[3] | 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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[2528] | 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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[3764] | 13 | !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot |
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[2528] | 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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[3294] | 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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[5120] | 18 | !! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity |
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[503] | 19 | !!---------------------------------------------------------------------- |
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[3] | 20 | |
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| 21 | !!---------------------------------------------------------------------- |
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[455] | 22 | !! dyn_hpg : update the momentum trend with the now horizontal |
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[3] | 23 | !! gradient of the hydrostatic pressure |
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[2528] | 24 | !! dyn_hpg_init : initialisation and control of options |
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[455] | 25 | !! hpg_zco : z-coordinate scheme |
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| 26 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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| 27 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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[5120] | 28 | !! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf |
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[455] | 29 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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[3294] | 30 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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[3] | 31 | !!---------------------------------------------------------------------- |
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| 32 | USE oce ! ocean dynamics and tracers |
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[4990] | 33 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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[3] | 34 | USE dom_oce ! ocean space and time domain |
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| 35 | USE phycst ! physical constants |
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[4990] | 36 | USE trd_oce ! trends: ocean variables |
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| 37 | USE trddyn ! trend manager: dynamics |
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[5930] | 38 | !jc USE zpshde ! partial step: hor. derivative (zps_hde routine) |
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[4990] | 39 | ! |
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[2715] | 40 | USE in_out_manager ! I/O manager |
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[258] | 41 | USE prtctl ! Print control |
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[4990] | 42 | USE lbclnk ! lateral boundary condition |
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[2715] | 43 | USE lib_mpp ! MPP library |
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[4990] | 44 | USE eosbn2 ! compute density |
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[3294] | 45 | USE wrk_nemo ! Memory Allocation |
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| 46 | USE timing ! Timing |
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[3] | 47 | |
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| 48 | IMPLICIT NONE |
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| 49 | PRIVATE |
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| 50 | |
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[2528] | 51 | PUBLIC dyn_hpg ! routine called by step module |
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| 52 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 53 | |
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[4147] | 54 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 55 | LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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| 56 | LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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| 57 | LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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| 58 | LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 59 | LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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[5120] | 60 | LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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[455] | 61 | |
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[3764] | 62 | INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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[455] | 63 | |
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[3] | 64 | !! * Substitutions |
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| 65 | # include "domzgr_substitute.h90" |
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| 66 | # include "vectopt_loop_substitute.h90" |
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| 67 | !!---------------------------------------------------------------------- |
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[2528] | 68 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 69 | !! $Id$ |
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| 70 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 71 | !!---------------------------------------------------------------------- |
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| 72 | CONTAINS |
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| 73 | |
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| 74 | SUBROUTINE dyn_hpg( kt ) |
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| 75 | !!--------------------------------------------------------------------- |
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| 76 | !! *** ROUTINE dyn_hpg *** |
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| 77 | !! |
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[3764] | 78 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 79 | !! using the scheme defined in the namelist |
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[3764] | 80 | !! |
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[455] | 81 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[4990] | 82 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 83 | !!---------------------------------------------------------------------- |
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| 84 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[3294] | 85 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[455] | 86 | !!---------------------------------------------------------------------- |
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[2528] | 87 | ! |
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[3294] | 88 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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[2715] | 89 | ! |
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[503] | 90 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[3294] | 91 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 92 | ztrdu(:,:,:) = ua(:,:,:) |
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| 93 | ztrdv(:,:,:) = va(:,:,:) |
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| 94 | ENDIF |
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[2528] | 95 | ! |
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[3294] | 96 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[503] | 97 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 98 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 99 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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[3294] | 100 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 101 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[5120] | 102 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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[455] | 103 | END SELECT |
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[2528] | 104 | ! |
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[503] | 105 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 106 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 107 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[4990] | 108 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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[3294] | 109 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 110 | ENDIF |
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[503] | 111 | ! |
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| 112 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 113 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 114 | ! |
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[3294] | 115 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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[2715] | 116 | ! |
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[455] | 117 | END SUBROUTINE dyn_hpg |
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| 118 | |
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| 119 | |
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[2528] | 120 | SUBROUTINE dyn_hpg_init |
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[455] | 121 | !!---------------------------------------------------------------------- |
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[2528] | 122 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 123 | !! |
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| 124 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 125 | !! computation and consistency control |
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| 126 | !! |
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[1601] | 127 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 128 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 129 | !!---------------------------------------------------------------------- |
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| 130 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 131 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 132 | !! |
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[3294] | 133 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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[5930] | 134 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf |
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[455] | 135 | !!---------------------------------------------------------------------- |
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[2528] | 136 | ! |
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[4147] | 137 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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| 138 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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| 139 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
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| 140 | |
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| 141 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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| 142 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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| 143 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
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[4624] | 144 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 145 | ! |
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| 146 | IF(lwp) THEN ! Control print |
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[455] | 147 | WRITE(numout,*) |
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[2528] | 148 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 149 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 150 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 151 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 152 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 153 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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[5120] | 154 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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[1601] | 155 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 156 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[455] | 157 | ENDIF |
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[2528] | 158 | ! |
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[3294] | 159 | IF( ln_hpg_djc ) & |
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| 160 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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| 161 | & currently disabled (bugs under investigation). Please select & |
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| 162 | & either ln_hpg_sco or ln_hpg_prj instead') |
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[2528] | 163 | ! |
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[5120] | 164 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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[3294] | 165 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
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| 166 | & the standard jacobian formulation hpg_sco or & |
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| 167 | & the pressure jacobian formulation hpg_prj') |
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[5120] | 168 | |
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| 169 | IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) & |
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| 170 | & CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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| 171 | IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) & |
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| 172 | & CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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[3294] | 173 | ! |
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[503] | 174 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 175 | IF( ln_hpg_zco ) nhpg = 0 |
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| 176 | IF( ln_hpg_zps ) nhpg = 1 |
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| 177 | IF( ln_hpg_sco ) nhpg = 2 |
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[3294] | 178 | IF( ln_hpg_djc ) nhpg = 3 |
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| 179 | IF( ln_hpg_prj ) nhpg = 4 |
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[5120] | 180 | IF( ln_hpg_isf ) nhpg = 5 |
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[2528] | 181 | ! |
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[3294] | 182 | ! ! Consistency check |
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[3764] | 183 | ioptio = 0 |
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[455] | 184 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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| 185 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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| 186 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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| 187 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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[3294] | 188 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[5120] | 189 | IF( ln_hpg_isf ) ioptio = ioptio + 1 |
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[2715] | 190 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[5120] | 191 | ! |
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| 192 | ! initialisation of ice load |
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| 193 | riceload(:,:)=0.0 |
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[503] | 194 | ! |
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[2528] | 195 | END SUBROUTINE dyn_hpg_init |
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[455] | 196 | |
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| 197 | |
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| 198 | SUBROUTINE hpg_zco( kt ) |
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| 199 | !!--------------------------------------------------------------------- |
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| 200 | !! *** ROUTINE hpg_zco *** |
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| 201 | !! |
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| 202 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 203 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 204 | !! is computed by taking the vertical integral of the in-situ |
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| 205 | !! density gradient along the model level from the suface to that |
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| 206 | !! level: zhpi = grav ..... |
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| 207 | !! zhpj = grav ..... |
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[3] | 208 | !! add it to the general momentum trend (ua,va). |
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[455] | 209 | !! ua = ua - 1/e1u * zhpi |
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| 210 | !! va = va - 1/e2v * zhpj |
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[3764] | 211 | !! |
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[3] | 212 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 213 | !!---------------------------------------------------------------------- |
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| 214 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 215 | !! |
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| 216 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 217 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3764] | 218 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 219 | !!---------------------------------------------------------------------- |
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[3764] | 220 | ! |
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[3294] | 221 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 222 | ! |
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[3] | 223 | IF( kt == nit000 ) THEN |
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| 224 | IF(lwp) WRITE(numout,*) |
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[455] | 225 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 226 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 227 | ENDIF |
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| 228 | |
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[3764] | 229 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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| 230 | |
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[455] | 231 | ! Surface value |
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[3] | 232 | DO jj = 2, jpjm1 |
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| 233 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 234 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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| 235 | ! hydrostatic pressure gradient |
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| 236 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 237 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 238 | ! add to the general momentum trend |
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[455] | 239 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 240 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 241 | END DO |
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| 242 | END DO |
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[3294] | 243 | |
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[503] | 244 | ! |
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[455] | 245 | ! interior value (2=<jk=<jpkm1) |
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[3] | 246 | DO jk = 2, jpkm1 |
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[455] | 247 | DO jj = 2, jpjm1 |
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[3] | 248 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 249 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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| 250 | ! hydrostatic pressure gradient |
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| 251 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 252 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 253 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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| 254 | |
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| 255 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 256 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 257 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 258 | ! add to the general momentum trend |
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[455] | 259 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 260 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[3] | 261 | END DO |
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| 262 | END DO |
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| 263 | END DO |
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[503] | 264 | ! |
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[3294] | 265 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 266 | ! |
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[455] | 267 | END SUBROUTINE hpg_zco |
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[216] | 268 | |
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[3] | 269 | |
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[455] | 270 | SUBROUTINE hpg_zps( kt ) |
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[3] | 271 | !!--------------------------------------------------------------------- |
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[455] | 272 | !! *** ROUTINE hpg_zps *** |
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[3764] | 273 | !! |
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[455] | 274 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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[3764] | 275 | !! |
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[3] | 276 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[3764] | 277 | !!---------------------------------------------------------------------- |
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[503] | 278 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 279 | !! |
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| 280 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 281 | INTEGER :: iku, ikv ! temporary integers |
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| 282 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[3764] | 283 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 284 | !!---------------------------------------------------------------------- |
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[3294] | 285 | ! |
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| 286 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 287 | ! |
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[3] | 288 | IF( kt == nit000 ) THEN |
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| 289 | IF(lwp) WRITE(numout,*) |
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[455] | 290 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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[503] | 291 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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[3] | 292 | ENDIF |
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| 293 | |
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[5930] | 294 | ! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level |
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| 295 | !jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv ) |
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[3294] | 296 | |
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[503] | 297 | ! Local constant initialization |
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[2528] | 298 | zcoef0 = - grav * 0.5_wp |
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[3] | 299 | |
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[2528] | 300 | ! Surface value (also valid in partial step case) |
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[3] | 301 | DO jj = 2, jpjm1 |
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| 302 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 303 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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[3] | 304 | ! hydrostatic pressure gradient |
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[455] | 305 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 306 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 307 | ! add to the general momentum trend |
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| 308 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 309 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 310 | END DO |
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| 311 | END DO |
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| 312 | |
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[3294] | 313 | |
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[503] | 314 | ! interior value (2=<jk=<jpkm1) |
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[3] | 315 | DO jk = 2, jpkm1 |
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| 316 | DO jj = 2, jpjm1 |
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| 317 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 318 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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[3] | 319 | ! hydrostatic pressure gradient |
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| 320 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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[455] | 321 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
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| 322 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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[3] | 323 | |
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| 324 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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[455] | 325 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
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| 326 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 327 | ! add to the general momentum trend |
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| 328 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 329 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[455] | 330 | END DO |
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[3] | 331 | END DO |
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| 332 | END DO |
---|
| 333 | |
---|
[3294] | 334 | |
---|
[2528] | 335 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
---|
[3] | 336 | DO jj = 2, jpjm1 |
---|
| 337 | DO ji = 2, jpim1 |
---|
[2528] | 338 | iku = mbku(ji,jj) |
---|
| 339 | ikv = mbkv(ji,jj) |
---|
[3] | 340 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
---|
| 341 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
---|
[2528] | 342 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 343 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 344 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
| 345 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
---|
| 346 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 347 | ENDIF |
---|
[2528] | 348 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 349 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 350 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 351 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
---|
| 352 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 353 | ENDIF |
---|
| 354 | END DO |
---|
| 355 | END DO |
---|
[503] | 356 | ! |
---|
[3294] | 357 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 358 | ! |
---|
[455] | 359 | END SUBROUTINE hpg_zps |
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[216] | 360 | |
---|
[455] | 361 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 362 | !!--------------------------------------------------------------------- |
---|
[455] | 363 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 364 | !! |
---|
[455] | 365 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 366 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 367 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 368 | !! density gradient along the model level from the suface to that |
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[455] | 369 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 370 | !! to the horizontal pressure gradient : |
---|
| 371 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
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| 372 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
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[3] | 373 | !! add it to the general momentum trend (ua,va). |
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[455] | 374 | !! ua = ua - 1/e1u * zhpi |
---|
| 375 | !! va = va - 1/e2v * zhpj |
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[3] | 376 | !! |
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| 377 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 378 | !!---------------------------------------------------------------------- |
---|
| 379 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 380 | !! |
---|
[5120] | 381 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 382 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
| 383 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
| 384 | !!---------------------------------------------------------------------- |
---|
| 385 | ! |
---|
| 386 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 387 | ! |
---|
| 388 | IF( kt == nit000 ) THEN |
---|
| 389 | IF(lwp) WRITE(numout,*) |
---|
| 390 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 391 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 392 | ENDIF |
---|
| 393 | |
---|
| 394 | ! Local constant initialization |
---|
| 395 | zcoef0 = - grav * 0.5_wp |
---|
| 396 | ! To use density and not density anomaly |
---|
| 397 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 398 | ELSE ; znad = 0._wp ! Fixed volume |
---|
| 399 | ENDIF |
---|
| 400 | |
---|
| 401 | ! Surface value |
---|
| 402 | DO jj = 2, jpjm1 |
---|
| 403 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 404 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 405 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 406 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 407 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 408 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 409 | ! s-coordinate pressure gradient correction |
---|
| 410 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 411 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
| 412 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 413 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 414 | ! add to the general momentum trend |
---|
| 415 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 416 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 417 | END DO |
---|
| 418 | END DO |
---|
| 419 | |
---|
| 420 | ! interior value (2=<jk=<jpkm1) |
---|
| 421 | DO jk = 2, jpkm1 |
---|
| 422 | DO jj = 2, jpjm1 |
---|
| 423 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 424 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 425 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 426 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 427 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 428 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 429 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 430 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
| 431 | ! s-coordinate pressure gradient correction |
---|
| 432 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 433 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 434 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 435 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 436 | ! add to the general momentum trend |
---|
| 437 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 438 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 439 | END DO |
---|
| 440 | END DO |
---|
| 441 | END DO |
---|
| 442 | ! |
---|
| 443 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 444 | ! |
---|
| 445 | END SUBROUTINE hpg_sco |
---|
| 446 | |
---|
| 447 | SUBROUTINE hpg_isf( kt ) |
---|
| 448 | !!--------------------------------------------------------------------- |
---|
| 449 | !! *** ROUTINE hpg_sco *** |
---|
| 450 | !! |
---|
| 451 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 452 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 453 | !! is computed by taking the vertical integral of the in-situ |
---|
| 454 | !! density gradient along the model level from the suface to that |
---|
| 455 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 456 | !! to the horizontal pressure gradient : |
---|
| 457 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 458 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 459 | !! add it to the general momentum trend (ua,va). |
---|
| 460 | !! ua = ua - 1/e1u * zhpi |
---|
| 461 | !! va = va - 1/e2v * zhpj |
---|
| 462 | !! iceload is added and partial cell case are added to the top and bottom |
---|
| 463 | !! |
---|
| 464 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 465 | !!---------------------------------------------------------------------- |
---|
| 466 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 467 | !! |
---|
[4990] | 468 | INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 469 | REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars |
---|
| 470 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd |
---|
| 471 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
---|
| 472 | REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj |
---|
[3] | 473 | !!---------------------------------------------------------------------- |
---|
[3294] | 474 | ! |
---|
[4990] | 475 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
---|
| 476 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 477 | CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 478 | ! |
---|
[4990] | 479 | IF( kt == nit000 ) THEN |
---|
[3] | 480 | IF(lwp) WRITE(numout,*) |
---|
[5120] | 481 | IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf' |
---|
[455] | 482 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
[3] | 483 | ENDIF |
---|
| 484 | |
---|
[503] | 485 | ! Local constant initialization |
---|
[2528] | 486 | zcoef0 = - grav * 0.5_wp |
---|
[592] | 487 | ! To use density and not density anomaly |
---|
[4990] | 488 | ! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 489 | ! ELSE ; znad = 0._wp ! Fixed volume |
---|
| 490 | ! ENDIF |
---|
| 491 | znad=1._wp |
---|
| 492 | ! iniitialised to 0. zhpi zhpi |
---|
| 493 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
---|
[455] | 494 | |
---|
[5930] | 495 | ! Partial steps: top & bottom before horizontal gradient |
---|
| 496 | !jc CALL zps_hde_isf( kt, jpts, tsn, gtsu, gtsv, gtui, gtvi, & |
---|
| 497 | !jc & rhd, gru , grv , aru , arv , gzu , gzv , ge3ru , ge3rv , & |
---|
| 498 | !jc & grui, grvi, arui, arvi, gzui, gzvi, ge3rui, ge3rvi ) |
---|
| 499 | |
---|
[4990] | 500 | !================================================================================== |
---|
| 501 | !=====Compute iceload and contribution of the half first wet layer ================= |
---|
| 502 | !=================================================================================== |
---|
| 503 | |
---|
| 504 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
---|
| 505 | ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp |
---|
| 506 | |
---|
| 507 | ! compute density of the water displaced by the ice shelf |
---|
| 508 | zrhd = rhd ! save rhd |
---|
| 509 | DO jk = 1, jpk |
---|
| 510 | zdept(:,:)=gdept_1d(jk) |
---|
| 511 | CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk)) |
---|
| 512 | END DO |
---|
| 513 | WHERE ( tmask(:,:,:) == 1._wp) |
---|
| 514 | rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd |
---|
| 515 | END WHERE |
---|
| 516 | |
---|
| 517 | ! compute rhd at the ice/oce interface (ice shelf side) |
---|
| 518 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
---|
| 519 | |
---|
| 520 | ! compute rhd at the ice/oce interface (ocean side) |
---|
| 521 | DO ji=1,jpi |
---|
| 522 | DO jj=1,jpj |
---|
| 523 | ikt=mikt(ji,jj) |
---|
| 524 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
---|
| 525 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
---|
| 526 | END DO |
---|
| 527 | END DO |
---|
| 528 | CALL eos(ztstop,risfdep,zrhdtop_oce) |
---|
| 529 | ! |
---|
| 530 | ! Surface value + ice shelf gradient |
---|
| 531 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
---|
| 532 | ziceload = 0._wp |
---|
| 533 | DO jj = 1, jpj |
---|
| 534 | DO ji = 1, jpi ! vector opt. |
---|
| 535 | ikt=mikt(ji,jj) |
---|
| 536 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
---|
| 537 | DO jk=2,ikt-1 |
---|
| 538 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) & |
---|
| 539 | & * (1._wp - tmask(ji,jj,jk)) |
---|
| 540 | END DO |
---|
| 541 | IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) & |
---|
| 542 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
---|
| 543 | END DO |
---|
| 544 | END DO |
---|
| 545 | riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5 |
---|
| 546 | ! compute zp from z=0 to first T wet point (correction due to zps not yet applied) |
---|
[455] | 547 | DO jj = 2, jpjm1 |
---|
[3764] | 548 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 549 | ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1) |
---|
| 550 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 551 | ! we assume ISF is in isostatic equilibrium |
---|
| 552 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) & |
---|
| 553 | & * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) & |
---|
| 554 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 555 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 556 | & + ( ziceload(ji+1,jj) - ziceload(ji,jj)) ) |
---|
| 557 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) & |
---|
| 558 | & * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) & |
---|
| 559 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 560 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 561 | & + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) ) |
---|
| 562 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
[2528] | 563 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 564 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 565 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 566 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 567 | ! add to the general momentum trend |
---|
[4990] | 568 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 569 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
[3764] | 570 | END DO |
---|
| 571 | END DO |
---|
[4990] | 572 | !================================================================================== |
---|
| 573 | !===== Compute partial cell contribution for the top cell ========================= |
---|
| 574 | !================================================================================== |
---|
| 575 | DO jj = 2, jpjm1 |
---|
| 576 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 577 | iku = miku(ji,jj) ; |
---|
| 578 | zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp |
---|
| 579 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
---|
| 580 | ! u direction |
---|
| 581 | IF ( iku .GT. 1 ) THEN |
---|
| 582 | ! case iku |
---|
| 583 | zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu & |
---|
| 584 | & * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) & |
---|
| 585 | & + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad ) |
---|
| 586 | ! corrective term ( = 0 if z coordinate ) |
---|
| 587 | zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj) |
---|
| 588 | ! zhpi will be added in interior loop |
---|
| 589 | ua(ji,jj,iku) = ua(ji,jj,iku) + zuap |
---|
| 590 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 591 | IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku) |
---|
[3764] | 592 | |
---|
[4990] | 593 | ! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps) |
---|
| 594 | zhpiint = zcoef0 / e1u(ji,jj) & |
---|
| 595 | & * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) & |
---|
| 596 | & + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) & |
---|
| 597 | & - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) & |
---|
| 598 | & + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) ) |
---|
| 599 | zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint |
---|
| 600 | END IF |
---|
| 601 | |
---|
| 602 | ! v direction |
---|
| 603 | ikv = mikv(ji,jj) |
---|
| 604 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
---|
| 605 | IF ( ikv .GT. 1 ) THEN |
---|
| 606 | ! case ikv |
---|
| 607 | zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv & |
---|
| 608 | & * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) & |
---|
| 609 | & + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad ) |
---|
| 610 | ! corrective term ( = 0 if z coordinate ) |
---|
| 611 | zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj) |
---|
| 612 | ! zhpi will be added in interior loop |
---|
| 613 | va(ji,jj,ikv) = va(ji,jj,ikv) + zvap |
---|
| 614 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 615 | IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv) |
---|
| 616 | |
---|
| 617 | ! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps) |
---|
| 618 | zhpjint = zcoef0 / e2v(ji,jj) & |
---|
| 619 | & * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) & |
---|
| 620 | & + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) & |
---|
| 621 | & - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) & |
---|
| 622 | & + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) ) |
---|
| 623 | zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint |
---|
| 624 | END IF |
---|
| 625 | END DO |
---|
| 626 | END DO |
---|
| 627 | |
---|
| 628 | !================================================================================== |
---|
| 629 | !===== Compute interior value ===================================================== |
---|
| 630 | !================================================================================== |
---|
| 631 | |
---|
| 632 | DO jj = 2, jpjm1 |
---|
| 633 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 634 | iku=miku(ji,jj); ikv=mikv(ji,jj) |
---|
| 635 | DO jk = 2, jpkm1 |
---|
[455] | 636 | ! hydrostatic pressure gradient along s-surfaces |
---|
[4990] | 637 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 638 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) & |
---|
| 639 | & + zcoef0 / e1u(ji,jj) & |
---|
| 640 | & * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) & |
---|
| 641 | & + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) & |
---|
| 642 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) & |
---|
| 643 | & + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) ) |
---|
[455] | 644 | ! s-coordinate pressure gradient correction |
---|
[4990] | 645 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 646 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 647 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1) |
---|
| 648 | ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 649 | |
---|
| 650 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 651 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 652 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) & |
---|
| 653 | & + zcoef0 / e2v(ji,jj) & |
---|
| 654 | & * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) & |
---|
| 655 | & + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) & |
---|
| 656 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) & |
---|
| 657 | & + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) ) |
---|
| 658 | ! s-coordinate pressure gradient correction |
---|
| 659 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 660 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 661 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1) |
---|
[455] | 662 | ! add to the general momentum trend |
---|
[4990] | 663 | va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk) |
---|
[455] | 664 | END DO |
---|
| 665 | END DO |
---|
| 666 | END DO |
---|
[4990] | 667 | |
---|
| 668 | !================================================================================== |
---|
| 669 | !===== Compute bottom cell contribution (partial cell) ============================ |
---|
| 670 | !================================================================================== |
---|
| 671 | |
---|
| 672 | DO jj = 2, jpjm1 |
---|
| 673 | DO ji = 2, jpim1 |
---|
| 674 | iku = mbku(ji,jj) |
---|
| 675 | ikv = mbkv(ji,jj) |
---|
| 676 | |
---|
| 677 | IF (iku .GT. 1) THEN |
---|
| 678 | ! remove old value (interior case) |
---|
| 679 | zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) & |
---|
| 680 | & * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj) |
---|
| 681 | ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap |
---|
| 682 | ! put new value |
---|
| 683 | ! -zpshpi to avoid double contribution of the partial step in the top layer |
---|
| 684 | zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj) |
---|
| 685 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj) |
---|
| 686 | ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap |
---|
| 687 | END IF |
---|
| 688 | ! v direction |
---|
| 689 | IF (ikv .GT. 1) THEN |
---|
| 690 | ! remove old value (interior case) |
---|
| 691 | zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) & |
---|
| 692 | & * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj) |
---|
| 693 | va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap |
---|
| 694 | ! put new value |
---|
| 695 | ! -zpshpj to avoid double contribution of the partial step in the top layer |
---|
| 696 | zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj) |
---|
| 697 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj) |
---|
| 698 | va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap |
---|
| 699 | END IF |
---|
| 700 | END DO |
---|
| 701 | END DO |
---|
| 702 | |
---|
| 703 | ! set back to original density value into the ice shelf cell (maybe useless because it is masked) |
---|
| 704 | rhd = zrhd |
---|
[503] | 705 | ! |
---|
[4990] | 706 | CALL wrk_dealloc( jpi,jpj,2, ztstop) |
---|
| 707 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 708 | CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 709 | ! |
---|
[5120] | 710 | END SUBROUTINE hpg_isf |
---|
[455] | 711 | |
---|
[4990] | 712 | |
---|
[455] | 713 | SUBROUTINE hpg_djc( kt ) |
---|
| 714 | !!--------------------------------------------------------------------- |
---|
| 715 | !! *** ROUTINE hpg_djc *** |
---|
| 716 | !! |
---|
| 717 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 718 | !! |
---|
[503] | 719 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 720 | !!---------------------------------------------------------------------- |
---|
[503] | 721 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 722 | !! |
---|
| 723 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 724 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 725 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 726 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3764] | 727 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3294] | 728 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 729 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 730 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 731 | !!---------------------------------------------------------------------- |
---|
[3294] | 732 | ! |
---|
[3764] | 733 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 734 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 735 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[3294] | 736 | ! |
---|
[455] | 737 | |
---|
| 738 | IF( kt == nit000 ) THEN |
---|
| 739 | IF(lwp) WRITE(numout,*) |
---|
| 740 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 741 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 742 | ENDIF |
---|
| 743 | |
---|
[503] | 744 | ! Local constant initialization |
---|
[2528] | 745 | zcoef0 = - grav * 0.5_wp |
---|
| 746 | z1_10 = 1._wp / 10._wp |
---|
| 747 | z1_12 = 1._wp / 12._wp |
---|
[455] | 748 | |
---|
| 749 | !---------------------------------------------------------------------------------------- |
---|
| 750 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 751 | !---------------------------------------------------------------------------------------- |
---|
| 752 | |
---|
| 753 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 754 | |
---|
| 755 | DO jk = 2, jpkm1 |
---|
| 756 | DO jj = 2, jpjm1 |
---|
| 757 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 758 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 759 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 760 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 761 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 762 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 763 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 764 | END DO |
---|
| 765 | END DO |
---|
| 766 | END DO |
---|
| 767 | |
---|
| 768 | !------------------------------------------------------------------------- |
---|
| 769 | ! compute harmonic averages using eq. 5.18 |
---|
| 770 | !------------------------------------------------------------------------- |
---|
| 771 | zep = 1.e-15 |
---|
| 772 | |
---|
[503] | 773 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 774 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 775 | |
---|
| 776 | DO jk = 2, jpkm1 |
---|
| 777 | DO jj = 2, jpjm1 |
---|
| 778 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 779 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 780 | |
---|
[2528] | 781 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 782 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 783 | |
---|
[2528] | 784 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 785 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 786 | |
---|
| 787 | IF( cffw > zep) THEN |
---|
[2528] | 788 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 789 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 790 | ELSE |
---|
[2528] | 791 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 792 | ENDIF |
---|
| 793 | |
---|
[2528] | 794 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 795 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 796 | |
---|
| 797 | IF( cffu > zep ) THEN |
---|
[2528] | 798 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 799 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 800 | ELSE |
---|
[2528] | 801 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 802 | ENDIF |
---|
| 803 | |
---|
| 804 | IF( cffx > zep ) THEN |
---|
[2528] | 805 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 806 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 807 | ELSE |
---|
[2528] | 808 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 809 | ENDIF |
---|
| 810 | |
---|
| 811 | IF( cffv > zep ) THEN |
---|
[2528] | 812 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 813 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 814 | ELSE |
---|
[2528] | 815 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 816 | ENDIF |
---|
| 817 | |
---|
| 818 | IF( cffy > zep ) THEN |
---|
[2528] | 819 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 820 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 821 | ELSE |
---|
[2528] | 822 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 823 | ENDIF |
---|
| 824 | |
---|
| 825 | END DO |
---|
| 826 | END DO |
---|
| 827 | END DO |
---|
| 828 | |
---|
| 829 | !---------------------------------------------------------------------------------- |
---|
| 830 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 831 | !---------------------------------------------------------------------------------- |
---|
[2528] | 832 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 833 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 834 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 835 | |
---|
[2528] | 836 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 837 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 838 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 839 | |
---|
| 840 | |
---|
| 841 | !-------------------------------------------------------------- |
---|
| 842 | ! Upper half of top-most grid box, compute and store |
---|
| 843 | !------------------------------------------------------------- |
---|
| 844 | |
---|
| 845 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 846 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 847 | |
---|
| 848 | DO jj = 2, jpjm1 |
---|
| 849 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 850 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 851 | & * ( rhd(ji,jj,1) & |
---|
| 852 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 853 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
[3764] | 854 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 855 | END DO |
---|
| 856 | END DO |
---|
| 857 | |
---|
| 858 | !!bug gm : here also, simplification is possible |
---|
| 859 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 860 | |
---|
| 861 | DO jk = 2, jpkm1 |
---|
| 862 | DO jj = 2, jpjm1 |
---|
| 863 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 864 | |
---|
| 865 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 866 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 867 | & - grav * z1_10 * ( & |
---|
| 868 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 869 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 870 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 871 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 872 | & ) |
---|
| 873 | |
---|
| 874 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 875 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 876 | & - grav* z1_10 * ( & |
---|
| 877 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 878 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 879 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 880 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 881 | & ) |
---|
| 882 | |
---|
| 883 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 884 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 885 | & - grav* z1_10 * ( & |
---|
| 886 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 887 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 888 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 889 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 890 | & ) |
---|
| 891 | |
---|
| 892 | END DO |
---|
| 893 | END DO |
---|
| 894 | END DO |
---|
| 895 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 896 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 897 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 898 | |
---|
| 899 | |
---|
| 900 | ! --------------- |
---|
| 901 | ! Surface value |
---|
| 902 | ! --------------- |
---|
| 903 | DO jj = 2, jpjm1 |
---|
| 904 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 905 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 906 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 907 | ! add to the general momentum trend |
---|
| 908 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 909 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 910 | END DO |
---|
| 911 | END DO |
---|
| 912 | |
---|
| 913 | ! ---------------- |
---|
| 914 | ! interior value (2=<jk=<jpkm1) |
---|
| 915 | ! ---------------- |
---|
| 916 | DO jk = 2, jpkm1 |
---|
[3764] | 917 | DO jj = 2, jpjm1 |
---|
[455] | 918 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 919 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 920 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 921 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 922 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 923 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 924 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 925 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 926 | ! add to the general momentum trend |
---|
| 927 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 928 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 929 | END DO |
---|
| 930 | END DO |
---|
| 931 | END DO |
---|
[503] | 932 | ! |
---|
[3764] | 933 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 934 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 935 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 936 | ! |
---|
[455] | 937 | END SUBROUTINE hpg_djc |
---|
| 938 | |
---|
| 939 | |
---|
[3294] | 940 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 941 | !!--------------------------------------------------------------------- |
---|
[3294] | 942 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 943 | !! |
---|
[3294] | 944 | !! ** Method : s-coordinate case. |
---|
| 945 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 946 | !! based on the constrained cubic-spline interpolation for |
---|
| 947 | !! all vertical coordinate systems |
---|
[455] | 948 | !! |
---|
[3294] | 949 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 950 | !!---------------------------------------------------------------------- |
---|
[3294] | 951 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 952 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 953 | !! |
---|
[3294] | 954 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 955 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 956 | !! |
---|
[3294] | 957 | !! The local variables for the correction term |
---|
| 958 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 959 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 960 | REAL(wp) :: zrhdt1 |
---|
[3294] | 961 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[3764] | 962 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
[3294] | 963 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[5224] | 964 | REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n |
---|
[455] | 965 | !!---------------------------------------------------------------------- |
---|
[3294] | 966 | ! |
---|
[3764] | 967 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 968 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 969 | CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[3294] | 970 | ! |
---|
[455] | 971 | IF( kt == nit000 ) THEN |
---|
| 972 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 973 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 974 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 975 | ENDIF |
---|
| 976 | |
---|
[3294] | 977 | !!---------------------------------------------------------------------- |
---|
| 978 | ! Local constant initialization |
---|
[3764] | 979 | zcoef0 = - grav |
---|
[3294] | 980 | znad = 0.0_wp |
---|
| 981 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 982 | |
---|
[3294] | 983 | ! Clean 3-D work arrays |
---|
| 984 | zhpi(:,:,:) = 0._wp |
---|
| 985 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 986 | |
---|
[3294] | 987 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 988 | DO jj = 1, jpj |
---|
[3764] | 989 | DO ji = 1, jpi |
---|
[3294] | 990 | jk = mbathy(ji,jj) |
---|
| 991 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 992 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 993 | ELSE IF(jk < jpkm1) THEN |
---|
| 994 | DO jkk = jk+1, jpk |
---|
| 995 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 996 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
[3764] | 997 | END DO |
---|
[3294] | 998 | ENDIF |
---|
| 999 | END DO |
---|
| 1000 | END DO |
---|
[3] | 1001 | |
---|
[3632] | 1002 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 1003 | DO jj = 1, jpj |
---|
| 1004 | DO ji = 1, jpi |
---|
| 1005 | zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 1006 | END DO |
---|
| 1007 | END DO |
---|
[455] | 1008 | |
---|
[4990] | 1009 | DO jk = 2, jpk |
---|
| 1010 | DO jj = 1, jpj |
---|
| 1011 | DO ji = 1, jpi |
---|
| 1012 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 1013 | END DO |
---|
| 1014 | END DO |
---|
| 1015 | END DO |
---|
[455] | 1016 | |
---|
[4990] | 1017 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 1018 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 1019 | |
---|
[3764] | 1020 | ! Construct the vertical density profile with the |
---|
[3294] | 1021 | ! constrained cubic spline interpolation |
---|
| 1022 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[3764] | 1023 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
[3294] | 1024 | |
---|
| 1025 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 1026 | DO jj = 2, jpj |
---|
[3764] | 1027 | DO ji = 2, jpi |
---|
[3632] | 1028 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), & |
---|
[3294] | 1029 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
[3632] | 1030 | dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1) |
---|
[3294] | 1031 | |
---|
| 1032 | ! assuming linear profile across the top half surface layer |
---|
[3764] | 1033 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
[3294] | 1034 | END DO |
---|
[455] | 1035 | END DO |
---|
| 1036 | |
---|
[3294] | 1037 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 1038 | DO jk = 2, jpkm1 |
---|
| 1039 | DO jj = 2, jpj |
---|
[3294] | 1040 | DO ji = 2, jpi |
---|
| 1041 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
[3632] | 1042 | integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),& |
---|
[3294] | 1043 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 1044 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 1045 | END DO |
---|
| 1046 | END DO |
---|
[455] | 1047 | END DO |
---|
| 1048 | |
---|
[3294] | 1049 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5224] | 1050 | |
---|
| 1051 | ! Prepare zsshu_n and zsshv_n |
---|
[3764] | 1052 | DO jj = 2, jpjm1 |
---|
| 1053 | DO ji = 2, jpim1 |
---|
[5836] | 1054 | zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
| 1055 | & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1056 | zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
| 1057 | & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
[3294] | 1058 | END DO |
---|
[455] | 1059 | END DO |
---|
| 1060 | |
---|
[5224] | 1061 | DO jj = 2, jpjm1 |
---|
| 1062 | DO ji = 2, jpim1 |
---|
| 1063 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
| 1064 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
| 1065 | END DO |
---|
| 1066 | END DO |
---|
| 1067 | |
---|
[3764] | 1068 | DO jk = 2, jpkm1 |
---|
| 1069 | DO jj = 2, jpjm1 |
---|
| 1070 | DO ji = 2, jpim1 |
---|
[3294] | 1071 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 1072 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 1073 | END DO |
---|
| 1074 | END DO |
---|
[455] | 1075 | END DO |
---|
[3764] | 1076 | |
---|
| 1077 | DO jk = 1, jpkm1 |
---|
| 1078 | DO jj = 2, jpjm1 |
---|
| 1079 | DO ji = 2, jpim1 |
---|
[3294] | 1080 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 1081 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 1082 | END DO |
---|
| 1083 | END DO |
---|
| 1084 | END DO |
---|
[455] | 1085 | |
---|
[3632] | 1086 | DO jk = 1, jpkm1 |
---|
| 1087 | DO jj = 2, jpjm1 |
---|
| 1088 | DO ji = 2, jpim1 |
---|
| 1089 | zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1090 | zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1091 | zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1092 | zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1093 | END DO |
---|
| 1094 | END DO |
---|
| 1095 | END DO |
---|
| 1096 | |
---|
| 1097 | |
---|
[3764] | 1098 | DO jk = 1, jpkm1 |
---|
| 1099 | DO jj = 2, jpjm1 |
---|
| 1100 | DO ji = 2, jpim1 |
---|
[3294] | 1101 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1102 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1103 | zuijk = zu(ji,jj,jk) |
---|
| 1104 | zvijk = zv(ji,jj,jk) |
---|
| 1105 | |
---|
| 1106 | !!!!! for u equation |
---|
| 1107 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 1108 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1109 | jis = ji + 1; jid = ji |
---|
| 1110 | ELSE |
---|
| 1111 | jis = ji; jid = ji +1 |
---|
| 1112 | ENDIF |
---|
| 1113 | |
---|
| 1114 | ! integrate the pressure on the shallow side |
---|
[3764] | 1115 | jk1 = jk |
---|
[3632] | 1116 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1117 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1118 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1119 | EXIT |
---|
| 1120 | ENDIF |
---|
[3632] | 1121 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1122 | zpwes = zpwes + & |
---|
[3632] | 1123 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1124 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1125 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1126 | jk1 = jk1 + 1 |
---|
| 1127 | END DO |
---|
[3764] | 1128 | |
---|
[3294] | 1129 | ! integrate the pressure on the deep side |
---|
[3764] | 1130 | jk1 = jk |
---|
[3632] | 1131 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1132 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1133 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1134 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1135 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1136 | dsp(jid,jj,1)) * zdeps |
---|
| 1137 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1138 | EXIT |
---|
| 1139 | ENDIF |
---|
[3632] | 1140 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1141 | zpwed = zpwed + & |
---|
[3632] | 1142 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1143 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1144 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1145 | jk1 = jk1 - 1 |
---|
| 1146 | END DO |
---|
[3764] | 1147 | |
---|
[3294] | 1148 | ! update the momentum trends in u direction |
---|
| 1149 | |
---|
| 1150 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1151 | IF( lk_vvl ) THEN |
---|
[3764] | 1152 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1153 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1154 | ELSE |
---|
[3764] | 1155 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1156 | ENDIF |
---|
| 1157 | |
---|
| 1158 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 1159 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 1160 | ENDIF |
---|
[3764] | 1161 | |
---|
[3294] | 1162 | !!!!! for v equation |
---|
| 1163 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1164 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1165 | jjs = jj + 1; jjd = jj |
---|
| 1166 | ELSE |
---|
| 1167 | jjs = jj ; jjd = jj + 1 |
---|
| 1168 | ENDIF |
---|
| 1169 | |
---|
| 1170 | ! integrate the pressure on the shallow side |
---|
[3764] | 1171 | jk1 = jk |
---|
[3632] | 1172 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1173 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1174 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1175 | EXIT |
---|
| 1176 | ENDIF |
---|
[3632] | 1177 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1178 | zpnss = zpnss + & |
---|
[3632] | 1179 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1180 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1181 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1182 | jk1 = jk1 + 1 |
---|
| 1183 | END DO |
---|
[3764] | 1184 | |
---|
[3294] | 1185 | ! integrate the pressure on the deep side |
---|
[3764] | 1186 | jk1 = jk |
---|
[3632] | 1187 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1188 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1189 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1190 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1191 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1192 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1193 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1194 | EXIT |
---|
| 1195 | ENDIF |
---|
[3632] | 1196 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1197 | zpnsd = zpnsd + & |
---|
[3632] | 1198 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1199 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1200 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1201 | jk1 = jk1 - 1 |
---|
| 1202 | END DO |
---|
| 1203 | |
---|
[3764] | 1204 | |
---|
[3294] | 1205 | ! update the momentum trends in v direction |
---|
| 1206 | |
---|
| 1207 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1208 | IF( lk_vvl ) THEN |
---|
| 1209 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
[3764] | 1210 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1211 | ELSE |
---|
[3764] | 1212 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1213 | ENDIF |
---|
| 1214 | |
---|
| 1215 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 1216 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 1217 | ENDIF |
---|
| 1218 | |
---|
[3764] | 1219 | |
---|
[3294] | 1220 | END DO |
---|
| 1221 | END DO |
---|
[455] | 1222 | END DO |
---|
[503] | 1223 | ! |
---|
[3764] | 1224 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1225 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 1226 | CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[2715] | 1227 | ! |
---|
[3294] | 1228 | END SUBROUTINE hpg_prj |
---|
[455] | 1229 | |
---|
[4990] | 1230 | |
---|
[3294] | 1231 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1232 | !!---------------------------------------------------------------------- |
---|
| 1233 | !! *** ROUTINE cspline *** |
---|
[3764] | 1234 | !! |
---|
[3294] | 1235 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1236 | !! |
---|
| 1237 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1238 | !! |
---|
[3294] | 1239 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1240 | !!---------------------------------------------------------------------- |
---|
| 1241 | IMPLICIT NONE |
---|
| 1242 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
[3764] | 1243 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
[3294] | 1244 | ! the interpoated function |
---|
[3764] | 1245 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
[3294] | 1246 | ! 2: Linear |
---|
[4990] | 1247 | ! |
---|
[3294] | 1248 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 1249 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1250 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1251 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1252 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1253 | !!---------------------------------------------------------------------- |
---|
| 1254 | |
---|
| 1255 | jpi = size(fsp,1) |
---|
| 1256 | jpj = size(fsp,2) |
---|
| 1257 | jpkm1 = size(fsp,3) - 1 |
---|
| 1258 | |
---|
[3764] | 1259 | |
---|
[3294] | 1260 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1261 | DO ji = 1, jpi |
---|
| 1262 | DO jj = 1, jpj |
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[3764] | 1263 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1264 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1265 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
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| 1266 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1267 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
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| 1268 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1269 | ! |
---|
| 1270 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
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[3764] | 1271 | ! |
---|
[3294] | 1272 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
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| 1273 | ! zdf(jk) = 0._wp |
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| 1274 | ! ELSE |
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| 1275 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
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| 1276 | ! ENDIF |
---|
| 1277 | ! END DO |
---|
[3764] | 1278 | |
---|
[3294] | 1279 | !!Simply geometric average |
---|
| 1280 | DO jk = 2, jpkm1-1 |
---|
| 1281 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 1282 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
[3764] | 1283 | |
---|
[3294] | 1284 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1285 | zdf(jk) = 0._wp |
---|
| 1286 | ELSE |
---|
| 1287 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1288 | ENDIF |
---|
| 1289 | END DO |
---|
[3764] | 1290 | |
---|
[3294] | 1291 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1292 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1293 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1294 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1295 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1296 | |
---|
[3294] | 1297 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1298 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1299 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1300 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
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[3764] | 1301 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1302 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1303 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1304 | |
---|
[3294] | 1305 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1306 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1307 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1308 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1309 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1310 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1311 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1312 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1313 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1314 | END DO |
---|
| 1315 | END DO |
---|
| 1316 | END DO |
---|
[3764] | 1317 | |
---|
[3294] | 1318 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1319 | DO ji = 1, jpi |
---|
| 1320 | DO jj = 1, jpj |
---|
| 1321 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1322 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1323 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1324 | |
---|
[3294] | 1325 | dsp(ji,jj,jk) = 0._wp |
---|
| 1326 | csp(ji,jj,jk) = 0._wp |
---|
| 1327 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1328 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1329 | END DO |
---|
| 1330 | END DO |
---|
| 1331 | END DO |
---|
| 1332 | |
---|
| 1333 | ELSE |
---|
| 1334 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1335 | ENDIF |
---|
| 1336 | |
---|
| 1337 | END SUBROUTINE cspline |
---|
| 1338 | |
---|
| 1339 | |
---|
[3764] | 1340 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1341 | !!---------------------------------------------------------------------- |
---|
| 1342 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1343 | !! |
---|
[3294] | 1344 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1345 | !! |
---|
[4990] | 1346 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1347 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1348 | !!---------------------------------------------------------------------- |
---|
| 1349 | IMPLICIT NONE |
---|
[3764] | 1350 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1351 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1352 | REAL(wp) :: zdeltx |
---|
| 1353 | !!---------------------------------------------------------------------- |
---|
| 1354 | |
---|
| 1355 | zdeltx = xr - xl |
---|
| 1356 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1357 | f = 0.5_wp * (fl + fr) |
---|
| 1358 | ELSE |
---|
| 1359 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1360 | ENDIF |
---|
[3764] | 1361 | |
---|
[3294] | 1362 | END FUNCTION interp1 |
---|
| 1363 | |
---|
[4990] | 1364 | |
---|
[3764] | 1365 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1366 | !!---------------------------------------------------------------------- |
---|
| 1367 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1368 | !! |
---|
[3294] | 1369 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1370 | !! |
---|
[3294] | 1371 | !! ** Method : cubic spline interpolation |
---|
| 1372 | !! |
---|
| 1373 | !!---------------------------------------------------------------------- |
---|
| 1374 | IMPLICIT NONE |
---|
[3764] | 1375 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1376 | REAL(wp) :: f ! value from the interpolation |
---|
| 1377 | !!---------------------------------------------------------------------- |
---|
| 1378 | |
---|
[3764] | 1379 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[3294] | 1380 | |
---|
| 1381 | END FUNCTION interp2 |
---|
| 1382 | |
---|
| 1383 | |
---|
[3764] | 1384 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1385 | !!---------------------------------------------------------------------- |
---|
| 1386 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1387 | !! |
---|
[3294] | 1388 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1389 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1390 | !! |
---|
[3294] | 1391 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1392 | !! |
---|
| 1393 | !!---------------------------------------------------------------------- |
---|
| 1394 | IMPLICIT NONE |
---|
[3764] | 1395 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1396 | REAL(wp) :: f ! value from the interpolation |
---|
| 1397 | !!---------------------------------------------------------------------- |
---|
| 1398 | |
---|
| 1399 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1400 | |
---|
| 1401 | END FUNCTION interp3 |
---|
| 1402 | |
---|
[3764] | 1403 | |
---|
| 1404 | FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f) |
---|
[3294] | 1405 | !!---------------------------------------------------------------------- |
---|
| 1406 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1407 | !! |
---|
[3294] | 1408 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1409 | !! |
---|
[3764] | 1410 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1411 | !! |
---|
[3294] | 1412 | !!---------------------------------------------------------------------- |
---|
| 1413 | IMPLICIT NONE |
---|
[3764] | 1414 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1415 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1416 | REAL(wp) :: f ! integration result |
---|
| 1417 | !!---------------------------------------------------------------------- |
---|
| 1418 | |
---|
[3764] | 1419 | za1 = 0.5_wp * b |
---|
| 1420 | za2 = c / 3.0_wp |
---|
| 1421 | za3 = 0.25_wp * d |
---|
[3294] | 1422 | |
---|
| 1423 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1424 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1425 | |
---|
[3632] | 1426 | END FUNCTION integ_spline |
---|
[3294] | 1427 | |
---|
[3] | 1428 | !!====================================================================== |
---|
| 1429 | END MODULE dynhpg |
---|
[3632] | 1430 | |
---|