| 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 | !! for convergence tests |
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| 44 | INTEGER :: ncvgid ! netcdf file id |
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| 45 | INTEGER :: nvarid_ucvg ! netcdf variable id |
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| 46 | INTEGER :: nvarid_ures |
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| 47 | INTEGER :: nvarid_vres |
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| 48 | INTEGER :: nvarid_velres |
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| 49 | INTEGER :: nvarid_udif |
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| 50 | INTEGER :: nvarid_vdif |
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| 51 | INTEGER :: nvarid_mke |
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| 52 | INTEGER :: nvarid_usub, nvarid_vsub |
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| 53 | |
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| 54 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zmsk00, zmsk15 |
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| 55 | |
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| 56 | !!---------------------------------------------------------------------- |
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| 57 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 58 | !! $Id: icedyn_rhg_vp.F90 13279 2020-07-09 10:39:43Z clem $ |
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| 59 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 60 | !!---------------------------------------------------------------------- |
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| 61 | |
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| 62 | CONTAINS |
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| 63 | |
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| 64 | SUBROUTINE ice_dyn_rhg_vp( kt, pshear_i, pdivu_i, pdelta_i ) |
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| 65 | !!------------------------------------------------------------------- |
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| 66 | !! |
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| 67 | !! *** SUBROUTINE ice_dyn_rhg_vp *** |
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| 68 | !! VP-LSR-C-grid |
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| 69 | !! |
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| 70 | !! ** Purpose : determines sea ice drift from wind stress, ice-ocean |
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| 71 | !! stress and sea-surface slope. Internal forces assume viscous-plastic rheology (Hibler, 1979) |
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| 72 | !! |
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| 73 | !! ** Method |
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| 74 | !! |
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| 75 | !! The resolution algorithm follows from Zhang and Hibler (1997) and Losch (2010) |
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| 76 | !! with elements from Lemieux and Tremblay (2008) and Lemieux and Tremblay (2009) |
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| 77 | !! |
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| 78 | !! The components of the momentum equations are arranged following the ideas of Zhang and Hibler (1997) |
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| 79 | !! |
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| 80 | !! f1(u) = g1(v) |
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| 81 | !! f2(v) = g2(v) |
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| 82 | !! |
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| 83 | !! The right-hand side (RHS) is explicit |
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| 84 | !! The left-hand side (LHS) is implicit |
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| 85 | !! Coriolis is part of explicit terms, whereas ice-ocean drag is implicit |
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| 86 | !! |
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| 87 | !! Two iteration levels (outer and inner loops) are used to solve the equations |
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| 88 | !! |
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| 89 | !! The outer loop (OL, typically 10 iterations) is there to deal with the (strong) non-linearities in the equation |
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| 90 | !! |
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| 91 | !! The inner loop (IL, typically 1500 iterations) is there to solve the linear problem with a line-successive-relaxation algorithm |
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| 92 | !! |
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| 93 | !! The velocity used in the non-linear terms uses a "modified euler time step" (not sure its the correct term), |
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| 94 | !!! with uk = ( uk-1 + uk-2 ) / 2. |
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| 95 | !! |
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| 96 | !! * Spatial discretization |
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| 97 | !! |
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| 98 | !! Assumes a C-grid |
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| 99 | !! |
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| 100 | !! The points in the C-grid look like this, my darling |
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| 101 | !! |
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| 102 | !! (ji,jj) |
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| 103 | !! | |
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| 104 | !! | |
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| 105 | !! (ji-1,jj) | (ji,jj) |
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| 106 | !! --------- |
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| 107 | !! | | |
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| 108 | !! | (ji,jj) |------(ji,jj) |
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| 109 | !! | | |
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| 110 | !! --------- |
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| 111 | !! (ji-1,jj-1) (ji,jj-1) |
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| 112 | !! |
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| 113 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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| 114 | !! ice total volume (vt_i) per unit area |
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| 115 | !! snow total volume (vt_s) per unit area |
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| 116 | !! |
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| 117 | !! ** Action : |
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| 118 | !! |
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| 119 | !! ** Steps : |
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| 120 | !! |
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| 121 | !! ** Notes : |
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| 122 | !! |
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| 123 | !! References : Zhang and Hibler, JGR 1997; Losch et al., OM 2010., Lemieux et al., 2008, 2009, ... |
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| 124 | !! |
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| 125 | !! |
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| 126 | !!------------------------------------------------------------------- |
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| 127 | !! |
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| 128 | INTEGER , INTENT(in ) :: kt ! time step |
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| 129 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
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| 130 | !! |
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| 131 | LOGICAL :: ll_u_iterate, ll_v_iterate ! continue iteration or not |
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| 132 | ! |
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| 133 | INTEGER :: ji, ji2, jj, jn ! dummy loop indices |
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| 134 | INTEGER :: jter, i_out, i_inn ! |
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| 135 | INTEGER :: ji_min, jj_min ! |
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| 136 | INTEGER :: nn_zebra_vp ! number of zebra steps |
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| 137 | |
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| 138 | INTEGER :: nn_thomas ! tridiagonal system version (1=mitgcm, 2=martin) |
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| 139 | |
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| 140 | INTEGER :: nn_nvp ! total number of VP iterations (n_out_vp*n_inn_vp) |
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| 141 | ! |
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| 142 | REAL(wp) :: zrhoco ! rau0 * rn_cio |
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| 143 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
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| 144 | REAL(wp) :: zglob_area ! global ice area for diagnostics |
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| 145 | REAL(wp) :: zkt ! isotropic tensile strength for landfast ice |
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| 146 | REAL(wp) :: zm2, zm3, zmassU, zmassV ! ice/snow mass and volume |
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| 147 | REAL(wp) :: zdeltat, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars |
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| 148 | REAL(wp) :: zp_deltastar_f ! |
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| 149 | REAL(wp) :: zu_cV, zv_cU ! |
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| 150 | REAL(wp) :: zfac, zfac1, zfac2, zfac3 |
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| 151 | REAL(wp) :: zt12U, zt11U, zt22U, zt21U, zt122U, zt121U |
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| 152 | REAL(wp) :: zt12V, zt11V, zt22V, zt21V, zt122V, zt121V |
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| 153 | REAL(wp) :: zAA3, zw, ztau, zuerr_max, zverr_max |
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| 154 | ! |
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| 155 | REAL(wp), DIMENSION(jpi,jpj) :: zfmask ! mask at F points for the ice |
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| 156 | REAL(wp), DIMENSION(jpi,jpj) :: za_iU , za_iV ! ice fraction on U/V points |
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| 157 | REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! Acceleration term contribution to RHS |
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| 158 | REAL(wp), DIMENSION(jpi,jpj) :: zmassU_t, zmassV_t ! Mass per unit area divided by time step |
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| 159 | ! |
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| 160 | REAL(wp), DIMENSION(jpi,jpj) :: zdeltastar_t ! Delta* at T-points |
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| 161 | REAL(wp), DIMENSION(jpi,jpj) :: zten_i ! Tension |
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| 162 | REAL(wp), DIMENSION(jpi,jpj) :: zp_deltastar_t ! P/delta* at T points |
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| 163 | REAL(wp), DIMENSION(jpi,jpj) :: zzt, zet ! Viscosity pre-factors at T points |
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| 164 | REAL(wp), DIMENSION(jpi,jpj) :: zef ! Viscosity pre-factor at F point |
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| 165 | ! |
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| 166 | REAL(wp), DIMENSION(jpi,jpj) :: zmt ! Mass per unit area at t-point |
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| 167 | REAL(wp), DIMENSION(jpi,jpj) :: zmf ! Coriolis factor (m*f) at t-point |
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| 168 | 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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| 169 | REAL(wp), DIMENSION(jpi,jpj) :: zu_c, zv_c ! "current" ice velocity (m/s), average of previous two OL iterates |
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| 170 | REAL(wp), DIMENSION(jpi,jpj) :: zu_b, zv_b ! velocity at previous sub-iterate |
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| 171 | REAL(wp), DIMENSION(jpi,jpj) :: zuerr, zverr ! absolute U/Vvelocity difference between current and previous sub-iterates |
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| 172 | ! |
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| 173 | REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear |
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| 174 | REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope: |
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| 175 | ! ! ocean surface (ssh_m) if ice is not embedded |
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| 176 | ! ! ice bottom surface if ice is embedded |
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| 177 | REAL(wp), DIMENSION(jpi,jpj) :: zCwU, zCwV ! ice-ocean drag pre-factor (rho*c*module(u)) |
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| 178 | REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points |
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| 179 | REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array |
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| 180 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points |
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| 181 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi_rhsu, ztauy_oi_rhsv ! ice-ocean stress RHS contribution at U-V points |
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| 182 | REAL(wp), DIMENSION(jpi,jpj) :: zs1_rhsu, zs2_rhsu, zs12_rhsu ! internal stress contributions to RHSU |
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| 183 | REAL(wp), DIMENSION(jpi,jpj) :: zs1_rhsv, zs2_rhsv, zs12_rhsv ! internal stress contributions to RHSV |
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| 184 | REAL(wp), DIMENSION(jpi,jpj) :: zf_rhsu, zf_rhsv ! U- and V- components of internal force RHS contributions |
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| 185 | REAL(wp), DIMENSION(jpi,jpj) :: zrhsu, zrhsv ! U and V RHS |
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| 186 | REAL(wp), DIMENSION(jpi,jpj) :: zAU, zBU, zCU, zDU, zEU ! Linear system coefficients, U equation |
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| 187 | REAL(wp), DIMENSION(jpi,jpj) :: zAV, zBV, zCV, zDV, zEV ! Linear system coefficients, V equation |
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| 188 | REAL(wp), DIMENSION(jpi,jpj) :: zFU, zFU_prime, zBU_prime ! Rearranged linear system coefficients, U equation |
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| 189 | REAL(wp), DIMENSION(jpi,jpj) :: zFV, zFV_prime, zBV_prime ! Rearranged linear system coefficients, V equation |
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| 190 | REAL(wp), DIMENSION(jpi,jpj) :: zCU_prime, zCV_prime ! Rearranged linear system coefficients, V equation |
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| 191 | !!! REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast) |
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| 192 | !!! REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast) |
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| 193 | ! |
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| 194 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! mask for lots of ice (1), little ice (0) |
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| 195 | REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence (1), no ice (0) |
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| 196 | ! |
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| 197 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
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| 198 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small |
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| 199 | REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small |
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| 200 | !! --- diags |
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| 201 | REAL(wp) :: zsig1, zsig2, zsig12, zdelta, z1_strength, zfac_x, zfac_y |
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| 202 | REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12, zs12f ! stress tensor components |
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| 203 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig_I, zsig_II, zsig1_p, zsig2_p |
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| 204 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztaux_oi, ztauy_oi |
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| 205 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice, zdiag_ymtrp_ice ! X/Y-component of ice mass transport (kg/s, SIMIP) |
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| 206 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw, zdiag_ymtrp_snw ! X/Y-component of snow mass transport (kg/s, SIMIP) |
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| 207 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp, zdiag_yatrp ! X/Y-component of area transport (m2/s, SIMIP) |
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| 208 | |
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| 209 | !!---------------------------------------------------------------------------------------------------------------------- |
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| 210 | ! DEBUG put all forcing terms to zero |
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| 211 | ! air-ice drag |
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| 212 | utau_ice(:,:) = 0._wp |
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| 213 | vtau_ice(:,:) = 0._wp |
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| 214 | ! coriolis |
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| 215 | ff_t(:,:) = 0._wp |
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| 216 | ! ice-ocean drag |
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| 217 | rn_cio = 0._wp |
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| 218 | ! ssh |
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| 219 | ! done line 330 !!! dont forget to act there |
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| 220 | ! END DEBUG |
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| 221 | |
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| 222 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_vp: VP sea-ice rheology (LSR solver)' |
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| 223 | IF( lwp ) WRITE(numout,*) '-- ice_dyn_rhg_vp: VP sea-ice rheology (LSR solver)' |
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| 224 | |
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| 225 | !------------------------------------------------------------------------------! |
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| 226 | ! |
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| 227 | ! --- Initialization |
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| 228 | ! |
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| 229 | !------------------------------------------------------------------------------! |
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| 230 | |
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| 231 | ! for diagnostics and convergence tests |
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| 232 | ALLOCATE( zmsk00(jpi,jpj), zmsk15(jpi,jpj) ) |
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| 233 | DO jj = 1, jpj |
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| 234 | DO ji = 1, jpi |
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| 235 | 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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| 236 | zmsk15(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - 0.15_wp ) ) ! 1 if 15% ice, 0 if less |
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| 237 | END DO |
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| 238 | END DO |
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| 239 | |
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| 240 | IF ( ln_zebra_vp ) THEN; nn_zebra_vp = 2 |
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| 241 | ELSE; nn_zebra_vp = 1; ENDIF |
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| 242 | |
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| 243 | nn_nvp = nn_nout_vp * nn_ninn_vp ! maximum number of iterations |
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| 244 | |
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| 245 | IF( lwp ) WRITE(numout,*) ' ln_zebra_vp : ', ln_zebra_vp |
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| 246 | IF( lwp ) WRITE(numout,*) ' nn_zebra_vp : ', nn_zebra_vp |
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| 247 | IF( lwp ) WRITE(numout,*) ' nn_nvp : ', nn_nvp |
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| 248 | |
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| 249 | zrhoco = rau0 * rn_cio |
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| 250 | |
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| 251 | ! ecc2: square of yield ellipse eccentricity |
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| 252 | ecc2 = rn_ecc * rn_ecc |
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| 253 | z1_ecc2 = 1._wp / ecc2 |
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| 254 | |
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| 255 | ! Initialise convergence checks |
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| 256 | IF( ln_rhg_chkcvg ) THEN |
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| 257 | |
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| 258 | ! ice area for global mean kinetic energy |
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| 259 | zglob_area = glob_sum( 'ice_rhg_vp', at_i(:,:) * e1e2t(:,:) ) ! global ice area (km2) |
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| 260 | |
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| 261 | ENDIF |
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| 262 | |
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| 263 | ! Landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) |
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| 264 | ! MV: Not working yet... |
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| 265 | IF( ln_landfast_L16 ) THEN ; zkt = rn_lf_tensile |
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| 266 | ELSE ; zkt = 0._wp |
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| 267 | ENDIF |
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| 268 | |
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| 269 | zs1_rhsu(:,:) = 0._wp; zs2_rhsu(:,:) = 0._wp; zs1_rhsv(:,:) = 0._wp; zs2_rhsv(:,:) = 0._wp |
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| 270 | zAU(:,:) = 0._wp; zBU(:,:) = 0._wp; zCU(:,:) = 0._wp; zDU(:,:) = 0._wp; zEU(:,:) = 0._wp; |
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| 271 | zAV(:,:) = 0._wp; zBV(:,:) = 0._wp; zCV(:,:) = 0._wp; zDV(:,:) = 0._wp; zEV(:,:) = 0._wp; |
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| 272 | zrhsu(:,:) = 0._wp; zrhsv(:,:) = 0._wp |
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| 273 | zf_rhsu(:,:) = 0._wp; zf_rhsv(:,:) = 0._wp |
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| 274 | |
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| 275 | !------------------------------------------------------------------------------! |
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| 276 | ! |
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| 277 | ! --- Time-independent quantities |
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| 278 | ! |
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| 279 | !------------------------------------------------------------------------------! |
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| 280 | |
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| 281 | CALL ice_strength ! strength at T points |
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| 282 | |
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| 283 | !------------------------------ |
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| 284 | ! -- F-mask (code from EVP) |
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| 285 | !------------------------------ |
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| 286 | ! MartinV: |
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| 287 | ! In EVP routine, zfmask is applied on shear at F-points, in order to enforce the lateral boundary condition (no-slip, ..., free-slip) |
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| 288 | ! I am not sure the same recipe applies here |
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| 289 | |
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| 290 | ! - ocean/land mask |
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| 291 | DO jj = 1, jpj - 1 |
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| 292 | DO ji = 1, jpi - 1 |
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| 293 | zfmask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) |
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| 294 | END DO |
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| 295 | END DO |
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| 296 | CALL lbc_lnk( 'icedyn_rhg_vp', zfmask, 'F', 1._wp ) |
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| 297 | |
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| 298 | ! Lateral boundary conditions on velocity (modify zfmask) |
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| 299 | ! Can be computed once for all, at first time step, for all rheologies |
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| 300 | DO jj = 2, jpj - 1 |
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| 301 | DO ji = 2, jpi - 1 ! vector opt. |
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| 302 | IF( zfmask(ji,jj) == 0._wp ) THEN |
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| 303 | zfmask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(ji,jj,1), umask(ji,jj+1,1), & |
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| 304 | & vmask(ji,jj,1), vmask(ji+1,jj,1) ) ) |
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| 305 | ENDIF |
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| 306 | END DO |
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| 307 | END DO |
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| 308 | DO jj = 2, jpj - 1 |
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| 309 | IF( zfmask(1,jj) == 0._wp ) THEN |
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| 310 | zfmask(1 ,jj) = rn_ishlat * MIN( 1._wp , MAX( vmask(2,jj,1), umask(1,jj+1,1), umask(1,jj,1) ) ) |
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| 311 | ENDIF |
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| 312 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
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| 313 | zfmask(jpi,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(jpi,jj+1,1), vmask(jpi - 1,jj,1), umask(jpi,jj-1,1) ) ) |
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| 314 | ENDIF |
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| 315 | END DO |
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| 316 | DO ji = 2, jpi - 1 |
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| 317 | IF( zfmask(ji,1) == 0._wp ) THEN |
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| 318 | zfmask(ji, 1 ) = rn_ishlat * MIN( 1._wp , MAX( vmask(ji+1,1,1), umask(ji,2,1), vmask(ji,1,1) ) ) |
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| 319 | ENDIF |
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| 320 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
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| 321 | zfmask(ji,jpj) = rn_ishlat * MIN( 1._wp , MAX( vmask(ji+1,jpj,1), vmask(ji-1,jpj,1), umask(ji,jpj - 1,1) ) ) |
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| 322 | ENDIF |
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| 323 | END DO |
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| 324 | |
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| 325 | CALL lbc_lnk( 'icedyn_rhg_vp', zfmask, 'F', 1._wp ) |
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| 326 | |
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| 327 | !---------------------------------------------------------------------------------------------------------- |
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| 328 | ! -- Time-independent pre-factors for acceleration, ocean drag, coriolis, atmospheric drag, surface tilt |
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| 329 | !---------------------------------------------------------------------------------------------------------- |
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| 330 | ! Compute all terms & factors independent of velocities, or only depending on velocities at previous time step |
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| 331 | |
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| 332 | ! sea surface height |
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| 333 | ! embedded sea ice: compute representative ice top surface |
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| 334 | ! non-embedded sea ice: use ocean surface for slope calculation |
|---|
| 335 | zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) |
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| 336 | zsshdyn(:,:) = 0._wp ! DEBUG CAREFUL !!! |
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| 337 | |
|---|
| 338 | DO jj = 2, jpj - 1 |
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| 339 | DO ji = 2, jpi - 1 |
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| 340 | |
|---|
| 341 | ! Ice fraction at U-V points |
|---|
| 342 | 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) |
|---|
| 343 | 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) |
|---|
| 344 | |
|---|
| 345 | ! Snow and ice mass at U-V points |
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| 346 | zmt(ji,jj) = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) ) |
|---|
| 347 | zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) ) |
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| 348 | zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) ) |
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| 349 | |
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| 350 | zmassU = 0.5_wp * ( zmt(ji,jj) * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
|---|
| 351 | zmassV = 0.5_wp * ( zmt(ji,jj) * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
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| 352 | |
|---|
| 353 | ! Mass per unit area divided by time step |
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| 354 | zmassU_t(ji,jj) = zmassU * r1_rdtice |
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| 355 | zmassV_t(ji,jj) = zmassV * r1_rdtice |
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| 356 | |
|---|
| 357 | ! Acceleration term contribution to RHS (depends on velocity at previous time step) |
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| 358 | zmU_t(ji,jj) = zmassU_t(ji,jj) * u_ice(ji,jj) |
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| 359 | zmV_t(ji,jj) = zmassV_t(ji,jj) * v_ice(ji,jj) |
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| 360 | |
|---|
| 361 | ! Ocean currents at U-V points |
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| 362 | 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) |
|---|
| 363 | 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) |
|---|
| 364 | |
|---|
| 365 | ! Coriolis factor at T points (m*f) |
|---|
| 366 | zmf(ji,jj) = zmt(ji,jj) * ff_t(ji,jj) |
|---|
| 367 | |
|---|
| 368 | ! Wind stress |
|---|
| 369 | ztaux_ai(ji,jj) = za_iU(ji,jj) * utau_ice(ji,jj) |
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| 370 | ztauy_ai(ji,jj) = za_iV(ji,jj) * vtau_ice(ji,jj) |
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| 371 | |
|---|
| 372 | ! Force due to sea surface tilt(- m*g*GRAD(ssh)) |
|---|
| 373 | zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) |
|---|
| 374 | zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) |
|---|
| 375 | |
|---|
| 376 | ! Mask for ice presence (1) or absence (0) |
|---|
| 377 | zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
|---|
| 378 | zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
|---|
| 379 | |
|---|
| 380 | ! Mask for lots of ice (1) or little ice (0) |
|---|
| 381 | IF( zmassU <= zmmin .AND. za_iU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp |
|---|
| 382 | ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF |
|---|
| 383 | IF( zmassV <= zmmin .AND. za_iV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp |
|---|
| 384 | ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF |
|---|
| 385 | |
|---|
| 386 | END DO |
|---|
| 387 | END DO |
|---|
| 388 | |
|---|
| 389 | CALL iom_put( 'zmsk00x' , zmsk00x ) ! MV DEBUG |
|---|
| 390 | CALL iom_put( 'zmsk00y' , zmsk00y ) ! MV DEBUG |
|---|
| 391 | CALL iom_put( 'zmsk01x' , zmsk01x ) ! MV DEBUG |
|---|
| 392 | CALL iom_put( 'zmsk01y' , zmsk01y ) ! MV DEBUG |
|---|
| 393 | CALL iom_put( 'ztauy_ai' , ztauy_ai ) ! MV DEBUG |
|---|
| 394 | CALL iom_put( 'ztaux_ai' , ztaux_ai ) ! MV DEBUG |
|---|
| 395 | CALL iom_put( 'ztauy_ai' , ztauy_ai ) ! MV DEBUG |
|---|
| 396 | CALL iom_put( 'zspgU' , zspgU ) ! MV DEBUG |
|---|
| 397 | CALL iom_put( 'zspgV' , zspgV ) ! MV DEBUG |
|---|
| 398 | |
|---|
| 399 | !------------------------------------------------------------------------------! |
|---|
| 400 | ! |
|---|
| 401 | ! --- Start outer loop |
|---|
| 402 | ! |
|---|
| 403 | !------------------------------------------------------------------------------! |
|---|
| 404 | |
|---|
| 405 | zu_c(:,:) = u_ice(:,:) |
|---|
| 406 | zv_c(:,:) = v_ice(:,:) |
|---|
| 407 | |
|---|
| 408 | jter = 0 |
|---|
| 409 | |
|---|
| 410 | DO i_out = 1, nn_nout_vp |
|---|
| 411 | |
|---|
| 412 | IF( lwp ) WRITE(numout,*) ' outer loop i_out : ', i_out |
|---|
| 413 | |
|---|
| 414 | ! Velocities used in the non linear terms are the average of the past two iterates |
|---|
| 415 | ! u_it = 0.5 * ( u_{it-1} + u_{it-2}) |
|---|
| 416 | ! Also used in Hibler and Ackley (1983); Zhang and Hibler (1997); Lemieux and Tremblay (2009) |
|---|
| 417 | zu_c(:,:) = 0.5_wp * ( u_ice(:,:) + zu_c(:,:) ) |
|---|
| 418 | zv_c(:,:) = 0.5_wp * ( v_ice(:,:) + zv_c(:,:) ) |
|---|
| 419 | |
|---|
| 420 | !------------------------------------------------------------------------------! |
|---|
| 421 | ! |
|---|
| 422 | ! --- Right-hand side (RHS) of the linear problem |
|---|
| 423 | ! |
|---|
| 424 | !------------------------------------------------------------------------------! |
|---|
| 425 | ! In the outer loop, one needs to update all RHS terms |
|---|
| 426 | ! with explicit velocity dependencies (viscosities, coriolis, ocean stress) |
|---|
| 427 | ! as a function of uc |
|---|
| 428 | ! |
|---|
| 429 | |
|---|
| 430 | !------------------------------------------ |
|---|
| 431 | ! -- Strain rates, viscosities and P/Delta |
|---|
| 432 | !------------------------------------------ |
|---|
| 433 | |
|---|
| 434 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 435 | DO jj = 1, jpj - 1 ! loops start at 1 since there is no boundary condition (lbc_lnk) at i=1 and j=1 for F points |
|---|
| 436 | DO ji = 1, jpi - 1 |
|---|
| 437 | |
|---|
| 438 | ! shear at F points |
|---|
| 439 | 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) & |
|---|
| 440 | & + ( zv_c(ji+1,jj) * r1_e2v(ji+1,jj) - zv_c(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 441 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 442 | |
|---|
| 443 | END DO |
|---|
| 444 | END DO |
|---|
| 445 | |
|---|
| 446 | CALL lbc_lnk( 'icedyn_rhg_vp', zds, 'F', 1. ) ! MV TEST could be un-necessary according to Gurvan |
|---|
| 447 | CALL iom_put( 'zds' , zds ) ! MV DEBUG |
|---|
| 448 | |
|---|
| 449 | IF( lwp ) WRITE(numout,*) ' outer loop 1a i_out : ', i_out |
|---|
| 450 | |
|---|
| 451 | DO jj = 2, jpj - 1 ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 |
|---|
| 452 | DO ji = 2, jpi - 1 ! |
|---|
| 453 | |
|---|
| 454 | ! shear**2 at T points (doc eq. A16) |
|---|
| 455 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 456 | & + 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) & |
|---|
| 457 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 458 | |
|---|
| 459 | ! divergence at T points |
|---|
| 460 | zdiv = ( e2u(ji,jj) * zu_c(ji,jj) - e2u(ji-1,jj) * zu_c(ji-1,jj) & |
|---|
| 461 | & + e1v(ji,jj) * zv_c(ji,jj) - e1v(ji,jj-1) * zv_c(ji,jj-1) & |
|---|
| 462 | & ) * r1_e1e2t(ji,jj) |
|---|
| 463 | zdiv2 = zdiv * zdiv |
|---|
| 464 | |
|---|
| 465 | ! tension at T points |
|---|
| 466 | 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) & |
|---|
| 467 | & - ( zv_c(ji,jj) * r1_e1v(ji,jj) - zv_c(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 468 | & ) * r1_e1e2t(ji,jj) |
|---|
| 469 | zdt2 = zdt * zdt |
|---|
| 470 | |
|---|
| 471 | ! delta at T points |
|---|
| 472 | zdeltat = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 473 | |
|---|
| 474 | ! delta* at T points (following Lemieux and Dupont, GMD 2020) |
|---|
| 475 | zdeltastar_t(ji,jj) = zdeltat + rn_creepl |
|---|
| 476 | |
|---|
| 477 | ! P/delta at T-points |
|---|
| 478 | zp_deltastar_t(ji,jj) = strength(ji,jj) / zdeltastar_t(ji,jj) |
|---|
| 479 | |
|---|
| 480 | ! Temporary zzt and zet factors at T-points |
|---|
| 481 | zzt(ji,jj) = zp_deltastar_t(ji,jj) * r1_e1e2t(ji,jj) |
|---|
| 482 | zet(ji,jj) = zzt(ji,jj) * z1_ecc2 |
|---|
| 483 | |
|---|
| 484 | END DO |
|---|
| 485 | END DO |
|---|
| 486 | |
|---|
| 487 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zp_deltastar_t , 'T', 1. , zzt , 'T', 1., zet, 'T', 1. ) |
|---|
| 488 | |
|---|
| 489 | CALL iom_put( 'zzt' , zzt ) ! MV DEBUG |
|---|
| 490 | CALL iom_put( 'zet' , zet ) ! MV DEBUG |
|---|
| 491 | CALL iom_put( 'zp_deltastar_t', zp_deltastar_t ) ! MV DEBUG |
|---|
| 492 | |
|---|
| 493 | IF( lwp ) WRITE(numout,*) ' outer loop 1b i_out : ', i_out |
|---|
| 494 | |
|---|
| 495 | DO jj = 1, jpj - 1 |
|---|
| 496 | DO ji = 1, jpi - 1 |
|---|
| 497 | |
|---|
| 498 | ! P/delta* at F points |
|---|
| 499 | zp_deltastar_f = 0.25_wp * ( zp_deltastar_t(ji,jj) + zp_deltastar_t(ji+1,jj) + zp_deltastar_t(ji,jj+1) + zp_deltastar_t(ji+1,jj+1) ) |
|---|
| 500 | |
|---|
| 501 | ! Temporary zef factor at F-point |
|---|
| 502 | zef(ji,jj) = zp_deltastar_f * r1_e1e2f(ji,jj) * z1_ecc2 |
|---|
| 503 | |
|---|
| 504 | END DO |
|---|
| 505 | END DO |
|---|
| 506 | |
|---|
| 507 | CALL lbc_lnk( 'icedyn_rhg_vp', zef, 'F', 1. ) |
|---|
| 508 | CALL iom_put( 'zef' , zef ) ! MV DEBUG |
|---|
| 509 | IF( lwp ) WRITE(numout,*) ' outer loop 1c i_out : ', i_out |
|---|
| 510 | |
|---|
| 511 | !--------------------------------------------------- |
|---|
| 512 | ! -- Ocean-ice drag and Coriolis RHS contributions |
|---|
| 513 | !--------------------------------------------------- |
|---|
| 514 | |
|---|
| 515 | DO jj = 2, jpj - 1 |
|---|
| 516 | DO ji = 2, jpi - 1 |
|---|
| 517 | |
|---|
| 518 | !--- ice u-velocity @V points, v-velocity @U points (for non-linear drag computation) |
|---|
| 519 | 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) |
|---|
| 520 | 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) |
|---|
| 521 | |
|---|
| 522 | !--- non-linear drag coefficients (need to be updated at each outer loop, see Lemieux and Tremblay JGR09, p.3, beginning of Section 3) |
|---|
| 523 | 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) ) & |
|---|
| 524 | & + ( zv_cU - v_oceU(ji,jj) ) * ( zv_cU - v_oceU(ji,jj) ) ) |
|---|
| 525 | 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) ) & |
|---|
| 526 | & + ( zu_cV - u_oceV(ji,jj) ) * ( zu_cV - u_oceV(ji,jj) ) ) |
|---|
| 527 | |
|---|
| 528 | !--- Ocean-ice drag contributions to RHS |
|---|
| 529 | ztaux_oi_rhsu(ji,jj) = zCwU(ji,jj) * u_oce(ji,jj) |
|---|
| 530 | ztauy_oi_rhsv(ji,jj) = zCwV(ji,jj) * v_oce(ji,jj) |
|---|
| 531 | |
|---|
| 532 | ! --- U-component of Coriolis Force (energy conserving formulation) |
|---|
| 533 | ! Note Lemieux et al 2008 recommend to do that implicitly, but I don't really see how this could be done |
|---|
| 534 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 535 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * zv_c(ji ,jj) + e1v(ji ,jj-1) * zv_c(ji ,jj-1) ) & |
|---|
| 536 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * zv_c(ji+1,jj) + e1v(ji+1,jj-1) * zv_c(ji+1,jj-1) ) ) |
|---|
| 537 | |
|---|
| 538 | ! --- V-component of Coriolis Force (energy conserving formulation) |
|---|
| 539 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 540 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * zu_c(ji,jj ) + e2u(ji-1,jj ) * zu_c(ji-1,jj ) ) & |
|---|
| 541 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * zu_c(ji,jj+1) + e2u(ji-1,jj+1) * zu_c(ji-1,jj+1) ) ) |
|---|
| 542 | |
|---|
| 543 | END DO |
|---|
| 544 | END DO |
|---|
| 545 | |
|---|
| 546 | IF( lwp ) WRITE(numout,*) ' outer loop 1d i_out : ', i_out |
|---|
| 547 | CALL lbc_lnk( 'icedyn_rhg_vp', zCwU, 'U', 1. ) |
|---|
| 548 | CALL lbc_lnk( 'icedyn_rhg_vp', zCwV, 'V', 1. ) |
|---|
| 549 | |
|---|
| 550 | CALL iom_put( 'zCwU' , zCwU ) ! MV DEBUG |
|---|
| 551 | CALL iom_put( 'zCwV' , zCwV ) ! MV DEBUG |
|---|
| 552 | IF( lwp ) WRITE(numout,*) ' outer loop 1e i_out : ', i_out |
|---|
| 553 | CALL iom_put( 'zCorU' , zCorU ) ! MV DEBUG |
|---|
| 554 | CALL iom_put( 'zCorV' , zCorV ) ! MV DEBUG |
|---|
| 555 | IF( lwp ) WRITE(numout,*) ' outer loop 1f i_out : ', i_out |
|---|
| 556 | |
|---|
| 557 | ! a priori, Coriolis and drag terms only affect diagonal or independent term of the linear system, |
|---|
| 558 | ! so there is no need for lbclnk on drag and coriolis |
|---|
| 559 | |
|---|
| 560 | !------------------------------------- |
|---|
| 561 | ! -- Internal stress RHS contribution |
|---|
| 562 | !------------------------------------- |
|---|
| 563 | |
|---|
| 564 | ! --- Stress contributions at T-points |
|---|
| 565 | DO jj = 2, jpj ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 |
|---|
| 566 | DO ji = 2, jpi ! |
|---|
| 567 | |
|---|
| 568 | ! sig1 contribution to RHS of U-equation at T-points |
|---|
| 569 | zs1_rhsu(ji,jj) = zzt(ji,jj) * ( e1v(ji,jj) * zv_c(ji,jj) - e1v(ji,jj-1) * zv_c(ji,jj-1) - 1.0_wp ) |
|---|
| 570 | |
|---|
| 571 | ! sig2 contribution to RHS of U-equation at T-points |
|---|
| 572 | 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) |
|---|
| 573 | |
|---|
| 574 | ! sig1 contribution to RHS of V-equation at T-points |
|---|
| 575 | zs1_rhsv(ji,jj) = zzt(ji,jj) * ( e2u(ji,jj) * zu_c(ji,jj) - e2u(ji-1,jj) * zu_c(ji-1,jj) - 1.0_wp ) |
|---|
| 576 | |
|---|
| 577 | ! sig2 contribution to RHS of V-equation at T-points |
|---|
| 578 | 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) |
|---|
| 579 | |
|---|
| 580 | END DO |
|---|
| 581 | END DO |
|---|
| 582 | |
|---|
| 583 | CALL iom_put( 'zs1_rhsu' , zs1_rhsu ) ! MV DEBUG |
|---|
| 584 | CALL iom_put( 'zs2_rhsu' , zs2_rhsu ) ! MV DEBUG |
|---|
| 585 | CALL iom_put( 'zs1_rhsv' , zs1_rhsv ) ! MV DEBUG |
|---|
| 586 | CALL iom_put( 'zs2_rhsv' , zs2_rhsv ) ! MV DEBUG |
|---|
| 587 | |
|---|
| 588 | ! a priori, no lbclnk, because rhsu is only used in the inner domain |
|---|
| 589 | |
|---|
| 590 | ! --- Stress contributions at f-points |
|---|
| 591 | ! MV NOTE: I applied zfmask on zds, by mimetism on EVP, but without deep understanding of what I was doing |
|---|
| 592 | ! My guess is that this is the way to enforce boundary conditions on strain rate tensor |
|---|
| 593 | |
|---|
| 594 | IF( lwp ) WRITE(numout,*) ' outer loop 2 i_out : ', i_out |
|---|
| 595 | |
|---|
| 596 | DO jj = 1, jpj - 1 |
|---|
| 597 | DO ji = 1, jpi - 1 |
|---|
| 598 | |
|---|
| 599 | ! sig12 contribution to RHS of U equation at F-points |
|---|
| 600 | 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) * zfmask(ji,jj) |
|---|
| 601 | |
|---|
| 602 | ! sig12 contribution to RHS of V equation at F-points |
|---|
| 603 | 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) * zfmask(ji,jj) |
|---|
| 604 | |
|---|
| 605 | END DO |
|---|
| 606 | END DO |
|---|
| 607 | |
|---|
| 608 | CALL lbc_lnk( 'icedyn_rhg_vp', zs12_rhsu, 'F', 1. ) |
|---|
| 609 | CALL lbc_lnk( 'icedyn_rhg_vp', zs12_rhsv, 'F', 1. ) |
|---|
| 610 | |
|---|
| 611 | CALL iom_put( 'zs12_rhsu' , zs12_rhsu ) ! MV DEBUG |
|---|
| 612 | CALL iom_put( 'zs12_rhsv' , zs12_rhsv ) ! MV DEBUG |
|---|
| 613 | |
|---|
| 614 | ! a priori, no lbclnk, because rhsu are only used in the inner domain |
|---|
| 615 | |
|---|
| 616 | ! --- Internal force contributions to RHS, taken as divergence of stresses (Appendix C of Hunke and Dukowicz, 2002) |
|---|
| 617 | ! OPT: merge with next loop and use intermediate scalars for zf_rhsu |
|---|
| 618 | |
|---|
| 619 | DO jj = 2, jpj - 1 |
|---|
| 620 | DO ji = 2, jpi - 1 |
|---|
| 621 | ! --- U component of internal force contribution to RHS at U points |
|---|
| 622 | zf_rhsu(ji,jj) = 0.5_wp * r1_e1e2u(ji,jj) * & |
|---|
| 623 | ( e2u(ji,jj) * ( zs1_rhsu(ji+1,jj) - zs1_rhsu(ji,jj) ) & |
|---|
| 624 | & + 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) ) & |
|---|
| 625 | & + 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) ) ) |
|---|
| 626 | |
|---|
| 627 | ! --- V component of internal force contribution to RHS at V points |
|---|
| 628 | zf_rhsv(ji,jj) = 0.5_wp * r1_e1e2v(ji,jj) * & |
|---|
| 629 | & ( e1v(ji,jj) * ( zs1_rhsv(ji,jj+1) - zs1_rhsv(ji,jj) ) & |
|---|
| 630 | & + 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) ) & |
|---|
| 631 | & + 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) ) ) |
|---|
| 632 | |
|---|
| 633 | END DO |
|---|
| 634 | END DO |
|---|
| 635 | |
|---|
| 636 | CALL iom_put( 'zf_rhsu' , zf_rhsu ) ! MV DEBUG |
|---|
| 637 | CALL iom_put( 'zf_rhsv' , zf_rhsv ) ! MV DEBUG |
|---|
| 638 | |
|---|
| 639 | !--------------------------- |
|---|
| 640 | ! -- Sum RHS contributions |
|---|
| 641 | !--------------------------- |
|---|
| 642 | ! |
|---|
| 643 | ! OPT: could use intermediate scalars to reduce memory access |
|---|
| 644 | DO jj = 2, jpj - 1 |
|---|
| 645 | DO ji = 2, jpi - 1 |
|---|
| 646 | |
|---|
| 647 | ! still miss ice ocean stress and acceleration contribution |
|---|
| 648 | 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) |
|---|
| 649 | zrhsv(ji,jj) = zmV_t(ji,jj) + ztauy_ai(ji,jj) + ztauy_oi_rhsv(ji,jj) + zspgV(ji,jj) + zCorV(ji,jj) + zf_rhsu(ji,jj) |
|---|
| 650 | |
|---|
| 651 | END DO |
|---|
| 652 | END DO |
|---|
| 653 | |
|---|
| 654 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zrhsu, 'U', 1., zrhsv, 'V', 1. ) |
|---|
| 655 | |
|---|
| 656 | CALL iom_put( 'zrhsu' , zrhsu ) ! MV DEBUG |
|---|
| 657 | CALL iom_put( 'zrhsv' , zrhsv ) ! MV DEBUG |
|---|
| 658 | |
|---|
| 659 | ! inner domain calculations -> no lbclnk |
|---|
| 660 | |
|---|
| 661 | IF( lwp ) WRITE(numout,*) ' outer loop 4 i_out : ', i_out |
|---|
| 662 | |
|---|
| 663 | !---------------------------------------------------------------------------------------! |
|---|
| 664 | ! |
|---|
| 665 | ! --- Linear system matrix |
|---|
| 666 | ! |
|---|
| 667 | !---------------------------------------------------------------------------------------! |
|---|
| 668 | |
|---|
| 669 | ! Linear system matrix contains all implicit contributions |
|---|
| 670 | ! 1) internal forces, 2) acceleration, 3) ice-ocean drag |
|---|
| 671 | |
|---|
| 672 | ! The linear system equation is written as follows |
|---|
| 673 | ! AU * u_{i-1,j} + BU * u_{i,j} + CU * u_{i+1,j} |
|---|
| 674 | ! = DU * u_{i,j-1} + EU * u_{i,j+1} + RHS (! my convention, not the same as ZH97 ) |
|---|
| 675 | |
|---|
| 676 | ! MV Note 1: martin losch applies boundary condition to BU in mitGCM - check whether it is necessary here ? |
|---|
| 677 | ! MV Note 2: "T" factor calculations can be optimized by putting things out of the loop |
|---|
| 678 | ! only zzt and zet are iteration-dependent, other only depend on scale factors |
|---|
| 679 | |
|---|
| 680 | DO ji = 2, jpi - 1 ! internal domain do loop |
|---|
| 681 | DO jj = 2, jpj - 1 |
|---|
| 682 | |
|---|
| 683 | !------------------------------------- |
|---|
| 684 | ! -- Internal forces LHS contribution |
|---|
| 685 | !------------------------------------- |
|---|
| 686 | ! |
|---|
| 687 | ! --- U-component |
|---|
| 688 | ! |
|---|
| 689 | ! "T" factors (intermediate results) |
|---|
| 690 | ! |
|---|
| 691 | zfac = 0.5_wp * r1_e1e2u(ji,jj) |
|---|
| 692 | zfac1 = zfac * e2u(ji,jj) |
|---|
| 693 | zfac2 = zfac * r1_e2u(ji,jj) |
|---|
| 694 | zfac3 = 2._wp * zfac * r1_e1u(ji,jj) |
|---|
| 695 | |
|---|
| 696 | zt12U = - zfac1 * zzt(ji+1,jj) |
|---|
| 697 | zt11U = zfac1 * zzt(ji,jj) |
|---|
| 698 | |
|---|
| 699 | zt22U = - zfac2 * zet(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) |
|---|
| 700 | zt21U = zfac2 * zet(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) |
|---|
| 701 | |
|---|
| 702 | zt122U = - zfac3 * zef(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) |
|---|
| 703 | zt121U = zfac3 * zef(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) |
|---|
| 704 | |
|---|
| 705 | ! |
|---|
| 706 | ! Linear system coefficients |
|---|
| 707 | ! |
|---|
| 708 | zAU(ji,jj) = - zt11U * e2u(ji-1,jj) - zt21U * r1_e2u(ji-1,jj) |
|---|
| 709 | zBU(ji,jj) = ( zt12U + zt11U ) * e2u(ji,jj) + ( zt22U + zt21U ) * r1_e2u(ji,jj) + ( zt122U + zt121U ) * r1_e1u(ji,jj) |
|---|
| 710 | zCU(ji,jj) = - zt12U * e2u(ji+1,jj) - zt22U * r1_e2u(ji+1,jj) |
|---|
| 711 | |
|---|
| 712 | zDU(ji,jj) = zt121U * r1_e1u(ji,jj-1) |
|---|
| 713 | zEU(ji,jj) = zt122U * r1_e1u(ji,jj+1) |
|---|
| 714 | |
|---|
| 715 | ! |
|---|
| 716 | ! --- V-component |
|---|
| 717 | ! |
|---|
| 718 | ! "T" factors (intermediate results) |
|---|
| 719 | ! |
|---|
| 720 | zfac = 0.5_wp * r1_e1e2v(ji,jj) |
|---|
| 721 | zfac1 = zfac * e2v(ji,jj) |
|---|
| 722 | zfac2 = zfac * r1_e1v(ji,jj) |
|---|
| 723 | zfac3 = 2._wp * zfac * r1_e2v(ji,jj) |
|---|
| 724 | |
|---|
| 725 | zt12V = - zfac1 * zzt(ji,jj+1) |
|---|
| 726 | zt11V = zfac1 * zzt(ji,jj) |
|---|
| 727 | |
|---|
| 728 | zt22V = zfac2 * zet(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) |
|---|
| 729 | zt21V = - zfac2 * zet(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) |
|---|
| 730 | |
|---|
| 731 | zt122V = zfac3 * zef(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) |
|---|
| 732 | zt121V = - zfac3 * zef(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) |
|---|
| 733 | |
|---|
| 734 | ! |
|---|
| 735 | ! Linear system coefficients |
|---|
| 736 | ! |
|---|
| 737 | zAV(ji,jj) = - zt11V * e1v(ji,jj-1) + zt21V * r1_e1v(ji,jj-1) |
|---|
| 738 | zBV(ji,jj) = ( zt12V + zt11V ) * e1v(ji,jj) - ( zt22V + zt21V ) * r1_e1v(ji,jj) - ( zt122V + zt121V ) * r1_e2v(ji,jj) |
|---|
| 739 | zCV(ji,jj) = - zt12V * e1v(ji,jj+1) + zt22V * r1_e1v(ji,jj+1) |
|---|
| 740 | |
|---|
| 741 | zDV(ji,jj) = - zt121V * r1_e2v(ji-1,jj) ! mistake is in the pdf notes not here |
|---|
| 742 | zEV(ji,jj) = - zt122V * r1_e2v(ji+1,jj) |
|---|
| 743 | |
|---|
| 744 | !----------------------------------------------------- |
|---|
| 745 | ! -- Ocean-ice drag and acceleration LHS contribution |
|---|
| 746 | !----------------------------------------------------- |
|---|
| 747 | zBU(ji,jj) = zBU(ji,jj) + zCwU(ji,jj) + zmassU_t(ji,jj) |
|---|
| 748 | zBV(ji,jj) = ZBV(ji,jj) + zCwV(ji,jj) + zmassV_t(ji,jj) |
|---|
| 749 | |
|---|
| 750 | END DO |
|---|
| 751 | END DO |
|---|
| 752 | |
|---|
| 753 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zAU , 'U', 1., zAV , 'V', 1. ) |
|---|
| 754 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zBU , 'U', 1., zBV , 'V', 1. ) |
|---|
| 755 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zCU , 'U', 1., zCV , 'V', 1. ) |
|---|
| 756 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zDU , 'U', 1., zDV , 'V', 1. ) |
|---|
| 757 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zEU , 'U', 1., zEV , 'V', 1. ) |
|---|
| 758 | |
|---|
| 759 | CALL iom_put( 'zAU' , zAU ) ! MV DEBUG |
|---|
| 760 | CALL iom_put( 'zBU' , zBU ) ! MV DEBUG |
|---|
| 761 | CALL iom_put( 'zCU' , zCU ) ! MV DEBUG |
|---|
| 762 | CALL iom_put( 'zDU' , zDU ) ! MV DEBUG |
|---|
| 763 | CALL iom_put( 'zEU' , zEU ) ! MV DEBUG |
|---|
| 764 | CALL iom_put( 'zAV' , zAV ) ! MV DEBUG |
|---|
| 765 | CALL iom_put( 'zBV' , zBV ) ! MV DEBUG |
|---|
| 766 | CALL iom_put( 'zCV' , zCV ) ! MV DEBUG |
|---|
| 767 | CALL iom_put( 'zDV' , zDV ) ! MV DEBUG |
|---|
| 768 | CALL iom_put( 'zEV' , zEV ) ! MV DEBUG |
|---|
| 769 | |
|---|
| 770 | !------------------------------------------------------------------------------! |
|---|
| 771 | ! |
|---|
| 772 | ! --- Inner loop: solve linear system, check convergence |
|---|
| 773 | ! |
|---|
| 774 | !------------------------------------------------------------------------------! |
|---|
| 775 | |
|---|
| 776 | ! Inner loop solves the linear problem .. requires 1500 iterations |
|---|
| 777 | ll_u_iterate = .TRUE. |
|---|
| 778 | ll_v_iterate = .TRUE. |
|---|
| 779 | |
|---|
| 780 | ! zBU |
|---|
| 781 | ! it is probably the way zBU is used that is problematic... |
|---|
| 782 | ! because zBU itself does not have the zipper!!! |
|---|
| 783 | ! BUG only occurs when zBU is different from zero |
|---|
| 784 | ! H1 - the jj loop does not work well with jpj = 149 ? |
|---|
| 785 | ! zBU(:,:) = 0._wp; zBV(:,:) = 0._wp |
|---|
| 786 | |
|---|
| 787 | DO i_inn = 1, nn_ninn_vp ! inner loop iterations |
|---|
| 788 | |
|---|
| 789 | IF( lwp ) WRITE(numout,*) ' inner loop 1 i_inn : ', i_inn |
|---|
| 790 | |
|---|
| 791 | !--- mitgcm computes initial value of residual here... |
|---|
| 792 | |
|---|
| 793 | jter = jter + 1 |
|---|
| 794 | ! l_full_nf_update = jter == nn_nvp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 |
|---|
| 795 | |
|---|
| 796 | zu_b(:,:) = u_ice(:,:) ! velocity at previous sub-iterate |
|---|
| 797 | zv_b(:,:) = v_ice(:,:) |
|---|
| 798 | |
|---|
| 799 | zFU(:,:) = 0._wp ; zFU_prime(:,:) = 0._wp ; zBU_prime(:,:) = 0._wp |
|---|
| 800 | zFV(:,:) = 0._wp ; zFV_prime(:,:) = 0._wp ; zBV_prime(:,:) = 0._wp |
|---|
| 801 | |
|---|
| 802 | IF ( ll_u_iterate .OR. ll_v_iterate ) THEN |
|---|
| 803 | |
|---|
| 804 | ! ---------------------------- ! |
|---|
| 805 | IF ( ll_u_iterate ) THEN ! --- Solve for u-velocity --- ! |
|---|
| 806 | ! ---------------------------- ! |
|---|
| 807 | |
|---|
| 808 | ! Thomas Algorithm for tridiagonal solver |
|---|
| 809 | ! what follows could be subroutinized... |
|---|
| 810 | |
|---|
| 811 | DO jn = 1, nn_zebra_vp ! "zebra" loop (! red-black-sor!!! ) |
|---|
| 812 | |
|---|
| 813 | ! OPT: could be even better optimized with a true red-black SOR |
|---|
| 814 | |
|---|
| 815 | IF ( jn == 1 ) THEN ; jj_min = 2 |
|---|
| 816 | ELSE ; jj_min = 3 |
|---|
| 817 | ENDIF |
|---|
| 818 | |
|---|
| 819 | IF ( lwp ) WRITE(numout,*) ' Into the U-zebra loop at step jn = ', jn, ', with jj_min = ', jj_min |
|---|
| 820 | |
|---|
| 821 | !---------------------------------------------------------- |
|---|
| 822 | ! -- Boundary condition (link with neighbouring processor) |
|---|
| 823 | !---------------------------------------------------------- |
|---|
| 824 | |
|---|
| 825 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 826 | |
|---|
| 827 | ! |
|---|
| 828 | ! MV - I am in doubts whether the way I coded it is reproducible - ask Gurvan |
|---|
| 829 | ! |
|---|
| 830 | ! A*u(i-1,j)+B*u(i,j)+C*u(i+1,j) = F |
|---|
| 831 | |
|---|
| 832 | ! - Right-hand side of tridiagonal system (zFU) |
|---|
| 833 | DO ji = 2, jpi - 1 |
|---|
| 834 | |
|---|
| 835 | ! boundary condition substitution |
|---|
| 836 | ! see Zhang and Hibler, 1997, Appendix B |
|---|
| 837 | ! MV NOTE possibly not fully appropriate |
|---|
| 838 | zAA3 = 0._wp |
|---|
| 839 | IF ( ji == 2 ) zAA3 = zAA3 - zAU(ji,jj) * u_ice(ji-1,jj) |
|---|
| 840 | IF ( ji == jpi - 1 ) zAA3 = zAA3 - zCU(ji,jj) * u_ice(ji+1,jj) |
|---|
| 841 | |
|---|
| 842 | ! right hand side |
|---|
| 843 | zFU(ji,jj) = ( zrhsu(ji,jj) & ! right-hand side terms |
|---|
| 844 | & + zAA3 & ! boundary condition translation |
|---|
| 845 | & + zDU(ji,jj) * u_ice(ji,jj-1) & ! internal force, j-1 |
|---|
| 846 | & + zEU(ji,jj) * u_ice(ji,jj+1) ) * umask(ji,jj,1) ! internal force, j+1 |
|---|
| 847 | |
|---|
| 848 | END DO |
|---|
| 849 | |
|---|
| 850 | END DO |
|---|
| 851 | |
|---|
| 852 | ! CALL lbc_lnk( 'icedyn_rhg_vp', zFU, 'U', 1. ) |
|---|
| 853 | |
|---|
| 854 | !--------------- |
|---|
| 855 | ! Forward sweep |
|---|
| 856 | !--------------- |
|---|
| 857 | nn_thomas = 2 ! 1 = martin, 2 = mitgcm |
|---|
| 858 | |
|---|
| 859 | IF ( nn_thomas == 1 ) THEN ! MV version seemingly more than mitGCM algorithm |
|---|
| 860 | |
|---|
| 861 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 862 | |
|---|
| 863 | DO ji = 3, jpi - 1 |
|---|
| 864 | |
|---|
| 865 | zfac = SIGN( 1._wp , zBU(ji-1,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU(ji-1,jj) ) - epsi20 ) ) |
|---|
| 866 | zw = zfac * zAU(ji,jj) / MAX ( ABS( zBU(ji-1,jj) ) , epsi20 ) |
|---|
| 867 | zBU_prime(ji,jj) = zBU(ji,jj) - zw * zCU(ji-1,jj) |
|---|
| 868 | zFU_prime(ji,jj) = zFU(ji,jj) - zw * zFU(ji-1,jj) |
|---|
| 869 | |
|---|
| 870 | END DO |
|---|
| 871 | |
|---|
| 872 | END DO |
|---|
| 873 | |
|---|
| 874 | ELSE ! nn_thomas == 2 ! mitGCM algorithm |
|---|
| 875 | |
|---|
| 876 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 877 | |
|---|
| 878 | ! ji = 2 |
|---|
| 879 | zw = zBU(2,jj) |
|---|
| 880 | zfac = SIGN( 1._wp , zw ) * MAX( 0._wp , SIGN( 1._wp , ABS(zw) - epsi20 ) ) |
|---|
| 881 | zw = zfac * 1.0_wp / MAX ( ABS( zw ) , epsi20 ) |
|---|
| 882 | zCU_prime(2,jj) = zw * zCU(2,jj) |
|---|
| 883 | zFU_prime(2,jj) = zw * zFU(2,jj) |
|---|
| 884 | |
|---|
| 885 | DO ji = 3, jpi - 1 |
|---|
| 886 | |
|---|
| 887 | zw = zBU(ji,jj) - zAU(ji,jj) * zCU_prime(ji-1,jj) |
|---|
| 888 | zfac = SIGN( 1._wp , zw ) * MAX( 0._wp , SIGN( 1._wp , ABS(zw) - epsi20 ) ) |
|---|
| 889 | zw = zfac * 1.0_wp / MAX ( ABS( zw ) , epsi20 ) |
|---|
| 890 | zCU_prime(ji,jj) = zw * zCU(ji,jj) |
|---|
| 891 | zFU_prime(ji,jj) = zw * ( zFU(ji,jj) - zAU(ji,jj) * zFU_prime(ji-1,jj) ) |
|---|
| 892 | |
|---|
| 893 | END DO |
|---|
| 894 | |
|---|
| 895 | END DO |
|---|
| 896 | |
|---|
| 897 | ENDIF |
|---|
| 898 | |
|---|
| 899 | ! CALL lbc_lnk_multi( 'icedyn_rhg_vp', zBU_prime , 'U', 1., zFU_prime, 'U', 1. ) |
|---|
| 900 | |
|---|
| 901 | !---------------- |
|---|
| 902 | ! Backward sweep |
|---|
| 903 | !---------------- |
|---|
| 904 | IF ( nn_thomas == 1 ) THEN ! MV version |
|---|
| 905 | |
|---|
| 906 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 907 | |
|---|
| 908 | ! last row |
|---|
| 909 | zfac = SIGN( 1._wp , zBU_prime(jpi-1,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU_prime(jpi-1,jj) ) - epsi20 ) ) |
|---|
| 910 | u_ice(jpi-1,jj) = zfac * zFU_prime(jpi-1,jj) / MAX( ABS ( zBU_prime(jpi-1,jj) ) , epsi20 ) & |
|---|
| 911 | & * umask(jpi-1,jj,1) |
|---|
| 912 | |
|---|
| 913 | DO ji2 = 2 , jpi-2 ! all other rows |
|---|
| 914 | !DO ji = jpi-2 , 2, -1 ! all other rows ! ---> original backward loop |
|---|
| 915 | ji = jpi - ji2 |
|---|
| 916 | ! ji2 = 2 -> ji = jpi - 2 |
|---|
| 917 | ! ji2 = jpi - 2 -> ji = 2 |
|---|
| 918 | zfac = SIGN( 1._wp , zBU_prime(ji,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU_prime(ji,jj) ) - epsi20 ) ) |
|---|
| 919 | u_ice(ji,jj) = zfac * ( zFU_prime(ji,jj) - zCU(ji,jj) * u_ice(ji+1,jj) * umask(ji,jj,1) ) & ! this |
|---|
| 920 | ! line is guilty |
|---|
| 921 | & / MAX ( ABS ( zBU_prime(ji,jj) ) , epsi20 ) |
|---|
| 922 | END DO |
|---|
| 923 | |
|---|
| 924 | END DO |
|---|
| 925 | |
|---|
| 926 | ELSE ! nn_thomas == 2 ! mitGCM version |
|---|
| 927 | |
|---|
| 928 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 929 | |
|---|
| 930 | u_ice(jpi-1,jpj) = zFU_prime(jpi-1,jpj) |
|---|
| 931 | |
|---|
| 932 | DO ji2 = 2 , jpi-2 ! all other rows ! MV OPT: could be turned into forward loop (by substituting ji) |
|---|
| 933 | ji = jpi - ji2 |
|---|
| 934 | u_ice(ji,jj) = zFU_prime(ji,jj) - zCU_prime(ji,jj) * u_ice(ji+1,jj) |
|---|
| 935 | END DO |
|---|
| 936 | |
|---|
| 937 | END DO |
|---|
| 938 | |
|---|
| 939 | ENDIF |
|---|
| 940 | |
|---|
| 941 | !--------------- |
|---|
| 942 | ! -- Relaxation |
|---|
| 943 | !--------------- |
|---|
| 944 | |
|---|
| 945 | DO jj = jj_min, jpj - 1, nn_zebra_vp |
|---|
| 946 | |
|---|
| 947 | DO ji = 2, jpi - 1 |
|---|
| 948 | |
|---|
| 949 | u_ice(ji,jj) = zu_b(ji,jj) + rn_relaxu_vp * ( u_ice(ji,jj) - zu_b(ji,jj) ) |
|---|
| 950 | |
|---|
| 951 | ! velocity masking for little-ice and no-ice cases |
|---|
| 952 | u_ice(ji,jj) = zmsk00x(ji,jj) & |
|---|
| 953 | & * ( zmsk01x(ji,jj) * u_ice(ji,jj) & |
|---|
| 954 | & + ( 1._wp - zmsk01x(ji,jj) ) * u_oce(ji,jj) * 0.01_wp ) * umask(ji,jj,1) |
|---|
| 955 | |
|---|
| 956 | END DO |
|---|
| 957 | |
|---|
| 958 | END DO ! jj |
|---|
| 959 | |
|---|
| 960 | END DO ! zebra loop |
|---|
| 961 | |
|---|
| 962 | ENDIF ! ll_u_iterate |
|---|
| 963 | |
|---|
| 964 | ! ! ---------------------------- ! |
|---|
| 965 | IF ( ll_v_iterate ) THEN ! --- Solve for V-velocity --- ! |
|---|
| 966 | ! ! ---------------------------- ! |
|---|
| 967 | |
|---|
| 968 | ! MV OPT: what follows could be subroutinized... |
|---|
| 969 | |
|---|
| 970 | DO jn = 1, nn_zebra_vp ! "zebra" loop |
|---|
| 971 | |
|---|
| 972 | IF ( jn == 1 ) THEN ; ji_min = 2 |
|---|
| 973 | ELSE ; ji_min = 3 |
|---|
| 974 | ENDIF |
|---|
| 975 | |
|---|
| 976 | IF ( lwp ) WRITE(numout,*) ' Into the V-zebra loop at step jn = ', jn, ', with ji_min = ', ji_min |
|---|
| 977 | |
|---|
| 978 | DO ji = ji_min, jpi - 1, nn_zebra_vp |
|---|
| 979 | |
|---|
| 980 | !!! It is intentional to have a ji then jj loop for V-velocity |
|---|
| 981 | !!! ZH97 explain it is critical for convergence speed |
|---|
| 982 | |
|---|
| 983 | !------------------------------------------- |
|---|
| 984 | ! -- Tridiagonal system solver for each row |
|---|
| 985 | !------------------------------------------- |
|---|
| 986 | ! A*v(i,j-1)+B*v(i,j)+C*v(i,j+1) = F |
|---|
| 987 | |
|---|
| 988 | ! --- Right-hand side of tridiagonal system (zFU) |
|---|
| 989 | DO jj = 2, jpj - 1 |
|---|
| 990 | |
|---|
| 991 | ! boundary condition substitution (check it is correctly applied !!!) |
|---|
| 992 | ! see Zhang and Hibler, 1997, Appendix B |
|---|
| 993 | zAA3 = 0._wp |
|---|
| 994 | IF ( jj == 2 ) zAA3 = zAA3 - zAV(ji,jj) * v_ice(ji,jj-1) |
|---|
| 995 | IF ( jj == jpj - 1 ) zAA3 = zAA3 - zCV(ji,jj) * v_ice(ji,jj+1) |
|---|
| 996 | |
|---|
| 997 | ! right hand side |
|---|
| 998 | zFV(ji,jj) = ( zrhsv(ji,jj) & ! right-hand side terms |
|---|
| 999 | & + zAA3 & ! boundary condition translation |
|---|
| 1000 | & + zDV(ji,jj) * v_ice(ji-1,jj) & ! internal force, j-1 |
|---|
| 1001 | & + zEV(ji,jj) * v_ice(ji+1,jj) ) * vmask(ji,jj,1) ! internal force, j+1 |
|---|
| 1002 | |
|---|
| 1003 | END DO |
|---|
| 1004 | |
|---|
| 1005 | ! --- Thomas Algorithm |
|---|
| 1006 | ! (MV: I chose a seemingly more efficient form of the algorithm than in mitGCM - not sure) |
|---|
| 1007 | ! Forward sweep |
|---|
| 1008 | DO jj = 3, jpj - 1 |
|---|
| 1009 | zfac = SIGN( 1._wp , zBV(ji,jj-1) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV(ji,jj-1) ) - epsi20 ) ) |
|---|
| 1010 | zw = zfac * zAV(ji,jj) / MAX ( ABS( zBV(ji,jj-1) ) , epsi20 ) |
|---|
| 1011 | zBV_prime(ji,jj) = zBV(ji,jj) - zw * zCV(ji,jj-1) |
|---|
| 1012 | zFV_prime(ji,jj) = zFV(ji,jj) - zw * zFV(ji,jj-1) |
|---|
| 1013 | END DO |
|---|
| 1014 | |
|---|
| 1015 | ! Backward sweep |
|---|
| 1016 | zfac = SIGN( 1._wp , zBV_prime(ji,jpj-1) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV_prime(ji,jpj-1) ) - epsi20 ) ) |
|---|
| 1017 | v_ice(ji,jpj-1) = zfac * zFV_prime(ji,jpj-1) / MAX ( ABS(zBV_prime(ji,jpj-1) ) , epsi20 ) & |
|---|
| 1018 | & * vmask(ji,jpj-1,1) ! last row |
|---|
| 1019 | |
|---|
| 1020 | DO jj = jpj-2, 2, -1 ! can be turned into forward row by substituting jj if needed |
|---|
| 1021 | zfac = SIGN( 1._wp , zBV_prime(ji,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV_prime(ji,jj) ) - epsi20 ) ) |
|---|
| 1022 | v_ice(ji,jj) = zfac * ( zFV_prime(ji,jj) - zCV(ji,jj) * v_ice(ji,jj+1) * vmask(ji,jj,1) ) & |
|---|
| 1023 | & / MAX ( ABS( zBV_prime(ji,jj) ) , epsi20 ) |
|---|
| 1024 | END DO |
|---|
| 1025 | |
|---|
| 1026 | !--------------- |
|---|
| 1027 | ! -- Relaxation |
|---|
| 1028 | !--------------- |
|---|
| 1029 | DO jj = 2, jpj - 1 |
|---|
| 1030 | v_ice(ji,jj) = zv_b(ji,jj) + rn_relaxv_vp * ( v_ice(ji,jj) - zv_b(ji,jj) ) |
|---|
| 1031 | |
|---|
| 1032 | ! mask velocity for no-ice and little-ice cases |
|---|
| 1033 | v_ice(ji,jj) = zmsk00y(ji,jj) & |
|---|
| 1034 | & * ( zmsk01y(ji,jj) * v_ice(ji,jj) & |
|---|
| 1035 | & + ( 1._wp - zmsk01y(ji,jj) ) * v_oce(ji,jj) * 0.01_wp ) * vmask(ji,jj,1) |
|---|
| 1036 | |
|---|
| 1037 | END DO |
|---|
| 1038 | |
|---|
| 1039 | END DO ! ji |
|---|
| 1040 | |
|---|
| 1041 | END DO ! zebra loop |
|---|
| 1042 | |
|---|
| 1043 | ENDIF ! ll_v_iterate |
|---|
| 1044 | |
|---|
| 1045 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', u_ice, 'U', -1., v_ice, 'V', -1. ) |
|---|
| 1046 | |
|---|
| 1047 | !-------------------------------------------------------------------------------------- |
|---|
| 1048 | ! -- Check convergence based on maximum velocity difference, continue or stop the loop |
|---|
| 1049 | !-------------------------------------------------------------------------------------- |
|---|
| 1050 | |
|---|
| 1051 | !------ |
|---|
| 1052 | ! on U |
|---|
| 1053 | !------ |
|---|
| 1054 | ! MV OPT: if the number of iterations to convergence is really variable, and keep the convergence check |
|---|
| 1055 | ! then we must optimize the use of the mpp_max, which is prohibitive |
|---|
| 1056 | zuerr_max = 0._wp |
|---|
| 1057 | |
|---|
| 1058 | IF ( ll_u_iterate .AND. MOD ( i_inn, nn_cvgchk_vp ) == 0 ) THEN |
|---|
| 1059 | |
|---|
| 1060 | ! - Maximum U-velocity difference |
|---|
| 1061 | zuerr(:,:) = 0._wp |
|---|
| 1062 | DO jj = 2, jpj - 1 |
|---|
| 1063 | DO ji = 2, jpi - 1 |
|---|
| 1064 | zuerr(ji,jj) = ABS ( ( u_ice(ji,jj) - zu_b(ji,jj) ) ) * umask(ji,jj,1) |
|---|
| 1065 | END DO |
|---|
| 1066 | END DO |
|---|
| 1067 | zuerr_max = MAXVAL( zuerr ) |
|---|
| 1068 | CALL mpp_max( 'icedyn_rhg_evp', zuerr_max ) ! max over the global domain - damned! |
|---|
| 1069 | |
|---|
| 1070 | ! - Stop if error is too large ("safeguard against bad forcing" of original Zhang routine) |
|---|
| 1071 | IF ( i_inn > 1 .AND. zuerr_max > rn_uerr_max_vp ) THEN |
|---|
| 1072 | IF ( lwp ) WRITE(numout,*) " VP rheology error was too large : ", zuerr_max, " in outer U-iteration ", i_out, " after ", i_inn, " iterations, we stopped " |
|---|
| 1073 | ll_u_iterate = .FALSE. |
|---|
| 1074 | ENDIF |
|---|
| 1075 | |
|---|
| 1076 | ! - Stop if error small enough |
|---|
| 1077 | IF ( zuerr_max < rn_uerr_min_vp ) THEN |
|---|
| 1078 | IF ( lwp ) WRITE(numout,*) " VP rheology nicely done in outer U-iteration ", i_out, " after ", i_inn, " iterations, finished! " |
|---|
| 1079 | ll_u_iterate = .FALSE. |
|---|
| 1080 | ENDIF |
|---|
| 1081 | |
|---|
| 1082 | ENDIF ! ll_u_iterate |
|---|
| 1083 | |
|---|
| 1084 | !------ |
|---|
| 1085 | ! on V |
|---|
| 1086 | !------ |
|---|
| 1087 | zverr_max = 0._wp |
|---|
| 1088 | |
|---|
| 1089 | IF ( ll_v_iterate .AND. MOD ( i_inn, nn_cvgchk_vp ) == 0 ) THEN |
|---|
| 1090 | |
|---|
| 1091 | ! - Maximum V-velocity difference |
|---|
| 1092 | zverr(:,:) = 0._wp |
|---|
| 1093 | DO jj = 2, jpj - 1 |
|---|
| 1094 | DO ji = 2, jpi - 1 |
|---|
| 1095 | zverr(ji,jj) = ABS ( ( v_ice(ji,jj) - zv_b(ji,jj) ) ) * vmask(ji,jj,1) |
|---|
| 1096 | END DO |
|---|
| 1097 | END DO |
|---|
| 1098 | |
|---|
| 1099 | zverr_max = MAXVAL( zverr ) |
|---|
| 1100 | CALL mpp_max( 'icedyn_rhg_evp', zverr_max ) ! max over the global domain - damned! |
|---|
| 1101 | |
|---|
| 1102 | ! - Stop if error is too large ("safeguard against bad forcing" of original Zhang routine) |
|---|
| 1103 | IF ( i_inn > 1 .AND. zverr_max > rn_uerr_max_vp ) THEN |
|---|
| 1104 | IF ( lwp ) WRITE(numout,*) " VP rheology error was too large : ", zverr_max, " in outer V-iteration ", i_out, " after ", i_inn, " iterations, we stopped " |
|---|
| 1105 | ll_v_iterate = .FALSE. |
|---|
| 1106 | ENDIF |
|---|
| 1107 | |
|---|
| 1108 | ! - Stop if error small enough |
|---|
| 1109 | IF ( zverr_max < rn_uerr_min_vp ) THEN |
|---|
| 1110 | IF ( lwp ) WRITE(numout,*) " VP rheology nicely done in outer V-iteration ", i_out, " after ", i_inn, " iterations, finished! " |
|---|
| 1111 | ll_v_iterate = .FALSE. |
|---|
| 1112 | ENDIF |
|---|
| 1113 | |
|---|
| 1114 | ENDIF ! ll_v_iterate |
|---|
| 1115 | |
|---|
| 1116 | !--------------------------------------------------------------------------------------- |
|---|
| 1117 | ! |
|---|
| 1118 | ! --- Calculate extra convergence diagnostics and save them |
|---|
| 1119 | ! |
|---|
| 1120 | !--------------------------------------------------------------------------------------- |
|---|
| 1121 | IF( ln_rhg_chkcvg .AND. MOD ( i_inn - 1, nn_cvgchk_vp ) == 0 ) CALL rhg_cvg_vp( kt, jter, nn_nvp, u_ice, v_ice, zmt, zuerr_max, zverr_max, zglob_area, & |
|---|
| 1122 | & zrhsu, zAU, zBU, zCU, zDU, zEU, zrhsv, zAV, zBV, zCV, zDV, zEV ) |
|---|
| 1123 | |
|---|
| 1124 | IF ( lwp ) WRITE(numout,*) ' Done convergence tests ' |
|---|
| 1125 | |
|---|
| 1126 | ENDIF ! --- end ll_u_iterate or ll_v_iterate |
|---|
| 1127 | |
|---|
| 1128 | END DO ! i_inn, end of inner loop |
|---|
| 1129 | |
|---|
| 1130 | END DO ! End of outer loop (i_out) ============================================================================================= |
|---|
| 1131 | |
|---|
| 1132 | IF ( lwp ) WRITE(numout,*) ' We are out of outer loop ' |
|---|
| 1133 | |
|---|
| 1134 | CALL iom_put( 'zFU' , zFU ) ! MV DEBUG |
|---|
| 1135 | CALL iom_put( 'zBU_prime' , zBU_prime ) ! MV DEBUG |
|---|
| 1136 | CALL iom_put( 'zFU_prime' , zFU_prime ) ! MV DEBUG |
|---|
| 1137 | |
|---|
| 1138 | CALL iom_put( 'zFV' , zFV ) ! MV DEBUG |
|---|
| 1139 | CALL iom_put( 'zBV_prime' , zBV_prime ) ! MV DEBUG |
|---|
| 1140 | CALL iom_put( 'zFV_prime' , zFV_prime ) ! MV DEBUG |
|---|
| 1141 | |
|---|
| 1142 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', u_ice, 'U', -1., v_ice, 'V', -1. ) |
|---|
| 1143 | |
|---|
| 1144 | IF ( lwp ) WRITE(numout,*) ' We are about to output uice_dbg ' |
|---|
| 1145 | IF( iom_use('uice_dbg' ) ) CALL iom_put( 'uice_dbg' , u_ice ) ! ice velocity u after solver |
|---|
| 1146 | IF( iom_use('vice_dbg' ) ) CALL iom_put( 'vice_dbg' , v_ice ) ! ice velocity v after solver |
|---|
| 1147 | |
|---|
| 1148 | !------------------------------------------------------------------------------! |
|---|
| 1149 | ! |
|---|
| 1150 | ! --- Convergence diagnostics |
|---|
| 1151 | ! |
|---|
| 1152 | !------------------------------------------------------------------------------! |
|---|
| 1153 | |
|---|
| 1154 | IF( ln_rhg_chkcvg ) THEN |
|---|
| 1155 | |
|---|
| 1156 | IF( iom_use('uice_cvg') ) THEN |
|---|
| 1157 | CALL iom_put( 'uice_cvg', MAX( ABS( u_ice(:,:) - zu_b(:,:) ) * umask(:,:,1) , & ! ice velocity difference at last iteration |
|---|
| 1158 | & ABS( v_ice(:,:) - zv_b(:,:) ) * vmask(:,:,1) ) * zmsk15(:,:) ) |
|---|
| 1159 | ENDIF |
|---|
| 1160 | |
|---|
| 1161 | ENDIF ! ln_rhg_chkcvg |
|---|
| 1162 | |
|---|
| 1163 | ! MV DEBUG test - replace ice velocity by ocean current to give the model the means to go ahead |
|---|
| 1164 | DO jj = 2, jpj - 1 |
|---|
| 1165 | DO ji = 2, jpi - 1 |
|---|
| 1166 | |
|---|
| 1167 | u_ice(ji,jj) = zmsk00x(ji,jj) & |
|---|
| 1168 | & * ( zmsk01x(ji,jj) * u_oce(ji,jj) * 0.01_wp & |
|---|
| 1169 | + ( 1._wp - zmsk01x(ji,jj) ) * u_oce(ji,jj) * 0.01_wp ) |
|---|
| 1170 | |
|---|
| 1171 | v_ice(ji,jj) = zmsk00y(ji,jj) & |
|---|
| 1172 | & * ( zmsk01y(ji,jj) * v_oce(ji,jj) * 0.01_wp & |
|---|
| 1173 | + ( 1._wp - zmsk01y(ji,jj) ) * v_oce(ji,jj) * 0.01_wp ) |
|---|
| 1174 | |
|---|
| 1175 | END DO |
|---|
| 1176 | END DO |
|---|
| 1177 | |
|---|
| 1178 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', u_ice, 'U', -1., v_ice, 'V', -1. ) |
|---|
| 1179 | |
|---|
| 1180 | ! END DEBUG |
|---|
| 1181 | |
|---|
| 1182 | !------------------------------------------------------------------------------! |
|---|
| 1183 | ! |
|---|
| 1184 | ! --- Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 1185 | ! |
|---|
| 1186 | !------------------------------------------------------------------------------! |
|---|
| 1187 | ! |
|---|
| 1188 | ! MV OPT: subroutinize ? |
|---|
| 1189 | |
|---|
| 1190 | DO jj = 1, jpj - 1 |
|---|
| 1191 | DO ji = 1, jpi - 1 |
|---|
| 1192 | |
|---|
| 1193 | ! shear at F points |
|---|
| 1194 | 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) & |
|---|
| 1195 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 1196 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 1197 | |
|---|
| 1198 | END DO |
|---|
| 1199 | END DO |
|---|
| 1200 | |
|---|
| 1201 | DO jj = 2, jpj - 1 |
|---|
| 1202 | DO ji = 2, jpi - 1 ! |
|---|
| 1203 | |
|---|
| 1204 | ! tension**2 at T points |
|---|
| 1205 | 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) & |
|---|
| 1206 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 1207 | & ) * r1_e1e2t(ji,jj) |
|---|
| 1208 | zdt2 = zdt * zdt |
|---|
| 1209 | |
|---|
| 1210 | zten_i(ji,jj) = zdt |
|---|
| 1211 | |
|---|
| 1212 | ! shear**2 at T points (doc eq. A16) |
|---|
| 1213 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 1214 | & + 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) & |
|---|
| 1215 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 1216 | |
|---|
| 1217 | ! shear at T points |
|---|
| 1218 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
|---|
| 1219 | |
|---|
| 1220 | ! divergence at T points |
|---|
| 1221 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 1222 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 1223 | & ) * r1_e1e2t(ji,jj) |
|---|
| 1224 | |
|---|
| 1225 | ! delta at T points |
|---|
| 1226 | zdelta = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 1227 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 |
|---|
| 1228 | |
|---|
| 1229 | !pdelta_i(ji,jj) = zdelta + rn_creepl * rswitch |
|---|
| 1230 | pdelta_i(ji,jj) = zdelta + rn_creepl |
|---|
| 1231 | |
|---|
| 1232 | END DO |
|---|
| 1233 | END DO |
|---|
| 1234 | |
|---|
| 1235 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', pshear_i, 'T', 1., pdivu_i, 'T', 1., pdelta_i, 'T', 1. ) |
|---|
| 1236 | |
|---|
| 1237 | !------------------------------------------------------------------------------! |
|---|
| 1238 | ! |
|---|
| 1239 | ! --- Diagnostics |
|---|
| 1240 | ! |
|---|
| 1241 | !------------------------------------------------------------------------------! |
|---|
| 1242 | ! |
|---|
| 1243 | ! MV OPT: subroutinize ? |
|---|
| 1244 | ! |
|---|
| 1245 | !---------------------------------- |
|---|
| 1246 | ! --- Recompute stresses if needed |
|---|
| 1247 | !---------------------------------- |
|---|
| 1248 | ! |
|---|
| 1249 | ! ---- Sea ice stresses at T-points |
|---|
| 1250 | IF ( iom_use('normstr') .OR. iom_use('sheastr') .OR. iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 1251 | |
|---|
| 1252 | DO jj = 2, jpj - 1 |
|---|
| 1253 | DO ji = 2, jpi - 1 |
|---|
| 1254 | zp_deltastar_t(ji,jj) = strength(ji,jj) / pdelta_i(ji,jj) |
|---|
| 1255 | zfac = zp_deltastar_t(ji,jj) |
|---|
| 1256 | zs1(ji,jj) = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) ) |
|---|
| 1257 | zs2(ji,jj) = zfac * z1_ecc2 * zten_i(ji,jj) |
|---|
| 1258 | zs12(ji,jj) = zfac * z1_ecc2 * pshear_i(ji,jj) |
|---|
| 1259 | END DO |
|---|
| 1260 | END DO |
|---|
| 1261 | |
|---|
| 1262 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zs1, 'T', 1., zs2, 'T', 1., zs12, 'T', 1. ) |
|---|
| 1263 | |
|---|
| 1264 | ENDIF |
|---|
| 1265 | |
|---|
| 1266 | ! ---- s12 at F-points |
|---|
| 1267 | IF ( iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 1268 | |
|---|
| 1269 | DO jj = 1, jpj - 1 |
|---|
| 1270 | DO ji = 1, jpi - 1 |
|---|
| 1271 | |
|---|
| 1272 | ! P/delta* at F points |
|---|
| 1273 | zp_deltastar_f = 0.25_wp * ( zp_deltastar_t(ji,jj) + zp_deltastar_t(ji+1,jj) + zp_deltastar_t(ji,jj+1) + zp_deltastar_t(ji+1,jj+1) ) |
|---|
| 1274 | |
|---|
| 1275 | ! s12 at F-points |
|---|
| 1276 | zs12f(ji,jj) = zp_deltastar_f * z1_ecc2 * zds(ji,jj) |
|---|
| 1277 | |
|---|
| 1278 | END DO |
|---|
| 1279 | END DO |
|---|
| 1280 | |
|---|
| 1281 | CALL lbc_lnk( 'icedyn_rhg_vp', zs12f, 'F', 1. ) |
|---|
| 1282 | |
|---|
| 1283 | ENDIF |
|---|
| 1284 | ! |
|---|
| 1285 | !----------------------- |
|---|
| 1286 | ! --- Store diagnostics |
|---|
| 1287 | !----------------------- |
|---|
| 1288 | ! |
|---|
| 1289 | ! --- Ice-ocean, ice-atm. & ice-ocean bottom (landfast) stresses --- ! |
|---|
| 1290 | IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. & |
|---|
| 1291 | & iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN |
|---|
| 1292 | |
|---|
| 1293 | ALLOCATE( ztaux_oi(jpi,jpj) , ztauy_oi(jpi,jpj) ) |
|---|
| 1294 | |
|---|
| 1295 | !--- Recalculate oceanic stress at last inner iteration |
|---|
| 1296 | DO jj = 2, jpj - 1 |
|---|
| 1297 | DO ji = 2, jpi - 1 |
|---|
| 1298 | |
|---|
| 1299 | !--- ice u-velocity @V points, v-velocity @U points (for non-linear drag computation) |
|---|
| 1300 | 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) |
|---|
| 1301 | 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) |
|---|
| 1302 | |
|---|
| 1303 | !--- non-linear drag coefficients (need to be updated at each outer loop, see Lemieux and Tremblay JGR09, p.3, beginning of Section 3) |
|---|
| 1304 | 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) ) & |
|---|
| 1305 | & + ( zv_cU - v_oceU(ji,jj) ) * ( zv_cU - v_oceU(ji,jj) ) ) |
|---|
| 1306 | 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) ) & |
|---|
| 1307 | & + ( zu_cV - u_oceV(ji,jj) ) * ( zu_cV - u_oceV(ji,jj) ) ) |
|---|
| 1308 | |
|---|
| 1309 | !--- Ocean-ice stress |
|---|
| 1310 | ztaux_oi(ji,jj) = zCwU(ji,jj) * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 1311 | ztauy_oi(ji,jj) = zCwV(ji,jj) * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 1312 | |
|---|
| 1313 | END DO |
|---|
| 1314 | END DO |
|---|
| 1315 | |
|---|
| 1316 | ! |
|---|
| 1317 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', ztaux_oi, 'U', -1., ztauy_oi, 'V', -1., ztaux_ai, 'U', -1., ztauy_ai, 'V', -1. ) !, & |
|---|
| 1318 | ! & ztaux_bi, 'U', -1., ztauy_bi, 'V', -1. ) |
|---|
| 1319 | ! |
|---|
| 1320 | CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 ) |
|---|
| 1321 | CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 ) |
|---|
| 1322 | CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 ) |
|---|
| 1323 | CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 ) |
|---|
| 1324 | ! CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 ) |
|---|
| 1325 | ! CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 ) |
|---|
| 1326 | |
|---|
| 1327 | DEALLOCATE( ztaux_oi , ztauy_oi ) |
|---|
| 1328 | |
|---|
| 1329 | ENDIF |
|---|
| 1330 | |
|---|
| 1331 | ! --- Divergence, shear and strength --- ! |
|---|
| 1332 | IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence |
|---|
| 1333 | IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! shear |
|---|
| 1334 | IF( iom_use('icedlt') ) CALL iom_put( 'icedlt' , pdelta_i * zmsk00 ) ! delta |
|---|
| 1335 | IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength |
|---|
| 1336 | |
|---|
| 1337 | ! --- Stress tensor invariants (SIMIP diags) --- ! |
|---|
| 1338 | IF( iom_use('normstr') .OR. iom_use('sheastr') ) THEN |
|---|
| 1339 | ! |
|---|
| 1340 | ! Stress tensor invariants (normal and shear stress N/m) - SIMIP diags. |
|---|
| 1341 | ! Definitions following Coon (1974) and Feltham (2008) |
|---|
| 1342 | ! |
|---|
| 1343 | ! sigma1, sigma2, sigma12 are useful (Hunke and Dukowicz MWR 2002, Bouillon et al., OM2013) |
|---|
| 1344 | ! however these are NOT stress tensor components, neither stress invariants, nor stress principal components |
|---|
| 1345 | ! |
|---|
| 1346 | ALLOCATE( zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 1347 | ! |
|---|
| 1348 | DO jj = 2, jpj - 1 |
|---|
| 1349 | DO ji = 2, jpi - 1 |
|---|
| 1350 | ! Stress invariants |
|---|
| 1351 | zsig_I(ji,jj) = zs1(ji,jj) * 0.5_wp ! 1st invariant, aka average normal stress aka negative pressure |
|---|
| 1352 | zsig_II(ji,jj) = SQRT ( zs2(ji,jj) * zs2(ji,jj) * 0.25_wp + zs12(ji,jj) ) ! 2nd invariant, aka maximum shear stress |
|---|
| 1353 | END DO |
|---|
| 1354 | END DO |
|---|
| 1355 | |
|---|
| 1356 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zsig_I, 'T', 1., zsig_II, 'T', 1.) |
|---|
| 1357 | |
|---|
| 1358 | IF( iom_use('normstr') ) CALL iom_put( 'normstr' , zsig_I(:,:) * zmsk00(:,:) ) ! Normal stress |
|---|
| 1359 | IF( iom_use('sheastr') ) CALL iom_put( 'sheastr' , zsig_II(:,:) * zmsk00(:,:) ) ! Maximum shear stress |
|---|
| 1360 | |
|---|
| 1361 | DEALLOCATE ( zsig_I, zsig_II ) |
|---|
| 1362 | |
|---|
| 1363 | ENDIF |
|---|
| 1364 | |
|---|
| 1365 | ! --- Normalized stress tensor principal components --- ! |
|---|
| 1366 | ! These are used to plot the normalized yield curve (Lemieux & Dupont, GMD 2020) |
|---|
| 1367 | ! To plot the yield curve and evaluate physical convergence, they have two recommendations |
|---|
| 1368 | ! Recommendation 1 : Use ice strength, not replacement pressure |
|---|
| 1369 | ! Recommendation 2 : Need to use deformations at PREVIOUS iterate for viscosities (see p. 1765) |
|---|
| 1370 | ! R2 means we need to recompute stresses |
|---|
| 1371 | |
|---|
| 1372 | IF( iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN |
|---|
| 1373 | ! |
|---|
| 1374 | ALLOCATE( zsig1_p(jpi,jpj) , zsig2_p(jpi,jpj) , zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) |
|---|
| 1375 | ! |
|---|
| 1376 | DO jj = 2, jpj - 1 |
|---|
| 1377 | DO ji = 2, jpi - 1 |
|---|
| 1378 | ! Ice stresses computed with **viscosities** (delta, p/delta) at **previous** iterates |
|---|
| 1379 | ! and **deformations** at current iterates |
|---|
| 1380 | ! following Lemieux & Dupont (2020) |
|---|
| 1381 | zfac = zp_deltastar_t(ji,jj) |
|---|
| 1382 | zsig1 = zfac * ( pdivu_i(ji,jj) - zdeltastar_t(ji,jj) ) |
|---|
| 1383 | zsig2 = zfac * z1_ecc2 * zten_i(ji,jj) |
|---|
| 1384 | zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj) |
|---|
| 1385 | |
|---|
| 1386 | ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008), T-point |
|---|
| 1387 | zsig_I(ji,jj) = zsig1 * 0.5_wp ! 1st invariant |
|---|
| 1388 | zsig_II(ji,jj) = SQRT ( zsig2 * zsig2 * 0.25_wp + zsig12 ) ! 2nd invariant |
|---|
| 1389 | |
|---|
| 1390 | ! Normalized principal stresses (used to display the ellipse) |
|---|
| 1391 | z1_strength = 1._wp / MAX ( 1._wp , strength(ji,jj) ) |
|---|
| 1392 | zsig1_p(ji,jj) = ( zsig_I(ji,jj) + zsig_II(ji,jj) ) * z1_strength |
|---|
| 1393 | zsig2_p(ji,jj) = ( zsig_I(ji,jj) - zsig_II(ji,jj) ) * z1_strength |
|---|
| 1394 | END DO |
|---|
| 1395 | END DO |
|---|
| 1396 | ! |
|---|
| 1397 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zsig1_p, 'T', 1., zsig2_p, 'T', 1.) |
|---|
| 1398 | ! |
|---|
| 1399 | ! |
|---|
| 1400 | CALL iom_put( 'sig1_pnorm' , zsig1_p ) |
|---|
| 1401 | CALL iom_put( 'sig2_pnorm' , zsig2_p ) |
|---|
| 1402 | |
|---|
| 1403 | DEALLOCATE( zsig1_p , zsig2_p , zsig_I , zsig_II ) |
|---|
| 1404 | |
|---|
| 1405 | ENDIF |
|---|
| 1406 | |
|---|
| 1407 | ! --- SIMIP, terms of tendency for momentum equation --- ! |
|---|
| 1408 | IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. & |
|---|
| 1409 | & iom_use('corstrx') .OR. iom_use('corstry') ) THEN |
|---|
| 1410 | |
|---|
| 1411 | ! --- Recalculate Coriolis stress at last inner iteration |
|---|
| 1412 | DO jj = 2, jpj - 1 |
|---|
| 1413 | DO ji = 2, jpi - 1 |
|---|
| 1414 | ! --- U-component |
|---|
| 1415 | zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 1416 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 1417 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 1418 | zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 1419 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 1420 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 1421 | END DO |
|---|
| 1422 | END DO |
|---|
| 1423 | ! |
|---|
| 1424 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zspgU, 'U', -1., zspgV, 'V', -1., & |
|---|
| 1425 | & zCorU, 'U', -1., zCorV, 'V', -1. ) |
|---|
| 1426 | ! |
|---|
| 1427 | CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x) |
|---|
| 1428 | CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y) |
|---|
| 1429 | CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x) |
|---|
| 1430 | CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y) |
|---|
| 1431 | |
|---|
| 1432 | ENDIF |
|---|
| 1433 | |
|---|
| 1434 | IF ( iom_use('intstrx') .OR. iom_use('intstry') ) THEN |
|---|
| 1435 | |
|---|
| 1436 | ! Recalculate internal forces (divergence of stress tensor) at last inner iteration |
|---|
| 1437 | DO jj = 2, jpj - 1 |
|---|
| 1438 | DO ji = 2, jpi - 1 |
|---|
| 1439 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 1440 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 1441 | & ) * r1_e2u(ji,jj) & |
|---|
| 1442 | & + ( zs12f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 1443 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 1444 | & ) * r1_e1e2u(ji,jj) |
|---|
| 1445 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 1446 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 1447 | & ) * r1_e1v(ji,jj) & |
|---|
| 1448 | & + ( zs12f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 1449 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 1450 | & ) * r1_e1e2v(ji,jj) |
|---|
| 1451 | END DO |
|---|
| 1452 | END DO |
|---|
| 1453 | |
|---|
| 1454 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zfU, 'U', -1., zfV, 'V', -1. ) |
|---|
| 1455 | |
|---|
| 1456 | CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x) |
|---|
| 1457 | CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y) |
|---|
| 1458 | |
|---|
| 1459 | ENDIF |
|---|
| 1460 | |
|---|
| 1461 | ! --- Ice & snow mass and ice area transports |
|---|
| 1462 | IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. & |
|---|
| 1463 | & iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN |
|---|
| 1464 | ! |
|---|
| 1465 | ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 1466 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) ) |
|---|
| 1467 | ! |
|---|
| 1468 | DO jj = 2, jpj - 1 |
|---|
| 1469 | DO ji = 2, jpi - 1 |
|---|
| 1470 | ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 1471 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj) |
|---|
| 1472 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj) |
|---|
| 1473 | |
|---|
| 1474 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 1475 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 1476 | |
|---|
| 1477 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 1478 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 1479 | |
|---|
| 1480 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 1481 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 1482 | |
|---|
| 1483 | END DO |
|---|
| 1484 | END DO |
|---|
| 1485 | |
|---|
| 1486 | CALL lbc_lnk_multi( 'icedyn_rhg_vp', zdiag_xmtrp_ice, 'U', -1., zdiag_ymtrp_ice, 'V', -1., & |
|---|
| 1487 | & zdiag_xmtrp_snw, 'U', -1., zdiag_ymtrp_snw, 'V', -1., & |
|---|
| 1488 | & zdiag_xatrp , 'U', -1., zdiag_yatrp , 'V', -1. ) |
|---|
| 1489 | |
|---|
| 1490 | CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 1491 | CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport |
|---|
| 1492 | CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s) |
|---|
| 1493 | CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport |
|---|
| 1494 | CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport |
|---|
| 1495 | CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport |
|---|
| 1496 | |
|---|
| 1497 | DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 1498 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 1499 | |
|---|
| 1500 | ENDIF |
|---|
| 1501 | |
|---|
| 1502 | DEALLOCATE( zmsk00, zmsk15 ) |
|---|
| 1503 | |
|---|
| 1504 | END SUBROUTINE ice_dyn_rhg_vp |
|---|
| 1505 | |
|---|
| 1506 | |
|---|
| 1507 | |
|---|
| 1508 | SUBROUTINE rhg_cvg_vp( kt, kiter, kitermax, pu, pv, pmt, puerr_max, pverr_max, pglob_area, & |
|---|
| 1509 | & prhsu, pAU, pBU, pCU, pDU, pEU, prhsv, pAV, pBV, pCV, pDV, pEV ) |
|---|
| 1510 | |
|---|
| 1511 | !!---------------------------------------------------------------------- |
|---|
| 1512 | !! *** ROUTINE rhg_cvg_vp *** |
|---|
| 1513 | !! |
|---|
| 1514 | !! ** Purpose : check convergence of VP ice rheology |
|---|
| 1515 | !! |
|---|
| 1516 | !! ** Method : create a file ice_cvg.nc containing a few convergence diagnostics |
|---|
| 1517 | !! This routine is called every sub-iteration, so it is cpu expensive |
|---|
| 1518 | !! |
|---|
| 1519 | !! Calculates / stores |
|---|
| 1520 | !! - maximum absolute U-V difference (uice_cvg, u_dif, v_dif, m/s) |
|---|
| 1521 | !! - 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) |
|---|
| 1522 | !! - mean kinetic energy (mke_ice, J/m2) |
|---|
| 1523 | !! |
|---|
| 1524 | !! ** Note : for the first sub-iteration, uice_cvg is set to 0 (too large otherwise) |
|---|
| 1525 | !!---------------------------------------------------------------------- |
|---|
| 1526 | INTEGER , INTENT(in) :: kt, kiter, kitermax ! ocean time-step index |
|---|
| 1527 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pmt ! now velocity and mass per unit area |
|---|
| 1528 | REAL(wp), INTENT(in) :: puerr_max, pverr_max ! absolute mean velocity difference |
|---|
| 1529 | REAL(wp), INTENT(in) :: pglob_area ! global ice area |
|---|
| 1530 | REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsu, pAU, pBU, pCU, pDU, pEU ! linear system coefficients |
|---|
| 1531 | REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsv, pAV, pBV, pCV, pDV, pEV |
|---|
| 1532 | !! |
|---|
| 1533 | INTEGER :: it, idtime, istatus, ix_dim, iy_dim |
|---|
| 1534 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 1535 | REAL(wp) :: zveldif, zu_res_mean, zv_res_mean, zvelres, zmke, zu, zv ! local scalars |
|---|
| 1536 | REAL(wp) :: z1_pglob_area |
|---|
| 1537 | REAL(wp), DIMENSION(jpi,jpj) :: zu_res, zv_res, zvel2 ! local arrays |
|---|
| 1538 | |
|---|
| 1539 | CHARACTER(len=20) :: clname |
|---|
| 1540 | !!---------------------------------------------------------------------- |
|---|
| 1541 | |
|---|
| 1542 | IF( lwp ) THEN |
|---|
| 1543 | WRITE(numout,*) |
|---|
| 1544 | WRITE(numout,*) 'rhg_cvg_vp : ice rheology convergence control' |
|---|
| 1545 | WRITE(numout,*) '~~~~~~~~~~~' |
|---|
| 1546 | WRITE(numout,*) ' kiter = : ', kiter |
|---|
| 1547 | WRITE(numout,*) ' kitermax = : ', kitermax |
|---|
| 1548 | ENDIF |
|---|
| 1549 | |
|---|
| 1550 | ! create file |
|---|
| 1551 | IF( kt == nit000 .AND. kiter == 1 ) THEN |
|---|
| 1552 | ! |
|---|
| 1553 | IF( lwm ) THEN |
|---|
| 1554 | |
|---|
| 1555 | clname = 'ice_cvg.nc' |
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| 1556 | IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname) |
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| 1557 | istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid ) |
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| 1558 | |
|---|
| 1559 | istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime ) |
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| 1560 | istatus = NF90_DEF_DIM( ncvgid, 'x' , jpi, ix_dim ) |
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| 1561 | istatus = NF90_DEF_DIM( ncvgid, 'y' , jpj, iy_dim ) |
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| 1562 | |
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| 1563 | istatus = NF90_DEF_VAR( ncvgid, 'uice_cvg', NF90_DOUBLE , (/ idtime /), nvarid_ucvg ) ! the name uice_cvg sucks, no ? |
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| 1564 | ! i suggest vel_dif instead |
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| 1565 | istatus = NF90_DEF_VAR( ncvgid, 'u_res', NF90_DOUBLE , (/ idtime /), nvarid_ures ) |
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| 1566 | istatus = NF90_DEF_VAR( ncvgid, 'v_res', NF90_DOUBLE , (/ idtime /), nvarid_vres ) |
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| 1567 | istatus = NF90_DEF_VAR( ncvgid, 'vel_res', NF90_DOUBLE , (/ idtime /), nvarid_velres ) |
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| 1568 | istatus = NF90_DEF_VAR( ncvgid, 'u_dif', NF90_DOUBLE , (/ idtime /), nvarid_udif ) |
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| 1569 | istatus = NF90_DEF_VAR( ncvgid, 'v_dif', NF90_DOUBLE , (/ idtime /), nvarid_vdif ) |
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| 1570 | istatus = NF90_DEF_VAR( ncvgid, 'mke_ice', NF90_DOUBLE , (/ idtime /), nvarid_mke ) |
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| 1571 | |
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| 1572 | istatus = NF90_DEF_VAR( ncvgid, 'usub' , NF90_DOUBLE, (/ ix_dim, iy_dim, idtime /), nvarid_usub) ! --> u-velocity in sub-iterations |
|---|
| 1573 | istatus = NF90_DEF_VAR( ncvgid, 'vsub' , NF90_DOUBLE, (/ ix_dim, iy_dim, idtime /), nvarid_vsub) ! --> v-velocity in sub-iterations |
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| 1574 | |
|---|
| 1575 | istatus = NF90_ENDDEF(ncvgid) |
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| 1576 | |
|---|
| 1577 | ENDIF |
|---|
| 1578 | ! |
|---|
| 1579 | ENDIF |
|---|
| 1580 | |
|---|
| 1581 | IF ( lwp ) WRITE(numout,*) ' File created ' |
|---|
| 1582 | |
|---|
| 1583 | ! --- Max absolute velocity difference with previous iterate (zveldif) |
|---|
| 1584 | zveldif = MAX( puerr_max, pverr_max ) ! velocity difference with previous iterate, should nearly be equivalent to evp code |
|---|
| 1585 | ! if puerrmask and pverrmax are masked at 15% (TEST) |
|---|
| 1586 | |
|---|
| 1587 | IF ( lwp ) WRITE(numout,*) ' zfeldif : ', zveldif |
|---|
| 1588 | |
|---|
| 1589 | ! --- Mean residual and kinetic energy |
|---|
| 1590 | IF ( kiter == 1 ) THEN |
|---|
| 1591 | |
|---|
| 1592 | zu_res_mean = 0._wp |
|---|
| 1593 | zv_res_mean = 0._wp |
|---|
| 1594 | zvelres = 0._wp |
|---|
| 1595 | zmke = 0._wp |
|---|
| 1596 | |
|---|
| 1597 | ELSE |
|---|
| 1598 | |
|---|
| 1599 | ! -- Mean residual (N/m^2), zu_res_mean |
|---|
| 1600 | ! Here we take the residual of the linear system (N/m^2), |
|---|
| 1601 | ! We define it as in mitgcm: square-root of area-weighted mean square residual |
|---|
| 1602 | ! Local residual r = Ax - B expresses to which extent the momentum balance is verified |
|---|
| 1603 | ! i.e., how close we are to a solution |
|---|
| 1604 | |
|---|
| 1605 | IF ( lwp ) WRITE(numout,*) ' TEST 1 ' |
|---|
| 1606 | |
|---|
| 1607 | z1_pglob_area = 1._wp / pglob_area |
|---|
| 1608 | |
|---|
| 1609 | DO jj = 2, jpj - 1 |
|---|
| 1610 | DO ji = 2, jpi - 1 |
|---|
| 1611 | zu_res(ji,jj) = ( prhsu(ji,jj) + pDU(ji,jj) * pu(ji,jj-1) + pEU(ji,jj) * pu(ji,jj+1) & |
|---|
| 1612 | & - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) ) |
|---|
| 1613 | |
|---|
| 1614 | zv_res(ji,jj) = ( prhsv(ji,jj) + pDV(ji,jj) * pv(ji-1,jj) + pEV(ji,jj) * pv(ji+1,jj) & |
|---|
| 1615 | & - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) ) |
|---|
| 1616 | |
|---|
| 1617 | zu_res(ji,jj) = SQRT( zu_res(ji,jj) * zu_res(ji,jj) ) * umask(ji,jj,1) * e1e2u(ji,jj) * z1_pglob_area |
|---|
| 1618 | zv_res(ji,jj) = SQRT( zv_res(ji,jj) * zv_res(ji,jj) ) * vmask(ji,jj,1) * e1e2v(ji,jj) * z1_pglob_area |
|---|
| 1619 | |
|---|
| 1620 | END DO |
|---|
| 1621 | END DO |
|---|
| 1622 | |
|---|
| 1623 | IF ( lwp ) WRITE(numout,*) ' TEST 2 ' |
|---|
| 1624 | zu_res_mean = glob_sum( 'ice_rhg_vp', zu_res(:,:) ) |
|---|
| 1625 | zv_res_mean = glob_sum( 'ice_rhg_vp', zv_res(:,:) ) |
|---|
| 1626 | IF ( lwp ) WRITE(numout,*) ' TEST 3 ' |
|---|
| 1627 | zvelres = 0.5_wp * ( zu_res_mean + zv_res_mean ) |
|---|
| 1628 | |
|---|
| 1629 | IF ( lwp ) WRITE(numout,*) ' TEST 4 ' |
|---|
| 1630 | |
|---|
| 1631 | ! -- Global mean kinetic energy per unit area (J/m2) |
|---|
| 1632 | DO jj = 2, jpj - 1 |
|---|
| 1633 | DO ji = 2, jpi - 1 |
|---|
| 1634 | zu = 0.5_wp * ( pu(ji-1,jj) + pu(ji,jj) ) ! u-vel at T-point |
|---|
| 1635 | zv = 0.5_wp * ( pv(ji,jj-1) + pv(ji,jj) ) |
|---|
| 1636 | zvel2(:,:) = zu*zu + zv*zv ! square of ice velocity at T-point |
|---|
| 1637 | END DO |
|---|
| 1638 | END DO |
|---|
| 1639 | |
|---|
| 1640 | IF ( lwp ) WRITE(numout,*) ' TEST 5 ' |
|---|
| 1641 | zmke = 0.5_wp * glob_sum( 'ice_rhg_vp', pmt(:,:) * e1e2t(:,:) * zvel2(:,:) ) / pglob_area |
|---|
| 1642 | IF ( lwp ) WRITE(numout,*) ' TEST 6 ' |
|---|
| 1643 | |
|---|
| 1644 | ENDIF |
|---|
| 1645 | |
|---|
| 1646 | ! ! ==================== ! |
|---|
| 1647 | |
|---|
| 1648 | ! time |
|---|
| 1649 | it = ( kt - 1 ) * kitermax + kiter |
|---|
| 1650 | |
|---|
| 1651 | |
|---|
| 1652 | IF( lwm ) THEN |
|---|
| 1653 | ! write variables |
|---|
| 1654 | istatus = NF90_PUT_VAR( ncvgid, nvarid_ucvg, (/zveldif/), (/it/), (/1/) ) ! max U or V velocity diff between subiterations |
|---|
| 1655 | istatus = NF90_PUT_VAR( ncvgid, nvarid_ures, (/zu_res_mean/), (/it/), (/1/) ) ! U-residual of the linear system |
|---|
| 1656 | istatus = NF90_PUT_VAR( ncvgid, nvarid_vres, (/zv_res_mean/), (/it/), (/1/) ) ! V-residual of the linear system |
|---|
| 1657 | istatus = NF90_PUT_VAR( ncvgid, nvarid_velres, (/zvelres/), (/it/), (/1/) ) ! average of u- and v- residuals |
|---|
| 1658 | istatus = NF90_PUT_VAR( ncvgid, nvarid_udif, (/puerr_max/), (/it/), (/1/) ) ! max U velocity difference, inner iterations |
|---|
| 1659 | istatus = NF90_PUT_VAR( ncvgid, nvarid_vdif, (/pverr_max/), (/it/), (/1/) ) ! max V velocity difference, inner iterations |
|---|
| 1660 | istatus = NF90_PUT_VAR( ncvgid, nvarid_mke, (/zmke/), (/it/), (/1/) ) ! mean kinetic energy |
|---|
| 1661 | |
|---|
| 1662 | istatus = NF90_PUT_VAR( ncvgid, nvarid_usub, (/pu/), (/it/) ) ! u-velocity |
|---|
| 1663 | istatus = NF90_PUT_VAR( ncvgid, nvarid_vsub, (/pv/), (/it/) ) ! v-velocity |
|---|
| 1664 | |
|---|
| 1665 | ! close file |
|---|
| 1666 | IF( kt == nitend ) istatus = NF90_CLOSE( ncvgid ) |
|---|
| 1667 | ENDIF |
|---|
| 1668 | |
|---|
| 1669 | END SUBROUTINE rhg_cvg_vp |
|---|
| 1670 | |
|---|
| 1671 | |
|---|
| 1672 | |
|---|
| 1673 | #else |
|---|
| 1674 | !!---------------------------------------------------------------------- |
|---|
| 1675 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 1676 | !!---------------------------------------------------------------------- |
|---|
| 1677 | #endif |
|---|
| 1678 | |
|---|
| 1679 | !!============================================================================== |
|---|
| 1680 | END MODULE icedyn_rhg_vp |
|---|
| 1681 | |
|---|
