| 1 | MODULE icedyn_rhg_evp |
|---|
| 2 | !!====================================================================== |
|---|
| 3 | !! *** MODULE icedyn_rhg_evp *** |
|---|
| 4 | !! Sea-Ice dynamics : rheology Elasto-Viscous-Plastic |
|---|
| 5 | !!====================================================================== |
|---|
| 6 | !! History : - ! 2007-03 (M.A. Morales Maqueda, S. Bouillon) Original code |
|---|
| 7 | !! 3.0 ! 2008-03 (M. Vancoppenolle) adaptation to new model |
|---|
| 8 | !! - ! 2008-11 (M. Vancoppenolle, S. Bouillon, Y. Aksenov) add surface tilt in ice rheolohy |
|---|
| 9 | !! 3.3 ! 2009-05 (G.Garric) addition of the evp case |
|---|
| 10 | !! 3.4 ! 2011-01 (A. Porter) dynamical allocation |
|---|
| 11 | !! 3.5 ! 2012-08 (R. Benshila) AGRIF |
|---|
| 12 | !! 3.6 ! 2016-06 (C. Rousset) Rewriting + landfast ice + mEVP (Bouillon 2013) |
|---|
| 13 | !! 3.7 ! 2017 (C. Rousset) add aEVP (Kimmritz 2016-2017) |
|---|
| 14 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
|---|
| 15 | !!---------------------------------------------------------------------- |
|---|
| 16 | #if defined key_si3 |
|---|
| 17 | !!---------------------------------------------------------------------- |
|---|
| 18 | !! 'key_si3' SI3 sea-ice model |
|---|
| 19 | !!---------------------------------------------------------------------- |
|---|
| 20 | !! ice_dyn_rhg_evp : computes ice velocities from EVP rheology |
|---|
| 21 | !! rhg_evp_rst : read/write EVP fields in ice restart |
|---|
| 22 | !!---------------------------------------------------------------------- |
|---|
| 23 | USE phycst ! Physical constant |
|---|
| 24 | USE dom_oce ! Ocean domain |
|---|
| 25 | USE sbc_oce , ONLY : ln_ice_embd, nn_fsbc, ssh_m |
|---|
| 26 | USE sbc_ice , ONLY : utau_ice, vtau_ice, snwice_mass, snwice_mass_b |
|---|
| 27 | USE ice ! sea-ice: ice variables |
|---|
| 28 | USE icevar ! ice_var_sshdyn |
|---|
| 29 | USE icedyn_rdgrft ! sea-ice: ice strength |
|---|
| 30 | USE bdy_oce , ONLY : ln_bdy |
|---|
| 31 | USE bdyice |
|---|
| 32 | #if defined key_agrif |
|---|
| 33 | USE agrif_ice_interp |
|---|
| 34 | #endif |
|---|
| 35 | ! |
|---|
| 36 | USE in_out_manager ! I/O manager |
|---|
| 37 | USE iom ! I/O manager library |
|---|
| 38 | USE lib_mpp ! MPP library |
|---|
| 39 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
|---|
| 40 | USE lbclnk ! lateral boundary conditions (or mpp links) |
|---|
| 41 | USE prtctl ! Print control |
|---|
| 42 | |
|---|
| 43 | IMPLICIT NONE |
|---|
| 44 | PRIVATE |
|---|
| 45 | |
|---|
| 46 | PUBLIC ice_dyn_rhg_evp ! called by icedyn_rhg.F90 |
|---|
| 47 | PUBLIC rhg_evp_rst ! called by icedyn_rhg.F90 |
|---|
| 48 | |
|---|
| 49 | !! * Substitutions |
|---|
| 50 | # include "vectopt_loop_substitute.h90" |
|---|
| 51 | !!---------------------------------------------------------------------- |
|---|
| 52 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
|---|
| 53 | !! $Id$ |
|---|
| 54 | !! Software governed by the CeCILL license (see ./LICENSE) |
|---|
| 55 | !!---------------------------------------------------------------------- |
|---|
| 56 | CONTAINS |
|---|
| 57 | |
|---|
| 58 | SUBROUTINE ice_dyn_rhg_evp( kt, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i ) |
|---|
| 59 | !!------------------------------------------------------------------- |
|---|
| 60 | !! *** SUBROUTINE ice_dyn_rhg_evp *** |
|---|
| 61 | !! EVP-C-grid |
|---|
| 62 | !! |
|---|
| 63 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
|---|
| 64 | !! stress and sea-surface slope. Ice-ice interaction is described by |
|---|
| 65 | !! a non-linear elasto-viscous-plastic (EVP) law including shear |
|---|
| 66 | !! strength and a bulk rheology (Hunke and Dukowicz, 2002). |
|---|
| 67 | !! |
|---|
| 68 | !! The points in the C-grid look like this, dear reader |
|---|
| 69 | !! |
|---|
| 70 | !! (ji,jj) |
|---|
| 71 | !! | |
|---|
| 72 | !! | |
|---|
| 73 | !! (ji-1,jj) | (ji,jj) |
|---|
| 74 | !! --------- |
|---|
| 75 | !! | | |
|---|
| 76 | !! | (ji,jj) |------(ji,jj) |
|---|
| 77 | !! | | |
|---|
| 78 | !! --------- |
|---|
| 79 | !! (ji-1,jj-1) (ji,jj-1) |
|---|
| 80 | !! |
|---|
| 81 | !! ** Inputs : - wind forcing (stress), oceanic currents |
|---|
| 82 | !! ice total volume (vt_i) per unit area |
|---|
| 83 | !! snow total volume (vt_s) per unit area |
|---|
| 84 | !! |
|---|
| 85 | !! ** Action : - compute u_ice, v_ice : the components of the |
|---|
| 86 | !! sea-ice velocity vector |
|---|
| 87 | !! - compute delta_i, shear_i, divu_i, which are inputs |
|---|
| 88 | !! of the ice thickness distribution |
|---|
| 89 | !! |
|---|
| 90 | !! ** Steps : 0) compute mask at F point |
|---|
| 91 | !! 1) Compute ice snow mass, ice strength |
|---|
| 92 | !! 2) Compute wind, oceanic stresses, mass terms and |
|---|
| 93 | !! coriolis terms of the momentum equation |
|---|
| 94 | !! 3) Solve the momentum equation (iterative procedure) |
|---|
| 95 | !! 4) Recompute delta, shear and divergence |
|---|
| 96 | !! (which are inputs of the ITD) & store stress |
|---|
| 97 | !! for the next time step |
|---|
| 98 | !! 5) Diagnostics including charge ellipse |
|---|
| 99 | !! |
|---|
| 100 | !! ** Notes : There is the possibility to use aEVP from the nice work of Kimmritz et al. (2016 & 2017) |
|---|
| 101 | !! by setting up ln_aEVP=T (i.e. changing alpha and beta parameters). |
|---|
| 102 | !! This is an upgraded version of mEVP from Bouillon et al. 2013 |
|---|
| 103 | !! (i.e. more stable and better convergence) |
|---|
| 104 | !! |
|---|
| 105 | !! References : Hunke and Dukowicz, JPO97 |
|---|
| 106 | !! Bouillon et al., Ocean Modelling 2009 |
|---|
| 107 | !! Bouillon et al., Ocean Modelling 2013 |
|---|
| 108 | !! Kimmritz et al., Ocean Modelling 2016 & 2017 |
|---|
| 109 | !!------------------------------------------------------------------- |
|---|
| 110 | INTEGER , INTENT(in ) :: kt ! time step |
|---|
| 111 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pstress1_i, pstress2_i, pstress12_i ! |
|---|
| 112 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
|---|
| 113 | !! |
|---|
| 114 | LOGICAL, PARAMETER :: ll_bdy_substep = .TRUE. ! temporary option to call bdy at each sub-time step (T) |
|---|
| 115 | ! or only at the main time step (F) |
|---|
| 116 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 117 | INTEGER :: jter ! local integers |
|---|
| 118 | ! |
|---|
| 119 | REAL(wp) :: zrhoco ! rau0 * rn_cio |
|---|
| 120 | REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling |
|---|
| 121 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
|---|
| 122 | REAL(wp) :: zalph1, z1_alph1, zalph2, z1_alph2 ! alpha coef from Bouillon 2009 or Kimmritz 2017 |
|---|
| 123 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV, zvU, zvV ! ice/snow mass and volume |
|---|
| 124 | REAL(wp) :: zdelta, zp_delf, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars |
|---|
| 125 | REAL(wp) :: zTauO, zTauB, zTauE, zvel ! temporary scalars |
|---|
| 126 | REAL(wp) :: zkt ! isotropic tensile strength for landfast ice |
|---|
| 127 | REAL(wp) :: zvCr ! critical ice volume above which ice is landfast |
|---|
| 128 | ! |
|---|
| 129 | REAL(wp) :: zresm ! Maximal error on ice velocity |
|---|
| 130 | REAL(wp) :: zintb, zintn ! dummy argument |
|---|
| 131 | REAL(wp) :: zfac_x, zfac_y |
|---|
| 132 | REAL(wp) :: zshear, zdum1, zdum2 |
|---|
| 133 | ! |
|---|
| 134 | REAL(wp), DIMENSION(jpi,jpj) :: z1_e1t0, z1_e2t0 ! scale factors |
|---|
| 135 | REAL(wp), DIMENSION(jpi,jpj) :: zp_delt ! P/delta at T points |
|---|
| 136 | REAL(wp), DIMENSION(jpi,jpj) :: zbeta ! beta coef from Kimmritz 2017 |
|---|
| 137 | ! |
|---|
| 138 | REAL(wp), DIMENSION(jpi,jpj) :: zdt_m ! (dt / ice-snow_mass) on T points |
|---|
| 139 | REAL(wp), DIMENSION(jpi,jpj) :: zaU , zaV ! ice fraction on U/V points |
|---|
| 140 | REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! (ice-snow_mass / dt) on U/V points |
|---|
| 141 | REAL(wp), DIMENSION(jpi,jpj) :: zmf ! coriolis parameter at T points |
|---|
| 142 | REAL(wp), DIMENSION(jpi,jpj) :: zTauU_ia , ztauV_ia ! ice-atm. stress at U-V points |
|---|
| 143 | REAL(wp), DIMENSION(jpi,jpj) :: zTauU_ib , ztauV_ib ! ice-bottom stress at U-V points (landfast param) |
|---|
| 144 | REAL(wp), DIMENSION(jpi,jpj) :: zspgU , zspgV ! surface pressure gradient at U/V points |
|---|
| 145 | REAL(wp), DIMENSION(jpi,jpj) :: v_oceU, u_oceV, v_iceU, u_iceV ! ocean/ice u/v component on V/U points |
|---|
| 146 | REAL(wp), DIMENSION(jpi,jpj) :: zfU , zfV ! internal stresses |
|---|
| 147 | ! |
|---|
| 148 | REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear |
|---|
| 149 | REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12 ! stress tensor components |
|---|
| 150 | !!$ REAL(wp), DIMENSION(jpi,jpj) :: zu_ice, zv_ice, zresr ! check convergence |
|---|
| 151 | REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope: |
|---|
| 152 | ! ! ocean surface (ssh_m) if ice is not embedded |
|---|
| 153 | ! ! ice bottom surface if ice is embedded |
|---|
| 154 | REAL(wp), DIMENSION(jpi,jpj) :: zCorx, zCory ! Coriolis stress array |
|---|
| 155 | REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi, ztauy_oi ! Ocean-to-ice stress array |
|---|
| 156 | ! |
|---|
| 157 | REAL(wp), DIMENSION(jpi,jpj) :: zswitchU, zswitchV ! dummy arrays |
|---|
| 158 | REAL(wp), DIMENSION(jpi,jpj) :: zmaskU, zmaskV ! mask for ice presence |
|---|
| 159 | REAL(wp), DIMENSION(jpi,jpj) :: zfmask, zwf ! mask at F points for the ice |
|---|
| 160 | |
|---|
| 161 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
|---|
| 162 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small |
|---|
| 163 | REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small |
|---|
| 164 | !! --- diags |
|---|
| 165 | REAL(wp), DIMENSION(jpi,jpj) :: zswi |
|---|
| 166 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig1, zsig2, zsig3 |
|---|
| 167 | !! --- SIMIP diags |
|---|
| 168 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_sig1 ! Average normal stress in sea ice |
|---|
| 169 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_sig2 ! Maximum shear stress in sea ice |
|---|
| 170 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_dssh_dx ! X-direction sea-surface tilt term (N/m2) |
|---|
| 171 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_dssh_dy ! X-direction sea-surface tilt term (N/m2) |
|---|
| 172 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_corstrx ! X-direction coriolis stress (N/m2) |
|---|
| 173 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_corstry ! Y-direction coriolis stress (N/m2) |
|---|
| 174 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_intstrx ! X-direction internal stress (N/m2) |
|---|
| 175 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_intstry ! Y-direction internal stress (N/m2) |
|---|
| 176 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_utau_oi ! X-direction ocean-ice stress |
|---|
| 177 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_vtau_oi ! Y-direction ocean-ice stress |
|---|
| 178 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice ! X-component of ice mass transport (kg/s) |
|---|
| 179 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_ice ! Y-component of ice mass transport (kg/s) |
|---|
| 180 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw ! X-component of snow mass transport (kg/s) |
|---|
| 181 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_snw ! Y-component of snow mass transport (kg/s) |
|---|
| 182 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp ! X-component of area transport (m2/s) |
|---|
| 183 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_yatrp ! Y-component of area transport (m2/s) |
|---|
| 184 | !!------------------------------------------------------------------- |
|---|
| 185 | |
|---|
| 186 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_evp: EVP sea-ice rheology' |
|---|
| 187 | |
|---|
| 188 | write(numout,*)'ice_dyn_rhg_evp 1: u_ice = ',u_ice(3,4) |
|---|
| 189 | ! |
|---|
| 190 | !!gm for Clem: OPTIMIZATION: I think zfmask can be computed one for all at the initialization.... |
|---|
| 191 | !------------------------------------------------------------------------------! |
|---|
| 192 | ! 0) mask at F points for the ice |
|---|
| 193 | !------------------------------------------------------------------------------! |
|---|
| 194 | ! ocean/land mask |
|---|
| 195 | DO jj = 1, jpjm1 |
|---|
| 196 | DO ji = 1, jpim1 ! NO vector opt. |
|---|
| 197 | zfmask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) |
|---|
| 198 | END DO |
|---|
| 199 | END DO |
|---|
| 200 | CALL lbc_lnk( 'icedyn_rhg_evp', zfmask, 'F', 1._wp ) |
|---|
| 201 | |
|---|
| 202 | ! Lateral boundary conditions on velocity (modify zfmask) |
|---|
| 203 | zwf(:,:) = zfmask(:,:) |
|---|
| 204 | DO jj = 2, jpjm1 |
|---|
| 205 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 206 | IF( zfmask(ji,jj) == 0._wp ) THEN |
|---|
| 207 | zfmask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,jj), zwf(ji,jj+1), zwf(ji-1,jj), zwf(ji,jj-1) ) ) |
|---|
| 208 | ENDIF |
|---|
| 209 | END DO |
|---|
| 210 | END DO |
|---|
| 211 | DO jj = 2, jpjm1 |
|---|
| 212 | IF( zfmask(1,jj) == 0._wp ) THEN |
|---|
| 213 | zfmask(1 ,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(2,jj), zwf(1,jj+1), zwf(1,jj-1) ) ) |
|---|
| 214 | ENDIF |
|---|
| 215 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
|---|
| 216 | zfmask(jpi,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(jpi,jj+1), zwf(jpim1,jj), zwf(jpi,jj-1) ) ) |
|---|
| 217 | ENDIF |
|---|
| 218 | END DO |
|---|
| 219 | DO ji = 2, jpim1 |
|---|
| 220 | IF( zfmask(ji,1) == 0._wp ) THEN |
|---|
| 221 | zfmask(ji,1 ) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,1), zwf(ji,2), zwf(ji-1,1) ) ) |
|---|
| 222 | ENDIF |
|---|
| 223 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
|---|
| 224 | zfmask(ji,jpj) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,jpj), zwf(ji-1,jpj), zwf(ji,jpjm1) ) ) |
|---|
| 225 | ENDIF |
|---|
| 226 | END DO |
|---|
| 227 | CALL lbc_lnk( 'icedyn_rhg_evp', zfmask, 'F', 1._wp ) |
|---|
| 228 | |
|---|
| 229 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 230 | |
|---|
| 231 | !------------------------------------------------------------------------------! |
|---|
| 232 | ! 1) define some variables and initialize arrays |
|---|
| 233 | !------------------------------------------------------------------------------! |
|---|
| 234 | zrhoco = rau0 * rn_cio |
|---|
| 235 | |
|---|
| 236 | ! ecc2: square of yield ellipse eccenticrity |
|---|
| 237 | ecc2 = rn_ecc * rn_ecc |
|---|
| 238 | z1_ecc2 = 1._wp / ecc2 |
|---|
| 239 | |
|---|
| 240 | ! Time step for subcycling |
|---|
| 241 | zdtevp = rdt_ice / REAL( nn_nevp ) |
|---|
| 242 | z1_dtevp = 1._wp / zdtevp |
|---|
| 243 | |
|---|
| 244 | ! alpha parameters (Bouillon 2009) |
|---|
| 245 | IF( .NOT. ln_aEVP ) THEN |
|---|
| 246 | zalph1 = ( 2._wp * rn_relast * rdt_ice ) * z1_dtevp |
|---|
| 247 | zalph2 = zalph1 * z1_ecc2 |
|---|
| 248 | |
|---|
| 249 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 250 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
|---|
| 251 | ENDIF |
|---|
| 252 | |
|---|
| 253 | ! Initialise stress tensor |
|---|
| 254 | zs1 (:,:) = pstress1_i (:,:) |
|---|
| 255 | zs2 (:,:) = pstress2_i (:,:) |
|---|
| 256 | zs12(:,:) = pstress12_i(:,:) |
|---|
| 257 | |
|---|
| 258 | ! Ice strength |
|---|
| 259 | CALL ice_strength |
|---|
| 260 | |
|---|
| 261 | ! scale factors |
|---|
| 262 | DO jj = 2, jpjm1 |
|---|
| 263 | DO ji = fs_2, fs_jpim1 |
|---|
| 264 | z1_e1t0(ji,jj) = 1._wp / ( e1t(ji+1,jj ) + e1t(ji,jj ) ) |
|---|
| 265 | z1_e2t0(ji,jj) = 1._wp / ( e2t(ji ,jj+1) + e2t(ji,jj ) ) |
|---|
| 266 | END DO |
|---|
| 267 | END DO |
|---|
| 268 | |
|---|
| 269 | ! landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010) |
|---|
| 270 | IF( ln_landfast_L16 .OR. ln_landfast_home ) THEN ; zkt = rn_tensile |
|---|
| 271 | ELSE ; zkt = 0._wp |
|---|
| 272 | ENDIF |
|---|
| 273 | |
|---|
| 274 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 275 | ! |
|---|
| 276 | !------------------------------------------------------------------------------! |
|---|
| 277 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
|---|
| 278 | !------------------------------------------------------------------------------! |
|---|
| 279 | ! sea surface height |
|---|
| 280 | ! embedded sea ice: compute representative ice top surface |
|---|
| 281 | ! non-embedded sea ice: use ocean surface for slope calculation |
|---|
| 282 | zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b) |
|---|
| 283 | |
|---|
| 284 | DO jj = 2, jpjm1 |
|---|
| 285 | DO ji = fs_2, fs_jpim1 |
|---|
| 286 | |
|---|
| 287 | ! ice fraction at U-V points |
|---|
| 288 | zaU(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) |
|---|
| 289 | zaV(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) |
|---|
| 290 | |
|---|
| 291 | ! Ice/snow mass at U-V points |
|---|
| 292 | zm1 = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) ) |
|---|
| 293 | zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) ) |
|---|
| 294 | zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) ) |
|---|
| 295 | zmassU = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
|---|
| 296 | zmassV = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 297 | |
|---|
| 298 | ! Ocean currents at U-V points |
|---|
| 299 | v_oceU(ji,jj) = 0.5_wp * ( ( v_oce(ji ,jj) + v_oce(ji ,jj-1) ) * e1t(ji+1,jj) & |
|---|
| 300 | & + ( v_oce(ji+1,jj) + v_oce(ji+1,jj-1) ) * e1t(ji ,jj) ) * z1_e1t0(ji,jj) * umask(ji,jj,1) |
|---|
| 301 | |
|---|
| 302 | u_oceV(ji,jj) = 0.5_wp * ( ( u_oce(ji,jj ) + u_oce(ji-1,jj ) ) * e2t(ji,jj+1) & |
|---|
| 303 | & + ( u_oce(ji,jj+1) + u_oce(ji-1,jj+1) ) * e2t(ji,jj ) ) * z1_e2t0(ji,jj) * vmask(ji,jj,1) |
|---|
| 304 | |
|---|
| 305 | ! Coriolis at T points (m*f) |
|---|
| 306 | zmf(ji,jj) = zm1 * ff_t(ji,jj) |
|---|
| 307 | |
|---|
| 308 | ! dt/m at T points (for alpha and beta coefficients) |
|---|
| 309 | zdt_m(ji,jj) = zdtevp / MAX( zm1, zmmin ) |
|---|
| 310 | |
|---|
| 311 | ! m/dt |
|---|
| 312 | zmU_t(ji,jj) = zmassU * z1_dtevp |
|---|
| 313 | zmV_t(ji,jj) = zmassV * z1_dtevp |
|---|
| 314 | |
|---|
| 315 | ! Drag ice-atm. |
|---|
| 316 | zTauU_ia(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj) |
|---|
| 317 | zTauV_ia(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj) |
|---|
| 318 | |
|---|
| 319 | ! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points |
|---|
| 320 | zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj) |
|---|
| 321 | zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj) |
|---|
| 322 | |
|---|
| 323 | ! masks |
|---|
| 324 | zmaskU(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
|---|
| 325 | zmaskV(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
|---|
| 326 | |
|---|
| 327 | ! switches |
|---|
| 328 | IF( zmassU <= zmmin .AND. zaU(ji,jj) <= zamin ) THEN ; zswitchU(ji,jj) = 0._wp |
|---|
| 329 | ELSE ; zswitchU(ji,jj) = 1._wp ; ENDIF |
|---|
| 330 | IF( zmassV <= zmmin .AND. zaV(ji,jj) <= zamin ) THEN ; zswitchV(ji,jj) = 0._wp |
|---|
| 331 | ELSE ; zswitchV(ji,jj) = 1._wp ; ENDIF |
|---|
| 332 | |
|---|
| 333 | END DO |
|---|
| 334 | END DO |
|---|
| 335 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zmf, 'T', 1., zdt_m, 'T', 1. ) |
|---|
| 336 | |
|---|
| 337 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 338 | ! |
|---|
| 339 | ! !== Landfast ice parameterization ==! |
|---|
| 340 | ! |
|---|
| 341 | IF( ln_landfast_L16 ) THEN !-- Lemieux 2016 |
|---|
| 342 | DO jj = 2, jpjm1 |
|---|
| 343 | DO ji = fs_2, fs_jpim1 |
|---|
| 344 | ! ice thickness at U-V points |
|---|
| 345 | zvU = 0.5_wp * ( vt_i(ji,jj) * e1e2t(ji,jj) + vt_i(ji+1,jj) * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
|---|
| 346 | zvV = 0.5_wp * ( vt_i(ji,jj) * e1e2t(ji,jj) + vt_i(ji,jj+1) * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 347 | ! ice-bottom stress at U points |
|---|
| 348 | zvCr = zaU(ji,jj) * rn_depfra * hu_n(ji,jj) |
|---|
| 349 | zTauU_ib(ji,jj) = rn_icebfr * MAX( 0._wp, zvU - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaU(ji,jj) ) ) |
|---|
| 350 | ! ice-bottom stress at V points |
|---|
| 351 | zvCr = zaV(ji,jj) * rn_depfra * hv_n(ji,jj) |
|---|
| 352 | zTauV_ib(ji,jj) = rn_icebfr * MAX( 0._wp, zvV - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaV(ji,jj) ) ) |
|---|
| 353 | ! ice_bottom stress at T points |
|---|
| 354 | zvCr = at_i(ji,jj) * rn_depfra * ht_n(ji,jj) |
|---|
| 355 | tau_icebfr(ji,jj) = rn_icebfr * MAX( 0._wp, vt_i(ji,jj) - zvCr ) * EXP( -rn_crhg * ( 1._wp - at_i(ji,jj) ) ) |
|---|
| 356 | END DO |
|---|
| 357 | END DO |
|---|
| 358 | CALL lbc_lnk( 'icedyn_rhg_evp', tau_icebfr(:,:), 'T', 1. ) |
|---|
| 359 | ! |
|---|
| 360 | ELSEIF( ln_landfast_home ) THEN !-- Home made |
|---|
| 361 | DO jj = 2, jpjm1 |
|---|
| 362 | DO ji = fs_2, fs_jpim1 |
|---|
| 363 | zTauU_ib(ji,jj) = tau_icebfr(ji,jj) |
|---|
| 364 | zTauV_ib(ji,jj) = tau_icebfr(ji,jj) |
|---|
| 365 | END DO |
|---|
| 366 | END DO |
|---|
| 367 | ! |
|---|
| 368 | ELSE !-- no landfast |
|---|
| 369 | DO jj = 2, jpjm1 |
|---|
| 370 | DO ji = fs_2, fs_jpim1 |
|---|
| 371 | zTauU_ib(ji,jj) = 0._wp |
|---|
| 372 | zTauV_ib(ji,jj) = 0._wp |
|---|
| 373 | END DO |
|---|
| 374 | END DO |
|---|
| 375 | ENDIF |
|---|
| 376 | IF( iom_use('tau_icebfr') ) CALL iom_put( 'tau_icebfr', tau_icebfr(:,:) ) |
|---|
| 377 | |
|---|
| 378 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 379 | |
|---|
| 380 | !------------------------------------------------------------------------------! |
|---|
| 381 | ! 3) Solution of the momentum equation, iterative procedure |
|---|
| 382 | !------------------------------------------------------------------------------! |
|---|
| 383 | ! |
|---|
| 384 | ! !----------------------! |
|---|
| 385 | DO jter = 1 , nn_nevp ! loop over jter ! |
|---|
| 386 | ! !----------------------! |
|---|
| 387 | l_full_nf_update = jter == nn_nevp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1 |
|---|
| 388 | ! |
|---|
| 389 | !!$ IF(ln_ctl) THEN ! Convergence test |
|---|
| 390 | !!$ DO jj = 1, jpjm1 |
|---|
| 391 | !!$ zu_ice(:,jj) = u_ice(:,jj) ! velocity at previous time step |
|---|
| 392 | !!$ zv_ice(:,jj) = v_ice(:,jj) |
|---|
| 393 | !!$ END DO |
|---|
| 394 | !!$ ENDIF |
|---|
| 395 | |
|---|
| 396 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 397 | DO jj = 1, jpjm1 ! loops start at 1 since there is no boundary condition (lbc_lnk) at i=1 and j=1 for F points |
|---|
| 398 | DO ji = 1, jpim1 |
|---|
| 399 | |
|---|
| 400 | ! shear at F points |
|---|
| 401 | 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) & |
|---|
| 402 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 403 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 404 | |
|---|
| 405 | END DO |
|---|
| 406 | END DO |
|---|
| 407 | CALL lbc_lnk( 'icedyn_rhg_evp', zds, 'F', 1. ) |
|---|
| 408 | |
|---|
| 409 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 410 | |
|---|
| 411 | DO jj = 2, jpj ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 |
|---|
| 412 | DO ji = 2, jpi ! no vector loop |
|---|
| 413 | |
|---|
| 414 | ! shear**2 at T points (doc eq. A16) |
|---|
| 415 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 416 | & + 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) & |
|---|
| 417 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 418 | |
|---|
| 419 | ! divergence at T points |
|---|
| 420 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 421 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 422 | & ) * r1_e1e2t(ji,jj) |
|---|
| 423 | zdiv2 = zdiv * zdiv |
|---|
| 424 | |
|---|
| 425 | ! tension at T points |
|---|
| 426 | 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) & |
|---|
| 427 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 428 | & ) * r1_e1e2t(ji,jj) |
|---|
| 429 | zdt2 = zdt * zdt |
|---|
| 430 | |
|---|
| 431 | ! delta at T points |
|---|
| 432 | zdelta = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 433 | |
|---|
| 434 | ! P/delta at T points |
|---|
| 435 | zp_delt(ji,jj) = strength(ji,jj) / ( zdelta + rn_creepl ) |
|---|
| 436 | |
|---|
| 437 | ! alpha & beta for aEVP |
|---|
| 438 | ! gamma = 0.5*P/(delta+creepl) * (c*pi)**2/Area * dt/m |
|---|
| 439 | ! alpha = beta = sqrt(4*gamma) |
|---|
| 440 | IF( ln_aEVP ) THEN |
|---|
| 441 | zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 442 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 443 | zalph2 = zalph1 |
|---|
| 444 | z1_alph2 = z1_alph1 |
|---|
| 445 | ENDIF |
|---|
| 446 | |
|---|
| 447 | ! stress at T points (zkt/=0 if landfast) |
|---|
| 448 | zs1(ji,jj) = ( zs1(ji,jj) * zalph1 + zp_delt(ji,jj) * ( zdiv * (1._wp + zkt) - zdelta * (1._wp - zkt) ) ) * z1_alph1 |
|---|
| 449 | zs2(ji,jj) = ( zs2(ji,jj) * zalph2 + zp_delt(ji,jj) * ( zdt * z1_ecc2 * (1._wp + zkt) ) ) * z1_alph2 |
|---|
| 450 | |
|---|
| 451 | END DO |
|---|
| 452 | END DO |
|---|
| 453 | CALL lbc_lnk( 'icedyn_rhg_evp', zp_delt, 'T', 1. ) |
|---|
| 454 | |
|---|
| 455 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 456 | |
|---|
| 457 | DO jj = 1, jpjm1 |
|---|
| 458 | DO ji = 1, jpim1 |
|---|
| 459 | |
|---|
| 460 | ! alpha & beta for aEVP |
|---|
| 461 | IF( ln_aEVP ) THEN |
|---|
| 462 | zalph2 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 463 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
|---|
| 464 | zbeta(ji,jj) = zalph2 |
|---|
| 465 | ENDIF |
|---|
| 466 | |
|---|
| 467 | ! P/delta at F points |
|---|
| 468 | zp_delf = 0.25_wp * ( zp_delt(ji,jj) + zp_delt(ji+1,jj) + zp_delt(ji,jj+1) + zp_delt(ji+1,jj+1) ) |
|---|
| 469 | |
|---|
| 470 | ! stress at F points (zkt/=0 if landfast) |
|---|
| 471 | zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 * (1._wp + zkt) ) * 0.5_wp ) * z1_alph2 |
|---|
| 472 | |
|---|
| 473 | END DO |
|---|
| 474 | END DO |
|---|
| 475 | |
|---|
| 476 | ! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- ! |
|---|
| 477 | DO jj = 2, jpjm1 |
|---|
| 478 | DO ji = fs_2, fs_jpim1 |
|---|
| 479 | ! !--- U points |
|---|
| 480 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 481 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 482 | & ) * r1_e2u(ji,jj) & |
|---|
| 483 | & + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 484 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 485 | & ) * r1_e1e2u(ji,jj) |
|---|
| 486 | ! |
|---|
| 487 | ! !--- V points |
|---|
| 488 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 489 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 490 | & ) * r1_e1v(ji,jj) & |
|---|
| 491 | & + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 492 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 493 | & ) * r1_e1e2v(ji,jj) |
|---|
| 494 | ! |
|---|
| 495 | ! !--- u_ice at V point |
|---|
| 496 | u_iceV(ji,jj) = 0.5_wp * ( ( u_ice(ji,jj ) + u_ice(ji-1,jj ) ) * e2t(ji,jj+1) & |
|---|
| 497 | & + ( u_ice(ji,jj+1) + u_ice(ji-1,jj+1) ) * e2t(ji,jj ) ) * z1_e2t0(ji,jj) * vmask(ji,jj,1) |
|---|
| 498 | ! |
|---|
| 499 | ! !--- v_ice at U point |
|---|
| 500 | v_iceU(ji,jj) = 0.5_wp * ( ( v_ice(ji ,jj) + v_ice(ji ,jj-1) ) * e1t(ji+1,jj) & |
|---|
| 501 | & + ( v_ice(ji+1,jj) + v_ice(ji+1,jj-1) ) * e1t(ji ,jj) ) * z1_e1t0(ji,jj) * umask(ji,jj,1) |
|---|
| 502 | END DO |
|---|
| 503 | END DO |
|---|
| 504 | write(numout,*)'ice_dyn_rhg_evp 3: u_ice = ',u_ice(3,4) |
|---|
| 505 | |
|---|
| 506 | ! |
|---|
| 507 | ! --- Computation of ice velocity --- ! |
|---|
| 508 | ! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta vary as in Kimmritz 2016 & 2017 |
|---|
| 509 | ! Bouillon et al. 2009 (eq 34-35) => stable |
|---|
| 510 | IF( MOD(jter,2) == 0 ) THEN ! even iterations |
|---|
| 511 | ! |
|---|
| 512 | DO jj = 2, jpjm1 |
|---|
| 513 | DO ji = fs_2, fs_jpim1 |
|---|
| 514 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 515 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 516 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 517 | ! !--- Ocean-to-Ice stress |
|---|
| 518 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 519 | ! |
|---|
| 520 | ! !--- tau_bottom/v_ice |
|---|
| 521 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 522 | zTauB = - zTauV_ib(ji,jj) / zvel |
|---|
| 523 | ! |
|---|
| 524 | ! !--- Coriolis at V-points (energy conserving formulation) |
|---|
| 525 | zCory(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 526 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 527 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 528 | ! |
|---|
| 529 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 530 | zTauE = zfV(ji,jj) + zTauV_ia(ji,jj) + zCory(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 531 | ! |
|---|
| 532 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 533 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, ztauE - zTauV_ib(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 534 | ! |
|---|
| 535 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 536 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbeta(ji,jj) * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 537 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 538 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 539 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 540 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 541 | & ) * zmaskV(ji,jj) |
|---|
| 542 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 543 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 544 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 545 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 546 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 547 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 548 | & ) * zmaskV(ji,jj) |
|---|
| 549 | ENDIF |
|---|
| 550 | END DO |
|---|
| 551 | END DO |
|---|
| 552 | CALL lbc_lnk( 'icedyn_rhg_evp', v_ice, 'V', -1. ) |
|---|
| 553 | ! |
|---|
| 554 | #if defined key_agrif |
|---|
| 555 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 556 | CALL agrif_interp_ice( 'V' ) |
|---|
| 557 | #endif |
|---|
| 558 | IF( ln_bdy .AND. ll_bdy_substep ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 559 | ! |
|---|
| 560 | DO jj = 2, jpjm1 |
|---|
| 561 | DO ji = fs_2, fs_jpim1 |
|---|
| 562 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 563 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 564 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 565 | ! !--- Ocean-to-Ice stress |
|---|
| 566 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 567 | ! |
|---|
| 568 | ! !--- tau_bottom/u_ice |
|---|
| 569 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 570 | zTauB = - zTauU_ib(ji,jj) / zvel |
|---|
| 571 | ! |
|---|
| 572 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 573 | zCorx(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 574 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 575 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 576 | |
|---|
| 577 | IF (ji == 3 .AND. jj == 4) THEN |
|---|
| 578 | write(numout,*)'ice_dyn_rhg_evp 6: u_ice(ji,jj), u_oce(ji,jj), v_iceU(ji,jj), v_oceU(ji,jj) = ',u_ice(ji,jj), u_oce(ji,jj), v_iceU(ji,jj), v_oceU(ji,jj) |
|---|
| 579 | write(numout,*)'ice_dyn_rhg_evp 6: zTauO, zTauU_ib(ji,jj), zvel =',zTauO, zTauU_ib(ji,jj), zvel |
|---|
| 580 | write(numout,*)'ice_dyn_rhg_evp 6: r1_e1u(ji,jj), zmf(ji,jj), e1v(ji,jj) = ',r1_e1u(ji,jj), zmf(ji,jj), e1v(ji,jj) |
|---|
| 581 | ENDIF |
|---|
| 582 | |
|---|
| 583 | ! |
|---|
| 584 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 585 | zTauE = zfU(ji,jj) + zTauU_ia(ji,jj) + zCorx(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 586 | ! |
|---|
| 587 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 588 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, ztauE - zTauU_ib(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 589 | ! |
|---|
| 590 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 591 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbeta(ji,jj) * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 592 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 593 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 594 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 595 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 596 | & ) * zmaskU(ji,jj) |
|---|
| 597 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 598 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 599 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 600 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 601 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 602 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 603 | & ) * zmaskU(ji,jj) |
|---|
| 604 | ENDIF |
|---|
| 605 | |
|---|
| 606 | IF (ji == 3 .AND. jj == 4) THEN |
|---|
| 607 | write(numout,*)'ice_dyn_rhg_evp 7: u_ice(ji,jj), zmU_t(ji,jj), zTauE, zTauO = ',u_ice(ji,jj), zmU_t(ji,jj), zTauE, zTauO |
|---|
| 608 | write(numout,*)'ice_dyn_rhg_evp 7: zepsi, zTauO, zTauB, rswitch = ', zepsi, zTauO, zTauB, rswitch |
|---|
| 609 | write(numout,*)'ice_dyn_rhg_evp 7: zdtevp, rn_lfrelax, zswitchU(ji,jj), zmaskU(ji,jj) = ', zdtevp, rn_lfrelax, zswitchU(ji,jj), zmaskU(ji,jj) |
|---|
| 610 | ENDIF |
|---|
| 611 | |
|---|
| 612 | END DO |
|---|
| 613 | END DO |
|---|
| 614 | CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1. ) |
|---|
| 615 | ! |
|---|
| 616 | #if defined key_agrif |
|---|
| 617 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 618 | CALL agrif_interp_ice( 'U' ) |
|---|
| 619 | #endif |
|---|
| 620 | IF( ln_bdy .AND. ll_bdy_substep ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 621 | ! |
|---|
| 622 | ELSE ! odd iterations |
|---|
| 623 | ! |
|---|
| 624 | DO jj = 2, jpjm1 |
|---|
| 625 | DO ji = fs_2, fs_jpim1 |
|---|
| 626 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 627 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 628 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 629 | ! !--- Ocean-to-Ice stress |
|---|
| 630 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 631 | ! |
|---|
| 632 | ! !--- tau_bottom/u_ice |
|---|
| 633 | zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) |
|---|
| 634 | zTauB = - zTauU_ib(ji,jj) / zvel |
|---|
| 635 | ! |
|---|
| 636 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 637 | zCorx(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 638 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 639 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 640 | |
|---|
| 641 | IF (ji == 3 .AND. jj == 4) THEN |
|---|
| 642 | write(numout,*)'ice_dyn_rhg_evp 8: u_ice(ji,jj), u_oce(ji,jj), v_iceU(ji,jj), v_oceU(ji,jj) = ',u_ice(ji,jj), u_oce(ji,jj), v_iceU(ji,jj), v_oceU(ji,jj) |
|---|
| 643 | write(numout,*)'ice_dyn_rhg_evp 8: zTauO, zTauU_ib(ji,jj), zvel =',zTauO, zTauU_ib(ji,jj), zvel |
|---|
| 644 | write(numout,*)'ice_dyn_rhg_evp 8: r1_e1u(ji,jj), zmf(ji,jj), e1v(ji,jj) = ',r1_e1u(ji,jj), zmf(ji,jj), e1v(ji,jj) |
|---|
| 645 | ENDIF |
|---|
| 646 | |
|---|
| 647 | ! |
|---|
| 648 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 649 | zTauE = zfU(ji,jj) + zTauU_ia(ji,jj) + zCorx(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 650 | ! |
|---|
| 651 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 652 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, ztauE - zTauU_ib(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 653 | ! |
|---|
| 654 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 655 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbeta(ji,jj) * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 656 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 657 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 658 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 659 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 660 | & ) * zmaskU(ji,jj) |
|---|
| 661 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 662 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 663 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 664 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 665 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 666 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 667 | & ) * zmaskU(ji,jj) |
|---|
| 668 | ENDIF |
|---|
| 669 | |
|---|
| 670 | IF (ji == 3 .AND. jj == 4) THEN |
|---|
| 671 | write(numout,*)'ice_dyn_rhg_evp 9: u_ice(ji,jj), zmU_t(ji,jj), zTauE, zTauO = ',u_ice(ji,jj), zmU_t(ji,jj), zTauE, zTauO |
|---|
| 672 | write(numout,*)'ice_dyn_rhg_evp 9: zepsi, zTauO, zTauB, rswitch = ', zepsi, zTauO, zTauB, rswitch |
|---|
| 673 | write(numout,*)'ice_dyn_rhg_evp 9: zdtevp, rn_lfrelax, zswitchU(ji,jj), zmaskU(ji,jj) = ', zdtevp, rn_lfrelax, zswitchU(ji,jj), zmaskU(ji,jj) |
|---|
| 674 | ENDIF |
|---|
| 675 | END DO |
|---|
| 676 | END DO |
|---|
| 677 | CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1. ) |
|---|
| 678 | |
|---|
| 679 | write(numout,*)'ice_dyn_rhg_evp 10: u_ice = ',u_ice(3,4) |
|---|
| 680 | ! |
|---|
| 681 | #if defined key_agrif |
|---|
| 682 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 683 | CALL agrif_interp_ice( 'U' ) |
|---|
| 684 | #endif |
|---|
| 685 | IF( ln_bdy .AND. ll_bdy_substep ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 686 | ! |
|---|
| 687 | DO jj = 2, jpjm1 |
|---|
| 688 | DO ji = fs_2, fs_jpim1 |
|---|
| 689 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 690 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 691 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 692 | ! !--- Ocean-to-Ice stress |
|---|
| 693 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 694 | ! |
|---|
| 695 | ! !--- tau_bottom/v_ice |
|---|
| 696 | zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) |
|---|
| 697 | zTauB = - zTauV_ib(ji,jj) / zvel |
|---|
| 698 | ! |
|---|
| 699 | ! !--- Coriolis at v-points (energy conserving formulation) |
|---|
| 700 | zCory(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 701 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 702 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 703 | ! |
|---|
| 704 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 705 | zTauE = zfV(ji,jj) + zTauV_ia(ji,jj) + zCory(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 706 | ! |
|---|
| 707 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 708 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zTauE - zTauV_ib(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 709 | ! |
|---|
| 710 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 711 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbeta(ji,jj) * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 712 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 713 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 714 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 715 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 716 | & ) * zmaskV(ji,jj) |
|---|
| 717 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 718 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 719 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 720 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 721 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 722 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin |
|---|
| 723 | & ) * zmaskV(ji,jj) |
|---|
| 724 | ENDIF |
|---|
| 725 | END DO |
|---|
| 726 | END DO |
|---|
| 727 | CALL lbc_lnk( 'icedyn_rhg_evp', v_ice, 'V', -1. ) |
|---|
| 728 | ! |
|---|
| 729 | #if defined key_agrif |
|---|
| 730 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 731 | CALL agrif_interp_ice( 'V' ) |
|---|
| 732 | #endif |
|---|
| 733 | IF( ln_bdy .AND. ll_bdy_substep ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 734 | ! |
|---|
| 735 | ENDIF |
|---|
| 736 | |
|---|
| 737 | !!$ IF(ln_ctl) THEN ! Convergence test |
|---|
| 738 | !!$ DO jj = 2 , jpjm1 |
|---|
| 739 | !!$ zresr(:,jj) = MAX( ABS( u_ice(:,jj) - zu_ice(:,jj) ), ABS( v_ice(:,jj) - zv_ice(:,jj) ) ) |
|---|
| 740 | !!$ END DO |
|---|
| 741 | !!$ zresm = MAXVAL( zresr( 1:jpi, 2:jpjm1 ) ) |
|---|
| 742 | !!$ CALL mpp_max( 'icedyn_rhg_evp', zresm ) ! max over the global domain |
|---|
| 743 | !!$ ENDIF |
|---|
| 744 | ! |
|---|
| 745 | ! ! ==================== ! |
|---|
| 746 | END DO ! end loop over jter ! |
|---|
| 747 | ! ! ==================== ! |
|---|
| 748 | ! |
|---|
| 749 | IF( ln_bdy .AND. .NOT.ll_bdy_substep ) THEN |
|---|
| 750 | CALL bdy_ice_dyn( 'U' ) |
|---|
| 751 | CALL bdy_ice_dyn( 'V' ) |
|---|
| 752 | ENDIF |
|---|
| 753 | write(numout,*)'ice_dyn_rhg_evp 5: u_ice = ',u_ice(3,4) |
|---|
| 754 | ! |
|---|
| 755 | !------------------------------------------------------------------------------! |
|---|
| 756 | ! 4) Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 757 | !------------------------------------------------------------------------------! |
|---|
| 758 | DO jj = 1, jpjm1 |
|---|
| 759 | DO ji = 1, jpim1 |
|---|
| 760 | |
|---|
| 761 | ! shear at F points |
|---|
| 762 | 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) & |
|---|
| 763 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 764 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 765 | |
|---|
| 766 | END DO |
|---|
| 767 | END DO |
|---|
| 768 | |
|---|
| 769 | DO jj = 2, jpjm1 |
|---|
| 770 | DO ji = 2, jpim1 ! no vector loop |
|---|
| 771 | |
|---|
| 772 | ! tension**2 at T points |
|---|
| 773 | 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) & |
|---|
| 774 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 775 | & ) * r1_e1e2t(ji,jj) |
|---|
| 776 | zdt2 = zdt * zdt |
|---|
| 777 | |
|---|
| 778 | ! shear**2 at T points (doc eq. A16) |
|---|
| 779 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 780 | & + 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) & |
|---|
| 781 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 782 | |
|---|
| 783 | ! shear at T points |
|---|
| 784 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
|---|
| 785 | |
|---|
| 786 | ! divergence at T points |
|---|
| 787 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 788 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 789 | & ) * r1_e1e2t(ji,jj) |
|---|
| 790 | |
|---|
| 791 | ! delta at T points |
|---|
| 792 | zdelta = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 793 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 |
|---|
| 794 | pdelta_i(ji,jj) = zdelta + rn_creepl * rswitch |
|---|
| 795 | |
|---|
| 796 | END DO |
|---|
| 797 | END DO |
|---|
| 798 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', pshear_i, 'T', 1., pdivu_i, 'T', 1., pdelta_i, 'T', 1. ) |
|---|
| 799 | |
|---|
| 800 | ! --- Store the stress tensor for the next time step --- ! |
|---|
| 801 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zs1, 'T', 1., zs2, 'T', 1., zs12, 'F', 1. ) |
|---|
| 802 | pstress1_i (:,:) = zs1 (:,:) |
|---|
| 803 | pstress2_i (:,:) = zs2 (:,:) |
|---|
| 804 | pstress12_i(:,:) = zs12(:,:) |
|---|
| 805 | write(numout,*)'ice_dyn_rhg_evp 4: u_ice = ',u_ice(3,4) |
|---|
| 806 | ! |
|---|
| 807 | |
|---|
| 808 | !------------------------------------------------------------------------------! |
|---|
| 809 | ! 5) diagnostics |
|---|
| 810 | !------------------------------------------------------------------------------! |
|---|
| 811 | DO jj = 1, jpj |
|---|
| 812 | DO ji = 1, jpi |
|---|
| 813 | zswi(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice, 0 if no ice |
|---|
| 814 | END DO |
|---|
| 815 | END DO |
|---|
| 816 | |
|---|
| 817 | ! --- divergence, shear and strength --- ! |
|---|
| 818 | IF( iom_use('icediv') ) CALL iom_put( "icediv" , pdivu_i (:,:) * zswi(:,:) ) ! divergence |
|---|
| 819 | IF( iom_use('iceshe') ) CALL iom_put( "iceshe" , pshear_i(:,:) * zswi(:,:) ) ! shear |
|---|
| 820 | IF( iom_use('icestr') ) CALL iom_put( "icestr" , strength(:,:) * zswi(:,:) ) ! Ice strength |
|---|
| 821 | |
|---|
| 822 | ! --- charge ellipse --- ! |
|---|
| 823 | IF( iom_use('isig1') .OR. iom_use('isig2') .OR. iom_use('isig3') ) THEN |
|---|
| 824 | ! |
|---|
| 825 | ALLOCATE( zsig1(jpi,jpj) , zsig2(jpi,jpj) , zsig3(jpi,jpj) ) |
|---|
| 826 | ! |
|---|
| 827 | DO jj = 2, jpjm1 |
|---|
| 828 | DO ji = 2, jpim1 |
|---|
| 829 | zdum1 = ( zswi(ji-1,jj) * pstress12_i(ji-1,jj) + zswi(ji ,jj-1) * pstress12_i(ji ,jj-1) + & ! stress12_i at T-point |
|---|
| 830 | & zswi(ji ,jj) * pstress12_i(ji ,jj) + zswi(ji-1,jj-1) * pstress12_i(ji-1,jj-1) ) & |
|---|
| 831 | & / MAX( 1._wp, zswi(ji-1,jj) + zswi(ji,jj-1) + zswi(ji,jj) + zswi(ji-1,jj-1) ) |
|---|
| 832 | |
|---|
| 833 | zshear = SQRT( pstress2_i(ji,jj) * pstress2_i(ji,jj) + 4._wp * zdum1 * zdum1 ) ! shear stress |
|---|
| 834 | |
|---|
| 835 | zdum2 = zswi(ji,jj) / MAX( 1._wp, strength(ji,jj) ) |
|---|
| 836 | |
|---|
| 837 | !! zsig1(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) + zshear ) ! principal stress (y-direction, see Hunke & Dukowicz 2002) |
|---|
| 838 | !! zsig2(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) - zshear ) ! principal stress (x-direction, see Hunke & Dukowicz 2002) |
|---|
| 839 | !! zsig3(ji,jj) = zdum2**2 * ( ( pstress1_i(ji,jj) + strength(ji,jj) )**2 + ( rn_ecc * zshear )**2 ) ! quadratic relation linking compressive stress to shear stress |
|---|
| 840 | !! ! (scheme converges if this value is ~1, see Bouillon et al 2009 (eq. 11)) |
|---|
| 841 | zsig1(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) ) ! compressive stress, see Bouillon et al. 2015 |
|---|
| 842 | zsig2(ji,jj) = 0.5_wp * zdum2 * ( zshear ) ! shear stress |
|---|
| 843 | zsig3(ji,jj) = zdum2**2 * ( ( pstress1_i(ji,jj) + strength(ji,jj) )**2 + ( rn_ecc * zshear )**2 ) |
|---|
| 844 | END DO |
|---|
| 845 | END DO |
|---|
| 846 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zsig1, 'T', 1., zsig2, 'T', 1., zsig3, 'T', 1. ) |
|---|
| 847 | ! |
|---|
| 848 | IF( iom_use('isig1') ) CALL iom_put( "isig1" , zsig1 ) |
|---|
| 849 | IF( iom_use('isig2') ) CALL iom_put( "isig2" , zsig2 ) |
|---|
| 850 | IF( iom_use('isig3') ) CALL iom_put( "isig3" , zsig3 ) |
|---|
| 851 | ! |
|---|
| 852 | DEALLOCATE( zsig1 , zsig2 , zsig3 ) |
|---|
| 853 | ENDIF |
|---|
| 854 | |
|---|
| 855 | ! --- SIMIP --- ! |
|---|
| 856 | IF ( iom_use( 'normstr' ) .OR. iom_use( 'sheastr' ) .OR. iom_use( 'dssh_dx' ) .OR. iom_use( 'dssh_dy' ) .OR. & |
|---|
| 857 | & iom_use( 'corstrx' ) .OR. iom_use( 'corstry' ) .OR. iom_use( 'intstrx' ) .OR. iom_use( 'intstry' ) .OR. & |
|---|
| 858 | & iom_use( 'utau_oi' ) .OR. iom_use( 'vtau_oi' ) .OR. iom_use( 'xmtrpice' ) .OR. iom_use( 'ymtrpice' ) .OR. & |
|---|
| 859 | & iom_use( 'xmtrpsnw' ) .OR. iom_use( 'ymtrpsnw' ) .OR. iom_use( 'xatrp' ) .OR. iom_use( 'yatrp' ) ) THEN |
|---|
| 860 | |
|---|
| 861 | ALLOCATE( zdiag_sig1 (jpi,jpj) , zdiag_sig2 (jpi,jpj) , zdiag_dssh_dx (jpi,jpj) , zdiag_dssh_dy (jpi,jpj) , & |
|---|
| 862 | & zdiag_corstrx (jpi,jpj) , zdiag_corstry (jpi,jpj) , zdiag_intstrx (jpi,jpj) , zdiag_intstry (jpi,jpj) , & |
|---|
| 863 | & zdiag_utau_oi (jpi,jpj) , zdiag_vtau_oi (jpi,jpj) , zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 864 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp (jpi,jpj) , zdiag_yatrp (jpi,jpj) ) |
|---|
| 865 | |
|---|
| 866 | DO jj = 2, jpjm1 |
|---|
| 867 | DO ji = 2, jpim1 |
|---|
| 868 | rswitch = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice, 0 if no ice |
|---|
| 869 | |
|---|
| 870 | ! Stress tensor invariants (normal and shear stress N/m) |
|---|
| 871 | zdiag_sig1(ji,jj) = ( zs1(ji,jj) + zs2(ji,jj) ) * rswitch ! normal stress |
|---|
| 872 | zdiag_sig2(ji,jj) = SQRT( ( zs1(ji,jj) - zs2(ji,jj) )**2 + 4*zs12(ji,jj)**2 ) * rswitch ! shear stress |
|---|
| 873 | |
|---|
| 874 | ! Stress terms of the momentum equation (N/m2) |
|---|
| 875 | zdiag_dssh_dx(ji,jj) = zspgU(ji,jj) * rswitch ! sea surface slope stress term |
|---|
| 876 | zdiag_dssh_dy(ji,jj) = zspgV(ji,jj) * rswitch |
|---|
| 877 | |
|---|
| 878 | zdiag_corstrx(ji,jj) = zCorx(ji,jj) * rswitch ! Coriolis stress term |
|---|
| 879 | zdiag_corstry(ji,jj) = zCory(ji,jj) * rswitch |
|---|
| 880 | |
|---|
| 881 | zdiag_intstrx(ji,jj) = zfU(ji,jj) * rswitch ! internal stress term |
|---|
| 882 | zdiag_intstry(ji,jj) = zfV(ji,jj) * rswitch |
|---|
| 883 | |
|---|
| 884 | zdiag_utau_oi(ji,jj) = ztaux_oi(ji,jj) * rswitch ! oceanic stress |
|---|
| 885 | zdiag_vtau_oi(ji,jj) = ztauy_oi(ji,jj) * rswitch |
|---|
| 886 | |
|---|
| 887 | ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 888 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * rswitch |
|---|
| 889 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * rswitch |
|---|
| 890 | |
|---|
| 891 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 892 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 893 | |
|---|
| 894 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 895 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 896 | |
|---|
| 897 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 898 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 899 | |
|---|
| 900 | END DO |
|---|
| 901 | END DO |
|---|
| 902 | |
|---|
| 903 | write(numout,*)'ice_dyn_rhg_evp 11: u_ice = ',u_ice(3,4) |
|---|
| 904 | |
|---|
| 905 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zdiag_sig1 , 'T', 1., zdiag_sig2 , 'T', 1., & |
|---|
| 906 | & zdiag_dssh_dx, 'U', -1., zdiag_dssh_dy, 'V', -1., & |
|---|
| 907 | & zdiag_corstrx, 'U', -1., zdiag_corstry, 'V', -1., & |
|---|
| 908 | & zdiag_intstrx, 'U', -1., zdiag_intstry, 'V', -1. ) |
|---|
| 909 | |
|---|
| 910 | CALL lbc_lnk_multi( 'icedyn_rhg_evp', zdiag_utau_oi , 'U', -1., zdiag_vtau_oi , 'V', -1., & |
|---|
| 911 | & zdiag_xmtrp_ice, 'U', -1., zdiag_xmtrp_snw, 'U', -1., & |
|---|
| 912 | & zdiag_xatrp , 'U', -1., zdiag_ymtrp_ice, 'V', -1., & |
|---|
| 913 | & zdiag_ymtrp_snw, 'V', -1., zdiag_yatrp , 'V', -1. ) |
|---|
| 914 | |
|---|
| 915 | IF( iom_use('normstr' ) ) CALL iom_put( 'normstr' , zdiag_sig1(:,:) ) ! Normal stress |
|---|
| 916 | IF( iom_use('sheastr' ) ) CALL iom_put( 'sheastr' , zdiag_sig2(:,:) ) ! Shear stress |
|---|
| 917 | IF( iom_use('dssh_dx' ) ) CALL iom_put( 'dssh_dx' , zdiag_dssh_dx(:,:) ) ! Sea-surface tilt term in force balance (x) |
|---|
| 918 | IF( iom_use('dssh_dy' ) ) CALL iom_put( 'dssh_dy' , zdiag_dssh_dy(:,:) ) ! Sea-surface tilt term in force balance (y) |
|---|
| 919 | IF( iom_use('corstrx' ) ) CALL iom_put( 'corstrx' , zdiag_corstrx(:,:) ) ! Coriolis force term in force balance (x) |
|---|
| 920 | IF( iom_use('corstry' ) ) CALL iom_put( 'corstry' , zdiag_corstry(:,:) ) ! Coriolis force term in force balance (y) |
|---|
| 921 | IF( iom_use('intstrx' ) ) CALL iom_put( 'intstrx' , zdiag_intstrx(:,:) ) ! Internal force term in force balance (x) |
|---|
| 922 | IF( iom_use('intstry' ) ) CALL iom_put( 'intstry' , zdiag_intstry(:,:) ) ! Internal force term in force balance (y) |
|---|
| 923 | IF( iom_use('utau_oi' ) ) CALL iom_put( 'utau_oi' , zdiag_utau_oi(:,:) ) ! Ocean stress term in force balance (x) |
|---|
| 924 | IF( iom_use('vtau_oi' ) ) CALL iom_put( 'vtau_oi' , zdiag_vtau_oi(:,:) ) ! Ocean stress term in force balance (y) |
|---|
| 925 | IF( iom_use('xmtrpice') ) CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice(:,:) ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 926 | IF( iom_use('ymtrpice') ) CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice(:,:) ) ! Y-component of sea-ice mass transport |
|---|
| 927 | IF( iom_use('xmtrpsnw') ) CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw(:,:) ) ! X-component of snow mass transport (kg/s) |
|---|
| 928 | IF( iom_use('ymtrpsnw') ) CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw(:,:) ) ! Y-component of snow mass transport |
|---|
| 929 | IF( iom_use('xatrp' ) ) CALL iom_put( 'xatrp' , zdiag_xatrp(:,:) ) ! X-component of ice area transport |
|---|
| 930 | IF( iom_use('yatrp' ) ) CALL iom_put( 'yatrp' , zdiag_yatrp(:,:) ) ! Y-component of ice area transport |
|---|
| 931 | |
|---|
| 932 | DEALLOCATE( zdiag_sig1 , zdiag_sig2 , zdiag_dssh_dx , zdiag_dssh_dy , & |
|---|
| 933 | & zdiag_corstrx , zdiag_corstry , zdiag_intstrx , zdiag_intstry , & |
|---|
| 934 | & zdiag_utau_oi , zdiag_vtau_oi , zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 935 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 936 | |
|---|
| 937 | ENDIF |
|---|
| 938 | |
|---|
| 939 | write(numout,*)'ice_dyn_rhg_evp 2: u_ice = ',u_ice(3,4) |
|---|
| 940 | ! |
|---|
| 941 | END SUBROUTINE ice_dyn_rhg_evp |
|---|
| 942 | |
|---|
| 943 | |
|---|
| 944 | SUBROUTINE rhg_evp_rst( cdrw, kt ) |
|---|
| 945 | !!--------------------------------------------------------------------- |
|---|
| 946 | !! *** ROUTINE rhg_evp_rst *** |
|---|
| 947 | !! |
|---|
| 948 | !! ** Purpose : Read or write RHG file in restart file |
|---|
| 949 | !! |
|---|
| 950 | !! ** Method : use of IOM library |
|---|
| 951 | !!---------------------------------------------------------------------- |
|---|
| 952 | CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag |
|---|
| 953 | INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step |
|---|
| 954 | ! |
|---|
| 955 | INTEGER :: iter ! local integer |
|---|
| 956 | INTEGER :: id1, id2, id3 ! local integers |
|---|
| 957 | !!---------------------------------------------------------------------- |
|---|
| 958 | ! |
|---|
| 959 | IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialize |
|---|
| 960 | ! ! --------------- |
|---|
| 961 | IF( ln_rstart ) THEN !* Read the restart file |
|---|
| 962 | ! |
|---|
| 963 | id1 = iom_varid( numrir, 'stress1_i' , ldstop = .FALSE. ) |
|---|
| 964 | id2 = iom_varid( numrir, 'stress2_i' , ldstop = .FALSE. ) |
|---|
| 965 | id3 = iom_varid( numrir, 'stress12_i', ldstop = .FALSE. ) |
|---|
| 966 | ! |
|---|
| 967 | IF( MIN( id1, id2, id3 ) > 0 ) THEN ! fields exist |
|---|
| 968 | CALL iom_get( numrir, jpdom_autoglo, 'stress1_i' , stress1_i ) |
|---|
| 969 | CALL iom_get( numrir, jpdom_autoglo, 'stress2_i' , stress2_i ) |
|---|
| 970 | CALL iom_get( numrir, jpdom_autoglo, 'stress12_i', stress12_i ) |
|---|
| 971 | ELSE ! start rheology from rest |
|---|
| 972 | IF(lwp) WRITE(numout,*) |
|---|
| 973 | IF(lwp) WRITE(numout,*) ' ==>>> previous run without rheology, set stresses to 0' |
|---|
| 974 | stress1_i (:,:) = 0._wp |
|---|
| 975 | stress2_i (:,:) = 0._wp |
|---|
| 976 | stress12_i(:,:) = 0._wp |
|---|
| 977 | ENDIF |
|---|
| 978 | ELSE !* Start from rest |
|---|
| 979 | IF(lwp) WRITE(numout,*) |
|---|
| 980 | IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set stresses to 0' |
|---|
| 981 | stress1_i (:,:) = 0._wp |
|---|
| 982 | stress2_i (:,:) = 0._wp |
|---|
| 983 | stress12_i(:,:) = 0._wp |
|---|
| 984 | ENDIF |
|---|
| 985 | ! |
|---|
| 986 | ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file |
|---|
| 987 | ! ! ------------------- |
|---|
| 988 | IF(lwp) WRITE(numout,*) '---- rhg-rst ----' |
|---|
| 989 | iter = kt + nn_fsbc - 1 ! ice restarts are written at kt == nitrst - nn_fsbc + 1 |
|---|
| 990 | ! |
|---|
| 991 | CALL iom_rstput( iter, nitrst, numriw, 'stress1_i' , stress1_i ) |
|---|
| 992 | CALL iom_rstput( iter, nitrst, numriw, 'stress2_i' , stress2_i ) |
|---|
| 993 | CALL iom_rstput( iter, nitrst, numriw, 'stress12_i', stress12_i ) |
|---|
| 994 | ! |
|---|
| 995 | ENDIF |
|---|
| 996 | ! |
|---|
| 997 | END SUBROUTINE rhg_evp_rst |
|---|
| 998 | |
|---|
| 999 | #else |
|---|
| 1000 | !!---------------------------------------------------------------------- |
|---|
| 1001 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 1002 | !!---------------------------------------------------------------------- |
|---|
| 1003 | #endif |
|---|
| 1004 | |
|---|
| 1005 | !!============================================================================== |
|---|
| 1006 | END MODULE icedyn_rhg_evp |
|---|
