[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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| 13 | !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot |
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| 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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| 31 | USE dom_oce ! ocean space and time domain |
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| 32 | USE phycst ! physical constants |
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[216] | 33 | USE trdmod ! ocean dynamics trends |
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| 34 | USE trdmod_oce ! ocean variables trends |
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[2715] | 35 | USE in_out_manager ! I/O manager |
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[258] | 36 | USE prtctl ! Print control |
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[455] | 37 | USE lbclnk ! lateral boundary condition |
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[2715] | 38 | USE lib_mpp ! MPP library |
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[3294] | 39 | USE wrk_nemo ! Memory Allocation |
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| 40 | USE timing ! Timing |
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[3] | 41 | |
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| 42 | IMPLICIT NONE |
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| 43 | PRIVATE |
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| 44 | |
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[2528] | 45 | PUBLIC dyn_hpg ! routine called by step module |
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| 46 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 47 | |
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[1601] | 48 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 49 | LOGICAL , PUBLIC :: ln_hpg_zco = .TRUE. !: z-coordinate - full steps |
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| 50 | LOGICAL , PUBLIC :: ln_hpg_zps = .FALSE. !: z-coordinate - partial steps (interpolation) |
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| 51 | LOGICAL , PUBLIC :: ln_hpg_sco = .FALSE. !: s-coordinate (standard jacobian formulation) |
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| 52 | LOGICAL , PUBLIC :: ln_hpg_djc = .FALSE. !: s-coordinate (Density Jacobian with Cubic polynomial) |
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[3294] | 53 | LOGICAL , PUBLIC :: ln_hpg_prj = .FALSE. !: s-coordinate (Pressure Jacobian scheme) |
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[1601] | 54 | LOGICAL , PUBLIC :: ln_dynhpg_imp = .FALSE. !: semi-implicite hpg flag |
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[455] | 55 | |
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[3294] | 56 | INTEGER :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) |
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[455] | 57 | |
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[3] | 58 | !! * Substitutions |
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| 59 | # include "domzgr_substitute.h90" |
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| 60 | # include "vectopt_loop_substitute.h90" |
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| 61 | !!---------------------------------------------------------------------- |
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[2528] | 62 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 63 | !! $Id$ |
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| 64 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 65 | !!---------------------------------------------------------------------- |
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| 66 | CONTAINS |
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| 67 | |
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| 68 | SUBROUTINE dyn_hpg( kt ) |
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| 69 | !!--------------------------------------------------------------------- |
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| 70 | !! *** ROUTINE dyn_hpg *** |
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| 71 | !! |
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[455] | 72 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 73 | !! using the scheme defined in the namelist |
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[455] | 74 | !! |
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| 75 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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| 76 | !! - Save the trend (l_trddyn=T) |
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[503] | 77 | !!---------------------------------------------------------------------- |
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| 78 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[3294] | 79 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[455] | 80 | !!---------------------------------------------------------------------- |
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[2528] | 81 | ! |
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[3294] | 82 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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[2715] | 83 | ! |
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[503] | 84 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[3294] | 85 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[455] | 86 | ztrdu(:,:,:) = ua(:,:,:) |
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| 87 | ztrdv(:,:,:) = va(:,:,:) |
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| 88 | ENDIF |
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[2528] | 89 | ! |
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[3294] | 90 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[503] | 91 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 92 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 93 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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[3294] | 94 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 95 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[455] | 96 | END SELECT |
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[2528] | 97 | ! |
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[503] | 98 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 99 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 100 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[503] | 101 | CALL trd_mod( ztrdu, ztrdv, jpdyn_trd_hpg, 'DYN', kt ) |
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[3294] | 102 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[455] | 103 | ENDIF |
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[503] | 104 | ! |
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| 105 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 106 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 107 | ! |
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[3294] | 108 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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[2715] | 109 | ! |
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[455] | 110 | END SUBROUTINE dyn_hpg |
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| 111 | |
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| 112 | |
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[2528] | 113 | SUBROUTINE dyn_hpg_init |
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[455] | 114 | !!---------------------------------------------------------------------- |
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[2528] | 115 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 116 | !! |
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| 117 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 118 | !! computation and consistency control |
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| 119 | !! |
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[1601] | 120 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 121 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 122 | !!---------------------------------------------------------------------- |
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| 123 | INTEGER :: ioptio = 0 ! temporary integer |
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[1601] | 124 | !! |
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[3294] | 125 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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| 126 | & ln_hpg_djc, ln_hpg_prj, ln_dynhpg_imp |
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[455] | 127 | !!---------------------------------------------------------------------- |
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[2528] | 128 | ! |
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| 129 | REWIND( numnam ) ! Read Namelist namdyn_hpg |
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| 130 | READ ( numnam, namdyn_hpg ) |
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| 131 | ! |
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| 132 | IF(lwp) THEN ! Control print |
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[455] | 133 | WRITE(numout,*) |
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[2528] | 134 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 135 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 136 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 137 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 138 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 139 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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| 140 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 141 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[1601] | 142 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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[455] | 143 | ENDIF |
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[2528] | 144 | ! |
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[3294] | 145 | IF( ln_hpg_djc ) & |
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| 146 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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| 147 | & currently disabled (bugs under investigation). Please select & |
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| 148 | & either ln_hpg_sco or ln_hpg_prj instead') |
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[2528] | 149 | ! |
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[3294] | 150 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) & |
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| 151 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
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| 152 | & the standard jacobian formulation hpg_sco or & |
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| 153 | & the pressure jacobian formulation hpg_prj') |
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| 154 | ! |
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[503] | 155 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 156 | IF( ln_hpg_zco ) nhpg = 0 |
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| 157 | IF( ln_hpg_zps ) nhpg = 1 |
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| 158 | IF( ln_hpg_sco ) nhpg = 2 |
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[3294] | 159 | IF( ln_hpg_djc ) nhpg = 3 |
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| 160 | IF( ln_hpg_prj ) nhpg = 4 |
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[2528] | 161 | ! |
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[3294] | 162 | ! ! Consistency check |
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[455] | 163 | ioptio = 0 |
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| 164 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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| 165 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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| 166 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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| 167 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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[3294] | 168 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[2715] | 169 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[503] | 170 | ! |
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[2528] | 171 | END SUBROUTINE dyn_hpg_init |
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[455] | 172 | |
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| 173 | |
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| 174 | SUBROUTINE hpg_zco( kt ) |
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| 175 | !!--------------------------------------------------------------------- |
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| 176 | !! *** ROUTINE hpg_zco *** |
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| 177 | !! |
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| 178 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 179 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 180 | !! is computed by taking the vertical integral of the in-situ |
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| 181 | !! density gradient along the model level from the suface to that |
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| 182 | !! level: zhpi = grav ..... |
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| 183 | !! zhpj = grav ..... |
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[3] | 184 | !! add it to the general momentum trend (ua,va). |
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[455] | 185 | !! ua = ua - 1/e1u * zhpi |
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| 186 | !! va = va - 1/e2v * zhpj |
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| 187 | !! |
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[3] | 188 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 189 | !!---------------------------------------------------------------------- |
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| 190 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 191 | !! |
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| 192 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 193 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3294] | 194 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 195 | !!---------------------------------------------------------------------- |
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[3294] | 196 | ! |
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| 197 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 198 | ! |
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[3] | 199 | IF( kt == nit000 ) THEN |
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| 200 | IF(lwp) WRITE(numout,*) |
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[455] | 201 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 202 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 203 | ENDIF |
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[455] | 204 | |
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[2715] | 205 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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[3] | 206 | |
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[455] | 207 | ! Surface value |
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[3] | 208 | DO jj = 2, jpjm1 |
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| 209 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 210 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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| 211 | ! hydrostatic pressure gradient |
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| 212 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 213 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 214 | ! add to the general momentum trend |
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[455] | 215 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 216 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 217 | END DO |
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| 218 | END DO |
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[3294] | 219 | |
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[503] | 220 | ! |
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[455] | 221 | ! interior value (2=<jk=<jpkm1) |
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[3] | 222 | DO jk = 2, jpkm1 |
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[455] | 223 | DO jj = 2, jpjm1 |
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[3] | 224 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 225 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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| 226 | ! hydrostatic pressure gradient |
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| 227 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 228 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 229 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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| 230 | |
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| 231 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 232 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 233 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 234 | ! add to the general momentum trend |
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[455] | 235 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 236 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[3] | 237 | END DO |
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| 238 | END DO |
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| 239 | END DO |
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[503] | 240 | ! |
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[3294] | 241 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 242 | ! |
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[455] | 243 | END SUBROUTINE hpg_zco |
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[216] | 244 | |
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[3] | 245 | |
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[455] | 246 | SUBROUTINE hpg_zps( kt ) |
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[3] | 247 | !!--------------------------------------------------------------------- |
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[455] | 248 | !! *** ROUTINE hpg_zps *** |
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[3] | 249 | !! |
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[455] | 250 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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| 251 | !! |
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[3] | 252 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[455] | 253 | !!---------------------------------------------------------------------- |
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[503] | 254 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 255 | !! |
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| 256 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 257 | INTEGER :: iku, ikv ! temporary integers |
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| 258 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[3294] | 259 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 260 | !!---------------------------------------------------------------------- |
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[3294] | 261 | ! |
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| 262 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 263 | ! |
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[3] | 264 | IF( kt == nit000 ) THEN |
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| 265 | IF(lwp) WRITE(numout,*) |
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[455] | 266 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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[503] | 267 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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[3] | 268 | ENDIF |
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| 269 | |
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[3294] | 270 | |
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[503] | 271 | ! Local constant initialization |
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[2528] | 272 | zcoef0 = - grav * 0.5_wp |
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[3] | 273 | |
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[2528] | 274 | ! Surface value (also valid in partial step case) |
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[3] | 275 | DO jj = 2, jpjm1 |
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| 276 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 277 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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[3] | 278 | ! hydrostatic pressure gradient |
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[455] | 279 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 280 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 281 | ! add to the general momentum trend |
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| 282 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 283 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 284 | END DO |
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| 285 | END DO |
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| 286 | |
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[3294] | 287 | |
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[503] | 288 | ! interior value (2=<jk=<jpkm1) |
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[3] | 289 | DO jk = 2, jpkm1 |
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| 290 | DO jj = 2, jpjm1 |
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| 291 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 292 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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[3] | 293 | ! hydrostatic pressure gradient |
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| 294 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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[455] | 295 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
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| 296 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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[3] | 297 | |
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| 298 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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[455] | 299 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
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| 300 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 301 | ! add to the general momentum trend |
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| 302 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 303 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[455] | 304 | END DO |
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[3] | 305 | END DO |
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| 306 | END DO |
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| 307 | |
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[3294] | 308 | |
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[2528] | 309 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
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[3] | 310 | # if defined key_vectopt_loop |
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| 311 | jj = 1 |
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| 312 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
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| 313 | # else |
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| 314 | DO jj = 2, jpjm1 |
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| 315 | DO ji = 2, jpim1 |
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| 316 | # endif |
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[2528] | 317 | iku = mbku(ji,jj) |
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| 318 | ikv = mbkv(ji,jj) |
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[3] | 319 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
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| 320 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
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[2528] | 321 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
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| 322 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
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| 323 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
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| 324 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
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| 325 | 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] | 326 | ENDIF |
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[2528] | 327 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
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| 328 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
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| 329 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
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| 330 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
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| 331 | 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] | 332 | ENDIF |
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| 333 | # if ! defined key_vectopt_loop |
---|
| 334 | END DO |
---|
| 335 | # endif |
---|
| 336 | END DO |
---|
[503] | 337 | ! |
---|
[3294] | 338 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 339 | ! |
---|
[455] | 340 | END SUBROUTINE hpg_zps |
---|
[216] | 341 | |
---|
[3] | 342 | |
---|
[455] | 343 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 344 | !!--------------------------------------------------------------------- |
---|
[455] | 345 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 346 | !! |
---|
[455] | 347 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 348 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 349 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 350 | !! density gradient along the model level from the suface to that |
---|
[455] | 351 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 352 | !! to the horizontal pressure gradient : |
---|
| 353 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 354 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[3] | 355 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 356 | !! ua = ua - 1/e1u * zhpi |
---|
| 357 | !! va = va - 1/e2v * zhpj |
---|
[3] | 358 | !! |
---|
| 359 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 360 | !!---------------------------------------------------------------------- |
---|
| 361 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 362 | !! |
---|
[592] | 363 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 364 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
[3294] | 365 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3] | 366 | !!---------------------------------------------------------------------- |
---|
[3294] | 367 | ! |
---|
| 368 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 369 | ! |
---|
[3] | 370 | IF( kt == nit000 ) THEN |
---|
| 371 | IF(lwp) WRITE(numout,*) |
---|
[455] | 372 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 373 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
[3] | 374 | ENDIF |
---|
| 375 | |
---|
[503] | 376 | ! Local constant initialization |
---|
[2528] | 377 | zcoef0 = - grav * 0.5_wp |
---|
[592] | 378 | ! To use density and not density anomaly |
---|
[2528] | 379 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 380 | ELSE ; znad = 0._wp ! Fixed volume |
---|
[592] | 381 | ENDIF |
---|
[455] | 382 | |
---|
[503] | 383 | ! Surface value |
---|
[455] | 384 | DO jj = 2, jpjm1 |
---|
| 385 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 386 | ! hydrostatic pressure gradient along s-surfaces |
---|
[592] | 387 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 388 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 389 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 390 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
[455] | 391 | ! s-coordinate pressure gradient correction |
---|
[2528] | 392 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 393 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 394 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 395 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 396 | ! add to the general momentum trend |
---|
| 397 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 398 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 399 | END DO |
---|
| 400 | END DO |
---|
| 401 | |
---|
[503] | 402 | ! interior value (2=<jk=<jpkm1) |
---|
[455] | 403 | DO jk = 2, jpkm1 |
---|
| 404 | DO jj = 2, jpjm1 |
---|
| 405 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 406 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 407 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
[592] | 408 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 409 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
[455] | 410 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
[592] | 411 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 412 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
[455] | 413 | ! s-coordinate pressure gradient correction |
---|
[2528] | 414 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
[455] | 415 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
[2528] | 416 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
[455] | 417 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 418 | ! add to the general momentum trend |
---|
| 419 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 420 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 421 | END DO |
---|
| 422 | END DO |
---|
| 423 | END DO |
---|
[503] | 424 | ! |
---|
[3294] | 425 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 426 | ! |
---|
[455] | 427 | END SUBROUTINE hpg_sco |
---|
| 428 | |
---|
| 429 | SUBROUTINE hpg_djc( kt ) |
---|
| 430 | !!--------------------------------------------------------------------- |
---|
| 431 | !! *** ROUTINE hpg_djc *** |
---|
| 432 | !! |
---|
| 433 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
| 434 | !! |
---|
[503] | 435 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 436 | !!---------------------------------------------------------------------- |
---|
[503] | 437 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 438 | !! |
---|
| 439 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 440 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 441 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 442 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3294] | 443 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
| 444 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 445 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 446 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 447 | !!---------------------------------------------------------------------- |
---|
[3294] | 448 | ! |
---|
| 449 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 450 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 451 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
| 452 | ! |
---|
[455] | 453 | |
---|
| 454 | IF( kt == nit000 ) THEN |
---|
| 455 | IF(lwp) WRITE(numout,*) |
---|
| 456 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 457 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 458 | ENDIF |
---|
| 459 | |
---|
[503] | 460 | ! Local constant initialization |
---|
[2528] | 461 | zcoef0 = - grav * 0.5_wp |
---|
| 462 | z1_10 = 1._wp / 10._wp |
---|
| 463 | z1_12 = 1._wp / 12._wp |
---|
[455] | 464 | |
---|
| 465 | !---------------------------------------------------------------------------------------- |
---|
| 466 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 467 | !---------------------------------------------------------------------------------------- |
---|
| 468 | |
---|
| 469 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 470 | |
---|
| 471 | DO jk = 2, jpkm1 |
---|
| 472 | DO jj = 2, jpjm1 |
---|
| 473 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 474 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 475 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 476 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 477 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 478 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 479 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 480 | END DO |
---|
| 481 | END DO |
---|
| 482 | END DO |
---|
| 483 | |
---|
| 484 | !------------------------------------------------------------------------- |
---|
| 485 | ! compute harmonic averages using eq. 5.18 |
---|
| 486 | !------------------------------------------------------------------------- |
---|
| 487 | zep = 1.e-15 |
---|
| 488 | |
---|
[503] | 489 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 490 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 491 | |
---|
| 492 | DO jk = 2, jpkm1 |
---|
| 493 | DO jj = 2, jpjm1 |
---|
| 494 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 495 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 496 | |
---|
[2528] | 497 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 498 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[455] | 499 | |
---|
[2528] | 500 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 501 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 502 | |
---|
| 503 | IF( cffw > zep) THEN |
---|
[2528] | 504 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 505 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 506 | ELSE |
---|
[2528] | 507 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 508 | ENDIF |
---|
| 509 | |
---|
[2528] | 510 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 511 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 512 | |
---|
| 513 | IF( cffu > zep ) THEN |
---|
[2528] | 514 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 515 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 516 | ELSE |
---|
[2528] | 517 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 518 | ENDIF |
---|
| 519 | |
---|
| 520 | IF( cffx > zep ) THEN |
---|
[2528] | 521 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 522 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 523 | ELSE |
---|
[2528] | 524 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 525 | ENDIF |
---|
| 526 | |
---|
| 527 | IF( cffv > zep ) THEN |
---|
[2528] | 528 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 529 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 530 | ELSE |
---|
[2528] | 531 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 532 | ENDIF |
---|
| 533 | |
---|
| 534 | IF( cffy > zep ) THEN |
---|
[2528] | 535 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 536 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 537 | ELSE |
---|
[2528] | 538 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 539 | ENDIF |
---|
| 540 | |
---|
| 541 | END DO |
---|
| 542 | END DO |
---|
| 543 | END DO |
---|
| 544 | |
---|
| 545 | !---------------------------------------------------------------------------------- |
---|
| 546 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 547 | !---------------------------------------------------------------------------------- |
---|
[2528] | 548 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 549 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 550 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 551 | |
---|
[2528] | 552 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 553 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 554 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 555 | |
---|
| 556 | |
---|
| 557 | !-------------------------------------------------------------- |
---|
| 558 | ! Upper half of top-most grid box, compute and store |
---|
| 559 | !------------------------------------------------------------- |
---|
| 560 | |
---|
| 561 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 562 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 563 | |
---|
| 564 | DO jj = 2, jpjm1 |
---|
| 565 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 566 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 567 | & * ( rhd(ji,jj,1) & |
---|
| 568 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 569 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 570 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 571 | END DO |
---|
| 572 | END DO |
---|
| 573 | |
---|
| 574 | !!bug gm : here also, simplification is possible |
---|
| 575 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 576 | |
---|
| 577 | DO jk = 2, jpkm1 |
---|
| 578 | DO jj = 2, jpjm1 |
---|
| 579 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 580 | |
---|
| 581 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 582 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 583 | & - grav * z1_10 * ( & |
---|
| 584 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 585 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 586 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 587 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 588 | & ) |
---|
| 589 | |
---|
| 590 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 591 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 592 | & - grav* z1_10 * ( & |
---|
| 593 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 594 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 595 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 596 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 597 | & ) |
---|
| 598 | |
---|
| 599 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 600 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 601 | & - grav* z1_10 * ( & |
---|
| 602 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 603 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 604 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 605 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 606 | & ) |
---|
| 607 | |
---|
| 608 | END DO |
---|
| 609 | END DO |
---|
| 610 | END DO |
---|
| 611 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 612 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 613 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 614 | |
---|
| 615 | |
---|
| 616 | ! --------------- |
---|
| 617 | ! Surface value |
---|
| 618 | ! --------------- |
---|
| 619 | DO jj = 2, jpjm1 |
---|
| 620 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 621 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 622 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 623 | ! add to the general momentum trend |
---|
| 624 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 625 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 626 | END DO |
---|
| 627 | END DO |
---|
| 628 | |
---|
| 629 | ! ---------------- |
---|
| 630 | ! interior value (2=<jk=<jpkm1) |
---|
| 631 | ! ---------------- |
---|
| 632 | DO jk = 2, jpkm1 |
---|
| 633 | DO jj = 2, jpjm1 |
---|
| 634 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 635 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 636 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 637 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 638 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 639 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 640 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 641 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 642 | ! add to the general momentum trend |
---|
| 643 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 644 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 645 | END DO |
---|
| 646 | END DO |
---|
| 647 | END DO |
---|
[503] | 648 | ! |
---|
[3294] | 649 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 650 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 651 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 652 | ! |
---|
[455] | 653 | END SUBROUTINE hpg_djc |
---|
| 654 | |
---|
| 655 | |
---|
[3294] | 656 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 657 | !!--------------------------------------------------------------------- |
---|
[3294] | 658 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 659 | !! |
---|
[3294] | 660 | !! ** Method : s-coordinate case. |
---|
| 661 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 662 | !! based on the constrained cubic-spline interpolation for |
---|
| 663 | !! all vertical coordinate systems |
---|
[455] | 664 | !! |
---|
[3294] | 665 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 666 | !! - Save the trend (l_trddyn=T) |
---|
| 667 | !! |
---|
[455] | 668 | !!---------------------------------------------------------------------- |
---|
[3294] | 669 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 670 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 671 | !! |
---|
[3294] | 672 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 673 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 674 | !! |
---|
[3294] | 675 | !! The local variables for the correction term |
---|
| 676 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 677 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
| 678 | REAL(wp) :: zrhdt1 |
---|
| 679 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
| 680 | INTEGER :: zbhitwe, zbhitns |
---|
| 681 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdeptht, zrhh |
---|
| 682 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[455] | 683 | !!---------------------------------------------------------------------- |
---|
[3294] | 684 | ! |
---|
| 685 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 686 | CALL wrk_alloc( jpi,jpj,jpk, zdeptht, zrhh ) |
---|
| 687 | ! |
---|
[455] | 688 | IF( kt == nit000 ) THEN |
---|
| 689 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 690 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 691 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 692 | ENDIF |
---|
| 693 | |
---|
[3294] | 694 | !!---------------------------------------------------------------------- |
---|
| 695 | ! Local constant initialization |
---|
| 696 | zcoef0 = - grav |
---|
| 697 | znad = 0.0_wp |
---|
| 698 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 699 | |
---|
[3294] | 700 | ! Clean 3-D work arrays |
---|
| 701 | zhpi(:,:,:) = 0._wp |
---|
| 702 | zrhh(:,:,:) = rhd(:,:,:) |
---|
| 703 | |
---|
| 704 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 705 | DO jj = 1, jpj |
---|
| 706 | DO ji = 1, jpi |
---|
| 707 | jk = mbathy(ji,jj) |
---|
| 708 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 709 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 710 | ELSE IF(jk < jpkm1) THEN |
---|
| 711 | DO jkk = jk+1, jpk |
---|
| 712 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 713 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
| 714 | END DO |
---|
| 715 | ENDIF |
---|
| 716 | END DO |
---|
| 717 | END DO |
---|
[3] | 718 | |
---|
[3294] | 719 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdeptht(:,:,:)" |
---|
| 720 | DO jj = 1, jpj |
---|
| 721 | DO ji = 1, jpi |
---|
| 722 | zdeptht(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) |
---|
| 723 | zdeptht(ji,jj,1) = zdeptht(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 724 | DO jk = 2, jpk |
---|
| 725 | zdeptht(ji,jj,jk) = zdeptht(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 726 | END DO |
---|
| 727 | END DO |
---|
| 728 | END DO |
---|
[455] | 729 | |
---|
[3294] | 730 | DO jk = 1, jpkm1 |
---|
| 731 | DO jj = 1, jpj |
---|
| 732 | DO ji = 1, jpi |
---|
| 733 | fsp(ji,jj,jk) = zrhh(ji,jj,jk) |
---|
| 734 | xsp(ji,jj,jk) = zdeptht(ji,jj,jk) |
---|
| 735 | END DO |
---|
| 736 | END DO |
---|
[455] | 737 | END DO |
---|
| 738 | |
---|
[3294] | 739 | ! Construct the vertical density profile with the |
---|
| 740 | ! constrained cubic spline interpolation |
---|
| 741 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
| 742 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
| 743 | |
---|
| 744 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 745 | DO jj = 2, jpj |
---|
| 746 | DO ji = 2, jpi |
---|
| 747 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdeptht(ji,jj,1),asp(ji,jj,1), & |
---|
| 748 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
| 749 | dsp(ji,jj,1) ) * 0.5_wp * zdeptht(ji,jj,1) |
---|
| 750 | zrhdt1 = MAX(zrhdt1, 1000._wp - rau0) ! no lighter than fresh water |
---|
| 751 | |
---|
| 752 | ! assuming linear profile across the top half surface layer |
---|
| 753 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
| 754 | END DO |
---|
[455] | 755 | END DO |
---|
| 756 | |
---|
[3294] | 757 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
| 758 | DO jk = 2, jpkm1 |
---|
| 759 | DO jj = 2, jpj |
---|
| 760 | DO ji = 2, jpi |
---|
| 761 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
| 762 | integ2(zdeptht(ji,jj,jk-1), zdeptht(ji,jj,jk),& |
---|
| 763 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 764 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 765 | END DO |
---|
| 766 | END DO |
---|
[455] | 767 | END DO |
---|
| 768 | |
---|
[3294] | 769 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
| 770 | DO jj = 2, jpjm1 |
---|
| 771 | DO ji = 2, jpim1 |
---|
| 772 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshu_n(ji,jj) * znad) |
---|
| 773 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshv_n(ji,jj) * znad) |
---|
| 774 | END DO |
---|
[455] | 775 | END DO |
---|
| 776 | |
---|
[3294] | 777 | DO jk = 2, jpkm1 |
---|
| 778 | DO jj = 2, jpjm1 |
---|
| 779 | DO ji = 2, jpim1 |
---|
| 780 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 781 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 782 | END DO |
---|
| 783 | END DO |
---|
[455] | 784 | END DO |
---|
[3294] | 785 | |
---|
| 786 | DO jk = 1, jpkm1 |
---|
| 787 | DO jj = 2, jpjm1 |
---|
| 788 | DO ji = 2, jpim1 |
---|
| 789 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 790 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 791 | END DO |
---|
| 792 | END DO |
---|
| 793 | END DO |
---|
[455] | 794 | |
---|
[3294] | 795 | DO jk = 1, jpkm1 |
---|
| 796 | DO jj = 2, jpjm1 |
---|
| 797 | DO ji = 2, jpim1 |
---|
| 798 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 799 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 800 | zuijk = zu(ji,jj,jk) |
---|
| 801 | zvijk = zv(ji,jj,jk) |
---|
| 802 | |
---|
| 803 | !!!!! for u equation |
---|
| 804 | IF( jk <= mbku(ji,jj) ) THEN |
---|
| 805 | IF( -zdeptht(ji+1,jj,mbku(ji,jj)) >= -zdeptht(ji,jj,mbku(ji,jj)) ) THEN |
---|
| 806 | jis = ji + 1; jid = ji |
---|
| 807 | ELSE |
---|
| 808 | jis = ji; jid = ji +1 |
---|
| 809 | ENDIF |
---|
| 810 | |
---|
| 811 | ! integrate the pressure on the shallow side |
---|
| 812 | jk1 = jk |
---|
| 813 | zbhitwe = 0 |
---|
| 814 | DO WHILE ( -zdeptht(jis,jj,jk1) > zuijk ) |
---|
| 815 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
| 816 | zbhitwe = 1 |
---|
| 817 | EXIT |
---|
| 818 | ENDIF |
---|
| 819 | zdeps = MIN(zdeptht(jis,jj,jk1+1), -zuijk) |
---|
| 820 | zpwes = zpwes + & |
---|
| 821 | integ2(zdeptht(jis,jj,jk1), zdeps, & |
---|
| 822 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 823 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 824 | jk1 = jk1 + 1 |
---|
| 825 | END DO |
---|
| 826 | |
---|
| 827 | IF(zbhitwe == 1) THEN |
---|
| 828 | zuijk = -zdeptht(jis,jj,jk1) |
---|
| 829 | ENDIF |
---|
| 830 | |
---|
| 831 | ! integrate the pressure on the deep side |
---|
| 832 | jk1 = jk |
---|
| 833 | zbhitwe = 0 |
---|
| 834 | DO WHILE ( -zdeptht(jid,jj,jk1) < zuijk ) |
---|
| 835 | IF( jk1 == 1 ) THEN |
---|
| 836 | zbhitwe = 1 |
---|
| 837 | EXIT |
---|
| 838 | ENDIF |
---|
| 839 | zdeps = MAX(zdeptht(jid,jj,jk1-1), -zuijk) |
---|
| 840 | zpwed = zpwed + & |
---|
| 841 | integ2(zdeps, zdeptht(jid,jj,jk1), & |
---|
| 842 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 843 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 844 | jk1 = jk1 - 1 |
---|
| 845 | END DO |
---|
| 846 | |
---|
| 847 | IF( zbhitwe == 1 ) THEN |
---|
| 848 | zdeps = zdeptht(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 849 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdeptht(jid,jj,1), asp(jid,jj,1), & |
---|
| 850 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 851 | dsp(jid,jj,1)) * zdeps |
---|
| 852 | zrhdt1 = MAX(zrhdt1, 1000._wp - rau0) ! no lighter than fresh water |
---|
| 853 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
| 854 | ENDIF |
---|
| 855 | |
---|
| 856 | ! update the momentum trends in u direction |
---|
| 857 | |
---|
| 858 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 859 | IF( lk_vvl ) THEN |
---|
| 860 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 861 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
| 862 | ELSE |
---|
| 863 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
| 864 | ENDIF |
---|
| 865 | |
---|
| 866 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 867 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 868 | ENDIF |
---|
| 869 | |
---|
| 870 | !!!!! for v equation |
---|
| 871 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
| 872 | IF( -zdeptht(ji,jj+1,mbkv(ji,jj)) >= -zdeptht(ji,jj,mbkv(ji,jj)) ) THEN |
---|
| 873 | jjs = jj + 1; jjd = jj |
---|
| 874 | ELSE |
---|
| 875 | jjs = jj ; jjd = jj + 1 |
---|
| 876 | ENDIF |
---|
| 877 | |
---|
| 878 | ! integrate the pressure on the shallow side |
---|
| 879 | jk1 = jk |
---|
| 880 | zbhitns = 0 |
---|
| 881 | DO WHILE ( -zdeptht(ji,jjs,jk1) > zvijk ) |
---|
| 882 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
| 883 | zbhitns = 1 |
---|
| 884 | EXIT |
---|
| 885 | ENDIF |
---|
| 886 | zdeps = MIN(zdeptht(ji,jjs,jk1+1), -zvijk) |
---|
| 887 | zpnss = zpnss + & |
---|
| 888 | integ2(zdeptht(ji,jjs,jk1), zdeps, & |
---|
| 889 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 890 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 891 | jk1 = jk1 + 1 |
---|
| 892 | END DO |
---|
| 893 | |
---|
| 894 | IF(zbhitns == 1) THEN |
---|
| 895 | zvijk = -zdeptht(ji,jjs,jk1) |
---|
| 896 | ENDIF |
---|
| 897 | |
---|
| 898 | ! integrate the pressure on the deep side |
---|
| 899 | jk1 = jk |
---|
| 900 | zbhitns = 0 |
---|
| 901 | DO WHILE ( -zdeptht(ji,jjd,jk1) < zvijk ) |
---|
| 902 | IF( jk1 == 1 ) THEN |
---|
| 903 | zbhitns = 1 |
---|
| 904 | EXIT |
---|
| 905 | ENDIF |
---|
| 906 | zdeps = MAX(zdeptht(ji,jjd,jk1-1), -zvijk) |
---|
| 907 | zpnsd = zpnsd + & |
---|
| 908 | integ2(zdeps, zdeptht(ji,jjd,jk1), & |
---|
| 909 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 910 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 911 | jk1 = jk1 - 1 |
---|
| 912 | END DO |
---|
| 913 | |
---|
| 914 | IF( zbhitns == 1 ) THEN |
---|
| 915 | zdeps = zdeptht(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 916 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdeptht(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 917 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 918 | dsp(ji,jjd,1) ) * zdeps |
---|
| 919 | zrhdt1 = MAX(zrhdt1, 1000._wp - rau0) ! no lighter than fresh water |
---|
| 920 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
| 921 | ENDIF |
---|
| 922 | |
---|
| 923 | ! update the momentum trends in v direction |
---|
| 924 | |
---|
| 925 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 926 | IF( lk_vvl ) THEN |
---|
| 927 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
| 928 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
| 929 | ELSE |
---|
| 930 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
| 931 | ENDIF |
---|
| 932 | |
---|
| 933 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 934 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 935 | ENDIF |
---|
| 936 | |
---|
| 937 | |
---|
| 938 | END DO |
---|
| 939 | END DO |
---|
[455] | 940 | END DO |
---|
[503] | 941 | ! |
---|
[3294] | 942 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 943 | CALL wrk_dealloc( jpi,jpj,jpk, zdeptht, zrhh ) |
---|
[2715] | 944 | ! |
---|
[3294] | 945 | END SUBROUTINE hpg_prj |
---|
[455] | 946 | |
---|
[3294] | 947 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 948 | !!---------------------------------------------------------------------- |
---|
| 949 | !! *** ROUTINE cspline *** |
---|
| 950 | !! |
---|
| 951 | !! ** Purpose : constrained cubic spline interpolation |
---|
| 952 | !! |
---|
| 953 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
| 954 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 955 | !! |
---|
| 956 | !!---------------------------------------------------------------------- |
---|
| 957 | IMPLICIT NONE |
---|
| 958 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
| 959 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
| 960 | ! the interpoated function |
---|
| 961 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
| 962 | ! 2: Linear |
---|
| 963 | |
---|
| 964 | ! Local Variables |
---|
| 965 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 966 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 967 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 968 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 969 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 970 | !!---------------------------------------------------------------------- |
---|
| 971 | |
---|
| 972 | jpi = size(fsp,1) |
---|
| 973 | jpj = size(fsp,2) |
---|
| 974 | jpkm1 = size(fsp,3) - 1 |
---|
| 975 | |
---|
| 976 | |
---|
| 977 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 978 | DO ji = 1, jpi |
---|
| 979 | DO jj = 1, jpj |
---|
| 980 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
| 981 | ! DO jk = 2, jpkm1-1 |
---|
| 982 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 983 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
| 984 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 985 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 986 | ! |
---|
| 987 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
| 988 | ! |
---|
| 989 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 990 | ! zdf(jk) = 0._wp |
---|
| 991 | ! ELSE |
---|
| 992 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 993 | ! ENDIF |
---|
| 994 | ! END DO |
---|
| 995 | |
---|
| 996 | !!Simply geometric average |
---|
| 997 | DO jk = 2, jpkm1-1 |
---|
| 998 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 999 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
| 1000 | |
---|
| 1001 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1002 | zdf(jk) = 0._wp |
---|
| 1003 | ELSE |
---|
| 1004 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1005 | ENDIF |
---|
| 1006 | END DO |
---|
| 1007 | |
---|
| 1008 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1009 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1010 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1011 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1012 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
| 1013 | |
---|
| 1014 | DO jk = 1, jpkm1 - 1 |
---|
| 1015 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
| 1016 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1017 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
| 1018 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
| 1019 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
| 1020 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1021 | |
---|
| 1022 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1023 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
| 1024 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
| 1025 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1026 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1027 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1028 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1029 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1030 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1031 | END DO |
---|
| 1032 | END DO |
---|
| 1033 | END DO |
---|
| 1034 | |
---|
| 1035 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1036 | DO ji = 1, jpi |
---|
| 1037 | DO jj = 1, jpj |
---|
| 1038 | DO jk = 1, jpkm1-1 |
---|
| 1039 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
| 1040 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
| 1041 | |
---|
| 1042 | dsp(ji,jj,jk) = 0._wp |
---|
| 1043 | csp(ji,jj,jk) = 0._wp |
---|
| 1044 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1045 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1046 | END DO |
---|
| 1047 | END DO |
---|
| 1048 | END DO |
---|
| 1049 | |
---|
| 1050 | ELSE |
---|
| 1051 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1052 | ENDIF |
---|
| 1053 | |
---|
| 1054 | |
---|
| 1055 | END SUBROUTINE cspline |
---|
| 1056 | |
---|
| 1057 | |
---|
| 1058 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
| 1059 | !!---------------------------------------------------------------------- |
---|
| 1060 | !! *** ROUTINE interp1 *** |
---|
| 1061 | !! |
---|
| 1062 | !! ** Purpose : 1-d linear interpolation |
---|
| 1063 | !! |
---|
| 1064 | !! ** Method : |
---|
| 1065 | !! interpolation is straight forward |
---|
| 1066 | !! extrapolation is also permitted (no value limit) |
---|
| 1067 | !! |
---|
| 1068 | !!---------------------------------------------------------------------- |
---|
| 1069 | IMPLICIT NONE |
---|
| 1070 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
| 1071 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1072 | REAL(wp) :: zdeltx |
---|
| 1073 | !!---------------------------------------------------------------------- |
---|
| 1074 | |
---|
| 1075 | zdeltx = xr - xl |
---|
| 1076 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1077 | f = 0.5_wp * (fl + fr) |
---|
| 1078 | ELSE |
---|
| 1079 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1080 | ENDIF |
---|
| 1081 | |
---|
| 1082 | END FUNCTION interp1 |
---|
| 1083 | |
---|
| 1084 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
| 1085 | !!---------------------------------------------------------------------- |
---|
| 1086 | !! *** ROUTINE interp1 *** |
---|
| 1087 | !! |
---|
| 1088 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
| 1089 | !! |
---|
| 1090 | !! ** Method : cubic spline interpolation |
---|
| 1091 | !! |
---|
| 1092 | !!---------------------------------------------------------------------- |
---|
| 1093 | IMPLICIT NONE |
---|
| 1094 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
| 1095 | REAL(wp) :: f ! value from the interpolation |
---|
| 1096 | !!---------------------------------------------------------------------- |
---|
| 1097 | |
---|
| 1098 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
| 1099 | |
---|
| 1100 | END FUNCTION interp2 |
---|
| 1101 | |
---|
| 1102 | |
---|
| 1103 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
| 1104 | !!---------------------------------------------------------------------- |
---|
| 1105 | !! *** ROUTINE interp1 *** |
---|
| 1106 | !! |
---|
| 1107 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1108 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
| 1109 | !! |
---|
| 1110 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1111 | !! |
---|
| 1112 | !!---------------------------------------------------------------------- |
---|
| 1113 | IMPLICIT NONE |
---|
| 1114 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
| 1115 | REAL(wp) :: f ! value from the interpolation |
---|
| 1116 | !!---------------------------------------------------------------------- |
---|
| 1117 | |
---|
| 1118 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1119 | |
---|
| 1120 | END FUNCTION interp3 |
---|
| 1121 | |
---|
| 1122 | |
---|
| 1123 | FUNCTION integ2(xl, xr, a, b, c, d) RESULT(f) |
---|
| 1124 | !!---------------------------------------------------------------------- |
---|
| 1125 | !! *** ROUTINE interp1 *** |
---|
| 1126 | !! |
---|
| 1127 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1128 | !! |
---|
| 1129 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1130 | !! |
---|
| 1131 | !!---------------------------------------------------------------------- |
---|
| 1132 | IMPLICIT NONE |
---|
| 1133 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1134 | REAL(wp) :: za1, za2, za3 |
---|
| 1135 | REAL(wp) :: f ! integration result |
---|
| 1136 | !!---------------------------------------------------------------------- |
---|
| 1137 | |
---|
| 1138 | za1 = 0.5_wp * b |
---|
| 1139 | za2 = c / 3.0_wp |
---|
| 1140 | za3 = 0.25_wp * d |
---|
| 1141 | |
---|
| 1142 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1143 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1144 | |
---|
| 1145 | END FUNCTION integ2 |
---|
| 1146 | |
---|
| 1147 | |
---|
[3] | 1148 | !!====================================================================== |
---|
| 1149 | END MODULE dynhpg |
---|