[825] | 1 | MODULE limrhg |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE limrhg *** |
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[834] | 4 | !! Ice rheology : sea ice rheology |
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[825] | 5 | !!====================================================================== |
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[1244] | 6 | !! History : - ! 2007-03 (M.A. Morales Maqueda, S. Bouillon) Original code |
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| 7 | !! 3.0 ! 2008-03 (M. Vancoppenolle) LIM3 |
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| 8 | !! - ! 2008-11 (M. Vancoppenolle, S. Bouillon, Y. Aksenov) add surface tilt in ice rheolohy |
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[2528] | 9 | !! 3.3 ! 2009-05 (G.Garric) addition of the lim2_evp cas |
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[2715] | 10 | !! 4.0 ! 2011-01 (A Porter) dynamical allocation |
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[1244] | 11 | !!---------------------------------------------------------------------- |
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[2528] | 12 | #if defined key_lim3 || ( defined key_lim2 && ! defined key_lim2_vp ) |
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[825] | 13 | !!---------------------------------------------------------------------- |
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[2528] | 14 | !! 'key_lim3' OR LIM-3 sea-ice model |
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[2717] | 15 | !! 'key_lim2' AND NOT 'key_lim2_vp' EVP LIM-2 sea-ice model |
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[825] | 16 | !!---------------------------------------------------------------------- |
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| 17 | !! lim_rhg : computes ice velocities |
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| 18 | !!---------------------------------------------------------------------- |
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[2528] | 19 | USE phycst ! Physical constant |
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| 20 | USE par_oce ! Ocean parameters |
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| 21 | USE dom_oce ! Ocean domain |
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| 22 | USE sbc_oce ! Surface boundary condition: ocean fields |
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| 23 | USE sbc_ice ! Surface boundary condition: ice fields |
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| 24 | USE lbclnk ! Lateral Boundary Condition / MPP link |
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| 25 | USE lib_mpp ! MPP library |
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| 26 | USE in_out_manager ! I/O manager |
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| 27 | USE prtctl ! Print control |
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| 28 | #if defined key_lim3 |
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| 29 | USE ice ! LIM-3: ice variables |
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| 30 | USE dom_ice ! LIM-3: ice domain |
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| 31 | USE limitd_me ! LIM-3: |
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| 32 | #else |
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| 33 | USE ice_2 ! LIM2: ice variables |
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| 34 | USE dom_ice_2 ! LIM2: ice domain |
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| 35 | #endif |
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[2804] | 36 | #if defined key_agrif && defined key_lim2 |
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| 37 | USE agrif_lim2_interp |
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| 38 | #endif |
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[825] | 39 | |
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| 40 | IMPLICIT NONE |
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| 41 | PRIVATE |
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| 42 | |
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[2715] | 43 | PUBLIC lim_rhg ! routine called by lim_dyn (or lim_dyn_2) |
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| 44 | PUBLIC lim_rhg_alloc ! routine called by nemo_alloc in nemogcm.F90 |
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[825] | 45 | |
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[2528] | 46 | REAL(wp) :: rzero = 0._wp ! constant values |
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| 47 | REAL(wp) :: rone = 1._wp ! constant values |
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| 48 | |
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[2715] | 49 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zpresh ! temporary array for ice strength |
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| 50 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zpreshc ! Ice strength on grid cell corners (zpreshc) |
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| 51 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zfrld1, zfrld2 ! lead fraction on U/V points |
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| 52 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zmass1, zmass2 ! ice/snow mass on U/V points |
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| 53 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zcorl1, zcorl2 ! coriolis parameter on U/V points |
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| 54 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: za1ct , za2ct ! temporary arrays |
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| 55 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zc1 ! ice mass |
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| 56 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zusw ! temporary weight for ice strength computation |
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| 57 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: u_oce1, v_oce1 ! ocean u/v component on U points |
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| 58 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: u_oce2, v_oce2 ! ocean u/v component on V points |
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| 59 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: u_ice2, v_ice1 ! ice u/v component on V/U point |
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| 60 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zf1 , zf2 ! arrays for internal stresses |
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| 61 | |
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| 62 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zdd , zdt ! Divergence and tension at centre of grid cells |
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| 63 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zds ! Shear on northeast corner of grid cells |
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| 64 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: deltat, deltac ! Delta at centre and corners of grid cells |
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| 65 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zs1 , zs2 ! Diagonal stress tensor components zs1 and zs2 |
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| 66 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zs12 ! Non-diagonal stress tensor component zs12 |
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| 67 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zu_ice, zv_ice, zresr ! Local error on velocity |
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| 68 | |
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[868] | 69 | !! * Substitutions |
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| 70 | # include "vectopt_loop_substitute.h90" |
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[825] | 71 | !!---------------------------------------------------------------------- |
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[2715] | 72 | !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011) |
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[1156] | 73 | !! $Id$ |
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[2528] | 74 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 75 | !!---------------------------------------------------------------------- |
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| 76 | CONTAINS |
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| 77 | |
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[2715] | 78 | FUNCTION lim_rhg_alloc() |
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| 79 | !!------------------------------------------------------------------- |
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| 80 | !! *** FUNCTION lim_rhg_alloc *** |
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| 81 | !!------------------------------------------------------------------- |
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| 82 | INTEGER :: lim_rhg_alloc ! return value |
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| 83 | INTEGER :: ierr(2) ! local integer |
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| 84 | !!------------------------------------------------------------------- |
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| 85 | ! |
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| 86 | ierr(:) = 0 |
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| 87 | ! |
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| 88 | ALLOCATE( zpresh (jpi,jpj) , zfrld1(jpi,jpj), zmass1(jpi,jpj), zcorl1(jpi,jpj), za1ct(jpi,jpj) , & |
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| 89 | & zpreshc(jpi,jpj) , zfrld2(jpi,jpj), zmass2(jpi,jpj), zcorl2(jpi,jpj), za2ct(jpi,jpj) , & |
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| 90 | & zc1 (jpi,jpj) , u_oce1(jpi,jpj), u_oce2(jpi,jpj), u_ice2(jpi,jpj), & |
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| 91 | & zusw (jpi,jpj) , v_oce1(jpi,jpj), v_oce2(jpi,jpj), v_ice1(jpi,jpj) , STAT=ierr(1) ) |
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| 92 | ! |
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| 93 | ALLOCATE( zf1(jpi,jpj) , deltat(jpi,jpj) , zu_ice(jpi,jpj) , & |
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| 94 | & zf2(jpi,jpj) , deltac(jpi,jpj) , zv_ice(jpi,jpj) , & |
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| 95 | & zdd(jpi,jpj) , zdt (jpi,jpj) , zds (jpi,jpj) , & |
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| 96 | & zs1(jpi,jpj) , zs2 (jpi,jpj) , zs12 (jpi,jpj) , zresr(jpi,jpj), STAT=ierr(2) ) |
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[2804] | 97 | ! |
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[2715] | 98 | lim_rhg_alloc = MAXVAL(ierr) |
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| 99 | ! |
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| 100 | END FUNCTION lim_rhg_alloc |
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| 101 | |
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| 102 | |
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[825] | 103 | SUBROUTINE lim_rhg( k_j1, k_jpj ) |
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| 104 | !!------------------------------------------------------------------- |
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[834] | 105 | !! *** SUBROUTINE lim_rhg *** |
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| 106 | !! EVP-C-grid |
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[825] | 107 | !! |
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[834] | 108 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
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[825] | 109 | !! stress and sea-surface slope. Ice-ice interaction is described by |
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[834] | 110 | !! a non-linear elasto-viscous-plastic (EVP) law including shear |
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| 111 | !! strength and a bulk rheology (Hunke and Dukowicz, 2002). |
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[825] | 112 | !! |
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[834] | 113 | !! The points in the C-grid look like this, dear reader |
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[825] | 114 | !! |
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[834] | 115 | !! (ji,jj) |
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| 116 | !! | |
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| 117 | !! | |
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| 118 | !! (ji-1,jj) | (ji,jj) |
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| 119 | !! --------- |
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| 120 | !! | | |
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| 121 | !! | (ji,jj) |------(ji,jj) |
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| 122 | !! | | |
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| 123 | !! --------- |
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| 124 | !! (ji-1,jj-1) (ji,jj-1) |
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[825] | 125 | !! |
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[834] | 126 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 127 | !! ice total volume (vt_i) per unit area |
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| 128 | !! snow total volume (vt_s) per unit area |
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[825] | 129 | !! |
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[834] | 130 | !! ** Action : - compute u_ice, v_ice : the components of the |
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| 131 | !! sea-ice velocity vector |
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| 132 | !! - compute delta_i, shear_i, divu_i, which are inputs |
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| 133 | !! of the ice thickness distribution |
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[825] | 134 | !! |
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[834] | 135 | !! ** Steps : 1) Compute ice snow mass, ice strength |
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| 136 | !! 2) Compute wind, oceanic stresses, mass terms and |
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| 137 | !! coriolis terms of the momentum equation |
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| 138 | !! 3) Solve the momentum equation (iterative procedure) |
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| 139 | !! 4) Prevent high velocities if the ice is thin |
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| 140 | !! 5) Recompute invariants of the strain rate tensor |
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| 141 | !! which are inputs of the ITD, store stress |
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| 142 | !! for the next time step |
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| 143 | !! 6) Control prints of residual (convergence) |
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| 144 | !! and charge ellipse. |
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| 145 | !! The user should make sure that the parameters |
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| 146 | !! nevp, telast and creepl maintain stress state |
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| 147 | !! on the charge ellipse for plastic flow |
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| 148 | !! e.g. in the Canadian Archipelago |
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| 149 | !! |
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[2528] | 150 | !! References : Hunke and Dukowicz, JPO97 |
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| 151 | !! Bouillon et al., Ocean Modelling 2009 |
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| 152 | !! Vancoppenolle et al., Ocean Modelling 2008 |
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| 153 | !!------------------------------------------------------------------- |
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| 154 | INTEGER, INTENT(in) :: k_j1 ! southern j-index for ice computation |
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| 155 | INTEGER, INTENT(in) :: k_jpj ! northern j-index for ice computation |
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[834] | 156 | !! |
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[2528] | 157 | INTEGER :: ji, jj ! dummy loop indices |
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| 158 | INTEGER :: jter ! local integers |
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[825] | 159 | CHARACTER (len=50) :: charout |
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[2528] | 160 | REAL(wp) :: zt11, zt12, zt21, zt22, ztagnx, ztagny, delta ! |
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| 161 | REAL(wp) :: za, zstms, zsang, zmask ! local scalars |
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[825] | 162 | |
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[2715] | 163 | REAL(wp) :: dtevp ! time step for subcycling |
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| 164 | REAL(wp) :: dtotel, ecc2 ! square of yield ellipse eccenticity |
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| 165 | REAL(wp) :: z0, zr, zcca, zccb ! temporary scalars |
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| 166 | REAL(wp) :: zu_ice2, zv_ice1 ! |
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| 167 | REAL(wp) :: zddc, zdtc, zdst ! delta on corners and on centre |
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| 168 | REAL(wp) :: zdsshx, zdsshy ! term for the gradient of ocean surface |
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| 169 | REAL(wp) :: sigma1, sigma2 ! internal ice stress |
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[825] | 170 | |
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[2715] | 171 | REAL(wp) :: zresm ! Maximal error on ice velocity |
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| 172 | REAL(wp) :: zindb ! ice (1) or not (0) |
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| 173 | REAL(wp) :: zdummy ! dummy argument |
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[2528] | 174 | !!------------------------------------------------------------------- |
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| 175 | #if defined key_lim2 && ! defined key_lim2_vp |
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| 176 | # if defined key_agrif |
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| 177 | USE ice_2, vt_s => hsnm |
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| 178 | USE ice_2, vt_i => hicm |
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| 179 | # else |
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| 180 | vt_s => hsnm |
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| 181 | vt_i => hicm |
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| 182 | # endif |
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| 183 | at_i(:,:) = 1. - frld(:,:) |
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| 184 | #endif |
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[921] | 185 | ! |
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| 186 | !------------------------------------------------------------------------------! |
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| 187 | ! 1) Ice-Snow mass (zc1), ice strength (zpresh) ! |
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| 188 | !------------------------------------------------------------------------------! |
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| 189 | ! |
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[825] | 190 | ! Put every vector to 0 |
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[2528] | 191 | zpresh (:,:) = 0._wp ; zc1 (:,:) = 0._wp |
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| 192 | zpreshc(:,:) = 0._wp |
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| 193 | u_ice2 (:,:) = 0._wp ; v_ice1(:,:) = 0._wp |
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| 194 | zdd (:,:) = 0._wp ; zdt (:,:) = 0._wp ; zds(:,:) = 0._wp |
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[825] | 195 | |
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[2528] | 196 | #if defined key_lim3 |
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| 197 | CALL lim_itd_me_icestrength( ridge_scheme_swi ) ! LIM-3: Ice strength on T-points |
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| 198 | #endif |
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[825] | 199 | |
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[868] | 200 | !CDIR NOVERRCHK |
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[2528] | 201 | DO jj = k_j1 , k_jpj ! Ice mass and temp variables |
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[868] | 202 | !CDIR NOVERRCHK |
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[825] | 203 | DO ji = 1 , jpi |
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| 204 | zc1(ji,jj) = tms(ji,jj) * ( rhosn * vt_s(ji,jj) + rhoic * vt_i(ji,jj) ) |
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[2528] | 205 | #if defined key_lim3 |
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| 206 | zpresh(ji,jj) = tms(ji,jj) * strength(ji,jj) * 0.5_wp |
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| 207 | #endif |
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[2580] | 208 | #if defined key_lim2 |
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| 209 | zpresh(ji,jj) = tms(ji,jj) * pstar * vt_i(ji,jj) * EXP( -c_rhg * (1. - at_i(ji,jj) ) ) |
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| 210 | #endif |
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[866] | 211 | ! tmi = 1 where there is ice or on land |
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[2528] | 212 | tmi(ji,jj) = 1._wp - ( 1._wp - MAX( 0._wp , SIGN ( 1._wp , vt_i(ji,jj) - epsd ) ) ) * tms(ji,jj) |
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[825] | 213 | END DO |
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| 214 | END DO |
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| 215 | |
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[834] | 216 | ! Ice strength on grid cell corners (zpreshc) |
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| 217 | ! needed for calculation of shear stress |
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[868] | 218 | !CDIR NOVERRCHK |
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[825] | 219 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 220 | !CDIR NOVERRCHK |
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| 221 | DO ji = 2, jpim1 !RB caution no fs_ (ji+1,jj+1) |
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[921] | 222 | zstms = tms(ji+1,jj+1) * wght(ji+1,jj+1,2,2) + & |
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| 223 | & tms(ji,jj+1) * wght(ji+1,jj+1,1,2) + & |
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| 224 | & tms(ji+1,jj) * wght(ji+1,jj+1,2,1) + & |
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| 225 | & tms(ji,jj) * wght(ji+1,jj+1,1,1) |
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| 226 | zusw(ji,jj) = 1.0 / MAX( zstms, epsd ) |
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| 227 | zpreshc(ji,jj) = ( zpresh(ji+1,jj+1) * wght(ji+1,jj+1,2,2) + & |
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| 228 | & zpresh(ji,jj+1) * wght(ji+1,jj+1,1,2) + & |
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| 229 | & zpresh(ji+1,jj) * wght(ji+1,jj+1,2,1) + & |
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| 230 | & zpresh(ji,jj) * wght(ji+1,jj+1,1,1) & |
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| 231 | & ) * zusw(ji,jj) |
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[825] | 232 | END DO |
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| 233 | END DO |
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| 234 | |
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| 235 | CALL lbc_lnk( zpreshc(:,:), 'F', 1. ) |
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[921] | 236 | ! |
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| 237 | !------------------------------------------------------------------------------! |
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| 238 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
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| 239 | !------------------------------------------------------------------------------! |
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| 240 | ! |
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[825] | 241 | ! Wind stress, coriolis and mass terms on the sides of the squares |
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| 242 | ! zfrld1: lead fraction on U-points |
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| 243 | ! zfrld2: lead fraction on V-points |
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| 244 | ! zmass1: ice/snow mass on U-points |
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| 245 | ! zmass2: ice/snow mass on V-points |
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| 246 | ! zcorl1: Coriolis parameter on U-points |
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| 247 | ! zcorl2: Coriolis parameter on V-points |
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| 248 | ! (ztagnx,ztagny): wind stress on U/V points |
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| 249 | ! u_oce1: ocean u component on u points |
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| 250 | ! v_oce1: ocean v component on u points |
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| 251 | ! u_oce2: ocean u component on v points |
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| 252 | ! v_oce2: ocean v component on v points |
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[921] | 253 | |
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[825] | 254 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 255 | DO ji = fs_2, fs_jpim1 |
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[825] | 256 | |
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[2528] | 257 | zt11 = tms(ji ,jj) * e1t(ji ,jj) |
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| 258 | zt12 = tms(ji+1,jj) * e1t(ji+1,jj) |
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| 259 | zt21 = tms(ji,jj ) * e2t(ji,jj ) |
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| 260 | zt22 = tms(ji,jj+1) * e2t(ji,jj+1) |
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[825] | 261 | |
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| 262 | ! Leads area. |
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[2528] | 263 | zfrld1(ji,jj) = ( zt12 * ( 1.0 - at_i(ji,jj) ) + zt11 * ( 1.0 - at_i(ji+1,jj) ) ) / ( zt11 + zt12 + epsd ) |
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| 264 | zfrld2(ji,jj) = ( zt22 * ( 1.0 - at_i(ji,jj) ) + zt21 * ( 1.0 - at_i(ji,jj+1) ) ) / ( zt21 + zt22 + epsd ) |
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[825] | 265 | |
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| 266 | ! Mass, coriolis coeff. and currents |
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[834] | 267 | zmass1(ji,jj) = ( zt12*zc1(ji,jj) + zt11*zc1(ji+1,jj) ) / (zt11+zt12+epsd) |
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| 268 | zmass2(ji,jj) = ( zt22*zc1(ji,jj) + zt21*zc1(ji,jj+1) ) / (zt21+zt22+epsd) |
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[2528] | 269 | zcorl1(ji,jj) = zmass1(ji,jj) * ( e1t(ji+1,jj)*fcor(ji,jj) + e1t(ji,jj)*fcor(ji+1,jj) ) & |
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| 270 | & / ( e1t(ji,jj) + e1t(ji+1,jj) + epsd ) |
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| 271 | zcorl2(ji,jj) = zmass2(ji,jj) * ( e2t(ji,jj+1)*fcor(ji,jj) + e2t(ji,jj)*fcor(ji,jj+1) ) & |
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| 272 | & / ( e2t(ji,jj+1) + e2t(ji,jj) + epsd ) |
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[825] | 273 | ! |
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[888] | 274 | u_oce1(ji,jj) = u_oce(ji,jj) |
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| 275 | v_oce2(ji,jj) = v_oce(ji,jj) |
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[825] | 276 | |
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[834] | 277 | ! Ocean has no slip boundary condition |
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[888] | 278 | v_oce1(ji,jj) = 0.5*( (v_oce(ji,jj)+v_oce(ji,jj-1))*e1t(ji,jj) & |
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[921] | 279 | & +(v_oce(ji+1,jj)+v_oce(ji+1,jj-1))*e1t(ji+1,jj)) & |
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| 280 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
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[825] | 281 | |
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[888] | 282 | u_oce2(ji,jj) = 0.5*((u_oce(ji,jj)+u_oce(ji-1,jj))*e2t(ji,jj) & |
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[921] | 283 | & +(u_oce(ji,jj+1)+u_oce(ji-1,jj+1))*e2t(ji,jj+1)) & |
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| 284 | & / (e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
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[825] | 285 | |
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[1469] | 286 | ! Wind stress at U,V-point |
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| 287 | ztagnx = ( 1. - zfrld1(ji,jj) ) * utau_ice(ji,jj) |
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| 288 | ztagny = ( 1. - zfrld2(ji,jj) ) * vtau_ice(ji,jj) |
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[825] | 289 | |
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[834] | 290 | ! Computation of the velocity field taking into account the ice internal interaction. |
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[825] | 291 | ! Terms that are independent of the velocity field. |
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| 292 | |
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| 293 | ! SB On utilise maintenant le gradient de la pente de l'ocean |
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| 294 | ! include it later |
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[834] | 295 | |
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[2528] | 296 | zdsshx = ( ssh_m(ji+1,jj) - ssh_m(ji,jj) ) / e1u(ji,jj) |
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| 297 | zdsshy = ( ssh_m(ji,jj+1) - ssh_m(ji,jj) ) / e2v(ji,jj) |
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[825] | 298 | |
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| 299 | za1ct(ji,jj) = ztagnx - zmass1(ji,jj) * grav * zdsshx |
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| 300 | za2ct(ji,jj) = ztagny - zmass2(ji,jj) * grav * zdsshy |
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| 301 | |
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| 302 | END DO |
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| 303 | END DO |
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| 304 | |
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[921] | 305 | ! |
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| 306 | !------------------------------------------------------------------------------! |
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| 307 | ! 3) Solution of the momentum equation, iterative procedure |
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| 308 | !------------------------------------------------------------------------------! |
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| 309 | ! |
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[825] | 310 | ! Time step for subcycling |
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| 311 | dtevp = rdt_ice / nevp |
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[2528] | 312 | dtotel = dtevp / ( 2._wp * telast ) |
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[825] | 313 | |
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| 314 | !-ecc2: square of yield ellipse eccenticrity (reminder: must become a namelist parameter) |
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[2528] | 315 | ecc2 = ecc * ecc |
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[825] | 316 | |
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| 317 | !-Initialise stress tensor |
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[2528] | 318 | zs1 (:,:) = stress1_i (:,:) |
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| 319 | zs2 (:,:) = stress2_i (:,:) |
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[866] | 320 | zs12(:,:) = stress12_i(:,:) |
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[825] | 321 | |
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[2528] | 322 | ! !----------------------! |
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[868] | 323 | DO jter = 1 , nevp ! loop over jter ! |
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[2528] | 324 | ! !----------------------! |
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[825] | 325 | DO jj = k_j1, k_jpj-1 |
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[2528] | 326 | zu_ice(:,jj) = u_ice(:,jj) ! velocity at previous time step |
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[825] | 327 | zv_ice(:,jj) = v_ice(:,jj) |
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[921] | 328 | END DO |
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[825] | 329 | |
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[834] | 330 | DO jj = k_j1+1, k_jpj-1 |
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[988] | 331 | DO ji = fs_2, jpim1 !RB bug no vect opt due to tmi |
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[825] | 332 | |
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[921] | 333 | ! |
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| 334 | !- Divergence, tension and shear (Section a. Appendix B of Hunke & Dukowicz, 2002) |
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| 335 | !- zdd(:,:), zdt(:,:): divergence and tension at centre of grid cells |
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| 336 | !- zds(:,:): shear on northeast corner of grid cells |
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| 337 | ! |
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| 338 | !- IMPORTANT REMINDER: Dear Gurvan, note that, the way these terms are coded, |
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| 339 | ! there are many repeated calculations. |
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| 340 | ! Speed could be improved by regrouping terms. For |
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| 341 | ! the moment, however, the stress is on clarity of coding to avoid |
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| 342 | ! bugs (Martin, for Miguel). |
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| 343 | ! |
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| 344 | !- ALSO: arrays zdd, zdt, zds and delta could |
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| 345 | ! be removed in the future to minimise memory demand. |
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| 346 | ! |
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| 347 | !- MORE NOTES: Note that we are calculating deformation rates and stresses on the corners of |
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| 348 | ! grid cells, exactly as in the B grid case. For simplicity, the indexation on |
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| 349 | ! the corners is the same as in the B grid. |
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| 350 | ! |
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| 351 | ! |
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| 352 | zdd(ji,jj) = ( e2u(ji,jj)*u_ice(ji,jj) & |
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| 353 | & -e2u(ji-1,jj)*u_ice(ji-1,jj) & |
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| 354 | & +e1v(ji,jj)*v_ice(ji,jj) & |
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| 355 | & -e1v(ji,jj-1)*v_ice(ji,jj-1) & |
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| 356 | & ) & |
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| 357 | & / area(ji,jj) |
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[825] | 358 | |
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[921] | 359 | zdt(ji,jj) = ( ( u_ice(ji,jj)/e2u(ji,jj) & |
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| 360 | & -u_ice(ji-1,jj)/e2u(ji-1,jj) & |
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| 361 | & )*e2t(ji,jj)*e2t(ji,jj) & |
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| 362 | & -( v_ice(ji,jj)/e1v(ji,jj) & |
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| 363 | & -v_ice(ji,jj-1)/e1v(ji,jj-1) & |
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| 364 | & )*e1t(ji,jj)*e1t(ji,jj) & |
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| 365 | & ) & |
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| 366 | & / area(ji,jj) |
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[825] | 367 | |
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[921] | 368 | ! |
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| 369 | zds(ji,jj) = ( ( u_ice(ji,jj+1)/e1u(ji,jj+1) & |
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| 370 | & -u_ice(ji,jj)/e1u(ji,jj) & |
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| 371 | & )*e1f(ji,jj)*e1f(ji,jj) & |
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| 372 | & +( v_ice(ji+1,jj)/e2v(ji+1,jj) & |
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| 373 | & -v_ice(ji,jj)/e2v(ji,jj) & |
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| 374 | & )*e2f(ji,jj)*e2f(ji,jj) & |
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| 375 | & ) & |
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| 376 | & / ( e1f(ji,jj) * e2f(ji,jj) ) * ( 2.0 - tmf(ji,jj) ) & |
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| 377 | & * tmi(ji,jj) * tmi(ji,jj+1) & |
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| 378 | & * tmi(ji+1,jj) * tmi(ji+1,jj+1) |
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[825] | 379 | |
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| 380 | |
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[921] | 381 | v_ice1(ji,jj) = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji+1,jj) & |
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| 382 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji,jj)) & |
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| 383 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
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[825] | 384 | |
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[921] | 385 | u_ice2(ji,jj) = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj+1) & |
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| 386 | & +(u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj)) & |
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| 387 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
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[825] | 388 | |
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[921] | 389 | END DO |
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| 390 | END DO |
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[2528] | 391 | CALL lbc_lnk( v_ice1, 'U', -1. ) ; CALL lbc_lnk( u_ice2, 'V', -1. ) ! lateral boundary cond. |
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[921] | 392 | |
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[868] | 393 | !CDIR NOVERRCHK |
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[921] | 394 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 395 | !CDIR NOVERRCHK |
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[921] | 396 | DO ji = fs_2, fs_jpim1 |
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[825] | 397 | |
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[921] | 398 | !- Calculate Delta at centre of grid cells |
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[2528] | 399 | zdst = ( e2u(ji , jj) * v_ice1(ji ,jj) & |
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| 400 | & - e2u(ji-1, jj) * v_ice1(ji-1,jj) & |
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| 401 | & + e1v(ji, jj ) * u_ice2(ji,jj ) & |
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| 402 | & - e1v(ji, jj-1) * u_ice2(ji,jj-1) & |
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| 403 | & ) & |
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[921] | 404 | & / area(ji,jj) |
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[825] | 405 | |
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[2528] | 406 | delta = SQRT( zdd(ji,jj)*zdd(ji,jj) + ( zdt(ji,jj)*zdt(ji,jj) + zdst*zdst ) * usecc2 ) |
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| 407 | deltat(ji,jj) = MAX( SQRT(zdd(ji,jj)**2 + (zdt(ji,jj)**2 + zdst**2)*usecc2), creepl ) |
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[825] | 408 | |
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[921] | 409 | !-Calculate stress tensor components zs1 and zs2 |
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| 410 | !-at centre of grid cells (see section 3.5 of CICE user's guide). |
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| 411 | zs1(ji,jj) = ( zs1(ji,jj) & |
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| 412 | & - dtotel*( ( 1.0 - alphaevp) * zs1(ji,jj) + & |
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| 413 | & ( delta / deltat(ji,jj) - zdd(ji,jj) / deltat(ji,jj) ) & |
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| 414 | * zpresh(ji,jj) ) ) & |
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| 415 | & / ( 1.0 + alphaevp * dtotel ) |
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[825] | 416 | |
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[921] | 417 | zs2(ji,jj) = ( zs2(ji,jj) & |
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| 418 | & - dtotel*((1.0-alphaevp)*ecc2*zs2(ji,jj) - & |
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| 419 | zdt(ji,jj)/deltat(ji,jj)*zpresh(ji,jj)) ) & |
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| 420 | & / ( 1.0 + alphaevp*ecc2*dtotel ) |
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[825] | 421 | |
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[921] | 422 | END DO |
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| 423 | END DO |
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[825] | 424 | |
---|
[921] | 425 | CALL lbc_lnk( zs1(:,:), 'T', 1. ) |
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| 426 | CALL lbc_lnk( zs2(:,:), 'T', 1. ) |
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[825] | 427 | |
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[868] | 428 | !CDIR NOVERRCHK |
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[921] | 429 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 430 | !CDIR NOVERRCHK |
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[921] | 431 | DO ji = fs_2, fs_jpim1 |
---|
| 432 | !- Calculate Delta on corners |
---|
| 433 | zddc = ( ( v_ice1(ji,jj+1)/e1u(ji,jj+1) & |
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| 434 | & -v_ice1(ji,jj)/e1u(ji,jj) & |
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| 435 | & )*e1f(ji,jj)*e1f(ji,jj) & |
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| 436 | & +( u_ice2(ji+1,jj)/e2v(ji+1,jj) & |
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| 437 | & -u_ice2(ji,jj)/e2v(ji,jj) & |
---|
| 438 | & )*e2f(ji,jj)*e2f(ji,jj) & |
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| 439 | & ) & |
---|
| 440 | & / ( e1f(ji,jj) * e2f(ji,jj) ) |
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[825] | 441 | |
---|
[921] | 442 | zdtc = (-( v_ice1(ji,jj+1)/e1u(ji,jj+1) & |
---|
| 443 | & -v_ice1(ji,jj)/e1u(ji,jj) & |
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| 444 | & )*e1f(ji,jj)*e1f(ji,jj) & |
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| 445 | & +( u_ice2(ji+1,jj)/e2v(ji+1,jj) & |
---|
| 446 | & -u_ice2(ji,jj)/e2v(ji,jj) & |
---|
| 447 | & )*e2f(ji,jj)*e2f(ji,jj) & |
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| 448 | & ) & |
---|
| 449 | & / ( e1f(ji,jj) * e2f(ji,jj) ) |
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[825] | 450 | |
---|
[921] | 451 | deltac(ji,jj) = SQRT(zddc**2+(zdtc**2+zds(ji,jj)**2)*usecc2) + creepl |
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[825] | 452 | |
---|
[921] | 453 | !-Calculate stress tensor component zs12 at corners (see section 3.5 of CICE user's guide). |
---|
| 454 | zs12(ji,jj) = ( zs12(ji,jj) & |
---|
| 455 | & - dtotel*( (1.0-alphaevp)*ecc2*zs12(ji,jj) - zds(ji,jj) / & |
---|
| 456 | & ( 2.0*deltac(ji,jj) ) * zpreshc(ji,jj))) & |
---|
| 457 | & / ( 1.0 + alphaevp*ecc2*dtotel ) |
---|
[825] | 458 | |
---|
[921] | 459 | END DO ! ji |
---|
| 460 | END DO ! jj |
---|
[825] | 461 | |
---|
[921] | 462 | CALL lbc_lnk( zs12(:,:), 'F', 1. ) |
---|
[825] | 463 | |
---|
[921] | 464 | ! Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) |
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| 465 | DO jj = k_j1+1, k_jpj-1 |
---|
| 466 | DO ji = fs_2, fs_jpim1 |
---|
| 467 | !- contribution of zs1, zs2 and zs12 to zf1 |
---|
| 468 | zf1(ji,jj) = 0.5*( (zs1(ji+1,jj)-zs1(ji,jj))*e2u(ji,jj) & |
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| 469 | & +(zs2(ji+1,jj)*e2t(ji+1,jj)**2-zs2(ji,jj)*e2t(ji,jj)**2)/e2u(ji,jj) & |
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| 470 | & +2.0*(zs12(ji,jj)*e1f(ji,jj)**2-zs12(ji,jj-1)*e1f(ji,jj-1)**2)/e1u(ji,jj) & |
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| 471 | & ) / ( e1u(ji,jj)*e2u(ji,jj) ) |
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| 472 | ! contribution of zs1, zs2 and zs12 to zf2 |
---|
| 473 | zf2(ji,jj) = 0.5*( (zs1(ji,jj+1)-zs1(ji,jj))*e1v(ji,jj) & |
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| 474 | & -(zs2(ji,jj+1)*e1t(ji,jj+1)**2 - zs2(ji,jj)*e1t(ji,jj)**2)/e1v(ji,jj) & |
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| 475 | & + 2.0*(zs12(ji,jj)*e2f(ji,jj)**2 - & |
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| 476 | zs12(ji-1,jj)*e2f(ji-1,jj)**2)/e2v(ji,jj) & |
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| 477 | & ) / ( e1v(ji,jj)*e2v(ji,jj) ) |
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| 478 | END DO |
---|
| 479 | END DO |
---|
[825] | 480 | ! |
---|
| 481 | ! Computation of ice velocity |
---|
| 482 | ! |
---|
| 483 | ! Both the Coriolis term and the ice-ocean drag are solved semi-implicitly. |
---|
| 484 | ! |
---|
[921] | 485 | IF (MOD(jter,2).eq.0) THEN |
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[825] | 486 | |
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[868] | 487 | !CDIR NOVERRCHK |
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[921] | 488 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 489 | !CDIR NOVERRCHK |
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[921] | 490 | DO ji = fs_2, fs_jpim1 |
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| 491 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass1(ji,jj))))*tmu(ji,jj) |
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| 492 | zsang = SIGN ( 1.0 , fcor(ji,jj) ) * sangvg |
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| 493 | z0 = zmass1(ji,jj)/dtevp |
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[825] | 494 | |
---|
[921] | 495 | ! SB modif because ocean has no slip boundary condition |
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| 496 | zv_ice1 = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji,jj) & |
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| 497 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji+1,jj)) & |
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| 498 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
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| 499 | za = rhoco*SQRT((u_ice(ji,jj)-u_oce1(ji,jj))**2 + & |
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| 500 | (zv_ice1-v_oce1(ji,jj))**2) * (1.0-zfrld1(ji,jj)) |
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| 501 | zr = z0*u_ice(ji,jj) + zf1(ji,jj) + za1ct(ji,jj) + & |
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| 502 | za*(cangvg*u_oce1(ji,jj)-zsang*v_oce1(ji,jj)) |
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| 503 | zcca = z0+za*cangvg |
---|
| 504 | zccb = zcorl1(ji,jj)+za*zsang |
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| 505 | u_ice(ji,jj) = (zr+zccb*zv_ice1)/(zcca+epsd)*zmask |
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[825] | 506 | |
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[921] | 507 | END DO |
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| 508 | END DO |
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[825] | 509 | |
---|
[921] | 510 | CALL lbc_lnk( u_ice(:,:), 'U', -1. ) |
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[2804] | 511 | #if defined key_agrif |
---|
| 512 | CALL agrif_dyn_lim(jter ,nevp , 'U') |
---|
| 513 | #endif |
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[868] | 514 | !CDIR NOVERRCHK |
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[921] | 515 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 516 | !CDIR NOVERRCHK |
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[921] | 517 | DO ji = fs_2, fs_jpim1 |
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[834] | 518 | |
---|
[921] | 519 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass2(ji,jj))))*tmv(ji,jj) |
---|
| 520 | zsang = SIGN(1.0,fcor(ji,jj))*sangvg |
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| 521 | z0 = zmass2(ji,jj)/dtevp |
---|
| 522 | ! SB modif because ocean has no slip boundary condition |
---|
| 523 | zu_ice2 = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj) & |
---|
| 524 | & + (u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj+1)) & |
---|
| 525 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
---|
| 526 | za = rhoco*SQRT((zu_ice2-u_oce2(ji,jj))**2 + & |
---|
| 527 | (v_ice(ji,jj)-v_oce2(ji,jj))**2)*(1.0-zfrld2(ji,jj)) |
---|
| 528 | zr = z0*v_ice(ji,jj) + zf2(ji,jj) + & |
---|
| 529 | za2ct(ji,jj) + za*(cangvg*v_oce2(ji,jj)+zsang*u_oce2(ji,jj)) |
---|
| 530 | zcca = z0+za*cangvg |
---|
| 531 | zccb = zcorl2(ji,jj)+za*zsang |
---|
| 532 | v_ice(ji,jj) = (zr-zccb*zu_ice2)/(zcca+epsd)*zmask |
---|
[825] | 533 | |
---|
[921] | 534 | END DO |
---|
| 535 | END DO |
---|
[825] | 536 | |
---|
[921] | 537 | CALL lbc_lnk( v_ice(:,:), 'V', -1. ) |
---|
[2804] | 538 | #if defined key_agrif |
---|
| 539 | CALL agrif_dyn_lim(jter ,nevp , 'U') |
---|
| 540 | #endif |
---|
[834] | 541 | ELSE |
---|
[868] | 542 | !CDIR NOVERRCHK |
---|
[921] | 543 | DO jj = k_j1+1, k_jpj-1 |
---|
[868] | 544 | !CDIR NOVERRCHK |
---|
[921] | 545 | DO ji = fs_2, fs_jpim1 |
---|
| 546 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass2(ji,jj))))*tmv(ji,jj) |
---|
| 547 | zsang = SIGN(1.0,fcor(ji,jj))*sangvg |
---|
| 548 | z0 = zmass2(ji,jj)/dtevp |
---|
| 549 | ! SB modif because ocean has no slip boundary condition |
---|
| 550 | zu_ice2 = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj) & |
---|
| 551 | & +(u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj+1)) & |
---|
| 552 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
---|
[825] | 553 | |
---|
[921] | 554 | za = rhoco*SQRT((zu_ice2-u_oce2(ji,jj))**2 + & |
---|
| 555 | (v_ice(ji,jj)-v_oce2(ji,jj))**2)*(1.0-zfrld2(ji,jj)) |
---|
| 556 | zr = z0*v_ice(ji,jj) + zf2(ji,jj) + & |
---|
| 557 | za2ct(ji,jj) + za*(cangvg*v_oce2(ji,jj)+zsang*u_oce2(ji,jj)) |
---|
| 558 | zcca = z0+za*cangvg |
---|
| 559 | zccb = zcorl2(ji,jj)+za*zsang |
---|
| 560 | v_ice(ji,jj) = (zr-zccb*zu_ice2)/(zcca+epsd)*zmask |
---|
[825] | 561 | |
---|
[921] | 562 | END DO |
---|
| 563 | END DO |
---|
[825] | 564 | |
---|
[921] | 565 | CALL lbc_lnk( v_ice(:,:), 'V', -1. ) |
---|
[2804] | 566 | #if defined key_agrif |
---|
| 567 | CALL agrif_dyn_lim(jter ,nevp , 'V') |
---|
| 568 | #endif |
---|
[868] | 569 | !CDIR NOVERRCHK |
---|
[921] | 570 | DO jj = k_j1+1, k_jpj-1 |
---|
[868] | 571 | !CDIR NOVERRCHK |
---|
[921] | 572 | DO ji = fs_2, fs_jpim1 |
---|
| 573 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass1(ji,jj))))*tmu(ji,jj) |
---|
| 574 | zsang = SIGN(1.0,fcor(ji,jj))*sangvg |
---|
| 575 | z0 = zmass1(ji,jj)/dtevp |
---|
| 576 | ! SB modif because ocean has no slip boundary condition |
---|
| 577 | ! GG Bug |
---|
| 578 | ! zv_ice1 = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji+1,jj) & |
---|
| 579 | ! & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji,jj)) & |
---|
| 580 | ! & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
---|
| 581 | zv_ice1 = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji,jj) & |
---|
| 582 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji+1,jj)) & |
---|
| 583 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
---|
[825] | 584 | |
---|
[921] | 585 | za = rhoco*SQRT((u_ice(ji,jj)-u_oce1(ji,jj))**2 + & |
---|
| 586 | (zv_ice1-v_oce1(ji,jj))**2)*(1.0-zfrld1(ji,jj)) |
---|
| 587 | zr = z0*u_ice(ji,jj) + zf1(ji,jj) + za1ct(ji,jj) + & |
---|
| 588 | za*(cangvg*u_oce1(ji,jj)-zsang*v_oce1(ji,jj)) |
---|
| 589 | zcca = z0+za*cangvg |
---|
| 590 | zccb = zcorl1(ji,jj)+za*zsang |
---|
| 591 | u_ice(ji,jj) = (zr+zccb*zv_ice1)/(zcca+epsd)*zmask |
---|
| 592 | END DO ! ji |
---|
| 593 | END DO ! jj |
---|
[825] | 594 | |
---|
[921] | 595 | CALL lbc_lnk( u_ice(:,:), 'U', -1. ) |
---|
[2804] | 596 | #if defined key_agrif |
---|
| 597 | CALL agrif_dyn_lim(jter ,nevp , 'U') |
---|
| 598 | #endif |
---|
[921] | 599 | ENDIF |
---|
[825] | 600 | |
---|
[921] | 601 | IF(ln_ctl) THEN |
---|
| 602 | !--- Convergence test. |
---|
| 603 | DO jj = k_j1+1 , k_jpj-1 |
---|
| 604 | zresr(:,jj) = MAX( ABS( u_ice(:,jj) - zu_ice(:,jj) ) , & |
---|
| 605 | ABS( v_ice(:,jj) - zv_ice(:,jj) ) ) |
---|
| 606 | END DO |
---|
| 607 | zresm = MAXVAL( zresr( 1:jpi , k_j1+1:k_jpj-1 ) ) |
---|
| 608 | IF( lk_mpp ) CALL mpp_max( zresm ) ! max over the global domain |
---|
| 609 | ENDIF |
---|
| 610 | |
---|
| 611 | ! ! ==================== ! |
---|
[868] | 612 | END DO ! end loop over jter ! |
---|
[825] | 613 | ! ! ==================== ! |
---|
| 614 | |
---|
[921] | 615 | ! |
---|
| 616 | !------------------------------------------------------------------------------! |
---|
| 617 | ! 4) Prevent ice velocities when the ice is thin |
---|
| 618 | !------------------------------------------------------------------------------! |
---|
| 619 | ! |
---|
[825] | 620 | ! If the ice thickness is below 1cm then ice velocity should equal the |
---|
[834] | 621 | ! ocean velocity, |
---|
| 622 | ! This prevents high velocity when ice is thin |
---|
[868] | 623 | !CDIR NOVERRCHK |
---|
[825] | 624 | DO jj = k_j1+1, k_jpj-1 |
---|
[868] | 625 | !CDIR NOVERRCHK |
---|
| 626 | DO ji = fs_2, fs_jpim1 |
---|
[825] | 627 | zindb = MAX( 0.0, SIGN( 1.0, at_i(ji,jj) - 1.0e-6 ) ) |
---|
| 628 | zdummy = zindb * vt_i(ji,jj) / MAX(at_i(ji,jj) , 1.0e-06 ) |
---|
| 629 | IF ( zdummy .LE. 5.0e-2 ) THEN |
---|
[888] | 630 | u_ice(ji,jj) = u_oce(ji,jj) |
---|
| 631 | v_ice(ji,jj) = v_oce(ji,jj) |
---|
[825] | 632 | ENDIF ! zdummy |
---|
| 633 | END DO |
---|
| 634 | END DO |
---|
[866] | 635 | |
---|
[869] | 636 | CALL lbc_lnk( u_ice(:,:), 'U', -1. ) |
---|
| 637 | CALL lbc_lnk( v_ice(:,:), 'V', -1. ) |
---|
[2804] | 638 | #if defined key_agrif_lim2 |
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| 639 | CALL agrif_dyn_lim(nevp ,nevp , 'U') |
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| 640 | CALL agrif_dyn_lim(nevp ,nevp , 'V') |
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| 641 | #endif |
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[869] | 642 | |
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[868] | 643 | DO jj = k_j1+1, k_jpj-1 |
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| 644 | DO ji = fs_2, fs_jpim1 |
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| 645 | zindb = MAX( 0.0, SIGN( 1.0, at_i(ji,jj) - 1.0e-6 ) ) |
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| 646 | zdummy = zindb * vt_i(ji,jj) / MAX(at_i(ji,jj) , 1.0e-06 ) |
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| 647 | IF ( zdummy .LE. 5.0e-2 ) THEN |
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[921] | 648 | v_ice1(ji,jj) = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji+1,jj) & |
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| 649 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji,jj)) & |
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| 650 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
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[868] | 651 | |
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[921] | 652 | u_ice2(ji,jj) = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj+1) & |
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| 653 | & +(u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj)) & |
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| 654 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
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| 655 | ENDIF ! zdummy |
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[868] | 656 | END DO |
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| 657 | END DO |
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| 658 | |
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[869] | 659 | CALL lbc_lnk( u_ice2(:,:), 'V', -1. ) |
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| 660 | CALL lbc_lnk( v_ice1(:,:), 'U', -1. ) |
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[868] | 661 | |
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[866] | 662 | ! Recompute delta, shear and div, inputs for mechanical redistribution |
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[868] | 663 | !CDIR NOVERRCHK |
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[825] | 664 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 665 | !CDIR NOVERRCHK |
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[988] | 666 | DO ji = fs_2, jpim1 !RB bug no vect opt due to tmi |
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[825] | 667 | !- zdd(:,:), zdt(:,:): divergence and tension at centre |
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| 668 | !- zds(:,:): shear on northeast corner of grid cells |
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| 669 | zindb = MAX( 0.0, SIGN( 1.0, at_i(ji,jj) - 1.0e-6 ) ) |
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| 670 | zdummy = zindb * vt_i(ji,jj) / MAX(at_i(ji,jj) , 1.0e-06 ) |
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| 671 | |
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| 672 | IF ( zdummy .LE. 5.0e-2 ) THEN |
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| 673 | |
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[921] | 674 | zdd(ji,jj) = ( e2u(ji,jj)*u_ice(ji,jj) & |
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| 675 | & -e2u(ji-1,jj)*u_ice(ji-1,jj) & |
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| 676 | & +e1v(ji,jj)*v_ice(ji,jj) & |
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| 677 | & -e1v(ji,jj-1)*v_ice(ji,jj-1) & |
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| 678 | & ) & |
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| 679 | & / area(ji,jj) |
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[825] | 680 | |
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[921] | 681 | zdt(ji,jj) = ( ( u_ice(ji,jj)/e2u(ji,jj) & |
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| 682 | & -u_ice(ji-1,jj)/e2u(ji-1,jj) & |
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| 683 | & )*e2t(ji,jj)*e2t(ji,jj) & |
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| 684 | & -( v_ice(ji,jj)/e1v(ji,jj) & |
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| 685 | & -v_ice(ji,jj-1)/e1v(ji,jj-1) & |
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| 686 | & )*e1t(ji,jj)*e1t(ji,jj) & |
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| 687 | & ) & |
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| 688 | & / area(ji,jj) |
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| 689 | ! |
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| 690 | ! SB modif because ocean has no slip boundary condition |
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| 691 | zds(ji,jj) = ( ( u_ice(ji,jj+1) / e1u(ji,jj+1) & |
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| 692 | & - u_ice(ji,jj) / e1u(ji,jj) ) & |
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| 693 | & * e1f(ji,jj) * e1f(ji,jj) & |
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| 694 | & + ( v_ice(ji+1,jj) / e2v(ji+1,jj) & |
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| 695 | & - v_ice(ji,jj) / e2v(ji,jj) ) & |
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| 696 | & * e2f(ji,jj) * e2f(ji,jj) ) & |
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| 697 | & / ( e1f(ji,jj) * e2f(ji,jj) ) * ( 2.0 - tmf(ji,jj) ) & |
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| 698 | & * tmi(ji,jj) * tmi(ji,jj+1) & |
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| 699 | & * tmi(ji+1,jj) * tmi(ji+1,jj+1) |
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[825] | 700 | |
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[921] | 701 | zdst = ( e2u( ji , jj ) * v_ice1(ji,jj) & |
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| 702 | & - e2u( ji-1, jj ) * v_ice1(ji-1,jj) & |
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| 703 | & + e1v( ji , jj ) * u_ice2(ji,jj) & |
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| 704 | & - e1v( ji , jj-1 ) * u_ice2(ji,jj-1) & |
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| 705 | & ) & |
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| 706 | & / area(ji,jj) |
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[825] | 707 | |
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[921] | 708 | deltat(ji,jj) = SQRT( zdd(ji,jj)*zdd(ji,jj) + & |
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| 709 | & ( zdt(ji,jj)*zdt(ji,jj) + zdst*zdst ) * usecc2 & |
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| 710 | & ) + creepl |
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[825] | 711 | |
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[921] | 712 | ENDIF ! zdummy |
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[825] | 713 | |
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| 714 | END DO !jj |
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| 715 | END DO !ji |
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[921] | 716 | ! |
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| 717 | !------------------------------------------------------------------------------! |
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| 718 | ! 5) Store stress tensor and its invariants |
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| 719 | !------------------------------------------------------------------------------! |
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| 720 | ! |
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[866] | 721 | ! * Invariants of the stress tensor are required for limitd_me |
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| 722 | ! accelerates convergence and improves stability |
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| 723 | DO jj = k_j1+1, k_jpj-1 |
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[868] | 724 | DO ji = fs_2, fs_jpim1 |
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| 725 | divu_i (ji,jj) = zdd (ji,jj) |
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| 726 | delta_i(ji,jj) = deltat(ji,jj) |
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| 727 | shear_i(ji,jj) = zds (ji,jj) |
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[825] | 728 | END DO |
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[866] | 729 | END DO |
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[825] | 730 | |
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[866] | 731 | ! Lateral boundary condition |
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[868] | 732 | CALL lbc_lnk( divu_i (:,:), 'T', 1. ) |
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[825] | 733 | CALL lbc_lnk( delta_i(:,:), 'T', 1. ) |
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| 734 | CALL lbc_lnk( shear_i(:,:), 'F', 1. ) |
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[866] | 735 | |
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[868] | 736 | ! * Store the stress tensor for the next time step |
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| 737 | stress1_i (:,:) = zs1 (:,:) |
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| 738 | stress2_i (:,:) = zs2 (:,:) |
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| 739 | stress12_i(:,:) = zs12(:,:) |
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| 740 | |
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[921] | 741 | ! |
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| 742 | !------------------------------------------------------------------------------! |
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| 743 | ! 6) Control prints of residual and charge ellipse |
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| 744 | !------------------------------------------------------------------------------! |
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| 745 | ! |
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[834] | 746 | ! print the residual for convergence |
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| 747 | IF(ln_ctl) THEN |
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[868] | 748 | WRITE(charout,FMT="('lim_rhg : res =',D23.16, ' iter =',I4)") zresm, jter |
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[834] | 749 | CALL prt_ctl_info(charout) |
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| 750 | CALL prt_ctl(tab2d_1=u_ice, clinfo1=' lim_rhg : u_ice :', tab2d_2=v_ice, clinfo2=' v_ice :') |
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| 751 | ENDIF |
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[825] | 752 | |
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[834] | 753 | ! print charge ellipse |
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| 754 | ! This can be desactivated once the user is sure that the stress state |
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| 755 | ! lie on the charge ellipse. See Bouillon et al. 08 for more details |
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[825] | 756 | IF(ln_ctl) THEN |
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| 757 | CALL prt_ctl_info('lim_rhg : numit :',ivar1=numit) |
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| 758 | CALL prt_ctl_info('lim_rhg : nwrite :',ivar1=nwrite) |
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| 759 | CALL prt_ctl_info('lim_rhg : MOD :',ivar1=MOD(numit,nwrite)) |
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| 760 | IF( MOD(numit,nwrite) .EQ. 0 ) THEN |
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| 761 | WRITE(charout,FMT="('lim_rhg :', I4, I6, I1, I1, A10)") 1000, numit, 0, 0, ' ch. ell. ' |
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| 762 | CALL prt_ctl_info(charout) |
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| 763 | DO jj = k_j1+1, k_jpj-1 |
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| 764 | DO ji = 2, jpim1 |
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| 765 | IF (zpresh(ji,jj) .GT. 1.0) THEN |
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| 766 | sigma1 = ( zs1(ji,jj) + (zs2(ji,jj)**2 + 4*zs12(ji,jj)**2 )**0.5 ) / ( 2*zpresh(ji,jj) ) |
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| 767 | sigma2 = ( zs1(ji,jj) - (zs2(ji,jj)**2 + 4*zs12(ji,jj)**2 )**0.5 ) / ( 2*zpresh(ji,jj) ) |
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| 768 | WRITE(charout,FMT="('lim_rhg :', I4, I4, D23.16, D23.16, D23.16, D23.16, A10)") |
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| 769 | CALL prt_ctl_info(charout) |
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| 770 | ENDIF |
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| 771 | END DO |
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| 772 | END DO |
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| 773 | WRITE(charout,FMT="('lim_rhg :', I4, I6, I1, I1, A10)") 2000, numit, 0, 0, ' ch. ell. ' |
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| 774 | CALL prt_ctl_info(charout) |
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| 775 | ENDIF |
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| 776 | ENDIF |
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[2715] | 777 | ! |
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[825] | 778 | END SUBROUTINE lim_rhg |
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| 779 | |
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| 780 | #else |
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| 781 | !!---------------------------------------------------------------------- |
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| 782 | !! Default option Dummy module NO LIM sea-ice model |
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| 783 | !!---------------------------------------------------------------------- |
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| 784 | CONTAINS |
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| 785 | SUBROUTINE lim_rhg( k1 , k2 ) ! Dummy routine |
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| 786 | WRITE(*,*) 'lim_rhg: You should not have seen this print! error?', k1, k2 |
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| 787 | END SUBROUTINE lim_rhg |
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| 788 | #endif |
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| 789 | |
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| 790 | !!============================================================================== |
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| 791 | END MODULE limrhg |
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