[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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[11556] | 19 | !! 3.6 ! 2019-08 (M. Bell) Revisions to bias pressure correction |
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[503] | 20 | !!---------------------------------------------------------------------- |
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[3] | 21 | |
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| 22 | !!---------------------------------------------------------------------- |
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[455] | 23 | !! dyn_hpg : update the momentum trend with the now horizontal |
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[3] | 24 | !! gradient of the hydrostatic pressure |
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[2528] | 25 | !! dyn_hpg_init : initialisation and control of options |
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[455] | 26 | !! hpg_zco : z-coordinate scheme |
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| 27 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
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| 28 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
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[5120] | 29 | !! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf |
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[455] | 30 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
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[3294] | 31 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
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[3] | 32 | !!---------------------------------------------------------------------- |
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| 33 | USE oce ! ocean dynamics and tracers |
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[4990] | 34 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
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[3] | 35 | USE dom_oce ! ocean space and time domain |
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| 36 | USE phycst ! physical constants |
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[4990] | 37 | USE trd_oce ! trends: ocean variables |
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| 38 | USE trddyn ! trend manager: dynamics |
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| 39 | ! |
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[2715] | 40 | USE in_out_manager ! I/O manager |
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[258] | 41 | USE prtctl ! Print control |
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[4990] | 42 | USE lbclnk ! lateral boundary condition |
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[2715] | 43 | USE lib_mpp ! MPP library |
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[4990] | 44 | USE eosbn2 ! compute density |
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[3294] | 45 | USE wrk_nemo ! Memory Allocation |
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| 46 | USE timing ! Timing |
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[8400] | 47 | USE biaspar ! bias correction variables |
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[3] | 48 | |
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| 49 | IMPLICIT NONE |
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| 50 | PRIVATE |
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| 51 | |
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[2528] | 52 | PUBLIC dyn_hpg ! routine called by step module |
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| 53 | PUBLIC dyn_hpg_init ! routine called by opa module |
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[3] | 54 | |
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[4147] | 55 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
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| 56 | LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
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| 57 | LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
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| 58 | LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
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| 59 | LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
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| 60 | LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
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[5120] | 61 | LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
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[4147] | 62 | LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag |
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[455] | 63 | |
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[3764] | 64 | 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] | 65 | |
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[3] | 66 | !! * Substitutions |
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| 67 | # include "domzgr_substitute.h90" |
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| 68 | # include "vectopt_loop_substitute.h90" |
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| 69 | !!---------------------------------------------------------------------- |
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[2528] | 70 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 71 | !! $Id$ |
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| 72 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 73 | !!---------------------------------------------------------------------- |
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| 74 | CONTAINS |
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| 75 | |
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| 76 | SUBROUTINE dyn_hpg( kt ) |
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| 77 | !!--------------------------------------------------------------------- |
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| 78 | !! *** ROUTINE dyn_hpg *** |
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| 79 | !! |
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[3764] | 80 | !! ** Method : Call the hydrostatic pressure gradient routine |
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[503] | 81 | !! using the scheme defined in the namelist |
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[3764] | 82 | !! |
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[455] | 83 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[4990] | 84 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
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[503] | 85 | !!---------------------------------------------------------------------- |
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| 86 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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[11556] | 87 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 88 | INTEGER :: iku, ikv ! k indices for bottom level at u and v points |
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| 89 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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| 90 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_rhd_st ! tmp density storage for pressure corr |
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| 91 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_ua, z_va ! tmp store for ua and va including hpg but not pressure correction |
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| 92 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_ua_bpc, z_va_bpc ! ua calculated with bias pressure correction |
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| 93 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_gru_st, z_grv_st ! tmp ua and va trends storage for pressure corr |
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| 94 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_ua_bpc_bot, z_va_bpc_bot ! bias pc fields calculated at the ocean bottom |
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| 95 | |
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[455] | 96 | !!---------------------------------------------------------------------- |
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[2528] | 97 | ! |
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[3294] | 98 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
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[2715] | 99 | ! |
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[503] | 100 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
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[3294] | 101 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 102 | ztrdu(:,:,:) = ua(:,:,:) |
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| 103 | ztrdv(:,:,:) = va(:,:,:) |
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| 104 | ENDIF |
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[2528] | 105 | ! |
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[11556] | 106 | |
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[8400] | 107 | IF ( ln_bias .AND. ln_bias_pc_app ) THEN |
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| 108 | |
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[11556] | 109 | ! allocate space for tempory variables for the bias pressure correction (bpc) |
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[8400] | 110 | ALLOCATE( z_rhd_st(jpi,jpj,jpk), & |
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| 111 | & z_gru_st(jpi,jpj), & |
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[11556] | 112 | & z_grv_st(jpi,jpj), & |
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| 113 | & z_ua(jpi,jpj,jpk), & |
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| 114 | & z_va(jpi,jpj,jpk), & |
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| 115 | & z_ua_bpc(jpi,jpj,jpk), & |
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| 116 | & z_va_bpc(jpi,jpj,jpk), & |
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| 117 | & z_ua_bpc_bot(jpi,jpj), & |
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| 118 | & z_va_bpc_bot(jpi,jpj) & |
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| 119 | & ) |
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[8400] | 120 | |
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[11556] | 121 | ! save the original acceleration trends |
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| 122 | ! (z_ua_bpc, z_va_bpc are used as temporary storage) |
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| 123 | z_ua_bpc(:,:,:) = ua(:,:,:) |
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| 124 | z_va_bpc(:,:,:) = va(:,:,:) |
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| 125 | |
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| 126 | END IF |
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[8400] | 127 | |
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[3294] | 128 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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[503] | 129 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 130 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 131 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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[3294] | 132 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 133 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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[5120] | 134 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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[455] | 135 | END SELECT |
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[2528] | 136 | ! |
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[11556] | 137 | |
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| 138 | IF ( ln_bias .AND. ln_bias_pc_app ) THEN |
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| 139 | |
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| 140 | ! The aim here is to calculate the contribution of the bpc to the acceleration terms. |
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| 141 | ! This is done so that the effect of the bpc on the hpg at the bottom can be removed. |
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| 142 | ! In order to do that: |
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| 143 | ! 1. The hpg calculation is done again, but with the contributions of the bpc included. |
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| 144 | ! 2. The difference between the acceleration terms (w and w/o bpc) is then calculated. |
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| 145 | ! 3. The effect of the bpc on the bottom hpg is then removed. |
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| 146 | ! 4. The total change to the acceleration terms is then calculated. |
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| 147 | |
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| 148 | ! The original density fields etc (without the bpc) are stored. |
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| 149 | z_rhd_st(:,:,:) = rhd(:,:,:) |
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| 150 | z_gru_st(:,:) = gru(:,:) |
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| 151 | z_grv_st(:,:) = grv(:,:) |
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| 152 | |
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| 153 | ! Set the density etc used in the hpc calculations to the value including the effect of the bpc. |
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| 154 | rhd(:,:,:) = rhd_pc(:,:,:) |
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| 155 | gru(:,:) = gru_pc(:,:) |
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| 156 | grv(:,:) = grv_pc(:,:) |
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| 157 | |
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| 158 | ! save the acceleration trends including hpg field but calculated without the bpc fields |
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| 159 | z_ua(:,:,:) = ua(:,:,:) |
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| 160 | z_va(:,:,:) = va(:,:,:) |
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| 161 | |
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| 162 | ! reset the acceleration trends to their original values |
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| 163 | ua(:,:,:) = z_ua_bpc(:,:,:) |
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| 164 | va(:,:,:) = z_va_bpc(:,:,:) |
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| 165 | |
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| 166 | ! re-calculate the horizontal pressure gradients with the bpc fields |
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| 167 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
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| 168 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
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| 169 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
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| 170 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
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| 171 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
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| 172 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
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| 173 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
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| 174 | END SELECT |
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| 175 | |
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| 176 | ! calculate the bpc contribution to ua and va |
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| 177 | z_ua_bpc(:,:,:) = ua(:,:,:) - z_ua(:,:,:) |
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| 178 | z_va_bpc(:,:,:) = va(:,:,:) - z_va(:,:,:) |
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| 179 | |
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| 180 | ! calculate the bpc contribution to ua and va at the bottom |
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| 181 | DO jj = 2, jpjm1 |
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| 182 | DO ji = 2, jpim1 |
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| 183 | iku = mbku(ji,jj) |
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| 184 | ikv = mbkv(ji,jj) |
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| 185 | z_ua_bpc_bot(ji,jj) = z_ua_bpc(ji,jj,iku) |
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| 186 | z_va_bpc_bot(ji,jj) = z_va_bpc(ji,jj,ikv) |
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| 187 | END DO ! ji |
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| 188 | END DO ! jj |
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| 189 | |
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| 190 | ! subtract off the bottom values of bpc contribution to ua and va |
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| 191 | DO jk = 1, jpk - 1 |
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| 192 | z_ua_bpc(:,:,jk) = z_ua_bpc(:,:,jk) - z_ua_bpc_bot(:,:) |
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| 193 | z_va_bpc(:,:,jk) = z_va_bpc(:,:,jk) - z_va_bpc_bot(:,:) |
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| 194 | END DO |
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| 195 | |
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| 196 | ! calculate ua using the original hpg (z_ua) and the bias hpg |
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| 197 | ! with the bottom pressure gradients subtracted off |
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| 198 | ua(:,:,:) = z_ua(:,:,:) + z_ua_bpc(:,:,:) |
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| 199 | va(:,:,:) = z_va(:,:,:) + z_va_bpc(:,:,:) |
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| 200 | |
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| 201 | ! restore original density, gru and grv fields |
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| 202 | rhd(:,:,:) = z_rhd_st(:,:,:) |
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| 203 | gru(:,:) = z_gru_st(:,:) |
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| 204 | grv(:,:) = z_grv_st(:,:) |
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| 205 | |
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| 206 | ! deallocate tempory variables |
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| 207 | DEALLOCATE( z_rhd_st, z_gru_st, z_grv_st, & |
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| 208 | & z_ua, z_va, z_ua_bpc, z_va_bpc, & |
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| 209 | & z_ua_bpc_bot, z_va_bpc_bot & |
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| 210 | & ) |
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| 211 | |
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| 212 | ENDIF ! ln_bias .AND. ln_bias_pc_app |
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| 213 | |
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| 214 | |
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[503] | 215 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
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[455] | 216 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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| 217 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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[4990] | 218 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
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[3294] | 219 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
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[3764] | 220 | ENDIF |
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[503] | 221 | ! |
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| 222 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
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| 223 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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| 224 | ! |
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[3294] | 225 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
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[2715] | 226 | ! |
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[455] | 227 | END SUBROUTINE dyn_hpg |
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| 228 | |
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| 229 | |
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[2528] | 230 | SUBROUTINE dyn_hpg_init |
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[455] | 231 | !!---------------------------------------------------------------------- |
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[2528] | 232 | !! *** ROUTINE dyn_hpg_init *** |
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[455] | 233 | !! |
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| 234 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
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| 235 | !! computation and consistency control |
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| 236 | !! |
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[1601] | 237 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
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[455] | 238 | !! with the type of vertical coordinate used (zco, zps, sco) |
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| 239 | !!---------------------------------------------------------------------- |
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| 240 | INTEGER :: ioptio = 0 ! temporary integer |
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[4147] | 241 | INTEGER :: ios ! Local integer output status for namelist read |
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[1601] | 242 | !! |
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[3294] | 243 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
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[5120] | 244 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp |
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[455] | 245 | !!---------------------------------------------------------------------- |
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[2528] | 246 | ! |
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[4147] | 247 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
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| 248 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
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| 249 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
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| 250 | |
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| 251 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
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| 252 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
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| 253 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
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[4624] | 254 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
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[2528] | 255 | ! |
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| 256 | IF(lwp) THEN ! Control print |
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[455] | 257 | WRITE(numout,*) |
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[2528] | 258 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
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| 259 | WRITE(numout,*) '~~~~~~~~~~~~' |
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[1601] | 260 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
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| 261 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
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| 262 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
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| 263 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
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[5120] | 264 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
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[1601] | 265 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
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[3294] | 266 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
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[1601] | 267 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
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[455] | 268 | ENDIF |
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[2528] | 269 | ! |
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[3294] | 270 | IF( ln_hpg_djc ) & |
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| 271 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
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| 272 | & currently disabled (bugs under investigation). Please select & |
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| 273 | & either ln_hpg_sco or ln_hpg_prj instead') |
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[2528] | 274 | ! |
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[5120] | 275 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
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[3294] | 276 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
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| 277 | & the standard jacobian formulation hpg_sco or & |
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| 278 | & the pressure jacobian formulation hpg_prj') |
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[5120] | 279 | |
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| 280 | IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) & |
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| 281 | & CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
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| 282 | IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) & |
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| 283 | & CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
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[3294] | 284 | ! |
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[503] | 285 | ! ! Set nhpg from ln_hpg_... flags |
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[455] | 286 | IF( ln_hpg_zco ) nhpg = 0 |
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| 287 | IF( ln_hpg_zps ) nhpg = 1 |
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| 288 | IF( ln_hpg_sco ) nhpg = 2 |
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[3294] | 289 | IF( ln_hpg_djc ) nhpg = 3 |
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| 290 | IF( ln_hpg_prj ) nhpg = 4 |
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[5120] | 291 | IF( ln_hpg_isf ) nhpg = 5 |
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[2528] | 292 | ! |
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[3294] | 293 | ! ! Consistency check |
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[3764] | 294 | ioptio = 0 |
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[455] | 295 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
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| 296 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
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| 297 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
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| 298 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
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[3294] | 299 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
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[5120] | 300 | IF( ln_hpg_isf ) ioptio = ioptio + 1 |
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[2715] | 301 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
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[5120] | 302 | ! |
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| 303 | ! initialisation of ice load |
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| 304 | riceload(:,:)=0.0 |
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[503] | 305 | ! |
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[2528] | 306 | END SUBROUTINE dyn_hpg_init |
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[455] | 307 | |
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| 308 | |
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| 309 | SUBROUTINE hpg_zco( kt ) |
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| 310 | !!--------------------------------------------------------------------- |
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| 311 | !! *** ROUTINE hpg_zco *** |
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| 312 | !! |
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| 313 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
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| 314 | !! The now hydrostatic pressure gradient at a given level, jk, |
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| 315 | !! is computed by taking the vertical integral of the in-situ |
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| 316 | !! density gradient along the model level from the suface to that |
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| 317 | !! level: zhpi = grav ..... |
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| 318 | !! zhpj = grav ..... |
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[3] | 319 | !! add it to the general momentum trend (ua,va). |
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[455] | 320 | !! ua = ua - 1/e1u * zhpi |
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| 321 | !! va = va - 1/e2v * zhpj |
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[3764] | 322 | !! |
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[3] | 323 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
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[503] | 324 | !!---------------------------------------------------------------------- |
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| 325 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 326 | !! |
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| 327 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 328 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
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[3764] | 329 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
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[3] | 330 | !!---------------------------------------------------------------------- |
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[3764] | 331 | ! |
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[3294] | 332 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
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| 333 | ! |
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[3] | 334 | IF( kt == nit000 ) THEN |
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| 335 | IF(lwp) WRITE(numout,*) |
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[455] | 336 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
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| 337 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
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[3] | 338 | ENDIF |
---|
| 339 | |
---|
[3764] | 340 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
---|
| 341 | |
---|
[455] | 342 | ! Surface value |
---|
[3] | 343 | DO jj = 2, jpjm1 |
---|
| 344 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 345 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
---|
| 346 | ! hydrostatic pressure gradient |
---|
| 347 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
---|
| 348 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
---|
[3] | 349 | ! add to the general momentum trend |
---|
[455] | 350 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 351 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 352 | END DO |
---|
| 353 | END DO |
---|
[3294] | 354 | |
---|
[503] | 355 | ! |
---|
[455] | 356 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 357 | DO jk = 2, jpkm1 |
---|
[455] | 358 | DO jj = 2, jpjm1 |
---|
[3] | 359 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 360 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
---|
| 361 | ! hydrostatic pressure gradient |
---|
| 362 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 363 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
---|
| 364 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 365 | |
---|
| 366 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 367 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
---|
| 368 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
---|
[3] | 369 | ! add to the general momentum trend |
---|
[455] | 370 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 371 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[3] | 372 | END DO |
---|
| 373 | END DO |
---|
| 374 | END DO |
---|
[503] | 375 | ! |
---|
[3294] | 376 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 377 | ! |
---|
[455] | 378 | END SUBROUTINE hpg_zco |
---|
[216] | 379 | |
---|
[3] | 380 | |
---|
[455] | 381 | SUBROUTINE hpg_zps( kt ) |
---|
[3] | 382 | !!--------------------------------------------------------------------- |
---|
[455] | 383 | !! *** ROUTINE hpg_zps *** |
---|
[3764] | 384 | !! |
---|
[455] | 385 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
---|
[3764] | 386 | !! |
---|
[3] | 387 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[3764] | 388 | !!---------------------------------------------------------------------- |
---|
[503] | 389 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 390 | !! |
---|
| 391 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 392 | INTEGER :: iku, ikv ! temporary integers |
---|
| 393 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
---|
[3764] | 394 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3] | 395 | !!---------------------------------------------------------------------- |
---|
[3294] | 396 | ! |
---|
| 397 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 398 | ! |
---|
[3] | 399 | IF( kt == nit000 ) THEN |
---|
| 400 | IF(lwp) WRITE(numout,*) |
---|
[455] | 401 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
---|
[503] | 402 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
---|
[3] | 403 | ENDIF |
---|
| 404 | |
---|
[3294] | 405 | |
---|
[503] | 406 | ! Local constant initialization |
---|
[2528] | 407 | zcoef0 = - grav * 0.5_wp |
---|
[3] | 408 | |
---|
[2528] | 409 | ! Surface value (also valid in partial step case) |
---|
[3] | 410 | DO jj = 2, jpjm1 |
---|
| 411 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 412 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
---|
[3] | 413 | ! hydrostatic pressure gradient |
---|
[455] | 414 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
---|
| 415 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
---|
[3] | 416 | ! add to the general momentum trend |
---|
| 417 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 418 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 419 | END DO |
---|
| 420 | END DO |
---|
| 421 | |
---|
[3294] | 422 | |
---|
[503] | 423 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 424 | DO jk = 2, jpkm1 |
---|
| 425 | DO jj = 2, jpjm1 |
---|
| 426 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 427 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
---|
[3] | 428 | ! hydrostatic pressure gradient |
---|
| 429 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
[455] | 430 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
| 431 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
---|
[3] | 432 | |
---|
| 433 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
[455] | 434 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
| 435 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
---|
[3] | 436 | ! add to the general momentum trend |
---|
| 437 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 438 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[455] | 439 | END DO |
---|
[3] | 440 | END DO |
---|
| 441 | END DO |
---|
| 442 | |
---|
[3294] | 443 | |
---|
[2528] | 444 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
---|
[3] | 445 | DO jj = 2, jpjm1 |
---|
| 446 | DO ji = 2, jpim1 |
---|
[2528] | 447 | iku = mbku(ji,jj) |
---|
| 448 | ikv = mbkv(ji,jj) |
---|
[3] | 449 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
---|
| 450 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
---|
[2528] | 451 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 452 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 453 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
| 454 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
---|
| 455 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 456 | ENDIF |
---|
[2528] | 457 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 458 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 459 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 460 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
---|
| 461 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 462 | ENDIF |
---|
| 463 | END DO |
---|
| 464 | END DO |
---|
[503] | 465 | ! |
---|
[3294] | 466 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 467 | ! |
---|
[455] | 468 | END SUBROUTINE hpg_zps |
---|
[216] | 469 | |
---|
[455] | 470 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 471 | !!--------------------------------------------------------------------- |
---|
[455] | 472 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 473 | !! |
---|
[455] | 474 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 475 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 476 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 477 | !! density gradient along the model level from the suface to that |
---|
[455] | 478 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 479 | !! to the horizontal pressure gradient : |
---|
| 480 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 481 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[3] | 482 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 483 | !! ua = ua - 1/e1u * zhpi |
---|
| 484 | !! va = va - 1/e2v * zhpj |
---|
[3] | 485 | !! |
---|
| 486 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 487 | !!---------------------------------------------------------------------- |
---|
| 488 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 489 | !! |
---|
[5120] | 490 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 491 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
| 492 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
| 493 | !!---------------------------------------------------------------------- |
---|
| 494 | ! |
---|
| 495 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 496 | ! |
---|
| 497 | IF( kt == nit000 ) THEN |
---|
| 498 | IF(lwp) WRITE(numout,*) |
---|
| 499 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 500 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 501 | ENDIF |
---|
| 502 | |
---|
| 503 | ! Local constant initialization |
---|
| 504 | zcoef0 = - grav * 0.5_wp |
---|
| 505 | ! To use density and not density anomaly |
---|
| 506 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 507 | ELSE ; znad = 0._wp ! Fixed volume |
---|
| 508 | ENDIF |
---|
| 509 | |
---|
| 510 | ! Surface value |
---|
| 511 | DO jj = 2, jpjm1 |
---|
| 512 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 513 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 514 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 515 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 516 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 517 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 518 | ! s-coordinate pressure gradient correction |
---|
| 519 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 520 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
| 521 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 522 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 523 | ! add to the general momentum trend |
---|
| 524 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 525 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 526 | END DO |
---|
| 527 | END DO |
---|
| 528 | |
---|
| 529 | ! interior value (2=<jk=<jpkm1) |
---|
| 530 | DO jk = 2, jpkm1 |
---|
| 531 | DO jj = 2, jpjm1 |
---|
| 532 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 533 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 534 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 535 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 536 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 537 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 538 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 539 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
| 540 | ! s-coordinate pressure gradient correction |
---|
| 541 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 542 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 543 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 544 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 545 | ! add to the general momentum trend |
---|
| 546 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 547 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 548 | END DO |
---|
| 549 | END DO |
---|
| 550 | END DO |
---|
| 551 | ! |
---|
| 552 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 553 | ! |
---|
| 554 | END SUBROUTINE hpg_sco |
---|
| 555 | |
---|
| 556 | SUBROUTINE hpg_isf( kt ) |
---|
| 557 | !!--------------------------------------------------------------------- |
---|
| 558 | !! *** ROUTINE hpg_sco *** |
---|
| 559 | !! |
---|
| 560 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 561 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 562 | !! is computed by taking the vertical integral of the in-situ |
---|
| 563 | !! density gradient along the model level from the suface to that |
---|
| 564 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 565 | !! to the horizontal pressure gradient : |
---|
| 566 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 567 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 568 | !! add it to the general momentum trend (ua,va). |
---|
| 569 | !! ua = ua - 1/e1u * zhpi |
---|
| 570 | !! va = va - 1/e2v * zhpj |
---|
| 571 | !! iceload is added and partial cell case are added to the top and bottom |
---|
| 572 | !! |
---|
| 573 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 574 | !!---------------------------------------------------------------------- |
---|
| 575 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 576 | !! |
---|
[4990] | 577 | INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 578 | REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars |
---|
| 579 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd |
---|
| 580 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
---|
| 581 | REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj |
---|
[3] | 582 | !!---------------------------------------------------------------------- |
---|
[3294] | 583 | ! |
---|
[4990] | 584 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
---|
| 585 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 586 | CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 587 | ! |
---|
[4990] | 588 | IF( kt == nit000 ) THEN |
---|
[3] | 589 | IF(lwp) WRITE(numout,*) |
---|
[5120] | 590 | IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf' |
---|
[455] | 591 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
[3] | 592 | ENDIF |
---|
| 593 | |
---|
[503] | 594 | ! Local constant initialization |
---|
[2528] | 595 | zcoef0 = - grav * 0.5_wp |
---|
[592] | 596 | ! To use density and not density anomaly |
---|
[4990] | 597 | ! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 598 | ! ELSE ; znad = 0._wp ! Fixed volume |
---|
| 599 | ! ENDIF |
---|
| 600 | znad=1._wp |
---|
| 601 | ! iniitialised to 0. zhpi zhpi |
---|
| 602 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
---|
[455] | 603 | |
---|
[4990] | 604 | !================================================================================== |
---|
| 605 | !=====Compute iceload and contribution of the half first wet layer ================= |
---|
| 606 | !=================================================================================== |
---|
| 607 | |
---|
| 608 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
---|
| 609 | ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp |
---|
| 610 | |
---|
| 611 | ! compute density of the water displaced by the ice shelf |
---|
| 612 | zrhd = rhd ! save rhd |
---|
| 613 | DO jk = 1, jpk |
---|
| 614 | zdept(:,:)=gdept_1d(jk) |
---|
| 615 | CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk)) |
---|
| 616 | END DO |
---|
| 617 | WHERE ( tmask(:,:,:) == 1._wp) |
---|
| 618 | rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd |
---|
| 619 | END WHERE |
---|
| 620 | |
---|
| 621 | ! compute rhd at the ice/oce interface (ice shelf side) |
---|
| 622 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
---|
| 623 | |
---|
| 624 | ! compute rhd at the ice/oce interface (ocean side) |
---|
| 625 | DO ji=1,jpi |
---|
| 626 | DO jj=1,jpj |
---|
| 627 | ikt=mikt(ji,jj) |
---|
| 628 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
---|
| 629 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
---|
| 630 | END DO |
---|
| 631 | END DO |
---|
| 632 | CALL eos(ztstop,risfdep,zrhdtop_oce) |
---|
| 633 | ! |
---|
| 634 | ! Surface value + ice shelf gradient |
---|
| 635 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
---|
| 636 | ziceload = 0._wp |
---|
| 637 | DO jj = 1, jpj |
---|
| 638 | DO ji = 1, jpi ! vector opt. |
---|
| 639 | ikt=mikt(ji,jj) |
---|
| 640 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
---|
| 641 | DO jk=2,ikt-1 |
---|
| 642 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) & |
---|
| 643 | & * (1._wp - tmask(ji,jj,jk)) |
---|
| 644 | END DO |
---|
| 645 | IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) & |
---|
| 646 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
---|
| 647 | END DO |
---|
| 648 | END DO |
---|
| 649 | riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5 |
---|
| 650 | ! compute zp from z=0 to first T wet point (correction due to zps not yet applied) |
---|
[455] | 651 | DO jj = 2, jpjm1 |
---|
[3764] | 652 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 653 | ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1) |
---|
| 654 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 655 | ! we assume ISF is in isostatic equilibrium |
---|
| 656 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) & |
---|
| 657 | & * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) & |
---|
| 658 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 659 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 660 | & + ( ziceload(ji+1,jj) - ziceload(ji,jj)) ) |
---|
| 661 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) & |
---|
| 662 | & * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) & |
---|
| 663 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 664 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 665 | & + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) ) |
---|
| 666 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
[2528] | 667 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 668 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 669 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 670 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 671 | ! add to the general momentum trend |
---|
[4990] | 672 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 673 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
[3764] | 674 | END DO |
---|
| 675 | END DO |
---|
[4990] | 676 | !================================================================================== |
---|
| 677 | !===== Compute partial cell contribution for the top cell ========================= |
---|
| 678 | !================================================================================== |
---|
| 679 | DO jj = 2, jpjm1 |
---|
| 680 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 681 | iku = miku(ji,jj) ; |
---|
| 682 | zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp |
---|
| 683 | 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)) |
---|
| 684 | ! u direction |
---|
| 685 | IF ( iku .GT. 1 ) THEN |
---|
| 686 | ! case iku |
---|
| 687 | zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu & |
---|
| 688 | & * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) & |
---|
| 689 | & + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad ) |
---|
| 690 | ! corrective term ( = 0 if z coordinate ) |
---|
| 691 | zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj) |
---|
| 692 | ! zhpi will be added in interior loop |
---|
| 693 | ua(ji,jj,iku) = ua(ji,jj,iku) + zuap |
---|
| 694 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 695 | IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku) |
---|
[3764] | 696 | |
---|
[4990] | 697 | ! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps) |
---|
| 698 | zhpiint = zcoef0 / e1u(ji,jj) & |
---|
| 699 | & * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) & |
---|
| 700 | & + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) & |
---|
| 701 | & - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) & |
---|
| 702 | & + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) ) |
---|
| 703 | zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint |
---|
| 704 | END IF |
---|
| 705 | |
---|
| 706 | ! v direction |
---|
| 707 | ikv = mikv(ji,jj) |
---|
| 708 | 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)) |
---|
| 709 | IF ( ikv .GT. 1 ) THEN |
---|
| 710 | ! case ikv |
---|
| 711 | zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv & |
---|
| 712 | & * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) & |
---|
| 713 | & + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad ) |
---|
| 714 | ! corrective term ( = 0 if z coordinate ) |
---|
| 715 | zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj) |
---|
| 716 | ! zhpi will be added in interior loop |
---|
| 717 | va(ji,jj,ikv) = va(ji,jj,ikv) + zvap |
---|
| 718 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 719 | IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv) |
---|
| 720 | |
---|
| 721 | ! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps) |
---|
| 722 | zhpjint = zcoef0 / e2v(ji,jj) & |
---|
| 723 | & * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) & |
---|
| 724 | & + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) & |
---|
| 725 | & - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) & |
---|
| 726 | & + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) ) |
---|
| 727 | zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint |
---|
| 728 | END IF |
---|
| 729 | END DO |
---|
| 730 | END DO |
---|
| 731 | |
---|
| 732 | !================================================================================== |
---|
| 733 | !===== Compute interior value ===================================================== |
---|
| 734 | !================================================================================== |
---|
| 735 | |
---|
| 736 | DO jj = 2, jpjm1 |
---|
| 737 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 738 | iku=miku(ji,jj); ikv=mikv(ji,jj) |
---|
| 739 | DO jk = 2, jpkm1 |
---|
[455] | 740 | ! hydrostatic pressure gradient along s-surfaces |
---|
[4990] | 741 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 742 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) & |
---|
| 743 | & + zcoef0 / e1u(ji,jj) & |
---|
| 744 | & * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) & |
---|
| 745 | & + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) & |
---|
| 746 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) & |
---|
| 747 | & + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) ) |
---|
[455] | 748 | ! s-coordinate pressure gradient correction |
---|
[4990] | 749 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 750 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 751 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1) |
---|
| 752 | ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 753 | |
---|
| 754 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 755 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 756 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) & |
---|
| 757 | & + zcoef0 / e2v(ji,jj) & |
---|
| 758 | & * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) & |
---|
| 759 | & + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) & |
---|
| 760 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) & |
---|
| 761 | & + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) ) |
---|
| 762 | ! s-coordinate pressure gradient correction |
---|
| 763 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 764 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 765 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1) |
---|
[455] | 766 | ! add to the general momentum trend |
---|
[4990] | 767 | va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk) |
---|
[455] | 768 | END DO |
---|
| 769 | END DO |
---|
| 770 | END DO |
---|
[4990] | 771 | |
---|
| 772 | !================================================================================== |
---|
| 773 | !===== Compute bottom cell contribution (partial cell) ============================ |
---|
| 774 | !================================================================================== |
---|
| 775 | |
---|
| 776 | DO jj = 2, jpjm1 |
---|
| 777 | DO ji = 2, jpim1 |
---|
| 778 | iku = mbku(ji,jj) |
---|
| 779 | ikv = mbkv(ji,jj) |
---|
| 780 | |
---|
| 781 | IF (iku .GT. 1) THEN |
---|
| 782 | ! remove old value (interior case) |
---|
| 783 | zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) & |
---|
| 784 | & * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj) |
---|
| 785 | ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap |
---|
| 786 | ! put new value |
---|
| 787 | ! -zpshpi to avoid double contribution of the partial step in the top layer |
---|
| 788 | zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj) |
---|
| 789 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj) |
---|
| 790 | ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap |
---|
| 791 | END IF |
---|
| 792 | ! v direction |
---|
| 793 | IF (ikv .GT. 1) THEN |
---|
| 794 | ! remove old value (interior case) |
---|
| 795 | zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) & |
---|
| 796 | & * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj) |
---|
| 797 | va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap |
---|
| 798 | ! put new value |
---|
| 799 | ! -zpshpj to avoid double contribution of the partial step in the top layer |
---|
| 800 | zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj) |
---|
| 801 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj) |
---|
| 802 | va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap |
---|
| 803 | END IF |
---|
| 804 | END DO |
---|
| 805 | END DO |
---|
| 806 | |
---|
| 807 | ! set back to original density value into the ice shelf cell (maybe useless because it is masked) |
---|
| 808 | rhd = zrhd |
---|
[503] | 809 | ! |
---|
[4990] | 810 | CALL wrk_dealloc( jpi,jpj,2, ztstop) |
---|
| 811 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 812 | CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 813 | ! |
---|
[5120] | 814 | END SUBROUTINE hpg_isf |
---|
[455] | 815 | |
---|
[4990] | 816 | |
---|
[455] | 817 | SUBROUTINE hpg_djc( kt ) |
---|
| 818 | !!--------------------------------------------------------------------- |
---|
| 819 | !! *** ROUTINE hpg_djc *** |
---|
| 820 | !! |
---|
| 821 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 822 | !! |
---|
[503] | 823 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 824 | !!---------------------------------------------------------------------- |
---|
[503] | 825 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 826 | !! |
---|
| 827 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 828 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 829 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 830 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3764] | 831 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3294] | 832 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 833 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 834 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 835 | !!---------------------------------------------------------------------- |
---|
[3294] | 836 | ! |
---|
[3764] | 837 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 838 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 839 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[3294] | 840 | ! |
---|
[455] | 841 | |
---|
| 842 | IF( kt == nit000 ) THEN |
---|
| 843 | IF(lwp) WRITE(numout,*) |
---|
| 844 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 845 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 846 | ENDIF |
---|
| 847 | |
---|
[503] | 848 | ! Local constant initialization |
---|
[2528] | 849 | zcoef0 = - grav * 0.5_wp |
---|
| 850 | z1_10 = 1._wp / 10._wp |
---|
| 851 | z1_12 = 1._wp / 12._wp |
---|
[455] | 852 | |
---|
| 853 | !---------------------------------------------------------------------------------------- |
---|
| 854 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 855 | !---------------------------------------------------------------------------------------- |
---|
| 856 | |
---|
| 857 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 858 | |
---|
| 859 | DO jk = 2, jpkm1 |
---|
| 860 | DO jj = 2, jpjm1 |
---|
| 861 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 862 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 863 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 864 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 865 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 866 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 867 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 868 | END DO |
---|
| 869 | END DO |
---|
| 870 | END DO |
---|
| 871 | |
---|
| 872 | !------------------------------------------------------------------------- |
---|
| 873 | ! compute harmonic averages using eq. 5.18 |
---|
| 874 | !------------------------------------------------------------------------- |
---|
| 875 | zep = 1.e-15 |
---|
| 876 | |
---|
[503] | 877 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 878 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 879 | |
---|
| 880 | DO jk = 2, jpkm1 |
---|
| 881 | DO jj = 2, jpjm1 |
---|
| 882 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 883 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 884 | |
---|
[2528] | 885 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 886 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 887 | |
---|
[2528] | 888 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 889 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 890 | |
---|
| 891 | IF( cffw > zep) THEN |
---|
[2528] | 892 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 893 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 894 | ELSE |
---|
[2528] | 895 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 896 | ENDIF |
---|
| 897 | |
---|
[2528] | 898 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 899 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 900 | |
---|
| 901 | IF( cffu > zep ) THEN |
---|
[2528] | 902 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 903 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 904 | ELSE |
---|
[2528] | 905 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 906 | ENDIF |
---|
| 907 | |
---|
| 908 | IF( cffx > zep ) THEN |
---|
[2528] | 909 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 910 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 911 | ELSE |
---|
[2528] | 912 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 913 | ENDIF |
---|
| 914 | |
---|
| 915 | IF( cffv > zep ) THEN |
---|
[2528] | 916 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 917 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 918 | ELSE |
---|
[2528] | 919 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 920 | ENDIF |
---|
| 921 | |
---|
| 922 | IF( cffy > zep ) THEN |
---|
[2528] | 923 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 924 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 925 | ELSE |
---|
[2528] | 926 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 927 | ENDIF |
---|
| 928 | |
---|
| 929 | END DO |
---|
| 930 | END DO |
---|
| 931 | END DO |
---|
| 932 | |
---|
| 933 | !---------------------------------------------------------------------------------- |
---|
| 934 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 935 | !---------------------------------------------------------------------------------- |
---|
[2528] | 936 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 937 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 938 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 939 | |
---|
[2528] | 940 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 941 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 942 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 943 | |
---|
| 944 | |
---|
| 945 | !-------------------------------------------------------------- |
---|
| 946 | ! Upper half of top-most grid box, compute and store |
---|
| 947 | !------------------------------------------------------------- |
---|
| 948 | |
---|
| 949 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 950 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 951 | |
---|
| 952 | DO jj = 2, jpjm1 |
---|
| 953 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 954 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 955 | & * ( rhd(ji,jj,1) & |
---|
| 956 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 957 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
[3764] | 958 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 959 | END DO |
---|
| 960 | END DO |
---|
| 961 | |
---|
| 962 | !!bug gm : here also, simplification is possible |
---|
| 963 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 964 | |
---|
| 965 | DO jk = 2, jpkm1 |
---|
| 966 | DO jj = 2, jpjm1 |
---|
| 967 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 968 | |
---|
| 969 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 970 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 971 | & - grav * z1_10 * ( & |
---|
| 972 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 973 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 974 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 975 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 976 | & ) |
---|
| 977 | |
---|
| 978 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 979 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 980 | & - grav* z1_10 * ( & |
---|
| 981 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 982 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 983 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 984 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 985 | & ) |
---|
| 986 | |
---|
| 987 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 988 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 989 | & - grav* z1_10 * ( & |
---|
| 990 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 991 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 992 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 993 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 994 | & ) |
---|
| 995 | |
---|
| 996 | END DO |
---|
| 997 | END DO |
---|
| 998 | END DO |
---|
| 999 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 1000 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 1001 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 1002 | |
---|
| 1003 | |
---|
| 1004 | ! --------------- |
---|
| 1005 | ! Surface value |
---|
| 1006 | ! --------------- |
---|
| 1007 | DO jj = 2, jpjm1 |
---|
| 1008 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1009 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 1010 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 1011 | ! add to the general momentum trend |
---|
| 1012 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 1013 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 1014 | END DO |
---|
| 1015 | END DO |
---|
| 1016 | |
---|
| 1017 | ! ---------------- |
---|
| 1018 | ! interior value (2=<jk=<jpkm1) |
---|
| 1019 | ! ---------------- |
---|
| 1020 | DO jk = 2, jpkm1 |
---|
[3764] | 1021 | DO jj = 2, jpjm1 |
---|
[455] | 1022 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1023 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 1024 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 1025 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 1026 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 1027 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 1028 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 1029 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 1030 | ! add to the general momentum trend |
---|
| 1031 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 1032 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 1033 | END DO |
---|
| 1034 | END DO |
---|
| 1035 | END DO |
---|
[503] | 1036 | ! |
---|
[3764] | 1037 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 1038 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 1039 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 1040 | ! |
---|
[455] | 1041 | END SUBROUTINE hpg_djc |
---|
| 1042 | |
---|
| 1043 | |
---|
[3294] | 1044 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 1045 | !!--------------------------------------------------------------------- |
---|
[3294] | 1046 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 1047 | !! |
---|
[3294] | 1048 | !! ** Method : s-coordinate case. |
---|
| 1049 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 1050 | !! based on the constrained cubic-spline interpolation for |
---|
| 1051 | !! all vertical coordinate systems |
---|
[455] | 1052 | !! |
---|
[3294] | 1053 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 1054 | !!---------------------------------------------------------------------- |
---|
[3294] | 1055 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 1056 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 1057 | !! |
---|
[3294] | 1058 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 1059 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 1060 | !! |
---|
[3294] | 1061 | !! The local variables for the correction term |
---|
| 1062 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 1063 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 1064 | REAL(wp) :: zrhdt1 |
---|
[3294] | 1065 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[3764] | 1066 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
[3294] | 1067 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[5224] | 1068 | REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n |
---|
[455] | 1069 | !!---------------------------------------------------------------------- |
---|
[3294] | 1070 | ! |
---|
[3764] | 1071 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1072 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 1073 | CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[3294] | 1074 | ! |
---|
[455] | 1075 | IF( kt == nit000 ) THEN |
---|
| 1076 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 1077 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 1078 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 1079 | ENDIF |
---|
| 1080 | |
---|
[3294] | 1081 | !!---------------------------------------------------------------------- |
---|
| 1082 | ! Local constant initialization |
---|
[3764] | 1083 | zcoef0 = - grav |
---|
[3294] | 1084 | znad = 0.0_wp |
---|
| 1085 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 1086 | |
---|
[3294] | 1087 | ! Clean 3-D work arrays |
---|
| 1088 | zhpi(:,:,:) = 0._wp |
---|
| 1089 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 1090 | |
---|
[3294] | 1091 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 1092 | DO jj = 1, jpj |
---|
[3764] | 1093 | DO ji = 1, jpi |
---|
[3294] | 1094 | jk = mbathy(ji,jj) |
---|
| 1095 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 1096 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 1097 | ELSE IF(jk < jpkm1) THEN |
---|
| 1098 | DO jkk = jk+1, jpk |
---|
| 1099 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 1100 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
[3764] | 1101 | END DO |
---|
[3294] | 1102 | ENDIF |
---|
| 1103 | END DO |
---|
| 1104 | END DO |
---|
[3] | 1105 | |
---|
[3632] | 1106 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 1107 | DO jj = 1, jpj |
---|
| 1108 | DO ji = 1, jpi |
---|
| 1109 | zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 1110 | END DO |
---|
| 1111 | END DO |
---|
[455] | 1112 | |
---|
[4990] | 1113 | DO jk = 2, jpk |
---|
| 1114 | DO jj = 1, jpj |
---|
| 1115 | DO ji = 1, jpi |
---|
| 1116 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 1117 | END DO |
---|
| 1118 | END DO |
---|
| 1119 | END DO |
---|
[455] | 1120 | |
---|
[4990] | 1121 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 1122 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 1123 | |
---|
[3764] | 1124 | ! Construct the vertical density profile with the |
---|
[3294] | 1125 | ! constrained cubic spline interpolation |
---|
| 1126 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[3764] | 1127 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
[3294] | 1128 | |
---|
| 1129 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 1130 | DO jj = 2, jpj |
---|
[3764] | 1131 | DO ji = 2, jpi |
---|
[3632] | 1132 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), & |
---|
[3294] | 1133 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
[3632] | 1134 | dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1) |
---|
[3294] | 1135 | |
---|
| 1136 | ! assuming linear profile across the top half surface layer |
---|
[3764] | 1137 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
[3294] | 1138 | END DO |
---|
[455] | 1139 | END DO |
---|
| 1140 | |
---|
[3294] | 1141 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 1142 | DO jk = 2, jpkm1 |
---|
| 1143 | DO jj = 2, jpj |
---|
[3294] | 1144 | DO ji = 2, jpi |
---|
| 1145 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
[3632] | 1146 | integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),& |
---|
[3294] | 1147 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 1148 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 1149 | END DO |
---|
| 1150 | END DO |
---|
[455] | 1151 | END DO |
---|
| 1152 | |
---|
[3294] | 1153 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5224] | 1154 | |
---|
| 1155 | ! Prepare zsshu_n and zsshv_n |
---|
[3764] | 1156 | DO jj = 2, jpjm1 |
---|
| 1157 | DO ji = 2, jpim1 |
---|
[5224] | 1158 | zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
| 1159 | & r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1160 | zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
| 1161 | & r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
[3294] | 1162 | END DO |
---|
[455] | 1163 | END DO |
---|
| 1164 | |
---|
[5224] | 1165 | DO jj = 2, jpjm1 |
---|
| 1166 | DO ji = 2, jpim1 |
---|
| 1167 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
| 1168 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
| 1169 | END DO |
---|
| 1170 | END DO |
---|
| 1171 | |
---|
[3764] | 1172 | DO jk = 2, jpkm1 |
---|
| 1173 | DO jj = 2, jpjm1 |
---|
| 1174 | DO ji = 2, jpim1 |
---|
[3294] | 1175 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 1176 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 1177 | END DO |
---|
| 1178 | END DO |
---|
[455] | 1179 | END DO |
---|
[3764] | 1180 | |
---|
| 1181 | DO jk = 1, jpkm1 |
---|
| 1182 | DO jj = 2, jpjm1 |
---|
| 1183 | DO ji = 2, jpim1 |
---|
[3294] | 1184 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 1185 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 1186 | END DO |
---|
| 1187 | END DO |
---|
| 1188 | END DO |
---|
[455] | 1189 | |
---|
[3632] | 1190 | DO jk = 1, jpkm1 |
---|
| 1191 | DO jj = 2, jpjm1 |
---|
| 1192 | DO ji = 2, jpim1 |
---|
| 1193 | zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1194 | zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1195 | zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1196 | zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1197 | END DO |
---|
| 1198 | END DO |
---|
| 1199 | END DO |
---|
| 1200 | |
---|
| 1201 | |
---|
[3764] | 1202 | DO jk = 1, jpkm1 |
---|
| 1203 | DO jj = 2, jpjm1 |
---|
| 1204 | DO ji = 2, jpim1 |
---|
[3294] | 1205 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1206 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1207 | zuijk = zu(ji,jj,jk) |
---|
| 1208 | zvijk = zv(ji,jj,jk) |
---|
| 1209 | |
---|
| 1210 | !!!!! for u equation |
---|
| 1211 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 1212 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1213 | jis = ji + 1; jid = ji |
---|
| 1214 | ELSE |
---|
| 1215 | jis = ji; jid = ji +1 |
---|
| 1216 | ENDIF |
---|
| 1217 | |
---|
| 1218 | ! integrate the pressure on the shallow side |
---|
[3764] | 1219 | jk1 = jk |
---|
[3632] | 1220 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1221 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1222 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1223 | EXIT |
---|
| 1224 | ENDIF |
---|
[3632] | 1225 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1226 | zpwes = zpwes + & |
---|
[3632] | 1227 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1228 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1229 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1230 | jk1 = jk1 + 1 |
---|
| 1231 | END DO |
---|
[3764] | 1232 | |
---|
[3294] | 1233 | ! integrate the pressure on the deep side |
---|
[3764] | 1234 | jk1 = jk |
---|
[3632] | 1235 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1236 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1237 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1238 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1239 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1240 | dsp(jid,jj,1)) * zdeps |
---|
| 1241 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1242 | EXIT |
---|
| 1243 | ENDIF |
---|
[3632] | 1244 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1245 | zpwed = zpwed + & |
---|
[3632] | 1246 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1247 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1248 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1249 | jk1 = jk1 - 1 |
---|
| 1250 | END DO |
---|
[3764] | 1251 | |
---|
[3294] | 1252 | ! update the momentum trends in u direction |
---|
| 1253 | |
---|
| 1254 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1255 | IF( lk_vvl ) THEN |
---|
[3764] | 1256 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1257 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1258 | ELSE |
---|
[3764] | 1259 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1260 | ENDIF |
---|
| 1261 | |
---|
| 1262 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 1263 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 1264 | ENDIF |
---|
[3764] | 1265 | |
---|
[3294] | 1266 | !!!!! for v equation |
---|
| 1267 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1268 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1269 | jjs = jj + 1; jjd = jj |
---|
| 1270 | ELSE |
---|
| 1271 | jjs = jj ; jjd = jj + 1 |
---|
| 1272 | ENDIF |
---|
| 1273 | |
---|
| 1274 | ! integrate the pressure on the shallow side |
---|
[3764] | 1275 | jk1 = jk |
---|
[3632] | 1276 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1277 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1278 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1279 | EXIT |
---|
| 1280 | ENDIF |
---|
[3632] | 1281 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1282 | zpnss = zpnss + & |
---|
[3632] | 1283 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1284 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1285 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1286 | jk1 = jk1 + 1 |
---|
| 1287 | END DO |
---|
[3764] | 1288 | |
---|
[3294] | 1289 | ! integrate the pressure on the deep side |
---|
[3764] | 1290 | jk1 = jk |
---|
[3632] | 1291 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1292 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1293 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1294 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1295 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1296 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1297 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1298 | EXIT |
---|
| 1299 | ENDIF |
---|
[3632] | 1300 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1301 | zpnsd = zpnsd + & |
---|
[3632] | 1302 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1303 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1304 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1305 | jk1 = jk1 - 1 |
---|
| 1306 | END DO |
---|
| 1307 | |
---|
[3764] | 1308 | |
---|
[3294] | 1309 | ! update the momentum trends in v direction |
---|
| 1310 | |
---|
| 1311 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1312 | IF( lk_vvl ) THEN |
---|
| 1313 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
[3764] | 1314 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1315 | ELSE |
---|
[3764] | 1316 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1317 | ENDIF |
---|
| 1318 | |
---|
| 1319 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 1320 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 1321 | ENDIF |
---|
| 1322 | |
---|
[3764] | 1323 | |
---|
[3294] | 1324 | END DO |
---|
| 1325 | END DO |
---|
[455] | 1326 | END DO |
---|
[503] | 1327 | ! |
---|
[3764] | 1328 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1329 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 1330 | CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[2715] | 1331 | ! |
---|
[3294] | 1332 | END SUBROUTINE hpg_prj |
---|
[455] | 1333 | |
---|
[4990] | 1334 | |
---|
[3294] | 1335 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1336 | !!---------------------------------------------------------------------- |
---|
| 1337 | !! *** ROUTINE cspline *** |
---|
[3764] | 1338 | !! |
---|
[3294] | 1339 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1340 | !! |
---|
| 1341 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1342 | !! |
---|
[3294] | 1343 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1344 | !!---------------------------------------------------------------------- |
---|
| 1345 | IMPLICIT NONE |
---|
| 1346 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
[3764] | 1347 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
[3294] | 1348 | ! the interpoated function |
---|
[3764] | 1349 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
[3294] | 1350 | ! 2: Linear |
---|
[4990] | 1351 | ! |
---|
[3294] | 1352 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1353 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1354 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1355 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1356 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1357 | !!---------------------------------------------------------------------- |
---|
| 1358 | |
---|
| 1359 | jpi = size(fsp,1) |
---|
| 1360 | jpj = size(fsp,2) |
---|
| 1361 | jpkm1 = size(fsp,3) - 1 |
---|
| 1362 | |
---|
[3764] | 1363 | |
---|
[3294] | 1364 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1365 | DO ji = 1, jpi |
---|
| 1366 | DO jj = 1, jpj |
---|
[3764] | 1367 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1368 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1369 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1370 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1371 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1372 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1373 | ! |
---|
| 1374 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1375 | ! |
---|
[3294] | 1376 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1377 | ! zdf(jk) = 0._wp |
---|
| 1378 | ! ELSE |
---|
| 1379 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1380 | ! ENDIF |
---|
| 1381 | ! END DO |
---|
[3764] | 1382 | |
---|
[3294] | 1383 | !!Simply geometric average |
---|
| 1384 | DO jk = 2, jpkm1-1 |
---|
| 1385 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 1386 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
[3764] | 1387 | |
---|
[3294] | 1388 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1389 | zdf(jk) = 0._wp |
---|
| 1390 | ELSE |
---|
| 1391 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1392 | ENDIF |
---|
| 1393 | END DO |
---|
[3764] | 1394 | |
---|
[3294] | 1395 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1396 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1397 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1398 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1399 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1400 | |
---|
[3294] | 1401 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1402 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1403 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1404 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1405 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1406 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1407 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1408 | |
---|
[3294] | 1409 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1410 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1411 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1412 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1413 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1414 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1415 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1416 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1417 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1418 | END DO |
---|
| 1419 | END DO |
---|
| 1420 | END DO |
---|
[3764] | 1421 | |
---|
[3294] | 1422 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1423 | DO ji = 1, jpi |
---|
| 1424 | DO jj = 1, jpj |
---|
| 1425 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1426 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1427 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1428 | |
---|
[3294] | 1429 | dsp(ji,jj,jk) = 0._wp |
---|
| 1430 | csp(ji,jj,jk) = 0._wp |
---|
| 1431 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1432 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1433 | END DO |
---|
| 1434 | END DO |
---|
| 1435 | END DO |
---|
| 1436 | |
---|
| 1437 | ELSE |
---|
| 1438 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1439 | ENDIF |
---|
| 1440 | |
---|
| 1441 | END SUBROUTINE cspline |
---|
| 1442 | |
---|
| 1443 | |
---|
[3764] | 1444 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1445 | !!---------------------------------------------------------------------- |
---|
| 1446 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1447 | !! |
---|
[3294] | 1448 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1449 | !! |
---|
[4990] | 1450 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1451 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1452 | !!---------------------------------------------------------------------- |
---|
| 1453 | IMPLICIT NONE |
---|
[3764] | 1454 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1455 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1456 | REAL(wp) :: zdeltx |
---|
| 1457 | !!---------------------------------------------------------------------- |
---|
| 1458 | |
---|
| 1459 | zdeltx = xr - xl |
---|
| 1460 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1461 | f = 0.5_wp * (fl + fr) |
---|
| 1462 | ELSE |
---|
| 1463 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1464 | ENDIF |
---|
[3764] | 1465 | |
---|
[3294] | 1466 | END FUNCTION interp1 |
---|
| 1467 | |
---|
[4990] | 1468 | |
---|
[3764] | 1469 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1470 | !!---------------------------------------------------------------------- |
---|
| 1471 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1472 | !! |
---|
[3294] | 1473 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1474 | !! |
---|
[3294] | 1475 | !! ** Method : cubic spline interpolation |
---|
| 1476 | !! |
---|
| 1477 | !!---------------------------------------------------------------------- |
---|
| 1478 | IMPLICIT NONE |
---|
[3764] | 1479 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1480 | REAL(wp) :: f ! value from the interpolation |
---|
| 1481 | !!---------------------------------------------------------------------- |
---|
| 1482 | |
---|
[3764] | 1483 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[3294] | 1484 | |
---|
| 1485 | END FUNCTION interp2 |
---|
| 1486 | |
---|
| 1487 | |
---|
[3764] | 1488 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1489 | !!---------------------------------------------------------------------- |
---|
| 1490 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1491 | !! |
---|
[3294] | 1492 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1493 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1494 | !! |
---|
[3294] | 1495 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1496 | !! |
---|
| 1497 | !!---------------------------------------------------------------------- |
---|
| 1498 | IMPLICIT NONE |
---|
[3764] | 1499 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1500 | REAL(wp) :: f ! value from the interpolation |
---|
| 1501 | !!---------------------------------------------------------------------- |
---|
| 1502 | |
---|
| 1503 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1504 | |
---|
| 1505 | END FUNCTION interp3 |
---|
| 1506 | |
---|
[3764] | 1507 | |
---|
| 1508 | FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f) |
---|
[3294] | 1509 | !!---------------------------------------------------------------------- |
---|
| 1510 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1511 | !! |
---|
[3294] | 1512 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1513 | !! |
---|
[3764] | 1514 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1515 | !! |
---|
[3294] | 1516 | !!---------------------------------------------------------------------- |
---|
| 1517 | IMPLICIT NONE |
---|
[3764] | 1518 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1519 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1520 | REAL(wp) :: f ! integration result |
---|
| 1521 | !!---------------------------------------------------------------------- |
---|
| 1522 | |
---|
[3764] | 1523 | za1 = 0.5_wp * b |
---|
| 1524 | za2 = c / 3.0_wp |
---|
| 1525 | za3 = 0.25_wp * d |
---|
[3294] | 1526 | |
---|
| 1527 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1528 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1529 | |
---|
[3632] | 1530 | END FUNCTION integ_spline |
---|
[3294] | 1531 | |
---|
[3] | 1532 | !!====================================================================== |
---|
| 1533 | END MODULE dynhpg |
---|
[3632] | 1534 | |
---|