[3] | 1 | MODULE dynhpg |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE dynhpg *** |
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| 4 | !! Ocean dynamics: hydrostatic pressure gradient trend |
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| 5 | !!====================================================================== |
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[2528] | 6 | !! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code |
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| 7 | !! 5.0 ! 1991-11 (G. Madec) |
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| 8 | !! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates |
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| 9 | !! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg |
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| 10 | !! 8.5 ! 2002-07 (G. Madec) F90: Free form and module |
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| 11 | !! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code |
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| 12 | !! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options |
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[3764] | 13 | !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot |
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[2528] | 14 | !! - ! 2005-11 (G. Madec) style & small optimisation |
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| 15 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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[3294] | 16 | !! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates |
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| 17 | !! ! (A. Coward) suppression of hel, wdj and rot options |
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[5120] | 18 | !! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity |
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[503] | 19 | !!---------------------------------------------------------------------- |
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[3] | 20 | |
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| 21 | !!---------------------------------------------------------------------- |
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[455] | 22 | !! dyn_hpg : update the momentum trend with the now horizontal |
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[3] | 23 | !! gradient of the hydrostatic pressure |
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[2528] | 24 | !! dyn_hpg_init : initialisation and control of options |
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[455] | 25 | !! hpg_zco : z-coordinate scheme |
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| 26 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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| 27 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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[5120] | 28 | !! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf |
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[455] | 29 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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[3294] | 30 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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[3] | 31 | !!---------------------------------------------------------------------- |
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| 32 | USE oce ! ocean dynamics and tracers |
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[4990] | 33 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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[3] | 34 | USE dom_oce ! ocean space and time domain |
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| 35 | USE phycst ! physical constants |
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[4990] | 36 | USE trd_oce ! trends: ocean variables |
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| 37 | USE trddyn ! trend manager: dynamics |
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| 38 | ! |
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[2715] | 39 | USE in_out_manager ! I/O manager |
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[258] | 40 | USE prtctl ! Print control |
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[4990] | 41 | USE lbclnk ! lateral boundary condition |
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[2715] | 42 | USE lib_mpp ! MPP library |
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[4990] | 43 | USE eosbn2 ! compute density |
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[3294] | 44 | USE wrk_nemo ! Memory Allocation |
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| 45 | USE timing ! Timing |
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[6278] | 46 | USE biaspar ! bias correction variables |
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[3] | 47 | |
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| 48 | IMPLICIT NONE |
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| 49 | PRIVATE |
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| 50 | |
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[2528] | 51 | PUBLIC dyn_hpg ! routine called by step module |
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| 52 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 53 | |
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[4147] | 54 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 55 | LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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| 56 | LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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| 57 | LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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| 58 | LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 59 | LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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[5120] | 60 | LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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[4147] | 61 | LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag |
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[455] | 62 | |
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[3764] | 63 | INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
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[455] | 64 | |
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[3] | 65 | !! * Substitutions |
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| 66 | # include "domzgr_substitute.h90" |
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| 67 | # include "vectopt_loop_substitute.h90" |
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| 68 | !!---------------------------------------------------------------------- |
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[2528] | 69 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 70 | !! $Id$ |
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| 71 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 72 | !!---------------------------------------------------------------------- |
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| 73 | CONTAINS |
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| 74 | |
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| 75 | SUBROUTINE dyn_hpg( kt ) |
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| 76 | !!--------------------------------------------------------------------- |
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| 77 | !! *** ROUTINE dyn_hpg *** |
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| 78 | !! |
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[3764] | 79 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 80 | !! using the scheme defined in the namelist |
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[3764] | 81 | !! |
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[455] | 82 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[4990] | 83 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 84 | !!---------------------------------------------------------------------- |
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| 85 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[3294] | 86 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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[6328] | 87 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rhd_st ! tmp density storage for pressure corr |
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| 88 | REAL(wp), DIMENSION(jpi,jpj) :: z_gru_st ! tmp ua trends storage for pressure corr |
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| 89 | REAL(wp), DIMENSION(jpi,jpj) :: z_grv_st ! tmp va trends storage for pressure corr |
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[455] | 90 | !!---------------------------------------------------------------------- |
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[2528] | 91 | ! |
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[3294] | 92 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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[2715] | 93 | ! |
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[503] | 94 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[3294] | 95 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 96 | ztrdu(:,:,:) = ua(:,:,:) |
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| 97 | ztrdv(:,:,:) = va(:,:,:) |
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| 98 | ENDIF |
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[2528] | 99 | ! |
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[6278] | 100 | IF ( ln_bias .AND. ln_bias_pc_app ) THEN |
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[7652] | 101 | IF(lwp) THEN |
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[7657] | 102 | WRITE(numout,*) " ! store orig density, use pressure corrected density using gru_pc and grv_pc" |
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[7652] | 103 | ENDIF |
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[6278] | 104 | z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density |
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| 105 | rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density |
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| 106 | z_gru_st(:,:) = gru(:,:) |
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| 107 | gru(:,:) = gru_pc(:,:) |
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| 108 | z_grv_st(:,:) = grv(:,:) |
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| 109 | grv(:,:) = grv_pc(:,:) |
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| 110 | ENDIF |
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| 111 | ! |
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[3294] | 112 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[7657] | 113 | IF(lwp) THEN |
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| 114 | WRITE(numout,*) " computing pressure gradient with nhpg = ",nhpg |
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| 115 | ENDIF |
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[503] | 116 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 117 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 118 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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[3294] | 119 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 120 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[5120] | 121 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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[455] | 122 | END SELECT |
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[2528] | 123 | ! |
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[503] | 124 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 125 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 126 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[4990] | 127 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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[3294] | 128 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 129 | ENDIF |
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[503] | 130 | ! |
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| 131 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 132 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 133 | ! |
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[6278] | 134 | IF ( ln_bias .AND. ln_bias_pc_app ) THEN |
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[7652] | 135 | IF(lwp) THEN |
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| 136 | WRITE(numout,*) " ! restore original density" |
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| 137 | ENDIF |
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[6278] | 138 | rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density |
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| 139 | gru(:,:) = z_gru_st(:,:) |
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| 140 | grv(:,:) = z_grv_st(:,:) |
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| 141 | ENDIF |
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| 142 | ! |
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[3294] | 143 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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[2715] | 144 | ! |
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[455] | 145 | END SUBROUTINE dyn_hpg |
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| 146 | |
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| 147 | |
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[2528] | 148 | SUBROUTINE dyn_hpg_init |
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[455] | 149 | !!---------------------------------------------------------------------- |
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[2528] | 150 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 151 | !! |
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| 152 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 153 | !! computation and consistency control |
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| 154 | !! |
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[1601] | 155 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 156 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 157 | !!---------------------------------------------------------------------- |
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| 158 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 159 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 160 | !! |
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[3294] | 161 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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[5120] | 162 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp |
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[455] | 163 | !!---------------------------------------------------------------------- |
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[2528] | 164 | ! |
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[4147] | 165 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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| 166 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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| 167 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
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| 168 | |
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| 169 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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| 170 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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| 171 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
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[4624] | 172 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 173 | ! |
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| 174 | IF(lwp) THEN ! Control print |
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[455] | 175 | WRITE(numout,*) |
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[2528] | 176 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 177 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 178 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 179 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 180 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 181 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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[5120] | 182 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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[1601] | 183 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 184 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[1601] | 185 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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[455] | 186 | ENDIF |
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[2528] | 187 | ! |
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[3294] | 188 | IF( ln_hpg_djc ) & |
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| 189 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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| 190 | & currently disabled (bugs under investigation). Please select & |
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| 191 | & either ln_hpg_sco or ln_hpg_prj instead') |
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[2528] | 192 | ! |
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[5120] | 193 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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[3294] | 194 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
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| 195 | & the standard jacobian formulation hpg_sco or & |
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| 196 | & the pressure jacobian formulation hpg_prj') |
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[5120] | 197 | |
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| 198 | IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) & |
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| 199 | & CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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| 200 | IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) & |
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| 201 | & CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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[3294] | 202 | ! |
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[503] | 203 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 204 | IF( ln_hpg_zco ) nhpg = 0 |
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| 205 | IF( ln_hpg_zps ) nhpg = 1 |
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| 206 | IF( ln_hpg_sco ) nhpg = 2 |
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[3294] | 207 | IF( ln_hpg_djc ) nhpg = 3 |
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| 208 | IF( ln_hpg_prj ) nhpg = 4 |
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[5120] | 209 | IF( ln_hpg_isf ) nhpg = 5 |
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[2528] | 210 | ! |
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[3294] | 211 | ! ! Consistency check |
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[3764] | 212 | ioptio = 0 |
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[455] | 213 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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| 214 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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| 215 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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| 216 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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[3294] | 217 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[5120] | 218 | IF( ln_hpg_isf ) ioptio = ioptio + 1 |
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[2715] | 219 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[5120] | 220 | ! |
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| 221 | ! initialisation of ice load |
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| 222 | riceload(:,:)=0.0 |
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[503] | 223 | ! |
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[2528] | 224 | END SUBROUTINE dyn_hpg_init |
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[455] | 225 | |
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| 226 | |
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| 227 | SUBROUTINE hpg_zco( kt ) |
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| 228 | !!--------------------------------------------------------------------- |
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| 229 | !! *** ROUTINE hpg_zco *** |
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| 230 | !! |
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| 231 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 232 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 233 | !! is computed by taking the vertical integral of the in-situ |
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| 234 | !! density gradient along the model level from the suface to that |
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| 235 | !! level: zhpi = grav ..... |
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| 236 | !! zhpj = grav ..... |
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[3] | 237 | !! add it to the general momentum trend (ua,va). |
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[455] | 238 | !! ua = ua - 1/e1u * zhpi |
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| 239 | !! va = va - 1/e2v * zhpj |
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[3764] | 240 | !! |
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[3] | 241 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 242 | !!---------------------------------------------------------------------- |
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| 243 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 244 | !! |
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| 245 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 246 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3764] | 247 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 248 | !!---------------------------------------------------------------------- |
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[3764] | 249 | ! |
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[3294] | 250 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 251 | ! |
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[3] | 252 | IF( kt == nit000 ) THEN |
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| 253 | IF(lwp) WRITE(numout,*) |
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[455] | 254 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 255 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 256 | ENDIF |
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| 257 | |
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[3764] | 258 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
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| 259 | |
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[455] | 260 | ! Surface value |
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[3] | 261 | DO jj = 2, jpjm1 |
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| 262 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 263 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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| 264 | ! hydrostatic pressure gradient |
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| 265 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 266 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 267 | ! add to the general momentum trend |
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[455] | 268 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
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| 269 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
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| 270 | END DO |
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| 271 | END DO |
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[3294] | 272 | |
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[503] | 273 | ! |
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[455] | 274 | ! interior value (2=<jk=<jpkm1) |
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[3] | 275 | DO jk = 2, jpkm1 |
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[455] | 276 | DO jj = 2, jpjm1 |
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[3] | 277 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[455] | 278 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
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| 279 | ! hydrostatic pressure gradient |
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| 280 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
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| 281 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
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| 282 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
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| 283 | |
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| 284 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
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| 285 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
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| 286 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
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[3] | 287 | ! add to the general momentum trend |
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[455] | 288 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
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| 289 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
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[3] | 290 | END DO |
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| 291 | END DO |
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| 292 | END DO |
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[503] | 293 | ! |
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[3294] | 294 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 295 | ! |
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[455] | 296 | END SUBROUTINE hpg_zco |
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[216] | 297 | |
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[3] | 298 | |
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[455] | 299 | SUBROUTINE hpg_zps( kt ) |
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[3] | 300 | !!--------------------------------------------------------------------- |
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[455] | 301 | !! *** ROUTINE hpg_zps *** |
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[3764] | 302 | !! |
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[455] | 303 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
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[3764] | 304 | !! |
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[3] | 305 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[3764] | 306 | !!---------------------------------------------------------------------- |
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[503] | 307 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 308 | !! |
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| 309 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 310 | INTEGER :: iku, ikv ! temporary integers |
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| 311 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
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[3764] | 312 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 313 | !!---------------------------------------------------------------------- |
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[3294] | 314 | ! |
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| 315 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 316 | ! |
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[3] | 317 | IF( kt == nit000 ) THEN |
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| 318 | IF(lwp) WRITE(numout,*) |
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[455] | 319 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
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[503] | 320 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
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[3] | 321 | ENDIF |
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| 322 | |
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[3294] | 323 | |
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[503] | 324 | ! Local constant initialization |
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[2528] | 325 | zcoef0 = - grav * 0.5_wp |
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[3] | 326 | |
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[2528] | 327 | ! Surface value (also valid in partial step case) |
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[3] | 328 | DO jj = 2, jpjm1 |
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| 329 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[170] | 330 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
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[3] | 331 | ! hydrostatic pressure gradient |
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[455] | 332 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
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| 333 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
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[3] | 334 | ! add to the general momentum trend |
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| 335 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 336 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 337 | END DO |
---|
| 338 | END DO |
---|
| 339 | |
---|
[3294] | 340 | |
---|
[503] | 341 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 342 | DO jk = 2, jpkm1 |
---|
| 343 | DO jj = 2, jpjm1 |
---|
| 344 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 345 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
---|
[3] | 346 | ! hydrostatic pressure gradient |
---|
| 347 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
[455] | 348 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
| 349 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
---|
[3] | 350 | |
---|
| 351 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
[455] | 352 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
| 353 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
---|
[3] | 354 | ! add to the general momentum trend |
---|
| 355 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 356 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[455] | 357 | END DO |
---|
[3] | 358 | END DO |
---|
| 359 | END DO |
---|
| 360 | |
---|
[3294] | 361 | |
---|
[2528] | 362 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
---|
[3] | 363 | DO jj = 2, jpjm1 |
---|
| 364 | DO ji = 2, jpim1 |
---|
[2528] | 365 | iku = mbku(ji,jj) |
---|
| 366 | ikv = mbkv(ji,jj) |
---|
[3] | 367 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
---|
| 368 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
---|
[2528] | 369 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 370 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 371 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
| 372 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
---|
| 373 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 374 | ENDIF |
---|
[2528] | 375 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 376 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 377 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 378 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
---|
| 379 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 380 | ENDIF |
---|
| 381 | END DO |
---|
| 382 | END DO |
---|
[503] | 383 | ! |
---|
[3294] | 384 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 385 | ! |
---|
[455] | 386 | END SUBROUTINE hpg_zps |
---|
[216] | 387 | |
---|
[455] | 388 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 389 | !!--------------------------------------------------------------------- |
---|
[455] | 390 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 391 | !! |
---|
[455] | 392 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 393 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 394 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 395 | !! density gradient along the model level from the suface to that |
---|
[455] | 396 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 397 | !! to the horizontal pressure gradient : |
---|
| 398 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 399 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[3] | 400 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 401 | !! ua = ua - 1/e1u * zhpi |
---|
| 402 | !! va = va - 1/e2v * zhpj |
---|
[3] | 403 | !! |
---|
| 404 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 405 | !!---------------------------------------------------------------------- |
---|
| 406 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 407 | !! |
---|
[5120] | 408 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 409 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
| 410 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
| 411 | !!---------------------------------------------------------------------- |
---|
| 412 | ! |
---|
| 413 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 414 | ! |
---|
| 415 | IF( kt == nit000 ) THEN |
---|
| 416 | IF(lwp) WRITE(numout,*) |
---|
| 417 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 418 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 419 | ENDIF |
---|
| 420 | |
---|
| 421 | ! Local constant initialization |
---|
| 422 | zcoef0 = - grav * 0.5_wp |
---|
| 423 | ! To use density and not density anomaly |
---|
| 424 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 425 | ELSE ; znad = 0._wp ! Fixed volume |
---|
| 426 | ENDIF |
---|
| 427 | |
---|
| 428 | ! Surface value |
---|
| 429 | DO jj = 2, jpjm1 |
---|
| 430 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 431 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 432 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 433 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 434 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 435 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 436 | ! s-coordinate pressure gradient correction |
---|
| 437 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 438 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
| 439 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 440 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 441 | ! add to the general momentum trend |
---|
| 442 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 443 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 444 | END DO |
---|
| 445 | END DO |
---|
| 446 | |
---|
| 447 | ! interior value (2=<jk=<jpkm1) |
---|
| 448 | DO jk = 2, jpkm1 |
---|
| 449 | DO jj = 2, jpjm1 |
---|
| 450 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 451 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 452 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 453 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 454 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 455 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 456 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 457 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
| 458 | ! s-coordinate pressure gradient correction |
---|
| 459 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 460 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 461 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 462 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 463 | ! add to the general momentum trend |
---|
| 464 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 465 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 466 | END DO |
---|
| 467 | END DO |
---|
| 468 | END DO |
---|
| 469 | ! |
---|
| 470 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 471 | ! |
---|
| 472 | END SUBROUTINE hpg_sco |
---|
| 473 | |
---|
| 474 | SUBROUTINE hpg_isf( kt ) |
---|
| 475 | !!--------------------------------------------------------------------- |
---|
| 476 | !! *** ROUTINE hpg_sco *** |
---|
| 477 | !! |
---|
| 478 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 479 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 480 | !! is computed by taking the vertical integral of the in-situ |
---|
| 481 | !! density gradient along the model level from the suface to that |
---|
| 482 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 483 | !! to the horizontal pressure gradient : |
---|
| 484 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 485 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 486 | !! add it to the general momentum trend (ua,va). |
---|
| 487 | !! ua = ua - 1/e1u * zhpi |
---|
| 488 | !! va = va - 1/e2v * zhpj |
---|
| 489 | !! iceload is added and partial cell case are added to the top and bottom |
---|
| 490 | !! |
---|
| 491 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 492 | !!---------------------------------------------------------------------- |
---|
| 493 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 494 | !! |
---|
[4990] | 495 | INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 496 | REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars |
---|
| 497 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd |
---|
| 498 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
---|
| 499 | REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj |
---|
[3] | 500 | !!---------------------------------------------------------------------- |
---|
[3294] | 501 | ! |
---|
[4990] | 502 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
---|
| 503 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 504 | CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 505 | ! |
---|
[4990] | 506 | IF( kt == nit000 ) THEN |
---|
[3] | 507 | IF(lwp) WRITE(numout,*) |
---|
[5120] | 508 | IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf' |
---|
[455] | 509 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
[3] | 510 | ENDIF |
---|
| 511 | |
---|
[503] | 512 | ! Local constant initialization |
---|
[2528] | 513 | zcoef0 = - grav * 0.5_wp |
---|
[592] | 514 | ! To use density and not density anomaly |
---|
[4990] | 515 | ! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 516 | ! ELSE ; znad = 0._wp ! Fixed volume |
---|
| 517 | ! ENDIF |
---|
| 518 | znad=1._wp |
---|
| 519 | ! iniitialised to 0. zhpi zhpi |
---|
| 520 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
---|
[455] | 521 | |
---|
[4990] | 522 | !================================================================================== |
---|
| 523 | !=====Compute iceload and contribution of the half first wet layer ================= |
---|
| 524 | !=================================================================================== |
---|
| 525 | |
---|
| 526 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
---|
| 527 | ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp |
---|
| 528 | |
---|
| 529 | ! compute density of the water displaced by the ice shelf |
---|
| 530 | zrhd = rhd ! save rhd |
---|
| 531 | DO jk = 1, jpk |
---|
| 532 | zdept(:,:)=gdept_1d(jk) |
---|
| 533 | CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk)) |
---|
| 534 | END DO |
---|
| 535 | WHERE ( tmask(:,:,:) == 1._wp) |
---|
| 536 | rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd |
---|
| 537 | END WHERE |
---|
| 538 | |
---|
| 539 | ! compute rhd at the ice/oce interface (ice shelf side) |
---|
| 540 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
---|
| 541 | |
---|
| 542 | ! compute rhd at the ice/oce interface (ocean side) |
---|
| 543 | DO ji=1,jpi |
---|
| 544 | DO jj=1,jpj |
---|
| 545 | ikt=mikt(ji,jj) |
---|
| 546 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
---|
| 547 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
---|
| 548 | END DO |
---|
| 549 | END DO |
---|
| 550 | CALL eos(ztstop,risfdep,zrhdtop_oce) |
---|
| 551 | ! |
---|
| 552 | ! Surface value + ice shelf gradient |
---|
| 553 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
---|
| 554 | ziceload = 0._wp |
---|
| 555 | DO jj = 1, jpj |
---|
| 556 | DO ji = 1, jpi ! vector opt. |
---|
| 557 | ikt=mikt(ji,jj) |
---|
| 558 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
---|
| 559 | DO jk=2,ikt-1 |
---|
| 560 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) & |
---|
| 561 | & * (1._wp - tmask(ji,jj,jk)) |
---|
| 562 | END DO |
---|
| 563 | IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) & |
---|
| 564 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
---|
| 565 | END DO |
---|
| 566 | END DO |
---|
| 567 | riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5 |
---|
| 568 | ! compute zp from z=0 to first T wet point (correction due to zps not yet applied) |
---|
[455] | 569 | DO jj = 2, jpjm1 |
---|
[3764] | 570 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 571 | ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1) |
---|
| 572 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 573 | ! we assume ISF is in isostatic equilibrium |
---|
| 574 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) & |
---|
| 575 | & * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) & |
---|
| 576 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 577 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 578 | & + ( ziceload(ji+1,jj) - ziceload(ji,jj)) ) |
---|
| 579 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) & |
---|
| 580 | & * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) & |
---|
| 581 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 582 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 583 | & + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) ) |
---|
| 584 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
[2528] | 585 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 586 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 587 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 588 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 589 | ! add to the general momentum trend |
---|
[4990] | 590 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 591 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
[3764] | 592 | END DO |
---|
| 593 | END DO |
---|
[4990] | 594 | !================================================================================== |
---|
| 595 | !===== Compute partial cell contribution for the top cell ========================= |
---|
| 596 | !================================================================================== |
---|
| 597 | DO jj = 2, jpjm1 |
---|
| 598 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 599 | iku = miku(ji,jj) ; |
---|
| 600 | zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp |
---|
| 601 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
---|
| 602 | ! u direction |
---|
| 603 | IF ( iku .GT. 1 ) THEN |
---|
| 604 | ! case iku |
---|
| 605 | zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu & |
---|
| 606 | & * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) & |
---|
| 607 | & + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad ) |
---|
| 608 | ! corrective term ( = 0 if z coordinate ) |
---|
| 609 | zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj) |
---|
| 610 | ! zhpi will be added in interior loop |
---|
| 611 | ua(ji,jj,iku) = ua(ji,jj,iku) + zuap |
---|
| 612 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 613 | IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku) |
---|
[3764] | 614 | |
---|
[4990] | 615 | ! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps) |
---|
| 616 | zhpiint = zcoef0 / e1u(ji,jj) & |
---|
| 617 | & * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) & |
---|
| 618 | & + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) & |
---|
| 619 | & - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) & |
---|
| 620 | & + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) ) |
---|
| 621 | zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint |
---|
| 622 | END IF |
---|
| 623 | |
---|
| 624 | ! v direction |
---|
| 625 | ikv = mikv(ji,jj) |
---|
| 626 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
---|
| 627 | IF ( ikv .GT. 1 ) THEN |
---|
| 628 | ! case ikv |
---|
| 629 | zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv & |
---|
| 630 | & * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) & |
---|
| 631 | & + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad ) |
---|
| 632 | ! corrective term ( = 0 if z coordinate ) |
---|
| 633 | zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj) |
---|
| 634 | ! zhpi will be added in interior loop |
---|
| 635 | va(ji,jj,ikv) = va(ji,jj,ikv) + zvap |
---|
| 636 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 637 | IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv) |
---|
| 638 | |
---|
| 639 | ! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps) |
---|
| 640 | zhpjint = zcoef0 / e2v(ji,jj) & |
---|
| 641 | & * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) & |
---|
| 642 | & + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) & |
---|
| 643 | & - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) & |
---|
| 644 | & + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) ) |
---|
| 645 | zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint |
---|
| 646 | END IF |
---|
| 647 | END DO |
---|
| 648 | END DO |
---|
| 649 | |
---|
| 650 | !================================================================================== |
---|
| 651 | !===== Compute interior value ===================================================== |
---|
| 652 | !================================================================================== |
---|
| 653 | |
---|
| 654 | DO jj = 2, jpjm1 |
---|
| 655 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 656 | iku=miku(ji,jj); ikv=mikv(ji,jj) |
---|
| 657 | DO jk = 2, jpkm1 |
---|
[455] | 658 | ! hydrostatic pressure gradient along s-surfaces |
---|
[4990] | 659 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 660 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) & |
---|
| 661 | & + zcoef0 / e1u(ji,jj) & |
---|
| 662 | & * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) & |
---|
| 663 | & + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) & |
---|
| 664 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) & |
---|
| 665 | & + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) ) |
---|
[455] | 666 | ! s-coordinate pressure gradient correction |
---|
[4990] | 667 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 668 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 669 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1) |
---|
| 670 | ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 671 | |
---|
| 672 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 673 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 674 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) & |
---|
| 675 | & + zcoef0 / e2v(ji,jj) & |
---|
| 676 | & * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) & |
---|
| 677 | & + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) & |
---|
| 678 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) & |
---|
| 679 | & + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) ) |
---|
| 680 | ! s-coordinate pressure gradient correction |
---|
| 681 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 682 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 683 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1) |
---|
[455] | 684 | ! add to the general momentum trend |
---|
[4990] | 685 | va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk) |
---|
[455] | 686 | END DO |
---|
| 687 | END DO |
---|
| 688 | END DO |
---|
[4990] | 689 | |
---|
| 690 | !================================================================================== |
---|
| 691 | !===== Compute bottom cell contribution (partial cell) ============================ |
---|
| 692 | !================================================================================== |
---|
| 693 | |
---|
| 694 | DO jj = 2, jpjm1 |
---|
| 695 | DO ji = 2, jpim1 |
---|
| 696 | iku = mbku(ji,jj) |
---|
| 697 | ikv = mbkv(ji,jj) |
---|
| 698 | |
---|
| 699 | IF (iku .GT. 1) THEN |
---|
| 700 | ! remove old value (interior case) |
---|
| 701 | zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) & |
---|
| 702 | & * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj) |
---|
| 703 | ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap |
---|
| 704 | ! put new value |
---|
| 705 | ! -zpshpi to avoid double contribution of the partial step in the top layer |
---|
| 706 | zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj) |
---|
| 707 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj) |
---|
| 708 | ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap |
---|
| 709 | END IF |
---|
| 710 | ! v direction |
---|
| 711 | IF (ikv .GT. 1) THEN |
---|
| 712 | ! remove old value (interior case) |
---|
| 713 | zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) & |
---|
| 714 | & * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj) |
---|
| 715 | va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap |
---|
| 716 | ! put new value |
---|
| 717 | ! -zpshpj to avoid double contribution of the partial step in the top layer |
---|
| 718 | zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj) |
---|
| 719 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj) |
---|
| 720 | va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap |
---|
| 721 | END IF |
---|
| 722 | END DO |
---|
| 723 | END DO |
---|
| 724 | |
---|
| 725 | ! set back to original density value into the ice shelf cell (maybe useless because it is masked) |
---|
| 726 | rhd = zrhd |
---|
[503] | 727 | ! |
---|
[4990] | 728 | CALL wrk_dealloc( jpi,jpj,2, ztstop) |
---|
| 729 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 730 | CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 731 | ! |
---|
[5120] | 732 | END SUBROUTINE hpg_isf |
---|
[455] | 733 | |
---|
[4990] | 734 | |
---|
[455] | 735 | SUBROUTINE hpg_djc( kt ) |
---|
| 736 | !!--------------------------------------------------------------------- |
---|
| 737 | !! *** ROUTINE hpg_djc *** |
---|
| 738 | !! |
---|
| 739 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 740 | !! |
---|
[503] | 741 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 742 | !!---------------------------------------------------------------------- |
---|
[503] | 743 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 744 | !! |
---|
| 745 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 746 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 747 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 748 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3764] | 749 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3294] | 750 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 751 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 752 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 753 | !!---------------------------------------------------------------------- |
---|
[3294] | 754 | ! |
---|
[3764] | 755 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 756 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 757 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[3294] | 758 | ! |
---|
[455] | 759 | |
---|
| 760 | IF( kt == nit000 ) THEN |
---|
| 761 | IF(lwp) WRITE(numout,*) |
---|
| 762 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 763 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 764 | ENDIF |
---|
| 765 | |
---|
[503] | 766 | ! Local constant initialization |
---|
[2528] | 767 | zcoef0 = - grav * 0.5_wp |
---|
| 768 | z1_10 = 1._wp / 10._wp |
---|
| 769 | z1_12 = 1._wp / 12._wp |
---|
[455] | 770 | |
---|
| 771 | !---------------------------------------------------------------------------------------- |
---|
| 772 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 773 | !---------------------------------------------------------------------------------------- |
---|
| 774 | |
---|
| 775 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 776 | |
---|
| 777 | DO jk = 2, jpkm1 |
---|
| 778 | DO jj = 2, jpjm1 |
---|
| 779 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 780 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 781 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 782 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 783 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 784 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 785 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 786 | END DO |
---|
| 787 | END DO |
---|
| 788 | END DO |
---|
| 789 | |
---|
| 790 | !------------------------------------------------------------------------- |
---|
| 791 | ! compute harmonic averages using eq. 5.18 |
---|
| 792 | !------------------------------------------------------------------------- |
---|
| 793 | zep = 1.e-15 |
---|
| 794 | |
---|
[503] | 795 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 796 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 797 | |
---|
| 798 | DO jk = 2, jpkm1 |
---|
| 799 | DO jj = 2, jpjm1 |
---|
| 800 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 801 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 802 | |
---|
[2528] | 803 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 804 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 805 | |
---|
[2528] | 806 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 807 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 808 | |
---|
| 809 | IF( cffw > zep) THEN |
---|
[2528] | 810 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 811 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 812 | ELSE |
---|
[2528] | 813 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 814 | ENDIF |
---|
| 815 | |
---|
[2528] | 816 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 817 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 818 | |
---|
| 819 | IF( cffu > zep ) THEN |
---|
[2528] | 820 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 821 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 822 | ELSE |
---|
[2528] | 823 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 824 | ENDIF |
---|
| 825 | |
---|
| 826 | IF( cffx > zep ) THEN |
---|
[2528] | 827 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 828 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 829 | ELSE |
---|
[2528] | 830 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 831 | ENDIF |
---|
| 832 | |
---|
| 833 | IF( cffv > zep ) THEN |
---|
[2528] | 834 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 835 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 836 | ELSE |
---|
[2528] | 837 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 838 | ENDIF |
---|
| 839 | |
---|
| 840 | IF( cffy > zep ) THEN |
---|
[2528] | 841 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 842 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 843 | ELSE |
---|
[2528] | 844 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 845 | ENDIF |
---|
| 846 | |
---|
| 847 | END DO |
---|
| 848 | END DO |
---|
| 849 | END DO |
---|
| 850 | |
---|
| 851 | !---------------------------------------------------------------------------------- |
---|
| 852 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 853 | !---------------------------------------------------------------------------------- |
---|
[2528] | 854 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 855 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 856 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 857 | |
---|
[2528] | 858 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 859 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 860 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 861 | |
---|
| 862 | |
---|
| 863 | !-------------------------------------------------------------- |
---|
| 864 | ! Upper half of top-most grid box, compute and store |
---|
| 865 | !------------------------------------------------------------- |
---|
| 866 | |
---|
| 867 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 868 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 869 | |
---|
| 870 | DO jj = 2, jpjm1 |
---|
| 871 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 872 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 873 | & * ( rhd(ji,jj,1) & |
---|
| 874 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 875 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
[3764] | 876 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 877 | END DO |
---|
| 878 | END DO |
---|
| 879 | |
---|
| 880 | !!bug gm : here also, simplification is possible |
---|
| 881 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 882 | |
---|
| 883 | DO jk = 2, jpkm1 |
---|
| 884 | DO jj = 2, jpjm1 |
---|
| 885 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 886 | |
---|
| 887 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 888 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 889 | & - grav * z1_10 * ( & |
---|
| 890 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 891 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 892 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 893 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 894 | & ) |
---|
| 895 | |
---|
| 896 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 897 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 898 | & - grav* z1_10 * ( & |
---|
| 899 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 900 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 901 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 902 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 903 | & ) |
---|
| 904 | |
---|
| 905 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 906 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 907 | & - grav* z1_10 * ( & |
---|
| 908 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 909 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 910 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 911 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 912 | & ) |
---|
| 913 | |
---|
| 914 | END DO |
---|
| 915 | END DO |
---|
| 916 | END DO |
---|
| 917 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 918 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 919 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 920 | |
---|
| 921 | |
---|
| 922 | ! --------------- |
---|
| 923 | ! Surface value |
---|
| 924 | ! --------------- |
---|
| 925 | DO jj = 2, jpjm1 |
---|
| 926 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 927 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 928 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 929 | ! add to the general momentum trend |
---|
| 930 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 931 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 932 | END DO |
---|
| 933 | END DO |
---|
| 934 | |
---|
| 935 | ! ---------------- |
---|
| 936 | ! interior value (2=<jk=<jpkm1) |
---|
| 937 | ! ---------------- |
---|
| 938 | DO jk = 2, jpkm1 |
---|
[3764] | 939 | DO jj = 2, jpjm1 |
---|
[455] | 940 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 941 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 942 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 943 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 944 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 945 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 946 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 947 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 948 | ! add to the general momentum trend |
---|
| 949 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 950 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 951 | END DO |
---|
| 952 | END DO |
---|
| 953 | END DO |
---|
[503] | 954 | ! |
---|
[3764] | 955 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 956 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 957 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 958 | ! |
---|
[455] | 959 | END SUBROUTINE hpg_djc |
---|
| 960 | |
---|
| 961 | |
---|
[3294] | 962 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 963 | !!--------------------------------------------------------------------- |
---|
[3294] | 964 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 965 | !! |
---|
[3294] | 966 | !! ** Method : s-coordinate case. |
---|
| 967 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 968 | !! based on the constrained cubic-spline interpolation for |
---|
| 969 | !! all vertical coordinate systems |
---|
[455] | 970 | !! |
---|
[3294] | 971 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 972 | !!---------------------------------------------------------------------- |
---|
[3294] | 973 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 974 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 975 | !! |
---|
[3294] | 976 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 977 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 978 | !! |
---|
[3294] | 979 | !! The local variables for the correction term |
---|
| 980 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 981 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 982 | REAL(wp) :: zrhdt1 |
---|
[3294] | 983 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[3764] | 984 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
[3294] | 985 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[5224] | 986 | REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n |
---|
[455] | 987 | !!---------------------------------------------------------------------- |
---|
[3294] | 988 | ! |
---|
[3764] | 989 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 990 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 991 | CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[3294] | 992 | ! |
---|
[455] | 993 | IF( kt == nit000 ) THEN |
---|
| 994 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 995 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 996 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 997 | ENDIF |
---|
| 998 | |
---|
[3294] | 999 | !!---------------------------------------------------------------------- |
---|
| 1000 | ! Local constant initialization |
---|
[3764] | 1001 | zcoef0 = - grav |
---|
[3294] | 1002 | znad = 0.0_wp |
---|
| 1003 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 1004 | |
---|
[3294] | 1005 | ! Clean 3-D work arrays |
---|
| 1006 | zhpi(:,:,:) = 0._wp |
---|
| 1007 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 1008 | |
---|
[3294] | 1009 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 1010 | DO jj = 1, jpj |
---|
[3764] | 1011 | DO ji = 1, jpi |
---|
[3294] | 1012 | jk = mbathy(ji,jj) |
---|
| 1013 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 1014 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 1015 | ELSE IF(jk < jpkm1) THEN |
---|
| 1016 | DO jkk = jk+1, jpk |
---|
| 1017 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 1018 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
[3764] | 1019 | END DO |
---|
[3294] | 1020 | ENDIF |
---|
| 1021 | END DO |
---|
| 1022 | END DO |
---|
[3] | 1023 | |
---|
[3632] | 1024 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 1025 | DO jj = 1, jpj |
---|
| 1026 | DO ji = 1, jpi |
---|
| 1027 | zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 1028 | END DO |
---|
| 1029 | END DO |
---|
[455] | 1030 | |
---|
[4990] | 1031 | DO jk = 2, jpk |
---|
| 1032 | DO jj = 1, jpj |
---|
| 1033 | DO ji = 1, jpi |
---|
| 1034 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 1035 | END DO |
---|
| 1036 | END DO |
---|
| 1037 | END DO |
---|
[455] | 1038 | |
---|
[4990] | 1039 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 1040 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 1041 | |
---|
[3764] | 1042 | ! Construct the vertical density profile with the |
---|
[3294] | 1043 | ! constrained cubic spline interpolation |
---|
| 1044 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[3764] | 1045 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
[3294] | 1046 | |
---|
| 1047 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 1048 | DO jj = 2, jpj |
---|
[3764] | 1049 | DO ji = 2, jpi |
---|
[3632] | 1050 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), & |
---|
[3294] | 1051 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
[3632] | 1052 | dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1) |
---|
[3294] | 1053 | |
---|
| 1054 | ! assuming linear profile across the top half surface layer |
---|
[3764] | 1055 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
[3294] | 1056 | END DO |
---|
[455] | 1057 | END DO |
---|
| 1058 | |
---|
[3294] | 1059 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 1060 | DO jk = 2, jpkm1 |
---|
| 1061 | DO jj = 2, jpj |
---|
[3294] | 1062 | DO ji = 2, jpi |
---|
| 1063 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
[3632] | 1064 | integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),& |
---|
[3294] | 1065 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 1066 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 1067 | END DO |
---|
| 1068 | END DO |
---|
[455] | 1069 | END DO |
---|
| 1070 | |
---|
[3294] | 1071 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5224] | 1072 | |
---|
| 1073 | ! Prepare zsshu_n and zsshv_n |
---|
[3764] | 1074 | DO jj = 2, jpjm1 |
---|
| 1075 | DO ji = 2, jpim1 |
---|
[5224] | 1076 | zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
| 1077 | & r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1078 | zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
| 1079 | & r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
[3294] | 1080 | END DO |
---|
[455] | 1081 | END DO |
---|
| 1082 | |
---|
[5224] | 1083 | DO jj = 2, jpjm1 |
---|
| 1084 | DO ji = 2, jpim1 |
---|
| 1085 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
| 1086 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
| 1087 | END DO |
---|
| 1088 | END DO |
---|
| 1089 | |
---|
[3764] | 1090 | DO jk = 2, jpkm1 |
---|
| 1091 | DO jj = 2, jpjm1 |
---|
| 1092 | DO ji = 2, jpim1 |
---|
[3294] | 1093 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 1094 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 1095 | END DO |
---|
| 1096 | END DO |
---|
[455] | 1097 | END DO |
---|
[3764] | 1098 | |
---|
| 1099 | DO jk = 1, jpkm1 |
---|
| 1100 | DO jj = 2, jpjm1 |
---|
| 1101 | DO ji = 2, jpim1 |
---|
[3294] | 1102 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 1103 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 1104 | END DO |
---|
| 1105 | END DO |
---|
| 1106 | END DO |
---|
[455] | 1107 | |
---|
[3632] | 1108 | DO jk = 1, jpkm1 |
---|
| 1109 | DO jj = 2, jpjm1 |
---|
| 1110 | DO ji = 2, jpim1 |
---|
| 1111 | zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1112 | zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1113 | zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1114 | zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1115 | END DO |
---|
| 1116 | END DO |
---|
| 1117 | END DO |
---|
| 1118 | |
---|
| 1119 | |
---|
[3764] | 1120 | DO jk = 1, jpkm1 |
---|
| 1121 | DO jj = 2, jpjm1 |
---|
| 1122 | DO ji = 2, jpim1 |
---|
[3294] | 1123 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1124 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1125 | zuijk = zu(ji,jj,jk) |
---|
| 1126 | zvijk = zv(ji,jj,jk) |
---|
| 1127 | |
---|
| 1128 | !!!!! for u equation |
---|
| 1129 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 1130 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1131 | jis = ji + 1; jid = ji |
---|
| 1132 | ELSE |
---|
| 1133 | jis = ji; jid = ji +1 |
---|
| 1134 | ENDIF |
---|
| 1135 | |
---|
| 1136 | ! integrate the pressure on the shallow side |
---|
[3764] | 1137 | jk1 = jk |
---|
[3632] | 1138 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1139 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1140 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1141 | EXIT |
---|
| 1142 | ENDIF |
---|
[3632] | 1143 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1144 | zpwes = zpwes + & |
---|
[3632] | 1145 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1146 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1147 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1148 | jk1 = jk1 + 1 |
---|
| 1149 | END DO |
---|
[3764] | 1150 | |
---|
[3294] | 1151 | ! integrate the pressure on the deep side |
---|
[3764] | 1152 | jk1 = jk |
---|
[3632] | 1153 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1154 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1155 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1156 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1157 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1158 | dsp(jid,jj,1)) * zdeps |
---|
| 1159 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1160 | EXIT |
---|
| 1161 | ENDIF |
---|
[3632] | 1162 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1163 | zpwed = zpwed + & |
---|
[3632] | 1164 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1165 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1166 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1167 | jk1 = jk1 - 1 |
---|
| 1168 | END DO |
---|
[3764] | 1169 | |
---|
[3294] | 1170 | ! update the momentum trends in u direction |
---|
| 1171 | |
---|
| 1172 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1173 | IF( lk_vvl ) THEN |
---|
[3764] | 1174 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1175 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1176 | ELSE |
---|
[3764] | 1177 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1178 | ENDIF |
---|
| 1179 | |
---|
| 1180 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 1181 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 1182 | ENDIF |
---|
[3764] | 1183 | |
---|
[3294] | 1184 | !!!!! for v equation |
---|
| 1185 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1186 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1187 | jjs = jj + 1; jjd = jj |
---|
| 1188 | ELSE |
---|
| 1189 | jjs = jj ; jjd = jj + 1 |
---|
| 1190 | ENDIF |
---|
| 1191 | |
---|
| 1192 | ! integrate the pressure on the shallow side |
---|
[3764] | 1193 | jk1 = jk |
---|
[3632] | 1194 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1195 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1196 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1197 | EXIT |
---|
| 1198 | ENDIF |
---|
[3632] | 1199 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1200 | zpnss = zpnss + & |
---|
[3632] | 1201 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1202 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1203 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1204 | jk1 = jk1 + 1 |
---|
| 1205 | END DO |
---|
[3764] | 1206 | |
---|
[3294] | 1207 | ! integrate the pressure on the deep side |
---|
[3764] | 1208 | jk1 = jk |
---|
[3632] | 1209 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1210 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1211 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1212 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1213 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1214 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1215 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1216 | EXIT |
---|
| 1217 | ENDIF |
---|
[3632] | 1218 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1219 | zpnsd = zpnsd + & |
---|
[3632] | 1220 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1221 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1222 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1223 | jk1 = jk1 - 1 |
---|
| 1224 | END DO |
---|
| 1225 | |
---|
[3764] | 1226 | |
---|
[3294] | 1227 | ! update the momentum trends in v direction |
---|
| 1228 | |
---|
| 1229 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1230 | IF( lk_vvl ) THEN |
---|
| 1231 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
[3764] | 1232 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1233 | ELSE |
---|
[3764] | 1234 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1235 | ENDIF |
---|
| 1236 | |
---|
| 1237 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 1238 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 1239 | ENDIF |
---|
| 1240 | |
---|
[3764] | 1241 | |
---|
[3294] | 1242 | END DO |
---|
| 1243 | END DO |
---|
[455] | 1244 | END DO |
---|
[503] | 1245 | ! |
---|
[3764] | 1246 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1247 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 1248 | CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[2715] | 1249 | ! |
---|
[3294] | 1250 | END SUBROUTINE hpg_prj |
---|
[455] | 1251 | |
---|
[4990] | 1252 | |
---|
[3294] | 1253 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1254 | !!---------------------------------------------------------------------- |
---|
| 1255 | !! *** ROUTINE cspline *** |
---|
[3764] | 1256 | !! |
---|
[3294] | 1257 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1258 | !! |
---|
| 1259 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1260 | !! |
---|
[3294] | 1261 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1262 | !!---------------------------------------------------------------------- |
---|
| 1263 | IMPLICIT NONE |
---|
| 1264 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
[3764] | 1265 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
[3294] | 1266 | ! the interpoated function |
---|
[3764] | 1267 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
[3294] | 1268 | ! 2: Linear |
---|
[4990] | 1269 | ! |
---|
[3294] | 1270 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1271 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1272 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1273 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1274 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1275 | !!---------------------------------------------------------------------- |
---|
| 1276 | |
---|
| 1277 | jpi = size(fsp,1) |
---|
| 1278 | jpj = size(fsp,2) |
---|
| 1279 | jpkm1 = size(fsp,3) - 1 |
---|
| 1280 | |
---|
[3764] | 1281 | |
---|
[3294] | 1282 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1283 | DO ji = 1, jpi |
---|
| 1284 | DO jj = 1, jpj |
---|
[3764] | 1285 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1286 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1287 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1288 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1289 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1290 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1291 | ! |
---|
| 1292 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1293 | ! |
---|
[3294] | 1294 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1295 | ! zdf(jk) = 0._wp |
---|
| 1296 | ! ELSE |
---|
| 1297 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1298 | ! ENDIF |
---|
| 1299 | ! END DO |
---|
[3764] | 1300 | |
---|
[3294] | 1301 | !!Simply geometric average |
---|
| 1302 | DO jk = 2, jpkm1-1 |
---|
| 1303 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 1304 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
[3764] | 1305 | |
---|
[3294] | 1306 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1307 | zdf(jk) = 0._wp |
---|
| 1308 | ELSE |
---|
| 1309 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1310 | ENDIF |
---|
| 1311 | END DO |
---|
[3764] | 1312 | |
---|
[3294] | 1313 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1314 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1315 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1316 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1317 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1318 | |
---|
[3294] | 1319 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1320 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1321 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1322 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1323 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1324 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1325 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1326 | |
---|
[3294] | 1327 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1328 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1329 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1330 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1331 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1332 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1333 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1334 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1335 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1336 | END DO |
---|
| 1337 | END DO |
---|
| 1338 | END DO |
---|
[3764] | 1339 | |
---|
[3294] | 1340 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1341 | DO ji = 1, jpi |
---|
| 1342 | DO jj = 1, jpj |
---|
| 1343 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1344 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1345 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1346 | |
---|
[3294] | 1347 | dsp(ji,jj,jk) = 0._wp |
---|
| 1348 | csp(ji,jj,jk) = 0._wp |
---|
| 1349 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1350 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1351 | END DO |
---|
| 1352 | END DO |
---|
| 1353 | END DO |
---|
| 1354 | |
---|
| 1355 | ELSE |
---|
| 1356 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1357 | ENDIF |
---|
| 1358 | |
---|
| 1359 | END SUBROUTINE cspline |
---|
| 1360 | |
---|
| 1361 | |
---|
[3764] | 1362 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1363 | !!---------------------------------------------------------------------- |
---|
| 1364 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1365 | !! |
---|
[3294] | 1366 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1367 | !! |
---|
[4990] | 1368 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1369 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1370 | !!---------------------------------------------------------------------- |
---|
| 1371 | IMPLICIT NONE |
---|
[3764] | 1372 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1373 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1374 | REAL(wp) :: zdeltx |
---|
| 1375 | !!---------------------------------------------------------------------- |
---|
| 1376 | |
---|
| 1377 | zdeltx = xr - xl |
---|
| 1378 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1379 | f = 0.5_wp * (fl + fr) |
---|
| 1380 | ELSE |
---|
| 1381 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1382 | ENDIF |
---|
[3764] | 1383 | |
---|
[3294] | 1384 | END FUNCTION interp1 |
---|
| 1385 | |
---|
[4990] | 1386 | |
---|
[3764] | 1387 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1388 | !!---------------------------------------------------------------------- |
---|
| 1389 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1390 | !! |
---|
[3294] | 1391 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1392 | !! |
---|
[3294] | 1393 | !! ** Method : cubic spline interpolation |
---|
| 1394 | !! |
---|
| 1395 | !!---------------------------------------------------------------------- |
---|
| 1396 | IMPLICIT NONE |
---|
[3764] | 1397 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1398 | REAL(wp) :: f ! value from the interpolation |
---|
| 1399 | !!---------------------------------------------------------------------- |
---|
| 1400 | |
---|
[3764] | 1401 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[3294] | 1402 | |
---|
| 1403 | END FUNCTION interp2 |
---|
| 1404 | |
---|
| 1405 | |
---|
[3764] | 1406 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1407 | !!---------------------------------------------------------------------- |
---|
| 1408 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1409 | !! |
---|
[3294] | 1410 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1411 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1412 | !! |
---|
[3294] | 1413 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1414 | !! |
---|
| 1415 | !!---------------------------------------------------------------------- |
---|
| 1416 | IMPLICIT NONE |
---|
[3764] | 1417 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1418 | REAL(wp) :: f ! value from the interpolation |
---|
| 1419 | !!---------------------------------------------------------------------- |
---|
| 1420 | |
---|
| 1421 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1422 | |
---|
| 1423 | END FUNCTION interp3 |
---|
| 1424 | |
---|
[3764] | 1425 | |
---|
| 1426 | FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f) |
---|
[3294] | 1427 | !!---------------------------------------------------------------------- |
---|
| 1428 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1429 | !! |
---|
[3294] | 1430 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1431 | !! |
---|
[3764] | 1432 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1433 | !! |
---|
[3294] | 1434 | !!---------------------------------------------------------------------- |
---|
| 1435 | IMPLICIT NONE |
---|
[3764] | 1436 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1437 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1438 | REAL(wp) :: f ! integration result |
---|
| 1439 | !!---------------------------------------------------------------------- |
---|
| 1440 | |
---|
[3764] | 1441 | za1 = 0.5_wp * b |
---|
| 1442 | za2 = c / 3.0_wp |
---|
| 1443 | za3 = 0.25_wp * d |
---|
[3294] | 1444 | |
---|
| 1445 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1446 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1447 | |
---|
[3632] | 1448 | END FUNCTION integ_spline |
---|
[3294] | 1449 | |
---|
[3] | 1450 | !!====================================================================== |
---|
| 1451 | END MODULE dynhpg |
---|
[3632] | 1452 | |
---|