
---|
816 | |
---|
817 | cffv = 2._wp * zdrhoy(ji ,jj-1,jk) * zdrhoy(ji,jj,jk ) |
---|
818 | IF( cffv > zep ) THEN |
---|
819 | zdrho_j(ji,jj,jk) = cffv / ( zdrhoy(ji,jj-1,jk) + zdrhoy(ji,jj,jk) ) |
---|
820 | ELSE |
---|
821 | zdrho_j(ji,jj,jk) = 0._wp |
---|
822 | ENDIF |
---|
823 | |
---|
824 | cffy = 2._wp * zdzy (ji ,jj-1,jk) * zdzy (ji,jj,jk ) |
---|
825 | IF( cffy > zep ) THEN |
---|
826 | zdz_j(ji,jj,jk) = cffy / ( zdzy(ji,jj-1,jk) + zdzy(ji,jj,jk) ) |
---|
827 | ELSE |
---|
828 | zdz_j(ji,jj,jk) = 0._wp |
---|
829 | ENDIF |
---|
830 | END_3D |
---|
831 | |
---|
832 | !!! Note that zdzx, zdzy, zdzz, zdrhox, zdrhoy and zdrhoz should NOT be used beyond this point |
---|
833 | |
---|
834 | !---------------------------------------------------------------------------------- |
---|
835 | ! 6B. apply boundary conditions at side boundaries using 5.36-5.37 |
---|
836 | !---------------------------------------------------------------------------------- |
---|
837 | |
---|
838 | DO jk = 1, jpkm1 |
---|
839 | zz_drho_i(:,:) = zdrho_i(:,:,jk) |
---|
840 | zz_dz_i (:,:) = zdz_i (:,:,jk) |
---|
841 | zz_drho_j(:,:) = zdrho_j(:,:,jk) |
---|
842 | zz_dz_j (:,:) = zdz_j (:,:,jk) |
---|
843 | DO_2D( 0, 1, 0, 1) |
---|
844 | ! Walls coming from left: should check from 2 to jpi-1 (and jpj=2-jpj) |
---|
845 | IF (ji < jpi) THEN |
---|
846 | IF ( umask(ji,jj,jk) > 0.5_wp .AND. umask(ji-1,jj,jk) < 0.5_wp .AND. umask(ji+1,jj,jk) > 0.5_wp) THEN |
---|
847 | zz_drho_i(ji,jj) = aco_bc_hor * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) ) - bco_bc_hor * zdrho_i(ji+1,jj,jk) |
---|
848 | zz_dz_i (ji,jj) = aco_bc_hor * (-gde3w(ji+1,jj,jk) + gde3w(ji,jj,jk) ) - bco_bc_hor * zdz_i (ji+1,jj,jk) |
---|
849 | END IF |
---|
850 | END IF |
---|
851 | ! Walls coming from right: should check from 3 to jpi (and jpj=2-jpj) |
---|
852 | IF (ji > 2) THEN |
---|
853 | IF ( umask(ji,jj,jk) < 0.5_wp .AND. umask(ji-1,jj,jk) > 0.5_wp .AND. umask(ji-2,jj,jk) > 0.5_wp) THEN |
---|
854 | zz_drho_i(ji,jj) = aco_bc_hor * ( rhd (ji,jj,jk) - rhd (ji-1,jj,jk) ) - bco_bc_hor * zdrho_i(ji-1,jj,jk) |
---|
855 | zz_dz_i (ji,jj) = aco_bc_hor * (-gde3w(ji,jj,jk) + gde3w(ji-1,jj,jk) ) - bco_bc_hor * zdz_i (ji-1,jj,jk) |
---|
856 | END IF |
---|
857 | END IF |
---|
858 | ! Walls coming from left: should check from 2 to jpj-1 (and jpi=2-jpi) |
---|
859 | IF (jj < jpj) THEN |
---|
860 | IF ( vmask(ji,jj,jk) > 0.5_wp .AND. vmask(ji,jj-1,jk) < 0.5_wp .AND. vmask(ji,jj+1,jk) > 0.5_wp) THEN |
---|
861 | zz_drho_j(ji,jj) = aco_bc_hor * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) ) - bco_bc_hor * zdrho_j(ji,jj+1,jk) |
---|
862 | zz_dz_j (ji,jj) = aco_bc_hor * (-gde3w(ji,jj+1,jk) + gde3w(ji,jj,jk) ) - bco_bc_hor * zdz_j (ji,jj+1,jk) |
---|
863 | END IF |
---|
864 | END IF |
---|
865 | ! Walls coming from right: should check from 3 to jpj (and jpi=2-jpi) |
---|
866 | IF (jj > 2) THEN |
---|
867 | IF ( vmask(ji,jj,jk) < 0.5_wp .AND. vmask(ji,jj-1,jk) > 0.5_wp .AND. vmask(ji,jj-2,jk) > 0.5_wp) THEN |
---|
868 | zz_drho_j(ji,jj) = aco_bc_hor * ( rhd (ji,jj,jk) - rhd (ji,jj-1,jk) ) - bco_bc_hor * zdrho_j(ji,jj-1,jk) |
---|
869 | zz_dz_j (ji,jj) = aco_bc_hor * (-gde3w(ji,jj,jk) + gde3w(ji,jj-1,jk) ) - bco_bc_hor * zdz_j (ji,jj-1,jk) |
---|
870 | END IF |
---|
871 | END IF |
---|
872 | END_2D |
---|
873 | zdrho_i(:,:,jk) = zz_drho_i(:,:) |
---|
874 | zdz_i (:,:,jk) = zz_dz_i (:,:) |
---|
875 | zdrho_j(:,:,jk) = zz_drho_j(:,:) |
---|
876 | zdz_j (:,:,jk) = zz_dz_j (:,:) |
---|
877 | END DO |
---|
878 | |
---|
879 | !-------------------------------------------------------------- |
---|
880 | ! 7. Calculate integrals on side faces |
---|
881 | !------------------------------------------------------------- |
---|
882 | |
---|
883 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
884 | ! two -ve signs cancel in next two lines (within zcoef0 and because gde3w is a depth not a height) |
---|
885 | z_rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
886 | & * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) ) |
---|
887 | IF ( umask(ji-1, jj, jk) > 0.5 .OR. umask(ji+1, jj, jk) > 0.5 ) THEN |
---|
888 | z_rho_i(ji,jj,jk) = z_rho_i(ji,jj,jk) - z_grav_10 * ( & |
---|
889 | & ( zdrho_i (ji+1,jj,jk) - zdrho_i (ji,jj,jk) ) & |
---|
890 | & * ( - gde3w(ji+1,jj,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_i (ji+1,jj,jk) + zdz_i (ji,jj,jk) ) ) & |
---|
891 | & - ( zdz_i (ji+1,jj,jk) - zdz_i (ji,jj,jk) ) & |
---|
892 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_i(ji+1,jj,jk) + zdrho_i(ji,jj,jk) ) ) & |
---|
893 | & ) |
---|
894 | END IF |
---|
895 | |
---|
896 | z_rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
897 | & * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) ) |
---|
898 | IF ( vmask(ji, jj-1, jk) > 0.5 .OR. vmask(ji, jj+1, jk) > 0.5 ) THEN |
---|
899 | z_rho_j(ji,jj,jk) = z_rho_j(ji,jj,jk) - z_grav_10 * ( & |
---|
900 | & ( zdrho_j (ji,jj+1,jk) - zdrho_j (ji,jj,jk) ) & |
---|
901 | & * ( - gde3w(ji,jj+1,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_j (ji,jj+1,jk) + zdz_j (ji,jj,jk) ) ) & |
---|
902 | & - ( zdz_j (ji,jj+1,jk) - zdz_j (ji,jj,jk) ) & |
---|
903 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_j(ji,jj+1,jk) + zdrho_j(ji,jj,jk) ) ) & |
---|
904 | & ) |
---|
905 | END IF |
---|
906 | END_3D |
---|
907 | |
---|
908 | !-------------------------------------------------------------- |
---|
909 | ! 8. Integrate in the vertical |
---|
910 | !------------------------------------------------------------- |
---|
911 | ! |
---|
912 | ! --------------- |
---|
913 | ! Surface value |
---|
914 | ! --------------- |
---|
915 | DO_2D( 0, 0, 0, 0 ) |
---|
916 | zhpi(ji,jj,1) = ( z_rho_k(ji,jj,1) - z_rho_k(ji+1,jj ,1) - z_rho_i(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
917 | zhpj(ji,jj,1) = ( z_rho_k(ji,jj,1) - z_rho_k(ji ,jj+1,1) - z_rho_j(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
918 | IF( ln_wd_il ) THEN |
---|
919 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
920 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
921 | ENDIF |
---|
922 | ! add to the general momentum trend |
---|
923 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) |
---|
924 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) |
---|
925 | END_2D |
---|
926 | |
---|
927 | ! ---------------- |
---|
928 | ! interior value (2=<jk=<jpkm1) |
---|
929 | ! ---------------- |
---|
930 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
931 | ! hydrostatic pressure gradient along s-surfaces |
---|
932 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
933 | & + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji+1,jj,jk ) ) & |
---|
934 | & - ( z_rho_i(ji,jj,jk) - z_rho_i(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
---|
935 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
936 | & + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji,jj+1,jk ) ) & |
---|
937 | & -( z_rho_j(ji,jj,jk) - z_rho_j(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
---|
938 | IF( ln_wd_il ) THEN |
---|
939 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
940 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
941 | ENDIF |
---|
942 | ! add to the general momentum trend |
---|
943 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) |
---|
944 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) |
---|
945 | END_3D |
---|
946 | ! |
---|
947 | IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) |
---|
948 | ! |
---|
949 | END SUBROUTINE hpg_djc |
---|
950 | |
---|
951 | |
---|
952 | SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs ) |
---|
953 | !!--------------------------------------------------------------------- |
---|
954 | !! *** ROUTINE hpg_prj *** |
---|
955 | !! |
---|
956 | !! ** Method : s-coordinate case. |
---|
957 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
958 | !! based on the constrained cubic-spline interpolation for |
---|
959 | !! all vertical coordinate systems |
---|
960 | !! |
---|
961 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
---|
962 | !!---------------------------------------------------------------------- |
---|
963 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
964 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
965 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
966 | REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
967 | !! |
---|
968 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
969 | REAL(wp) :: zcoef0, znad ! local scalars |
---|
970 | ! |
---|
971 | !! The local variables for the correction term |
---|
972 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
973 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
974 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
975 | REAL(wp) :: zrhdt1 |
---|
976 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
977 | REAL(wp), DIMENSION(jpi,jpj) :: zpgu, zpgv ! 2D workspace |
---|
978 | REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n |
---|
979 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh |
---|
980 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
981 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
982 | !!---------------------------------------------------------------------- |
---|
983 | ! |
---|
984 | IF( kt == nit000 ) THEN |
---|
985 | IF(lwp) WRITE(numout,*) |
---|
986 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
987 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
988 | ENDIF |
---|
989 | |
---|
990 | ! Local constant initialization |
---|
991 | zcoef0 = - grav |
---|
992 | znad = 1._wp |
---|
993 | IF( ln_linssh ) znad = 1._wp |
---|
994 | ! |
---|
995 | ! --------------- |
---|
996 | ! Surface pressure gradient to be removed |
---|
997 | ! --------------- |
---|
998 | DO_2D( 0, 0, 0, 0 ) |
---|
999 | zpgu(ji,jj) = - grav * ( ssh(ji+1,jj,Kmm) - ssh(ji,jj,Kmm) ) * r1_e1u(ji,jj) |
---|
1000 | zpgv(ji,jj) = - grav * ( ssh(ji,jj+1,Kmm) - ssh(ji,jj,Kmm) ) * r1_e2v(ji,jj) |
---|
1001 | END_2D |
---|
1002 | ! |
---|
1003 | |
---|
1004 | IF( ln_wd_il ) THEN |
---|
1005 | ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) ) |
---|
1006 | DO_2D( 0, 0, 0, 0 ) |
---|
1007 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
1008 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
1009 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) & |
---|
1010 | & > rn_wdmin1 + rn_wdmin2 |
---|
1011 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
1012 | & MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
1013 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
1014 | |
---|
1015 | IF(ll_tmp1) THEN |
---|
1016 | zcpx(ji,jj) = 1.0_wp |
---|
1017 | ELSE IF(ll_tmp2) THEN |
---|
1018 | ! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here |
---|
1019 | zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
1020 | & / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) ) |
---|
1021 | |
---|
1022 | zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp) |
---|
1023 | ELSE |
---|
1024 | zcpx(ji,jj) = 0._wp |
---|
1025 | END IF |
---|
1026 | |
---|
1027 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
1028 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
1029 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) & |
---|
1030 | & > rn_wdmin1 + rn_wdmin2 |
---|
1031 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
1032 | & MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
1033 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
1034 | |
---|
1035 | IF(ll_tmp1) THEN |
---|
1036 | zcpy(ji,jj) = 1.0_wp |
---|
1037 | ELSE IF(ll_tmp2) THEN |
---|
1038 | ! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here |
---|
1039 | zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
1040 | & / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) ) |
---|
1041 | zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp) |
---|
1042 | |
---|
1043 | ELSE |
---|
1044 | zcpy(ji,jj) = 0._wp |
---|
1045 | ENDIF |
---|
1046 | END_2D |
---|
1047 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp ) |
---|
1048 | ENDIF |
---|
1049 | |
---|
1050 | ! Clean 3-D work arrays |
---|
1051 | zhpi(:,:,:) = 0._wp |
---|
1052 | zrhh(:,:,:) = rhd(:,:,:) |
---|
1053 | |
---|
1054 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
1055 | DO_2D( 1, 1, 1, 1 ) |
---|
1056 | jk = mbkt(ji,jj) |
---|
1057 | IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp |
---|
1058 | ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk) |
---|
1059 | ELSEIF( jk < jpkm1 ) THEN |
---|
1060 | DO jkk = jk+1, jpk |
---|
1061 | zrhh(ji,jj,jkk) = interp1(CASTWP(gde3w(ji,jj,jkk )), CASTWP(gde3w(ji,jj,jkk-1)), & |
---|
1062 | & CASTWP(gde3w(ji,jj,jkk-2)), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2)) |
---|
1063 | |
---|
1064 | END DO |
---|
1065 | ENDIF |
---|
1066 | END_2D |
---|
1067 | |
---|
1068 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
1069 | DO_2D( 1, 1, 1, 1 ) |
---|
1070 | zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm) |
---|
1071 | END_2D |
---|
1072 | |
---|
1073 | DO_3D( 1, 1, 1, 1, 2, jpk ) |
---|
1074 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm) |
---|
1075 | END_3D |
---|
1076 | |
---|
1077 | fsp(:,:,:) = zrhh (:,:,:) |
---|
1078 | xsp(:,:,:) = zdept(:,:,:) |
---|
1079 | |
---|
1080 | ! Construct the vertical density profile with the |
---|
1081 | ! constrained cubic spline interpolation |
---|
1082 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
1083 | CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
1084 | |
---|
1085 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
1086 | DO_2D( 0, 1, 0, 1 ) |
---|
1087 | zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), & |
---|
1088 | & csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm) |
---|
1089 | |
---|
1090 | ! assuming linear profile across the top half surface layer |
---|
1091 | zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1 |
---|
1092 | END_2D |
---|
1093 | |
---|
1094 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
1095 | DO_3D( 0, 1, 0, 1, 2, jpkm1 ) |
---|
1096 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
1097 | & integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), & |
---|
1098 | & asp (ji,jj,jk-1), bsp (ji,jj,jk-1), & |
---|
1099 | & csp (ji,jj,jk-1), dsp (ji,jj,jk-1) ) |
---|
1100 | END_3D |
---|
1101 | |
---|
1102 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
1103 | |
---|
1104 | ! Prepare zsshu_n and zsshv_n |
---|
1105 | DO_2D( 0, 0, 0, 0 ) |
---|
1106 | !!gm BUG ? if it is ssh at u- & v-point then it should be: |
---|
1107 | ! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * & |
---|
1108 | ! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
1109 | ! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * & |
---|
1110 | ! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
1111 | !!gm not this: |
---|
1112 | zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * & |
---|
1113 | & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
1114 | zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * & |
---|
1115 | & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
1116 | END_2D |
---|
1117 | |
---|
1118 | CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1.0_wp, zsshv_n, 'V', 1.0_wp ) |
---|
1119 | |
---|
1120 | DO_2D( 0, 0, 0, 0 ) |
---|
1121 | zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) ) |
---|
1122 | zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) ) |
---|
1123 | END_2D |
---|
1124 | |
---|
1125 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
1126 | zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm) |
---|
1127 | zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm) |
---|
1128 | END_3D |
---|
1129 | |
---|
1130 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
1131 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm) |
---|
1132 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm) |
---|
1133 | END_3D |
---|
1134 | |
---|
1135 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
1136 | zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
1137 | zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
1138 | zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
1139 | zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
1140 | END_3D |
---|
1141 | |
---|
1142 | |
---|
1143 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
1144 | zpwes = 0._wp; zpwed = 0._wp |
---|
1145 | zpnss = 0._wp; zpnsd = 0._wp |
---|
1146 | zuijk = zu(ji,jj,jk) |
---|
1147 | zvijk = zv(ji,jj,jk) |
---|
1148 | |
---|
1149 | !!!!! for u equation |
---|
1150 | IF( jk <= mbku(ji,jj) ) THEN |
---|
1151 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
1152 | jis = ji + 1; jid = ji |
---|
1153 | ELSE |
---|
1154 | jis = ji; jid = ji +1 |
---|
1155 | ENDIF |
---|
1156 | |
---|
1157 | ! integrate the pressure on the shallow side |
---|
1158 | jk1 = jk |
---|
1159 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
1160 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
1161 | zuijk = -zdept(jis,jj,jk1) |
---|
1162 | EXIT |
---|
1163 | ENDIF |
---|
1164 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
1165 | zpwes = zpwes + & |
---|
1166 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
1167 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
1168 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
1169 | jk1 = jk1 + 1 |
---|
1170 | END DO |
---|
1171 | |
---|
1172 | ! integrate the pressure on the deep side |
---|
1173 | jk1 = jk |
---|
1174 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
1175 | IF( jk1 == 1 ) THEN |
---|
1176 | zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad) |
---|
1177 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
1178 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
1179 | dsp(jid,jj,1)) * zdeps |
---|
1180 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
1181 | EXIT |
---|
1182 | ENDIF |
---|
1183 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
1184 | zpwed = zpwed + & |
---|
1185 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
1186 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
1187 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
1188 | jk1 = jk1 - 1 |
---|
1189 | END DO |
---|
1190 | |
---|
1191 | ! update the momentum trends in u direction |
---|
1192 | |
---|
1193 | zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) ) |
---|
1194 | IF( .NOT.ln_linssh ) THEN |
---|
1195 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * & |
---|
1196 | & ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) ) |
---|
1197 | ELSE |
---|
1198 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
1199 | ENDIF |
---|
1200 | IF( ln_wd_il ) THEN |
---|
1201 | zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj) |
---|
1202 | zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj) |
---|
1203 | ENDIF |
---|
1204 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2 - zpgu(ji,jj)) * umask(ji,jj,jk) |
---|
1205 | ENDIF |
---|
1206 | |
---|
1207 | !!!!! for v equation |
---|
1208 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
1209 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
1210 | jjs = jj + 1; jjd = jj |
---|
1211 | ELSE |
---|
1212 | jjs = jj ; jjd = jj + 1 |
---|
1213 | ENDIF |
---|
1214 | |
---|
1215 | ! integrate the pressure on the shallow side |
---|
1216 | jk1 = jk |
---|
1217 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
1218 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
1219 | zvijk = -zdept(ji,jjs,jk1) |
---|
1220 | EXIT |
---|
1221 | ENDIF |
---|
1222 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
1223 | zpnss = zpnss + & |
---|
1224 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
1225 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
1226 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
1227 | jk1 = jk1 + 1 |
---|
1228 | END DO |
---|
1229 | |
---|
1230 | ! integrate the pressure on the deep side |
---|
1231 | jk1 = jk |
---|
1232 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
1233 | IF( jk1 == 1 ) THEN |
---|
1234 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad) |
---|
1235 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
1236 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
1237 | dsp(ji,jjd,1) ) * zdeps |
---|
1238 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
1239 | EXIT |
---|
1240 | ENDIF |
---|
1241 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
1242 | zpnsd = zpnsd + & |
---|
1243 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
1244 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
1245 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
1246 | jk1 = jk1 - 1 |
---|
1247 | END DO |
---|
1248 | |
---|
1249 | |
---|
1250 | ! update the momentum trends in v direction |
---|
1251 | |
---|
1252 | zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) ) |
---|
1253 | IF( .NOT.ln_linssh ) THEN |
---|
1254 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * & |
---|
1255 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) ) |
---|
1256 | ELSE |
---|
1257 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
1258 | ENDIF |
---|
1259 | IF( ln_wd_il ) THEN |
---|
1260 | zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj) |
---|
1261 | zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj) |
---|
1262 | ENDIF |
---|
1263 | |
---|
1264 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2 - zpgv(ji,jj)) * vmask(ji,jj,jk) |
---|
1265 | ENDIF |
---|
1266 | ! |
---|
1267 | END_3D |
---|
1268 | ! |
---|
1269 | IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) |
---|
1270 | ! |
---|
1271 | END SUBROUTINE hpg_prj |
---|
1272 | |
---|
1273 | |
---|
1274 | SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
1275 | !!---------------------------------------------------------------------- |
---|
1276 | !! *** ROUTINE cspline *** |
---|
1277 | !! |
---|
1278 | !! ** Purpose : constrained cubic spline interpolation |
---|
1279 | !! |
---|
1280 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
1281 | !! |
---|
1282 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
1283 | !!---------------------------------------------------------------------- |
---|
1284 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate |
---|
1285 | REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function |
---|
1286 | INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear |
---|
1287 | ! |
---|
1288 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1289 | INTEGER :: jpi, jpj, jpkm1 |
---|
1290 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
1291 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
1292 | REAL(wp) :: zdf(size(fsp,3)) |
---|
1293 | !!---------------------------------------------------------------------- |
---|
1294 | ! |
---|
1295 | !!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!! |
---|
1296 | jpi = size(fsp,1) |
---|
1297 | jpj = size(fsp,2) |
---|
1298 | jpkm1 = MAX( 1, size(fsp,3) - 1 ) |
---|
1299 | ! |
---|
1300 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
1301 | DO ji = 1, jpi |
---|
1302 | DO jj = 1, jpj |
---|
1303 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
1304 | ! DO jk = 2, jpkm1-1 |
---|
1305 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
1306 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1307 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
1308 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
1309 | ! |
---|
1310 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
1311 | ! |
---|
1312 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
1313 | ! zdf(jk) = 0._wp |
---|
1314 | ! ELSE |
---|
1315 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
1316 | ! ENDIF |
---|
1317 | ! END DO |
---|
1318 | |
---|
1319 | !!Simply geometric average |
---|
1320 | DO jk = 2, jpkm1-1 |
---|
1321 | zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1)) |
---|
1322 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk )) |
---|
1323 | |
---|
1324 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
1325 | zdf(jk) = 0._wp |
---|
1326 | ELSE |
---|
1327 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
1328 | ENDIF |
---|
1329 | END DO |
---|
1330 | |
---|
1331 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
1332 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
1333 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
1334 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1) |
---|
1335 | |
---|
1336 | DO jk = 1, jpkm1 - 1 |
---|
1337 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1338 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
1339 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
1340 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
1341 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
1342 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
1343 | |
---|
1344 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
1345 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
1346 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
1347 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
1348 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
1349 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
1350 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
1351 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
1352 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
1353 | END DO |
---|
1354 | END DO |
---|
1355 | END DO |
---|
1356 | |
---|
1357 | ELSEIF ( polynomial_type == 2 ) THEN ! Linear |
---|
1358 | DO ji = 1, jpi |
---|
1359 | DO jj = 1, jpj |
---|
1360 | DO jk = 1, jpkm1-1 |
---|
1361 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
1362 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
1363 | |
---|
1364 | dsp(ji,jj,jk) = 0._wp |
---|
1365 | csp(ji,jj,jk) = 0._wp |
---|
1366 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
1367 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
1368 | END DO |
---|
1369 | END DO |
---|
1370 | END DO |
---|
1371 | ! |
---|
1372 | ELSE |
---|
1373 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
1374 | ENDIF |
---|
1375 | ! |
---|
1376 | END SUBROUTINE cspline |
---|
1377 | |
---|
1378 | |
---|
1379 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
1380 | !!---------------------------------------------------------------------- |
---|
1381 | !! *** ROUTINE interp1 *** |
---|
1382 | !! |
---|
1383 | !! ** Purpose : 1-d linear interpolation |
---|
1384 | !! |
---|
1385 | !! ** Method : interpolation is straight forward |
---|
1386 | !! extrapolation is also permitted (no value limit) |
---|
1387 | !!---------------------------------------------------------------------- |
---|
1388 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
1389 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
1390 | REAL(wp) :: zdeltx |
---|
1391 | !!---------------------------------------------------------------------- |
---|
1392 | ! |
---|
1393 | zdeltx = xr - xl |
---|
1394 | IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN |
---|
1395 | f = 0.5_wp * (fl + fr) |
---|
1396 | ELSE |
---|
1397 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
1398 | ENDIF |
---|
1399 | ! |
---|
1400 | END FUNCTION interp1 |
---|
1401 | |
---|
1402 | |
---|
1403 | FUNCTION interp2( x, a, b, c, d ) RESULT(f) |
---|
1404 | !!---------------------------------------------------------------------- |
---|
1405 | !! *** ROUTINE interp1 *** |
---|
1406 | !! |
---|
1407 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
1408 | !! |
---|
1409 | !! ** Method : cubic spline interpolation |
---|
1410 | !! |
---|
1411 | !!---------------------------------------------------------------------- |
---|
1412 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
1413 | REAL(wp) :: f ! value from the interpolation |
---|
1414 | !!---------------------------------------------------------------------- |
---|
1415 | ! |
---|
1416 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
1417 | ! |
---|
1418 | END FUNCTION interp2 |
---|
1419 | |
---|
1420 | |
---|
1421 | FUNCTION interp3( x, a, b, c, d ) RESULT(f) |
---|
1422 | !!---------------------------------------------------------------------- |
---|
1423 | !! *** ROUTINE interp1 *** |
---|
1424 | !! |
---|
1425 | !! ** Purpose : Calculate the first order of derivative of |
---|
1426 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
1427 | !! |
---|
1428 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
1429 | !! |
---|
1430 | !!---------------------------------------------------------------------- |
---|
1431 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
1432 | REAL(wp) :: f ! value from the interpolation |
---|
1433 | !!---------------------------------------------------------------------- |
---|
1434 | ! |
---|
1435 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
1436 | ! |
---|
1437 | END FUNCTION interp3 |
---|
1438 | |
---|
1439 | |
---|
1440 | FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f) |
---|
1441 | !!---------------------------------------------------------------------- |
---|
1442 | !! *** ROUTINE interp1 *** |
---|
1443 | !! |
---|
1444 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
1445 | !! |
---|
1446 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
1447 | !! |
---|
1448 | !!---------------------------------------------------------------------- |
---|
1449 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
1450 | REAL(wp) :: za1, za2, za3 |
---|
1451 | REAL(wp) :: f ! integration result |
---|
1452 | !!---------------------------------------------------------------------- |
---|
1453 | ! |
---|
1454 | za1 = 0.5_wp * b |
---|
1455 | za2 = c / 3.0_wp |
---|
1456 | za3 = 0.25_wp * d |
---|
1457 | ! |
---|
1458 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
1459 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
1460 | ! |
---|
1461 | END FUNCTION integ_spline |
---|
1462 | |
---|
1463 | !!====================================================================== |
---|
1464 | END MODULE dynhpg |
---|