| 1 | MODULE dynzdf_imp |
|---|
| 2 | !!============================================================================== |
|---|
| 3 | !! *** MODULE dynzdf_imp *** |
|---|
| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
|---|
| 5 | !!============================================================================== |
|---|
| 6 | !! History : OPA ! 1990-10 (B. Blanke) Original code |
|---|
| 7 | !! 8.0 ! 1997-05 (G. Madec) vertical component of isopycnal |
|---|
| 8 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
|---|
| 9 | !! 3.3 ! 2010-04 (M. Leclair, G. Madec) Forcing averaged over 2 time steps |
|---|
| 10 | !!---------------------------------------------------------------------- |
|---|
| 11 | |
|---|
| 12 | !!---------------------------------------------------------------------- |
|---|
| 13 | !! dyn_zdf_imp : update the momentum trend with the vertical diffu- |
|---|
| 14 | !! sion using a implicit time-stepping. |
|---|
| 15 | !!---------------------------------------------------------------------- |
|---|
| 16 | USE oce ! ocean dynamics and tracers |
|---|
| 17 | USE dom_oce ! ocean space and time domain |
|---|
| 18 | USE sbc_oce ! surface boundary condition: ocean |
|---|
| 19 | USE zdf_oce ! ocean vertical physics |
|---|
| 20 | USE phycst ! physical constants |
|---|
| 21 | USE in_out_manager ! I/O manager |
|---|
| 22 | |
|---|
| 23 | IMPLICIT NONE |
|---|
| 24 | PRIVATE |
|---|
| 25 | |
|---|
| 26 | PUBLIC dyn_zdf_imp ! called by step.F90 |
|---|
| 27 | |
|---|
| 28 | !! * Substitutions |
|---|
| 29 | # include "domzgr_substitute.h90" |
|---|
| 30 | # include "vectopt_loop_substitute.h90" |
|---|
| 31 | !!---------------------------------------------------------------------- |
|---|
| 32 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
|---|
| 33 | !! $Id$ |
|---|
| 34 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
|---|
| 35 | !!---------------------------------------------------------------------- |
|---|
| 36 | CONTAINS |
|---|
| 37 | |
|---|
| 38 | SUBROUTINE dyn_zdf_imp( kt, p2dt ) |
|---|
| 39 | !!---------------------------------------------------------------------- |
|---|
| 40 | !! *** ROUTINE dyn_zdf_imp *** |
|---|
| 41 | !! |
|---|
| 42 | !! ** Purpose : Compute the trend due to the vert. momentum diffusion |
|---|
| 43 | !! and the surface forcing, and add it to the general trend of |
|---|
| 44 | !! the momentum equations. |
|---|
| 45 | !! |
|---|
| 46 | !! ** Method : The vertical momentum mixing trend is given by : |
|---|
| 47 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
|---|
| 48 | !! backward time stepping |
|---|
| 49 | !! Surface boundary conditions: wind stress input (averaged over kt-1/2 & kt+1/2) |
|---|
| 50 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
|---|
| 51 | !! Add this trend to the general trend ua : |
|---|
| 52 | !! ua = ua + dz( avmu dz(u) ) |
|---|
| 53 | !! |
|---|
| 54 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive mixing trend. |
|---|
| 55 | !!--------------------------------------------------------------------- |
|---|
| 56 | USE oce, ONLY : zwd => ta ! use ta as workspace |
|---|
| 57 | USE oce, ONLY : zws => sa ! use sa as workspace |
|---|
| 58 | !! |
|---|
| 59 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
|---|
| 60 | REAL(wp), INTENT( in ) :: p2dt ! vertical profile of tracer time-step |
|---|
| 61 | !! |
|---|
| 62 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 63 | REAL(wp) :: z1_p2dt, zcoef ! temporary scalars |
|---|
| 64 | REAL(wp) :: zzwi, zzws, zrhs ! temporary scalars |
|---|
| 65 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi ! 3D workspace |
|---|
| 66 | !!---------------------------------------------------------------------- |
|---|
| 67 | |
|---|
| 68 | IF( kt == nit000 ) THEN |
|---|
| 69 | IF(lwp) WRITE(numout,*) |
|---|
| 70 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
|---|
| 71 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
|---|
| 72 | ENDIF |
|---|
| 73 | |
|---|
| 74 | ! 0. Local constant initialization |
|---|
| 75 | ! -------------------------------- |
|---|
| 76 | z1_p2dt = 1._wp / p2dt ! inverse of the timestep |
|---|
| 77 | |
|---|
| 78 | ! 1. Vertical diffusion on u |
|---|
| 79 | ! --------------------------- |
|---|
| 80 | ! Matrix and second member construction |
|---|
| 81 | ! bottom boundary condition: both zwi and zws must be masked as avmu can take |
|---|
| 82 | ! non zero value at the ocean bottom depending on the bottom friction |
|---|
| 83 | ! used but the bottom velocities have already been updated with the bottom |
|---|
| 84 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
|---|
| 85 | ! is no need to include these in the implicit calculation. |
|---|
| 86 | ! |
|---|
| 87 | DO jk = 1, jpkm1 ! Matrix |
|---|
| 88 | DO jj = 2, jpjm1 |
|---|
| 89 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 90 | zcoef = - p2dt / fse3u(ji,jj,jk) |
|---|
| 91 | zzwi = zcoef * avmu (ji,jj,jk ) / fse3uw(ji,jj,jk ) |
|---|
| 92 | zwi(ji,jj,jk) = zzwi * umask(ji,jj,jk) |
|---|
| 93 | zzws = zcoef * avmu (ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
|---|
| 94 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
|---|
| 95 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
|---|
| 96 | END DO |
|---|
| 97 | END DO |
|---|
| 98 | END DO |
|---|
| 99 | DO jj = 2, jpjm1 ! Surface boudary conditions |
|---|
| 100 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 101 | zwi(ji,jj,1) = 0._wp |
|---|
| 102 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
|---|
| 103 | END DO |
|---|
| 104 | END DO |
|---|
| 105 | |
|---|
| 106 | ! Matrix inversion starting from the first level |
|---|
| 107 | !----------------------------------------------------------------------- |
|---|
| 108 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 109 | ! |
|---|
| 110 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
|---|
| 111 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
|---|
| 112 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
|---|
| 113 | ! ( ... )( ... ) ( ... ) |
|---|
| 114 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 115 | ! |
|---|
| 116 | ! m is decomposed in the product of an upper and a lower triangular matrix |
|---|
| 117 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 118 | ! The solution (the after velocity) is in ua |
|---|
| 119 | !----------------------------------------------------------------------- |
|---|
| 120 | ! |
|---|
| 121 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
|---|
| 122 | DO jj = 2, jpjm1 |
|---|
| 123 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 124 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
|---|
| 125 | END DO |
|---|
| 126 | END DO |
|---|
| 127 | END DO |
|---|
| 128 | ! |
|---|
| 129 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 == |
|---|
| 130 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 131 | ua(ji,jj,1) = ub(ji,jj,1) + p2dt * ( ua(ji,jj,1) + 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & |
|---|
| 132 | & / ( fse3u(ji,jj,1) * rau0 ) ) |
|---|
| 133 | END DO |
|---|
| 134 | END DO |
|---|
| 135 | DO jk = 2, jpkm1 |
|---|
| 136 | DO jj = 2, jpjm1 |
|---|
| 137 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 138 | zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk) ! zrhs=right hand side |
|---|
| 139 | ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) |
|---|
| 140 | END DO |
|---|
| 141 | END DO |
|---|
| 142 | END DO |
|---|
| 143 | ! |
|---|
| 144 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk == |
|---|
| 145 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 146 | ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
|---|
| 147 | END DO |
|---|
| 148 | END DO |
|---|
| 149 | DO jk = jpk-2, 1, -1 |
|---|
| 150 | DO jj = 2, jpjm1 |
|---|
| 151 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 152 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
|---|
| 153 | END DO |
|---|
| 154 | END DO |
|---|
| 155 | END DO |
|---|
| 156 | |
|---|
| 157 | ! Normalization to obtain the general momentum trend ua |
|---|
| 158 | DO jk = 1, jpkm1 |
|---|
| 159 | DO jj = 2, jpjm1 |
|---|
| 160 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 161 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) * z1_p2dt |
|---|
| 162 | END DO |
|---|
| 163 | END DO |
|---|
| 164 | END DO |
|---|
| 165 | |
|---|
| 166 | |
|---|
| 167 | ! 2. Vertical diffusion on v |
|---|
| 168 | ! --------------------------- |
|---|
| 169 | ! Matrix and second member construction |
|---|
| 170 | ! bottom boundary condition: both zwi and zws must be masked as avmv can take |
|---|
| 171 | ! non zero value at the ocean bottom depending on the bottom friction |
|---|
| 172 | ! used but the bottom velocities have already been updated with the bottom |
|---|
| 173 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
|---|
| 174 | ! is no need to include these in the implicit calculation. |
|---|
| 175 | ! |
|---|
| 176 | DO jk = 1, jpkm1 ! Matrix |
|---|
| 177 | DO jj = 2, jpjm1 |
|---|
| 178 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 179 | zcoef = -p2dt / fse3v(ji,jj,jk) |
|---|
| 180 | zzwi = zcoef * avmv (ji,jj,jk ) / fse3vw(ji,jj,jk ) |
|---|
| 181 | zwi(ji,jj,jk) = zzwi * vmask(ji,jj,jk) |
|---|
| 182 | zzws = zcoef * avmv (ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
|---|
| 183 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
|---|
| 184 | zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws |
|---|
| 185 | END DO |
|---|
| 186 | END DO |
|---|
| 187 | END DO |
|---|
| 188 | DO jj = 2, jpjm1 ! Surface boudary conditions |
|---|
| 189 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 190 | zwi(ji,jj,1) = 0._wp |
|---|
| 191 | zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) |
|---|
| 192 | END DO |
|---|
| 193 | END DO |
|---|
| 194 | |
|---|
| 195 | ! Matrix inversion |
|---|
| 196 | !----------------------------------------------------------------------- |
|---|
| 197 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 198 | ! |
|---|
| 199 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
|---|
| 200 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
|---|
| 201 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
|---|
| 202 | ! ( ... )( ... ) ( ... ) |
|---|
| 203 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 204 | ! |
|---|
| 205 | ! m is decomposed in the product of an upper and lower triangular matrix |
|---|
| 206 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 207 | ! The solution (after velocity) is in 2d array va |
|---|
| 208 | !----------------------------------------------------------------------- |
|---|
| 209 | ! |
|---|
| 210 | DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == |
|---|
| 211 | DO jj = 2, jpjm1 |
|---|
| 212 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 213 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
|---|
| 214 | END DO |
|---|
| 215 | END DO |
|---|
| 216 | END DO |
|---|
| 217 | ! |
|---|
| 218 | DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 == |
|---|
| 219 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 220 | va(ji,jj,1) = vb(ji,jj,1) + p2dt * ( va(ji,jj,1) + 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & |
|---|
| 221 | & / ( fse3v(ji,jj,1) * rau0 ) ) |
|---|
| 222 | END DO |
|---|
| 223 | END DO |
|---|
| 224 | DO jk = 2, jpkm1 |
|---|
| 225 | DO jj = 2, jpjm1 |
|---|
| 226 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 227 | zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk) ! zrhs=right hand side |
|---|
| 228 | va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) |
|---|
| 229 | END DO |
|---|
| 230 | END DO |
|---|
| 231 | END DO |
|---|
| 232 | ! |
|---|
| 233 | DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk == |
|---|
| 234 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 235 | va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
|---|
| 236 | END DO |
|---|
| 237 | END DO |
|---|
| 238 | DO jk = jpk-2, 1, -1 |
|---|
| 239 | DO jj = 2, jpjm1 |
|---|
| 240 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 241 | va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
|---|
| 242 | END DO |
|---|
| 243 | END DO |
|---|
| 244 | END DO |
|---|
| 245 | |
|---|
| 246 | ! Normalization to obtain the general momentum trend va |
|---|
| 247 | DO jk = 1, jpkm1 |
|---|
| 248 | DO jj = 2, jpjm1 |
|---|
| 249 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 250 | va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) * z1_p2dt |
|---|
| 251 | END DO |
|---|
| 252 | END DO |
|---|
| 253 | END DO |
|---|
| 254 | ! |
|---|
| 255 | END SUBROUTINE dyn_zdf_imp |
|---|
| 256 | |
|---|
| 257 | !!============================================================================== |
|---|
| 258 | END MODULE dynzdf_imp |
|---|
