| 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 icedyn_rdgrft ! sea-ice: ice strength |
|---|
| 29 | USE bdy_oce , ONLY : ln_bdy |
|---|
| 30 | USE bdyice |
|---|
| 31 | #if defined key_agrif |
|---|
| 32 | USE agrif_ice_interp |
|---|
| 33 | #endif |
|---|
| 34 | ! |
|---|
| 35 | USE in_out_manager ! I/O manager |
|---|
| 36 | USE iom ! I/O manager library |
|---|
| 37 | USE lib_mpp ! MPP library |
|---|
| 38 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
|---|
| 39 | USE lbclnk ! lateral boundary conditions (or mpp links) |
|---|
| 40 | USE prtctl ! Print control |
|---|
| 41 | |
|---|
| 42 | IMPLICIT NONE |
|---|
| 43 | PRIVATE |
|---|
| 44 | |
|---|
| 45 | PUBLIC ice_dyn_rhg_evp ! called by icedyn_rhg.F90 |
|---|
| 46 | PUBLIC rhg_evp_rst ! called by icedyn_rhg.F90 |
|---|
| 47 | |
|---|
| 48 | !! * Substitutions |
|---|
| 49 | # include "vectopt_loop_substitute.h90" |
|---|
| 50 | !!---------------------------------------------------------------------- |
|---|
| 51 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
|---|
| 52 | !! $Id$ |
|---|
| 53 | !! Software governed by the CeCILL license (see ./LICENSE) |
|---|
| 54 | !!---------------------------------------------------------------------- |
|---|
| 55 | CONTAINS |
|---|
| 56 | |
|---|
| 57 | SUBROUTINE ice_dyn_rhg_evp( kt, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i ) |
|---|
| 58 | !!------------------------------------------------------------------- |
|---|
| 59 | !! *** SUBROUTINE ice_dyn_rhg_evp *** |
|---|
| 60 | !! EVP-C-grid |
|---|
| 61 | !! |
|---|
| 62 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
|---|
| 63 | !! stress and sea-surface slope. Ice-ice interaction is described by |
|---|
| 64 | !! a non-linear elasto-viscous-plastic (EVP) law including shear |
|---|
| 65 | !! strength and a bulk rheology (Hunke and Dukowicz, 2002). |
|---|
| 66 | !! |
|---|
| 67 | !! The points in the C-grid look like this, dear reader |
|---|
| 68 | !! |
|---|
| 69 | !! (ji,jj) |
|---|
| 70 | !! | |
|---|
| 71 | !! | |
|---|
| 72 | !! (ji-1,jj) | (ji,jj) |
|---|
| 73 | !! --------- |
|---|
| 74 | !! | | |
|---|
| 75 | !! | (ji,jj) |------(ji,jj) |
|---|
| 76 | !! | | |
|---|
| 77 | !! --------- |
|---|
| 78 | !! (ji-1,jj-1) (ji,jj-1) |
|---|
| 79 | !! |
|---|
| 80 | !! ** Inputs : - wind forcing (stress), oceanic currents |
|---|
| 81 | !! ice total volume (vt_i) per unit area |
|---|
| 82 | !! snow total volume (vt_s) per unit area |
|---|
| 83 | !! |
|---|
| 84 | !! ** Action : - compute u_ice, v_ice : the components of the |
|---|
| 85 | !! sea-ice velocity vector |
|---|
| 86 | !! - compute delta_i, shear_i, divu_i, which are inputs |
|---|
| 87 | !! of the ice thickness distribution |
|---|
| 88 | !! |
|---|
| 89 | !! ** Steps : 0) compute mask at F point |
|---|
| 90 | !! 1) Compute ice snow mass, ice strength |
|---|
| 91 | !! 2) Compute wind, oceanic stresses, mass terms and |
|---|
| 92 | !! coriolis terms of the momentum equation |
|---|
| 93 | !! 3) Solve the momentum equation (iterative procedure) |
|---|
| 94 | !! 4) Recompute delta, shear and divergence |
|---|
| 95 | !! (which are inputs of the ITD) & store stress |
|---|
| 96 | !! for the next time step |
|---|
| 97 | !! 5) Diagnostics including charge ellipse |
|---|
| 98 | !! |
|---|
| 99 | !! ** Notes : There is the possibility to use aEVP from the nice work of Kimmritz et al. (2016 & 2017) |
|---|
| 100 | !! by setting up ln_aEVP=T (i.e. changing alpha and beta parameters). |
|---|
| 101 | !! This is an upgraded version of mEVP from Bouillon et al. 2013 |
|---|
| 102 | !! (i.e. more stable and better convergence) |
|---|
| 103 | !! |
|---|
| 104 | !! References : Hunke and Dukowicz, JPO97 |
|---|
| 105 | !! Bouillon et al., Ocean Modelling 2009 |
|---|
| 106 | !! Bouillon et al., Ocean Modelling 2013 |
|---|
| 107 | !! Kimmritz et al., Ocean Modelling 2016 & 2017 |
|---|
| 108 | !!------------------------------------------------------------------- |
|---|
| 109 | USE scoce, ONLY : z1_e1t0 => scr2D1, z1_e2t0 => scr2D2, & ! scale factors |
|---|
| 110 | zp_delt => scr2D3, & ! P/delta at T points |
|---|
| 111 | zbeta => scr2D4, & ! beta coef from Kimmritz 2017 |
|---|
| 112 | ! |
|---|
| 113 | zdt_m => scr2D5, & ! (dt / ice-snow_mass) on T points |
|---|
| 114 | zaU => scr2D6 , zaV => scr2D7, & ! ice fraction on U/V points |
|---|
| 115 | zmU_t => scr2D8, zmV_t => scr2D9, & ! (ice-snow_mass / dt) on U/V points |
|---|
| 116 | zmf => scr2D10, & ! coriolis parameter at T points |
|---|
| 117 | zTauU_ia => scr2D11, ztauV_ia => scr2D12, & ! ice-atm. stress at U-V points |
|---|
| 118 | zspgU => scr2D13, zspgV => scr2D14, & ! surface pressure gradient at U/V points |
|---|
| 119 | v_oceU => scr2D15, u_oceV => scr2D16, v_iceU => scr2D17, u_iceV => scr2D18, & ! ocean/ice u/v component on V/U points |
|---|
| 120 | zfU => scr2D19 , zfV => scr2D20, & ! internal stresses |
|---|
| 121 | ! |
|---|
| 122 | zds => scr2D21, & ! shear |
|---|
| 123 | zs1 => scr2D22, zs2 => scr2D23, zs12 => scr2D38, & ! stress tensor components |
|---|
| 124 | zu_ice => scr2D24, zv_ice => scr2D25, zresr => scr2D26, & ! check convergence |
|---|
| 125 | zpice => scr2D27, & ! array used for the calculation of ice surface slope: |
|---|
| 126 | ! ! ocean surface (ssh_m) if ice is not embedded |
|---|
| 127 | ! ! ice top surface if ice is embedded |
|---|
| 128 | zCorx => scr2D28, zCory => scr2D29, & ! Coriolis stress array |
|---|
| 129 | ztaux_oi => scr2D30, ztauy_oi => scr2D31, & ! Ocean-to-ice stress array |
|---|
| 130 | ! |
|---|
| 131 | zswitchU => scr2D32, zswitchV => scr2D33, & ! dummy arrays |
|---|
| 132 | zmaskU => scr2D34, zmaskV => scr2D35, & ! mask for ice presence |
|---|
| 133 | zfmask => scr2D36, zwf => scr2D37 ! mask at F points for the ice |
|---|
| 134 | |
|---|
| 135 | |
|---|
| 136 | |
|---|
| 137 | INTEGER , INTENT(in ) :: kt ! time step |
|---|
| 138 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: pstress1_i, pstress2_i, pstress12_i ! |
|---|
| 139 | REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i ! |
|---|
| 140 | !! |
|---|
| 141 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 142 | INTEGER :: jter ! local integers |
|---|
| 143 | ! |
|---|
| 144 | REAL(wp) :: zrhoco ! rau0 * rn_cio |
|---|
| 145 | REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling |
|---|
| 146 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
|---|
| 147 | REAL(wp) :: zalph1, z1_alph1, zalph2, z1_alph2 ! alpha coef from Bouillon 2009 or Kimmritz 2017 |
|---|
| 148 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV ! ice/snow mass |
|---|
| 149 | REAL(wp) :: zdelta, zp_delf, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars |
|---|
| 150 | REAL(wp) :: zTauO, zTauB, zTauE, zvel ! temporary scalars |
|---|
| 151 | ! |
|---|
| 152 | REAL(wp) :: zresm ! Maximal error on ice velocity |
|---|
| 153 | REAL(wp) :: zintb, zintn ! dummy argument |
|---|
| 154 | REAL(wp) :: zfac_x, zfac_y |
|---|
| 155 | REAL(wp) :: zshear, zdum1, zdum2 |
|---|
| 156 | ! |
|---|
| 157 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
|---|
| 158 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity equals ocean velocity |
|---|
| 159 | !! --- diags |
|---|
| 160 | REAL(wp), DIMENSION(jpi,jpj) :: zswi |
|---|
| 161 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig1, zsig2, zsig3 |
|---|
| 162 | !! --- SIMIP diags |
|---|
| 163 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_sig1 ! Average normal stress in sea ice |
|---|
| 164 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_sig2 ! Maximum shear stress in sea ice |
|---|
| 165 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_dssh_dx ! X-direction sea-surface tilt term (N/m2) |
|---|
| 166 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_dssh_dy ! X-direction sea-surface tilt term (N/m2) |
|---|
| 167 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_corstrx ! X-direction coriolis stress (N/m2) |
|---|
| 168 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_corstry ! Y-direction coriolis stress (N/m2) |
|---|
| 169 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_intstrx ! X-direction internal stress (N/m2) |
|---|
| 170 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_intstry ! Y-direction internal stress (N/m2) |
|---|
| 171 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_utau_oi ! X-direction ocean-ice stress |
|---|
| 172 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_vtau_oi ! Y-direction ocean-ice stress |
|---|
| 173 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice ! X-component of ice mass transport (kg/s) |
|---|
| 174 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_ice ! Y-component of ice mass transport (kg/s) |
|---|
| 175 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw ! X-component of snow mass transport (kg/s) |
|---|
| 176 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_snw ! Y-component of snow mass transport (kg/s) |
|---|
| 177 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp ! X-component of area transport (m2/s) |
|---|
| 178 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_yatrp ! Y-component of area transport (m2/s) |
|---|
| 179 | !!------------------------------------------------------------------- |
|---|
| 180 | |
|---|
| 181 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_evp: EVP sea-ice rheology' |
|---|
| 182 | ! |
|---|
| 183 | !!gm for Clem: OPTIMIZATION: I think zfmask can be computed one for all at the initialization.... |
|---|
| 184 | !------------------------------------------------------------------------------! |
|---|
| 185 | ! 0) mask at F points for the ice |
|---|
| 186 | !------------------------------------------------------------------------------! |
|---|
| 187 | ! ocean/land mask |
|---|
| 188 | DO jj = 1, jpjm1 |
|---|
| 189 | DO ji = 1, jpim1 ! NO vector opt. |
|---|
| 190 | zfmask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) |
|---|
| 191 | END DO |
|---|
| 192 | END DO |
|---|
| 193 | CALL lbc_lnk( zfmask, 'F', 1._wp ) |
|---|
| 194 | |
|---|
| 195 | ! Lateral boundary conditions on velocity (modify zfmask) |
|---|
| 196 | zwf(:,:) = zfmask(:,:) |
|---|
| 197 | DO jj = 2, jpjm1 |
|---|
| 198 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 199 | IF( zfmask(ji,jj) == 0._wp ) THEN |
|---|
| 200 | 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) ) ) |
|---|
| 201 | ENDIF |
|---|
| 202 | END DO |
|---|
| 203 | END DO |
|---|
| 204 | DO jj = 2, jpjm1 |
|---|
| 205 | IF( zfmask(1,jj) == 0._wp ) THEN |
|---|
| 206 | zfmask(1 ,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(2,jj), zwf(1,jj+1), zwf(1,jj-1) ) ) |
|---|
| 207 | ENDIF |
|---|
| 208 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
|---|
| 209 | zfmask(jpi,jj) = rn_ishlat * MIN( 1._wp , MAX( zwf(jpi,jj+1), zwf(jpim1,jj), zwf(jpi,jj-1) ) ) |
|---|
| 210 | ENDIF |
|---|
| 211 | END DO |
|---|
| 212 | DO ji = 2, jpim1 |
|---|
| 213 | IF( zfmask(ji,1) == 0._wp ) THEN |
|---|
| 214 | zfmask(ji,1 ) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,1), zwf(ji,2), zwf(ji-1,1) ) ) |
|---|
| 215 | ENDIF |
|---|
| 216 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
|---|
| 217 | zfmask(ji,jpj) = rn_ishlat * MIN( 1._wp , MAX( zwf(ji+1,jpj), zwf(ji-1,jpj), zwf(ji,jpjm1) ) ) |
|---|
| 218 | ENDIF |
|---|
| 219 | END DO |
|---|
| 220 | CALL lbc_lnk( zfmask, 'F', 1._wp ) |
|---|
| 221 | |
|---|
| 222 | !------------------------------------------------------------------------------! |
|---|
| 223 | ! 1) define some variables and initialize arrays |
|---|
| 224 | !------------------------------------------------------------------------------! |
|---|
| 225 | zrhoco = rau0 * rn_cio |
|---|
| 226 | |
|---|
| 227 | ! ecc2: square of yield ellipse eccenticrity |
|---|
| 228 | ecc2 = rn_ecc * rn_ecc |
|---|
| 229 | z1_ecc2 = 1._wp / ecc2 |
|---|
| 230 | |
|---|
| 231 | ! Time step for subcycling |
|---|
| 232 | zdtevp = rdt_ice / REAL( nn_nevp ) |
|---|
| 233 | z1_dtevp = 1._wp / zdtevp |
|---|
| 234 | |
|---|
| 235 | ! alpha parameters (Bouillon 2009) |
|---|
| 236 | IF( .NOT. ln_aEVP ) THEN |
|---|
| 237 | zalph1 = ( 2._wp * rn_relast * rdt_ice ) * z1_dtevp |
|---|
| 238 | zalph2 = zalph1 * z1_ecc2 |
|---|
| 239 | |
|---|
| 240 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 241 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
|---|
| 242 | ENDIF |
|---|
| 243 | |
|---|
| 244 | ! Initialise stress tensor |
|---|
| 245 | zs1 (:,:) = pstress1_i (:,:) |
|---|
| 246 | zs2 (:,:) = pstress2_i (:,:) |
|---|
| 247 | zs12(:,:) = pstress12_i(:,:) |
|---|
| 248 | |
|---|
| 249 | ! Ice strength |
|---|
| 250 | CALL ice_strength |
|---|
| 251 | |
|---|
| 252 | ! scale factors |
|---|
| 253 | DO jj = 2, jpjm1 |
|---|
| 254 | DO ji = fs_2, fs_jpim1 |
|---|
| 255 | z1_e1t0(ji,jj) = 1._wp / ( e1t(ji+1,jj ) + e1t(ji,jj ) ) |
|---|
| 256 | z1_e2t0(ji,jj) = 1._wp / ( e2t(ji ,jj+1) + e2t(ji,jj ) ) |
|---|
| 257 | END DO |
|---|
| 258 | END DO |
|---|
| 259 | |
|---|
| 260 | ! |
|---|
| 261 | !------------------------------------------------------------------------------! |
|---|
| 262 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
|---|
| 263 | !------------------------------------------------------------------------------! |
|---|
| 264 | |
|---|
| 265 | IF( ln_ice_embd ) THEN !== embedded sea ice: compute representative ice top surface ==! |
|---|
| 266 | ! |
|---|
| 267 | ! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[n/nn_fsbc], n=0,nn_fsbc-1} |
|---|
| 268 | ! = (1/nn_fsbc)^2 * {SUM[n] , n=0,nn_fsbc-1} |
|---|
| 269 | zintn = REAL( nn_fsbc - 1 ) / REAL( nn_fsbc ) * 0.5_wp |
|---|
| 270 | ! |
|---|
| 271 | ! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[1-n/nn_fsbc], n=0,nn_fsbc-1} |
|---|
| 272 | ! = (1/nn_fsbc)^2 * (nn_fsbc^2 - {SUM[n], n=0,nn_fsbc-1}) |
|---|
| 273 | zintb = REAL( nn_fsbc + 1 ) / REAL( nn_fsbc ) * 0.5_wp |
|---|
| 274 | ! |
|---|
| 275 | zpice(:,:) = ssh_m(:,:) + ( zintn * snwice_mass(:,:) + zintb * snwice_mass_b(:,:) ) * r1_rau0 |
|---|
| 276 | ! |
|---|
| 277 | ELSE !== non-embedded sea ice: use ocean surface for slope calculation ==! |
|---|
| 278 | zpice(:,:) = ssh_m(:,:) |
|---|
| 279 | ENDIF |
|---|
| 280 | |
|---|
| 281 | DO jj = 2, jpjm1 |
|---|
| 282 | DO ji = fs_2, fs_jpim1 |
|---|
| 283 | |
|---|
| 284 | ! ice fraction at U-V points |
|---|
| 285 | 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) |
|---|
| 286 | 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) |
|---|
| 287 | |
|---|
| 288 | ! Ice/snow mass at U-V points |
|---|
| 289 | zm1 = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) ) |
|---|
| 290 | zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) ) |
|---|
| 291 | zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) ) |
|---|
| 292 | zmassU = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1) |
|---|
| 293 | zmassV = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 294 | |
|---|
| 295 | ! Ocean currents at U-V points |
|---|
| 296 | v_oceU(ji,jj) = 0.5_wp * ( ( v_oce(ji ,jj) + v_oce(ji ,jj-1) ) * e1t(ji+1,jj) & |
|---|
| 297 | & + ( v_oce(ji+1,jj) + v_oce(ji+1,jj-1) ) * e1t(ji ,jj) ) * z1_e1t0(ji,jj) * umask(ji,jj,1) |
|---|
| 298 | |
|---|
| 299 | u_oceV(ji,jj) = 0.5_wp * ( ( u_oce(ji,jj ) + u_oce(ji-1,jj ) ) * e2t(ji,jj+1) & |
|---|
| 300 | & + ( u_oce(ji,jj+1) + u_oce(ji-1,jj+1) ) * e2t(ji,jj ) ) * z1_e2t0(ji,jj) * vmask(ji,jj,1) |
|---|
| 301 | |
|---|
| 302 | ! Coriolis at T points (m*f) |
|---|
| 303 | zmf(ji,jj) = zm1 * ff_t(ji,jj) |
|---|
| 304 | |
|---|
| 305 | ! dt/m at T points (for alpha and beta coefficients) |
|---|
| 306 | zdt_m(ji,jj) = zdtevp / MAX( zm1, zmmin ) |
|---|
| 307 | |
|---|
| 308 | ! m/dt |
|---|
| 309 | zmU_t(ji,jj) = zmassU * z1_dtevp |
|---|
| 310 | zmV_t(ji,jj) = zmassV * z1_dtevp |
|---|
| 311 | |
|---|
| 312 | ! Drag ice-atm. |
|---|
| 313 | zTauU_ia(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj) |
|---|
| 314 | zTauV_ia(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj) |
|---|
| 315 | |
|---|
| 316 | ! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points |
|---|
| 317 | zspgU(ji,jj) = - zmassU * grav * ( zpice(ji+1,jj) - zpice(ji,jj) ) * r1_e1u(ji,jj) |
|---|
| 318 | zspgV(ji,jj) = - zmassV * grav * ( zpice(ji,jj+1) - zpice(ji,jj) ) * r1_e2v(ji,jj) |
|---|
| 319 | |
|---|
| 320 | ! masks |
|---|
| 321 | zmaskU(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
|---|
| 322 | zmaskV(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
|---|
| 323 | |
|---|
| 324 | ! switches |
|---|
| 325 | zswitchU(ji,jj) = MAX( 0._wp, SIGN( 1._wp, zmassU - zmmin ) ) ! 0 if ice mass < zmmin |
|---|
| 326 | zswitchV(ji,jj) = MAX( 0._wp, SIGN( 1._wp, zmassV - zmmin ) ) ! 0 if ice mass < zmmin |
|---|
| 327 | |
|---|
| 328 | END DO |
|---|
| 329 | END DO |
|---|
| 330 | CALL lbc_lnk_multi( zmf, 'T', 1., zdt_m, 'T', 1. ) |
|---|
| 331 | ! |
|---|
| 332 | !------------------------------------------------------------------------------! |
|---|
| 333 | ! 3) Solution of the momentum equation, iterative procedure |
|---|
| 334 | !------------------------------------------------------------------------------! |
|---|
| 335 | ! |
|---|
| 336 | ! !----------------------! |
|---|
| 337 | DO jter = 1 , nn_nevp ! loop over jter ! |
|---|
| 338 | ! !----------------------! |
|---|
| 339 | IF(ln_ctl) THEN ! Convergence test |
|---|
| 340 | DO jj = 1, jpjm1 |
|---|
| 341 | zu_ice(:,jj) = u_ice(:,jj) ! velocity at previous time step |
|---|
| 342 | zv_ice(:,jj) = v_ice(:,jj) |
|---|
| 343 | END DO |
|---|
| 344 | ENDIF |
|---|
| 345 | |
|---|
| 346 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
|---|
| 347 | 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 |
|---|
| 348 | DO ji = 1, jpim1 |
|---|
| 349 | |
|---|
| 350 | ! shear at F points |
|---|
| 351 | 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) & |
|---|
| 352 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 353 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 354 | |
|---|
| 355 | END DO |
|---|
| 356 | END DO |
|---|
| 357 | CALL lbc_lnk( zds, 'F', 1. ) |
|---|
| 358 | |
|---|
| 359 | DO jj = 2, jpj ! loop to jpi,jpj to avoid making a communication for zs1,zs2,zs12 |
|---|
| 360 | DO ji = 2, jpi ! no vector loop |
|---|
| 361 | |
|---|
| 362 | ! shear**2 at T points (doc eq. A16) |
|---|
| 363 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 364 | & + 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) & |
|---|
| 365 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 366 | |
|---|
| 367 | ! divergence at T points |
|---|
| 368 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 369 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 370 | & ) * r1_e1e2t(ji,jj) |
|---|
| 371 | zdiv2 = zdiv * zdiv |
|---|
| 372 | |
|---|
| 373 | ! tension at T points |
|---|
| 374 | 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) & |
|---|
| 375 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 376 | & ) * r1_e1e2t(ji,jj) |
|---|
| 377 | zdt2 = zdt * zdt |
|---|
| 378 | |
|---|
| 379 | ! delta at T points |
|---|
| 380 | zdelta = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 381 | |
|---|
| 382 | ! P/delta at T points |
|---|
| 383 | zp_delt(ji,jj) = strength(ji,jj) / ( zdelta + rn_creepl ) |
|---|
| 384 | |
|---|
| 385 | ! alpha & beta for aEVP |
|---|
| 386 | ! gamma = 0.5*P/(delta+creepl) * (c*pi)**2/Area * dt/m |
|---|
| 387 | ! alpha = beta = sqrt(4*gamma) |
|---|
| 388 | IF( ln_aEVP ) THEN |
|---|
| 389 | zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 390 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
|---|
| 391 | zalph2 = zalph1 |
|---|
| 392 | z1_alph2 = z1_alph1 |
|---|
| 393 | ENDIF |
|---|
| 394 | |
|---|
| 395 | ! stress at T points |
|---|
| 396 | zs1(ji,jj) = ( zs1(ji,jj) * zalph1 + zp_delt(ji,jj) * ( zdiv - zdelta ) ) * z1_alph1 |
|---|
| 397 | zs2(ji,jj) = ( zs2(ji,jj) * zalph2 + zp_delt(ji,jj) * ( zdt * z1_ecc2 ) ) * z1_alph2 |
|---|
| 398 | |
|---|
| 399 | END DO |
|---|
| 400 | END DO |
|---|
| 401 | CALL lbc_lnk( zp_delt, 'T', 1. ) |
|---|
| 402 | |
|---|
| 403 | IF( ln_aEVP ) THEN |
|---|
| 404 | DO jj = 1, jpjm1 |
|---|
| 405 | DO ji = 1, jpim1 |
|---|
| 406 | |
|---|
| 407 | ! alpha & beta for aEVP |
|---|
| 408 | zalph2 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) ) |
|---|
| 409 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
|---|
| 410 | zbeta(ji,jj) = zalph2 |
|---|
| 411 | |
|---|
| 412 | ! P/delta at F points |
|---|
| 413 | 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) ) |
|---|
| 414 | |
|---|
| 415 | ! stress at F points |
|---|
| 416 | zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 ) * 0.5_wp ) * z1_alph2 |
|---|
| 417 | |
|---|
| 418 | END DO |
|---|
| 419 | END DO |
|---|
| 420 | ELSE |
|---|
| 421 | DO jj = 1, jpjm1 |
|---|
| 422 | DO ji = 1, jpim1 |
|---|
| 423 | |
|---|
| 424 | ! P/delta at F points |
|---|
| 425 | 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) ) |
|---|
| 426 | |
|---|
| 427 | ! stress at F points |
|---|
| 428 | zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 ) * 0.5_wp ) * z1_alph2 |
|---|
| 429 | |
|---|
| 430 | END DO |
|---|
| 431 | END DO |
|---|
| 432 | ENDIF |
|---|
| 433 | |
|---|
| 434 | ! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- ! |
|---|
| 435 | DO jj = 2, jpjm1 |
|---|
| 436 | DO ji = fs_2, fs_jpim1 |
|---|
| 437 | ! !--- U points |
|---|
| 438 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
|---|
| 439 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
|---|
| 440 | & ) * r1_e2u(ji,jj) & |
|---|
| 441 | & + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
|---|
| 442 | & ) * 2._wp * r1_e1u(ji,jj) & |
|---|
| 443 | & ) * r1_e1e2u(ji,jj) |
|---|
| 444 | ! |
|---|
| 445 | ! !--- V points |
|---|
| 446 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
|---|
| 447 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 448 | & ) * r1_e1v(ji,jj) & |
|---|
| 449 | & + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
|---|
| 450 | & ) * 2._wp * r1_e2v(ji,jj) & |
|---|
| 451 | & ) * r1_e1e2v(ji,jj) |
|---|
| 452 | ! |
|---|
| 453 | ! !--- u_ice at V point |
|---|
| 454 | u_iceV(ji,jj) = 0.5_wp * ( ( u_ice(ji,jj ) + u_ice(ji-1,jj ) ) * e2t(ji,jj+1) & |
|---|
| 455 | & + ( u_ice(ji,jj+1) + u_ice(ji-1,jj+1) ) * e2t(ji,jj ) ) * z1_e2t0(ji,jj) * vmask(ji,jj,1) |
|---|
| 456 | ! |
|---|
| 457 | ! !--- v_ice at U point |
|---|
| 458 | v_iceU(ji,jj) = 0.5_wp * ( ( v_ice(ji ,jj) + v_ice(ji ,jj-1) ) * e1t(ji+1,jj) & |
|---|
| 459 | & + ( v_ice(ji+1,jj) + v_ice(ji+1,jj-1) ) * e1t(ji ,jj) ) * z1_e1t0(ji,jj) * umask(ji,jj,1) |
|---|
| 460 | END DO |
|---|
| 461 | END DO |
|---|
| 462 | ! |
|---|
| 463 | ! --- Computation of ice velocity --- ! |
|---|
| 464 | ! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta vary as in Kimmritz 2016 & 2017 |
|---|
| 465 | ! Bouillon et al. 2009 (eq 34-35) => stable |
|---|
| 466 | IF( MOD(jter,2) == 0 ) THEN ! even iterations |
|---|
| 467 | ! |
|---|
| 468 | DO jj = 2, jpjm1 |
|---|
| 469 | DO ji = fs_2, fs_jpim1 |
|---|
| 470 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 471 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 472 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 473 | ! !--- Ocean-to-Ice stress |
|---|
| 474 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 475 | ! |
|---|
| 476 | ! !--- tau_bottom/v_ice |
|---|
| 477 | zvel = MAX( zepsi, SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) ) |
|---|
| 478 | zTauB = - tau_icebfr(ji,jj) / zvel |
|---|
| 479 | ! |
|---|
| 480 | ! !--- Coriolis at V-points (energy conserving formulation) |
|---|
| 481 | zCory(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 482 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 483 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 484 | ! |
|---|
| 485 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 486 | zTauE = zfV(ji,jj) + zTauV_ia(ji,jj) + zCory(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 487 | ! |
|---|
| 488 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 489 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, ztauE - tau_icebfr(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 490 | ! |
|---|
| 491 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 492 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbeta(ji,jj) * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 493 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 494 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 495 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 496 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 497 | & ) * zmaskV(ji,jj) |
|---|
| 498 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 499 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 500 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 501 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 502 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 503 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 504 | & ) * zmaskV(ji,jj) |
|---|
| 505 | ENDIF |
|---|
| 506 | END DO |
|---|
| 507 | END DO |
|---|
| 508 | CALL lbc_lnk( v_ice, 'V', -1. ) |
|---|
| 509 | ! |
|---|
| 510 | #if defined key_agrif |
|---|
| 511 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 512 | CALL agrif_interp_ice( 'V' ) |
|---|
| 513 | #endif |
|---|
| 514 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 515 | ! |
|---|
| 516 | DO jj = 2, jpjm1 |
|---|
| 517 | DO ji = fs_2, fs_jpim1 |
|---|
| 518 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 519 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 520 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 521 | ! !--- Ocean-to-Ice stress |
|---|
| 522 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 523 | ! |
|---|
| 524 | ! !--- tau_bottom/u_ice |
|---|
| 525 | zvel = MAX( zepsi, SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) ) |
|---|
| 526 | zTauB = - tau_icebfr(ji,jj) / zvel |
|---|
| 527 | ! |
|---|
| 528 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 529 | zCorx(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 530 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 531 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 532 | ! |
|---|
| 533 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 534 | zTauE = zfU(ji,jj) + zTauU_ia(ji,jj) + zCorx(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 535 | ! |
|---|
| 536 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 537 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, ztauE - tau_icebfr(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 538 | ! |
|---|
| 539 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 540 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbeta(ji,jj) * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 541 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 542 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 543 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 544 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 545 | & ) * zmaskU(ji,jj) |
|---|
| 546 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 547 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 548 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 549 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 550 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 551 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 552 | & ) * zmaskU(ji,jj) |
|---|
| 553 | ENDIF |
|---|
| 554 | END DO |
|---|
| 555 | END DO |
|---|
| 556 | CALL lbc_lnk( u_ice, 'U', -1. ) |
|---|
| 557 | ! |
|---|
| 558 | #if defined key_agrif |
|---|
| 559 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 560 | CALL agrif_interp_ice( 'U' ) |
|---|
| 561 | #endif |
|---|
| 562 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 563 | ! |
|---|
| 564 | ELSE ! odd iterations |
|---|
| 565 | ! |
|---|
| 566 | DO jj = 2, jpjm1 |
|---|
| 567 | DO ji = fs_2, fs_jpim1 |
|---|
| 568 | ! !--- tau_io/(u_oce - u_ice) |
|---|
| 569 | zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
|---|
| 570 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
|---|
| 571 | ! !--- Ocean-to-Ice stress |
|---|
| 572 | ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
|---|
| 573 | ! |
|---|
| 574 | ! !--- tau_bottom/u_ice |
|---|
| 575 | zvel = MAX( zepsi, SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) ) ) |
|---|
| 576 | zTauB = - tau_icebfr(ji,jj) / zvel |
|---|
| 577 | ! |
|---|
| 578 | ! !--- Coriolis at U-points (energy conserving formulation) |
|---|
| 579 | zCorx(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * & |
|---|
| 580 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
|---|
| 581 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
|---|
| 582 | ! |
|---|
| 583 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 584 | zTauE = zfU(ji,jj) + zTauU_ia(ji,jj) + zCorx(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj) |
|---|
| 585 | ! |
|---|
| 586 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 587 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, ztauE - tau_icebfr(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 588 | ! |
|---|
| 589 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 590 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbeta(ji,jj) * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 591 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 592 | & ) / MAX( zepsi, zmU_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 593 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 594 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 595 | & ) * zmaskU(ji,jj) |
|---|
| 596 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 597 | u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity |
|---|
| 598 | & + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 599 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 600 | & + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 601 | & ) * zswitchU(ji,jj) + u_oce(ji,jj) * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 602 | & ) * zmaskU(ji,jj) |
|---|
| 603 | ENDIF |
|---|
| 604 | END DO |
|---|
| 605 | END DO |
|---|
| 606 | CALL lbc_lnk( u_ice, 'U', -1. ) |
|---|
| 607 | ! |
|---|
| 608 | #if defined key_agrif |
|---|
| 609 | !! CALL agrif_interp_ice( 'U', jter, nn_nevp ) |
|---|
| 610 | CALL agrif_interp_ice( 'U' ) |
|---|
| 611 | #endif |
|---|
| 612 | IF( ln_bdy ) CALL bdy_ice_dyn( 'U' ) |
|---|
| 613 | ! |
|---|
| 614 | DO jj = 2, jpjm1 |
|---|
| 615 | DO ji = fs_2, fs_jpim1 |
|---|
| 616 | ! !--- tau_io/(v_oce - v_ice) |
|---|
| 617 | zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
|---|
| 618 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
|---|
| 619 | ! !--- Ocean-to-Ice stress |
|---|
| 620 | ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
|---|
| 621 | ! |
|---|
| 622 | ! !--- tau_bottom/v_ice |
|---|
| 623 | zvel = MAX( zepsi, SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) ) ) |
|---|
| 624 | ztauB = - tau_icebfr(ji,jj) / zvel |
|---|
| 625 | ! |
|---|
| 626 | ! !--- Coriolis at v-points (energy conserving formulation) |
|---|
| 627 | zCory(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * & |
|---|
| 628 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
|---|
| 629 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
|---|
| 630 | ! |
|---|
| 631 | ! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
|---|
| 632 | zTauE = zfV(ji,jj) + zTauV_ia(ji,jj) + zCory(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj) |
|---|
| 633 | ! |
|---|
| 634 | ! !--- landfast switch => 0 = static friction ; 1 = sliding friction |
|---|
| 635 | rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zTauE - tau_icebfr(ji,jj) ) - SIGN( 1._wp, zTauE ) ) ) |
|---|
| 636 | ! |
|---|
| 637 | IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017) |
|---|
| 638 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbeta(ji,jj) * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity |
|---|
| 639 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 640 | & ) / MAX( zepsi, zmV_t(ji,jj) * ( zbeta(ji,jj) + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 641 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 642 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 643 | & ) * zmaskV(ji,jj) |
|---|
| 644 | ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009) |
|---|
| 645 | v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity |
|---|
| 646 | & + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
|---|
| 647 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast |
|---|
| 648 | & + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lfrelax ) & ! static friction => slow decrease to v=0 |
|---|
| 649 | & ) * zswitchV(ji,jj) + v_oce(ji,jj) * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
|---|
| 650 | & ) * zmaskV(ji,jj) |
|---|
| 651 | ENDIF |
|---|
| 652 | END DO |
|---|
| 653 | END DO |
|---|
| 654 | CALL lbc_lnk( v_ice, 'V', -1. ) |
|---|
| 655 | ! |
|---|
| 656 | #if defined key_agrif |
|---|
| 657 | !! CALL agrif_interp_ice( 'V', jter, nn_nevp ) |
|---|
| 658 | CALL agrif_interp_ice( 'V' ) |
|---|
| 659 | #endif |
|---|
| 660 | IF( ln_bdy ) CALL bdy_ice_dyn( 'V' ) |
|---|
| 661 | ! |
|---|
| 662 | ENDIF |
|---|
| 663 | |
|---|
| 664 | IF(ln_ctl) THEN ! Convergence test |
|---|
| 665 | DO jj = 2 , jpjm1 |
|---|
| 666 | zresr(:,jj) = MAX( ABS( u_ice(:,jj) - zu_ice(:,jj) ), ABS( v_ice(:,jj) - zv_ice(:,jj) ) ) |
|---|
| 667 | END DO |
|---|
| 668 | zresm = MAXVAL( zresr( 1:jpi, 2:jpjm1 ) ) |
|---|
| 669 | IF( lk_mpp ) CALL mpp_max( zresm ) ! max over the global domain |
|---|
| 670 | ENDIF |
|---|
| 671 | ! |
|---|
| 672 | ! ! ==================== ! |
|---|
| 673 | END DO ! end loop over jter ! |
|---|
| 674 | ! ! ==================== ! |
|---|
| 675 | ! |
|---|
| 676 | !------------------------------------------------------------------------------! |
|---|
| 677 | ! 4) Recompute delta, shear and div (inputs for mechanical redistribution) |
|---|
| 678 | !------------------------------------------------------------------------------! |
|---|
| 679 | DO jj = 1, jpjm1 |
|---|
| 680 | DO ji = 1, jpim1 |
|---|
| 681 | |
|---|
| 682 | ! shear at F points |
|---|
| 683 | 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) & |
|---|
| 684 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
|---|
| 685 | & ) * r1_e1e2f(ji,jj) * zfmask(ji,jj) |
|---|
| 686 | |
|---|
| 687 | END DO |
|---|
| 688 | END DO |
|---|
| 689 | |
|---|
| 690 | DO jj = 2, jpjm1 |
|---|
| 691 | DO ji = 2, jpim1 ! no vector loop |
|---|
| 692 | |
|---|
| 693 | ! tension**2 at T points |
|---|
| 694 | 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) & |
|---|
| 695 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
|---|
| 696 | & ) * r1_e1e2t(ji,jj) |
|---|
| 697 | zdt2 = zdt * zdt |
|---|
| 698 | |
|---|
| 699 | ! shear**2 at T points (doc eq. A16) |
|---|
| 700 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) & |
|---|
| 701 | & + 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) & |
|---|
| 702 | & ) * 0.25_wp * r1_e1e2t(ji,jj) |
|---|
| 703 | |
|---|
| 704 | ! shear at T points |
|---|
| 705 | pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
|---|
| 706 | |
|---|
| 707 | ! divergence at T points |
|---|
| 708 | pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
|---|
| 709 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
|---|
| 710 | & ) * r1_e1e2t(ji,jj) |
|---|
| 711 | |
|---|
| 712 | ! delta at T points |
|---|
| 713 | zdelta = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) |
|---|
| 714 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 |
|---|
| 715 | pdelta_i(ji,jj) = zdelta + rn_creepl * rswitch |
|---|
| 716 | |
|---|
| 717 | END DO |
|---|
| 718 | END DO |
|---|
| 719 | CALL lbc_lnk_multi( pshear_i, 'T', 1., pdivu_i, 'T', 1., pdelta_i, 'T', 1. ) |
|---|
| 720 | |
|---|
| 721 | ! --- Store the stress tensor for the next time step --- ! |
|---|
| 722 | CALL lbc_lnk_multi( zs1, 'T', 1., zs2, 'T', 1., zs12, 'F', 1. ) |
|---|
| 723 | pstress1_i (:,:) = zs1 (:,:) |
|---|
| 724 | pstress2_i (:,:) = zs2 (:,:) |
|---|
| 725 | pstress12_i(:,:) = zs12(:,:) |
|---|
| 726 | ! |
|---|
| 727 | |
|---|
| 728 | !------------------------------------------------------------------------------! |
|---|
| 729 | ! 5) diagnostics |
|---|
| 730 | !------------------------------------------------------------------------------! |
|---|
| 731 | DO jj = 1, jpj |
|---|
| 732 | DO ji = 1, jpi |
|---|
| 733 | zswi(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice, 0 if no ice |
|---|
| 734 | END DO |
|---|
| 735 | END DO |
|---|
| 736 | |
|---|
| 737 | ! --- divergence, shear and strength --- ! |
|---|
| 738 | IF( iom_use('icediv') ) CALL iom_put( "icediv" , pdivu_i (:,:) * zswi(:,:) ) ! divergence |
|---|
| 739 | IF( iom_use('iceshe') ) CALL iom_put( "iceshe" , pshear_i(:,:) * zswi(:,:) ) ! shear |
|---|
| 740 | IF( iom_use('icestr') ) CALL iom_put( "icestr" , strength(:,:) * zswi(:,:) ) ! Ice strength |
|---|
| 741 | |
|---|
| 742 | ! --- charge ellipse --- ! |
|---|
| 743 | IF( iom_use('isig1') .OR. iom_use('isig2') .OR. iom_use('isig3') ) THEN |
|---|
| 744 | ! |
|---|
| 745 | ALLOCATE( zsig1(jpi,jpj) , zsig2(jpi,jpj) , zsig3(jpi,jpj) ) |
|---|
| 746 | ! |
|---|
| 747 | DO jj = 2, jpjm1 |
|---|
| 748 | DO ji = 2, jpim1 |
|---|
| 749 | zdum1 = ( zswi(ji-1,jj) * pstress12_i(ji-1,jj) + zswi(ji ,jj-1) * pstress12_i(ji ,jj-1) + & ! stress12_i at T-point |
|---|
| 750 | & zswi(ji ,jj) * pstress12_i(ji ,jj) + zswi(ji-1,jj-1) * pstress12_i(ji-1,jj-1) ) & |
|---|
| 751 | & / MAX( 1._wp, zswi(ji-1,jj) + zswi(ji,jj-1) + zswi(ji,jj) + zswi(ji-1,jj-1) ) |
|---|
| 752 | |
|---|
| 753 | zshear = SQRT( pstress2_i(ji,jj) * pstress2_i(ji,jj) + 4._wp * zdum1 * zdum1 ) ! shear stress |
|---|
| 754 | |
|---|
| 755 | zdum2 = zswi(ji,jj) / MAX( 1._wp, strength(ji,jj) ) |
|---|
| 756 | |
|---|
| 757 | !! zsig1(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) + zshear ) ! principal stress (y-direction, see Hunke & Dukowicz 2002) |
|---|
| 758 | !! zsig2(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) - zshear ) ! principal stress (x-direction, see Hunke & Dukowicz 2002) |
|---|
| 759 | !! 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 |
|---|
| 760 | !! ! (scheme converges if this value is ~1, see Bouillon et al 2009 (eq. 11)) |
|---|
| 761 | zsig1(ji,jj) = 0.5_wp * zdum2 * ( pstress1_i(ji,jj) ) ! compressive stress, see Bouillon et al. 2015 |
|---|
| 762 | zsig2(ji,jj) = 0.5_wp * zdum2 * ( zshear ) ! shear stress |
|---|
| 763 | zsig3(ji,jj) = zdum2**2 * ( ( pstress1_i(ji,jj) + strength(ji,jj) )**2 + ( rn_ecc * zshear )**2 ) |
|---|
| 764 | END DO |
|---|
| 765 | END DO |
|---|
| 766 | CALL lbc_lnk_multi( zsig1, 'T', 1., zsig2, 'T', 1., zsig3, 'T', 1. ) |
|---|
| 767 | ! |
|---|
| 768 | IF( iom_use('isig1') ) CALL iom_put( "isig1" , zsig1 ) |
|---|
| 769 | IF( iom_use('isig2') ) CALL iom_put( "isig2" , zsig2 ) |
|---|
| 770 | IF( iom_use('isig3') ) CALL iom_put( "isig3" , zsig3 ) |
|---|
| 771 | ! |
|---|
| 772 | DEALLOCATE( zsig1 , zsig2 , zsig3 ) |
|---|
| 773 | ENDIF |
|---|
| 774 | |
|---|
| 775 | ! --- SIMIP --- ! |
|---|
| 776 | IF ( iom_use( 'normstr' ) .OR. iom_use( 'sheastr' ) .OR. iom_use( 'dssh_dx' ) .OR. iom_use( 'dssh_dy' ) .OR. & |
|---|
| 777 | & iom_use( 'corstrx' ) .OR. iom_use( 'corstry' ) .OR. iom_use( 'intstrx' ) .OR. iom_use( 'intstry' ) .OR. & |
|---|
| 778 | & iom_use( 'utau_oi' ) .OR. iom_use( 'vtau_oi' ) .OR. iom_use( 'xmtrpice' ) .OR. iom_use( 'ymtrpice' ) .OR. & |
|---|
| 779 | & iom_use( 'xmtrpsnw' ) .OR. iom_use( 'ymtrpsnw' ) .OR. iom_use( 'xatrp' ) .OR. iom_use( 'yatrp' ) ) THEN |
|---|
| 780 | |
|---|
| 781 | ALLOCATE( zdiag_sig1 (jpi,jpj) , zdiag_sig2 (jpi,jpj) , zdiag_dssh_dx (jpi,jpj) , zdiag_dssh_dy (jpi,jpj) , & |
|---|
| 782 | & zdiag_corstrx (jpi,jpj) , zdiag_corstry (jpi,jpj) , zdiag_intstrx (jpi,jpj) , zdiag_intstry (jpi,jpj) , & |
|---|
| 783 | & zdiag_utau_oi (jpi,jpj) , zdiag_vtau_oi (jpi,jpj) , zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , & |
|---|
| 784 | & zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp (jpi,jpj) , zdiag_yatrp (jpi,jpj) ) |
|---|
| 785 | |
|---|
| 786 | DO jj = 2, jpjm1 |
|---|
| 787 | DO ji = 2, jpim1 |
|---|
| 788 | rswitch = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice, 0 if no ice |
|---|
| 789 | |
|---|
| 790 | ! Stress tensor invariants (normal and shear stress N/m) |
|---|
| 791 | zdiag_sig1(ji,jj) = ( zs1(ji,jj) + zs2(ji,jj) ) * rswitch ! normal stress |
|---|
| 792 | zdiag_sig2(ji,jj) = SQRT( ( zs1(ji,jj) - zs2(ji,jj) )**2 + 4*zs12(ji,jj)**2 ) * rswitch ! shear stress |
|---|
| 793 | |
|---|
| 794 | ! Stress terms of the momentum equation (N/m2) |
|---|
| 795 | zdiag_dssh_dx(ji,jj) = zspgU(ji,jj) * rswitch ! sea surface slope stress term |
|---|
| 796 | zdiag_dssh_dy(ji,jj) = zspgV(ji,jj) * rswitch |
|---|
| 797 | |
|---|
| 798 | zdiag_corstrx(ji,jj) = zCorx(ji,jj) * rswitch ! Coriolis stress term |
|---|
| 799 | zdiag_corstry(ji,jj) = zCory(ji,jj) * rswitch |
|---|
| 800 | |
|---|
| 801 | zdiag_intstrx(ji,jj) = zfU(ji,jj) * rswitch ! internal stress term |
|---|
| 802 | zdiag_intstry(ji,jj) = zfV(ji,jj) * rswitch |
|---|
| 803 | |
|---|
| 804 | zdiag_utau_oi(ji,jj) = ztaux_oi(ji,jj) * rswitch ! oceanic stress |
|---|
| 805 | zdiag_vtau_oi(ji,jj) = ztauy_oi(ji,jj) * rswitch |
|---|
| 806 | |
|---|
| 807 | ! 2D ice mass, snow mass, area transport arrays (X, Y) |
|---|
| 808 | zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * rswitch |
|---|
| 809 | zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * rswitch |
|---|
| 810 | |
|---|
| 811 | zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component |
|---|
| 812 | zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- '' |
|---|
| 813 | |
|---|
| 814 | zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component |
|---|
| 815 | zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- '' |
|---|
| 816 | |
|---|
| 817 | zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component |
|---|
| 818 | zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- '' |
|---|
| 819 | |
|---|
| 820 | END DO |
|---|
| 821 | END DO |
|---|
| 822 | |
|---|
| 823 | CALL lbc_lnk_multi( zdiag_sig1 , 'T', 1., zdiag_sig2 , 'T', 1., & |
|---|
| 824 | & zdiag_dssh_dx, 'U', -1., zdiag_dssh_dy, 'V', -1., & |
|---|
| 825 | & zdiag_corstrx, 'U', -1., zdiag_corstry, 'V', -1., & |
|---|
| 826 | & zdiag_intstrx, 'U', -1., zdiag_intstry, 'V', -1. ) |
|---|
| 827 | |
|---|
| 828 | CALL lbc_lnk_multi( zdiag_utau_oi , 'U', -1., zdiag_vtau_oi , 'V', -1., & |
|---|
| 829 | & zdiag_xmtrp_ice, 'U', -1., zdiag_xmtrp_snw, 'U', -1., & |
|---|
| 830 | & zdiag_xatrp , 'U', -1., zdiag_ymtrp_ice, 'V', -1., & |
|---|
| 831 | & zdiag_ymtrp_snw, 'V', -1., zdiag_yatrp , 'V', -1. ) |
|---|
| 832 | |
|---|
| 833 | IF( iom_use('normstr' ) ) CALL iom_put( 'normstr' , zdiag_sig1(:,:) ) ! Normal stress |
|---|
| 834 | IF( iom_use('sheastr' ) ) CALL iom_put( 'sheastr' , zdiag_sig2(:,:) ) ! Shear stress |
|---|
| 835 | IF( iom_use('dssh_dx' ) ) CALL iom_put( 'dssh_dx' , zdiag_dssh_dx(:,:) ) ! Sea-surface tilt term in force balance (x) |
|---|
| 836 | IF( iom_use('dssh_dy' ) ) CALL iom_put( 'dssh_dy' , zdiag_dssh_dy(:,:) ) ! Sea-surface tilt term in force balance (y) |
|---|
| 837 | IF( iom_use('corstrx' ) ) CALL iom_put( 'corstrx' , zdiag_corstrx(:,:) ) ! Coriolis force term in force balance (x) |
|---|
| 838 | IF( iom_use('corstry' ) ) CALL iom_put( 'corstry' , zdiag_corstry(:,:) ) ! Coriolis force term in force balance (y) |
|---|
| 839 | IF( iom_use('intstrx' ) ) CALL iom_put( 'intstrx' , zdiag_intstrx(:,:) ) ! Internal force term in force balance (x) |
|---|
| 840 | IF( iom_use('intstry' ) ) CALL iom_put( 'intstry' , zdiag_intstry(:,:) ) ! Internal force term in force balance (y) |
|---|
| 841 | IF( iom_use('utau_oi' ) ) CALL iom_put( 'utau_oi' , zdiag_utau_oi(:,:) ) ! Ocean stress term in force balance (x) |
|---|
| 842 | IF( iom_use('vtau_oi' ) ) CALL iom_put( 'vtau_oi' , zdiag_vtau_oi(:,:) ) ! Ocean stress term in force balance (y) |
|---|
| 843 | IF( iom_use('xmtrpice') ) CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice(:,:) ) ! X-component of sea-ice mass transport (kg/s) |
|---|
| 844 | IF( iom_use('ymtrpice') ) CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice(:,:) ) ! Y-component of sea-ice mass transport |
|---|
| 845 | IF( iom_use('xmtrpsnw') ) CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw(:,:) ) ! X-component of snow mass transport (kg/s) |
|---|
| 846 | IF( iom_use('ymtrpsnw') ) CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw(:,:) ) ! Y-component of snow mass transport |
|---|
| 847 | IF( iom_use('xatrp' ) ) CALL iom_put( 'xatrp' , zdiag_xatrp(:,:) ) ! X-component of ice area transport |
|---|
| 848 | IF( iom_use('yatrp' ) ) CALL iom_put( 'yatrp' , zdiag_yatrp(:,:) ) ! Y-component of ice area transport |
|---|
| 849 | |
|---|
| 850 | DEALLOCATE( zdiag_sig1 , zdiag_sig2 , zdiag_dssh_dx , zdiag_dssh_dy , & |
|---|
| 851 | & zdiag_corstrx , zdiag_corstry , zdiag_intstrx , zdiag_intstry , & |
|---|
| 852 | & zdiag_utau_oi , zdiag_vtau_oi , zdiag_xmtrp_ice , zdiag_ymtrp_ice , & |
|---|
| 853 | & zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp ) |
|---|
| 854 | |
|---|
| 855 | ENDIF |
|---|
| 856 | ! |
|---|
| 857 | END SUBROUTINE ice_dyn_rhg_evp |
|---|
| 858 | |
|---|
| 859 | |
|---|
| 860 | SUBROUTINE rhg_evp_rst( cdrw, kt ) |
|---|
| 861 | !!--------------------------------------------------------------------- |
|---|
| 862 | !! *** ROUTINE rhg_evp_rst *** |
|---|
| 863 | !! |
|---|
| 864 | !! ** Purpose : Read or write RHG file in restart file |
|---|
| 865 | !! |
|---|
| 866 | !! ** Method : use of IOM library |
|---|
| 867 | !!---------------------------------------------------------------------- |
|---|
| 868 | CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag |
|---|
| 869 | INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step |
|---|
| 870 | ! |
|---|
| 871 | INTEGER :: iter ! local integer |
|---|
| 872 | INTEGER :: id1, id2, id3 ! local integers |
|---|
| 873 | !!---------------------------------------------------------------------- |
|---|
| 874 | ! |
|---|
| 875 | IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialize |
|---|
| 876 | ! ! --------------- |
|---|
| 877 | IF( ln_rstart ) THEN !* Read the restart file |
|---|
| 878 | ! |
|---|
| 879 | id1 = iom_varid( numrir, 'stress1_i' , ldstop = .FALSE. ) |
|---|
| 880 | id2 = iom_varid( numrir, 'stress2_i' , ldstop = .FALSE. ) |
|---|
| 881 | id3 = iom_varid( numrir, 'stress12_i', ldstop = .FALSE. ) |
|---|
| 882 | ! |
|---|
| 883 | IF( MIN( id1, id2, id3 ) > 0 ) THEN ! fields exist |
|---|
| 884 | CALL iom_get( numrir, jpdom_autoglo, 'stress1_i' , stress1_i ) |
|---|
| 885 | CALL iom_get( numrir, jpdom_autoglo, 'stress2_i' , stress2_i ) |
|---|
| 886 | CALL iom_get( numrir, jpdom_autoglo, 'stress12_i', stress12_i ) |
|---|
| 887 | ELSE ! start rheology from rest |
|---|
| 888 | IF(lwp) WRITE(numout,*) |
|---|
| 889 | IF(lwp) WRITE(numout,*) ' ==>>> previous run without rheology, set stresses to 0' |
|---|
| 890 | stress1_i (:,:) = 0._wp |
|---|
| 891 | stress2_i (:,:) = 0._wp |
|---|
| 892 | stress12_i(:,:) = 0._wp |
|---|
| 893 | ENDIF |
|---|
| 894 | ELSE !* Start from rest |
|---|
| 895 | IF(lwp) WRITE(numout,*) |
|---|
| 896 | IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set stresses to 0' |
|---|
| 897 | stress1_i (:,:) = 0._wp |
|---|
| 898 | stress2_i (:,:) = 0._wp |
|---|
| 899 | stress12_i(:,:) = 0._wp |
|---|
| 900 | ENDIF |
|---|
| 901 | ! |
|---|
| 902 | ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file |
|---|
| 903 | ! ! ------------------- |
|---|
| 904 | IF(lwp) WRITE(numout,*) '---- rhg-rst ----' |
|---|
| 905 | iter = kt + nn_fsbc - 1 ! ice restarts are written at kt == nitrst - nn_fsbc + 1 |
|---|
| 906 | ! |
|---|
| 907 | CALL iom_rstput( iter, nitrst, numriw, 'stress1_i' , stress1_i ) |
|---|
| 908 | CALL iom_rstput( iter, nitrst, numriw, 'stress2_i' , stress2_i ) |
|---|
| 909 | CALL iom_rstput( iter, nitrst, numriw, 'stress12_i', stress12_i ) |
|---|
| 910 | ! |
|---|
| 911 | ENDIF |
|---|
| 912 | ! |
|---|
| 913 | END SUBROUTINE rhg_evp_rst |
|---|
| 914 | |
|---|
| 915 | #else |
|---|
| 916 | !!---------------------------------------------------------------------- |
|---|
| 917 | !! Default option Empty module NO SI3 sea-ice model |
|---|
| 918 | !!---------------------------------------------------------------------- |
|---|
| 919 | #endif |
|---|
| 920 | |
|---|
| 921 | !!============================================================================== |
|---|
| 922 | END MODULE icedyn_rhg_evp |
|---|
