[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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[12377] | 33 | USE isf_oce , ONLY : risfload ! ice shelf (risfload variable) |
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| 34 | USE isfload , ONLY : isf_load ! ice shelf (isf_load routine ) |
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[4990] | 35 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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[3] | 36 | USE dom_oce ! ocean space and time domain |
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[6152] | 37 | USE wet_dry ! wetting and drying |
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[3] | 38 | USE phycst ! physical constants |
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[4990] | 39 | USE trd_oce ! trends: ocean variables |
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| 40 | USE trddyn ! trend manager: dynamics |
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[11416] | 41 | USE zpshde ! partial step: hor. derivative (zps_hde routine) |
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[4990] | 42 | ! |
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[2715] | 43 | USE in_out_manager ! I/O manager |
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[258] | 44 | USE prtctl ! Print control |
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[4990] | 45 | USE lbclnk ! lateral boundary condition |
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[2715] | 46 | USE lib_mpp ! MPP library |
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[4990] | 47 | USE eosbn2 ! compute density |
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[3294] | 48 | USE timing ! Timing |
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[6140] | 49 | USE iom |
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[3] | 50 | |
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| 51 | IMPLICIT NONE |
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| 52 | PRIVATE |
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| 53 | |
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[2528] | 54 | PUBLIC dyn_hpg ! routine called by step module |
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| 55 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 56 | |
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[9490] | 57 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 58 | LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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| 59 | LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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| 60 | LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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| 61 | LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 62 | LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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| 63 | LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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[455] | 64 | |
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[9490] | 65 | ! !! Flag to control the type of hydrostatic pressure gradient |
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| 66 | INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion |
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| 67 | INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps |
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| 68 | INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation) |
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| 69 | INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation) |
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| 70 | INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 71 | INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme) |
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| 72 | INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf |
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| 73 | ! |
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| 74 | INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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[455] | 75 | |
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[3] | 76 | !! * Substitutions |
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[12377] | 77 | # include "do_loop_substitute.h90" |
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[13237] | 78 | # include "domzgr_substitute.h90" |
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| 79 | |
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[3] | 80 | !!---------------------------------------------------------------------- |
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[9598] | 81 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[2528] | 82 | !! $Id$ |
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[10068] | 83 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[3] | 84 | !!---------------------------------------------------------------------- |
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| 85 | CONTAINS |
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| 86 | |
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[12377] | 87 | SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs ) |
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[3] | 88 | !!--------------------------------------------------------------------- |
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| 89 | !! *** ROUTINE dyn_hpg *** |
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| 90 | !! |
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[3764] | 91 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 92 | !! using the scheme defined in the namelist |
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[3764] | 93 | !! |
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[12377] | 94 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
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[4990] | 95 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 96 | !!---------------------------------------------------------------------- |
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[12377] | 97 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 98 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
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| 99 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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| 100 | ! |
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[9019] | 101 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[455] | 102 | !!---------------------------------------------------------------------- |
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[2528] | 103 | ! |
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[9019] | 104 | IF( ln_timing ) CALL timing_start('dyn_hpg') |
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[2715] | 105 | ! |
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[12377] | 106 | IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn) |
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[9019] | 107 | ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) ) |
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[12377] | 108 | ztrdu(:,:,:) = puu(:,:,:,Krhs) |
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| 109 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) |
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[3764] | 110 | ENDIF |
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[2528] | 111 | ! |
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[3294] | 112 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[12377] | 113 | CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate |
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| 114 | CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation) |
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| 115 | CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation) |
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| 116 | CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 117 | CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme) |
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| 118 | CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf |
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[455] | 119 | END SELECT |
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[2528] | 120 | ! |
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[503] | 121 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[12377] | 122 | ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:) |
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| 123 | ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:) |
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| 124 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm ) |
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[9019] | 125 | DEALLOCATE( ztrdu , ztrdv ) |
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[3764] | 126 | ENDIF |
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[503] | 127 | ! |
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[12377] | 128 | IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 129 | & tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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[503] | 130 | ! |
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[9019] | 131 | IF( ln_timing ) CALL timing_stop('dyn_hpg') |
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[2715] | 132 | ! |
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[455] | 133 | END SUBROUTINE dyn_hpg |
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| 134 | |
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| 135 | |
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[12377] | 136 | SUBROUTINE dyn_hpg_init( Kmm ) |
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[455] | 137 | !!---------------------------------------------------------------------- |
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[2528] | 138 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 139 | !! |
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| 140 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 141 | !! computation and consistency control |
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| 142 | !! |
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[1601] | 143 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 144 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 145 | !!---------------------------------------------------------------------- |
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[12377] | 146 | INTEGER, INTENT( in ) :: Kmm ! ocean time level index |
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| 147 | ! |
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[455] | 148 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 149 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 150 | !! |
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[6140] | 151 | INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF |
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| 152 | REAL(wp) :: znad |
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[9019] | 153 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density |
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| 154 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF |
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| 155 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF |
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[6140] | 156 | !! |
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[3294] | 157 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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[5930] | 158 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf |
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[455] | 159 | !!---------------------------------------------------------------------- |
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[2528] | 160 | ! |
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[4147] | 161 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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[11536] | 162 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' ) |
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[6140] | 163 | ! |
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[4147] | 164 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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[11536] | 165 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' ) |
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[4624] | 166 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 167 | ! |
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| 168 | IF(lwp) THEN ! Control print |
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[455] | 169 | WRITE(numout,*) |
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[2528] | 170 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 171 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 172 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 173 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 174 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 175 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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[5120] | 176 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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[1601] | 177 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 178 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[455] | 179 | ENDIF |
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[2528] | 180 | ! |
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[3294] | 181 | IF( ln_hpg_djc ) & |
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[9019] | 182 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method', & |
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| 183 | & ' currently disabled (bugs under investigation).' , & |
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| 184 | & ' Please select either ln_hpg_sco or ln_hpg_prj instead' ) |
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| 185 | ! |
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| 186 | IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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| 187 | & CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', & |
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| 188 | & ' the standard jacobian formulation hpg_sco or ' , & |
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| 189 | & ' the pressure jacobian formulation hpg_prj' ) |
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| 190 | ! |
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| 191 | IF( ln_hpg_isf ) THEN |
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| 192 | IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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| 193 | ELSE |
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| 194 | IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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| 195 | ENDIF |
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[2528] | 196 | ! |
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[9490] | 197 | ! ! Set nhpg from ln_hpg_... flags & consistency check |
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| 198 | nhpg = np_ERROR |
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| 199 | ioptio = 0 |
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| 200 | IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF |
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| 201 | IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF |
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| 202 | IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF |
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| 203 | IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF |
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| 204 | IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF |
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| 205 | IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF |
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[2528] | 206 | ! |
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[2715] | 207 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[5120] | 208 | ! |
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[9490] | 209 | IF(lwp) THEN |
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| 210 | WRITE(numout,*) |
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| 211 | SELECT CASE( nhpg ) |
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| 212 | CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps ' |
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| 213 | CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)' |
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| 214 | CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)' |
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| 215 | CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)' |
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| 216 | CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)' |
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| 217 | CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf' |
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| 218 | END SELECT |
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| 219 | WRITE(numout,*) |
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| 220 | ENDIF |
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[9019] | 221 | ! |
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[2528] | 222 | END SUBROUTINE dyn_hpg_init |
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[455] | 223 | |
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| 224 | |
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[12377] | 225 | SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs ) |
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[455] | 226 | !!--------------------------------------------------------------------- |
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| 227 | !! *** ROUTINE hpg_zco *** |
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| 228 | !! |
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| 229 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 230 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 231 | !! is computed by taking the vertical integral of the in-situ |
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| 232 | !! density gradient along the model level from the suface to that |
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| 233 | !! level: zhpi = grav ..... |
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| 234 | !! zhpj = grav ..... |
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[12377] | 235 | !! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)). |
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| 236 | !! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi |
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| 237 | !! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj |
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[3764] | 238 | !! |
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[12377] | 239 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
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[503] | 240 | !!---------------------------------------------------------------------- |
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[12377] | 241 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 242 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
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| 243 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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[6140] | 244 | ! |
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[503] | 245 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 246 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[9019] | 247 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
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[3] | 248 | !!---------------------------------------------------------------------- |
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[3764] | 249 | ! |
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[3] | 250 | IF( kt == nit000 ) THEN |
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| 251 | IF(lwp) WRITE(numout,*) |
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[455] | 252 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 253 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 254 | ENDIF |
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| 255 | |
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[3764] | 256 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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| 257 | |
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[455] | 258 | ! Surface value |
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[13899] | 259 | DO_2D( 0, 0, 0, 0 ) |
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[12377] | 260 | zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm) |
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| 261 | ! hydrostatic pressure gradient |
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| 262 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
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| 263 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
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| 264 | ! add to the general momentum trend |
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| 265 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) |
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| 266 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) |
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| 267 | END_2D |
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[3294] | 268 | |
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[503] | 269 | ! |
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[455] | 270 | ! interior value (2=<jk=<jpkm1) |
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[13899] | 271 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
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[12377] | 272 | zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm) |
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| 273 | ! hydrostatic pressure gradient |
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| 274 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 275 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 276 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
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[455] | 277 | |
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[12377] | 278 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 279 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 280 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
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| 281 | ! add to the general momentum trend |
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| 282 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) |
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| 283 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) |
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| 284 | END_3D |
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[503] | 285 | ! |
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[455] | 286 | END SUBROUTINE hpg_zco |
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[216] | 287 | |
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[3] | 288 | |
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[12377] | 289 | SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs ) |
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[3] | 290 | !!--------------------------------------------------------------------- |
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[455] | 291 | !! *** ROUTINE hpg_zps *** |
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[3764] | 292 | !! |
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[455] | 293 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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[3764] | 294 | !! |
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[12377] | 295 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
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[3764] | 296 | !!---------------------------------------------------------------------- |
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[12377] | 297 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 298 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
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| 299 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
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[503] | 300 | !! |
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| 301 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 302 | INTEGER :: iku, ikv ! temporary integers |
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| 303 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[9019] | 304 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
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[11416] | 305 | REAL(wp), DIMENSION(jpi,jpj) :: zgtsu, zgtsv, zgru, zgrv |
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[3] | 306 | !!---------------------------------------------------------------------- |
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[3294] | 307 | ! |
---|
[3] | 308 | IF( kt == nit000 ) THEN |
---|
| 309 | IF(lwp) WRITE(numout,*) |
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[455] | 310 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
---|
[503] | 311 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
---|
[3] | 312 | ENDIF |
---|
| 313 | |
---|
[11416] | 314 | ! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level |
---|
[12377] | 315 | CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv ) |
---|
[3294] | 316 | |
---|
[503] | 317 | ! Local constant initialization |
---|
[2528] | 318 | zcoef0 = - grav * 0.5_wp |
---|
[3] | 319 | |
---|
[2528] | 320 | ! Surface value (also valid in partial step case) |
---|
[13899] | 321 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 322 | zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm) |
---|
| 323 | ! hydrostatic pressure gradient |
---|
| 324 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 325 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
| 326 | ! add to the general momentum trend |
---|
| 327 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) |
---|
| 328 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) |
---|
| 329 | END_2D |
---|
[3] | 330 | |
---|
[503] | 331 | ! interior value (2=<jk=<jpkm1) |
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[13899] | 332 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 333 | zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm) |
---|
| 334 | ! hydrostatic pressure gradient |
---|
| 335 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 336 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
| 337 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj) |
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[3] | 338 | |
---|
[12377] | 339 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 340 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
| 341 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj) |
---|
| 342 | ! add to the general momentum trend |
---|
| 343 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) |
---|
| 344 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) |
---|
| 345 | END_3D |
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[3] | 346 | |
---|
[11416] | 347 | ! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90) |
---|
[13899] | 348 | DO_2D( 0, 0, 0, 0 ) |
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[12377] | 349 | iku = mbku(ji,jj) |
---|
| 350 | ikv = mbkv(ji,jj) |
---|
| 351 | zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) ) |
---|
| 352 | zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) ) |
---|
| 353 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 354 | puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 355 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
| 356 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj) |
---|
| 357 | puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
| 358 | ENDIF |
---|
| 359 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 360 | pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 361 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 362 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj) |
---|
| 363 | pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
| 364 | ENDIF |
---|
| 365 | END_2D |
---|
[503] | 366 | ! |
---|
[455] | 367 | END SUBROUTINE hpg_zps |
---|
[216] | 368 | |
---|
[6140] | 369 | |
---|
[12377] | 370 | SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs ) |
---|
[3] | 371 | !!--------------------------------------------------------------------- |
---|
[455] | 372 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 373 | !! |
---|
[455] | 374 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 375 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 376 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 377 | !! density gradient along the model level from the suface to that |
---|
[455] | 378 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 379 | !! to the horizontal pressure gradient : |
---|
| 380 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 381 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[12377] | 382 | !! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)). |
---|
| 383 | !! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi |
---|
| 384 | !! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj |
---|
[3] | 385 | !! |
---|
[12377] | 386 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
---|
[503] | 387 | !!---------------------------------------------------------------------- |
---|
[12377] | 388 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
| 389 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
| 390 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
[503] | 391 | !! |
---|
[6152] | 392 | INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices |
---|
| 393 | REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars |
---|
[7646] | 394 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
[9019] | 395 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
---|
| 396 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
[5120] | 397 | !!---------------------------------------------------------------------- |
---|
| 398 | ! |
---|
[9039] | 399 | IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj)) |
---|
[9023] | 400 | ! |
---|
[5120] | 401 | IF( kt == nit000 ) THEN |
---|
| 402 | IF(lwp) WRITE(numout,*) |
---|
| 403 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 404 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 405 | ENDIF |
---|
[6140] | 406 | ! |
---|
[5120] | 407 | zcoef0 = - grav * 0.5_wp |
---|
[6140] | 408 | IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly |
---|
| 409 | ELSE ; znad = 1._wp ! Variable volume: density |
---|
[5120] | 410 | ENDIF |
---|
[6140] | 411 | ! |
---|
[9023] | 412 | IF( ln_wd_il ) THEN |
---|
[13899] | 413 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 414 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
| 415 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
| 416 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) & |
---|
| 417 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 418 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
| 419 | & MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
| 420 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 421 | |
---|
[12377] | 422 | IF(ll_tmp1) THEN |
---|
| 423 | zcpx(ji,jj) = 1.0_wp |
---|
| 424 | ELSE IF(ll_tmp2) THEN |
---|
| 425 | ! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here |
---|
| 426 | zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
| 427 | & / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) ) |
---|
| 428 | ELSE |
---|
| 429 | zcpx(ji,jj) = 0._wp |
---|
| 430 | END IF |
---|
| 431 | |
---|
| 432 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
| 433 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
| 434 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) & |
---|
| 435 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 436 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
| 437 | & MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
| 438 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 439 | |
---|
[12377] | 440 | IF(ll_tmp1) THEN |
---|
| 441 | zcpy(ji,jj) = 1.0_wp |
---|
| 442 | ELSE IF(ll_tmp2) THEN |
---|
| 443 | ! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here |
---|
| 444 | zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
| 445 | & / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) ) |
---|
| 446 | ELSE |
---|
| 447 | zcpy(ji,jj) = 0._wp |
---|
| 448 | END IF |
---|
| 449 | END_2D |
---|
[13226] | 450 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp ) |
---|
[9023] | 451 | END IF |
---|
| 452 | |
---|
[5120] | 453 | ! Surface value |
---|
[13899] | 454 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 455 | ! hydrostatic pressure gradient along s-surfaces |
---|
[13237] | 456 | zhpi(ji,jj,1) = & |
---|
| 457 | & zcoef0 * ( e3w(ji+1,jj ,1,Kmm) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 458 | & - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) & |
---|
| 459 | & * r1_e1u(ji,jj) |
---|
| 460 | zhpj(ji,jj,1) = & |
---|
| 461 | & zcoef0 * ( e3w(ji ,jj+1,1,Kmm) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 462 | & - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) & |
---|
| 463 | & * r1_e2v(ji,jj) |
---|
[12377] | 464 | ! s-coordinate pressure gradient correction |
---|
| 465 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 466 | & * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 467 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 468 | & * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
| 469 | ! |
---|
| 470 | IF( ln_wd_il ) THEN |
---|
| 471 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
| 472 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
| 473 | zuap = zuap * zcpx(ji,jj) |
---|
| 474 | zvap = zvap * zcpy(ji,jj) |
---|
| 475 | ENDIF |
---|
| 476 | ! |
---|
| 477 | ! add to the general momentum trend |
---|
| 478 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap |
---|
| 479 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap |
---|
| 480 | END_2D |
---|
[5120] | 481 | |
---|
| 482 | ! interior value (2=<jk=<jpkm1) |
---|
[13899] | 483 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 484 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 485 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) & |
---|
| 486 | & * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 487 | & - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 488 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) & |
---|
| 489 | & * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 490 | & - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
| 491 | ! s-coordinate pressure gradient correction |
---|
| 492 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 493 | & * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj) |
---|
| 494 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 495 | & * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj) |
---|
| 496 | ! |
---|
| 497 | IF( ln_wd_il ) THEN |
---|
| 498 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
| 499 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
| 500 | zuap = zuap * zcpx(ji,jj) |
---|
| 501 | zvap = zvap * zcpy(ji,jj) |
---|
| 502 | ENDIF |
---|
| 503 | ! |
---|
| 504 | ! add to the general momentum trend |
---|
| 505 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap |
---|
| 506 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap |
---|
| 507 | END_3D |
---|
[5120] | 508 | ! |
---|
[9039] | 509 | IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy ) |
---|
[5120] | 510 | ! |
---|
| 511 | END SUBROUTINE hpg_sco |
---|
| 512 | |
---|
[6140] | 513 | |
---|
[12377] | 514 | SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs ) |
---|
[5120] | 515 | !!--------------------------------------------------------------------- |
---|
[6140] | 516 | !! *** ROUTINE hpg_isf *** |
---|
[5120] | 517 | !! |
---|
| 518 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 519 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 520 | !! is computed by taking the vertical integral of the in-situ |
---|
| 521 | !! density gradient along the model level from the suface to that |
---|
| 522 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 523 | !! to the horizontal pressure gradient : |
---|
| 524 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 525 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[12377] | 526 | !! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)). |
---|
| 527 | !! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi |
---|
| 528 | !! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj |
---|
| 529 | !! iceload is added |
---|
[5120] | 530 | !! |
---|
[12377] | 531 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
---|
[5120] | 532 | !!---------------------------------------------------------------------- |
---|
[12377] | 533 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
| 534 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
| 535 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
[5120] | 536 | !! |
---|
[6140] | 537 | INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 538 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
[9019] | 539 | REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj |
---|
| 540 | REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top |
---|
| 541 | REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce |
---|
[3] | 542 | !!---------------------------------------------------------------------- |
---|
[3294] | 543 | ! |
---|
[9019] | 544 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
---|
[3294] | 545 | ! |
---|
[9019] | 546 | znad=1._wp ! To use density and not density anomaly |
---|
| 547 | ! |
---|
| 548 | ! ! iniitialised to 0. zhpi zhpi |
---|
| 549 | zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp |
---|
[6140] | 550 | |
---|
[4990] | 551 | ! compute rhd at the ice/oce interface (ocean side) |
---|
[6140] | 552 | ! usefull to reduce residual current in the test case ISOMIP with no melting |
---|
[9019] | 553 | DO ji = 1, jpi |
---|
| 554 | DO jj = 1, jpj |
---|
| 555 | ikt = mikt(ji,jj) |
---|
[12377] | 556 | zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm) |
---|
| 557 | zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm) |
---|
[4990] | 558 | END DO |
---|
| 559 | END DO |
---|
[9019] | 560 | CALL eos( zts_top, risfdep, zrhdtop_oce ) |
---|
[6140] | 561 | |
---|
| 562 | !================================================================================== |
---|
| 563 | !===== Compute surface value ===================================================== |
---|
| 564 | !================================================================================== |
---|
[13899] | 565 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 566 | ikt = mikt(ji,jj) |
---|
| 567 | iktp1i = mikt(ji+1,jj) |
---|
| 568 | iktp1j = mikt(ji,jj+1) |
---|
| 569 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 570 | ! we assume ISF is in isostatic equilibrium |
---|
| 571 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w(ji+1,jj,iktp1i,Kmm) & |
---|
| 572 | & * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) & |
---|
| 573 | & - 0.5_wp * e3w(ji,jj,ikt,Kmm) & |
---|
| 574 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
| 575 | & + ( risfload(ji+1,jj) - risfload(ji,jj)) ) |
---|
| 576 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w(ji,jj+1,iktp1j,Kmm) & |
---|
| 577 | & * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) & |
---|
| 578 | & - 0.5_wp * e3w(ji,jj,ikt,Kmm) & |
---|
| 579 | & * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) & |
---|
| 580 | & + ( risfload(ji,jj+1) - risfload(ji,jj)) ) |
---|
| 581 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
| 582 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 583 | & * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 584 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 585 | & * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
| 586 | ! add to the general momentum trend |
---|
| 587 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 588 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
| 589 | END_2D |
---|
[4990] | 590 | !================================================================================== |
---|
| 591 | !===== Compute interior value ===================================================== |
---|
| 592 | !================================================================================== |
---|
[6140] | 593 | ! interior value (2=<jk=<jpkm1) |
---|
[13899] | 594 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 595 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 596 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
[13237] | 597 | & * ( e3w(ji+1,jj,jk,Kmm) & |
---|
| 598 | & * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) * wmask(ji+1,jj,jk) & |
---|
| 599 | & - e3w(ji ,jj,jk,Kmm) & |
---|
| 600 | & * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) * wmask(ji ,jj,jk) ) |
---|
[12377] | 601 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
[13237] | 602 | & * ( e3w(ji,jj+1,jk,Kmm) & |
---|
| 603 | & * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) * wmask(ji,jj+1,jk) & |
---|
| 604 | & - e3w(ji,jj ,jk,Kmm) & |
---|
| 605 | & * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) * wmask(ji,jj ,jk) ) |
---|
[12377] | 606 | ! s-coordinate pressure gradient correction |
---|
| 607 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 608 | & * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 609 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 610 | & * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 611 | ! add to the general momentum trend |
---|
| 612 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 613 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk) |
---|
| 614 | END_3D |
---|
[503] | 615 | ! |
---|
[5120] | 616 | END SUBROUTINE hpg_isf |
---|
[455] | 617 | |
---|
[4990] | 618 | |
---|
[12377] | 619 | SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs ) |
---|
[455] | 620 | !!--------------------------------------------------------------------- |
---|
| 621 | !! *** ROUTINE hpg_djc *** |
---|
| 622 | !! |
---|
| 623 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 624 | !! |
---|
[503] | 625 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 626 | !!---------------------------------------------------------------------- |
---|
[12377] | 627 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
| 628 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
| 629 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
[503] | 630 | !! |
---|
| 631 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 632 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 633 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 634 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[6152] | 635 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
[9019] | 636 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj |
---|
| 637 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 638 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 639 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k |
---|
| 640 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
[455] | 641 | !!---------------------------------------------------------------------- |
---|
[3294] | 642 | ! |
---|
[9023] | 643 | IF( ln_wd_il ) THEN |
---|
[9019] | 644 | ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) ) |
---|
[13899] | 645 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 646 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
| 647 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
| 648 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) & |
---|
| 649 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 650 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
| 651 | & MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
| 652 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
| 653 | IF(ll_tmp1) THEN |
---|
| 654 | zcpx(ji,jj) = 1.0_wp |
---|
| 655 | ELSE IF(ll_tmp2) THEN |
---|
| 656 | ! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here |
---|
| 657 | zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
| 658 | & / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) ) |
---|
| 659 | ELSE |
---|
| 660 | zcpx(ji,jj) = 0._wp |
---|
| 661 | END IF |
---|
| 662 | |
---|
| 663 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
| 664 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
| 665 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) & |
---|
| 666 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 667 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
| 668 | & MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
| 669 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 670 | |
---|
[12377] | 671 | IF(ll_tmp1) THEN |
---|
| 672 | zcpy(ji,jj) = 1.0_wp |
---|
| 673 | ELSE IF(ll_tmp2) THEN |
---|
| 674 | ! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here |
---|
| 675 | zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
| 676 | & / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) ) |
---|
| 677 | ELSE |
---|
| 678 | zcpy(ji,jj) = 0._wp |
---|
| 679 | END IF |
---|
| 680 | END_2D |
---|
[13226] | 681 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp ) |
---|
[9023] | 682 | END IF |
---|
[6152] | 683 | |
---|
[455] | 684 | IF( kt == nit000 ) THEN |
---|
| 685 | IF(lwp) WRITE(numout,*) |
---|
| 686 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 687 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 688 | ENDIF |
---|
| 689 | |
---|
[503] | 690 | ! Local constant initialization |
---|
[2528] | 691 | zcoef0 = - grav * 0.5_wp |
---|
| 692 | z1_10 = 1._wp / 10._wp |
---|
| 693 | z1_12 = 1._wp / 12._wp |
---|
[455] | 694 | |
---|
| 695 | !---------------------------------------------------------------------------------------- |
---|
| 696 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 697 | !---------------------------------------------------------------------------------------- |
---|
| 698 | |
---|
| 699 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 700 | |
---|
[13899] | 701 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 702 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 703 | dzz (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji,jj,jk-1) |
---|
| 704 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 705 | dzx (ji,jj,jk) = gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk ) |
---|
| 706 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 707 | dzy (ji,jj,jk) = gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk ) |
---|
| 708 | END_3D |
---|
[455] | 709 | |
---|
| 710 | !------------------------------------------------------------------------- |
---|
| 711 | ! compute harmonic averages using eq. 5.18 |
---|
| 712 | !------------------------------------------------------------------------- |
---|
| 713 | zep = 1.e-15 |
---|
| 714 | |
---|
[503] | 715 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 716 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 717 | |
---|
[13899] | 718 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 719 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 720 | |
---|
[12377] | 721 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 722 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 723 | |
---|
[12377] | 724 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 725 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 726 | |
---|
[12377] | 727 | IF( cffw > zep) THEN |
---|
| 728 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 729 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
| 730 | ELSE |
---|
| 731 | drhow(ji,jj,jk) = 0._wp |
---|
| 732 | ENDIF |
---|
[455] | 733 | |
---|
[12377] | 734 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 735 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 736 | |
---|
[12377] | 737 | IF( cffu > zep ) THEN |
---|
| 738 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 739 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
| 740 | ELSE |
---|
| 741 | drhou(ji,jj,jk ) = 0._wp |
---|
| 742 | ENDIF |
---|
[455] | 743 | |
---|
[12377] | 744 | IF( cffx > zep ) THEN |
---|
| 745 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 746 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
| 747 | ELSE |
---|
| 748 | dzu(ji,jj,jk) = 0._wp |
---|
| 749 | ENDIF |
---|
[455] | 750 | |
---|
[12377] | 751 | IF( cffv > zep ) THEN |
---|
| 752 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 753 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
| 754 | ELSE |
---|
| 755 | drhov(ji,jj,jk) = 0._wp |
---|
| 756 | ENDIF |
---|
[455] | 757 | |
---|
[12377] | 758 | IF( cffy > zep ) THEN |
---|
| 759 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 760 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
| 761 | ELSE |
---|
| 762 | dzv(ji,jj,jk) = 0._wp |
---|
| 763 | ENDIF |
---|
[455] | 764 | |
---|
[12377] | 765 | END_3D |
---|
[455] | 766 | |
---|
| 767 | !---------------------------------------------------------------------------------- |
---|
| 768 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 769 | !---------------------------------------------------------------------------------- |
---|
[2528] | 770 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 771 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 772 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 773 | |
---|
[2528] | 774 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 775 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 776 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 777 | |
---|
| 778 | |
---|
| 779 | !-------------------------------------------------------------- |
---|
| 780 | ! Upper half of top-most grid box, compute and store |
---|
| 781 | !------------------------------------------------------------- |
---|
| 782 | |
---|
[13237] | 783 | !!bug gm : e3w-gde3w(:,:,:) = 0.5*e3w .... and gde3w(:,:,2)-gde3w(:,:,1)=e3w(:,:,2,Kmm) .... to be verified |
---|
| 784 | ! true if gde3w(:,:,:) is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
[455] | 785 | |
---|
[13899] | 786 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 787 | rho_k(ji,jj,1) = -grav * ( e3w(ji,jj,1,Kmm) - gde3w(ji,jj,1) ) & |
---|
| 788 | & * ( rhd(ji,jj,1) & |
---|
| 789 | & + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) & |
---|
| 790 | & * ( e3w (ji,jj,1,Kmm) - gde3w(ji,jj,1) ) & |
---|
| 791 | & / ( gde3w(ji,jj,2) - gde3w(ji,jj,1) ) ) |
---|
| 792 | END_2D |
---|
[455] | 793 | |
---|
| 794 | !!bug gm : here also, simplification is possible |
---|
| 795 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 796 | |
---|
[13899] | 797 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[455] | 798 | |
---|
[12377] | 799 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 800 | & * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) ) & |
---|
| 801 | & - grav * z1_10 * ( & |
---|
| 802 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 803 | & * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 804 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 805 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 806 | & ) |
---|
[455] | 807 | |
---|
[12377] | 808 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 809 | & * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) ) & |
---|
| 810 | & - grav* z1_10 * ( & |
---|
| 811 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 812 | & * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 813 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 814 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 815 | & ) |
---|
[455] | 816 | |
---|
[12377] | 817 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 818 | & * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) ) & |
---|
| 819 | & - grav* z1_10 * ( & |
---|
| 820 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 821 | & * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 822 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 823 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 824 | & ) |
---|
[455] | 825 | |
---|
[12377] | 826 | END_3D |
---|
[13226] | 827 | CALL lbc_lnk_multi( 'dynhpg', rho_k, 'W', 1.0_wp, rho_i, 'U', 1.0_wp, rho_j, 'V', 1.0_wp ) |
---|
[455] | 828 | |
---|
| 829 | ! --------------- |
---|
| 830 | ! Surface value |
---|
| 831 | ! --------------- |
---|
[13899] | 832 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 833 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj) |
---|
| 834 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj) |
---|
| 835 | IF( ln_wd_il ) THEN |
---|
| 836 | zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj) |
---|
| 837 | zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj) |
---|
| 838 | ENDIF |
---|
| 839 | ! add to the general momentum trend |
---|
| 840 | puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) |
---|
| 841 | pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) |
---|
| 842 | END_2D |
---|
[455] | 843 | |
---|
| 844 | ! ---------------- |
---|
| 845 | ! interior value (2=<jk=<jpkm1) |
---|
| 846 | ! ---------------- |
---|
[13899] | 847 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 848 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 849 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 850 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 851 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj) |
---|
| 852 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 853 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 854 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj) |
---|
| 855 | IF( ln_wd_il ) THEN |
---|
| 856 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj) |
---|
| 857 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj) |
---|
| 858 | ENDIF |
---|
| 859 | ! add to the general momentum trend |
---|
| 860 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) |
---|
| 861 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) |
---|
| 862 | END_3D |
---|
[503] | 863 | ! |
---|
[9023] | 864 | IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) |
---|
[2715] | 865 | ! |
---|
[455] | 866 | END SUBROUTINE hpg_djc |
---|
| 867 | |
---|
| 868 | |
---|
[12377] | 869 | SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs ) |
---|
[455] | 870 | !!--------------------------------------------------------------------- |
---|
[3294] | 871 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 872 | !! |
---|
[3294] | 873 | !! ** Method : s-coordinate case. |
---|
| 874 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 875 | !! based on the constrained cubic-spline interpolation for |
---|
| 876 | !! all vertical coordinate systems |
---|
[455] | 877 | !! |
---|
[12377] | 878 | !! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend |
---|
[455] | 879 | !!---------------------------------------------------------------------- |
---|
[3294] | 880 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
[12377] | 881 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
---|
| 882 | INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices |
---|
| 883 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation |
---|
[503] | 884 | !! |
---|
[3294] | 885 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
[6140] | 886 | REAL(wp) :: zcoef0, znad ! local scalars |
---|
| 887 | ! |
---|
[3294] | 888 | !! The local variables for the correction term |
---|
| 889 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
[6152] | 890 | LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables |
---|
[3294] | 891 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 892 | REAL(wp) :: zrhdt1 |
---|
[3294] | 893 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[9019] | 894 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh |
---|
| 895 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
| 896 | REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n |
---|
| 897 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter |
---|
[455] | 898 | !!---------------------------------------------------------------------- |
---|
[3294] | 899 | ! |
---|
[455] | 900 | IF( kt == nit000 ) THEN |
---|
| 901 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 902 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 903 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 904 | ENDIF |
---|
| 905 | |
---|
[3294] | 906 | ! Local constant initialization |
---|
[3764] | 907 | zcoef0 = - grav |
---|
[6140] | 908 | znad = 1._wp |
---|
| 909 | IF( ln_linssh ) znad = 0._wp |
---|
[3] | 910 | |
---|
[9023] | 911 | IF( ln_wd_il ) THEN |
---|
[9019] | 912 | ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) ) |
---|
[13899] | 913 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 914 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
| 915 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. & |
---|
| 916 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) & |
---|
| 917 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 918 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
| 919 | & MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > & |
---|
| 920 | & MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 921 | |
---|
[12377] | 922 | IF(ll_tmp1) THEN |
---|
| 923 | zcpx(ji,jj) = 1.0_wp |
---|
| 924 | ELSE IF(ll_tmp2) THEN |
---|
| 925 | ! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here |
---|
| 926 | zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
| 927 | & / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) ) |
---|
| 928 | |
---|
| 929 | zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp) |
---|
| 930 | ELSE |
---|
| 931 | zcpx(ji,jj) = 0._wp |
---|
| 932 | END IF |
---|
| 933 | |
---|
| 934 | ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
| 935 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. & |
---|
| 936 | & MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) & |
---|
| 937 | & > rn_wdmin1 + rn_wdmin2 |
---|
| 938 | ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( & |
---|
| 939 | & MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > & |
---|
| 940 | & MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 ) |
---|
[6152] | 941 | |
---|
[12377] | 942 | IF(ll_tmp1) THEN |
---|
| 943 | zcpy(ji,jj) = 1.0_wp |
---|
| 944 | ELSE IF(ll_tmp2) THEN |
---|
| 945 | ! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here |
---|
| 946 | zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) & |
---|
| 947 | & / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) ) |
---|
| 948 | zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp) |
---|
[9023] | 949 | |
---|
[12377] | 950 | ELSE |
---|
| 951 | zcpy(ji,jj) = 0._wp |
---|
| 952 | ENDIF |
---|
| 953 | END_2D |
---|
[13226] | 954 | CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp ) |
---|
[9019] | 955 | ENDIF |
---|
[6152] | 956 | |
---|
[3294] | 957 | ! Clean 3-D work arrays |
---|
| 958 | zhpi(:,:,:) = 0._wp |
---|
| 959 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 960 | |
---|
[3294] | 961 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
[13899] | 962 | DO_2D( 1, 1, 1, 1 ) |
---|
| 963 | jk = mbkt(ji,jj) |
---|
| 964 | IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp |
---|
| 965 | ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk) |
---|
[12377] | 966 | ELSEIF( jk < jpkm1 ) THEN |
---|
| 967 | DO jkk = jk+1, jpk |
---|
| 968 | zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), & |
---|
[13899] | 969 | & gde3w(ji,jj,jkk-2), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2)) |
---|
[12377] | 970 | END DO |
---|
| 971 | ENDIF |
---|
| 972 | END_2D |
---|
[3] | 973 | |
---|
[3632] | 974 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[13899] | 975 | DO_2D( 1, 1, 1, 1 ) |
---|
[12377] | 976 | zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm) * znad |
---|
| 977 | END_2D |
---|
[455] | 978 | |
---|
[13899] | 979 | DO_3D( 1, 1, 1, 1, 2, jpk ) |
---|
[12377] | 980 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm) |
---|
| 981 | END_3D |
---|
[455] | 982 | |
---|
[4990] | 983 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 984 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 985 | |
---|
[3764] | 986 | ! Construct the vertical density profile with the |
---|
[3294] | 987 | ! constrained cubic spline interpolation |
---|
| 988 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[6140] | 989 | CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
[3294] | 990 | |
---|
| 991 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
[13899] | 992 | DO_2D( 0, 1, 0, 1 ) |
---|
[12377] | 993 | zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), & |
---|
| 994 | & csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm) |
---|
[3294] | 995 | |
---|
[12377] | 996 | ! assuming linear profile across the top half surface layer |
---|
| 997 | zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1 |
---|
| 998 | END_2D |
---|
[455] | 999 | |
---|
[3294] | 1000 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[13899] | 1001 | DO_3D( 0, 1, 0, 1, 2, jpkm1 ) |
---|
[12377] | 1002 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
| 1003 | & integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), & |
---|
| 1004 | & asp (ji,jj,jk-1), bsp (ji,jj,jk-1), & |
---|
| 1005 | & csp (ji,jj,jk-1), dsp (ji,jj,jk-1) ) |
---|
| 1006 | END_3D |
---|
[455] | 1007 | |
---|
[3294] | 1008 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5224] | 1009 | |
---|
| 1010 | ! Prepare zsshu_n and zsshv_n |
---|
[13899] | 1011 | DO_2D( 0, 0, 0, 0 ) |
---|
[6140] | 1012 | !!gm BUG ? if it is ssh at u- & v-point then it should be: |
---|
[12377] | 1013 | ! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * & |
---|
[6140] | 1014 | ! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
[12377] | 1015 | ! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * & |
---|
[6140] | 1016 | ! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
| 1017 | !!gm not this: |
---|
[12377] | 1018 | zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * & |
---|
| 1019 | & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1020 | zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * & |
---|
| 1021 | & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
| 1022 | END_2D |
---|
[455] | 1023 | |
---|
[13226] | 1024 | CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1.0_wp, zsshv_n, 'V', 1.0_wp ) |
---|
[6152] | 1025 | |
---|
[13899] | 1026 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1027 | zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) * znad) |
---|
| 1028 | zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) * znad) |
---|
| 1029 | END_2D |
---|
[5224] | 1030 | |
---|
[13899] | 1031 | DO_3D( 0, 0, 0, 0, 2, jpkm1 ) |
---|
[12377] | 1032 | zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm) |
---|
| 1033 | zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm) |
---|
| 1034 | END_3D |
---|
[3764] | 1035 | |
---|
[13899] | 1036 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
[12377] | 1037 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm) |
---|
| 1038 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm) |
---|
| 1039 | END_3D |
---|
[455] | 1040 | |
---|
[13899] | 1041 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
[12377] | 1042 | zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
| 1043 | zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) ) |
---|
| 1044 | zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
| 1045 | zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) ) |
---|
| 1046 | END_3D |
---|
[3632] | 1047 | |
---|
| 1048 | |
---|
[13899] | 1049 | DO_3D( 0, 0, 0, 0, 1, jpkm1 ) |
---|
[12377] | 1050 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1051 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1052 | zuijk = zu(ji,jj,jk) |
---|
| 1053 | zvijk = zv(ji,jj,jk) |
---|
[3294] | 1054 | |
---|
[12377] | 1055 | !!!!! for u equation |
---|
| 1056 | IF( jk <= mbku(ji,jj) ) THEN |
---|
| 1057 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
| 1058 | jis = ji + 1; jid = ji |
---|
| 1059 | ELSE |
---|
| 1060 | jis = ji; jid = ji +1 |
---|
| 1061 | ENDIF |
---|
[3294] | 1062 | |
---|
[12377] | 1063 | ! integrate the pressure on the shallow side |
---|
| 1064 | jk1 = jk |
---|
| 1065 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
| 1066 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
| 1067 | zuijk = -zdept(jis,jj,jk1) |
---|
| 1068 | EXIT |
---|
| 1069 | ENDIF |
---|
| 1070 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
| 1071 | zpwes = zpwes + & |
---|
| 1072 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
| 1073 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1074 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1075 | jk1 = jk1 + 1 |
---|
| 1076 | END DO |
---|
[3764] | 1077 | |
---|
[12377] | 1078 | ! integrate the pressure on the deep side |
---|
| 1079 | jk1 = jk |
---|
| 1080 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
| 1081 | IF( jk1 == 1 ) THEN |
---|
| 1082 | zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad) |
---|
| 1083 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1084 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1085 | dsp(jid,jj,1)) * zdeps |
---|
| 1086 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
| 1087 | EXIT |
---|
| 1088 | ENDIF |
---|
| 1089 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
| 1090 | zpwed = zpwed + & |
---|
| 1091 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
| 1092 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1093 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1094 | jk1 = jk1 - 1 |
---|
| 1095 | END DO |
---|
[3764] | 1096 | |
---|
[12377] | 1097 | ! update the momentum trends in u direction |
---|
[3294] | 1098 | |
---|
[12377] | 1099 | zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) ) |
---|
| 1100 | IF( .NOT.ln_linssh ) THEN |
---|
| 1101 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * & |
---|
| 1102 | & ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) ) |
---|
| 1103 | ELSE |
---|
| 1104 | zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
| 1105 | ENDIF |
---|
| 1106 | IF( ln_wd_il ) THEN |
---|
| 1107 | zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj) |
---|
| 1108 | zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj) |
---|
| 1109 | ENDIF |
---|
| 1110 | puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk) |
---|
| 1111 | ENDIF |
---|
[3764] | 1112 | |
---|
[12377] | 1113 | !!!!! for v equation |
---|
| 1114 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
| 1115 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
| 1116 | jjs = jj + 1; jjd = jj |
---|
| 1117 | ELSE |
---|
| 1118 | jjs = jj ; jjd = jj + 1 |
---|
| 1119 | ENDIF |
---|
[3294] | 1120 | |
---|
[12377] | 1121 | ! integrate the pressure on the shallow side |
---|
| 1122 | jk1 = jk |
---|
| 1123 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
| 1124 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
| 1125 | zvijk = -zdept(ji,jjs,jk1) |
---|
| 1126 | EXIT |
---|
| 1127 | ENDIF |
---|
| 1128 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
| 1129 | zpnss = zpnss + & |
---|
| 1130 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
| 1131 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1132 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1133 | jk1 = jk1 + 1 |
---|
| 1134 | END DO |
---|
[3764] | 1135 | |
---|
[12377] | 1136 | ! integrate the pressure on the deep side |
---|
| 1137 | jk1 = jk |
---|
| 1138 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
| 1139 | IF( jk1 == 1 ) THEN |
---|
| 1140 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad) |
---|
| 1141 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1142 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1143 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1144 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
| 1145 | EXIT |
---|
| 1146 | ENDIF |
---|
| 1147 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
| 1148 | zpnsd = zpnsd + & |
---|
| 1149 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
| 1150 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1151 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1152 | jk1 = jk1 - 1 |
---|
| 1153 | END DO |
---|
[3294] | 1154 | |
---|
[3764] | 1155 | |
---|
[12377] | 1156 | ! update the momentum trends in v direction |
---|
[3294] | 1157 | |
---|
[12377] | 1158 | zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) ) |
---|
| 1159 | IF( .NOT.ln_linssh ) THEN |
---|
| 1160 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * & |
---|
| 1161 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) ) |
---|
| 1162 | ELSE |
---|
| 1163 | zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
| 1164 | ENDIF |
---|
| 1165 | IF( ln_wd_il ) THEN |
---|
| 1166 | zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj) |
---|
| 1167 | zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj) |
---|
| 1168 | ENDIF |
---|
[6152] | 1169 | |
---|
[12377] | 1170 | pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk) |
---|
| 1171 | ENDIF |
---|
| 1172 | ! |
---|
| 1173 | END_3D |
---|
[503] | 1174 | ! |
---|
[9023] | 1175 | IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy ) |
---|
[2715] | 1176 | ! |
---|
[3294] | 1177 | END SUBROUTINE hpg_prj |
---|
[455] | 1178 | |
---|
[4990] | 1179 | |
---|
[6140] | 1180 | SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type ) |
---|
[3294] | 1181 | !!---------------------------------------------------------------------- |
---|
| 1182 | !! *** ROUTINE cspline *** |
---|
[3764] | 1183 | !! |
---|
[3294] | 1184 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1185 | !! |
---|
| 1186 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1187 | !! |
---|
[3294] | 1188 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1189 | !!---------------------------------------------------------------------- |
---|
[6140] | 1190 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate |
---|
| 1191 | REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function |
---|
| 1192 | INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear |
---|
[4990] | 1193 | ! |
---|
[3294] | 1194 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1195 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1196 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1197 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1198 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1199 | !!---------------------------------------------------------------------- |
---|
[6140] | 1200 | ! |
---|
| 1201 | !!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!! |
---|
[3294] | 1202 | jpi = size(fsp,1) |
---|
| 1203 | jpj = size(fsp,2) |
---|
[7761] | 1204 | jpkm1 = MAX( 1, size(fsp,3) - 1 ) |
---|
[6140] | 1205 | ! |
---|
[3294] | 1206 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1207 | DO ji = 1, jpi |
---|
| 1208 | DO jj = 1, jpj |
---|
[3764] | 1209 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1210 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1211 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1212 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1213 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1214 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1215 | ! |
---|
| 1216 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1217 | ! |
---|
[3294] | 1218 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1219 | ! zdf(jk) = 0._wp |
---|
| 1220 | ! ELSE |
---|
| 1221 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1222 | ! ENDIF |
---|
| 1223 | ! END DO |
---|
[3764] | 1224 | |
---|
[3294] | 1225 | !!Simply geometric average |
---|
| 1226 | DO jk = 2, jpkm1-1 |
---|
[9019] | 1227 | zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1)) |
---|
| 1228 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk )) |
---|
[3764] | 1229 | |
---|
[3294] | 1230 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1231 | zdf(jk) = 0._wp |
---|
| 1232 | ELSE |
---|
| 1233 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1234 | ENDIF |
---|
| 1235 | END DO |
---|
[3764] | 1236 | |
---|
[3294] | 1237 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
[6140] | 1238 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
[3294] | 1239 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
[6140] | 1240 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1241 | |
---|
[3294] | 1242 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1243 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1244 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1245 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1246 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1247 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1248 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1249 | |
---|
[3294] | 1250 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1251 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1252 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1253 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1254 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1255 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1256 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1257 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1258 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1259 | END DO |
---|
| 1260 | END DO |
---|
| 1261 | END DO |
---|
[3764] | 1262 | |
---|
[6140] | 1263 | ELSEIF ( polynomial_type == 2 ) THEN ! Linear |
---|
[3294] | 1264 | DO ji = 1, jpi |
---|
| 1265 | DO jj = 1, jpj |
---|
| 1266 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1267 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1268 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1269 | |
---|
[3294] | 1270 | dsp(ji,jj,jk) = 0._wp |
---|
| 1271 | csp(ji,jj,jk) = 0._wp |
---|
| 1272 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1273 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1274 | END DO |
---|
| 1275 | END DO |
---|
| 1276 | END DO |
---|
[9019] | 1277 | ! |
---|
[3294] | 1278 | ELSE |
---|
[9019] | 1279 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
[3294] | 1280 | ENDIF |
---|
[9019] | 1281 | ! |
---|
[3294] | 1282 | END SUBROUTINE cspline |
---|
| 1283 | |
---|
| 1284 | |
---|
[3764] | 1285 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1286 | !!---------------------------------------------------------------------- |
---|
| 1287 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1288 | !! |
---|
[3294] | 1289 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1290 | !! |
---|
[4990] | 1291 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1292 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1293 | !!---------------------------------------------------------------------- |
---|
[3764] | 1294 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1295 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1296 | REAL(wp) :: zdeltx |
---|
| 1297 | !!---------------------------------------------------------------------- |
---|
[6140] | 1298 | ! |
---|
[3294] | 1299 | zdeltx = xr - xl |
---|
[6140] | 1300 | IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN |
---|
| 1301 | f = 0.5_wp * (fl + fr) |
---|
[3294] | 1302 | ELSE |
---|
[6140] | 1303 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
[3294] | 1304 | ENDIF |
---|
[6140] | 1305 | ! |
---|
[3294] | 1306 | END FUNCTION interp1 |
---|
| 1307 | |
---|
[4990] | 1308 | |
---|
[6140] | 1309 | FUNCTION interp2( x, a, b, c, d ) RESULT(f) |
---|
[3294] | 1310 | !!---------------------------------------------------------------------- |
---|
| 1311 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1312 | !! |
---|
[3294] | 1313 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1314 | !! |
---|
[3294] | 1315 | !! ** Method : cubic spline interpolation |
---|
| 1316 | !! |
---|
| 1317 | !!---------------------------------------------------------------------- |
---|
[3764] | 1318 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1319 | REAL(wp) :: f ! value from the interpolation |
---|
| 1320 | !!---------------------------------------------------------------------- |
---|
[6140] | 1321 | ! |
---|
[3764] | 1322 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[6140] | 1323 | ! |
---|
[3294] | 1324 | END FUNCTION interp2 |
---|
| 1325 | |
---|
| 1326 | |
---|
[6140] | 1327 | FUNCTION interp3( x, a, b, c, d ) RESULT(f) |
---|
[3294] | 1328 | !!---------------------------------------------------------------------- |
---|
| 1329 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1330 | !! |
---|
[9019] | 1331 | !! ** Purpose : Calculate the first order of derivative of |
---|
[3294] | 1332 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1333 | !! |
---|
[3294] | 1334 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1335 | !! |
---|
| 1336 | !!---------------------------------------------------------------------- |
---|
[3764] | 1337 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1338 | REAL(wp) :: f ! value from the interpolation |
---|
| 1339 | !!---------------------------------------------------------------------- |
---|
[6140] | 1340 | ! |
---|
[3294] | 1341 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
[6140] | 1342 | ! |
---|
[3294] | 1343 | END FUNCTION interp3 |
---|
| 1344 | |
---|
[3764] | 1345 | |
---|
[6140] | 1346 | FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f) |
---|
[3294] | 1347 | !!---------------------------------------------------------------------- |
---|
| 1348 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1349 | !! |
---|
[3294] | 1350 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1351 | !! |
---|
[3764] | 1352 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1353 | !! |
---|
[3294] | 1354 | !!---------------------------------------------------------------------- |
---|
[3764] | 1355 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1356 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1357 | REAL(wp) :: f ! integration result |
---|
| 1358 | !!---------------------------------------------------------------------- |
---|
[6140] | 1359 | ! |
---|
[3764] | 1360 | za1 = 0.5_wp * b |
---|
| 1361 | za2 = c / 3.0_wp |
---|
| 1362 | za3 = 0.25_wp * d |
---|
[6140] | 1363 | ! |
---|
[3294] | 1364 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1365 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
[6140] | 1366 | ! |
---|
[3632] | 1367 | END FUNCTION integ_spline |
---|
[3294] | 1368 | |
---|
[3] | 1369 | !!====================================================================== |
---|
| 1370 | END MODULE dynhpg |
---|