| 1 | MODULE icedyn_rhg_eap |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icedyn_rhg_eap *** |
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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 | !! ! 2019 (S. Rynders, Y. Aksenov, C. Rousset) change into eap rheology from |
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| 16 | !! CICE code (Tsamados, Heorton) |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | #if defined key_si3 |
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| 19 | !!---------------------------------------------------------------------- |
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| 20 | !! 'key_si3' SI3 sea-ice model |
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| 21 | !!---------------------------------------------------------------------- |
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| 22 | !! ice_dyn_rhg_eap : computes ice velocities from EVP rheology |
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| 23 | !! rhg_eap_rst : read/write EVP fields in ice restart |
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| 24 | !!---------------------------------------------------------------------- |
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| 25 | USE phycst ! Physical constant |
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| 26 | USE dom_oce ! Ocean domain |
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| 27 | USE sbc_oce , ONLY : ln_ice_embd, nn_fsbc, ssh_m |
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| 28 | USE sbc_ice , ONLY : utau_ice, vtau_ice, snwice_mass, snwice_mass_b |
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| 29 | USE ice ! sea-ice: ice variables |
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| 30 | USE icevar ! ice_var_sshdyn |
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| 31 | USE icedyn_rdgrft ! sea-ice: ice strength |
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| 32 | USE bdy_oce , ONLY : ln_bdy |
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| 33 | USE bdyice |
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| 34 | #if defined key_agrif |
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| 35 | USE agrif_ice_interp |
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| 36 | #endif |
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| 37 | ! |
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| 38 | USE in_out_manager ! I/O manager |
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| 39 | USE iom ! I/O manager library |
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| 40 | USE lib_mpp ! MPP library |
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| 41 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 42 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 43 | USE prtctl ! Print control |
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| 44 | |
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| 45 | USE netcdf ! NetCDF library for convergence test |
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| 46 | IMPLICIT NONE |
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| 47 | PRIVATE |
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| 48 | |
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| 49 | PUBLIC ice_dyn_rhg_eap ! called by icedyn_rhg.F90 |
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| 50 | PUBLIC rhg_eap_rst ! called by icedyn_rhg.F90 |
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| 51 | |
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| 52 | REAL(wp), PARAMETER :: pphi = 3.141592653589793_wp/12._wp ! diamond shaped floe smaller angle (default phi = 30 deg) |
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| 53 | |
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| 54 | ! look-up table for calculating structure tensor |
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| 55 | INTEGER, PARAMETER :: nx_yield = 41 |
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| 56 | INTEGER, PARAMETER :: ny_yield = 41 |
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| 57 | INTEGER, PARAMETER :: na_yield = 21 |
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| 58 | |
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| 59 | REAL(wp), DIMENSION(nx_yield, ny_yield, na_yield) :: s11r, s12r, s22r, s11s, s12s, s22s |
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| 60 | |
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| 61 | !! * Substitutions |
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| 62 | # include "do_loop_substitute.h90" |
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| 63 | # include "domzgr_substitute.h90" |
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| 64 | |
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| 65 | !! for convergence tests |
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| 66 | INTEGER :: ncvgid ! netcdf file id |
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| 67 | INTEGER :: nvarid ! netcdf variable id |
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| 68 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zmsk00, zmsk15 |
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| 69 | !!---------------------------------------------------------------------- |
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| 70 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 71 | !! $Id: icedyn_rhg_eap.F90 11536 2019-09-11 13:54:18Z smasson $ |
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| 72 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 73 | !!---------------------------------------------------------------------- |
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| 74 | CONTAINS |
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| 75 | |
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| 76 | SUBROUTINE ice_dyn_rhg_eap( kt, Kmm, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i, paniso_11, paniso_12, prdg_conv ) |
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| 77 | !!------------------------------------------------------------------- |
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| 78 | !! *** SUBROUTINE ice_dyn_rhg_eap *** |
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| 79 | !! EAP-C-grid |
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| 80 | !! |
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| 81 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
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| 82 | !! stress and sea-surface slope. Ice-ice interaction is described by |
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| 83 | !! a non-linear elasto-anisotropic-plastic (EAP) law including shear |
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| 84 | !! strength and a bulk rheology . |
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| 85 | !! |
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| 86 | !! The points in the C-grid look like this, dear reader |
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| 87 | !! |
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| 88 | !! (ji,jj) |
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| 89 | !! | |
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| 90 | !! | |
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| 91 | !! (ji-1,jj) | (ji,jj) |
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| 92 | !! --------- |
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| 93 | !! | | |
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| 94 | !! | (ji,jj) |------(ji,jj) |
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| 95 | !! | | |
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| 96 | !! --------- |
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| 97 | !! (ji-1,jj-1) (ji,jj-1) |
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| 98 | !! |
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| 99 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 100 | !! ice total volume (vt_i) per unit area |
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| 101 | !! snow total volume (vt_s) per unit area |
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| 102 | !! |
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| 103 | !! ** Action : - compute u_ice, v_ice : the components of the |
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| 104 | !! sea-ice velocity vector |
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| 105 | !! - compute delta_i, shear_i, divu_i, which are inputs |
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| 106 | !! of the ice thickness distribution |
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| 107 | !! |
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| 108 | !! ** Steps : 0) compute mask at F point |
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| 109 | !! 1) Compute ice snow mass, ice strength |
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| 110 | !! 2) Compute wind, oceanic stresses, mass terms and |
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| 111 | !! coriolis terms of the momentum equation |
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| 112 | !! 3) Solve the momentum equation (iterative procedure) |
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| 113 | !! 4) Recompute delta, shear and divergence |
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| 114 | !! (which are inputs of the ITD) & store stress |
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| 115 | !! for the next time step |
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| 116 | !! 5) Diagnostics including charge ellipse |
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| 117 | !! |
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| 118 | !! ** Notes : There is the possibility to use aEVP from the nice work of Kimmritz et al. (2016 & 2017) |
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| 119 | !! by setting up ln_aEVP=T (i.e. changing alpha and beta parameters). |
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| 120 | !! This is an upgraded version of mEVP from Bouillon et al. 2013 |
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| 121 | !! (i.e. more stable and better convergence) |
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| 122 | !! |
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| 123 | !! References : Hunke and Dukowicz, JPO97 |
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| 124 | !! Bouillon et al., Ocean Modelling 2009 |
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| 125 | !! Bouillon et al., Ocean Modelling 2013 |
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| 126 | !! Kimmritz et al., Ocean Modelling 2016 & 2017 |
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| 127 | !!------------------------------------------------------------------- |
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| 128 | INTEGER , INTENT(in ) :: kt ! time step |
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| 129 | INTEGER , INTENT(in ) :: Kmm ! ocean time level index |
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| 130 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pstress1_i, pstress2_i, pstress12_i ! |
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| 131 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
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| 132 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: paniso_11 , paniso_12 ! structure tensor components |
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| 133 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: prdg_conv ! for ridging |
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| 134 | !! |
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| 135 | INTEGER :: ji, jj ! dummy loop indices |
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| 136 | INTEGER :: jter ! local integers |
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| 137 | ! |
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| 138 | REAL(wp) :: zrhoco ! rau0 * rn_cio |
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| 139 | REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling |
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| 140 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
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| 141 | REAL(wp) :: zalph1, z1_alph1, zalph2, z1_alph2 ! alpha coef from Bouillon 2009 or Kimmritz 2017 |
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| 142 | REAl(wp) :: zbetau, zbetav |
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| 143 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV, zvU, zvV ! ice/snow mass and volume |
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| 144 | REAL(wp) :: zds2, zdt, zdt2, zdiv, zdiv2, zdsT ! temporary scalars |
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| 145 | REAL(wp) :: zTauO, zTauB, zRHS, zvel ! temporary scalars |
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| 146 | REAL(wp) :: zkt ! isotropic tensile strength for landfast ice |
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| 147 | REAL(wp) :: zvCr ! critical ice volume above which ice is landfast |
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| 148 | ! |
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| 149 | REAL(wp) :: zintb, zintn ! dummy argument |
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| 150 | REAL(wp) :: zfac_x, zfac_y |
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| 151 | REAL(wp) :: zshear, zdum1, zdum2 |
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| 152 | REAL(wp) :: zstressptmp, zstressmtmp, zstress12tmpF ! anisotropic stress tensor components |
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| 153 | REAL(wp) :: zalphar, zalphas ! for mechanical redistribution |
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| 154 | REAL(wp) :: zmresult11, zmresult12, z1dtevpkth, zp5kth, z1_dtevp_A ! for structure tensor evolution |
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| 155 | ! |
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| 156 | REAL(wp), DIMENSION(jpi,jpj) :: zstress12tmp ! anisotropic stress tensor component for regridding |
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| 157 | REAL(wp), DIMENSION(jpi,jpj) :: zyield11, zyield22, zyield12 ! yield surface tensor for history |
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| 158 | REAL(wp), DIMENSION(jpi,jpj) :: zdelta, zp_delt ! delta and P/delta at T points |
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| 159 | REAL(wp), DIMENSION(jpi,jpj) :: zten_i ! tension |
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| 160 | REAL(wp), DIMENSION(jpi,jpj) :: zbeta ! beta coef from Kimmritz 2017 |
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| 161 | ! |
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| 162 | REAL(wp), DIMENSION(jpi,jpj) :: zdt_m ! (dt / ice-snow_mass) on T points |
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| 163 | REAL(wp), DIMENSION(jpi,jpj) :: zaU , zaV ! ice fraction on U/V points |
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| 164 | REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! (ice-snow_mass / dt) on U/V points |
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| 165 | REAL(wp), DIMENSION(jpi,jpj) :: zmf ! coriolis parameter at T points |
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| 166 | 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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| 167 | ! |
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| 168 | REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear |
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| 169 | REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12 ! stress tensor components |
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| 170 | REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope: |
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| 171 | ! ! ocean surface (ssh_m) if ice is not embedded |
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| 172 | ! ! ice bottom surface if ice is embedded |
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| 173 | REAL(wp), DIMENSION(jpi,jpj) :: zfU , zfV ! internal stresses |
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| 174 | REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points |
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| 175 | REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array |
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| 176 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points |
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| 177 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi, ztauy_oi ! ice-ocean stress at U-V points |
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| 178 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast) |
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| 179 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast) |
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| 180 | ! |
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| 181 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! dummy arrays |
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| 182 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence |
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| 183 | REAL(wp), DIMENSION(jpi,jpj) :: zfmask ! mask at F points for the ice |
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| 184 | |
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| 185 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
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| 186 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small |
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| 187 | REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small |
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| 188 | !! --- check convergence |
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| 189 | REAL(wp), DIMENSION(jpi,jpj) :: zu_ice, zv_ice |
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| 190 | !! --- diags |
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| 191 | REAL(wp) :: zsig1, zsig2, zsig12, zfac, z1_strength |
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| 192 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig_I, zsig_II, zsig1_p, zsig2_p |
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| 193 | !! --- SIMIP diags |
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| 194 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice ! X-component of ice mass transport (kg/s) |
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| 195 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_ice ! Y-component of ice mass transport (kg/s) |
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| 196 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw ! X-component of snow mass transport (kg/s) |
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| 197 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_snw ! Y-component of snow mass transport (kg/s) |
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| 198 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp ! X-component of area transport (m2/s) |
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| 199 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_yatrp ! Y-component of area transport (m2/s) |
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| 200 | !!------------------------------------------------------------------- |
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| 201 | |
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| 202 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_eap: EAP sea-ice rheology' |
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| 203 | ! |
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| 204 | ! for diagnostics and convergence tests |
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| 205 | ALLOCATE( zmsk00(jpi,jpj), zmsk15(jpi,jpj) ) |
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| 206 | DO_2D( 1, 1, 1, 1 ) |
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| 207 | 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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| 208 | 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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| 209 | END_2D |
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| 210 | ! |
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| 211 | !!gm for Clem: OPTIMIZATION: I think zfmask can be computed one for all at the initialization.... |
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| 212 | !------------------------------------------------------------------------------! |
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| 213 | ! 0) mask at F points for the ice |
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| 214 | !------------------------------------------------------------------------------! |
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| 215 | ! ocean/land mask |
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| 216 | DO_2D( 1, 0, 1, 0 ) |
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| 217 | 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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| 218 | END_2D |
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| 219 | CALL lbc_lnk( 'icedyn_rhg_eap', zfmask, 'F', 1._wp ) |
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| 220 | |
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| 221 | ! Lateral boundary conditions on velocity (modify zfmask) |
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| 222 | DO_2D( 0, 0, 0, 0 ) |
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| 223 | IF( zfmask(ji,jj) == 0._wp ) THEN |
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| 224 | zfmask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(ji,jj,1), umask(ji,jj+1,1), & |
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| 225 | & vmask(ji,jj,1), vmask(ji+1,jj,1) ) ) |
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| 226 | ENDIF |
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| 227 | END_2D |
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| 228 | DO jj = 2, jpjm1 |
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| 229 | IF( zfmask(1,jj) == 0._wp ) THEN |
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| 230 | 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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| 231 | ENDIF |
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| 232 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
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| 233 | 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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| 234 | ENDIF |
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| 235 | END DO |
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| 236 | DO ji = 2, jpim1 |
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| 237 | IF( zfmask(ji,1) == 0._wp ) THEN |
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| 238 | 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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| 239 | ENDIF |
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| 240 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
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| 241 | 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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| 242 | ENDIF |
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| 243 | END DO |
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| 244 | CALL lbc_lnk( 'icedyn_rhg_eap', zfmask, 'F', 1.0_wp ) |
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| 245 | |
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| 246 | !------------------------------------------------------------------------------! |
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| 247 | ! 1) define some variables and initialize arrays |
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| 248 | !------------------------------------------------------------------------------! |
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| 249 | zrhoco = rho0 * rn_cio |
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| 250 | |
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| 251 | ! ecc2: square of yield ellipse eccenticrity |
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| 252 | ecc2 = rn_ecc * rn_ecc |
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| 253 | z1_ecc2 = 1._wp / ecc2 |
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| 254 | |
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| 255 | ! alpha parameters (Bouillon 2009) |
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| 256 | IF( .NOT. ln_aEVP ) THEN |
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| 257 | zdtevp = rDt_ice / REAL( nn_nevp ) |
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| 258 | zalph1 = 2._wp * rn_relast * REAL( nn_nevp ) |
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| 259 | zalph2 = zalph1 * z1_ecc2 |
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| 260 | |
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| 261 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
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| 262 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
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| 263 | ELSE |
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| 264 | zdtevp = rdt_ice |
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| 265 | ! zalpha parameters set later on adaptatively |
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| 266 | ENDIF |
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| 267 | z1_dtevp = 1._wp / zdtevp |
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| 268 | |
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| 269 | ! Initialise stress tensor |
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| 270 | zs1 (:,:) = pstress1_i (:,:) |
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| 271 | zs2 (:,:) = pstress2_i (:,:) |
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| 272 | zs12(:,:) = pstress12_i(:,:) |
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| 273 | |
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| 274 | ! constants for structure tensor |
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| 275 | z1_dtevp_A = z1_dtevp/10.0_wp |
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| 276 | z1dtevpkth = 1._wp / (z1_dtevp_A + 0.00002_wp) |
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| 277 | zp5kth = 0.5_wp * 0.00002_wp |
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| 278 | |
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| 279 | ! Ice strength |
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| 280 | CALL ice_strength |
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| 281 | |
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| 282 | ! landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) |
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| 283 | IF( ln_landfast_L16 ) THEN ; zkt = rn_lf_tensile |
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| 284 | ELSE ; zkt = 0._wp |
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| 285 | ENDIF |
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| 286 | ! |
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| 287 | !------------------------------------------------------------------------------! |
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| 288 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
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| 289 | !------------------------------------------------------------------------------! |
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| 290 | ! sea surface height |
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| 291 | ! embedded sea ice: compute representative ice top surface |
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| 292 | ! non-embedded sea ice: use ocean surface for slope calculation |
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| 293 | zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) |
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| 294 | |
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| 295 | DO_2D( 0, 0, 0, 0 ) |
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| 296 | |
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| 297 | ! ice fraction at U-V points |
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| 298 | 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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| 299 | 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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| 300 | |
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| 301 | ! Ice/snow mass at U-V points |
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| 302 | zm1 = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) ) |
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| 303 | zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) ) |
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| 304 | zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) ) |
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| 305 | 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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| 306 | 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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| 307 | |
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| 308 | ! Ocean currents at U-V points |
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| 309 | 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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| 310 | 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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| 311 | |
|---|
| 312 | ! Coriolis at T points (m*f) |
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| 313 | zmf(ji,jj) = zm1 * ff_t(ji,jj) |
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| 314 | |
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| 315 | ! dt/m at T points (for alpha and beta coefficients) |
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| 316 | zdt_m(ji,jj) = zdtevp / MAX( zm1, zmmin ) |
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| 317 | |
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| 318 | ! m/dt |
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| 319 | zmU_t(ji,jj) = zmassU * z1_dtevp |
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| 320 | zmV_t(ji,jj) = zmassV * z1_dtevp |
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| 321 | |
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| 322 | ! Drag ice-atm. |
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| 323 | ztaux_ai(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj) |
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| 324 | ztauy_ai(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj) |
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| 325 | |
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| 326 | ! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points |
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| 327 | zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) |
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| 328 | zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) |
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| 329 | |
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| 330 | ! masks |
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| 331 | zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
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| 332 | zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
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| 333 | |
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| 334 | ! switches |
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| 335 | IF( zmassU <= zmmin .AND. zaU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp |
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| 336 | ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF |
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| 337 | IF( zmassV <= zmmin .AND. zaV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp |
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| 338 | ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF |
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| 339 | |
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| 340 | END_2D |
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| 341 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zmf, 'T', 1.0_wp, zdt_m, 'T', 1.0_wp ) |
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| 342 | ! |
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| 343 | ! !== Landfast ice parameterization ==! |
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| 344 | ! |
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| 345 | IF( ln_landfast_L16 ) THEN !-- Lemieux 2016 |
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| 346 | DO_2D( 0, 0, 0, 0 ) |
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| 347 | ! ice thickness at U-V points |
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| 348 | 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) |
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| 349 | 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) |
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| 350 | ! ice-bottom stress at U points |
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| 351 | zvCr = zaU(ji,jj) * rn_lf_depfra * hu(ji,jj,Kmm) |
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| 352 | ztaux_base(ji,jj) = - rn_lf_bfr * MAX( 0._wp, zvU - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaU(ji,jj) ) ) |
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| 353 | ! ice-bottom stress at V points |
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| 354 | zvCr = zaV(ji,jj) * rn_lf_depfra * hv(ji,jj,Kmm) |
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| 355 | ztauy_base(ji,jj) = - rn_lf_bfr * MAX( 0._wp, zvV - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaV(ji,jj) ) ) |
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| 356 | ! ice_bottom stress at T points |
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| 357 | zvCr = at_i(ji,jj) * rn_lf_depfra * ht(ji,jj) |
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| 358 | tau_icebfr(ji,jj) = - rn_lf_bfr * MAX( 0._wp, vt_i(ji,jj) - zvCr ) * EXP( -rn_crhg * ( 1._wp - at_i(ji,jj) ) ) |
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| 359 | END_2D |
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| 360 | CALL lbc_lnk( 'icedyn_rhg_eap', tau_icebfr(:,:), 'T', 1.0_wp ) |
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| 361 | ! |
|---|
| 362 | ELSE !-- no landfast |
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| 363 | DO_2D( 0, 0, 0, 0 ) |
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| 364 | ztaux_base(ji,jj) = 0._wp |
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| 365 | ztauy_base(ji,jj) = 0._wp |
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| 366 | END_2D |
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| 367 | ENDIF |
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| 368 | |
|---|
| 369 | !------------------------------------------------------------------------------! |
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| 370 | ! 3) Solution of the momentum equation, iterative procedure |
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| 371 | !------------------------------------------------------------------------------! |
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| 372 | ! |
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| 373 | ! ! ==================== ! |
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| 374 | DO jter = 1 , nn_nevp ! loop over jter ! |
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| 375 | ! ! ==================== ! |
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| 376 | 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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| 377 | ! |
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| 378 | ! convergence test |
|---|
| 379 | IF( nn_rhg_chkcvg == 1 .OR. nn_rhg_chkcvg == 2 ) THEN |
|---|
| 380 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 381 | zu_ice(ji,jj) = u_ice(ji,jj) * umask(ji,jj,1) ! velocity at previous time step |
|---|
| 382 | zv_ice(ji,jj) = v_ice(ji,jj) * vmask(ji,jj,1) |
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| 383 | END_2D |
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| 384 | ENDIF |
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| 385 | |
|---|
| 386 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 387 | DO_2D( 1, 0, 1, 0 ) |
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| 388 | |
|---|
| 389 | ! shear at F points |
|---|
| 390 | 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) & |
|---|
| 391 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 392 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 393 | |
|---|
| 394 | END_2D |
|---|
| 395 | |
|---|
| 396 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 397 | |
|---|
| 398 | ! shear**2 at T points (doc eq. A16) |
|---|
| 399 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 400 | & + 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) & |
|---|
| 401 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 402 | |
|---|
| 403 | ! divergence at T points |
|---|
| 404 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 405 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 406 | & ) * r1_e1e2t(ji,jj) |
|---|
| 407 | zdiv2 = zdiv * zdiv |
|---|
| 408 | |
|---|
| 409 | ! tension at T points |
|---|
| 410 | 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) & |
|---|
| 411 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 412 | & ) * r1_e1e2t(ji,jj) |
|---|
| 413 | zdt2 = zdt * zdt |
|---|
| 414 | |
|---|
| 415 | ! delta at T points |
|---|
| 416 | zdelta(ji,jj) = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 417 | |
|---|
| 418 | END_2D |
|---|
| 419 | CALL lbc_lnk( 'icedyn_rhg_eap', zdelta, 'T', 1.0_wp ) |
|---|
| 420 | |
|---|
| 421 | ! P/delta at T points |
|---|
| 422 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 423 | zp_delt(ji,jj) = strength(ji,jj) / ( zdelta(ji,jj) + rn_creepl ) |
|---|
| 424 | END_2D |
|---|
| 425 | |
|---|
| 426 | DO_2D( 0, 1, 0, 1 ) ! loop ends at jpi,jpj so that no lbc_lnk are needed for zs1 and zs2 |
|---|
| 427 | |
|---|
| 428 | ! shear at T points |
|---|
| 429 | zdsT = ( zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 430 | & + zds(ji,jj-1) * e1e2f(ji,jj-1) + zds(ji-1,jj-1) * e1e2f(ji-1,jj-1) & |
|---|
| 431 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 432 | |
|---|
| 433 | ! divergence at T points (duplication to avoid communications) |
|---|
| 434 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 435 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 436 | & ) * r1_e1e2t(ji,jj) |
|---|
| 437 | |
|---|
| 438 | ! tension at T points (duplication to avoid communications) |
|---|
| 439 | 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) & |
|---|
| 440 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 441 | & ) * r1_e1e2t(ji,jj) |
|---|
| 442 | |
|---|
| 443 | ! --- anisotropic stress calculation --- ! |
|---|
| 444 | CALL update_stress_rdg (jter, nn_nevp, zdiv, zdt, zdsT, paniso_11(ji,jj), paniso_12(ji,jj), & |
|---|
| 445 | zstressptmp, zstressmtmp, zstress12tmp(ji,jj), strength(ji,jj), zalphar, zalphas) |
|---|
| 446 | |
|---|
| 447 | ! structure tensor update |
|---|
| 448 | CALL calc_ffrac(zstressptmp, zstressmtmp, zstress12tmp(ji,jj), paniso_11(ji,jj), paniso_12(ji,jj), zmresult11, zmresult12) |
|---|
| 449 | |
|---|
| 450 | paniso_11(ji,jj) = (paniso_11(ji,jj) + 0.5*2.e-5*zdtevp + zmresult11*zdtevp) / (1. + 2.e-5*zdtevp) ! implicit |
|---|
| 451 | paniso_12(ji,jj) = (paniso_12(ji,jj) + zmresult12*zdtevp) / (1. + 2.e-5*zdtevp) ! implicit |
|---|
| 452 | |
|---|
| 453 | IF (jter == nn_nevp) THEN |
|---|
| 454 | zyield11(ji,jj) = 0.5_wp * (zstressptmp + zstressmtmp) |
|---|
| 455 | zyield22(ji,jj) = 0.5_wp * (zstressptmp - zstressmtmp) |
|---|
| 456 | zyield12(ji,jj) = zstress12tmp(ji,jj) |
|---|
| 457 | prdg_conv(ji,jj) = -min( zalphar, 0._wp) |
|---|
| 458 | ENDIF |
|---|
| 459 | |
|---|
| 460 | ! alpha for aEVP |
|---|
| 461 | ! gamma = 0.5*P/(delta+creepl) * (c*pi)**2/Area * dt/m |
|---|
| 462 | ! alpha = beta = sqrt(4*gamma) |
|---|
| 463 | IF( ln_aEVP ) THEN |
|---|
| 464 | zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 465 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 466 | zalph2 = zalph1 |
|---|
| 467 | z1_alph2 = z1_alph1 |
|---|
| 468 | ! explicit: |
|---|
| 469 | ! z1_alph1 = 1._wp / zalph1 |
|---|
| 470 | ! z1_alph2 = 1._wp / zalph1 |
|---|
| 471 | ! zalph1 = zalph1 - 1._wp |
|---|
| 472 | ! zalph2 = zalph1 |
|---|
| 473 | ENDIF |
|---|
| 474 | |
|---|
| 475 | ! stress at T points (zkt/=0 if landfast) |
|---|
| 476 | zs1(ji,jj) = ( zs1(ji,jj) * zalph1 + zstressptmp ) * z1_alph1 |
|---|
| 477 | zs2(ji,jj) = ( zs2(ji,jj) * zalph1 + zstressmtmp ) * z1_alph1 |
|---|
| 478 | END_2D |
|---|
| 479 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zstress12tmp, 'T', 1.0_wp , paniso_11, 'T', 1.0_wp , paniso_12, 'T', 1.0_wp) |
|---|
| 480 | |
|---|
| 481 | ! Save beta at T-points for further computations |
|---|
| 482 | IF( ln_aEVP ) THEN |
|---|
| 483 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 484 | zbeta(ji,jj) = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 485 | END_2D |
|---|
| 486 | ENDIF |
|---|
| 487 | |
|---|
| 488 | DO_2D( 1, 0, 1, 0 ) |
|---|
| 489 | ! stress12tmp at F points |
|---|
| 490 | zstress12tmpF = ( zstress12tmp(ji,jj+1) * e1e2t(ji,jj+1) + zstress12tmp(ji+1,jj+1) * e1e2t(ji+1,jj+1) & |
|---|
| 491 | & + zstress12tmp(ji,jj ) * e1e2t(ji,jj ) + zstress12tmp(ji+1,jj ) * e1e2t(ji+1,jj ) & |
|---|
| 492 | & ) * 0.25_wp * r1_e1e2f(ji,jj) |
|---|
| 493 | |
|---|
| 494 | ! alpha for aEVP |
|---|
| 495 | IF( ln_aEVP ) THEN |
|---|
| 496 | zalph2 = MAX( zbeta(ji,jj), zbeta(ji+1,jj), zbeta(ji,jj+1), zbeta(ji+1,jj+1) ) |
|---|
| 497 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
|---|
| 498 | ! explicit: |
|---|
| 499 | ! z1_alph2 = 1._wp / zalph2 |
|---|
| 500 | ! zalph2 = zalph2 - 1._wp |
|---|
| 501 | ENDIF |
|---|
| 502 | |
|---|
| 503 | ! stress at F points (zkt/=0 if landfast) |
|---|
| 504 | zs12(ji,jj) = ( zs12(ji,jj) * zalph1 + zstress12tmpF ) * z1_alph1 |
|---|
| 505 | |
|---|
| 506 | END_2D |
|---|
| 507 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zs1, 'T', 1.0_wp, zs2, 'T', 1.0_wp, zs12, 'F', 1.0_wp ) |
|---|
| 508 | |
|---|
| 509 | ! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- ! |
|---|
| 510 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 511 | ! !--- U points |
|---|
| 512 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 513 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 514 | & ) * r1_e2u(ji,jj) & |
|---|
| 515 | & + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 516 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 517 | & ) * r1_e1e2u(ji,jj) |
|---|
| 518 | ! |
|---|
| 519 | ! !--- V points |
|---|
| 520 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 521 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 522 | & ) * r1_e1v(ji,jj) & |
|---|
| 523 | & + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 524 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 525 | & ) * r1_e1e2v(ji,jj) |
|---|
| 526 | ! |
|---|
| 527 | ! !--- ice currents at U-V point |
|---|
| 528 | 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) |
|---|
| 529 | 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) |
|---|
| 530 | ! |
|---|
| 531 | END_2D |
|---|
| 532 | ! |
|---|
| 533 | ! --- Computation of ice velocity --- ! |
|---|
| 534 | ! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta vary as in Kimmritz 2016 & 2017 |
|---|
| 535 | ! Bouillon et al. 2009 (eq 34-35) => stable |
|---|
| 536 | IF( MOD(jter,2) == 0 ) THEN ! even iterations |
|---|
| 537 | ! |
|---|
| 538 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 539 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 540 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 541 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 542 | ! !--- Ocean-to-Ice stress |
|---|
| 543 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 544 | ! |
|---|
| 545 | ! !--- tau_bottom/v_ice |
|---|
| 546 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 547 | zTauB = ztauy_base(ji,jj) / zvel |
|---|
| 548 | ! !--- OceanBottom-to-Ice stress |
|---|
| 549 | ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj) |
|---|
| 550 | ! |
|---|
| 551 | ! !--- Coriolis at V-points (energy conserving formulation) |
|---|
| 552 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 553 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 554 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 555 | ! |
|---|
| 556 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 557 | zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 558 | ! |
|---|
| 559 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 560 | ! 1 = sliding friction : TauB < RHS |
|---|
| 561 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 562 | ! |
|---|
| 563 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 564 | zbetav = MAX( zbeta(ji,jj), zbeta(ji,jj+1) ) |
|---|
| 565 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbetav * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 566 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 567 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbetav + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 568 | & + ( 1._wp - rswitch ) * ( v_ice_b(ji,jj) & |
|---|
| 569 | & + v_ice (ji,jj) * MAX( 0._wp, zbetav - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 570 | & ) / ( zbetav + 1._wp ) & |
|---|
| 571 | & ) * 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 |
|---|
| 572 | & ) * zmsk00y(ji,jj) |
|---|
| 573 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 574 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 575 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 576 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 577 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 578 | & ) * 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 |
|---|
| 579 | & ) * zmsk00y(ji,jj) |
|---|
| 580 | ENDIF |
|---|
| 581 | END_2D |
|---|
| 582 | CALL lbc_lnk( 'icedyn_rhg_eap', v_ice, 'V', -1.0_wp ) |
|---|
| 583 | ! |
|---|
| 584 | #if defined key_agrif |
|---|
| 585 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 586 | CALL agrif_interp_ice( 'V' ) |
|---|
| 587 | #endif |
|---|
| 588 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 589 | ! |
|---|
| 590 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 591 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 592 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 593 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 594 | ! !--- Ocean-to-Ice stress |
|---|
| 595 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 596 | ! |
|---|
| 597 | ! !--- tau_bottom/u_ice |
|---|
| 598 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 599 | zTauB = ztaux_base(ji,jj) / zvel |
|---|
| 600 | ! !--- OceanBottom-to-Ice stress |
|---|
| 601 | ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj) |
|---|
| 602 | ! |
|---|
| 603 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 604 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 605 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 606 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 607 | ! |
|---|
| 608 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 609 | zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 610 | ! |
|---|
| 611 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 612 | ! 1 = sliding friction : TauB < RHS |
|---|
| 613 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 614 | ! |
|---|
| 615 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 616 | zbetau = MAX( zbeta(ji,jj), zbeta(ji+1,jj) ) |
|---|
| 617 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbetau * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 618 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 619 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbetau + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 620 | & + ( 1._wp - rswitch ) * ( u_ice_b(ji,jj) & |
|---|
| 621 | & + u_ice (ji,jj) * MAX( 0._wp, zbetau - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 622 | & ) / ( zbetau + 1._wp ) & |
|---|
| 623 | & ) * 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 |
|---|
| 624 | & ) * zmsk00x(ji,jj) |
|---|
| 625 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 626 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 627 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 628 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 629 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 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 | ENDIF |
|---|
| 633 | END_2D |
|---|
| 634 | CALL lbc_lnk( 'icedyn_rhg_eap', u_ice, 'U', -1.0_wp ) |
|---|
| 635 | ! |
|---|
| 636 | #if defined key_agrif |
|---|
| 637 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 638 | CALL agrif_interp_ice( 'U' ) |
|---|
| 639 | #endif |
|---|
| 640 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 641 | ! |
|---|
| 642 | ELSE ! odd iterations |
|---|
| 643 | ! |
|---|
| 644 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 645 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 646 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 647 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 648 | ! !--- Ocean-to-Ice stress |
|---|
| 649 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 650 | ! |
|---|
| 651 | ! !--- tau_bottom/u_ice |
|---|
| 652 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 653 | zTauB = ztaux_base(ji,jj) / zvel |
|---|
| 654 | ! !--- OceanBottom-to-Ice stress |
|---|
| 655 | ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj) |
|---|
| 656 | ! |
|---|
| 657 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 658 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 659 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 660 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 661 | ! |
|---|
| 662 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 663 | zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 664 | ! |
|---|
| 665 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 666 | ! 1 = sliding friction : TauB < RHS |
|---|
| 667 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 668 | ! |
|---|
| 669 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 670 | zbetau = MAX( zbeta(ji,jj), zbeta(ji+1,jj) ) |
|---|
| 671 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbetau * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 672 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 673 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbetau + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 674 | & + ( 1._wp - rswitch ) * ( u_ice_b(ji,jj) & |
|---|
| 675 | & + u_ice (ji,jj) * MAX( 0._wp, zbetau - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 676 | & ) / ( zbetau + 1._wp ) & |
|---|
| 677 | & ) * 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 |
|---|
| 678 | & ) * zmsk00x(ji,jj) |
|---|
| 679 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 680 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 681 | & + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 682 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 683 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 684 | & ) * 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 |
|---|
| 685 | & ) * zmsk00x(ji,jj) |
|---|
| 686 | ENDIF |
|---|
| 687 | END_2D |
|---|
| 688 | CALL lbc_lnk( 'icedyn_rhg_eap', u_ice, 'U', -1.0_wp ) |
|---|
| 689 | ! |
|---|
| 690 | #if defined key_agrif |
|---|
| 691 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 692 | CALL agrif_interp_ice( 'U' ) |
|---|
| 693 | #endif |
|---|
| 694 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 695 | ! |
|---|
| 696 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 697 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 698 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 699 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 700 | ! !--- Ocean-to-Ice stress |
|---|
| 701 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 702 | ! |
|---|
| 703 | ! !--- tau_bottom/v_ice |
|---|
| 704 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 705 | zTauB = ztauy_base(ji,jj) / zvel |
|---|
| 706 | ! !--- OceanBottom-to-Ice stress |
|---|
| 707 | ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj) |
|---|
| 708 | ! |
|---|
| 709 | ! !--- Coriolis at v-points (energy conserving formulation) |
|---|
| 710 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 711 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 712 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 713 | ! |
|---|
| 714 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 715 | zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 716 | ! |
|---|
| 717 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 718 | ! 1 = sliding friction : TauB < RHS |
|---|
| 719 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 720 | ! |
|---|
| 721 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 722 | zbetav = MAX( zbeta(ji,jj), zbeta(ji,jj+1) ) |
|---|
| 723 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbetav * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 724 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 725 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbetav + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 726 | & + ( 1._wp - rswitch ) * ( v_ice_b(ji,jj) & |
|---|
| 727 | & + v_ice (ji,jj) * MAX( 0._wp, zbetav - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 728 | & ) / ( zbetav + 1._wp ) & |
|---|
| 729 | & ) * 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 |
|---|
| 730 | & ) * zmsk00y(ji,jj) |
|---|
| 731 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 732 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 733 | & + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 734 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 735 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0 |
|---|
| 736 | & ) * 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 |
|---|
| 737 | & ) * zmsk00y(ji,jj) |
|---|
| 738 | ENDIF |
|---|
| 739 | END_2D |
|---|
| 740 | CALL lbc_lnk( 'icedyn_rhg_eap', v_ice, 'V', -1.0_wp ) |
|---|
| 741 | ! |
|---|
| 742 | #if defined key_agrif |
|---|
| 743 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 744 | CALL agrif_interp_ice( 'V' ) |
|---|
| 745 | #endif |
|---|
| 746 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 747 | ! |
|---|
| 748 | ENDIF |
|---|
| 749 | |
|---|
| 750 | ! convergence test |
|---|
| 751 | IF( nn_rhg_chkcvg == 2 ) CALL rhg_cvg( kt, jter, nn_nevp, u_ice, v_ice, zu_ice, zv_ice ) |
|---|
| 752 | ! |
|---|
| 753 | ! ! ==================== ! |
|---|
| 754 | END DO ! end loop over jter ! |
|---|
| 755 | ! ! ==================== ! |
|---|
| 756 | IF( ln_aEVP ) CALL iom_put( 'beta_evp' , zbeta ) |
|---|
| 757 | ! |
|---|
| 758 | CALL lbc_lnk( 'icedyn_rhg_eap', prdg_conv, 'T', 1.0_wp ) ! only need this in ridging module after rheology completed |
|---|
| 759 | ! |
|---|
| 760 | !------------------------------------------------------------------------------! |
|---|
| 761 | ! 4) Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 762 | !------------------------------------------------------------------------------! |
|---|
| 763 | DO_2D( 1, 0, 1, 0 ) |
|---|
| 764 | |
|---|
| 765 | ! shear at F points |
|---|
| 766 | 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) & |
|---|
| 767 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 768 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 769 | |
|---|
| 770 | END_2D |
|---|
| 771 | |
|---|
| 772 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 773 | |
|---|
| 774 | ! tension**2 at T points |
|---|
| 775 | 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) & |
|---|
| 776 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 777 | & ) * r1_e1e2t(ji,jj) |
|---|
| 778 | zdt2 = zdt * zdt |
|---|
| 779 | |
|---|
| 780 | zten_i(ji,jj) = zdt |
|---|
| 781 | |
|---|
| 782 | ! shear**2 at T points (doc eq. A16) |
|---|
| 783 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 784 | & + 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) & |
|---|
| 785 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 786 | |
|---|
| 787 | ! shear at T points |
|---|
| 788 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
|---|
| 789 | |
|---|
| 790 | ! divergence at T points |
|---|
| 791 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 792 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 793 | & ) * r1_e1e2t(ji,jj) |
|---|
| 794 | |
|---|
| 795 | ! delta at T points |
|---|
| 796 | zfac = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) ! delta |
|---|
| 797 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zfac ) ) ! 0 if delta=0 |
|---|
| 798 | pdelta_i(ji,jj) = zfac + rn_creepl * rswitch ! delta+creepl |
|---|
| 799 | |
|---|
| 800 | END_2D |
|---|
| 801 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', pshear_i, 'T', 1.0_wp, pdivu_i, 'T', 1.0_wp, pdelta_i, 'T', 1.0_wp, & |
|---|
| 802 | & zten_i, 'T', 1.0_wp, zs1 , 'T', 1.0_wp, zs2 , 'T', 1.0_wp, & |
|---|
| 803 | & zs12, 'F', 1.0_wp ) |
|---|
| 804 | |
|---|
| 805 | ! --- Store the stress tensor for the next time step --- ! |
|---|
| 806 | pstress1_i (:,:) = zs1 (:,:) |
|---|
| 807 | pstress2_i (:,:) = zs2 (:,:) |
|---|
| 808 | pstress12_i(:,:) = zs12(:,:) |
|---|
| 809 | ! |
|---|
| 810 | |
|---|
| 811 | !------------------------------------------------------------------------------! |
|---|
| 812 | ! 5) diagnostics |
|---|
| 813 | !------------------------------------------------------------------------------! |
|---|
| 814 | ! --- ice-ocean, ice-atm. & ice-oceanbottom(landfast) stresses --- ! |
|---|
| 815 | IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. & |
|---|
| 816 | & iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN |
|---|
| 817 | ! |
|---|
| 818 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', ztaux_oi, 'U', -1.0_wp, ztauy_oi, 'V', -1.0_wp, ztaux_ai, 'U', -1.0_wp, & |
|---|
| 819 | & ztauy_ai, 'V', -1.0_wp, ztaux_bi, 'U', -1.0_wp, ztauy_bi, 'V', -1.0_wp ) |
|---|
| 820 | ! |
|---|
| 821 | CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 ) |
|---|
| 822 | CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 ) |
|---|
| 823 | CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 ) |
|---|
| 824 | CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 ) |
|---|
| 825 | CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 ) |
|---|
| 826 | CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 ) |
|---|
| 827 | ENDIF |
|---|
| 828 | |
|---|
| 829 | ! --- divergence, shear and strength --- ! |
|---|
| 830 | IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence |
|---|
| 831 | IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! shear |
|---|
| 832 | IF( iom_use('icedlt') ) CALL iom_put( 'icedlt' , pdelta_i * zmsk00 ) ! delta |
|---|
| 833 | IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength |
|---|
| 834 | |
|---|
| 835 | ! --- Stress tensor invariants (SIMIP diags) --- ! |
|---|
| 836 | IF( iom_use('normstr') .OR. iom_use('sheastr') ) THEN |
|---|
| 837 | ! |
|---|
| 838 | ALLOCATE( zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 839 | ! |
|---|
| 840 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 841 | |
|---|
| 842 | ! Ice stresses |
|---|
| 843 | ! sigma1, sigma2, sigma12 are some useful recombination of the stresses (Hunke and Dukowicz MWR 2002, Bouillon et al., OM2013) |
|---|
| 844 | ! These are NOT stress tensor components, neither stress invariants, neither stress principal components |
|---|
| 845 | ! I know, this can be confusing... |
|---|
| 846 | zfac = strength(ji,jj) / ( pdelta_i(ji,jj) + rn_creepl ) |
|---|
| 847 | zsig1 = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) ) |
|---|
| 848 | zsig2 = zfac * z1_ecc2 * zten_i(ji,jj) |
|---|
| 849 | zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj) |
|---|
| 850 | |
|---|
| 851 | ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008) |
|---|
| 852 | zsig_I (ji,jj) = zsig1 * 0.5_wp ! 1st stress invariant, aka average normal stress, aka negative pressure |
|---|
| 853 | zsig_II(ji,jj) = SQRT ( MAX( 0._wp, zsig2 * zsig2 * 0.25_wp + zsig12 ) ) ! 2nd '' '', aka maximum shear stress |
|---|
| 854 | |
|---|
| 855 | END_2D |
|---|
| 856 | ! |
|---|
| 857 | ! Stress tensor invariants (normal and shear stress N/m) - SIMIP diags - definitions following Coon (1974) and Feltham (2008) |
|---|
| 858 | IF( iom_use('normstr') ) CALL iom_put( 'normstr', zsig_I (:,:) * zmsk00(:,:) ) ! Normal stress |
|---|
| 859 | IF( iom_use('sheastr') ) CALL iom_put( 'sheastr', zsig_II(:,:) * zmsk00(:,:) ) ! Maximum shear stress |
|---|
| 860 | |
|---|
| 861 | DEALLOCATE ( zsig_I, zsig_II ) |
|---|
| 862 | |
|---|
| 863 | ENDIF |
|---|
| 864 | |
|---|
| 865 | ! --- Normalized stress tensor principal components --- ! |
|---|
| 866 | ! This are used to plot the normalized yield curve, see Lemieux & Dupont, 2020 |
|---|
| 867 | ! Recommendation 1 : we use ice strength, not replacement pressure |
|---|
| 868 | ! Recommendation 2 : need to use deformations at PREVIOUS iterate for viscosities |
|---|
| 869 | IF( iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN |
|---|
| 870 | ! |
|---|
| 871 | ALLOCATE( zsig1_p(jpi,jpj) , zsig2_p(jpi,jpj) , zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 872 | ! |
|---|
| 873 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 874 | |
|---|
| 875 | ! Ice stresses computed with **viscosities** (delta, p/delta) at **previous** iterates |
|---|
| 876 | ! and **deformations** at current iterates |
|---|
| 877 | ! following Lemieux & Dupont (2020) |
|---|
| 878 | zfac = zp_delt(ji,jj) |
|---|
| 879 | zsig1 = zfac * ( pdivu_i(ji,jj) - ( zdelta(ji,jj) + rn_creepl ) ) |
|---|
| 880 | zsig2 = zfac * z1_ecc2 * zten_i(ji,jj) |
|---|
| 881 | zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj) |
|---|
| 882 | |
|---|
| 883 | ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008), T-point |
|---|
| 884 | zsig_I(ji,jj) = zsig1 * 0.5_wp ! 1st stress invariant, aka average normal stress, aka negative pressure |
|---|
| 885 | zsig_II(ji,jj) = SQRT ( MAX( 0._wp, zsig2 * zsig2 * 0.25_wp + zsig12 ) ) ! 2nd '' '', aka maximum shear stress |
|---|
| 886 | |
|---|
| 887 | ! Normalized principal stresses (used to display the ellipse) |
|---|
| 888 | z1_strength = 1._wp / MAX( 1._wp, strength(ji,jj) ) |
|---|
| 889 | zsig1_p(ji,jj) = ( zsig_I(ji,jj) + zsig_II(ji,jj) ) * z1_strength |
|---|
| 890 | zsig2_p(ji,jj) = ( zsig_I(ji,jj) - zsig_II(ji,jj) ) * z1_strength |
|---|
| 891 | END_2D |
|---|
| 892 | ! |
|---|
| 893 | CALL iom_put( 'sig1_pnorm' , zsig1_p ) |
|---|
| 894 | CALL iom_put( 'sig2_pnorm' , zsig2_p ) |
|---|
| 895 | |
|---|
| 896 | DEALLOCATE( zsig1_p , zsig2_p , zsig_I, zsig_II ) |
|---|
| 897 | |
|---|
| 898 | ENDIF |
|---|
| 899 | |
|---|
| 900 | ! --- yieldcurve --- ! |
|---|
| 901 | IF( iom_use('yield11') .OR. iom_use('yield12') .OR. iom_use('yield22')) THEN |
|---|
| 902 | |
|---|
| 903 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zyield11, 'T', 1.0_wp, zyield22, 'T', 1.0_wp, zyield12, 'T', 1.0_wp ) |
|---|
| 904 | |
|---|
| 905 | CALL iom_put( 'yield11', zyield11 * zmsk00 ) |
|---|
| 906 | CALL iom_put( 'yield22', zyield22 * zmsk00 ) |
|---|
| 907 | CALL iom_put( 'yield12', zyield12 * zmsk00 ) |
|---|
| 908 | ENDIF |
|---|
| 909 | |
|---|
| 910 | ! --- anisotropy tensor --- ! |
|---|
| 911 | IF( iom_use('aniso') ) THEN |
|---|
| 912 | CALL lbc_lnk( 'icedyn_rhg_eap', paniso_11, 'T', 1.0_wp ) |
|---|
| 913 | CALL iom_put( 'aniso' , paniso_11 * zmsk00 ) |
|---|
| 914 | ENDIF |
|---|
| 915 | |
|---|
| 916 | ! --- SIMIP --- ! |
|---|
| 917 | IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. & |
|---|
| 918 | & iom_use('corstrx') .OR. iom_use('corstry') .OR. iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 919 | ! |
|---|
| 920 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zspgU, 'U', -1.0_wp, zspgV, 'V', -1.0_wp, & |
|---|
| 921 | & zCorU, 'U', -1.0_wp, zCorV, 'V', -1.0_wp, & |
|---|
| 922 | & zfU, 'U', -1.0_wp, zfV, 'V', -1.0_wp ) |
|---|
| 923 | |
|---|
| 924 | CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x) |
|---|
| 925 | CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y) |
|---|
| 926 | CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x) |
|---|
| 927 | CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y) |
|---|
| 928 | CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x) |
|---|
| 929 | CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y) |
|---|
| 930 | ENDIF |
|---|
| 931 | |
|---|
| 932 | IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. & |
|---|
| 933 | & iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN |
|---|
| 934 | ! |
|---|
| 935 | ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 936 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) ) |
|---|
| 937 | ! |
|---|
| 938 | DO_2D( 0, 0, 0, 0 ) |
|---|
| 939 | ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 940 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj) |
|---|
| 941 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj) |
|---|
| 942 | |
|---|
| 943 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 944 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 945 | |
|---|
| 946 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 947 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 948 | |
|---|
| 949 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 950 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 951 | |
|---|
| 952 | END_2D |
|---|
| 953 | |
|---|
| 954 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zdiag_xmtrp_ice, 'U', -1.0_wp, zdiag_ymtrp_ice, 'V', -1.0_wp, & |
|---|
| 955 | & zdiag_xmtrp_snw, 'U', -1.0_wp, zdiag_ymtrp_snw, 'V', -1.0_wp, & |
|---|
| 956 | & zdiag_xatrp , 'U', -1.0_wp, zdiag_yatrp , 'V', -1.0_wp ) |
|---|
| 957 | |
|---|
| 958 | CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 959 | CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport |
|---|
| 960 | CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s) |
|---|
| 961 | CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport |
|---|
| 962 | CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport |
|---|
| 963 | CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport |
|---|
| 964 | |
|---|
| 965 | DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 966 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 967 | |
|---|
| 968 | ENDIF |
|---|
| 969 | ! |
|---|
| 970 | ! --- convergence tests --- ! |
|---|
| 971 | IF( nn_rhg_chkcvg == 1 .OR. nn_rhg_chkcvg == 2 ) THEN |
|---|
| 972 | IF( iom_use('uice_cvg') ) THEN |
|---|
| 973 | IF( ln_aEVP ) THEN ! output: beta * ( u(t=nn_nevp) - u(t=nn_nevp-1) ) |
|---|
| 974 | CALL iom_put( 'uice_cvg', MAX( ABS( u_ice(:,:) - zu_ice(:,:) ) * zbeta(:,:) * umask(:,:,1) , & |
|---|
| 975 | & ABS( v_ice(:,:) - zv_ice(:,:) ) * zbeta(:,:) * vmask(:,:,1) ) * zmsk15(:,:) ) |
|---|
| 976 | ELSE ! output: nn_nevp * ( u(t=nn_nevp) - u(t=nn_nevp-1) ) |
|---|
| 977 | CALL iom_put( 'uice_cvg', REAL( nn_nevp ) * MAX( ABS( u_ice(:,:) - zu_ice(:,:) ) * umask(:,:,1) , & |
|---|
| 978 | & ABS( v_ice(:,:) - zv_ice(:,:) ) * vmask(:,:,1) ) * zmsk15(:,:) ) |
|---|
| 979 | ENDIF |
|---|
| 980 | ENDIF |
|---|
| 981 | ENDIF |
|---|
| 982 | ! |
|---|
| 983 | DEALLOCATE( zmsk00, zmsk15 ) |
|---|
| 984 | ! |
|---|
| 985 | END SUBROUTINE ice_dyn_rhg_eap |
|---|
| 986 | |
|---|
| 987 | |
|---|
| 988 | SUBROUTINE rhg_cvg( kt, kiter, kitermax, pu, pv, pub, pvb ) |
|---|
| 989 | !!---------------------------------------------------------------------- |
|---|
| 990 | !! *** ROUTINE rhg_cvg *** |
|---|
| 991 | !! |
|---|
| 992 | !! ** Purpose : check convergence of oce rheology |
|---|
| 993 | !! |
|---|
| 994 | !! ** Method : create a file ice_cvg.nc containing the convergence of ice velocity |
|---|
| 995 | !! during the sub timestepping of rheology so as: |
|---|
| 996 | !! uice_cvg = MAX( u(t+1) - u(t) , v(t+1) - v(t) ) |
|---|
| 997 | !! This routine is called every sub-iteration, so it is cpu expensive |
|---|
| 998 | !! |
|---|
| 999 | !! ** Note : for the first sub-iteration, uice_cvg is set to 0 (too large otherwise) |
|---|
| 1000 | !!---------------------------------------------------------------------- |
|---|
| 1001 | INTEGER , INTENT(in) :: kt, kiter, kitermax ! ocean time-step index |
|---|
| 1002 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pub, pvb ! now and before velocities |
|---|
| 1003 | !! |
|---|
| 1004 | INTEGER :: it, idtime, istatus |
|---|
| 1005 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 1006 | REAL(wp) :: zresm ! local real |
|---|
| 1007 | CHARACTER(len=20) :: clname |
|---|
| 1008 | REAL(wp), DIMENSION(jpi,jpj) :: zres ! check convergence |
|---|
| 1009 | !!---------------------------------------------------------------------- |
|---|
| 1010 | |
|---|
| 1011 | ! create file |
|---|
| 1012 | IF( kt == nit000 .AND. kiter == 1 ) THEN |
|---|
| 1013 | ! |
|---|
| 1014 | IF( lwp ) THEN |
|---|
| 1015 | WRITE(numout,*) |
|---|
| 1016 | WRITE(numout,*) 'rhg_cvg : ice rheology convergence control' |
|---|
| 1017 | WRITE(numout,*) '~~~~~~~' |
|---|
| 1018 | ENDIF |
|---|
| 1019 | ! |
|---|
| 1020 | IF( lwm ) THEN |
|---|
| 1021 | clname = 'ice_cvg.nc' |
|---|
| 1022 | IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname) |
|---|
| 1023 | istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid ) |
|---|
| 1024 | istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime ) |
|---|
| 1025 | istatus = NF90_DEF_VAR( ncvgid, 'uice_cvg', NF90_DOUBLE , (/ idtime /), nvarid ) |
|---|
| 1026 | istatus = NF90_ENDDEF(ncvgid) |
|---|
| 1027 | ENDIF |
|---|
| 1028 | ! |
|---|
| 1029 | ENDIF |
|---|
| 1030 | |
|---|
| 1031 | ! time |
|---|
| 1032 | it = ( kt - 1 ) * kitermax + kiter |
|---|
| 1033 | |
|---|
| 1034 | ! convergence |
|---|
| 1035 | IF( kiter == 1 ) THEN ! remove the first iteration for calculations of convergence (always very large) |
|---|
| 1036 | zresm = 0._wp |
|---|
| 1037 | ELSE |
|---|
| 1038 | DO_2D( 1, 1, 1, 1 ) |
|---|
| 1039 | zres(ji,jj) = MAX( ABS( pu(ji,jj) - pub(ji,jj) ) * umask(ji,jj,1), & |
|---|
| 1040 | & ABS( pv(ji,jj) - pvb(ji,jj) ) * vmask(ji,jj,1) ) * zmsk15(ji,jj) |
|---|
| 1041 | END_2D |
|---|
| 1042 | zresm = MAXVAL( zres ) |
|---|
| 1043 | CALL mpp_max( 'icedyn_rhg_evp', zresm ) ! max over the global domain |
|---|
| 1044 | ENDIF |
|---|
| 1045 | |
|---|
| 1046 | IF( lwm ) THEN |
|---|
| 1047 | ! write variables |
|---|
| 1048 | istatus = NF90_PUT_VAR( ncvgid, nvarid, (/zresm/), (/it/), (/1/) ) |
|---|
| 1049 | ! close file |
|---|
| 1050 | IF( kt == nitend ) istatus = NF90_CLOSE(ncvgid) |
|---|
| 1051 | ENDIF |
|---|
| 1052 | |
|---|
| 1053 | END SUBROUTINE rhg_cvg |
|---|
| 1054 | |
|---|
| 1055 | |
|---|
| 1056 | SUBROUTINE update_stress_rdg( ksub, kndte, pdivu, ptension, pshear, pa11, pa12, & |
|---|
| 1057 | & pstressp, pstressm, pstress12, pstrength, palphar, palphas ) |
|---|
| 1058 | !!--------------------------------------------------------------------- |
|---|
| 1059 | !! *** SUBROUTINE update_stress_rdg *** |
|---|
| 1060 | !! |
|---|
| 1061 | !! ** Purpose : Updates the stress depending on values of strain rate and structure |
|---|
| 1062 | !! tensor and for the last subcycle step it computes closing and sliding rate |
|---|
| 1063 | !!--------------------------------------------------------------------- |
|---|
| 1064 | INTEGER, INTENT(in ) :: ksub, kndte |
|---|
| 1065 | REAL(wp), INTENT(in ) :: pstrength |
|---|
| 1066 | REAL(wp), INTENT(in ) :: pdivu, ptension, pshear |
|---|
| 1067 | REAL(wp), INTENT(in ) :: pa11, pa12 |
|---|
| 1068 | REAL(wp), INTENT( out) :: pstressp, pstressm, pstress12 |
|---|
| 1069 | REAL(wp), INTENT( out) :: palphar, palphas |
|---|
| 1070 | |
|---|
| 1071 | INTEGER :: kx ,ky, ka |
|---|
| 1072 | |
|---|
| 1073 | REAL(wp) :: zstemp11r, zstemp12r, zstemp22r |
|---|
| 1074 | REAL(wp) :: zstemp11s, zstemp12s, zstemp22s |
|---|
| 1075 | REAL(wp) :: za22, zQd11Qd11, zQd11Qd12, zQd12Qd12 |
|---|
| 1076 | REAL(wp) :: zQ11Q11, zQ11Q12, zQ12Q12 |
|---|
| 1077 | REAL(wp) :: zdtemp11, zdtemp12, zdtemp22 |
|---|
| 1078 | REAL(wp) :: zrotstemp11r, zrotstemp12r, zrotstemp22r |
|---|
| 1079 | REAL(wp) :: zrotstemp11s, zrotstemp12s, zrotstemp22s |
|---|
| 1080 | REAL(wp) :: zsig11, zsig12, zsig22 |
|---|
| 1081 | REAL(wp) :: zsgprm11, zsgprm12, zsgprm22 |
|---|
| 1082 | REAL(wp) :: zinvstressconviso |
|---|
| 1083 | REAL(wp) :: zAngle_denom_gamma, zAngle_denom_alpha |
|---|
| 1084 | REAL(wp) :: zTany_1, zTany_2 |
|---|
| 1085 | REAL(wp) :: zx, zy, zdx, zdy, zda, zkxw, kyw, kaw |
|---|
| 1086 | REAL(wp) :: zinvdx, zinvdy, zinvda |
|---|
| 1087 | REAL(wp) :: zdtemp1, zdtemp2, zatempprime, zinvsin |
|---|
| 1088 | |
|---|
| 1089 | REAL(wp), PARAMETER :: kfriction = 0.45_wp |
|---|
| 1090 | !!--------------------------------------------------------------------- |
|---|
| 1091 | ! Factor to maintain the same stress as in EVP (see Section 3) |
|---|
| 1092 | ! Can be set to 1 otherwise |
|---|
| 1093 | ! zinvstressconviso = 1._wp/(1._wp+kfriction*kfriction) |
|---|
| 1094 | zinvstressconviso = 1._wp |
|---|
| 1095 | |
|---|
| 1096 | zinvsin = 1._wp/sin(2._wp*pphi) * zinvstressconviso |
|---|
| 1097 | !now uses phi as set in higher code |
|---|
| 1098 | |
|---|
| 1099 | ! compute eigenvalues, eigenvectors and angles for structure tensor, strain |
|---|
| 1100 | ! rates |
|---|
| 1101 | |
|---|
| 1102 | ! 1) structure tensor |
|---|
| 1103 | za22 = 1._wp-pa11 |
|---|
| 1104 | zQ11Q11 = 1._wp |
|---|
| 1105 | zQ12Q12 = rsmall |
|---|
| 1106 | zQ11Q12 = rsmall |
|---|
| 1107 | |
|---|
| 1108 | ! gamma: angle between general coordiantes and principal axis of A |
|---|
| 1109 | ! here Tan2gamma = 2 a12 / (a11 - a22) |
|---|
| 1110 | IF((ABS(pa11 - za22) > rsmall).OR.(ABS(pa12) > rsmall)) THEN |
|---|
| 1111 | zAngle_denom_gamma = 1._wp/sqrt( ( pa11 - za22 )*( pa11 - za22) + & |
|---|
| 1112 | 4._wp*pa12*pa12 ) |
|---|
| 1113 | |
|---|
| 1114 | zQ11Q11 = 0.5_wp + ( pa11 - za22 )*0.5_wp*zAngle_denom_gamma !Cos^2 |
|---|
| 1115 | zQ12Q12 = 0.5_wp - ( pa11 - za22 )*0.5_wp*zAngle_denom_gamma !Sin^2 |
|---|
| 1116 | zQ11Q12 = pa12*zAngle_denom_gamma !CosSin |
|---|
| 1117 | ENDIF |
|---|
| 1118 | |
|---|
| 1119 | ! rotation Q*atemp*Q^T |
|---|
| 1120 | zatempprime = zQ11Q11*pa11 + 2.0_wp*zQ11Q12*pa12 + zQ12Q12*za22 |
|---|
| 1121 | |
|---|
| 1122 | ! make first principal value the largest |
|---|
| 1123 | zatempprime = max(zatempprime, 1.0_wp - zatempprime) |
|---|
| 1124 | |
|---|
| 1125 | ! 2) strain rate |
|---|
| 1126 | zdtemp11 = 0.5_wp*(pdivu + ptension) |
|---|
| 1127 | zdtemp12 = pshear*0.5_wp |
|---|
| 1128 | zdtemp22 = 0.5_wp*(pdivu - ptension) |
|---|
| 1129 | |
|---|
| 1130 | ! here Tan2alpha = 2 dtemp12 / (dtemp11 - dtemp22) |
|---|
| 1131 | |
|---|
| 1132 | zQd11Qd11 = 1.0_wp |
|---|
| 1133 | zQd12Qd12 = rsmall |
|---|
| 1134 | zQd11Qd12 = rsmall |
|---|
| 1135 | |
|---|
| 1136 | IF((ABS( zdtemp11 - zdtemp22) > rsmall).OR. (ABS(zdtemp12) > rsmall)) THEN |
|---|
| 1137 | |
|---|
| 1138 | zAngle_denom_alpha = 1.0_wp/sqrt( ( zdtemp11 - zdtemp22 )* & |
|---|
| 1139 | ( zdtemp11 - zdtemp22 ) + 4.0_wp*zdtemp12*zdtemp12) |
|---|
| 1140 | |
|---|
| 1141 | zQd11Qd11 = 0.5_wp + ( zdtemp11 - zdtemp22 )*0.5_wp*zAngle_denom_alpha !Cos^2 |
|---|
| 1142 | zQd12Qd12 = 0.5_wp - ( zdtemp11 - zdtemp22 )*0.5_wp*zAngle_denom_alpha !Sin^2 |
|---|
| 1143 | zQd11Qd12 = zdtemp12*zAngle_denom_alpha !CosSin |
|---|
| 1144 | ENDIF |
|---|
| 1145 | |
|---|
| 1146 | zdtemp1 = zQd11Qd11*zdtemp11 + 2.0_wp*zQd11Qd12*zdtemp12 + zQd12Qd12*zdtemp22 |
|---|
| 1147 | zdtemp2 = zQd12Qd12*zdtemp11 - 2.0_wp*zQd11Qd12*zdtemp12 + zQd11Qd11*zdtemp22 |
|---|
| 1148 | ! In cos and sin values |
|---|
| 1149 | zx = 0._wp |
|---|
| 1150 | IF ((ABS(zdtemp1) > rsmall).OR.(ABS(zdtemp2) > rsmall)) THEN |
|---|
| 1151 | zx = atan2(zdtemp2,zdtemp1) |
|---|
| 1152 | ENDIF |
|---|
| 1153 | |
|---|
| 1154 | ! to ensure the angle lies between pi/4 and 9 pi/4 |
|---|
| 1155 | IF (zx < rpi*0.25_wp) zx = zx + rpi*2.0_wp |
|---|
| 1156 | |
|---|
| 1157 | ! y: angle between major principal axis of strain rate and structure |
|---|
| 1158 | ! tensor |
|---|
| 1159 | ! y = gamma - alpha |
|---|
| 1160 | ! Expressesed componently with |
|---|
| 1161 | ! Tany = (Singamma*Cosgamma - Sinalpha*Cosgamma)/(Cos^2gamma - Sin^alpha) |
|---|
| 1162 | |
|---|
| 1163 | zTany_1 = zQ11Q12 - zQd11Qd12 |
|---|
| 1164 | zTany_2 = zQ11Q11 - zQd12Qd12 |
|---|
| 1165 | |
|---|
| 1166 | zy = 0._wp |
|---|
| 1167 | |
|---|
| 1168 | IF ((ABS(zTany_1) > rsmall).OR.(ABS(zTany_2) > rsmall)) THEN |
|---|
| 1169 | zy = atan2(zTany_1,zTany_2) |
|---|
| 1170 | ENDIF |
|---|
| 1171 | |
|---|
| 1172 | ! to make sure y is between 0 and pi |
|---|
| 1173 | IF (zy > rpi) zy = zy - rpi |
|---|
| 1174 | IF (zy < 0) zy = zy + rpi |
|---|
| 1175 | |
|---|
| 1176 | ! 3) update anisotropic stress tensor |
|---|
| 1177 | zdx = rpi/real(nx_yield-1,kind=wp) |
|---|
| 1178 | zdy = rpi/real(ny_yield-1,kind=wp) |
|---|
| 1179 | zda = 0.5_wp/real(na_yield-1,kind=wp) |
|---|
| 1180 | zinvdx = 1._wp/zdx |
|---|
| 1181 | zinvdy = 1._wp/zdy |
|---|
| 1182 | zinvda = 1._wp/zda |
|---|
| 1183 | |
|---|
| 1184 | ! % need 8 coords and 8 weights |
|---|
| 1185 | ! % range in kx |
|---|
| 1186 | kx = int((zx-rpi*0.25_wp-rpi)*zinvdx) + 1 |
|---|
| 1187 | !!clem kx = MAX( 1, MIN( nx_yield-1, INT((zx-rpi*0.25_wp-rpi)*zinvdx) + 1 ) ) |
|---|
| 1188 | zkxw = kx - (zx-rpi*0.25_wp-rpi)*zinvdx |
|---|
| 1189 | |
|---|
| 1190 | ky = int(zy*zinvdy) + 1 |
|---|
| 1191 | !!clem ky = MAX( 1, MIN( ny_yield-1, INT(zy*zinvdy) + 1 ) ) |
|---|
| 1192 | kyw = ky - zy*zinvdy |
|---|
| 1193 | |
|---|
| 1194 | ka = int((zatempprime-0.5_wp)*zinvda) + 1 |
|---|
| 1195 | !!clem ka = MAX( 1, MIN( na_yield-1, INT((zatempprime-0.5_wp)*zinvda) + 1 ) ) |
|---|
| 1196 | kaw = ka - (zatempprime-0.5_wp)*zinvda |
|---|
| 1197 | |
|---|
| 1198 | ! % Determine sigma_r(A1,Zeta,y) and sigma_s (see Section A1 of Tsamados 2013) |
|---|
| 1199 | !!$ zstemp11r = zkxw * kyw * kaw * s11r(kx ,ky ,ka ) & |
|---|
| 1200 | !!$ & + (1._wp-zkxw) * kyw * kaw * s11r(kx+1,ky ,ka ) & |
|---|
| 1201 | !!$ & + zkxw * (1._wp-kyw) * kaw * s11r(kx ,ky+1,ka ) & |
|---|
| 1202 | !!$ & + zkxw * kyw * (1._wp-kaw) * s11r(kx ,ky ,ka+1) & |
|---|
| 1203 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s11r(kx+1,ky+1,ka ) & |
|---|
| 1204 | !!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s11r(kx+1,ky ,ka+1) & |
|---|
| 1205 | !!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s11r(kx ,ky+1,ka+1) & |
|---|
| 1206 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s11r(kx+1,ky+1,ka+1) |
|---|
| 1207 | !!$ zstemp12r = zkxw * kyw * kaw * s12r(kx ,ky ,ka ) & |
|---|
| 1208 | !!$ & + (1._wp-zkxw) * kyw * kaw * s12r(kx+1,ky ,ka ) & |
|---|
| 1209 | !!$ & + zkxw * (1._wp-kyw) * kaw * s12r(kx ,ky+1,ka ) & |
|---|
| 1210 | !!$ & + zkxw * kyw * (1._wp-kaw) * s12r(kx ,ky ,ka+1) & |
|---|
| 1211 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s12r(kx+1,ky+1,ka ) & |
|---|
| 1212 | !!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s12r(kx+1,ky ,ka+1) & |
|---|
| 1213 | !!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s12r(kx ,ky+1,ka+1) & |
|---|
| 1214 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s12r(kx+1,ky+1,ka+1) |
|---|
| 1215 | !!$ zstemp22r = zkxw * kyw * kaw * s22r(kx ,ky ,ka ) & |
|---|
| 1216 | !!$ & + (1._wp-zkxw) * kyw * kaw * s22r(kx+1,ky ,ka ) & |
|---|
| 1217 | !!$ & + zkxw * (1._wp-kyw) * kaw * s22r(kx ,ky+1,ka ) & |
|---|
| 1218 | !!$ & + zkxw * kyw * (1._wp-kaw) * s22r(kx ,ky ,ka+1) & |
|---|
| 1219 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s22r(kx+1,ky+1,ka ) & |
|---|
| 1220 | !!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s22r(kx+1,ky ,ka+1) & |
|---|
| 1221 | !!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s22r(kx ,ky+1,ka+1) & |
|---|
| 1222 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s22r(kx+1,ky+1,ka+1) |
|---|
| 1223 | !!$ |
|---|
| 1224 | !!$ zstemp11s = zkxw * kyw * kaw * s11s(kx ,ky ,ka ) & |
|---|
| 1225 | !!$ & + (1._wp-zkxw) * kyw * kaw * s11s(kx+1,ky ,ka ) & |
|---|
| 1226 | !!$ & + zkxw * (1._wp-kyw) * kaw * s11s(kx ,ky+1,ka ) & |
|---|
| 1227 | !!$ & + zkxw * kyw * (1._wp-kaw) * s11s(kx ,ky ,ka+1) & |
|---|
| 1228 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s11s(kx+1,ky+1,ka ) & |
|---|
| 1229 | !!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s11s(kx+1,ky ,ka+1) & |
|---|
| 1230 | !!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s11s(kx ,ky+1,ka+1) & |
|---|
| 1231 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s11s(kx+1,ky+1,ka+1) |
|---|
| 1232 | !!$ zstemp12s = zkxw * kyw * kaw * s12s(kx ,ky ,ka ) & |
|---|
| 1233 | !!$ & + (1._wp-zkxw) * kyw * kaw * s12s(kx+1,ky ,ka ) & |
|---|
| 1234 | !!$ & + zkxw * (1._wp-kyw) * kaw * s12s(kx ,ky+1,ka ) & |
|---|
| 1235 | !!$ & + zkxw * kyw * (1._wp-kaw) * s12s(kx ,ky ,ka+1) & |
|---|
| 1236 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s12s(kx+1,ky+1,ka ) & |
|---|
| 1237 | !!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s12s(kx+1,ky ,ka+1) & |
|---|
| 1238 | !!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s12s(kx ,ky+1,ka+1) & |
|---|
| 1239 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s12s(kx+1,ky+1,ka+1) |
|---|
| 1240 | !!$ zstemp22s = zkxw * kyw * kaw * s22s(kx ,ky ,ka ) & |
|---|
| 1241 | !!$ & + (1._wp-zkxw) * kyw * kaw * s22s(kx+1,ky ,ka ) & |
|---|
| 1242 | !!$ & + zkxw * (1._wp-kyw) * kaw * s22s(kx ,ky+1,ka ) & |
|---|
| 1243 | !!$ & + zkxw * kyw * (1._wp-kaw) * s22s(kx ,ky ,ka+1) & |
|---|
| 1244 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s22s(kx+1,ky+1,ka ) & |
|---|
| 1245 | !!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s22s(kx+1,ky ,ka+1) & |
|---|
| 1246 | !!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s22s(kx ,ky+1,ka+1) & |
|---|
| 1247 | !!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s22s(kx+1,ky+1,ka+1) |
|---|
| 1248 | |
|---|
| 1249 | zstemp11r = s11r(kx,ky,ka) |
|---|
| 1250 | zstemp12r = s12r(kx,ky,ka) |
|---|
| 1251 | zstemp22r = s22r(kx,ky,ka) |
|---|
| 1252 | zstemp11s = s11s(kx,ky,ka) |
|---|
| 1253 | zstemp12s = s12s(kx,ky,ka) |
|---|
| 1254 | zstemp22s = s22s(kx,ky,ka) |
|---|
| 1255 | |
|---|
| 1256 | |
|---|
| 1257 | ! Calculate mean ice stress over a collection of floes (Equation 3 in |
|---|
| 1258 | ! Tsamados 2013) |
|---|
| 1259 | |
|---|
| 1260 | zsig11 = pstrength*(zstemp11r + kfriction*zstemp11s) * zinvsin |
|---|
| 1261 | zsig12 = pstrength*(zstemp12r + kfriction*zstemp12s) * zinvsin |
|---|
| 1262 | zsig22 = pstrength*(zstemp22r + kfriction*zstemp22s) * zinvsin |
|---|
| 1263 | |
|---|
| 1264 | ! Back - rotation of the stress from principal axes into general coordinates |
|---|
| 1265 | |
|---|
| 1266 | ! Update stress |
|---|
| 1267 | zsgprm11 = zQ11Q11*zsig11 + zQ12Q12*zsig22 - 2._wp*zQ11Q12 *zsig12 |
|---|
| 1268 | zsgprm12 = zQ11Q12*zsig11 - zQ11Q12*zsig22 + (zQ11Q11 - zQ12Q12)*zsig12 |
|---|
| 1269 | zsgprm22 = zQ12Q12*zsig11 + zQ11Q11*zsig22 + 2._wp*zQ11Q12 *zsig12 |
|---|
| 1270 | |
|---|
| 1271 | pstressp = zsgprm11 + zsgprm22 |
|---|
| 1272 | pstress12 = zsgprm12 |
|---|
| 1273 | pstressm = zsgprm11 - zsgprm22 |
|---|
| 1274 | |
|---|
| 1275 | ! Compute ridging and sliding functions in general coordinates |
|---|
| 1276 | ! (Equation 11 in Tsamados 2013) |
|---|
| 1277 | IF (ksub == kndte) THEN |
|---|
| 1278 | zrotstemp11r = zQ11Q11*zstemp11r - 2._wp*zQ11Q12* zstemp12r & |
|---|
| 1279 | + zQ12Q12*zstemp22r |
|---|
| 1280 | zrotstemp12r = zQ11Q11*zstemp12r + zQ11Q12*(zstemp11r-zstemp22r) & |
|---|
| 1281 | - zQ12Q12*zstemp12r |
|---|
| 1282 | zrotstemp22r = zQ12Q12*zstemp11r + 2._wp*zQ11Q12* zstemp12r & |
|---|
| 1283 | + zQ11Q11*zstemp22r |
|---|
| 1284 | |
|---|
| 1285 | zrotstemp11s = zQ11Q11*zstemp11s - 2._wp*zQ11Q12* zstemp12s & |
|---|
| 1286 | + zQ12Q12*zstemp22s |
|---|
| 1287 | zrotstemp12s = zQ11Q11*zstemp12s + zQ11Q12*(zstemp11s-zstemp22s) & |
|---|
| 1288 | - zQ12Q12*zstemp12s |
|---|
| 1289 | zrotstemp22s = zQ12Q12*zstemp11s + 2._wp*zQ11Q12* zstemp12s & |
|---|
| 1290 | + zQ11Q11*zstemp22s |
|---|
| 1291 | |
|---|
| 1292 | palphar = zrotstemp11r*zdtemp11 + 2._wp*zrotstemp12r*zdtemp12 & |
|---|
| 1293 | + zrotstemp22r*zdtemp22 |
|---|
| 1294 | palphas = zrotstemp11s*zdtemp11 + 2._wp*zrotstemp12s*zdtemp12 & |
|---|
| 1295 | + zrotstemp22s*zdtemp22 |
|---|
| 1296 | ENDIF |
|---|
| 1297 | END SUBROUTINE update_stress_rdg |
|---|
| 1298 | |
|---|
| 1299 | !======================================================================= |
|---|
| 1300 | |
|---|
| 1301 | |
|---|
| 1302 | SUBROUTINE calc_ffrac( pstressp, pstressm, pstress12, pa11, pa12, & |
|---|
| 1303 | & pmresult11, pmresult12 ) |
|---|
| 1304 | !!--------------------------------------------------------------------- |
|---|
| 1305 | !! *** ROUTINE calc_ffrac *** |
|---|
| 1306 | !! |
|---|
| 1307 | !! ** Purpose : Computes term in evolution equation for structure tensor |
|---|
| 1308 | !! which determines the ice floe re-orientation due to fracture |
|---|
| 1309 | !! ** Method : Eq. 7: Ffrac = -kf(A-S) or = 0 depending on sigma_1 and sigma_2 |
|---|
| 1310 | !!--------------------------------------------------------------------- |
|---|
| 1311 | REAL (wp), INTENT(in) :: pstressp, pstressm, pstress12, pa11, pa12 |
|---|
| 1312 | REAL (wp), INTENT(out) :: pmresult11, pmresult12 |
|---|
| 1313 | |
|---|
| 1314 | ! local variables |
|---|
| 1315 | |
|---|
| 1316 | REAL (wp) :: zsigma11, zsigma12, zsigma22 ! stress tensor elements |
|---|
| 1317 | REAL (wp) :: zAngle_denom ! angle with principal component axis |
|---|
| 1318 | REAL (wp) :: zsigma_1, zsigma_2 ! principal components of stress |
|---|
| 1319 | REAL (wp) :: zQ11, zQ12, zQ11Q11, zQ11Q12, zQ12Q12 |
|---|
| 1320 | |
|---|
| 1321 | !!$ REAL (wp), PARAMETER :: kfrac = 0.0001_wp ! rate of fracture formation |
|---|
| 1322 | REAL (wp), PARAMETER :: kfrac = 1.e-3_wp ! rate of fracture formation |
|---|
| 1323 | REAL (wp), PARAMETER :: threshold = 0.3_wp ! critical confinement ratio |
|---|
| 1324 | !!--------------------------------------------------------------- |
|---|
| 1325 | ! |
|---|
| 1326 | zsigma11 = 0.5_wp*(pstressp+pstressm) |
|---|
| 1327 | zsigma12 = pstress12 |
|---|
| 1328 | zsigma22 = 0.5_wp*(pstressp-pstressm) |
|---|
| 1329 | |
|---|
| 1330 | ! Here's the change - no longer calculate gamma, |
|---|
| 1331 | ! use trig formulation, angle signs are kept correct, don't worry |
|---|
| 1332 | |
|---|
| 1333 | ! rotate tensor to get into sigma principal axis |
|---|
| 1334 | |
|---|
| 1335 | ! here Tan2gamma = 2 sig12 / (sig11 - sig12) |
|---|
| 1336 | ! add rsmall to the denominator to stop 1/0 errors, makes very little |
|---|
| 1337 | ! error to the calculated angles < rsmall |
|---|
| 1338 | |
|---|
| 1339 | zQ11Q11 = 0.1_wp |
|---|
| 1340 | zQ12Q12 = rsmall |
|---|
| 1341 | zQ11Q12 = rsmall |
|---|
| 1342 | |
|---|
| 1343 | IF((ABS( zsigma11 - zsigma22) > rsmall).OR.(ABS(zsigma12) > rsmall)) THEN |
|---|
| 1344 | |
|---|
| 1345 | zAngle_denom = 1.0_wp/sqrt( ( zsigma11 - zsigma22 )*( zsigma11 - & |
|---|
| 1346 | zsigma22 ) + 4.0_wp*zsigma12*zsigma12) |
|---|
| 1347 | |
|---|
| 1348 | zQ11Q11 = 0.5_wp + ( zsigma11 - zsigma22 )*0.5_wp*zAngle_denom !Cos^2 |
|---|
| 1349 | zQ12Q12 = 0.5_wp - ( zsigma11 - zsigma22 )*0.5_wp*zAngle_denom !Sin^2 |
|---|
| 1350 | zQ11Q12 = zsigma12*zAngle_denom !CosSin |
|---|
| 1351 | ENDIF |
|---|
| 1352 | |
|---|
| 1353 | zsigma_1 = zQ11Q11*zsigma11 + 2.0_wp*zQ11Q12*zsigma12 + zQ12Q12*zsigma22 ! S(1,1) |
|---|
| 1354 | zsigma_2 = zQ12Q12*zsigma11 - 2.0_wp*zQ11Q12*zsigma12 + zQ11Q11*zsigma22 ! S(2,2) |
|---|
| 1355 | |
|---|
| 1356 | ! Pure divergence |
|---|
| 1357 | IF ((zsigma_1 >= 0.0_wp).AND.(zsigma_2 >= 0.0_wp)) THEN |
|---|
| 1358 | pmresult11 = 0.0_wp |
|---|
| 1359 | pmresult12 = 0.0_wp |
|---|
| 1360 | |
|---|
| 1361 | ! Unconfined compression: cracking of blocks not along the axial splitting |
|---|
| 1362 | ! direction |
|---|
| 1363 | ! which leads to the loss of their shape, so we again model it through diffusion |
|---|
| 1364 | ELSEIF ((zsigma_1 >= 0.0_wp).AND.(zsigma_2 < 0.0_wp)) THEN |
|---|
| 1365 | pmresult11 = - kfrac * (pa11 - zQ12Q12) |
|---|
| 1366 | pmresult12 = - kfrac * (pa12 + zQ11Q12) |
|---|
| 1367 | |
|---|
| 1368 | ! Shear faulting |
|---|
| 1369 | ELSEIF (zsigma_2 == 0.0_wp) THEN |
|---|
| 1370 | pmresult11 = 0.0_wp |
|---|
| 1371 | pmresult12 = 0.0_wp |
|---|
| 1372 | ELSEIF ((zsigma_1 <= 0.0_wp).AND.(zsigma_1/zsigma_2 <= threshold)) THEN |
|---|
| 1373 | pmresult11 = - kfrac * (pa11 - zQ12Q12) |
|---|
| 1374 | pmresult12 = - kfrac * (pa12 + zQ11Q12) |
|---|
| 1375 | |
|---|
| 1376 | ! Horizontal spalling |
|---|
| 1377 | ELSE |
|---|
| 1378 | pmresult11 = 0.0_wp |
|---|
| 1379 | pmresult12 = 0.0_wp |
|---|
| 1380 | ENDIF |
|---|
| 1381 | |
|---|
| 1382 | END SUBROUTINE calc_ffrac |
|---|
| 1383 | |
|---|
| 1384 | |
|---|
| 1385 | SUBROUTINE rhg_eap_rst( cdrw, kt ) |
|---|
| 1386 | !!--------------------------------------------------------------------- |
|---|
| 1387 | !! *** ROUTINE rhg_eap_rst *** |
|---|
| 1388 | !! |
|---|
| 1389 | !! ** Purpose : Read or write RHG file in restart file |
|---|
| 1390 | !! |
|---|
| 1391 | !! ** Method : use of IOM library |
|---|
| 1392 | !!---------------------------------------------------------------------- |
|---|
| 1393 | CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag |
|---|
| 1394 | INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step |
|---|
| 1395 | ! |
|---|
| 1396 | INTEGER :: iter ! local integer |
|---|
| 1397 | INTEGER :: id1, id2, id3, id4, id5 ! local integers |
|---|
| 1398 | INTEGER :: ix, iy, ip, iz, n, ia ! local integers |
|---|
| 1399 | |
|---|
| 1400 | INTEGER, PARAMETER :: nz = 100 |
|---|
| 1401 | |
|---|
| 1402 | REAL(wp) :: ainit, xinit, yinit, pinit, zinit |
|---|
| 1403 | REAL(wp) :: da, dx, dy, dp, dz, a1 |
|---|
| 1404 | |
|---|
| 1405 | !!clem |
|---|
| 1406 | REAL(wp) :: zw1, zw2, zfac, ztemp |
|---|
| 1407 | REAL(wp) :: idx, idy, idz |
|---|
| 1408 | |
|---|
| 1409 | REAL(wp), PARAMETER :: eps6 = 1.0e-6_wp |
|---|
| 1410 | !!---------------------------------------------------------------------- |
|---|
| 1411 | ! |
|---|
| 1412 | IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialize |
|---|
| 1413 | ! ! --------------- |
|---|
| 1414 | IF( ln_rstart ) THEN !* Read the restart file |
|---|
| 1415 | ! |
|---|
| 1416 | id1 = iom_varid( numrir, 'stress1_i' , ldstop = .FALSE. ) |
|---|
| 1417 | id2 = iom_varid( numrir, 'stress2_i' , ldstop = .FALSE. ) |
|---|
| 1418 | id3 = iom_varid( numrir, 'stress12_i', ldstop = .FALSE. ) |
|---|
| 1419 | id4 = iom_varid( numrir, 'aniso_11' , ldstop = .FALSE. ) |
|---|
| 1420 | id5 = iom_varid( numrir, 'aniso_12' , ldstop = .FALSE. ) |
|---|
| 1421 | ! |
|---|
| 1422 | IF( MIN( id1, id2, id3, id4, id5 ) > 0 ) THEN ! fields exist |
|---|
| 1423 | CALL iom_get( numrir, jpdom_auto, 'stress1_i' , stress1_i , cd_type = 'T' ) |
|---|
| 1424 | CALL iom_get( numrir, jpdom_auto, 'stress2_i' , stress2_i , cd_type = 'T' ) |
|---|
| 1425 | CALL iom_get( numrir, jpdom_auto, 'stress12_i', stress12_i, cd_type = 'F' ) |
|---|
| 1426 | CALL iom_get( numrir, jpdom_auto, 'aniso_11' , aniso_11 , cd_type = 'T' ) |
|---|
| 1427 | CALL iom_get( numrir, jpdom_auto, 'aniso_12' , aniso_12 , cd_type = 'T' ) |
|---|
| 1428 | ELSE ! start rheology from rest |
|---|
| 1429 | IF(lwp) WRITE(numout,*) |
|---|
| 1430 | IF(lwp) WRITE(numout,*) ' ==>>> previous run without rheology, set stresses to 0' |
|---|
| 1431 | stress1_i (:,:) = 0._wp |
|---|
| 1432 | stress2_i (:,:) = 0._wp |
|---|
| 1433 | stress12_i(:,:) = 0._wp |
|---|
| 1434 | aniso_11 (:,:) = 0.5_wp |
|---|
| 1435 | aniso_12 (:,:) = 0._wp |
|---|
| 1436 | ENDIF |
|---|
| 1437 | ELSE !* Start from rest |
|---|
| 1438 | IF(lwp) WRITE(numout,*) |
|---|
| 1439 | IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set stresses to 0' |
|---|
| 1440 | stress1_i (:,:) = 0._wp |
|---|
| 1441 | stress2_i (:,:) = 0._wp |
|---|
| 1442 | stress12_i(:,:) = 0._wp |
|---|
| 1443 | aniso_11 (:,:) = 0.5_wp |
|---|
| 1444 | aniso_12 (:,:) = 0._wp |
|---|
| 1445 | ENDIF |
|---|
| 1446 | ! |
|---|
| 1447 | |
|---|
| 1448 | da = 0.5_wp/real(na_yield-1,kind=wp) |
|---|
| 1449 | ainit = 0.5_wp - da |
|---|
| 1450 | dx = rpi/real(nx_yield-1,kind=wp) |
|---|
| 1451 | xinit = rpi + 0.25_wp*rpi - dx |
|---|
| 1452 | dz = rpi/real(nz,kind=wp) |
|---|
| 1453 | zinit = -rpi*0.5_wp |
|---|
| 1454 | dy = rpi/real(ny_yield-1,kind=wp) |
|---|
| 1455 | yinit = -dy |
|---|
| 1456 | |
|---|
| 1457 | s11r(:,:,:) = 0._wp |
|---|
| 1458 | s12r(:,:,:) = 0._wp |
|---|
| 1459 | s22r(:,:,:) = 0._wp |
|---|
| 1460 | s11s(:,:,:) = 0._wp |
|---|
| 1461 | s12s(:,:,:) = 0._wp |
|---|
| 1462 | s22s(:,:,:) = 0._wp |
|---|
| 1463 | |
|---|
| 1464 | !!$ DO ia=1,na_yield |
|---|
| 1465 | !!$ DO ix=1,nx_yield |
|---|
| 1466 | !!$ DO iy=1,ny_yield |
|---|
| 1467 | !!$ s11r(ix,iy,ia) = 0._wp |
|---|
| 1468 | !!$ s12r(ix,iy,ia) = 0._wp |
|---|
| 1469 | !!$ s22r(ix,iy,ia) = 0._wp |
|---|
| 1470 | !!$ s11s(ix,iy,ia) = 0._wp |
|---|
| 1471 | !!$ s12s(ix,iy,ia) = 0._wp |
|---|
| 1472 | !!$ s22s(ix,iy,ia) = 0._wp |
|---|
| 1473 | !!$ IF (ia <= na_yield-1) THEN |
|---|
| 1474 | !!$ DO iz=1,nz |
|---|
| 1475 | !!$ s11r(ix,iy,ia) = s11r(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1476 | !!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1477 | !!$ s11kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi) |
|---|
| 1478 | !!$ s12r(ix,iy,ia) = s12r(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1479 | !!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1480 | !!$ s12kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi) |
|---|
| 1481 | !!$ s22r(ix,iy,ia) = s22r(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1482 | !!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1483 | !!$ s22kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi) |
|---|
| 1484 | !!$ s11s(ix,iy,ia) = s11s(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1485 | !!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1486 | !!$ s11ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi) |
|---|
| 1487 | !!$ s12s(ix,iy,ia) = s12s(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1488 | !!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1489 | !!$ s12ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi) |
|---|
| 1490 | !!$ s22s(ix,iy,ia) = s22s(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1491 | !!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1492 | !!$ s22ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi) |
|---|
| 1493 | !!$ ENDDO |
|---|
| 1494 | !!$ IF (abs(s11r(ix,iy,ia)) < eps6) s11r(ix,iy,ia) = 0._wp |
|---|
| 1495 | !!$ IF (abs(s12r(ix,iy,ia)) < eps6) s12r(ix,iy,ia) = 0._wp |
|---|
| 1496 | !!$ IF (abs(s22r(ix,iy,ia)) < eps6) s22r(ix,iy,ia) = 0._wp |
|---|
| 1497 | !!$ IF (abs(s11s(ix,iy,ia)) < eps6) s11s(ix,iy,ia) = 0._wp |
|---|
| 1498 | !!$ IF (abs(s12s(ix,iy,ia)) < eps6) s12s(ix,iy,ia) = 0._wp |
|---|
| 1499 | !!$ IF (abs(s22s(ix,iy,ia)) < eps6) s22s(ix,iy,ia) = 0._wp |
|---|
| 1500 | !!$ ELSE |
|---|
| 1501 | !!$ s11r(ix,iy,ia) = 0.5_wp*s11kr(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi) |
|---|
| 1502 | !!$ s12r(ix,iy,ia) = 0.5_wp*s12kr(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi) |
|---|
| 1503 | !!$ s22r(ix,iy,ia) = 0.5_wp*s22kr(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi) |
|---|
| 1504 | !!$ s11s(ix,iy,ia) = 0.5_wp*s11ks(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi) |
|---|
| 1505 | !!$ s12s(ix,iy,ia) = 0.5_wp*s12ks(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi) |
|---|
| 1506 | !!$ s22s(ix,iy,ia) = 0.5_wp*s22ks(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi) |
|---|
| 1507 | !!$ IF (abs(s11r(ix,iy,ia)) < eps6) s11r(ix,iy,ia) = 0._wp |
|---|
| 1508 | !!$ IF (abs(s12r(ix,iy,ia)) < eps6) s12r(ix,iy,ia) = 0._wp |
|---|
| 1509 | !!$ IF (abs(s22r(ix,iy,ia)) < eps6) s22r(ix,iy,ia) = 0._wp |
|---|
| 1510 | !!$ IF (abs(s11s(ix,iy,ia)) < eps6) s11s(ix,iy,ia) = 0._wp |
|---|
| 1511 | !!$ IF (abs(s12s(ix,iy,ia)) < eps6) s12s(ix,iy,ia) = 0._wp |
|---|
| 1512 | !!$ IF (abs(s22s(ix,iy,ia)) < eps6) s22s(ix,iy,ia) = 0._wp |
|---|
| 1513 | !!$ ENDIF |
|---|
| 1514 | !!$ ENDDO |
|---|
| 1515 | !!$ ENDDO |
|---|
| 1516 | !!$ ENDDO |
|---|
| 1517 | |
|---|
| 1518 | !! faster but still very slow => to be improved |
|---|
| 1519 | zfac = dz/sin(2._wp*pphi) |
|---|
| 1520 | DO ia = 1, na_yield-1 |
|---|
| 1521 | zw1 = w1(ainit+ia*da) |
|---|
| 1522 | zw2 = w2(ainit+ia*da) |
|---|
| 1523 | DO iz = 1, nz |
|---|
| 1524 | idz = zinit+iz*dz |
|---|
| 1525 | ztemp = zw1 * EXP(-zw2*(zinit+iz*dz)*(zinit+iz*dz)) |
|---|
| 1526 | DO iy = 1, ny_yield |
|---|
| 1527 | idy = yinit+iy*dy |
|---|
| 1528 | DO ix = 1, nx_yield |
|---|
| 1529 | idx = xinit+ix*dx |
|---|
| 1530 | s11r(ix,iy,ia) = s11r(ix,iy,ia) + ztemp * s11kr(idx,idy,idz)*zfac |
|---|
| 1531 | s12r(ix,iy,ia) = s12r(ix,iy,ia) + ztemp * s12kr(idx,idy,idz)*zfac |
|---|
| 1532 | s22r(ix,iy,ia) = s22r(ix,iy,ia) + ztemp * s22kr(idx,idy,idz)*zfac |
|---|
| 1533 | s11s(ix,iy,ia) = s11s(ix,iy,ia) + ztemp * s11ks(idx,idy,idz)*zfac |
|---|
| 1534 | s12s(ix,iy,ia) = s12s(ix,iy,ia) + ztemp * s12ks(idx,idy,idz)*zfac |
|---|
| 1535 | s22s(ix,iy,ia) = s22s(ix,iy,ia) + ztemp * s22ks(idx,idy,idz)*zfac |
|---|
| 1536 | END DO |
|---|
| 1537 | END DO |
|---|
| 1538 | END DO |
|---|
| 1539 | END DO |
|---|
| 1540 | |
|---|
| 1541 | zfac = 1._wp/sin(2._wp*pphi) |
|---|
| 1542 | ia = na_yield |
|---|
| 1543 | DO iy = 1, ny_yield |
|---|
| 1544 | idy = yinit+iy*dy |
|---|
| 1545 | DO ix = 1, nx_yield |
|---|
| 1546 | idx = xinit+ix*dx |
|---|
| 1547 | s11r(ix,iy,ia) = 0.5_wp*s11kr(idx,idy,0._wp)*zfac |
|---|
| 1548 | s12r(ix,iy,ia) = 0.5_wp*s12kr(idx,idy,0._wp)*zfac |
|---|
| 1549 | s22r(ix,iy,ia) = 0.5_wp*s22kr(idx,idy,0._wp)*zfac |
|---|
| 1550 | s11s(ix,iy,ia) = 0.5_wp*s11ks(idx,idy,0._wp)*zfac |
|---|
| 1551 | s12s(ix,iy,ia) = 0.5_wp*s12ks(idx,idy,0._wp)*zfac |
|---|
| 1552 | s22s(ix,iy,ia) = 0.5_wp*s22ks(idx,idy,0._wp)*zfac |
|---|
| 1553 | ENDDO |
|---|
| 1554 | ENDDO |
|---|
| 1555 | WHERE (ABS(s11r(:,:,:)) < eps6) s11r(:,:,:) = 0._wp |
|---|
| 1556 | WHERE (ABS(s12r(:,:,:)) < eps6) s12r(:,:,:) = 0._wp |
|---|
| 1557 | WHERE (ABS(s22r(:,:,:)) < eps6) s22r(:,:,:) = 0._wp |
|---|
| 1558 | WHERE (ABS(s11s(:,:,:)) < eps6) s11s(:,:,:) = 0._wp |
|---|
| 1559 | WHERE (ABS(s12s(:,:,:)) < eps6) s12s(:,:,:) = 0._wp |
|---|
| 1560 | WHERE (ABS(s22s(:,:,:)) < eps6) s22s(:,:,:) = 0._wp |
|---|
| 1561 | |
|---|
| 1562 | |
|---|
| 1563 | ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file |
|---|
| 1564 | ! ! ------------------- |
|---|
| 1565 | IF(lwp) WRITE(numout,*) '---- rhg-rst ----' |
|---|
| 1566 | iter = kt + nn_fsbc - 1 ! ice restarts are written at kt == nitrst - nn_fsbc + 1 |
|---|
| 1567 | ! |
|---|
| 1568 | CALL iom_rstput( iter, nitrst, numriw, 'stress1_i' , stress1_i ) |
|---|
| 1569 | CALL iom_rstput( iter, nitrst, numriw, 'stress2_i' , stress2_i ) |
|---|
| 1570 | CALL iom_rstput( iter, nitrst, numriw, 'stress12_i', stress12_i ) |
|---|
| 1571 | CALL iom_rstput( iter, nitrst, numriw, 'aniso_11' , aniso_11 ) |
|---|
| 1572 | CALL iom_rstput( iter, nitrst, numriw, 'aniso_12' , aniso_12 ) |
|---|
| 1573 | ! |
|---|
| 1574 | ENDIF |
|---|
| 1575 | ! |
|---|
| 1576 | END SUBROUTINE rhg_eap_rst |
|---|
| 1577 | |
|---|
| 1578 | |
|---|
| 1579 | FUNCTION w1(pa) |
|---|
| 1580 | !!------------------------------------------------------------------- |
|---|
| 1581 | !! Function : w1 (see Gaussian function psi in Tsamados et al 2013) |
|---|
| 1582 | !!------------------------------------------------------------------- |
|---|
| 1583 | REAL(wp), INTENT(in ) :: pa |
|---|
| 1584 | REAL(wp) :: w1 |
|---|
| 1585 | !!------------------------------------------------------------------- |
|---|
| 1586 | |
|---|
| 1587 | w1 = - 223.87569446_wp & |
|---|
| 1588 | & + 2361.21986630_wp*pa & |
|---|
| 1589 | & - 10606.56079975_wp*pa*pa & |
|---|
| 1590 | & + 26315.50025642_wp*pa*pa*pa & |
|---|
| 1591 | & - 38948.30444297_wp*pa*pa*pa*pa & |
|---|
| 1592 | & + 34397.72407466_wp*pa*pa*pa*pa*pa & |
|---|
| 1593 | & - 16789.98003081_wp*pa*pa*pa*pa*pa*pa & |
|---|
| 1594 | & + 3495.82839237_wp*pa*pa*pa*pa*pa*pa*pa |
|---|
| 1595 | |
|---|
| 1596 | END FUNCTION w1 |
|---|
| 1597 | |
|---|
| 1598 | |
|---|
| 1599 | FUNCTION w2(pa) |
|---|
| 1600 | !!------------------------------------------------------------------- |
|---|
| 1601 | !! Function : w2 (see Gaussian function psi in Tsamados et al 2013) |
|---|
| 1602 | !!------------------------------------------------------------------- |
|---|
| 1603 | REAL(wp), INTENT(in ) :: pa |
|---|
| 1604 | REAL(wp) :: w2 |
|---|
| 1605 | !!------------------------------------------------------------------- |
|---|
| 1606 | |
|---|
| 1607 | w2 = - 6670.68911883_wp & |
|---|
| 1608 | & + 70222.33061536_wp*pa & |
|---|
| 1609 | & - 314871.71525448_wp*pa*pa & |
|---|
| 1610 | & + 779570.02793492_wp*pa*pa*pa & |
|---|
| 1611 | & - 1151098.82436864_wp*pa*pa*pa*pa & |
|---|
| 1612 | & + 1013896.59464498_wp*pa*pa*pa*pa*pa & |
|---|
| 1613 | & - 493379.44906738_wp*pa*pa*pa*pa*pa*pa & |
|---|
| 1614 | & + 102356.55151800_wp*pa*pa*pa*pa*pa*pa*pa |
|---|
| 1615 | |
|---|
| 1616 | END FUNCTION w2 |
|---|
| 1617 | |
|---|
| 1618 | FUNCTION s11kr(px,py,pz) |
|---|
| 1619 | !!------------------------------------------------------------------- |
|---|
| 1620 | !! Function : s11kr |
|---|
| 1621 | !!------------------------------------------------------------------- |
|---|
| 1622 | REAL(wp), INTENT(in ) :: px,py,pz |
|---|
| 1623 | |
|---|
| 1624 | REAL(wp) :: s11kr, zpih |
|---|
| 1625 | |
|---|
| 1626 | REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22 |
|---|
| 1627 | REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22 |
|---|
| 1628 | REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22 |
|---|
| 1629 | REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22 |
|---|
| 1630 | REAL(wp) :: zd11, zd12, zd22 |
|---|
| 1631 | REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2 |
|---|
| 1632 | REAL(wp) :: zHen1t2, zHen2t1 |
|---|
| 1633 | !!------------------------------------------------------------------- |
|---|
| 1634 | |
|---|
| 1635 | zpih = 0.5_wp*rpi |
|---|
| 1636 | |
|---|
| 1637 | zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1638 | zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1639 | zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1640 | zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1641 | zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1642 | zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1643 | zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1644 | zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1645 | zt1t2i11 = cos(pz-pphi) * cos(pz+pphi) |
|---|
| 1646 | zt1t2i12 = cos(pz-pphi) * sin(pz+pphi) |
|---|
| 1647 | zt1t2i21 = sin(pz-pphi) * cos(pz+pphi) |
|---|
| 1648 | zt1t2i22 = sin(pz-pphi) * sin(pz+pphi) |
|---|
| 1649 | zt2t1i11 = cos(pz+pphi) * cos(pz-pphi) |
|---|
| 1650 | zt2t1i12 = cos(pz+pphi) * sin(pz-pphi) |
|---|
| 1651 | zt2t1i21 = sin(pz+pphi) * cos(pz-pphi) |
|---|
| 1652 | zt2t1i22 = sin(pz+pphi) * sin(pz-pphi) |
|---|
| 1653 | ! In expression of tensor d, with this formulatin d(x)=-d(x+pi) |
|---|
| 1654 | ! Solution, when diagonalizing always check sgn(a11-a22) if > then keep x else |
|---|
| 1655 | ! x=x-pi/2 |
|---|
| 1656 | zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py)) |
|---|
| 1657 | zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px)) |
|---|
| 1658 | zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py)) |
|---|
| 1659 | zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22 |
|---|
| 1660 | zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22 |
|---|
| 1661 | zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22 |
|---|
| 1662 | |
|---|
| 1663 | IF (-zIIn1t2>=rsmall) THEN |
|---|
| 1664 | zHen1t2 = 1._wp |
|---|
| 1665 | ELSE |
|---|
| 1666 | zHen1t2 = 0._wp |
|---|
| 1667 | ENDIF |
|---|
| 1668 | |
|---|
| 1669 | IF (-zIIn2t1>=rsmall) THEN |
|---|
| 1670 | zHen2t1 = 1._wp |
|---|
| 1671 | ELSE |
|---|
| 1672 | zHen2t1 = 0._wp |
|---|
| 1673 | ENDIF |
|---|
| 1674 | |
|---|
| 1675 | s11kr = (- zHen1t2 * zn1t2i11 - zHen2t1 * zn2t1i11) |
|---|
| 1676 | |
|---|
| 1677 | END FUNCTION s11kr |
|---|
| 1678 | |
|---|
| 1679 | FUNCTION s12kr(px,py,pz) |
|---|
| 1680 | !!------------------------------------------------------------------- |
|---|
| 1681 | !! Function : s12kr |
|---|
| 1682 | !!------------------------------------------------------------------- |
|---|
| 1683 | REAL(wp), INTENT(in ) :: px,py,pz |
|---|
| 1684 | |
|---|
| 1685 | REAL(wp) :: s12kr, zs12r0, zs21r0, zpih |
|---|
| 1686 | |
|---|
| 1687 | REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22 |
|---|
| 1688 | REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22 |
|---|
| 1689 | REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22 |
|---|
| 1690 | REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22 |
|---|
| 1691 | REAL(wp) :: zd11, zd12, zd22 |
|---|
| 1692 | REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2 |
|---|
| 1693 | REAL(wp) :: zHen1t2, zHen2t1 |
|---|
| 1694 | !!------------------------------------------------------------------- |
|---|
| 1695 | zpih = 0.5_wp*rpi |
|---|
| 1696 | |
|---|
| 1697 | zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1698 | zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1699 | zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1700 | zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1701 | zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1702 | zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1703 | zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1704 | zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1705 | zt1t2i11 = cos(pz-pphi) * cos(pz+pphi) |
|---|
| 1706 | zt1t2i12 = cos(pz-pphi) * sin(pz+pphi) |
|---|
| 1707 | zt1t2i21 = sin(pz-pphi) * cos(pz+pphi) |
|---|
| 1708 | zt1t2i22 = sin(pz-pphi) * sin(pz+pphi) |
|---|
| 1709 | zt2t1i11 = cos(pz+pphi) * cos(pz-pphi) |
|---|
| 1710 | zt2t1i12 = cos(pz+pphi) * sin(pz-pphi) |
|---|
| 1711 | zt2t1i21 = sin(pz+pphi) * cos(pz-pphi) |
|---|
| 1712 | zt2t1i22 = sin(pz+pphi) * sin(pz-pphi) |
|---|
| 1713 | zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py)) |
|---|
| 1714 | zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px)) |
|---|
| 1715 | zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py)) |
|---|
| 1716 | zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22 |
|---|
| 1717 | zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22 |
|---|
| 1718 | zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22 |
|---|
| 1719 | |
|---|
| 1720 | IF (-zIIn1t2>=rsmall) THEN |
|---|
| 1721 | zHen1t2 = 1._wp |
|---|
| 1722 | ELSE |
|---|
| 1723 | zHen1t2 = 0._wp |
|---|
| 1724 | ENDIF |
|---|
| 1725 | |
|---|
| 1726 | IF (-zIIn2t1>=rsmall) THEN |
|---|
| 1727 | zHen2t1 = 1._wp |
|---|
| 1728 | ELSE |
|---|
| 1729 | zHen2t1 = 0._wp |
|---|
| 1730 | ENDIF |
|---|
| 1731 | |
|---|
| 1732 | zs12r0 = (- zHen1t2 * zn1t2i12 - zHen2t1 * zn2t1i12) |
|---|
| 1733 | zs21r0 = (- zHen1t2 * zn1t2i21 - zHen2t1 * zn2t1i21) |
|---|
| 1734 | s12kr=0.5_wp*(zs12r0+zs21r0) |
|---|
| 1735 | |
|---|
| 1736 | END FUNCTION s12kr |
|---|
| 1737 | |
|---|
| 1738 | FUNCTION s22kr(px,py,pz) |
|---|
| 1739 | !!------------------------------------------------------------------- |
|---|
| 1740 | !! Function : s22kr |
|---|
| 1741 | !!------------------------------------------------------------------- |
|---|
| 1742 | REAL(wp), INTENT(in ) :: px,py,pz |
|---|
| 1743 | |
|---|
| 1744 | REAL(wp) :: s22kr, zpih |
|---|
| 1745 | |
|---|
| 1746 | REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22 |
|---|
| 1747 | REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22 |
|---|
| 1748 | REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22 |
|---|
| 1749 | REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22 |
|---|
| 1750 | REAL(wp) :: zd11, zd12, zd22 |
|---|
| 1751 | REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2 |
|---|
| 1752 | REAL(wp) :: zHen1t2, zHen2t1 |
|---|
| 1753 | !!------------------------------------------------------------------- |
|---|
| 1754 | zpih = 0.5_wp*rpi |
|---|
| 1755 | |
|---|
| 1756 | zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1757 | zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1758 | zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1759 | zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1760 | zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1761 | zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1762 | zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1763 | zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1764 | zt1t2i11 = cos(pz-pphi) * cos(pz+pphi) |
|---|
| 1765 | zt1t2i12 = cos(pz-pphi) * sin(pz+pphi) |
|---|
| 1766 | zt1t2i21 = sin(pz-pphi) * cos(pz+pphi) |
|---|
| 1767 | zt1t2i22 = sin(pz-pphi) * sin(pz+pphi) |
|---|
| 1768 | zt2t1i11 = cos(pz+pphi) * cos(pz-pphi) |
|---|
| 1769 | zt2t1i12 = cos(pz+pphi) * sin(pz-pphi) |
|---|
| 1770 | zt2t1i21 = sin(pz+pphi) * cos(pz-pphi) |
|---|
| 1771 | zt2t1i22 = sin(pz+pphi) * sin(pz-pphi) |
|---|
| 1772 | zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py)) |
|---|
| 1773 | zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px)) |
|---|
| 1774 | zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py)) |
|---|
| 1775 | zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22 |
|---|
| 1776 | zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22 |
|---|
| 1777 | zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22 |
|---|
| 1778 | |
|---|
| 1779 | IF (-zIIn1t2>=rsmall) THEN |
|---|
| 1780 | zHen1t2 = 1._wp |
|---|
| 1781 | ELSE |
|---|
| 1782 | zHen1t2 = 0._wp |
|---|
| 1783 | ENDIF |
|---|
| 1784 | |
|---|
| 1785 | IF (-zIIn2t1>=rsmall) THEN |
|---|
| 1786 | zHen2t1 = 1._wp |
|---|
| 1787 | ELSE |
|---|
| 1788 | zHen2t1 = 0._wp |
|---|
| 1789 | ENDIF |
|---|
| 1790 | |
|---|
| 1791 | s22kr = (- zHen1t2 * zn1t2i22 - zHen2t1 * zn2t1i22) |
|---|
| 1792 | |
|---|
| 1793 | END FUNCTION s22kr |
|---|
| 1794 | |
|---|
| 1795 | FUNCTION s11ks(px,py,pz) |
|---|
| 1796 | !!------------------------------------------------------------------- |
|---|
| 1797 | !! Function : s11ks |
|---|
| 1798 | !!------------------------------------------------------------------- |
|---|
| 1799 | REAL(wp), INTENT(in ) :: px,py,pz |
|---|
| 1800 | |
|---|
| 1801 | REAL(wp) :: s11ks, zpih |
|---|
| 1802 | |
|---|
| 1803 | REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22 |
|---|
| 1804 | REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22 |
|---|
| 1805 | REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22 |
|---|
| 1806 | REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22 |
|---|
| 1807 | REAL(wp) :: zd11, zd12, zd22 |
|---|
| 1808 | REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2 |
|---|
| 1809 | REAL(wp) :: zHen1t2, zHen2t1 |
|---|
| 1810 | !!------------------------------------------------------------------- |
|---|
| 1811 | zpih = 0.5_wp*rpi |
|---|
| 1812 | |
|---|
| 1813 | zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1814 | zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1815 | zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1816 | zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1817 | zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1818 | zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1819 | zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1820 | zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1821 | zt1t2i11 = cos(pz-pphi) * cos(pz+pphi) |
|---|
| 1822 | zt1t2i12 = cos(pz-pphi) * sin(pz+pphi) |
|---|
| 1823 | zt1t2i21 = sin(pz-pphi) * cos(pz+pphi) |
|---|
| 1824 | zt1t2i22 = sin(pz-pphi) * sin(pz+pphi) |
|---|
| 1825 | zt2t1i11 = cos(pz+pphi) * cos(pz-pphi) |
|---|
| 1826 | zt2t1i12 = cos(pz+pphi) * sin(pz-pphi) |
|---|
| 1827 | zt2t1i21 = sin(pz+pphi) * cos(pz-pphi) |
|---|
| 1828 | zt2t1i22 = sin(pz+pphi) * sin(pz-pphi) |
|---|
| 1829 | zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py)) |
|---|
| 1830 | zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px)) |
|---|
| 1831 | zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py)) |
|---|
| 1832 | zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22 |
|---|
| 1833 | zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22 |
|---|
| 1834 | zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22 |
|---|
| 1835 | |
|---|
| 1836 | IF (-zIIn1t2>=rsmall) THEN |
|---|
| 1837 | zHen1t2 = 1._wp |
|---|
| 1838 | ELSE |
|---|
| 1839 | zHen1t2 = 0._wp |
|---|
| 1840 | ENDIF |
|---|
| 1841 | |
|---|
| 1842 | IF (-zIIn2t1>=rsmall) THEN |
|---|
| 1843 | zHen2t1 = 1._wp |
|---|
| 1844 | ELSE |
|---|
| 1845 | zHen2t1 = 0._wp |
|---|
| 1846 | ENDIF |
|---|
| 1847 | |
|---|
| 1848 | s11ks = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i11 + zHen2t1 * zt2t1i11) |
|---|
| 1849 | |
|---|
| 1850 | END FUNCTION s11ks |
|---|
| 1851 | |
|---|
| 1852 | FUNCTION s12ks(px,py,pz) |
|---|
| 1853 | !!------------------------------------------------------------------- |
|---|
| 1854 | !! Function : s12ks |
|---|
| 1855 | !!------------------------------------------------------------------- |
|---|
| 1856 | REAL(wp), INTENT(in ) :: px,py,pz |
|---|
| 1857 | |
|---|
| 1858 | REAL(wp) :: s12ks, zs12s0, zs21s0, zpih |
|---|
| 1859 | |
|---|
| 1860 | REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22 |
|---|
| 1861 | REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22 |
|---|
| 1862 | REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22 |
|---|
| 1863 | REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22 |
|---|
| 1864 | REAL(wp) :: zd11, zd12, zd22 |
|---|
| 1865 | REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2 |
|---|
| 1866 | REAL(wp) :: zHen1t2, zHen2t1 |
|---|
| 1867 | !!------------------------------------------------------------------- |
|---|
| 1868 | zpih = 0.5_wp*rpi |
|---|
| 1869 | |
|---|
| 1870 | zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1871 | zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1872 | zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1873 | zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1874 | zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1875 | zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1876 | zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1877 | zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1878 | zt1t2i11 = cos(pz-pphi) * cos(pz+pphi) |
|---|
| 1879 | zt1t2i12 = cos(pz-pphi) * sin(pz+pphi) |
|---|
| 1880 | zt1t2i21 = sin(pz-pphi) * cos(pz+pphi) |
|---|
| 1881 | zt1t2i22 = sin(pz-pphi) * sin(pz+pphi) |
|---|
| 1882 | zt2t1i11 = cos(pz+pphi) * cos(pz-pphi) |
|---|
| 1883 | zt2t1i12 = cos(pz+pphi) * sin(pz-pphi) |
|---|
| 1884 | zt2t1i21 = sin(pz+pphi) * cos(pz-pphi) |
|---|
| 1885 | zt2t1i22 = sin(pz+pphi) * sin(pz-pphi) |
|---|
| 1886 | zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py)) |
|---|
| 1887 | zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px)) |
|---|
| 1888 | zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py)) |
|---|
| 1889 | zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22 |
|---|
| 1890 | zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22 |
|---|
| 1891 | zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22 |
|---|
| 1892 | |
|---|
| 1893 | IF (-zIIn1t2>=rsmall) THEN |
|---|
| 1894 | zHen1t2 = 1._wp |
|---|
| 1895 | ELSE |
|---|
| 1896 | zHen1t2 = 0._wp |
|---|
| 1897 | ENDIF |
|---|
| 1898 | |
|---|
| 1899 | IF (-zIIn2t1>=rsmall) THEN |
|---|
| 1900 | zHen2t1 = 1._wp |
|---|
| 1901 | ELSE |
|---|
| 1902 | zHen2t1 = 0._wp |
|---|
| 1903 | ENDIF |
|---|
| 1904 | |
|---|
| 1905 | zs12s0 = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i12 + zHen2t1 * zt2t1i12) |
|---|
| 1906 | zs21s0 = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i21 + zHen2t1 * zt2t1i21) |
|---|
| 1907 | s12ks=0.5_wp*(zs12s0+zs21s0) |
|---|
| 1908 | |
|---|
| 1909 | END FUNCTION s12ks |
|---|
| 1910 | |
|---|
| 1911 | FUNCTION s22ks(px,py,pz) |
|---|
| 1912 | !!------------------------------------------------------------------- |
|---|
| 1913 | !! Function : s22ks |
|---|
| 1914 | !!------------------------------------------------------------------- |
|---|
| 1915 | REAL(wp), INTENT(in ) :: px,py,pz |
|---|
| 1916 | |
|---|
| 1917 | REAL(wp) :: s22ks, zpih |
|---|
| 1918 | |
|---|
| 1919 | REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22 |
|---|
| 1920 | REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22 |
|---|
| 1921 | REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22 |
|---|
| 1922 | REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22 |
|---|
| 1923 | REAL(wp) :: zd11, zd12, zd22 |
|---|
| 1924 | REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2 |
|---|
| 1925 | REAL(wp) :: zHen1t2, zHen2t1 |
|---|
| 1926 | !!------------------------------------------------------------------- |
|---|
| 1927 | zpih = 0.5_wp*rpi |
|---|
| 1928 | |
|---|
| 1929 | zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1930 | zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1931 | zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi) |
|---|
| 1932 | zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi) |
|---|
| 1933 | zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1934 | zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1935 | zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi) |
|---|
| 1936 | zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi) |
|---|
| 1937 | zt1t2i11 = cos(pz-pphi) * cos(pz+pphi) |
|---|
| 1938 | zt1t2i12 = cos(pz-pphi) * sin(pz+pphi) |
|---|
| 1939 | zt1t2i21 = sin(pz-pphi) * cos(pz+pphi) |
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| 1940 | zt1t2i22 = sin(pz-pphi) * sin(pz+pphi) |
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| 1941 | zt2t1i11 = cos(pz+pphi) * cos(pz-pphi) |
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| 1942 | zt2t1i12 = cos(pz+pphi) * sin(pz-pphi) |
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| 1943 | zt2t1i21 = sin(pz+pphi) * cos(pz-pphi) |
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| 1944 | zt2t1i22 = sin(pz+pphi) * sin(pz-pphi) |
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| 1945 | zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py)) |
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| 1946 | zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px)) |
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| 1947 | zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py)) |
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| 1948 | zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22 |
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| 1949 | zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22 |
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| 1950 | zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22 |
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| 1951 | |
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| 1952 | IF (-zIIn1t2>=rsmall) THEN |
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| 1953 | zHen1t2 = 1._wp |
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| 1954 | ELSE |
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| 1955 | zHen1t2 = 0._wp |
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| 1956 | ENDIF |
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| 1957 | |
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| 1958 | IF (-zIIn2t1>=rsmall) THEN |
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| 1959 | zHen2t1 = 1._wp |
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| 1960 | ELSE |
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| 1961 | zHen2t1 = 0._wp |
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| 1962 | ENDIF |
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| 1963 | |
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| 1964 | s22ks = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i22 + zHen2t1 * zt2t1i22) |
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| 1965 | |
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| 1966 | END FUNCTION s22ks |
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| 1967 | |
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| 1968 | #else |
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| 1969 | !!---------------------------------------------------------------------- |
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| 1970 | !! Default option Empty module NO SI3 sea-ice model |
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| 1971 | !!---------------------------------------------------------------------- |
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| 1972 | #endif |
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| 1973 | |
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| 1974 | !!============================================================================== |
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| 1975 | END MODULE icedyn_rhg_eap |
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