| 1 | MODULE dynzdf_imp_tam |
|---|
| 2 | #ifdef key_tam |
|---|
| 3 | !!============================================================================== |
|---|
| 4 | !! *** MODULE dynzdf_imp_tam *** |
|---|
| 5 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
|---|
| 6 | !! Tangent and Adjoint Module |
|---|
| 7 | !!============================================================================== |
|---|
| 8 | !! History of the direct module: |
|---|
| 9 | !! ! 90-10 (B. Blanke) Original code |
|---|
| 10 | !! ! 97-05 (G. Madec) vertical component of isopycnal |
|---|
| 11 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
|---|
| 12 | !! History of the TAM module: |
|---|
| 13 | !! 9.0 ! 09-01 (A. Vidard) TAM of the 02-08 version |
|---|
| 14 | !!---------------------------------------------------------------------- |
|---|
| 15 | |
|---|
| 16 | !!---------------------------------------------------------------------- |
|---|
| 17 | !! dyn_zdf_imp : update the momentum trend with the vertical diffu- |
|---|
| 18 | !! sion using an implicit time-stepping scheme. |
|---|
| 19 | !!---------------------------------------------------------------------- |
|---|
| 20 | !! * Modules used |
|---|
| 21 | USE par_kind , ONLY: & ! Precision variables |
|---|
| 22 | & wp |
|---|
| 23 | USE par_oce , ONLY: & ! Ocean space and time domain variables |
|---|
| 24 | & jpi, & |
|---|
| 25 | & jpj, & |
|---|
| 26 | & jpk, & |
|---|
| 27 | & jpim1, & |
|---|
| 28 | & jpjm1, & |
|---|
| 29 | & jpkm1 |
|---|
| 30 | USE oce_tam , ONLY: & ! ocean dynamics and tracers |
|---|
| 31 | & ub_tl, & |
|---|
| 32 | & ua_tl, & |
|---|
| 33 | & vb_tl, & |
|---|
| 34 | & va_tl, & |
|---|
| 35 | & ub_ad, & |
|---|
| 36 | & ua_ad, & |
|---|
| 37 | & vb_ad, & |
|---|
| 38 | & va_ad |
|---|
| 39 | USE zdf_oce , ONLY: & ! ocean vertical physics |
|---|
| 40 | & avmu, & |
|---|
| 41 | & avmv |
|---|
| 42 | USE dom_oce , ONLY: & ! ocean space and time domain |
|---|
| 43 | #if defined key_zco |
|---|
| 44 | & e3t_0, & |
|---|
| 45 | & e3w_0, & |
|---|
| 46 | #else |
|---|
| 47 | & e3u, & |
|---|
| 48 | & e3v, & |
|---|
| 49 | & e3uw, & |
|---|
| 50 | & e3vw, & |
|---|
| 51 | #endif |
|---|
| 52 | & umask, & |
|---|
| 53 | & vmask |
|---|
| 54 | USE phycst , ONLY: & ! physical constants |
|---|
| 55 | & rau0 |
|---|
| 56 | USE in_out_manager, ONLY: & ! I/O manager |
|---|
| 57 | & nit000, & |
|---|
| 58 | & nitend, & |
|---|
| 59 | & numout, & |
|---|
| 60 | & lwp |
|---|
| 61 | |
|---|
| 62 | |
|---|
| 63 | IMPLICIT NONE |
|---|
| 64 | PRIVATE |
|---|
| 65 | |
|---|
| 66 | !! * Routine accessibility |
|---|
| 67 | PUBLIC dyn_zdf_imp_tan ! called by dynzdf_tam.F90 |
|---|
| 68 | PUBLIC dyn_zdf_imp_adj ! called by dynzdf_tam.F90 |
|---|
| 69 | |
|---|
| 70 | !! * Substitutions |
|---|
| 71 | # include "domzgr_substitute.h90" |
|---|
| 72 | # include "vectopt_loop_substitute.h90" |
|---|
| 73 | !!---------------------------------------------------------------------- |
|---|
| 74 | |
|---|
| 75 | CONTAINS |
|---|
| 76 | |
|---|
| 77 | SUBROUTINE dyn_zdf_imp_tan( kt, p2dt ) |
|---|
| 78 | !!---------------------------------------------------------------------- |
|---|
| 79 | !! *** ROUTINE dyn_zdf_imp_tan *** |
|---|
| 80 | !! |
|---|
| 81 | !! ** Purpose of the direct routine: |
|---|
| 82 | !! Compute the trend due to the vert. momentum diffusion |
|---|
| 83 | !! and the surface forcing, and add it to the general trend of |
|---|
| 84 | !! the momentum equations. |
|---|
| 85 | !! |
|---|
| 86 | !! ** Method of the direct routine: |
|---|
| 87 | !! The vertical momentum mixing trend is given by : |
|---|
| 88 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
|---|
| 89 | !! backward time stepping |
|---|
| 90 | !! Surface boundary conditions: wind stress input |
|---|
| 91 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
|---|
| 92 | !! Add this trend to the general trend ua : |
|---|
| 93 | !! ua = ua + dz( avmu dz(u) )E |
|---|
| 94 | !! |
|---|
| 95 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
|---|
| 96 | !! mixing trend. |
|---|
| 97 | !!--------------------------------------------------------------------- |
|---|
| 98 | !! * Modules used |
|---|
| 99 | !! * Arguments |
|---|
| 100 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
|---|
| 101 | REAL(wp), INTENT( in ) :: p2dt ! time-step |
|---|
| 102 | |
|---|
| 103 | !! * Local declarations |
|---|
| 104 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 105 | REAL(wp) :: zrau0r, z2dtf, zcoef, zzws, zrhstl ! temporary scalars |
|---|
| 106 | REAL(wp), DIMENSION(jpi,jpj,jpk):: zwi, zws, zwd ! temporary workspace arrays |
|---|
| 107 | !!---------------------------------------------------------------------- |
|---|
| 108 | |
|---|
| 109 | IF( kt == nit000 ) THEN |
|---|
| 110 | IF(lwp) WRITE(numout,*) |
|---|
| 111 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_tan : vertical momentum diffusion explicit operator' |
|---|
| 112 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ ' |
|---|
| 113 | ENDIF |
|---|
| 114 | ! 0. Local constant initialization |
|---|
| 115 | ! -------------------------------- |
|---|
| 116 | zrau0r = 1. / rau0 ! inverse of the reference density |
|---|
| 117 | |
|---|
| 118 | ! 1. Vertical diffusion on u |
|---|
| 119 | ! --------------------------- |
|---|
| 120 | ! Matrix and second member construction |
|---|
| 121 | ! bottom boundary condition: only zws must be masked as avmu can take |
|---|
| 122 | ! non zero value at the ocean bottom depending on the bottom friction |
|---|
| 123 | ! used (see zdfmix.F) |
|---|
| 124 | DO jk = 1, jpkm1 |
|---|
| 125 | DO jj = 2, jpjm1 |
|---|
| 126 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 127 | zcoef = - p2dt / fse3u(ji,jj,jk) |
|---|
| 128 | zwi(ji,jj,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) * umask(ji,jj,jk) |
|---|
| 129 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
|---|
| 130 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
|---|
| 131 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zzws |
|---|
| 132 | END DO |
|---|
| 133 | END DO |
|---|
| 134 | END DO |
|---|
| 135 | |
|---|
| 136 | ! Surface boudary conditions |
|---|
| 137 | DO jj = 2, jpjm1 |
|---|
| 138 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 139 | zwi(ji,jj,1) = 0. |
|---|
| 140 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
|---|
| 141 | END DO |
|---|
| 142 | END DO |
|---|
| 143 | |
|---|
| 144 | ! Matrix inversion starting from the first level |
|---|
| 145 | !----------------------------------------------------------------------- |
|---|
| 146 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 147 | ! |
|---|
| 148 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
|---|
| 149 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
|---|
| 150 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
|---|
| 151 | ! ( ... )( ... ) ( ... ) |
|---|
| 152 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 153 | ! |
|---|
| 154 | ! m is decomposed in the product of an upper and a lower triangular matrix |
|---|
| 155 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 156 | ! The solution (the after velocity) is in ua |
|---|
| 157 | !----------------------------------------------------------------------- |
|---|
| 158 | |
|---|
| 159 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
|---|
| 160 | DO jk = 2, jpkm1 |
|---|
| 161 | DO jj = 2, jpjm1 |
|---|
| 162 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 163 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
|---|
| 164 | END DO |
|---|
| 165 | END DO |
|---|
| 166 | END DO |
|---|
| 167 | |
|---|
| 168 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
|---|
| 169 | DO jj = 2, jpjm1 |
|---|
| 170 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 171 | ua_tl(ji,jj,1) = ub_tl(ji,jj,1) & |
|---|
| 172 | + p2dt * ua_tl(ji,jj,1) |
|---|
| 173 | END DO |
|---|
| 174 | END DO |
|---|
| 175 | DO jk = 2, jpkm1 |
|---|
| 176 | DO jj = 2, jpjm1 |
|---|
| 177 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 178 | zrhstl = ub_tl(ji,jj,jk) + p2dt * ua_tl(ji,jj,jk) ! zrhs=right hand side |
|---|
| 179 | ua_tl(ji,jj,jk) = zrhstl - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua_tl(ji,jj,jk-1) |
|---|
| 180 | END DO |
|---|
| 181 | END DO |
|---|
| 182 | END DO |
|---|
| 183 | |
|---|
| 184 | ! thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk |
|---|
| 185 | DO jj = 2, jpjm1 |
|---|
| 186 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 187 | ua_tl(ji,jj,jpkm1) = ua_tl(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
|---|
| 188 | END DO |
|---|
| 189 | END DO |
|---|
| 190 | DO jk = jpk-2, 1, -1 |
|---|
| 191 | DO jj = 2, jpjm1 |
|---|
| 192 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 193 | ua_tl(ji,jj,jk) = ( ua_tl(ji,jj,jk) - zws(ji,jj,jk) * ua_tl(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
|---|
| 194 | END DO |
|---|
| 195 | END DO |
|---|
| 196 | END DO |
|---|
| 197 | |
|---|
| 198 | ! Normalization to obtain the general momentum trend ua |
|---|
| 199 | DO jk = 1, jpkm1 |
|---|
| 200 | DO jj = 2, jpjm1 |
|---|
| 201 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 202 | ua_tl(ji,jj,jk) = ( ua_tl(ji,jj,jk) - ub_tl(ji,jj,jk) ) / p2dt |
|---|
| 203 | END DO |
|---|
| 204 | END DO |
|---|
| 205 | END DO |
|---|
| 206 | |
|---|
| 207 | |
|---|
| 208 | ! 2. Vertical diffusion on v |
|---|
| 209 | ! --------------------------- |
|---|
| 210 | ! Matrix and second member construction |
|---|
| 211 | ! bottom boundary condition: only zws must be masked as avmv can take |
|---|
| 212 | ! non zero value at the ocean bottom depending on the bottom friction |
|---|
| 213 | ! used (see zdfmix.F) |
|---|
| 214 | DO jk = 1, jpkm1 |
|---|
| 215 | DO jj = 2, jpjm1 |
|---|
| 216 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 217 | zcoef = -p2dt / fse3v(ji,jj,jk) |
|---|
| 218 | zwi(ji,jj,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
|---|
| 219 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
|---|
| 220 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
|---|
| 221 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zzws |
|---|
| 222 | END DO |
|---|
| 223 | END DO |
|---|
| 224 | END DO |
|---|
| 225 | |
|---|
| 226 | ! Surface boudary conditions |
|---|
| 227 | DO jj = 2, jpjm1 |
|---|
| 228 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 229 | zwi(ji,jj,1) = 0._wp |
|---|
| 230 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
|---|
| 231 | END DO |
|---|
| 232 | END DO |
|---|
| 233 | |
|---|
| 234 | ! Matrix inversion |
|---|
| 235 | !----------------------------------------------------------------------- |
|---|
| 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 solution (after velocity) is in 2d array va |
|---|
| 248 | !----------------------------------------------------------------------- |
|---|
| 249 | |
|---|
| 250 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
|---|
| 251 | DO jk = 2, jpkm1 |
|---|
| 252 | DO jj = 2, jpjm1 |
|---|
| 253 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 254 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
|---|
| 255 | END DO |
|---|
| 256 | END DO |
|---|
| 257 | END DO |
|---|
| 258 | |
|---|
| 259 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
|---|
| 260 | DO jj = 2, jpjm1 |
|---|
| 261 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 262 | va_tl(ji,jj,1) = vb_tl(ji,jj,1) & |
|---|
| 263 | + p2dt * va_tl(ji,jj,1) |
|---|
| 264 | END DO |
|---|
| 265 | END DO |
|---|
| 266 | DO jk = 2, jpkm1 |
|---|
| 267 | DO jj = 2, jpjm1 |
|---|
| 268 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 269 | zrhstl = vb_tl(ji,jj,jk) + p2dt * va_tl(ji,jj,jk) ! zrhs=right hand side |
|---|
| 270 | va_tl(ji,jj,jk) = zrhstl - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va_tl(ji,jj,jk-1) |
|---|
| 271 | END DO |
|---|
| 272 | END DO |
|---|
| 273 | END DO |
|---|
| 274 | |
|---|
| 275 | ! thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk |
|---|
| 276 | DO jj = 2, jpjm1 |
|---|
| 277 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 278 | va_tl(ji,jj,jpkm1) = va_tl(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
|---|
| 279 | END DO |
|---|
| 280 | END DO |
|---|
| 281 | DO jk = jpk-2, 1, -1 |
|---|
| 282 | DO jj = 2, jpjm1 |
|---|
| 283 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 284 | va_tl(ji,jj,jk) = ( va_tl(ji,jj,jk) - zws(ji,jj,jk) * va_tl(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
|---|
| 285 | END DO |
|---|
| 286 | END DO |
|---|
| 287 | END DO |
|---|
| 288 | |
|---|
| 289 | ! Normalization to obtain the general momentum trend va |
|---|
| 290 | DO jk = 1, jpkm1 |
|---|
| 291 | DO jj = 2, jpjm1 |
|---|
| 292 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 293 | va_tl(ji,jj,jk) = ( va_tl(ji,jj,jk) - vb_tl(ji,jj,jk) ) / p2dt |
|---|
| 294 | END DO |
|---|
| 295 | END DO |
|---|
| 296 | END DO |
|---|
| 297 | |
|---|
| 298 | END SUBROUTINE dyn_zdf_imp_tan |
|---|
| 299 | SUBROUTINE dyn_zdf_imp_adj( kt, p2dt ) |
|---|
| 300 | !!---------------------------------------------------------------------- |
|---|
| 301 | !! *** ROUTINE dyn_zdf_imp_adj *** |
|---|
| 302 | !! |
|---|
| 303 | !! ** Purpose of the direct routine: |
|---|
| 304 | !! Compute the trend due to the vert. momentum diffusion |
|---|
| 305 | !! and the surface forcing, and add it to the general trend of |
|---|
| 306 | !! the momentum equations. |
|---|
| 307 | !! |
|---|
| 308 | !! ** Method of the direct routine: |
|---|
| 309 | !! The vertical momentum mixing trend is given by : |
|---|
| 310 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
|---|
| 311 | !! backward time stepping |
|---|
| 312 | !! Surface boundary conditions: wind stress input |
|---|
| 313 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
|---|
| 314 | !! Add this trend to the general trend ua : |
|---|
| 315 | !! ua = ua + dz( avmu dz(u) )E |
|---|
| 316 | !! |
|---|
| 317 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
|---|
| 318 | !! mixing trend. |
|---|
| 319 | !!--------------------------------------------------------------------- |
|---|
| 320 | !! * Modules used |
|---|
| 321 | !! * Arguments |
|---|
| 322 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
|---|
| 323 | REAL(wp), INTENT( in ) :: p2dt ! time-step |
|---|
| 324 | |
|---|
| 325 | !! * Local declarations |
|---|
| 326 | !! * Local declarations |
|---|
| 327 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 328 | REAL(wp) :: zrau0r, z2dtf, zcoef, zzws, zrhsad ! temporary scalars |
|---|
| 329 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zws, zwd! temporary workspace arrays |
|---|
| 330 | !!---------------------------------------------------------------------- |
|---|
| 331 | |
|---|
| 332 | IF( kt == nit000 ) THEN |
|---|
| 333 | IF(lwp) WRITE(numout,*) |
|---|
| 334 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_adj : vertical momentum diffusion explicit operator' |
|---|
| 335 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ ' |
|---|
| 336 | ENDIF |
|---|
| 337 | ! 0. Local constant initialization |
|---|
| 338 | ! -------------------------------- |
|---|
| 339 | zrau0r = 1. / rau0 ! inverse of the reference density |
|---|
| 340 | zrhsad = 0.0_wp |
|---|
| 341 | |
|---|
| 342 | |
|---|
| 343 | |
|---|
| 344 | |
|---|
| 345 | ! 2. Vertical diffusion on v |
|---|
| 346 | ! --------------------------- |
|---|
| 347 | ! Matrix and second member construction |
|---|
| 348 | ! bottom boundary condition: only zws must be masked as avmv can take |
|---|
| 349 | ! non zero value at the ocean bottom depending on the bottom friction |
|---|
| 350 | ! used (see zdfmix.F) |
|---|
| 351 | DO jk = 1, jpkm1 |
|---|
| 352 | DO jj = 2, jpjm1 |
|---|
| 353 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 354 | zcoef = -p2dt / fse3v(ji,jj,jk) |
|---|
| 355 | zwi(ji,jj,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
|---|
| 356 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
|---|
| 357 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
|---|
| 358 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
|---|
| 359 | END DO |
|---|
| 360 | END DO |
|---|
| 361 | END DO |
|---|
| 362 | |
|---|
| 363 | ! Surface boudary conditions |
|---|
| 364 | DO jj = 2, jpjm1 |
|---|
| 365 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 366 | zwi(ji,jj,1) = 0._wp |
|---|
| 367 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
|---|
| 368 | END DO |
|---|
| 369 | END DO |
|---|
| 370 | |
|---|
| 371 | ! Matrix inversion |
|---|
| 372 | !----------------------------------------------------------------------- |
|---|
| 373 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 374 | ! |
|---|
| 375 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
|---|
| 376 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
|---|
| 377 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
|---|
| 378 | ! ( ... )( ... ) ( ... ) |
|---|
| 379 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 380 | ! |
|---|
| 381 | ! m is decomposed in the product of an upper and lower triangular |
|---|
| 382 | ! matrix |
|---|
| 383 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 384 | ! The solution (after velocity) is in 2d array va |
|---|
| 385 | !----------------------------------------------------------------------- |
|---|
| 386 | |
|---|
| 387 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
|---|
| 388 | DO jk = 2, jpkm1 |
|---|
| 389 | DO jj = 2, jpjm1 |
|---|
| 390 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 391 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
|---|
| 392 | END DO |
|---|
| 393 | END DO |
|---|
| 394 | END DO |
|---|
| 395 | |
|---|
| 396 | ! Normalization to obtain the general momentum trend va |
|---|
| 397 | DO jk = jpkm1, 1, -1 |
|---|
| 398 | DO jj = jpjm1, 2, -1 |
|---|
| 399 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 400 | vb_ad(ji,jj,jk) = vb_ad(ji,jj,jk) - va_ad(ji,jj,jk) / p2dt |
|---|
| 401 | va_ad(ji,jj,jk) = va_ad(ji,jj,jk) / p2dt |
|---|
| 402 | END DO |
|---|
| 403 | END DO |
|---|
| 404 | END DO |
|---|
| 405 | ! thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk |
|---|
| 406 | DO jk = 1, jpk-2 |
|---|
| 407 | DO jj = jpjm1, 2, -1 |
|---|
| 408 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 409 | va_ad(ji,jj,jk+1) = va_ad(ji,jj,jk+1) - zws(ji,jj,jk) * va_ad(ji,jj,jk) / zwd(ji,jj,jk) |
|---|
| 410 | va_ad(ji,jj,jk ) = va_ad(ji,jj,jk ) / zwd(ji,jj,jk) |
|---|
| 411 | END DO |
|---|
| 412 | END DO |
|---|
| 413 | END DO |
|---|
| 414 | DO jj = jpjm1, 2, -1 |
|---|
| 415 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 416 | va_ad(ji,jj,jpkm1) = va_ad(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
|---|
| 417 | END DO |
|---|
| 418 | END DO |
|---|
| 419 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
|---|
| 420 | DO jk = jpkm1, 2, -1 |
|---|
| 421 | DO jj = jpjm1, 2, -1 |
|---|
| 422 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 423 | zrhsad = zrhsad + va_ad(ji,jj,jk) |
|---|
| 424 | va_ad(ji,jj,jk-1) = va_ad(ji,jj,jk-1) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va_ad(ji,jj,jk) |
|---|
| 425 | va_ad(ji,jj,jk ) = 0.0_wp |
|---|
| 426 | vb_ad(ji,jj,jk) = vb_ad(ji,jj,jk) + zrhsad |
|---|
| 427 | va_ad(ji,jj,jk) = va_ad(ji,jj,jk) + p2dt * zrhsad |
|---|
| 428 | zrhsad = 0.0_wp |
|---|
| 429 | END DO |
|---|
| 430 | END DO |
|---|
| 431 | END DO |
|---|
| 432 | DO jj = jpjm1, 2, -1 |
|---|
| 433 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 434 | vb_ad(ji,jj,1) = vb_ad(ji,jj,1) + va_ad(ji,jj,1) |
|---|
| 435 | va_ad(ji,jj,1) = va_ad(ji,jj,1) * p2dt |
|---|
| 436 | END DO |
|---|
| 437 | END DO |
|---|
| 438 | |
|---|
| 439 | ! 1. Vertical diffusion on u |
|---|
| 440 | ! --------------------------- |
|---|
| 441 | ! Matrix and second member construction |
|---|
| 442 | ! bottom boundary condition: only zws must be masked as avmu can take |
|---|
| 443 | ! non zero value at the ocean bottom depending on the bottom friction |
|---|
| 444 | ! used (see zdfmix.F) |
|---|
| 445 | DO jk = 1, jpkm1 |
|---|
| 446 | DO jj = 2, jpjm1 |
|---|
| 447 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 448 | zcoef = - p2dt / fse3u(ji,jj,jk) |
|---|
| 449 | zwi(ji,jj,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
|---|
| 450 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
|---|
| 451 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
|---|
| 452 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
|---|
| 453 | END DO |
|---|
| 454 | END DO |
|---|
| 455 | END DO |
|---|
| 456 | |
|---|
| 457 | ! Surface boudary conditions |
|---|
| 458 | DO jj = 2, jpjm1 |
|---|
| 459 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 460 | zwi(ji,jj,1) = 0._wp |
|---|
| 461 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
|---|
| 462 | END DO |
|---|
| 463 | END DO |
|---|
| 464 | |
|---|
| 465 | ! Matrix inversion starting from the first level |
|---|
| 466 | !----------------------------------------------------------------------- |
|---|
| 467 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 468 | ! |
|---|
| 469 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
|---|
| 470 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
|---|
| 471 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
|---|
| 472 | ! ( ... )( ... ) ( ... ) |
|---|
| 473 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 474 | ! |
|---|
| 475 | ! m is decomposed in the product of an upper and a lower triangular matrix |
|---|
| 476 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 477 | ! The solution (the after velocity) is in ua |
|---|
| 478 | !----------------------------------------------------------------------- |
|---|
| 479 | |
|---|
| 480 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
|---|
| 481 | DO jk = 2, jpkm1 |
|---|
| 482 | DO jj = 2, jpjm1 |
|---|
| 483 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 484 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
|---|
| 485 | END DO |
|---|
| 486 | END DO |
|---|
| 487 | END DO |
|---|
| 488 | ! Normalization to obtain the general momentum trend ua |
|---|
| 489 | DO jk = jpkm1, 1, -1 |
|---|
| 490 | DO jj = jpjm1, 2, -1 |
|---|
| 491 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 492 | ub_ad(ji,jj,jk) = ub_ad(ji,jj,jk) - ua_ad(ji,jj,jk) / p2dt |
|---|
| 493 | ua_ad(ji,jj,jk) = ua_ad(ji,jj,jk) / p2dt |
|---|
| 494 | END DO |
|---|
| 495 | END DO |
|---|
| 496 | END DO |
|---|
| 497 | ! thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk |
|---|
| 498 | DO jk = 1, jpk-2 |
|---|
| 499 | DO jj = jpjm1, 2, -1 |
|---|
| 500 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 501 | ua_ad(ji,jj,jk+1) = ua_ad(ji,jj,jk+1) - ua_ad(ji,jj,jk) * zws(ji,jj,jk) / zwd(ji,jj,jk) |
|---|
| 502 | ua_ad(ji,jj,jk) = ua_ad(ji,jj,jk) / zwd(ji,jj,jk) |
|---|
| 503 | END DO |
|---|
| 504 | END DO |
|---|
| 505 | END DO |
|---|
| 506 | DO jj = jpjm1, 2, -1 |
|---|
| 507 | DO ji = fs_jpim1, fs_2, -1 |
|---|
| 508 | ua_ad(ji,jj,jpkm1) = ua_ad(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
|---|
| 509 | END DO |
|---|
| 510 | END DO |
|---|
| 511 | DO jk = jpkm1, 2, -1 |
|---|
| 512 | DO jj = jpjm1, 2, -1 |
|---|
| 513 | DO ji = fs_jpim1, fs_2, -1 ! vector opt. |
|---|
| 514 | zrhsad = zrhsad + ua_ad(ji,jj,jk) |
|---|
| 515 | ua_ad(ji,jj,jk-1) = ua_ad(ji,jj,jk-1) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua_ad(ji,jj,jk) |
|---|
| 516 | ua_ad(ji,jj,jk) = 0.0_wp |
|---|
| 517 | ub_ad(ji,jj,jk) = ub_ad(ji,jj,jk) + zrhsad |
|---|
| 518 | ua_ad(ji,jj,jk) = ua_ad(ji,jj,jk) + zrhsad * p2dt |
|---|
| 519 | zrhsad = 0.0_wp |
|---|
| 520 | END DO |
|---|
| 521 | END DO |
|---|
| 522 | END DO |
|---|
| 523 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
|---|
| 524 | DO jj = 2, jpjm1 |
|---|
| 525 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 526 | ub_ad(ji,jj,1) = ub_ad(ji,jj,1) + ua_ad(ji,jj,1) |
|---|
| 527 | ua_ad(ji,jj,1) = p2dt * ua_ad(ji,jj,1) |
|---|
| 528 | END DO |
|---|
| 529 | END DO |
|---|
| 530 | |
|---|
| 531 | |
|---|
| 532 | |
|---|
| 533 | END SUBROUTINE dyn_zdf_imp_adj |
|---|
| 534 | #endif |
|---|
| 535 | !!============================================================================== |
|---|
| 536 | END MODULE dynzdf_imp_tam |
|---|
