[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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[503] | 16 | !!---------------------------------------------------------------------- |
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[3] | 17 | |
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| 18 | !!---------------------------------------------------------------------- |
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[455] | 19 | !! dyn_hpg : update the momentum trend with the now horizontal |
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[3] | 20 | !! gradient of the hydrostatic pressure |
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[2528] | 21 | !! dyn_hpg_init : initialisation and control of options |
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[455] | 22 | !! hpg_zco : z-coordinate scheme |
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| 23 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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| 24 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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| 25 | !! hpg_hel : s-coordinate (helsinki modification) |
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| 26 | !! hpg_wdj : s-coordinate (weighted density jacobian) |
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| 27 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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| 28 | !! hpg_rot : s-coordinate (ROTated axes scheme) |
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[2873] | 29 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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[3] | 30 | !!---------------------------------------------------------------------- |
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| 31 | USE oce ! ocean dynamics and tracers |
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| 32 | USE dom_oce ! ocean space and time domain |
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| 33 | USE phycst ! physical constants |
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[216] | 34 | USE trdmod ! ocean dynamics trends |
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| 35 | USE trdmod_oce ! ocean variables trends |
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[2715] | 36 | USE in_out_manager ! I/O manager |
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[258] | 37 | USE prtctl ! Print control |
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[455] | 38 | USE lbclnk ! lateral boundary condition |
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[2715] | 39 | USE lib_mpp ! MPP library |
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[3] | 40 | |
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| 41 | IMPLICIT NONE |
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| 42 | PRIVATE |
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| 43 | |
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[2528] | 44 | PUBLIC dyn_hpg ! routine called by step module |
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| 45 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 46 | |
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[1601] | 47 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 48 | LOGICAL , PUBLIC :: ln_hpg_zco = .TRUE. !: z-coordinate - full steps |
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| 49 | LOGICAL , PUBLIC :: ln_hpg_zps = .FALSE. !: z-coordinate - partial steps (interpolation) |
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| 50 | LOGICAL , PUBLIC :: ln_hpg_sco = .FALSE. !: s-coordinate (standard jacobian formulation) |
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| 51 | LOGICAL , PUBLIC :: ln_hpg_hel = .FALSE. !: s-coordinate (helsinki modification) |
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| 52 | LOGICAL , PUBLIC :: ln_hpg_wdj = .FALSE. !: s-coordinate (weighted density jacobian) |
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| 53 | LOGICAL , PUBLIC :: ln_hpg_djc = .FALSE. !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 54 | LOGICAL , PUBLIC :: ln_hpg_rot = .FALSE. !: s-coordinate (ROTated axes scheme) |
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[2873] | 55 | LOGICAL , PUBLIC :: ln_hpg_prj = .FALSE. !: s-coordinate (Pressure Jacobian scheme) |
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[2528] | 56 | REAL(wp), PUBLIC :: rn_gamma = 0._wp !: weighting coefficient |
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[1601] | 57 | LOGICAL , PUBLIC :: ln_dynhpg_imp = .FALSE. !: semi-implicite hpg flag |
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[455] | 58 | |
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[2873] | 59 | INTEGER :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) |
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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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[455] | 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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[455] | 77 | !! |
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| 78 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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| 79 | !! - Save the trend (l_trddyn=T) |
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[503] | 80 | !!---------------------------------------------------------------------- |
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[2715] | 81 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
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| 82 | USE wrk_nemo, ONLY: ztrdu => wrk_3d_1 , ztrdv => wrk_3d_2 ! 3D workspace |
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| 83 | !! |
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[503] | 84 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[455] | 85 | !!---------------------------------------------------------------------- |
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[2528] | 86 | ! |
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[2715] | 87 | IF( wrk_in_use(3, 1,2) ) THEN |
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| 88 | CALL ctl_stop('dyn_hpg: requested workspace arrays are unavailable') ; RETURN |
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| 89 | ENDIF |
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| 90 | ! |
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[503] | 91 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[455] | 92 | ztrdu(:,:,:) = ua(:,:,:) |
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| 93 | ztrdv(:,:,:) = va(:,:,:) |
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| 94 | ENDIF |
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[2528] | 95 | ! |
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[455] | 96 | SELECT CASE ( nhpg ) ! Hydrastatic pressure gradient computation |
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[503] | 97 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 98 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 99 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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| 100 | CASE ( 3 ) ; CALL hpg_hel ( kt ) ! s-coordinate (helsinki modification) |
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| 101 | CASE ( 4 ) ; CALL hpg_wdj ( kt ) ! s-coordinate (weighted density jacobian) |
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| 102 | CASE ( 5 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 103 | CASE ( 6 ) ; CALL hpg_rot ( kt ) ! s-coordinate (ROTated axes scheme) |
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[2873] | 104 | CASE ( 7 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[455] | 105 | END SELECT |
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[2528] | 106 | ! |
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[503] | 107 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 108 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 109 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[503] | 110 | CALL trd_mod( ztrdu, ztrdv, jpdyn_trd_hpg, 'DYN', kt ) |
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[455] | 111 | ENDIF |
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[503] | 112 | ! |
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| 113 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 114 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 115 | ! |
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[2715] | 116 | IF( wrk_not_released(3, 1,2) ) CALL ctl_stop('dyn_hpg: failed to release workspace arrays') |
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| 117 | ! |
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[455] | 118 | END SUBROUTINE dyn_hpg |
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| 119 | |
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| 120 | |
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[2528] | 121 | SUBROUTINE dyn_hpg_init |
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[455] | 122 | !!---------------------------------------------------------------------- |
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[2528] | 123 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 124 | !! |
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| 125 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 126 | !! computation and consistency control |
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| 127 | !! |
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[1601] | 128 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 129 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 130 | !!---------------------------------------------------------------------- |
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| 131 | INTEGER :: ioptio = 0 ! temporary integer |
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[1601] | 132 | !! |
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[2528] | 133 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, ln_hpg_hel, & |
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[2873] | 134 | & ln_hpg_wdj, ln_hpg_djc, ln_hpg_rot, ln_hpg_prj, rn_gamma , ln_dynhpg_imp |
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[455] | 135 | !!---------------------------------------------------------------------- |
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[2528] | 136 | ! |
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| 137 | REWIND( numnam ) ! Read Namelist namdyn_hpg |
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| 138 | READ ( numnam, namdyn_hpg ) |
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| 139 | ! |
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| 140 | IF(lwp) THEN ! Control print |
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[455] | 141 | WRITE(numout,*) |
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[2528] | 142 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 143 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 144 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 145 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 146 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 147 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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| 148 | WRITE(numout,*) ' s-coord. (helsinki modification) ln_hpg_hel = ', ln_hpg_hel |
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| 149 | WRITE(numout,*) ' s-coord. (weighted density jacobian) ln_hpg_wdj = ', ln_hpg_wdj |
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| 150 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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| 151 | WRITE(numout,*) ' s-coord. (ROTated axes scheme) ln_hpg_rot = ', ln_hpg_rot |
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[2873] | 152 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[1601] | 153 | WRITE(numout,*) ' weighting coeff. (wdj scheme) rn_gamma = ', rn_gamma |
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| 154 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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[455] | 155 | ENDIF |
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[2528] | 156 | ! |
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[2873] | 157 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) & |
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| 158 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl require:& |
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| 159 | & the standard jacobian formulation hpg_sco or & |
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| 160 | & the pressure jacobian formulation hpg_prj') |
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[2528] | 161 | ! |
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[503] | 162 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 163 | IF( ln_hpg_zco ) nhpg = 0 |
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| 164 | IF( ln_hpg_zps ) nhpg = 1 |
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| 165 | IF( ln_hpg_sco ) nhpg = 2 |
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| 166 | IF( ln_hpg_hel ) nhpg = 3 |
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| 167 | IF( ln_hpg_wdj ) nhpg = 4 |
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| 168 | IF( ln_hpg_djc ) nhpg = 5 |
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| 169 | IF( ln_hpg_rot ) nhpg = 6 |
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[2873] | 170 | IF( ln_hpg_prj ) nhpg = 7 |
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[2528] | 171 | ! |
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[503] | 172 | ! ! Consitency check |
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[455] | 173 | ioptio = 0 |
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| 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_hel ) ioptio = ioptio + 1 |
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| 178 | IF( ln_hpg_wdj ) ioptio = ioptio + 1 |
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| 179 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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| 180 | IF( ln_hpg_rot ) ioptio = ioptio + 1 |
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[2873] | 181 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[2715] | 182 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[503] | 183 | ! |
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[2528] | 184 | END SUBROUTINE dyn_hpg_init |
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[455] | 185 | |
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| 186 | |
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| 187 | SUBROUTINE hpg_zco( kt ) |
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| 188 | !!--------------------------------------------------------------------- |
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| 189 | !! *** ROUTINE hpg_zco *** |
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| 190 | !! |
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| 191 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 192 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 193 | !! is computed by taking the vertical integral of the in-situ |
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| 194 | !! density gradient along the model level from the suface to that |
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| 195 | !! level: zhpi = grav ..... |
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| 196 | !! zhpj = grav ..... |
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[3] | 197 | !! add it to the general momentum trend (ua,va). |
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[455] | 198 | !! ua = ua - 1/e1u * zhpi |
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| 199 | !! va = va - 1/e2v * zhpj |
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| 200 | !! |
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[3] | 201 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 202 | !!---------------------------------------------------------------------- |
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[2715] | 203 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
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[3] | 204 | !! |
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[503] | 205 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 206 | !! |
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| 207 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 208 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3] | 209 | !!---------------------------------------------------------------------- |
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[455] | 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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[455] | 216 | |
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[2715] | 217 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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[3] | 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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[503] | 231 | ! |
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[455] | 232 | ! interior value (2=<jk=<jpkm1) |
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[3] | 233 | DO jk = 2, jpkm1 |
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[455] | 234 | DO jj = 2, jpjm1 |
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[3] | 235 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 236 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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| 237 | ! hydrostatic pressure gradient |
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| 238 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 239 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 240 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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| 241 | |
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| 242 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 243 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 244 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 245 | ! add to the general momentum trend |
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[455] | 246 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 247 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[3] | 248 | END DO |
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| 249 | END DO |
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| 250 | END DO |
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[503] | 251 | ! |
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[455] | 252 | END SUBROUTINE hpg_zco |
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[216] | 253 | |
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[3] | 254 | |
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[455] | 255 | SUBROUTINE hpg_zps( kt ) |
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[3] | 256 | !!--------------------------------------------------------------------- |
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[455] | 257 | !! *** ROUTINE hpg_zps *** |
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[3] | 258 | !! |
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[455] | 259 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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| 260 | !! |
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[3] | 261 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[455] | 262 | !!---------------------------------------------------------------------- |
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[2715] | 263 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
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[503] | 264 | !! |
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| 265 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 266 | !! |
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| 267 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 268 | INTEGER :: iku, ikv ! temporary integers |
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| 269 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[3] | 270 | !!---------------------------------------------------------------------- |
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| 271 | |
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| 272 | IF( kt == nit000 ) THEN |
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| 273 | IF(lwp) WRITE(numout,*) |
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[455] | 274 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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[503] | 275 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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[3] | 276 | ENDIF |
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| 277 | |
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[503] | 278 | ! Local constant initialization |
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[2528] | 279 | zcoef0 = - grav * 0.5_wp |
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[3] | 280 | |
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[2528] | 281 | ! Surface value (also valid in partial step case) |
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[3] | 282 | DO jj = 2, jpjm1 |
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| 283 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 284 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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[3] | 285 | ! hydrostatic pressure gradient |
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[455] | 286 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 287 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 288 | ! add to the general momentum trend |
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| 289 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 290 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 291 | END DO |
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| 292 | END DO |
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| 293 | |
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[503] | 294 | ! interior value (2=<jk=<jpkm1) |
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[3] | 295 | DO jk = 2, jpkm1 |
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| 296 | DO jj = 2, jpjm1 |
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| 297 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 298 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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[3] | 299 | ! hydrostatic pressure gradient |
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| 300 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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[455] | 301 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
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| 302 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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[3] | 303 | |
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| 304 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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[455] | 305 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
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| 306 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 307 | ! add to the general momentum trend |
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| 308 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 309 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[455] | 310 | END DO |
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[3] | 311 | END DO |
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| 312 | END DO |
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| 313 | |
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[2528] | 314 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
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[3] | 315 | # if defined key_vectopt_loop |
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| 316 | jj = 1 |
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| 317 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
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| 318 | # else |
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| 319 | DO jj = 2, jpjm1 |
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| 320 | DO ji = 2, jpim1 |
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| 321 | # endif |
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[2528] | 322 | iku = mbku(ji,jj) |
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| 323 | ikv = mbkv(ji,jj) |
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[3] | 324 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
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| 325 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
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[2528] | 326 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
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| 327 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
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| 328 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
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| 329 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
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| 330 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 331 | ENDIF |
---|
[2528] | 332 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 333 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 334 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 335 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
---|
| 336 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 337 | ENDIF |
---|
| 338 | # if ! defined key_vectopt_loop |
---|
| 339 | END DO |
---|
| 340 | # endif |
---|
| 341 | END DO |
---|
[503] | 342 | ! |
---|
[455] | 343 | END SUBROUTINE hpg_zps |
---|
[216] | 344 | |
---|
[3] | 345 | |
---|
[455] | 346 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 347 | !!--------------------------------------------------------------------- |
---|
[455] | 348 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 349 | !! |
---|
[455] | 350 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 351 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 352 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 353 | !! density gradient along the model level from the suface to that |
---|
[455] | 354 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 355 | !! to the horizontal pressure gradient : |
---|
| 356 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 357 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
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[3] | 358 | !! add it to the general momentum trend (ua,va). |
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[455] | 359 | !! ua = ua - 1/e1u * zhpi |
---|
| 360 | !! va = va - 1/e2v * zhpj |
---|
[3] | 361 | !! |
---|
| 362 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 363 | !!---------------------------------------------------------------------- |
---|
[2715] | 364 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
[3] | 365 | !! |
---|
[503] | 366 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 367 | !! |
---|
[592] | 368 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 369 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
[3] | 370 | !!---------------------------------------------------------------------- |
---|
| 371 | |
---|
| 372 | IF( kt == nit000 ) THEN |
---|
| 373 | IF(lwp) WRITE(numout,*) |
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[455] | 374 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 375 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
[3] | 376 | ENDIF |
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| 377 | |
---|
[503] | 378 | ! Local constant initialization |
---|
[2528] | 379 | zcoef0 = - grav * 0.5_wp |
---|
[592] | 380 | ! To use density and not density anomaly |
---|
[2528] | 381 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 382 | ELSE ; znad = 0._wp ! Fixed volume |
---|
[592] | 383 | ENDIF |
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[455] | 384 | |
---|
[503] | 385 | ! Surface value |
---|
[455] | 386 | DO jj = 2, jpjm1 |
---|
| 387 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 388 | ! hydrostatic pressure gradient along s-surfaces |
---|
[592] | 389 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 390 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 391 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 392 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
[455] | 393 | ! s-coordinate pressure gradient correction |
---|
[2528] | 394 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 395 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 396 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 397 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 398 | ! add to the general momentum trend |
---|
| 399 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 400 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 401 | END DO |
---|
| 402 | END DO |
---|
| 403 | |
---|
[503] | 404 | ! interior value (2=<jk=<jpkm1) |
---|
[455] | 405 | DO jk = 2, jpkm1 |
---|
| 406 | DO jj = 2, jpjm1 |
---|
| 407 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 408 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 409 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
[592] | 410 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 411 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
[455] | 412 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
[592] | 413 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 414 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
[455] | 415 | ! s-coordinate pressure gradient correction |
---|
[2528] | 416 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
[455] | 417 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
[2528] | 418 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
[455] | 419 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 420 | ! add to the general momentum trend |
---|
| 421 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 422 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 423 | END DO |
---|
| 424 | END DO |
---|
| 425 | END DO |
---|
[503] | 426 | ! |
---|
[455] | 427 | END SUBROUTINE hpg_sco |
---|
| 428 | |
---|
| 429 | |
---|
| 430 | SUBROUTINE hpg_hel( kt ) |
---|
| 431 | !!--------------------------------------------------------------------- |
---|
| 432 | !! *** ROUTINE hpg_hel *** |
---|
| 433 | !! |
---|
| 434 | !! ** Method : s-coordinate case. |
---|
| 435 | !! The now hydrostatic pressure gradient at a given level |
---|
| 436 | !! jk is computed by taking the vertical integral of the in-situ |
---|
| 437 | !! density gradient along the model level from the suface to that |
---|
| 438 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 439 | !! to the horizontal pressure gradient : |
---|
| 440 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 441 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 442 | !! add it to the general momentum trend (ua,va). |
---|
| 443 | !! ua = ua - 1/e1u * zhpi |
---|
| 444 | !! va = va - 1/e2v * zhpj |
---|
| 445 | !! |
---|
| 446 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 447 | !! - Save the trend (l_trddyn=T) |
---|
[503] | 448 | !!---------------------------------------------------------------------- |
---|
[2715] | 449 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
[455] | 450 | !! |
---|
[503] | 451 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 452 | !! |
---|
| 453 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 454 | REAL(wp) :: zcoef0, zuap, zvap ! temporary scalars |
---|
[455] | 455 | !!---------------------------------------------------------------------- |
---|
| 456 | |
---|
| 457 | IF( kt == nit000 ) THEN |
---|
| 458 | IF(lwp) WRITE(numout,*) |
---|
| 459 | IF(lwp) WRITE(numout,*) 'dyn:hpg_hel : hydrostatic pressure gradient trend' |
---|
| 460 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, helsinki modified scheme' |
---|
[216] | 461 | ENDIF |
---|
| 462 | |
---|
[503] | 463 | ! Local constant initialization |
---|
[2528] | 464 | zcoef0 = - grav * 0.5_wp |
---|
[455] | 465 | |
---|
[503] | 466 | ! Surface value |
---|
[3] | 467 | DO jj = 2, jpjm1 |
---|
| 468 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 469 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 470 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj ,1) * rhd(ji+1,jj ,1) & |
---|
| 471 | & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
| 472 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3t(ji ,jj+1,1) * rhd(ji ,jj+1,1) & |
---|
| 473 | & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
| 474 | ! s-coordinate pressure gradient correction |
---|
| 475 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & |
---|
| 476 | & * ( fsdept(ji+1,jj,1) - fsdept(ji,jj,1) ) / e1u(ji,jj) |
---|
| 477 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & |
---|
| 478 | & * ( fsdept(ji,jj+1,1) - fsdept(ji,jj,1) ) / e2v(ji,jj) |
---|
[3] | 479 | ! add to the general momentum trend |
---|
[455] | 480 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 481 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
[3] | 482 | END DO |
---|
| 483 | END DO |
---|
[503] | 484 | ! |
---|
| 485 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 486 | DO jk = 2, jpkm1 |
---|
| 487 | DO jj = 2, jpjm1 |
---|
| 488 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 489 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 490 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 491 | & + zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,jk ) * rhd(ji+1,jj,jk) & |
---|
| 492 | & -fse3t(ji ,jj,jk ) * rhd(ji ,jj,jk) ) & |
---|
| 493 | & + zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,jk-1) * rhd(ji+1,jj,jk-1) & |
---|
| 494 | & -fse3t(ji ,jj,jk-1) * rhd(ji ,jj,jk-1) ) |
---|
| 495 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
[2528] | 496 | & + zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,jk ) * rhd(ji,jj+1,jk) & |
---|
[455] | 497 | & -fse3t(ji,jj ,jk ) * rhd(ji,jj, jk) ) & |
---|
[2528] | 498 | & + zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,jk-1) * rhd(ji,jj+1,jk-1) & |
---|
[455] | 499 | & -fse3t(ji,jj ,jk-1) * rhd(ji,jj, jk-1) ) |
---|
| 500 | ! s-coordinate pressure gradient correction |
---|
| 501 | zuap = - zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 502 | & * ( fsdept(ji+1,jj,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 503 | zvap = - zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 504 | & * ( fsdept(ji,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 505 | ! add to the general momentum trend |
---|
| 506 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 507 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 508 | END DO |
---|
| 509 | END DO |
---|
| 510 | END DO |
---|
[503] | 511 | ! |
---|
[455] | 512 | END SUBROUTINE hpg_hel |
---|
| 513 | |
---|
| 514 | |
---|
| 515 | SUBROUTINE hpg_wdj( kt ) |
---|
| 516 | !!--------------------------------------------------------------------- |
---|
| 517 | !! *** ROUTINE hpg_wdj *** |
---|
| 518 | !! |
---|
| 519 | !! ** Method : Weighted Density Jacobian (wdj) scheme (song 1998) |
---|
[1601] | 520 | !! The weighting coefficients from the namelist parameter rn_gamma |
---|
| 521 | !! (alpha=0.5-rn_gamma ; beta=1-alpha=0.5+rn_gamma |
---|
[455] | 522 | !! |
---|
| 523 | !! Reference : Song, Mon. Wea. Rev., 126, 3213-3230, 1998. |
---|
[503] | 524 | !!---------------------------------------------------------------------- |
---|
[2715] | 525 | USE oce, ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
[455] | 526 | !! |
---|
[503] | 527 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 528 | !! |
---|
| 529 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 530 | REAL(wp) :: zcoef0, zuap, zvap ! temporary scalars |
---|
| 531 | REAL(wp) :: zalph , zbeta ! " " |
---|
[455] | 532 | !!---------------------------------------------------------------------- |
---|
| 533 | |
---|
| 534 | IF( kt == nit000 ) THEN |
---|
| 535 | IF(lwp) WRITE(numout,*) |
---|
| 536 | IF(lwp) WRITE(numout,*) 'dyn:hpg_wdj : hydrostatic pressure gradient trend' |
---|
| 537 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ Weighted Density Jacobian' |
---|
| 538 | ENDIF |
---|
| 539 | |
---|
| 540 | ! Local constant initialization |
---|
[2528] | 541 | zcoef0 = - grav * 0.5_wp |
---|
| 542 | zalph = 0.5_wp - rn_gamma ! weighting coefficients (alpha=0.5-rn_gamma |
---|
| 543 | zbeta = 0.5_wp + rn_gamma ! (beta =1-alpha=0.5+rn_gamma |
---|
[455] | 544 | |
---|
| 545 | ! Surface value (no ponderation) |
---|
| 546 | DO jj = 2, jpjm1 |
---|
| 547 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 548 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 549 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * rhd(ji+1,jj ,1) & |
---|
| 550 | & - fse3w(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
| 551 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * rhd(ji ,jj+1,1) & |
---|
| 552 | & - fse3w(ji ,jj ,1) * rhd(ji, jj ,1) ) |
---|
| 553 | ! s-coordinate pressure gradient correction |
---|
| 554 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & |
---|
| 555 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
| 556 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & |
---|
| 557 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 558 | ! add to the general momentum trend |
---|
| 559 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 560 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 561 | END DO |
---|
| 562 | END DO |
---|
| 563 | |
---|
| 564 | ! Interior value (2=<jk=<jpkm1) (weighted with zalph & zbeta) |
---|
| 565 | DO jk = 2, jpkm1 |
---|
| 566 | DO jj = 2, jpjm1 |
---|
| 567 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 568 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 569 | & * ( ( fsde3w(ji+1,jj,jk ) + fsde3w(ji,jj,jk ) & |
---|
| 570 | & - fsde3w(ji+1,jj,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
| 571 | & * ( zalph * ( rhd (ji+1,jj,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
| 572 | & + zbeta * ( rhd (ji+1,jj,jk ) - rhd (ji,jj,jk ) ) ) & |
---|
| 573 | & - ( rhd (ji+1,jj,jk ) + rhd (ji,jj,jk ) & |
---|
| 574 | & - rhd (ji+1,jj,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
| 575 | & * ( zalph * ( fsde3w(ji+1,jj,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
| 576 | & + zbeta * ( fsde3w(ji+1,jj,jk ) - fsde3w(ji,jj,jk ) ) ) ) |
---|
| 577 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 578 | & * ( ( fsde3w(ji,jj+1,jk ) + fsde3w(ji,jj,jk ) & |
---|
| 579 | & - fsde3w(ji,jj+1,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
| 580 | & * ( zalph * ( rhd (ji,jj+1,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
| 581 | & + zbeta * ( rhd (ji,jj+1,jk ) - rhd (ji,jj,jk ) ) ) & |
---|
| 582 | & - ( rhd (ji,jj+1,jk ) + rhd (ji,jj,jk ) & |
---|
| 583 | & - rhd (ji,jj+1,jk-1) - rhd (ji,jj,jk-1) ) & |
---|
| 584 | & * ( zalph * ( fsde3w(ji,jj+1,jk-1) - fsde3w(ji,jj,jk-1) ) & |
---|
| 585 | & + zbeta * ( fsde3w(ji,jj+1,jk ) - fsde3w(ji,jj,jk ) ) ) ) |
---|
[3] | 586 | ! add to the general momentum trend |
---|
| 587 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 588 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[455] | 589 | END DO |
---|
[3] | 590 | END DO |
---|
| 591 | END DO |
---|
[503] | 592 | ! |
---|
[455] | 593 | END SUBROUTINE hpg_wdj |
---|
[216] | 594 | |
---|
[455] | 595 | |
---|
| 596 | SUBROUTINE hpg_djc( kt ) |
---|
| 597 | !!--------------------------------------------------------------------- |
---|
| 598 | !! *** ROUTINE hpg_djc *** |
---|
| 599 | !! |
---|
| 600 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
| 601 | !! |
---|
[503] | 602 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 603 | !!---------------------------------------------------------------------- |
---|
[2715] | 604 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
---|
| 605 | USE oce , ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
| 606 | USE wrk_nemo, ONLY: drhox => wrk_3d_1 , dzx => wrk_3d_2 |
---|
| 607 | USE wrk_nemo, ONLY: drhou => wrk_3d_3 , dzu => wrk_3d_4 , rho_i => wrk_3d_5 |
---|
| 608 | USE wrk_nemo, ONLY: drhoy => wrk_3d_6 , dzy => wrk_3d_7 |
---|
| 609 | USE wrk_nemo, ONLY: drhov => wrk_3d_8 , dzv => wrk_3d_9 , rho_j => wrk_3d_10 |
---|
| 610 | USE wrk_nemo, ONLY: drhoz => wrk_3d_11 , dzz => wrk_3d_12 |
---|
| 611 | USE wrk_nemo, ONLY: drhow => wrk_3d_13 , dzw => wrk_3d_14 |
---|
| 612 | USE wrk_nemo, ONLY: rho_k => wrk_3d_15 |
---|
[503] | 613 | !! |
---|
| 614 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 615 | !! |
---|
| 616 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 617 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 618 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 619 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[455] | 620 | !!---------------------------------------------------------------------- |
---|
| 621 | |
---|
[2715] | 622 | IF( wrk_in_use(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) THEN |
---|
| 623 | CALL ctl_stop('dyn:hpg_djc: requested workspace arrays unavailable') ; RETURN |
---|
| 624 | ENDIF |
---|
| 625 | |
---|
[455] | 626 | IF( kt == nit000 ) THEN |
---|
| 627 | IF(lwp) WRITE(numout,*) |
---|
| 628 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 629 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 630 | ENDIF |
---|
| 631 | |
---|
[503] | 632 | ! Local constant initialization |
---|
[2528] | 633 | zcoef0 = - grav * 0.5_wp |
---|
| 634 | z1_10 = 1._wp / 10._wp |
---|
| 635 | z1_12 = 1._wp / 12._wp |
---|
[455] | 636 | |
---|
| 637 | !---------------------------------------------------------------------------------------- |
---|
| 638 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 639 | !---------------------------------------------------------------------------------------- |
---|
| 640 | |
---|
| 641 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 642 | |
---|
| 643 | DO jk = 2, jpkm1 |
---|
| 644 | DO jj = 2, jpjm1 |
---|
| 645 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 646 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 647 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 648 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 649 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 650 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 651 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 652 | END DO |
---|
| 653 | END DO |
---|
| 654 | END DO |
---|
| 655 | |
---|
| 656 | !------------------------------------------------------------------------- |
---|
| 657 | ! compute harmonic averages using eq. 5.18 |
---|
| 658 | !------------------------------------------------------------------------- |
---|
| 659 | zep = 1.e-15 |
---|
| 660 | |
---|
[503] | 661 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 662 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 663 | |
---|
| 664 | DO jk = 2, jpkm1 |
---|
| 665 | DO jj = 2, jpjm1 |
---|
| 666 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 667 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 668 | |
---|
[2528] | 669 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 670 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[455] | 671 | |
---|
[2528] | 672 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 673 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 674 | |
---|
| 675 | IF( cffw > zep) THEN |
---|
[2528] | 676 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 677 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 678 | ELSE |
---|
[2528] | 679 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 680 | ENDIF |
---|
| 681 | |
---|
[2528] | 682 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 683 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 684 | |
---|
| 685 | IF( cffu > zep ) THEN |
---|
[2528] | 686 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 687 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 688 | ELSE |
---|
[2528] | 689 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 690 | ENDIF |
---|
| 691 | |
---|
| 692 | IF( cffx > zep ) THEN |
---|
[2528] | 693 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 694 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 695 | ELSE |
---|
[2528] | 696 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 697 | ENDIF |
---|
| 698 | |
---|
| 699 | IF( cffv > zep ) THEN |
---|
[2528] | 700 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 701 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 702 | ELSE |
---|
[2528] | 703 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 704 | ENDIF |
---|
| 705 | |
---|
| 706 | IF( cffy > zep ) THEN |
---|
[2528] | 707 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 708 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 709 | ELSE |
---|
[2528] | 710 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 711 | ENDIF |
---|
| 712 | |
---|
| 713 | END DO |
---|
| 714 | END DO |
---|
| 715 | END DO |
---|
| 716 | |
---|
| 717 | !---------------------------------------------------------------------------------- |
---|
| 718 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 719 | !---------------------------------------------------------------------------------- |
---|
[2528] | 720 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 721 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 722 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 723 | |
---|
[2528] | 724 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 725 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 726 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 727 | |
---|
| 728 | |
---|
| 729 | !-------------------------------------------------------------- |
---|
| 730 | ! Upper half of top-most grid box, compute and store |
---|
| 731 | !------------------------------------------------------------- |
---|
| 732 | |
---|
| 733 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 734 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 735 | |
---|
| 736 | DO jj = 2, jpjm1 |
---|
| 737 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 738 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 739 | & * ( rhd(ji,jj,1) & |
---|
| 740 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 741 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 742 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 743 | END DO |
---|
| 744 | END DO |
---|
| 745 | |
---|
| 746 | !!bug gm : here also, simplification is possible |
---|
| 747 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 748 | |
---|
| 749 | DO jk = 2, jpkm1 |
---|
| 750 | DO jj = 2, jpjm1 |
---|
| 751 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 752 | |
---|
| 753 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 754 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 755 | & - grav * z1_10 * ( & |
---|
| 756 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 757 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 758 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 759 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 760 | & ) |
---|
| 761 | |
---|
| 762 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 763 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 764 | & - grav* z1_10 * ( & |
---|
| 765 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 766 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 767 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 768 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 769 | & ) |
---|
| 770 | |
---|
| 771 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 772 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 773 | & - grav* z1_10 * ( & |
---|
| 774 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 775 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 776 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 777 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 778 | & ) |
---|
| 779 | |
---|
| 780 | END DO |
---|
| 781 | END DO |
---|
| 782 | END DO |
---|
| 783 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 784 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 785 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 786 | |
---|
| 787 | |
---|
| 788 | ! --------------- |
---|
| 789 | ! Surface value |
---|
| 790 | ! --------------- |
---|
| 791 | DO jj = 2, jpjm1 |
---|
| 792 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 793 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 794 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 795 | ! add to the general momentum trend |
---|
| 796 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 797 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 798 | END DO |
---|
| 799 | END DO |
---|
| 800 | |
---|
| 801 | ! ---------------- |
---|
| 802 | ! interior value (2=<jk=<jpkm1) |
---|
| 803 | ! ---------------- |
---|
| 804 | DO jk = 2, jpkm1 |
---|
| 805 | DO jj = 2, jpjm1 |
---|
| 806 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 807 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 808 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 809 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 810 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 811 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 812 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 813 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 814 | ! add to the general momentum trend |
---|
| 815 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 816 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 817 | END DO |
---|
| 818 | END DO |
---|
| 819 | END DO |
---|
[503] | 820 | ! |
---|
[2715] | 821 | IF( wrk_not_released(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) & |
---|
| 822 | CALL ctl_stop('dyn:hpg_djc: failed to release workspace arrays') |
---|
| 823 | ! |
---|
[455] | 824 | END SUBROUTINE hpg_djc |
---|
| 825 | |
---|
| 826 | |
---|
| 827 | SUBROUTINE hpg_rot( kt ) |
---|
| 828 | !!--------------------------------------------------------------------- |
---|
| 829 | !! *** ROUTINE hpg_rot *** |
---|
| 830 | !! |
---|
| 831 | !! ** Method : rotated axes scheme (Thiem and Berntsen 2005) |
---|
| 832 | !! |
---|
| 833 | !! Reference: Thiem & Berntsen, Ocean Modelling, In press, 2005. |
---|
| 834 | !!---------------------------------------------------------------------- |
---|
[2715] | 835 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
---|
| 836 | USE oce , ONLY: zhpi => ta , zhpj => sa ! (ta,sa) used as 3D workspace |
---|
| 837 | USE wrk_nemo, ONLY: zdistr => wrk_2d_1 , zsina => wrk_2d_2 , zcosa => wrk_2d_3 |
---|
| 838 | USE wrk_nemo, ONLY: zhpiorg => wrk_3d_1 , zhpirot => wrk_3d_2 |
---|
| 839 | USE wrk_nemo, ONLY: zhpitra => wrk_3d_3 , zhpine => wrk_3d_4 |
---|
| 840 | USE wrk_nemo, ONLY: zhpjorg => wrk_3d_5 , zhpjrot => wrk_3d_6 |
---|
| 841 | USE wrk_nemo, ONLY: zhpjtra => wrk_3d_7 , zhpjne => wrk_3d_8 |
---|
[503] | 842 | !! |
---|
| 843 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 844 | !! |
---|
| 845 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 846 | REAL(wp) :: zforg, zcoef0, zuap, zmskd1, zmskd1m ! temporary scalar |
---|
| 847 | REAL(wp) :: zfrot , zvap, zmskd2, zmskd2m ! " " |
---|
[455] | 848 | !!---------------------------------------------------------------------- |
---|
| 849 | |
---|
[2715] | 850 | IF( wrk_in_use(2, 1,2,3) .OR. & |
---|
| 851 | wrk_in_use(3, 1,2,3,4,5,6,7,8) ) THEN |
---|
| 852 | CALL ctl_stop('dyn:hpg_rot: requested workspace arrays unavailable') ; RETURN |
---|
| 853 | ENDIF |
---|
| 854 | |
---|
[455] | 855 | IF( kt == nit000 ) THEN |
---|
| 856 | IF(lwp) WRITE(numout,*) |
---|
| 857 | IF(lwp) WRITE(numout,*) 'dyn:hpg_rot : hydrostatic pressure gradient trend' |
---|
| 858 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, rotated axes scheme used' |
---|
[3] | 859 | ENDIF |
---|
| 860 | |
---|
[455] | 861 | ! ------------------------------- |
---|
| 862 | ! Local constant initialization |
---|
| 863 | ! ------------------------------- |
---|
[2528] | 864 | zcoef0 = - grav * 0.5_wp |
---|
| 865 | zforg = 0.95_wp |
---|
| 866 | zfrot = 1._wp - zforg |
---|
[3] | 867 | |
---|
[455] | 868 | ! inverse of the distance between 2 diagonal T-points (defined at F-point) (here zcoef0/distance) |
---|
| 869 | zdistr(:,:) = zcoef0 / SQRT( e1f(:,:)*e1f(:,:) + e2f(:,:)*e1f(:,:) ) |
---|
[3] | 870 | |
---|
[455] | 871 | ! sinus and cosinus of diagonal angle at F-point |
---|
| 872 | zsina(:,:) = ATAN2( e2f(:,:), e1f(:,:) ) |
---|
| 873 | zcosa(:,:) = COS( zsina(:,:) ) |
---|
| 874 | zsina(:,:) = SIN( zsina(:,:) ) |
---|
| 875 | |
---|
| 876 | ! --------------- |
---|
| 877 | ! Surface value |
---|
| 878 | ! --------------- |
---|
| 879 | ! compute and add to the general trend the pressure gradients along the axes |
---|
| 880 | DO jj = 2, jpjm1 |
---|
| 881 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 882 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 883 | zhpiorg(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,1) * rhd(ji+1,jj,1) & |
---|
| 884 | & - fse3t(ji ,jj,1) * rhd(ji ,jj,1) ) |
---|
| 885 | zhpjorg(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,1) * rhd(ji,jj+1,1) & |
---|
| 886 | & - fse3t(ji,jj ,1) * rhd(ji,jj ,1) ) |
---|
| 887 | ! s-coordinate pressure gradient correction |
---|
| 888 | zuap = -zcoef0 * ( rhd (ji+1,jj ,1) + rhd (ji,jj,1) ) & |
---|
| 889 | & * ( fsdept(ji+1,jj ,1) - fsdept(ji,jj,1) ) / e1u(ji,jj) |
---|
| 890 | zvap = -zcoef0 * ( rhd (ji ,jj+1,1) + rhd (ji,jj,1) ) & |
---|
| 891 | & * ( fsdept(ji ,jj+1,1) - fsdept(ji,jj,1) ) / e2v(ji,jj) |
---|
| 892 | ! add to the general momentum trend |
---|
| 893 | ua(ji,jj,1) = ua(ji,jj,1) + zforg * ( zhpiorg(ji,jj,1) + zuap ) |
---|
| 894 | va(ji,jj,1) = va(ji,jj,1) + zforg * ( zhpjorg(ji,jj,1) + zvap ) |
---|
| 895 | END DO |
---|
| 896 | END DO |
---|
| 897 | |
---|
| 898 | ! compute the pressure gradients in the diagonal directions |
---|
| 899 | DO jj = 1, jpjm1 |
---|
| 900 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 901 | zmskd1 = tmask(ji+1,jj+1,1) * tmask(ji ,jj,1) ! mask in the 1st diagnonal |
---|
| 902 | zmskd2 = tmask(ji ,jj+1,1) * tmask(ji+1,jj,1) ! mask in the 2nd diagnonal |
---|
| 903 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 904 | zhpitra(ji,jj,1) = zdistr(ji,jj) * zmskd1 * ( fse3t(ji+1,jj+1,1) * rhd(ji+1,jj+1,1) & |
---|
| 905 | & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) |
---|
| 906 | zhpjtra(ji,jj,1) = zdistr(ji,jj) * zmskd2 * ( fse3t(ji ,jj+1,1) * rhd(ji ,jj+1,1) & |
---|
| 907 | & - fse3t(ji+1,jj ,1) * rhd(ji+1,jj ,1) ) |
---|
| 908 | ! s-coordinate pressure gradient correction |
---|
| 909 | zuap = -zdistr(ji,jj) * zmskd1 * ( rhd (ji+1,jj+1,1) + rhd (ji ,jj,1) ) & |
---|
| 910 | & * ( fsdept(ji+1,jj+1,1) - fsdept(ji ,jj,1) ) |
---|
| 911 | zvap = -zdistr(ji,jj) * zmskd2 * ( rhd (ji ,jj+1,1) + rhd (ji+1,jj,1) ) & |
---|
| 912 | & * ( fsdept(ji ,jj+1,1) - fsdept(ji+1,jj,1) ) |
---|
| 913 | ! back rotation |
---|
| 914 | zhpine(ji,jj,1) = zcosa(ji,jj) * ( zhpitra(ji,jj,1) + zuap ) & |
---|
| 915 | & - zsina(ji,jj) * ( zhpjtra(ji,jj,1) + zvap ) |
---|
| 916 | zhpjne(ji,jj,1) = zsina(ji,jj) * ( zhpitra(ji,jj,1) + zuap ) & |
---|
| 917 | & + zcosa(ji,jj) * ( zhpjtra(ji,jj,1) + zvap ) |
---|
| 918 | END DO |
---|
| 919 | END DO |
---|
| 920 | |
---|
| 921 | ! interpolate and add to the general trend the diagonal gradient |
---|
| 922 | DO jj = 2, jpjm1 |
---|
| 923 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 924 | ! averaging |
---|
| 925 | zhpirot(ji,jj,1) = 0.5 * ( zhpine(ji,jj,1) + zhpine(ji ,jj-1,1) ) |
---|
| 926 | zhpjrot(ji,jj,1) = 0.5 * ( zhpjne(ji,jj,1) + zhpjne(ji-1,jj ,1) ) |
---|
| 927 | ! add to the general momentum trend |
---|
| 928 | ua(ji,jj,1) = ua(ji,jj,1) + zfrot * zhpirot(ji,jj,1) |
---|
| 929 | va(ji,jj,1) = va(ji,jj,1) + zfrot * zhpjrot(ji,jj,1) |
---|
| 930 | END DO |
---|
| 931 | END DO |
---|
| 932 | |
---|
| 933 | ! ----------------- |
---|
| 934 | ! 2. interior value (2=<jk=<jpkm1) |
---|
| 935 | ! ----------------- |
---|
| 936 | ! compute and add to the general trend the pressure gradients along the axes |
---|
| 937 | DO jk = 2, jpkm1 |
---|
| 938 | DO jj = 2, jpjm1 |
---|
| 939 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 940 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 941 | zhpiorg(ji,jj,jk) = zhpiorg(ji,jj,jk-1) & |
---|
| 942 | & + zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,jk ) * rhd(ji+1,jj,jk ) & |
---|
| 943 | & - fse3t(ji ,jj,jk ) * rhd(ji ,jj,jk ) & |
---|
| 944 | & + fse3t(ji+1,jj,jk-1) * rhd(ji+1,jj,jk-1) & |
---|
| 945 | & - fse3t(ji ,jj,jk-1) * rhd(ji ,jj,jk-1) ) |
---|
| 946 | zhpjorg(ji,jj,jk) = zhpjorg(ji,jj,jk-1) & |
---|
| 947 | & + zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,jk ) * rhd(ji,jj+1,jk ) & |
---|
| 948 | & - fse3t(ji,jj ,jk ) * rhd(ji,jj, jk ) & |
---|
| 949 | & + fse3t(ji,jj+1,jk-1) * rhd(ji,jj+1,jk-1) & |
---|
| 950 | & - fse3t(ji,jj ,jk-1) * rhd(ji,jj, jk-1) ) |
---|
| 951 | ! s-coordinate pressure gradient correction |
---|
| 952 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) & |
---|
| 953 | & * ( fsdept(ji+1,jj ,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 954 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 955 | & * ( fsdept(ji ,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 956 | ! add to the general momentum trend |
---|
| 957 | ua(ji,jj,jk) = ua(ji,jj,jk) + zforg*( zhpiorg(ji,jj,jk) + zuap ) |
---|
| 958 | va(ji,jj,jk) = va(ji,jj,jk) + zforg*( zhpjorg(ji,jj,jk) + zvap ) |
---|
| 959 | END DO |
---|
| 960 | END DO |
---|
| 961 | END DO |
---|
| 962 | |
---|
| 963 | ! compute the pressure gradients in the diagonal directions |
---|
| 964 | DO jk = 2, jpkm1 |
---|
| 965 | DO jj = 1, jpjm1 |
---|
| 966 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 967 | zmskd1 = tmask(ji+1,jj+1,jk ) * tmask(ji ,jj,jk ) ! level jk mask in the 1st diagnonal |
---|
| 968 | zmskd1m = tmask(ji+1,jj+1,jk-1) * tmask(ji ,jj,jk-1) ! level jk-1 " " |
---|
| 969 | zmskd2 = tmask(ji ,jj+1,jk ) * tmask(ji+1,jj,jk ) ! level jk mask in the 2nd diagnonal |
---|
| 970 | zmskd2m = tmask(ji ,jj+1,jk-1) * tmask(ji+1,jj,jk-1) ! level jk-1 " " |
---|
| 971 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 972 | zhpitra(ji,jj,jk) = zhpitra(ji,jj,jk-1) & |
---|
| 973 | & + zdistr(ji,jj) * zmskd1 * ( fse3t(ji+1,jj+1,jk ) * rhd(ji+1,jj+1,jk) & |
---|
| 974 | & -fse3t(ji ,jj ,jk ) * rhd(ji ,jj ,jk) ) & |
---|
| 975 | & + zdistr(ji,jj) * zmskd1m * ( fse3t(ji+1,jj+1,jk-1) * rhd(ji+1,jj+1,jk-1) & |
---|
| 976 | & -fse3t(ji ,jj ,jk-1) * rhd(ji ,jj ,jk-1) ) |
---|
| 977 | zhpjtra(ji,jj,jk) = zhpjtra(ji,jj,jk-1) & |
---|
| 978 | & + zdistr(ji,jj) * zmskd2 * ( fse3t(ji ,jj+1,jk ) * rhd(ji ,jj+1,jk) & |
---|
| 979 | & -fse3t(ji+1,jj ,jk ) * rhd(ji+1,jj, jk) ) & |
---|
| 980 | & + zdistr(ji,jj) * zmskd2m * ( fse3t(ji ,jj+1,jk-1) * rhd(ji ,jj+1,jk-1) & |
---|
| 981 | & -fse3t(ji+1,jj ,jk-1) * rhd(ji+1,jj, jk-1) ) |
---|
| 982 | ! s-coordinate pressure gradient correction |
---|
| 983 | zuap = - zdistr(ji,jj) * zmskd1 * ( rhd (ji+1,jj+1,jk) + rhd (ji ,jj,jk) ) & |
---|
| 984 | & * ( fsdept(ji+1,jj+1,jk) - fsdept(ji ,jj,jk) ) |
---|
| 985 | zvap = - zdistr(ji,jj) * zmskd2 * ( rhd (ji ,jj+1,jk) + rhd (ji+1,jj,jk) ) & |
---|
| 986 | & * ( fsdept(ji ,jj+1,jk) - fsdept(ji+1,jj,jk) ) |
---|
| 987 | ! back rotation |
---|
| 988 | zhpine(ji,jj,jk) = zcosa(ji,jj) * ( zhpitra(ji,jj,jk) + zuap ) & |
---|
| 989 | & - zsina(ji,jj) * ( zhpjtra(ji,jj,jk) + zvap ) |
---|
| 990 | zhpjne(ji,jj,jk) = zsina(ji,jj) * ( zhpitra(ji,jj,jk) + zuap ) & |
---|
| 991 | & + zcosa(ji,jj) * ( zhpjtra(ji,jj,jk) + zvap ) |
---|
| 992 | END DO |
---|
| 993 | END DO |
---|
| 994 | END DO |
---|
| 995 | |
---|
| 996 | ! interpolate and add to the general trend |
---|
| 997 | DO jk = 2, jpkm1 |
---|
| 998 | DO jj = 2, jpjm1 |
---|
| 999 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1000 | ! averaging |
---|
| 1001 | zhpirot(ji,jj,jk) = 0.5 * ( zhpine(ji,jj,jk) + zhpine(ji ,jj-1,jk) ) |
---|
| 1002 | zhpjrot(ji,jj,jk) = 0.5 * ( zhpjne(ji,jj,jk) + zhpjne(ji-1,jj ,jk) ) |
---|
| 1003 | ! add to the general momentum trend |
---|
| 1004 | ua(ji,jj,jk) = ua(ji,jj,jk) + zfrot * zhpirot(ji,jj,jk) |
---|
| 1005 | va(ji,jj,jk) = va(ji,jj,jk) + zfrot * zhpjrot(ji,jj,jk) |
---|
| 1006 | END DO |
---|
| 1007 | END DO |
---|
| 1008 | END DO |
---|
[503] | 1009 | ! |
---|
[2715] | 1010 | IF( wrk_not_released(2, 1,2,3) .OR. & |
---|
| 1011 | wrk_not_released(3, 1,2,3,4,5,6,7,8) ) CALL ctl_stop('dyn:hpg_rot: failed to release workspace arrays') |
---|
| 1012 | ! |
---|
[455] | 1013 | END SUBROUTINE hpg_rot |
---|
| 1014 | |
---|
[2873] | 1015 | |
---|
| 1016 | SUBROUTINE hpg_prj( kt ) |
---|
| 1017 | !!--------------------------------------------------------------------- |
---|
| 1018 | !! *** ROUTINE hpg_prj *** |
---|
| 1019 | !! |
---|
| 1020 | !! ** Method : s-coordinate case. |
---|
| 1021 | !! Reformulate the horizontal hydrostatical pressure gradient |
---|
| 1022 | !! term using Pressure Jacobian. A new correction term |
---|
| 1023 | !! is developed to eliminate the sigma-coordinate error. |
---|
| 1024 | !! |
---|
| 1025 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 1026 | !! - Save the trend (l_trddyn=T) |
---|
| 1027 | !! |
---|
| 1028 | !!---------------------------------------------------------------------- |
---|
| 1029 | |
---|
| 1030 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
---|
| 1031 | USE oce , ONLY: fsde3w_tmp => ta ! (ta,sa) used as 3D workspace |
---|
| 1032 | USE oce , ONLY: rhd_tmp => sa |
---|
| 1033 | USE wrk_nemo, ONLY: zhpi => wrk_3d_3 |
---|
| 1034 | USE wrk_nemo, ONLY: zu => wrk_3d_4 |
---|
| 1035 | USE wrk_nemo, ONLY: zv => wrk_3d_5 |
---|
| 1036 | USE wrk_nemo, ONLY: fsp => wrk_3d_6 |
---|
| 1037 | USE wrk_nemo, ONLY: xsp => wrk_3d_7 |
---|
| 1038 | USE wrk_nemo, ONLY: asp => wrk_3d_8 |
---|
| 1039 | USE wrk_nemo, ONLY: bsp => wrk_3d_9 |
---|
| 1040 | USE wrk_nemo, ONLY: csp => wrk_3d_10 |
---|
| 1041 | USE wrk_nemo, ONLY: dsp => wrk_3d_11 |
---|
| 1042 | !! |
---|
| 1043 | !!---------------------------------------------------------------------- |
---|
| 1044 | !! |
---|
| 1045 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 1046 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 1047 | !! |
---|
| 1048 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 1049 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
| 1050 | !! |
---|
| 1051 | !! The local varialbes for the correction term |
---|
[3080] | 1052 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 1053 | REAL(wp) :: zuijk, zvijk, pwes, pwed, pnss, pnsd, deps |
---|
| 1054 | REAL(wp) :: rhdt1 |
---|
[2873] | 1055 | REAL(wp) :: dpdx1, dpdx2, dpdy1, dpdy2 |
---|
| 1056 | INTEGER :: bhitwe, bhitns |
---|
| 1057 | !!---------------------------------------------------------------------- |
---|
| 1058 | |
---|
| 1059 | IF( wrk_in_use(3, 3,4,5,6,7,8,9,10,11) ) THEN |
---|
| 1060 | CALL ctl_stop('dyn:hpg_prj: requested workspace arrays unavailable') ; RETURN |
---|
| 1061 | ENDIF |
---|
| 1062 | |
---|
| 1063 | IF( kt == nit000 ) THEN |
---|
| 1064 | IF(lwp) WRITE(numout,*) |
---|
| 1065 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 1066 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
| 1067 | ENDIF |
---|
| 1068 | |
---|
| 1069 | !!---------------------------------------------------------------------- |
---|
| 1070 | ! Local constant initialization |
---|
| 1071 | zcoef0 = - grav |
---|
| 1072 | znad = 0.0_wp |
---|
| 1073 | IF(lk_vvl) znad = 1._wp |
---|
| 1074 | |
---|
| 1075 | ! Save fsde3w and rhd |
---|
| 1076 | fsde3w_tmp(:,:,:) = fsde3w(:,:,:) |
---|
| 1077 | rhd_tmp(:,:,:) = rhd(:,:,:) |
---|
| 1078 | |
---|
| 1079 | ! Clean 3-D work arraies |
---|
| 1080 | zhpi(:,:,:) = 0. |
---|
| 1081 | |
---|
| 1082 | !how to add vector opt.? N.B., jpi&jpi rather than jpim1&jpjm1 are needed here |
---|
| 1083 | |
---|
| 1084 | ! Preparing vertical density profile for hybrid-sco coordinate |
---|
| 1085 | DO jj = 1, jpj |
---|
| 1086 | DO ji = 1, jpi |
---|
| 1087 | jk = mbathy(ji,jj) |
---|
| 1088 | IF(jk <= 0) THEN; rhd(ji,jj,:) = 0._wp |
---|
| 1089 | ELSE IF(jk == 1) THEN; rhd(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 1090 | ELSE IF(jk < jpkm1) THEN |
---|
| 1091 | DO jkk = jk+1, jpk |
---|
| 1092 | rhd(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1),& |
---|
| 1093 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
| 1094 | END DO |
---|
| 1095 | END IF |
---|
| 1096 | END DO |
---|
| 1097 | END DO |
---|
| 1098 | |
---|
| 1099 | DO jj = 1, jpj |
---|
| 1100 | DO ji = 1, jpi |
---|
| 1101 | fsde3w(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) |
---|
| 1102 | fsde3w(ji,jj,1) = fsde3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 1103 | DO jk = 2, jpk |
---|
| 1104 | fsde3w(ji,jj,jk) = fsde3w(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 1105 | END DO |
---|
| 1106 | END DO |
---|
| 1107 | END DO |
---|
| 1108 | |
---|
| 1109 | DO jk = 1, jpkm1 |
---|
| 1110 | DO jj = 1, jpj |
---|
| 1111 | DO ji = 1, jpi |
---|
| 1112 | fsp(ji,jj,jk) = rhd(ji,jj,jk) |
---|
| 1113 | xsp(ji,jj,jk) = fsde3w(ji,jj,jk) |
---|
| 1114 | END DO |
---|
| 1115 | END DO |
---|
| 1116 | END DO |
---|
| 1117 | |
---|
[3068] | 1118 | ! ! Construct the vertical density profile with the |
---|
| 1119 | ! !Constrained cubic spline interpolation |
---|
[2873] | 1120 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
| 1121 | |
---|
[3068] | 1122 | ! Calculate the hydrostatic pressure at T(ji,jj,1) |
---|
[2873] | 1123 | DO jj = 2, jpj |
---|
| 1124 | DO ji = 2, jpi |
---|
| 1125 | rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & |
---|
| 1126 | bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & |
---|
| 1127 | * 0.5_wp * fsde3w(ji,jj,1) |
---|
[3068] | 1128 | rhdt1 = max(rhdt1, 1000._wp - rau0) ! no lighter than fresh water |
---|
| 1129 | |
---|
| 1130 | ! ! assuming linear profile across the top half surface layer |
---|
| 1131 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * rhdt1 |
---|
[2873] | 1132 | END DO |
---|
| 1133 | END DO |
---|
| 1134 | |
---|
| 1135 | ! Calculate the pressure at T(ji,jj,2:jpkm1) |
---|
| 1136 | DO jk = 2, jpkm1 |
---|
| 1137 | DO jj = 2, jpj |
---|
| 1138 | DO ji = 2, jpi |
---|
| 1139 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
| 1140 | integ2(fsde3w(ji,jj,jk-1),fsde3w(ji,jj,jk),& |
---|
| 1141 | asp(ji,jj,jk-1),bsp(ji,jj,jk-1),& |
---|
| 1142 | csp(ji,jj,jk-1),dsp(ji,jj,jk-1)) |
---|
| 1143 | END DO |
---|
| 1144 | END DO |
---|
| 1145 | END DO |
---|
| 1146 | |
---|
| 1147 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
| 1148 | |
---|
| 1149 | DO jj = 2, jpjm1 |
---|
| 1150 | DO ji = 2, jpim1 |
---|
[3079] | 1151 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshu_n(ji,jj) * znad) |
---|
| 1152 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshv_n(ji,jj) * znad) |
---|
[2873] | 1153 | END DO |
---|
| 1154 | END DO |
---|
| 1155 | |
---|
| 1156 | DO jk = 2, jpkm1 |
---|
| 1157 | DO jj = 2, jpjm1 |
---|
| 1158 | DO ji = 2, jpim1 |
---|
[3079] | 1159 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 1160 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
[2873] | 1161 | END DO |
---|
| 1162 | END DO |
---|
| 1163 | END DO |
---|
| 1164 | |
---|
[3079] | 1165 | DO jk = 1, jpkm1 |
---|
| 1166 | DO jj = 2, jpjm1 |
---|
| 1167 | DO ji = 2, jpim1 |
---|
| 1168 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 1169 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 1170 | END DO |
---|
| 1171 | END DO |
---|
| 1172 | END DO |
---|
[2873] | 1173 | |
---|
| 1174 | DO jk = 1, jpkm1 |
---|
| 1175 | DO jj = 2, jpjm1 |
---|
| 1176 | DO ji = 2, jpim1 |
---|
[3068] | 1177 | pwes = 0._wp; pwed = 0._wp |
---|
| 1178 | pnss = 0._wp; pnsd = 0._wp |
---|
[2873] | 1179 | zuijk = zu(ji,jj,jk) |
---|
| 1180 | zvijk = zv(ji,jj,jk) |
---|
| 1181 | |
---|
[3068] | 1182 | !!!!! for u equation |
---|
[3079] | 1183 | IF(jk <= mbku(ji,jj)) THEN |
---|
| 1184 | IF(-fsde3w(ji+1,jj,mbku(ji,jj)) >= -fsde3w(ji,jj,mbku(ji,jj))) THEN |
---|
[3068] | 1185 | jis = ji + 1; jid = ji |
---|
| 1186 | ELSE |
---|
| 1187 | jis = ji; jid = ji +1 |
---|
| 1188 | ENDIF |
---|
[2873] | 1189 | |
---|
[3068] | 1190 | ! !integrate the pressure on the shallow side |
---|
| 1191 | jk1 = jk |
---|
| 1192 | bhitwe = 0 |
---|
[3079] | 1193 | DO WHILE ( -fsde3w(jis,jj,jk1) > zuijk ) |
---|
| 1194 | IF(jk1 == mbku(ji,jj)) THEN |
---|
| 1195 | bhitwe = 1 |
---|
| 1196 | EXIT |
---|
| 1197 | ENDIF |
---|
| 1198 | deps = min(fsde3w(jis,jj,jk1+1), -zuijk) |
---|
[3068] | 1199 | pwes = pwes + & |
---|
[3079] | 1200 | integ2(fsde3w(jis,jj,jk1),deps,& |
---|
[3068] | 1201 | asp(jis,jj,jk1),bsp(jis,jj,jk1),& |
---|
| 1202 | csp(jis,jj,jk1),dsp(jis,jj,jk1)) |
---|
[3079] | 1203 | jk1 = jk1 + 1 |
---|
| 1204 | END DO |
---|
| 1205 | |
---|
| 1206 | IF(bhitwe == 1) THEN |
---|
| 1207 | zuijk = -fsde3w(jis,jj,jk1) |
---|
[3068] | 1208 | ENDIF |
---|
[2873] | 1209 | |
---|
[3068] | 1210 | ! !integrate the pressure on the deep side |
---|
| 1211 | jk1 = jk |
---|
| 1212 | bhitwe = 0 |
---|
[3079] | 1213 | DO WHILE ( -fsde3w(jid,jj,jk1) < zuijk ) |
---|
| 1214 | IF(jk1 == 1) THEN |
---|
| 1215 | bhitwe = 1 |
---|
| 1216 | EXIT |
---|
| 1217 | END IF |
---|
| 1218 | deps = max(fsde3w(jid,jj,jk1-1), -zuijk) |
---|
[3068] | 1219 | pwed = pwed + & |
---|
[3079] | 1220 | integ2(deps,fsde3w(jid,jj,jk1),& |
---|
[3068] | 1221 | asp(jid,jj,jk1-1),bsp(jid,jj,jk1-1),& |
---|
| 1222 | csp(jid,jj,jk1-1),dsp(jid,jj,jk1-1)) |
---|
[3079] | 1223 | jk1 = jk1 - 1 |
---|
| 1224 | END DO |
---|
| 1225 | |
---|
| 1226 | IF(bhitwe == 1) THEN |
---|
[3068] | 1227 | deps = fsde3w(jid,jj,1) + min(zuijk, sshn(jid,jj)*znad) |
---|
| 1228 | rhdt1 = rhd(jid,jj,1) - interp3(fsde3w(jid,jj,1),asp(jid,jj,1), & |
---|
| 1229 | bsp(jid,jj,1),csp(jid,jj,1),dsp(jid,jj,1)) * deps |
---|
| 1230 | rhdt1 = max(rhdt1, 1000._wp - rau0) ! no lighter than fresh water |
---|
| 1231 | pwed = pwed + 0.5_wp * (rhd(jid,jj,1) + rhdt1) * deps |
---|
| 1232 | ENDIF |
---|
[2873] | 1233 | |
---|
| 1234 | |
---|
| 1235 | dpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1236 | IF(lk_vvl) THEN |
---|
[3079] | 1237 | dpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1238 | (REAL(jis-jid, wp) * (pwes + pwed) + (sshn(ji+1,jj)-sshn(ji,jj))) |
---|
[2873] | 1239 | ELSE |
---|
[3079] | 1240 | dpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (pwes + pwed) |
---|
[2873] | 1241 | ENDIF |
---|
| 1242 | |
---|
| 1243 | ua(ji,jj,jk) = ua(ji,jj,jk) + (dpdx1 + dpdx2)*& |
---|
| 1244 | & umask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji+1,jj,jk) |
---|
[3079] | 1245 | ENDIF |
---|
[3068] | 1246 | |
---|
| 1247 | !!!!! for v equation |
---|
[3079] | 1248 | IF(jk <= mbkv(ji,jj)) THEN |
---|
| 1249 | IF(-fsde3w(ji,jj+1,mbkv(ji,jj)) >= -fsde3w(ji,jj,mbkv(ji,jj))) THEN |
---|
[3068] | 1250 | jjs = jj + 1; jjd = jj |
---|
| 1251 | ELSE |
---|
| 1252 | jjs = jj ; jjd = jj + 1 |
---|
| 1253 | ENDIF |
---|
[2873] | 1254 | |
---|
[3068] | 1255 | ! !integrate the pressure on the shallow side |
---|
| 1256 | jk1 = jk |
---|
| 1257 | bhitns = 0 |
---|
[3079] | 1258 | DO WHILE ( -fsde3w(ji,jjs,jk1) > zvijk ) |
---|
| 1259 | IF(jk1 == mbkv(ji,jj)) THEN |
---|
| 1260 | bhitns = 1 |
---|
| 1261 | EXIT |
---|
| 1262 | ENDIF |
---|
| 1263 | deps = min(fsde3w(ji,jjs,jk1+1), -zvijk) |
---|
[3068] | 1264 | pnss = pnss + & |
---|
[3079] | 1265 | integ2(fsde3w(ji,jjs,jk1),deps,& |
---|
[3068] | 1266 | asp(ji,jjs,jk1),bsp(ji,jjs,jk1),& |
---|
| 1267 | csp(ji,jjs,jk1),dsp(ji,jjs,jk1)) |
---|
[3079] | 1268 | jk1 = jk1 + 1 |
---|
| 1269 | END DO |
---|
| 1270 | |
---|
| 1271 | IF(bhitns == 1) THEN |
---|
| 1272 | zvijk = -fsde3w(ji,jjs,jk1) |
---|
[3068] | 1273 | ENDIF |
---|
[2873] | 1274 | |
---|
[3068] | 1275 | ! !integrate the pressure on the deep side |
---|
| 1276 | jk1 = jk |
---|
| 1277 | bhitns = 0 |
---|
[3079] | 1278 | DO WHILE ( -fsde3w(ji,jjd,jk1) < zvijk ) |
---|
| 1279 | IF(jk1 == 1) THEN |
---|
| 1280 | bhitns = 1 |
---|
| 1281 | EXIT |
---|
| 1282 | END IF |
---|
| 1283 | deps = max(fsde3w(ji,jjd,jk1-1), -zvijk) |
---|
[3068] | 1284 | pnsd = pnsd + & |
---|
[3079] | 1285 | integ2(deps,fsde3w(ji,jjd,jk1),& |
---|
[3068] | 1286 | asp(ji,jjd,jk1-1),bsp(ji,jjd,jk1-1),& |
---|
| 1287 | csp(ji,jjd,jk1-1),dsp(ji,jjd,jk1-1)) |
---|
[3079] | 1288 | jk1 = jk1 - 1 |
---|
| 1289 | END DO |
---|
| 1290 | |
---|
| 1291 | IF(bhitns == 1) THEN |
---|
[3068] | 1292 | deps = fsde3w(ji,jjd,1) + min(zvijk, sshn(ji,jjd)*znad) |
---|
| 1293 | rhdt1 = rhd(ji,jjd,1) - interp3(fsde3w(ji,jjd,1),asp(ji,jjd,1), & |
---|
| 1294 | bsp(ji,jjd,1),csp(ji,jjd,1),dsp(ji,jjd,1)) * deps |
---|
| 1295 | rhdt1 = max(rhdt1, 1000._wp - rau0) ! no lighter than fresh water |
---|
| 1296 | pnsd = pnsd + 0.5_wp * (rhd(ji,jjd,1) + rhdt1) * deps |
---|
| 1297 | ENDIF |
---|
[2873] | 1298 | |
---|
| 1299 | |
---|
[3068] | 1300 | dpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1301 | if(lk_vvl) then |
---|
[3079] | 1302 | dpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
| 1303 | (REAL(jjs-jjd, wp) * (pnss + pnsd) + (sshn(ji,jj+1)-sshn(ji,jj))) |
---|
[3068] | 1304 | else |
---|
[3079] | 1305 | dpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (pnss + pnsd ) |
---|
[3068] | 1306 | end if |
---|
[2873] | 1307 | |
---|
[3068] | 1308 | va(ji,jj,jk) = va(ji,jj,jk) + (dpdy1 + dpdy2)*& |
---|
| 1309 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
[3079] | 1310 | ENDIF |
---|
[2873] | 1311 | |
---|
| 1312 | |
---|
| 1313 | END DO |
---|
| 1314 | END DO |
---|
| 1315 | END DO |
---|
| 1316 | |
---|
| 1317 | ! Restore fsde3w and rhd |
---|
| 1318 | fsde3w(:,:,:) = fsde3w_tmp(:,:,:) |
---|
| 1319 | rhd(:,:,:) = rhd_tmp(:,:,:) |
---|
| 1320 | |
---|
| 1321 | ! |
---|
| 1322 | IF( wrk_not_released(3, 3,4,5,6,7,8,9,10,11) ) & |
---|
| 1323 | CALL ctl_stop('dyn:hpg_prj: failed to release workspace arrays') |
---|
| 1324 | ! |
---|
| 1325 | END SUBROUTINE hpg_prj |
---|
| 1326 | |
---|
| 1327 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1328 | !!---------------------------------------------------------------------- |
---|
| 1329 | !! *** ROUTINE cspline *** |
---|
| 1330 | !! |
---|
| 1331 | !! ** Purpose : constrained cubic spline interpolation |
---|
| 1332 | !! |
---|
| 1333 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
| 1334 | !! Reference: K.W. Brodlie, A review of mehtods for curve and function |
---|
| 1335 | !! drawing, 1980 |
---|
| 1336 | !! |
---|
| 1337 | !!---------------------------------------------------------------------- |
---|
| 1338 | IMPLICIT NONE |
---|
| 1339 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
| 1340 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
| 1341 | ! the interpoated function |
---|
| 1342 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
| 1343 | ! 2: Linear |
---|
| 1344 | |
---|
| 1345 | ! Local Variables |
---|
| 1346 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1347 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1348 | REAL(wp) :: df1, df2, ddf1, ddf2, tmp1, tmp2, dxtmp |
---|
| 1349 | REAL(wp) :: dxtmp1, dxtmp2, alpha |
---|
| 1350 | REAL(wp) :: df(size(fsp,3)) |
---|
| 1351 | !!---------------------------------------------------------------------- |
---|
| 1352 | |
---|
| 1353 | jpi = size(fsp,1) |
---|
| 1354 | jpj = size(fsp,2) |
---|
| 1355 | jpkm1 = size(fsp,3) - 1 |
---|
| 1356 | |
---|
| 1357 | ! Clean output arrays |
---|
| 1358 | asp = 0.0_wp |
---|
| 1359 | bsp = 0.0_wp |
---|
| 1360 | csp = 0.0_wp |
---|
| 1361 | dsp = 0.0_wp |
---|
| 1362 | |
---|
| 1363 | |
---|
| 1364 | Do ji = 1, jpi |
---|
| 1365 | Do jj = 1, jpj |
---|
| 1366 | |
---|
| 1367 | If (polynomial_type == 1) Then !Constrained Cubic Spline |
---|
| 1368 | Do jk = 2, jpkm1-1 |
---|
| 1369 | dxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1370 | dxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
| 1371 | df1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / dxtmp1 |
---|
| 1372 | df2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / dxtmp2 |
---|
| 1373 | |
---|
| 1374 | alpha = ( dxtmp1 + 2._wp * dxtmp2 ) / ( dxtmp1 + dxtmp2 ) / 3._wp |
---|
| 1375 | |
---|
| 1376 | If(df1 * df2 <= 0._wp) Then |
---|
| 1377 | df(jk) = 0._wp |
---|
| 1378 | Else |
---|
| 1379 | df(jk) = df1 * df2 / ( ( 1._wp - alpha ) * df1 + alpha * df2 ) |
---|
| 1380 | End If |
---|
| 1381 | End Do |
---|
| 1382 | |
---|
| 1383 | df(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - & |
---|
| 1384 | & 0.5_wp * df(2) |
---|
| 1385 | df(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1386 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1387 | & 0.5_wp * df(jpkm1 - 1) |
---|
| 1388 | |
---|
| 1389 | Do jk = 1, jpkm1 - 1 |
---|
| 1390 | dxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
| 1391 | tmp1 = (df(jk+1) + 2._wp * df(jk)) / dxtmp |
---|
| 1392 | tmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / dxtmp / dxtmp |
---|
| 1393 | ddf1 = -2._wp * tmp1 + tmp2 |
---|
| 1394 | tmp1 = (2._wp * df(jk+1) + df(jk)) / dxtmp |
---|
| 1395 | ddf2 = 2._wp * tmp1 - tmp2 |
---|
| 1396 | |
---|
| 1397 | dsp(ji,jj,jk) = (ddf2 - ddf1) / 6._wp / dxtmp |
---|
| 1398 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * ddf1 - xsp(ji,jj,jk)*ddf2 ) / 2._wp / dxtmp |
---|
| 1399 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / dxtmp - & |
---|
| 1400 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1401 | & dsp(ji,jj,jk) * ( xsp(ji,jj,jk+1)**2 + & |
---|
| 1402 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk) + & |
---|
| 1403 | & xsp(ji,jj,jk)**2 ) |
---|
| 1404 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) - & |
---|
| 1405 | & csp(ji,jj,jk) * xsp(ji,jj,jk)**2 - & |
---|
| 1406 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)**3 |
---|
| 1407 | End Do |
---|
| 1408 | |
---|
| 1409 | Else If (polynomial_type == 2) Then !Linear |
---|
| 1410 | |
---|
| 1411 | Do jk = 1, jpkm1-1 |
---|
| 1412 | dxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
| 1413 | tmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
| 1414 | |
---|
| 1415 | dsp(ji,jj,jk) = 0._wp |
---|
| 1416 | csp(ji,jj,jk) = 0._wp |
---|
| 1417 | bsp(ji,jj,jk) = tmp1 / dxtmp |
---|
| 1418 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1419 | End Do |
---|
| 1420 | |
---|
| 1421 | Else |
---|
| 1422 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1423 | End If |
---|
| 1424 | |
---|
| 1425 | End Do |
---|
| 1426 | End Do |
---|
| 1427 | |
---|
| 1428 | End Subroutine cspline |
---|
| 1429 | |
---|
| 1430 | |
---|
| 1431 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
| 1432 | !!---------------------------------------------------------------------- |
---|
| 1433 | !! *** ROUTINE interp1 *** |
---|
| 1434 | !! |
---|
| 1435 | !! ** Purpose : 1-d linear interpolation |
---|
| 1436 | !! |
---|
| 1437 | !! ** Method : |
---|
| 1438 | !! interpolation is straigt forward |
---|
| 1439 | !! extrapolation is also permitted (no value limit) |
---|
| 1440 | !! |
---|
| 1441 | !! H.Liu, Jan 2009, POL |
---|
| 1442 | !!---------------------------------------------------------------------- |
---|
| 1443 | IMPLICIT NONE |
---|
| 1444 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
| 1445 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1446 | REAL(wp) :: deltx |
---|
| 1447 | !!---------------------------------------------------------------------- |
---|
| 1448 | |
---|
| 1449 | deltx = xr - xl |
---|
| 1450 | IF(abs(deltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1451 | f = 0.5_wp * (fl + fr) |
---|
| 1452 | ELSE |
---|
| 1453 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / deltx |
---|
| 1454 | END IF |
---|
| 1455 | |
---|
| 1456 | END FUNCTION interp1 |
---|
| 1457 | |
---|
| 1458 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
| 1459 | !!---------------------------------------------------------------------- |
---|
| 1460 | !! *** ROUTINE interp1 *** |
---|
| 1461 | !! |
---|
| 1462 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
| 1463 | !! |
---|
| 1464 | !! ** Method : cubic spline interpolation |
---|
| 1465 | !! |
---|
| 1466 | !!---------------------------------------------------------------------- |
---|
| 1467 | IMPLICIT NONE |
---|
| 1468 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
| 1469 | REAL(wp) :: f ! value from the interpolation |
---|
| 1470 | !!---------------------------------------------------------------------- |
---|
| 1471 | |
---|
| 1472 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
| 1473 | |
---|
| 1474 | END FUNCTION interp2 |
---|
| 1475 | |
---|
| 1476 | |
---|
| 1477 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
| 1478 | !!---------------------------------------------------------------------- |
---|
| 1479 | !! *** ROUTINE interp1 *** |
---|
| 1480 | !! |
---|
| 1481 | !! ** Purpose : deriavtive of a cubic spline function |
---|
| 1482 | !! |
---|
| 1483 | !! ** Method : |
---|
| 1484 | !! |
---|
| 1485 | !!---------------------------------------------------------------------- |
---|
| 1486 | IMPLICIT NONE |
---|
| 1487 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
| 1488 | REAL(wp) :: f ! value from the interpolation |
---|
| 1489 | !!---------------------------------------------------------------------- |
---|
| 1490 | |
---|
| 1491 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1492 | |
---|
| 1493 | END FUNCTION interp3 |
---|
| 1494 | |
---|
| 1495 | |
---|
| 1496 | FUNCTION integ2(xl, xr, a, b, c, d) RESULT(f) |
---|
| 1497 | !!---------------------------------------------------------------------- |
---|
| 1498 | !! *** ROUTINE interp1 *** |
---|
| 1499 | !! |
---|
| 1500 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1501 | !! |
---|
| 1502 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1503 | !! |
---|
| 1504 | !!---------------------------------------------------------------------- |
---|
| 1505 | IMPLICIT NONE |
---|
| 1506 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1507 | REAL(wp) :: a1, a2,a3 |
---|
| 1508 | REAL(wp) :: f ! integration result |
---|
| 1509 | !!---------------------------------------------------------------------- |
---|
| 1510 | |
---|
| 1511 | a1 = 0.5_wp * b |
---|
| 1512 | a2 = c / 3.0_wp |
---|
| 1513 | a3 = 0.25_wp * d |
---|
| 1514 | |
---|
| 1515 | f = xr * ( a + xr * ( a1 + xr * ( a2 + a3 * xr ) ) ) - & |
---|
| 1516 | & xl * ( a + xl * ( a1 + xl * ( a2 + a3 * xl ) ) ) |
---|
| 1517 | |
---|
| 1518 | END FUNCTION integ2 |
---|
| 1519 | |
---|
| 1520 | |
---|
[3] | 1521 | !!====================================================================== |
---|
| 1522 | END MODULE dynhpg |
---|