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 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 INTEGER :: nvarid_vres INTEGER :: nvarid_velres INTEGER :: nvarid_udif INTEGER :: nvarid_vdif INTEGER :: nvarid_veldif INTEGER :: nvarid_mke INTEGER :: nvarid_ures_xy, nvarid_vres_xy REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zmsk00, zmsk15 !!---------------------------------------------------------------------- !! 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(v) !! !! 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 :: jter, i_out, i_inn ! INTEGER :: ji_min, jj_min ! INTEGER :: nn_zebra_vp ! number of zebra steps INTEGER :: nn_nvp ! total number of VP iterations (n_out_vp*n_inn_vp) ! 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) :: zdeltat, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars REAL(wp) :: zp_deltastar_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) :: zfmask ! mask at F points for the ice 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) :: zdeltastar_t ! Delta* at T-points REAL(wp), DIMENSION(jpi,jpj) :: zten_i ! Tension REAL(wp), DIMENSION(jpi,jpj) :: zp_deltastar_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) :: zCU_prime, zCV_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) :: 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) CALL ctl_stop( 'STOP', 'icedyn_rhg_vp: stop because vp rheology is an ongoing work and should not be used' ) !!---------------------------------------------------------------------------------------------------------------------- ! DEBUG put all forcing terms to zero ! air-ice drag utau_ice(:,:) = 0._wp vtau_ice(:,:) = 0._wp ! coriolis ff_t(:,:) = 0._wp ! ice-ocean drag rn_cio = 0._wp ! ssh ! done line 330 !!! dont forget to act there ! END DEBUG 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 ALLOCATE( zmsk00(jpi,jpj), zmsk15(jpi,jpj) ) DO jj = 1, jpj DO ji = 1, jpi zmsk00(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice , 0 if no ice zmsk15(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - 0.15_wp ) ) ! 1 if 15% ice, 0 if less END DO END DO 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 zglob_area = glob_sum( 'ice_rhg_vp', at_i(:,:) * e1e2t(:,:) ) ! global ice area (km2) 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 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; zrhsu(:,:) = 0._wp; zrhsv(:,:) = 0._wp zf_rhsu(:,:) = 0._wp; zf_rhsv(:,:) = 0._wp !------------------------------------------------------------------------------! ! ! --- Time-independent quantities ! !------------------------------------------------------------------------------! CALL ice_strength ! strength at T points !------------------------------ ! -- F-mask (code from EVP) !------------------------------ ! MartinV: ! In EVP routine, zfmask 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 DO jj = 1, jpj - 1 DO ji = 1, jpi - 1 zfmask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) END DO END DO ! Lateral boundary conditions on velocity (modify zfmask) ! Can be computed once for all, at first time step, for all rheologies DO jj = 2, jpj - 1 DO ji = 2, jpi - 1 ! vector opt. IF( zfmask(ji,jj) == 0._wp ) THEN zfmask(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 DO END DO DO jj = 2, jpj - 1 IF( zfmask(1,jj) == 0._wp ) THEN zfmask(1 ,jj) = rn_ishlat * MIN( 1._wp , MAX( vmask(2,jj,1), umask(1,jj+1,1), umask(1,jj,1) ) ) ENDIF IF( zfmask(jpi,jj) == 0._wp ) THEN zfmask(jpi,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(jpi,jj+1,1), vmask(jpi - 1,jj,1), umask(jpi,jj-1,1) ) ) ENDIF END DO DO ji = 2, jpi - 1 IF( zfmask(ji,1) == 0._wp ) THEN zfmask(ji, 1 ) = rn_ishlat * MIN( 1._wp , MAX( vmask(ji+1,1,1), umask(ji,2,1), vmask(ji,1,1) ) ) ENDIF IF( zfmask(ji,jpj) == 0._wp ) THEN zfmask(ji,jpj) = rn_ishlat * MIN( 1._wp , MAX( vmask(ji+1,jpj,1), vmask(ji-1,jpj,1), umask(ji,jpj - 1,1) ) ) ENDIF END DO CALL lbc_lnk( 'icedyn_rhg_vp', zfmask, 'F', 1._wp ) !---------------------------------------------------------------------------------------------------------- ! -- 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) zsshdyn(:,:) = 0._wp ! DEBUG CAREFUL !!! zmt(:,:) = rhos * vt_s(:,:) + rhoi * vt_i(:,:) ! Snow and ice mass at T-point zmf(:,:) = zmt(:,:) * ff_t(:,:) ! Coriolis factor at T points (m*f) DO jj = 2, jpj - 1 DO ji = 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 ! MV TEST DEBUG IF ( ( zmt(ji,jj) <= zmmin .OR. zmt(ji+1,jj) <= zmmin ) .AND. & & ( at_i(ji,jj) <= zamin .OR. at_i(ji+1,jj) <= zamin ) ) THEN ; zmsk01x(ji,jj) = 0._wp ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF IF ( ( zmt(ji,jj) <= zmmin .OR. zmt(ji,jj+1) <= zmmin ) .AND. & & ( at_i(ji,jj) <= zamin .OR. at_i(ji,jj+1) <= zamin ) ) THEN ; zmsk01y(ji,jj) = 0._wp ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF ! END MV TEST DEBUG END DO END DO CALL iom_put( 'zmsk00x' , zmsk00x ) ! MV DEBUG CALL iom_put( 'zmsk00y' , zmsk00y ) ! MV DEBUG CALL iom_put( 'zmsk01x' , zmsk01x ) ! MV DEBUG CALL iom_put( 'zmsk01y' , zmsk01y ) ! MV DEBUG CALL iom_put( 'ztaux_ai' , ztaux_ai ) ! MV DEBUG CALL iom_put( 'ztauy_ai' , ztauy_ai ) ! MV DEBUG CALL iom_put( 'zspgU' , zspgU ) ! MV DEBUG CALL iom_put( 'zspgV' , zspgV ) ! MV DEBUG !------------------------------------------------------------------------------! ! ! --- Start outer loop ! !------------------------------------------------------------------------------! zu_c(:,:) = u_ice(:,:) zv_c(:,:) = v_ice(:,:) jter = 0 DO i_out = 1, nn_vp_nout IF( lwp ) WRITE(numout,*) ' outer loop i_out : ', i_out ! 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 uc ! !------------------------------------------ ! -- Strain rates, viscosities and P/Delta !------------------------------------------ ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! 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 DO ji = 1, jpi - 1 ! 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) * zfmask(ji,jj) END DO END DO CALL lbc_lnk( 'icedyn_rhg_vp', zds, 'F', 1. ) ! MV TEST could be un-necessary according to Gurvan CALL iom_put( 'zds' , zds ) ! MV DEBUG IF( lwp ) WRITE(numout,*) ' outer loop 1a i_out : ', i_out !DO jj = 2, jpj - 1 ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 ! DO ji = 2, jpi - 1 ! ! MV DEBUG DO jj = 2, jpj ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 DO ji = 2, jpi ! ! END MV DEBUG ! 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 = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) ! delta* at T points (following Lemieux and Dupont, GMD 2020) zdeltastar_t(ji,jj) = zdeltat + rn_creepl ! P/delta at T-points zp_deltastar_t(ji,jj) = strength(ji,jj) / zdeltastar_t(ji,jj) ! Temporary zzt and zet factors at T-points zzt(ji,jj) = zp_deltastar_t(ji,jj) * r1_e1e2t(ji,jj) zet(ji,jj) = zzt(ji,jj) * z1_ecc2 END DO END DO CALL lbc_lnk_multi( 'icedyn_rhg_vp', zp_deltastar_t , 'T', 1. , zzt , 'T', 1., zet, 'T', 1. ) CALL iom_put( 'zzt' , zzt ) ! MV DEBUG CALL iom_put( 'zet' , zet ) ! MV DEBUG CALL iom_put( 'zp_deltastar_t', zp_deltastar_t ) ! MV DEBUG IF( lwp ) WRITE(numout,*) ' outer loop 1b i_out : ', i_out DO jj = 1, jpj - 1 DO ji = 1, jpi - 1 ! P/delta* at F points 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) ) ! Temporary zef factor at F-point zef(ji,jj) = zp_deltastar_f * r1_e1e2f(ji,jj) * z1_ecc2 * zfmask(ji,jj) END DO END DO CALL lbc_lnk( 'icedyn_rhg_vp', zef, 'F', 1. ) CALL iom_put( 'zef' , zef ) ! MV DEBUG IF( lwp ) WRITE(numout,*) ' outer loop 1c i_out : ', i_out !--------------------------------------------------- ! -- Ocean-ice drag and Coriolis RHS contributions !--------------------------------------------------- DO jj = 2, jpj - 1 DO ji = 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) ! Note Lemieux et al 2008 recommend to do that implicitly, but I don't really see how this could be done 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 DO END DO IF( lwp ) WRITE(numout,*) ' outer loop 1d i_out : ', i_out CALL lbc_lnk_multi( 'icedyn_rhg_vp', zCwU , 'U', -1., zCwV, 'V', -1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zCorU, 'U', -1., zCorV, 'V', -1. ) CALL iom_put( 'zCwU' , zCwU ) ! MV DEBUG CALL iom_put( 'zCwV' , zCwV ) ! MV DEBUG CALL iom_put( 'zCorU' , zCorU ) ! MV DEBUG CALL iom_put( 'zCorV' , zCorV ) ! MV DEBUG IF( lwp ) WRITE(numout,*) ' outer loop 1f i_out : ', i_out ! a priori, Coriolis and drag terms only affect diagonal or independent term of the linear system, ! so there is no need for lbclnk on drag and coriolis !------------------------------------- ! -- Internal stress RHS contribution !------------------------------------- ! --- Stress contributions at T-points DO jj = 2, jpj ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 DO ji = 2, jpi ! ! 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) - 1.0_wp ) ! 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) - 1.0_wp ) ! 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 DO END DO CALL iom_put( 'zs1_rhsu' , zs1_rhsu ) ! MV DEBUG CALL iom_put( 'zs2_rhsu' , zs2_rhsu ) ! MV DEBUG CALL iom_put( 'zs1_rhsv' , zs1_rhsv ) ! MV DEBUG CALL iom_put( 'zs2_rhsv' , zs2_rhsv ) ! MV DEBUG ! a priori, no lbclnk, because rhsu is only used in the inner domain ! --- Stress contributions at f-points ! MV NOTE: I applied zfmask 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 IF( lwp ) WRITE(numout,*) ' outer loop 2 i_out : ', i_out DO jj = 1, jpj - 1 DO ji = 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) * zfmask(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) * zfmask(ji,jj) END DO END DO CALL lbc_lnk( 'icedyn_rhg_vp', zs12_rhsu, 'F', 1. ) CALL lbc_lnk( 'icedyn_rhg_vp', zs12_rhsv, 'F', 1. ) CALL iom_put( 'zs12_rhsu' , zs12_rhsu ) ! MV DEBUG CALL iom_put( 'zs12_rhsv' , zs12_rhsv ) ! MV DEBUG ! a priori, no lbclnk, because rhsu are only used in the inner domain ! --- 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 jj = 2, jpj - 1 DO ji = 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 DO END DO CALL iom_put( 'zf_rhsu' , zf_rhsu ) ! MV DEBUG CALL iom_put( 'zf_rhsv' , zf_rhsv ) ! MV DEBUG !--------------------------- ! -- Sum RHS contributions !--------------------------- ! ! OPT: could use intermediate scalars to reduce memory access DO jj = 2, jpj - 1 DO ji = 2, jpi - 1 ! still miss ice ocean stress and acceleration contribution 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_rhsu(ji,jj) END DO END DO CALL lbc_lnk_multi( 'icedyn_rhg_vp', zrhsu, 'U', -1., zrhsv, 'V', -1.) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zmU_t, 'U', -1., zmV_t, 'V', -1.) CALL lbc_lnk_multi( 'icedyn_rhg_vp', ztaux_oi_rhsu, 'U', -1., ztauy_oi_rhsv, 'V', -1.) CALL iom_put( 'zmU_t' , zmU_t ) ! MV DEBUG CALL iom_put( 'zmV_t' , zmV_t ) ! MV DEBUG CALL iom_put( 'ztaux_oi_rhsu' , ztaux_oi_rhsu ) ! MV DEBUG CALL iom_put( 'ztauy_oi_rhsv' , ztauy_oi_rhsv ) ! MV DEBUG CALL iom_put( 'zrhsu' , zrhsu ) ! MV DEBUG CALL iom_put( 'zrhsv' , zrhsv ) ! MV DEBUG ! inner domain calculations -> no lbclnk IF( lwp ) WRITE(numout,*) ' outer loop 4 i_out : ', i_out !---------------------------------------------------------------------------------------! ! ! --- 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 ji = 2, jpi - 1 ! internal domain do loop DO jj = 2, jpj - 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) zt12U = - zfac1 * zzt(ji+1,jj) zt11U = zfac1 * zzt(ji,jj) zt22U = - zfac2 * zet(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) zt21U = zfac2 * zet(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) * e2t(ji,jj) zt122U = - zfac3 * zef(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) * e1f(ji,jj) zt121U = zfac3 * zef(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) ! ! Linear system coefficients ! zAU(ji,jj) = - zt11U * e2u(ji-1,jj) - zt21U * r1_e2u(ji-1,jj) zBU(ji,jj) = ( zt12U + zt11U ) * e2u(ji,jj) + ( zt22U + zt21U ) * r1_e2u(ji,jj) + ( zt122U + zt121U ) * 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 * e2v(ji,jj) zfac2 = zfac * r1_e1v(ji,jj) zfac3 = 2._wp * zfac * r1_e2v(ji,jj) zt12V = - zfac1 * zzt(ji,jj+1) zt11V = zfac1 * zzt(ji,jj) zt22V = zfac2 * zet(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) zt21V = - zfac2 * zet(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) * e1t(ji,jj) zt122V = zfac3 * zef(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) * e2f(ji,jj) zt121V = - zfac3 * zef(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) ! ! Linear system coefficients ! zAV(ji,jj) = - zt11V * e1v(ji,jj-1) + zt21V * r1_e1v(ji,jj-1) zBV(ji,jj) = ( zt12V + zt11V ) * e1v(ji,jj) - ( zt22V + zt21V ) * 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) ! mistake is in the pdf notes not here 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 DO END DO CALL lbc_lnk_multi( 'icedyn_rhg_vp', zAU , 'U', 1., zAV , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zBU , 'U', 1., zBV , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zCU , 'U', 1., zCV , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zDU , 'U', 1., zDV , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zEU , 'U', 1., zEV , 'V', 1. ) CALL iom_put( 'zAU' , zAU ) ! MV DEBUG CALL iom_put( 'zBU' , zBU ) ! MV DEBUG CALL iom_put( 'zCU' , zCU ) ! MV DEBUG CALL iom_put( 'zDU' , zDU ) ! MV DEBUG CALL iom_put( 'zEU' , zEU ) ! MV DEBUG CALL iom_put( 'zAV' , zAV ) ! MV DEBUG CALL iom_put( 'zBV' , zBV ) ! MV DEBUG CALL iom_put( 'zCV' , zCV ) ! MV DEBUG CALL iom_put( 'zDV' , zDV ) ! MV DEBUG CALL iom_put( 'zEV' , zEV ) ! MV DEBUG !------------------------------------------------------------------------------! ! ! --- 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 IF( lwp ) WRITE(numout,*) ' inner loop 1 i_inn : ', i_inn !--- mitgcm computes initial value of residual here... jter = jter + 1 ! l_full_nf_update = jter == nn_nvp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 zu_b(:,:) = u_ice(:,:) ! velocity at previous sub-iterate zv_b(:,:) = v_ice(:,:) ! 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 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; zCU_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 IF ( lwp ) WRITE(numout,*) ' Into the U-zebra loop at step jn = ', jn, ', with jj_min = ', jj_min DO jj = jj_min, jpj - 1, nn_zebra_vp !------------------------ ! Independent term (zFU) !------------------------ DO ji = 2, jpi - 1 ! 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 CALL lbc_lnk( 'icedyn_rhg_vp', zFU, 'U', 1. ) !--------------- ! Forward sweep !--------------- DO jj = jj_min, jpj - 1, nn_zebra_vp 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 CALL lbc_lnk_multi( 'icedyn_rhg_vp', zFU_prime, 'U', 1., zBU_prime, 'U', 1. ) !----------------------------- ! 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 velocity masking for little-ice and 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 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; zCV_prime(:,:) = 0._wp DO jn = 1, nn_zebra_vp ! "zebra" loop IF ( jn == 1 ) THEN ; ji_min = 2 ELSE ; ji_min = 3 ENDIF IF ( lwp ) WRITE(numout,*) ' Into the V-zebra loop at step jn = ', jn, ', with ji_min = ', ji_min DO ji = ji_min, jpi - 1, nn_zebra_vp !------------------------ ! Independent term (zFV) !------------------------ DO jj = 2, jpj - 1 ! 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 CALL lbc_lnk_multi( 'icedyn_rhg_vp', zFV, 'V', 1.) !--------------- ! Forward sweep !--------------- DO ji = ji_min, jpi - 1, nn_zebra_vp 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 CALL lbc_lnk_multi( 'icedyn_rhg_vp', zFV_prime, 'V', 1., zBV_prime, 'V', 1. ) !----------------------------- ! 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 (should it be now or later) 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 END DO ! zebra loop ENDIF ! ll_v_iterate CALL lbc_lnk_multi( 'icedyn_rhg_vp', u_ice, 'U', -1., v_ice, 'V', -1. ) !-------------------------------------------------------------------------------------- ! -- 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 jj = 2, jpj - 1 DO ji = 2, jpi - 1 zuerr(ji,jj) = ABS ( ( u_ice(ji,jj) - zu_b(ji,jj) ) ) * umask(ji,jj,1) END DO END DO zuerr_max = MAXVAL( zuerr ) CALL mpp_max( 'icedyn_rhg_evp', zuerr_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. 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 jj = 2, jpj - 1 DO ji = 2, jpi - 1 zverr(ji,jj) = ABS ( ( v_ice(ji,jj) - zv_b(ji,jj) ) ) * vmask(ji,jj,1) END DO END DO 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 ) CALL rhg_cvg_vp( kt, jter, nn_nvp, u_ice, v_ice, zmt, zuerr_max, zverr_max, zglob_area, & & zrhsu, zAU, zBU, zCU, zDU, zEU, zrhsv, zAV, zBV, zCV, zDV, zEV ) IF ( lwp ) WRITE(numout,*) ' Done convergence tests ' END DO ! i_inn, end of inner loop END DO ! End of outer loop (i_out) ============================================================================================= IF ( lwp ) WRITE(numout,*) ' We are out of outer loop ' CALL lbc_lnk_multi( 'icedyn_rhg_vp', zFU , 'U', 1., zFV , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zBU_prime , 'U', 1., zBV_prime , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zFU_prime , 'U', 1., zFV_prime , 'V', 1. ) CALL lbc_lnk_multi( 'icedyn_rhg_vp', zCU_prime , 'U', 1., zCV_prime , 'V', 1. ) CALL iom_put( 'zFU' , zFU ) ! MV DEBUG CALL iom_put( 'zBU_prime' , zBU_prime ) ! MV DEBUG CALL iom_put( 'zCU_prime' , zCU_prime ) ! MV DEBUG CALL iom_put( 'zFU_prime' , zFU_prime ) ! MV DEBUG CALL iom_put( 'zFV' , zFV ) ! MV DEBUG CALL iom_put( 'zBV_prime' , zBV_prime ) ! MV DEBUG CALL iom_put( 'zCV_prime' , zCV_prime ) ! MV DEBUG CALL iom_put( 'zFV_prime' , zFV_prime ) ! MV DEBUG CALL lbc_lnk_multi( 'icedyn_rhg_vp', u_ice, 'U', -1., v_ice, 'V', -1. ) IF ( lwp ) WRITE(numout,*) ' We are about to output uice_dbg ' IF( iom_use('uice_dbg' ) ) CALL iom_put( 'uice_dbg' , u_ice ) ! ice velocity u after solver IF( iom_use('vice_dbg' ) ) CALL iom_put( 'vice_dbg' , v_ice ) ! ice velocity v after solver !------------------------------------------------------------------------------! ! ! --- Convergence diagnostics ! !------------------------------------------------------------------------------! IF( nn_rhg_chkcvg /= 0 ) THEN IF( iom_use('uice_cvg') ) THEN CALL iom_put( 'uice_cvg', MAX( ABS( u_ice(:,:) - zu_b(:,:) ) * umask(:,:,1) , & ! ice velocity difference at last iteration & ABS( v_ice(:,:) - zv_b(:,:) ) * vmask(:,:,1) ) * zmsk15(:,:) ) ENDIF ENDIF ! MV DEBUG test - replace ice velocity by ocean current to give the model the means to go ahead DO jj = 2, jpj - 1 DO ji = 2, jpi - 1 u_ice(ji,jj) = zmsk00x(ji,jj) & & * ( zmsk01x(ji,jj) * u_oce(ji,jj) * 0.01_wp & + ( 1._wp - zmsk01x(ji,jj) ) * u_oce(ji,jj) * 0.01_wp ) v_ice(ji,jj) = zmsk00y(ji,jj) & & * ( zmsk01y(ji,jj) * v_oce(ji,jj) * 0.01_wp & + ( 1._wp - zmsk01y(ji,jj) ) * v_oce(ji,jj) * 0.01_wp ) END DO END DO CALL lbc_lnk_multi( 'icedyn_rhg_vp', u_ice, 'U', -1., v_ice, 'V', -1. ) IF ( lwp ) WRITE(numout,*) ' Velocity replaced ' ! END DEBUG !------------------------------------------------------------------------------! ! ! --- Recompute delta, shear and div (inputs for mechanical redistribution) ! !------------------------------------------------------------------------------! ! ! MV OPT: subroutinize ? DO jj = 1, jpj - 1 DO ji = 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) * zfmask(ji,jj) END DO END DO DO jj = 2, jpj - 1 DO ji = 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 zten_i(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) ! shear at T points pshear_i(ji,jj) = SQRT( zdt2 + 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) ! delta at T points zdelta = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( 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 pdelta_i(ji,jj) = zdelta + rn_creepl END DO END DO IF ( lwp ) WRITE(numout,*) ' Deformation recalculated ' CALL lbc_lnk_multi( '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') ) THEN DO jj = 2, jpj - 1 DO ji = 2, jpi - 1 zp_deltastar_t(ji,jj) = strength(ji,jj) / pdelta_i(ji,jj) zfac = zp_deltastar_t(ji,jj) zs1(ji,jj) = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) ) zs2(ji,jj) = zfac * z1_ecc2 * zten_i(ji,jj) zs12(ji,jj) = zfac * z1_ecc2 * pshear_i(ji,jj) END DO END DO CALL lbc_lnk_multi( '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 jj = 1, jpj - 1 DO ji = 1, jpi - 1 ! P/delta* at F points 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) ) ! s12 at F-points zs12f(ji,jj) = zp_deltastar_f * z1_ecc2 * zds(ji,jj) END DO END DO CALL lbc_lnk( 'icedyn_rhg_vp', zs12f, 'F', 1. ) ENDIF IF ( lwp ) WRITE(numout,*) ' zs12f recalculated ' ! !----------------------- ! --- 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 jj = 2, jpj - 1 DO ji = 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 DO END DO ! CALL lbc_lnk_multi( '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 ) ! shear IF( iom_use('icedlt') ) CALL iom_put( 'icedlt' , pdelta_i * zmsk00 ) ! delta IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength IF ( lwp ) WRITE(numout,*) 'Some terms recalculated ' ! --- 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 jj = 2, jpj - 1 DO ji = 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) = SQRT ( zs2(ji,jj) * zs2(ji,jj) * 0.25_wp + zs12(ji,jj) ) ! 2nd invariant, aka maximum shear stress END DO END DO CALL lbc_lnk_multi( '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 IF ( lwp ) WRITE(numout,*) 'SIMIP work done' ! --- 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 jj = 2, jpj - 1 DO ji = 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_deltastar_t(ji,jj) zsig1 = zfac * ( pdivu_i(ji,jj) - zdeltastar_t(ji,jj) ) zsig1 = 0._wp !!! FUCKING DEBUG TEST !!! zsig2 = zfac * z1_ecc2 * zten_i(ji,jj) zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj) ! 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) = SQRT ( zsig2 * zsig2 * 0.25_wp + 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 DO END DO IF ( lwp ) WRITE(numout,*) 'Some shitty stress work done' ! CALL lbc_lnk_multi( 'icedyn_rhg_vp', zsig1_p, 'T', 1., zsig2_p, 'T', 1.) ! IF ( lwp ) WRITE(numout,*) ' Beauaaaarflblbllll ' ! CALL iom_put( 'sig1_pnorm' , zsig1_p ) CALL iom_put( 'sig2_pnorm' , zsig2_p ) DEALLOCATE( zsig1_p , zsig2_p , zsig_I , zsig_II ) IF ( lwp ) WRITE(numout,*) ' So what ??? ' 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 jj = 2, jpj - 1 DO ji = 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 DO END DO ! CALL lbc_lnk_multi( '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 jj = 2, jpj - 1 DO ji = 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 DO END DO CALL lbc_lnk_multi( '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 jj = 2, jpj - 1 DO ji = 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 DO END DO CALL lbc_lnk_multi( '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 DEALLOCATE( zmsk00, zmsk15 ) END SUBROUTINE ice_dyn_rhg_vp SUBROUTINE rhg_cvg_vp( kt, kiter, kitermax, pu, pv, pmt, puerr_max, pverr_max, pglob_area, & & prhsu, pAU, pBU, pCU, pDU, pEU, prhsv, pAV, pBV, pCV, pDV, pEV ) !!---------------------------------------------------------------------- !! *** 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, kiter, kitermax ! ocean time-step index REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pmt ! now velocity and mass per unit area 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 ! linear system coefficients REAL(wp), DIMENSION(:,:), INTENT(in) :: prhsv, pAV, pBV, pCV, pDV, pEV !! INTEGER :: it, idtime, istatus, ix_dim, iy_dim INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zveldif, zu_res_mean, zv_res_mean, zvelres, zmke, zu, zv ! local scalars REAL(wp) :: z1_pglob_area REAL(wp), DIMENSION(jpi,jpj) :: zu_res, zv_res, zvel2 ! local arrays CHARACTER(len=20) :: clname !!---------------------------------------------------------------------- IF( lwp ) THEN WRITE(numout,*) WRITE(numout,*) 'rhg_cvg_vp : ice rheology convergence control' WRITE(numout,*) '~~~~~~~~~~~' WRITE(numout,*) ' kiter = : ', kiter WRITE(numout,*) ' kitermax = : ', kitermax ENDIF ! create file IF( kt == nit000 .AND. kiter == 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 ) ! i suggest vel_dif instead 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, 'u_dif' , NF90_DOUBLE , (/ idtime /), nvarid_udif ) istatus = NF90_DEF_VAR( ncvgid, 'v_dif' , NF90_DOUBLE , (/ idtime /), nvarid_vdif ) istatus = NF90_DEF_VAR( ncvgid, 'vel_dif', NF90_DOUBLE , (/ idtime /), nvarid_veldif ) istatus = NF90_DEF_VAR( ncvgid, 'mke_ice', NF90_DOUBLE , (/ idtime /), nvarid_mke ) istatus = NF90_DEF_VAR( ncvgid, 'u_res_xy', NF90_DOUBLE, (/ ix_dim, iy_dim /), nvarid_ures_xy) istatus = NF90_DEF_VAR( ncvgid, 'v_res_xy', NF90_DOUBLE, (/ ix_dim, iy_dim /), nvarid_vres_xy) istatus = NF90_ENDDEF(ncvgid) ENDIF ! ENDIF IF ( lwp ) WRITE(numout,*) ' File created ' ! --- Max absolute velocity difference with previous iterate (zveldif) zveldif = MAX( puerr_max, pverr_max ) ! velocity difference with previous iterate, should nearly be equivalent to evp code ! if puerrmask and pverrmax are masked at 15% (TEST) ! --- Mean residual and kinetic energy IF ( kiter == 1 ) THEN zu_res_mean = 0._wp zv_res_mean = 0._wp zvelres = 0._wp zmke = 0._wp ELSE ! -- Mean residual (N/m^2), zu_res_mean ! Here we take the residual of the linear system (N/m^2), ! We define it as in mitgcm: square-root of area-weighted mean square residual ! Local residual r = Ax - B expresses to which extent the momentum balance is verified ! i.e., how close we are to a solution IF ( lwp ) WRITE(numout,*) ' TEST 1 ' z1_pglob_area = 1._wp / pglob_area zu_res(:,:) = 0._wp; zv_res(:,:) = 0._wp DO jj = 2, jpj - 1 DO ji = 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) * e1e2u(ji,jj) * z1_pglob_area zv_res(ji,jj) = SQRT( zv_res(ji,jj) * zv_res(ji,jj) ) * vmask(ji,jj,1) * e1e2v(ji,jj) * z1_pglob_area END DO END DO IF ( lwp ) WRITE(numout,*) ' TEST 2 ' zu_res_mean = glob_sum( 'ice_rhg_vp', zu_res(:,:) ) zv_res_mean = glob_sum( 'ice_rhg_vp', zv_res(:,:) ) IF ( lwp ) WRITE(numout,*) ' TEST 3 ' zvelres = 0.5_wp * ( zu_res_mean + zv_res_mean ) IF ( lwp ) WRITE(numout,*) ' TEST 4 ' ! -- Global mean kinetic energy per unit area (J/m2) zvel2(:,:) = 0._wp DO jj = 2, jpj - 1 DO ji = 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 DO END DO IF ( lwp ) WRITE(numout,*) ' TEST 5 ' zmke = 0.5_wp * glob_sum( 'ice_rhg_vp', pmt(:,:) * e1e2t(:,:) * zvel2(:,:) ) / pglob_area IF ( lwp ) WRITE(numout,*) ' TEST 6 ' ENDIF ! kiter ! ! ==================== ! ! time it = ( kt - 1 ) * kitermax + kiter IF( lwm ) THEN ! write variables istatus = NF90_PUT_VAR( ncvgid, nvarid_ures, (/zu_res_mean/), (/it/), (/1/) ) ! U-residual of the linear system istatus = NF90_PUT_VAR( ncvgid, nvarid_vres, (/zv_res_mean/), (/it/), (/1/) ) ! V-residual of the linear system istatus = NF90_PUT_VAR( ncvgid, nvarid_velres, (/zvelres/), (/it/), (/1/) ) ! average of u- and v- residuals istatus = NF90_PUT_VAR( ncvgid, nvarid_udif, (/puerr_max/), (/it/), (/1/) ) ! max U velocity difference, inner iterations istatus = NF90_PUT_VAR( ncvgid, nvarid_vdif, (/pverr_max/), (/it/), (/1/) ) ! max V velocity difference, inner iterations istatus = NF90_PUT_VAR( ncvgid, nvarid_veldif, (/zveldif/), (/it/), (/1/) ) ! max U or V velocity diff between subiterations istatus = NF90_PUT_VAR( ncvgid, nvarid_mke, (/zmke/), (/it/), (/1/) ) ! mean kinetic energy ! IF ( kiter == kitermax ) THEN WRITE(numout,*) ' Should plot the spatially dependent residual ' istatus = NF90_PUT_VAR( ncvgid, nvarid_ures_xy, (/zu_res/) ) ! U-residual, spatially dependent istatus = NF90_PUT_VAR( ncvgid, nvarid_vres_xy, (/zv_res/) ) ! V-residual, spatially dependent ENDIF ! close file IF( kt == nitend ) 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