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- 2010-11-17T12:09:36+01:00 (13 years ago)
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branches/nemo_v3_3_beta/NEMOGCM/NEMO/OPA_SRC/LDF/ldfslp.F90
r2371 r2401 10 10 !! 1.0 ! 2005-10 (A. Beckmann) correction for s-coordinates 11 11 !! 3.3 ! 2010-10 (G. Nurser, C. Harris, G. Madec) add Griffies operator 12 !! - ! 2010-11 (F. Dupond, G. Madec) bug correction in slopes just below the ML 12 13 !!---------------------------------------------------------------------- 13 14 #if defined key_ldfslp || defined key_esopa … … 93 94 USE oce , zgru => ua ! use ua as workspace 94 95 USE oce , zgrv => va ! use va as workspace 95 USE oce , zw y=> ta ! use ta as workspace96 USE oce , zww => ta ! use ta as workspace 96 97 USE oce , zwz => sa ! use sa as workspace 97 98 !! … … 103 104 INTEGER :: ii0, ii1, iku ! temporary integer 104 105 INTEGER :: ij0, ij1, ikv ! temporary integer 105 REAL(wp) :: zeps, zmg, zm05g, zalpha ! temporary scalars 106 REAL(wp) :: zcoef1, zcoef2, zcoef3 ! - - 107 REAL(wp) :: zcofu , zcofv , zcofw ! - - 108 REAL(wp) :: zau, zbu, zai, zbi, z1u, z1wu ! - - 109 REAL(wp) :: zav, zbv, zaj, zbj, z1v, z1wv ! 110 REAL(wp), DIMENSION(jpi,jpj,jpk) :: zww ! 3D workspace 106 REAL(wp) :: zeps, zm1_g, zm1_2g, z1_16 ! local scalars 107 REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - 108 REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - 109 REAL(wp) :: zck, zfk, zbw ! - - 110 REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdzr ! 3D workspace 111 111 !!---------------------------------------------------------------------- 112 112 113 zeps = 1.e-20 ! Local constant initialization 114 zmg = -1.0 / grav 115 zm05g = -0.5 / grav 113 zeps = 1.e-20_wp !== Local constant initialization ==! 114 z1_16 = 1.0_wp / 16._wp 115 zm1_g = -1.0_wp / grav 116 zm1_2g = -0.5_wp / grav 116 117 ! 117 118 zww(:,:,:) = 0.e0 118 119 zwz(:,:,:) = 0.e0 119 ! ! horizontal density gradient computation120 DO jk = 1, jpk 120 ! 121 DO jk = 1, jpk !== i- & j-gradient of density ==! 121 122 DO jj = 1, jpjm1 122 123 DO ji = 1, fs_jpim1 ! vector opt. … … 141 142 END DO 142 143 ENDIF 143 144 CALL ldf_slp_mxl( prd, pn2 ) ! Slopes of isopycnal surfaces just below the mixed layer 144 ! 145 zdzr(:,:,1) = 0._wp !== Local vertical density gradient at T-point == ! (evaluated from N^2) 146 DO jk = 2, jpkm1 147 ! ! zdzr = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point 148 ! ! trick: tmask(ik ) = 0 => all pn2 = 0 => zdzr = 0 149 ! ! else tmask(ik+1) = 0 => pn2(ik+1) = 0 => zdzr divides by 1 150 ! ! umask(ik+1) /= 0 => all pn2 /= 0 => zdzr divides by 2 151 ! ! NB: 1/(tmask+1) = (1-.5*tmask) substitute a / by a * ==> faster 152 zdzr(:,:,jk) = zm1_g * ( prd(:,:,jk) + 1._wp ) & 153 & * ( pn2(:,:,jk) + pn2(:,:,jk+1) ) * ( 1._wp - 0.5_wp * tmask(:,:,jk+1) ) 154 END DO 155 ! 156 ! !== Slopes just below the mixed layer ==! 157 CALL ldf_slp_mxl( prd, pn2, zgru, zgrv, zdzr ) ! output: uslpml, vslpml, wslpiml, wslpjml 145 158 146 159 … … 148 161 ! =========================== | vslp = d/dj( prd ) / d/dz( prd ) 149 162 ! 150 ! !* Local vertical density gradient evaluated from N^2151 DO jk = 2, jpkm1 ! zwy = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point152 DO jj = 1, jpj153 DO ji = 1, jpi154 zwy(ji,jj,jk) = zmg * ( prd(ji,jj,jk) + 1. ) * ( pn2 (ji,jj,jk) + pn2 (ji,jj,jk+1) ) &155 & / MAX( tmask(ji,jj,jk) + tmask(ji,jj,jk+1), 1. )156 END DO157 END DO158 END DO159 163 DO jk = 2, jpkm1 !* Slopes at u and v points 160 164 DO jj = 2, jpjm1 161 165 DO ji = fs_2, fs_jpim1 ! vector opt. 162 ! horizontal and vertical density gradient at u- and v-points 163 zau = 1. / e1u(ji,jj) * zgru(ji,jj,jk) 164 zav = 1. / e2v(ji,jj) * zgrv(ji,jj,jk) 165 zbu = 0.5 * ( zwy(ji,jj,jk) + zwy(ji+1,jj ,jk) ) 166 zbv = 0.5 * ( zwy(ji,jj,jk) + zwy(ji ,jj+1,jk) ) 167 ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 168 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 169 zbu = MIN( zbu, -100.*ABS( zau ), -7.e+3/fse3u(ji,jj,jk)*ABS( zau ) ) 170 zbv = MIN( zbv, -100.*ABS( zav ), -7.e+3/fse3v(ji,jj,jk)*ABS( zav ) ) 171 ! uslp and vslp output in zwz and zww, resp. 172 zalpha = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj,jk) ) 173 zwz (ji,jj,jk) = ( ( 1. - zalpha) * zau / ( zbu - zeps ) & 174 & + zalpha * uslpml(ji,jj) & 175 & * 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk)-fse3u(ji,jj,1) ) & 176 & / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 5. ) ) * umask(ji,jj,jk) 177 zalpha = MAX( omlmask(ji,jj,jk), omlmask(ji,jj+1,jk) ) 178 zww (ji,jj,jk) = ( ( 1. - zalpha) * zav / ( zbv - zeps ) & 179 & + zalpha * vslpml(ji,jj) & 180 & * 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk)-fse3v(ji,jj,1) ) & 181 & / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 5. ) ) * vmask(ji,jj,jk) 166 ! ! horizontal and vertical density gradient at u- and v-points 167 zau = zgru(ji,jj,jk) / e1u(ji,jj) 168 zav = zgrv(ji,jj,jk) / e2v(ji,jj) 169 zbu = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji+1,jj ,jk) ) 170 zbv = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji ,jj+1,jk) ) 171 ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 172 ! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 173 zbu = MIN( zbu, -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,jk)* ABS( zau ) ) 174 zbv = MIN( zbv, -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,jk)* ABS( zav ) ) 175 ! ! uslp and vslp output in zwz and zww, resp. 176 zfi = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj,jk) ) 177 zfj = MAX( omlmask(ji,jj,jk), omlmask(ji,jj+1,jk) ) 178 zwz(ji,jj,jk) = ( ( 1. - zfi) * zau / ( zbu - zeps ) & 179 & + zfi * uslpml(ji,jj) & 180 & * 0.5_wp * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk)-fse3u(ji,jj,1) ) & 181 & / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 5._wp ) ) * umask(ji,jj,jk) 182 zww(ji,jj,jk) = ( ( 1. - zfj) * zav / ( zbv - zeps ) & 183 & + zfj * vslpml(ji,jj) & 184 & * 0.5_wp * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk)-fse3v(ji,jj,1) ) & 185 & / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 5. ) ) * vmask(ji,jj,jk) 186 !!gm modif to suppress omlmask.... (as in Griffies case) 187 ! ! ! jk must be >= ML level for zf=1. otherwise zf=0. 188 ! zfi = REAL( 1 - 1/(1 + jk / MAX( nmln(ji+1,jj), nmln(ji,jj) ) ), wp ) 189 ! zfj = REAL( 1 - 1/(1 + jk / MAX( nmln(ji,jj+1), nmln(ji,jj) ) ), wp ) 190 ! zci = 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) ) 191 ! zcj = 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 10. ) ) 192 ! zwz(ji,jj,jk) = ( zfi * zai / ( zbi - zeps ) + ( 1._wp - zfi ) * wslpiml(ji,jj) * zci ) * tmask(ji,jj,jk) 193 ! zww(ji,jj,jk) = ( zfj * zaj / ( zbj - zeps ) + ( 1._wp - zfj ) * wslpjml(ji,jj) * zcj ) * tmask(ji,jj,jk) 194 !!gm end modif 182 195 END DO 183 196 END DO … … 185 198 CALL lbc_lnk( zwz, 'U', -1. ) ; CALL lbc_lnk( zww, 'V', -1. ) ! lateral boundary conditions 186 199 ! 187 zcofu = 1. / 16. !* horizontal Shapiro filter 188 zcofv = 1. / 16. 200 ! !* horizontal Shapiro filter 189 201 DO jk = 2, jpkm1 190 202 DO jj = 2, jpjm1, jpj-3 ! rows jj=2 and =jpjm1 only 191 203 DO ji = 2, jpim1 192 uslp(ji,jj,jk) = z cofu* ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &204 uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & 193 205 & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & 194 206 & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & 195 207 & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & 196 208 & + 4.* zwz(ji ,jj ,jk) ) 197 vslp(ji,jj,jk) = z cofv* ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &209 vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & 198 210 & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & 199 211 & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & … … 204 216 DO jj = 3, jpj-2 ! other rows 205 217 DO ji = fs_2, fs_jpim1 ! vector opt. 206 uslp(ji,jj,jk) = z cofu* ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &218 uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & 207 219 & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & 208 220 & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & 209 221 & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & 210 222 & + 4.* zwz(ji ,jj ,jk) ) 211 vslp(ji,jj,jk) = z cofv* ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &223 vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & 212 224 & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & 213 225 & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & … … 219 231 DO jj = 2, jpjm1 220 232 DO ji = fs_2, fs_jpim1 ! vector opt. 221 z1u = ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk) )*.5 222 z1v = ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk) )*.5 223 z1wu = ( umask(ji,jj,jk) + umask(ji,jj,jk+1) )*.5 224 z1wv = ( vmask(ji,jj,jk) + vmask(ji,jj,jk+1) )*.5 225 uslp(ji,jj,jk) = uslp(ji,jj,jk) * z1u * z1wu 226 vslp(ji,jj,jk) = vslp(ji,jj,jk) * z1v * z1wv 233 uslp(ji,jj,jk) = uslp(ji,jj,jk) * ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk ) ) * 0.5_wp & 234 & * ( umask(ji,jj ,jk) + umask(ji,jj ,jk+1) ) * 0.5_wp 235 vslp(ji,jj,jk) = vslp(ji,jj,jk) * ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk ) ) * 0.5_wp & 236 & * ( vmask(ji ,jj,jk) + vmask(ji ,jj,jk+1) ) * 0.5_wp 227 237 END DO 228 238 END DO … … 233 243 ! =========================== | wslpj = mij( d/dj( prd ) / d/dz( prd ) 234 244 ! 235 ! !* Local vertical density gradient evaluated from N^2 236 DO jk = 2, jpkm1 ! zwy = d/dz(prd)= - mk ( prd ) / grav * pn2 -- at w point 237 DO jj = 1, jpj 238 DO ji = 1, jpi 239 zwy(ji,jj,jk) = zm05g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. ) 240 END DO 241 END DO 242 END DO 243 DO jk = 2, jpkm1 !* Slopes at w point 245 DO jk = 2, jpkm1 244 246 DO jj = 2, jpjm1 245 247 DO ji = fs_2, fs_jpim1 ! vector opt. 246 ! ! horizontal density i-gradient at w-points247 z coef1 = MAX( zeps, umask(ji-1,jj,jk )+umask(ji,jj,jk ) &248 & +umask(ji-1,jj,jk-1)+umask(ji,jj,jk-1) )249 zcoef1 = 1. / ( zcoef1 * e1t (ji,jj) )250 z ai = zcoef1 * ( zgru(ji ,jj,jk ) + zgru(ji ,jj,jk-1)&251 & + zgru(ji-1,jj,jk-1) + zgru(ji-1,jj,jk ) ) * tmask (ji,jj,jk)252 ! ! horizontal density j-gradient at w-points253 zcoef2 = MAX( zeps, vmask(ji,jj-1,jk )+vmask(ji,jj,jk-1) &254 & +vmask(ji,jj-1,jk-1)+vmask(ji,jj,jk ) )255 zcoef2 = 1.0 / ( zcoef2 * e2t (ji,jj))256 zaj = zcoef2 * ( zgrv(ji,jj ,jk ) + zgrv(ji,jj ,jk-1)&257 & + zgrv(ji,jj-1,jk-1) + zgrv(ji,jj-1,jk ) )* tmask (ji,jj,jk)248 ! !* Local vertical density gradient evaluated from N^2 249 zbw = zm1_2g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. ) 250 ! !* Slopes at w point 251 ! ! i- & j-gradient of density at w-points 252 zci = MAX( umask(ji-1,jj,jk ) + umask(ji,jj,jk ) & 253 & + umask(ji-1,jj,jk-1) + umask(ji,jj,jk-1) , zeps ) * e1t(ji,jj) 254 zcj = MAX( vmask(ji,jj-1,jk ) + vmask(ji,jj,jk-1) & 255 & + vmask(ji,jj-1,jk-1) + vmask(ji,jj,jk ) , zeps ) * e2t(ji,jj) 256 zai = ( zgru (ji-1,jj,jk ) + zgru (ji,jj,jk-1) & 257 & + zgru (ji-1,jj,jk-1) + zgru (ji,jj,jk ) ) / zci * tmask (ji,jj,jk) 258 zaj = ( zgrv (ji,jj-1,jk ) + zgrv (ji,jj,jk-1) & 259 & + zgrv (ji,jj-1,jk-1) + zgrv (ji,jj,jk ) ) / zcj * tmask (ji,jj,jk) 258 260 ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0. 259 ! ! static instability: kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 260 zbi = MIN( zwy (ji,jj,jk),- 100.*ABS(zai), -7.e+3/fse3w(ji,jj,jk)*ABS(zai) ) 261 zbj = MIN( zwy (ji,jj,jk), -100.*ABS(zaj), -7.e+3/fse3w(ji,jj,jk)*ABS(zaj) ) 262 ! ! wslpi and wslpj output in zwz and zww, resp. 263 zalpha = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) 264 zcoef3 = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. ) 265 zwz(ji,jj,jk) = ( zai / ( zbi - zeps) * ( 1. - zalpha ) & 266 & + zcoef3 * wslpiml(ji,jj) * zalpha ) * tmask (ji,jj,jk) 267 zww(ji,jj,jk) = ( zaj / ( zbj - zeps) * ( 1. - zalpha ) & 268 & + zcoef3 * wslpjml(ji,jj) * zalpha ) * tmask (ji,jj,jk) 269 END DO 270 END DO 271 END DO 272 CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions on zwz and zww 261 ! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 262 zbi = MIN( zbw ,- 100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zai ) ) 263 zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zaj ) ) 264 ! ! wslpi and wslpj with ML flattening (output in zwz and zww, resp.) 265 zfk = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) ! zfk=1 in the ML otherwise zfk=0 266 zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10._wp ) 267 zwz(ji,jj,jk) = ( zai / ( zbi - zeps ) * ( 1._wp - zfk ) + zck * wslpiml(ji,jj) * zfk ) * tmask(ji,jj,jk) 268 zww(ji,jj,jk) = ( zaj / ( zbj - zeps ) * ( 1._wp - zfk ) + zck * wslpjml(ji,jj) * zfk ) * tmask(ji,jj,jk) 269 270 !!gm modif to suppress omlmask.... (as in Griffies operator) 271 ! ! ! jk must be >= ML level for zfk=1. otherwise zfk=0. 272 ! zfk = REAL( 1 - 1/(1 + jk / nmln(ji+1,jj)), wp ) 273 ! zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. ) 274 ! zwz(ji,jj,jk) = ( zfk * zai / ( zbi - zeps ) + ( 1._wp - zfk ) * wslpiml(ji,jj) * zck ) * tmask(ji,jj,jk) 275 ! zww(ji,jj,jk) = ( zfk * zaj / ( zbj - zeps ) + ( 1._wp - zfk ) * wslpjml(ji,jj) * zck ) * tmask(ji,jj,jk) 276 !!gm end modif 277 END DO 278 END DO 279 END DO 280 CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions 273 281 ! 274 282 ! !* horizontal Shapiro filter … … 276 284 DO jj = 2, jpjm1, jpj-3 ! rows jj=2 and =jpjm1 277 285 DO ji = 2, jpim1 278 zcofw = tmask(ji,jj,jk) / 16.279 286 wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & 280 287 & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & 281 288 & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & 282 289 & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & 283 & + 4.* zwz(ji ,jj ,jk) ) * zcofw290 & + 4.* zwz(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) 284 291 285 292 wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & … … 287 294 & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & 288 295 & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & 289 & + 4.* zww(ji ,jj ,jk) ) * zcofw296 & + 4.* zww(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) 290 297 END DO 291 298 END DO 292 299 DO jj = 3, jpj-2 ! other rows 293 300 DO ji = fs_2, fs_jpim1 ! vector opt. 294 zcofw = tmask(ji,jj,jk) / 16.295 301 wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & 296 302 & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & 297 303 & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & 298 304 & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & 299 & + 4.* zwz(ji ,jj ,jk) ) * zcofw305 & + 4.* zwz(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) 300 306 301 307 wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & … … 303 309 & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & 304 310 & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & 305 & + 4.* zww(ji ,jj ,jk) ) * zcofw311 & + 4.* zww(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) 306 312 END DO 307 313 END DO … … 309 315 DO jj = 2, jpjm1 310 316 DO ji = fs_2, fs_jpim1 ! vector opt. 311 z 1u = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) *.5312 z1v = ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) *.5313 wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * z 1u * z1v314 wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * z 1u * z1v317 zck = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) & 318 & * ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) * 0.25 319 wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * zck 320 wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * zck 315 321 END DO 316 322 END DO … … 573 579 574 580 575 SUBROUTINE ldf_slp_mxl( prd, pn2 )581 SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr ) 576 582 !!---------------------------------------------------------------------- 577 583 !! *** ROUTINE ldf_slp_mxl *** … … 580 586 !! the mixed layer. 581 587 !! 582 !! ** Method : 583 !! The slope in the i-direction is computed at u- and w-points 584 !! (uslp, wslpi) and the slope in the j-direction is computed at 585 !! v- and w-points (vslp, wslpj). 586 !! They are bounded by 1/100 over the whole ocean, and within the 587 !! surface layer they are bounded by the distance to the surface 588 !! ( slope<= depth/l where l is the length scale of horizontal 589 !! diffusion (here, aht=2000m2/s ==> l=20km with a typical velocity 590 !! of 10cm/s) 591 !! 592 !! ** Action : Compute uslp, wslpi, and vslp, wslpj, the i- and j-slopes 593 !! of now neutral surfaces at u-, w- and v- w-points, resp. 594 !!---------------------------------------------------------------------- 595 USE oce , zgru => ua ! ua, va used as workspace and set to hor. 596 USE oce , zgrv => va ! density gradient in ldf_slp 597 !! 598 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: prd ! in situ density 599 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.) 600 !! 601 INTEGER :: ji, jj, jk ! dummy loop indices 602 INTEGER :: ik, ikm1 ! temporary integers 603 REAL(wp) :: zeps, zmg, zm05g ! temporary scalars 604 REAL(wp) :: zcoef1, zcoef2 ! - - 605 REAL(wp) :: zau, zbu, zai, zbi ! - - 606 REAL(wp) :: zav, zbv, zaj, zbj ! - - 607 REAL(wp), DIMENSION(jpi,jpj) :: zwy ! 2D workspace 608 !!---------------------------------------------------------------------- 609 610 zeps = 1.e-20 ! Local constant initialization 611 zmg = -1.0 / grav 612 zm05g = -0.5 / grav 588 !! ** Method : The slope in the i-direction is computed at u- & w-points 589 !! (uslpml, wslpiml) and the slope in the j-direction is computed 590 !! at v- and w-points (vslpml, wslpjml) with the same bounds as 591 !! in ldf_slp. 592 !! 593 !! ** Action : uslpml, wslpiml : i- & j-slopes of neutral surfaces 594 !! vslpml, wslpjml just below the mixed layer 595 !! omlmask : mixed layer mask 596 !!---------------------------------------------------------------------- 597 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: prd ! in situ density 598 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.) 599 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: p_gru, p_grv ! i- & j-gradient of density (u- & v-pts) 600 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: p_dzr ! z-gradient of density (T-point) 601 !! 602 INTEGER :: ji , jj , jk ! dummy loop indices 603 INTEGER :: iku, ikv, ik, ikm1 ! local integers 604 REAL(wp) :: zeps, zm1_g, zm1_2g ! local scalars 605 REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - 606 REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - 607 REAL(wp) :: zck, zfk, zbw ! - - 608 !!---------------------------------------------------------------------- 609 610 zeps = 1.e-20_wp !== Local constant initialization ==! 611 zm1_g = -1.0_wp / grav 612 zm1_2g = -0.5_wp / grav 613 613 ! 614 614 uslpml (1,:) = 0.e0 ; uslpml (jpi,:) = 0.e0 … … 616 616 wslpiml(1,:) = 0.e0 ; wslpiml(jpi,:) = 0.e0 617 617 wslpjml(1,:) = 0.e0 ; wslpjml(jpi,:) = 0.e0 618 619 ! ! surface mixed layer mask620 DO jk = 1, jpk 618 ! 619 ! !== surface mixed layer mask ! 620 DO jk = 1, jpk ! =1 inside the mixed layer, =0 otherwise 621 621 # if defined key_vectopt_loop 622 622 DO jj = 1, 1 … … 645 645 !----------------------------------------------------------------------- 646 646 ! 647 zwy(:,jpj) = 0.e0 !* vertical density gradient for u-slope (from N^2)648 zwy(jpi,:) = 0.e0649 # if defined key_vectopt_loop650 DO jj = 1, 1651 DO ji = 1, jpij-jpi ! vector opt. (forced unrolling)652 # else653 DO jj = 1, jpjm1654 DO ji = 1, jpim1655 # endif656 ik = MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) ! avoid spurious recirculation657 ik = MIN( ik, jpkm1 ) ! if ik = jpk take jpkm1 values658 zwy(ji,jj) = zmg * ( prd(ji,jj,ik) + 1. ) * ( pn2 (ji,jj,ik) + pn2 (ji,jj,ik+1) ) &659 & / MAX( tmask(ji,jj,ik) + tmask(ji,jj,ik+1), 1. )660 END DO661 END DO662 CALL lbc_lnk( zwy, 'U', 1. ) ! lateral boundary conditions NO sign change663 664 ! !* Slope at u points665 647 # if defined key_vectopt_loop 666 648 DO jj = 1, 1 … … 670 652 DO ji = 2, jpim1 671 653 # endif 672 ! horizontal and vertical density gradient at u-points 673 ik = MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) 674 ik = MIN( ik, jpkm1 ) 675 zau = 1./ e1u(ji,jj) * zgru(ji,jj,ik) 676 zbu = 0.5*( zwy(ji,jj) + zwy(ji+1,jj) ) 677 ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 678 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 679 zbu = MIN( zbu, -100.*ABS(zau), -7.e+3/fse3u(ji,jj,ik)*ABS(zau) ) 680 ! uslpml 681 uslpml (ji,jj) = zau / ( zbu - zeps ) * umask (ji,jj,ik) 682 END DO 683 END DO 684 CALL lbc_lnk( uslpml, 'U', -1. ) ! lateral boundary conditions (i-gradient => sign change) 685 686 ! !* vertical density gradient for v-slope (from N^2) 687 # if defined key_vectopt_loop 688 DO jj = 1, 1 689 DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) 690 # else 691 DO jj = 1, jpjm1 692 DO ji = 1, jpim1 693 # endif 694 ik = MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) 695 ik = MIN( ik, jpkm1 ) 696 zwy(ji,jj) = zmg * ( prd(ji,jj,ik) + 1. ) * ( pn2 (ji,jj,ik) + pn2 (ji,jj,ik+1) ) & 697 & / MAX( tmask(ji,jj,ik) + tmask(ji,jj,ik+1), 1. ) 698 END DO 699 END DO 700 CALL lbc_lnk( zwy, 'V', 1. ) ! lateral boundary conditions NO sign change 701 702 ! !* Slope at v points 703 # if defined key_vectopt_loop 704 DO jj = 1, 1 705 DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) 706 # else 707 DO jj = 2, jpjm1 708 DO ji = 2, jpim1 709 # endif 710 ! horizontal and vertical density gradient at v-points 711 ik = MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) 712 ik = MIN( ik,jpkm1 ) 713 zav = 1./ e2v(ji,jj) * zgrv(ji,jj,ik) 714 zbv = 0.5*( zwy(ji,jj) + zwy(ji,jj+1) ) 715 ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 716 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 717 zbv = MIN( zbv, -100.*ABS(zav), -7.e+3/fse3v(ji,jj,ik)*ABS( zav ) ) 718 ! vslpml 719 vslpml (ji,jj) = zav / ( zbv - zeps ) * vmask (ji,jj,ik) 720 END DO 721 END DO 722 CALL lbc_lnk( vslpml, 'V', -1. ) ! lateral boundary conditions (j-gradient => sign change) 723 724 725 ! !* vertical density gradient for w-slope (from N^2) 726 # if defined key_vectopt_loop 727 DO jj = 1, 1 728 DO ji = 1, jpij ! vector opt. (forced unrolling) 729 # else 730 DO jj = 1, jpj 731 DO ji = 1, jpi 732 # endif 733 ik = nmln(ji,jj) + 1 734 ik = MIN( ik, jpk ) 735 ikm1 = MAX ( 1, ik-1) 736 zwy (ji,jj) = zm05g * pn2 (ji,jj,ik) * & 737 & ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. ) 738 END DO 739 END DO 740 741 ! !* Slopes at w points 742 # if defined key_vectopt_loop 743 DO jj = 1, 1 744 DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) 745 # else 746 DO jj = 2, jpjm1 747 DO ji = 2, jpim1 748 # endif 749 ik = nmln(ji,jj) + 1 750 ik = MIN( ik, jpk ) 751 ikm1 = MAX ( 1, ik-1 ) 752 ! horizontal density i-gradient at w-points 753 zcoef1 = MAX( zeps, umask(ji-1,jj,ik )+umask(ji,jj,ik ) & 754 & +umask(ji-1,jj,ikm1)+umask(ji,jj,ikm1) ) 755 zcoef1 = 1. / ( zcoef1 * e1t (ji,jj) ) 756 zai = zcoef1 * ( zgru(ji ,jj,ik ) + zgru(ji ,jj,ikm1) & 757 & + zgru(ji-1,jj,ikm1) + zgru(ji-1,jj,ik ) ) * tmask (ji,jj,ik) 758 ! horizontal density j-gradient at w-points 759 zcoef2 = MAX( zeps, vmask(ji,jj-1,ik )+vmask(ji,jj,ikm1) & 760 & +vmask(ji,jj-1,ikm1)+vmask(ji,jj,ik ) ) 761 zcoef2 = 1.0 / ( zcoef2 * e2t (ji,jj) ) 762 zaj = zcoef2 * ( zgrv(ji,jj ,ik ) + zgrv(ji,jj ,ikm1) & 763 & + zgrv(ji,jj-1,ikm1) + zgrv(ji,jj-1,ik ) ) * tmask (ji,jj,ik) 764 ! bound the slopes: abs(zw.)<= 1/100 and zb..<0. 765 ! static instability: 766 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 767 zbi = MIN ( zwy (ji,jj),- 100.*ABS(zai), -7.e+3/fse3w(ji,jj,ik)*ABS(zai) ) 768 zbj = MIN ( zwy (ji,jj), -100.*ABS(zaj), -7.e+3/fse3w(ji,jj,ik)*ABS(zaj) ) 769 ! wslpiml and wslpjml 770 wslpiml (ji,jj) = zai / ( zbi - zeps) * tmask (ji,jj,ik) 771 wslpjml (ji,jj) = zaj / ( zbj - zeps) * tmask (ji,jj,ik) 772 END DO 773 END DO 774 CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions 654 ! !== Slope at u- & v-points just below the Mixed Layer ==! 655 ! 656 ! !- vertical density gradient for u- and v-slopes (from dzr at T-point) 657 iku = MIN( MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) , jpkm1 ) ! ML (MAX of T-pts, bound by jpkm1) 658 ikv = MIN( MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) , jpkm1 ) ! 659 zbu = 0.5_wp * ( p_dzr(ji,jj,iku) + p_dzr(ji+1,jj ,iku) ) 660 zbv = 0.5_wp * ( p_dzr(ji,jj,ikv) + p_dzr(ji ,jj+1,ikv) ) 661 ! !- horizontal density gradient at u- & v-points 662 zau = p_gru(ji,jj,iku) / e1u(ji,jj) 663 zav = p_grv(ji,jj,ikv) / e2v(ji,jj) 664 ! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0 665 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 666 zbu = MIN( zbu , -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,ik)* ABS( zau ) ) 667 zbv = MIN( zbv , -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,ik)* ABS( zav ) ) 668 ! !- Slope at u- & v-points (uslpml, vslpml) 669 uslpml(ji,jj) = zau / ( zbu - zeps ) * umask(ji,jj,ik) 670 vslpml(ji,jj) = zav / ( zbv - zeps ) * vmask(ji,jj,ik) 671 ! 672 ! !== i- & j-slopes at w-points just below the Mixed Layer ==! 673 ! 674 ik = MIN( nmln(ji,jj) + 1, jpk ) 675 ikm1 = MAX( 1, ik-1 ) 676 ! !- vertical density gradient for w-slope (from N^2) 677 zbw = zm1_2g * pn2 (ji,jj,ik) * ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. ) 678 ! !- horizontal density i- & j-gradient at w-points 679 zci = MAX( umask(ji-1,jj,ik ) + umask(ji,jj,ik ) & 680 & + umask(ji-1,jj,ikm1) + umask(ji,jj,ikm1) , zeps ) * e1t(ji,jj) 681 zcj = MAX( vmask(ji,jj-1,ik ) + vmask(ji,jj,ik ) & 682 & + vmask(ji,jj-1,ikm1) + vmask(ji,jj,ikm1) , zeps ) * e2t(ji,jj) 683 zai = ( p_gru(ji-1,jj,ik ) + p_gru(ji,jj,ik) & 684 & + p_gru(ji-1,jj,ikm1) + p_gru(ji,jj,ikm1 ) ) / zci * tmask(ji,jj,ik) 685 zaj = ( p_grv(ji,jj-1,ik ) + p_grv(ji,jj,ik ) & 686 & + p_grv(ji,jj-1,ikm1) + p_grv(ji,jj,ikm1) ) / zcj * tmask(ji,jj,ik) 687 ! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0. 688 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) 689 zbi = MIN( zbw , -100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zai ) ) 690 zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zaj ) ) 691 ! !- i- & j-slope at w-points (wslpiml, wslpjml) 692 wslpiml(ji,jj) = zai / ( zbi - zeps ) * tmask (ji,jj,ik) 693 wslpjml(ji,jj) = zaj / ( zbj - zeps ) * tmask (ji,jj,ik) 694 END DO 695 END DO 696 !!gm this lbc_lnk should be useless.... 697 CALL lbc_lnk( uslpml , 'U', -1. ) ; CALL lbc_lnk( vslpml , 'V', -1. ) ! lateral boundary cond. (sign change) 698 CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions 775 699 ! 776 700 END SUBROUTINE ldf_slp_mxl
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