[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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[503] | 18 | !!---------------------------------------------------------------------- |
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[3] | 19 | |
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| 20 | !!---------------------------------------------------------------------- |
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[455] | 21 | !! dyn_hpg : update the momentum trend with the now horizontal |
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[3] | 22 | !! gradient of the hydrostatic pressure |
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[2528] | 23 | !! dyn_hpg_init : initialisation and control of options |
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[455] | 24 | !! hpg_zco : z-coordinate scheme |
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| 25 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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| 26 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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| 27 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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[3294] | 28 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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[3] | 29 | !!---------------------------------------------------------------------- |
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| 30 | USE oce ! ocean dynamics and tracers |
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[4990] | 31 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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[3] | 32 | USE dom_oce ! ocean space and time domain |
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| 33 | USE phycst ! physical constants |
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[4990] | 34 | USE trd_oce ! trends: ocean variables |
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| 35 | USE trddyn ! trend manager: dynamics |
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| 36 | ! |
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[2715] | 37 | USE in_out_manager ! I/O manager |
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[258] | 38 | USE prtctl ! Print control |
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[4990] | 39 | USE lbclnk ! lateral boundary condition |
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[2715] | 40 | USE lib_mpp ! MPP library |
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[4990] | 41 | USE eosbn2 ! compute density |
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[3294] | 42 | USE wrk_nemo ! Memory Allocation |
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| 43 | USE timing ! Timing |
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[3] | 44 | |
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| 45 | IMPLICIT NONE |
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| 46 | PRIVATE |
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| 47 | |
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[2528] | 48 | PUBLIC dyn_hpg ! routine called by step module |
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| 49 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 50 | |
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[4147] | 51 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 52 | LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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| 53 | LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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| 54 | LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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| 55 | LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 56 | LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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| 57 | LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag |
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[455] | 58 | |
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[3764] | 59 | INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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[455] | 60 | |
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[3] | 61 | !! * Substitutions |
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| 62 | # include "domzgr_substitute.h90" |
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| 63 | # include "vectopt_loop_substitute.h90" |
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| 64 | !!---------------------------------------------------------------------- |
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[2528] | 65 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 66 | !! $Id$ |
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| 67 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 68 | !!---------------------------------------------------------------------- |
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| 69 | CONTAINS |
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| 70 | |
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| 71 | SUBROUTINE dyn_hpg( kt ) |
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| 72 | !!--------------------------------------------------------------------- |
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| 73 | !! *** ROUTINE dyn_hpg *** |
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| 74 | !! |
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[3764] | 75 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 76 | !! using the scheme defined in the namelist |
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[3764] | 77 | !! |
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[455] | 78 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[4990] | 79 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 80 | !!---------------------------------------------------------------------- |
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| 81 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[3294] | 82 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[455] | 83 | !!---------------------------------------------------------------------- |
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[2528] | 84 | ! |
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[3294] | 85 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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[2715] | 86 | ! |
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[503] | 87 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[3294] | 88 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 89 | ztrdu(:,:,:) = ua(:,:,:) |
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| 90 | ztrdv(:,:,:) = va(:,:,:) |
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| 91 | ENDIF |
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[2528] | 92 | ! |
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[3294] | 93 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[503] | 94 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 95 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 96 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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[3294] | 97 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 98 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[455] | 99 | END SELECT |
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[2528] | 100 | ! |
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[503] | 101 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 102 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 103 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[4990] | 104 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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[3294] | 105 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 106 | ENDIF |
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[503] | 107 | ! |
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| 108 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 109 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 110 | ! |
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[3294] | 111 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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[2715] | 112 | ! |
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[455] | 113 | END SUBROUTINE dyn_hpg |
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| 114 | |
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| 115 | |
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[2528] | 116 | SUBROUTINE dyn_hpg_init |
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[455] | 117 | !!---------------------------------------------------------------------- |
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[2528] | 118 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 119 | !! |
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| 120 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 121 | !! computation and consistency control |
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| 122 | !! |
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[1601] | 123 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 124 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 125 | !!---------------------------------------------------------------------- |
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| 126 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 127 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 128 | !! |
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[3294] | 129 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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| 130 | & ln_hpg_djc, ln_hpg_prj, ln_dynhpg_imp |
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[455] | 131 | !!---------------------------------------------------------------------- |
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[2528] | 132 | ! |
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[4147] | 133 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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| 134 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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| 135 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
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| 136 | |
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| 137 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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| 138 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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| 139 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
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[4624] | 140 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 141 | ! |
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| 142 | IF(lwp) THEN ! Control print |
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[455] | 143 | WRITE(numout,*) |
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[2528] | 144 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 145 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 146 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 147 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 148 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 149 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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| 150 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 151 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[1601] | 152 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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[455] | 153 | ENDIF |
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[2528] | 154 | ! |
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[3294] | 155 | IF( ln_hpg_djc ) & |
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| 156 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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| 157 | & currently disabled (bugs under investigation). Please select & |
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| 158 | & either ln_hpg_sco or ln_hpg_prj instead') |
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[2528] | 159 | ! |
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[3294] | 160 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) & |
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| 161 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
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| 162 | & the standard jacobian formulation hpg_sco or & |
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| 163 | & the pressure jacobian formulation hpg_prj') |
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| 164 | ! |
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[503] | 165 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 166 | IF( ln_hpg_zco ) nhpg = 0 |
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| 167 | IF( ln_hpg_zps ) nhpg = 1 |
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| 168 | IF( ln_hpg_sco ) nhpg = 2 |
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[3294] | 169 | IF( ln_hpg_djc ) nhpg = 3 |
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| 170 | IF( ln_hpg_prj ) nhpg = 4 |
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[2528] | 171 | ! |
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[3294] | 172 | ! ! Consistency check |
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[3764] | 173 | ioptio = 0 |
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[455] | 174 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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| 175 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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| 176 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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| 177 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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[3294] | 178 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[2715] | 179 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[4990] | 180 | IF( (ln_hpg_zco .OR. ln_hpg_zps .OR. ln_hpg_djc .OR. ln_hpg_prj ) .AND. nn_isf .NE. 0 ) & |
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| 181 | & CALL ctl_stop( 'Only hpg_sco has been corrected to work with ice shelf cavity.' ) |
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[503] | 182 | ! |
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[2528] | 183 | END SUBROUTINE dyn_hpg_init |
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[455] | 184 | |
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| 185 | |
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| 186 | SUBROUTINE hpg_zco( kt ) |
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| 187 | !!--------------------------------------------------------------------- |
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| 188 | !! *** ROUTINE hpg_zco *** |
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| 189 | !! |
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| 190 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 191 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 192 | !! is computed by taking the vertical integral of the in-situ |
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| 193 | !! density gradient along the model level from the suface to that |
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| 194 | !! level: zhpi = grav ..... |
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| 195 | !! zhpj = grav ..... |
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[3] | 196 | !! add it to the general momentum trend (ua,va). |
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[455] | 197 | !! ua = ua - 1/e1u * zhpi |
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| 198 | !! va = va - 1/e2v * zhpj |
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[3764] | 199 | !! |
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[3] | 200 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 201 | !!---------------------------------------------------------------------- |
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| 202 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 203 | !! |
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| 204 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 205 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3764] | 206 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 207 | !!---------------------------------------------------------------------- |
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[3764] | 208 | ! |
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[3294] | 209 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 210 | ! |
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[3] | 211 | IF( kt == nit000 ) THEN |
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| 212 | IF(lwp) WRITE(numout,*) |
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[455] | 213 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 214 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 215 | ENDIF |
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| 216 | |
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[3764] | 217 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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| 218 | |
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[455] | 219 | ! Surface value |
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[3] | 220 | DO jj = 2, jpjm1 |
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| 221 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 222 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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| 223 | ! hydrostatic pressure gradient |
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| 224 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 225 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 226 | ! add to the general momentum trend |
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[455] | 227 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 228 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 229 | END DO |
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| 230 | END DO |
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[3294] | 231 | |
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[503] | 232 | ! |
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[455] | 233 | ! interior value (2=<jk=<jpkm1) |
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[3] | 234 | DO jk = 2, jpkm1 |
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[455] | 235 | DO jj = 2, jpjm1 |
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[3] | 236 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 237 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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| 238 | ! hydrostatic pressure gradient |
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| 239 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 240 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 241 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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| 242 | |
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| 243 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 244 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 245 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 246 | ! add to the general momentum trend |
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[455] | 247 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 248 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[3] | 249 | END DO |
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| 250 | END DO |
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| 251 | END DO |
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[503] | 252 | ! |
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[3294] | 253 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 254 | ! |
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[455] | 255 | END SUBROUTINE hpg_zco |
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[216] | 256 | |
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[3] | 257 | |
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[455] | 258 | SUBROUTINE hpg_zps( kt ) |
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[3] | 259 | !!--------------------------------------------------------------------- |
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[455] | 260 | !! *** ROUTINE hpg_zps *** |
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[3764] | 261 | !! |
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[455] | 262 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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[3764] | 263 | !! |
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[3] | 264 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[3764] | 265 | !!---------------------------------------------------------------------- |
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[503] | 266 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 267 | !! |
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| 268 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 269 | INTEGER :: iku, ikv ! temporary integers |
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| 270 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[3764] | 271 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 272 | !!---------------------------------------------------------------------- |
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[3294] | 273 | ! |
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| 274 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 275 | ! |
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[3] | 276 | IF( kt == nit000 ) THEN |
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| 277 | IF(lwp) WRITE(numout,*) |
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[455] | 278 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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[503] | 279 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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[3] | 280 | ENDIF |
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| 281 | |
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[3294] | 282 | |
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[503] | 283 | ! Local constant initialization |
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[2528] | 284 | zcoef0 = - grav * 0.5_wp |
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[3] | 285 | |
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[2528] | 286 | ! Surface value (also valid in partial step case) |
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[3] | 287 | DO jj = 2, jpjm1 |
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| 288 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 289 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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[3] | 290 | ! hydrostatic pressure gradient |
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[455] | 291 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 292 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 293 | ! add to the general momentum trend |
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| 294 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 295 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 296 | END DO |
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| 297 | END DO |
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| 298 | |
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[3294] | 299 | |
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[503] | 300 | ! interior value (2=<jk=<jpkm1) |
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[3] | 301 | DO jk = 2, jpkm1 |
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| 302 | DO jj = 2, jpjm1 |
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| 303 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 304 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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[3] | 305 | ! hydrostatic pressure gradient |
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| 306 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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[455] | 307 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
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| 308 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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[3] | 309 | |
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| 310 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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[455] | 311 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
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| 312 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 313 | ! add to the general momentum trend |
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| 314 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 315 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[455] | 316 | END DO |
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[3] | 317 | END DO |
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| 318 | END DO |
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| 319 | |
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[3294] | 320 | |
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[2528] | 321 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
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[3] | 322 | DO jj = 2, jpjm1 |
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| 323 | DO ji = 2, jpim1 |
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[2528] | 324 | iku = mbku(ji,jj) |
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| 325 | ikv = mbkv(ji,jj) |
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[3] | 326 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
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| 327 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
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[2528] | 328 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
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| 329 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
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| 330 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
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| 331 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
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| 332 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
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[3] | 333 | ENDIF |
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[2528] | 334 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
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| 335 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
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| 336 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
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| 337 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
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| 338 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
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[3] | 339 | ENDIF |
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| 340 | END DO |
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| 341 | END DO |
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[503] | 342 | ! |
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[3294] | 343 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 344 | ! |
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[455] | 345 | END SUBROUTINE hpg_zps |
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[216] | 346 | |
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[3] | 347 | |
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[455] | 348 | SUBROUTINE hpg_sco( kt ) |
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[3] | 349 | !!--------------------------------------------------------------------- |
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[455] | 350 | !! *** ROUTINE hpg_sco *** |
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[3] | 351 | !! |
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[455] | 352 | !! ** Method : s-coordinate case. Jacobian scheme. |
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| 353 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 354 | !! is computed by taking the vertical integral of the in-situ |
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[3] | 355 | !! density gradient along the model level from the suface to that |
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[455] | 356 | !! level. s-coordinates (ln_sco): a corrective term is added |
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| 357 | !! to the horizontal pressure gradient : |
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| 358 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
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| 359 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
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[3] | 360 | !! add it to the general momentum trend (ua,va). |
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[455] | 361 | !! ua = ua - 1/e1u * zhpi |
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| 362 | !! va = va - 1/e2v * zhpj |
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[3] | 363 | !! |
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| 364 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 365 | !!---------------------------------------------------------------------- |
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| 366 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 367 | !! |
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[4990] | 368 | INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices |
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| 369 | REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars |
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| 370 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd |
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| 371 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
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| 372 | REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj |
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[3] | 373 | !!---------------------------------------------------------------------- |
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[3294] | 374 | ! |
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[4990] | 375 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
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| 376 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
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| 377 | CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
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[3294] | 378 | ! |
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[4990] | 379 | IF( kt == nit000 ) THEN |
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[3] | 380 | IF(lwp) WRITE(numout,*) |
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[455] | 381 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
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| 382 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
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[3] | 383 | ENDIF |
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| 384 | |
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[503] | 385 | ! Local constant initialization |
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[2528] | 386 | zcoef0 = - grav * 0.5_wp |
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[592] | 387 | ! To use density and not density anomaly |
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[4990] | 388 | ! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
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| 389 | ! ELSE ; znad = 0._wp ! Fixed volume |
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| 390 | ! ENDIF |
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| 391 | znad=1._wp |
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| 392 | ! iniitialised to 0. zhpi zhpi |
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| 393 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
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[455] | 394 | |
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[4990] | 395 | !================================================================================== |
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| 396 | !=====Compute iceload and contribution of the half first wet layer ================= |
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| 397 | !=================================================================================== |
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| 398 | |
---|
| 399 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
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| 400 | ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp |
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| 401 | |
---|
| 402 | ! compute density of the water displaced by the ice shelf |
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| 403 | zrhd = rhd ! save rhd |
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| 404 | DO jk = 1, jpk |
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| 405 | zdept(:,:)=gdept_1d(jk) |
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| 406 | CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk)) |
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| 407 | END DO |
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| 408 | WHERE ( tmask(:,:,:) == 1._wp) |
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| 409 | rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd |
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| 410 | END WHERE |
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| 411 | |
---|
| 412 | ! compute rhd at the ice/oce interface (ice shelf side) |
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| 413 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
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| 414 | |
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| 415 | ! compute rhd at the ice/oce interface (ocean side) |
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| 416 | DO ji=1,jpi |
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| 417 | DO jj=1,jpj |
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| 418 | ikt=mikt(ji,jj) |
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| 419 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
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| 420 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
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| 421 | END DO |
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| 422 | END DO |
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| 423 | CALL eos(ztstop,risfdep,zrhdtop_oce) |
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| 424 | ! |
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| 425 | ! Surface value + ice shelf gradient |
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| 426 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
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| 427 | ziceload = 0._wp |
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| 428 | DO jj = 1, jpj |
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| 429 | DO ji = 1, jpi ! vector opt. |
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| 430 | ikt=mikt(ji,jj) |
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| 431 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
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| 432 | DO jk=2,ikt-1 |
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| 433 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) & |
---|
| 434 | & * (1._wp - tmask(ji,jj,jk)) |
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| 435 | END DO |
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| 436 | IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) & |
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| 437 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
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| 438 | END DO |
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| 439 | END DO |
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| 440 | riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5 |
---|
| 441 | ! compute zp from z=0 to first T wet point (correction due to zps not yet applied) |
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[455] | 442 | DO jj = 2, jpjm1 |
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[3764] | 443 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 444 | ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1) |
---|
| 445 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 446 | ! we assume ISF is in isostatic equilibrium |
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| 447 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) & |
---|
| 448 | & * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) & |
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| 449 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 450 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 451 | & + ( ziceload(ji+1,jj) - ziceload(ji,jj)) ) |
---|
| 452 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) & |
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| 453 | & * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) & |
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| 454 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
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| 455 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
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| 456 | & + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) ) |
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| 457 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
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[2528] | 458 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
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[455] | 459 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
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[2528] | 460 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
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[455] | 461 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
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| 462 | ! add to the general momentum trend |
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[4990] | 463 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
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| 464 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
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[3764] | 465 | END DO |
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| 466 | END DO |
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[4990] | 467 | !================================================================================== |
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| 468 | !===== Compute partial cell contribution for the top cell ========================= |
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| 469 | !================================================================================== |
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| 470 | DO jj = 2, jpjm1 |
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| 471 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 472 | iku = miku(ji,jj) ; |
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| 473 | zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp |
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| 474 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
---|
| 475 | ! u direction |
---|
| 476 | IF ( iku .GT. 1 ) THEN |
---|
| 477 | ! case iku |
---|
| 478 | zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu & |
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| 479 | & * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) & |
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| 480 | & + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad ) |
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| 481 | ! corrective term ( = 0 if z coordinate ) |
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| 482 | zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj) |
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| 483 | ! zhpi will be added in interior loop |
---|
| 484 | ua(ji,jj,iku) = ua(ji,jj,iku) + zuap |
---|
| 485 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 486 | IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku) |
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[3764] | 487 | |
---|
[4990] | 488 | ! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps) |
---|
| 489 | zhpiint = zcoef0 / e1u(ji,jj) & |
---|
| 490 | & * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) & |
---|
| 491 | & + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) & |
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| 492 | & - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) & |
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| 493 | & + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) ) |
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| 494 | zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint |
---|
| 495 | END IF |
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| 496 | |
---|
| 497 | ! v direction |
---|
| 498 | ikv = mikv(ji,jj) |
---|
| 499 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
---|
| 500 | IF ( ikv .GT. 1 ) THEN |
---|
| 501 | ! case ikv |
---|
| 502 | zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv & |
---|
| 503 | & * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) & |
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| 504 | & + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad ) |
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| 505 | ! corrective term ( = 0 if z coordinate ) |
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| 506 | zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj) |
---|
| 507 | ! zhpi will be added in interior loop |
---|
| 508 | va(ji,jj,ikv) = va(ji,jj,ikv) + zvap |
---|
| 509 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 510 | IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv) |
---|
| 511 | |
---|
| 512 | ! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps) |
---|
| 513 | zhpjint = zcoef0 / e2v(ji,jj) & |
---|
| 514 | & * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) & |
---|
| 515 | & + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) & |
---|
| 516 | & - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) & |
---|
| 517 | & + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) ) |
---|
| 518 | zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint |
---|
| 519 | END IF |
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| 520 | END DO |
---|
| 521 | END DO |
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| 522 | |
---|
| 523 | !================================================================================== |
---|
| 524 | !===== Compute interior value ===================================================== |
---|
| 525 | !================================================================================== |
---|
| 526 | |
---|
| 527 | DO jj = 2, jpjm1 |
---|
| 528 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 529 | iku=miku(ji,jj); ikv=mikv(ji,jj) |
---|
| 530 | DO jk = 2, jpkm1 |
---|
[455] | 531 | ! hydrostatic pressure gradient along s-surfaces |
---|
[4990] | 532 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 533 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) & |
---|
| 534 | & + zcoef0 / e1u(ji,jj) & |
---|
| 535 | & * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) & |
---|
| 536 | & + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) & |
---|
| 537 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) & |
---|
| 538 | & + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) ) |
---|
[455] | 539 | ! s-coordinate pressure gradient correction |
---|
[4990] | 540 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 541 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 542 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1) |
---|
| 543 | ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 544 | |
---|
| 545 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 546 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 547 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) & |
---|
| 548 | & + zcoef0 / e2v(ji,jj) & |
---|
| 549 | & * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) & |
---|
| 550 | & + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) & |
---|
| 551 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) & |
---|
| 552 | & + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) ) |
---|
| 553 | ! s-coordinate pressure gradient correction |
---|
| 554 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 555 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 556 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1) |
---|
[455] | 557 | ! add to the general momentum trend |
---|
[4990] | 558 | va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk) |
---|
[455] | 559 | END DO |
---|
| 560 | END DO |
---|
| 561 | END DO |
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[4990] | 562 | |
---|
| 563 | !================================================================================== |
---|
| 564 | !===== Compute bottom cell contribution (partial cell) ============================ |
---|
| 565 | !================================================================================== |
---|
| 566 | |
---|
| 567 | # if defined key_vectopt_loop |
---|
| 568 | jj = 1 |
---|
| 569 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
---|
| 570 | # else |
---|
| 571 | DO jj = 2, jpjm1 |
---|
| 572 | DO ji = 2, jpim1 |
---|
| 573 | # endif |
---|
| 574 | iku = mbku(ji,jj) |
---|
| 575 | ikv = mbkv(ji,jj) |
---|
| 576 | |
---|
| 577 | IF (iku .GT. 1) THEN |
---|
| 578 | ! remove old value (interior case) |
---|
| 579 | zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) & |
---|
| 580 | & * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj) |
---|
| 581 | ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap |
---|
| 582 | ! put new value |
---|
| 583 | ! -zpshpi to avoid double contribution of the partial step in the top layer |
---|
| 584 | zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj) |
---|
| 585 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj) |
---|
| 586 | ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap |
---|
| 587 | END IF |
---|
| 588 | ! v direction |
---|
| 589 | IF (ikv .GT. 1) THEN |
---|
| 590 | ! remove old value (interior case) |
---|
| 591 | zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) & |
---|
| 592 | & * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj) |
---|
| 593 | va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap |
---|
| 594 | ! put new value |
---|
| 595 | ! -zpshpj to avoid double contribution of the partial step in the top layer |
---|
| 596 | zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj) |
---|
| 597 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj) |
---|
| 598 | va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap |
---|
| 599 | END IF |
---|
| 600 | # if ! defined key_vectopt_loop |
---|
| 601 | END DO |
---|
| 602 | # endif |
---|
| 603 | END DO |
---|
| 604 | |
---|
| 605 | ! set back to original density value into the ice shelf cell (maybe useless because it is masked) |
---|
| 606 | rhd = zrhd |
---|
[503] | 607 | ! |
---|
[4990] | 608 | CALL wrk_dealloc( jpi,jpj,2, ztstop) |
---|
| 609 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 610 | CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 611 | ! |
---|
[455] | 612 | END SUBROUTINE hpg_sco |
---|
| 613 | |
---|
[4990] | 614 | |
---|
[455] | 615 | SUBROUTINE hpg_djc( kt ) |
---|
| 616 | !!--------------------------------------------------------------------- |
---|
| 617 | !! *** ROUTINE hpg_djc *** |
---|
| 618 | !! |
---|
| 619 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 620 | !! |
---|
[503] | 621 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 622 | !!---------------------------------------------------------------------- |
---|
[503] | 623 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 624 | !! |
---|
| 625 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 626 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 627 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 628 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3764] | 629 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3294] | 630 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 631 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 632 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 633 | !!---------------------------------------------------------------------- |
---|
[3294] | 634 | ! |
---|
[3764] | 635 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 636 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 637 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[3294] | 638 | ! |
---|
[455] | 639 | |
---|
| 640 | IF( kt == nit000 ) THEN |
---|
| 641 | IF(lwp) WRITE(numout,*) |
---|
| 642 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 643 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 644 | ENDIF |
---|
| 645 | |
---|
[503] | 646 | ! Local constant initialization |
---|
[2528] | 647 | zcoef0 = - grav * 0.5_wp |
---|
| 648 | z1_10 = 1._wp / 10._wp |
---|
| 649 | z1_12 = 1._wp / 12._wp |
---|
[455] | 650 | |
---|
| 651 | !---------------------------------------------------------------------------------------- |
---|
| 652 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 653 | !---------------------------------------------------------------------------------------- |
---|
| 654 | |
---|
| 655 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 656 | |
---|
| 657 | DO jk = 2, jpkm1 |
---|
| 658 | DO jj = 2, jpjm1 |
---|
| 659 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 660 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 661 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 662 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 663 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 664 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 665 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 666 | END DO |
---|
| 667 | END DO |
---|
| 668 | END DO |
---|
| 669 | |
---|
| 670 | !------------------------------------------------------------------------- |
---|
| 671 | ! compute harmonic averages using eq. 5.18 |
---|
| 672 | !------------------------------------------------------------------------- |
---|
| 673 | zep = 1.e-15 |
---|
| 674 | |
---|
[503] | 675 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 676 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 677 | |
---|
| 678 | DO jk = 2, jpkm1 |
---|
| 679 | DO jj = 2, jpjm1 |
---|
| 680 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 681 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 682 | |
---|
[2528] | 683 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 684 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 685 | |
---|
[2528] | 686 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 687 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 688 | |
---|
| 689 | IF( cffw > zep) THEN |
---|
[2528] | 690 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 691 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 692 | ELSE |
---|
[2528] | 693 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 694 | ENDIF |
---|
| 695 | |
---|
[2528] | 696 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 697 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 698 | |
---|
| 699 | IF( cffu > zep ) THEN |
---|
[2528] | 700 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 701 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 702 | ELSE |
---|
[2528] | 703 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 704 | ENDIF |
---|
| 705 | |
---|
| 706 | IF( cffx > zep ) THEN |
---|
[2528] | 707 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 708 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 709 | ELSE |
---|
[2528] | 710 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 711 | ENDIF |
---|
| 712 | |
---|
| 713 | IF( cffv > zep ) THEN |
---|
[2528] | 714 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 715 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 716 | ELSE |
---|
[2528] | 717 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 718 | ENDIF |
---|
| 719 | |
---|
| 720 | IF( cffy > zep ) THEN |
---|
[2528] | 721 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 722 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 723 | ELSE |
---|
[2528] | 724 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 725 | ENDIF |
---|
| 726 | |
---|
| 727 | END DO |
---|
| 728 | END DO |
---|
| 729 | END DO |
---|
| 730 | |
---|
| 731 | !---------------------------------------------------------------------------------- |
---|
| 732 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 733 | !---------------------------------------------------------------------------------- |
---|
[2528] | 734 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 735 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 736 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 737 | |
---|
[2528] | 738 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 739 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 740 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 741 | |
---|
| 742 | |
---|
| 743 | !-------------------------------------------------------------- |
---|
| 744 | ! Upper half of top-most grid box, compute and store |
---|
| 745 | !------------------------------------------------------------- |
---|
| 746 | |
---|
| 747 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 748 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 749 | |
---|
| 750 | DO jj = 2, jpjm1 |
---|
| 751 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 752 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 753 | & * ( rhd(ji,jj,1) & |
---|
| 754 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 755 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
[3764] | 756 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 757 | END DO |
---|
| 758 | END DO |
---|
| 759 | |
---|
| 760 | !!bug gm : here also, simplification is possible |
---|
| 761 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 762 | |
---|
| 763 | DO jk = 2, jpkm1 |
---|
| 764 | DO jj = 2, jpjm1 |
---|
| 765 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 766 | |
---|
| 767 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 768 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 769 | & - grav * z1_10 * ( & |
---|
| 770 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 771 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 772 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 773 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 774 | & ) |
---|
| 775 | |
---|
| 776 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 777 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 778 | & - grav* z1_10 * ( & |
---|
| 779 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 780 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 781 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 782 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 783 | & ) |
---|
| 784 | |
---|
| 785 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 786 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 787 | & - grav* z1_10 * ( & |
---|
| 788 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 789 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 790 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 791 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 792 | & ) |
---|
| 793 | |
---|
| 794 | END DO |
---|
| 795 | END DO |
---|
| 796 | END DO |
---|
| 797 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 798 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 799 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 800 | |
---|
| 801 | |
---|
| 802 | ! --------------- |
---|
| 803 | ! Surface value |
---|
| 804 | ! --------------- |
---|
| 805 | DO jj = 2, jpjm1 |
---|
| 806 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 807 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 808 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 809 | ! add to the general momentum trend |
---|
| 810 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 811 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 812 | END DO |
---|
| 813 | END DO |
---|
| 814 | |
---|
| 815 | ! ---------------- |
---|
| 816 | ! interior value (2=<jk=<jpkm1) |
---|
| 817 | ! ---------------- |
---|
| 818 | DO jk = 2, jpkm1 |
---|
[3764] | 819 | DO jj = 2, jpjm1 |
---|
[455] | 820 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 821 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 822 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 823 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 824 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 825 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 826 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 827 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 828 | ! add to the general momentum trend |
---|
| 829 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 830 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 831 | END DO |
---|
| 832 | END DO |
---|
| 833 | END DO |
---|
[503] | 834 | ! |
---|
[3764] | 835 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 836 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 837 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 838 | ! |
---|
[455] | 839 | END SUBROUTINE hpg_djc |
---|
| 840 | |
---|
| 841 | |
---|
[3294] | 842 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 843 | !!--------------------------------------------------------------------- |
---|
[3294] | 844 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 845 | !! |
---|
[3294] | 846 | !! ** Method : s-coordinate case. |
---|
| 847 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 848 | !! based on the constrained cubic-spline interpolation for |
---|
| 849 | !! all vertical coordinate systems |
---|
[455] | 850 | !! |
---|
[3294] | 851 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 852 | !!---------------------------------------------------------------------- |
---|
[3294] | 853 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 854 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 855 | !! |
---|
[3294] | 856 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 857 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 858 | !! |
---|
[3294] | 859 | !! The local variables for the correction term |
---|
| 860 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 861 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 862 | REAL(wp) :: zrhdt1 |
---|
[3294] | 863 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[3764] | 864 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
[3294] | 865 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[455] | 866 | !!---------------------------------------------------------------------- |
---|
[3294] | 867 | ! |
---|
[3764] | 868 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 869 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[3294] | 870 | ! |
---|
[455] | 871 | IF( kt == nit000 ) THEN |
---|
| 872 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 873 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 874 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 875 | ENDIF |
---|
| 876 | |
---|
[3294] | 877 | !!---------------------------------------------------------------------- |
---|
| 878 | ! Local constant initialization |
---|
[3764] | 879 | zcoef0 = - grav |
---|
[3294] | 880 | znad = 0.0_wp |
---|
| 881 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 882 | |
---|
[3294] | 883 | ! Clean 3-D work arrays |
---|
| 884 | zhpi(:,:,:) = 0._wp |
---|
| 885 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 886 | |
---|
[3294] | 887 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 888 | DO jj = 1, jpj |
---|
[3764] | 889 | DO ji = 1, jpi |
---|
[3294] | 890 | jk = mbathy(ji,jj) |
---|
| 891 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 892 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 893 | ELSE IF(jk < jpkm1) THEN |
---|
| 894 | DO jkk = jk+1, jpk |
---|
| 895 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 896 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
[3764] | 897 | END DO |
---|
[3294] | 898 | ENDIF |
---|
| 899 | END DO |
---|
| 900 | END DO |
---|
[3] | 901 | |
---|
[3632] | 902 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 903 | DO jj = 1, jpj |
---|
| 904 | DO ji = 1, jpi |
---|
| 905 | zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 906 | END DO |
---|
| 907 | END DO |
---|
[455] | 908 | |
---|
[4990] | 909 | DO jk = 2, jpk |
---|
| 910 | DO jj = 1, jpj |
---|
| 911 | DO ji = 1, jpi |
---|
| 912 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 913 | END DO |
---|
| 914 | END DO |
---|
| 915 | END DO |
---|
[455] | 916 | |
---|
[4990] | 917 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 918 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 919 | |
---|
[3764] | 920 | ! Construct the vertical density profile with the |
---|
[3294] | 921 | ! constrained cubic spline interpolation |
---|
| 922 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[3764] | 923 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
[3294] | 924 | |
---|
| 925 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 926 | DO jj = 2, jpj |
---|
[3764] | 927 | DO ji = 2, jpi |
---|
[3632] | 928 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), & |
---|
[3294] | 929 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
[3632] | 930 | dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1) |
---|
[3294] | 931 | |
---|
| 932 | ! assuming linear profile across the top half surface layer |
---|
[3764] | 933 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
[3294] | 934 | END DO |
---|
[455] | 935 | END DO |
---|
| 936 | |
---|
[3294] | 937 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 938 | DO jk = 2, jpkm1 |
---|
| 939 | DO jj = 2, jpj |
---|
[3294] | 940 | DO ji = 2, jpi |
---|
| 941 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
[3632] | 942 | integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),& |
---|
[3294] | 943 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 944 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 945 | END DO |
---|
| 946 | END DO |
---|
[455] | 947 | END DO |
---|
| 948 | |
---|
[3294] | 949 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[3764] | 950 | DO jj = 2, jpjm1 |
---|
| 951 | DO ji = 2, jpim1 |
---|
[4292] | 952 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshu_n for ztilde compilation |
---|
| 953 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshv_n for ztilde compilation |
---|
[3294] | 954 | END DO |
---|
[455] | 955 | END DO |
---|
| 956 | |
---|
[3764] | 957 | DO jk = 2, jpkm1 |
---|
| 958 | DO jj = 2, jpjm1 |
---|
| 959 | DO ji = 2, jpim1 |
---|
[3294] | 960 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 961 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 962 | END DO |
---|
| 963 | END DO |
---|
[455] | 964 | END DO |
---|
[3764] | 965 | |
---|
| 966 | DO jk = 1, jpkm1 |
---|
| 967 | DO jj = 2, jpjm1 |
---|
| 968 | DO ji = 2, jpim1 |
---|
[3294] | 969 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 970 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 971 | END DO |
---|
| 972 | END DO |
---|
| 973 | END DO |
---|
[455] | 974 | |
---|
[3632] | 975 | DO jk = 1, jpkm1 |
---|
| 976 | DO jj = 2, jpjm1 |
---|
| 977 | DO ji = 2, jpim1 |
---|
| 978 | zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 979 | zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 980 | zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 981 | zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 982 | END DO |
---|
| 983 | END DO |
---|
| 984 | END DO |
---|
| 985 | |
---|
| 986 | |
---|
[3764] | 987 | DO jk = 1, jpkm1 |
---|
| 988 | DO jj = 2, jpjm1 |
---|
| 989 | DO ji = 2, jpim1 |
---|
[3294] | 990 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 991 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 992 | zuijk = zu(ji,jj,jk) |
---|
| 993 | zvijk = zv(ji,jj,jk) |
---|
| 994 | |
---|
| 995 | !!!!! for u equation |
---|
| 996 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 997 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 998 | jis = ji + 1; jid = ji |
---|
| 999 | ELSE |
---|
| 1000 | jis = ji; jid = ji +1 |
---|
| 1001 | ENDIF |
---|
| 1002 | |
---|
| 1003 | ! integrate the pressure on the shallow side |
---|
[3764] | 1004 | jk1 = jk |
---|
[3632] | 1005 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1006 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1007 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1008 | EXIT |
---|
| 1009 | ENDIF |
---|
[3632] | 1010 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1011 | zpwes = zpwes + & |
---|
[3632] | 1012 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1013 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1014 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1015 | jk1 = jk1 + 1 |
---|
| 1016 | END DO |
---|
[3764] | 1017 | |
---|
[3294] | 1018 | ! integrate the pressure on the deep side |
---|
[3764] | 1019 | jk1 = jk |
---|
[3632] | 1020 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1021 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1022 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1023 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1024 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1025 | dsp(jid,jj,1)) * zdeps |
---|
| 1026 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1027 | EXIT |
---|
| 1028 | ENDIF |
---|
[3632] | 1029 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1030 | zpwed = zpwed + & |
---|
[3632] | 1031 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1032 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1033 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1034 | jk1 = jk1 - 1 |
---|
| 1035 | END DO |
---|
[3764] | 1036 | |
---|
[3294] | 1037 | ! update the momentum trends in u direction |
---|
| 1038 | |
---|
| 1039 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1040 | IF( lk_vvl ) THEN |
---|
[3764] | 1041 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1042 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1043 | ELSE |
---|
[3764] | 1044 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1045 | ENDIF |
---|
| 1046 | |
---|
| 1047 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 1048 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 1049 | ENDIF |
---|
[3764] | 1050 | |
---|
[3294] | 1051 | !!!!! for v equation |
---|
| 1052 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1053 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1054 | jjs = jj + 1; jjd = jj |
---|
| 1055 | ELSE |
---|
| 1056 | jjs = jj ; jjd = jj + 1 |
---|
| 1057 | ENDIF |
---|
| 1058 | |
---|
| 1059 | ! integrate the pressure on the shallow side |
---|
[3764] | 1060 | jk1 = jk |
---|
[3632] | 1061 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1062 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1063 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1064 | EXIT |
---|
| 1065 | ENDIF |
---|
[3632] | 1066 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1067 | zpnss = zpnss + & |
---|
[3632] | 1068 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1069 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1070 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1071 | jk1 = jk1 + 1 |
---|
| 1072 | END DO |
---|
[3764] | 1073 | |
---|
[3294] | 1074 | ! integrate the pressure on the deep side |
---|
[3764] | 1075 | jk1 = jk |
---|
[3632] | 1076 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1077 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1078 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1079 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1080 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1081 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1082 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1083 | EXIT |
---|
| 1084 | ENDIF |
---|
[3632] | 1085 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1086 | zpnsd = zpnsd + & |
---|
[3632] | 1087 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1088 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1089 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1090 | jk1 = jk1 - 1 |
---|
| 1091 | END DO |
---|
| 1092 | |
---|
[3764] | 1093 | |
---|
[3294] | 1094 | ! update the momentum trends in v direction |
---|
| 1095 | |
---|
| 1096 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1097 | IF( lk_vvl ) THEN |
---|
| 1098 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
[3764] | 1099 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1100 | ELSE |
---|
[3764] | 1101 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1102 | ENDIF |
---|
| 1103 | |
---|
| 1104 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 1105 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 1106 | ENDIF |
---|
| 1107 | |
---|
[3764] | 1108 | |
---|
[3294] | 1109 | END DO |
---|
| 1110 | END DO |
---|
[455] | 1111 | END DO |
---|
[503] | 1112 | ! |
---|
[3764] | 1113 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1114 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[2715] | 1115 | ! |
---|
[3294] | 1116 | END SUBROUTINE hpg_prj |
---|
[455] | 1117 | |
---|
[4990] | 1118 | |
---|
[3294] | 1119 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1120 | !!---------------------------------------------------------------------- |
---|
| 1121 | !! *** ROUTINE cspline *** |
---|
[3764] | 1122 | !! |
---|
[3294] | 1123 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1124 | !! |
---|
| 1125 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1126 | !! |
---|
[3294] | 1127 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1128 | !!---------------------------------------------------------------------- |
---|
| 1129 | IMPLICIT NONE |
---|
| 1130 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
[3764] | 1131 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
[3294] | 1132 | ! the interpoated function |
---|
[3764] | 1133 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
[3294] | 1134 | ! 2: Linear |
---|
[4990] | 1135 | ! |
---|
[3294] | 1136 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1137 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1138 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1139 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1140 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1141 | !!---------------------------------------------------------------------- |
---|
| 1142 | |
---|
| 1143 | jpi = size(fsp,1) |
---|
| 1144 | jpj = size(fsp,2) |
---|
| 1145 | jpkm1 = size(fsp,3) - 1 |
---|
| 1146 | |
---|
[3764] | 1147 | |
---|
[3294] | 1148 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1149 | DO ji = 1, jpi |
---|
| 1150 | DO jj = 1, jpj |
---|
[3764] | 1151 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1152 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1153 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1154 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1155 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1156 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1157 | ! |
---|
| 1158 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1159 | ! |
---|
[3294] | 1160 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1161 | ! zdf(jk) = 0._wp |
---|
| 1162 | ! ELSE |
---|
| 1163 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1164 | ! ENDIF |
---|
| 1165 | ! END DO |
---|
[3764] | 1166 | |
---|
[3294] | 1167 | !!Simply geometric average |
---|
| 1168 | DO jk = 2, jpkm1-1 |
---|
| 1169 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 1170 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
[3764] | 1171 | |
---|
[3294] | 1172 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1173 | zdf(jk) = 0._wp |
---|
| 1174 | ELSE |
---|
| 1175 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1176 | ENDIF |
---|
| 1177 | END DO |
---|
[3764] | 1178 | |
---|
[3294] | 1179 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1180 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1181 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1182 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1183 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1184 | |
---|
[3294] | 1185 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1186 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1187 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1188 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1189 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1190 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1191 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1192 | |
---|
[3294] | 1193 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1194 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1195 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1196 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1197 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1198 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1199 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1200 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1201 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1202 | END DO |
---|
| 1203 | END DO |
---|
| 1204 | END DO |
---|
[3764] | 1205 | |
---|
[3294] | 1206 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1207 | DO ji = 1, jpi |
---|
| 1208 | DO jj = 1, jpj |
---|
| 1209 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1210 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1211 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1212 | |
---|
[3294] | 1213 | dsp(ji,jj,jk) = 0._wp |
---|
| 1214 | csp(ji,jj,jk) = 0._wp |
---|
| 1215 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1216 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1217 | END DO |
---|
| 1218 | END DO |
---|
| 1219 | END DO |
---|
| 1220 | |
---|
| 1221 | ELSE |
---|
| 1222 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1223 | ENDIF |
---|
| 1224 | |
---|
| 1225 | END SUBROUTINE cspline |
---|
| 1226 | |
---|
| 1227 | |
---|
[3764] | 1228 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1229 | !!---------------------------------------------------------------------- |
---|
| 1230 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1231 | !! |
---|
[3294] | 1232 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1233 | !! |
---|
[4990] | 1234 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1235 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1236 | !!---------------------------------------------------------------------- |
---|
| 1237 | IMPLICIT NONE |
---|
[3764] | 1238 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1239 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1240 | REAL(wp) :: zdeltx |
---|
| 1241 | !!---------------------------------------------------------------------- |
---|
| 1242 | |
---|
| 1243 | zdeltx = xr - xl |
---|
| 1244 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1245 | f = 0.5_wp * (fl + fr) |
---|
| 1246 | ELSE |
---|
| 1247 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1248 | ENDIF |
---|
[3764] | 1249 | |
---|
[3294] | 1250 | END FUNCTION interp1 |
---|
| 1251 | |
---|
[4990] | 1252 | |
---|
[3764] | 1253 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1254 | !!---------------------------------------------------------------------- |
---|
| 1255 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1256 | !! |
---|
[3294] | 1257 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1258 | !! |
---|
[3294] | 1259 | !! ** Method : cubic spline interpolation |
---|
| 1260 | !! |
---|
| 1261 | !!---------------------------------------------------------------------- |
---|
| 1262 | IMPLICIT NONE |
---|
[3764] | 1263 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1264 | REAL(wp) :: f ! value from the interpolation |
---|
| 1265 | !!---------------------------------------------------------------------- |
---|
| 1266 | |
---|
[3764] | 1267 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[3294] | 1268 | |
---|
| 1269 | END FUNCTION interp2 |
---|
| 1270 | |
---|
| 1271 | |
---|
[3764] | 1272 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1273 | !!---------------------------------------------------------------------- |
---|
| 1274 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1275 | !! |
---|
[3294] | 1276 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1277 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1278 | !! |
---|
[3294] | 1279 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1280 | !! |
---|
| 1281 | !!---------------------------------------------------------------------- |
---|
| 1282 | IMPLICIT NONE |
---|
[3764] | 1283 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1284 | REAL(wp) :: f ! value from the interpolation |
---|
| 1285 | !!---------------------------------------------------------------------- |
---|
| 1286 | |
---|
| 1287 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1288 | |
---|
| 1289 | END FUNCTION interp3 |
---|
| 1290 | |
---|
[3764] | 1291 | |
---|
| 1292 | FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f) |
---|
[3294] | 1293 | !!---------------------------------------------------------------------- |
---|
| 1294 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1295 | !! |
---|
[3294] | 1296 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1297 | !! |
---|
[3764] | 1298 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1299 | !! |
---|
[3294] | 1300 | !!---------------------------------------------------------------------- |
---|
| 1301 | IMPLICIT NONE |
---|
[3764] | 1302 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1303 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1304 | REAL(wp) :: f ! integration result |
---|
| 1305 | !!---------------------------------------------------------------------- |
---|
| 1306 | |
---|
[3764] | 1307 | za1 = 0.5_wp * b |
---|
| 1308 | za2 = c / 3.0_wp |
---|
| 1309 | za3 = 0.25_wp * d |
---|
[3294] | 1310 | |
---|
| 1311 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1312 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1313 | |
---|
[3632] | 1314 | END FUNCTION integ_spline |
---|
[3294] | 1315 | |
---|
[3] | 1316 | !!====================================================================== |
---|
| 1317 | END MODULE dynhpg |
---|
[3632] | 1318 | |
---|