[3] | 1 | MODULE dynzdf_imp_atsk |
---|
| 2 | !!============================================================================== |
---|
| 3 | !! *** MODULE dynzdf_imp_atsk *** |
---|
| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
---|
| 5 | !!============================================================================== |
---|
| 6 | |
---|
| 7 | !!---------------------------------------------------------------------- |
---|
| 8 | !! dyn_zdf_imp_tsk : update the momentum trend with the vertical |
---|
| 9 | !! diffusion using an implicit time-stepping and |
---|
| 10 | !! j-k-i loops. |
---|
| 11 | !!---------------------------------------------------------------------- |
---|
| 12 | !! * Modules used |
---|
| 13 | USE oce ! ocean dynamics and tracers |
---|
| 14 | USE dom_oce ! ocean space and time domain |
---|
| 15 | USE phycst ! physical constants |
---|
| 16 | USE zdf_oce ! ocean vertical physics |
---|
| 17 | USE in_out_manager ! I/O manager |
---|
| 18 | USE taumod ! surface ocean stress |
---|
| 19 | USE trddyn_oce ! dynamics trends diagnostics variables |
---|
| 20 | |
---|
| 21 | IMPLICIT NONE |
---|
| 22 | PRIVATE |
---|
| 23 | |
---|
| 24 | !! * Routine accessibility |
---|
| 25 | PUBLIC dyn_zdf_imp_tsk ! called by step.F90 |
---|
| 26 | |
---|
| 27 | !! * Substitutions |
---|
| 28 | # include "domzgr_substitute.h90" |
---|
| 29 | # include "vectopt_loop_substitute.h90" |
---|
| 30 | !!---------------------------------------------------------------------- |
---|
| 31 | !! OPA 9.0 , LODYC-IPSL (2003) |
---|
| 32 | !!---------------------------------------------------------------------- |
---|
| 33 | |
---|
| 34 | CONTAINS |
---|
| 35 | |
---|
| 36 | SUBROUTINE dyn_zdf_imp_tsk( kt ) |
---|
| 37 | !!---------------------------------------------------------------------- |
---|
| 38 | !! *** ROUTINE dyn_zdf_imp_tsk *** |
---|
| 39 | !! |
---|
| 40 | !! ** Purpose : Compute the trend due to the vert. momentum diffusion |
---|
| 41 | !! and the surface forcing, and add it to the general trend of |
---|
| 42 | !! the momentum equations. |
---|
| 43 | !! |
---|
| 44 | !! ** Method : The vertical momentum mixing trend is given by : |
---|
| 45 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
---|
| 46 | !! backward time stepping |
---|
| 47 | !! Surface boundary conditions: wind stress input |
---|
| 48 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
---|
| 49 | !! Add this trend to the general trend ua : |
---|
| 50 | !! ua = ua + dz( avmu dz(u) ) |
---|
| 51 | !! |
---|
| 52 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
---|
| 53 | !! mixing trend. |
---|
| 54 | !! - Save the trends in (utrd,vtrd) ('key_diatrends') |
---|
| 55 | !! |
---|
| 56 | !! History : |
---|
| 57 | !! 8.5 ! 02-08 (G. Madec) auto-tasking option |
---|
| 58 | !!--------------------------------------------------------------------- |
---|
| 59 | !! * Arguments |
---|
| 60 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
---|
| 61 | |
---|
| 62 | !! * Local declarations |
---|
| 63 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 64 | INTEGER :: ikst, ikenm2, ikstp1 ! temporary integers |
---|
| 65 | REAL(wp) :: & |
---|
| 66 | zrau0r, z2dt, zua, zva, & ! temporary scalars |
---|
| 67 | z2dtf, zcoef, zzws |
---|
| 68 | REAL(wp), DIMENSION(jpi,jpk) :: & |
---|
| 69 | zwx, zwy, zwz, & ! workspace |
---|
| 70 | zwd, zws, zwi, zwt |
---|
| 71 | #if defined key_trddyn |
---|
| 72 | INTEGER :: & |
---|
| 73 | ikbu, ikbum1, ikbv, ikbvm1 & ! temporary integers |
---|
| 74 | #endif |
---|
| 75 | !!---------------------------------------------------------------------- |
---|
| 76 | |
---|
| 77 | IF( kt == nit000 ) THEN |
---|
| 78 | IF(lwp) WRITE(numout,*) |
---|
| 79 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_tsk : vertical momentum diffusion implicit operator' |
---|
| 80 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ auto-task case (j-k-i loop)' |
---|
| 81 | ENDIF |
---|
| 82 | |
---|
| 83 | |
---|
| 84 | ! 0. Local constant initialization |
---|
| 85 | ! -------------------------------- |
---|
| 86 | zrau0r = 1. / rau0 ! inverse of the reference density |
---|
| 87 | z2dt = 2. * rdt ! Leap-frog environnement |
---|
| 88 | ! Euler time stepping when starting from rest |
---|
| 89 | IF( neuler == 0 .AND. kt == nit000 ) z2dt = rdt |
---|
| 90 | |
---|
| 91 | ! ! =============== |
---|
| 92 | DO jj = 2, jpjm1 ! Vertical slab |
---|
| 93 | ! ! =============== |
---|
| 94 | ! 1. Vertical diffusion on u |
---|
| 95 | ! --------------------------- |
---|
| 96 | |
---|
| 97 | ! Matrix and second member construction |
---|
| 98 | ! bottom boundary condition: only zws must be masked as avmu can take |
---|
| 99 | ! non zero value at the ocean bottom depending on the bottom friction |
---|
| 100 | ! used (see zdfmix.F) |
---|
| 101 | DO jk = 1, jpkm1 |
---|
| 102 | DO ji = 2, jpim1 |
---|
| 103 | zcoef = - z2dt / fse3u(ji,jj,jk) |
---|
| 104 | zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
---|
| 105 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
---|
| 106 | zws(ji,jk) = zzws * umask(ji,jj,jk+1) |
---|
| 107 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
---|
| 108 | zwy(ji,jk) = ub(ji,jj,jk) + z2dt * ua(ji,jj,jk) |
---|
| 109 | END DO |
---|
| 110 | END DO |
---|
| 111 | |
---|
| 112 | ! Surface boudary conditions |
---|
| 113 | DO ji = 2, jpim1 |
---|
| 114 | z2dtf = z2dt / ( fse3u(ji,jj,1)*rau0 ) |
---|
| 115 | zwi(ji,1) = 0. |
---|
| 116 | zwd(ji,1) = 1. - zws(ji,1) |
---|
| 117 | zwy(ji,1) = zwy(ji,1) + z2dtf * taux(ji,jj) |
---|
| 118 | END DO |
---|
| 119 | |
---|
| 120 | ! Matrix inversion starting from the first level |
---|
| 121 | ikst = 1 |
---|
| 122 | !!---------------------------------------------------------------------- |
---|
| 123 | !! ZDF.MATRIXSOLVER |
---|
| 124 | !! ******************** |
---|
| 125 | !!---------------------------------------------------------------------- |
---|
| 126 | !! Matrix inversion |
---|
| 127 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
---|
| 128 | ! |
---|
| 129 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
---|
| 130 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
---|
| 131 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
---|
| 132 | ! ( ... )( ... ) ( ... ) |
---|
| 133 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
---|
| 134 | ! |
---|
| 135 | ! m is decomposed in the product of an upper and lower triangular |
---|
| 136 | ! matrix |
---|
| 137 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
---|
| 138 | ! The second member is in 2d array zwy |
---|
| 139 | ! The solution is in 2d array zwx |
---|
| 140 | ! The 2d arry zwt and zwz are work space arrays |
---|
| 141 | ! |
---|
| 142 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
---|
| 143 | ! the resolution of tke matrix where surface tke value is prescribed |
---|
| 144 | ! so that ikstrt=2. |
---|
| 145 | !!---------------------------------------------------------------------- |
---|
| 146 | |
---|
| 147 | ikstp1 = ikst + 1 |
---|
| 148 | ikenm2 = jpk - 2 |
---|
| 149 | DO ji = 2, jpim1 |
---|
| 150 | zwt(ji,ikst) = zwd(ji,ikst) |
---|
| 151 | END DO |
---|
| 152 | DO jk = ikstp1, jpkm1 |
---|
| 153 | DO ji = 2, jpim1 |
---|
| 154 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
---|
| 155 | END DO |
---|
| 156 | END DO |
---|
| 157 | DO ji = 2, jpim1 |
---|
| 158 | zwz(ji,ikst) = zwy(ji,ikst) |
---|
| 159 | END DO |
---|
| 160 | DO jk = ikstp1, jpkm1 |
---|
| 161 | DO ji = 2, jpim1 |
---|
| 162 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
---|
| 163 | END DO |
---|
| 164 | END DO |
---|
| 165 | DO ji = 2, jpim1 |
---|
| 166 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
---|
| 167 | END DO |
---|
| 168 | DO jk = ikenm2, ikst, -1 |
---|
| 169 | DO ji = 2, jpim1 |
---|
| 170 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
---|
| 171 | END DO |
---|
| 172 | END DO |
---|
| 173 | |
---|
| 174 | ! Normalization to obtain the general momentum trend ua |
---|
| 175 | DO jk = 1, jpkm1 |
---|
| 176 | DO ji = 2, jpim1 |
---|
| 177 | zua = ( zwx(ji,jk) - ub(ji,jj,jk) ) / z2dt |
---|
| 178 | #if defined key_trddyn |
---|
| 179 | ! save the vertical diffusive momentum trend |
---|
| 180 | utrd(ji,jj,jk,7) = zua - ua(ji,jj,jk) |
---|
| 181 | #endif |
---|
| 182 | ua(ji,jj,jk) = zua |
---|
| 183 | END DO |
---|
| 184 | END DO |
---|
| 185 | |
---|
| 186 | #if defined key_trddyn |
---|
| 187 | ! diagnose surface and bottom momentum fluxes |
---|
| 188 | DO ji = 2, jpim1 |
---|
| 189 | ! save the surface forcing momentum fluxes |
---|
| 190 | tautrd(ji,jj,1) = taux(ji,jj) / ( fse3u(ji,jj,1)*rau0 ) |
---|
| 191 | ! save bottom friction momentum fluxes |
---|
| 192 | ikbu = MIN( mbathy(ji+1,jj), mbathy(ji,jj) ) |
---|
| 193 | ikbum1 = MAX( ikbu-1, 1 ) |
---|
| 194 | tautrd(ji,jj,3) = - avmu(ji,jj,ikbu) * zwx(ji,ikbum1) & |
---|
| 195 | / ( fse3u(ji,jj,ikbum1)*fse3uw(ji,jj,ikbu) ) |
---|
| 196 | ! subtract surface forcing and bottom friction trend from vertical |
---|
| 197 | ! diffusive momentum trend |
---|
| 198 | utrd(ji,jj,1 ,7) = utrd(ji,jj,1 ,7) - tautrd(ji,jj,1) |
---|
| 199 | utrd(ji,jj,ikbum1,7) = utrd(ji,jj,ikbum1,7) - tautrd(ji,jj,3) |
---|
| 200 | END DO |
---|
| 201 | #endif |
---|
| 202 | |
---|
| 203 | ! 2. Vertical diffusion on v |
---|
| 204 | ! --------------------------- |
---|
| 205 | |
---|
| 206 | ! Matrix and second member construction |
---|
| 207 | ! bottom boundary condition: only zws must be masked as avmv can take |
---|
| 208 | ! non zero value at the ocean bottom depending on the bottom friction |
---|
| 209 | ! used (see zdfmix.F) |
---|
| 210 | DO jk = 1, jpkm1 |
---|
| 211 | DO ji = 2, jpim1 |
---|
| 212 | zcoef = -z2dt/fse3v(ji,jj,jk) |
---|
| 213 | zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
---|
| 214 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
---|
| 215 | zws(ji,jk) = zzws * vmask(ji,jj,jk+1) |
---|
| 216 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
---|
| 217 | zwy(ji,jk) = vb(ji,jj,jk) + z2dt * va(ji,jj,jk) |
---|
| 218 | END DO |
---|
| 219 | END DO |
---|
| 220 | |
---|
| 221 | ! Surface boudary conditions |
---|
| 222 | DO ji = 2, jpim1 |
---|
| 223 | z2dtf = z2dt / ( fse3v(ji,jj,1)*rau0 ) |
---|
| 224 | zwi(ji,1) = 0.e0 |
---|
| 225 | zwd(ji,1) = 1. - zws(ji,1) |
---|
| 226 | zwy(ji,1) = zwy(ji,1) + z2dtf * tauy(ji,jj) |
---|
| 227 | END DO |
---|
| 228 | |
---|
| 229 | ! Matrix inversion starting from the first level |
---|
| 230 | ikst = 1 |
---|
| 231 | !!---------------------------------------------------------------------- |
---|
| 232 | !! ZDF.MATRIXSOLVER |
---|
| 233 | !! ******************** |
---|
| 234 | !!---------------------------------------------------------------------- |
---|
| 235 | !! Matrix inversion |
---|
| 236 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
---|
| 237 | ! |
---|
| 238 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
---|
| 239 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
---|
| 240 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
---|
| 241 | ! ( ... )( ... ) ( ... ) |
---|
| 242 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
---|
| 243 | ! |
---|
| 244 | ! m is decomposed in the product of an upper and lower triangular |
---|
| 245 | ! matrix |
---|
| 246 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
---|
| 247 | ! The second member is in 2d array zwy |
---|
| 248 | ! The solution is in 2d array zwx |
---|
| 249 | ! The 2d arry zwt and zwz are work space arrays |
---|
| 250 | ! |
---|
| 251 | ! N.B. the starting vertical index (ikst) is equal to 1 except for |
---|
| 252 | ! the resolution of tke matrix where surface tke value is prescribed |
---|
| 253 | ! so that ikstrt=2. |
---|
| 254 | !!---------------------------------------------------------------------- |
---|
| 255 | |
---|
| 256 | ikstp1 = ikst + 1 |
---|
| 257 | ikenm2 = jpk - 2 |
---|
| 258 | DO ji = 2, jpim1 |
---|
| 259 | zwt(ji,ikst) = zwd(ji,ikst) |
---|
| 260 | END DO |
---|
| 261 | DO jk = ikstp1, jpkm1 |
---|
| 262 | DO ji = 2, jpim1 |
---|
| 263 | zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) |
---|
| 264 | END DO |
---|
| 265 | END DO |
---|
| 266 | DO ji = 2, jpim1 |
---|
| 267 | zwz(ji,ikst) = zwy(ji,ikst) |
---|
| 268 | END DO |
---|
| 269 | DO jk = ikstp1, jpkm1 |
---|
| 270 | DO ji = 2, jpim1 |
---|
| 271 | zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) |
---|
| 272 | END DO |
---|
| 273 | END DO |
---|
| 274 | DO ji = 2, jpim1 |
---|
| 275 | zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) |
---|
| 276 | END DO |
---|
| 277 | DO jk = ikenm2, ikst, -1 |
---|
| 278 | DO ji = 2, jpim1 |
---|
| 279 | zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) |
---|
| 280 | END DO |
---|
| 281 | END DO |
---|
| 282 | |
---|
| 283 | ! Normalization to obtain the general momentum trend va |
---|
| 284 | DO jk = 1, jpkm1 |
---|
| 285 | DO ji = 2, jpim1 |
---|
| 286 | zva = ( zwx(ji,jk) - vb(ji,jj,jk) ) / z2dt |
---|
| 287 | #if defined key_trddyn |
---|
| 288 | ! save the vertical diffusive momentum fluxes |
---|
| 289 | vtrd(ji,jj,jk,7) = zva - va(ji,jj,jk) |
---|
| 290 | #endif |
---|
| 291 | va(ji,jj,jk) = zva |
---|
| 292 | END DO |
---|
| 293 | END DO |
---|
| 294 | |
---|
| 295 | #if defined key_trddyn |
---|
| 296 | ! diagnose surface and bottom momentum fluxes |
---|
| 297 | DO ji = 2, jpim1 |
---|
| 298 | ! save the surface forcing momentum fluxes |
---|
| 299 | tautrd(ji,jj,2) = tauy(ji,jj) / ( fse3v(ji,jj,1)*rau0 ) |
---|
| 300 | ! save bottom friction momentum fluxes |
---|
| 301 | ikbv = MIN( mbathy(ji,jj+1), mbathy(ji,jj) ) |
---|
| 302 | ikbvm1 = MAX( ikbv-1, 1 ) |
---|
| 303 | tautrd(ji,jj,4) = - avmv(ji,jj,ikbv) * zwx(ji,ikbvm1) & |
---|
| 304 | / ( fse3v(ji,jj,ikbvm1)*fse3vw(ji,jj,ikbv) ) |
---|
| 305 | ! subtract surface forcing and bottom friction trend from vertical |
---|
| 306 | ! diffusive momentum trend |
---|
| 307 | vtrd(ji,jj,1 ,7) = vtrd(ji,jj,1 ,7) - tautrd(ji,jj,2) |
---|
| 308 | vtrd(ji,jj,ikbvm1,7) = vtrd(ji,jj,ikbvm1,7) - tautrd(ji,jj,4) |
---|
| 309 | END DO |
---|
| 310 | #endif |
---|
| 311 | ! ! =============== |
---|
| 312 | END DO ! End of slab |
---|
| 313 | ! ! =============== |
---|
| 314 | END SUBROUTINE dyn_zdf_imp_tsk |
---|
| 315 | |
---|
| 316 | !!============================================================================== |
---|
| 317 | END MODULE dynzdf_imp_atsk |
---|