[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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[6152] | 35 | USE wet_dry ! wetting and drying |
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[3] | 36 | USE phycst ! physical constants |
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[4990] | 37 | USE trd_oce ! trends: ocean variables |
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| 38 | USE trddyn ! trend manager: dynamics |
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[11416] | 39 | USE zpshde ! partial step: hor. derivative (zps_hde routine) |
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[4990] | 40 | ! |
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[2715] | 41 | USE in_out_manager ! I/O manager |
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[258] | 42 | USE prtctl ! Print control |
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[4990] | 43 | USE lbclnk ! lateral boundary condition |
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[2715] | 44 | USE lib_mpp ! MPP library |
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[4990] | 45 | USE eosbn2 ! compute density |
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[3294] | 46 | USE timing ! Timing |
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[6140] | 47 | USE iom |
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[3] | 48 | |
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| 49 | IMPLICIT NONE |
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| 50 | PRIVATE |
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| 51 | |
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[2528] | 52 | PUBLIC dyn_hpg ! routine called by step module |
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| 53 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 54 | |
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[9490] | 55 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 56 | LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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| 57 | LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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| 58 | LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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| 59 | LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 60 | LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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| 61 | LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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[455] | 62 | |
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[9490] | 63 | ! !! Flag to control the type of hydrostatic pressure gradient |
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| 64 | INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion |
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| 65 | INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps |
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| 66 | INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation) |
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| 67 | INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation) |
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| 68 | INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 69 | INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme) |
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| 70 | INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf |
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| 71 | ! |
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| 72 | INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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[455] | 73 | |
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[3] | 74 | !! * Substitutions |
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| 75 | # include "vectopt_loop_substitute.h90" |
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| 76 | !!---------------------------------------------------------------------- |
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[9598] | 77 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[2528] | 78 | !! $Id$ |
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[10068] | 79 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[3] | 80 | !!---------------------------------------------------------------------- |
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| 81 | CONTAINS |
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| 82 | |
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| 83 | SUBROUTINE dyn_hpg( kt ) |
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| 84 | !!--------------------------------------------------------------------- |
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| 85 | !! *** ROUTINE dyn_hpg *** |
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| 86 | !! |
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[3764] | 87 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 88 | !! using the scheme defined in the namelist |
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[3764] | 89 | !! |
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[455] | 90 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[4990] | 91 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 92 | !!---------------------------------------------------------------------- |
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| 93 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[9019] | 94 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[455] | 95 | !!---------------------------------------------------------------------- |
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[2528] | 96 | ! |
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[9019] | 97 | IF( ln_timing ) CALL timing_start('dyn_hpg') |
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[2715] | 98 | ! |
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[503] | 99 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[9019] | 100 | ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) ) |
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[7753] | 101 | ztrdu(:,:,:) = ua(:,:,:) |
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| 102 | ztrdv(:,:,:) = va(:,:,:) |
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[3764] | 103 | ENDIF |
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[2528] | 104 | ! |
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[3294] | 105 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[9490] | 106 | CASE ( np_zco ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 107 | CASE ( np_zps ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 108 | CASE ( np_sco ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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| 109 | CASE ( np_djc ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 110 | CASE ( np_prj ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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| 111 | CASE ( np_isf ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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[455] | 112 | END SELECT |
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[2528] | 113 | ! |
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[503] | 114 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[7753] | 115 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 116 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[4990] | 117 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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[9019] | 118 | DEALLOCATE( ztrdu , ztrdv ) |
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[3764] | 119 | ENDIF |
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[503] | 120 | ! |
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| 121 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 122 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 123 | ! |
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[9019] | 124 | IF( ln_timing ) CALL timing_stop('dyn_hpg') |
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[2715] | 125 | ! |
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[455] | 126 | END SUBROUTINE dyn_hpg |
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| 127 | |
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| 128 | |
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[2528] | 129 | SUBROUTINE dyn_hpg_init |
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[455] | 130 | !!---------------------------------------------------------------------- |
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[2528] | 131 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 132 | !! |
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| 133 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 134 | !! computation and consistency control |
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| 135 | !! |
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[1601] | 136 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 137 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 138 | !!---------------------------------------------------------------------- |
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| 139 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 140 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 141 | !! |
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[6140] | 142 | INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF |
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| 143 | REAL(wp) :: znad |
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[9019] | 144 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density |
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| 145 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF |
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| 146 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF |
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[6140] | 147 | !! |
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[3294] | 148 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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[5930] | 149 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf |
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[455] | 150 | !!---------------------------------------------------------------------- |
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[2528] | 151 | ! |
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[4147] | 152 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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| 153 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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[11536] | 154 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' ) |
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[6140] | 155 | ! |
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[4147] | 156 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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| 157 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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[11536] | 158 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' ) |
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[4624] | 159 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 160 | ! |
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| 161 | IF(lwp) THEN ! Control print |
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[455] | 162 | WRITE(numout,*) |
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[2528] | 163 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 164 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 165 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 166 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 167 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 168 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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[5120] | 169 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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[1601] | 170 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 171 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[455] | 172 | ENDIF |
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[2528] | 173 | ! |
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[3294] | 174 | IF( ln_hpg_djc ) & |
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[9019] | 175 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method', & |
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| 176 | & ' currently disabled (bugs under investigation).' , & |
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| 177 | & ' Please select either ln_hpg_sco or ln_hpg_prj instead' ) |
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| 178 | ! |
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| 179 | IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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| 180 | & CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', & |
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| 181 | & ' the standard jacobian formulation hpg_sco or ' , & |
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| 182 | & ' the pressure jacobian formulation hpg_prj' ) |
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| 183 | ! |
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| 184 | IF( ln_hpg_isf ) THEN |
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| 185 | IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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| 186 | ELSE |
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| 187 | IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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| 188 | ENDIF |
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[2528] | 189 | ! |
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[9490] | 190 | ! ! Set nhpg from ln_hpg_... flags & consistency check |
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| 191 | nhpg = np_ERROR |
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| 192 | ioptio = 0 |
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| 193 | IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF |
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| 194 | IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF |
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| 195 | IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF |
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| 196 | IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF |
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| 197 | IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF |
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| 198 | IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF |
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[2528] | 199 | ! |
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[2715] | 200 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[5120] | 201 | ! |
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[9490] | 202 | IF(lwp) THEN |
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| 203 | WRITE(numout,*) |
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| 204 | SELECT CASE( nhpg ) |
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| 205 | CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps ' |
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| 206 | CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)' |
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| 207 | CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)' |
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| 208 | CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)' |
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| 209 | CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)' |
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| 210 | CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf' |
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| 211 | END SELECT |
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| 212 | WRITE(numout,*) |
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| 213 | ENDIF |
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[9019] | 214 | ! |
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| 215 | IF ( .NOT. ln_isfcav ) THEN !--- no ice shelf load |
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| 216 | riceload(:,:) = 0._wp |
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[6140] | 217 | ! |
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[9019] | 218 | ELSE !--- set an ice shelf load |
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| 219 | ! |
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[6140] | 220 | IF(lwp) WRITE(numout,*) |
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[9019] | 221 | IF(lwp) WRITE(numout,*) ' ice shelf case: set the ice-shelf load' |
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| 222 | ALLOCATE( zts_top(jpi,jpj,jpts) , zrhd(jpi,jpj,jpk) , zrhdtop_isf(jpi,jpj) , ziceload(jpi,jpj) ) |
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| 223 | ! |
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| 224 | znad = 1._wp !- To use density and not density anomaly |
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| 225 | ! |
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| 226 | ! !- assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
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| 227 | zts_top(:,:,jp_tem) = -1.9_wp ; zts_top(:,:,jp_sal) = 34.4_wp |
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| 228 | ! |
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| 229 | DO jk = 1, jpk !- compute density of the water displaced by the ice shelf |
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| 230 | CALL eos( zts_top(:,:,:), gdept_n(:,:,jk), zrhd(:,:,jk) ) |
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[6140] | 231 | END DO |
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[9019] | 232 | ! |
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| 233 | ! !- compute rhd at the ice/oce interface (ice shelf side) |
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| 234 | CALL eos( zts_top , risfdep, zrhdtop_isf ) |
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| 235 | ! |
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| 236 | ! !- Surface value + ice shelf gradient |
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| 237 | ziceload = 0._wp ! compute pressure due to ice shelf load |
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| 238 | DO jj = 1, jpj ! (used to compute hpgi/j for all the level from 1 to miku/v) |
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| 239 | DO ji = 1, jpi ! divided by 2 later |
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| 240 | ikt = mikt(ji,jj) |
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[6140] | 241 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
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[9019] | 242 | DO jk = 2, ikt-1 |
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[6140] | 243 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) & |
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| 244 | & * (1._wp - tmask(ji,jj,jk)) |
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| 245 | END DO |
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| 246 | 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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[10491] | 247 | & * ( risfdep(ji,jj) - gdept_n(ji,jj,ikt-1) ) |
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[6140] | 248 | END DO |
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| 249 | END DO |
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[9019] | 250 | riceload(:,:) = ziceload(:,:) ! need to be saved for diaar5 |
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| 251 | ! |
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| 252 | DEALLOCATE( zts_top , zrhd , zrhdtop_isf , ziceload ) |
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| 253 | ENDIF |
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[503] | 254 | ! |
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[2528] | 255 | END SUBROUTINE dyn_hpg_init |
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[455] | 256 | |
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| 257 | |
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| 258 | SUBROUTINE hpg_zco( kt ) |
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| 259 | !!--------------------------------------------------------------------- |
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| 260 | !! *** ROUTINE hpg_zco *** |
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| 261 | !! |
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| 262 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 263 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 264 | !! is computed by taking the vertical integral of the in-situ |
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| 265 | !! density gradient along the model level from the suface to that |
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| 266 | !! level: zhpi = grav ..... |
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| 267 | !! zhpj = grav ..... |
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[3] | 268 | !! add it to the general momentum trend (ua,va). |
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[455] | 269 | !! ua = ua - 1/e1u * zhpi |
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| 270 | !! va = va - 1/e2v * zhpj |
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[3764] | 271 | !! |
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[3] | 272 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 273 | !!---------------------------------------------------------------------- |
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| 274 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[6140] | 275 | ! |
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[503] | 276 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 277 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[9019] | 278 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
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[3] | 279 | !!---------------------------------------------------------------------- |
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[3764] | 280 | ! |
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[3] | 281 | IF( kt == nit000 ) THEN |
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| 282 | IF(lwp) WRITE(numout,*) |
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[455] | 283 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 284 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 285 | ENDIF |
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| 286 | |
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[3764] | 287 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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| 288 | |
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[455] | 289 | ! Surface value |
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[3] | 290 | DO jj = 2, jpjm1 |
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| 291 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 292 | zcoef1 = zcoef0 * e3w_n(ji,jj,1) |
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[455] | 293 | ! hydrostatic pressure gradient |
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[6140] | 294 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
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| 295 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
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[3] | 296 | ! add to the general momentum trend |
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[455] | 297 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 298 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 299 | END DO |
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| 300 | END DO |
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[3294] | 301 | |
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[503] | 302 | ! |
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[455] | 303 | ! interior value (2=<jk=<jpkm1) |
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[3] | 304 | DO jk = 2, jpkm1 |
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[455] | 305 | DO jj = 2, jpjm1 |
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[3] | 306 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 307 | zcoef1 = zcoef0 * e3w_n(ji,jj,jk) |
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[455] | 308 | ! hydrostatic pressure gradient |
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| 309 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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[6140] | 310 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 311 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
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[455] | 312 | |
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| 313 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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[6140] | 314 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 315 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
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[3] | 316 | ! add to the general momentum trend |
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[455] | 317 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 318 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[3] | 319 | END DO |
---|
| 320 | END DO |
---|
| 321 | END DO |
---|
[503] | 322 | ! |
---|
[455] | 323 | END SUBROUTINE hpg_zco |
---|
[216] | 324 | |
---|
[3] | 325 | |
---|
[455] | 326 | SUBROUTINE hpg_zps( kt ) |
---|
[3] | 327 | !!--------------------------------------------------------------------- |
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[455] | 328 | !! *** ROUTINE hpg_zps *** |
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[3764] | 329 | !! |
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[455] | 330 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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[3764] | 331 | !! |
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[3] | 332 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[3764] | 333 | !!---------------------------------------------------------------------- |
---|
[503] | 334 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 335 | !! |
---|
| 336 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 337 | INTEGER :: iku, ikv ! temporary integers |
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| 338 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[9019] | 339 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
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[11416] | 340 | REAL(wp), DIMENSION(jpi,jpj) :: zgtsu, zgtsv, zgru, zgrv |
---|
[3] | 341 | !!---------------------------------------------------------------------- |
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[3294] | 342 | ! |
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[3] | 343 | IF( kt == nit000 ) THEN |
---|
| 344 | IF(lwp) WRITE(numout,*) |
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[455] | 345 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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[503] | 346 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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[3] | 347 | ENDIF |
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| 348 | |
---|
[11416] | 349 | ! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level |
---|
| 350 | CALL zps_hde( kt, jpts, tsn, zgtsu, zgtsv, rhd, zgru , zgrv ) |
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[3294] | 351 | |
---|
[503] | 352 | ! Local constant initialization |
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[2528] | 353 | zcoef0 = - grav * 0.5_wp |
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[3] | 354 | |
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[2528] | 355 | ! Surface value (also valid in partial step case) |
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[3] | 356 | DO jj = 2, jpjm1 |
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| 357 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 358 | zcoef1 = zcoef0 * e3w_n(ji,jj,1) |
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[3] | 359 | ! hydrostatic pressure gradient |
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[6140] | 360 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
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| 361 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
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[3] | 362 | ! add to the general momentum trend |
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| 363 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 364 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 365 | END DO |
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| 366 | END DO |
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| 367 | |
---|
[503] | 368 | ! interior value (2=<jk=<jpkm1) |
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[3] | 369 | DO jk = 2, jpkm1 |
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| 370 | DO jj = 2, jpjm1 |
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| 371 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 372 | zcoef1 = zcoef0 * e3w_n(ji,jj,jk) |
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[3] | 373 | ! hydrostatic pressure gradient |
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| 374 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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[455] | 375 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
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[6140] | 376 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
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[3] | 377 | |
---|
| 378 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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[455] | 379 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
[6140] | 380 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
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[3] | 381 | ! add to the general momentum trend |
---|
| 382 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 383 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[455] | 384 | END DO |
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[3] | 385 | END DO |
---|
| 386 | END DO |
---|
| 387 | |
---|
[11416] | 388 | ! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90) |
---|
[3] | 389 | DO jj = 2, jpjm1 |
---|
| 390 | DO ji = 2, jpim1 |
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[2528] | 391 | iku = mbku(ji,jj) |
---|
| 392 | ikv = mbkv(ji,jj) |
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[6140] | 393 | zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) ) |
---|
| 394 | zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) ) |
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[2528] | 395 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 396 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 397 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
[11416] | 398 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj) |
---|
[2528] | 399 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 400 | ENDIF |
---|
[2528] | 401 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 402 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 403 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
[11416] | 404 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj) |
---|
[2528] | 405 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 406 | ENDIF |
---|
| 407 | END DO |
---|
| 408 | END DO |
---|
[503] | 409 | ! |
---|
[455] | 410 | END SUBROUTINE hpg_zps |
---|
[216] | 411 | |
---|
[6140] | 412 | |
---|
[455] | 413 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 414 | !!--------------------------------------------------------------------- |
---|
[455] | 415 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 416 | !! |
---|
[455] | 417 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 418 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 419 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 420 | !! density gradient along the model level from the suface to that |
---|
[455] | 421 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 422 | !! to the horizontal pressure gradient : |
---|
| 423 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 424 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[3] | 425 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 426 | !! ua = ua - 1/e1u * zhpi |
---|
| 427 | !! va = va - 1/e2v * zhpj |
---|
[3] | 428 | !! |
---|
| 429 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 430 | !!---------------------------------------------------------------------- |
---|
| 431 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 432 | !! |
---|
[6152] | 433 | INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices |
---|
| 434 | REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars |
---|
[7646] | 435 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
[9019] | 436 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
---|
| 437 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
[5120] | 438 | !!---------------------------------------------------------------------- |
---|
| 439 | ! |
---|
[9039] | 440 | IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj)) |
---|
[9023] | 441 | ! |
---|
[5120] | 442 | IF( kt == nit000 ) THEN |
---|
| 443 | IF(lwp) WRITE(numout,*) |
---|
| 444 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 445 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 446 | ENDIF |
---|
[6140] | 447 | ! |
---|
[5120] | 448 | zcoef0 = - grav * 0.5_wp |
---|
[6140] | 449 | IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly |
---|
| 450 | ELSE ; znad = 1._wp ! Variable volume: density |
---|
[5120] | 451 | ENDIF |
---|
[6140] | 452 | ! |
---|
[9023] | 453 | IF( ln_wd_il ) THEN |
---|
| 454 | DO jj = 2, jpjm1 |
---|
| 455 | DO ji = 2, jpim1 |
---|
| 456 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
| 457 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
| 458 | & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji+1,jj) + ht_0(ji+1,jj) ) & |
---|
| 459 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 460 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & |
---|
| 461 | & MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
| 462 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 463 | |
---|
[9023] | 464 | IF(ll_tmp1) THEN |
---|
| 465 | zcpx(ji,jj) = 1.0_wp |
---|
| 466 | ELSE IF(ll_tmp2) THEN |
---|
| 467 | ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here |
---|
| 468 | zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) & |
---|
| 469 | & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) |
---|
| 470 | ELSE |
---|
| 471 | zcpx(ji,jj) = 0._wp |
---|
| 472 | END IF |
---|
| 473 | |
---|
| 474 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
| 475 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
| 476 | & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji,jj+1) + ht_0(ji,jj+1) ) & |
---|
| 477 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 478 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & |
---|
| 479 | & MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
| 480 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 481 | |
---|
[9023] | 482 | IF(ll_tmp1) THEN |
---|
| 483 | zcpy(ji,jj) = 1.0_wp |
---|
| 484 | ELSE IF(ll_tmp2) THEN |
---|
| 485 | ! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here |
---|
| 486 | zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) & |
---|
| 487 | & / (sshn(ji,jj+1) - sshn(ji,jj )) ) |
---|
| 488 | ELSE |
---|
| 489 | zcpy(ji,jj) = 0._wp |
---|
| 490 | END IF |
---|
| 491 | END DO |
---|
| 492 | END DO |
---|
[10425] | 493 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. ) |
---|
[9023] | 494 | END IF |
---|
| 495 | |
---|
[5120] | 496 | ! Surface value |
---|
| 497 | DO jj = 2, jpjm1 |
---|
| 498 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 499 | ! hydrostatic pressure gradient along s-surfaces |
---|
[6140] | 500 | zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 501 | & - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj) |
---|
| 502 | zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 503 | & - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj) |
---|
[5120] | 504 | ! s-coordinate pressure gradient correction |
---|
[6140] | 505 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 506 | & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 507 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 508 | & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
[9019] | 509 | ! |
---|
[9023] | 510 | IF( ln_wd_il ) THEN |
---|
[9019] | 511 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
| 512 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
| 513 | zuap = zuap * zcpx(ji,jj) |
---|
| 514 | zvap = zvap * zcpy(ji,jj) |
---|
[6152] | 515 | ENDIF |
---|
[9019] | 516 | ! |
---|
[5120] | 517 | ! add to the general momentum trend |
---|
| 518 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 519 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 520 | END DO |
---|
| 521 | END DO |
---|
| 522 | |
---|
| 523 | ! interior value (2=<jk=<jpkm1) |
---|
| 524 | DO jk = 2, jpkm1 |
---|
| 525 | DO jj = 2, jpjm1 |
---|
| 526 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 527 | ! hydrostatic pressure gradient along s-surfaces |
---|
[6140] | 528 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) & |
---|
| 529 | & * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 530 | & - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 531 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) & |
---|
| 532 | & * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 533 | & - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
[5120] | 534 | ! s-coordinate pressure gradient correction |
---|
[6140] | 535 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 536 | & * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj) |
---|
| 537 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 538 | & * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj) |
---|
[9019] | 539 | ! |
---|
[9023] | 540 | IF( ln_wd_il ) THEN |
---|
[9019] | 541 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
| 542 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
| 543 | zuap = zuap * zcpx(ji,jj) |
---|
| 544 | zvap = zvap * zcpy(ji,jj) |
---|
[6152] | 545 | ENDIF |
---|
[9019] | 546 | ! |
---|
[5120] | 547 | ! add to the general momentum trend |
---|
| 548 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 549 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 550 | END DO |
---|
| 551 | END DO |
---|
| 552 | END DO |
---|
| 553 | ! |
---|
[9039] | 554 | IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy ) |
---|
[5120] | 555 | ! |
---|
| 556 | END SUBROUTINE hpg_sco |
---|
| 557 | |
---|
[6140] | 558 | |
---|
[5120] | 559 | SUBROUTINE hpg_isf( kt ) |
---|
| 560 | !!--------------------------------------------------------------------- |
---|
[6140] | 561 | !! *** ROUTINE hpg_isf *** |
---|
[5120] | 562 | !! |
---|
| 563 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 564 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 565 | !! is computed by taking the vertical integral of the in-situ |
---|
| 566 | !! density gradient along the model level from the suface to that |
---|
| 567 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 568 | !! to the horizontal pressure gradient : |
---|
| 569 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 570 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 571 | !! add it to the general momentum trend (ua,va). |
---|
| 572 | !! ua = ua - 1/e1u * zhpi |
---|
| 573 | !! va = va - 1/e2v * zhpj |
---|
| 574 | !! iceload is added and partial cell case are added to the top and bottom |
---|
| 575 | !! |
---|
| 576 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 577 | !!---------------------------------------------------------------------- |
---|
| 578 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 579 | !! |
---|
[6140] | 580 | INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 581 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
[9019] | 582 | REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj |
---|
| 583 | REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top |
---|
| 584 | REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce |
---|
[3] | 585 | !!---------------------------------------------------------------------- |
---|
[3294] | 586 | ! |
---|
[9019] | 587 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
---|
[3294] | 588 | ! |
---|
[9019] | 589 | znad=1._wp ! To use density and not density anomaly |
---|
| 590 | ! |
---|
| 591 | ! ! iniitialised to 0. zhpi zhpi |
---|
| 592 | zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp |
---|
[6140] | 593 | |
---|
[4990] | 594 | ! compute rhd at the ice/oce interface (ocean side) |
---|
[6140] | 595 | ! usefull to reduce residual current in the test case ISOMIP with no melting |
---|
[9019] | 596 | DO ji = 1, jpi |
---|
| 597 | DO jj = 1, jpj |
---|
| 598 | ikt = mikt(ji,jj) |
---|
| 599 | zts_top(ji,jj,1) = tsn(ji,jj,ikt,1) |
---|
| 600 | zts_top(ji,jj,2) = tsn(ji,jj,ikt,2) |
---|
[4990] | 601 | END DO |
---|
| 602 | END DO |
---|
[9019] | 603 | CALL eos( zts_top, risfdep, zrhdtop_oce ) |
---|
[6140] | 604 | |
---|
| 605 | !================================================================================== |
---|
| 606 | !===== Compute surface value ===================================================== |
---|
| 607 | !================================================================================== |
---|
[455] | 608 | DO jj = 2, jpjm1 |
---|
[3764] | 609 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[6140] | 610 | ikt = mikt(ji,jj) |
---|
| 611 | iktp1i = mikt(ji+1,jj) |
---|
| 612 | iktp1j = mikt(ji,jj+1) |
---|
[4990] | 613 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 614 | ! we assume ISF is in isostatic equilibrium |
---|
[6140] | 615 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) & |
---|
| 616 | & * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) & |
---|
| 617 | & - 0.5_wp * e3w_n(ji,jj,ikt) & |
---|
| 618 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
| 619 | & + ( riceload(ji+1,jj) - riceload(ji,jj)) ) |
---|
| 620 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) & |
---|
| 621 | & * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) & |
---|
| 622 | & - 0.5_wp * e3w_n(ji,jj,ikt) & |
---|
| 623 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
| 624 | & + ( riceload(ji,jj+1) - riceload(ji,jj)) ) |
---|
[4990] | 625 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
[6140] | 626 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 627 | & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 628 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 629 | & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
[455] | 630 | ! add to the general momentum trend |
---|
[4990] | 631 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 632 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
[3764] | 633 | END DO |
---|
| 634 | END DO |
---|
[4990] | 635 | !================================================================================== |
---|
| 636 | !===== Compute interior value ===================================================== |
---|
| 637 | !================================================================================== |
---|
[6140] | 638 | ! interior value (2=<jk=<jpkm1) |
---|
| 639 | DO jk = 2, jpkm1 |
---|
| 640 | DO jj = 2, jpjm1 |
---|
| 641 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 642 | ! hydrostatic pressure gradient along s-surfaces |
---|
[6140] | 643 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 644 | & * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) * wmask(ji+1,jj,jk) & |
---|
| 645 | & - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) * wmask(ji ,jj,jk) ) |
---|
| 646 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 647 | & * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) * wmask(ji,jj+1,jk) & |
---|
| 648 | & - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) * wmask(ji,jj ,jk) ) |
---|
[455] | 649 | ! s-coordinate pressure gradient correction |
---|
[6140] | 650 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 651 | & * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 652 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 653 | & * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj) |
---|
[455] | 654 | ! add to the general momentum trend |
---|
[6140] | 655 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 656 | va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk) |
---|
[455] | 657 | END DO |
---|
| 658 | END DO |
---|
| 659 | END DO |
---|
[503] | 660 | ! |
---|
[5120] | 661 | END SUBROUTINE hpg_isf |
---|
[455] | 662 | |
---|
[4990] | 663 | |
---|
[455] | 664 | SUBROUTINE hpg_djc( kt ) |
---|
| 665 | !!--------------------------------------------------------------------- |
---|
| 666 | !! *** ROUTINE hpg_djc *** |
---|
| 667 | !! |
---|
| 668 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 669 | !! |
---|
[503] | 670 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 671 | !!---------------------------------------------------------------------- |
---|
[503] | 672 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 673 | !! |
---|
| 674 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 675 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 676 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 677 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[6152] | 678 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
[9019] | 679 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
---|
| 680 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 681 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 682 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k |
---|
| 683 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
[455] | 684 | !!---------------------------------------------------------------------- |
---|
[3294] | 685 | ! |
---|
[9023] | 686 | IF( ln_wd_il ) THEN |
---|
[9019] | 687 | ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) ) |
---|
[9023] | 688 | DO jj = 2, jpjm1 |
---|
| 689 | DO ji = 2, jpim1 |
---|
| 690 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
| 691 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
| 692 | & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji+1,jj) + ht_0(ji+1,jj) ) & |
---|
| 693 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 694 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & |
---|
| 695 | & MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
| 696 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
| 697 | IF(ll_tmp1) THEN |
---|
| 698 | zcpx(ji,jj) = 1.0_wp |
---|
| 699 | ELSE IF(ll_tmp2) THEN |
---|
| 700 | ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here |
---|
| 701 | zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) & |
---|
| 702 | & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) |
---|
| 703 | ELSE |
---|
| 704 | zcpx(ji,jj) = 0._wp |
---|
| 705 | END IF |
---|
[6152] | 706 | |
---|
[9023] | 707 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
| 708 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
| 709 | & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji,jj+1) + ht_0(ji,jj+1) ) & |
---|
| 710 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 711 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & |
---|
| 712 | & MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
| 713 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 714 | |
---|
[9023] | 715 | IF(ll_tmp1) THEN |
---|
| 716 | zcpy(ji,jj) = 1.0_wp |
---|
| 717 | ELSE IF(ll_tmp2) THEN |
---|
| 718 | ! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here |
---|
| 719 | zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) & |
---|
| 720 | & / (sshn(ji,jj+1) - sshn(ji,jj )) ) |
---|
| 721 | ELSE |
---|
| 722 | zcpy(ji,jj) = 0._wp |
---|
| 723 | END IF |
---|
| 724 | END DO |
---|
| 725 | END DO |
---|
[10425] | 726 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. ) |
---|
[9023] | 727 | END IF |
---|
[6152] | 728 | |
---|
[455] | 729 | IF( kt == nit000 ) THEN |
---|
| 730 | IF(lwp) WRITE(numout,*) |
---|
| 731 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 732 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 733 | ENDIF |
---|
| 734 | |
---|
[503] | 735 | ! Local constant initialization |
---|
[2528] | 736 | zcoef0 = - grav * 0.5_wp |
---|
| 737 | z1_10 = 1._wp / 10._wp |
---|
| 738 | z1_12 = 1._wp / 12._wp |
---|
[455] | 739 | |
---|
| 740 | !---------------------------------------------------------------------------------------- |
---|
| 741 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 742 | !---------------------------------------------------------------------------------------- |
---|
| 743 | |
---|
| 744 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 745 | |
---|
| 746 | DO jk = 2, jpkm1 |
---|
| 747 | DO jj = 2, jpjm1 |
---|
| 748 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[6140] | 749 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 750 | dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1) |
---|
| 751 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 752 | dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk ) |
---|
| 753 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 754 | dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk ) |
---|
[455] | 755 | END DO |
---|
| 756 | END DO |
---|
| 757 | END DO |
---|
| 758 | |
---|
| 759 | !------------------------------------------------------------------------- |
---|
| 760 | ! compute harmonic averages using eq. 5.18 |
---|
| 761 | !------------------------------------------------------------------------- |
---|
| 762 | zep = 1.e-15 |
---|
| 763 | |
---|
[503] | 764 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 765 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 766 | |
---|
| 767 | DO jk = 2, jpkm1 |
---|
| 768 | DO jj = 2, jpjm1 |
---|
| 769 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 770 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 771 | |
---|
[2528] | 772 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 773 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 774 | |
---|
[2528] | 775 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 776 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 777 | |
---|
| 778 | IF( cffw > zep) THEN |
---|
[2528] | 779 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 780 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 781 | ELSE |
---|
[2528] | 782 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 783 | ENDIF |
---|
| 784 | |
---|
[2528] | 785 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 786 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 787 | |
---|
| 788 | IF( cffu > zep ) THEN |
---|
[2528] | 789 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 790 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 791 | ELSE |
---|
[2528] | 792 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 793 | ENDIF |
---|
| 794 | |
---|
| 795 | IF( cffx > zep ) THEN |
---|
[2528] | 796 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 797 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 798 | ELSE |
---|
[2528] | 799 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 800 | ENDIF |
---|
| 801 | |
---|
| 802 | IF( cffv > zep ) THEN |
---|
[2528] | 803 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 804 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 805 | ELSE |
---|
[2528] | 806 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 807 | ENDIF |
---|
| 808 | |
---|
| 809 | IF( cffy > zep ) THEN |
---|
[2528] | 810 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 811 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 812 | ELSE |
---|
[2528] | 813 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 814 | ENDIF |
---|
| 815 | |
---|
| 816 | END DO |
---|
| 817 | END DO |
---|
| 818 | END DO |
---|
| 819 | |
---|
| 820 | !---------------------------------------------------------------------------------- |
---|
| 821 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 822 | !---------------------------------------------------------------------------------- |
---|
[2528] | 823 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 824 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 825 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 826 | |
---|
[2528] | 827 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 828 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 829 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 830 | |
---|
| 831 | |
---|
| 832 | !-------------------------------------------------------------- |
---|
| 833 | ! Upper half of top-most grid box, compute and store |
---|
| 834 | !------------------------------------------------------------- |
---|
| 835 | |
---|
[6140] | 836 | !!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified |
---|
| 837 | ! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
[455] | 838 | |
---|
| 839 | DO jj = 2, jpjm1 |
---|
| 840 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[6140] | 841 | rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) & |
---|
| 842 | & * ( rhd(ji,jj,1) & |
---|
| 843 | & + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) & |
---|
| 844 | & * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) & |
---|
| 845 | & / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) ) |
---|
[455] | 846 | END DO |
---|
| 847 | END DO |
---|
| 848 | |
---|
| 849 | !!bug gm : here also, simplification is possible |
---|
| 850 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 851 | |
---|
| 852 | DO jk = 2, jpkm1 |
---|
| 853 | DO jj = 2, jpjm1 |
---|
| 854 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 855 | |
---|
[6140] | 856 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 857 | & * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) & |
---|
| 858 | & - grav * z1_10 * ( & |
---|
| 859 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 860 | & * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 861 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 862 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
[455] | 863 | & ) |
---|
| 864 | |
---|
[6140] | 865 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 866 | & * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) & |
---|
| 867 | & - grav* z1_10 * ( & |
---|
| 868 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 869 | & * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 870 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 871 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
[455] | 872 | & ) |
---|
| 873 | |
---|
[6140] | 874 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 875 | & * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) & |
---|
| 876 | & - grav* z1_10 * ( & |
---|
| 877 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 878 | & * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 879 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 880 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
[455] | 881 | & ) |
---|
| 882 | |
---|
| 883 | END DO |
---|
| 884 | END DO |
---|
| 885 | END DO |
---|
[10425] | 886 | CALL lbc_lnk_multi( 'dynhpg', rho_k, 'W', 1., rho_i, 'U', 1., rho_j, 'V', 1. ) |
---|
[455] | 887 | |
---|
| 888 | ! --------------- |
---|
| 889 | ! Surface value |
---|
| 890 | ! --------------- |
---|
| 891 | DO jj = 2, jpjm1 |
---|
| 892 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[6140] | 893 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 894 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
[9023] | 895 | IF( ln_wd_il ) THEN |
---|
[6152] | 896 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
| 897 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
| 898 | ENDIF |
---|
[455] | 899 | ! add to the general momentum trend |
---|
| 900 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 901 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 902 | END DO |
---|
| 903 | END DO |
---|
| 904 | |
---|
| 905 | ! ---------------- |
---|
| 906 | ! interior value (2=<jk=<jpkm1) |
---|
| 907 | ! ---------------- |
---|
| 908 | DO jk = 2, jpkm1 |
---|
[3764] | 909 | DO jj = 2, jpjm1 |
---|
[455] | 910 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 911 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 912 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 913 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
[6140] | 914 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj) |
---|
[455] | 915 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 916 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
[6140] | 917 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj) |
---|
[9023] | 918 | IF( ln_wd_il ) THEN |
---|
[6152] | 919 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
| 920 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
| 921 | ENDIF |
---|
[455] | 922 | ! add to the general momentum trend |
---|
| 923 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 924 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 925 | END DO |
---|
| 926 | END DO |
---|
| 927 | END DO |
---|
[503] | 928 | ! |
---|
[9023] | 929 | IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) |
---|
[2715] | 930 | ! |
---|
[455] | 931 | END SUBROUTINE hpg_djc |
---|
| 932 | |
---|
| 933 | |
---|
[3294] | 934 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 935 | !!--------------------------------------------------------------------- |
---|
[3294] | 936 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 937 | !! |
---|
[3294] | 938 | !! ** Method : s-coordinate case. |
---|
| 939 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 940 | !! based on the constrained cubic-spline interpolation for |
---|
| 941 | !! all vertical coordinate systems |
---|
[455] | 942 | !! |
---|
[3294] | 943 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 944 | !!---------------------------------------------------------------------- |
---|
[3294] | 945 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 946 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 947 | !! |
---|
[3294] | 948 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
[6140] | 949 | REAL(wp) :: zcoef0, znad ! local scalars |
---|
| 950 | ! |
---|
[3294] | 951 | !! The local variables for the correction term |
---|
| 952 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
[6152] | 953 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
[3294] | 954 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 955 | REAL(wp) :: zrhdt1 |
---|
[3294] | 956 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[9019] | 957 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh |
---|
| 958 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
| 959 | REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n |
---|
| 960 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
[455] | 961 | !!---------------------------------------------------------------------- |
---|
[3294] | 962 | ! |
---|
[455] | 963 | IF( kt == nit000 ) THEN |
---|
| 964 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 965 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 966 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 967 | ENDIF |
---|
| 968 | |
---|
[3294] | 969 | ! Local constant initialization |
---|
[3764] | 970 | zcoef0 = - grav |
---|
[6140] | 971 | znad = 1._wp |
---|
| 972 | IF( ln_linssh ) znad = 0._wp |
---|
[3] | 973 | |
---|
[9023] | 974 | IF( ln_wd_il ) THEN |
---|
[9019] | 975 | ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) ) |
---|
| 976 | DO jj = 2, jpjm1 |
---|
[9023] | 977 | DO ji = 2, jpim1 |
---|
| 978 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
| 979 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
| 980 | & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji+1,jj) + ht_0(ji+1,jj) ) & |
---|
| 981 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 982 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( & |
---|
| 983 | & MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > & |
---|
| 984 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 985 | |
---|
[9023] | 986 | IF(ll_tmp1) THEN |
---|
| 987 | zcpx(ji,jj) = 1.0_wp |
---|
| 988 | ELSE IF(ll_tmp2) THEN |
---|
| 989 | ! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here |
---|
| 990 | zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) & |
---|
| 991 | & / (sshn(ji+1,jj) - sshn(ji ,jj)) ) |
---|
| 992 | |
---|
| 993 | zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp) |
---|
| 994 | ELSE |
---|
| 995 | zcpx(ji,jj) = 0._wp |
---|
| 996 | END IF |
---|
[6152] | 997 | |
---|
[9023] | 998 | ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
| 999 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
| 1000 | & MAX( sshn(ji,jj) + ht_0(ji,jj), sshn(ji,jj+1) + ht_0(ji,jj+1) ) & |
---|
| 1001 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 1002 | ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( & |
---|
| 1003 | & MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > & |
---|
| 1004 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 1005 | |
---|
[9023] | 1006 | IF(ll_tmp1) THEN |
---|
| 1007 | zcpy(ji,jj) = 1.0_wp |
---|
| 1008 | ELSE IF(ll_tmp2) THEN |
---|
| 1009 | ! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here |
---|
| 1010 | zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) & |
---|
| 1011 | & / (sshn(ji,jj+1) - sshn(ji,jj )) ) |
---|
| 1012 | zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp) |
---|
| 1013 | |
---|
[9019] | 1014 | ELSE |
---|
| 1015 | zcpy(ji,jj) = 0._wp |
---|
| 1016 | ENDIF |
---|
| 1017 | END DO |
---|
| 1018 | END DO |
---|
[10425] | 1019 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. ) |
---|
[9019] | 1020 | ENDIF |
---|
[6152] | 1021 | |
---|
[3294] | 1022 | ! Clean 3-D work arrays |
---|
| 1023 | zhpi(:,:,:) = 0._wp |
---|
| 1024 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 1025 | |
---|
[3294] | 1026 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 1027 | DO jj = 1, jpj |
---|
[3764] | 1028 | DO ji = 1, jpi |
---|
[13095] | 1029 | jk = mbkt(ji,jj) |
---|
| 1030 | IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp |
---|
| 1031 | ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk) |
---|
[6140] | 1032 | ELSEIF( jk < jpkm1 ) THEN |
---|
[3294] | 1033 | DO jkk = jk+1, jpk |
---|
[6140] | 1034 | zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), & |
---|
[13095] | 1035 | & gde3w_n(ji,jj,jkk-2), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2)) |
---|
[3764] | 1036 | END DO |
---|
[3294] | 1037 | ENDIF |
---|
| 1038 | END DO |
---|
| 1039 | END DO |
---|
[3] | 1040 | |
---|
[3632] | 1041 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 1042 | DO jj = 1, jpj |
---|
| 1043 | DO ji = 1, jpi |
---|
[6140] | 1044 | zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad |
---|
[4990] | 1045 | END DO |
---|
| 1046 | END DO |
---|
[455] | 1047 | |
---|
[4990] | 1048 | DO jk = 2, jpk |
---|
| 1049 | DO jj = 1, jpj |
---|
| 1050 | DO ji = 1, jpi |
---|
[6140] | 1051 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk) |
---|
[4990] | 1052 | END DO |
---|
| 1053 | END DO |
---|
| 1054 | END DO |
---|
[455] | 1055 | |
---|
[4990] | 1056 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 1057 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 1058 | |
---|
[3764] | 1059 | ! Construct the vertical density profile with the |
---|
[3294] | 1060 | ! constrained cubic spline interpolation |
---|
| 1061 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[6140] | 1062 | CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
[3294] | 1063 | |
---|
| 1064 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 1065 | DO jj = 2, jpj |
---|
[3764] | 1066 | DO ji = 2, jpi |
---|
[6140] | 1067 | zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), & |
---|
| 1068 | & csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1) |
---|
[3294] | 1069 | |
---|
| 1070 | ! assuming linear profile across the top half surface layer |
---|
[6140] | 1071 | zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1 |
---|
[3294] | 1072 | END DO |
---|
[455] | 1073 | END DO |
---|
| 1074 | |
---|
[3294] | 1075 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 1076 | DO jk = 2, jpkm1 |
---|
| 1077 | DO jj = 2, jpj |
---|
[3294] | 1078 | DO ji = 2, jpi |
---|
[6140] | 1079 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
| 1080 | & integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), & |
---|
| 1081 | & asp (ji,jj,jk-1), bsp (ji,jj,jk-1), & |
---|
| 1082 | & csp (ji,jj,jk-1), dsp (ji,jj,jk-1) ) |
---|
[3294] | 1083 | END DO |
---|
| 1084 | END DO |
---|
[455] | 1085 | END DO |
---|
| 1086 | |
---|
[3294] | 1087 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5224] | 1088 | |
---|
| 1089 | ! Prepare zsshu_n and zsshv_n |
---|
[3764] | 1090 | DO jj = 2, jpjm1 |
---|
| 1091 | DO ji = 2, jpim1 |
---|
[6140] | 1092 | !!gm BUG ? if it is ssh at u- & v-point then it should be: |
---|
| 1093 | ! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * & |
---|
| 1094 | ! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1095 | ! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * & |
---|
| 1096 | ! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
| 1097 | !!gm not this: |
---|
[5836] | 1098 | zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
| 1099 | & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1100 | zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
| 1101 | & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
[3294] | 1102 | END DO |
---|
[455] | 1103 | END DO |
---|
| 1104 | |
---|
[10425] | 1105 | CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1., zsshv_n, 'V', 1. ) |
---|
[6152] | 1106 | |
---|
[5224] | 1107 | DO jj = 2, jpjm1 |
---|
| 1108 | DO ji = 2, jpim1 |
---|
[6140] | 1109 | zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
| 1110 | zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
[5224] | 1111 | END DO |
---|
| 1112 | END DO |
---|
| 1113 | |
---|
[3764] | 1114 | DO jk = 2, jpkm1 |
---|
| 1115 | DO jj = 2, jpjm1 |
---|
| 1116 | DO ji = 2, jpim1 |
---|
[6140] | 1117 | zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk) |
---|
| 1118 | zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk) |
---|
[3294] | 1119 | END DO |
---|
| 1120 | END DO |
---|
[455] | 1121 | END DO |
---|
[3764] | 1122 | |
---|
| 1123 | DO jk = 1, jpkm1 |
---|
| 1124 | DO jj = 2, jpjm1 |
---|
| 1125 | DO ji = 2, jpim1 |
---|
[6140] | 1126 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk) |
---|
| 1127 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk) |
---|
[3294] | 1128 | END DO |
---|
| 1129 | END DO |
---|
| 1130 | END DO |
---|
[455] | 1131 | |
---|
[3632] | 1132 | DO jk = 1, jpkm1 |
---|
| 1133 | DO jj = 2, jpjm1 |
---|
| 1134 | DO ji = 2, jpim1 |
---|
[6140] | 1135 | zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
| 1136 | zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
| 1137 | zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
| 1138 | zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
[3632] | 1139 | END DO |
---|
| 1140 | END DO |
---|
| 1141 | END DO |
---|
| 1142 | |
---|
| 1143 | |
---|
[3764] | 1144 | DO jk = 1, jpkm1 |
---|
| 1145 | DO jj = 2, jpjm1 |
---|
| 1146 | DO ji = 2, jpim1 |
---|
[3294] | 1147 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1148 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1149 | zuijk = zu(ji,jj,jk) |
---|
| 1150 | zvijk = zv(ji,jj,jk) |
---|
| 1151 | |
---|
| 1152 | !!!!! for u equation |
---|
| 1153 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 1154 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1155 | jis = ji + 1; jid = ji |
---|
| 1156 | ELSE |
---|
| 1157 | jis = ji; jid = ji +1 |
---|
| 1158 | ENDIF |
---|
| 1159 | |
---|
| 1160 | ! integrate the pressure on the shallow side |
---|
[3764] | 1161 | jk1 = jk |
---|
[3632] | 1162 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1163 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1164 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1165 | EXIT |
---|
| 1166 | ENDIF |
---|
[3632] | 1167 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1168 | zpwes = zpwes + & |
---|
[3632] | 1169 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1170 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1171 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1172 | jk1 = jk1 + 1 |
---|
| 1173 | END DO |
---|
[3764] | 1174 | |
---|
[3294] | 1175 | ! integrate the pressure on the deep side |
---|
[3764] | 1176 | jk1 = jk |
---|
[3632] | 1177 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1178 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1179 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1180 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1181 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1182 | dsp(jid,jj,1)) * zdeps |
---|
| 1183 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1184 | EXIT |
---|
| 1185 | ENDIF |
---|
[3632] | 1186 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1187 | zpwed = zpwed + & |
---|
[3632] | 1188 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1189 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1190 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1191 | jk1 = jk1 - 1 |
---|
| 1192 | END DO |
---|
[3764] | 1193 | |
---|
[3294] | 1194 | ! update the momentum trends in u direction |
---|
| 1195 | |
---|
[6140] | 1196 | zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) ) |
---|
| 1197 | IF( .NOT.ln_linssh ) THEN |
---|
| 1198 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * & |
---|
| 1199 | & ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1200 | ELSE |
---|
[6140] | 1201 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1202 | ENDIF |
---|
[9023] | 1203 | IF( ln_wd_il ) THEN |
---|
| 1204 | zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj) |
---|
| 1205 | zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj) |
---|
[6152] | 1206 | ENDIF |
---|
| 1207 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk) |
---|
[3294] | 1208 | ENDIF |
---|
[3764] | 1209 | |
---|
[3294] | 1210 | !!!!! for v equation |
---|
| 1211 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1212 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1213 | jjs = jj + 1; jjd = jj |
---|
| 1214 | ELSE |
---|
| 1215 | jjs = jj ; jjd = jj + 1 |
---|
| 1216 | ENDIF |
---|
| 1217 | |
---|
| 1218 | ! integrate the pressure on the shallow side |
---|
[3764] | 1219 | jk1 = jk |
---|
[3632] | 1220 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1221 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1222 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1223 | EXIT |
---|
| 1224 | ENDIF |
---|
[3632] | 1225 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1226 | zpnss = zpnss + & |
---|
[3632] | 1227 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1228 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1229 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1230 | jk1 = jk1 + 1 |
---|
| 1231 | END DO |
---|
[3764] | 1232 | |
---|
[3294] | 1233 | ! integrate the pressure on the deep side |
---|
[3764] | 1234 | jk1 = jk |
---|
[3632] | 1235 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1236 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1237 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1238 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1239 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1240 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1241 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1242 | EXIT |
---|
| 1243 | ENDIF |
---|
[3632] | 1244 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1245 | zpnsd = zpnsd + & |
---|
[3632] | 1246 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1247 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1248 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1249 | jk1 = jk1 - 1 |
---|
| 1250 | END DO |
---|
| 1251 | |
---|
[3764] | 1252 | |
---|
[3294] | 1253 | ! update the momentum trends in v direction |
---|
| 1254 | |
---|
[6140] | 1255 | zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) ) |
---|
| 1256 | IF( .NOT.ln_linssh ) THEN |
---|
| 1257 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * & |
---|
| 1258 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1259 | ELSE |
---|
[6140] | 1260 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1261 | ENDIF |
---|
[9023] | 1262 | IF( ln_wd_il ) THEN |
---|
| 1263 | zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj) |
---|
| 1264 | zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj) |
---|
[6152] | 1265 | ENDIF |
---|
| 1266 | |
---|
| 1267 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk) |
---|
[3294] | 1268 | ENDIF |
---|
[6140] | 1269 | ! |
---|
| 1270 | END DO |
---|
| 1271 | END DO |
---|
[455] | 1272 | END DO |
---|
[503] | 1273 | ! |
---|
[9023] | 1274 | IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) |
---|
[2715] | 1275 | ! |
---|
[3294] | 1276 | END SUBROUTINE hpg_prj |
---|
[455] | 1277 | |
---|
[4990] | 1278 | |
---|
[6140] | 1279 | SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
[3294] | 1280 | !!---------------------------------------------------------------------- |
---|
| 1281 | !! *** ROUTINE cspline *** |
---|
[3764] | 1282 | !! |
---|
[3294] | 1283 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1284 | !! |
---|
| 1285 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1286 | !! |
---|
[3294] | 1287 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1288 | !!---------------------------------------------------------------------- |
---|
[6140] | 1289 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate |
---|
| 1290 | REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function |
---|
| 1291 | INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear |
---|
[4990] | 1292 | ! |
---|
[3294] | 1293 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1294 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1295 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1296 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1297 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1298 | !!---------------------------------------------------------------------- |
---|
[6140] | 1299 | ! |
---|
| 1300 | !!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!! |
---|
[3294] | 1301 | jpi = size(fsp,1) |
---|
| 1302 | jpj = size(fsp,2) |
---|
[7761] | 1303 | jpkm1 = MAX( 1, size(fsp,3) - 1 ) |
---|
[6140] | 1304 | ! |
---|
[3294] | 1305 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1306 | DO ji = 1, jpi |
---|
| 1307 | DO jj = 1, jpj |
---|
[3764] | 1308 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1309 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1310 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1311 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1312 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1313 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1314 | ! |
---|
| 1315 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1316 | ! |
---|
[3294] | 1317 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1318 | ! zdf(jk) = 0._wp |
---|
| 1319 | ! ELSE |
---|
| 1320 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1321 | ! ENDIF |
---|
| 1322 | ! END DO |
---|
[3764] | 1323 | |
---|
[3294] | 1324 | !!Simply geometric average |
---|
| 1325 | DO jk = 2, jpkm1-1 |
---|
[9019] | 1326 | zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1)) |
---|
| 1327 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk )) |
---|
[3764] | 1328 | |
---|
[3294] | 1329 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1330 | zdf(jk) = 0._wp |
---|
| 1331 | ELSE |
---|
| 1332 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1333 | ENDIF |
---|
| 1334 | END DO |
---|
[3764] | 1335 | |
---|
[3294] | 1336 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
[6140] | 1337 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
[3294] | 1338 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
[6140] | 1339 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1340 | |
---|
[3294] | 1341 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1342 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1343 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1344 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1345 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1346 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1347 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1348 | |
---|
[3294] | 1349 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1350 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1351 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1352 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1353 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1354 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1355 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1356 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1357 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1358 | END DO |
---|
| 1359 | END DO |
---|
| 1360 | END DO |
---|
[3764] | 1361 | |
---|
[6140] | 1362 | ELSEIF ( polynomial_type == 2 ) THEN ! Linear |
---|
[3294] | 1363 | DO ji = 1, jpi |
---|
| 1364 | DO jj = 1, jpj |
---|
| 1365 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1366 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1367 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1368 | |
---|
[3294] | 1369 | dsp(ji,jj,jk) = 0._wp |
---|
| 1370 | csp(ji,jj,jk) = 0._wp |
---|
| 1371 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1372 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1373 | END DO |
---|
| 1374 | END DO |
---|
| 1375 | END DO |
---|
[9019] | 1376 | ! |
---|
[3294] | 1377 | ELSE |
---|
[9019] | 1378 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
[3294] | 1379 | ENDIF |
---|
[9019] | 1380 | ! |
---|
[3294] | 1381 | END SUBROUTINE cspline |
---|
| 1382 | |
---|
| 1383 | |
---|
[3764] | 1384 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1385 | !!---------------------------------------------------------------------- |
---|
| 1386 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1387 | !! |
---|
[3294] | 1388 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1389 | !! |
---|
[4990] | 1390 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1391 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1392 | !!---------------------------------------------------------------------- |
---|
[3764] | 1393 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1394 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1395 | REAL(wp) :: zdeltx |
---|
| 1396 | !!---------------------------------------------------------------------- |
---|
[6140] | 1397 | ! |
---|
[3294] | 1398 | zdeltx = xr - xl |
---|
[6140] | 1399 | IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN |
---|
| 1400 | f = 0.5_wp * (fl + fr) |
---|
[3294] | 1401 | ELSE |
---|
[6140] | 1402 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
[3294] | 1403 | ENDIF |
---|
[6140] | 1404 | ! |
---|
[3294] | 1405 | END FUNCTION interp1 |
---|
| 1406 | |
---|
[4990] | 1407 | |
---|
[6140] | 1408 | FUNCTION interp2( x, a, b, c, d ) RESULT(f) |
---|
[3294] | 1409 | !!---------------------------------------------------------------------- |
---|
| 1410 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1411 | !! |
---|
[3294] | 1412 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1413 | !! |
---|
[3294] | 1414 | !! ** Method : cubic spline interpolation |
---|
| 1415 | !! |
---|
| 1416 | !!---------------------------------------------------------------------- |
---|
[3764] | 1417 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1418 | REAL(wp) :: f ! value from the interpolation |
---|
| 1419 | !!---------------------------------------------------------------------- |
---|
[6140] | 1420 | ! |
---|
[3764] | 1421 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[6140] | 1422 | ! |
---|
[3294] | 1423 | END FUNCTION interp2 |
---|
| 1424 | |
---|
| 1425 | |
---|
[6140] | 1426 | FUNCTION interp3( x, a, b, c, d ) RESULT(f) |
---|
[3294] | 1427 | !!---------------------------------------------------------------------- |
---|
| 1428 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1429 | !! |
---|
[9019] | 1430 | !! ** Purpose : Calculate the first order of derivative of |
---|
[3294] | 1431 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1432 | !! |
---|
[3294] | 1433 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1434 | !! |
---|
| 1435 | !!---------------------------------------------------------------------- |
---|
[3764] | 1436 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1437 | REAL(wp) :: f ! value from the interpolation |
---|
| 1438 | !!---------------------------------------------------------------------- |
---|
[6140] | 1439 | ! |
---|
[3294] | 1440 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
[6140] | 1441 | ! |
---|
[3294] | 1442 | END FUNCTION interp3 |
---|
| 1443 | |
---|
[3764] | 1444 | |
---|
[6140] | 1445 | FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f) |
---|
[3294] | 1446 | !!---------------------------------------------------------------------- |
---|
| 1447 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1448 | !! |
---|
[3294] | 1449 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1450 | !! |
---|
[3764] | 1451 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1452 | !! |
---|
[3294] | 1453 | !!---------------------------------------------------------------------- |
---|
[3764] | 1454 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1455 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1456 | REAL(wp) :: f ! integration result |
---|
| 1457 | !!---------------------------------------------------------------------- |
---|
[6140] | 1458 | ! |
---|
[3764] | 1459 | za1 = 0.5_wp * b |
---|
| 1460 | za2 = c / 3.0_wp |
---|
| 1461 | za3 = 0.25_wp * d |
---|
[6140] | 1462 | ! |
---|
[3294] | 1463 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1464 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
[6140] | 1465 | ! |
---|
[3632] | 1466 | END FUNCTION integ_spline |
---|
[3294] | 1467 | |
---|
[3] | 1468 | !!====================================================================== |
---|
| 1469 | END MODULE dynhpg |
---|
[3632] | 1470 | |
---|