| 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) 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 | IMPLICIT NONE |
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| 46 | PRIVATE |
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| 47 | |
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| 48 | PUBLIC ice_dyn_rhg_eap ! called by icedyn_rhg.F90 |
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| 49 | PUBLIC rhg_eap_rst ! called by icedyn_rhg.F90 |
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| 50 | |
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| 51 | REAL(wp), PARAMETER :: phi = 3.141592653589793_wp/12._wp ! diamond shaped floe smaller angle (default phi = 30 deg) |
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| 52 | |
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| 53 | ! look-up table for calculating structure tensor |
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| 54 | INTEGER, PARAMETER :: nx_yield = 41 |
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| 55 | INTEGER, PARAMETER :: ny_yield = 41 |
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| 56 | INTEGER, PARAMETER :: na_yield = 21 |
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| 57 | |
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| 58 | REAL(wp), DIMENSION(nx_yield, ny_yield, na_yield) :: s11r, s12r, s22r, s11s, s12s, s22s |
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| 59 | |
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| 60 | !! * Substitutions |
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| 61 | # include "vectopt_loop_substitute.h90" |
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| 62 | !!---------------------------------------------------------------------- |
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| 63 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 64 | !! $Id: icedyn_rhg_eap.F90 11536 2019-09-11 13:54:18Z smasson $ |
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| 65 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 66 | !!---------------------------------------------------------------------- |
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| 67 | CONTAINS |
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| 68 | |
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| 69 | SUBROUTINE ice_dyn_rhg_eap( kt, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i, paniso_11, paniso_12 ) |
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| 70 | !!------------------------------------------------------------------- |
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| 71 | !! *** SUBROUTINE ice_dyn_rhg_eap *** |
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| 72 | !! EAP-C-grid |
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| 73 | !! |
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| 74 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
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| 75 | !! stress and sea-surface slope. Ice-ice interaction is described by |
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| 76 | !! a non-linear elasto-anisotropic-plastic (EAP) law including shear |
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| 77 | !! strength and a bulk rheology . |
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| 78 | !! |
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| 79 | !! The points in the C-grid look like this, dear reader |
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| 80 | !! |
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| 81 | !! (ji,jj) |
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| 82 | !! | |
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| 83 | !! | |
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| 84 | !! (ji-1,jj) | (ji,jj) |
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| 85 | !! --------- |
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| 86 | !! | | |
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| 87 | !! | (ji,jj) |------(ji,jj) |
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| 88 | !! | | |
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| 89 | !! --------- |
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| 90 | !! (ji-1,jj-1) (ji,jj-1) |
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| 91 | !! |
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| 92 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 93 | !! ice total volume (vt_i) per unit area |
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| 94 | !! snow total volume (vt_s) per unit area |
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| 95 | !! |
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| 96 | !! ** Action : - compute u_ice, v_ice : the components of the |
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| 97 | !! sea-ice velocity vector |
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| 98 | !! - compute delta_i, shear_i, divu_i, which are inputs |
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| 99 | !! of the ice thickness distribution |
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| 100 | !! |
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| 101 | !! ** Steps : 0) compute mask at F point |
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| 102 | !! 1) Compute ice snow mass, ice strength |
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| 103 | !! 2) Compute wind, oceanic stresses, mass terms and |
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| 104 | !! coriolis terms of the momentum equation |
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| 105 | !! 3) Solve the momentum equation (iterative procedure) |
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| 106 | !! 4) Recompute delta, shear and divergence |
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| 107 | !! (which are inputs of the ITD) & store stress |
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| 108 | !! for the next time step |
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| 109 | !! 5) Diagnostics including charge ellipse |
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| 110 | !! |
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| 111 | !! ** Notes : There is the possibility to use aEVP from the nice work of Kimmritz et al. (2016 & 2017) |
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| 112 | !! by setting up ln_aEVP=T (i.e. changing alpha and beta parameters). |
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| 113 | !! This is an upgraded version of mEVP from Bouillon et al. 2013 |
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| 114 | !! (i.e. more stable and better convergence) |
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| 115 | !! |
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| 116 | !! References : Hunke and Dukowicz, JPO97 |
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| 117 | !! Bouillon et al., Ocean Modelling 2009 |
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| 118 | !! Bouillon et al., Ocean Modelling 2013 |
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| 119 | !! Kimmritz et al., Ocean Modelling 2016 & 2017 |
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| 120 | !!------------------------------------------------------------------- |
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| 121 | INTEGER , INTENT(in ) :: kt ! time step |
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| 122 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pstress1_i, pstress2_i, pstress12_i ! |
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| 123 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
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| 124 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: paniso_11 , paniso_12 ! structure tensor components |
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| 125 | !! |
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| 126 | INTEGER :: ji, jj ! dummy loop indices |
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| 127 | INTEGER :: jter ! local integers |
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| 128 | ! |
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| 129 | REAL(wp) :: zrhoco ! rau0 * rn_cio |
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| 130 | REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling |
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| 131 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
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| 132 | REAL(wp) :: zalph1, z1_alph1 ! alpha coef from Bouillon 2009 or Kimmritz 2017 |
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| 133 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV, zvU, zvV ! ice/snow mass and volume |
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| 134 | REAL(wp) :: zdelta, zp_delf, zds2, zdt, zdt2, zdiv, zdiv2, zdsT ! temporary scalars |
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| 135 | REAL(wp) :: zTauO, zTauB, zRHS, zvel ! temporary scalars |
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| 136 | REAL(wp) :: zkt ! isotropic tensile strength for landfast ice |
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| 137 | REAL(wp) :: zvCr ! critical ice volume above which ice is landfast |
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| 138 | ! |
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| 139 | REAL(wp) :: zresm ! Maximal error on ice velocity |
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| 140 | REAL(wp) :: zintb, zintn ! dummy argument |
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| 141 | REAL(wp) :: zfac_x, zfac_y |
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| 142 | REAL(wp) :: zshear, zdum1, zdum2 |
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| 143 | REAL(wp) :: stressptmp, stressmtmp, stress12tmpF ! anisotropic stress tensor components |
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| 144 | REAL(wp) :: alphar, alphas ! for mechanical redistribution |
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| 145 | ! |
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| 146 | REAL(wp), DIMENSION(jpi,jpj) :: stress12tmp ! anisotropic stress tensor component for regridding |
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| 147 | REAL(wp), DIMENSION(jpi,jpj) :: zp_delt ! P/delta at T points |
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| 148 | REAL(wp), DIMENSION(jpi,jpj) :: zbeta ! beta coef from Kimmritz 2017 |
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| 149 | ! |
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| 150 | REAL(wp), DIMENSION(jpi,jpj) :: zdt_m ! (dt / ice-snow_mass) on T points |
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| 151 | REAL(wp), DIMENSION(jpi,jpj) :: zaU , zaV ! ice fraction on U/V points |
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| 152 | REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! (ice-snow_mass / dt) on U/V points |
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| 153 | REAL(wp), DIMENSION(jpi,jpj) :: zmf ! coriolis parameter at T points |
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| 154 | 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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| 155 | ! |
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| 156 | REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear |
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| 157 | REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12 ! stress tensor components |
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| 158 | !!$ REAL(wp), DIMENSION(jpi,jpj) :: zu_ice, zv_ice, zresr ! check convergence |
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| 159 | REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope: |
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| 160 | ! ! ocean surface (ssh_m) if ice is not embedded |
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| 161 | ! ! ice bottom surface if ice is embedded |
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| 162 | REAL(wp), DIMENSION(jpi,jpj) :: zfU , zfV ! internal stresses |
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| 163 | REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points |
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| 164 | REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array |
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| 165 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points |
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| 166 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi, ztauy_oi ! ice-ocean stress at U-V points |
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| 167 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast) |
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| 168 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast) |
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| 169 | ! |
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| 170 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! dummy arrays |
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| 171 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence |
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| 172 | REAL(wp), DIMENSION(jpi,jpj) :: zfmask, zwf ! mask at F points for the ice |
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| 173 | |
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| 174 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
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| 175 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small |
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| 176 | REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small |
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| 177 | !! --- diags |
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| 178 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00 |
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| 179 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig1, zsig2, zsig3 |
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| 180 | !! --- SIMIP diags |
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| 181 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice ! X-component of ice mass transport (kg/s) |
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| 182 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_ice ! Y-component of ice mass transport (kg/s) |
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| 183 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw ! X-component of snow mass transport (kg/s) |
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| 184 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_snw ! Y-component of snow mass transport (kg/s) |
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| 185 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp ! X-component of area transport (m2/s) |
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| 186 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_yatrp ! Y-component of area transport (m2/s) |
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| 187 | !!------------------------------------------------------------------- |
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| 188 | |
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| 189 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_eap: EAP sea-ice rheology' |
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| 190 | ! |
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| 191 | !!gm for Clem: OPTIMIZATION: I think zfmask can be computed one for all at the initialization.... |
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| 192 | !------------------------------------------------------------------------------! |
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| 193 | ! 0) mask at F points for the ice |
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| 194 | !------------------------------------------------------------------------------! |
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| 195 | ! ocean/land mask |
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| 196 | DO jj = 1, jpjm1 |
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| 197 | DO ji = 1, jpim1 ! NO vector opt. |
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| 198 | 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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| 199 | END DO |
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| 200 | END DO |
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| 201 | CALL lbc_lnk( 'icedyn_rhg_eap', zfmask, 'F', 1._wp ) |
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| 202 | |
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| 203 | ! Lateral boundary conditions on velocity (modify zfmask) |
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| 204 | zwf(:,:) = zfmask(:,:) |
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| 205 | DO jj = 2, jpjm1 |
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| 206 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 207 | IF( zfmask(ji,jj) == 0._wp ) THEN |
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| 208 | zfmask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,jj), zwf(ji,jj+1), zwf(ji-1,jj), zwf(ji,jj-1) ) ) |
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| 209 | ENDIF |
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| 210 | END DO |
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| 211 | END DO |
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| 212 | DO jj = 2, jpjm1 |
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| 213 | IF( zfmask(1,jj) == 0._wp ) THEN |
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| 214 | zfmask(1 ,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(2,jj), zwf(1,jj+1), zwf(1,jj-1) ) ) |
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| 215 | ENDIF |
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| 216 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
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| 217 | zfmask(jpi,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(jpi,jj+1), zwf(jpim1,jj), zwf(jpi,jj-1) ) ) |
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| 218 | ENDIF |
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| 219 | END DO |
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| 220 | DO ji = 2, jpim1 |
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| 221 | IF( zfmask(ji,1) == 0._wp ) THEN |
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| 222 | zfmask(ji,1 ) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,1), zwf(ji,2), zwf(ji-1,1) ) ) |
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| 223 | ENDIF |
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| 224 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
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| 225 | zfmask(ji,jpj) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,jpj), zwf(ji-1,jpj), zwf(ji,jpjm1) ) ) |
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| 226 | ENDIF |
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| 227 | END DO |
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| 228 | CALL lbc_lnk( 'icedyn_rhg_eap', zfmask, 'F', 1._wp ) |
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| 229 | |
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| 230 | !------------------------------------------------------------------------------! |
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| 231 | ! 1) define some variables and initialize arrays |
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| 232 | !------------------------------------------------------------------------------! |
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| 233 | zrhoco = rau0 * rn_cio |
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| 234 | |
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| 235 | ! ecc2: square of yield ellipse eccenticrity |
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| 236 | ecc2 = rn_ecc * rn_ecc |
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| 237 | z1_ecc2 = 1._wp / ecc2 |
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| 238 | |
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| 239 | ! Time step for subcycling |
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| 240 | zdtevp = rdt_ice / REAL( nn_nevp ) |
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| 241 | z1_dtevp = 1._wp / zdtevp |
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| 242 | |
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| 243 | ! alpha parameters (Bouillon 2009) |
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| 244 | IF( .NOT. ln_aEVP ) THEN |
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| 245 | zalph1 = ( 2._wp * rn_relast * rdt_ice ) * z1_dtevp |
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| 246 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
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| 247 | ENDIF |
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| 248 | |
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| 249 | ! Initialise stress tensor |
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| 250 | zs1 (:,:) = pstress1_i (:,:) |
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| 251 | zs2 (:,:) = pstress2_i (:,:) |
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| 252 | zs12(:,:) = pstress12_i(:,:) |
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| 253 | |
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| 254 | ! Ice strength |
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| 255 | CALL ice_strength |
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| 256 | |
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| 257 | ! landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) |
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| 258 | IF( ln_landfast_L16 ) THEN ; zkt = rn_tensile |
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| 259 | ELSE ; zkt = 0._wp |
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| 260 | ENDIF |
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| 261 | ! |
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| 262 | !------------------------------------------------------------------------------! |
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| 263 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
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| 264 | !------------------------------------------------------------------------------! |
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| 265 | ! sea surface height |
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| 266 | ! embedded sea ice: compute representative ice top surface |
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| 267 | ! non-embedded sea ice: use ocean surface for slope calculation |
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| 268 | zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) |
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| 269 | |
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| 270 | DO jj = 2, jpjm1 |
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| 271 | DO ji = fs_2, fs_jpim1 |
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| 272 | |
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| 273 | ! ice fraction at U-V points |
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| 274 | 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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| 275 | 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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| 276 | |
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| 277 | ! Ice/snow mass at U-V points |
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| 278 | zm1 = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) ) |
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| 279 | zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) ) |
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| 280 | zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) ) |
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| 281 | 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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| 282 | 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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| 283 | |
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| 284 | ! Ocean currents at U-V points |
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| 285 | 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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| 286 | 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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| 287 | |
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| 288 | ! Coriolis at T points (m*f) |
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| 289 | zmf(ji,jj) = zm1 * ff_t(ji,jj) |
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| 290 | |
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| 291 | ! dt/m at T points (for alpha and beta coefficients) |
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| 292 | zdt_m(ji,jj) = zdtevp / MAX( zm1, zmmin ) |
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| 293 | |
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| 294 | ! m/dt |
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| 295 | zmU_t(ji,jj) = zmassU * z1_dtevp |
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| 296 | zmV_t(ji,jj) = zmassV * z1_dtevp |
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| 297 | |
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| 298 | ! Drag ice-atm. |
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| 299 | ztaux_ai(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj) |
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| 300 | ztauy_ai(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj) |
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| 301 | |
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| 302 | ! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points |
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| 303 | zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) |
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| 304 | zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) |
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| 305 | |
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| 306 | ! masks |
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| 307 | zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
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| 308 | zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
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| 309 | |
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| 310 | ! switches |
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| 311 | IF( zmassU <= zmmin .AND. zaU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp |
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| 312 | ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF |
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| 313 | IF( zmassV <= zmmin .AND. zaV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp |
|---|
| 314 | ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF |
|---|
| 315 | |
|---|
| 316 | END DO |
|---|
| 317 | END DO |
|---|
| 318 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zmf, 'T', 1., zdt_m, 'T', 1. ) |
|---|
| 319 | ! |
|---|
| 320 | ! !== Landfast ice parameterization ==! |
|---|
| 321 | ! |
|---|
| 322 | IF( ln_landfast_L16 ) THEN !-- Lemieux 2016 |
|---|
| 323 | DO jj = 2, jpjm1 |
|---|
| 324 | DO ji = fs_2, fs_jpim1 |
|---|
| 325 | ! ice thickness at U-V points |
|---|
| 326 | 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) |
|---|
| 327 | 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) |
|---|
| 328 | ! ice-bottom stress at U points |
|---|
| 329 | zvCr = zaU(ji,jj) * rn_depfra * hu_n(ji,jj) |
|---|
| 330 | ztaux_base(ji,jj) = - rn_icebfr * MAX( 0._wp, zvU - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaU(ji,jj) ) ) |
|---|
| 331 | ! ice-bottom stress at V points |
|---|
| 332 | zvCr = zaV(ji,jj) * rn_depfra * hv_n(ji,jj) |
|---|
| 333 | ztauy_base(ji,jj) = - rn_icebfr * MAX( 0._wp, zvV - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaV(ji,jj) ) ) |
|---|
| 334 | ! ice_bottom stress at T points |
|---|
| 335 | zvCr = at_i(ji,jj) * rn_depfra * ht_n(ji,jj) |
|---|
| 336 | tau_icebfr(ji,jj) = - rn_icebfr * MAX( 0._wp, vt_i(ji,jj) - zvCr ) * EXP( -rn_crhg * ( 1._wp - at_i(ji,jj) ) ) |
|---|
| 337 | END DO |
|---|
| 338 | END DO |
|---|
| 339 | CALL lbc_lnk( 'icedyn_rhg_eap', tau_icebfr(:,:), 'T', 1. ) |
|---|
| 340 | ! |
|---|
| 341 | ELSE !-- no landfast |
|---|
| 342 | DO jj = 2, jpjm1 |
|---|
| 343 | DO ji = fs_2, fs_jpim1 |
|---|
| 344 | ztaux_base(ji,jj) = 0._wp |
|---|
| 345 | ztauy_base(ji,jj) = 0._wp |
|---|
| 346 | END DO |
|---|
| 347 | END DO |
|---|
| 348 | ENDIF |
|---|
| 349 | |
|---|
| 350 | !------------------------------------------------------------------------------! |
|---|
| 351 | ! 3) Solution of the momentum equation, iterative procedure |
|---|
| 352 | !------------------------------------------------------------------------------! |
|---|
| 353 | ! |
|---|
| 354 | ! ! ==================== ! |
|---|
| 355 | DO jter = 1 , nn_nevp ! loop over jter ! |
|---|
| 356 | ! ! ==================== ! |
|---|
| 357 | l_full_nf_update = jter == nn_nevp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 |
|---|
| 358 | ! |
|---|
| 359 | !!$ IF(ln_ctl) THEN ! Convergence test |
|---|
| 360 | !!$ DO jj = 1, jpjm1 |
|---|
| 361 | !!$ zu_ice(:,jj) = u_ice(:,jj) ! velocity at previous time step |
|---|
| 362 | !!$ zv_ice(:,jj) = v_ice(:,jj) |
|---|
| 363 | !!$ END DO |
|---|
| 364 | !!$ ENDIF |
|---|
| 365 | |
|---|
| 366 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 367 | DO jj = 1, jpjm1 ! loops start at 1 since there is no boundary condition (lbc_lnk) at i=1 and j=1 for F points |
|---|
| 368 | DO ji = 1, jpim1 |
|---|
| 369 | |
|---|
| 370 | ! shear at F points |
|---|
| 371 | 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) & |
|---|
| 372 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 373 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 374 | |
|---|
| 375 | END DO |
|---|
| 376 | END DO |
|---|
| 377 | CALL lbc_lnk( 'icedyn_rhg_eap', zds, 'F', 1. ) |
|---|
| 378 | |
|---|
| 379 | DO jj = 2, jpj ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 |
|---|
| 380 | DO ji = 2, jpi ! no vector loop |
|---|
| 381 | |
|---|
| 382 | ! shear at T points |
|---|
| 383 | zdsT = ( zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 384 | & + zds(ji,jj-1) * e1e2f(ji,jj-1) + zds(ji-1,jj-1) * e1e2f(ji-1,jj-1) & |
|---|
| 385 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 386 | |
|---|
| 387 | ! shear**2 at T points (doc eq. A16) |
|---|
| 388 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 389 | & + 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) & |
|---|
| 390 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 391 | |
|---|
| 392 | ! divergence at T points |
|---|
| 393 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 394 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 395 | & ) * r1_e1e2t(ji,jj) |
|---|
| 396 | zdiv2 = zdiv * zdiv |
|---|
| 397 | |
|---|
| 398 | ! tension at T points |
|---|
| 399 | 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) & |
|---|
| 400 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 401 | & ) * r1_e1e2t(ji,jj) |
|---|
| 402 | zdt2 = zdt * zdt |
|---|
| 403 | |
|---|
| 404 | ! --- anisotropic stress calculation --- ! |
|---|
| 405 | CALL update_stress_rdg (jter, nn_nevp, phi, zdiv, zdt, & |
|---|
| 406 | zdsT, paniso_11(ji,jj), paniso_12(ji,jj), & |
|---|
| 407 | stressptmp, stressmtmp, & |
|---|
| 408 | stress12tmp(ji,jj), strength(ji,jj), & |
|---|
| 409 | alphar, alphas) |
|---|
| 410 | IF (jter == nn_nevp) THEN |
|---|
| 411 | rdg_conv(ji,jj) = -min( alphar, 0._wp) |
|---|
| 412 | ENDIF |
|---|
| 413 | |
|---|
| 414 | ! delta at T points |
|---|
| 415 | zdelta = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 416 | |
|---|
| 417 | ! P/delta at T points |
|---|
| 418 | zp_delt(ji,jj) = strength(ji,jj) / ( zdelta + rn_creepl ) |
|---|
| 419 | |
|---|
| 420 | ! alpha & beta for aEVP |
|---|
| 421 | ! gamma = 0.5*P/(delta+creepl) * (c*pi)**2/Area * dt/m |
|---|
| 422 | ! alpha = beta = sqrt(4*gamma) |
|---|
| 423 | !IF( ln_aEVP ) THEN |
|---|
| 424 | ! zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 425 | ! z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 426 | !ENDIF |
|---|
| 427 | |
|---|
| 428 | ! stress at T points (zkt/=0 if landfast) |
|---|
| 429 | !zs1(ji,jj) = ( zs1(ji,jj) * zalph1 + zp_delt(ji,jj) * ( zdiv * (1._wp + zkt) - zdelta * (1._wp - zkt) ) ) * z1_alph1 |
|---|
| 430 | !zs2(ji,jj) = ( zs2(ji,jj) * zalph2 + zp_delt(ji,jj) * ( zdt * z1_ecc2 * (1._wp + zkt) ) ) * z1_alph2 |
|---|
| 431 | zs1(ji,jj) = ( zs1(ji,jj) + stressptmp * zalph1 ) * z1_alph1 |
|---|
| 432 | zs2(ji,jj) = ( zs2(ji,jj) + stressmtmp * zalph1 ) * z1_alph1 |
|---|
| 433 | !zs1(ji,jj) = ( stressptmp * zs1(ji,jj) + zalph1 ) * z1_alph1 |
|---|
| 434 | !zs2(ji,jj) = ( stressmtmp * zs2(ji,jj) + zalph1 ) * z1_alph1 |
|---|
| 435 | !WRITE(numout,*) 'stress output', ji, jj, zs1(ji,jj) |
|---|
| 436 | END DO |
|---|
| 437 | END DO |
|---|
| 438 | !CALL lbc_lnk( 'icedyn_rhg_eap', zp_delt, 'T', 1. ) |
|---|
| 439 | CALL lbc_lnk( 'icedyn_rhg_eap', stress12tmp, 'T', 1. ) |
|---|
| 440 | |
|---|
| 441 | DO jj = 1, jpjm1 |
|---|
| 442 | DO ji = 1, jpim1 |
|---|
| 443 | ! stress12tmp at F points |
|---|
| 444 | stress12tmpF = ( stress12tmp(ji,jj+1) * e1e2t(ji,jj+1) + stress12tmp(ji+1,jj+1) * e1e2t(ji+1,jj+1) & |
|---|
| 445 | & + stress12tmp(ji,jj ) * e1e2t(ji,jj ) + stress12tmp(ji+1,jj ) * e1e2t(ji+1,jj ) & |
|---|
| 446 | & ) * 0.25_wp * r1_e1e2f(ji,jj) |
|---|
| 447 | |
|---|
| 448 | ! alpha & beta for aEVP |
|---|
| 449 | !IF( ln_aEVP ) THEN |
|---|
| 450 | ! zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 451 | ! z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 452 | !ENDIF |
|---|
| 453 | |
|---|
| 454 | ! stress at F points (zkt/=0 if landfast) |
|---|
| 455 | !zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 * (1._wp + zkt) ) * 0.5_wp ) * z1_alph2 |
|---|
| 456 | zs12(ji,jj) = ( zs12(ji,jj) + stress12tmpF * zalph1 ) * z1_alph1 |
|---|
| 457 | !zs12(ji,jj) = ( stress12tmpF * zs12(ji,jj) + zalph1 ) * z1_alph1 |
|---|
| 458 | |
|---|
| 459 | END DO |
|---|
| 460 | END DO |
|---|
| 461 | |
|---|
| 462 | ! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- ! |
|---|
| 463 | DO jj = 2, jpjm1 |
|---|
| 464 | DO ji = fs_2, fs_jpim1 |
|---|
| 465 | ! !--- U points |
|---|
| 466 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 467 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 468 | & ) * r1_e2u(ji,jj) & |
|---|
| 469 | & + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 470 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 471 | & ) * r1_e1e2u(ji,jj) |
|---|
| 472 | ! |
|---|
| 473 | ! !--- V points |
|---|
| 474 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 475 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 476 | & ) * r1_e1v(ji,jj) & |
|---|
| 477 | & + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 478 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 479 | & ) * r1_e1e2v(ji,jj) |
|---|
| 480 | ! |
|---|
| 481 | ! !--- ice currents at U-V point |
|---|
| 482 | 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) |
|---|
| 483 | 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) |
|---|
| 484 | ! |
|---|
| 485 | END DO |
|---|
| 486 | END DO |
|---|
| 487 | ! |
|---|
| 488 | ! --- Computation of ice velocity --- ! |
|---|
| 489 | ! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta vary as in Kimmritz 2016 & 2017 |
|---|
| 490 | ! Bouillon et al. 2009 (eq 34-35) => stable |
|---|
| 491 | IF( MOD(jter,2) == 0 ) THEN ! even iterations |
|---|
| 492 | ! |
|---|
| 493 | DO jj = 2, jpjm1 |
|---|
| 494 | DO ji = fs_2, fs_jpim1 |
|---|
| 495 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 496 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 497 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 498 | ! !--- Ocean-to-Ice stress |
|---|
| 499 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 500 | ! |
|---|
| 501 | ! !--- tau_bottom/v_ice |
|---|
| 502 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 503 | zTauB = ztauy_base(ji,jj) / zvel |
|---|
| 504 | ! !--- OceanBottom-to-Ice stress |
|---|
| 505 | ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj) |
|---|
| 506 | ! |
|---|
| 507 | ! !--- Coriolis at V-points (energy conserving formulation) |
|---|
| 508 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 509 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 510 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 511 | ! |
|---|
| 512 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 513 | zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 514 | ! |
|---|
| 515 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 516 | ! 1 = sliding friction : TauB < RHS |
|---|
| 517 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 518 | ! |
|---|
| 519 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 520 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbeta(ji,jj) * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 521 | & + zRHS + zTauO * v_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 522 | & / MAX( zepsi, zmV_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 523 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 524 | & ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 525 | & ) * zmsk00y(ji,jj) |
|---|
| 526 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 527 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 528 | & + zRHS + zTauO * v_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 529 | & / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 530 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 531 | & ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 532 | & ) * zmsk00y(ji,jj) |
|---|
| 533 | ENDIF |
|---|
| 534 | END DO |
|---|
| 535 | END DO |
|---|
| 536 | CALL lbc_lnk( 'icedyn_rhg_eap', v_ice, 'V', -1. ) |
|---|
| 537 | ! |
|---|
| 538 | #if defined key_agrif |
|---|
| 539 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 540 | CALL agrif_interp_ice( 'V' ) |
|---|
| 541 | #endif |
|---|
| 542 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 543 | ! |
|---|
| 544 | DO jj = 2, jpjm1 |
|---|
| 545 | DO ji = fs_2, fs_jpim1 |
|---|
| 546 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 547 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 548 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 549 | ! !--- Ocean-to-Ice stress |
|---|
| 550 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 551 | ! |
|---|
| 552 | ! !--- tau_bottom/u_ice |
|---|
| 553 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 554 | zTauB = ztaux_base(ji,jj) / zvel |
|---|
| 555 | ! !--- OceanBottom-to-Ice stress |
|---|
| 556 | ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj) |
|---|
| 557 | ! |
|---|
| 558 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 559 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 560 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 561 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 562 | ! |
|---|
| 563 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 564 | zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 565 | ! |
|---|
| 566 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 567 | ! 1 = sliding friction : TauB < RHS |
|---|
| 568 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 569 | ! |
|---|
| 570 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 571 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbeta(ji,jj) * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 572 | & + zRHS + zTauO * u_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 573 | & / MAX( zepsi, zmU_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 574 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 575 | & ) * 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 |
|---|
| 576 | & ) * zmsk00x(ji,jj) |
|---|
| 577 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 578 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 579 | & + zRHS + zTauO * u_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 580 | & / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 581 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 582 | & ) * 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 |
|---|
| 583 | & ) * zmsk00x(ji,jj) |
|---|
| 584 | ENDIF |
|---|
| 585 | END DO |
|---|
| 586 | END DO |
|---|
| 587 | CALL lbc_lnk( 'icedyn_rhg_eap', u_ice, 'U', -1. ) |
|---|
| 588 | ! |
|---|
| 589 | #if defined key_agrif |
|---|
| 590 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 591 | CALL agrif_interp_ice( 'U' ) |
|---|
| 592 | #endif |
|---|
| 593 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 594 | ! |
|---|
| 595 | ELSE ! odd iterations |
|---|
| 596 | ! |
|---|
| 597 | DO jj = 2, jpjm1 |
|---|
| 598 | DO ji = fs_2, fs_jpim1 |
|---|
| 599 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 600 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 601 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 602 | ! !--- Ocean-to-Ice stress |
|---|
| 603 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 604 | ! |
|---|
| 605 | ! !--- tau_bottom/u_ice |
|---|
| 606 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 607 | zTauB = ztaux_base(ji,jj) / zvel |
|---|
| 608 | ! !--- OceanBottom-to-Ice stress |
|---|
| 609 | ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj) |
|---|
| 610 | ! |
|---|
| 611 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 612 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 613 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 614 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 615 | ! |
|---|
| 616 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 617 | zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 618 | ! |
|---|
| 619 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 620 | ! 1 = sliding friction : TauB < RHS |
|---|
| 621 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 622 | ! |
|---|
| 623 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 624 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbeta(ji,jj) * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 625 | & + zRHS + zTauO * u_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 626 | & / MAX( zepsi, zmU_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 627 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 628 | & ) * 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 |
|---|
| 629 | & ) * zmsk00x(ji,jj) |
|---|
| 630 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 631 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 632 | & + zRHS + zTauO * u_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 633 | & / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 634 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 635 | & ) * 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 |
|---|
| 636 | & ) * zmsk00x(ji,jj) |
|---|
| 637 | ENDIF |
|---|
| 638 | END DO |
|---|
| 639 | END DO |
|---|
| 640 | CALL lbc_lnk( 'icedyn_rhg_eap', u_ice, 'U', -1. ) |
|---|
| 641 | ! |
|---|
| 642 | #if defined key_agrif |
|---|
| 643 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 644 | CALL agrif_interp_ice( 'U' ) |
|---|
| 645 | #endif |
|---|
| 646 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 647 | ! |
|---|
| 648 | DO jj = 2, jpjm1 |
|---|
| 649 | DO ji = fs_2, fs_jpim1 |
|---|
| 650 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 651 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 652 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 653 | ! !--- Ocean-to-Ice stress |
|---|
| 654 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 655 | ! |
|---|
| 656 | ! !--- tau_bottom/v_ice |
|---|
| 657 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 658 | zTauB = ztauy_base(ji,jj) / zvel |
|---|
| 659 | ! !--- OceanBottom-to-Ice stress |
|---|
| 660 | ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj) |
|---|
| 661 | ! |
|---|
| 662 | ! !--- Coriolis at v-points (energy conserving formulation) |
|---|
| 663 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 664 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 665 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 666 | ! |
|---|
| 667 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 668 | zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 669 | ! |
|---|
| 670 | ! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS) |
|---|
| 671 | ! 1 = sliding friction : TauB < RHS |
|---|
| 672 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) ) |
|---|
| 673 | ! |
|---|
| 674 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 675 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbeta(ji,jj) * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 676 | & + zRHS + zTauO * v_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 677 | & / MAX( zepsi, zmV_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 678 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 679 | & ) * 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 |
|---|
| 680 | & ) * zmsk00y(ji,jj) |
|---|
| 681 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 682 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 683 | & + zRHS + zTauO * v_ice(ji,jj) ) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 684 | & / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 685 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 686 | & ) * 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 |
|---|
| 687 | & ) * zmsk00y(ji,jj) |
|---|
| 688 | ENDIF |
|---|
| 689 | END DO |
|---|
| 690 | END DO |
|---|
| 691 | CALL lbc_lnk( 'icedyn_rhg_eap', v_ice, 'V', -1. ) |
|---|
| 692 | ! |
|---|
| 693 | #if defined key_agrif |
|---|
| 694 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 695 | CALL agrif_interp_ice( 'V' ) |
|---|
| 696 | #endif |
|---|
| 697 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 698 | ! |
|---|
| 699 | ENDIF |
|---|
| 700 | |
|---|
| 701 | !!$ IF(ln_ctl) THEN ! Convergence test |
|---|
| 702 | !!$ DO jj = 2 , jpjm1 |
|---|
| 703 | !!$ zresr(:,jj) = MAX( ABS( u_ice(:,jj) - zu_ice(:,jj) ), ABS( v_ice(:,jj) - zv_ice(:,jj) ) ) |
|---|
| 704 | !!$ END DO |
|---|
| 705 | !!$ zresm = MAXVAL( zresr( 1:jpi, 2:jpjm1 ) ) |
|---|
| 706 | !!$ CALL mpp_max( 'icedyn_rhg_eap', zresm ) ! max over the global domain |
|---|
| 707 | !!$ ENDIF |
|---|
| 708 | ! |
|---|
| 709 | ! ! ==================== ! |
|---|
| 710 | END DO ! end loop over jter ! |
|---|
| 711 | ! ! ==================== ! |
|---|
| 712 | ! |
|---|
| 713 | !------------------------------------------------------------------------------! |
|---|
| 714 | ! 4) Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 715 | !------------------------------------------------------------------------------! |
|---|
| 716 | DO jj = 1, jpjm1 |
|---|
| 717 | DO ji = 1, jpim1 |
|---|
| 718 | |
|---|
| 719 | ! shear at F points |
|---|
| 720 | 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) & |
|---|
| 721 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 722 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 723 | |
|---|
| 724 | END DO |
|---|
| 725 | END DO |
|---|
| 726 | |
|---|
| 727 | DO jj = 2, jpjm1 |
|---|
| 728 | DO ji = 2, jpim1 ! no vector loop |
|---|
| 729 | |
|---|
| 730 | ! tension**2 at T points |
|---|
| 731 | 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) & |
|---|
| 732 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 733 | & ) * r1_e1e2t(ji,jj) |
|---|
| 734 | zdt2 = zdt * zdt |
|---|
| 735 | |
|---|
| 736 | ! shear**2 at T points (doc eq. A16) |
|---|
| 737 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 738 | & + 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) & |
|---|
| 739 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 740 | |
|---|
| 741 | ! shear at T points |
|---|
| 742 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
|---|
| 743 | |
|---|
| 744 | ! divergence at T points |
|---|
| 745 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 746 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 747 | & ) * r1_e1e2t(ji,jj) |
|---|
| 748 | |
|---|
| 749 | ! delta at T points |
|---|
| 750 | zdelta = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 751 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 |
|---|
| 752 | pdelta_i(ji,jj) = zdelta + rn_creepl * rswitch |
|---|
| 753 | |
|---|
| 754 | END DO |
|---|
| 755 | END DO |
|---|
| 756 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', pshear_i, 'T', 1., pdivu_i, 'T', 1., pdelta_i, 'T', 1. ) |
|---|
| 757 | !CALL lbc_lnk_multi( 'icedyn_rhg_eap', pshear_i, 'T', 1., pdivu_i, 'T', 1. ) |
|---|
| 758 | |
|---|
| 759 | ! --- Store the stress tensor for the next time step --- ! |
|---|
| 760 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zs1, 'T', 1., zs2, 'T', 1., zs12, 'F', 1. ) |
|---|
| 761 | pstress1_i (:,:) = zs1 (:,:) |
|---|
| 762 | pstress2_i (:,:) = zs2 (:,:) |
|---|
| 763 | pstress12_i(:,:) = zs12(:,:) |
|---|
| 764 | ! |
|---|
| 765 | |
|---|
| 766 | !------------------------------------------------------------------------------! |
|---|
| 767 | ! 5) diagnostics |
|---|
| 768 | !------------------------------------------------------------------------------! |
|---|
| 769 | DO jj = 1, jpj |
|---|
| 770 | DO ji = 1, jpi |
|---|
| 771 | zmsk00(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice, 0 if no ice |
|---|
| 772 | END DO |
|---|
| 773 | END DO |
|---|
| 774 | |
|---|
| 775 | ! --- ice-ocean, ice-atm. & ice-oceanbottom(landfast) stresses --- ! |
|---|
| 776 | IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. & |
|---|
| 777 | & iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN |
|---|
| 778 | ! |
|---|
| 779 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', ztaux_oi, 'U', -1., ztauy_oi, 'V', -1., ztaux_ai, 'U', -1., ztauy_ai, 'V', -1., & |
|---|
| 780 | & ztaux_bi, 'U', -1., ztauy_bi, 'V', -1. ) |
|---|
| 781 | ! |
|---|
| 782 | CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 ) |
|---|
| 783 | CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 ) |
|---|
| 784 | CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 ) |
|---|
| 785 | CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 ) |
|---|
| 786 | CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 ) |
|---|
| 787 | CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 ) |
|---|
| 788 | ENDIF |
|---|
| 789 | |
|---|
| 790 | ! --- divergence, shear and strength --- ! |
|---|
| 791 | IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence |
|---|
| 792 | IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! shear |
|---|
| 793 | IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength |
|---|
| 794 | |
|---|
| 795 | ! --- stress tensor --- ! |
|---|
| 796 | IF( iom_use('isig1') .OR. iom_use('isig2') .OR. iom_use('isig3') .OR. iom_use('normstr') .OR. iom_use('sheastr') ) THEN |
|---|
| 797 | ! |
|---|
| 798 | ALLOCATE( zsig1(jpi,jpj) , zsig2(jpi,jpj) , zsig3(jpi,jpj) ) |
|---|
| 799 | ! |
|---|
| 800 | DO jj = 2, jpjm1 |
|---|
| 801 | DO ji = 2, jpim1 |
|---|
| 802 | zdum1 = ( zmsk00(ji-1,jj) * pstress12_i(ji-1,jj) + zmsk00(ji ,jj-1) * pstress12_i(ji ,jj-1) + & ! stress12_i at T-point |
|---|
| 803 | & zmsk00(ji ,jj) * pstress12_i(ji ,jj) + zmsk00(ji-1,jj-1) * pstress12_i(ji-1,jj-1) ) & |
|---|
| 804 | & / MAX( 1._wp, zmsk00(ji-1,jj) + zmsk00(ji,jj-1) + zmsk00(ji,jj) + zmsk00(ji-1,jj-1) ) |
|---|
| 805 | |
|---|
| 806 | zshear = SQRT( pstress2_i(ji,jj) * pstress2_i(ji,jj) + 4._wp * zdum1 * zdum1 ) ! shear stress |
|---|
| 807 | |
|---|
| 808 | zdum2 = zmsk00(ji,jj) / MAX( 1._wp, strength(ji,jj) ) |
|---|
| 809 | |
|---|
| 810 | !! zsig1(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) + zshear ) ! principal stress (y-direction, see Hunke & Dukowicz 2002) |
|---|
| 811 | !! zsig2(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) - zshear ) ! principal stress (x-direction, see Hunke & Dukowicz 2002) |
|---|
| 812 | !! zsig3(ji,jj) = zdum2**2 * ( ( pstress1_i(ji,jj) + strength(ji,jj) )**2 + ( rn_ecc * zshear )**2 ) ! quadratic relation linking compressive stress to shear stress |
|---|
| 813 | !! ! (scheme converges if this value is ~1, see Bouillon et al 2009 (eq. 11)) |
|---|
| 814 | zsig1(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) ) ! compressive stress, see Bouillon et al. 2015 |
|---|
| 815 | zsig2(ji,jj) = 0.5_wp * zdum2 * ( zshear ) ! shear stress |
|---|
| 816 | zsig3(ji,jj) = zdum2**2 * ( ( pstress1_i(ji,jj) + strength(ji,jj) )**2 + ( rn_ecc * zshear )**2 ) |
|---|
| 817 | END DO |
|---|
| 818 | END DO |
|---|
| 819 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zsig1, 'T', 1., zsig2, 'T', 1., zsig3, 'T', 1. ) |
|---|
| 820 | ! |
|---|
| 821 | CALL iom_put( 'isig1' , zsig1 ) |
|---|
| 822 | CALL iom_put( 'isig2' , zsig2 ) |
|---|
| 823 | CALL iom_put( 'isig3' , zsig3 ) |
|---|
| 824 | ! |
|---|
| 825 | ! Stress tensor invariants (normal and shear stress N/m) |
|---|
| 826 | IF( iom_use('normstr') ) CALL iom_put( 'normstr' , ( zs1(:,:) + zs2(:,:) ) * zmsk00(:,:) ) ! Normal stress |
|---|
| 827 | IF( iom_use('sheastr') ) CALL iom_put( 'sheastr' , SQRT( ( zs1(:,:) - zs2(:,:) )**2 + 4*zs12(:,:)**2 ) * zmsk00(:,:) ) ! Shear stress |
|---|
| 828 | |
|---|
| 829 | DEALLOCATE( zsig1 , zsig2 , zsig3 ) |
|---|
| 830 | ENDIF |
|---|
| 831 | |
|---|
| 832 | ! --- anisotropy tensor --- ! |
|---|
| 833 | IF( iom_use('aniso') ) THEN |
|---|
| 834 | CALL iom_put( 'aniso' , aniso_11 * zmsk00 ) |
|---|
| 835 | ENDIF |
|---|
| 836 | |
|---|
| 837 | ! --- SIMIP --- ! |
|---|
| 838 | IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. & |
|---|
| 839 | & iom_use('corstrx') .OR. iom_use('corstry') .OR. iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 840 | ! |
|---|
| 841 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zspgU, 'U', -1., zspgV, 'V', -1., & |
|---|
| 842 | & zCorU, 'U', -1., zCorV, 'V', -1., zfU, 'U', -1., zfV, 'V', -1. ) |
|---|
| 843 | |
|---|
| 844 | CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x) |
|---|
| 845 | CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y) |
|---|
| 846 | CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x) |
|---|
| 847 | CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y) |
|---|
| 848 | CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x) |
|---|
| 849 | CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y) |
|---|
| 850 | ENDIF |
|---|
| 851 | |
|---|
| 852 | IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. & |
|---|
| 853 | & iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN |
|---|
| 854 | ! |
|---|
| 855 | ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 856 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) ) |
|---|
| 857 | ! |
|---|
| 858 | DO jj = 2, jpjm1 |
|---|
| 859 | DO ji = 2, jpim1 |
|---|
| 860 | ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 861 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj) |
|---|
| 862 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj) |
|---|
| 863 | |
|---|
| 864 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 865 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 866 | |
|---|
| 867 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 868 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 869 | |
|---|
| 870 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 871 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 872 | |
|---|
| 873 | END DO |
|---|
| 874 | END DO |
|---|
| 875 | |
|---|
| 876 | CALL lbc_lnk_multi( 'icedyn_rhg_eap', zdiag_xmtrp_ice, 'U', -1., zdiag_ymtrp_ice, 'V', -1., & |
|---|
| 877 | & zdiag_xmtrp_snw, 'U', -1., zdiag_ymtrp_snw, 'V', -1., & |
|---|
| 878 | & zdiag_xatrp , 'U', -1., zdiag_yatrp , 'V', -1. ) |
|---|
| 879 | |
|---|
| 880 | CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 881 | CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport |
|---|
| 882 | CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s) |
|---|
| 883 | CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport |
|---|
| 884 | CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport |
|---|
| 885 | CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport |
|---|
| 886 | |
|---|
| 887 | DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 888 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 889 | |
|---|
| 890 | ENDIF |
|---|
| 891 | ! |
|---|
| 892 | END SUBROUTINE ice_dyn_rhg_eap |
|---|
| 893 | |
|---|
| 894 | SUBROUTINE update_stress_rdg (ksub, ndte, phi, divu, tension, & |
|---|
| 895 | shear, a11, a12, & |
|---|
| 896 | stressp, stressm, & |
|---|
| 897 | stress12, strength, & |
|---|
| 898 | alphar, alphas) |
|---|
| 899 | !!--------------------------------------------------------------------- |
|---|
| 900 | !! *** SUBROUTINE rhg_eap_rst *** |
|---|
| 901 | !! Updates the stress depending on values of strain rate and structure |
|---|
| 902 | !! tensor and for ksub=ndte it computes closing and sliding rate |
|---|
| 903 | !!--------------------------------------------------------------------- |
|---|
| 904 | INTEGER, INTENT(in ) :: ksub, ndte |
|---|
| 905 | REAL(wp), INTENT(in ) :: phi, strength |
|---|
| 906 | REAL(wp), INTENT(in ) :: divu, tension, shear |
|---|
| 907 | REAL(wp), INTENT(in ) :: a11, a12 |
|---|
| 908 | REAL(wp), INTENT( out) :: stressp, stressm, stress12 |
|---|
| 909 | REAL(wp), INTENT( out) :: alphar, alphas |
|---|
| 910 | |
|---|
| 911 | INTEGER :: kx ,ky, ka |
|---|
| 912 | |
|---|
| 913 | REAL(wp) :: stemp11r, stemp12r, stemp22r |
|---|
| 914 | REAL(wp) :: stemp11s, stemp12s, stemp22s |
|---|
| 915 | REAL(wp) :: a22, Qd11Qd11, Qd11Qd12, Qd12Qd12 |
|---|
| 916 | REAL(wp) :: Q11Q11, Q11Q12, Q12Q12 |
|---|
| 917 | REAL(wp) :: dtemp11, dtemp12, dtemp22 |
|---|
| 918 | REAL(wp) :: rotstemp11r, rotstemp12r, rotstemp22r |
|---|
| 919 | REAL(wp) :: rotstemp11s, rotstemp12s, rotstemp22s |
|---|
| 920 | REAL(wp) :: sig11, sig12, sig22 |
|---|
| 921 | REAL(wp) :: sgprm11, sgprm12, sgprm22 |
|---|
| 922 | REAL(wp) :: invstressconviso |
|---|
| 923 | REAL(wp) :: Angle_denom_gamma, Angle_denom_alpha |
|---|
| 924 | REAL(wp) :: Tany_1, Tany_2 |
|---|
| 925 | REAL(wp) :: x, y, dx, dy, da, kxw, kyw, kaw |
|---|
| 926 | REAL(wp) :: invdx, invdy, invda |
|---|
| 927 | REAL(wp) :: dtemp1, dtemp2, atempprime, a, invsin |
|---|
| 928 | |
|---|
| 929 | REAL(wp), PARAMETER :: kfriction = 0.45_wp |
|---|
| 930 | !!--------------------------------------------------------------------- |
|---|
| 931 | ! Factor to maintain the same stress as in EVP (see Section 3) |
|---|
| 932 | ! Can be set to 1 otherwise |
|---|
| 933 | invstressconviso = 1._wp/(1._wp+kfriction*kfriction) |
|---|
| 934 | |
|---|
| 935 | invsin = 1._wp/sin(2._wp*phi) * invstressconviso |
|---|
| 936 | !now uses phi as set in higher code |
|---|
| 937 | |
|---|
| 938 | ! compute eigenvalues, eigenvectors and angles for structure tensor, strain |
|---|
| 939 | ! rates |
|---|
| 940 | |
|---|
| 941 | ! 1) structure tensor |
|---|
| 942 | a22 = 1._wp-a11 |
|---|
| 943 | Q11Q11 = 1._wp |
|---|
| 944 | Q12Q12 = rsmall |
|---|
| 945 | Q11Q12 = rsmall |
|---|
| 946 | |
|---|
| 947 | ! gamma: angle between general coordiantes and principal axis of A |
|---|
| 948 | ! here Tan2gamma = 2 a12 / (a11 - a22) |
|---|
| 949 | if((ABS(a11 - a22) > rsmall).or.(ABS(a12) > rsmall)) then |
|---|
| 950 | Angle_denom_gamma = 1._wp/sqrt( ( a11 - a22 )*( a11 - a22) + & |
|---|
| 951 | 4._wp*a12*a12 ) |
|---|
| 952 | |
|---|
| 953 | Q11Q11 = 0.5_wp + ( a11 - a22 )*0.5_wp*Angle_denom_gamma !Cos^2 |
|---|
| 954 | Q12Q12 = 0.5_wp - ( a11 - a22 )*0.5_wp*Angle_denom_gamma !Sin^2 |
|---|
| 955 | Q11Q12 = a12*Angle_denom_gamma !CosSin |
|---|
| 956 | endif |
|---|
| 957 | |
|---|
| 958 | ! rotation Q*atemp*Q^T |
|---|
| 959 | atempprime = Q11Q11*a11 + 2.0_wp*Q11Q12*a12 + Q12Q12*a22 |
|---|
| 960 | |
|---|
| 961 | ! make first principal value the largest |
|---|
| 962 | atempprime = max(atempprime, 1.0_wp - atempprime) |
|---|
| 963 | |
|---|
| 964 | ! 2) strain rate |
|---|
| 965 | dtemp11 = 0.5_wp*(divu + tension) |
|---|
| 966 | dtemp12 = shear*0.5_wp |
|---|
| 967 | dtemp22 = 0.5_wp*(divu - tension) |
|---|
| 968 | |
|---|
| 969 | !WRITE(numout,*) 'div, tension, shear inside loop', ksub, divu, tension, shear |
|---|
| 970 | |
|---|
| 971 | ! here Tan2alpha = 2 dtemp12 / (dtemp11 - dtemp22) |
|---|
| 972 | |
|---|
| 973 | Qd11Qd11 = 1.0_wp |
|---|
| 974 | Qd12Qd12 = rsmall |
|---|
| 975 | Qd11Qd12 = rsmall |
|---|
| 976 | |
|---|
| 977 | if((ABS( dtemp11 - dtemp22) > rsmall).or. (ABS(dtemp12) > rsmall)) then |
|---|
| 978 | |
|---|
| 979 | Angle_denom_alpha = 1.0_wp/sqrt( ( dtemp11 - dtemp22 )* & |
|---|
| 980 | ( dtemp11 - dtemp22 ) + 4.0_wp*dtemp12*dtemp12) |
|---|
| 981 | |
|---|
| 982 | Qd11Qd11 = 0.5_wp + ( dtemp11 - dtemp22 )*0.5_wp*Angle_denom_alpha !Cos^2 |
|---|
| 983 | Qd12Qd12 = 0.5_wp - ( dtemp11 - dtemp22 )*0.5_wp*Angle_denom_alpha !Sin^2 |
|---|
| 984 | Qd11Qd12 = dtemp12*Angle_denom_alpha !CosSin |
|---|
| 985 | endif |
|---|
| 986 | |
|---|
| 987 | dtemp1 = Qd11Qd11*dtemp11 + 2.0_wp*Qd11Qd12*dtemp12 + Qd12Qd12*dtemp22 |
|---|
| 988 | dtemp2 = Qd12Qd12*dtemp11 - 2.0_wp*Qd11Qd12*dtemp12 + Qd11Qd11*dtemp22 |
|---|
| 989 | ! In cos and sin values |
|---|
| 990 | x = 0._wp |
|---|
| 991 | if ((ABS(dtemp1) > rsmall).or.(ABS(dtemp2) > rsmall)) then |
|---|
| 992 | x = atan2(dtemp2,dtemp1) |
|---|
| 993 | endif |
|---|
| 994 | |
|---|
| 995 | ! to ensure the angle lies between pi/4 and 9 pi/4 |
|---|
| 996 | if (x < rpi*0.25_wp) x = x + rpi*2.0_wp |
|---|
| 997 | |
|---|
| 998 | ! y: angle between major principal axis of strain rate and structure |
|---|
| 999 | ! tensor |
|---|
| 1000 | ! y = gamma - alpha |
|---|
| 1001 | ! Expressesed componently with |
|---|
| 1002 | ! Tany = (Singamma*Cosgamma - Sinalpha*Cosgamma)/(Cos^2gamma - Sin^alpha) |
|---|
| 1003 | |
|---|
| 1004 | Tany_1 = Q11Q12 - Qd11Qd12 |
|---|
| 1005 | Tany_2 = Q11Q11 - Qd12Qd12 |
|---|
| 1006 | |
|---|
| 1007 | y = 0._wp |
|---|
| 1008 | |
|---|
| 1009 | if ((ABS(Tany_1) > rsmall).or.(ABS(Tany_2) > rsmall)) then |
|---|
| 1010 | y = atan2(Tany_1,Tany_2) |
|---|
| 1011 | endif |
|---|
| 1012 | |
|---|
| 1013 | ! to make sure y is between 0 and pi |
|---|
| 1014 | if (y > rpi) y = y - rpi |
|---|
| 1015 | if (y < 0) y = y + rpi |
|---|
| 1016 | |
|---|
| 1017 | ! 3) update anisotropic stress tensor |
|---|
| 1018 | dx = rpi/real(nx_yield-1,kind=wp) |
|---|
| 1019 | dy = rpi/real(ny_yield-1,kind=wp) |
|---|
| 1020 | da = 0.5_wp/real(na_yield-1,kind=wp) |
|---|
| 1021 | invdx = 1._wp/dx |
|---|
| 1022 | invdy = 1._wp/dy |
|---|
| 1023 | invda = 1._wp/da |
|---|
| 1024 | |
|---|
| 1025 | ! % need 8 coords and 8 weights |
|---|
| 1026 | ! % range in kx |
|---|
| 1027 | kx = int((x-rpi*0.25_wp-rpi)*invdx) + 1 |
|---|
| 1028 | kxw = kx - (x-rpi*0.25_wp-rpi)*invdx |
|---|
| 1029 | |
|---|
| 1030 | ky = int(y*invdy) + 1 |
|---|
| 1031 | kyw = ky - y*invdy |
|---|
| 1032 | |
|---|
| 1033 | ka = int((atempprime-0.5_wp)*invda) + 1 |
|---|
| 1034 | kaw = ka - (atempprime-0.5_wp)*invda |
|---|
| 1035 | |
|---|
| 1036 | ! % Determine sigma_r(A1,Zeta,y) and sigma_s (see Section A1 of Tsamados 2013) |
|---|
| 1037 | stemp11r = kxw * kyw * kaw * s11r(kx ,ky ,ka ) & |
|---|
| 1038 | & + (1._wp-kxw) * kyw * kaw * s11r(kx+1,ky ,ka ) & |
|---|
| 1039 | & + kxw * (1._wp-kyw) * kaw * s11r(kx ,ky+1,ka ) & |
|---|
| 1040 | & + kxw * kyw * (1._wp-kaw) * s11r(kx ,ky ,ka+1) & |
|---|
| 1041 | & + (1._wp-kxw) * (1._wp-kyw) * kaw * s11r(kx+1,ky+1,ka ) & |
|---|
| 1042 | & + (1._wp-kxw) * kyw * (1._wp-kaw) * s11r(kx+1,ky ,ka+1) & |
|---|
| 1043 | & + kxw * (1._wp-kyw) * (1._wp-kaw) * s11r(kx ,ky+1,ka+1) & |
|---|
| 1044 | & + (1._wp-kxw) * (1._wp-kyw) * (1._wp-kaw) * s11r(kx+1,ky+1,ka+1) |
|---|
| 1045 | stemp12r = kxw * kyw * kaw * s12r(kx ,ky ,ka ) & |
|---|
| 1046 | & + (1._wp-kxw) * kyw * kaw * s12r(kx+1,ky ,ka ) & |
|---|
| 1047 | & + kxw * (1._wp-kyw) * kaw * s12r(kx ,ky+1,ka ) & |
|---|
| 1048 | & + kxw * kyw * (1._wp-kaw) * s12r(kx ,ky ,ka+1) & |
|---|
| 1049 | & + (1._wp-kxw) * (1._wp-kyw) * kaw * s12r(kx+1,ky+1,ka ) & |
|---|
| 1050 | & + (1._wp-kxw) * kyw * (1._wp-kaw) * s12r(kx+1,ky ,ka+1) & |
|---|
| 1051 | & + kxw * (1._wp-kyw) * (1._wp-kaw) * s12r(kx ,ky+1,ka+1) & |
|---|
| 1052 | & + (1._wp-kxw) * (1._wp-kyw) * (1._wp-kaw) * s12r(kx+1,ky+1,ka+1) |
|---|
| 1053 | stemp22r = kxw * kyw * kaw * s22r(kx ,ky ,ka ) & |
|---|
| 1054 | & + (1._wp-kxw) * kyw * kaw * s22r(kx+1,ky ,ka ) & |
|---|
| 1055 | & + kxw * (1._wp-kyw) * kaw * s22r(kx ,ky+1,ka ) & |
|---|
| 1056 | & + kxw * kyw * (1._wp-kaw) * s22r(kx ,ky ,ka+1) & |
|---|
| 1057 | & + (1._wp-kxw) * (1._wp-kyw) * kaw * s22r(kx+1,ky+1,ka ) & |
|---|
| 1058 | & + (1._wp-kxw) * kyw * (1._wp-kaw) * s22r(kx+1,ky ,ka+1) & |
|---|
| 1059 | & + kxw * (1._wp-kyw) * (1._wp-kaw) * s22r(kx ,ky+1,ka+1) & |
|---|
| 1060 | & + (1._wp-kxw) * (1._wp-kyw) * (1._wp-kaw) * s22r(kx+1,ky+1,ka+1) |
|---|
| 1061 | |
|---|
| 1062 | stemp11s = kxw * kyw * kaw * s11s(kx ,ky ,ka ) & |
|---|
| 1063 | & + (1._wp-kxw) * kyw * kaw * s11s(kx+1,ky ,ka ) & |
|---|
| 1064 | & + kxw * (1._wp-kyw) * kaw * s11s(kx ,ky+1,ka ) & |
|---|
| 1065 | & + kxw * kyw * (1._wp-kaw) * s11s(kx ,ky ,ka+1) & |
|---|
| 1066 | & + (1._wp-kxw) * (1._wp-kyw) * kaw * s11s(kx+1,ky+1,ka ) & |
|---|
| 1067 | & + (1._wp-kxw) * kyw * (1._wp-kaw) * s11s(kx+1,ky ,ka+1) & |
|---|
| 1068 | & + kxw * (1._wp-kyw) * (1._wp-kaw) * s11s(kx ,ky+1,ka+1) & |
|---|
| 1069 | & + (1._wp-kxw) * (1._wp-kyw) * (1._wp-kaw) * s11s(kx+1,ky+1,ka+1) |
|---|
| 1070 | stemp12s = kxw * kyw * kaw * s12s(kx ,ky ,ka ) & |
|---|
| 1071 | & + (1._wp-kxw) * kyw * kaw * s12s(kx+1,ky ,ka ) & |
|---|
| 1072 | & + kxw * (1._wp-kyw) * kaw * s12s(kx ,ky+1,ka ) & |
|---|
| 1073 | & + kxw * kyw * (1._wp-kaw) * s12s(kx ,ky ,ka+1) & |
|---|
| 1074 | & + (1._wp-kxw) * (1._wp-kyw) * kaw * s12s(kx+1,ky+1,ka ) & |
|---|
| 1075 | & + (1._wp-kxw) * kyw * (1._wp-kaw) * s12s(kx+1,ky ,ka+1) & |
|---|
| 1076 | & + kxw * (1._wp-kyw) * (1._wp-kaw) * s12s(kx ,ky+1,ka+1) & |
|---|
| 1077 | & + (1._wp-kxw) * (1._wp-kyw) * (1._wp-kaw) * s12s(kx+1,ky+1,ka+1) |
|---|
| 1078 | stemp22s = kxw * kyw * kaw * s22s(kx ,ky ,ka ) & |
|---|
| 1079 | & + (1._wp-kxw) * kyw * kaw * s22s(kx+1,ky ,ka ) & |
|---|
| 1080 | & + kxw * (1._wp-kyw) * kaw * s22s(kx ,ky+1,ka ) & |
|---|
| 1081 | & + kxw * kyw * (1._wp-kaw) * s22s(kx ,ky ,ka+1) & |
|---|
| 1082 | & + (1._wp-kxw) * (1._wp-kyw) * kaw * s22s(kx+1,ky+1,ka ) & |
|---|
| 1083 | & + (1._wp-kxw) * kyw * (1._wp-kaw) * s22s(kx+1,ky ,ka+1) & |
|---|
| 1084 | & + kxw * (1._wp-kyw) * (1._wp-kaw) * s22s(kx ,ky+1,ka+1) & |
|---|
| 1085 | & + (1._wp-kxw) * (1._wp-kyw) * (1._wp-kaw) * s22s(kx+1,ky+1,ka+1) |
|---|
| 1086 | |
|---|
| 1087 | ! Calculate mean ice stress over a collection of floes (Equation 3 in |
|---|
| 1088 | ! Tsamados 2013) |
|---|
| 1089 | |
|---|
| 1090 | sig11 = strength*(stemp11r + kfriction*stemp11s) * invsin |
|---|
| 1091 | sig12 = strength*(stemp12r + kfriction*stemp12s) * invsin |
|---|
| 1092 | sig22 = strength*(stemp22r + kfriction*stemp22s) * invsin |
|---|
| 1093 | |
|---|
| 1094 | !WRITE(numout,*) 'strength inside loop', strength |
|---|
| 1095 | !WRITE(numout,*) 'principal axis stress inside loop', sig11, sig12, sig22 |
|---|
| 1096 | |
|---|
| 1097 | ! Back - rotation of the stress from principal axes into general coordinates |
|---|
| 1098 | |
|---|
| 1099 | ! Update stress |
|---|
| 1100 | sgprm11 = Q11Q11*sig11 + Q12Q12*sig22 - 2._wp*Q11Q12 *sig12 |
|---|
| 1101 | sgprm12 = Q11Q12*sig11 - Q11Q12*sig22 + (Q11Q11 - Q12Q12)*sig12 |
|---|
| 1102 | sgprm22 = Q12Q12*sig11 + Q11Q11*sig22 + 2._wp*Q11Q12 *sig12 |
|---|
| 1103 | |
|---|
| 1104 | stressp = sgprm11 + sgprm22 |
|---|
| 1105 | stress12 = sgprm12 |
|---|
| 1106 | stressm = sgprm11 - sgprm22 |
|---|
| 1107 | |
|---|
| 1108 | !WRITE(numout,*) 'stress output inside loop', ksub, stressp |
|---|
| 1109 | |
|---|
| 1110 | ! Compute ridging and sliding functions in general coordinates |
|---|
| 1111 | ! (Equation 11 in Tsamados 2013) |
|---|
| 1112 | if (ksub == ndte) then |
|---|
| 1113 | rotstemp11r = Q11Q11*stemp11r - 2._wp*Q11Q12* stemp12r & |
|---|
| 1114 | + Q12Q12*stemp22r |
|---|
| 1115 | rotstemp12r = Q11Q11*stemp12r + Q11Q12*(stemp11r-stemp22r) & |
|---|
| 1116 | - Q12Q12*stemp12r |
|---|
| 1117 | rotstemp22r = Q12Q12*stemp11r + 2._wp*Q11Q12* stemp12r & |
|---|
| 1118 | + Q11Q11*stemp22r |
|---|
| 1119 | |
|---|
| 1120 | rotstemp11s = Q11Q11*stemp11s - 2._wp*Q11Q12* stemp12s & |
|---|
| 1121 | + Q12Q12*stemp22s |
|---|
| 1122 | rotstemp12s = Q11Q11*stemp12s + Q11Q12*(stemp11s-stemp22s) & |
|---|
| 1123 | - Q12Q12*stemp12s |
|---|
| 1124 | rotstemp22s = Q12Q12*stemp11s + 2._wp*Q11Q12* stemp12s & |
|---|
| 1125 | + Q11Q11*stemp22s |
|---|
| 1126 | |
|---|
| 1127 | alphar = rotstemp11r*dtemp11 + 2._wp*rotstemp12r*dtemp12 & |
|---|
| 1128 | + rotstemp22r*dtemp22 |
|---|
| 1129 | alphas = rotstemp11s*dtemp11 + 2._wp*rotstemp12s*dtemp12 & |
|---|
| 1130 | + rotstemp22s*dtemp22 |
|---|
| 1131 | endif |
|---|
| 1132 | END SUBROUTINE update_stress_rdg |
|---|
| 1133 | |
|---|
| 1134 | SUBROUTINE rhg_eap_rst( cdrw, kt ) |
|---|
| 1135 | !!--------------------------------------------------------------------- |
|---|
| 1136 | !! *** ROUTINE rhg_eap_rst *** |
|---|
| 1137 | !! |
|---|
| 1138 | !! ** Purpose : Read or write RHG file in restart file |
|---|
| 1139 | !! |
|---|
| 1140 | !! ** Method : use of IOM library |
|---|
| 1141 | !!---------------------------------------------------------------------- |
|---|
| 1142 | CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag |
|---|
| 1143 | INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step |
|---|
| 1144 | ! |
|---|
| 1145 | INTEGER :: iter ! local integer |
|---|
| 1146 | INTEGER :: id1, id2, id3, id4, id5 ! local integers |
|---|
| 1147 | INTEGER :: ix, iy, ip, iz, n, ia ! local integers |
|---|
| 1148 | |
|---|
| 1149 | INTEGER, PARAMETER :: nz = 100 |
|---|
| 1150 | |
|---|
| 1151 | REAL(wp) :: ainit, xinit, yinit, pinit, zinit |
|---|
| 1152 | REAL(wp) :: da, dx, dy, dp, dz, a1 |
|---|
| 1153 | |
|---|
| 1154 | REAL(wp), PARAMETER :: eps6 = 1.0e-6_wp |
|---|
| 1155 | !!---------------------------------------------------------------------- |
|---|
| 1156 | ! |
|---|
| 1157 | IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialize |
|---|
| 1158 | ! ! --------------- |
|---|
| 1159 | IF( ln_rstart ) THEN !* Read the restart file |
|---|
| 1160 | ! |
|---|
| 1161 | id1 = iom_varid( numrir, 'stress1_i' , ldstop = .FALSE. ) |
|---|
| 1162 | id2 = iom_varid( numrir, 'stress2_i' , ldstop = .FALSE. ) |
|---|
| 1163 | id3 = iom_varid( numrir, 'stress12_i', ldstop = .FALSE. ) |
|---|
| 1164 | id4 = iom_varid( numrir, 'aniso_11' , ldstop = .FALSE. ) |
|---|
| 1165 | id5 = iom_varid( numrir, 'aniso_12' , ldstop = .FALSE. ) |
|---|
| 1166 | ! |
|---|
| 1167 | IF( MIN( id1, id2, id3, id4, id5 ) > 0 ) THEN ! fields exist |
|---|
| 1168 | CALL iom_get( numrir, jpdom_autoglo, 'stress1_i' , stress1_i ) |
|---|
| 1169 | CALL iom_get( numrir, jpdom_autoglo, 'stress2_i' , stress2_i ) |
|---|
| 1170 | CALL iom_get( numrir, jpdom_autoglo, 'stress12_i', stress12_i ) |
|---|
| 1171 | CALL iom_get( numrir, jpdom_autoglo, 'aniso_11' , aniso_11 ) |
|---|
| 1172 | CALL iom_get( numrir, jpdom_autoglo, 'aniso_12' , aniso_12 ) |
|---|
| 1173 | ELSE ! start rheology from rest |
|---|
| 1174 | IF(lwp) WRITE(numout,*) |
|---|
| 1175 | IF(lwp) WRITE(numout,*) ' ==>>> previous run without rheology, set stresses to 0' |
|---|
| 1176 | stress1_i (:,:) = 0._wp |
|---|
| 1177 | stress2_i (:,:) = 0._wp |
|---|
| 1178 | stress12_i(:,:) = 0._wp |
|---|
| 1179 | aniso_11 (:,:) = 0.5_wp |
|---|
| 1180 | aniso_12 (:,:) = 0._wp |
|---|
| 1181 | ENDIF |
|---|
| 1182 | ELSE !* Start from rest |
|---|
| 1183 | IF(lwp) WRITE(numout,*) |
|---|
| 1184 | IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set stresses to 0' |
|---|
| 1185 | stress1_i (:,:) = 0._wp |
|---|
| 1186 | stress2_i (:,:) = 0._wp |
|---|
| 1187 | stress12_i(:,:) = 0._wp |
|---|
| 1188 | aniso_11 (:,:) = 0.5_wp |
|---|
| 1189 | aniso_12 (:,:) = 0._wp |
|---|
| 1190 | ENDIF |
|---|
| 1191 | ! |
|---|
| 1192 | |
|---|
| 1193 | da = 0.5_wp/real(na_yield-1,kind=wp) |
|---|
| 1194 | ainit = 0.5_wp - da |
|---|
| 1195 | dx = rpi/real(nx_yield-1,kind=wp) |
|---|
| 1196 | xinit = rpi + 0.25_wp*rpi - dx |
|---|
| 1197 | dz = rpi/real(nz,kind=wp) |
|---|
| 1198 | zinit = -rpi*0.5_wp |
|---|
| 1199 | dy = rpi/real(ny_yield-1,kind=wp) |
|---|
| 1200 | yinit = -dy |
|---|
| 1201 | |
|---|
| 1202 | DO ia=1,na_yield |
|---|
| 1203 | DO ix=1,nx_yield |
|---|
| 1204 | DO iy=1,ny_yield |
|---|
| 1205 | s11r(ix,iy,ia) = 0._wp |
|---|
| 1206 | s12r(ix,iy,ia) = 0._wp |
|---|
| 1207 | s22r(ix,iy,ia) = 0._wp |
|---|
| 1208 | s11s(ix,iy,ia) = 0._wp |
|---|
| 1209 | s12s(ix,iy,ia) = 0._wp |
|---|
| 1210 | s22s(ix,iy,ia) = 0._wp |
|---|
| 1211 | IF (ia <= na_yield-1) then |
|---|
| 1212 | DO iz=1,nz |
|---|
| 1213 | s11r(ix,iy,ia) = s11r(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1214 | exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1215 | s11kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz,phi)*dz/sin(2._wp*phi) |
|---|
| 1216 | s12r(ix,iy,ia) = s12r(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1217 | exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1218 | s12kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz,phi)*dz/sin(2._wp*phi) |
|---|
| 1219 | s22r(ix,iy,ia) = s22r(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1220 | exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1221 | s22kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz,phi)*dz/sin(2._wp*phi) |
|---|
| 1222 | s11s(ix,iy,ia) = s11s(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1223 | exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1224 | s11ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz,phi)*dz/sin(2._wp*phi) |
|---|
| 1225 | s12s(ix,iy,ia) = s12s(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1226 | exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1227 | s12ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz,phi)*dz/sin(2._wp*phi) |
|---|
| 1228 | s22s(ix,iy,ia) = s22s(ix,iy,ia) + 1*w1(ainit+ia*da)* & |
|---|
| 1229 | exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* & |
|---|
| 1230 | s22ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz,phi)*dz/sin(2._wp*phi) |
|---|
| 1231 | ENDDO |
|---|
| 1232 | IF (abs(s11r(ix,iy,ia)) < eps6) s11r(ix,iy,ia) = 0._wp |
|---|
| 1233 | IF (abs(s12r(ix,iy,ia)) < eps6) s12r(ix,iy,ia) = 0._wp |
|---|
| 1234 | IF (abs(s22r(ix,iy,ia)) < eps6) s22r(ix,iy,ia) = 0._wp |
|---|
| 1235 | IF (abs(s11s(ix,iy,ia)) < eps6) s11s(ix,iy,ia) = 0._wp |
|---|
| 1236 | IF (abs(s12s(ix,iy,ia)) < eps6) s12s(ix,iy,ia) = 0._wp |
|---|
| 1237 | IF (abs(s22s(ix,iy,ia)) < eps6) s22s(ix,iy,ia) = 0._wp |
|---|
| 1238 | ELSE |
|---|
| 1239 | s11r(ix,iy,ia) = 0.5_wp*s11kr(xinit+ix*dx,yinit+iy*dy,0._wp,phi)/sin(2._wp*phi) |
|---|
| 1240 | s12r(ix,iy,ia) = 0.5_wp*s12kr(xinit+ix*dx,yinit+iy*dy,0._wp,phi)/sin(2._wp*phi) |
|---|
| 1241 | s22r(ix,iy,ia) = 0.5_wp*s22kr(xinit+ix*dx,yinit+iy*dy,0._wp,phi)/sin(2._wp*phi) |
|---|
| 1242 | s11s(ix,iy,ia) = 0.5_wp*s11ks(xinit+ix*dx,yinit+iy*dy,0._wp,phi)/sin(2._wp*phi) |
|---|
| 1243 | s12s(ix,iy,ia) = 0.5_wp*s12ks(xinit+ix*dx,yinit+iy*dy,0._wp,phi)/sin(2._wp*phi) |
|---|
| 1244 | s22s(ix,iy,ia) = 0.5_wp*s22ks(xinit+ix*dx,yinit+iy*dy,0._wp,phi)/sin(2._wp*phi) |
|---|
| 1245 | IF (abs(s11r(ix,iy,ia)) < eps6) s11r(ix,iy,ia) = 0._wp |
|---|
| 1246 | IF (abs(s12r(ix,iy,ia)) < eps6) s12r(ix,iy,ia) = 0._wp |
|---|
| 1247 | IF (abs(s22r(ix,iy,ia)) < eps6) s22r(ix,iy,ia) = 0._wp |
|---|
| 1248 | IF (abs(s11s(ix,iy,ia)) < eps6) s11s(ix,iy,ia) = 0._wp |
|---|
| 1249 | IF (abs(s12s(ix,iy,ia)) < eps6) s12s(ix,iy,ia) = 0._wp |
|---|
| 1250 | IF (abs(s22s(ix,iy,ia)) < eps6) s22s(ix,iy,ia) = 0._wp |
|---|
| 1251 | ENDIF |
|---|
| 1252 | ENDDO |
|---|
| 1253 | ENDDO |
|---|
| 1254 | ENDDO |
|---|
| 1255 | |
|---|
| 1256 | ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file |
|---|
| 1257 | ! ! ------------------- |
|---|
| 1258 | IF(lwp) WRITE(numout,*) '---- rhg-rst ----' |
|---|
| 1259 | iter = kt + nn_fsbc - 1 ! ice restarts are written at kt == nitrst - nn_fsbc + 1 |
|---|
| 1260 | ! |
|---|
| 1261 | CALL iom_rstput( iter, nitrst, numriw, 'stress1_i' , stress1_i ) |
|---|
| 1262 | CALL iom_rstput( iter, nitrst, numriw, 'stress2_i' , stress2_i ) |
|---|
| 1263 | CALL iom_rstput( iter, nitrst, numriw, 'stress12_i', stress12_i ) |
|---|
| 1264 | CALL iom_rstput( iter, nitrst, numriw, 'aniso_11' , aniso_11 ) |
|---|
| 1265 | CALL iom_rstput( iter, nitrst, numriw, 'aniso_12' , aniso_12 ) |
|---|
| 1266 | ! |
|---|
| 1267 | ENDIF |
|---|
| 1268 | ! |
|---|
| 1269 | END SUBROUTINE rhg_eap_rst |
|---|
| 1270 | |
|---|
| 1271 | |
|---|
| 1272 | FUNCTION w1(a) |
|---|
| 1273 | !!------------------------------------------------------------------- |
|---|
| 1274 | !! Function : w1 (see Gaussian function psi in Tsamados et al 2013) |
|---|
| 1275 | !!------------------------------------------------------------------- |
|---|
| 1276 | REAL(wp), INTENT(in ) :: a |
|---|
| 1277 | REAL(wp) :: w1 |
|---|
| 1278 | !!------------------------------------------------------------------- |
|---|
| 1279 | |
|---|
| 1280 | w1 = - 223.87569446_wp & |
|---|
| 1281 | + 2361.2198663_wp*a & |
|---|
| 1282 | - 10606.56079975_wp*a*a & |
|---|
| 1283 | + 26315.50025642_wp*a*a*a & |
|---|
| 1284 | - 38948.30444297_wp*a*a*a*a & |
|---|
| 1285 | + 34397.72407466_wp*a*a*a*a*a & |
|---|
| 1286 | - 16789.98003081_wp*a*a*a*a*a*a & |
|---|
| 1287 | + 3495.82839237_wp*a*a*a*a*a*a*a |
|---|
| 1288 | |
|---|
| 1289 | END FUNCTION w1 |
|---|
| 1290 | |
|---|
| 1291 | |
|---|
| 1292 | FUNCTION w2(a) |
|---|
| 1293 | !!------------------------------------------------------------------- |
|---|
| 1294 | !! Function : w2 (see Gaussian function psi in Tsamados et al 2013) |
|---|
| 1295 | !!------------------------------------------------------------------- |
|---|
| 1296 | REAL(wp), INTENT(in ) :: a |
|---|
| 1297 | REAL(wp) :: w2 |
|---|
| 1298 | !!------------------------------------------------------------------- |
|---|
| 1299 | |
|---|
| 1300 | w2 = - 6670.68911883_wp & |
|---|
| 1301 | + 70222.33061536_wp*a & |
|---|
| 1302 | - 314871.71525448_wp*a*a & |
|---|
| 1303 | + 779570.02793492_wp*a*a*a & |
|---|
| 1304 | - 1151098.82436864_wp*a*a*a*a & |
|---|
| 1305 | + 1013896.59464498_wp*a*a*a*a*a & |
|---|
| 1306 | - 493379.44906738_wp*a*a*a*a*a*a & |
|---|
| 1307 | + 102356.551518_wp*a*a*a*a*a*a*a |
|---|
| 1308 | |
|---|
| 1309 | END FUNCTION w2 |
|---|
| 1310 | |
|---|
| 1311 | FUNCTION s11kr(x,y,z,phi) |
|---|
| 1312 | !!------------------------------------------------------------------- |
|---|
| 1313 | !! Function : s11kr |
|---|
| 1314 | !!------------------------------------------------------------------- |
|---|
| 1315 | REAL(wp), INTENT(in ) :: x,y,z,phi |
|---|
| 1316 | |
|---|
| 1317 | REAL(wp) :: s11kr, p, pih |
|---|
| 1318 | |
|---|
| 1319 | REAL(wp) :: n1t2i11, n1t2i12, n1t2i21, n1t2i22 |
|---|
| 1320 | REAL(wp) :: n2t1i11, n2t1i12, n2t1i21, n2t1i22 |
|---|
| 1321 | REAL(wp) :: t1t2i11, t1t2i12, t1t2i21, t1t2i22 |
|---|
| 1322 | REAL(wp) :: t2t1i11, t2t1i12, t2t1i21, t2t1i22 |
|---|
| 1323 | REAL(wp) :: d11, d12, d22 |
|---|
| 1324 | REAL(wp) :: IIn1t2, IIn2t1, IIt1t2 |
|---|
| 1325 | REAL(wp) :: Hen1t2, Hen2t1 |
|---|
| 1326 | !!------------------------------------------------------------------- |
|---|
| 1327 | |
|---|
| 1328 | pih = 0.5_wp*rpi |
|---|
| 1329 | p = phi |
|---|
| 1330 | |
|---|
| 1331 | n1t2i11 = cos(z+pih-p) * cos(z+p) |
|---|
| 1332 | n1t2i12 = cos(z+pih-p) * sin(z+p) |
|---|
| 1333 | n1t2i21 = sin(z+pih-p) * cos(z+p) |
|---|
| 1334 | n1t2i22 = sin(z+pih-p) * sin(z+p) |
|---|
| 1335 | n2t1i11 = cos(z-pih+p) * cos(z-p) |
|---|
| 1336 | n2t1i12 = cos(z-pih+p) * sin(z-p) |
|---|
| 1337 | n2t1i21 = sin(z-pih+p) * cos(z-p) |
|---|
| 1338 | n2t1i22 = sin(z-pih+p) * sin(z-p) |
|---|
| 1339 | t1t2i11 = cos(z-p) * cos(z+p) |
|---|
| 1340 | t1t2i12 = cos(z-p) * sin(z+p) |
|---|
| 1341 | t1t2i21 = sin(z-p) * cos(z+p) |
|---|
| 1342 | t1t2i22 = sin(z-p) * sin(z+p) |
|---|
| 1343 | t2t1i11 = cos(z+p) * cos(z-p) |
|---|
| 1344 | t2t1i12 = cos(z+p) * sin(z-p) |
|---|
| 1345 | t2t1i21 = sin(z+p) * cos(z-p) |
|---|
| 1346 | t2t1i22 = sin(z+p) * sin(z-p) |
|---|
| 1347 | ! In expression of tensor d, with this formulatin d(x)=-d(x+pi) |
|---|
| 1348 | ! Solution, when diagonalizing always check sgn(a11-a22) if > then keep x else |
|---|
| 1349 | ! x=x-pi/2 |
|---|
| 1350 | d11 = cos(y)*cos(y)*(cos(x)+sin(x)*tan(y)*tan(y)) |
|---|
| 1351 | d12 = cos(y)*cos(y)*tan(y)*(-cos(x)+sin(x)) |
|---|
| 1352 | d22 = cos(y)*cos(y)*(sin(x)+cos(x)*tan(y)*tan(y)) |
|---|
| 1353 | IIn1t2 = n1t2i11 * d11 + (n1t2i12 + n1t2i21) * d12 + n1t2i22 * d22 |
|---|
| 1354 | IIn2t1 = n2t1i11 * d11 + (n2t1i12 + n2t1i21) * d12 + n2t1i22 * d22 |
|---|
| 1355 | IIt1t2 = t1t2i11 * d11 + (t1t2i12 + t1t2i21) * d12 + t1t2i22 * d22 |
|---|
| 1356 | |
|---|
| 1357 | IF (-IIn1t2>=rsmall) then |
|---|
| 1358 | Hen1t2 = 1._wp |
|---|
| 1359 | ELSE |
|---|
| 1360 | Hen1t2 = 0._wp |
|---|
| 1361 | ENDIF |
|---|
| 1362 | |
|---|
| 1363 | IF (-IIn2t1>=rsmall) then |
|---|
| 1364 | Hen2t1 = 1._wp |
|---|
| 1365 | ELSE |
|---|
| 1366 | Hen2t1 = 0._wp |
|---|
| 1367 | ENDIF |
|---|
| 1368 | |
|---|
| 1369 | s11kr = (- Hen1t2 * n1t2i11 - Hen2t1 * n2t1i11) |
|---|
| 1370 | |
|---|
| 1371 | END FUNCTION s11kr |
|---|
| 1372 | |
|---|
| 1373 | FUNCTION s12kr(x,y,z,phi) |
|---|
| 1374 | !!------------------------------------------------------------------- |
|---|
| 1375 | !! Function : s12kr |
|---|
| 1376 | !!------------------------------------------------------------------- |
|---|
| 1377 | REAL(wp), INTENT(in ) :: x,y,z,phi |
|---|
| 1378 | |
|---|
| 1379 | REAL(wp) :: s12kr, s12r0, s21r0, p, pih |
|---|
| 1380 | |
|---|
| 1381 | REAL(wp) :: n1t2i11, n1t2i12, n1t2i21, n1t2i22 |
|---|
| 1382 | REAL(wp) :: n2t1i11, n2t1i12, n2t1i21, n2t1i22 |
|---|
| 1383 | REAL(wp) :: t1t2i11, t1t2i12, t1t2i21, t1t2i22 |
|---|
| 1384 | REAL(wp) :: t2t1i11, t2t1i12, t2t1i21, t2t1i22 |
|---|
| 1385 | REAL(wp) :: d11, d12, d22 |
|---|
| 1386 | REAL(wp) :: IIn1t2, IIn2t1, IIt1t2 |
|---|
| 1387 | REAL(wp) :: Hen1t2, Hen2t1 |
|---|
| 1388 | !!------------------------------------------------------------------- |
|---|
| 1389 | pih = 0.5_wp*rpi |
|---|
| 1390 | p = phi |
|---|
| 1391 | |
|---|
| 1392 | n1t2i11 = cos(z+pih-p) * cos(z+p) |
|---|
| 1393 | n1t2i12 = cos(z+pih-p) * sin(z+p) |
|---|
| 1394 | n1t2i21 = sin(z+pih-p) * cos(z+p) |
|---|
| 1395 | n1t2i22 = sin(z+pih-p) * sin(z+p) |
|---|
| 1396 | n2t1i11 = cos(z-pih+p) * cos(z-p) |
|---|
| 1397 | n2t1i12 = cos(z-pih+p) * sin(z-p) |
|---|
| 1398 | n2t1i21 = sin(z-pih+p) * cos(z-p) |
|---|
| 1399 | n2t1i22 = sin(z-pih+p) * sin(z-p) |
|---|
| 1400 | t1t2i11 = cos(z-p) * cos(z+p) |
|---|
| 1401 | t1t2i12 = cos(z-p) * sin(z+p) |
|---|
| 1402 | t1t2i21 = sin(z-p) * cos(z+p) |
|---|
| 1403 | t1t2i22 = sin(z-p) * sin(z+p) |
|---|
| 1404 | t2t1i11 = cos(z+p) * cos(z-p) |
|---|
| 1405 | t2t1i12 = cos(z+p) * sin(z-p) |
|---|
| 1406 | t2t1i21 = sin(z+p) * cos(z-p) |
|---|
| 1407 | t2t1i22 = sin(z+p) * sin(z-p) |
|---|
| 1408 | d11 = cos(y)*cos(y)*(cos(x)+sin(x)*tan(y)*tan(y)) |
|---|
| 1409 | d12 = cos(y)*cos(y)*tan(y)*(-cos(x)+sin(x)) |
|---|
| 1410 | d22 = cos(y)*cos(y)*(sin(x)+cos(x)*tan(y)*tan(y)) |
|---|
| 1411 | IIn1t2 = n1t2i11 * d11 + (n1t2i12 + n1t2i21) * d12 + n1t2i22 * d22 |
|---|
| 1412 | IIn2t1 = n2t1i11 * d11 + (n2t1i12 + n2t1i21) * d12 + n2t1i22 * d22 |
|---|
| 1413 | IIt1t2 = t1t2i11 * d11 + (t1t2i12 + t1t2i21) * d12 + t1t2i22 * d22 |
|---|
| 1414 | |
|---|
| 1415 | IF (-IIn1t2>=rsmall) then |
|---|
| 1416 | Hen1t2 = 1._wp |
|---|
| 1417 | ELSE |
|---|
| 1418 | Hen1t2 = 0._wp |
|---|
| 1419 | ENDIF |
|---|
| 1420 | |
|---|
| 1421 | IF (-IIn2t1>=rsmall) then |
|---|
| 1422 | Hen2t1 = 1._wp |
|---|
| 1423 | ELSE |
|---|
| 1424 | Hen2t1 = 0._wp |
|---|
| 1425 | ENDIF |
|---|
| 1426 | |
|---|
| 1427 | s12r0 = (- Hen1t2 * n1t2i12 - Hen2t1 * n2t1i12) |
|---|
| 1428 | s21r0 = (- Hen1t2 * n1t2i21 - Hen2t1 * n2t1i21) |
|---|
| 1429 | s12kr=0.5_wp*(s12r0+s21r0) |
|---|
| 1430 | |
|---|
| 1431 | END FUNCTION s12kr |
|---|
| 1432 | |
|---|
| 1433 | FUNCTION s22kr(x,y,z,phi) |
|---|
| 1434 | !!------------------------------------------------------------------- |
|---|
| 1435 | !! Function : s22kr |
|---|
| 1436 | !!------------------------------------------------------------------- |
|---|
| 1437 | REAL(wp), INTENT(in ) :: x,y,z,phi |
|---|
| 1438 | |
|---|
| 1439 | REAL(wp) :: s22kr, p, pih |
|---|
| 1440 | |
|---|
| 1441 | REAL(wp) :: n1t2i11, n1t2i12, n1t2i21, n1t2i22 |
|---|
| 1442 | REAL(wp) :: n2t1i11, n2t1i12, n2t1i21, n2t1i22 |
|---|
| 1443 | REAL(wp) :: t1t2i11, t1t2i12, t1t2i21, t1t2i22 |
|---|
| 1444 | REAL(wp) :: t2t1i11, t2t1i12, t2t1i21, t2t1i22 |
|---|
| 1445 | REAL(wp) :: d11, d12, d22 |
|---|
| 1446 | REAL(wp) :: IIn1t2, IIn2t1, IIt1t2 |
|---|
| 1447 | REAL(wp) :: Hen1t2, Hen2t1 |
|---|
| 1448 | !!------------------------------------------------------------------- |
|---|
| 1449 | pih = 0.5_wp*rpi |
|---|
| 1450 | p = phi |
|---|
| 1451 | |
|---|
| 1452 | n1t2i11 = cos(z+pih-p) * cos(z+p) |
|---|
| 1453 | n1t2i12 = cos(z+pih-p) * sin(z+p) |
|---|
| 1454 | n1t2i21 = sin(z+pih-p) * cos(z+p) |
|---|
| 1455 | n1t2i22 = sin(z+pih-p) * sin(z+p) |
|---|
| 1456 | n2t1i11 = cos(z-pih+p) * cos(z-p) |
|---|
| 1457 | n2t1i12 = cos(z-pih+p) * sin(z-p) |
|---|
| 1458 | n2t1i21 = sin(z-pih+p) * cos(z-p) |
|---|
| 1459 | n2t1i22 = sin(z-pih+p) * sin(z-p) |
|---|
| 1460 | t1t2i11 = cos(z-p) * cos(z+p) |
|---|
| 1461 | t1t2i12 = cos(z-p) * sin(z+p) |
|---|
| 1462 | t1t2i21 = sin(z-p) * cos(z+p) |
|---|
| 1463 | t1t2i22 = sin(z-p) * sin(z+p) |
|---|
| 1464 | t2t1i11 = cos(z+p) * cos(z-p) |
|---|
| 1465 | t2t1i12 = cos(z+p) * sin(z-p) |
|---|
| 1466 | t2t1i21 = sin(z+p) * cos(z-p) |
|---|
| 1467 | t2t1i22 = sin(z+p) * sin(z-p) |
|---|
| 1468 | d11 = cos(y)*cos(y)*(cos(x)+sin(x)*tan(y)*tan(y)) |
|---|
| 1469 | d12 = cos(y)*cos(y)*tan(y)*(-cos(x)+sin(x)) |
|---|
| 1470 | d22 = cos(y)*cos(y)*(sin(x)+cos(x)*tan(y)*tan(y)) |
|---|
| 1471 | IIn1t2 = n1t2i11 * d11 + (n1t2i12 + n1t2i21) * d12 + n1t2i22 * d22 |
|---|
| 1472 | IIn2t1 = n2t1i11 * d11 + (n2t1i12 + n2t1i21) * d12 + n2t1i22 * d22 |
|---|
| 1473 | IIt1t2 = t1t2i11 * d11 + (t1t2i12 + t1t2i21) * d12 + t1t2i22 * d22 |
|---|
| 1474 | |
|---|
| 1475 | IF (-IIn1t2>=rsmall) then |
|---|
| 1476 | Hen1t2 = 1._wp |
|---|
| 1477 | ELSE |
|---|
| 1478 | Hen1t2 = 0._wp |
|---|
| 1479 | ENDIF |
|---|
| 1480 | |
|---|
| 1481 | IF (-IIn2t1>=rsmall) then |
|---|
| 1482 | Hen2t1 = 1._wp |
|---|
| 1483 | ELSE |
|---|
| 1484 | Hen2t1 = 0._wp |
|---|
| 1485 | ENDIF |
|---|
| 1486 | |
|---|
| 1487 | s22kr = (- Hen1t2 * n1t2i22 - Hen2t1 * n2t1i22) |
|---|
| 1488 | |
|---|
| 1489 | END FUNCTION s22kr |
|---|
| 1490 | |
|---|
| 1491 | FUNCTION s11ks(x,y,z,phi) |
|---|
| 1492 | !!------------------------------------------------------------------- |
|---|
| 1493 | !! Function : s11ks |
|---|
| 1494 | !!------------------------------------------------------------------- |
|---|
| 1495 | REAL(wp), INTENT(in ) :: x,y,z,phi |
|---|
| 1496 | |
|---|
| 1497 | REAL(wp) :: s11ks, p, pih |
|---|
| 1498 | |
|---|
| 1499 | REAL(wp) :: n1t2i11, n1t2i12, n1t2i21, n1t2i22 |
|---|
| 1500 | REAL(wp) :: n2t1i11, n2t1i12, n2t1i21, n2t1i22 |
|---|
| 1501 | REAL(wp) :: t1t2i11, t1t2i12, t1t2i21, t1t2i22 |
|---|
| 1502 | REAL(wp) :: t2t1i11, t2t1i12, t2t1i21, t2t1i22 |
|---|
| 1503 | REAL(wp) :: d11, d12, d22 |
|---|
| 1504 | REAL(wp) :: IIn1t2, IIn2t1, IIt1t2 |
|---|
| 1505 | REAL(wp) :: Hen1t2, Hen2t1 |
|---|
| 1506 | !!------------------------------------------------------------------- |
|---|
| 1507 | pih = 0.5_wp*rpi |
|---|
| 1508 | p = phi |
|---|
| 1509 | |
|---|
| 1510 | n1t2i11 = cos(z+pih-p) * cos(z+p) |
|---|
| 1511 | n1t2i12 = cos(z+pih-p) * sin(z+p) |
|---|
| 1512 | n1t2i21 = sin(z+pih-p) * cos(z+p) |
|---|
| 1513 | n1t2i22 = sin(z+pih-p) * sin(z+p) |
|---|
| 1514 | n2t1i11 = cos(z-pih+p) * cos(z-p) |
|---|
| 1515 | n2t1i12 = cos(z-pih+p) * sin(z-p) |
|---|
| 1516 | n2t1i21 = sin(z-pih+p) * cos(z-p) |
|---|
| 1517 | n2t1i22 = sin(z-pih+p) * sin(z-p) |
|---|
| 1518 | t1t2i11 = cos(z-p) * cos(z+p) |
|---|
| 1519 | t1t2i12 = cos(z-p) * sin(z+p) |
|---|
| 1520 | t1t2i21 = sin(z-p) * cos(z+p) |
|---|
| 1521 | t1t2i22 = sin(z-p) * sin(z+p) |
|---|
| 1522 | t2t1i11 = cos(z+p) * cos(z-p) |
|---|
| 1523 | t2t1i12 = cos(z+p) * sin(z-p) |
|---|
| 1524 | t2t1i21 = sin(z+p) * cos(z-p) |
|---|
| 1525 | t2t1i22 = sin(z+p) * sin(z-p) |
|---|
| 1526 | d11 = cos(y)*cos(y)*(cos(x)+sin(x)*tan(y)*tan(y)) |
|---|
| 1527 | d12 = cos(y)*cos(y)*tan(y)*(-cos(x)+sin(x)) |
|---|
| 1528 | d22 = cos(y)*cos(y)*(sin(x)+cos(x)*tan(y)*tan(y)) |
|---|
| 1529 | IIn1t2 = n1t2i11 * d11 + (n1t2i12 + n1t2i21) * d12 + n1t2i22 * d22 |
|---|
| 1530 | IIn2t1 = n2t1i11 * d11 + (n2t1i12 + n2t1i21) * d12 + n2t1i22 * d22 |
|---|
| 1531 | IIt1t2 = t1t2i11 * d11 + (t1t2i12 + t1t2i21) * d12 + t1t2i22 * d22 |
|---|
| 1532 | |
|---|
| 1533 | IF (-IIn1t2>=rsmall) then |
|---|
| 1534 | Hen1t2 = 1._wp |
|---|
| 1535 | ELSE |
|---|
| 1536 | Hen1t2 = 0._wp |
|---|
| 1537 | ENDIF |
|---|
| 1538 | |
|---|
| 1539 | IF (-IIn2t1>=rsmall) then |
|---|
| 1540 | Hen2t1 = 1._wp |
|---|
| 1541 | ELSE |
|---|
| 1542 | Hen2t1 = 0._wp |
|---|
| 1543 | ENDIF |
|---|
| 1544 | |
|---|
| 1545 | s11ks = sign(1._wp,IIt1t2+rsmall)*(Hen1t2 * t1t2i11 + Hen2t1 * t2t1i11) |
|---|
| 1546 | |
|---|
| 1547 | END FUNCTION s11ks |
|---|
| 1548 | |
|---|
| 1549 | FUNCTION s12ks(x,y,z,phi) |
|---|
| 1550 | !!------------------------------------------------------------------- |
|---|
| 1551 | !! Function : s12ks |
|---|
| 1552 | !!------------------------------------------------------------------- |
|---|
| 1553 | REAL(wp), INTENT(in ) :: x,y,z,phi |
|---|
| 1554 | |
|---|
| 1555 | REAL(wp) :: s12ks, s12s0, s21s0, p, pih |
|---|
| 1556 | |
|---|
| 1557 | REAL(wp) :: n1t2i11, n1t2i12, n1t2i21, n1t2i22 |
|---|
| 1558 | REAL(wp) :: n2t1i11, n2t1i12, n2t1i21, n2t1i22 |
|---|
| 1559 | REAL(wp) :: t1t2i11, t1t2i12, t1t2i21, t1t2i22 |
|---|
| 1560 | REAL(wp) :: t2t1i11, t2t1i12, t2t1i21, t2t1i22 |
|---|
| 1561 | REAL(wp) :: d11, d12, d22 |
|---|
| 1562 | REAL(wp) :: IIn1t2, IIn2t1, IIt1t2 |
|---|
| 1563 | REAL(wp) :: Hen1t2, Hen2t1 |
|---|
| 1564 | !!------------------------------------------------------------------- |
|---|
| 1565 | pih = 0.5_wp*rpi |
|---|
| 1566 | p =phi |
|---|
| 1567 | |
|---|
| 1568 | n1t2i11 = cos(z+pih-p) * cos(z+p) |
|---|
| 1569 | n1t2i12 = cos(z+pih-p) * sin(z+p) |
|---|
| 1570 | n1t2i21 = sin(z+pih-p) * cos(z+p) |
|---|
| 1571 | n1t2i22 = sin(z+pih-p) * sin(z+p) |
|---|
| 1572 | n2t1i11 = cos(z-pih+p) * cos(z-p) |
|---|
| 1573 | n2t1i12 = cos(z-pih+p) * sin(z-p) |
|---|
| 1574 | n2t1i21 = sin(z-pih+p) * cos(z-p) |
|---|
| 1575 | n2t1i22 = sin(z-pih+p) * sin(z-p) |
|---|
| 1576 | t1t2i11 = cos(z-p) * cos(z+p) |
|---|
| 1577 | t1t2i12 = cos(z-p) * sin(z+p) |
|---|
| 1578 | t1t2i21 = sin(z-p) * cos(z+p) |
|---|
| 1579 | t1t2i22 = sin(z-p) * sin(z+p) |
|---|
| 1580 | t2t1i11 = cos(z+p) * cos(z-p) |
|---|
| 1581 | t2t1i12 = cos(z+p) * sin(z-p) |
|---|
| 1582 | t2t1i21 = sin(z+p) * cos(z-p) |
|---|
| 1583 | t2t1i22 = sin(z+p) * sin(z-p) |
|---|
| 1584 | d11 = cos(y)*cos(y)*(cos(x)+sin(x)*tan(y)*tan(y)) |
|---|
| 1585 | d12 = cos(y)*cos(y)*tan(y)*(-cos(x)+sin(x)) |
|---|
| 1586 | d22 = cos(y)*cos(y)*(sin(x)+cos(x)*tan(y)*tan(y)) |
|---|
| 1587 | IIn1t2 = n1t2i11 * d11 + (n1t2i12 + n1t2i21) * d12 + n1t2i22 * d22 |
|---|
| 1588 | IIn2t1 = n2t1i11 * d11 + (n2t1i12 + n2t1i21) * d12 + n2t1i22 * d22 |
|---|
| 1589 | IIt1t2 = t1t2i11 * d11 + (t1t2i12 + t1t2i21) * d12 + t1t2i22 * d22 |
|---|
| 1590 | |
|---|
| 1591 | IF (-IIn1t2>=rsmall) then |
|---|
| 1592 | Hen1t2 = 1._wp |
|---|
| 1593 | ELSE |
|---|
| 1594 | Hen1t2 = 0._wp |
|---|
| 1595 | ENDIF |
|---|
| 1596 | |
|---|
| 1597 | IF (-IIn2t1>=rsmall) then |
|---|
| 1598 | Hen2t1 = 1._wp |
|---|
| 1599 | ELSE |
|---|
| 1600 | Hen2t1 = 0._wp |
|---|
| 1601 | ENDIF |
|---|
| 1602 | |
|---|
| 1603 | s12s0 = sign(1._wp,IIt1t2+rsmall)*(Hen1t2 * t1t2i12 + Hen2t1 * t2t1i12) |
|---|
| 1604 | s21s0 = sign(1._wp,IIt1t2+rsmall)*(Hen1t2 * t1t2i21 + Hen2t1 * t2t1i21) |
|---|
| 1605 | s12ks=0.5_wp*(s12s0+s21s0) |
|---|
| 1606 | |
|---|
| 1607 | END FUNCTION s12ks |
|---|
| 1608 | |
|---|
| 1609 | FUNCTION s22ks(x,y,z,phi) |
|---|
| 1610 | !!------------------------------------------------------------------- |
|---|
| 1611 | !! Function : s22ks |
|---|
| 1612 | !!------------------------------------------------------------------- |
|---|
| 1613 | REAL(wp), INTENT(in ) :: x,y,z,phi |
|---|
| 1614 | |
|---|
| 1615 | REAL(wp) :: s22ks, p, pih |
|---|
| 1616 | |
|---|
| 1617 | REAL(wp) :: n1t2i11, n1t2i12, n1t2i21, n1t2i22 |
|---|
| 1618 | REAL(wp) :: n2t1i11, n2t1i12, n2t1i21, n2t1i22 |
|---|
| 1619 | REAL(wp) :: t1t2i11, t1t2i12, t1t2i21, t1t2i22 |
|---|
| 1620 | REAL(wp) :: t2t1i11, t2t1i12, t2t1i21, t2t1i22 |
|---|
| 1621 | REAL(wp) :: d11, d12, d22 |
|---|
| 1622 | REAL(wp) :: IIn1t2, IIn2t1, IIt1t2 |
|---|
| 1623 | REAL(wp) :: Hen1t2, Hen2t1 |
|---|
| 1624 | !!------------------------------------------------------------------- |
|---|
| 1625 | pih = 0.5_wp*rpi |
|---|
| 1626 | p =phi |
|---|
| 1627 | |
|---|
| 1628 | n1t2i11 = cos(z+pih-p) * cos(z+p) |
|---|
| 1629 | n1t2i12 = cos(z+pih-p) * sin(z+p) |
|---|
| 1630 | n1t2i21 = sin(z+pih-p) * cos(z+p) |
|---|
| 1631 | n1t2i22 = sin(z+pih-p) * sin(z+p) |
|---|
| 1632 | n2t1i11 = cos(z-pih+p) * cos(z-p) |
|---|
| 1633 | n2t1i12 = cos(z-pih+p) * sin(z-p) |
|---|
| 1634 | n2t1i21 = sin(z-pih+p) * cos(z-p) |
|---|
| 1635 | n2t1i22 = sin(z-pih+p) * sin(z-p) |
|---|
| 1636 | t1t2i11 = cos(z-p) * cos(z+p) |
|---|
| 1637 | t1t2i12 = cos(z-p) * sin(z+p) |
|---|
| 1638 | t1t2i21 = sin(z-p) * cos(z+p) |
|---|
| 1639 | t1t2i22 = sin(z-p) * sin(z+p) |
|---|
| 1640 | t2t1i11 = cos(z+p) * cos(z-p) |
|---|
| 1641 | t2t1i12 = cos(z+p) * sin(z-p) |
|---|
| 1642 | t2t1i21 = sin(z+p) * cos(z-p) |
|---|
| 1643 | t2t1i22 = sin(z+p) * sin(z-p) |
|---|
| 1644 | d11 = cos(y)*cos(y)*(cos(x)+sin(x)*tan(y)*tan(y)) |
|---|
| 1645 | d12 = cos(y)*cos(y)*tan(y)*(-cos(x)+sin(x)) |
|---|
| 1646 | d22 = cos(y)*cos(y)*(sin(x)+cos(x)*tan(y)*tan(y)) |
|---|
| 1647 | IIn1t2 = n1t2i11 * d11 + (n1t2i12 + n1t2i21) * d12 + n1t2i22 * d22 |
|---|
| 1648 | IIn2t1 = n2t1i11 * d11 + (n2t1i12 + n2t1i21) * d12 + n2t1i22 * d22 |
|---|
| 1649 | IIt1t2 = t1t2i11 * d11 + (t1t2i12 + t1t2i21) * d12 + t1t2i22 * d22 |
|---|
| 1650 | |
|---|
| 1651 | IF (-IIn1t2>=rsmall) THEN |
|---|
| 1652 | Hen1t2 = 1._wp |
|---|
| 1653 | ELSE |
|---|
| 1654 | Hen1t2 = 0._wp |
|---|
| 1655 | ENDIF |
|---|
| 1656 | |
|---|
| 1657 | IF (-IIn2t1>=rsmall) THEN |
|---|
| 1658 | Hen2t1 = 1._wp |
|---|
| 1659 | ELSE |
|---|
| 1660 | Hen2t1 = 0._wp |
|---|
| 1661 | ENDIF |
|---|
| 1662 | |
|---|
| 1663 | s22ks = sign(1._wp,IIt1t2+rsmall)*(Hen1t2 * t1t2i22 + Hen2t1 * t2t1i22) |
|---|
| 1664 | |
|---|
| 1665 | END FUNCTION s22ks |
|---|
| 1666 | |
|---|
| 1667 | #else |
|---|
| 1668 | !!---------------------------------------------------------------------- |
|---|
| 1669 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 1670 | !!---------------------------------------------------------------------- |
|---|
| 1671 | |
|---|
| 1672 | #endif |
|---|
| 1673 | !!============================================================================== |
|---|
| 1674 | END MODULE icedyn_rhg_eap |
|---|
