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-04 ! minimum velocity error, beyond which convergence is assumed !! 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) :: zp_delstar_f ! 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) :: zdeltat, zdelstar_t ! Delta & Delta* at T-points REAL(wp), DIMENSION(jpi,jpj) :: ztens, zshear ! Tension, shear REAL(wp), DIMENSION(jpi,jpj) :: zp_delstar_t ! P/delta* at T points 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) :: 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) :: 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) ! REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small !! --- diags REAL(wp) :: zsig1, zsig2, zsig12, zdelta, z1_strength, zfac_x, zfac_y REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12, zs12f ! stress tensor components REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig_I, zsig_II, zsig1_p, zsig2_p REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztaux_oi, ztauy_oi REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice, zdiag_ymtrp_ice ! X/Y-component of ice mass transport (kg/s, SIMIP) REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw, zdiag_ymtrp_snw ! X/Y-component of snow mass transport (kg/s, SIMIP) REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp, zdiag_yatrp ! X/Y-component of area transport (m2/s, SIMIP) REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zvel_res ! Residual of the linear system at last iteration REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zvel_diff ! Absolute velocity difference @last outer iteration !!---------------------------------------------------------------------------------------------------------------------- IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_vp: VP sea-ice rheology (LSR solver)' IF( lwp ) WRITE(numout,*) '-- ice_dyn_rhg_vp: VP sea-ice rheology (LSR solver)' !------------------------------------------------------------------------------! ! ! --- Initialization ! !------------------------------------------------------------------------------! ! for diagnostics and convergence tests DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) zmsk00(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice , 0 if no ice END_2D IF ( lp_zebra_vp ) THEN; nn_zebra_vp = 2 ELSE; nn_zebra_vp = 1; ENDIF nn_nvp = nn_vp_nout * nn_vp_ninn ! maximum number of iterations IF( lwp ) WRITE(numout,*) ' lp_zebra_vp : ', lp_zebra_vp IF( lwp ) WRITE(numout,*) ' nn_zebra_vp : ', nn_zebra_vp IF( lwp ) WRITE(numout,*) ' nn_nvp : ', nn_nvp zrhoco = rho0 * rn_cio ! ecc2: square of yield ellipse eccentricity ecc2 = rn_ecc * rn_ecc z1_ecc2 = 1._wp / ecc2 ! Initialise convergence checks IF( nn_rhg_chkcvg /= 0 ) THEN ! ice area for global mean kinetic energy (m2) zglob_area = glob_sum( 'ice_rhg_vp', at_i(:,:) * e1e2t(:,:) * tmask(:,:,1) ) ENDIF ! Landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) ! MV: Not working yet... IF( ln_landfast_L16 ) THEN ; zkt = rn_lf_tensile ELSE ; zkt = 0._wp ENDIF zs1_rhsu(:,:) = 0._wp; zs2_rhsu(:,:) = 0._wp; zs1_rhsv(:,:) = 0._wp; zs2_rhsv(:,:) = 0._wp zrhsu (:,:) = 0._wp; zrhsv (:,:) = 0._wp; zf_rhsu(:,:) = 0._wp; zf_rhsv(:,:) = 0._wp zAU(:,:) = 0._wp; zBU(:,:) = 0._wp; zCU(:,:) = 0._wp; zDU(:,:) = 0._wp; zEU(:,:) = 0._wp zAV(:,:) = 0._wp; zBV(:,:) = 0._wp; zCV(:,:) = 0._wp; zDV(:,:) = 0._wp; zEV(:,:) = 0._wp !------------------------------------------------------------------------------! ! ! --- Time-independent quantities ! !------------------------------------------------------------------------------! CALL ice_strength ! strength at T points !--------------------------- ! -- F-mask (code from EVP) !--------------------------- IF( kt == nit000 ) THEN ! MartinV: ! In EVP routine, fimask is applied on shear at F-points, in order to enforce the lateral boundary condition (no-slip, ..., free-slip) ! I am not sure the same recipe applies here ! - ocean/land mask ALLOCATE( fimask(jpi,jpj) ) IF( rn_ishlat == 0._wp ) THEN DO_2D( 0, 0, 0, 0 ) fimask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) END_2D ELSE DO_2D( 0, 0, 0, 0 ) fimask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) ! Lateral boundary conditions on velocity (modify fimask) IF( fimask(ji,jj) == 0._wp ) THEN fimask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(ji,jj,1), umask(ji,jj+1,1), & & vmask(ji,jj,1), vmask(ji+1,jj,1) ) ) ENDIF END_2D ENDIF CALL lbc_lnk( 'icedyn_rhg_vp', fimask, 'F', 1._wp ) ENDIF !---------------------------------------------------------------------------------------------------------- ! -- Time-independent pre-factors for acceleration, ocean drag, coriolis, atmospheric drag, surface tilt !---------------------------------------------------------------------------------------------------------- ! Compute all terms & factors independent of velocities, or only depending on velocities at previous time step ! sea surface height ! embedded sea ice: compute representative ice top surface ! non-embedded sea ice: use ocean surface for slope calculation zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) zmt(ji,jj) = rhos * vt_s(ji,jj) + rhoi * vt_i(ji,jj) ! Snow and ice mass at T-point zmf(ji,jj) = zmt(ji,jj) * ff_t(ji,jj) ! Coriolis factor at T points (m*f) END_2D DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! Ice fraction at U-V points 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) 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) ! Snow and ice mass at U-V points zm1 = zmt(ji,jj) zm2 = zmt(ji+1,jj) zm3 = zmt(ji,jj+1) zmassU = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) zmassV = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) ! Mass per unit area divided by time step zmassU_t(ji,jj) = zmassU * r1_Dt_ice zmassV_t(ji,jj) = zmassV * r1_Dt_ice ! Acceleration term contribution to RHS (depends on velocity at previous time step) zmU_t(ji,jj) = zmassU_t(ji,jj) * u_ice(ji,jj) zmV_t(ji,jj) = zmassV_t(ji,jj) * v_ice(ji,jj) ! Ocean currents at U-V points 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) 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) ! Wind stress ztaux_ai(ji,jj) = za_iU(ji,jj) * utau_ice(ji,jj) ztauy_ai(ji,jj) = za_iV(ji,jj) * vtau_ice(ji,jj) ! Force due to sea surface tilt(- m*g*GRAD(ssh)) zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) ! Mask for ice presence (1) or absence (0) zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice ! Mask for lots of ice (1) or little ice (0) IF ( zmassU <= zmmin .AND. za_iU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF IF ( zmassV <= zmmin .AND. za_iV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF END_2D !------------------------------------------------------------------------------! ! ! --- Start outer loop ! !------------------------------------------------------------------------------! zu_c(:,:) = u_ice(:,:) zv_c(:,:) = v_ice(:,:) i_inn_tot = 0 DO i_out = 1, nn_vp_nout ! Velocities used in the non linear terms are the average of the past two iterates ! u_it = 0.5 * ( u_{it-1} + u_{it-2} ) ! Also used in Hibler and Ackley (1983); Zhang and Hibler (1997); Lemieux and Tremblay (2009) zu_c(:,:) = 0.5_wp * ( u_ice(:,:) + zu_c(:,:) ) zv_c(:,:) = 0.5_wp * ( v_ice(:,:) + zv_c(:,:) ) !------------------------------------------------------------------------------! ! ! --- Right-hand side (RHS) of the linear problem ! !------------------------------------------------------------------------------! ! In the outer loop, one needs to update all RHS terms ! with explicit velocity dependencies (viscosities, coriolis, ocean stress) ! as a function of "current" velocities (uc, vc) !------------------------------------------ ! -- Strain rates, viscosities and P/Delta !------------------------------------------ ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 ) ! 1->jpi-1 ! loops start at 1 since there is no boundary condition (lbc_lnk) at i=1 and j=1 for F points ! shear at F points 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) & & + ( zv_c(ji+1,jj) * r1_e2v(ji+1,jj) - zv_c(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & & ) * r1_e1e2f(ji,jj) * fimask(ji,jj) END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zds, 'F', 1. ) ! necessary, zds2 uses jpi/jpj values for zds DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls ) ! 2 -> jpj; 2,jpi !!! CHECK !!! ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 ! shear**2 at T points (doc eq. A16) zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & & + 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) & & ) * 0.25_wp * r1_e1e2t(ji,jj) ! divergence at T points zdiv = ( e2u(ji,jj) * zu_c(ji,jj) - e2u(ji-1,jj) * zu_c(ji-1,jj) & & + e1v(ji,jj) * zv_c(ji,jj) - e1v(ji,jj-1) * zv_c(ji,jj-1) & & ) * r1_e1e2t(ji,jj) zdiv2 = zdiv * zdiv ! tension at T points 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) & & - ( zv_c(ji,jj) * r1_e1v(ji,jj) - zv_c(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & & ) * r1_e1e2t(ji,jj) zdt2 = zdt * zdt ! delta at T points zdeltat(ji,jj) = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) ! delta* at T points (following Lemieux and Dupont, GMD 2020) zdelstar_t(ji,jj) = zdeltat(ji,jj) + rn_creepl ! OPT zdelstar_t can be totally removed and put into next line directly. Could change results ! P/delta* at T-points zp_delstar_t(ji,jj) = strength(ji,jj) / zdelstar_t(ji,jj) ! Temporary zzt and zet factors at T-points zzt(ji,jj) = zp_delstar_t(ji,jj) * r1_e1e2t(ji,jj) zet(ji,jj) = zzt(ji,jj) * z1_ecc2 END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zp_delstar_t , 'T', 1. ) ! necessary, used for ji = 1 and jj = 1 DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )! 1-> jpj-1; 1->jpi-1 ! P/delta* at F points zp_delstar_f = 0.25_wp * ( zp_delstar_t(ji,jj) + zp_delstar_t(ji+1,jj) + zp_delstar_t(ji,jj+1) + zp_delstar_t(ji+1,jj+1) ) ! Temporary zef factor at F-point zef(ji,jj) = zp_delstar_f * r1_e1e2f(ji,jj) * z1_ecc2 * fimask(ji,jj) * 0.5_wp END_2D !--------------------------------------------------- ! -- Ocean-ice drag and Coriolis RHS contributions !--------------------------------------------------- DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 !--- ice u-velocity @V points, v-velocity @U points (for non-linear drag computation) 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) 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) !--- non-linear drag coefficients (need to be updated at each outer loop, see Lemieux and Tremblay JGR09, p.3, beginning of Section 3) 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) ) & & + ( zv_cU - v_oceU(ji,jj) ) * ( zv_cU - v_oceU(ji,jj) ) ) 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) ) & & + ( zu_cV - u_oceV(ji,jj) ) * ( zu_cV - u_oceV(ji,jj) ) ) !--- Ocean-ice drag contributions to RHS ztaux_oi_rhsu(ji,jj) = zCwU(ji,jj) * u_oce(ji,jj) ztauy_oi_rhsv(ji,jj) = zCwV(ji,jj) * v_oce(ji,jj) !--- U-component of Coriolis Force (energy conserving formulation) zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & & ( zmf(ji ,jj) * ( e1v(ji ,jj) * zv_c(ji ,jj) + e1v(ji ,jj-1) * zv_c(ji ,jj-1) ) & & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * zv_c(ji+1,jj) + e1v(ji+1,jj-1) * zv_c(ji+1,jj-1) ) ) !--- V-component of Coriolis Force (energy conserving formulation) zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & & ( zmf(ji,jj ) * ( e2u(ji,jj ) * zu_c(ji,jj ) + e2u(ji-1,jj ) * zu_c(ji-1,jj ) ) & & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * zu_c(ji,jj+1) + e2u(ji-1,jj+1) * zu_c(ji-1,jj+1) ) ) END_2D !------------------------------------- ! -- Internal stress RHS contribution !------------------------------------- ! --- Stress contributions at T-points DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls ) ! 2 -> jpj; 2,jpi !!! CHECK !!! ! loop to jpi,jpj to avoid making a communication for zs1 & zs2 ! sig1 contribution to RHS of U-equation at T-points zs1_rhsu(ji,jj) = zzt(ji,jj) * ( e1v(ji,jj) * zv_c(ji,jj) - e1v(ji,jj-1) * zv_c(ji,jj-1) ) & & - zp_delstar_t(ji,jj) * zdeltat(ji,jj) ! sig2 contribution to RHS of U-equation at T-points 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) ! sig1 contribution to RHS of V-equation at T-points zs1_rhsv(ji,jj) = zzt(ji,jj) * ( e2u(ji,jj) * zu_c(ji,jj) - e2u(ji-1,jj) * zu_c(ji-1,jj) ) & & - zp_delstar_t(ji,jj) * zdeltat(ji,jj) ! sig2 contribution to RHS of V-equation at T-points 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) END_2D ! --- Stress contributions at F-points ! MV NOTE: I applied fimask on zds, by mimetism on EVP, but without deep understanding of what I was doing ! My guess is that this is the way to enforce boundary conditions on strain rate tensor DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 ) ! 1->jpi-1 ! sig12 contribution to RHS of U equation at F-points zs12_rhsu(ji,jj) = zef(ji,jj) * ( r1_e2v(ji+1,jj) * zv_c(ji+1,jj) + r1_e2v(ji,jj) * zv_c(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) * fimask(ji,jj) ! sig12 contribution to RHS of V equation at F-points zs12_rhsv(ji,jj) = zef(ji,jj) * ( r1_e1u(ji,jj+1) * zu_c(ji,jj+1) + r1_e1u(ji,jj) * zu_c(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) * fimask(ji,jj) END_2D ! --- Internal force contributions to RHS, taken as divergence of stresses (Appendix C of Hunke and Dukowicz, 2002) ! OPT: merge with next loop and use intermediate scalars for zf_rhsu DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! --- U component of internal force contribution to RHS at U points zf_rhsu(ji,jj) = 0.5_wp * r1_e1e2u(ji,jj) * & ( e2u(ji,jj) * ( zs1_rhsu(ji+1,jj) - zs1_rhsu(ji,jj) ) & & + 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) ) & & + 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) ) ) ! --- V component of internal force contribution to RHS at V points zf_rhsv(ji,jj) = 0.5_wp * r1_e1e2v(ji,jj) * & & ( e1v(ji,jj) * ( zs1_rhsv(ji,jj+1) - zs1_rhsv(ji,jj) ) & & - 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) ) & & + 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) ) ) END_2D !--------------------------- ! -- Sum RHS contributions !--------------------------- ! ! OPT: could use intermediate scalars to reduce memory access DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 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) zrhsv(ji,jj) = zmV_t(ji,jj) + ztauy_ai(ji,jj) + ztauy_oi_rhsv(ji,jj) + zspgV(ji,jj) + zCorV(ji,jj) + zf_rhsv(ji,jj) END_2D !---------------------------------------------------------------------------------------! ! ! --- Linear system matrix ! !---------------------------------------------------------------------------------------! ! Linear system matrix contains all implicit contributions ! 1) internal forces, 2) acceleration, 3) ice-ocean drag ! The linear system equation is written as follows ! AU * u_{i-1,j} + BU * u_{i,j} + CU * u_{i+1,j} ! = DU * u_{i,j-1} + EU * u_{i,j+1} + RHS (! my convention, not the same as ZH97 ) ! MV Note 1: martin losch applies boundary condition to BU in mitGCM - check whether it is necessary here ? ! MV Note 2: "T" factor calculations can be optimized by putting things out of the loop ! only zzt and zet are iteration-dependent, other only depend on scale factors DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 !------------------------------------- ! -- Internal forces LHS contribution !------------------------------------- ! ! --- U-component ! ! "T" factors (intermediate results) ! zfac = 0.5_wp * r1_e1e2u(ji,jj) zfac1 = zfac * e2u(ji,jj) zfac2 = zfac * r1_e2u(ji,jj) zfac3 = 2._wp * zfac * r1_e1u(ji,jj) zt11U = zfac1 * zzt(ji,jj) zt12U = zfac1 * zzt(ji+1,jj) zt21U = zfac2 * zet(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) zt22U = zfac2 * zet(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) zt121U = zfac3 * zef(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) zt122U = zfac3 * zef(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) ! ! Linear system coefficients ! zAU(ji,jj) = - zt11U * e2u(ji-1,jj) - zt21U * r1_e2u(ji-1,jj) zBU(ji,jj) = ( zt11U + zt12U ) * e2u(ji,jj) + ( zt21U + zt22U ) * r1_e2u(ji,jj) + ( zt121U + zt122U ) * r1_e1u(ji,jj) zCU(ji,jj) = - zt12U * e2u(ji+1,jj) - zt22U * r1_e2u(ji+1,jj) zDU(ji,jj) = zt121U * r1_e1u(ji,jj-1) zEU(ji,jj) = zt122U * r1_e1u(ji,jj+1) ! ! --- V-component ! ! "T" factors (intermediate results) ! zfac = 0.5_wp * r1_e1e2v(ji,jj) zfac1 = zfac * e1v(ji,jj) zfac2 = zfac * r1_e1v(ji,jj) zfac3 = 2._wp * zfac * r1_e2v(ji,jj) zt11V = zfac1 * zzt(ji,jj) zt12V = zfac1 * zzt(ji,jj+1) zt21V = zfac2 * zet(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) zt22V = zfac2 * zet(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) zt121V = zfac3 * zef(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) zt122V = zfac3 * zef(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) ! ! Linear system coefficients ! zAV(ji,jj) = - zt11V * e1v(ji,jj-1) - zt21V * r1_e1v(ji,jj-1) zBV(ji,jj) = ( zt11V + zt12V ) * e1v(ji,jj) + ( zt21V + zt22V ) * r1_e1v(ji,jj) + ( zt122V + zt121V ) * r1_e2v(ji,jj) zCV(ji,jj) = - zt12V * e1v(ji,jj+1) - zt22V * r1_e1v(ji,jj+1) zDV(ji,jj) = zt121V * r1_e2v(ji-1,jj) zEV(ji,jj) = zt122V * r1_e2v(ji+1,jj) !----------------------------------------------------- ! -- Ocean-ice drag and acceleration LHS contribution !----------------------------------------------------- zBU(ji,jj) = zBU(ji,jj) + zCwU(ji,jj) + zmassU_t(ji,jj) zBV(ji,jj) = zBV(ji,jj) + zCwV(ji,jj) + zmassV_t(ji,jj) END_2D !------------------------------------------------------------------------------! ! ! --- Inner loop: solve linear system, check convergence ! !------------------------------------------------------------------------------! ! Inner loop solves the linear problem .. requires 1500 iterations ll_u_iterate = .TRUE. ll_v_iterate = .TRUE. DO i_inn = 1, nn_vp_ninn ! inner loop iterations !--- mitgcm computes initial value of residual here... i_inn_tot = i_inn_tot + 1 ! l_full_nf_update = i_inn_tot == nn_nvp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 zu_b(:,:) = u_ice(:,:) ! velocity at previous inner-iterate zv_b(:,:) = v_ice(:,:) IF ( ll_u_iterate .OR. ll_v_iterate ) THEN ! ---------------------------- ! IF ( ll_u_iterate ) THEN ! --- Solve for u-velocity --- ! ! ---------------------------- ! ! What follows could be subroutinized... ! Thomas Algorithm for tridiagonal solver ! A*u(i-1,j)+B*u(i,j)+C*u(i+1,j) = F zFU(:,:) = 0._wp ; zFU_prime(:,:) = 0._wp ; zBU_prime(:,:) = 0._wp; DO jn = 1, nn_zebra_vp ! "zebra" loop (! red-black-sor!!! ) ! OPT: could be even better optimized with a true red-black SOR IF ( jn == 1 ) THEN ; jj_min = 2 ELSE ; jj_min = 3 ENDIF DO jj = jj_min, jpj - 1, nn_zebra_vp !------------------------ ! Independent term (zFU) !------------------------ DO ji = 2, jpi - 1 ! note: these are key lines linking information between processors ! u_ice/v_ice need to be lbc_linked ! sub-domain boundary condition substitution ! see Zhang and Hibler, 1997, Appendix B zAA3 = 0._wp IF ( ji == 2 ) zAA3 = zAA3 - zAU(ji,jj) * u_ice(ji-1,jj) IF ( ji == jpi - 1 ) zAA3 = zAA3 - zCU(ji,jj) * u_ice(ji+1,jj) ! right hand side zFU(ji,jj) = ( zrhsu(ji,jj) & ! right-hand side terms & + zAA3 & ! boundary condition translation & + zDU(ji,jj) * u_ice(ji,jj-1) & ! internal force, j-1 & + zEU(ji,jj) * u_ice(ji,jj+1) ) * umask(ji,jj,1) ! internal force, j+1 END DO END DO !--------------- ! Forward sweep !--------------- DO jj = jj_min, jpj - 1, nn_zebra_vp zBU_prime(2,jj) = zBU(2,jj) zFU_prime(2,jj) = zFU(2,jj) DO ji = 3, jpi - 1 zfac = SIGN( 1._wp , zBU(ji-1,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU(ji-1,jj) ) - epsi20 ) ) zw = zfac * zAU(ji,jj) / MAX ( ABS( zBU(ji-1,jj) ) , epsi20 ) zBU_prime(ji,jj) = zBU(ji,jj) - zw * zCU(ji-1,jj) zFU_prime(ji,jj) = zFU(ji,jj) - zw * zFU(ji-1,jj) END DO END DO !----------------------------- ! Backward sweep & relaxation !----------------------------- DO jj = jj_min, jpj - 1, nn_zebra_vp ! --- Backward sweep ! last row zfac = SIGN( 1._wp , zBU_prime(jpi-1,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU_prime(jpi-1,jj) ) - epsi20 ) ) u_ice(jpi-1,jj) = zfac * zFU_prime(jpi-1,jj) / MAX( ABS ( zBU_prime(jpi-1,jj) ) , epsi20 ) & & * umask(jpi-1,jj,1) DO ji = jpi - 2 , 2, -1 ! all other rows ! ---> original backward loop zfac = SIGN( 1._wp , zBU_prime(ji,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBU_prime(ji,jj) ) - epsi20 ) ) u_ice(ji,jj) = zfac * ( zFU_prime(ji,jj) - zCU(ji,jj) * u_ice(ji+1,jj) ) * umask(ji,jj,1) & & / MAX ( ABS ( zBU_prime(ji,jj) ) , epsi20 ) END DO !--- Relaxation and masking (for low-ice/no-ice cases) DO ji = 2, jpi - 1 u_ice(ji,jj) = zu_b(ji,jj) + zrelaxu_vp * ( u_ice(ji,jj) - zu_b(ji,jj) ) ! relaxation u_ice(ji,jj) = zmsk00x(ji,jj) & ! masking & * ( zmsk01x(ji,jj) * u_ice(ji,jj) & & + ( 1._wp - zmsk01x(ji,jj) ) * u_oce(ji,jj) * 0.01_wp ) * umask(ji,jj,1) END DO END DO ! jj CALL lbc_lnk( 'icedyn_rhg_vp', u_ice, 'U', -1. ) END DO ! zebra loop ENDIF ! ll_u_iterate ! ! ---------------------------- ! IF ( ll_v_iterate ) THEN ! --- Solve for V-velocity --- ! ! ! ---------------------------- ! ! MV OPT: what follows could be subroutinized... ! Thomas Algorithm for tridiagonal solver ! A*v(i,j-1)+B*v(i,j)+C*v(i,j+1) = F ! It is intentional to have a ji then jj loop for V-velocity !!! ZH97 explain it is critical for convergence speed zFV(:,:) = 0._wp ; zFV_prime(:,:) = 0._wp ; zBV_prime(:,:) = 0._wp; DO jn = 1, nn_zebra_vp ! "zebra" loop IF ( jn == 1 ) THEN ; ji_min = 2 ELSE ; ji_min = 3 ENDIF DO ji = ji_min, jpi - 1, nn_zebra_vp !------------------------ ! Independent term (zFV) !------------------------ DO jj = 2, jpj - 1 ! subdomain boundary condition substitution (check it is correctly applied !!!) ! see Zhang and Hibler, 1997, Appendix B zAA3 = 0._wp IF ( jj == 2 ) zAA3 = zAA3 - zAV(ji,jj) * v_ice(ji,jj-1) IF ( jj == jpj - 1 ) zAA3 = zAA3 - zCV(ji,jj) * v_ice(ji,jj+1) ! right hand side zFV(ji,jj) = ( zrhsv(ji,jj) & ! right-hand side terms & + zAA3 & ! boundary condition translation & + zDV(ji,jj) * v_ice(ji-1,jj) & ! internal force, j-1 & + zEV(ji,jj) * v_ice(ji+1,jj) ) * vmask(ji,jj,1) ! internal force, j+1 END DO END DO !--------------- ! Forward sweep !--------------- DO ji = ji_min, jpi - 1, nn_zebra_vp zBV_prime(ji,2) = zBV(ji,2) zFV_prime(ji,2) = zFV(ji,2) DO jj = 3, jpj - 1 zfac = SIGN( 1._wp , zBV(ji,jj-1) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV(ji,jj-1) ) - epsi20 ) ) zw = zfac * zAV(ji,jj) / MAX ( ABS( zBV(ji,jj-1) ) , epsi20 ) zBV_prime(ji,jj) = zBV(ji,jj) - zw * zCV(ji,jj-1) zFV_prime(ji,jj) = zFV(ji,jj) - zw * zFV(ji,jj-1) END DO END DO !----------------------------- ! Backward sweep & relaxation !----------------------------- DO ji = ji_min, jpi - 1, nn_zebra_vp ! --- Backward sweep ! last row zfac = SIGN( 1._wp , zBV_prime(ji,jpj-1) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV_prime(ji,jpj-1) ) - epsi20 ) ) v_ice(ji,jpj-1) = zfac * zFV_prime(ji,jpj-1) / MAX ( ABS(zBV_prime(ji,jpj-1) ) , epsi20 ) & & * vmask(ji,jpj-1,1) ! last row ! other rows DO jj = jpj-2, 2, -1 ! original back loop zfac = SIGN( 1._wp , zBV_prime(ji,jj) ) * MAX( 0._wp , SIGN( 1._wp , ABS( zBV_prime(ji,jj) ) - epsi20 ) ) v_ice(ji,jj) = zfac * ( zFV_prime(ji,jj) - zCV(ji,jj) * v_ice(ji,jj+1) ) * vmask(ji,jj,1) & & / MAX ( ABS( zBV_prime(ji,jj) ) , epsi20 ) END DO ! --- Relaxation & masking DO jj = 2, jpj - 1 v_ice(ji,jj) = zv_b(ji,jj) + zrelaxv_vp * ( v_ice(ji,jj) - zv_b(ji,jj) ) ! relaxation v_ice(ji,jj) = zmsk00y(ji,jj) & ! masking & * ( zmsk01y(ji,jj) * v_ice(ji,jj) & & + ( 1._wp - zmsk01y(ji,jj) ) * v_oce(ji,jj) * 0.01_wp ) * vmask(ji,jj,1) END DO ! jj END DO ! ji CALL lbc_lnk( 'icedyn_rhg_vp', v_ice, 'V', -1. ) END DO ! zebra loop ENDIF ! ll_v_iterate ! I suspect the communication should go into the zebra loop if we want reproducibility !-------------------------------------------------------------------------------------- ! -- Check convergence based on maximum velocity difference, continue or stop the loop !-------------------------------------------------------------------------------------- !------ ! on U !------ ! MV OPT: if the number of iterations to convergence is really variable, and keep the convergence check ! then we must optimize the use of the mpp_max, which is prohibitive zuerr_max = 0._wp IF ( ll_u_iterate .AND. MOD ( i_inn, nn_vp_chkcvg ) == 0 ) THEN ! - Maximum U-velocity difference zuerr(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zuerr(ji,jj) = ABS ( ( u_ice(ji,jj) - zu_b(ji,jj) ) ) * umask(ji,jj,1) END_2D zuerr_max = MAXVAL( zuerr ) CALL mpp_max( 'icedyn_rhg_evp', zuerr_max ) ! max over the global domain - damned! ! - Stop if max error is too large ("safeguard against bad forcing" of original Zhang routine) IF ( i_inn > 1 .AND. zuerr_max > zuerr_max_vp ) THEN IF ( lwp ) WRITE(numout,*) " VP rheology error was too large : ", zuerr_max, " in outer U-iteration ", i_out, " after ", i_inn, " iterations, we stopped " ll_u_iterate = .FALSE. ENDIF ! - Stop if error small enough IF ( zuerr_max < zuerr_min_vp ) THEN IF ( lwp ) WRITE(numout,*) " VP rheology nicely done in outer U-iteration ", i_out, " after ", i_inn, " iterations, finished! " ll_u_iterate = .FALSE. ENDIF ENDIF ! ll_u_iterate !------ ! on V !------ zverr_max = 0._wp IF ( ll_v_iterate .AND. MOD ( i_inn, nn_vp_chkcvg ) == 0 ) THEN ! - Maximum V-velocity difference zverr(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zverr(ji,jj) = ABS ( ( v_ice(ji,jj) - zv_b(ji,jj) ) ) * vmask(ji,jj,1) END_2D zverr_max = MAXVAL( zverr ) CALL mpp_max( 'icedyn_rhg_evp', zverr_max ) ! max over the global domain - damned! ! - Stop if error is too large ("safeguard against bad forcing" of original Zhang routine) IF ( i_inn > 1 .AND. zverr_max > zuerr_max_vp ) THEN IF ( lwp ) WRITE(numout,*) " VP rheology error was too large : ", zverr_max, " in outer V-iteration ", i_out, " after ", i_inn, " iterations, we stopped " ll_v_iterate = .FALSE. ENDIF ! - Stop if error small enough IF ( zverr_max < zuerr_min_vp ) THEN IF ( lwp ) WRITE(numout,*) " VP rheology nicely done in outer V-iteration ", i_out, " after ", i_inn, " iterations, finished! " ll_v_iterate = .FALSE. ENDIF ENDIF ! ll_v_iterate ENDIF ! --- end ll_u_iterate or ll_v_iterate !--------------------------------------------------------------------------------------- ! ! --- Calculate extra convergence diagnostics and save them ! !--------------------------------------------------------------------------------------- IF( nn_rhg_chkcvg/=0 .AND. MOD ( i_inn - 1, nn_vp_chkcvg ) == 0 ) THEN CALL rhg_cvg_vp( kt, i_out, i_inn, i_inn_tot, nn_vp_nout, nn_vp_ninn, nn_nvp, & & u_ice, v_ice, zu_b, zv_b, zu_c, zv_c, & & zmt, za_iU, za_iV, zuerr_max, zverr_max, zglob_area, & & zrhsu, zAU, zBU, zCU, zDU, zEU, zFU, & & zrhsv, zAV, zBV, zCV, zDV, zEV, zFV, & zvel_res, zvel_diff ) ENDIF END DO ! i_inn, end of inner loop END DO ! End of outer loop (i_out) ============================================================================================= IF( nn_rhg_chkcvg/=0 ) THEN IF( iom_use('velo_res') ) CALL iom_put( 'velo_res', zvel_res ) ! linear system residual @last inner&outer iteration IF( iom_use('velo_ero') ) CALL iom_put( 'velo_ero', zvel_diff ) ! abs velocity difference @last outer iteration IF( iom_use('uice_eri') ) CALL iom_put( 'uice_eri', zuerr ) ! abs velocity difference @last inner iteration IF( iom_use('vice_eri') ) CALL iom_put( 'vice_eri', zverr ) ! abs velocity difference @last inner iteration DEALLOCATE( zvel_res , zvel_diff ) ENDIF ! nn_rhg_chkcvg !------------------------------------------------------------------------------! ! ! --- Recompute delta, shear and div (inputs for mechanical redistribution) ! !------------------------------------------------------------------------------! ! ! MV OPT: subroutinize ? DO_2D( nn_hls, nn_hls, nn_hls-1, nn_hls-1 ) ! 1->jpj-1; 1->jpi-1 ! shear at F points 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) & & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & & ) * r1_e1e2f(ji,jj) * fimask(ji,jj) END_2D DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! tension**2 at T points 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) & & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & & ) * r1_e1e2t(ji,jj) zdt2 = zdt * zdt ztens(ji,jj) = zdt ! shear**2 at T points (doc eq. A16) zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & & + 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) & & ) * 0.25_wp * r1_e1e2t(ji,jj) ! maximum shear rate at T points (includees tension, output only) pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) ! i think this is maximum shear rate and not actual shear --- i'm not totally sure here ! shear at T-points zshear(ji,jj) = SQRT( zds2 ) ! divergence at T points pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & & ) * r1_e1e2t(ji,jj) zdiv2 = pdivu_i(ji,jj) * pdivu_i(ji,jj) ! delta at T points zdelta = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 pdelta_i(ji,jj) = zdelta + rn_creepl ! * rswitch END_2D CALL lbc_lnk( 'icedyn_rhg_vp', pshear_i, 'T', 1., pdivu_i, 'T', 1., pdelta_i, 'T', 1. ) !------------------------------------------------------------------------------! ! ! --- Diagnostics ! !------------------------------------------------------------------------------! ! ! MV OPT: subroutinize ? ! !---------------------------------- ! --- Recompute stresses if needed !---------------------------------- ! ! ---- Sea ice stresses at T-points IF ( iom_use('normstr') .OR. iom_use('sheastr') .OR. & & iom_use('intstrx') .OR. iom_use('intstry') .OR. & & iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zp_delstar_t(ji,jj) = strength(ji,jj) / pdelta_i(ji,jj) zfac = zp_delstar_t(ji,jj) zs1(ji,jj) = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) ) zs2(ji,jj) = zfac * z1_ecc2 * ztens(ji,jj) zs12(ji,jj) = zfac * z1_ecc2 * zshear(ji,jj) * 0.5_wp ! Bug 12 nov END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zs1, 'T', 1., zs2, 'T', 1., zs12, 'T', 1. ) ENDIF ! ---- s12 at F-points IF ( iom_use('intstrx') .OR. iom_use('intstry') ) THEN DO_2D( nn_hls, nn_hls, nn_hls-1, nn_hls-1 ) ! 1->jpj-1; 1->jpi-1 ! P/delta* at F points zp_delstar_f = 0.25_wp * ( zp_delstar_t(ji,jj) + zp_delstar_t(ji+1,jj) + zp_delstar_t(ji,jj+1) + zp_delstar_t(ji+1,jj+1) ) ! s12 at F-points zs12f(ji,jj) = zp_delstar_f * z1_ecc2 * zds(ji,jj) END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zs12f, 'F', 1. ) ENDIF ! !----------------------- ! --- Store diagnostics !----------------------- ! ! --- Ice-ocean, ice-atm. & ice-ocean bottom (landfast) stresses --- ! IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. & & iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN ALLOCATE( ztaux_oi(jpi,jpj) , ztauy_oi(jpi,jpj) ) !--- Recalculate oceanic stress at last inner iteration DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 !--- ice u-velocity @V points, v-velocity @U points (for non-linear drag computation) 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) 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) !--- non-linear drag coefficients (need to be updated at each outer loop, see Lemieux and Tremblay JGR09, p.3, beginning of Section 3) 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) ) & & + ( zv_cU - v_oceU(ji,jj) ) * ( zv_cU - v_oceU(ji,jj) ) ) 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) ) & & + ( zu_cV - u_oceV(ji,jj) ) * ( zu_cV - u_oceV(ji,jj) ) ) !--- Ocean-ice stress ztaux_oi(ji,jj) = zCwU(ji,jj) * ( u_oce(ji,jj) - u_ice(ji,jj) ) ztauy_oi(ji,jj) = zCwV(ji,jj) * ( v_oce(ji,jj) - v_ice(ji,jj) ) END_2D ! CALL lbc_lnk( 'icedyn_rhg_vp', ztaux_oi, 'U', -1., ztauy_oi, 'V', -1., ztaux_ai, 'U', -1., ztauy_ai, 'V', -1. ) !, & ! & ztaux_bi, 'U', -1., ztauy_bi, 'V', -1. ) ! CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 ) CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 ) CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 ) CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 ) ! CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 ) ! CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 ) DEALLOCATE( ztaux_oi , ztauy_oi ) ENDIF ! --- Divergence, shear and strength --- ! IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! maximum shear rate IF( iom_use('icedlt') ) CALL iom_put( 'icedlt' , pdelta_i * zmsk00 ) ! delta IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength ! --- Stress tensor invariants (SIMIP diags) --- ! IF( iom_use('normstr') .OR. iom_use('sheastr') ) THEN ! ! Stress tensor invariants (normal and shear stress N/m) - SIMIP diags. ! Definitions following Coon (1974) and Feltham (2008) ! ! sigma1, sigma2, sigma12 are useful (Hunke and Dukowicz MWR 2002, Bouillon et al., OM2013) ! however these are NOT stress tensor components, neither stress invariants, nor stress principal components ! ALLOCATE( zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) ! DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! Stress invariants zsig_I(ji,jj) = zs1(ji,jj) * 0.5_wp ! 1st invariant, aka average normal stress aka negative pressure zsig_II(ji,jj) = 0.5_wp * SQRT ( zs2(ji,jj) * zs2(ji,jj) + 4. * zs12(ji,jj) * zs12(ji,jj) ) ! 2nd invariant, aka maximum shear stress END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zsig_I, 'T', 1., zsig_II, 'T', 1.) IF( iom_use('normstr') ) CALL iom_put( 'normstr' , zsig_I(:,:) * zmsk00(:,:) ) ! Normal stress IF( iom_use('sheastr') ) CALL iom_put( 'sheastr' , zsig_II(:,:) * zmsk00(:,:) ) ! Maximum shear stress DEALLOCATE ( zsig_I, zsig_II ) ENDIF ! --- Normalized stress tensor principal components --- ! ! These are used to plot the normalized yield curve (Lemieux & Dupont, GMD 2020) ! To plot the yield curve and evaluate physical convergence, they have two recommendations ! Recommendation 1 : Use ice strength, not replacement pressure ! Recommendation 2 : Need to use deformations at PREVIOUS iterate for viscosities (see p. 1765) ! R2 means we need to recompute stresses IF( iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN ! ALLOCATE( zsig1_p(jpi,jpj) , zsig2_p(jpi,jpj) , zsig_I(jpi,jpj) , zsig_II(jpi,jpj) ) ! DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! Ice stresses computed with **viscosities** (delta, p/delta) at **previous** iterates ! and **deformations** at current iterates ! following Lemieux & Dupont (2020) zfac = zp_delstar_t(ji,jj) zsig1 = zfac * ( pdivu_i(ji,jj) - zdeltat(ji,jj) ) zsig2 = zfac * z1_ecc2 * ztens(ji,jj) zsig12 = zfac * z1_ecc2 * zshear(ji,jj) * 0.5_wp ! Bugfix 12 Nov ! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008), T-point zsig_I(ji,jj) = zsig1 * 0.5_wp ! 1st invariant zsig_II(ji,jj) = 0.5_wp * SQRT ( zsig2 * zsig2 + 4. *zsig12 * zsig12 ) ! 2nd invariant ! Normalized principal stresses (used to display the ellipse) z1_strength = 1._wp / MAX ( 1._wp , strength(ji,jj) ) zsig1_p(ji,jj) = ( zsig_I(ji,jj) + zsig_II(ji,jj) ) * z1_strength zsig2_p(ji,jj) = ( zsig_I(ji,jj) - zsig_II(ji,jj) ) * z1_strength END_2D ! CALL lbc_lnk( 'icedyn_rhg_vp', zsig1_p, 'T', 1., zsig2_p, 'T', 1.) ! CALL iom_put( 'sig1_pnorm' , zsig1_p ) CALL iom_put( 'sig2_pnorm' , zsig2_p ) DEALLOCATE( zsig1_p , zsig2_p , zsig_I , zsig_II ) ENDIF ! --- SIMIP, terms of tendency for momentum equation --- ! IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. & & iom_use('corstrx') .OR. iom_use('corstry') ) THEN ! --- Recalculate Coriolis stress at last inner iteration DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! --- U-component zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) END_2D ! CALL lbc_lnk( 'icedyn_rhg_vp', zspgU, 'U', -1., zspgV, 'V', -1., & & zCorU, 'U', -1., zCorV, 'V', -1. ) ! CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x) CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y) CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x) CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y) ENDIF IF ( iom_use('intstrx') .OR. iom_use('intstry') ) THEN ! Recalculate internal forces (divergence of stress tensor) at last inner iteration DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & & ) * r1_e2u(ji,jj) & & + ( zs12f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & & ) * 2._wp * r1_e1u(ji,jj) & & ) * r1_e1e2u(ji,jj) zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & & ) * r1_e1v(ji,jj) & & + ( zs12f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & & ) * 2._wp * r1_e2v(ji,jj) & & ) * r1_e1e2v(ji,jj) END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zfU, 'U', -1., zfV, 'V', -1. ) CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x) CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y) ENDIF ! --- Ice & snow mass and ice area transports IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. & & iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN ! ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) ) ! DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 ! 2D ice mass, snow mass, area transport arrays (X, Y) zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj) zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj) zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' END_2D CALL lbc_lnk( 'icedyn_rhg_vp', zdiag_xmtrp_ice, 'U', -1., zdiag_ymtrp_ice, 'V', -1., & & zdiag_xmtrp_snw, 'U', -1., zdiag_ymtrp_snw, 'V', -1., & & zdiag_xatrp , 'U', -1., zdiag_yatrp , 'V', -1. ) CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s) CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s) CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , & & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) ENDIF END SUBROUTINE ice_dyn_rhg_vp SUBROUTINE rhg_cvg_vp( kt, kitout, kitinn, kitinntot, kitoutmax, kitinnmax, kitinntotmax , & & pu, pv, pub, pvb, pub_outer, pvb_outer , & & pmt, pat_iu, pat_iv, puerr_max, pverr_max, pglob_area , & & prhsu, pAU, pBU, pCU, pDU, pEU, pFU , & & prhsv, pAV, pBV, pCV, pDV, pEV, pFV , & & pvel_res, pvel_diff ) !! !!---------------------------------------------------------------------- !! *** ROUTINE rhg_cvg_vp *** !! !! ** Purpose : check convergence of VP ice rheology !! !! ** Method : create a file ice_cvg.nc containing a few convergence diagnostics !! This routine is called every sub-iteration, so it is cpu expensive !! !! Calculates / stores !! - maximum absolute U-V difference (uice_cvg, u_dif, v_dif, m/s) !! - 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) !! - mean kinetic energy (mke_ice, J/m2) !! !! ** Note : for the first sub-iteration, uice_cvg is set to 0 (too large otherwise) !! !!---------------------------------------------------------------------- !! INTEGER , INTENT(in) :: kt, kitout, kitinn, kitinntot ! ocean model iterate, outer, inner and total n-iterations INTEGER , INTENT(in) :: kitoutmax, kitinnmax ! max number of outer & inner iterations INTEGER , INTENT(in) :: kitinntotmax ! max number of total sub-iterations REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pub, pvb ! now & sub-iter-before velocities REAL(wp), DIMENSION(:,:), INTENT(in) :: pub_outer, pvb_outer ! velocities @before outer iterations REAL(wp), DIMENSION(:,:), INTENT(in) :: pmt, pat_iu, pat_iv ! mass at T-point, ice concentration at U&V REAL(wp), INTENT(in) :: puerr_max, pverr_max ! absolute mean velocity difference REAL(wp), INTENT(in) :: pglob_area ! global ice area REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsu, pAU, pBU, pCU, pDU, pEU, pFU ! linear system coefficients REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsv, pAV, pBV, pCV, pDV, pEV, pFV REAL(wp), DIMENSION(:,:), INTENT(inout) :: pvel_res ! velocity residual @last inner iteration REAL(wp), DIMENSION(:,:), INTENT(inout) :: pvel_diff ! velocity difference @last outer iteration !! INTEGER :: idtime, istatus, ix_dim, iy_dim INTEGER :: ji, jj ! dummy loop indices INTEGER :: it_inn_file, it_out_file REAL(wp) :: zu_res_mean, zv_res_mean, zvel_res_mean ! mean residuals of the linear system REAL(wp) :: zu_mad, zv_mad, zvel_mad ! mean absolute deviation, sub-iterates REAL(wp) :: zu_mad_outer, zv_mad_outer, zvel_mad_outer ! mean absolute deviation, outer-iterates REAL(wp) :: zvel_err_max, zmke, zu, zv ! local scalars REAL(wp) :: z1_pglob_area ! inverse global ice area REAL(wp), DIMENSION(jpi,jpj) :: zu_res, zv_res, zvel2 ! local arrays REAL(wp), DIMENSION(jpi,jpj) :: zu_diff, zv_diff ! local arrays CHARACTER(len=20) :: clname !!---------------------------------------------------------------------- IF( lwp ) THEN WRITE(numout,*) WRITE(numout,*) 'rhg_cvg_vp : ice rheology convergence control' WRITE(numout,*) '~~~~~~~~~~~' WRITE(numout,*) ' kt = : ', kt WRITE(numout,*) ' kitout = : ', kitout WRITE(numout,*) ' kitinn = : ', kitinn WRITE(numout,*) ' kitinntot = : ', kitinntot WRITE(numout,*) ' kitoutmax (nn_vp_nout) = ', kitoutmax WRITE(numout,*) ' kitinnmax (nn_vp_ninn) = ', kitinnmax WRITE(numout,*) ' kitinntotmax (nn_nvp) = ', kitinntotmax WRITE(numout,*) ENDIF z1_pglob_area = 1._wp / pglob_area ! inverse global ice area ! create file IF( kt == nit000 .AND. kitinntot == 1 ) THEN ! IF( lwm ) THEN clname = 'ice_cvg.nc' IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname) istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid ) istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime ) istatus = NF90_DEF_DIM( ncvgid, 'x' , jpi, ix_dim ) istatus = NF90_DEF_DIM( ncvgid, 'y' , jpj, iy_dim ) istatus = NF90_DEF_VAR( ncvgid, 'u_res' , NF90_DOUBLE , (/ idtime /), nvarid_ures ) istatus = NF90_DEF_VAR( ncvgid, 'v_res' , NF90_DOUBLE , (/ idtime /), nvarid_vres ) istatus = NF90_DEF_VAR( ncvgid, 'vel_res' , NF90_DOUBLE , (/ idtime /), nvarid_velres ) istatus = NF90_DEF_VAR( ncvgid, 'uerr_max_sub' , NF90_DOUBLE , (/ idtime /), nvarid_uerr_max ) istatus = NF90_DEF_VAR( ncvgid, 'verr_max_sub' , NF90_DOUBLE , (/ idtime /), nvarid_verr_max ) istatus = NF90_DEF_VAR( ncvgid, 'velerr_max_sub', NF90_DOUBLE , (/ idtime /), nvarid_velerr_max ) istatus = NF90_DEF_VAR( ncvgid, 'umad_sub' , NF90_DOUBLE , (/ idtime /), nvarid_umad ) istatus = NF90_DEF_VAR( ncvgid, 'vmad_sub' , NF90_DOUBLE , (/ idtime /), nvarid_vmad ) istatus = NF90_DEF_VAR( ncvgid, 'velmad_sub' , NF90_DOUBLE , (/ idtime /), nvarid_velmad ) istatus = NF90_DEF_VAR( ncvgid, 'umad_outer' , NF90_DOUBLE , (/ idtime /), nvarid_umad_outer ) istatus = NF90_DEF_VAR( ncvgid, 'vmad_outer' , NF90_DOUBLE , (/ idtime /), nvarid_vmad_outer ) istatus = NF90_DEF_VAR( ncvgid, 'velmad_outer' , NF90_DOUBLE , (/ idtime /), nvarid_velmad_outer ) istatus = NF90_DEF_VAR( ncvgid, 'mke_ice', NF90_DOUBLE , (/ idtime /), nvarid_mke ) istatus = NF90_ENDDEF(ncvgid) ENDIF ! ENDIF !------------------------------------------------------------ ! ! Max absolute velocity difference with previous sub-iterate ! ( zvel_err_max ) ! !------------------------------------------------------------ ! ! This comes from the criterion used to stop the iterative procedure zvel_err_max = 0.5_wp * ( puerr_max + pverr_max ) ! average of U- and V- maximum error over the whole domain !---------------------------------------------- ! ! Mean-absolute-deviation (sub-iterates) ! ( zu_mad, zv_mad, zvel_mad) ! !---------------------------------------------- ! ! U zu_diff(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zu_diff(ji,jj) = ABS ( ( pu(ji,jj) - pub(ji,jj) ) ) * e1e2u(ji,jj) * pat_iu(ji,jj) * umask(ji,jj,1) * z1_pglob_area END_2D ! V zv_diff(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zv_diff(ji,jj) = ABS ( ( pv(ji,jj) - pvb(ji,jj) ) ) * e1e2v(ji,jj) * pat_iv(ji,jj) * vmask(ji,jj,1) * z1_pglob_area END_2D ! global sum & U-V average CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_diff, 'U', 1., zv_diff , 'V', 1. ) zu_mad = glob_sum( 'icedyn_rhg_vp : ', zu_diff ) zv_mad = glob_sum( 'icedyn_rhg_vp : ', zv_diff ) zvel_mad = 0.5_wp * ( zu_mad + zv_mad ) !----------------------------------------------- ! ! Mean-absolute-deviation (outer-iterates) ! ( zu_mad_outer, zv_mad_outer, zvel_mad_outer) ! !----------------------------------------------- ! IF ( kitinn == kitinnmax ) THEN ! only work at the end of outer iterates ! * U zu_diff(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zu_diff(ji,jj) = ABS ( ( pu(ji,jj) - pub_outer(ji,jj) ) ) * e1e2u(ji,jj) * pat_iu(ji,jj) * umask(ji,jj,1) * & & z1_pglob_area END_2D ! * V zv_diff(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zv_diff(ji,jj) = ABS ( ( pv(ji,jj) - pvb_outer(ji,jj) ) ) * e1e2v(ji,jj) * pat_iv(ji,jj) * vmask(ji,jj,1) * & & z1_pglob_area END_2D ! Global ice-concentration, grid-cell-area weighted mean CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_diff, 'U', 1., zv_diff , 'V', 1. ) ! abs behaves as a scalar no ? zu_mad_outer = glob_sum( 'icedyn_rhg_vp : ', zu_diff ) zv_mad_outer = glob_sum( 'icedyn_rhg_vp : ', zv_diff ) ! Average of both U & V zvel_mad_outer = 0.5_wp * ( zu_mad_outer + zv_mad_outer ) ENDIF ! --- Spatially-resolved absolute difference to send back to main routine ! (last iteration only, T-point) IF ( kitinntot == kitinntotmax) THEN zu_diff(:,:) = 0._wp zv_diff(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zu_diff(ji,jj) = ( ABS ( ( pu(ji-1,jj) - pub_outer(ji-1,jj) ) ) * umask(ji-1,jj,1) & & + ABS ( ( pu(ji,jj ) - pub_outer(ji,jj) ) ) * umask(ji,jj,1) ) & & / ( umask(ji-1,jj,1) + umask(ji,jj,1) ) zv_diff(ji,jj) = ( ABS ( ( pv(ji,jj-1) - pvb_outer(ji,jj-1) ) ) * vmask(ji,jj-1,1) & & + ABS ( ( pv(ji,jj ) - pvb_outer(ji,jj) ) ) * vmask(ji,jj,1) & & / ( vmask(ji,jj-1,1) + vmask(ji,jj,1) ) ) END_2D CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_diff, 'T', 1., zv_diff , 'T', 1. ) pvel_diff(:,:) = 0.5_wp * ( zu_diff(:,:) + zv_diff(:,:) ) ELSE pvel_diff(:,:) = 0._wp ENDIF !--------------------------------------- ! ! --- Mean residual & kinetic energy ! !--------------------------------------- IF ( kitinntot == 1 ) THEN zu_res_mean = 0._wp zv_res_mean = 0._wp zvel_res_mean = 0._wp zmke = 0._wp ELSE ! * Mean residual (N/m2) ! Here we take the residual of the linear system (N/m2), ! We define it as in mitgcm: global area-weighted mean of square-root residual ! Local residual r = Ax - B expresses to which extent the momentum balance is verified ! i.e., how close we are to a solution zu_res(:,:) = 0._wp; zv_res(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zu_res(ji,jj) = ( prhsu(ji,jj) + pDU(ji,jj) * pu(ji,jj-1) + pEU(ji,jj) * pu(ji,jj+1) & & - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) ) zv_res(ji,jj) = ( prhsv(ji,jj) + pDV(ji,jj) * pv(ji-1,jj) + pEV(ji,jj) * pv(ji+1,jj) & & - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) ) ! zu_res(ji,jj) = pFU(ji,jj) - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) ! zv_res(ji,jj) = pFV(ji,jj) - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) zu_res(ji,jj) = SQRT( zu_res(ji,jj) * zu_res(ji,jj) ) * umask(ji,jj,1) * pat_iu(ji,jj) * e1e2u(ji,jj) * z1_pglob_area zv_res(ji,jj) = SQRT( zv_res(ji,jj) * zv_res(ji,jj) ) * vmask(ji,jj,1) * pat_iv(ji,jj) * e1e2v(ji,jj) * z1_pglob_area END_2D ! Global ice-concentration, grid-cell-area weighted mean CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_res, 'U', 1., zv_res , 'V', 1. ) zu_res_mean = glob_sum( 'ice_rhg_vp', zu_res(:,:) ) zv_res_mean = glob_sum( 'ice_rhg_vp', zv_res(:,:) ) zvel_res_mean = 0.5_wp * ( zu_res_mean + zv_res_mean ) ! --- Global mean kinetic energy per unit area (J/m2) zvel2(:,:) = 0._wp DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zu = 0.5_wp * ( pu(ji-1,jj) + pu(ji,jj) ) ! u-vel at T-point zv = 0.5_wp * ( pv(ji,jj-1) + pv(ji,jj) ) zvel2(ji,jj) = zu*zu + zv*zv ! square of ice velocity at T-point END_2D zmke = 0.5_wp * glob_sum( 'ice_rhg_vp', pmt(:,:) * e1e2t(:,:) * zvel2(:,:) ) / pglob_area ENDIF ! kitinntot !--- Spatially-resolved residual at last iteration to send back to main routine (last iteration only) !--- Calculation @T-point IF ( kitinntot == kitinntotmax) THEN DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 zu_res(ji,jj) = ( prhsu(ji,jj) + pDU(ji,jj) * pu(ji,jj-1) + pEU(ji,jj) * pu(ji,jj+1) & & - pAU(ji,jj) * pu(ji-1,jj) - pBU(ji,jj) * pu(ji,jj) - pCU(ji,jj) * pu(ji+1,jj) ) zv_res(ji,jj) = ( prhsv(ji,jj) + pDV(ji,jj) * pv(ji-1,jj) + pEV(ji,jj) * pv(ji+1,jj) & & - pAV(ji,jj) * pv(ji,jj-1) - pBV(ji,jj) * pv(ji,jj) - pCV(ji,jj) * pv(ji,jj+1) ) zu_res(ji,jj) = SQRT( zu_res(ji,jj) * zu_res(ji,jj) ) * umask(ji,jj,1) zv_res(ji,jj) = SQRT( zv_res(ji,jj) * zv_res(ji,jj) ) * vmask(ji,jj,1) END_2D CALL lbc_lnk( 'icedyn_rhg_cvg_vp', zu_res, 'U', 1., zv_res , 'V', 1. ) DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2->jpj-1; 2->jpi-1 pvel_res(ji,jj) = 0.25_wp * ( zu_res(ji-1,jj) + zu_res(ji,jj) + zv_res(ji,jj-1) + zv_res(ji,jj) ) END_2D CALL lbc_lnk( 'icedyn_rhg_cvg_vp', pvel_res, 'T', 1. ) ELSE pvel_res(:,:) = 0._wp ENDIF ! ! ==================== ! it_inn_file = ( kt - nit000 ) * kitinntotmax + kitinntot ! time step in the file it_out_file = ( kt - nit000 ) * kitoutmax + kitout ! write variables IF( lwm ) THEN istatus = NF90_PUT_VAR( ncvgid, nvarid_ures , (/zu_res_mean/), (/it_inn_file/), (/1/) ) ! Residuals of the linear system, area weighted mean istatus = NF90_PUT_VAR( ncvgid, nvarid_vres , (/zv_res_mean/), (/it_inn_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_velres, (/zvel_res_mean/), (/it_inn_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_uerr_max , (/puerr_max/), (/it_inn_file/), (/1/) ) ! Max velocit_inn_filey error, sub-it_inn_fileerates istatus = NF90_PUT_VAR( ncvgid, nvarid_verr_max , (/pverr_max/), (/it_inn_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_velerr_max, (/zvel_err_max/), (/it_inn_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_umad , (/zu_mad/) , (/it_inn_file/), (/1/) ) ! velocit_inn_filey MAD, area/sic-weighted, sub-it_inn_fileerates istatus = NF90_PUT_VAR( ncvgid, nvarid_vmad , (/zv_mad/) , (/it_inn_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_velmad , (/zvel_mad/), (/it_inn_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_mke, (/zmke/), (/kitinntot/), (/1/) ) ! mean kinetic energy IF ( kitinn == kitinnmax ) THEN ! only print outer mad at the end of inner loop istatus = NF90_PUT_VAR( ncvgid, nvarid_umad_outer , (/zu_mad_outer/) , (/it_out_file/), (/1/) ) ! velocity MAD, area/sic-weighted, outer-iterates istatus = NF90_PUT_VAR( ncvgid, nvarid_vmad_outer , (/zv_mad_outer/) , (/it_out_file/), (/1/) ) ! istatus = NF90_PUT_VAR( ncvgid, nvarid_velmad_outer , (/zvel_mad_outer/), (/it_out_file/), (/1/) ) ! ENDIF IF( kt == nitend - nn_fsbc + 1 .AND. kitinntot == kitinntotmax ) istatus = NF90_CLOSE( ncvgid ) ENDIF END SUBROUTINE rhg_cvg_vp #else !!---------------------------------------------------------------------- !! Default option Empty module NO SI3 sea-ice model !!---------------------------------------------------------------------- #endif !!============================================================================== END MODULE icedyn_rhg_vp