| 1 | MODULE icedyn_rhg_vp |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icedyn_rhg_vp *** |
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| 4 | !! Sea-Ice dynamics : Viscous-plastic rheology with LSR technique |
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| 5 | !!====================================================================== |
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| 6 | !! |
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| 7 | !! History : - ! 1997-20 (J. Zhang, M. Losch) Original code, implementation into mitGCM |
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| 8 | !! 4.0 ! 2020-09 (M. Vancoppenolle) Adaptation to SI3 |
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| 9 | !! |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | #if defined key_si3 |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | !! 'key_si3' SI3 sea-ice model |
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| 14 | !!---------------------------------------------------------------------- |
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| 15 | !! ice_dyn_rhg_vp : computes ice velocities from VP rheolog with LSR solvery |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | USE phycst ! Physical constants |
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| 18 | USE dom_oce ! Ocean domain |
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| 19 | USE sbc_oce , ONLY : ln_ice_embd, nn_fsbc, ssh_m |
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| 20 | USE sbc_ice , ONLY : utau_ice, vtau_ice, snwice_mass, snwice_mass_b |
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| 21 | USE ice ! sea-ice: ice variables |
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| 22 | USE icevar ! ice_var_sshdyn |
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| 23 | USE icedyn_rdgrft ! sea-ice: ice strength |
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| 24 | USE bdy_oce , ONLY : ln_bdy |
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| 25 | USE bdyice |
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| 26 | #if defined key_agrif |
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| 27 | USE agrif_ice_interp |
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| 28 | #endif |
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| 29 | ! |
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| 30 | USE in_out_manager ! I/O manager |
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| 31 | USE iom ! I/O manager library |
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| 32 | USE lib_mpp ! MPP library |
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| 33 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 34 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 35 | USE prtctl ! Print control |
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| 36 | |
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| 37 | USE netcdf ! NetCDF library for convergence test |
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| 38 | IMPLICIT NONE |
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| 39 | PRIVATE |
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| 40 | |
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| 41 | PUBLIC ice_dyn_rhg_vp ! called by icedyn_rhg.F90 |
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| 42 | |
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| 43 | INTEGER :: nn_nvp ! total number of VP iterations (n_out_vp*n_inn_vp) |
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| 44 | LOGICAL :: lp_zebra_vp =.TRUE. ! activate zebra (solve the linear system problem every odd j-band, then one every even one) |
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| 45 | REAL(wp) :: zrelaxu_vp=0.95 ! U-relaxation factor (MV: can probably be merged with V-factor once ok) |
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| 46 | REAL(wp) :: zrelaxv_vp=0.95 ! V-relaxation factor |
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| 47 | REAL(wp) :: zuerr_max_vp=0.80 ! maximum velocity error, above which a forcing error is considered and solver is stopped |
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| 48 | REAL(wp) :: zuerr_min_vp=1.e-04 ! minimum velocity error, beyond which convergence is assumed |
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| 49 | |
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| 50 | !! for convergence tests |
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| 51 | INTEGER :: ncvgid ! netcdf file id |
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| 52 | INTEGER :: nvarid_ures, nvarid_vres, nvarid_velres |
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| 53 | INTEGER :: nvarid_uerr_max, nvarid_verr_max, nvarid_velerr_max |
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| 54 | INTEGER :: nvarid_umad, nvarid_vmad, nvarid_velmad |
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| 55 | INTEGER :: nvarid_umad_outer, nvarid_vmad_outer, nvarid_velmad_outer |
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| 56 | INTEGER :: nvarid_mke |
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| 57 | |
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| 58 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fimask ! mask at F points for the ice |
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| 59 | |
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| 60 | !! * Substitutions |
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| 61 | # include "do_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_vp.F90 13279 2020-07-09 10:39:43Z clem $ |
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| 65 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 66 | !!---------------------------------------------------------------------- |
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| 67 | |
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| 68 | CONTAINS |
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| 69 | |
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| 70 | SUBROUTINE ice_dyn_rhg_vp( kt, pshear_i, pdivu_i, pdelta_i ) |
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| 71 | !!------------------------------------------------------------------- |
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| 72 | !! |
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| 73 | !! *** SUBROUTINE ice_dyn_rhg_vp *** |
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| 74 | !! VP-LSR-C-grid |
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| 75 | !! |
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| 76 | !! ** Purpose : determines sea ice drift from wind stress, ice-ocean |
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| 77 | !! stress and sea-surface slope. Internal forces assume viscous-plastic rheology (Hibler, 1979) |
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| 78 | !! |
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| 79 | !! ** Method |
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| 80 | !! |
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| 81 | !! The resolution algorithm follows from Zhang and Hibler (1997) and Losch (2010) |
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| 82 | !! with elements from Lemieux and Tremblay (2008) and Lemieux and Tremblay (2009) |
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| 83 | !! |
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| 84 | !! The components of the momentum equations are arranged following the ideas of Zhang and Hibler (1997) |
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| 85 | !! |
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| 86 | !! f1(u) = g1(v) |
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| 87 | !! f2(v) = g2(u) |
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| 88 | !! |
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| 89 | !! The right-hand side (RHS) is explicit |
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| 90 | !! The left-hand side (LHS) is implicit |
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| 91 | !! Coriolis is part of explicit terms, whereas ice-ocean drag is implicit |
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| 92 | !! |
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| 93 | !! Two iteration levels (outer and inner loops) are used to solve the equations |
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| 94 | !! |
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| 95 | !! The outer loop (OL, typically 10 iterations) is there to deal with the (strong) non-linearities in the equation |
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| 96 | !! |
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| 97 | !! The inner loop (IL, typically 1500 iterations) is there to solve the linear problem with a line-successive-relaxation algorithm |
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| 98 | !! |
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| 99 | !! The velocity used in the non-linear terms uses a "modified euler time step" (not sure its the correct term), |
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| 100 | !!! with uk = ( uk-1 + uk-2 ) / 2. |
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| 101 | !! |
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| 102 | !! * Spatial discretization |
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| 103 | !! |
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| 104 | !! Assumes a C-grid |
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| 105 | !! |
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| 106 | !! The points in the C-grid look like this, my darling |
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| 107 | !! |
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| 108 | !! (ji,jj) |
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| 109 | !! | |
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| 110 | !! | |
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| 111 | !! (ji-1,jj) | (ji,jj) |
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| 112 | !! --------- |
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| 113 | !! | | |
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| 114 | !! | (ji,jj) |------(ji,jj) |
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| 115 | !! | | |
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| 116 | !! --------- |
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| 117 | !! (ji-1,jj-1) (ji,jj-1) |
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| 118 | !! |
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| 119 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 120 | !! ice total volume (vt_i) per unit area |
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| 121 | !! snow total volume (vt_s) per unit area |
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| 122 | !! |
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| 123 | !! ** Action : |
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| 124 | !! |
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| 125 | !! ** Steps : |
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| 126 | !! |
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| 127 | !! ** Notes : |
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| 128 | !! |
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| 129 | !! References : Zhang and Hibler, JGR 1997; Losch et al., OM 2010., Lemieux et al., 2008, 2009, ... |
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| 130 | !! |
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| 131 | !! |
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| 132 | !!------------------------------------------------------------------- |
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| 133 | !! |
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| 134 | INTEGER , INTENT(in ) :: kt ! time step |
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| 135 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
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| 136 | !! |
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| 137 | LOGICAL :: ll_u_iterate, ll_v_iterate ! continue iteration or not |
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| 138 | ! |
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| 139 | INTEGER :: ji, ji2, jj, jj2, jn ! dummy loop indices |
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| 140 | INTEGER :: i_out, i_inn, i_inn_tot ! |
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| 141 | INTEGER :: ji_min, jj_min ! |
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| 142 | INTEGER :: nn_zebra_vp ! number of zebra steps |
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| 143 | |
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| 144 | ! |
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| 145 | REAL(wp) :: zrhoco ! rho0 * rn_cio |
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| 146 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
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| 147 | REAL(wp) :: zglob_area ! global ice area for diagnostics |
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| 148 | REAL(wp) :: zkt ! isotropic tensile strength for landfast ice |
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| 149 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV ! ice/snow mass and volume |
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| 150 | REAL(wp) :: zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars |
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| 151 | REAL(wp) :: zp_delstar_f ! |
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| 152 | REAL(wp) :: zu_cV, zv_cU ! |
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| 153 | REAL(wp) :: zfac, zfac1, zfac2, zfac3 |
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| 154 | REAL(wp) :: zt12U, zt11U, zt22U, zt21U, zt122U, zt121U |
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| 155 | REAL(wp) :: zt12V, zt11V, zt22V, zt21V, zt122V, zt121V |
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| 156 | REAL(wp) :: zAA3, zw, ztau, zuerr_max, zverr_max |
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| 157 | ! |
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| 158 | REAL(wp), DIMENSION(jpi,jpj) :: za_iU , za_iV ! ice fraction on U/V points |
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| 159 | REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! Acceleration term contribution to RHS |
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| 160 | REAL(wp), DIMENSION(jpi,jpj) :: zmassU_t, zmassV_t ! Mass per unit area divided by time step |
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| 161 | ! |
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| 162 | REAL(wp), DIMENSION(jpi,jpj) :: zdeltat, zdelstar_t ! Delta & Delta* at T-points |
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| 163 | REAL(wp), DIMENSION(jpi,jpj) :: ztens, zshear ! Tension, shear |
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| 164 | REAL(wp), DIMENSION(jpi,jpj) :: zp_delstar_t ! P/delta* at T points |
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| 165 | REAL(wp), DIMENSION(jpi,jpj) :: zzt, zet ! Viscosity pre-factors at T points |
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| 166 | REAL(wp), DIMENSION(jpi,jpj) :: zef ! Viscosity pre-factor at F point |
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| 167 | ! |
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| 168 | REAL(wp), DIMENSION(jpi,jpj) :: zmt ! Mass per unit area at t-point |
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| 169 | REAL(wp), DIMENSION(jpi,jpj) :: zmf ! Coriolis factor (m*f) at t-point |
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| 170 | 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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| 171 | REAL(wp), DIMENSION(jpi,jpj) :: zu_c, zv_c ! "current" ice velocity (m/s), average of previous two OL iterates |
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| 172 | REAL(wp), DIMENSION(jpi,jpj) :: zu_b, zv_b ! velocity at previous sub-iterate |
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| 173 | REAL(wp), DIMENSION(jpi,jpj) :: zuerr, zverr ! absolute U/Vvelocity difference between current and previous sub-iterates |
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| 174 | ! |
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| 175 | REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear |
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| 176 | REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope: |
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| 177 | ! ! ocean surface (ssh_m) if ice is not embedded |
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| 178 | ! ! ice bottom surface if ice is embedded |
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| 179 | REAL(wp), DIMENSION(jpi,jpj) :: zCwU, zCwV ! ice-ocean drag pre-factor (rho*c*module(u)) |
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| 180 | REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points |
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| 181 | REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array |
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| 182 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points |
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| 183 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi_rhsu, ztauy_oi_rhsv ! ice-ocean stress RHS contribution at U-V points |
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| 184 | REAL(wp), DIMENSION(jpi,jpj) :: zs1_rhsu, zs2_rhsu, zs12_rhsu ! internal stress contributions to RHSU |
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| 185 | REAL(wp), DIMENSION(jpi,jpj) :: zs1_rhsv, zs2_rhsv, zs12_rhsv ! internal stress contributions to RHSV |
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| 186 | REAL(wp), DIMENSION(jpi,jpj) :: zf_rhsu, zf_rhsv ! U- and V- components of internal force RHS contributions |
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| 187 | REAL(wp), DIMENSION(jpi,jpj) :: zrhsu, zrhsv ! U and V RHS |
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| 188 | REAL(wp), DIMENSION(jpi,jpj) :: zAU, zBU, zCU, zDU, zEU ! Linear system coefficients, U equation |
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| 189 | REAL(wp), DIMENSION(jpi,jpj) :: zAV, zBV, zCV, zDV, zEV ! Linear system coefficients, V equation |
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| 190 | REAL(wp), DIMENSION(jpi,jpj) :: zFU, zFU_prime, zBU_prime ! Rearranged linear system coefficients, U equation |
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| 191 | REAL(wp), DIMENSION(jpi,jpj) :: zFV, zFV_prime, zBV_prime ! Rearranged linear system coefficients, V equation |
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| 192 | !!! REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast) |
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| 193 | !!! REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast) |
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| 194 | ! |
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| 195 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00 |
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| 196 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! mask for lots of ice (1), little ice (0) |
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| 197 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence (1), no ice (0) |
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| 198 | ! |
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| 199 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
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| 200 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small |
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| 201 | REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small |
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| 202 | !! --- diags |
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| 203 | REAL(wp) :: zsig1, zsig2, zsig12, zdelta, z1_strength, zfac_x, zfac_y |
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| 204 | REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12, zs12f ! stress tensor components |
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| 205 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig_I, zsig_II, zsig1_p, zsig2_p |
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| 206 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztaux_oi, ztauy_oi |
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| 207 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice, zdiag_ymtrp_ice ! X/Y-component of ice mass transport (kg/s, SIMIP) |
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| 208 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw, zdiag_ymtrp_snw ! X/Y-component of snow mass transport (kg/s, SIMIP) |
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| 209 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp, zdiag_yatrp ! X/Y-component of area transport (m2/s, SIMIP) |
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| 210 | |
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| 211 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zvel_res ! Residual of the linear system at last iteration |
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| 212 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zvel_diff ! Absolute velocity difference @last outer iteration |
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| 213 | |
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| 214 | |
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| 215 | !!---------------------------------------------------------------------------------------------------------------------- |
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| 216 | |
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| 217 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_vp: VP sea-ice rheology (LSR solver)' |
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| 218 | IF( lwp ) WRITE(numout,*) '-- ice_dyn_rhg_vp: VP sea-ice rheology (LSR solver)' |
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| 219 | |
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| 220 | !------------------------------------------------------------------------------! |
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| 221 | ! |
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| 222 | ! --- Initialization |
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| 223 | ! |
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| 224 | !------------------------------------------------------------------------------! |
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| 225 | |
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| 226 | ! for diagnostics and convergence tests |
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| 227 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 228 | zmsk00(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice , 0 if no ice |
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| 229 | END_2D |
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| 230 | |
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| 231 | IF ( lp_zebra_vp ) THEN; nn_zebra_vp = 2 |
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| 232 | ELSE; nn_zebra_vp = 1; ENDIF |
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| 233 | |
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| 234 | nn_nvp = nn_vp_nout * nn_vp_ninn ! maximum number of iterations |
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| 235 | |
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| 236 | IF( lwp ) WRITE(numout,*) ' lp_zebra_vp : ', lp_zebra_vp |
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| 237 | IF( lwp ) WRITE(numout,*) ' nn_zebra_vp : ', nn_zebra_vp |
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| 238 | IF( lwp ) WRITE(numout,*) ' nn_nvp : ', nn_nvp |
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| 239 | |
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| 240 | zrhoco = rho0 * rn_cio |
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| 241 | |
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| 242 | ! ecc2: square of yield ellipse eccentricity |
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| 243 | ecc2 = rn_ecc * rn_ecc |
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| 244 | z1_ecc2 = 1._wp / ecc2 |
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| 245 | |
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| 246 | ! Initialise convergence checks |
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| 247 | IF( nn_rhg_chkcvg /= 0 ) THEN |
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| 248 | |
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| 249 | ! ice area for global mean kinetic energy (m2) |
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| 250 | zglob_area = glob_sum( 'ice_rhg_vp', at_i(:,:) * e1e2t(:,:) * tmask(:,:,1) ) |
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| 251 | |
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| 252 | ENDIF |
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| 253 | |
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| 254 | ! Landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) |
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| 255 | ! MV: Not working yet... |
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| 256 | IF( ln_landfast_L16 ) THEN ; zkt = rn_lf_tensile |
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| 257 | ELSE ; zkt = 0._wp |
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| 258 | ENDIF |
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| 259 | |
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| 260 | zs1_rhsu(:,:) = 0._wp; zs2_rhsu(:,:) = 0._wp; zs1_rhsv(:,:) = 0._wp; zs2_rhsv(:,:) = 0._wp |
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| 261 | zrhsu (:,:) = 0._wp; zrhsv (:,:) = 0._wp; zf_rhsu(:,:) = 0._wp; zf_rhsv(:,:) = 0._wp |
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| 262 | zAU(:,:) = 0._wp; zBU(:,:) = 0._wp; zCU(:,:) = 0._wp; zDU(:,:) = 0._wp; zEU(:,:) = 0._wp |
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| 263 | zAV(:,:) = 0._wp; zBV(:,:) = 0._wp; zCV(:,:) = 0._wp; zDV(:,:) = 0._wp; zEV(:,:) = 0._wp |
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| 264 | |
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| 265 | !------------------------------------------------------------------------------! |
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| 266 | ! |
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| 267 | ! --- Time-independent quantities |
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| 268 | ! |
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| 269 | !------------------------------------------------------------------------------! |
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| 270 | |
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| 271 | CALL ice_strength ! strength at T points |
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| 272 | |
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| 273 | !--------------------------- |
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| 274 | ! -- F-mask (code from EVP) |
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| 275 | !--------------------------- |
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| 276 | IF( kt == nit000 ) THEN |
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| 277 | ! MartinV: |
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| 278 | ! In EVP routine, fimask is applied on shear at F-points, in order to enforce the lateral boundary condition (no-slip, ..., free-slip) |
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| 279 | ! I am not sure the same recipe applies here |
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| 280 | |
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| 281 | ! - ocean/land mask |
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| 282 | ALLOCATE( fimask(jpi,jpj) ) |
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| 283 | IF( rn_ishlat == 0._wp ) THEN |
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| 284 | DO_2D( 0, 0, 0, 0 ) |
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| 285 | fimask(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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| 286 | END_2D |
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| 287 | ELSE |
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| 288 | DO_2D( 0, 0, 0, 0 ) |
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| 289 | fimask(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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| 290 | ! Lateral boundary conditions on velocity (modify fimask) |
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| 291 | IF( fimask(ji,jj) == 0._wp ) THEN |
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| 292 | fimask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(ji,jj,1), umask(ji,jj+1,1), & |
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| 293 | & vmask(ji,jj,1), vmask(ji+1,jj,1) ) ) |
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| 294 | ENDIF |
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| 295 | END_2D |
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| 296 | ENDIF |
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| 297 | |
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| 298 | CALL lbc_lnk( 'icedyn_rhg_vp', fimask, 'F', 1._wp ) |
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| 299 | ENDIF |
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| 300 | |
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| 301 | !---------------------------------------------------------------------------------------------------------- |
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| 302 | ! -- Time-independent pre-factors for acceleration, ocean drag, coriolis, atmospheric drag, surface tilt |
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| 303 | !---------------------------------------------------------------------------------------------------------- |
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| 304 | ! Compute all terms & factors independent of velocities, or only depending on velocities at previous time step |
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| 305 | |
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| 306 | ! sea surface height |
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| 307 | ! embedded sea ice: compute representative ice top surface |
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| 308 | ! non-embedded sea ice: use ocean surface for slope calculation |
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| 309 | zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) |
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| 310 | |
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| 311 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 312 | zmt(ji,jj) = rhos * vt_s(ji,jj) + rhoi * vt_i(ji,jj) ! Snow and ice mass at T-point |
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| 313 | zmf(ji,jj) = zmt(ji,jj) * ff_t(ji,jj) ! Coriolis factor at T points (m*f) |
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| 314 | END_2D |
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| 315 | |
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| 316 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
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| 317 | |
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| 318 | ! Ice fraction at U-V points |
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| 319 | za_iU(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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| 320 | za_iV(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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| 321 | |
|---|
| 322 | ! Snow and ice mass at U-V points |
|---|
| 323 | zm1 = zmt(ji,jj) |
|---|
| 324 | zm2 = zmt(ji+1,jj) |
|---|
| 325 | zm3 = zmt(ji,jj+1) |
|---|
| 326 | zmassU = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
|---|
| 327 | zmassV = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 328 | |
|---|
| 329 | ! Mass per unit area divided by time step |
|---|
| 330 | zmassU_t(ji,jj) = zmassU * r1_Dt_ice |
|---|
| 331 | zmassV_t(ji,jj) = zmassV * r1_Dt_ice |
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| 332 | |
|---|
| 333 | ! Acceleration term contribution to RHS (depends on velocity at previous time step) |
|---|
| 334 | zmU_t(ji,jj) = zmassU_t(ji,jj) * u_ice(ji,jj) |
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| 335 | zmV_t(ji,jj) = zmassV_t(ji,jj) * v_ice(ji,jj) |
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| 336 | |
|---|
| 337 | ! Ocean currents at U-V points |
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| 338 | 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) |
|---|
| 339 | 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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| 340 | |
|---|
| 341 | ! Wind stress |
|---|
| 342 | ztaux_ai(ji,jj) = za_iU(ji,jj) * utau_ice(ji,jj) |
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| 343 | ztauy_ai(ji,jj) = za_iV(ji,jj) * vtau_ice(ji,jj) |
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| 344 | |
|---|
| 345 | ! Force due to sea surface tilt(- m*g*GRAD(ssh)) |
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| 346 | zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) |
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| 347 | zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) |
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| 348 | |
|---|
| 349 | ! Mask for ice presence (1) or absence (0) |
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| 350 | zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
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| 351 | zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
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| 352 | |
|---|
| 353 | ! Mask for lots of ice (1) or little ice (0) |
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| 354 | IF ( zmassU <= zmmin .AND. za_iU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp |
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| 355 | ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF |
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| 356 | IF ( zmassV <= zmmin .AND. za_iV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp |
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| 357 | ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF |
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| 358 | |
|---|
| 359 | END_2D |
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| 360 | |
|---|
| 361 | !------------------------------------------------------------------------------! |
|---|
| 362 | ! |
|---|
| 363 | ! --- Start outer loop |
|---|
| 364 | ! |
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| 365 | !------------------------------------------------------------------------------! |
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| 366 | |
|---|
| 367 | zu_c(:,:) = u_ice(:,:) |
|---|
| 368 | zv_c(:,:) = v_ice(:,:) |
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| 369 | |
|---|
| 370 | i_inn_tot = 0 |
|---|
| 371 | |
|---|
| 372 | DO i_out = 1, nn_vp_nout |
|---|
| 373 | |
|---|
| 374 | ! Velocities used in the non linear terms are the average of the past two iterates |
|---|
| 375 | ! u_it = 0.5 * ( u_{it-1} + u_{it-2} ) |
|---|
| 376 | ! Also used in Hibler and Ackley (1983); Zhang and Hibler (1997); Lemieux and Tremblay (2009) |
|---|
| 377 | zu_c(:,:) = 0.5_wp * ( u_ice(:,:) + zu_c(:,:) ) |
|---|
| 378 | zv_c(:,:) = 0.5_wp * ( v_ice(:,:) + zv_c(:,:) ) |
|---|
| 379 | |
|---|
| 380 | !------------------------------------------------------------------------------! |
|---|
| 381 | ! |
|---|
| 382 | ! --- Right-hand side (RHS) of the linear problem |
|---|
| 383 | ! |
|---|
| 384 | !------------------------------------------------------------------------------! |
|---|
| 385 | ! In the outer loop, one needs to update all RHS terms |
|---|
| 386 | ! with explicit velocity dependencies (viscosities, coriolis, ocean stress) |
|---|
| 387 | ! as a function of "current" velocities (uc, vc) |
|---|
| 388 | |
|---|
| 389 | !------------------------------------------ |
|---|
| 390 | ! -- Strain rates, viscosities and P/Delta |
|---|
| 391 | !------------------------------------------ |
|---|
| 392 | |
|---|
| 393 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 394 | DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 ) ! 1->jpi-1 |
|---|
| 395 | |
|---|
| 396 | ! loops start at 1 since there is no boundary condition (lbc_lnk) at i=1 and j=1 for F points |
|---|
| 397 | ! shear at F points |
|---|
| 398 | zds(ji,jj) = ( ( zu_c(ji,jj+1) * r1_e1u(ji,jj+1) - zu_c(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) & |
|---|
| 399 | & + ( zv_c(ji+1,jj) * r1_e2v(ji+1,jj) - zv_c(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 400 | & ) * r1_e1e2f(ji,jj) * fimask(ji,jj) |
|---|
| 401 | |
|---|
| 402 | END_2D |
|---|
| 403 | |
|---|
| 404 | CALL lbc_lnk( 'icedyn_rhg_vp', zds, 'F', 1. ) ! necessary, zds2 uses jpi/jpj values for zds |
|---|
| 405 | |
|---|
| 406 | DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls ) ! 2 -> jpj; 2,jpi !!! CHECK !!! |
|---|
| 407 | ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 |
|---|
| 408 | |
|---|
| 409 | ! shear**2 at T points (doc eq. A16) |
|---|
| 410 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 411 | & + 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) & |
|---|
| 412 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 413 | |
|---|
| 414 | ! divergence at T points |
|---|
| 415 | zdiv = ( e2u(ji,jj) * zu_c(ji,jj) - e2u(ji-1,jj) * zu_c(ji-1,jj) & |
|---|
| 416 | & + e1v(ji,jj) * zv_c(ji,jj) - e1v(ji,jj-1) * zv_c(ji,jj-1) & |
|---|
| 417 | & ) * r1_e1e2t(ji,jj) |
|---|
| 418 | zdiv2 = zdiv * zdiv |
|---|
| 419 | |
|---|
| 420 | ! tension at T points |
|---|
| 421 | zdt = ( ( zu_c(ji,jj) * r1_e2u(ji,jj) - zu_c(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 422 | & - ( zv_c(ji,jj) * r1_e1v(ji,jj) - zv_c(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 423 | & ) * r1_e1e2t(ji,jj) |
|---|
| 424 | zdt2 = zdt * zdt |
|---|
| 425 | |
|---|
| 426 | ! delta at T points |
|---|
| 427 | zdeltat(ji,jj) = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 428 | |
|---|
| 429 | ! delta* at T points (following Lemieux and Dupont, GMD 2020) |
|---|
| 430 | zdelstar_t(ji,jj) = zdeltat(ji,jj) + rn_creepl ! OPT zdelstar_t can be totally removed and put into next line directly. Could change results |
|---|
| 431 | |
|---|
| 432 | ! P/delta* at T-points |
|---|
| 433 | zp_delstar_t(ji,jj) = strength(ji,jj) / zdelstar_t(ji,jj) |
|---|
| 434 | |
|---|
| 435 | ! Temporary zzt and zet factors at T-points |
|---|
| 436 | zzt(ji,jj) = zp_delstar_t(ji,jj) * r1_e1e2t(ji,jj) |
|---|
| 437 | zet(ji,jj) = zzt(ji,jj) * z1_ecc2 |
|---|
| 438 | |
|---|
| 439 | END_2D |
|---|
| 440 | |
|---|
| 441 | CALL lbc_lnk( 'icedyn_rhg_vp', zp_delstar_t , 'T', 1. ) ! necessary, used for ji = 1 and jj = 1 |
|---|
| 442 | |
|---|
| 443 | DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )! 1-> jpj-1; 1->jpi-1 |
|---|
| 444 | |
|---|
| 445 | ! P/delta* at F points |
|---|
| 446 | zp_delstar_f = 0.25_wp * ( zp_delstar_t(ji,jj) + zp_delstar_t(ji+1,jj) + zp_delstar_t(ji,jj+1) + zp_delstar_t(ji+1,jj+1) ) |
|---|
| 447 | |
|---|
| 448 | ! Temporary zef factor at F-point |
|---|
| 449 | zef(ji,jj) = zp_delstar_f * r1_e1e2f(ji,jj) * z1_ecc2 * fimask(ji,jj) * 0.5_wp |
|---|
| 450 | |
|---|
| 451 | END_2D |
|---|
| 452 | |
|---|
| 453 | !--------------------------------------------------- |
|---|
| 454 | ! -- Ocean-ice drag and Coriolis RHS contributions |
|---|
| 455 | !--------------------------------------------------- |
|---|
| 456 | |
|---|
| 457 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 458 | |
|---|
| 459 | !--- ice u-velocity @V points, v-velocity @U points (for non-linear drag computation) |
|---|
| 460 | zu_cV = 0.25_wp * ( zu_c(ji,jj) + zu_c(ji-1,jj) + zu_c(ji,jj+1) + zu_c(ji-1,jj+1) ) * vmask(ji,jj,1) |
|---|
| 461 | zv_cU = 0.25_wp * ( zv_c(ji,jj) + zv_c(ji,jj-1) + zv_c(ji+1,jj) + zv_c(ji+1,jj-1) ) * umask(ji,jj,1) |
|---|
| 462 | |
|---|
| 463 | !--- non-linear drag coefficients (need to be updated at each outer loop, see Lemieux and Tremblay JGR09, p.3, beginning of Section 3) |
|---|
| 464 | zCwU(ji,jj) = za_iU(ji,jj) * zrhoco * SQRT( ( zu_c (ji,jj) - u_oce (ji,jj) ) * ( zu_c (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 465 | & + ( zv_cU - v_oceU(ji,jj) ) * ( zv_cU - v_oceU(ji,jj) ) ) |
|---|
| 466 | zCwV(ji,jj) = za_iV(ji,jj) * zrhoco * SQRT( ( zv_c (ji,jj) - v_oce (ji,jj) ) * ( zv_c (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 467 | & + ( zu_cV - u_oceV(ji,jj) ) * ( zu_cV - u_oceV(ji,jj) ) ) |
|---|
| 468 | |
|---|
| 469 | !--- Ocean-ice drag contributions to RHS |
|---|
| 470 | ztaux_oi_rhsu(ji,jj) = zCwU(ji,jj) * u_oce(ji,jj) |
|---|
| 471 | ztauy_oi_rhsv(ji,jj) = zCwV(ji,jj) * v_oce(ji,jj) |
|---|
| 472 | |
|---|
| 473 | !--- U-component of Coriolis Force (energy conserving formulation) |
|---|
| 474 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 475 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * zv_c(ji ,jj) + e1v(ji ,jj-1) * zv_c(ji ,jj-1) ) & |
|---|
| 476 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * zv_c(ji+1,jj) + e1v(ji+1,jj-1) * zv_c(ji+1,jj-1) ) ) |
|---|
| 477 | |
|---|
| 478 | !--- V-component of Coriolis Force (energy conserving formulation) |
|---|
| 479 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 480 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * zu_c(ji,jj ) + e2u(ji-1,jj ) * zu_c(ji-1,jj ) ) & |
|---|
| 481 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * zu_c(ji,jj+1) + e2u(ji-1,jj+1) * zu_c(ji-1,jj+1) ) ) |
|---|
| 482 | |
|---|
| 483 | END_2D |
|---|
| 484 | |
|---|
| 485 | !------------------------------------- |
|---|
| 486 | ! -- Internal stress RHS contribution |
|---|
| 487 | !------------------------------------- |
|---|
| 488 | |
|---|
| 489 | ! --- Stress contributions at T-points |
|---|
| 490 | DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls ) ! 2 -> jpj; 2,jpi !!! CHECK !!! |
|---|
| 491 | |
|---|
| 492 | ! loop to jpi,jpj to avoid making a communication for zs1 & zs2 |
|---|
| 493 | |
|---|
| 494 | ! sig1 contribution to RHS of U-equation at T-points |
|---|
| 495 | zs1_rhsu(ji,jj) = zzt(ji,jj) * ( e1v(ji,jj) * zv_c(ji,jj) - e1v(ji,jj-1) * zv_c(ji,jj-1) ) & |
|---|
| 496 | & - zp_delstar_t(ji,jj) * zdeltat(ji,jj) |
|---|
| 497 | |
|---|
| 498 | ! sig2 contribution to RHS of U-equation at T-points |
|---|
| 499 | zs2_rhsu(ji,jj) = - zet(ji,jj) * ( r1_e1v(ji,jj) * zv_c(ji,jj) - r1_e1v(ji,jj-1) * zv_c(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) |
|---|
| 500 | |
|---|
| 501 | ! sig1 contribution to RHS of V-equation at T-points |
|---|
| 502 | zs1_rhsv(ji,jj) = zzt(ji,jj) * ( e2u(ji,jj) * zu_c(ji,jj) - e2u(ji-1,jj) * zu_c(ji-1,jj) ) & |
|---|
| 503 | & - zp_delstar_t(ji,jj) * zdeltat(ji,jj) |
|---|
| 504 | |
|---|
| 505 | ! sig2 contribution to RHS of V-equation at T-points |
|---|
| 506 | zs2_rhsv(ji,jj) = zet(ji,jj) * ( r1_e2u(ji,jj) * zu_c(ji,jj) - r1_e2u(ji-1,jj) * zu_c(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) |
|---|
| 507 | |
|---|
| 508 | END_2D |
|---|
| 509 | |
|---|
| 510 | ! --- Stress contributions at F-points |
|---|
| 511 | ! MV NOTE: I applied fimask on zds, by mimetism on EVP, but without deep understanding of what I was doing |
|---|
| 512 | ! My guess is that this is the way to enforce boundary conditions on strain rate tensor |
|---|
| 513 | |
|---|
| 514 | DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 ) ! 1->jpi-1 |
|---|
| 515 | |
|---|
| 516 | ! sig12 contribution to RHS of U equation at F-points |
|---|
| 517 | zs12_rhsu(ji,jj) = zef(ji,jj) * ( r1_e2v(ji+1,jj) * zv_c(ji+1,jj) + r1_e2v(ji,jj) * zv_c(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) * fimask(ji,jj) |
|---|
| 518 | |
|---|
| 519 | ! sig12 contribution to RHS of V equation at F-points |
|---|
| 520 | zs12_rhsv(ji,jj) = zef(ji,jj) * ( r1_e1u(ji,jj+1) * zu_c(ji,jj+1) + r1_e1u(ji,jj) * zu_c(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) * fimask(ji,jj) |
|---|
| 521 | |
|---|
| 522 | END_2D |
|---|
| 523 | |
|---|
| 524 | ! --- Internal force contributions to RHS, taken as divergence of stresses (Appendix C of Hunke and Dukowicz, 2002) |
|---|
| 525 | ! OPT: merge with next loop and use intermediate scalars for zf_rhsu |
|---|
| 526 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 527 | |
|---|
| 528 | ! --- U component of internal force contribution to RHS at U points |
|---|
| 529 | zf_rhsu(ji,jj) = 0.5_wp * r1_e1e2u(ji,jj) * & |
|---|
| 530 | ( e2u(ji,jj) * ( zs1_rhsu(ji+1,jj) - zs1_rhsu(ji,jj) ) & |
|---|
| 531 | & + r1_e2u(ji,jj) * ( e2t(ji+1,jj) * e2t(ji+1,jj) * zs2_rhsu(ji+1,jj) - e2t(ji,jj) * e2t(ji,jj) * zs2_rhsu(ji,jj) ) & |
|---|
| 532 | & + 2._wp * r1_e1u(ji,jj) * ( e1f(ji,jj) * e1f(ji,jj) * zs12_rhsu(ji,jj) - e1f(ji,jj-1) * e1f(ji,jj-1) * zs12_rhsu(ji,jj-1) ) ) |
|---|
| 533 | |
|---|
| 534 | ! --- V component of internal force contribution to RHS at V points |
|---|
| 535 | zf_rhsv(ji,jj) = 0.5_wp * r1_e1e2v(ji,jj) * & |
|---|
| 536 | & ( e1v(ji,jj) * ( zs1_rhsv(ji,jj+1) - zs1_rhsv(ji,jj) ) & |
|---|
| 537 | & - r1_e1v(ji,jj) * ( e1t(ji,jj+1) * e1t(ji,jj+1) * zs2_rhsv(ji,jj+1) - e1t(ji,jj) * e1t(ji,jj) * zs2_rhsv(ji,jj) ) & |
|---|
| 538 | & + 2._wp * r1_e2v(ji,jj) * ( e2f(ji,jj) * e2f(ji,jj) * zs12_rhsv(ji,jj) - e2f(ji-1,jj) * e2f(ji-1,jj) * zs12_rhsv(ji-1,jj) ) ) |
|---|
| 539 | |
|---|
| 540 | END_2D |
|---|
| 541 | |
|---|
| 542 | !--------------------------- |
|---|
| 543 | ! -- Sum RHS contributions |
|---|
| 544 | !--------------------------- |
|---|
| 545 | ! |
|---|
| 546 | ! OPT: could use intermediate scalars to reduce memory access |
|---|
| 547 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 548 | |
|---|
| 549 | zrhsu(ji,jj) = zmU_t(ji,jj) + ztaux_ai(ji,jj) + ztaux_oi_rhsu(ji,jj) + zspgU(ji,jj) + zCorU(ji,jj) + zf_rhsu(ji,jj) |
|---|
| 550 | zrhsv(ji,jj) = zmV_t(ji,jj) + ztauy_ai(ji,jj) + ztauy_oi_rhsv(ji,jj) + zspgV(ji,jj) + zCorV(ji,jj) + zf_rhsv(ji,jj) |
|---|
| 551 | |
|---|
| 552 | END_2D |
|---|
| 553 | |
|---|
| 554 | !---------------------------------------------------------------------------------------! |
|---|
| 555 | ! |
|---|
| 556 | ! --- Linear system matrix |
|---|
| 557 | ! |
|---|
| 558 | !---------------------------------------------------------------------------------------! |
|---|
| 559 | |
|---|
| 560 | ! Linear system matrix contains all implicit contributions |
|---|
| 561 | ! 1) internal forces, 2) acceleration, 3) ice-ocean drag |
|---|
| 562 | |
|---|
| 563 | ! The linear system equation is written as follows |
|---|
| 564 | ! AU * u_{i-1,j} + BU * u_{i,j} + CU * u_{i+1,j} |
|---|
| 565 | ! = DU * u_{i,j-1} + EU * u_{i,j+1} + RHS (! my convention, not the same as ZH97 ) |
|---|
| 566 | |
|---|
| 567 | ! MV Note 1: martin losch applies boundary condition to BU in mitGCM - check whether it is necessary here ? |
|---|
| 568 | ! MV Note 2: "T" factor calculations can be optimized by putting things out of the loop |
|---|
| 569 | ! only zzt and zet are iteration-dependent, other only depend on scale factors |
|---|
| 570 | |
|---|
| 571 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 572 | |
|---|
| 573 | !------------------------------------- |
|---|
| 574 | ! -- Internal forces LHS contribution |
|---|
| 575 | !------------------------------------- |
|---|
| 576 | ! |
|---|
| 577 | ! --- U-component |
|---|
| 578 | ! |
|---|
| 579 | ! "T" factors (intermediate results) |
|---|
| 580 | ! |
|---|
| 581 | zfac = 0.5_wp * r1_e1e2u(ji,jj) |
|---|
| 582 | zfac1 = zfac * e2u(ji,jj) |
|---|
| 583 | zfac2 = zfac * r1_e2u(ji,jj) |
|---|
| 584 | zfac3 = 2._wp * zfac * r1_e1u(ji,jj) |
|---|
| 585 | |
|---|
| 586 | zt11U = zfac1 * zzt(ji,jj) |
|---|
| 587 | zt12U = zfac1 * zzt(ji+1,jj) |
|---|
| 588 | |
|---|
| 589 | zt21U = zfac2 * zet(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) |
|---|
| 590 | zt22U = zfac2 * zet(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) |
|---|
| 591 | |
|---|
| 592 | zt121U = zfac3 * zef(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) |
|---|
| 593 | zt122U = zfac3 * zef(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) |
|---|
| 594 | |
|---|
| 595 | ! |
|---|
| 596 | ! Linear system coefficients |
|---|
| 597 | ! |
|---|
| 598 | zAU(ji,jj) = - zt11U * e2u(ji-1,jj) - zt21U * r1_e2u(ji-1,jj) |
|---|
| 599 | zBU(ji,jj) = ( zt11U + zt12U ) * e2u(ji,jj) + ( zt21U + zt22U ) * r1_e2u(ji,jj) + ( zt121U + zt122U ) * r1_e1u(ji,jj) |
|---|
| 600 | zCU(ji,jj) = - zt12U * e2u(ji+1,jj) - zt22U * r1_e2u(ji+1,jj) |
|---|
| 601 | |
|---|
| 602 | zDU(ji,jj) = zt121U * r1_e1u(ji,jj-1) |
|---|
| 603 | zEU(ji,jj) = zt122U * r1_e1u(ji,jj+1) |
|---|
| 604 | |
|---|
| 605 | ! |
|---|
| 606 | ! --- V-component |
|---|
| 607 | ! |
|---|
| 608 | ! "T" factors (intermediate results) |
|---|
| 609 | ! |
|---|
| 610 | zfac = 0.5_wp * r1_e1e2v(ji,jj) |
|---|
| 611 | zfac1 = zfac * e1v(ji,jj) |
|---|
| 612 | zfac2 = zfac * r1_e1v(ji,jj) |
|---|
| 613 | zfac3 = 2._wp * zfac * r1_e2v(ji,jj) |
|---|
| 614 | |
|---|
| 615 | zt11V = zfac1 * zzt(ji,jj) |
|---|
| 616 | zt12V = zfac1 * zzt(ji,jj+1) |
|---|
| 617 | |
|---|
| 618 | zt21V = zfac2 * zet(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) |
|---|
| 619 | zt22V = zfac2 * zet(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) |
|---|
| 620 | |
|---|
| 621 | zt121V = zfac3 * zef(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) |
|---|
| 622 | zt122V = zfac3 * zef(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) |
|---|
| 623 | |
|---|
| 624 | ! |
|---|
| 625 | ! Linear system coefficients |
|---|
| 626 | ! |
|---|
| 627 | zAV(ji,jj) = - zt11V * e1v(ji,jj-1) - zt21V * r1_e1v(ji,jj-1) |
|---|
| 628 | zBV(ji,jj) = ( zt11V + zt12V ) * e1v(ji,jj) + ( zt21V + zt22V ) * r1_e1v(ji,jj) + ( zt122V + zt121V ) * r1_e2v(ji,jj) |
|---|
| 629 | zCV(ji,jj) = - zt12V * e1v(ji,jj+1) - zt22V * r1_e1v(ji,jj+1) |
|---|
| 630 | |
|---|
| 631 | zDV(ji,jj) = zt121V * r1_e2v(ji-1,jj) |
|---|
| 632 | zEV(ji,jj) = zt122V * r1_e2v(ji+1,jj) |
|---|
| 633 | |
|---|
| 634 | !----------------------------------------------------- |
|---|
| 635 | ! -- Ocean-ice drag and acceleration LHS contribution |
|---|
| 636 | !----------------------------------------------------- |
|---|
| 637 | zBU(ji,jj) = zBU(ji,jj) + zCwU(ji,jj) + zmassU_t(ji,jj) |
|---|
| 638 | zBV(ji,jj) = zBV(ji,jj) + zCwV(ji,jj) + zmassV_t(ji,jj) |
|---|
| 639 | |
|---|
| 640 | END_2D |
|---|
| 641 | |
|---|
| 642 | !------------------------------------------------------------------------------! |
|---|
| 643 | ! |
|---|
| 644 | ! --- Inner loop: solve linear system, check convergence |
|---|
| 645 | ! |
|---|
| 646 | !------------------------------------------------------------------------------! |
|---|
| 647 | |
|---|
| 648 | ! Inner loop solves the linear problem .. requires 1500 iterations |
|---|
| 649 | ll_u_iterate = .TRUE. |
|---|
| 650 | ll_v_iterate = .TRUE. |
|---|
| 651 | |
|---|
| 652 | DO i_inn = 1, nn_vp_ninn ! inner loop iterations |
|---|
| 653 | |
|---|
| 654 | !--- mitgcm computes initial value of residual here... |
|---|
| 655 | |
|---|
| 656 | i_inn_tot = i_inn_tot + 1 |
|---|
| 657 | ! l_full_nf_update = i_inn_tot == nn_nvp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 |
|---|
| 658 | |
|---|
| 659 | zu_b(:,:) = u_ice(:,:) ! velocity at previous inner-iterate |
|---|
| 660 | zv_b(:,:) = v_ice(:,:) |
|---|
| 661 | |
|---|
| 662 | IF ( ll_u_iterate .OR. ll_v_iterate ) THEN |
|---|
| 663 | |
|---|
| 664 | ! ---------------------------- ! |
|---|
| 665 | IF ( ll_u_iterate ) THEN ! --- Solve for u-velocity --- ! |
|---|
| 666 | ! ---------------------------- ! |
|---|
| 667 | |
|---|
| 668 | ! What follows could be subroutinized... |
|---|
| 669 | |
|---|
| 670 | ! Thomas Algorithm for tridiagonal solver |
|---|
| 671 | ! A*u(i-1,j)+B*u(i,j)+C*u(i+1,j) = F |
|---|
| 672 | |
|---|
| 673 | zFU(:,:) = 0._wp ; zFU_prime(:,:) = 0._wp ; zBU_prime(:,:) = 0._wp; |
|---|
| 674 | |
|---|
| 675 | DO jn = 1, nn_zebra_vp ! "zebra" loop (! red-black-sor!!! ) |
|---|
| 676 | |
|---|
| 677 | ! OPT: could be even better optimized with a true red-black SOR |
|---|
| 678 | |
|---|
| 679 | IF ( jn == 1 ) THEN ; jj_min = 2 |
|---|
| 680 | ELSE ; jj_min = 3 |
|---|
| 681 | ENDIF |
|---|
| 682 | |
|---|
| 683 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 684 | |
|---|
| 685 | !------------------------ |
|---|
| 686 | ! Independent term (zFU) |
|---|
| 687 | !------------------------ |
|---|
| 688 | DO ji = 2, jpi - 1 |
|---|
| 689 | ! note: these are key lines linking information between processors |
|---|
| 690 | ! u_ice/v_ice need to be lbc_linked |
|---|
| 691 | |
|---|
| 692 | ! sub-domain boundary condition substitution |
|---|
| 693 | ! see Zhang and Hibler, 1997, Appendix B |
|---|
| 694 | zAA3 = 0._wp |
|---|
| 695 | IF ( ji == 2 ) zAA3 = zAA3 - zAU(ji,jj) * u_ice(ji-1,jj) |
|---|
| 696 | IF ( ji == jpi - 1 ) zAA3 = zAA3 - zCU(ji,jj) * u_ice(ji+1,jj) |
|---|
| 697 | |
|---|
| 698 | ! right hand side |
|---|
| 699 | zFU(ji,jj) = ( zrhsu(ji,jj) & ! right-hand side terms |
|---|
| 700 | & + zAA3 & ! boundary condition translation |
|---|
| 701 | & + zDU(ji,jj) * u_ice(ji,jj-1) & ! internal force, j-1 |
|---|
| 702 | & + zEU(ji,jj) * u_ice(ji,jj+1) ) * umask(ji,jj,1) ! internal force, j+1 |
|---|
| 703 | |
|---|
| 704 | END DO |
|---|
| 705 | |
|---|
| 706 | END DO |
|---|
| 707 | |
|---|
| 708 | !--------------- |
|---|
| 709 | ! Forward sweep |
|---|
| 710 | !--------------- |
|---|
| 711 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 712 | |
|---|
| 713 | zBU_prime(2,jj) = zBU(2,jj) |
|---|
| 714 | zFU_prime(2,jj) = zFU(2,jj) |
|---|
| 715 | |
|---|
| 716 | DO ji = 3, jpi - 1 |
|---|
| 717 | |
|---|
| 718 | zfac = SIGN( 1._wp , zBU(ji-1,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU(ji-1,jj) ) - epsi20 ) ) |
|---|
| 719 | zw = zfac * zAU(ji,jj) / MAX ( ABS( zBU(ji-1,jj) ) , epsi20 ) |
|---|
| 720 | zBU_prime(ji,jj) = zBU(ji,jj) - zw * zCU(ji-1,jj) |
|---|
| 721 | zFU_prime(ji,jj) = zFU(ji,jj) - zw * zFU(ji-1,jj) |
|---|
| 722 | |
|---|
| 723 | END DO |
|---|
| 724 | |
|---|
| 725 | END DO |
|---|
| 726 | |
|---|
| 727 | !----------------------------- |
|---|
| 728 | ! Backward sweep & relaxation |
|---|
| 729 | !----------------------------- |
|---|
| 730 | |
|---|
| 731 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 732 | |
|---|
| 733 | ! --- Backward sweep |
|---|
| 734 | |
|---|
| 735 | ! last row |
|---|
| 736 | zfac = SIGN( 1._wp , zBU_prime(jpi-1,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU_prime(jpi-1,jj) ) - epsi20 ) ) |
|---|
| 737 | u_ice(jpi-1,jj) = zfac * zFU_prime(jpi-1,jj) / MAX( ABS ( zBU_prime(jpi-1,jj) ) , epsi20 ) & |
|---|
| 738 | & * umask(jpi-1,jj,1) |
|---|
| 739 | |
|---|
| 740 | DO ji = jpi - 2 , 2, -1 ! all other rows ! ---> original backward loop |
|---|
| 741 | zfac = SIGN( 1._wp , zBU_prime(ji,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU_prime(ji,jj) ) - epsi20 ) ) |
|---|
| 742 | u_ice(ji,jj) = zfac * ( zFU_prime(ji,jj) - zCU(ji,jj) * u_ice(ji+1,jj) ) * umask(ji,jj,1) & |
|---|
| 743 | & / MAX ( ABS ( zBU_prime(ji,jj) ) , epsi20 ) |
|---|
| 744 | END DO |
|---|
| 745 | |
|---|
| 746 | !--- Relaxation and masking (for low-ice/no-ice cases) |
|---|
| 747 | DO ji = 2, jpi - 1 |
|---|
| 748 | |
|---|
| 749 | u_ice(ji,jj) = zu_b(ji,jj) + zrelaxu_vp * ( u_ice(ji,jj) - zu_b(ji,jj) ) ! relaxation |
|---|
| 750 | |
|---|
| 751 | u_ice(ji,jj) = zmsk00x(ji,jj) & ! masking |
|---|
| 752 | & * ( zmsk01x(ji,jj) * u_ice(ji,jj) & |
|---|
| 753 | & + ( 1._wp - zmsk01x(ji,jj) ) * u_oce(ji,jj) * 0.01_wp ) * umask(ji,jj,1) |
|---|
| 754 | |
|---|
| 755 | END DO |
|---|
| 756 | |
|---|
| 757 | END DO ! jj |
|---|
| 758 | |
|---|
| 759 | CALL lbc_lnk( 'icedyn_rhg_vp', u_ice, 'U', -1. ) |
|---|
| 760 | |
|---|
| 761 | END DO ! zebra loop |
|---|
| 762 | |
|---|
| 763 | ENDIF ! ll_u_iterate |
|---|
| 764 | |
|---|
| 765 | ! ! ---------------------------- ! |
|---|
| 766 | IF ( ll_v_iterate ) THEN ! --- Solve for V-velocity --- ! |
|---|
| 767 | ! ! ---------------------------- ! |
|---|
| 768 | |
|---|
| 769 | ! MV OPT: what follows could be subroutinized... |
|---|
| 770 | ! Thomas Algorithm for tridiagonal solver |
|---|
| 771 | ! A*v(i,j-1)+B*v(i,j)+C*v(i,j+1) = F |
|---|
| 772 | ! It is intentional to have a ji then jj loop for V-velocity |
|---|
| 773 | !!! ZH97 explain it is critical for convergence speed |
|---|
| 774 | |
|---|
| 775 | zFV(:,:) = 0._wp ; zFV_prime(:,:) = 0._wp ; zBV_prime(:,:) = 0._wp; |
|---|
| 776 | |
|---|
| 777 | DO jn = 1, nn_zebra_vp ! "zebra" loop |
|---|
| 778 | |
|---|
| 779 | IF ( jn == 1 ) THEN ; ji_min = 2 |
|---|
| 780 | ELSE ; ji_min = 3 |
|---|
| 781 | ENDIF |
|---|
| 782 | |
|---|
| 783 | DO ji = ji_min, jpi - 1, nn_zebra_vp |
|---|
| 784 | |
|---|
| 785 | !------------------------ |
|---|
| 786 | ! Independent term (zFV) |
|---|
| 787 | !------------------------ |
|---|
| 788 | DO jj = 2, jpj - 1 |
|---|
| 789 | |
|---|
| 790 | ! subdomain boundary condition substitution (check it is correctly applied !!!) |
|---|
| 791 | ! see Zhang and Hibler, 1997, Appendix B |
|---|
| 792 | zAA3 = 0._wp |
|---|
| 793 | IF ( jj == 2 ) zAA3 = zAA3 - zAV(ji,jj) * v_ice(ji,jj-1) |
|---|
| 794 | IF ( jj == jpj - 1 ) zAA3 = zAA3 - zCV(ji,jj) * v_ice(ji,jj+1) |
|---|
| 795 | |
|---|
| 796 | ! right hand side |
|---|
| 797 | zFV(ji,jj) = ( zrhsv(ji,jj) & ! right-hand side terms |
|---|
| 798 | & + zAA3 & ! boundary condition translation |
|---|
| 799 | & + zDV(ji,jj) * v_ice(ji-1,jj) & ! internal force, j-1 |
|---|
| 800 | & + zEV(ji,jj) * v_ice(ji+1,jj) ) * vmask(ji,jj,1) ! internal force, j+1 |
|---|
| 801 | |
|---|
| 802 | END DO |
|---|
| 803 | |
|---|
| 804 | END DO |
|---|
| 805 | |
|---|
| 806 | !--------------- |
|---|
| 807 | ! Forward sweep |
|---|
| 808 | !--------------- |
|---|
| 809 | DO ji = ji_min, jpi - 1, nn_zebra_vp |
|---|
| 810 | |
|---|
| 811 | zBV_prime(ji,2) = zBV(ji,2) |
|---|
| 812 | zFV_prime(ji,2) = zFV(ji,2) |
|---|
| 813 | |
|---|
| 814 | DO jj = 3, jpj - 1 |
|---|
| 815 | |
|---|
| 816 | zfac = SIGN( 1._wp , zBV(ji,jj-1) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV(ji,jj-1) ) - epsi20 ) ) |
|---|
| 817 | zw = zfac * zAV(ji,jj) / MAX ( ABS( zBV(ji,jj-1) ) , epsi20 ) |
|---|
| 818 | zBV_prime(ji,jj) = zBV(ji,jj) - zw * zCV(ji,jj-1) |
|---|
| 819 | zFV_prime(ji,jj) = zFV(ji,jj) - zw * zFV(ji,jj-1) |
|---|
| 820 | |
|---|
| 821 | END DO |
|---|
| 822 | |
|---|
| 823 | END DO |
|---|
| 824 | |
|---|
| 825 | !----------------------------- |
|---|
| 826 | ! Backward sweep & relaxation |
|---|
| 827 | !----------------------------- |
|---|
| 828 | DO ji = ji_min, jpi - 1, nn_zebra_vp |
|---|
| 829 | |
|---|
| 830 | ! --- Backward sweep |
|---|
| 831 | ! last row |
|---|
| 832 | zfac = SIGN( 1._wp , zBV_prime(ji,jpj-1) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV_prime(ji,jpj-1) ) - epsi20 ) ) |
|---|
| 833 | v_ice(ji,jpj-1) = zfac * zFV_prime(ji,jpj-1) / MAX ( ABS(zBV_prime(ji,jpj-1) ) , epsi20 ) & |
|---|
| 834 | & * vmask(ji,jpj-1,1) ! last row |
|---|
| 835 | |
|---|
| 836 | ! other rows |
|---|
| 837 | DO jj = jpj-2, 2, -1 ! original back loop |
|---|
| 838 | zfac = SIGN( 1._wp , zBV_prime(ji,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV_prime(ji,jj) ) - epsi20 ) ) |
|---|
| 839 | v_ice(ji,jj) = zfac * ( zFV_prime(ji,jj) - zCV(ji,jj) * v_ice(ji,jj+1) ) * vmask(ji,jj,1) & |
|---|
| 840 | & / MAX ( ABS( zBV_prime(ji,jj) ) , epsi20 ) |
|---|
| 841 | END DO |
|---|
| 842 | |
|---|
| 843 | ! --- Relaxation & masking |
|---|
| 844 | DO jj = 2, jpj - 1 |
|---|
| 845 | |
|---|
| 846 | v_ice(ji,jj) = zv_b(ji,jj) + zrelaxv_vp * ( v_ice(ji,jj) - zv_b(ji,jj) ) ! relaxation |
|---|
| 847 | |
|---|
| 848 | v_ice(ji,jj) = zmsk00y(ji,jj) & ! masking |
|---|
| 849 | & * ( zmsk01y(ji,jj) * v_ice(ji,jj) & |
|---|
| 850 | & + ( 1._wp - zmsk01y(ji,jj) ) * v_oce(ji,jj) * 0.01_wp ) * vmask(ji,jj,1) |
|---|
| 851 | |
|---|
| 852 | END DO ! jj |
|---|
| 853 | |
|---|
| 854 | END DO ! ji |
|---|
| 855 | |
|---|
| 856 | CALL lbc_lnk( 'icedyn_rhg_vp', v_ice, 'V', -1. ) |
|---|
| 857 | |
|---|
| 858 | END DO ! zebra loop |
|---|
| 859 | |
|---|
| 860 | ENDIF ! ll_v_iterate |
|---|
| 861 | |
|---|
| 862 | ! I suspect the communication should go into the zebra loop if we want reproducibility |
|---|
| 863 | |
|---|
| 864 | !-------------------------------------------------------------------------------------- |
|---|
| 865 | ! -- Check convergence based on maximum velocity difference, continue or stop the loop |
|---|
| 866 | !-------------------------------------------------------------------------------------- |
|---|
| 867 | |
|---|
| 868 | !------ |
|---|
| 869 | ! on U |
|---|
| 870 | !------ |
|---|
| 871 | ! MV OPT: if the number of iterations to convergence is really variable, and keep the convergence check |
|---|
| 872 | ! then we must optimize the use of the mpp_max, which is prohibitive |
|---|
| 873 | zuerr_max = 0._wp |
|---|
| 874 | |
|---|
| 875 | IF ( ll_u_iterate .AND. MOD ( i_inn, nn_vp_chkcvg ) == 0 ) THEN |
|---|
| 876 | |
|---|
| 877 | ! - Maximum U-velocity difference |
|---|
| 878 | zuerr(:,:) = 0._wp |
|---|
| 879 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 880 | |
|---|
| 881 | zuerr(ji,jj) = ABS ( ( u_ice(ji,jj) - zu_b(ji,jj) ) ) * umask(ji,jj,1) |
|---|
| 882 | |
|---|
| 883 | END_2D |
|---|
| 884 | |
|---|
| 885 | zuerr_max = MAXVAL( zuerr ) |
|---|
| 886 | CALL mpp_max( 'icedyn_rhg_evp', zuerr_max ) ! max over the global domain - damned! |
|---|
| 887 | |
|---|
| 888 | ! - Stop if max error is too large ("safeguard against bad forcing" of original Zhang routine) |
|---|
| 889 | IF ( i_inn > 1 .AND. zuerr_max > zuerr_max_vp ) THEN |
|---|
| 890 | IF ( lwp ) WRITE(numout,*) " VP rheology error was too large : ", zuerr_max, " in outer U-iteration ", i_out, " after ", i_inn, " iterations, we stopped " |
|---|
| 891 | ll_u_iterate = .FALSE. |
|---|
| 892 | ENDIF |
|---|
| 893 | |
|---|
| 894 | ! - Stop if error small enough |
|---|
| 895 | IF ( zuerr_max < zuerr_min_vp ) THEN |
|---|
| 896 | IF ( lwp ) WRITE(numout,*) " VP rheology nicely done in outer U-iteration ", i_out, " after ", i_inn, " iterations, finished! " |
|---|
| 897 | ll_u_iterate = .FALSE. |
|---|
| 898 | ENDIF |
|---|
| 899 | |
|---|
| 900 | ENDIF ! ll_u_iterate |
|---|
| 901 | |
|---|
| 902 | !------ |
|---|
| 903 | ! on V |
|---|
| 904 | !------ |
|---|
| 905 | zverr_max = 0._wp |
|---|
| 906 | |
|---|
| 907 | IF ( ll_v_iterate .AND. MOD ( i_inn, nn_vp_chkcvg ) == 0 ) THEN |
|---|
| 908 | |
|---|
| 909 | ! - Maximum V-velocity difference |
|---|
| 910 | zverr(:,:) = 0._wp |
|---|
| 911 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 912 | |
|---|
| 913 | zverr(ji,jj) = ABS ( ( v_ice(ji,jj) - zv_b(ji,jj) ) ) * vmask(ji,jj,1) |
|---|
| 914 | |
|---|
| 915 | END_2D |
|---|
| 916 | |
|---|
| 917 | zverr_max = MAXVAL( zverr ) |
|---|
| 918 | CALL mpp_max( 'icedyn_rhg_evp', zverr_max ) ! max over the global domain - damned! |
|---|
| 919 | |
|---|
| 920 | ! - Stop if error is too large ("safeguard against bad forcing" of original Zhang routine) |
|---|
| 921 | IF ( i_inn > 1 .AND. zverr_max > zuerr_max_vp ) THEN |
|---|
| 922 | IF ( lwp ) WRITE(numout,*) " VP rheology error was too large : ", zverr_max, " in outer V-iteration ", i_out, " after ", i_inn, " iterations, we stopped " |
|---|
| 923 | ll_v_iterate = .FALSE. |
|---|
| 924 | ENDIF |
|---|
| 925 | |
|---|
| 926 | ! - Stop if error small enough |
|---|
| 927 | IF ( zverr_max < zuerr_min_vp ) THEN |
|---|
| 928 | IF ( lwp ) WRITE(numout,*) " VP rheology nicely done in outer V-iteration ", i_out, " after ", i_inn, " iterations, finished! " |
|---|
| 929 | ll_v_iterate = .FALSE. |
|---|
| 930 | ENDIF |
|---|
| 931 | |
|---|
| 932 | ENDIF ! ll_v_iterate |
|---|
| 933 | |
|---|
| 934 | ENDIF ! --- end ll_u_iterate or ll_v_iterate |
|---|
| 935 | |
|---|
| 936 | !--------------------------------------------------------------------------------------- |
|---|
| 937 | ! |
|---|
| 938 | ! --- Calculate extra convergence diagnostics and save them |
|---|
| 939 | ! |
|---|
| 940 | !--------------------------------------------------------------------------------------- |
|---|
| 941 | IF( nn_rhg_chkcvg/=0 .AND. MOD ( i_inn - 1, nn_vp_chkcvg ) == 0 ) THEN |
|---|
| 942 | |
|---|
| 943 | CALL rhg_cvg_vp( kt, i_out, i_inn, i_inn_tot, nn_vp_nout, nn_vp_ninn, nn_nvp, & |
|---|
| 944 | & u_ice, v_ice, zu_b, zv_b, zu_c, zv_c, & |
|---|
| 945 | & zmt, za_iU, za_iV, zuerr_max, zverr_max, zglob_area, & |
|---|
| 946 | & zrhsu, zAU, zBU, zCU, zDU, zEU, zFU, & |
|---|
| 947 | & zrhsv, zAV, zBV, zCV, zDV, zEV, zFV, & |
|---|
| 948 | zvel_res, zvel_diff ) |
|---|
| 949 | |
|---|
| 950 | ENDIF |
|---|
| 951 | |
|---|
| 952 | END DO ! i_inn, end of inner loop |
|---|
| 953 | |
|---|
| 954 | END DO ! End of outer loop (i_out) ============================================================================================= |
|---|
| 955 | |
|---|
| 956 | IF( nn_rhg_chkcvg/=0 ) THEN |
|---|
| 957 | |
|---|
| 958 | IF( iom_use('velo_res') ) CALL iom_put( 'velo_res', zvel_res ) ! linear system residual @last inner&outer iteration |
|---|
| 959 | IF( iom_use('velo_ero') ) CALL iom_put( 'velo_ero', zvel_diff ) ! abs velocity difference @last outer iteration |
|---|
| 960 | IF( iom_use('uice_eri') ) CALL iom_put( 'uice_eri', zuerr ) ! abs velocity difference @last inner iteration |
|---|
| 961 | IF( iom_use('vice_eri') ) CALL iom_put( 'vice_eri', zverr ) ! abs velocity difference @last inner iteration |
|---|
| 962 | |
|---|
| 963 | DEALLOCATE( zvel_res , zvel_diff ) |
|---|
| 964 | |
|---|
| 965 | ENDIF ! nn_rhg_chkcvg |
|---|
| 966 | |
|---|
| 967 | !------------------------------------------------------------------------------! |
|---|
| 968 | ! |
|---|
| 969 | ! --- Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 970 | ! |
|---|
| 971 | !------------------------------------------------------------------------------! |
|---|
| 972 | ! |
|---|
| 973 | ! MV OPT: subroutinize ? |
|---|
| 974 | DO_2D( nn_hls, nn_hls, nn_hls-1, nn_hls-1 ) ! 1->jpj-1; 1->jpi-1 |
|---|
| 975 | |
|---|
| 976 | ! shear at F points |
|---|
| 977 | 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) & |
|---|
| 978 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 979 | & ) * r1_e1e2f(ji,jj) * fimask(ji,jj) |
|---|
| 980 | |
|---|
| 981 | END_2D |
|---|
| 982 | |
|---|
| 983 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 984 | |
|---|
| 985 | ! tension**2 at T points |
|---|
| 986 | 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) & |
|---|
| 987 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 988 | & ) * r1_e1e2t(ji,jj) |
|---|
| 989 | zdt2 = zdt * zdt |
|---|
| 990 | |
|---|
| 991 | ztens(ji,jj) = zdt |
|---|
| 992 | |
|---|
| 993 | ! shear**2 at T points (doc eq. A16) |
|---|
| 994 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 995 | & + 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) & |
|---|
| 996 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 997 | |
|---|
| 998 | ! maximum shear rate at T points (includees tension, output only) |
|---|
| 999 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) ! i think this is maximum shear rate and not actual shear --- i'm not totally sure here |
|---|
| 1000 | |
|---|
| 1001 | ! shear at T-points |
|---|
| 1002 | zshear(ji,jj) = SQRT( zds2 ) |
|---|
| 1003 | |
|---|
| 1004 | ! divergence at T points |
|---|
| 1005 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 1006 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 1007 | & ) * r1_e1e2t(ji,jj) |
|---|
| 1008 | |
|---|
| 1009 | zdiv2 = pdivu_i(ji,jj) * pdivu_i(ji,jj) |
|---|
| 1010 | |
|---|
| 1011 | ! delta at T points |
|---|
| 1012 | zdelta = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 1013 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 |
|---|
| 1014 | |
|---|
| 1015 | pdelta_i(ji,jj) = zdelta + rn_creepl ! * rswitch |
|---|
| 1016 | |
|---|
| 1017 | END_2D |
|---|
| 1018 | |
|---|
| 1019 | CALL lbc_lnk( 'icedyn_rhg_vp', pshear_i, 'T', 1., pdivu_i, 'T', 1., pdelta_i, 'T', 1. ) |
|---|
| 1020 | |
|---|
| 1021 | !------------------------------------------------------------------------------! |
|---|
| 1022 | ! |
|---|
| 1023 | ! --- Diagnostics |
|---|
| 1024 | ! |
|---|
| 1025 | !------------------------------------------------------------------------------! |
|---|
| 1026 | ! |
|---|
| 1027 | ! MV OPT: subroutinize ? |
|---|
| 1028 | ! |
|---|
| 1029 | !---------------------------------- |
|---|
| 1030 | ! --- Recompute stresses if needed |
|---|
| 1031 | !---------------------------------- |
|---|
| 1032 | ! |
|---|
| 1033 | ! ---- Sea ice stresses at T-points |
|---|
| 1034 | IF ( iom_use('normstr') .OR. iom_use('sheastr') .OR. & |
|---|
| 1035 | & iom_use('intstrx') .OR. iom_use('intstry') .OR. & |
|---|
| 1036 | & iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN |
|---|
| 1037 | |
|---|
| 1038 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1039 | |
|---|
| 1040 | zp_delstar_t(ji,jj) = strength(ji,jj) / pdelta_i(ji,jj) |
|---|
| 1041 | zfac = zp_delstar_t(ji,jj) |
|---|
| 1042 | zs1(ji,jj) = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) ) |
|---|
| 1043 | zs2(ji,jj) = zfac * z1_ecc2 * ztens(ji,jj) |
|---|
| 1044 | zs12(ji,jj) = zfac * z1_ecc2 * zshear(ji,jj) * 0.5_wp ! Bug 12 nov |
|---|
| 1045 | |
|---|
| 1046 | END_2D |
|---|
| 1047 | |
|---|
| 1048 | CALL lbc_lnk( 'icedyn_rhg_vp', zs1, 'T', 1., zs2, 'T', 1., zs12, 'T', 1. ) |
|---|
| 1049 | |
|---|
| 1050 | ENDIF |
|---|
| 1051 | |
|---|
| 1052 | ! ---- s12 at F-points |
|---|
| 1053 | IF ( iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 1054 | |
|---|
| 1055 | DO_2D( nn_hls, nn_hls, nn_hls-1, nn_hls-1 ) ! 1->jpj-1; 1->jpi-1 |
|---|
| 1056 | |
|---|
| 1057 | ! P/delta* at F points |
|---|
| 1058 | zp_delstar_f = 0.25_wp * ( zp_delstar_t(ji,jj) + zp_delstar_t(ji+1,jj) + zp_delstar_t(ji,jj+1) + zp_delstar_t(ji+1,jj+1) ) |
|---|
| 1059 | |
|---|
| 1060 | ! s12 at F-points |
|---|
| 1061 | zs12f(ji,jj) = zp_delstar_f * z1_ecc2 * zds(ji,jj) |
|---|
| 1062 | |
|---|
| 1063 | END_2D |
|---|
| 1064 | |
|---|
| 1065 | CALL lbc_lnk( 'icedyn_rhg_vp', zs12f, 'F', 1. ) |
|---|
| 1066 | |
|---|
| 1067 | ENDIF |
|---|
| 1068 | |
|---|
| 1069 | ! |
|---|
| 1070 | !----------------------- |
|---|
| 1071 | ! --- Store diagnostics |
|---|
| 1072 | !----------------------- |
|---|
| 1073 | ! |
|---|
| 1074 | ! --- Ice-ocean, ice-atm. & ice-ocean bottom (landfast) stresses --- ! |
|---|
| 1075 | IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. & |
|---|
| 1076 | & iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN |
|---|
| 1077 | |
|---|
| 1078 | ALLOCATE( ztaux_oi(jpi,jpj) , ztauy_oi(jpi,jpj) ) |
|---|
| 1079 | |
|---|
| 1080 | !--- Recalculate oceanic stress at last inner iteration |
|---|
| 1081 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1082 | |
|---|
| 1083 | !--- ice u-velocity @V points, v-velocity @U points (for non-linear drag computation) |
|---|
| 1084 | zu_cV = 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) |
|---|
| 1085 | zv_cU = 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) |
|---|
| 1086 | |
|---|
| 1087 | !--- non-linear drag coefficients (need to be updated at each outer loop, see Lemieux and Tremblay JGR09, p.3, beginning of Section 3) |
|---|
| 1088 | zCwU(ji,jj) = za_iU(ji,jj) * zrhoco * SQRT( ( u_ice(ji,jj) - u_oce (ji,jj) ) * ( u_ice(ji,jj) - u_oce (ji,jj) ) & |
|---|
| 1089 | & + ( zv_cU - v_oceU(ji,jj) ) * ( zv_cU - v_oceU(ji,jj) ) ) |
|---|
| 1090 | zCwV(ji,jj) = za_iV(ji,jj) * zrhoco * SQRT( ( v_ice(ji,jj) - v_oce (ji,jj) ) * ( v_ice(ji,jj) - v_oce (ji,jj) ) & |
|---|
| 1091 | & + ( zu_cV - u_oceV(ji,jj) ) * ( zu_cV - u_oceV(ji,jj) ) ) |
|---|
| 1092 | |
|---|
| 1093 | !--- Ocean-ice stress |
|---|
| 1094 | ztaux_oi(ji,jj) = zCwU(ji,jj) * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 1095 | ztauy_oi(ji,jj) = zCwV(ji,jj) * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 1096 | |
|---|
| 1097 | END_2D |
|---|
| 1098 | |
|---|
| 1099 | ! |
|---|
| 1100 | CALL lbc_lnk( 'icedyn_rhg_vp', ztaux_oi, 'U', -1., ztauy_oi, 'V', -1., ztaux_ai, 'U', -1., ztauy_ai, 'V', -1. ) !, & |
|---|
| 1101 | ! & ztaux_bi, 'U', -1., ztauy_bi, 'V', -1. ) |
|---|
| 1102 | ! |
|---|
| 1103 | CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 ) |
|---|
| 1104 | CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 ) |
|---|
| 1105 | CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 ) |
|---|
| 1106 | CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 ) |
|---|
| 1107 | ! CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 ) |
|---|
| 1108 | ! CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 ) |
|---|
| 1109 | |
|---|
| 1110 | DEALLOCATE( ztaux_oi , ztauy_oi ) |
|---|
| 1111 | |
|---|
| 1112 | ENDIF |
|---|
| 1113 | |
|---|
| 1114 | ! --- Divergence, shear and strength --- ! |
|---|
| 1115 | IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence |
|---|
| 1116 | IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! maximum shear rate |
|---|
| 1117 | IF( iom_use('icedlt') ) CALL iom_put( 'icedlt' , pdelta_i * zmsk00 ) ! delta |
|---|
| 1118 | IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength |
|---|
| 1119 | |
|---|
| 1120 | ! --- Stress tensor invariants (SIMIP diags) --- ! |
|---|
| 1121 | IF( iom_use('normstr') .OR. iom_use('sheastr') ) THEN |
|---|
| 1122 | ! |
|---|
| 1123 | ! Stress tensor invariants (normal and shear stress N/m) - SIMIP diags. |
|---|
| 1124 | ! Definitions following Coon (1974) and Feltham (2008) |
|---|
| 1125 | ! |
|---|
| 1126 | ! sigma1, sigma2, sigma12 are useful (Hunke and Dukowicz MWR 2002, Bouillon et al., OM2013) |
|---|
| 1127 | ! however these are NOT stress tensor components, neither stress invariants, nor stress principal components |
|---|
| 1128 | ! |
|---|
| 1129 | ALLOCATE( zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 1130 | ! |
|---|
| 1131 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1132 | ! Stress invariants |
|---|
| 1133 | zsig_I(ji,jj) = zs1(ji,jj) * 0.5_wp ! 1st invariant, aka average normal stress aka negative pressure |
|---|
| 1134 | zsig_II(ji,jj) = 0.5_wp * SQRT ( zs2(ji,jj) * zs2(ji,jj) + 4. * zs12(ji,jj) * zs12(ji,jj) ) ! 2nd invariant, aka maximum shear stress |
|---|
| 1135 | END_2D |
|---|
| 1136 | |
|---|
| 1137 | CALL lbc_lnk( 'icedyn_rhg_vp', zsig_I, 'T', 1., zsig_II, 'T', 1.) |
|---|
| 1138 | |
|---|
| 1139 | IF( iom_use('normstr') ) CALL iom_put( 'normstr' , zsig_I(:,:) * zmsk00(:,:) ) ! Normal stress |
|---|
| 1140 | IF( iom_use('sheastr') ) CALL iom_put( 'sheastr' , zsig_II(:,:) * zmsk00(:,:) ) ! Maximum shear stress |
|---|
| 1141 | |
|---|
| 1142 | DEALLOCATE ( zsig_I, zsig_II ) |
|---|
| 1143 | |
|---|
| 1144 | ENDIF |
|---|
| 1145 | |
|---|
| 1146 | ! --- Normalized stress tensor principal components --- ! |
|---|
| 1147 | ! These are used to plot the normalized yield curve (Lemieux & Dupont, GMD 2020) |
|---|
| 1148 | ! To plot the yield curve and evaluate physical convergence, they have two recommendations |
|---|
| 1149 | ! Recommendation 1 : Use ice strength, not replacement pressure |
|---|
| 1150 | ! Recommendation 2 : Need to use deformations at PREVIOUS iterate for viscosities (see p. 1765) |
|---|
| 1151 | ! R2 means we need to recompute stresses |
|---|
| 1152 | |
|---|
| 1153 | IF( iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN |
|---|
| 1154 | ! |
|---|
| 1155 | ALLOCATE( zsig1_p(jpi,jpj) , zsig2_p(jpi,jpj) , zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 1156 | ! |
|---|
| 1157 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1158 | |
|---|
| 1159 | ! Ice stresses computed with **viscosities** (delta, p/delta) at **previous** iterates |
|---|
| 1160 | ! and **deformations** at current iterates |
|---|
| 1161 | ! following Lemieux & Dupont (2020) |
|---|
| 1162 | zfac = zp_delstar_t(ji,jj) |
|---|
| 1163 | zsig1 = zfac * ( pdivu_i(ji,jj) - zdeltat(ji,jj) ) |
|---|
| 1164 | zsig2 = zfac * z1_ecc2 * ztens(ji,jj) |
|---|
| 1165 | zsig12 = zfac * z1_ecc2 * zshear(ji,jj) * 0.5_wp ! Bugfix 12 Nov |
|---|
| 1166 | |
|---|
| 1167 | ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008), T-point |
|---|
| 1168 | zsig_I(ji,jj) = zsig1 * 0.5_wp ! 1st invariant |
|---|
| 1169 | zsig_II(ji,jj) = 0.5_wp * SQRT ( zsig2 * zsig2 + 4. *zsig12 * zsig12 ) ! 2nd invariant |
|---|
| 1170 | |
|---|
| 1171 | ! Normalized principal stresses (used to display the ellipse) |
|---|
| 1172 | z1_strength = 1._wp / MAX ( 1._wp , strength(ji,jj) ) |
|---|
| 1173 | zsig1_p(ji,jj) = ( zsig_I(ji,jj) + zsig_II(ji,jj) ) * z1_strength |
|---|
| 1174 | zsig2_p(ji,jj) = ( zsig_I(ji,jj) - zsig_II(ji,jj) ) * z1_strength |
|---|
| 1175 | |
|---|
| 1176 | END_2D |
|---|
| 1177 | ! |
|---|
| 1178 | CALL lbc_lnk( 'icedyn_rhg_vp', zsig1_p, 'T', 1., zsig2_p, 'T', 1.) |
|---|
| 1179 | ! |
|---|
| 1180 | CALL iom_put( 'sig1_pnorm' , zsig1_p ) |
|---|
| 1181 | CALL iom_put( 'sig2_pnorm' , zsig2_p ) |
|---|
| 1182 | |
|---|
| 1183 | DEALLOCATE( zsig1_p , zsig2_p , zsig_I , zsig_II ) |
|---|
| 1184 | |
|---|
| 1185 | ENDIF |
|---|
| 1186 | |
|---|
| 1187 | ! --- SIMIP, terms of tendency for momentum equation --- ! |
|---|
| 1188 | IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. & |
|---|
| 1189 | & iom_use('corstrx') .OR. iom_use('corstry') ) THEN |
|---|
| 1190 | |
|---|
| 1191 | ! --- Recalculate Coriolis stress at last inner iteration |
|---|
| 1192 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1193 | ! --- U-component |
|---|
| 1194 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 1195 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 1196 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 1197 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 1198 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 1199 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 1200 | END_2D |
|---|
| 1201 | ! |
|---|
| 1202 | CALL lbc_lnk( 'icedyn_rhg_vp', zspgU, 'U', -1., zspgV, 'V', -1., & |
|---|
| 1203 | & zCorU, 'U', -1., zCorV, 'V', -1. ) |
|---|
| 1204 | ! |
|---|
| 1205 | CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x) |
|---|
| 1206 | CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y) |
|---|
| 1207 | CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x) |
|---|
| 1208 | CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y) |
|---|
| 1209 | |
|---|
| 1210 | ENDIF |
|---|
| 1211 | |
|---|
| 1212 | IF ( iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 1213 | |
|---|
| 1214 | ! Recalculate internal forces (divergence of stress tensor) at last inner iteration |
|---|
| 1215 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1216 | |
|---|
| 1217 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 1218 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 1219 | & ) * r1_e2u(ji,jj) & |
|---|
| 1220 | & + ( zs12f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 1221 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 1222 | & ) * r1_e1e2u(ji,jj) |
|---|
| 1223 | |
|---|
| 1224 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 1225 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 1226 | & ) * r1_e1v(ji,jj) & |
|---|
| 1227 | & + ( zs12f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 1228 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 1229 | & ) * r1_e1e2v(ji,jj) |
|---|
| 1230 | |
|---|
| 1231 | END_2D |
|---|
| 1232 | |
|---|
| 1233 | CALL lbc_lnk( 'icedyn_rhg_vp', zfU, 'U', -1., zfV, 'V', -1. ) |
|---|
| 1234 | |
|---|
| 1235 | CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x) |
|---|
| 1236 | CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y) |
|---|
| 1237 | |
|---|
| 1238 | ENDIF |
|---|
| 1239 | |
|---|
| 1240 | ! --- Ice & snow mass and ice area transports |
|---|
| 1241 | IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. & |
|---|
| 1242 | & iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN |
|---|
| 1243 | ! |
|---|
| 1244 | ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 1245 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) ) |
|---|
| 1246 | ! |
|---|
| 1247 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 1248 | |
|---|
| 1249 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj) |
|---|
| 1250 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj) |
|---|
| 1251 | |
|---|
| 1252 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 1253 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 1254 | |
|---|
| 1255 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 1256 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 1257 | |
|---|
| 1258 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 1259 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 1260 | |
|---|
| 1261 | END_2D |
|---|
| 1262 | |
|---|
| 1263 | CALL lbc_lnk( 'icedyn_rhg_vp', zdiag_xmtrp_ice, 'U', -1., zdiag_ymtrp_ice, 'V', -1., & |
|---|
| 1264 | & zdiag_xmtrp_snw, 'U', -1., zdiag_ymtrp_snw, 'V', -1., & |
|---|
| 1265 | & zdiag_xatrp , 'U', -1., zdiag_yatrp , 'V', -1. ) |
|---|
| 1266 | |
|---|
| 1267 | CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 1268 | CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport |
|---|
| 1269 | CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s) |
|---|
| 1270 | CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport |
|---|
| 1271 | CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport |
|---|
| 1272 | CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport |
|---|
| 1273 | |
|---|
| 1274 | DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 1275 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 1276 | |
|---|
| 1277 | ENDIF |
|---|
| 1278 | |
|---|
| 1279 | END SUBROUTINE ice_dyn_rhg_vp |
|---|
| 1280 | |
|---|
| 1281 | |
|---|
| 1282 | SUBROUTINE rhg_cvg_vp( kt, kitout, kitinn, kitinntot, kitoutmax, kitinnmax, kitinntotmax , & |
|---|
| 1283 | & pu, pv, pub, pvb, pub_outer, pvb_outer , & |
|---|
| 1284 | & pmt, pat_iu, pat_iv, puerr_max, pverr_max, pglob_area , & |
|---|
| 1285 | & prhsu, pAU, pBU, pCU, pDU, pEU, pFU , & |
|---|
| 1286 | & prhsv, pAV, pBV, pCV, pDV, pEV, pFV , & |
|---|
| 1287 | & pvel_res, pvel_diff ) |
|---|
| 1288 | !! |
|---|
| 1289 | !!---------------------------------------------------------------------- |
|---|
| 1290 | !! *** ROUTINE rhg_cvg_vp *** |
|---|
| 1291 | !! |
|---|
| 1292 | !! ** Purpose : check convergence of VP ice rheology |
|---|
| 1293 | !! |
|---|
| 1294 | !! ** Method : create a file ice_cvg.nc containing a few convergence diagnostics |
|---|
| 1295 | !! This routine is called every sub-iteration, so it is cpu expensive |
|---|
| 1296 | !! |
|---|
| 1297 | !! Calculates / stores |
|---|
| 1298 | !! - maximum absolute U-V difference (uice_cvg, u_dif, v_dif, m/s) |
|---|
| 1299 | !! - residuals in U, V and UV-mean taken as square-root of area-weighted mean square residual (u_res, v_res, vel_res, N/m2) |
|---|
| 1300 | !! - mean kinetic energy (mke_ice, J/m2) |
|---|
| 1301 | !! |
|---|
| 1302 | !! ** Note : for the first sub-iteration, uice_cvg is set to 0 (too large otherwise) |
|---|
| 1303 | !! |
|---|
| 1304 | !!---------------------------------------------------------------------- |
|---|
| 1305 | !! |
|---|
| 1306 | INTEGER , INTENT(in) :: kt, kitout, kitinn, kitinntot ! ocean model iterate, outer, inner and total n-iterations |
|---|
| 1307 | INTEGER , INTENT(in) :: kitoutmax, kitinnmax ! max number of outer & inner iterations |
|---|
| 1308 | INTEGER , INTENT(in) :: kitinntotmax ! max number of total sub-iterations |
|---|
| 1309 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pub, pvb ! now & sub-iter-before velocities |
|---|
| 1310 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pub_outer, pvb_outer ! velocities @before outer iterations |
|---|
| 1311 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pmt, pat_iu, pat_iv ! mass at T-point, ice concentration at U&V |
|---|
| 1312 | REAL(wp), INTENT(in) :: puerr_max, pverr_max ! absolute mean velocity difference |
|---|
| 1313 | REAL(wp), INTENT(in) :: pglob_area ! global ice area |
|---|
| 1314 | REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsu, pAU, pBU, pCU, pDU, pEU, pFU ! linear system coefficients |
|---|
| 1315 | REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsv, pAV, pBV, pCV, pDV, pEV, pFV |
|---|
| 1316 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pvel_res ! velocity residual @last inner iteration |
|---|
| 1317 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pvel_diff ! velocity difference @last outer iteration |
|---|
| 1318 | !! |
|---|
| 1319 | |
|---|
| 1320 | INTEGER :: idtime, istatus, ix_dim, iy_dim |
|---|
| 1321 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 1322 | INTEGER :: it_inn_file, it_out_file |
|---|
| 1323 | REAL(wp) :: zu_res_mean, zv_res_mean, zvel_res_mean ! mean residuals of the linear system |
|---|
| 1324 | REAL(wp) :: zu_mad, zv_mad, zvel_mad ! mean absolute deviation, sub-iterates |
|---|
| 1325 | REAL(wp) :: zu_mad_outer, zv_mad_outer, zvel_mad_outer ! mean absolute deviation, outer-iterates |
|---|
| 1326 | REAL(wp) :: zvel_err_max, zmke, zu, zv ! local scalars |
|---|
| 1327 | REAL(wp) :: z1_pglob_area ! inverse global ice area |
|---|
| 1328 | |
|---|
| 1329 | REAL(wp), DIMENSION(jpi,jpj) :: zu_res, zv_res, zvel2 ! local arrays |
|---|
| 1330 | REAL(wp), DIMENSION(jpi,jpj) :: zu_diff, zv_diff ! local arrays |
|---|
| 1331 | |
|---|
| 1332 | CHARACTER(len=20) :: clname |
|---|
| 1333 | !!---------------------------------------------------------------------- |
|---|
| 1334 | |
|---|
| 1335 | |
|---|
| 1336 | IF( lwp ) THEN |
|---|
| 1337 | |
|---|
| 1338 | WRITE(numout,*) |
|---|
| 1339 | WRITE(numout,*) 'rhg_cvg_vp : ice rheology convergence control' |
|---|
| 1340 | WRITE(numout,*) '~~~~~~~~~~~' |
|---|
| 1341 | WRITE(numout,*) ' kt = : ', kt |
|---|
| 1342 | WRITE(numout,*) ' kitout = : ', kitout |
|---|
| 1343 | WRITE(numout,*) ' kitinn = : ', kitinn |
|---|
| 1344 | WRITE(numout,*) ' kitinntot = : ', kitinntot |
|---|
| 1345 | WRITE(numout,*) ' kitoutmax (nn_vp_nout) = ', kitoutmax |
|---|
| 1346 | WRITE(numout,*) ' kitinnmax (nn_vp_ninn) = ', kitinnmax |
|---|
| 1347 | WRITE(numout,*) ' kitinntotmax (nn_nvp) = ', kitinntotmax |
|---|
| 1348 | WRITE(numout,*) |
|---|
| 1349 | |
|---|
| 1350 | ENDIF |
|---|
| 1351 | |
|---|
| 1352 | z1_pglob_area = 1._wp / pglob_area ! inverse global ice area |
|---|
| 1353 | |
|---|
| 1354 | ! create file |
|---|
| 1355 | IF( kt == nit000 .AND. kitinntot == 1 ) THEN |
|---|
| 1356 | ! |
|---|
| 1357 | IF( lwm ) THEN |
|---|
| 1358 | |
|---|
| 1359 | clname = 'ice_cvg.nc' |
|---|
| 1360 | IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname) |
|---|
| 1361 | istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid ) |
|---|
| 1362 | |
|---|
| 1363 | istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime ) |
|---|
| 1364 | istatus = NF90_DEF_DIM( ncvgid, 'x' , jpi, ix_dim ) |
|---|
| 1365 | istatus = NF90_DEF_DIM( ncvgid, 'y' , jpj, iy_dim ) |
|---|
| 1366 | |
|---|
| 1367 | istatus = NF90_DEF_VAR( ncvgid, 'u_res' , NF90_DOUBLE , (/ idtime /), nvarid_ures ) |
|---|
| 1368 | istatus = NF90_DEF_VAR( ncvgid, 'v_res' , NF90_DOUBLE , (/ idtime /), nvarid_vres ) |
|---|
| 1369 | istatus = NF90_DEF_VAR( ncvgid, 'vel_res' , NF90_DOUBLE , (/ idtime /), nvarid_velres ) |
|---|
| 1370 | |
|---|
| 1371 | istatus = NF90_DEF_VAR( ncvgid, 'uerr_max_sub' , NF90_DOUBLE , (/ idtime /), nvarid_uerr_max ) |
|---|
| 1372 | istatus = NF90_DEF_VAR( ncvgid, 'verr_max_sub' , NF90_DOUBLE , (/ idtime /), nvarid_verr_max ) |
|---|
| 1373 | istatus = NF90_DEF_VAR( ncvgid, 'velerr_max_sub', NF90_DOUBLE , (/ idtime /), nvarid_velerr_max ) |
|---|
| 1374 | |
|---|
| 1375 | istatus = NF90_DEF_VAR( ncvgid, 'umad_sub' , NF90_DOUBLE , (/ idtime /), nvarid_umad ) |
|---|
| 1376 | istatus = NF90_DEF_VAR( ncvgid, 'vmad_sub' , NF90_DOUBLE , (/ idtime /), nvarid_vmad ) |
|---|
| 1377 | istatus = NF90_DEF_VAR( ncvgid, 'velmad_sub' , NF90_DOUBLE , (/ idtime /), nvarid_velmad ) |
|---|
| 1378 | |
|---|
| 1379 | istatus = NF90_DEF_VAR( ncvgid, 'umad_outer' , NF90_DOUBLE , (/ idtime /), nvarid_umad_outer ) |
|---|
| 1380 | istatus = NF90_DEF_VAR( ncvgid, 'vmad_outer' , NF90_DOUBLE , (/ idtime /), nvarid_vmad_outer ) |
|---|
| 1381 | istatus = NF90_DEF_VAR( ncvgid, 'velmad_outer' , NF90_DOUBLE , (/ idtime /), nvarid_velmad_outer ) |
|---|
| 1382 | |
|---|
| 1383 | istatus = NF90_DEF_VAR( ncvgid, 'mke_ice', NF90_DOUBLE , (/ idtime /), nvarid_mke ) |
|---|
| 1384 | |
|---|
| 1385 | istatus = NF90_ENDDEF(ncvgid) |
|---|
| 1386 | |
|---|
| 1387 | ENDIF |
|---|
| 1388 | ! |
|---|
| 1389 | ENDIF |
|---|
| 1390 | |
|---|
| 1391 | !------------------------------------------------------------ |
|---|
| 1392 | ! |
|---|
| 1393 | ! Max absolute velocity difference with previous sub-iterate |
|---|
| 1394 | ! ( zvel_err_max ) |
|---|
| 1395 | ! |
|---|
| 1396 | !------------------------------------------------------------ |
|---|
| 1397 | ! |
|---|
| 1398 | ! This comes from the criterion used to stop the iterative procedure |
|---|
| 1399 | zvel_err_max = 0.5_wp * ( puerr_max + pverr_max ) ! average of U- and V- maximum error over the whole domain |
|---|
| 1400 | |
|---|
| 1401 | !---------------------------------------------- |
|---|
| 1402 | ! |
|---|
| 1403 | ! Mean-absolute-deviation (sub-iterates) |
|---|
| 1404 | ! ( zu_mad, zv_mad, zvel_mad) |
|---|
| 1405 | ! |
|---|
| 1406 | !---------------------------------------------- |
|---|
| 1407 | ! |
|---|
| 1408 | ! U |
|---|
| 1409 | zu_diff(:,:) = 0._wp |
|---|
| 1410 | |
|---|
| 1411 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1412 | |
|---|
| 1413 | zu_diff(ji,jj) = ABS ( ( pu(ji,jj) - pub(ji,jj) ) ) * e1e2u(ji,jj) * pat_iu(ji,jj) * umask(ji,jj,1) * z1_pglob_area |
|---|
| 1414 | |
|---|
| 1415 | END_2D |
|---|
| 1416 | |
|---|
| 1417 | ! V |
|---|
| 1418 | zv_diff(:,:) = 0._wp |
|---|
| 1419 | |
|---|
| 1420 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1421 | |
|---|
| 1422 | zv_diff(ji,jj) = ABS ( ( pv(ji,jj) - pvb(ji,jj) ) ) * e1e2v(ji,jj) * pat_iv(ji,jj) * vmask(ji,jj,1) * z1_pglob_area |
|---|
| 1423 | |
|---|
| 1424 | END_2D |
|---|
| 1425 | |
|---|
| 1426 | ! global sum & U-V average |
|---|
| 1427 | CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_diff, 'U', 1., zv_diff , 'V', 1. ) |
|---|
| 1428 | zu_mad = glob_sum( 'icedyn_rhg_vp : ', zu_diff ) |
|---|
| 1429 | zv_mad = glob_sum( 'icedyn_rhg_vp : ', zv_diff ) |
|---|
| 1430 | |
|---|
| 1431 | zvel_mad = 0.5_wp * ( zu_mad + zv_mad ) |
|---|
| 1432 | |
|---|
| 1433 | !----------------------------------------------- |
|---|
| 1434 | ! |
|---|
| 1435 | ! Mean-absolute-deviation (outer-iterates) |
|---|
| 1436 | ! ( zu_mad_outer, zv_mad_outer, zvel_mad_outer) |
|---|
| 1437 | ! |
|---|
| 1438 | !----------------------------------------------- |
|---|
| 1439 | ! |
|---|
| 1440 | IF ( kitinn == kitinnmax ) THEN ! only work at the end of outer iterates |
|---|
| 1441 | |
|---|
| 1442 | ! * U |
|---|
| 1443 | zu_diff(:,:) = 0._wp |
|---|
| 1444 | |
|---|
| 1445 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1446 | |
|---|
| 1447 | zu_diff(ji,jj) = ABS ( ( pu(ji,jj) - pub_outer(ji,jj) ) ) * e1e2u(ji,jj) * pat_iu(ji,jj) * umask(ji,jj,1) * & |
|---|
| 1448 | & z1_pglob_area |
|---|
| 1449 | |
|---|
| 1450 | END_2D |
|---|
| 1451 | |
|---|
| 1452 | ! * V |
|---|
| 1453 | zv_diff(:,:) = 0._wp |
|---|
| 1454 | |
|---|
| 1455 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1456 | |
|---|
| 1457 | zv_diff(ji,jj) = ABS ( ( pv(ji,jj) - pvb_outer(ji,jj) ) ) * e1e2v(ji,jj) * pat_iv(ji,jj) * vmask(ji,jj,1) * & |
|---|
| 1458 | & z1_pglob_area |
|---|
| 1459 | |
|---|
| 1460 | END_2D |
|---|
| 1461 | |
|---|
| 1462 | ! Global ice-concentration, grid-cell-area weighted mean |
|---|
| 1463 | CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_diff, 'U', 1., zv_diff , 'V', 1. ) ! abs behaves as a scalar no ? |
|---|
| 1464 | |
|---|
| 1465 | zu_mad_outer = glob_sum( 'icedyn_rhg_vp : ', zu_diff ) |
|---|
| 1466 | zv_mad_outer = glob_sum( 'icedyn_rhg_vp : ', zv_diff ) |
|---|
| 1467 | |
|---|
| 1468 | ! Average of both U & V |
|---|
| 1469 | zvel_mad_outer = 0.5_wp * ( zu_mad_outer + zv_mad_outer ) |
|---|
| 1470 | |
|---|
| 1471 | ENDIF |
|---|
| 1472 | |
|---|
| 1473 | ! --- Spatially-resolved absolute difference to send back to main routine |
|---|
| 1474 | ! (last iteration only, T-point) |
|---|
| 1475 | |
|---|
| 1476 | IF ( kitinntot == kitinntotmax) THEN |
|---|
| 1477 | |
|---|
| 1478 | zu_diff(:,:) = 0._wp |
|---|
| 1479 | zv_diff(:,:) = 0._wp |
|---|
| 1480 | |
|---|
| 1481 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1482 | |
|---|
| 1483 | zu_diff(ji,jj) = ( ABS ( ( pu(ji-1,jj) - pub_outer(ji-1,jj) ) ) * umask(ji-1,jj,1) & |
|---|
| 1484 | & + ABS ( ( pu(ji,jj ) - pub_outer(ji,jj) ) ) * umask(ji,jj,1) ) & |
|---|
| 1485 | & / ( umask(ji-1,jj,1) + umask(ji,jj,1) ) |
|---|
| 1486 | |
|---|
| 1487 | zv_diff(ji,jj) = ( ABS ( ( pv(ji,jj-1) - pvb_outer(ji,jj-1) ) ) * vmask(ji,jj-1,1) & |
|---|
| 1488 | & + ABS ( ( pv(ji,jj ) - pvb_outer(ji,jj) ) ) * vmask(ji,jj,1) & |
|---|
| 1489 | & / ( vmask(ji,jj-1,1) + vmask(ji,jj,1) ) ) |
|---|
| 1490 | |
|---|
| 1491 | |
|---|
| 1492 | END_2D |
|---|
| 1493 | |
|---|
| 1494 | CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_diff, 'T', 1., zv_diff , 'T', 1. ) |
|---|
| 1495 | pvel_diff(:,:) = 0.5_wp * ( zu_diff(:,:) + zv_diff(:,:) ) |
|---|
| 1496 | |
|---|
| 1497 | ELSE |
|---|
| 1498 | |
|---|
| 1499 | pvel_diff(:,:) = 0._wp |
|---|
| 1500 | |
|---|
| 1501 | ENDIF |
|---|
| 1502 | |
|---|
| 1503 | !--------------------------------------- |
|---|
| 1504 | ! |
|---|
| 1505 | ! --- Mean residual & kinetic energy |
|---|
| 1506 | ! |
|---|
| 1507 | !--------------------------------------- |
|---|
| 1508 | |
|---|
| 1509 | IF ( kitinntot == 1 ) THEN |
|---|
| 1510 | |
|---|
| 1511 | zu_res_mean = 0._wp |
|---|
| 1512 | zv_res_mean = 0._wp |
|---|
| 1513 | zvel_res_mean = 0._wp |
|---|
| 1514 | zmke = 0._wp |
|---|
| 1515 | |
|---|
| 1516 | ELSE |
|---|
| 1517 | |
|---|
| 1518 | ! * Mean residual (N/m2) |
|---|
| 1519 | ! Here we take the residual of the linear system (N/m2), |
|---|
| 1520 | ! We define it as in mitgcm: global area-weighted mean of square-root residual |
|---|
| 1521 | ! Local residual r = Ax - B expresses to which extent the momentum balance is verified |
|---|
| 1522 | ! i.e., how close we are to a solution |
|---|
| 1523 | zu_res(:,:) = 0._wp; zv_res(:,:) = 0._wp |
|---|
| 1524 | |
|---|
| 1525 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1526 | |
|---|
| 1527 | zu_res(ji,jj) = ( prhsu(ji,jj) + pDU(ji,jj) * pu(ji,jj-1) + pEU(ji,jj) * pu(ji,jj+1) & |
|---|
| 1528 | & - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) ) |
|---|
| 1529 | zv_res(ji,jj) = ( prhsv(ji,jj) + pDV(ji,jj) * pv(ji-1,jj) + pEV(ji,jj) * pv(ji+1,jj) & |
|---|
| 1530 | & - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) ) |
|---|
| 1531 | |
|---|
| 1532 | ! zu_res(ji,jj) = pFU(ji,jj) - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) |
|---|
| 1533 | ! zv_res(ji,jj) = pFV(ji,jj) - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) |
|---|
| 1534 | |
|---|
| 1535 | zu_res(ji,jj) = SQRT( zu_res(ji,jj) * zu_res(ji,jj) ) * umask(ji,jj,1) * pat_iu(ji,jj) * e1e2u(ji,jj) * z1_pglob_area |
|---|
| 1536 | zv_res(ji,jj) = SQRT( zv_res(ji,jj) * zv_res(ji,jj) ) * vmask(ji,jj,1) * pat_iv(ji,jj) * e1e2v(ji,jj) * z1_pglob_area |
|---|
| 1537 | |
|---|
| 1538 | END_2D |
|---|
| 1539 | |
|---|
| 1540 | ! Global ice-concentration, grid-cell-area weighted mean |
|---|
| 1541 | CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_res, 'U', 1., zv_res , 'V', 1. ) |
|---|
| 1542 | |
|---|
| 1543 | zu_res_mean = glob_sum( 'ice_rhg_vp', zu_res(:,:) ) |
|---|
| 1544 | zv_res_mean = glob_sum( 'ice_rhg_vp', zv_res(:,:) ) |
|---|
| 1545 | zvel_res_mean = 0.5_wp * ( zu_res_mean + zv_res_mean ) |
|---|
| 1546 | |
|---|
| 1547 | ! --- Global mean kinetic energy per unit area (J/m2) |
|---|
| 1548 | zvel2(:,:) = 0._wp |
|---|
| 1549 | |
|---|
| 1550 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1551 | |
|---|
| 1552 | zu = 0.5_wp * ( pu(ji-1,jj) + pu(ji,jj) ) ! u-vel at T-point |
|---|
| 1553 | zv = 0.5_wp * ( pv(ji,jj-1) + pv(ji,jj) ) |
|---|
| 1554 | zvel2(ji,jj) = zu*zu + zv*zv ! square of ice velocity at T-point |
|---|
| 1555 | |
|---|
| 1556 | END_2D |
|---|
| 1557 | |
|---|
| 1558 | zmke = 0.5_wp * glob_sum( 'ice_rhg_vp', pmt(:,:) * e1e2t(:,:) * zvel2(:,:) ) / pglob_area |
|---|
| 1559 | |
|---|
| 1560 | ENDIF ! kitinntot |
|---|
| 1561 | |
|---|
| 1562 | !--- Spatially-resolved residual at last iteration to send back to main routine (last iteration only) |
|---|
| 1563 | !--- Calculation @T-point |
|---|
| 1564 | |
|---|
| 1565 | IF ( kitinntot == kitinntotmax) THEN |
|---|
| 1566 | |
|---|
| 1567 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1568 | |
|---|
| 1569 | zu_res(ji,jj) = ( prhsu(ji,jj) + pDU(ji,jj) * pu(ji,jj-1) + pEU(ji,jj) * pu(ji,jj+1) & |
|---|
| 1570 | & - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) ) |
|---|
| 1571 | zv_res(ji,jj) = ( prhsv(ji,jj) + pDV(ji,jj) * pv(ji-1,jj) + pEV(ji,jj) * pv(ji+1,jj) & |
|---|
| 1572 | & - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) ) |
|---|
| 1573 | |
|---|
| 1574 | zu_res(ji,jj) = SQRT( zu_res(ji,jj) * zu_res(ji,jj) ) * umask(ji,jj,1) |
|---|
| 1575 | zv_res(ji,jj) = SQRT( zv_res(ji,jj) * zv_res(ji,jj) ) * vmask(ji,jj,1) |
|---|
| 1576 | |
|---|
| 1577 | END_2D |
|---|
| 1578 | |
|---|
| 1579 | CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_res, 'U', 1., zv_res , 'V', 1. ) |
|---|
| 1580 | |
|---|
| 1581 | DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 |
|---|
| 1582 | |
|---|
| 1583 | pvel_res(ji,jj) = 0.25_wp * ( zu_res(ji-1,jj) + zu_res(ji,jj) + zv_res(ji,jj-1) + zv_res(ji,jj) ) |
|---|
| 1584 | |
|---|
| 1585 | END_2D |
|---|
| 1586 | CALL lbc_lnk( 'icedyn_rhg_cvg_vp', pvel_res, 'T', 1. ) |
|---|
| 1587 | |
|---|
| 1588 | ELSE |
|---|
| 1589 | |
|---|
| 1590 | pvel_res(:,:) = 0._wp |
|---|
| 1591 | |
|---|
| 1592 | ENDIF |
|---|
| 1593 | |
|---|
| 1594 | ! ! ==================== ! |
|---|
| 1595 | |
|---|
| 1596 | it_inn_file = ( kt - nit000 ) * kitinntotmax + kitinntot ! time step in the file |
|---|
| 1597 | it_out_file = ( kt - nit000 ) * kitoutmax + kitout |
|---|
| 1598 | |
|---|
| 1599 | ! write variables |
|---|
| 1600 | IF( lwm ) THEN |
|---|
| 1601 | |
|---|
| 1602 | istatus = NF90_PUT_VAR( ncvgid, nvarid_ures , (/zu_res_mean/), (/it_inn_file/), (/1/) ) ! Residuals of the linear system, area weighted mean |
|---|
| 1603 | istatus = NF90_PUT_VAR( ncvgid, nvarid_vres , (/zv_res_mean/), (/it_inn_file/), (/1/) ) ! |
|---|
| 1604 | istatus = NF90_PUT_VAR( ncvgid, nvarid_velres, (/zvel_res_mean/), (/it_inn_file/), (/1/) ) ! |
|---|
| 1605 | |
|---|
| 1606 | istatus = NF90_PUT_VAR( ncvgid, nvarid_uerr_max , (/puerr_max/), (/it_inn_file/), (/1/) ) ! Max velocit_inn_filey error, sub-it_inn_fileerates |
|---|
| 1607 | istatus = NF90_PUT_VAR( ncvgid, nvarid_verr_max , (/pverr_max/), (/it_inn_file/), (/1/) ) ! |
|---|
| 1608 | istatus = NF90_PUT_VAR( ncvgid, nvarid_velerr_max, (/zvel_err_max/), (/it_inn_file/), (/1/) ) ! |
|---|
| 1609 | |
|---|
| 1610 | istatus = NF90_PUT_VAR( ncvgid, nvarid_umad , (/zu_mad/) , (/it_inn_file/), (/1/) ) ! velocit_inn_filey MAD, area/sic-weighted, sub-it_inn_fileerates |
|---|
| 1611 | istatus = NF90_PUT_VAR( ncvgid, nvarid_vmad , (/zv_mad/) , (/it_inn_file/), (/1/) ) ! |
|---|
| 1612 | istatus = NF90_PUT_VAR( ncvgid, nvarid_velmad , (/zvel_mad/), (/it_inn_file/), (/1/) ) ! |
|---|
| 1613 | |
|---|
| 1614 | istatus = NF90_PUT_VAR( ncvgid, nvarid_mke, (/zmke/), (/kitinntot/), (/1/) ) ! mean kinetic energy |
|---|
| 1615 | |
|---|
| 1616 | IF ( kitinn == kitinnmax ) THEN ! only print outer mad at the end of inner loop |
|---|
| 1617 | |
|---|
| 1618 | istatus = NF90_PUT_VAR( ncvgid, nvarid_umad_outer , (/zu_mad_outer/) , (/it_out_file/), (/1/) ) ! velocity MAD, area/sic-weighted, outer-iterates |
|---|
| 1619 | istatus = NF90_PUT_VAR( ncvgid, nvarid_vmad_outer , (/zv_mad_outer/) , (/it_out_file/), (/1/) ) ! |
|---|
| 1620 | istatus = NF90_PUT_VAR( ncvgid, nvarid_velmad_outer , (/zvel_mad_outer/), (/it_out_file/), (/1/) ) ! |
|---|
| 1621 | |
|---|
| 1622 | ENDIF |
|---|
| 1623 | |
|---|
| 1624 | IF( kt == nitend - nn_fsbc + 1 .AND. kitinntot == kitinntotmax ) istatus = NF90_CLOSE( ncvgid ) |
|---|
| 1625 | ENDIF |
|---|
| 1626 | |
|---|
| 1627 | END SUBROUTINE rhg_cvg_vp |
|---|
| 1628 | |
|---|
| 1629 | |
|---|
| 1630 | |
|---|
| 1631 | #else |
|---|
| 1632 | !!---------------------------------------------------------------------- |
|---|
| 1633 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 1634 | !!---------------------------------------------------------------------- |
|---|
| 1635 | #endif |
|---|
| 1636 | |
|---|
| 1637 | !!============================================================================== |
|---|
| 1638 | END MODULE icedyn_rhg_vp |
|---|
| 1639 | |
|---|
