| 1 | MODULE icedyn_rhg_evp |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icedyn_rhg_evp *** |
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| 4 | !! Sea-Ice dynamics : rheology Elasto-Viscous-Plastic |
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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) adaptation to new model |
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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 evp case |
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| 10 | !! 3.4 ! 2011-01 (A. Porter) dynamical allocation |
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| 11 | !! 3.5 ! 2012-08 (R. Benshila) AGRIF |
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| 12 | !! 3.6 ! 2016-06 (C. Rousset) Rewriting + landfast ice + mEVP (Bouillon 2013) |
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| 13 | !! 3.7 ! 2017 (C. Rousset) add aEVP (Kimmritz 2016-2017) |
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| 14 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | #if defined key_si3 |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | !! 'key_si3' SI3 sea-ice model |
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| 19 | !!---------------------------------------------------------------------- |
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| 20 | !! ice_dyn_rhg_evp : computes ice velocities from EVP rheology |
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| 21 | !! rhg_evp_rst : read/write EVP fields in ice restart |
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| 22 | !!---------------------------------------------------------------------- |
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| 23 | USE phycst ! Physical constant |
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| 24 | USE dom_oce ! Ocean domain |
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| 25 | USE sbc_oce , ONLY : ln_ice_embd, nn_fsbc, ssh_m |
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| 26 | USE sbc_ice , ONLY : utau_ice, vtau_ice, snwice_mass, snwice_mass_b |
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| 27 | USE ice ! sea-ice: ice variables |
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| 28 | USE icevar ! ice_var_sshdyn |
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| 29 | USE icedyn_rdgrft ! sea-ice: ice strength |
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| 30 | USE bdy_oce , ONLY : ln_bdy |
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| 31 | USE bdyice |
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| 32 | #if defined key_agrif |
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| 33 | USE agrif_ice_interp |
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| 34 | #endif |
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| 35 | ! |
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| 36 | USE in_out_manager ! I/O manager |
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| 37 | USE iom ! I/O manager library |
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| 38 | USE lib_mpp ! MPP library |
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| 39 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 40 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 41 | USE prtctl ! Print control |
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| 42 | |
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| 43 | USE netcdf ! NetCDF library for convergence test |
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| 44 | IMPLICIT NONE |
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| 45 | PRIVATE |
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| 46 | |
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| 47 | PUBLIC ice_dyn_rhg_evp ! called by icedyn_rhg.F90 |
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| 48 | PUBLIC rhg_evp_rst ! called by icedyn_rhg.F90 |
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| 49 | |
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| 50 | !! * Substitutions |
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| 51 | # include "do_loop_substitute.h90" |
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| 52 | # include "domzgr_substitute.h90" |
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| 53 | |
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| 54 | !! for convergence tests |
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| 55 | INTEGER :: ncvgid ! netcdf file id |
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| 56 | INTEGER :: nvarid ! netcdf variable id |
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| 57 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zmsk00, zmsk15 |
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| 58 | !!---------------------------------------------------------------------- |
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| 59 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 60 | !! $Id$ |
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| 61 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 62 | !!---------------------------------------------------------------------- |
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| 63 | CONTAINS |
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| 64 | |
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| 65 | SUBROUTINE ice_dyn_rhg_evp( kt, Kmm, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i ) |
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| 66 | !!------------------------------------------------------------------- |
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| 67 | !! *** SUBROUTINE ice_dyn_rhg_evp *** |
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| 68 | !! EVP-C-grid |
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| 69 | !! |
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| 70 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
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| 71 | !! stress and sea-surface slope. Ice-ice interaction is described by |
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| 72 | !! a non-linear elasto-viscous-plastic (EVP) law including shear |
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| 73 | !! strength and a bulk rheology (Hunke and Dukowicz, 2002). |
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| 74 | !! |
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| 75 | !! The points in the C-grid look like this, dear reader |
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| 76 | !! |
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| 77 | !! (ji,jj) |
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| 78 | !! | |
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| 79 | !! | |
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| 80 | !! (ji-1,jj) | (ji,jj) |
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| 81 | !! --------- |
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| 82 | !! | | |
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| 83 | !! | (ji,jj) |------(ji,jj) |
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| 84 | !! | | |
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| 85 | !! --------- |
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| 86 | !! (ji-1,jj-1) (ji,jj-1) |
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| 87 | !! |
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| 88 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 89 | !! ice total volume (vt_i) per unit area |
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| 90 | !! snow total volume (vt_s) per unit area |
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| 91 | !! |
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| 92 | !! ** Action : - compute u_ice, v_ice : the components of the |
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| 93 | !! sea-ice velocity vector |
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| 94 | !! - compute delta_i, shear_i, divu_i, which are inputs |
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| 95 | !! of the ice thickness distribution |
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| 96 | !! |
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| 97 | !! ** Steps : 0) compute mask at F point |
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| 98 | !! 1) Compute ice snow mass, ice strength |
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| 99 | !! 2) Compute wind, oceanic stresses, mass terms and |
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| 100 | !! coriolis terms of the momentum equation |
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| 101 | !! 3) Solve the momentum equation (iterative procedure) |
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| 102 | !! 4) Recompute delta, shear and divergence |
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| 103 | !! (which are inputs of the ITD) & store stress |
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| 104 | !! for the next time step |
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| 105 | !! 5) Diagnostics including charge ellipse |
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| 106 | !! |
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| 107 | !! ** Notes : There is the possibility to use aEVP from the nice work of Kimmritz et al. (2016 & 2017) |
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| 108 | !! by setting up ln_aEVP=T (i.e. changing alpha and beta parameters). |
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| 109 | !! This is an upgraded version of mEVP from Bouillon et al. 2013 |
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| 110 | !! (i.e. more stable and better convergence) |
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| 111 | !! |
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| 112 | !! References : Hunke and Dukowicz, JPO97 |
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| 113 | !! Bouillon et al., Ocean Modelling 2009 |
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| 114 | !! Bouillon et al., Ocean Modelling 2013 |
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| 115 | !! Kimmritz et al., Ocean Modelling 2016 & 2017 |
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| 116 | !!------------------------------------------------------------------- |
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| 117 | INTEGER , INTENT(in ) :: kt ! time step |
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| 118 | INTEGER , INTENT(in ) :: Kmm ! ocean time level index |
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| 119 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pstress1_i, pstress2_i, pstress12_i ! |
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| 120 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
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| 121 | !! |
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| 122 | INTEGER :: ji, jj ! dummy loop indices |
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| 123 | INTEGER :: jter ! local integers |
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| 124 | ! |
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| 125 | REAL(wp) :: zrhoco ! rho0 * rn_cio |
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| 126 | REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling |
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| 127 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
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| 128 | REAL(wp) :: zalph1, z1_alph1, zalph2, z1_alph2 ! alpha coef from Bouillon 2009 or Kimmritz 2017 |
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| 129 | REAl(wp) :: zbetau, zbetav |
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| 130 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV, zvU, zvV ! ice/snow mass and volume |
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| 131 | REAL(wp) :: zp_delf, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars |
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| 132 | REAL(wp) :: zTauO, zTauB, zRHS, zvel ! temporary scalars |
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| 133 | REAL(wp) :: zkt ! isotropic tensile strength for landfast ice |
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| 134 | REAL(wp) :: zvCr ! critical ice volume above which ice is landfast |
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| 135 | ! |
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| 136 | REAL(wp) :: zintb, zintn ! dummy argument |
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| 137 | REAL(wp) :: zfac_x, zfac_y |
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| 138 | REAL(wp) :: zshear, zdum1, zdum2 |
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| 139 | ! |
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| 140 | REAL(wp), DIMENSION(jpi,jpj) :: zdelta, zp_delt ! delta and P/delta at T points |
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| 141 | REAL(wp), DIMENSION(jpi,jpj) :: zbeta ! beta coef from Kimmritz 2017 |
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| 142 | ! |
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| 143 | REAL(wp), DIMENSION(jpi,jpj) :: zdt_m ! (dt / ice-snow_mass) on T points |
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| 144 | REAL(wp), DIMENSION(jpi,jpj) :: zaU , zaV ! ice fraction on U/V points |
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| 145 | REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! (ice-snow_mass / dt) on U/V points |
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| 146 | REAL(wp), DIMENSION(jpi,jpj) :: zmf ! coriolis parameter at T points |
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| 147 | REAL(wp), DIMENSION(jpi,jpj) :: v_oceU, u_oceV, v_iceU, u_iceV ! ocean/ice u/v component on V/U points |
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| 148 | ! |
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| 149 | REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear |
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| 150 | REAL(wp), DIMENSION(jpi,jpj) :: zten_i ! tension |
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| 151 | REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12 ! stress tensor components |
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| 152 | REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope: |
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| 153 | ! ! ocean surface (ssh_m) if ice is not embedded |
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| 154 | ! ! ice bottom surface if ice is embedded |
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| 155 | REAL(wp), DIMENSION(jpi,jpj) :: zfU , zfV ! internal stresses |
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| 156 | REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points |
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| 157 | REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array |
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| 158 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points |
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| 159 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi, ztauy_oi ! ice-ocean stress at U-V points |
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| 160 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast) |
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| 161 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast) |
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| 162 | ! |
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| 163 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! dummy arrays |
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| 164 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence |
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| 165 | REAL(wp), DIMENSION(jpi,jpj) :: zfmask ! mask at F points for the ice |
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| 166 | |
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| 167 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
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| 168 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small |
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| 169 | REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small |
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| 170 | !! --- check convergence |
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| 171 | REAL(wp), DIMENSION(jpi,jpj) :: zu_ice, zv_ice |
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| 172 | !! --- diags |
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| 173 | REAL(wp) :: zsig1, zsig2, zsig12, zfac, z1_strength |
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| 174 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig_I, zsig_II, zsig1_p, zsig2_p |
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| 175 | !! --- SIMIP diags |
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| 176 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice ! X-component of ice mass transport (kg/s) |
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| 177 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_ice ! Y-component of ice mass transport (kg/s) |
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| 178 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw ! X-component of snow mass transport (kg/s) |
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| 179 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_snw ! Y-component of snow mass transport (kg/s) |
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| 180 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp ! X-component of area transport (m2/s) |
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| 181 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_yatrp ! Y-component of area transport (m2/s) |
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| 182 | !!------------------------------------------------------------------- |
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| 183 | |
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| 184 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_evp: EVP sea-ice rheology' |
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| 185 | ! |
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| 186 | ! for diagnostics and convergence tests |
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| 187 | ALLOCATE( zmsk00(jpi,jpj), zmsk15(jpi,jpj) ) |
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| 188 | DO_2D( 1, 1, 1, 1 ) |
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| 189 | zmsk00(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice , 0 if no ice |
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| 190 | zmsk15(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - 0.15_wp ) ) ! 1 if 15% ice, 0 if less |
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| 191 | END_2D |
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| 192 | ! |
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| 193 | !!gm for Clem: OPTIMIZATION: I think zfmask can be computed one for all at the initialization.... |
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| 194 | !------------------------------------------------------------------------------! |
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| 195 | ! 0) mask at F points for the ice |
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| 196 | !------------------------------------------------------------------------------! |
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| 197 | ! ocean/land mask |
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| 198 | DO_2D( 1, 0, 1, 0 ) |
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| 199 | zfmask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) |
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| 200 | END_2D |
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| 201 | CALL lbc_lnk( 'icedyn_rhg_evp', zfmask, 'F', 1._wp) |
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| 202 | |
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| 203 | ! Lateral boundary conditions on velocity (modify zfmask) |
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| 204 | DO_2D( 0, 0, 0, 0 ) |
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| 205 | IF( zfmask(ji,jj) == 0._wp ) THEN |
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| 206 | zfmask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(ji,jj,1), umask(ji,jj+1,1), & |
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| 207 | & vmask(ji,jj,1), vmask(ji+1,jj,1) ) ) |
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| 208 | ENDIF |
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| 209 | END_2D |
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| 210 | DO jj = 2, jpjm1 |
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| 211 | IF( zfmask(1,jj) == 0._wp ) THEN |
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| 212 | zfmask(1 ,jj) = rn_ishlat * MIN( 1._wp , MAX( vmask(2,jj,1), umask(1,jj+1,1), umask(1,jj,1) ) ) |
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| 213 | ENDIF |
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| 214 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
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| 215 | zfmask(jpi,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(jpi,jj+1,1), vmask(jpim1,jj,1), umask(jpi,jj-1,1) ) ) |
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| 216 | ENDIF |
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| 217 | END DO |
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| 218 | DO ji = 2, jpim1 |
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| 219 | IF( zfmask(ji,1) == 0._wp ) THEN |
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| 220 | zfmask(ji, 1 ) = rn_ishlat * MIN( 1._wp , MAX( vmask(ji+1,1,1), umask(ji,2,1), vmask(ji,1,1) ) ) |
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| 221 | ENDIF |
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| 222 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
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| 223 | zfmask(ji,jpj) = rn_ishlat * MIN( 1._wp , MAX( vmask(ji+1,jpj,1), vmask(ji-1,jpj,1), umask(ji,jpjm1,1) ) ) |
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| 224 | ENDIF |
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| 225 | END DO |
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| 226 | CALL lbc_lnk( 'icedyn_rhg_evp', zfmask, 'F', 1._wp ) |
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| 227 | |
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| 228 | !------------------------------------------------------------------------------! |
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| 229 | ! 1) define some variables and initialize arrays |
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| 230 | !------------------------------------------------------------------------------! |
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| 231 | zrhoco = rho0 * rn_cio |
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| 232 | |
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| 233 | ! ecc2: square of yield ellipse eccenticrity |
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| 234 | ecc2 = rn_ecc * rn_ecc |
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| 235 | z1_ecc2 = 1._wp / ecc2 |
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| 236 | |
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| 237 | ! alpha parameters (Bouillon 2009) |
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| 238 | IF( .NOT. ln_aEVP ) THEN |
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| 239 | zdtevp = rDt_ice / REAL( nn_nevp ) |
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| 240 | zalph1 = 2._wp * rn_relast * REAL( nn_nevp ) |
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| 241 | zalph2 = zalph1 * z1_ecc2 |
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| 242 | |
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| 243 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
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| 244 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
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| 245 | ELSE |
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| 246 | zdtevp = rdt_ice |
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| 247 | ! zalpha parameters set later on adaptatively |
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| 248 | ENDIF |
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| 249 | z1_dtevp = 1._wp / zdtevp |
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| 250 | |
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| 251 | ! Initialise stress tensor |
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| 252 | zs1 (:,:) = pstress1_i (:,:) |
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| 253 | zs2 (:,:) = pstress2_i (:,:) |
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| 254 | zs12(:,:) = pstress12_i(:,:) |
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| 255 | |
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| 256 | ! Ice strength |
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| 257 | CALL ice_strength |
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| 258 | |
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| 259 | ! landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) |
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| 260 | IF( ln_landfast_L16 ) THEN ; zkt = rn_lf_tensile |
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| 261 | ELSE ; zkt = 0._wp |
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| 262 | ENDIF |
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| 263 | ! |
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| 264 | !------------------------------------------------------------------------------! |
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| 265 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
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| 266 | !------------------------------------------------------------------------------! |
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| 267 | ! sea surface height |
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| 268 | ! embedded sea ice: compute representative ice top surface |
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| 269 | ! non-embedded sea ice: use ocean surface for slope calculation |
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| 270 | zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) |
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| 271 | |
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| 272 | DO_2D( 0, 0, 0, 0 ) |
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| 273 | |
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| 274 | ! ice fraction at U-V points |
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| 275 | zaU(ji,jj) = 0.5_wp * ( at_i(ji,jj) * e1e2t(ji,jj) + at_i(ji+1,jj) * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
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| 276 | zaV(ji,jj) = 0.5_wp * ( at_i(ji,jj) * e1e2t(ji,jj) + at_i(ji,jj+1) * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
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| 277 | |
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| 278 | ! Ice/snow mass at U-V points |
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| 279 | zm1 = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) ) |
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| 280 | zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) ) |
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| 281 | zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) ) |
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| 282 | zmassU = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
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| 283 | zmassV = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
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| 284 | |
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| 285 | ! Ocean currents at U-V points |
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| 286 | v_oceU(ji,jj) = 0.25_wp * ( v_oce(ji,jj) + v_oce(ji,jj-1) + v_oce(ji+1,jj) + v_oce(ji+1,jj-1) ) * umask(ji,jj,1) |
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| 287 | u_oceV(ji,jj) = 0.25_wp * ( u_oce(ji,jj) + u_oce(ji-1,jj) + u_oce(ji,jj+1) + u_oce(ji-1,jj+1) ) * vmask(ji,jj,1) |
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| 288 | |
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| 289 | ! Coriolis at T points (m*f) |
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| 290 | zmf(ji,jj) = zm1 * ff_t(ji,jj) |
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| 291 | |
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| 292 | ! dt/m at T points (for alpha and beta coefficients) |
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| 293 | zdt_m(ji,jj) = zdtevp / MAX( zm1, zmmin ) |
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| 294 | |
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| 295 | ! m/dt |
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| 296 | zmU_t(ji,jj) = zmassU * z1_dtevp |
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| 297 | zmV_t(ji,jj) = zmassV * z1_dtevp |
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| 298 | |
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| 299 | ! Drag ice-atm. |
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| 300 | ztaux_ai(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj) |
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| 301 | ztauy_ai(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj) |
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| 302 | |
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| 303 | ! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points |
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| 304 | zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) |
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| 305 | zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) |
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| 306 | |
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| 307 | ! masks |
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| 308 | zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
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| 309 | zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
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| 310 | |
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| 311 | ! switches |
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| 312 | IF( zmassU <= zmmin .AND. zaU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp |
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| 313 | ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF |
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| 314 | IF( zmassV <= zmmin .AND. zaV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp |
|---|
| 315 | ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF |
|---|
| 316 | |
|---|
| 317 | END_2D |
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| 318 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zmf, 'T', 1.0_wp, zdt_m, 'T', 1.0_wp ) |
|---|
| 319 | ! |
|---|
| 320 | ! !== Landfast ice parameterization ==! |
|---|
| 321 | ! |
|---|
| 322 | IF( ln_landfast_L16 ) THEN !-- Lemieux 2016 |
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| 323 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 324 | ! ice thickness at U-V points |
|---|
| 325 | zvU = 0.5_wp * ( vt_i(ji,jj) * e1e2t(ji,jj) + vt_i(ji+1,jj) * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
|---|
| 326 | zvV = 0.5_wp * ( vt_i(ji,jj) * e1e2t(ji,jj) + vt_i(ji,jj+1) * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 327 | ! ice-bottom stress at U points |
|---|
| 328 | zvCr = zaU(ji,jj) * rn_lf_depfra * hu(ji,jj,Kmm) |
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| 329 | ztaux_base(ji,jj) = - rn_lf_bfr * MAX( 0._wp, zvU - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaU(ji,jj) ) ) |
|---|
| 330 | ! ice-bottom stress at V points |
|---|
| 331 | zvCr = zaV(ji,jj) * rn_lf_depfra * hv(ji,jj,Kmm) |
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| 332 | ztauy_base(ji,jj) = - rn_lf_bfr * MAX( 0._wp, zvV - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaV(ji,jj) ) ) |
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| 333 | ! ice_bottom stress at T points |
|---|
| 334 | zvCr = at_i(ji,jj) * rn_lf_depfra * ht(ji,jj) |
|---|
| 335 | tau_icebfr(ji,jj) = - rn_lf_bfr * MAX( 0._wp, vt_i(ji,jj) - zvCr ) * EXP( -rn_crhg * ( 1._wp - at_i(ji,jj) ) ) |
|---|
| 336 | END_2D |
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| 337 | CALL lbc_lnk( 'icedyn_rhg_evp', tau_icebfr(:,:), 'T', 1.0_wp ) |
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| 338 | ! |
|---|
| 339 | ELSE !-- no landfast |
|---|
| 340 | DO_2D( 0, 0, 0, 0 ) |
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| 341 | ztaux_base(ji,jj) = 0._wp |
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| 342 | ztauy_base(ji,jj) = 0._wp |
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| 343 | END_2D |
|---|
| 344 | ENDIF |
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| 345 | |
|---|
| 346 | !------------------------------------------------------------------------------! |
|---|
| 347 | ! 3) Solution of the momentum equation, iterative procedure |
|---|
| 348 | !------------------------------------------------------------------------------! |
|---|
| 349 | ! |
|---|
| 350 | ! ! ==================== ! |
|---|
| 351 | DO jter = 1 , nn_nevp ! loop over jter ! |
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| 352 | ! ! ==================== ! |
|---|
| 353 | l_full_nf_update = jter == nn_nevp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 |
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| 354 | ! |
|---|
| 355 | ! convergence test |
|---|
| 356 | IF( nn_rhg_chkcvg == 1 .OR. nn_rhg_chkcvg == 2 ) THEN |
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| 357 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 358 | zu_ice(ji,jj) = u_ice(ji,jj) * umask(ji,jj,1) ! velocity at previous time step |
|---|
| 359 | zv_ice(ji,jj) = v_ice(ji,jj) * vmask(ji,jj,1) |
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| 360 | END_2D |
|---|
| 361 | ENDIF |
|---|
| 362 | |
|---|
| 363 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 364 | DO_2D( 1, 0, 1, 0 ) |
|---|
| 365 | |
|---|
| 366 | ! shear at F points |
|---|
| 367 | zds(ji,jj) = ( ( u_ice(ji,jj+1) * r1_e1u(ji,jj+1) - u_ice(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) & |
|---|
| 368 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 369 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 370 | |
|---|
| 371 | END_2D |
|---|
| 372 | |
|---|
| 373 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 374 | |
|---|
| 375 | ! shear**2 at T points (doc eq. A16) |
|---|
| 376 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 377 | & + zds(ji,jj-1) * zds(ji,jj-1) * e1e2f(ji,jj-1) + zds(ji-1,jj-1) * zds(ji-1,jj-1) * e1e2f(ji-1,jj-1) & |
|---|
| 378 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 379 | |
|---|
| 380 | ! divergence at T points |
|---|
| 381 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 382 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 383 | & ) * r1_e1e2t(ji,jj) |
|---|
| 384 | zdiv2 = zdiv * zdiv |
|---|
| 385 | |
|---|
| 386 | ! tension at T points |
|---|
| 387 | zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 388 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 389 | & ) * r1_e1e2t(ji,jj) |
|---|
| 390 | zdt2 = zdt * zdt |
|---|
| 391 | |
|---|
| 392 | ! delta at T points |
|---|
| 393 | zdelta(ji,jj) = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 394 | |
|---|
| 395 | END_2D |
|---|
| 396 | CALL lbc_lnk( 'icedyn_rhg_evp', zdelta, 'T', 1.0_wp ) |
|---|
| 397 | |
|---|
| 398 | ! P/delta at T points |
|---|
| 399 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 400 | zp_delt(ji,jj) = strength(ji,jj) / ( zdelta(ji,jj) + rn_creepl ) |
|---|
| 401 | END_2D |
|---|
| 402 | |
|---|
| 403 | DO_2D( 0, 1, 0, 1 ) ! loop ends at jpi,jpj so that no lbc_lnk are needed for zs1 and zs2 |
|---|
| 404 | |
|---|
| 405 | ! divergence at T points (duplication to avoid communications) |
|---|
| 406 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 407 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 408 | & ) * r1_e1e2t(ji,jj) |
|---|
| 409 | |
|---|
| 410 | ! tension at T points (duplication to avoid communications) |
|---|
| 411 | zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 412 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 413 | & ) * r1_e1e2t(ji,jj) |
|---|
| 414 | |
|---|
| 415 | ! alpha for aEVP |
|---|
| 416 | ! gamma = 0.5*P/(delta+creepl) * (c*pi)**2/Area * dt/m |
|---|
| 417 | ! alpha = beta = sqrt(4*gamma) |
|---|
| 418 | IF( ln_aEVP ) THEN |
|---|
| 419 | zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 420 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 421 | zalph2 = zalph1 |
|---|
| 422 | z1_alph2 = z1_alph1 |
|---|
| 423 | ! explicit: |
|---|
| 424 | ! z1_alph1 = 1._wp / zalph1 |
|---|
| 425 | ! z1_alph2 = 1._wp / zalph1 |
|---|
| 426 | ! zalph1 = zalph1 - 1._wp |
|---|
| 427 | ! zalph2 = zalph1 |
|---|
| 428 | ENDIF |
|---|
| 429 | |
|---|
| 430 | ! stress at T points (zkt/=0 if landfast) |
|---|
| 431 | zs1(ji,jj) = ( zs1(ji,jj)*zalph1 + zp_delt(ji,jj) * ( zdiv*(1._wp + zkt) - zdelta(ji,jj)*(1._wp - zkt) ) ) * z1_alph1 |
|---|
| 432 | zs2(ji,jj) = ( zs2(ji,jj)*zalph2 + zp_delt(ji,jj) * ( zdt * z1_ecc2 * (1._wp + zkt) ) ) * z1_alph2 |
|---|
| 433 | |
|---|
| 434 | END_2D |
|---|
| 435 | |
|---|
| 436 | ! Save beta at T-points for further computations |
|---|
| 437 | IF( ln_aEVP ) THEN |
|---|
| 438 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 439 | zbeta(ji,jj) = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 440 | END_2D |
|---|
| 441 | ENDIF |
|---|
| 442 | |
|---|
| 443 | DO_2D( 1, 0, 1, 0 ) |
|---|
| 444 | |
|---|
| 445 | ! alpha for aEVP |
|---|
| 446 | IF( ln_aEVP ) THEN |
|---|
| 447 | zalph2 = MAX( zbeta(ji,jj), zbeta(ji+1,jj), zbeta(ji,jj+1), zbeta(ji+1,jj+1) ) |
|---|
| 448 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
|---|
| 449 | ! explicit: |
|---|
| 450 | ! z1_alph2 = 1._wp / zalph2 |
|---|
| 451 | ! zalph2 = zalph2 - 1._wp |
|---|
| 452 | ENDIF |
|---|
| 453 | |
|---|
| 454 | ! P/delta at F points |
|---|
| 455 | zp_delf = 0.25_wp * ( zp_delt(ji,jj) + zp_delt(ji+1,jj) + zp_delt(ji,jj+1) + zp_delt(ji+1,jj+1) ) |
|---|
| 456 | |
|---|
| 457 | ! stress at F points (zkt/=0 if landfast) |
|---|
| 458 | zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 * (1._wp + zkt) ) * 0.5_wp ) * z1_alph2 |
|---|
| 459 | |
|---|
| 460 | END_2D |
|---|
| 461 | |
|---|
| 462 | ! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- ! |
|---|
| 463 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 464 | ! !--- U points |
|---|
| 465 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 466 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 467 | & ) * r1_e2u(ji,jj) & |
|---|
| 468 | & + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 469 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 470 | & ) * r1_e1e2u(ji,jj) |
|---|
| 471 | ! |
|---|
| 472 | ! !--- V points |
|---|
| 473 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 474 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 475 | & ) * r1_e1v(ji,jj) & |
|---|
| 476 | & + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 477 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 478 | & ) * r1_e1e2v(ji,jj) |
|---|
| 479 | ! |
|---|
| 480 | ! !--- ice currents at U-V point |
|---|
| 481 | v_iceU(ji,jj) = 0.25_wp * ( v_ice(ji,jj) + v_ice(ji,jj-1) + v_ice(ji+1,jj) + v_ice(ji+1,jj-1) ) * umask(ji,jj,1) |
|---|
| 482 | u_iceV(ji,jj) = 0.25_wp * ( u_ice(ji,jj) + u_ice(ji-1,jj) + u_ice(ji,jj+1) + u_ice(ji-1,jj+1) ) * vmask(ji,jj,1) |
|---|
| 483 | ! |
|---|
| 484 | END_2D |
|---|
| 485 | ! |
|---|
| 486 | ! --- Computation of ice velocity --- ! |
|---|
| 487 | ! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta vary as in Kimmritz 2016 & 2017 |
|---|
| 488 | ! Bouillon et al. 2009 (eq 34-35) => stable |
|---|
| 489 | IF( MOD(jter,2) == 0 ) THEN ! even iterations |
|---|
| 490 | ! |
|---|
| 491 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 492 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 493 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 494 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 495 | ! !--- Ocean-to-Ice stress |
|---|
| 496 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 497 | ! |
|---|
| 498 | ! !--- tau_bottom/v_ice |
|---|
| 499 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 500 | zTauB = ztauy_base(ji,jj) / zvel |
|---|
| 501 | ! !--- OceanBottom-to-Ice stress |
|---|
| 502 | ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj) |
|---|
| 503 | ! |
|---|
| 504 | ! !--- Coriolis at V-points (energy conserving formulation) |
|---|
| 505 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 506 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 507 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 508 | ! |
|---|
| 509 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 510 | zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 511 | ! |
|---|
| 512 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 513 | ! 1 = sliding friction : TauB < RHS |
|---|
| 514 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 515 | ! |
|---|
| 516 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 517 | zbetav = MAX( zbeta(ji,jj), zbeta(ji,jj+1) ) |
|---|
| 518 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbetav * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 519 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 520 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbetav + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 521 | & + ( 1._wp - rswitch ) * ( v_ice_b(ji,jj) & |
|---|
| 522 | & + v_ice (ji,jj) * MAX( 0._wp, zbetav - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 523 | & ) / ( zbetav + 1._wp ) & |
|---|
| 524 | & ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 525 | & ) * zmsk00y(ji,jj) |
|---|
| 526 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 527 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 528 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 529 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 530 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 531 | & ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 532 | & ) * zmsk00y(ji,jj) |
|---|
| 533 | ENDIF |
|---|
| 534 | END_2D |
|---|
| 535 | CALL lbc_lnk( 'icedyn_rhg_evp', v_ice, 'V', -1.0_wp ) |
|---|
| 536 | ! |
|---|
| 537 | #if defined key_agrif |
|---|
| 538 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 539 | CALL agrif_interp_ice( 'V' ) |
|---|
| 540 | #endif |
|---|
| 541 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 542 | ! |
|---|
| 543 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 544 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 545 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 546 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 547 | ! !--- Ocean-to-Ice stress |
|---|
| 548 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 549 | ! |
|---|
| 550 | ! !--- tau_bottom/u_ice |
|---|
| 551 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 552 | zTauB = ztaux_base(ji,jj) / zvel |
|---|
| 553 | ! !--- OceanBottom-to-Ice stress |
|---|
| 554 | ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj) |
|---|
| 555 | ! |
|---|
| 556 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 557 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 558 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 559 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 560 | ! |
|---|
| 561 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 562 | zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 563 | ! |
|---|
| 564 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 565 | ! 1 = sliding friction : TauB < RHS |
|---|
| 566 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 567 | ! |
|---|
| 568 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 569 | zbetau = MAX( zbeta(ji,jj), zbeta(ji+1,jj) ) |
|---|
| 570 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbetau * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 571 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 572 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbetau + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 573 | & + ( 1._wp - rswitch ) * ( u_ice_b(ji,jj) & |
|---|
| 574 | & + u_ice (ji,jj) * MAX( 0._wp, zbetau - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 575 | & ) / ( zbetau + 1._wp ) & |
|---|
| 576 | & ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 577 | & ) * zmsk00x(ji,jj) |
|---|
| 578 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 579 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 580 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 581 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 582 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 583 | & ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 584 | & ) * zmsk00x(ji,jj) |
|---|
| 585 | ENDIF |
|---|
| 586 | END_2D |
|---|
| 587 | CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1.0_wp ) |
|---|
| 588 | ! |
|---|
| 589 | #if defined key_agrif |
|---|
| 590 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 591 | CALL agrif_interp_ice( 'U' ) |
|---|
| 592 | #endif |
|---|
| 593 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 594 | ! |
|---|
| 595 | ELSE ! odd iterations |
|---|
| 596 | ! |
|---|
| 597 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 598 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 599 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 600 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 601 | ! !--- Ocean-to-Ice stress |
|---|
| 602 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 603 | ! |
|---|
| 604 | ! !--- tau_bottom/u_ice |
|---|
| 605 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 606 | zTauB = ztaux_base(ji,jj) / zvel |
|---|
| 607 | ! !--- OceanBottom-to-Ice stress |
|---|
| 608 | ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj) |
|---|
| 609 | ! |
|---|
| 610 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 611 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 612 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 613 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 614 | ! |
|---|
| 615 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 616 | zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 617 | ! |
|---|
| 618 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 619 | ! 1 = sliding friction : TauB < RHS |
|---|
| 620 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 621 | ! |
|---|
| 622 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 623 | zbetau = MAX( zbeta(ji,jj), zbeta(ji+1,jj) ) |
|---|
| 624 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbetau * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 625 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 626 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbetau + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 627 | & + ( 1._wp - rswitch ) * ( u_ice_b(ji,jj) & |
|---|
| 628 | & + u_ice (ji,jj) * MAX( 0._wp, zbetau - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 629 | & ) / ( zbetau + 1._wp ) & |
|---|
| 630 | & ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 631 | & ) * zmsk00x(ji,jj) |
|---|
| 632 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 633 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 634 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 635 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 636 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 637 | & ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 638 | & ) * zmsk00x(ji,jj) |
|---|
| 639 | ENDIF |
|---|
| 640 | END_2D |
|---|
| 641 | CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1.0_wp ) |
|---|
| 642 | ! |
|---|
| 643 | #if defined key_agrif |
|---|
| 644 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 645 | CALL agrif_interp_ice( 'U' ) |
|---|
| 646 | #endif |
|---|
| 647 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 648 | ! |
|---|
| 649 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 650 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 651 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 652 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 653 | ! !--- Ocean-to-Ice stress |
|---|
| 654 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 655 | ! |
|---|
| 656 | ! !--- tau_bottom/v_ice |
|---|
| 657 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 658 | zTauB = ztauy_base(ji,jj) / zvel |
|---|
| 659 | ! !--- OceanBottom-to-Ice stress |
|---|
| 660 | ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj) |
|---|
| 661 | ! |
|---|
| 662 | ! !--- Coriolis at v-points (energy conserving formulation) |
|---|
| 663 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 664 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 665 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 666 | ! |
|---|
| 667 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 668 | zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 669 | ! |
|---|
| 670 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 671 | ! 1 = sliding friction : TauB < RHS |
|---|
| 672 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 673 | ! |
|---|
| 674 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 675 | zbetav = MAX( zbeta(ji,jj), zbeta(ji,jj+1) ) |
|---|
| 676 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbetav * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 677 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 678 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbetav + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 679 | & + ( 1._wp - rswitch ) * ( v_ice_b(ji,jj) & |
|---|
| 680 | & + v_ice (ji,jj) * MAX( 0._wp, zbetav - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 681 | & ) / ( zbetav + 1._wp ) & |
|---|
| 682 | & ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 683 | & ) * zmsk00y(ji,jj) |
|---|
| 684 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 685 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 686 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 687 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 688 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 689 | & ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 690 | & ) * zmsk00y(ji,jj) |
|---|
| 691 | ENDIF |
|---|
| 692 | END_2D |
|---|
| 693 | CALL lbc_lnk( 'icedyn_rhg_evp', v_ice, 'V', -1.0_wp ) |
|---|
| 694 | ! |
|---|
| 695 | #if defined key_agrif |
|---|
| 696 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 697 | CALL agrif_interp_ice( 'V' ) |
|---|
| 698 | #endif |
|---|
| 699 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 700 | ! |
|---|
| 701 | ENDIF |
|---|
| 702 | |
|---|
| 703 | ! convergence test |
|---|
| 704 | IF( nn_rhg_chkcvg == 2 ) CALL rhg_cvg( kt, jter, nn_nevp, u_ice, v_ice, zu_ice, zv_ice ) |
|---|
| 705 | ! |
|---|
| 706 | ! ! ==================== ! |
|---|
| 707 | END DO ! end loop over jter ! |
|---|
| 708 | ! ! ==================== ! |
|---|
| 709 | IF( ln_aEVP ) CALL iom_put( 'beta_evp' , zbeta ) |
|---|
| 710 | ! |
|---|
| 711 | !------------------------------------------------------------------------------! |
|---|
| 712 | ! 4) Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 713 | !------------------------------------------------------------------------------! |
|---|
| 714 | DO_2D( 1, 0, 1, 0 ) |
|---|
| 715 | |
|---|
| 716 | ! shear at F points |
|---|
| 717 | zds(ji,jj) = ( ( u_ice(ji,jj+1) * r1_e1u(ji,jj+1) - u_ice(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) & |
|---|
| 718 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 719 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 720 | |
|---|
| 721 | END_2D |
|---|
| 722 | |
|---|
| 723 | DO_2D( 0, 0, 0, 0 ) ! no vector loop |
|---|
| 724 | |
|---|
| 725 | ! tension**2 at T points |
|---|
| 726 | zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 727 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 728 | & ) * r1_e1e2t(ji,jj) |
|---|
| 729 | zdt2 = zdt * zdt |
|---|
| 730 | |
|---|
| 731 | zten_i(ji,jj) = zdt |
|---|
| 732 | |
|---|
| 733 | ! shear**2 at T points (doc eq. A16) |
|---|
| 734 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 735 | & + zds(ji,jj-1) * zds(ji,jj-1) * e1e2f(ji,jj-1) + zds(ji-1,jj-1) * zds(ji-1,jj-1) * e1e2f(ji-1,jj-1) & |
|---|
| 736 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 737 | |
|---|
| 738 | ! shear at T points |
|---|
| 739 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
|---|
| 740 | |
|---|
| 741 | ! divergence at T points |
|---|
| 742 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 743 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 744 | & ) * r1_e1e2t(ji,jj) |
|---|
| 745 | |
|---|
| 746 | ! delta at T points |
|---|
| 747 | zfac = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) ! delta |
|---|
| 748 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zfac ) ) ! 0 if delta=0 |
|---|
| 749 | pdelta_i(ji,jj) = zfac + rn_creepl * rswitch ! delta+creepl |
|---|
| 750 | |
|---|
| 751 | END_2D |
|---|
| 752 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', pshear_i, 'T', 1._wp, pdivu_i, 'T', 1._wp, pdelta_i, 'T', 1._wp, zten_i, 'T', 1._wp, & |
|---|
| 753 | & zs1 , 'T', 1._wp, zs2 , 'T', 1._wp, zs12 , 'F', 1._wp ) |
|---|
| 754 | |
|---|
| 755 | ! --- Store the stress tensor for the next time step --- ! |
|---|
| 756 | pstress1_i (:,:) = zs1 (:,:) |
|---|
| 757 | pstress2_i (:,:) = zs2 (:,:) |
|---|
| 758 | pstress12_i(:,:) = zs12(:,:) |
|---|
| 759 | ! |
|---|
| 760 | |
|---|
| 761 | !------------------------------------------------------------------------------! |
|---|
| 762 | ! 5) diagnostics |
|---|
| 763 | !------------------------------------------------------------------------------! |
|---|
| 764 | ! --- ice-ocean, ice-atm. & ice-oceanbottom(landfast) stresses --- ! |
|---|
| 765 | IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. & |
|---|
| 766 | & iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN |
|---|
| 767 | ! |
|---|
| 768 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', ztaux_oi, 'U', -1.0_wp, ztauy_oi, 'V', -1.0_wp, ztaux_ai, 'U', -1.0_wp, ztauy_ai, 'V', -1.0_wp, & |
|---|
| 769 | & ztaux_bi, 'U', -1.0_wp, ztauy_bi, 'V', -1.0_wp ) |
|---|
| 770 | ! |
|---|
| 771 | CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 ) |
|---|
| 772 | CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 ) |
|---|
| 773 | CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 ) |
|---|
| 774 | CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 ) |
|---|
| 775 | CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 ) |
|---|
| 776 | CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 ) |
|---|
| 777 | ENDIF |
|---|
| 778 | |
|---|
| 779 | ! --- divergence, shear and strength --- ! |
|---|
| 780 | IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence |
|---|
| 781 | IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! shear |
|---|
| 782 | IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength |
|---|
| 783 | |
|---|
| 784 | ! --- Stress tensor invariants (SIMIP diags) --- ! |
|---|
| 785 | IF( iom_use('normstr') .OR. iom_use('sheastr') ) THEN |
|---|
| 786 | ! |
|---|
| 787 | ALLOCATE( zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 788 | ! |
|---|
| 789 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 790 | |
|---|
| 791 | ! Ice stresses |
|---|
| 792 | ! sigma1, sigma2, sigma12 are some useful recombination of the stresses (Hunke and Dukowicz MWR 2002, Bouillon et al., OM2013) |
|---|
| 793 | ! These are NOT stress tensor components, neither stress invariants, neither stress principal components |
|---|
| 794 | ! I know, this can be confusing... |
|---|
| 795 | zfac = strength(ji,jj) / ( pdelta_i(ji,jj) + rn_creepl ) |
|---|
| 796 | zsig1 = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) ) |
|---|
| 797 | zsig2 = zfac * z1_ecc2 * zten_i(ji,jj) |
|---|
| 798 | zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj) |
|---|
| 799 | |
|---|
| 800 | ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008) |
|---|
| 801 | zsig_I (ji,jj) = zsig1 * 0.5_wp ! 1st stress invariant, aka average normal stress, aka negative pressure |
|---|
| 802 | zsig_II(ji,jj) = SQRT ( MAX( 0._wp, zsig2 * zsig2 * 0.25_wp + zsig12 ) ) ! 2nd '' '', aka maximum shear stress |
|---|
| 803 | |
|---|
| 804 | END_2D |
|---|
| 805 | ! |
|---|
| 806 | ! Stress tensor invariants (normal and shear stress N/m) - SIMIP diags - definitions following Coon (1974) and Feltham (2008) |
|---|
| 807 | IF( iom_use('normstr') ) CALL iom_put( 'normstr', zsig_I (:,:) * zmsk00(:,:) ) ! Normal stress |
|---|
| 808 | IF( iom_use('sheastr') ) CALL iom_put( 'sheastr', zsig_II(:,:) * zmsk00(:,:) ) ! Maximum shear stress |
|---|
| 809 | |
|---|
| 810 | DEALLOCATE ( zsig_I, zsig_II ) |
|---|
| 811 | |
|---|
| 812 | ENDIF |
|---|
| 813 | |
|---|
| 814 | ! --- Normalized stress tensor principal components --- ! |
|---|
| 815 | ! This are used to plot the normalized yield curve, see Lemieux & Dupont, 2020 |
|---|
| 816 | ! Recommendation 1 : we use ice strength, not replacement pressure |
|---|
| 817 | ! Recommendation 2 : need to use deformations at PREVIOUS iterate for viscosities |
|---|
| 818 | IF( iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN |
|---|
| 819 | ! |
|---|
| 820 | ALLOCATE( zsig1_p(jpi,jpj) , zsig2_p(jpi,jpj) , zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 821 | ! |
|---|
| 822 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 823 | |
|---|
| 824 | ! Ice stresses computed with **viscosities** (delta, p/delta) at **previous** iterates |
|---|
| 825 | ! and **deformations** at current iterates |
|---|
| 826 | ! following Lemieux & Dupont (2020) |
|---|
| 827 | zfac = zp_delt(ji,jj) |
|---|
| 828 | zsig1 = zfac * ( pdivu_i(ji,jj) - ( zdelta(ji,jj) + rn_creepl ) ) |
|---|
| 829 | zsig2 = zfac * z1_ecc2 * zten_i(ji,jj) |
|---|
| 830 | zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj) |
|---|
| 831 | |
|---|
| 832 | ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008), T-point |
|---|
| 833 | zsig_I(ji,jj) = zsig1 * 0.5_wp ! 1st stress invariant, aka average normal stress, aka negative pressure |
|---|
| 834 | zsig_II(ji,jj) = SQRT ( MAX( 0._wp, zsig2 * zsig2 * 0.25_wp + zsig12 ) ) ! 2nd '' '', aka maximum shear stress |
|---|
| 835 | |
|---|
| 836 | ! Normalized principal stresses (used to display the ellipse) |
|---|
| 837 | z1_strength = 1._wp / MAX( 1._wp, strength(ji,jj) ) |
|---|
| 838 | zsig1_p(ji,jj) = ( zsig_I(ji,jj) + zsig_II(ji,jj) ) * z1_strength |
|---|
| 839 | zsig2_p(ji,jj) = ( zsig_I(ji,jj) - zsig_II(ji,jj) ) * z1_strength |
|---|
| 840 | END_2D |
|---|
| 841 | ! |
|---|
| 842 | CALL iom_put( 'sig1_pnorm' , zsig1_p ) |
|---|
| 843 | CALL iom_put( 'sig2_pnorm' , zsig2_p ) |
|---|
| 844 | |
|---|
| 845 | DEALLOCATE( zsig1_p , zsig2_p , zsig_I, zsig_II ) |
|---|
| 846 | |
|---|
| 847 | ENDIF |
|---|
| 848 | |
|---|
| 849 | ! --- SIMIP --- ! |
|---|
| 850 | IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. & |
|---|
| 851 | & iom_use('corstrx') .OR. iom_use('corstry') .OR. iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 852 | ! |
|---|
| 853 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zspgU, 'U', -1.0_wp, zspgV, 'V', -1.0_wp, & |
|---|
| 854 | & zCorU, 'U', -1.0_wp, zCorV, 'V', -1.0_wp, zfU, 'U', -1.0_wp, zfV, 'V', -1.0_wp ) |
|---|
| 855 | |
|---|
| 856 | CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x) |
|---|
| 857 | CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y) |
|---|
| 858 | CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x) |
|---|
| 859 | CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y) |
|---|
| 860 | CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x) |
|---|
| 861 | CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y) |
|---|
| 862 | ENDIF |
|---|
| 863 | |
|---|
| 864 | IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. & |
|---|
| 865 | & iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN |
|---|
| 866 | ! |
|---|
| 867 | ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 868 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) ) |
|---|
| 869 | ! |
|---|
| 870 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 871 | ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 872 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj) |
|---|
| 873 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj) |
|---|
| 874 | |
|---|
| 875 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 876 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 877 | |
|---|
| 878 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 879 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 880 | |
|---|
| 881 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 882 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 883 | |
|---|
| 884 | END_2D |
|---|
| 885 | |
|---|
| 886 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zdiag_xmtrp_ice, 'U', -1.0_wp, zdiag_ymtrp_ice, 'V', -1.0_wp, & |
|---|
| 887 | & zdiag_xmtrp_snw, 'U', -1.0_wp, zdiag_ymtrp_snw, 'V', -1.0_wp, & |
|---|
| 888 | & zdiag_xatrp , 'U', -1.0_wp, zdiag_yatrp , 'V', -1.0_wp ) |
|---|
| 889 | |
|---|
| 890 | CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 891 | CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport |
|---|
| 892 | CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s) |
|---|
| 893 | CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport |
|---|
| 894 | CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport |
|---|
| 895 | CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport |
|---|
| 896 | |
|---|
| 897 | DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 898 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 899 | |
|---|
| 900 | ENDIF |
|---|
| 901 | ! |
|---|
| 902 | ! --- convergence tests --- ! |
|---|
| 903 | IF( nn_rhg_chkcvg == 1 .OR. nn_rhg_chkcvg == 2 ) THEN |
|---|
| 904 | IF( iom_use('uice_cvg') ) THEN |
|---|
| 905 | IF( ln_aEVP ) THEN ! output: beta * ( u(t=nn_nevp) - u(t=nn_nevp-1) ) |
|---|
| 906 | CALL iom_put( 'uice_cvg', MAX( ABS( u_ice(:,:) - zu_ice(:,:) ) * zbeta(:,:) * umask(:,:,1) , & |
|---|
| 907 | & ABS( v_ice(:,:) - zv_ice(:,:) ) * zbeta(:,:) * vmask(:,:,1) ) * zmsk15(:,:) ) |
|---|
| 908 | ELSE ! output: nn_nevp * ( u(t=nn_nevp) - u(t=nn_nevp-1) ) |
|---|
| 909 | CALL iom_put( 'uice_cvg', REAL( nn_nevp ) * MAX( ABS( u_ice(:,:) - zu_ice(:,:) ) * umask(:,:,1) , & |
|---|
| 910 | & ABS( v_ice(:,:) - zv_ice(:,:) ) * vmask(:,:,1) ) * zmsk15(:,:) ) |
|---|
| 911 | ENDIF |
|---|
| 912 | ENDIF |
|---|
| 913 | ENDIF |
|---|
| 914 | ! |
|---|
| 915 | DEALLOCATE( zmsk00, zmsk15 ) |
|---|
| 916 | ! |
|---|
| 917 | END SUBROUTINE ice_dyn_rhg_evp |
|---|
| 918 | |
|---|
| 919 | |
|---|
| 920 | SUBROUTINE rhg_cvg( kt, kiter, kitermax, pu, pv, pub, pvb ) |
|---|
| 921 | !!---------------------------------------------------------------------- |
|---|
| 922 | !! *** ROUTINE rhg_cvg *** |
|---|
| 923 | !! |
|---|
| 924 | !! ** Purpose : check convergence of oce rheology |
|---|
| 925 | !! |
|---|
| 926 | !! ** Method : create a file ice_cvg.nc containing the convergence of ice velocity |
|---|
| 927 | !! during the sub timestepping of rheology so as: |
|---|
| 928 | !! uice_cvg = MAX( u(t+1) - u(t) , v(t+1) - v(t) ) |
|---|
| 929 | !! This routine is called every sub-iteration, so it is cpu expensive |
|---|
| 930 | !! |
|---|
| 931 | !! ** Note : for the first sub-iteration, uice_cvg is set to 0 (too large otherwise) |
|---|
| 932 | !!---------------------------------------------------------------------- |
|---|
| 933 | INTEGER , INTENT(in) :: kt, kiter, kitermax ! ocean time-step index |
|---|
| 934 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pub, pvb ! now and before velocities |
|---|
| 935 | !! |
|---|
| 936 | INTEGER :: it, idtime, istatus |
|---|
| 937 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 938 | REAL(wp) :: zresm ! local real |
|---|
| 939 | CHARACTER(len=20) :: clname |
|---|
| 940 | REAL(wp), DIMENSION(jpi,jpj) :: zres ! check convergence |
|---|
| 941 | !!---------------------------------------------------------------------- |
|---|
| 942 | |
|---|
| 943 | ! create file |
|---|
| 944 | IF( kt == nit000 .AND. kiter == 1 ) THEN |
|---|
| 945 | ! |
|---|
| 946 | IF( lwp ) THEN |
|---|
| 947 | WRITE(numout,*) |
|---|
| 948 | WRITE(numout,*) 'rhg_cvg : ice rheology convergence control' |
|---|
| 949 | WRITE(numout,*) '~~~~~~~' |
|---|
| 950 | ENDIF |
|---|
| 951 | ! |
|---|
| 952 | IF( lwm ) THEN |
|---|
| 953 | clname = 'ice_cvg.nc' |
|---|
| 954 | IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname) |
|---|
| 955 | istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid ) |
|---|
| 956 | istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime ) |
|---|
| 957 | istatus = NF90_DEF_VAR( ncvgid, 'uice_cvg', NF90_DOUBLE , (/ idtime /), nvarid ) |
|---|
| 958 | istatus = NF90_ENDDEF(ncvgid) |
|---|
| 959 | ENDIF |
|---|
| 960 | ! |
|---|
| 961 | ENDIF |
|---|
| 962 | |
|---|
| 963 | ! time |
|---|
| 964 | it = ( kt - 1 ) * kitermax + kiter |
|---|
| 965 | |
|---|
| 966 | ! convergence |
|---|
| 967 | IF( kiter == 1 ) THEN ! remove the first iteration for calculations of convergence (always very large) |
|---|
| 968 | zresm = 0._wp |
|---|
| 969 | ELSE |
|---|
| 970 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 971 | zres(ji,jj) = MAX( ABS( pu(ji,jj) - pub(ji,jj) ) * umask(ji,jj,1), & |
|---|
| 972 | & ABS( pv(ji,jj) - pvb(ji,jj) ) * vmask(ji,jj,1) ) * zmsk15(ji,jj) |
|---|
| 973 | END_2D |
|---|
| 974 | zresm = MAXVAL( zres ) |
|---|
| 975 | CALL mpp_max( 'icedyn_rhg_evp', zresm ) ! max over the global domain |
|---|
| 976 | ENDIF |
|---|
| 977 | |
|---|
| 978 | IF( lwm ) THEN |
|---|
| 979 | ! write variables |
|---|
| 980 | istatus = NF90_PUT_VAR( ncvgid, nvarid, (/zresm/), (/it/), (/1/) ) |
|---|
| 981 | ! close file |
|---|
| 982 | IF( kt == nitend - nn_fsbc + 1 ) istatus = NF90_CLOSE(ncvgid) |
|---|
| 983 | ENDIF |
|---|
| 984 | |
|---|
| 985 | END SUBROUTINE rhg_cvg |
|---|
| 986 | |
|---|
| 987 | |
|---|
| 988 | SUBROUTINE rhg_evp_rst( cdrw, kt ) |
|---|
| 989 | !!--------------------------------------------------------------------- |
|---|
| 990 | !! *** ROUTINE rhg_evp_rst *** |
|---|
| 991 | !! |
|---|
| 992 | !! ** Purpose : Read or write RHG file in restart file |
|---|
| 993 | !! |
|---|
| 994 | !! ** Method : use of IOM library |
|---|
| 995 | !!---------------------------------------------------------------------- |
|---|
| 996 | CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag |
|---|
| 997 | INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step |
|---|
| 998 | ! |
|---|
| 999 | INTEGER :: iter ! local integer |
|---|
| 1000 | INTEGER :: id1, id2, id3 ! local integers |
|---|
| 1001 | !!---------------------------------------------------------------------- |
|---|
| 1002 | ! |
|---|
| 1003 | IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialize |
|---|
| 1004 | ! ! --------------- |
|---|
| 1005 | IF( ln_rstart ) THEN !* Read the restart file |
|---|
| 1006 | ! |
|---|
| 1007 | id1 = iom_varid( numrir, 'stress1_i' , ldstop = .FALSE. ) |
|---|
| 1008 | id2 = iom_varid( numrir, 'stress2_i' , ldstop = .FALSE. ) |
|---|
| 1009 | id3 = iom_varid( numrir, 'stress12_i', ldstop = .FALSE. ) |
|---|
| 1010 | ! |
|---|
| 1011 | IF( MIN( id1, id2, id3 ) > 0 ) THEN ! fields exist |
|---|
| 1012 | CALL iom_get( numrir, jpdom_auto, 'stress1_i' , stress1_i , cd_type = 'T' ) |
|---|
| 1013 | CALL iom_get( numrir, jpdom_auto, 'stress2_i' , stress2_i , cd_type = 'T' ) |
|---|
| 1014 | CALL iom_get( numrir, jpdom_auto, 'stress12_i', stress12_i, cd_type = 'F' ) |
|---|
| 1015 | ELSE ! start rheology from rest |
|---|
| 1016 | IF(lwp) WRITE(numout,*) |
|---|
| 1017 | IF(lwp) WRITE(numout,*) ' ==>>> previous run without rheology, set stresses to 0' |
|---|
| 1018 | stress1_i (:,:) = 0._wp |
|---|
| 1019 | stress2_i (:,:) = 0._wp |
|---|
| 1020 | stress12_i(:,:) = 0._wp |
|---|
| 1021 | ENDIF |
|---|
| 1022 | ELSE !* Start from rest |
|---|
| 1023 | IF(lwp) WRITE(numout,*) |
|---|
| 1024 | IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set stresses to 0' |
|---|
| 1025 | stress1_i (:,:) = 0._wp |
|---|
| 1026 | stress2_i (:,:) = 0._wp |
|---|
| 1027 | stress12_i(:,:) = 0._wp |
|---|
| 1028 | ENDIF |
|---|
| 1029 | ! |
|---|
| 1030 | ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file |
|---|
| 1031 | ! ! ------------------- |
|---|
| 1032 | IF(lwp) WRITE(numout,*) '---- rhg-rst ----' |
|---|
| 1033 | iter = kt + nn_fsbc - 1 ! ice restarts are written at kt == nitrst - nn_fsbc + 1 |
|---|
| 1034 | ! |
|---|
| 1035 | CALL iom_rstput( iter, nitrst, numriw, 'stress1_i' , stress1_i ) |
|---|
| 1036 | CALL iom_rstput( iter, nitrst, numriw, 'stress2_i' , stress2_i ) |
|---|
| 1037 | CALL iom_rstput( iter, nitrst, numriw, 'stress12_i', stress12_i ) |
|---|
| 1038 | ! |
|---|
| 1039 | ENDIF |
|---|
| 1040 | ! |
|---|
| 1041 | END SUBROUTINE rhg_evp_rst |
|---|
| 1042 | |
|---|
| 1043 | |
|---|
| 1044 | #else |
|---|
| 1045 | !!---------------------------------------------------------------------- |
|---|
| 1046 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 1047 | !!---------------------------------------------------------------------- |
|---|
| 1048 | #endif |
|---|
| 1049 | |
|---|
| 1050 | !!============================================================================== |
|---|
| 1051 | END MODULE icedyn_rhg_evp |
|---|
