| 1 | MODULE limrhg |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE limrhg *** |
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| 4 | !! Ice rheology : sea ice rheology |
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| 5 | !!====================================================================== |
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| 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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| 9 | !! 3.3 ! 2009-05 (G.Garric) addition of the lim2_evp cas |
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| 10 | !! 4.0 ! 2011-01 (A Porter) dynamical allocation |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | #if defined key_lim3 || ( defined key_lim2 && ! defined key_lim2_vp ) |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | !! 'key_lim3' OR LIM-3 sea-ice model |
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| 15 | !! 'key_lim2' AND NOT 'key_lim2_vp' EVP LIM-2 sea-ice model |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | !! lim_rhg : computes ice velocities |
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| 18 | !!---------------------------------------------------------------------- |
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| 19 | USE phycst ! Physical constant |
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| 20 | USE oce , ONLY : snwice_mass, snwice_mass_b |
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| 21 | USE par_oce ! Ocean parameters |
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| 22 | USE dom_oce ! Ocean domain |
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| 23 | USE sbc_oce ! Surface boundary condition: ocean fields |
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| 24 | USE sbc_ice ! Surface boundary condition: ice fields |
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| 25 | #if defined key_lim3 |
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| 26 | USE ice ! LIM-3: ice variables |
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| 27 | USE dom_ice ! LIM-3: ice domain |
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| 28 | USE limitd_me ! LIM-3: |
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| 29 | #else |
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| 30 | USE ice_2 ! LIM-2: ice variables |
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| 31 | USE dom_ice_2 ! LIM-2: ice domain |
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| 32 | #endif |
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| 33 | USE lbclnk ! Lateral Boundary Condition / MPP link |
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| 34 | USE lib_mpp ! MPP library |
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| 35 | USE wrk_nemo ! work arrays |
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| 36 | USE in_out_manager ! I/O manager |
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| 37 | USE prtctl ! Print control |
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| 38 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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| 39 | |
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| 40 | IMPLICIT NONE |
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| 41 | PRIVATE |
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| 42 | |
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| 43 | PUBLIC lim_rhg ! routine called by lim_dyn (or lim_dyn_2) |
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| 44 | |
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| 45 | REAL(wp) :: rzero = 0._wp ! constant values |
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| 46 | REAL(wp) :: rone = 1._wp ! constant values |
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| 47 | |
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| 48 | !! * Substitutions |
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| 49 | # include "vectopt_loop_substitute.h90" |
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| 50 | !!---------------------------------------------------------------------- |
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| 51 | !! NEMO/LIM3 3.4 , UCL - NEMO Consortium (2011) |
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| 52 | !! $Id$ |
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| 53 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 54 | !!---------------------------------------------------------------------- |
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| 55 | CONTAINS |
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| 56 | |
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| 57 | SUBROUTINE lim_rhg( k_j1, k_jpj ) |
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| 58 | !!------------------------------------------------------------------- |
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| 59 | !! *** SUBROUTINE lim_rhg *** |
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| 60 | !! EVP-C-grid |
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| 61 | !! |
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| 62 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
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| 63 | !! stress and sea-surface slope. Ice-ice interaction is described by |
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| 64 | !! a non-linear elasto-viscous-plastic (EVP) law including shear |
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| 65 | !! strength and a bulk rheology (Hunke and Dukowicz, 2002). |
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| 66 | !! |
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| 67 | !! The points in the C-grid look like this, dear reader |
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| 68 | !! |
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| 69 | !! (ji,jj) |
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| 70 | !! | |
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| 71 | !! | |
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| 72 | !! (ji-1,jj) | (ji,jj) |
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| 73 | !! --------- |
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| 74 | !! | | |
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| 75 | !! | (ji,jj) |------(ji,jj) |
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| 76 | !! | | |
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| 77 | !! --------- |
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| 78 | !! (ji-1,jj-1) (ji,jj-1) |
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| 79 | !! |
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| 80 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 81 | !! ice total volume (vt_i) per unit area |
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| 82 | !! snow total volume (vt_s) per unit area |
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| 83 | !! |
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| 84 | !! ** Action : - compute u_ice, v_ice : the components of the |
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| 85 | !! sea-ice velocity vector |
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| 86 | !! - compute delta_i, shear_i, divu_i, which are inputs |
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| 87 | !! of the ice thickness distribution |
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| 88 | !! |
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| 89 | !! ** Steps : 1) Compute ice snow mass, ice strength |
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| 90 | !! 2) Compute wind, oceanic stresses, mass terms and |
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| 91 | !! coriolis terms of the momentum equation |
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| 92 | !! 3) Solve the momentum equation (iterative procedure) |
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| 93 | !! 4) Prevent high velocities if the ice is thin |
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| 94 | !! 5) Recompute invariants of the strain rate tensor |
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| 95 | !! which are inputs of the ITD, store stress |
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| 96 | !! for the next time step |
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| 97 | !! 6) Control prints of residual (convergence) |
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| 98 | !! and charge ellipse. |
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| 99 | !! The user should make sure that the parameters |
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| 100 | !! nevp, telast and creepl maintain stress state |
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| 101 | !! on the charge ellipse for plastic flow |
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| 102 | !! e.g. in the Canadian Archipelago |
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| 103 | !! |
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| 104 | !! References : Hunke and Dukowicz, JPO97 |
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| 105 | !! Bouillon et al., Ocean Modelling 2009 |
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| 106 | !! Vancoppenolle et al., Ocean Modelling 2008 |
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| 107 | !!------------------------------------------------------------------- |
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| 108 | INTEGER, INTENT(in) :: k_j1 ! southern j-index for ice computation |
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| 109 | INTEGER, INTENT(in) :: k_jpj ! northern j-index for ice computation |
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| 110 | !! |
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| 111 | INTEGER :: ji, jj ! dummy loop indices |
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| 112 | INTEGER :: jter ! local integers |
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| 113 | CHARACTER (len=50) :: charout |
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| 114 | REAL(wp) :: zt11, zt12, zt21, zt22, ztagnx, ztagny, delta ! |
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| 115 | REAL(wp) :: za, zstms, zsang, zmask ! local scalars |
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| 116 | |
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| 117 | REAL(wp) :: dtevp ! time step for subcycling |
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| 118 | REAL(wp) :: dtotel, ecc2 ! square of yield ellipse eccenticity |
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| 119 | REAL(wp) :: z0, zr, zcca, zccb ! temporary scalars |
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| 120 | REAL(wp) :: zu_ice2, zv_ice1 ! |
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| 121 | REAL(wp) :: zddc, zdtc, zdst ! delta on corners and on centre |
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| 122 | REAL(wp) :: zdsshx, zdsshy ! term for the gradient of ocean surface |
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| 123 | REAL(wp) :: sigma1, sigma2 ! internal ice stress |
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| 124 | |
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| 125 | REAL(wp) :: zresm ! Maximal error on ice velocity |
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| 126 | REAL(wp) :: zindb ! ice (1) or not (0) |
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| 127 | REAL(wp) :: zdummy ! dummy argument |
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| 128 | REAL(wp) :: zintb, zintn ! dummy argument |
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| 129 | |
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| 130 | REAL(wp), POINTER, DIMENSION(:,:) :: zpresh ! temporary array for ice strength |
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| 131 | REAL(wp), POINTER, DIMENSION(:,:) :: zpreshc ! Ice strength on grid cell corners (zpreshc) |
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| 132 | REAL(wp), POINTER, DIMENSION(:,:) :: zfrld1, zfrld2 ! lead fraction on U/V points |
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| 133 | REAL(wp), POINTER, DIMENSION(:,:) :: zmass1, zmass2 ! ice/snow mass on U/V points |
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| 134 | REAL(wp), POINTER, DIMENSION(:,:) :: zcorl1, zcorl2 ! coriolis parameter on U/V points |
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| 135 | REAL(wp), POINTER, DIMENSION(:,:) :: za1ct , za2ct ! temporary arrays |
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| 136 | REAL(wp), POINTER, DIMENSION(:,:) :: zc1 ! ice mass |
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| 137 | REAL(wp), POINTER, DIMENSION(:,:) :: zusw ! temporary weight for ice strength computation |
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| 138 | REAL(wp), POINTER, DIMENSION(:,:) :: u_oce1, v_oce1 ! ocean u/v component on U points |
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| 139 | REAL(wp), POINTER, DIMENSION(:,:) :: u_oce2, v_oce2 ! ocean u/v component on V points |
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| 140 | REAL(wp), POINTER, DIMENSION(:,:) :: u_ice2, v_ice1 ! ice u/v component on V/U point |
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| 141 | REAL(wp), POINTER, DIMENSION(:,:) :: zf1 , zf2 ! arrays for internal stresses |
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| 142 | |
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| 143 | REAL(wp), POINTER, DIMENSION(:,:) :: zdd , zdt ! Divergence and tension at centre of grid cells |
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| 144 | REAL(wp), POINTER, DIMENSION(:,:) :: zds ! Shear on northeast corner of grid cells |
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| 145 | REAL(wp), POINTER, DIMENSION(:,:) :: deltat, deltac ! Delta at centre and corners of grid cells |
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| 146 | REAL(wp), POINTER, DIMENSION(:,:) :: zs1 , zs2 ! Diagonal stress tensor components zs1 and zs2 |
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| 147 | REAL(wp), POINTER, DIMENSION(:,:) :: zs12 ! Non-diagonal stress tensor component zs12 |
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| 148 | REAL(wp), POINTER, DIMENSION(:,:) :: zu_ice, zv_ice, zresr ! Local error on velocity |
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| 149 | REAL(wp), POINTER, DIMENSION(:,:) :: zpice ! array used for the calculation of ice surface slope: |
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| 150 | ! ocean surface (ssh_m) if ice is not embedded |
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| 151 | ! ice top surface if ice is embedded |
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| 152 | |
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| 153 | !!------------------------------------------------------------------- |
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| 154 | |
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| 155 | CALL wrk_alloc( jpi,jpj, zpresh, zfrld1, zmass1, zcorl1, za1ct , zpreshc, zfrld2, zmass2, zcorl2, za2ct ) |
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| 156 | CALL wrk_alloc( jpi,jpj, zc1 , u_oce1, u_oce2, u_ice2, zusw , v_oce1 , v_oce2, v_ice1 ) |
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| 157 | CALL wrk_alloc( jpi,jpj, zf1 , deltat, zu_ice, zf2 , deltac, zv_ice , zdd , zdt , zds ) |
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| 158 | CALL wrk_alloc( jpi,jpj, zdd , zdt , zds , zs1 , zs2 , zs12 , zresr , zpice ) |
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| 159 | |
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| 160 | #if defined key_lim2 && ! defined key_lim2_vp |
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| 161 | # if defined key_agrif |
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| 162 | USE ice_2, vt_s => hsnm |
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| 163 | USE ice_2, vt_i => hicm |
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| 164 | # else |
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| 165 | vt_s => hsnm |
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| 166 | vt_i => hicm |
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| 167 | # endif |
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| 168 | at_i(:,:) = 1. - frld(:,:) |
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| 169 | #endif |
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| 170 | ! |
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| 171 | !------------------------------------------------------------------------------! |
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| 172 | ! 1) Ice-Snow mass (zc1), ice strength (zpresh) ! |
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| 173 | !------------------------------------------------------------------------------! |
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| 174 | ! |
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| 175 | ! Put every vector to 0 |
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| 176 | zpresh (:,:) = 0._wp ; zc1 (:,:) = 0._wp |
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| 177 | zpreshc(:,:) = 0._wp |
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| 178 | u_ice2 (:,:) = 0._wp ; v_ice1(:,:) = 0._wp |
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| 179 | zdd (:,:) = 0._wp ; zdt (:,:) = 0._wp ; zds(:,:) = 0._wp |
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| 180 | |
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| 181 | #if defined key_lim3 |
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| 182 | CALL lim_itd_me_icestrength( ridge_scheme_swi ) ! LIM-3: Ice strength on T-points |
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| 183 | #endif |
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| 184 | |
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| 185 | !CDIR NOVERRCHK |
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| 186 | DO jj = k_j1 , k_jpj ! Ice mass and temp variables |
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| 187 | !CDIR NOVERRCHK |
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| 188 | DO ji = 1 , jpi |
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| 189 | zc1(ji,jj) = tms(ji,jj) * ( rhosn * vt_s(ji,jj) + rhoic * vt_i(ji,jj) ) |
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| 190 | #if defined key_lim3 |
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| 191 | zpresh(ji,jj) = tms(ji,jj) * strength(ji,jj) * 0.5_wp |
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| 192 | #endif |
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| 193 | #if defined key_lim2 |
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| 194 | zpresh(ji,jj) = tms(ji,jj) * pstar * vt_i(ji,jj) * EXP( -c_rhg * (1. - at_i(ji,jj) ) ) |
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| 195 | #endif |
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| 196 | ! tmi = 1 where there is ice or on land |
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| 197 | 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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| 198 | END DO |
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| 199 | END DO |
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| 200 | |
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| 201 | ! Ice strength on grid cell corners (zpreshc) |
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| 202 | ! needed for calculation of shear stress |
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| 203 | !CDIR NOVERRCHK |
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| 204 | DO jj = k_j1+1, k_jpj-1 |
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| 205 | !CDIR NOVERRCHK |
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| 206 | DO ji = 2, jpim1 !RB caution no fs_ (ji+1,jj+1) |
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| 207 | zstms = tms(ji+1,jj+1) * wght(ji+1,jj+1,2,2) + & |
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| 208 | & tms(ji,jj+1) * wght(ji+1,jj+1,1,2) + & |
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| 209 | & tms(ji+1,jj) * wght(ji+1,jj+1,2,1) + & |
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| 210 | & tms(ji,jj) * wght(ji+1,jj+1,1,1) |
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| 211 | zusw(ji,jj) = 1.0 / MAX( zstms, epsd ) |
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| 212 | zpreshc(ji,jj) = ( zpresh(ji+1,jj+1) * wght(ji+1,jj+1,2,2) + & |
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| 213 | & zpresh(ji,jj+1) * wght(ji+1,jj+1,1,2) + & |
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| 214 | & zpresh(ji+1,jj) * wght(ji+1,jj+1,2,1) + & |
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| 215 | & zpresh(ji,jj) * wght(ji+1,jj+1,1,1) & |
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| 216 | & ) * zusw(ji,jj) |
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| 217 | END DO |
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| 218 | END DO |
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| 219 | |
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| 220 | CALL lbc_lnk( zpreshc(:,:), 'F', 1. ) |
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| 221 | ! |
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| 222 | !------------------------------------------------------------------------------! |
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| 223 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
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| 224 | !------------------------------------------------------------------------------! |
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| 225 | ! |
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| 226 | ! Wind stress, coriolis and mass terms on the sides of the squares |
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| 227 | ! zfrld1: lead fraction on U-points |
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| 228 | ! zfrld2: lead fraction on V-points |
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| 229 | ! zmass1: ice/snow mass on U-points |
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| 230 | ! zmass2: ice/snow mass on V-points |
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| 231 | ! zcorl1: Coriolis parameter on U-points |
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| 232 | ! zcorl2: Coriolis parameter on V-points |
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| 233 | ! (ztagnx,ztagny): wind stress on U/V points |
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| 234 | ! u_oce1: ocean u component on u points |
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| 235 | ! v_oce1: ocean v component on u points |
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| 236 | ! u_oce2: ocean u component on v points |
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| 237 | ! v_oce2: ocean v component on v points |
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| 238 | |
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| 239 | IF( nn_ice_embd == 2 ) THEN !== embedded sea ice: compute representative ice top surface ==! |
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| 240 | ! |
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| 241 | ! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[n/nn_fsbc], n=0,nn_fsbc-1} |
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| 242 | ! = (1/nn_fsbc)^2 * {SUM[n], n=0,nn_fsbc-1} |
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| 243 | zintn = REAL( nn_fsbc - 1 ) / REAL( nn_fsbc ) * 0.5_wp |
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| 244 | ! |
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| 245 | ! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[1-n/nn_fsbc], n=0,nn_fsbc-1} |
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| 246 | ! = (1/nn_fsbc)^2 * (nn_fsbc^2 - {SUM[n], n=0,nn_fsbc-1}) |
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| 247 | zintb = REAL( nn_fsbc + 1 ) / REAL( nn_fsbc ) * 0.5_wp |
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| 248 | ! |
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| 249 | zpice(:,:) = ssh_m(:,:) + ( zintn * snwice_mass(:,:) + zintb * snwice_mass_b(:,:) ) * r1_rau0 |
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| 250 | ! |
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| 251 | ELSE !== non-embedded sea ice: use ocean surface for slope calculation ==! |
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| 252 | zpice(:,:) = ssh_m(:,:) |
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| 253 | ENDIF |
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| 254 | |
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| 255 | DO jj = k_j1+1, k_jpj-1 |
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| 256 | DO ji = fs_2, fs_jpim1 |
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| 257 | |
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| 258 | zt11 = tms(ji ,jj) * e1t(ji ,jj) |
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| 259 | zt12 = tms(ji+1,jj) * e1t(ji+1,jj) |
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| 260 | zt21 = tms(ji,jj ) * e2t(ji,jj ) |
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| 261 | zt22 = tms(ji,jj+1) * e2t(ji,jj+1) |
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| 262 | |
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| 263 | ! Leads area. |
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| 264 | 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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| 265 | 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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| 266 | |
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| 267 | ! Mass, coriolis coeff. and currents |
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| 268 | zmass1(ji,jj) = ( zt12*zc1(ji,jj) + zt11*zc1(ji+1,jj) ) / (zt11+zt12+epsd) |
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| 269 | zmass2(ji,jj) = ( zt22*zc1(ji,jj) + zt21*zc1(ji,jj+1) ) / (zt21+zt22+epsd) |
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| 270 | zcorl1(ji,jj) = zmass1(ji,jj) * ( e1t(ji+1,jj)*fcor(ji,jj) + e1t(ji,jj)*fcor(ji+1,jj) ) & |
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| 271 | & / ( e1t(ji,jj) + e1t(ji+1,jj) + epsd ) |
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| 272 | zcorl2(ji,jj) = zmass2(ji,jj) * ( e2t(ji,jj+1)*fcor(ji,jj) + e2t(ji,jj)*fcor(ji,jj+1) ) & |
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| 273 | & / ( e2t(ji,jj+1) + e2t(ji,jj) + epsd ) |
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| 274 | ! |
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| 275 | u_oce1(ji,jj) = u_oce(ji,jj) |
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| 276 | v_oce2(ji,jj) = v_oce(ji,jj) |
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| 277 | |
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| 278 | ! Ocean has no slip boundary condition |
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| 279 | v_oce1(ji,jj) = 0.5*( (v_oce(ji,jj)+v_oce(ji,jj-1))*e1t(ji,jj) & |
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| 280 | & +(v_oce(ji+1,jj)+v_oce(ji+1,jj-1))*e1t(ji+1,jj)) & |
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| 281 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
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| 282 | |
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| 283 | u_oce2(ji,jj) = 0.5*((u_oce(ji,jj)+u_oce(ji-1,jj))*e2t(ji,jj) & |
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| 284 | & +(u_oce(ji,jj+1)+u_oce(ji-1,jj+1))*e2t(ji,jj+1)) & |
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| 285 | & / (e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
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| 286 | |
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| 287 | ! Wind stress at U,V-point |
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| 288 | ztagnx = ( 1. - zfrld1(ji,jj) ) * utau_ice(ji,jj) |
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| 289 | ztagny = ( 1. - zfrld2(ji,jj) ) * vtau_ice(ji,jj) |
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| 290 | |
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| 291 | ! Computation of the velocity field taking into account the ice internal interaction. |
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| 292 | ! Terms that are independent of the velocity field. |
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| 293 | |
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| 294 | ! SB On utilise maintenant le gradient de la pente de l'ocean |
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| 295 | ! include it later |
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| 296 | |
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| 297 | zdsshx = ( zpice(ji+1,jj) - zpice(ji,jj) ) / e1u(ji,jj) |
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| 298 | zdsshy = ( zpice(ji,jj+1) - zpice(ji,jj) ) / e2v(ji,jj) |
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| 299 | |
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| 300 | za1ct(ji,jj) = ztagnx - zmass1(ji,jj) * grav * zdsshx |
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| 301 | za2ct(ji,jj) = ztagny - zmass2(ji,jj) * grav * zdsshy |
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| 302 | |
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| 303 | END DO |
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| 304 | END DO |
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| 305 | |
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| 306 | ! |
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| 307 | !------------------------------------------------------------------------------! |
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| 308 | ! 3) Solution of the momentum equation, iterative procedure |
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| 309 | !------------------------------------------------------------------------------! |
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| 310 | ! |
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| 311 | ! Time step for subcycling |
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| 312 | dtevp = rdt_ice / nevp |
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| 313 | dtotel = dtevp / ( 2._wp * telast ) |
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| 314 | |
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| 315 | !-ecc2: square of yield ellipse eccenticrity (reminder: must become a namelist parameter) |
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| 316 | ecc2 = ecc * ecc |
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| 317 | |
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| 318 | !-Initialise stress tensor |
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| 319 | zs1 (:,:) = stress1_i (:,:) |
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| 320 | zs2 (:,:) = stress2_i (:,:) |
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| 321 | zs12(:,:) = stress12_i(:,:) |
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| 322 | |
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| 323 | ! !----------------------! |
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| 324 | DO jter = 1 , nevp ! loop over jter ! |
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| 325 | ! !----------------------! |
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| 326 | DO jj = k_j1, k_jpj-1 |
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| 327 | zu_ice(:,jj) = u_ice(:,jj) ! velocity at previous time step |
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| 328 | zv_ice(:,jj) = v_ice(:,jj) |
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| 329 | END DO |
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| 330 | |
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| 331 | DO jj = k_j1+1, k_jpj-1 |
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| 332 | DO ji = fs_2, jpim1 !RB bug no vect opt due to tmi |
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| 333 | |
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| 334 | ! |
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| 335 | !- Divergence, tension and shear (Section a. Appendix B of Hunke & Dukowicz, 2002) |
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| 336 | !- zdd(:,:), zdt(:,:): divergence and tension at centre of grid cells |
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| 337 | !- zds(:,:): shear on northeast corner of grid cells |
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| 338 | ! |
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| 339 | !- IMPORTANT REMINDER: Dear Gurvan, note that, the way these terms are coded, |
|---|
| 340 | ! there are many repeated calculations. |
|---|
| 341 | ! Speed could be improved by regrouping terms. For |
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| 342 | ! the moment, however, the stress is on clarity of coding to avoid |
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| 343 | ! bugs (Martin, for Miguel). |
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| 344 | ! |
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| 345 | !- ALSO: arrays zdd, zdt, zds and delta could |
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| 346 | ! be removed in the future to minimise memory demand. |
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| 347 | ! |
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| 348 | !- MORE NOTES: Note that we are calculating deformation rates and stresses on the corners of |
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| 349 | ! grid cells, exactly as in the B grid case. For simplicity, the indexation on |
|---|
| 350 | ! the corners is the same as in the B grid. |
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| 351 | ! |
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| 352 | ! |
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| 353 | zdd(ji,jj) = ( e2u(ji,jj)*u_ice(ji,jj) & |
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| 354 | & -e2u(ji-1,jj)*u_ice(ji-1,jj) & |
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| 355 | & +e1v(ji,jj)*v_ice(ji,jj) & |
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| 356 | & -e1v(ji,jj-1)*v_ice(ji,jj-1) & |
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| 357 | & ) & |
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| 358 | & / area(ji,jj) |
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| 359 | |
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| 360 | zdt(ji,jj) = ( ( u_ice(ji,jj)/e2u(ji,jj) & |
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| 361 | & -u_ice(ji-1,jj)/e2u(ji-1,jj) & |
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| 362 | & )*e2t(ji,jj)*e2t(ji,jj) & |
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| 363 | & -( v_ice(ji,jj)/e1v(ji,jj) & |
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| 364 | & -v_ice(ji,jj-1)/e1v(ji,jj-1) & |
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| 365 | & )*e1t(ji,jj)*e1t(ji,jj) & |
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| 366 | & ) & |
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| 367 | & / area(ji,jj) |
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| 368 | |
|---|
| 369 | ! |
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| 370 | zds(ji,jj) = ( ( u_ice(ji,jj+1)/e1u(ji,jj+1) & |
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| 371 | & -u_ice(ji,jj)/e1u(ji,jj) & |
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| 372 | & )*e1f(ji,jj)*e1f(ji,jj) & |
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| 373 | & +( v_ice(ji+1,jj)/e2v(ji+1,jj) & |
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| 374 | & -v_ice(ji,jj)/e2v(ji,jj) & |
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| 375 | & )*e2f(ji,jj)*e2f(ji,jj) & |
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| 376 | & ) & |
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| 377 | & / ( e1f(ji,jj) * e2f(ji,jj) ) * ( 2.0 - tmf(ji,jj) ) & |
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| 378 | & * tmi(ji,jj) * tmi(ji,jj+1) & |
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| 379 | & * tmi(ji+1,jj) * tmi(ji+1,jj+1) |
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| 380 | |
|---|
| 381 | |
|---|
| 382 | v_ice1(ji,jj) = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji+1,jj) & |
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| 383 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji,jj)) & |
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| 384 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
|---|
| 385 | |
|---|
| 386 | u_ice2(ji,jj) = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj+1) & |
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| 387 | & +(u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj)) & |
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| 388 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
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| 389 | |
|---|
| 390 | END DO |
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| 391 | END DO |
|---|
| 392 | CALL lbc_lnk( v_ice1, 'U', -1. ) ; CALL lbc_lnk( u_ice2, 'V', -1. ) ! lateral boundary cond. |
|---|
| 393 | |
|---|
| 394 | !CDIR NOVERRCHK |
|---|
| 395 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 396 | !CDIR NOVERRCHK |
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| 397 | DO ji = fs_2, fs_jpim1 |
|---|
| 398 | |
|---|
| 399 | !- Calculate Delta at centre of grid cells |
|---|
| 400 | zdst = ( e2u(ji , jj) * v_ice1(ji ,jj) & |
|---|
| 401 | & - e2u(ji-1, jj) * v_ice1(ji-1,jj) & |
|---|
| 402 | & + e1v(ji, jj ) * u_ice2(ji,jj ) & |
|---|
| 403 | & - e1v(ji, jj-1) * u_ice2(ji,jj-1) & |
|---|
| 404 | & ) & |
|---|
| 405 | & / area(ji,jj) |
|---|
| 406 | |
|---|
| 407 | delta = SQRT( zdd(ji,jj)*zdd(ji,jj) + ( zdt(ji,jj)*zdt(ji,jj) + zdst*zdst ) * usecc2 ) |
|---|
| 408 | deltat(ji,jj) = MAX( SQRT(zdd(ji,jj)**2 + (zdt(ji,jj)**2 + zdst**2)*usecc2), creepl ) |
|---|
| 409 | |
|---|
| 410 | !-Calculate stress tensor components zs1 and zs2 |
|---|
| 411 | !-at centre of grid cells (see section 3.5 of CICE user's guide). |
|---|
| 412 | zs1(ji,jj) = ( zs1(ji,jj) & |
|---|
| 413 | & - dtotel*( ( 1.0 - alphaevp) * zs1(ji,jj) + & |
|---|
| 414 | & ( delta / deltat(ji,jj) - zdd(ji,jj) / deltat(ji,jj) ) & |
|---|
| 415 | * zpresh(ji,jj) ) ) & |
|---|
| 416 | & / ( 1.0 + alphaevp * dtotel ) |
|---|
| 417 | |
|---|
| 418 | zs2(ji,jj) = ( zs2(ji,jj) & |
|---|
| 419 | & - dtotel*((1.0-alphaevp)*ecc2*zs2(ji,jj) - & |
|---|
| 420 | zdt(ji,jj)/deltat(ji,jj)*zpresh(ji,jj)) ) & |
|---|
| 421 | & / ( 1.0 + alphaevp*ecc2*dtotel ) |
|---|
| 422 | |
|---|
| 423 | END DO |
|---|
| 424 | END DO |
|---|
| 425 | |
|---|
| 426 | CALL lbc_lnk( zs1(:,:), 'T', 1. ) |
|---|
| 427 | CALL lbc_lnk( zs2(:,:), 'T', 1. ) |
|---|
| 428 | |
|---|
| 429 | !CDIR NOVERRCHK |
|---|
| 430 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 431 | !CDIR NOVERRCHK |
|---|
| 432 | DO ji = fs_2, fs_jpim1 |
|---|
| 433 | !- Calculate Delta on corners |
|---|
| 434 | zddc = ( ( v_ice1(ji,jj+1)/e1u(ji,jj+1) & |
|---|
| 435 | & -v_ice1(ji,jj)/e1u(ji,jj) & |
|---|
| 436 | & )*e1f(ji,jj)*e1f(ji,jj) & |
|---|
| 437 | & +( u_ice2(ji+1,jj)/e2v(ji+1,jj) & |
|---|
| 438 | & -u_ice2(ji,jj)/e2v(ji,jj) & |
|---|
| 439 | & )*e2f(ji,jj)*e2f(ji,jj) & |
|---|
| 440 | & ) & |
|---|
| 441 | & / ( e1f(ji,jj) * e2f(ji,jj) ) |
|---|
| 442 | |
|---|
| 443 | zdtc = (-( v_ice1(ji,jj+1)/e1u(ji,jj+1) & |
|---|
| 444 | & -v_ice1(ji,jj)/e1u(ji,jj) & |
|---|
| 445 | & )*e1f(ji,jj)*e1f(ji,jj) & |
|---|
| 446 | & +( u_ice2(ji+1,jj)/e2v(ji+1,jj) & |
|---|
| 447 | & -u_ice2(ji,jj)/e2v(ji,jj) & |
|---|
| 448 | & )*e2f(ji,jj)*e2f(ji,jj) & |
|---|
| 449 | & ) & |
|---|
| 450 | & / ( e1f(ji,jj) * e2f(ji,jj) ) |
|---|
| 451 | |
|---|
| 452 | deltac(ji,jj) = SQRT(zddc**2+(zdtc**2+zds(ji,jj)**2)*usecc2) + creepl |
|---|
| 453 | |
|---|
| 454 | !-Calculate stress tensor component zs12 at corners (see section 3.5 of CICE user's guide). |
|---|
| 455 | zs12(ji,jj) = ( zs12(ji,jj) & |
|---|
| 456 | & - dtotel*( (1.0-alphaevp)*ecc2*zs12(ji,jj) - zds(ji,jj) / & |
|---|
| 457 | & ( 2.0*deltac(ji,jj) ) * zpreshc(ji,jj))) & |
|---|
| 458 | & / ( 1.0 + alphaevp*ecc2*dtotel ) |
|---|
| 459 | |
|---|
| 460 | END DO ! ji |
|---|
| 461 | END DO ! jj |
|---|
| 462 | |
|---|
| 463 | CALL lbc_lnk( zs12(:,:), 'F', 1. ) |
|---|
| 464 | |
|---|
| 465 | ! Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) |
|---|
| 466 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 467 | DO ji = fs_2, fs_jpim1 |
|---|
| 468 | !- contribution of zs1, zs2 and zs12 to zf1 |
|---|
| 469 | zf1(ji,jj) = 0.5*( (zs1(ji+1,jj)-zs1(ji,jj))*e2u(ji,jj) & |
|---|
| 470 | & +(zs2(ji+1,jj)*e2t(ji+1,jj)**2-zs2(ji,jj)*e2t(ji,jj)**2)/e2u(ji,jj) & |
|---|
| 471 | & +2.0*(zs12(ji,jj)*e1f(ji,jj)**2-zs12(ji,jj-1)*e1f(ji,jj-1)**2)/e1u(ji,jj) & |
|---|
| 472 | & ) / ( e1u(ji,jj)*e2u(ji,jj) ) |
|---|
| 473 | ! contribution of zs1, zs2 and zs12 to zf2 |
|---|
| 474 | zf2(ji,jj) = 0.5*( (zs1(ji,jj+1)-zs1(ji,jj))*e1v(ji,jj) & |
|---|
| 475 | & -(zs2(ji,jj+1)*e1t(ji,jj+1)**2 - zs2(ji,jj)*e1t(ji,jj)**2)/e1v(ji,jj) & |
|---|
| 476 | & + 2.0*(zs12(ji,jj)*e2f(ji,jj)**2 - & |
|---|
| 477 | zs12(ji-1,jj)*e2f(ji-1,jj)**2)/e2v(ji,jj) & |
|---|
| 478 | & ) / ( e1v(ji,jj)*e2v(ji,jj) ) |
|---|
| 479 | END DO |
|---|
| 480 | END DO |
|---|
| 481 | ! |
|---|
| 482 | ! Computation of ice velocity |
|---|
| 483 | ! |
|---|
| 484 | ! Both the Coriolis term and the ice-ocean drag are solved semi-implicitly. |
|---|
| 485 | ! |
|---|
| 486 | IF (MOD(jter,2).eq.0) THEN |
|---|
| 487 | |
|---|
| 488 | !CDIR NOVERRCHK |
|---|
| 489 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 490 | !CDIR NOVERRCHK |
|---|
| 491 | DO ji = fs_2, fs_jpim1 |
|---|
| 492 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass1(ji,jj))))*tmu(ji,jj) |
|---|
| 493 | zsang = SIGN ( 1.0 , fcor(ji,jj) ) * sangvg |
|---|
| 494 | z0 = zmass1(ji,jj)/dtevp |
|---|
| 495 | |
|---|
| 496 | ! SB modif because ocean has no slip boundary condition |
|---|
| 497 | zv_ice1 = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji,jj) & |
|---|
| 498 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji+1,jj)) & |
|---|
| 499 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
|---|
| 500 | za = rhoco*SQRT((u_ice(ji,jj)-u_oce1(ji,jj))**2 + & |
|---|
| 501 | (zv_ice1-v_oce1(ji,jj))**2) * (1.0-zfrld1(ji,jj)) |
|---|
| 502 | zr = z0*u_ice(ji,jj) + zf1(ji,jj) + za1ct(ji,jj) + & |
|---|
| 503 | za*(cangvg*u_oce1(ji,jj)-zsang*v_oce1(ji,jj)) |
|---|
| 504 | zcca = z0+za*cangvg |
|---|
| 505 | zccb = zcorl1(ji,jj)+za*zsang |
|---|
| 506 | u_ice(ji,jj) = (zr+zccb*zv_ice1)/(zcca+epsd)*zmask |
|---|
| 507 | |
|---|
| 508 | END DO |
|---|
| 509 | END DO |
|---|
| 510 | |
|---|
| 511 | CALL lbc_lnk( u_ice(:,:), 'U', -1. ) |
|---|
| 512 | |
|---|
| 513 | !CDIR NOVERRCHK |
|---|
| 514 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 515 | !CDIR NOVERRCHK |
|---|
| 516 | DO ji = fs_2, fs_jpim1 |
|---|
| 517 | |
|---|
| 518 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass2(ji,jj))))*tmv(ji,jj) |
|---|
| 519 | zsang = SIGN(1.0,fcor(ji,jj))*sangvg |
|---|
| 520 | z0 = zmass2(ji,jj)/dtevp |
|---|
| 521 | ! SB modif because ocean has no slip boundary condition |
|---|
| 522 | zu_ice2 = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj) & |
|---|
| 523 | & + (u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj+1)) & |
|---|
| 524 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
|---|
| 525 | za = rhoco*SQRT((zu_ice2-u_oce2(ji,jj))**2 + & |
|---|
| 526 | (v_ice(ji,jj)-v_oce2(ji,jj))**2)*(1.0-zfrld2(ji,jj)) |
|---|
| 527 | zr = z0*v_ice(ji,jj) + zf2(ji,jj) + & |
|---|
| 528 | za2ct(ji,jj) + za*(cangvg*v_oce2(ji,jj)+zsang*u_oce2(ji,jj)) |
|---|
| 529 | zcca = z0+za*cangvg |
|---|
| 530 | zccb = zcorl2(ji,jj)+za*zsang |
|---|
| 531 | v_ice(ji,jj) = (zr-zccb*zu_ice2)/(zcca+epsd)*zmask |
|---|
| 532 | |
|---|
| 533 | END DO |
|---|
| 534 | END DO |
|---|
| 535 | |
|---|
| 536 | CALL lbc_lnk( v_ice(:,:), 'V', -1. ) |
|---|
| 537 | |
|---|
| 538 | ELSE |
|---|
| 539 | !CDIR NOVERRCHK |
|---|
| 540 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 541 | !CDIR NOVERRCHK |
|---|
| 542 | DO ji = fs_2, fs_jpim1 |
|---|
| 543 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass2(ji,jj))))*tmv(ji,jj) |
|---|
| 544 | zsang = SIGN(1.0,fcor(ji,jj))*sangvg |
|---|
| 545 | z0 = zmass2(ji,jj)/dtevp |
|---|
| 546 | ! SB modif because ocean has no slip boundary condition |
|---|
| 547 | zu_ice2 = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj) & |
|---|
| 548 | & +(u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj+1)) & |
|---|
| 549 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
|---|
| 550 | |
|---|
| 551 | za = rhoco*SQRT((zu_ice2-u_oce2(ji,jj))**2 + & |
|---|
| 552 | (v_ice(ji,jj)-v_oce2(ji,jj))**2)*(1.0-zfrld2(ji,jj)) |
|---|
| 553 | zr = z0*v_ice(ji,jj) + zf2(ji,jj) + & |
|---|
| 554 | za2ct(ji,jj) + za*(cangvg*v_oce2(ji,jj)+zsang*u_oce2(ji,jj)) |
|---|
| 555 | zcca = z0+za*cangvg |
|---|
| 556 | zccb = zcorl2(ji,jj)+za*zsang |
|---|
| 557 | v_ice(ji,jj) = (zr-zccb*zu_ice2)/(zcca+epsd)*zmask |
|---|
| 558 | |
|---|
| 559 | END DO |
|---|
| 560 | END DO |
|---|
| 561 | |
|---|
| 562 | CALL lbc_lnk( v_ice(:,:), 'V', -1. ) |
|---|
| 563 | |
|---|
| 564 | !CDIR NOVERRCHK |
|---|
| 565 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 566 | !CDIR NOVERRCHK |
|---|
| 567 | DO ji = fs_2, fs_jpim1 |
|---|
| 568 | zmask = (1.0-MAX(rzero,SIGN(rone,-zmass1(ji,jj))))*tmu(ji,jj) |
|---|
| 569 | zsang = SIGN(1.0,fcor(ji,jj))*sangvg |
|---|
| 570 | z0 = zmass1(ji,jj)/dtevp |
|---|
| 571 | ! SB modif because ocean has no slip boundary condition |
|---|
| 572 | ! GG Bug |
|---|
| 573 | ! zv_ice1 = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji+1,jj) & |
|---|
| 574 | ! & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji,jj)) & |
|---|
| 575 | ! & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
|---|
| 576 | zv_ice1 = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji,jj) & |
|---|
| 577 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji+1,jj)) & |
|---|
| 578 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
|---|
| 579 | |
|---|
| 580 | za = rhoco*SQRT((u_ice(ji,jj)-u_oce1(ji,jj))**2 + & |
|---|
| 581 | (zv_ice1-v_oce1(ji,jj))**2)*(1.0-zfrld1(ji,jj)) |
|---|
| 582 | zr = z0*u_ice(ji,jj) + zf1(ji,jj) + za1ct(ji,jj) + & |
|---|
| 583 | za*(cangvg*u_oce1(ji,jj)-zsang*v_oce1(ji,jj)) |
|---|
| 584 | zcca = z0+za*cangvg |
|---|
| 585 | zccb = zcorl1(ji,jj)+za*zsang |
|---|
| 586 | u_ice(ji,jj) = (zr+zccb*zv_ice1)/(zcca+epsd)*zmask |
|---|
| 587 | END DO ! ji |
|---|
| 588 | END DO ! jj |
|---|
| 589 | |
|---|
| 590 | CALL lbc_lnk( u_ice(:,:), 'U', -1. ) |
|---|
| 591 | |
|---|
| 592 | ENDIF |
|---|
| 593 | |
|---|
| 594 | IF(ln_ctl) THEN |
|---|
| 595 | !--- Convergence test. |
|---|
| 596 | DO jj = k_j1+1 , k_jpj-1 |
|---|
| 597 | zresr(:,jj) = MAX( ABS( u_ice(:,jj) - zu_ice(:,jj) ) , & |
|---|
| 598 | ABS( v_ice(:,jj) - zv_ice(:,jj) ) ) |
|---|
| 599 | END DO |
|---|
| 600 | zresm = MAXVAL( zresr( 1:jpi , k_j1+1:k_jpj-1 ) ) |
|---|
| 601 | IF( lk_mpp ) CALL mpp_max( zresm ) ! max over the global domain |
|---|
| 602 | ENDIF |
|---|
| 603 | |
|---|
| 604 | ! ! ==================== ! |
|---|
| 605 | END DO ! end loop over jter ! |
|---|
| 606 | ! ! ==================== ! |
|---|
| 607 | |
|---|
| 608 | ! |
|---|
| 609 | !------------------------------------------------------------------------------! |
|---|
| 610 | ! 4) Prevent ice velocities when the ice is thin |
|---|
| 611 | !------------------------------------------------------------------------------! |
|---|
| 612 | ! |
|---|
| 613 | ! If the ice thickness is below 1cm then ice velocity should equal the |
|---|
| 614 | ! ocean velocity, |
|---|
| 615 | ! This prevents high velocity when ice is thin |
|---|
| 616 | !CDIR NOVERRCHK |
|---|
| 617 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 618 | !CDIR NOVERRCHK |
|---|
| 619 | DO ji = fs_2, fs_jpim1 |
|---|
| 620 | zindb = MAX( 0.0, SIGN( 1.0, at_i(ji,jj) - 1.0e-6 ) ) |
|---|
| 621 | zdummy = zindb * vt_i(ji,jj) / MAX(at_i(ji,jj) , 1.0e-06 ) |
|---|
| 622 | IF ( zdummy .LE. 5.0e-2 ) THEN |
|---|
| 623 | u_ice(ji,jj) = u_oce(ji,jj) |
|---|
| 624 | v_ice(ji,jj) = v_oce(ji,jj) |
|---|
| 625 | ENDIF ! zdummy |
|---|
| 626 | END DO |
|---|
| 627 | END DO |
|---|
| 628 | |
|---|
| 629 | CALL lbc_lnk( u_ice(:,:), 'U', -1. ) |
|---|
| 630 | CALL lbc_lnk( v_ice(:,:), 'V', -1. ) |
|---|
| 631 | |
|---|
| 632 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 633 | DO ji = fs_2, fs_jpim1 |
|---|
| 634 | zindb = MAX( 0.0, SIGN( 1.0, at_i(ji,jj) - 1.0e-6 ) ) |
|---|
| 635 | zdummy = zindb * vt_i(ji,jj) / MAX(at_i(ji,jj) , 1.0e-06 ) |
|---|
| 636 | IF ( zdummy .LE. 5.0e-2 ) THEN |
|---|
| 637 | v_ice1(ji,jj) = 0.5*( (v_ice(ji,jj)+v_ice(ji,jj-1))*e1t(ji+1,jj) & |
|---|
| 638 | & +(v_ice(ji+1,jj)+v_ice(ji+1,jj-1))*e1t(ji,jj)) & |
|---|
| 639 | & /(e1t(ji+1,jj)+e1t(ji,jj)) * tmu(ji,jj) |
|---|
| 640 | |
|---|
| 641 | u_ice2(ji,jj) = 0.5*( (u_ice(ji,jj)+u_ice(ji-1,jj))*e2t(ji,jj+1) & |
|---|
| 642 | & +(u_ice(ji,jj+1)+u_ice(ji-1,jj+1))*e2t(ji,jj)) & |
|---|
| 643 | & /(e2t(ji,jj+1)+e2t(ji,jj)) * tmv(ji,jj) |
|---|
| 644 | ENDIF ! zdummy |
|---|
| 645 | END DO |
|---|
| 646 | END DO |
|---|
| 647 | |
|---|
| 648 | CALL lbc_lnk( u_ice2(:,:), 'V', -1. ) |
|---|
| 649 | CALL lbc_lnk( v_ice1(:,:), 'U', -1. ) |
|---|
| 650 | |
|---|
| 651 | ! Recompute delta, shear and div, inputs for mechanical redistribution |
|---|
| 652 | !CDIR NOVERRCHK |
|---|
| 653 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 654 | !CDIR NOVERRCHK |
|---|
| 655 | DO ji = fs_2, jpim1 !RB bug no vect opt due to tmi |
|---|
| 656 | !- zdd(:,:), zdt(:,:): divergence and tension at centre |
|---|
| 657 | !- zds(:,:): shear on northeast corner of grid cells |
|---|
| 658 | zindb = MAX( 0.0, SIGN( 1.0, at_i(ji,jj) - 1.0e-6 ) ) |
|---|
| 659 | zdummy = zindb * vt_i(ji,jj) / MAX(at_i(ji,jj) , 1.0e-06 ) |
|---|
| 660 | |
|---|
| 661 | IF ( zdummy .LE. 5.0e-2 ) THEN |
|---|
| 662 | |
|---|
| 663 | zdd(ji,jj) = ( e2u(ji,jj)*u_ice(ji,jj) & |
|---|
| 664 | & -e2u(ji-1,jj)*u_ice(ji-1,jj) & |
|---|
| 665 | & +e1v(ji,jj)*v_ice(ji,jj) & |
|---|
| 666 | & -e1v(ji,jj-1)*v_ice(ji,jj-1) & |
|---|
| 667 | & ) & |
|---|
| 668 | & / area(ji,jj) |
|---|
| 669 | |
|---|
| 670 | zdt(ji,jj) = ( ( u_ice(ji,jj)/e2u(ji,jj) & |
|---|
| 671 | & -u_ice(ji-1,jj)/e2u(ji-1,jj) & |
|---|
| 672 | & )*e2t(ji,jj)*e2t(ji,jj) & |
|---|
| 673 | & -( v_ice(ji,jj)/e1v(ji,jj) & |
|---|
| 674 | & -v_ice(ji,jj-1)/e1v(ji,jj-1) & |
|---|
| 675 | & )*e1t(ji,jj)*e1t(ji,jj) & |
|---|
| 676 | & ) & |
|---|
| 677 | & / area(ji,jj) |
|---|
| 678 | ! |
|---|
| 679 | ! SB modif because ocean has no slip boundary condition |
|---|
| 680 | zds(ji,jj) = ( ( u_ice(ji,jj+1) / e1u(ji,jj+1) & |
|---|
| 681 | & - u_ice(ji,jj) / e1u(ji,jj) ) & |
|---|
| 682 | & * e1f(ji,jj) * e1f(ji,jj) & |
|---|
| 683 | & + ( v_ice(ji+1,jj) / e2v(ji+1,jj) & |
|---|
| 684 | & - v_ice(ji,jj) / e2v(ji,jj) ) & |
|---|
| 685 | & * e2f(ji,jj) * e2f(ji,jj) ) & |
|---|
| 686 | & / ( e1f(ji,jj) * e2f(ji,jj) ) * ( 2.0 - tmf(ji,jj) ) & |
|---|
| 687 | & * tmi(ji,jj) * tmi(ji,jj+1) & |
|---|
| 688 | & * tmi(ji+1,jj) * tmi(ji+1,jj+1) |
|---|
| 689 | |
|---|
| 690 | zdst = ( e2u( ji , jj ) * v_ice1(ji,jj) & |
|---|
| 691 | & - e2u( ji-1, jj ) * v_ice1(ji-1,jj) & |
|---|
| 692 | & + e1v( ji , jj ) * u_ice2(ji,jj) & |
|---|
| 693 | & - e1v( ji , jj-1 ) * u_ice2(ji,jj-1) & |
|---|
| 694 | & ) & |
|---|
| 695 | & / area(ji,jj) |
|---|
| 696 | |
|---|
| 697 | deltat(ji,jj) = SQRT( zdd(ji,jj)*zdd(ji,jj) + & |
|---|
| 698 | & ( zdt(ji,jj)*zdt(ji,jj) + zdst*zdst ) * usecc2 & |
|---|
| 699 | & ) + creepl |
|---|
| 700 | |
|---|
| 701 | ENDIF ! zdummy |
|---|
| 702 | |
|---|
| 703 | END DO !jj |
|---|
| 704 | END DO !ji |
|---|
| 705 | ! |
|---|
| 706 | !------------------------------------------------------------------------------! |
|---|
| 707 | ! 5) Store stress tensor and its invariants |
|---|
| 708 | !------------------------------------------------------------------------------! |
|---|
| 709 | ! |
|---|
| 710 | ! * Invariants of the stress tensor are required for limitd_me |
|---|
| 711 | ! accelerates convergence and improves stability |
|---|
| 712 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 713 | DO ji = fs_2, fs_jpim1 |
|---|
| 714 | divu_i (ji,jj) = zdd (ji,jj) |
|---|
| 715 | delta_i(ji,jj) = deltat(ji,jj) |
|---|
| 716 | shear_i(ji,jj) = zds (ji,jj) |
|---|
| 717 | END DO |
|---|
| 718 | END DO |
|---|
| 719 | |
|---|
| 720 | ! Lateral boundary condition |
|---|
| 721 | CALL lbc_lnk( divu_i (:,:), 'T', 1. ) |
|---|
| 722 | CALL lbc_lnk( delta_i(:,:), 'T', 1. ) |
|---|
| 723 | CALL lbc_lnk( shear_i(:,:), 'F', 1. ) |
|---|
| 724 | |
|---|
| 725 | ! * Store the stress tensor for the next time step |
|---|
| 726 | stress1_i (:,:) = zs1 (:,:) |
|---|
| 727 | stress2_i (:,:) = zs2 (:,:) |
|---|
| 728 | stress12_i(:,:) = zs12(:,:) |
|---|
| 729 | |
|---|
| 730 | ! |
|---|
| 731 | !------------------------------------------------------------------------------! |
|---|
| 732 | ! 6) Control prints of residual and charge ellipse |
|---|
| 733 | !------------------------------------------------------------------------------! |
|---|
| 734 | ! |
|---|
| 735 | ! print the residual for convergence |
|---|
| 736 | IF(ln_ctl) THEN |
|---|
| 737 | WRITE(charout,FMT="('lim_rhg : res =',D23.16, ' iter =',I4)") zresm, jter |
|---|
| 738 | CALL prt_ctl_info(charout) |
|---|
| 739 | CALL prt_ctl(tab2d_1=u_ice, clinfo1=' lim_rhg : u_ice :', tab2d_2=v_ice, clinfo2=' v_ice :') |
|---|
| 740 | ENDIF |
|---|
| 741 | |
|---|
| 742 | ! print charge ellipse |
|---|
| 743 | ! This can be desactivated once the user is sure that the stress state |
|---|
| 744 | ! lie on the charge ellipse. See Bouillon et al. 08 for more details |
|---|
| 745 | IF(ln_ctl) THEN |
|---|
| 746 | CALL prt_ctl_info('lim_rhg : numit :',ivar1=numit) |
|---|
| 747 | CALL prt_ctl_info('lim_rhg : nwrite :',ivar1=nwrite) |
|---|
| 748 | CALL prt_ctl_info('lim_rhg : MOD :',ivar1=MOD(numit,nwrite)) |
|---|
| 749 | IF( MOD(numit,nwrite) .EQ. 0 ) THEN |
|---|
| 750 | WRITE(charout,FMT="('lim_rhg :', I4, I6, I1, I1, A10)") 1000, numit, 0, 0, ' ch. ell. ' |
|---|
| 751 | CALL prt_ctl_info(charout) |
|---|
| 752 | DO jj = k_j1+1, k_jpj-1 |
|---|
| 753 | DO ji = 2, jpim1 |
|---|
| 754 | IF (zpresh(ji,jj) .GT. 1.0) THEN |
|---|
| 755 | sigma1 = ( zs1(ji,jj) + (zs2(ji,jj)**2 + 4*zs12(ji,jj)**2 )**0.5 ) / ( 2*zpresh(ji,jj) ) |
|---|
| 756 | sigma2 = ( zs1(ji,jj) - (zs2(ji,jj)**2 + 4*zs12(ji,jj)**2 )**0.5 ) / ( 2*zpresh(ji,jj) ) |
|---|
| 757 | WRITE(charout,FMT="('lim_rhg :', I4, I4, D23.16, D23.16, D23.16, D23.16, A10)") |
|---|
| 758 | CALL prt_ctl_info(charout) |
|---|
| 759 | ENDIF |
|---|
| 760 | END DO |
|---|
| 761 | END DO |
|---|
| 762 | WRITE(charout,FMT="('lim_rhg :', I4, I6, I1, I1, A10)") 2000, numit, 0, 0, ' ch. ell. ' |
|---|
| 763 | CALL prt_ctl_info(charout) |
|---|
| 764 | ENDIF |
|---|
| 765 | ENDIF |
|---|
| 766 | ! |
|---|
| 767 | CALL wrk_dealloc( jpi,jpj, zpresh, zfrld1, zmass1, zcorl1, za1ct , zpreshc, zfrld2, zmass2, zcorl2, za2ct ) |
|---|
| 768 | CALL wrk_dealloc( jpi,jpj, zc1 , u_oce1, u_oce2, u_ice2, zusw , v_oce1 , v_oce2, v_ice1 ) |
|---|
| 769 | CALL wrk_dealloc( jpi,jpj, zf1 , deltat, zu_ice, zf2 , deltac, zv_ice , zdd , zdt , zds ) |
|---|
| 770 | CALL wrk_dealloc( jpi,jpj, zdd , zdt , zds , zs1 , zs2 , zs12 , zresr , zpice ) |
|---|
| 771 | |
|---|
| 772 | END SUBROUTINE lim_rhg |
|---|
| 773 | |
|---|
| 774 | #else |
|---|
| 775 | !!---------------------------------------------------------------------- |
|---|
| 776 | !! Default option Dummy module NO LIM sea-ice model |
|---|
| 777 | !!---------------------------------------------------------------------- |
|---|
| 778 | CONTAINS |
|---|
| 779 | SUBROUTINE lim_rhg( k1 , k2 ) ! Dummy routine |
|---|
| 780 | WRITE(*,*) 'lim_rhg: You should not have seen this print! error?', k1, k2 |
|---|
| 781 | END SUBROUTINE lim_rhg |
|---|
| 782 | #endif |
|---|
| 783 | |
|---|
| 784 | !!============================================================================== |
|---|
| 785 | END MODULE limrhg |
|---|
