[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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| 38 | ! |
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[2715] | 39 | USE in_out_manager ! I/O manager |
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[258] | 40 | USE prtctl ! Print control |
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[4990] | 41 | USE lbclnk ! lateral boundary condition |
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[2715] | 42 | USE lib_mpp ! MPP library |
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[4990] | 43 | USE eosbn2 ! compute density |
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[3294] | 44 | USE wrk_nemo ! Memory Allocation |
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| 45 | USE timing ! Timing |
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[5189] | 46 | USE iom |
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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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[4147] | 61 | LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag |
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[455] | 62 | |
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[3764] | 63 | 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] | 64 | |
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[3] | 65 | !! * Substitutions |
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| 66 | # include "domzgr_substitute.h90" |
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| 67 | # include "vectopt_loop_substitute.h90" |
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| 68 | !!---------------------------------------------------------------------- |
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[2528] | 69 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 70 | !! $Id$ |
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| 71 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 72 | !!---------------------------------------------------------------------- |
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| 73 | CONTAINS |
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| 74 | |
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| 75 | SUBROUTINE dyn_hpg( kt ) |
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| 76 | !!--------------------------------------------------------------------- |
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| 77 | !! *** ROUTINE dyn_hpg *** |
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| 78 | !! |
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[3764] | 79 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 80 | !! using the scheme defined in the namelist |
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[3764] | 81 | !! |
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[455] | 82 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[4990] | 83 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 84 | !!---------------------------------------------------------------------- |
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| 85 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[3294] | 86 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[455] | 87 | !!---------------------------------------------------------------------- |
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[2528] | 88 | ! |
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[3294] | 89 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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[2715] | 90 | ! |
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[503] | 91 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[3294] | 92 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 93 | ztrdu(:,:,:) = ua(:,:,:) |
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| 94 | ztrdv(:,:,:) = va(:,:,:) |
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| 95 | ENDIF |
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[2528] | 96 | ! |
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[3294] | 97 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[503] | 98 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 99 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 100 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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[3294] | 101 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 102 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[5120] | 103 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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[455] | 104 | END SELECT |
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[2528] | 105 | ! |
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[503] | 106 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 107 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 108 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[4990] | 109 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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[3294] | 110 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 111 | ENDIF |
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[503] | 112 | ! |
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| 113 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 114 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 115 | ! |
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[3294] | 116 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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[2715] | 117 | ! |
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[455] | 118 | END SUBROUTINE dyn_hpg |
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| 119 | |
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| 120 | |
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[2528] | 121 | SUBROUTINE dyn_hpg_init |
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[455] | 122 | !!---------------------------------------------------------------------- |
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[2528] | 123 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 124 | !! |
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| 125 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 126 | !! computation and consistency control |
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| 127 | !! |
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[1601] | 128 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 129 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 130 | !!---------------------------------------------------------------------- |
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| 131 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 132 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 133 | !! |
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[5189] | 134 | INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF |
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| 135 | REAL(wp) :: znad |
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| 136 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop, zrhd ! hypothesys on isf density |
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| 137 | REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF |
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| 138 | REAL(wp), POINTER, DIMENSION(:,:) :: ziceload ! density at bottom of ISF |
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| 139 | !! |
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[3294] | 140 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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[5120] | 141 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp |
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[455] | 142 | !!---------------------------------------------------------------------- |
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[2528] | 143 | ! |
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[4147] | 144 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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| 145 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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| 146 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
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| 147 | |
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| 148 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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| 149 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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| 150 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
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[4624] | 151 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 152 | ! |
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| 153 | IF(lwp) THEN ! Control print |
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[455] | 154 | WRITE(numout,*) |
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[2528] | 155 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 156 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 157 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 158 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 159 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 160 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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[5120] | 161 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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[1601] | 162 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 163 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[1601] | 164 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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[455] | 165 | ENDIF |
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[2528] | 166 | ! |
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[3294] | 167 | IF( ln_hpg_djc ) & |
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| 168 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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| 169 | & currently disabled (bugs under investigation). Please select & |
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| 170 | & either ln_hpg_sco or ln_hpg_prj instead') |
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[2528] | 171 | ! |
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[5120] | 172 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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[3294] | 173 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
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| 174 | & the standard jacobian formulation hpg_sco or & |
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| 175 | & the pressure jacobian formulation hpg_prj') |
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[5120] | 176 | |
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| 177 | IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) & |
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| 178 | & CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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| 179 | IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) & |
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| 180 | & CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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[3294] | 181 | ! |
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[503] | 182 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 183 | IF( ln_hpg_zco ) nhpg = 0 |
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| 184 | IF( ln_hpg_zps ) nhpg = 1 |
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| 185 | IF( ln_hpg_sco ) nhpg = 2 |
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[3294] | 186 | IF( ln_hpg_djc ) nhpg = 3 |
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| 187 | IF( ln_hpg_prj ) nhpg = 4 |
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[5120] | 188 | IF( ln_hpg_isf ) nhpg = 5 |
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[2528] | 189 | ! |
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[3294] | 190 | ! ! Consistency check |
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[3764] | 191 | ioptio = 0 |
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[455] | 192 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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| 193 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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| 194 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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| 195 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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[3294] | 196 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[5120] | 197 | IF( ln_hpg_isf ) ioptio = ioptio + 1 |
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[2715] | 198 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[5120] | 199 | ! |
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[5189] | 200 | ! initialisation of ice shelf load |
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| 201 | IF ( .NOT. ln_isfcav ) riceload(:,:)=0.0 |
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| 202 | IF ( ln_isfcav ) THEN |
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| 203 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
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| 204 | CALL wrk_alloc( jpi,jpj,jpk, zrhd ) |
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| 205 | CALL wrk_alloc( jpi,jpj, zrhdtop_isf, ziceload) |
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| 206 | ! |
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| 207 | IF(lwp) WRITE(numout,*) |
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| 208 | IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf' |
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| 209 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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| 210 | |
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| 211 | ! To use density and not density anomaly |
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| 212 | znad=1._wp |
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| 213 | |
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| 214 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
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| 215 | ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp |
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| 216 | |
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| 217 | ! compute density of the water displaced by the ice shelf |
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| 218 | DO jk = 1, jpk |
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| 219 | CALL eos(ztstop(:,:,:),fsdept_n(:,:,jk),zrhd(:,:,jk)) |
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| 220 | END DO |
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| 221 | |
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| 222 | ! compute rhd at the ice/oce interface (ice shelf side) |
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| 223 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
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| 224 | |
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| 225 | ! Surface value + ice shelf gradient |
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| 226 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
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[5834] | 227 | ! divided by 2 later |
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[5189] | 228 | ziceload = 0._wp |
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| 229 | DO jj = 1, jpj |
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[5921] | 230 | DO ji = 1, jpi |
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[5189] | 231 | ikt=mikt(ji,jj) |
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| 232 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
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| 233 | DO jk=2,ikt-1 |
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| 234 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * fse3w(ji,jj,jk) & |
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| 235 | & * (1._wp - tmask(ji,jj,jk)) |
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| 236 | END DO |
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[5944] | 237 | IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) & |
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[5189] | 238 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
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| 239 | END DO |
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| 240 | END DO |
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| 241 | riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5 |
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| 242 | |
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| 243 | CALL wrk_dealloc( jpi,jpj, 2, ztstop) |
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| 244 | CALL wrk_dealloc( jpi,jpj,jpk, zrhd ) |
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| 245 | CALL wrk_dealloc( jpi,jpj, zrhdtop_isf, ziceload) |
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| 246 | END IF |
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[503] | 247 | ! |
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[2528] | 248 | END SUBROUTINE dyn_hpg_init |
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[455] | 249 | |
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| 250 | |
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| 251 | SUBROUTINE hpg_zco( kt ) |
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| 252 | !!--------------------------------------------------------------------- |
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| 253 | !! *** ROUTINE hpg_zco *** |
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| 254 | !! |
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| 255 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 256 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 257 | !! is computed by taking the vertical integral of the in-situ |
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| 258 | !! density gradient along the model level from the suface to that |
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| 259 | !! level: zhpi = grav ..... |
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| 260 | !! zhpj = grav ..... |
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[3] | 261 | !! add it to the general momentum trend (ua,va). |
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[455] | 262 | !! ua = ua - 1/e1u * zhpi |
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| 263 | !! va = va - 1/e2v * zhpj |
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[3764] | 264 | !! |
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[3] | 265 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 266 | !!---------------------------------------------------------------------- |
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| 267 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 268 | !! |
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| 269 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 270 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3764] | 271 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 272 | !!---------------------------------------------------------------------- |
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[3764] | 273 | ! |
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[3294] | 274 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 275 | ! |
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[3] | 276 | IF( kt == nit000 ) THEN |
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| 277 | IF(lwp) WRITE(numout,*) |
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[455] | 278 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 279 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 280 | ENDIF |
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| 281 | |
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[3764] | 282 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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| 283 | |
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[455] | 284 | ! Surface value |
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[3] | 285 | DO jj = 2, jpjm1 |
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| 286 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 287 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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| 288 | ! hydrostatic pressure gradient |
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| 289 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 290 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 291 | ! add to the general momentum trend |
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[455] | 292 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 293 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 294 | END DO |
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| 295 | END DO |
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[3294] | 296 | |
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[503] | 297 | ! |
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[455] | 298 | ! interior value (2=<jk=<jpkm1) |
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[3] | 299 | DO jk = 2, jpkm1 |
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[455] | 300 | DO jj = 2, jpjm1 |
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[3] | 301 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 302 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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| 303 | ! hydrostatic pressure gradient |
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| 304 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 305 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 306 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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| 307 | |
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| 308 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 309 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 310 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 311 | ! add to the general momentum trend |
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[455] | 312 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 313 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[3] | 314 | END DO |
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| 315 | END DO |
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| 316 | END DO |
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[503] | 317 | ! |
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[3294] | 318 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 319 | ! |
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[455] | 320 | END SUBROUTINE hpg_zco |
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[216] | 321 | |
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[3] | 322 | |
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[455] | 323 | SUBROUTINE hpg_zps( kt ) |
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[3] | 324 | !!--------------------------------------------------------------------- |
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[455] | 325 | !! *** ROUTINE hpg_zps *** |
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[3764] | 326 | !! |
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[455] | 327 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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[3764] | 328 | !! |
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[3] | 329 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[3764] | 330 | !!---------------------------------------------------------------------- |
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[503] | 331 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 332 | !! |
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| 333 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 334 | INTEGER :: iku, ikv ! temporary integers |
---|
| 335 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
---|
[3764] | 336 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3] | 337 | !!---------------------------------------------------------------------- |
---|
[3294] | 338 | ! |
---|
| 339 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 340 | ! |
---|
[3] | 341 | IF( kt == nit000 ) THEN |
---|
| 342 | IF(lwp) WRITE(numout,*) |
---|
[455] | 343 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
---|
[503] | 344 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
---|
[3] | 345 | ENDIF |
---|
| 346 | |
---|
[3294] | 347 | |
---|
[503] | 348 | ! Local constant initialization |
---|
[2528] | 349 | zcoef0 = - grav * 0.5_wp |
---|
[3] | 350 | |
---|
[2528] | 351 | ! Surface value (also valid in partial step case) |
---|
[3] | 352 | DO jj = 2, jpjm1 |
---|
| 353 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 354 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
---|
[3] | 355 | ! hydrostatic pressure gradient |
---|
[455] | 356 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
---|
| 357 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
---|
[3] | 358 | ! add to the general momentum trend |
---|
| 359 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 360 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 361 | END DO |
---|
| 362 | END DO |
---|
| 363 | |
---|
[3294] | 364 | |
---|
[503] | 365 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 366 | DO jk = 2, jpkm1 |
---|
| 367 | DO jj = 2, jpjm1 |
---|
| 368 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 369 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
---|
[3] | 370 | ! hydrostatic pressure gradient |
---|
| 371 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
[455] | 372 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
| 373 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
---|
[3] | 374 | |
---|
| 375 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
[455] | 376 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
| 377 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
---|
[3] | 378 | ! add to the general momentum trend |
---|
| 379 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 380 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[455] | 381 | END DO |
---|
[3] | 382 | END DO |
---|
| 383 | END DO |
---|
| 384 | |
---|
[3294] | 385 | |
---|
[2528] | 386 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
---|
[3] | 387 | DO jj = 2, jpjm1 |
---|
| 388 | DO ji = 2, jpim1 |
---|
[2528] | 389 | iku = mbku(ji,jj) |
---|
| 390 | ikv = mbkv(ji,jj) |
---|
[3] | 391 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
---|
| 392 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
---|
[2528] | 393 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 394 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 395 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
| 396 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
---|
| 397 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 398 | ENDIF |
---|
[2528] | 399 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 400 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 401 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 402 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
---|
| 403 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 404 | ENDIF |
---|
| 405 | END DO |
---|
| 406 | END DO |
---|
[503] | 407 | ! |
---|
[3294] | 408 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 409 | ! |
---|
[455] | 410 | END SUBROUTINE hpg_zps |
---|
[216] | 411 | |
---|
[455] | 412 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 413 | !!--------------------------------------------------------------------- |
---|
[455] | 414 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 415 | !! |
---|
[455] | 416 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 417 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 418 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 419 | !! density gradient along the model level from the suface to that |
---|
[455] | 420 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 421 | !! to the horizontal pressure gradient : |
---|
| 422 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 423 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[3] | 424 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 425 | !! ua = ua - 1/e1u * zhpi |
---|
| 426 | !! va = va - 1/e2v * zhpj |
---|
[3] | 427 | !! |
---|
| 428 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 429 | !!---------------------------------------------------------------------- |
---|
| 430 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 431 | !! |
---|
[5120] | 432 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 433 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
| 434 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
| 435 | !!---------------------------------------------------------------------- |
---|
| 436 | ! |
---|
| 437 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 438 | ! |
---|
| 439 | IF( kt == nit000 ) THEN |
---|
| 440 | IF(lwp) WRITE(numout,*) |
---|
| 441 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 442 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 443 | ENDIF |
---|
| 444 | |
---|
| 445 | ! Local constant initialization |
---|
| 446 | zcoef0 = - grav * 0.5_wp |
---|
| 447 | ! To use density and not density anomaly |
---|
| 448 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 449 | ELSE ; znad = 0._wp ! Fixed volume |
---|
| 450 | ENDIF |
---|
| 451 | |
---|
| 452 | ! Surface value |
---|
| 453 | DO jj = 2, jpjm1 |
---|
| 454 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 455 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 456 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 457 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 458 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 459 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 460 | ! s-coordinate pressure gradient correction |
---|
| 461 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 462 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
| 463 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 464 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 465 | ! add to the general momentum trend |
---|
| 466 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 467 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 468 | END DO |
---|
| 469 | END DO |
---|
| 470 | |
---|
| 471 | ! interior value (2=<jk=<jpkm1) |
---|
| 472 | DO jk = 2, jpkm1 |
---|
| 473 | DO jj = 2, jpjm1 |
---|
| 474 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 475 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 476 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 477 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 478 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 479 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 480 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 481 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
| 482 | ! s-coordinate pressure gradient correction |
---|
| 483 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 484 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 485 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 486 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 487 | ! add to the general momentum trend |
---|
| 488 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 489 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 490 | END DO |
---|
| 491 | END DO |
---|
| 492 | END DO |
---|
| 493 | ! |
---|
| 494 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 495 | ! |
---|
| 496 | END SUBROUTINE hpg_sco |
---|
| 497 | |
---|
| 498 | SUBROUTINE hpg_isf( kt ) |
---|
| 499 | !!--------------------------------------------------------------------- |
---|
[5921] | 500 | !! *** ROUTINE hpg_isf *** |
---|
[5120] | 501 | !! |
---|
| 502 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 503 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 504 | !! is computed by taking the vertical integral of the in-situ |
---|
| 505 | !! density gradient along the model level from the suface to that |
---|
| 506 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 507 | !! to the horizontal pressure gradient : |
---|
| 508 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 509 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 510 | !! add it to the general momentum trend (ua,va). |
---|
| 511 | !! ua = ua - 1/e1u * zhpi |
---|
| 512 | !! va = va - 1/e2v * zhpj |
---|
| 513 | !! iceload is added and partial cell case are added to the top and bottom |
---|
| 514 | !! |
---|
| 515 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 516 | !!---------------------------------------------------------------------- |
---|
| 517 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 518 | !! |
---|
[5200] | 519 | INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 520 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
[5189] | 521 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[4990] | 522 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
---|
[5944] | 523 | REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_oce |
---|
[3] | 524 | !!---------------------------------------------------------------------- |
---|
[3294] | 525 | ! |
---|
[5189] | 526 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
---|
| 527 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj) |
---|
[5944] | 528 | CALL wrk_alloc( jpi,jpj, zrhdtop_oce ) |
---|
[3294] | 529 | ! |
---|
[503] | 530 | ! Local constant initialization |
---|
[2528] | 531 | zcoef0 = - grav * 0.5_wp |
---|
[5189] | 532 | |
---|
[592] | 533 | ! To use density and not density anomaly |
---|
[4990] | 534 | znad=1._wp |
---|
[5189] | 535 | |
---|
[4990] | 536 | ! iniitialised to 0. zhpi zhpi |
---|
| 537 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
---|
[455] | 538 | |
---|
[5921] | 539 | ! compute rhd at the ice/oce interface (ocean side) |
---|
| 540 | ! usefull to reduce residual current in the test case ISOMIP with no melting |
---|
| 541 | DO ji=1,jpi |
---|
| 542 | DO jj=1,jpj |
---|
| 543 | ikt=mikt(ji,jj) |
---|
| 544 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
---|
| 545 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
---|
| 546 | END DO |
---|
| 547 | END DO |
---|
| 548 | CALL eos(ztstop,risfdep,zrhdtop_oce) |
---|
[4990] | 549 | |
---|
[5834] | 550 | !================================================================================== |
---|
| 551 | !===== Compute surface value ===================================================== |
---|
| 552 | !================================================================================== |
---|
[455] | 553 | DO jj = 2, jpjm1 |
---|
[3764] | 554 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 555 | ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1) |
---|
| 556 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 557 | ! we assume ISF is in isostatic equilibrium |
---|
[5921] | 558 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj,iktp1i) & |
---|
| 559 | & * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) & |
---|
| 560 | & - 0.5_wp * fse3w(ji,jj,ikt) & |
---|
| 561 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
| 562 | & + ( riceload(ji+1,jj) - riceload(ji,jj)) ) |
---|
| 563 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji,jj+1,iktp1j) & |
---|
| 564 | & * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) & |
---|
| 565 | & - 0.5_wp * fse3w(ji,jj,ikt) & |
---|
| 566 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
| 567 | & + ( riceload(ji,jj+1) - riceload(ji,jj)) ) |
---|
[4990] | 568 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
[2528] | 569 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 570 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 571 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 572 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 573 | ! add to the general momentum trend |
---|
[4990] | 574 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 575 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
[3764] | 576 | END DO |
---|
| 577 | END DO |
---|
| 578 | |
---|
[4990] | 579 | !================================================================================== |
---|
| 580 | !===== Compute interior value ===================================================== |
---|
| 581 | !================================================================================== |
---|
[5189] | 582 | ! interior value (2=<jk=<jpkm1) |
---|
| 583 | DO jk = 2, jpkm1 |
---|
| 584 | DO jj = 2, jpjm1 |
---|
| 585 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 586 | ! hydrostatic pressure gradient along s-surfaces |
---|
[5189] | 587 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 588 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) * wmask(ji+1,jj,jk) & |
---|
| 589 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) * wmask(ji ,jj,jk) ) |
---|
| 590 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 591 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) * wmask(ji,jj+1,jk) & |
---|
| 592 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) * wmask(ji,jj ,jk) ) |
---|
[455] | 593 | ! s-coordinate pressure gradient correction |
---|
[5189] | 594 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 595 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 596 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 597 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
[455] | 598 | ! add to the general momentum trend |
---|
[5189] | 599 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 600 | va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk) |
---|
[455] | 601 | END DO |
---|
| 602 | END DO |
---|
| 603 | END DO |
---|
[503] | 604 | ! |
---|
[5189] | 605 | CALL wrk_dealloc( jpi,jpj,2 , ztstop) |
---|
| 606 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj) |
---|
[5944] | 607 | CALL wrk_dealloc( jpi,jpj , zrhdtop_oce ) |
---|
[3294] | 608 | ! |
---|
[5120] | 609 | END SUBROUTINE hpg_isf |
---|
[455] | 610 | |
---|
[4990] | 611 | |
---|
[455] | 612 | SUBROUTINE hpg_djc( kt ) |
---|
| 613 | !!--------------------------------------------------------------------- |
---|
| 614 | !! *** ROUTINE hpg_djc *** |
---|
| 615 | !! |
---|
| 616 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 617 | !! |
---|
[503] | 618 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 619 | !!---------------------------------------------------------------------- |
---|
[503] | 620 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 621 | !! |
---|
| 622 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 623 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 624 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 625 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3764] | 626 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3294] | 627 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 628 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 629 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 630 | !!---------------------------------------------------------------------- |
---|
[3294] | 631 | ! |
---|
[3764] | 632 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 633 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 634 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[3294] | 635 | ! |
---|
[455] | 636 | |
---|
| 637 | IF( kt == nit000 ) THEN |
---|
| 638 | IF(lwp) WRITE(numout,*) |
---|
| 639 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 640 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 641 | ENDIF |
---|
| 642 | |
---|
[503] | 643 | ! Local constant initialization |
---|
[2528] | 644 | zcoef0 = - grav * 0.5_wp |
---|
| 645 | z1_10 = 1._wp / 10._wp |
---|
| 646 | z1_12 = 1._wp / 12._wp |
---|
[455] | 647 | |
---|
| 648 | !---------------------------------------------------------------------------------------- |
---|
| 649 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 650 | !---------------------------------------------------------------------------------------- |
---|
| 651 | |
---|
| 652 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 653 | |
---|
| 654 | DO jk = 2, jpkm1 |
---|
| 655 | DO jj = 2, jpjm1 |
---|
| 656 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 657 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 658 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 659 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 660 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 661 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 662 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 663 | END DO |
---|
| 664 | END DO |
---|
| 665 | END DO |
---|
| 666 | |
---|
| 667 | !------------------------------------------------------------------------- |
---|
| 668 | ! compute harmonic averages using eq. 5.18 |
---|
| 669 | !------------------------------------------------------------------------- |
---|
| 670 | zep = 1.e-15 |
---|
| 671 | |
---|
[503] | 672 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 673 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 674 | |
---|
| 675 | DO jk = 2, jpkm1 |
---|
| 676 | DO jj = 2, jpjm1 |
---|
| 677 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 678 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 679 | |
---|
[2528] | 680 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 681 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 682 | |
---|
[2528] | 683 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 684 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 685 | |
---|
| 686 | IF( cffw > zep) THEN |
---|
[2528] | 687 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 688 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 689 | ELSE |
---|
[2528] | 690 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 691 | ENDIF |
---|
| 692 | |
---|
[2528] | 693 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 694 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 695 | |
---|
| 696 | IF( cffu > zep ) THEN |
---|
[2528] | 697 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 698 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 699 | ELSE |
---|
[2528] | 700 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 701 | ENDIF |
---|
| 702 | |
---|
| 703 | IF( cffx > zep ) THEN |
---|
[2528] | 704 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 705 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 706 | ELSE |
---|
[2528] | 707 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 708 | ENDIF |
---|
| 709 | |
---|
| 710 | IF( cffv > zep ) THEN |
---|
[2528] | 711 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 712 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 713 | ELSE |
---|
[2528] | 714 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 715 | ENDIF |
---|
| 716 | |
---|
| 717 | IF( cffy > zep ) THEN |
---|
[2528] | 718 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 719 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 720 | ELSE |
---|
[2528] | 721 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 722 | ENDIF |
---|
| 723 | |
---|
| 724 | END DO |
---|
| 725 | END DO |
---|
| 726 | END DO |
---|
| 727 | |
---|
| 728 | !---------------------------------------------------------------------------------- |
---|
| 729 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 730 | !---------------------------------------------------------------------------------- |
---|
[2528] | 731 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 732 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 733 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 734 | |
---|
[2528] | 735 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 736 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 737 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 738 | |
---|
| 739 | |
---|
| 740 | !-------------------------------------------------------------- |
---|
| 741 | ! Upper half of top-most grid box, compute and store |
---|
| 742 | !------------------------------------------------------------- |
---|
| 743 | |
---|
| 744 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 745 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 746 | |
---|
| 747 | DO jj = 2, jpjm1 |
---|
| 748 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 749 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 750 | & * ( rhd(ji,jj,1) & |
---|
| 751 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 752 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
[3764] | 753 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 754 | END DO |
---|
| 755 | END DO |
---|
| 756 | |
---|
| 757 | !!bug gm : here also, simplification is possible |
---|
| 758 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 759 | |
---|
| 760 | DO jk = 2, jpkm1 |
---|
| 761 | DO jj = 2, jpjm1 |
---|
| 762 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 763 | |
---|
| 764 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 765 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 766 | & - grav * z1_10 * ( & |
---|
| 767 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 768 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 769 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 770 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 771 | & ) |
---|
| 772 | |
---|
| 773 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 774 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 775 | & - grav* z1_10 * ( & |
---|
| 776 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 777 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 778 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 779 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 780 | & ) |
---|
| 781 | |
---|
| 782 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 783 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 784 | & - grav* z1_10 * ( & |
---|
| 785 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 786 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 787 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 788 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 789 | & ) |
---|
| 790 | |
---|
| 791 | END DO |
---|
| 792 | END DO |
---|
| 793 | END DO |
---|
| 794 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 795 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 796 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 797 | |
---|
| 798 | |
---|
| 799 | ! --------------- |
---|
| 800 | ! Surface value |
---|
| 801 | ! --------------- |
---|
| 802 | DO jj = 2, jpjm1 |
---|
| 803 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 804 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 805 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 806 | ! add to the general momentum trend |
---|
| 807 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 808 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 809 | END DO |
---|
| 810 | END DO |
---|
| 811 | |
---|
| 812 | ! ---------------- |
---|
| 813 | ! interior value (2=<jk=<jpkm1) |
---|
| 814 | ! ---------------- |
---|
| 815 | DO jk = 2, jpkm1 |
---|
[3764] | 816 | DO jj = 2, jpjm1 |
---|
[455] | 817 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 818 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 819 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 820 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 821 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 822 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 823 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 824 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 825 | ! add to the general momentum trend |
---|
| 826 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 827 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 828 | END DO |
---|
| 829 | END DO |
---|
| 830 | END DO |
---|
[503] | 831 | ! |
---|
[3764] | 832 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 833 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 834 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 835 | ! |
---|
[455] | 836 | END SUBROUTINE hpg_djc |
---|
| 837 | |
---|
| 838 | |
---|
[3294] | 839 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 840 | !!--------------------------------------------------------------------- |
---|
[3294] | 841 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 842 | !! |
---|
[3294] | 843 | !! ** Method : s-coordinate case. |
---|
| 844 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 845 | !! based on the constrained cubic-spline interpolation for |
---|
| 846 | !! all vertical coordinate systems |
---|
[455] | 847 | !! |
---|
[3294] | 848 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 849 | !!---------------------------------------------------------------------- |
---|
[3294] | 850 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 851 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 852 | !! |
---|
[3294] | 853 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 854 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 855 | !! |
---|
[3294] | 856 | !! The local variables for the correction term |
---|
| 857 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 858 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 859 | REAL(wp) :: zrhdt1 |
---|
[3294] | 860 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[3764] | 861 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
[3294] | 862 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[5621] | 863 | REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n |
---|
[455] | 864 | !!---------------------------------------------------------------------- |
---|
[3294] | 865 | ! |
---|
[3764] | 866 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 867 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5621] | 868 | CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[3294] | 869 | ! |
---|
[455] | 870 | IF( kt == nit000 ) THEN |
---|
| 871 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 872 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 873 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 874 | ENDIF |
---|
| 875 | |
---|
[3294] | 876 | !!---------------------------------------------------------------------- |
---|
| 877 | ! Local constant initialization |
---|
[3764] | 878 | zcoef0 = - grav |
---|
[3294] | 879 | znad = 0.0_wp |
---|
| 880 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 881 | |
---|
[3294] | 882 | ! Clean 3-D work arrays |
---|
| 883 | zhpi(:,:,:) = 0._wp |
---|
| 884 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 885 | |
---|
[3294] | 886 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 887 | DO jj = 1, jpj |
---|
[3764] | 888 | DO ji = 1, jpi |
---|
[3294] | 889 | jk = mbathy(ji,jj) |
---|
| 890 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 891 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 892 | ELSE IF(jk < jpkm1) THEN |
---|
| 893 | DO jkk = jk+1, jpk |
---|
| 894 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 895 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
[3764] | 896 | END DO |
---|
[3294] | 897 | ENDIF |
---|
| 898 | END DO |
---|
| 899 | END DO |
---|
[3] | 900 | |
---|
[3632] | 901 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 902 | DO jj = 1, jpj |
---|
| 903 | DO ji = 1, jpi |
---|
| 904 | zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 905 | END DO |
---|
| 906 | END DO |
---|
[455] | 907 | |
---|
[4990] | 908 | DO jk = 2, jpk |
---|
| 909 | DO jj = 1, jpj |
---|
| 910 | DO ji = 1, jpi |
---|
| 911 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 912 | END DO |
---|
| 913 | END DO |
---|
| 914 | END DO |
---|
[455] | 915 | |
---|
[4990] | 916 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 917 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 918 | |
---|
[3764] | 919 | ! Construct the vertical density profile with the |
---|
[3294] | 920 | ! constrained cubic spline interpolation |
---|
| 921 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[3764] | 922 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
[3294] | 923 | |
---|
| 924 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 925 | DO jj = 2, jpj |
---|
[3764] | 926 | DO ji = 2, jpi |
---|
[3632] | 927 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), & |
---|
[3294] | 928 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
[3632] | 929 | dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1) |
---|
[3294] | 930 | |
---|
| 931 | ! assuming linear profile across the top half surface layer |
---|
[3764] | 932 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
[3294] | 933 | END DO |
---|
[455] | 934 | END DO |
---|
| 935 | |
---|
[3294] | 936 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 937 | DO jk = 2, jpkm1 |
---|
| 938 | DO jj = 2, jpj |
---|
[3294] | 939 | DO ji = 2, jpi |
---|
| 940 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
[3632] | 941 | integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),& |
---|
[3294] | 942 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 943 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 944 | END DO |
---|
| 945 | END DO |
---|
[455] | 946 | END DO |
---|
| 947 | |
---|
[3294] | 948 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5621] | 949 | |
---|
| 950 | ! Prepare zsshu_n and zsshv_n |
---|
[3764] | 951 | DO jj = 2, jpjm1 |
---|
| 952 | DO ji = 2, jpim1 |
---|
[5621] | 953 | zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
| 954 | & r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 955 | zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
| 956 | & r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
[3294] | 957 | END DO |
---|
[455] | 958 | END DO |
---|
| 959 | |
---|
[5621] | 960 | DO jj = 2, jpjm1 |
---|
| 961 | DO ji = 2, jpim1 |
---|
| 962 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
| 963 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
| 964 | END DO |
---|
| 965 | END DO |
---|
| 966 | |
---|
[3764] | 967 | DO jk = 2, jpkm1 |
---|
| 968 | DO jj = 2, jpjm1 |
---|
| 969 | DO ji = 2, jpim1 |
---|
[3294] | 970 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 971 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 972 | END DO |
---|
| 973 | END DO |
---|
[455] | 974 | END DO |
---|
[3764] | 975 | |
---|
| 976 | DO jk = 1, jpkm1 |
---|
| 977 | DO jj = 2, jpjm1 |
---|
| 978 | DO ji = 2, jpim1 |
---|
[3294] | 979 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 980 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 981 | END DO |
---|
| 982 | END DO |
---|
| 983 | END DO |
---|
[455] | 984 | |
---|
[3632] | 985 | DO jk = 1, jpkm1 |
---|
| 986 | DO jj = 2, jpjm1 |
---|
| 987 | DO ji = 2, jpim1 |
---|
| 988 | zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 989 | zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 990 | zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 991 | zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 992 | END DO |
---|
| 993 | END DO |
---|
| 994 | END DO |
---|
| 995 | |
---|
| 996 | |
---|
[3764] | 997 | DO jk = 1, jpkm1 |
---|
| 998 | DO jj = 2, jpjm1 |
---|
| 999 | DO ji = 2, jpim1 |
---|
[3294] | 1000 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1001 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1002 | zuijk = zu(ji,jj,jk) |
---|
| 1003 | zvijk = zv(ji,jj,jk) |
---|
| 1004 | |
---|
| 1005 | !!!!! for u equation |
---|
| 1006 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 1007 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1008 | jis = ji + 1; jid = ji |
---|
| 1009 | ELSE |
---|
| 1010 | jis = ji; jid = ji +1 |
---|
| 1011 | ENDIF |
---|
| 1012 | |
---|
| 1013 | ! integrate the pressure on the shallow side |
---|
[3764] | 1014 | jk1 = jk |
---|
[3632] | 1015 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1016 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1017 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1018 | EXIT |
---|
| 1019 | ENDIF |
---|
[3632] | 1020 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1021 | zpwes = zpwes + & |
---|
[3632] | 1022 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1023 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1024 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1025 | jk1 = jk1 + 1 |
---|
| 1026 | END DO |
---|
[3764] | 1027 | |
---|
[3294] | 1028 | ! integrate the pressure on the deep side |
---|
[3764] | 1029 | jk1 = jk |
---|
[3632] | 1030 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1031 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1032 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1033 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1034 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1035 | dsp(jid,jj,1)) * zdeps |
---|
| 1036 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1037 | EXIT |
---|
| 1038 | ENDIF |
---|
[3632] | 1039 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1040 | zpwed = zpwed + & |
---|
[3632] | 1041 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1042 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1043 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1044 | jk1 = jk1 - 1 |
---|
| 1045 | END DO |
---|
[3764] | 1046 | |
---|
[3294] | 1047 | ! update the momentum trends in u direction |
---|
| 1048 | |
---|
| 1049 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1050 | IF( lk_vvl ) THEN |
---|
[3764] | 1051 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1052 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1053 | ELSE |
---|
[3764] | 1054 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1055 | ENDIF |
---|
| 1056 | |
---|
| 1057 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 1058 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 1059 | ENDIF |
---|
[3764] | 1060 | |
---|
[3294] | 1061 | !!!!! for v equation |
---|
| 1062 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1063 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1064 | jjs = jj + 1; jjd = jj |
---|
| 1065 | ELSE |
---|
| 1066 | jjs = jj ; jjd = jj + 1 |
---|
| 1067 | ENDIF |
---|
| 1068 | |
---|
| 1069 | ! integrate the pressure on the shallow side |
---|
[3764] | 1070 | jk1 = jk |
---|
[3632] | 1071 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1072 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1073 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1074 | EXIT |
---|
| 1075 | ENDIF |
---|
[3632] | 1076 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1077 | zpnss = zpnss + & |
---|
[3632] | 1078 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1079 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1080 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1081 | jk1 = jk1 + 1 |
---|
| 1082 | END DO |
---|
[3764] | 1083 | |
---|
[3294] | 1084 | ! integrate the pressure on the deep side |
---|
[3764] | 1085 | jk1 = jk |
---|
[3632] | 1086 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1087 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1088 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1089 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1090 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1091 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1092 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1093 | EXIT |
---|
| 1094 | ENDIF |
---|
[3632] | 1095 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1096 | zpnsd = zpnsd + & |
---|
[3632] | 1097 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1098 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1099 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1100 | jk1 = jk1 - 1 |
---|
| 1101 | END DO |
---|
| 1102 | |
---|
[3764] | 1103 | |
---|
[3294] | 1104 | ! update the momentum trends in v direction |
---|
| 1105 | |
---|
| 1106 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1107 | IF( lk_vvl ) THEN |
---|
| 1108 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
[3764] | 1109 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1110 | ELSE |
---|
[3764] | 1111 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1112 | ENDIF |
---|
| 1113 | |
---|
| 1114 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 1115 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 1116 | ENDIF |
---|
| 1117 | |
---|
[3764] | 1118 | |
---|
[3294] | 1119 | END DO |
---|
| 1120 | END DO |
---|
[455] | 1121 | END DO |
---|
[503] | 1122 | ! |
---|
[3764] | 1123 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1124 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5621] | 1125 | CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[2715] | 1126 | ! |
---|
[3294] | 1127 | END SUBROUTINE hpg_prj |
---|
[455] | 1128 | |
---|
[4990] | 1129 | |
---|
[3294] | 1130 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1131 | !!---------------------------------------------------------------------- |
---|
| 1132 | !! *** ROUTINE cspline *** |
---|
[3764] | 1133 | !! |
---|
[3294] | 1134 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1135 | !! |
---|
| 1136 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1137 | !! |
---|
[3294] | 1138 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1139 | !!---------------------------------------------------------------------- |
---|
| 1140 | IMPLICIT NONE |
---|
| 1141 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
[3764] | 1142 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
[3294] | 1143 | ! the interpoated function |
---|
[3764] | 1144 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
[3294] | 1145 | ! 2: Linear |
---|
[4990] | 1146 | ! |
---|
[3294] | 1147 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1148 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1149 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1150 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1151 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1152 | !!---------------------------------------------------------------------- |
---|
| 1153 | |
---|
| 1154 | jpi = size(fsp,1) |
---|
| 1155 | jpj = size(fsp,2) |
---|
| 1156 | jpkm1 = size(fsp,3) - 1 |
---|
| 1157 | |
---|
[3764] | 1158 | |
---|
[3294] | 1159 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1160 | DO ji = 1, jpi |
---|
| 1161 | DO jj = 1, jpj |
---|
[3764] | 1162 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1163 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1164 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1165 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1166 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1167 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1168 | ! |
---|
| 1169 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1170 | ! |
---|
[3294] | 1171 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1172 | ! zdf(jk) = 0._wp |
---|
| 1173 | ! ELSE |
---|
| 1174 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1175 | ! ENDIF |
---|
| 1176 | ! END DO |
---|
[3764] | 1177 | |
---|
[3294] | 1178 | !!Simply geometric average |
---|
| 1179 | DO jk = 2, jpkm1-1 |
---|
| 1180 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 1181 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
[3764] | 1182 | |
---|
[3294] | 1183 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1184 | zdf(jk) = 0._wp |
---|
| 1185 | ELSE |
---|
| 1186 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1187 | ENDIF |
---|
| 1188 | END DO |
---|
[3764] | 1189 | |
---|
[3294] | 1190 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1191 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1192 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1193 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1194 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1195 | |
---|
[3294] | 1196 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1197 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1198 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1199 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1200 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1201 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1202 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1203 | |
---|
[3294] | 1204 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1205 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1206 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1207 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1208 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1209 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1210 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1211 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1212 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1213 | END DO |
---|
| 1214 | END DO |
---|
| 1215 | END DO |
---|
[3764] | 1216 | |
---|
[3294] | 1217 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1218 | DO ji = 1, jpi |
---|
| 1219 | DO jj = 1, jpj |
---|
| 1220 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1221 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1222 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1223 | |
---|
[3294] | 1224 | dsp(ji,jj,jk) = 0._wp |
---|
| 1225 | csp(ji,jj,jk) = 0._wp |
---|
| 1226 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1227 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1228 | END DO |
---|
| 1229 | END DO |
---|
| 1230 | END DO |
---|
| 1231 | |
---|
| 1232 | ELSE |
---|
| 1233 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1234 | ENDIF |
---|
| 1235 | |
---|
| 1236 | END SUBROUTINE cspline |
---|
| 1237 | |
---|
| 1238 | |
---|
[3764] | 1239 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1240 | !!---------------------------------------------------------------------- |
---|
| 1241 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1242 | !! |
---|
[3294] | 1243 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1244 | !! |
---|
[4990] | 1245 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1246 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1247 | !!---------------------------------------------------------------------- |
---|
| 1248 | IMPLICIT NONE |
---|
[3764] | 1249 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1250 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1251 | REAL(wp) :: zdeltx |
---|
| 1252 | !!---------------------------------------------------------------------- |
---|
| 1253 | |
---|
| 1254 | zdeltx = xr - xl |
---|
| 1255 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1256 | f = 0.5_wp * (fl + fr) |
---|
| 1257 | ELSE |
---|
| 1258 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1259 | ENDIF |
---|
[3764] | 1260 | |
---|
[3294] | 1261 | END FUNCTION interp1 |
---|
| 1262 | |
---|
[4990] | 1263 | |
---|
[3764] | 1264 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1265 | !!---------------------------------------------------------------------- |
---|
| 1266 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1267 | !! |
---|
[3294] | 1268 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1269 | !! |
---|
[3294] | 1270 | !! ** Method : cubic spline interpolation |
---|
| 1271 | !! |
---|
| 1272 | !!---------------------------------------------------------------------- |
---|
| 1273 | IMPLICIT NONE |
---|
[3764] | 1274 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1275 | REAL(wp) :: f ! value from the interpolation |
---|
| 1276 | !!---------------------------------------------------------------------- |
---|
| 1277 | |
---|
[3764] | 1278 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[3294] | 1279 | |
---|
| 1280 | END FUNCTION interp2 |
---|
| 1281 | |
---|
| 1282 | |
---|
[3764] | 1283 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1284 | !!---------------------------------------------------------------------- |
---|
| 1285 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1286 | !! |
---|
[3294] | 1287 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1288 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1289 | !! |
---|
[3294] | 1290 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1291 | !! |
---|
| 1292 | !!---------------------------------------------------------------------- |
---|
| 1293 | IMPLICIT NONE |
---|
[3764] | 1294 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1295 | REAL(wp) :: f ! value from the interpolation |
---|
| 1296 | !!---------------------------------------------------------------------- |
---|
| 1297 | |
---|
| 1298 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1299 | |
---|
| 1300 | END FUNCTION interp3 |
---|
| 1301 | |
---|
[3764] | 1302 | |
---|
| 1303 | FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f) |
---|
[3294] | 1304 | !!---------------------------------------------------------------------- |
---|
| 1305 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1306 | !! |
---|
[3294] | 1307 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1308 | !! |
---|
[3764] | 1309 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1310 | !! |
---|
[3294] | 1311 | !!---------------------------------------------------------------------- |
---|
| 1312 | IMPLICIT NONE |
---|
[3764] | 1313 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1314 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1315 | REAL(wp) :: f ! integration result |
---|
| 1316 | !!---------------------------------------------------------------------- |
---|
| 1317 | |
---|
[3764] | 1318 | za1 = 0.5_wp * b |
---|
| 1319 | za2 = c / 3.0_wp |
---|
| 1320 | za3 = 0.25_wp * d |
---|
[3294] | 1321 | |
---|
| 1322 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1323 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1324 | |
---|
[3632] | 1325 | END FUNCTION integ_spline |
---|
[3294] | 1326 | |
---|
[3] | 1327 | !!====================================================================== |
---|
| 1328 | END MODULE dynhpg |
---|
[3632] | 1329 | |
---|