[8586] | 1 | MODULE icedyn_adv_umx |
---|
| 2 | !!============================================================================== |
---|
| 3 | !! *** MODULE icedyn_adv_umx *** |
---|
| 4 | !! sea-ice : advection using the ULTIMATE-MACHO scheme |
---|
| 5 | !!============================================================================== |
---|
| 6 | !! History : 3.6 ! 2014-11 (C. Rousset, G. Madec) Original code |
---|
[9604] | 7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
---|
[8586] | 8 | !!---------------------------------------------------------------------- |
---|
[9570] | 9 | #if defined key_si3 |
---|
[8586] | 10 | !!---------------------------------------------------------------------- |
---|
[9570] | 11 | !! 'key_si3' SI3 sea-ice model |
---|
[8586] | 12 | !!---------------------------------------------------------------------- |
---|
[10911] | 13 | !! ice_dyn_adv_umx : update the tracer fields |
---|
[8586] | 14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
---|
[10911] | 15 | !! macho : compute the fluxes |
---|
| 16 | !! nonosc_ice : limit the fluxes using a non-oscillatory algorithm |
---|
[8586] | 17 | !!---------------------------------------------------------------------- |
---|
| 18 | USE phycst ! physical constant |
---|
| 19 | USE dom_oce ! ocean domain |
---|
| 20 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
---|
| 21 | USE ice ! sea-ice variables |
---|
[10413] | 22 | USE icevar ! sea-ice: operations |
---|
[8586] | 23 | ! |
---|
| 24 | USE in_out_manager ! I/O manager |
---|
[10786] | 25 | USE iom ! I/O manager library |
---|
[8586] | 26 | USE lib_mpp ! MPP library |
---|
| 27 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
---|
| 28 | USE lbclnk ! lateral boundary conditions (or mpp links) |
---|
| 29 | |
---|
| 30 | IMPLICIT NONE |
---|
| 31 | PRIVATE |
---|
| 32 | |
---|
| 33 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
---|
[10930] | 34 | ! |
---|
[10945] | 35 | INTEGER, PARAMETER :: np_advS = 1 ! advection for S and T: dVS/dt = -div( uVS ) => np_advS = 1 |
---|
| 36 | ! or dVS/dt = -div( uA * uHS / u ) => np_advS = 2 |
---|
| 37 | ! or dVS/dt = -div( uV * uS / u ) => np_advS = 3 |
---|
| 38 | INTEGER, PARAMETER :: np_limiter = 1 ! limiter: 1 = nonosc |
---|
| 39 | ! 2 = superbee |
---|
| 40 | ! 3 = h3 |
---|
| 41 | LOGICAL :: ll_upsxy = .TRUE. ! alternate directions for upstream |
---|
| 42 | LOGICAL :: ll_hoxy = .TRUE. ! alternate directions for high order |
---|
| 43 | LOGICAL :: ll_neg = .TRUE. ! if T interpolated at u/v points is negative or v_i < 1.e-6 |
---|
| 44 | ! then interpolate T at u/v points using the upstream scheme |
---|
| 45 | LOGICAL :: ll_prelim = .FALSE. ! prelimiter from: Zalesak(1979) eq. 14 => not well defined in 2D |
---|
[10930] | 46 | ! |
---|
[10945] | 47 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
---|
| 48 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
---|
[10930] | 49 | ! |
---|
[10945] | 50 | INTEGER, ALLOCATABLE, DIMENSION(:,:,:) :: imsk_small, jmsk_small |
---|
[10930] | 51 | ! |
---|
[8586] | 52 | !! * Substitutions |
---|
[12377] | 53 | # include "do_loop_substitute.h90" |
---|
[8586] | 54 | !!---------------------------------------------------------------------- |
---|
[9598] | 55 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
---|
[10069] | 56 | !! $Id$ |
---|
[10413] | 57 | !! Software governed by the CeCILL licence (./LICENSE) |
---|
[8586] | 58 | !!---------------------------------------------------------------------- |
---|
| 59 | CONTAINS |
---|
| 60 | |
---|
[10911] | 61 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, ph_i, ph_s, ph_ip, & |
---|
[10413] | 62 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
[8586] | 63 | !!---------------------------------------------------------------------- |
---|
| 64 | !! *** ROUTINE ice_dyn_adv_umx *** |
---|
| 65 | !! |
---|
| 66 | !! ** Purpose : Compute the now trend due to total advection of |
---|
| 67 | !! tracers and add it to the general trend of tracer equations |
---|
| 68 | !! using an "Ultimate-Macho" scheme |
---|
| 69 | !! |
---|
| 70 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 71 | !!---------------------------------------------------------------------- |
---|
[10413] | 72 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
[8586] | 73 | INTEGER , INTENT(in ) :: kt ! time step |
---|
| 74 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
---|
| 75 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
---|
[10911] | 76 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_i ! ice thickness |
---|
| 77 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_s ! snw thickness |
---|
| 78 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_ip ! ice pond thickness |
---|
[8586] | 79 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
---|
| 80 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
---|
| 81 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
---|
| 82 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
---|
| 83 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
---|
| 84 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
---|
[11627] | 85 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond concentration |
---|
[8586] | 86 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
---|
| 87 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
---|
| 88 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
---|
| 89 | ! |
---|
| 90 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
---|
[10413] | 91 | INTEGER :: icycle ! number of sub-timestep for the advection |
---|
| 92 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
---|
[10930] | 93 | REAL(wp) :: zdt, zvi_cen |
---|
[10911] | 94 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! for global communication |
---|
[10945] | 95 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
---|
[10439] | 96 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
---|
[10945] | 97 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zu_cat, zv_cat |
---|
[10911] | 98 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho, zua_ups, zva_ups |
---|
[10945] | 99 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai , z1_aip, zhvar |
---|
[10911] | 100 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhi_max, zhs_max, zhip_max |
---|
[10945] | 101 | ! |
---|
| 102 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs |
---|
[8586] | 103 | !!---------------------------------------------------------------------- |
---|
| 104 | ! |
---|
| 105 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
---|
| 106 | ! |
---|
[10911] | 107 | ! --- Record max of the surrounding 9-pts ice thick. (for call Hbig) --- ! |
---|
| 108 | DO jl = 1, jpl |
---|
[12377] | 109 | DO_2D_00_00 |
---|
| 110 | zhip_max(ji,jj,jl) = MAX( epsi20, ph_ip(ji,jj,jl), ph_ip(ji+1,jj ,jl), ph_ip(ji ,jj+1,jl), & |
---|
| 111 | & ph_ip(ji-1,jj ,jl), ph_ip(ji ,jj-1,jl), & |
---|
| 112 | & ph_ip(ji+1,jj+1,jl), ph_ip(ji-1,jj-1,jl), & |
---|
| 113 | & ph_ip(ji+1,jj-1,jl), ph_ip(ji-1,jj+1,jl) ) |
---|
| 114 | zhi_max (ji,jj,jl) = MAX( epsi20, ph_i (ji,jj,jl), ph_i (ji+1,jj ,jl), ph_i (ji ,jj+1,jl), & |
---|
| 115 | & ph_i (ji-1,jj ,jl), ph_i (ji ,jj-1,jl), & |
---|
| 116 | & ph_i (ji+1,jj+1,jl), ph_i (ji-1,jj-1,jl), & |
---|
| 117 | & ph_i (ji+1,jj-1,jl), ph_i (ji-1,jj+1,jl) ) |
---|
| 118 | zhs_max (ji,jj,jl) = MAX( epsi20, ph_s (ji,jj,jl), ph_s (ji+1,jj ,jl), ph_s (ji ,jj+1,jl), & |
---|
| 119 | & ph_s (ji-1,jj ,jl), ph_s (ji ,jj-1,jl), & |
---|
| 120 | & ph_s (ji+1,jj+1,jl), ph_s (ji-1,jj-1,jl), & |
---|
| 121 | & ph_s (ji+1,jj-1,jl), ph_s (ji-1,jj+1,jl) ) |
---|
| 122 | END_2D |
---|
[10911] | 123 | END DO |
---|
[10930] | 124 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zhi_max, 'T', 1., zhs_max, 'T', 1., zhip_max, 'T', 1. ) |
---|
[10911] | 125 | ! |
---|
| 126 | ! |
---|
| 127 | ! --- If ice drift is too fast, use subtime steps for advection (CFL test for stability) --- ! |
---|
| 128 | ! Note: the advection split is applied at the next time-step in order to avoid blocking global comm. |
---|
| 129 | ! this should not affect too much the stability |
---|
[12489] | 130 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rDt_ice * r1_e1u(:,:) ) |
---|
| 131 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rDt_ice * r1_e2v(:,:) ) ) |
---|
[10425] | 132 | |
---|
| 133 | ! non-blocking global communication send zcflnow and receive zcflprv |
---|
| 134 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
---|
[8586] | 135 | |
---|
[10425] | 136 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
---|
| 137 | ELSE ; icycle = 1 |
---|
[8586] | 138 | ENDIF |
---|
[12489] | 139 | zdt = rDt_ice / REAL(icycle) |
---|
[8586] | 140 | |
---|
| 141 | ! --- transport --- ! |
---|
| 142 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
---|
| 143 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
---|
[10945] | 144 | ! |
---|
| 145 | ! setup transport for each ice cat |
---|
| 146 | DO jl = 1, jpl |
---|
| 147 | zu_cat(:,:,jl) = zudy(:,:) |
---|
| 148 | zv_cat(:,:,jl) = zvdx(:,:) |
---|
| 149 | END DO |
---|
| 150 | ! |
---|
[8586] | 151 | ! --- define velocity for advection: u*grad(H) --- ! |
---|
[12377] | 152 | DO_2D_00_00 |
---|
| 153 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
---|
| 154 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
---|
| 155 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
---|
| 156 | ENDIF |
---|
[8586] | 157 | |
---|
[12377] | 158 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
---|
| 159 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
---|
| 160 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
---|
| 161 | ENDIF |
---|
| 162 | END_2D |
---|
[8586] | 163 | |
---|
| 164 | !---------------! |
---|
| 165 | !== advection ==! |
---|
| 166 | !---------------! |
---|
[10413] | 167 | DO jt = 1, icycle |
---|
| 168 | |
---|
[10439] | 169 | ! record at_i before advection (for open water) |
---|
| 170 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
---|
[10413] | 171 | |
---|
[10439] | 172 | ! inverse of A and Ap |
---|
[10425] | 173 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
---|
| 174 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
---|
| 175 | END WHERE |
---|
| 176 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
---|
| 177 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
---|
| 178 | END WHERE |
---|
| 179 | ! |
---|
[10930] | 180 | ! setup a mask where advection will be upstream |
---|
| 181 | IF( ll_neg ) THEN |
---|
[10945] | 182 | IF( .NOT. ALLOCATED(imsk_small) ) ALLOCATE( imsk_small(jpi,jpj,jpl) ) |
---|
| 183 | IF( .NOT. ALLOCATED(jmsk_small) ) ALLOCATE( jmsk_small(jpi,jpj,jpl) ) |
---|
[10930] | 184 | DO jl = 1, jpl |
---|
[12377] | 185 | DO_2D_10_10 |
---|
| 186 | zvi_cen = 0.5_wp * ( pv_i(ji+1,jj,jl) + pv_i(ji,jj,jl) ) |
---|
| 187 | IF( zvi_cen < epsi06) THEN ; imsk_small(ji,jj,jl) = 0 |
---|
| 188 | ELSE ; imsk_small(ji,jj,jl) = 1 ; ENDIF |
---|
| 189 | zvi_cen = 0.5_wp * ( pv_i(ji,jj+1,jl) + pv_i(ji,jj,jl) ) |
---|
| 190 | IF( zvi_cen < epsi06) THEN ; jmsk_small(ji,jj,jl) = 0 |
---|
| 191 | ELSE ; jmsk_small(ji,jj,jl) = 1 ; ENDIF |
---|
| 192 | END_2D |
---|
[10930] | 193 | END DO |
---|
| 194 | ENDIF |
---|
| 195 | ! |
---|
| 196 | ! ----------------------- ! |
---|
| 197 | ! ==> start advection <== ! |
---|
| 198 | ! ----------------------- ! |
---|
| 199 | ! |
---|
[10911] | 200 | !== Ice area ==! |
---|
[10425] | 201 | zamsk = 1._wp |
---|
[10945] | 202 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zu_cat , zv_cat , zcu_box, zcv_box, & |
---|
[10911] | 203 | & pa_i, pa_i, zua_ups, zva_ups, zua_ho , zva_ho ) |
---|
[10945] | 204 | ! |
---|
| 205 | ! ! --------------------------------- ! |
---|
| 206 | IF( np_advS == 1 ) THEN ! -- advection form: -div( uVS ) -- ! |
---|
| 207 | ! ! --------------------------------- ! |
---|
| 208 | zamsk = 0._wp |
---|
[10911] | 209 | !== Ice volume ==! |
---|
| 210 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
---|
| 211 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 212 | & zhvar, pv_i, zua_ups, zva_ups ) |
---|
| 213 | !== Snw volume ==! |
---|
| 214 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
---|
| 215 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 216 | & zhvar, pv_s, zua_ups, zva_ups ) |
---|
| 217 | ! |
---|
[10945] | 218 | zamsk = 1._wp |
---|
[10911] | 219 | !== Salt content ==! |
---|
[10945] | 220 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
---|
| 221 | & psv_i, psv_i ) |
---|
| 222 | !== Ice heat content ==! |
---|
| 223 | DO jk = 1, nlay_i |
---|
| 224 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
---|
| 225 | & pe_i(:,:,jk,:), pe_i(:,:,jk,:) ) |
---|
| 226 | END DO |
---|
| 227 | !== Snw heat content ==! |
---|
| 228 | DO jk = 1, nlay_s |
---|
| 229 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
---|
| 230 | & pe_s(:,:,jk,:), pe_s(:,:,jk,:) ) |
---|
| 231 | END DO |
---|
| 232 | ! |
---|
| 233 | ! ! ------------------------------------------ ! |
---|
| 234 | ELSEIF( np_advS == 2 ) THEN ! -- advection form: -div( uA * uHS / u ) -- ! |
---|
| 235 | ! ! ------------------------------------------ ! |
---|
| 236 | zamsk = 0._wp |
---|
| 237 | !== Ice volume ==! |
---|
| 238 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
---|
| 239 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 240 | & zhvar, pv_i, zua_ups, zva_ups ) |
---|
| 241 | !== Snw volume ==! |
---|
| 242 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
---|
| 243 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 244 | & zhvar, pv_s, zua_ups, zva_ups ) |
---|
| 245 | !== Salt content ==! |
---|
[10911] | 246 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
---|
| 247 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 248 | & zhvar, psv_i, zua_ups, zva_ups ) |
---|
| 249 | !== Ice heat content ==! |
---|
| 250 | DO jk = 1, nlay_i |
---|
| 251 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
---|
| 252 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
---|
| 253 | & zhvar, pe_i(:,:,jk,:), zua_ups, zva_ups ) |
---|
| 254 | END DO |
---|
| 255 | !== Snw heat content ==! |
---|
| 256 | DO jk = 1, nlay_s |
---|
| 257 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
---|
| 258 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
---|
| 259 | & zhvar, pe_s(:,:,jk,:), zua_ups, zva_ups ) |
---|
| 260 | END DO |
---|
| 261 | ! |
---|
[10945] | 262 | ! ! ----------------------------------------- ! |
---|
| 263 | ELSEIF( np_advS == 3 ) THEN ! -- advection form: -div( uV * uS / u ) -- ! |
---|
| 264 | ! ! ----------------------------------------- ! |
---|
| 265 | zamsk = 0._wp |
---|
| 266 | ! |
---|
| 267 | ALLOCATE( zuv_ho (jpi,jpj,jpl), zvv_ho (jpi,jpj,jpl), & |
---|
| 268 | & zuv_ups(jpi,jpj,jpl), zvv_ups(jpi,jpj,jpl), z1_vi(jpi,jpj,jpl), z1_vs(jpi,jpj,jpl) ) |
---|
| 269 | ! |
---|
[10911] | 270 | ! inverse of Vi |
---|
| 271 | WHERE( pv_i(:,:,:) >= epsi20 ) ; z1_vi(:,:,:) = 1._wp / pv_i(:,:,:) |
---|
| 272 | ELSEWHERE ; z1_vi(:,:,:) = 0. |
---|
| 273 | END WHERE |
---|
| 274 | ! inverse of Vs |
---|
| 275 | WHERE( pv_s(:,:,:) >= epsi20 ) ; z1_vs(:,:,:) = 1._wp / pv_s(:,:,:) |
---|
| 276 | ELSEWHERE ; z1_vs(:,:,:) = 0. |
---|
| 277 | END WHERE |
---|
| 278 | ! |
---|
| 279 | ! It is important to first calculate the ice fields and then the snow fields (because we use the same arrays) |
---|
| 280 | ! |
---|
| 281 | !== Ice volume ==! |
---|
| 282 | zuv_ups = zua_ups |
---|
| 283 | zvv_ups = zva_ups |
---|
| 284 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
---|
| 285 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 286 | & zhvar, pv_i, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
---|
| 287 | !== Salt content ==! |
---|
| 288 | zhvar(:,:,:) = psv_i(:,:,:) * z1_vi(:,:,:) |
---|
| 289 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zuv_ho , zvv_ho , zcu_box, zcv_box, & |
---|
| 290 | & zhvar, psv_i, zuv_ups, zvv_ups ) |
---|
| 291 | !== Ice heat content ==! |
---|
| 292 | DO jk = 1, nlay_i |
---|
| 293 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_vi(:,:,:) |
---|
| 294 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
---|
| 295 | & zhvar, pe_i(:,:,jk,:), zuv_ups, zvv_ups ) |
---|
| 296 | END DO |
---|
| 297 | !== Snow volume ==! |
---|
| 298 | zuv_ups = zua_ups |
---|
| 299 | zvv_ups = zva_ups |
---|
| 300 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
---|
| 301 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 302 | & zhvar, pv_s, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
---|
| 303 | !== Snw heat content ==! |
---|
| 304 | DO jk = 1, nlay_s |
---|
| 305 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_vs(:,:,:) |
---|
| 306 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
---|
| 307 | & zhvar, pe_s(:,:,jk,:), zuv_ups, zvv_ups ) |
---|
| 308 | END DO |
---|
| 309 | ! |
---|
[10945] | 310 | DEALLOCATE( zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs ) |
---|
| 311 | ! |
---|
[10911] | 312 | ENDIF |
---|
[10425] | 313 | ! |
---|
[10911] | 314 | !== Ice age ==! |
---|
[11612] | 315 | zamsk = 1._wp |
---|
| 316 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
---|
| 317 | & poa_i, poa_i ) |
---|
[10786] | 318 | ! |
---|
[10911] | 319 | !== melt ponds ==! |
---|
| 320 | IF ( ln_pnd_H12 ) THEN |
---|
[11627] | 321 | ! concentration |
---|
[10425] | 322 | zamsk = 1._wp |
---|
[10945] | 323 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat , zv_cat , zcu_box, zcv_box, & |
---|
[10911] | 324 | & pa_ip, pa_ip, zua_ups, zva_ups, zua_ho , zva_ho ) |
---|
[10945] | 325 | ! volume |
---|
[10425] | 326 | zamsk = 0._wp |
---|
[10475] | 327 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
---|
[10911] | 328 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 329 | & zhvar, pv_ip, zua_ups, zva_ups ) |
---|
[10425] | 330 | ENDIF |
---|
[10418] | 331 | ! |
---|
[10911] | 332 | !== Open water area ==! |
---|
[10439] | 333 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
---|
[12377] | 334 | DO_2D_00_00 |
---|
| 335 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & |
---|
| 336 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
---|
| 337 | END_2D |
---|
[10930] | 338 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i, 'T', 1. ) |
---|
[10418] | 339 | ! |
---|
[10911] | 340 | ! |
---|
| 341 | ! --- Ensure non-negative fields and in-bound thicknesses --- ! |
---|
| 342 | ! Remove negative values (conservation is ensured) |
---|
| 343 | ! (because advected fields are not perfectly bounded and tiny negative values can occur, e.g. -1.e-20) |
---|
[10930] | 344 | CALL ice_var_zapneg( zdt, pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
[10911] | 345 | ! |
---|
[12197] | 346 | ! --- Make sure ice thickness is not too big --- ! |
---|
| 347 | ! (because ice thickness can be too large where ice concentration is very small) |
---|
| 348 | CALL Hbig( zdt, zhi_max, zhs_max, zhip_max, pv_i, pv_s, pa_i, pa_ip, pv_ip, pe_s ) |
---|
| 349 | ! |
---|
| 350 | ! --- Ensure snow load is not too big --- ! |
---|
| 351 | CALL Hsnow( zdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
| 352 | ! |
---|
[8586] | 353 | END DO |
---|
| 354 | ! |
---|
| 355 | END SUBROUTINE ice_dyn_adv_umx |
---|
[9929] | 356 | |
---|
[8586] | 357 | |
---|
[10911] | 358 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, & |
---|
| 359 | & pt, ptc, pua_ups, pva_ups, pua_ho, pva_ho ) |
---|
[8586] | 360 | !!---------------------------------------------------------------------- |
---|
| 361 | !! *** ROUTINE adv_umx *** |
---|
| 362 | !! |
---|
| 363 | !! ** Purpose : Compute the now trend due to total advection of |
---|
[10446] | 364 | !! tracers and add it to the general trend of tracer equations |
---|
[8586] | 365 | !! |
---|
[10911] | 366 | !! ** Method : - calculate upstream fluxes and upstream solution for tracers V/A(=H) etc |
---|
[10446] | 367 | !! - calculate tracer H at u and v points (Ultimate) |
---|
[10911] | 368 | !! - calculate the high order fluxes using alterning directions (Macho) |
---|
[10519] | 369 | !! - apply a limiter on the fluxes (nonosc_ice) |
---|
[10911] | 370 | !! - convert this tracer flux to a "volume" flux (uH -> uV) |
---|
| 371 | !! - apply a limiter a second time on the volumes fluxes (nonosc_ice) |
---|
| 372 | !! - calculate the high order solution for V |
---|
[8586] | 373 | !! |
---|
[10911] | 374 | !! ** Action : solve 3 equations => a) dA/dt = -div(uA) |
---|
| 375 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
---|
| 376 | !! c) dVS/dt = -div(uVS) using either dHS/dt = -u.grad(HS) or dS/dt = -u.grad(S) |
---|
[10446] | 377 | !! |
---|
[10911] | 378 | !! in eq. b), - fluxes uH are evaluated (with UMx) and limited with nonosc_ice. This step is necessary to get a good H. |
---|
| 379 | !! - then we convert this flux to a "volume" flux this way => uH * uA / u |
---|
| 380 | !! where uA is the flux from eq. a) |
---|
| 381 | !! this "volume" flux is also limited with nonosc_ice (otherwise overshoots can occur) |
---|
| 382 | !! - at last we estimate dV/dt = -div(uH * uA / u) |
---|
| 383 | !! |
---|
| 384 | !! in eq. c), one can solve the equation for S (ln_advS=T), then dVS/dt = -div(uV * uS / u) |
---|
| 385 | !! or for HS (ln_advS=F), then dVS/dt = -div(uA * uHS / u) |
---|
| 386 | !! |
---|
| 387 | !! ** Note : - this method can lead to tiny negative V (-1.e-20) => set it to 0 while conserving mass etc. |
---|
| 388 | !! - At the ice edge, Ultimate scheme can lead to: |
---|
| 389 | !! 1) negative interpolated tracers at u-v points |
---|
| 390 | !! 2) non-zero interpolated tracers at u-v points eventhough there is no ice and velocity is outward |
---|
| 391 | !! Solution for 1): apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
---|
| 392 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
---|
| 393 | !! Solution for 2): we set it to 0 in this case |
---|
[10446] | 394 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
---|
| 395 | !! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we |
---|
[10911] | 396 | !! work on H (and not V). It is partly related to the multi-category approach |
---|
[10446] | 397 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
---|
[10911] | 398 | !! concentration is small). Since we do not limit S and T, large values can occur at the edge but it does not really matter |
---|
| 399 | !! since sv_i and e_i are still good. |
---|
[8586] | 400 | !!---------------------------------------------------------------------- |
---|
[10911] | 401 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 402 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 403 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 404 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 405 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 406 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
---|
| 407 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
---|
| 408 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
| 409 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
---|
| 410 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
---|
| 411 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT(inout), OPTIONAL :: pua_ups, pva_ups ! upstream u*a fluxes |
---|
| 412 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
---|
[8586] | 413 | ! |
---|
[10425] | 414 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[8586] | 415 | REAL(wp) :: ztra ! local scalar |
---|
[10446] | 416 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
---|
[10439] | 417 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
---|
[8586] | 418 | !!---------------------------------------------------------------------- |
---|
| 419 | ! |
---|
[10446] | 420 | ! Upstream (_ups) fluxes |
---|
| 421 | ! ----------------------- |
---|
| 422 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
---|
| 423 | |
---|
| 424 | ! High order (_ho) fluxes |
---|
| 425 | ! ----------------------- |
---|
| 426 | SELECT CASE( kn_umx ) |
---|
| 427 | ! |
---|
| 428 | CASE ( 20 ) !== centered second order ==! |
---|
| 429 | ! |
---|
[10475] | 430 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 431 | ! |
---|
| 432 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
---|
| 433 | ! |
---|
[10475] | 434 | CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 435 | ! |
---|
| 436 | END SELECT |
---|
[10439] | 437 | ! |
---|
[10446] | 438 | ! --ho --ho |
---|
| 439 | ! new fluxes = u*H * u*a / u |
---|
| 440 | ! ---------------------------- |
---|
[10475] | 441 | IF( pamsk == 0._wp ) THEN |
---|
[10446] | 442 | DO jl = 1, jpl |
---|
[12377] | 443 | DO_2D_10_10 |
---|
| 444 | IF( ABS( pu(ji,jj) ) > epsi10 ) THEN |
---|
| 445 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc (ji,jj,jl) / pu(ji,jj) |
---|
| 446 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * pua_ups(ji,jj,jl) / pu(ji,jj) |
---|
| 447 | ELSE |
---|
| 448 | zfu_ho (ji,jj,jl) = 0._wp |
---|
| 449 | zfu_ups(ji,jj,jl) = 0._wp |
---|
| 450 | ENDIF |
---|
| 451 | ! |
---|
| 452 | IF( ABS( pv(ji,jj) ) > epsi10 ) THEN |
---|
| 453 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc (ji,jj,jl) / pv(ji,jj) |
---|
| 454 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pva_ups(ji,jj,jl) / pv(ji,jj) |
---|
| 455 | ELSE |
---|
| 456 | zfv_ho (ji,jj,jl) = 0._wp |
---|
| 457 | zfv_ups(ji,jj,jl) = 0._wp |
---|
| 458 | ENDIF |
---|
| 459 | END_2D |
---|
[10446] | 460 | END DO |
---|
[10911] | 461 | |
---|
| 462 | ! the new "volume" fluxes must also be "flux corrected" |
---|
| 463 | ! thus we calculate the upstream solution and apply a limiter again |
---|
| 464 | DO jl = 1, jpl |
---|
[12377] | 465 | DO_2D_00_00 |
---|
| 466 | ztra = - ( zfu_ups(ji,jj,jl) - zfu_ups(ji-1,jj,jl) + zfv_ups(ji,jj,jl) - zfv_ups(ji,jj-1,jl) ) |
---|
| 467 | ! |
---|
| 468 | zt_ups(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 469 | END_2D |
---|
[10911] | 470 | END DO |
---|
| 471 | CALL lbc_lnk( 'icedyn_adv_umx', zt_ups, 'T', 1. ) |
---|
| 472 | ! |
---|
[10945] | 473 | IF ( np_limiter == 1 ) THEN |
---|
[10911] | 474 | CALL nonosc_ice( 1._wp, pdt, pu, pv, ptc, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10945] | 475 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
[10911] | 476 | CALL limiter_x( pdt, pu, ptc, zfu_ups, zfu_ho ) |
---|
| 477 | CALL limiter_y( pdt, pv, ptc, zfv_ups, zfv_ho ) |
---|
| 478 | ENDIF |
---|
| 479 | ! |
---|
[10446] | 480 | ENDIF |
---|
[10911] | 481 | ! --ho --ups |
---|
| 482 | ! in case of advection of A: output u*a and u*a |
---|
| 483 | ! ----------------------------------------------- |
---|
[10446] | 484 | IF( PRESENT( pua_ho ) ) THEN |
---|
| 485 | DO jl = 1, jpl |
---|
[12377] | 486 | DO_2D_10_10 |
---|
| 487 | pua_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) ; pva_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) |
---|
| 488 | pua_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) ; pva_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) |
---|
| 489 | END_2D |
---|
[10446] | 490 | END DO |
---|
| 491 | ENDIF |
---|
| 492 | ! |
---|
| 493 | ! final trend with corrected fluxes |
---|
| 494 | ! --------------------------------- |
---|
| 495 | DO jl = 1, jpl |
---|
[12377] | 496 | DO_2D_00_00 |
---|
| 497 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
---|
| 498 | ! |
---|
| 499 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 500 | END_2D |
---|
[10446] | 501 | END DO |
---|
| 502 | CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1. ) |
---|
| 503 | ! |
---|
| 504 | END SUBROUTINE adv_umx |
---|
| 505 | |
---|
| 506 | |
---|
| 507 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
---|
| 508 | !!--------------------------------------------------------------------- |
---|
| 509 | !! *** ROUTINE upstream *** |
---|
| 510 | !! |
---|
| 511 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
---|
| 512 | !!---------------------------------------------------------------------- |
---|
| 513 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 514 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 515 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 516 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 517 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 518 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 519 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
---|
| 520 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
| 521 | ! |
---|
| 522 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 523 | REAL(wp) :: ztra ! local scalar |
---|
| 524 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
| 525 | !!---------------------------------------------------------------------- |
---|
| 526 | |
---|
[10439] | 527 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
---|
[10446] | 528 | ! |
---|
[10425] | 529 | DO jl = 1, jpl |
---|
[12377] | 530 | DO_2D_10_10 |
---|
| 531 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
| 532 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
| 533 | END_2D |
---|
[10413] | 534 | END DO |
---|
[10446] | 535 | ! |
---|
[10439] | 536 | ELSE !** alternate directions **! |
---|
[10413] | 537 | ! |
---|
| 538 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[10439] | 539 | ! |
---|
| 540 | DO jl = 1, jpl !-- flux in x-direction |
---|
[12377] | 541 | DO_2D_10_10 |
---|
| 542 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
| 543 | END_2D |
---|
[10413] | 544 | END DO |
---|
[10439] | 545 | ! |
---|
| 546 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[12377] | 547 | DO_2D_00_00 |
---|
| 548 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
---|
| 549 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 550 | ! |
---|
| 551 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 552 | END_2D |
---|
[10413] | 553 | END DO |
---|
[10425] | 554 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 555 | ! |
---|
[10439] | 556 | DO jl = 1, jpl !-- flux in y-direction |
---|
[12377] | 557 | DO_2D_10_10 |
---|
| 558 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * zpt(ji,jj+1,jl) |
---|
| 559 | END_2D |
---|
[10413] | 560 | END DO |
---|
[10439] | 561 | ! |
---|
[10413] | 562 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
[10439] | 563 | ! |
---|
| 564 | DO jl = 1, jpl !-- flux in y-direction |
---|
[12377] | 565 | DO_2D_10_10 |
---|
| 566 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
| 567 | END_2D |
---|
[10413] | 568 | END DO |
---|
[10439] | 569 | ! |
---|
| 570 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[12377] | 571 | DO_2D_00_00 |
---|
| 572 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
---|
| 573 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 574 | ! |
---|
| 575 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 576 | END_2D |
---|
[10413] | 577 | END DO |
---|
[10425] | 578 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 579 | ! |
---|
[10439] | 580 | DO jl = 1, jpl !-- flux in x-direction |
---|
[12377] | 581 | DO_2D_10_10 |
---|
| 582 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * zpt(ji+1,jj,jl) |
---|
| 583 | END_2D |
---|
[10413] | 584 | END DO |
---|
| 585 | ! |
---|
| 586 | ENDIF |
---|
| 587 | |
---|
| 588 | ENDIF |
---|
[10439] | 589 | ! |
---|
| 590 | DO jl = 1, jpl !-- after tracer with upstream scheme |
---|
[12377] | 591 | DO_2D_00_00 |
---|
| 592 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
---|
| 593 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
---|
| 594 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
---|
| 595 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 596 | ! |
---|
| 597 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 598 | END_2D |
---|
[8586] | 599 | END DO |
---|
[10446] | 600 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1. ) |
---|
[10413] | 601 | |
---|
[10446] | 602 | END SUBROUTINE upstream |
---|
[8586] | 603 | |
---|
[10446] | 604 | |
---|
[10475] | 605 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 606 | !!--------------------------------------------------------------------- |
---|
[10446] | 607 | !! *** ROUTINE cen2 *** |
---|
[8586] | 608 | !! |
---|
[10446] | 609 | !! ** Purpose : compute the high order fluxes using a centered |
---|
| 610 | !! second order scheme |
---|
[8586] | 611 | !!---------------------------------------------------------------------- |
---|
[10439] | 612 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 613 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 614 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 615 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 616 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 617 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
[10446] | 618 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 619 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 620 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[8586] | 621 | ! |
---|
[10425] | 622 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 623 | REAL(wp) :: ztra ! local scalar |
---|
| 624 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
[8586] | 625 | !!---------------------------------------------------------------------- |
---|
| 626 | ! |
---|
[10439] | 627 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
---|
[8586] | 628 | ! |
---|
[10425] | 629 | DO jl = 1, jpl |
---|
[12377] | 630 | DO_2D_10_10 |
---|
| 631 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
---|
| 632 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
---|
| 633 | END_2D |
---|
[8586] | 634 | END DO |
---|
[10475] | 635 | ! |
---|
[10945] | 636 | IF ( np_limiter == 1 ) THEN |
---|
[10519] | 637 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10945] | 638 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
[10446] | 639 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 640 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 641 | ENDIF |
---|
[8586] | 642 | ! |
---|
[10439] | 643 | ELSE !** alternate directions **! |
---|
[8586] | 644 | ! |
---|
[10413] | 645 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
| 646 | ! |
---|
[10439] | 647 | DO jl = 1, jpl !-- flux in x-direction |
---|
[12377] | 648 | DO_2D_10_10 |
---|
| 649 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
---|
| 650 | END_2D |
---|
[10413] | 651 | END DO |
---|
[10945] | 652 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 653 | |
---|
[10439] | 654 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[12377] | 655 | DO_2D_00_00 |
---|
| 656 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
---|
| 657 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 658 | ! |
---|
| 659 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 660 | END_2D |
---|
[10413] | 661 | END DO |
---|
[10446] | 662 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 663 | |
---|
[10439] | 664 | DO jl = 1, jpl !-- flux in y-direction |
---|
[12377] | 665 | DO_2D_10_10 |
---|
| 666 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
---|
| 667 | END_2D |
---|
[10413] | 668 | END DO |
---|
[10945] | 669 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 670 | |
---|
| 671 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 672 | ! |
---|
[10439] | 673 | DO jl = 1, jpl !-- flux in y-direction |
---|
[12377] | 674 | DO_2D_10_10 |
---|
| 675 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
---|
| 676 | END_2D |
---|
[10413] | 677 | END DO |
---|
[10945] | 678 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 679 | ! |
---|
[10439] | 680 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[12377] | 681 | DO_2D_00_00 |
---|
| 682 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
---|
| 683 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 684 | ! |
---|
| 685 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 686 | END_2D |
---|
[10413] | 687 | END DO |
---|
[10446] | 688 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 689 | ! |
---|
[10439] | 690 | DO jl = 1, jpl !-- flux in x-direction |
---|
[12377] | 691 | DO_2D_10_10 |
---|
| 692 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
---|
| 693 | END_2D |
---|
[10413] | 694 | END DO |
---|
[10945] | 695 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 696 | |
---|
| 697 | ENDIF |
---|
[10945] | 698 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 699 | |
---|
| 700 | ENDIF |
---|
| 701 | |
---|
| 702 | END SUBROUTINE cen2 |
---|
| 703 | |
---|
| 704 | |
---|
[10475] | 705 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 706 | !!--------------------------------------------------------------------- |
---|
| 707 | !! *** ROUTINE macho *** |
---|
| 708 | !! |
---|
[10446] | 709 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
---|
[10413] | 710 | !! |
---|
[10446] | 711 | !! ** Method : ... |
---|
[10413] | 712 | !! |
---|
| 713 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 714 | !!---------------------------------------------------------------------- |
---|
[10439] | 715 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 716 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 717 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 718 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 719 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 720 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 721 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 722 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
[10446] | 723 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 724 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 725 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[10413] | 726 | ! |
---|
[10425] | 727 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 728 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
---|
[10413] | 729 | !!---------------------------------------------------------------------- |
---|
| 730 | ! |
---|
| 731 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[8586] | 732 | ! |
---|
[10413] | 733 | ! !-- ultimate interpolation of pt at u-point --! |
---|
[10911] | 734 | CALL ultimate_x( pamsk, kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
---|
[10413] | 735 | ! !-- limiter in x --! |
---|
[10945] | 736 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10446] | 737 | ! !-- advective form update in zpt --! |
---|
[10439] | 738 | DO jl = 1, jpl |
---|
[12377] | 739 | DO_2D_00_00 |
---|
| 740 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pubox(ji,jj ) * ( zt_u(ji,jj,jl) - zt_u(ji-1,jj,jl) ) * r1_e1t (ji,jj) & |
---|
| 741 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
---|
| 742 | & * pamsk & |
---|
| 743 | & ) * pdt ) * tmask(ji,jj,1) |
---|
| 744 | END_2D |
---|
[10439] | 745 | END DO |
---|
[10446] | 746 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 747 | ! |
---|
[10413] | 748 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 749 | IF( ll_hoxy ) THEN |
---|
[10911] | 750 | CALL ultimate_y( pamsk, kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
---|
[10413] | 751 | ELSE |
---|
[10911] | 752 | CALL ultimate_y( pamsk, kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
---|
[10413] | 753 | ENDIF |
---|
| 754 | ! !-- limiter in y --! |
---|
[10945] | 755 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 756 | ! |
---|
| 757 | ! |
---|
| 758 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 759 | ! |
---|
| 760 | ! !-- ultimate interpolation of pt at v-point --! |
---|
[10911] | 761 | CALL ultimate_y( pamsk, kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
---|
[10413] | 762 | ! !-- limiter in y --! |
---|
[10945] | 763 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10446] | 764 | ! !-- advective form update in zpt --! |
---|
[10439] | 765 | DO jl = 1, jpl |
---|
[12377] | 766 | DO_2D_00_00 |
---|
| 767 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pvbox(ji,jj ) * ( zt_v(ji,jj,jl) - zt_v(ji,jj-1,jl) ) * r1_e2t (ji,jj) & |
---|
| 768 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
---|
| 769 | & * pamsk & |
---|
| 770 | & ) * pdt ) * tmask(ji,jj,1) |
---|
| 771 | END_2D |
---|
[10439] | 772 | END DO |
---|
[10446] | 773 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 774 | ! |
---|
| 775 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 776 | IF( ll_hoxy ) THEN |
---|
[10911] | 777 | CALL ultimate_x( pamsk, kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
---|
[10413] | 778 | ELSE |
---|
[10911] | 779 | CALL ultimate_x( pamsk, kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
---|
[10413] | 780 | ENDIF |
---|
| 781 | ! !-- limiter in x --! |
---|
[10945] | 782 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 783 | ! |
---|
| 784 | ENDIF |
---|
| 785 | |
---|
[10945] | 786 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 787 | ! |
---|
| 788 | END SUBROUTINE macho |
---|
| 789 | |
---|
| 790 | |
---|
[10911] | 791 | SUBROUTINE ultimate_x( pamsk, kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
---|
[8586] | 792 | !!--------------------------------------------------------------------- |
---|
| 793 | !! *** ROUTINE ultimate_x *** |
---|
| 794 | !! |
---|
[10446] | 795 | !! ** Purpose : compute tracer at u-points |
---|
[8586] | 796 | !! |
---|
[10446] | 797 | !! ** Method : ... |
---|
[8586] | 798 | !! |
---|
| 799 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 800 | !!---------------------------------------------------------------------- |
---|
[10911] | 801 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 802 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 803 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 804 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
---|
| 805 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 806 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
---|
| 807 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
---|
[8586] | 808 | ! |
---|
[10425] | 809 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10930] | 810 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
[10425] | 811 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
---|
[8586] | 812 | !!---------------------------------------------------------------------- |
---|
| 813 | ! |
---|
| 814 | ! !-- Laplacian in i-direction --! |
---|
[10425] | 815 | DO jl = 1, jpl |
---|
| 816 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
[12377] | 817 | DO ji = 1, jpim1 |
---|
[10425] | 818 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 819 | END DO |
---|
| 820 | ! ! Second derivative (Laplacian) |
---|
[12377] | 821 | DO ji = 2, jpim1 |
---|
[10425] | 822 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 823 | END DO |
---|
[8586] | 824 | END DO |
---|
| 825 | END DO |
---|
[10425] | 826 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1. ) |
---|
[8586] | 827 | ! |
---|
| 828 | ! !-- BiLaplacian in i-direction --! |
---|
[10425] | 829 | DO jl = 1, jpl |
---|
| 830 | DO jj = 2, jpjm1 ! Third derivative |
---|
[12377] | 831 | DO ji = 1, jpim1 |
---|
[10425] | 832 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 833 | END DO |
---|
| 834 | ! ! Fourth derivative |
---|
[12377] | 835 | DO ji = 2, jpim1 |
---|
[10425] | 836 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 837 | END DO |
---|
[8586] | 838 | END DO |
---|
| 839 | END DO |
---|
[10425] | 840 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1. ) |
---|
[8586] | 841 | ! |
---|
| 842 | ! |
---|
[10413] | 843 | SELECT CASE (kn_umx ) |
---|
[8586] | 844 | ! |
---|
| 845 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 846 | ! |
---|
[10425] | 847 | DO jl = 1, jpl |
---|
[12377] | 848 | DO_2D_10_10 |
---|
| 849 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 850 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
| 851 | END_2D |
---|
[8586] | 852 | END DO |
---|
| 853 | ! |
---|
| 854 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 855 | ! |
---|
[10425] | 856 | DO jl = 1, jpl |
---|
[12377] | 857 | DO_2D_10_10 |
---|
| 858 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 859 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 860 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
| 861 | END_2D |
---|
[8586] | 862 | END DO |
---|
| 863 | ! |
---|
| 864 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 865 | ! |
---|
[10425] | 866 | DO jl = 1, jpl |
---|
[12377] | 867 | DO_2D_10_10 |
---|
| 868 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 869 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 870 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[12377] | 871 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 872 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 873 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 874 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
| 875 | END_2D |
---|
[8586] | 876 | END DO |
---|
| 877 | ! |
---|
| 878 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 879 | ! |
---|
[10425] | 880 | DO jl = 1, jpl |
---|
[12377] | 881 | DO_2D_10_10 |
---|
| 882 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 883 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 884 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[12377] | 885 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 886 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 887 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 888 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
| 889 | END_2D |
---|
[8586] | 890 | END DO |
---|
| 891 | ! |
---|
| 892 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 893 | ! |
---|
[10425] | 894 | DO jl = 1, jpl |
---|
[12377] | 895 | DO_2D_10_10 |
---|
| 896 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 897 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 898 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[12377] | 899 | zdx4 = zdx2 * zdx2 |
---|
| 900 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 901 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 902 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 903 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
---|
| 904 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
---|
| 905 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
---|
| 906 | END_2D |
---|
[8586] | 907 | END DO |
---|
| 908 | ! |
---|
| 909 | END SELECT |
---|
[10439] | 910 | ! |
---|
| 911 | ! if pt at u-point is negative then use the upstream value |
---|
| 912 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 913 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 914 | IF( ll_neg ) THEN |
---|
[10425] | 915 | DO jl = 1, jpl |
---|
[12377] | 916 | DO_2D_10_10 |
---|
| 917 | IF( pt_u(ji,jj,jl) < 0._wp .OR. ( imsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
| 918 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 919 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
| 920 | ENDIF |
---|
| 921 | END_2D |
---|
[10413] | 922 | END DO |
---|
| 923 | ENDIF |
---|
[10439] | 924 | ! !-- High order flux in i-direction --! |
---|
[10425] | 925 | DO jl = 1, jpl |
---|
[12377] | 926 | DO_2D_10_10 |
---|
| 927 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
---|
| 928 | END_2D |
---|
[10413] | 929 | END DO |
---|
[8586] | 930 | ! |
---|
| 931 | END SUBROUTINE ultimate_x |
---|
| 932 | |
---|
| 933 | |
---|
[10911] | 934 | SUBROUTINE ultimate_y( pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
---|
[8586] | 935 | !!--------------------------------------------------------------------- |
---|
| 936 | !! *** ROUTINE ultimate_y *** |
---|
| 937 | !! |
---|
[10446] | 938 | !! ** Purpose : compute tracer at v-points |
---|
[8586] | 939 | !! |
---|
[10446] | 940 | !! ** Method : ... |
---|
[8586] | 941 | !! |
---|
| 942 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 943 | !!---------------------------------------------------------------------- |
---|
[10911] | 944 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 945 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 946 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 947 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
---|
| 948 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 949 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
---|
| 950 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
---|
[8586] | 951 | ! |
---|
[10439] | 952 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10930] | 953 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
[10425] | 954 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
---|
[8586] | 955 | !!---------------------------------------------------------------------- |
---|
| 956 | ! |
---|
| 957 | ! !-- Laplacian in j-direction --! |
---|
[10425] | 958 | DO jl = 1, jpl |
---|
[12377] | 959 | DO_2D_10_00 |
---|
| 960 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 961 | END_2D |
---|
| 962 | DO_2D_00_00 |
---|
| 963 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 964 | END_2D |
---|
[8586] | 965 | END DO |
---|
[10425] | 966 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1. ) |
---|
[8586] | 967 | ! |
---|
| 968 | ! !-- BiLaplacian in j-direction --! |
---|
[10425] | 969 | DO jl = 1, jpl |
---|
[12377] | 970 | DO_2D_10_00 |
---|
| 971 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 972 | END_2D |
---|
| 973 | DO_2D_00_00 |
---|
| 974 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 975 | END_2D |
---|
[8586] | 976 | END DO |
---|
[10425] | 977 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1. ) |
---|
[8586] | 978 | ! |
---|
| 979 | ! |
---|
[10413] | 980 | SELECT CASE (kn_umx ) |
---|
[10425] | 981 | ! |
---|
[8586] | 982 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
[10425] | 983 | DO jl = 1, jpl |
---|
[12377] | 984 | DO_2D_10_10 |
---|
| 985 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 986 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
| 987 | END_2D |
---|
[8586] | 988 | END DO |
---|
| 989 | ! |
---|
| 990 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
[10425] | 991 | DO jl = 1, jpl |
---|
[12377] | 992 | DO_2D_10_10 |
---|
| 993 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 994 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 995 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
| 996 | END_2D |
---|
[8586] | 997 | END DO |
---|
| 998 | ! |
---|
| 999 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
[10425] | 1000 | DO jl = 1, jpl |
---|
[12377] | 1001 | DO_2D_10_10 |
---|
| 1002 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1003 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1004 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[12377] | 1005 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1006 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1007 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1008 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 1009 | END_2D |
---|
[8586] | 1010 | END DO |
---|
| 1011 | ! |
---|
| 1012 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
[10425] | 1013 | DO jl = 1, jpl |
---|
[12377] | 1014 | DO_2D_10_10 |
---|
| 1015 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1016 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1017 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[12377] | 1018 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1019 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1020 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1021 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 1022 | END_2D |
---|
[8586] | 1023 | END DO |
---|
| 1024 | ! |
---|
| 1025 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
[10425] | 1026 | DO jl = 1, jpl |
---|
[12377] | 1027 | DO_2D_10_10 |
---|
| 1028 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1029 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1030 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[12377] | 1031 | zdy4 = zdy2 * zdy2 |
---|
| 1032 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1033 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1034 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1035 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
---|
| 1036 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
---|
| 1037 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
---|
| 1038 | END_2D |
---|
[8586] | 1039 | END DO |
---|
| 1040 | ! |
---|
| 1041 | END SELECT |
---|
[10439] | 1042 | ! |
---|
| 1043 | ! if pt at v-point is negative then use the upstream value |
---|
| 1044 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 1045 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 1046 | IF( ll_neg ) THEN |
---|
[10425] | 1047 | DO jl = 1, jpl |
---|
[12377] | 1048 | DO_2D_10_10 |
---|
| 1049 | IF( pt_v(ji,jj,jl) < 0._wp .OR. ( jmsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
| 1050 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
---|
| 1051 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
| 1052 | ENDIF |
---|
| 1053 | END_2D |
---|
[10413] | 1054 | END DO |
---|
| 1055 | ENDIF |
---|
[10439] | 1056 | ! !-- High order flux in j-direction --! |
---|
[10425] | 1057 | DO jl = 1, jpl |
---|
[12377] | 1058 | DO_2D_10_10 |
---|
| 1059 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
---|
| 1060 | END_2D |
---|
[10413] | 1061 | END DO |
---|
[8586] | 1062 | ! |
---|
| 1063 | END SUBROUTINE ultimate_y |
---|
[10413] | 1064 | |
---|
| 1065 | |
---|
[10519] | 1066 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 1067 | !!--------------------------------------------------------------------- |
---|
[10519] | 1068 | !! *** ROUTINE nonosc_ice *** |
---|
[8586] | 1069 | !! |
---|
[10446] | 1070 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
[10519] | 1071 | !! scheme and the before field by a non-oscillatory algorithm |
---|
[8586] | 1072 | !! |
---|
[10446] | 1073 | !! ** Method : ... |
---|
[8586] | 1074 | !!---------------------------------------------------------------------- |
---|
[10439] | 1075 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 1076 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10425] | 1077 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1078 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
---|
[10446] | 1079 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
---|
| 1080 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
[10425] | 1081 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
[8586] | 1082 | ! |
---|
[10425] | 1083 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10475] | 1084 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
---|
| 1085 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
---|
[10425] | 1086 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
---|
[10439] | 1087 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
---|
[8586] | 1088 | !!---------------------------------------------------------------------- |
---|
| 1089 | zbig = 1.e+40_wp |
---|
[10425] | 1090 | |
---|
[10413] | 1091 | ! antidiffusive flux : high order minus low order |
---|
| 1092 | ! -------------------------------------------------- |
---|
[10425] | 1093 | DO jl = 1, jpl |
---|
[12377] | 1094 | DO_2D_10_10 |
---|
| 1095 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1096 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1097 | END_2D |
---|
[8586] | 1098 | END DO |
---|
| 1099 | |
---|
[10413] | 1100 | ! extreme case where pfu_ho has to be zero |
---|
| 1101 | ! ---------------------------------------- |
---|
| 1102 | ! pfu_ho |
---|
| 1103 | ! * ---> |
---|
| 1104 | ! | | * | | |
---|
| 1105 | ! | | | * | |
---|
| 1106 | ! | | | | * |
---|
[10439] | 1107 | ! t_ups : i-1 i i+1 i+2 |
---|
[10945] | 1108 | IF( ll_prelim ) THEN |
---|
[10413] | 1109 | |
---|
[10425] | 1110 | DO jl = 1, jpl |
---|
[12377] | 1111 | DO_2D_00_00 |
---|
| 1112 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
---|
| 1113 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
---|
| 1114 | END_2D |
---|
[10413] | 1115 | END DO |
---|
[10439] | 1116 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1., ztj_ups, 'T', 1. ) |
---|
[8586] | 1117 | |
---|
[10425] | 1118 | DO jl = 1, jpl |
---|
[12377] | 1119 | DO_2D_00_00 |
---|
| 1120 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1121 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1122 | ! |
---|
| 1123 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1124 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1125 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1126 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10425] | 1127 | ENDIF |
---|
[12377] | 1128 | ! |
---|
| 1129 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
---|
| 1130 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
---|
| 1131 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1132 | pfv_ho(ji,jj,jl)=0._wp |
---|
| 1133 | ENDIF |
---|
| 1134 | ! |
---|
| 1135 | ENDIF |
---|
| 1136 | END_2D |
---|
[10413] | 1137 | END DO |
---|
[10425] | 1138 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
---|
[10413] | 1139 | |
---|
| 1140 | ENDIF |
---|
[10425] | 1141 | |
---|
[8586] | 1142 | ! Search local extrema |
---|
| 1143 | ! -------------------- |
---|
[10439] | 1144 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
[10425] | 1145 | z1_dt = 1._wp / pdt |
---|
| 1146 | DO jl = 1, jpl |
---|
| 1147 | |
---|
[12377] | 1148 | DO_2D_11_11 |
---|
| 1149 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
| 1150 | zbup(ji,jj) = -zbig |
---|
| 1151 | zbdo(ji,jj) = zbig |
---|
| 1152 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
---|
| 1153 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1154 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1155 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
| 1156 | zbup(ji,jj) = pt(ji,jj,jl) |
---|
| 1157 | zbdo(ji,jj) = pt(ji,jj,jl) |
---|
| 1158 | ELSE |
---|
| 1159 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1160 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1161 | ENDIF |
---|
| 1162 | END_2D |
---|
[8586] | 1163 | |
---|
[12377] | 1164 | DO_2D_00_00 |
---|
| 1165 | ! |
---|
| 1166 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj), zbup(ji+1,jj), zbup(ji,jj-1), zbup(ji,jj+1) ) ! search max/min in neighbourhood |
---|
| 1167 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
| 1168 | ! |
---|
| 1169 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
---|
| 1170 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
---|
| 1171 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
---|
| 1172 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
---|
| 1173 | ! |
---|
| 1174 | zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
| 1175 | & ) * ( 1. - pamsk ) |
---|
| 1176 | zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
| 1177 | & ) * ( 1. - pamsk ) |
---|
| 1178 | ! |
---|
| 1179 | ! ! up & down beta terms |
---|
| 1180 | ! clem: zbetup and zbetdo must be 0 for zpos>1.e-10 & zneg>1.e-10 (do not put 0 instead of 1.e-10 !!!) |
---|
| 1181 | IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
| 1182 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1183 | ENDIF |
---|
| 1184 | ! |
---|
| 1185 | IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
| 1186 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
| 1187 | ENDIF |
---|
| 1188 | ! |
---|
| 1189 | ! if all the points are outside ice cover |
---|
| 1190 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1191 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
| 1192 | ! |
---|
| 1193 | END_2D |
---|
[8586] | 1194 | END DO |
---|
[10425] | 1195 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
[8586] | 1196 | |
---|
[10413] | 1197 | |
---|
| 1198 | ! monotonic flux in the y direction |
---|
| 1199 | ! --------------------------------- |
---|
[10425] | 1200 | DO jl = 1, jpl |
---|
[12377] | 1201 | DO_2D_10_10 |
---|
| 1202 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
---|
| 1203 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
---|
| 1204 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
---|
| 1205 | ! |
---|
| 1206 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
---|
| 1207 | ! |
---|
| 1208 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
---|
| 1209 | ! |
---|
| 1210 | END_2D |
---|
[10413] | 1211 | |
---|
[12377] | 1212 | DO_2D_10_10 |
---|
| 1213 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
---|
| 1214 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
---|
| 1215 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
---|
| 1216 | ! |
---|
| 1217 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
---|
| 1218 | ! |
---|
| 1219 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
---|
| 1220 | ! |
---|
| 1221 | END_2D |
---|
[10413] | 1222 | |
---|
| 1223 | END DO |
---|
[8586] | 1224 | ! |
---|
[10519] | 1225 | END SUBROUTINE nonosc_ice |
---|
[8586] | 1226 | |
---|
[10446] | 1227 | |
---|
| 1228 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 1229 | !!--------------------------------------------------------------------- |
---|
| 1230 | !! *** ROUTINE limiter_x *** |
---|
| 1231 | !! |
---|
| 1232 | !! ** Purpose : compute flux limiter |
---|
| 1233 | !!---------------------------------------------------------------------- |
---|
[10446] | 1234 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1235 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1236 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1237 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
---|
| 1238 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
---|
[10413] | 1239 | ! |
---|
| 1240 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1241 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1242 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
---|
[10413] | 1243 | !!---------------------------------------------------------------------- |
---|
| 1244 | ! |
---|
[10425] | 1245 | DO jl = 1, jpl |
---|
[12377] | 1246 | DO_2D_00_00 |
---|
| 1247 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
---|
| 1248 | END_2D |
---|
[10413] | 1249 | END DO |
---|
[10425] | 1250 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1251 | |
---|
[10425] | 1252 | DO jl = 1, jpl |
---|
[12377] | 1253 | DO_2D_00_00 |
---|
| 1254 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
| 1255 | |
---|
| 1256 | Rjm = zslpx(ji-1,jj,jl) |
---|
| 1257 | Rj = zslpx(ji ,jj,jl) |
---|
| 1258 | Rjp = zslpx(ji+1,jj,jl) |
---|
[10413] | 1259 | |
---|
[12377] | 1260 | IF( np_limiter == 3 ) THEN |
---|
[10413] | 1261 | |
---|
[12377] | 1262 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1263 | ELSE ; Rr = Rjp |
---|
| 1264 | ENDIF |
---|
[10413] | 1265 | |
---|
[12377] | 1266 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1267 | IF( Rj > 0. ) THEN |
---|
| 1268 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1269 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1270 | ELSE |
---|
| 1271 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1272 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1273 | ENDIF |
---|
| 1274 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1275 | |
---|
[12377] | 1276 | ELSEIF( np_limiter == 2 ) THEN |
---|
| 1277 | IF( Rj /= 0. ) THEN |
---|
| 1278 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1279 | ELSE ; Cr = Rjp / Rj |
---|
[10413] | 1280 | ENDIF |
---|
[12377] | 1281 | ELSE |
---|
| 1282 | Cr = 0. |
---|
| 1283 | ENDIF |
---|
[10425] | 1284 | |
---|
[12377] | 1285 | ! -- superbee -- |
---|
| 1286 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1287 | ! -- van albada 2 -- |
---|
| 1288 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1289 | ! -- sweby (with beta=1) -- |
---|
| 1290 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1291 | ! -- van Leer -- |
---|
| 1292 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1293 | ! -- ospre -- |
---|
| 1294 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1295 | ! -- koren -- |
---|
| 1296 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1297 | ! -- charm -- |
---|
| 1298 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1299 | !ELSE ; zpsi = 0. |
---|
| 1300 | !ENDIF |
---|
| 1301 | ! -- van albada 1 -- |
---|
| 1302 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1303 | ! -- smart -- |
---|
| 1304 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1305 | ! -- umist -- |
---|
| 1306 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1307 | |
---|
[12377] | 1308 | ! high order flux corrected by the limiter |
---|
| 1309 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
[10413] | 1310 | |
---|
[12377] | 1311 | ENDIF |
---|
| 1312 | END_2D |
---|
[10413] | 1313 | END DO |
---|
[10425] | 1314 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1315 | ! |
---|
| 1316 | END SUBROUTINE limiter_x |
---|
| 1317 | |
---|
[10446] | 1318 | |
---|
| 1319 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 1320 | !!--------------------------------------------------------------------- |
---|
| 1321 | !! *** ROUTINE limiter_y *** |
---|
| 1322 | !! |
---|
| 1323 | !! ** Purpose : compute flux limiter |
---|
| 1324 | !!---------------------------------------------------------------------- |
---|
[10446] | 1325 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1326 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
| 1327 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1328 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
---|
| 1329 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
---|
[10413] | 1330 | ! |
---|
| 1331 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1332 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1333 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
---|
[10413] | 1334 | !!---------------------------------------------------------------------- |
---|
| 1335 | ! |
---|
[10425] | 1336 | DO jl = 1, jpl |
---|
[12377] | 1337 | DO_2D_00_00 |
---|
| 1338 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
---|
| 1339 | END_2D |
---|
[10413] | 1340 | END DO |
---|
[10425] | 1341 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1342 | |
---|
[10425] | 1343 | DO jl = 1, jpl |
---|
[12377] | 1344 | DO_2D_00_00 |
---|
| 1345 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
[10413] | 1346 | |
---|
[12377] | 1347 | Rjm = zslpy(ji,jj-1,jl) |
---|
| 1348 | Rj = zslpy(ji,jj ,jl) |
---|
| 1349 | Rjp = zslpy(ji,jj+1,jl) |
---|
[10413] | 1350 | |
---|
[12377] | 1351 | IF( np_limiter == 3 ) THEN |
---|
[10413] | 1352 | |
---|
[12377] | 1353 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1354 | ELSE ; Rr = Rjp |
---|
| 1355 | ENDIF |
---|
[10413] | 1356 | |
---|
[12377] | 1357 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1358 | IF( Rj > 0. ) THEN |
---|
| 1359 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1360 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1361 | ELSE |
---|
| 1362 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1363 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1364 | ENDIF |
---|
| 1365 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1366 | |
---|
[12377] | 1367 | ELSEIF( np_limiter == 2 ) THEN |
---|
[10413] | 1368 | |
---|
[12377] | 1369 | IF( Rj /= 0. ) THEN |
---|
| 1370 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1371 | ELSE ; Cr = Rjp / Rj |
---|
[10425] | 1372 | ENDIF |
---|
[12377] | 1373 | ELSE |
---|
| 1374 | Cr = 0. |
---|
| 1375 | ENDIF |
---|
[10413] | 1376 | |
---|
[12377] | 1377 | ! -- superbee -- |
---|
| 1378 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1379 | ! -- van albada 2 -- |
---|
| 1380 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1381 | ! -- sweby (with beta=1) -- |
---|
| 1382 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1383 | ! -- van Leer -- |
---|
| 1384 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1385 | ! -- ospre -- |
---|
| 1386 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1387 | ! -- koren -- |
---|
| 1388 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1389 | ! -- charm -- |
---|
| 1390 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1391 | !ELSE ; zpsi = 0. |
---|
| 1392 | !ENDIF |
---|
| 1393 | ! -- van albada 1 -- |
---|
| 1394 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1395 | ! -- smart -- |
---|
| 1396 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1397 | ! -- umist -- |
---|
| 1398 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1399 | |
---|
[12377] | 1400 | ! high order flux corrected by the limiter |
---|
| 1401 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
[10425] | 1402 | |
---|
[12377] | 1403 | ENDIF |
---|
| 1404 | END_2D |
---|
[10413] | 1405 | END DO |
---|
[10425] | 1406 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1407 | ! |
---|
| 1408 | END SUBROUTINE limiter_y |
---|
| 1409 | |
---|
[10911] | 1410 | |
---|
[12197] | 1411 | SUBROUTINE Hbig( pdt, phi_max, phs_max, phip_max, pv_i, pv_s, pa_i, pa_ip, pv_ip, pe_s ) |
---|
[10911] | 1412 | !!------------------------------------------------------------------- |
---|
| 1413 | !! *** ROUTINE Hbig *** |
---|
| 1414 | !! |
---|
| 1415 | !! ** Purpose : Thickness correction in case advection scheme creates |
---|
| 1416 | !! abnormally tick ice or snow |
---|
| 1417 | !! |
---|
| 1418 | !! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points |
---|
| 1419 | !! (before advection) and reduce it by adapting ice concentration |
---|
| 1420 | !! 2- check whether snow thickness is larger than the surrounding 9-points |
---|
| 1421 | !! (before advection) and reduce it by sending the excess in the ocean |
---|
| 1422 | !! |
---|
| 1423 | !! ** input : Max thickness of the surrounding 9-points |
---|
| 1424 | !!------------------------------------------------------------------- |
---|
[10930] | 1425 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10911] | 1426 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max ! max ice thick from surrounding 9-pts |
---|
[12197] | 1427 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip, pv_ip |
---|
[10911] | 1428 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
| 1429 | ! |
---|
[12197] | 1430 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1431 | REAL(wp) :: z1_dt, zhip, zhi, zhs, zfra |
---|
[10911] | 1432 | !!------------------------------------------------------------------- |
---|
| 1433 | ! |
---|
[10930] | 1434 | z1_dt = 1._wp / pdt |
---|
[10911] | 1435 | ! |
---|
| 1436 | DO jl = 1, jpl |
---|
| 1437 | |
---|
[12377] | 1438 | DO_2D_11_11 |
---|
| 1439 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
| 1440 | ! |
---|
| 1441 | ! ! -- check h_ip -- ! |
---|
| 1442 | ! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip |
---|
| 1443 | IF( ln_pnd_H12 .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN |
---|
| 1444 | zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) ) |
---|
| 1445 | IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN |
---|
| 1446 | pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl) |
---|
[10911] | 1447 | ENDIF |
---|
[12377] | 1448 | ENDIF |
---|
| 1449 | ! |
---|
| 1450 | ! ! -- check h_i -- ! |
---|
| 1451 | ! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i |
---|
| 1452 | zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
| 1453 | IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1454 | pa_i(ji,jj,jl) = pv_i(ji,jj,jl) / MIN( phi_max(ji,jj,jl), hi_max(jpl) ) !-- bound h_i to hi_max (99 m) |
---|
| 1455 | ENDIF |
---|
| 1456 | ! |
---|
| 1457 | ! ! -- check h_s -- ! |
---|
| 1458 | ! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean |
---|
| 1459 | zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
| 1460 | IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1461 | zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 ) |
---|
[10911] | 1462 | ! |
---|
[12377] | 1463 | wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * z1_dt |
---|
| 1464 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
[10911] | 1465 | ! |
---|
[12377] | 1466 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
| 1467 | pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl) |
---|
| 1468 | ENDIF |
---|
| 1469 | ! |
---|
| 1470 | ENDIF |
---|
| 1471 | END_2D |
---|
[12197] | 1472 | END DO |
---|
| 1473 | ! |
---|
| 1474 | END SUBROUTINE Hbig |
---|
| 1475 | |
---|
| 1476 | |
---|
| 1477 | SUBROUTINE Hsnow( pdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
| 1478 | !!------------------------------------------------------------------- |
---|
| 1479 | !! *** ROUTINE Hsnow *** |
---|
| 1480 | !! |
---|
| 1481 | !! ** Purpose : 1- Check snow load after advection |
---|
| 1482 | !! 2- Correct pond concentration to avoid a_ip > a_i |
---|
| 1483 | !! |
---|
| 1484 | !! ** Method : If snow load makes snow-ice interface to deplet below the ocean surface |
---|
| 1485 | !! then put the snow excess in the ocean |
---|
| 1486 | !! |
---|
| 1487 | !! ** Notes : This correction is crucial because of the call to routine icecor afterwards |
---|
| 1488 | !! which imposes a mini of ice thick. (rn_himin). This imposed mini can artificially |
---|
| 1489 | !! make the snow very thick (if concentration decreases drastically) |
---|
| 1490 | !! This behavior has been seen in Ultimate-Macho and supposedly it can also be true for Prather |
---|
| 1491 | !!------------------------------------------------------------------- |
---|
| 1492 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1493 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip |
---|
| 1494 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
| 1495 | ! |
---|
| 1496 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1497 | REAL(wp) :: z1_dt, zvs_excess, zfra |
---|
| 1498 | !!------------------------------------------------------------------- |
---|
| 1499 | ! |
---|
| 1500 | z1_dt = 1._wp / pdt |
---|
| 1501 | ! |
---|
| 1502 | ! -- check snow load -- ! |
---|
| 1503 | DO jl = 1, jpl |
---|
[12377] | 1504 | DO_2D_11_11 |
---|
| 1505 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
| 1506 | ! |
---|
[12489] | 1507 | zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rho0-rhoi) * r1_rhos ) |
---|
[12377] | 1508 | ! |
---|
| 1509 | IF( zvs_excess > 0._wp ) THEN ! snow-ice interface deplets below the ocean surface |
---|
| 1510 | ! put snow excess in the ocean |
---|
| 1511 | zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 ) |
---|
| 1512 | wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * z1_dt |
---|
| 1513 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
| 1514 | ! correct snow volume and heat content |
---|
| 1515 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
| 1516 | pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess |
---|
[10911] | 1517 | ENDIF |
---|
[12377] | 1518 | ! |
---|
| 1519 | ENDIF |
---|
| 1520 | END_2D |
---|
[12197] | 1521 | END DO |
---|
| 1522 | ! |
---|
| 1523 | !-- correct pond concentration to avoid a_ip > a_i -- ! |
---|
[10911] | 1524 | WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:) |
---|
| 1525 | ! |
---|
[12197] | 1526 | END SUBROUTINE Hsnow |
---|
| 1527 | |
---|
| 1528 | |
---|
[8586] | 1529 | #else |
---|
| 1530 | !!---------------------------------------------------------------------- |
---|
[9570] | 1531 | !! Default option Dummy module NO SI3 sea-ice model |
---|
[8586] | 1532 | !!---------------------------------------------------------------------- |
---|
| 1533 | #endif |
---|
| 1534 | |
---|
| 1535 | !!====================================================================== |
---|
| 1536 | END MODULE icedyn_adv_umx |
---|