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MODULE icedyn_rhg_vp
!!======================================================================
!! *** MODULE icedyn_rhg_vp ***
!! Sea-Ice dynamics : Viscous-plastic rheology with LSR technique
!!======================================================================
!!
!! History : - ! 1997-20 (J. Zhang, M. Losch) Original code, implementation into mitGCM
!! 4.0 ! 2020-09 (M. Vancoppenolle) Adaptation to SI3
!!
!!----------------------------------------------------------------------
#if defined key_si3
!!----------------------------------------------------------------------
!! 'key_si3' SI3 sea-ice model
!!----------------------------------------------------------------------
!! ice_dyn_rhg_vp : computes ice velocities from VP rheolog with LSR solvery
!!----------------------------------------------------------------------
USE phycst ! Physical constants
USE dom_oce ! Ocean domain
USE sbc_oce , ONLY : ln_ice_embd, nn_fsbc, ssh_m
USE sbc_ice , ONLY : utau_ice, vtau_ice, snwice_mass, snwice_mass_b
USE ice ! sea-ice: ice variables
USE icevar ! ice_var_sshdyn
USE icedyn_rdgrft ! sea-ice: ice strength
USE bdy_oce , ONLY : ln_bdy
USE bdyice
#if defined key_agrif
USE agrif_ice_interp
#endif
!
USE in_out_manager ! I/O manager
USE iom ! I/O manager library
USE lib_mpp ! MPP library
USE lib_fortran ! fortran utilities (glob_sum + no signed zero)
USE lbclnk ! lateral boundary conditions (or mpp links)
USE prtctl ! Print control
USE netcdf ! NetCDF library for convergence test
IMPLICIT NONE
PRIVATE
PUBLIC ice_dyn_rhg_vp ! called by icedyn_rhg.F90
INTEGER :: nn_nvp ! total number of VP iterations (n_out_vp*n_inn_vp)
LOGICAL :: lp_zebra_vp =.TRUE. ! activate zebra (solve the linear system problem every odd j-band, then one every even one)
REAL(wp) :: zrelaxu_vp=0.95 ! U-relaxation factor (MV: can probably be merged with V-factor once ok)
REAL(wp) :: zrelaxv_vp=0.95 ! V-relaxation factor
REAL(wp) :: zuerr_max_vp=0.80 ! maximum velocity error, above which a forcing error is considered and solver is stopped
REAL(wp) :: zuerr_min_vp=1.e-06 ! minimum velocity error, beyond which convergence is assumed
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!! for convergence tests
INTEGER :: ncvgid ! netcdf file id
INTEGER :: nvarid_ures, nvarid_vres, nvarid_velres
INTEGER :: nvarid_uerr_max, nvarid_verr_max, nvarid_velerr_max
INTEGER :: nvarid_umad, nvarid_vmad, nvarid_velmad
INTEGER :: nvarid_umad_outer, nvarid_vmad_outer, nvarid_velmad_outer
INTEGER :: nvarid_mke
REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fimask ! mask at F points for the ice
!! * Substitutions
# include "do_loop_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/ICE 4.0 , NEMO Consortium (2018)
!! $Id: icedyn_rhg_vp.F90 13279 2020-07-09 10:39:43Z clem $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE ice_dyn_rhg_vp( kt, pshear_i, pdivu_i, pdelta_i )
!!-------------------------------------------------------------------
!!
!! *** SUBROUTINE ice_dyn_rhg_vp ***
!! VP-LSR-C-grid
!!
!! ** Purpose : determines sea ice drift from wind stress, ice-ocean
!! stress and sea-surface slope. Internal forces assume viscous-plastic rheology (Hibler, 1979)
!!
!! ** Method
!!
!! The resolution algorithm follows from Zhang and Hibler (1997) and Losch (2010)
!! with elements from Lemieux and Tremblay (2008) and Lemieux and Tremblay (2009)
!!
!! The components of the momentum equations are arranged following the ideas of Zhang and Hibler (1997)
!!
!! f1(u) = g1(v)
!! f2(v) = g2(u)
!!
!! The right-hand side (RHS) is explicit
!! The left-hand side (LHS) is implicit
!! Coriolis is part of explicit terms, whereas ice-ocean drag is implicit
!!
!! Two iteration levels (outer and inner loops) are used to solve the equations
!!
!! The outer loop (OL, typically 10 iterations) is there to deal with the (strong) non-linearities in the equation
!!
!! The inner loop (IL, typically 1500 iterations) is there to solve the linear problem with a line-successive-relaxation algorithm
!!
!! The velocity used in the non-linear terms uses a "modified euler time step" (not sure its the correct term),
!!! with uk = ( uk-1 + uk-2 ) / 2.
!!
!! * Spatial discretization
!!
!! Assumes a C-grid
!!
!! The points in the C-grid look like this, my darling
!!
!! (ji,jj)
!! |
!! |
!! (ji-1,jj) | (ji,jj)
!! ---------
!! | |
!! | (ji,jj) |------(ji,jj)
!! | |
!! ---------
!! (ji-1,jj-1) (ji,jj-1)
!!
!! ** Inputs : - wind forcing (stress), oceanic currents
!! ice total volume (vt_i) per unit area
!! snow total volume (vt_s) per unit area
!!
!! ** Action :
!!
!! ** Steps :
!!
!! ** Notes :
!!
!! References : Zhang and Hibler, JGR 1997; Losch et al., OM 2010., Lemieux et al., 2008, 2009, ...
!!
!!
!!-------------------------------------------------------------------
!!
INTEGER , INTENT(in ) :: kt ! time step
REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i !
!!
LOGICAL :: ll_u_iterate, ll_v_iterate ! continue iteration or not
!
INTEGER :: ji, ji2, jj, jj2, jn ! dummy loop indices
INTEGER :: i_out, i_inn, i_inn_tot !
INTEGER :: ji_min, jj_min !
INTEGER :: nn_zebra_vp ! number of zebra steps
!
REAL(wp) :: zrhoco ! rho0 * rn_cio
REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity
REAL(wp) :: zglob_area ! global ice area for diagnostics
REAL(wp) :: zkt ! isotropic tensile strength for landfast ice
REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV ! ice/snow mass and volume
REAL(wp) :: zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars
REAL(wp) :: zu_cV, zv_cU !
REAL(wp) :: zfac, zfac1, zfac2, zfac3
REAL(wp) :: zt12U, zt11U, zt22U, zt21U, zt122U, zt121U
REAL(wp) :: zt12V, zt11V, zt22V, zt21V, zt122V, zt121V
REAL(wp) :: zAA3, zw, ztau, zuerr_max, zverr_max
!
REAL(wp), DIMENSION(jpi,jpj) :: za_iU , za_iV ! ice fraction on U/V points
REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! Acceleration term contribution to RHS
REAL(wp), DIMENSION(jpi,jpj) :: zmassU_t, zmassV_t ! Mass per unit area divided by time step
!
REAL(wp), DIMENSION(jpi,jpj) :: zdelta ! Delta at T-points (now value)
REAL(wp), DIMENSION(jpi,jpj) :: zten_i, zshear ! Tension, shear
REAL(wp), DIMENSION(jpi,jpj) :: zvisc_t ! Bulk viscosity (P/delta*) at T points
REAL(wp), DIMENSION(jpi,jpj) :: zvisc_t_prev ! Bulk viscosity (next to last iterate) - for yield curve diag
REAL(wp), DIMENSION(jpi,jpj) :: zzt, zet ! Viscosity pre-factors at T points
REAL(wp), DIMENSION(jpi,jpj) :: zef ! Viscosity pre-factor at F point
!
REAL(wp), DIMENSION(jpi,jpj) :: zmt ! Mass per unit area at t-point
REAL(wp), DIMENSION(jpi,jpj) :: zmf ! Coriolis factor (m*f) at t-point
REAL(wp), DIMENSION(jpi,jpj) :: v_oceU, u_oceV, v_iceU, u_iceV ! ocean/ice u/v component on V/U points
REAL(wp), DIMENSION(jpi,jpj) :: zu_c, zv_c ! "current" ice velocity (m/s), average of previous two OL iterates
REAL(wp), DIMENSION(jpi,jpj) :: zu_b, zv_b ! velocity at previous sub-iterate
REAL(wp), DIMENSION(jpi,jpj) :: zuerr, zverr ! absolute U/Vvelocity difference between current and previous sub-iterates
REAL(wp), DIMENSION(jpi,jpj) :: zvel_res ! Residual of the linear system at last iteration
REAL(wp), DIMENSION(jpi,jpj) :: zvel_diff ! Absolute velocity difference @last outer iteration
!
REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear
REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope:
! ! ocean surface (ssh_m) if ice is not embedded
! ! ice bottom surface if ice is embedded
REAL(wp), DIMENSION(jpi,jpj) :: zCwU, zCwV ! ice-ocean drag pre-factor (rho*c*module(u))
REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points
REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array
REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points
REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi_rhsu, ztauy_oi_rhsv ! ice-ocean stress RHS contribution at U-V points
REAL(wp), DIMENSION(jpi,jpj) :: zs1_rhsu, zs2_rhsu, zs12_rhsu ! internal stress contributions to RHSU
REAL(wp), DIMENSION(jpi,jpj) :: zs1_rhsv, zs2_rhsv, zs12_rhsv ! internal stress contributions to RHSV
REAL(wp), DIMENSION(jpi,jpj) :: zf_rhsu, zf_rhsv ! U- and V- components of internal force RHS contributions
REAL(wp), DIMENSION(jpi,jpj) :: zrhsu, zrhsv ! U and V RHS
REAL(wp), DIMENSION(jpi,jpj) :: zAU, zBU, zCU, zDU, zEU ! Linear system coefficients, U equation
REAL(wp), DIMENSION(jpi,jpj) :: zAV, zBV, zCV, zDV, zEV ! Linear system coefficients, V equation
REAL(wp), DIMENSION(jpi,jpj) :: zFU, zFU_prime, zBU_prime ! Rearranged linear system coefficients, U equation
REAL(wp), DIMENSION(jpi,jpj) :: zFV, zFV_prime, zBV_prime ! Rearranged linear system coefficients, V equation
!!! REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast)
!!! REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast)
!
REAL(wp), DIMENSION(jpi,jpj) :: zmsk, zmsk00
REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! mask for lots of ice (1), little ice (0)
REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence (1), no ice (0)
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