[5770] | 1 | MODULE traadv_fct |
---|
[3] | 2 | !!============================================================================== |
---|
[5770] | 3 | !! *** MODULE traadv_fct *** |
---|
| 4 | !! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method) |
---|
[3] | 5 | !!============================================================================== |
---|
[5770] | 6 | !! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90) |
---|
[503] | 7 | !!---------------------------------------------------------------------- |
---|
[3] | 8 | |
---|
| 9 | !!---------------------------------------------------------------------- |
---|
[5770] | 10 | !! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme |
---|
| 11 | !! with sub-time-stepping in the vertical direction |
---|
| 12 | !! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm |
---|
| 13 | !! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection |
---|
[3] | 14 | !!---------------------------------------------------------------------- |
---|
[3625] | 15 | USE oce ! ocean dynamics and active tracers |
---|
| 16 | USE dom_oce ! ocean space and time domain |
---|
[4990] | 17 | USE trc_oce ! share passive tracers/Ocean variables |
---|
| 18 | USE trd_oce ! trends: ocean variables |
---|
[3625] | 19 | USE trdtra ! tracers trends |
---|
[4990] | 20 | USE diaptr ! poleward transport diagnostics |
---|
[7646] | 21 | USE diaar5 ! AR5 diagnostics |
---|
[9019] | 22 | USE phycst , ONLY : rau0_rcp |
---|
[11407] | 23 | USE zdf_oce , ONLY : ln_zad_Aimp |
---|
[4990] | 24 | ! |
---|
[5770] | 25 | USE in_out_manager ! I/O manager |
---|
[9019] | 26 | USE iom ! |
---|
[3625] | 27 | USE lib_mpp ! MPP library |
---|
| 28 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
---|
[5770] | 29 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
---|
[3] | 30 | |
---|
| 31 | IMPLICIT NONE |
---|
| 32 | PRIVATE |
---|
| 33 | |
---|
[9019] | 34 | PUBLIC tra_adv_fct ! called by traadv.F90 |
---|
| 35 | PUBLIC interp_4th_cpt ! called by traadv_cen.F90 |
---|
[3] | 36 | |
---|
[5770] | 37 | LOGICAL :: l_trd ! flag to compute trends |
---|
[7646] | 38 | LOGICAL :: l_ptr ! flag to compute poleward transport |
---|
| 39 | LOGICAL :: l_hst ! flag to compute heat/salt transport |
---|
[5770] | 40 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
---|
[2528] | 41 | |
---|
[7646] | 42 | ! ! tridiag solver associated indices: |
---|
| 43 | INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition |
---|
| 44 | INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition |
---|
| 45 | |
---|
[3] | 46 | !! * Substitutions |
---|
| 47 | # include "vectopt_loop_substitute.h90" |
---|
| 48 | !!---------------------------------------------------------------------- |
---|
[9598] | 49 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
---|
[1152] | 50 | !! $Id$ |
---|
[10068] | 51 | !! Software governed by the CeCILL license (see ./LICENSE) |
---|
[3] | 52 | !!---------------------------------------------------------------------- |
---|
| 53 | CONTAINS |
---|
| 54 | |
---|
[5770] | 55 | SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & |
---|
| 56 | & ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v ) |
---|
[3] | 57 | !!---------------------------------------------------------------------- |
---|
[5770] | 58 | !! *** ROUTINE tra_adv_fct *** |
---|
[3] | 59 | !! |
---|
[6140] | 60 | !! ** Purpose : Compute the now trend due to total advection of tracers |
---|
| 61 | !! and add it to the general trend of tracer equations |
---|
[3] | 62 | !! |
---|
[5770] | 63 | !! ** Method : - 2nd or 4th FCT scheme on the horizontal direction |
---|
| 64 | !! (choice through the value of kn_fct) |
---|
[6140] | 65 | !! - on the vertical the 4th order is a compact scheme |
---|
[5770] | 66 | !! - corrected flux (monotonic correction) |
---|
[3] | 67 | !! |
---|
[6140] | 68 | !! ** Action : - update pta with the now advective tracer trends |
---|
[9019] | 69 | !! - send trends to trdtra module for further diagnostics (l_trdtra=T) |
---|
[6140] | 70 | !! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T) |
---|
[503] | 71 | !!---------------------------------------------------------------------- |
---|
[2528] | 72 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
[3294] | 73 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
---|
[2528] | 74 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
---|
| 75 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
---|
[5770] | 76 | INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4) |
---|
| 77 | INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4) |
---|
[6140] | 78 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
---|
[2528] | 79 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components |
---|
| 80 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields |
---|
| 81 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
---|
[2715] | 82 | ! |
---|
[5770] | 83 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
---|
[6140] | 84 | REAL(wp) :: ztra ! local scalar |
---|
[5770] | 85 | REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - - |
---|
| 86 | REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - - |
---|
[9019] | 87 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw |
---|
| 88 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry |
---|
[11407] | 89 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup |
---|
| 90 | LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection |
---|
[3] | 91 | !!---------------------------------------------------------------------- |
---|
[3294] | 92 | ! |
---|
| 93 | IF( kt == kit000 ) THEN |
---|
[2528] | 94 | IF(lwp) WRITE(numout,*) |
---|
[5770] | 95 | IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype |
---|
[2528] | 96 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
[3] | 97 | ENDIF |
---|
[2528] | 98 | ! |
---|
[9019] | 99 | l_trd = .FALSE. ! set local switches |
---|
[7646] | 100 | l_hst = .FALSE. |
---|
| 101 | l_ptr = .FALSE. |
---|
[11407] | 102 | ll_zAimp = .FALSE. |
---|
[9019] | 103 | IF( ( cdtype =='TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. |
---|
| 104 | IF( cdtype =='TRA' .AND. ln_diaptr ) l_ptr = .TRUE. |
---|
| 105 | IF( cdtype =='TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. & |
---|
| 106 | & iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE. |
---|
[5770] | 107 | ! |
---|
[7646] | 108 | IF( l_trd .OR. l_hst ) THEN |
---|
[9019] | 109 | ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) ) |
---|
[7753] | 110 | ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp |
---|
[3294] | 111 | ENDIF |
---|
[2528] | 112 | ! |
---|
[7646] | 113 | IF( l_ptr ) THEN |
---|
[9019] | 114 | ALLOCATE( zptry(jpi,jpj,jpk) ) |
---|
[7753] | 115 | zptry(:,:,:) = 0._wp |
---|
[7646] | 116 | ENDIF |
---|
[6140] | 117 | ! ! surface & bottom value : flux set to zero one for all |
---|
[7753] | 118 | zwz(:,:, 1 ) = 0._wp |
---|
| 119 | zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp |
---|
[2528] | 120 | ! |
---|
[7753] | 121 | zwi(:,:,:) = 0._wp |
---|
| 122 | ! |
---|
[11407] | 123 | ! If adaptive vertical advection, check if it is needed on this PE at this time |
---|
| 124 | IF( ln_zad_Aimp ) THEN |
---|
| 125 | IF( MAXVAL( ABS( wi(:,:,:) ) ) > 0._wp ) ll_zAimp = .TRUE. |
---|
| 126 | END IF |
---|
| 127 | ! If active adaptive vertical advection, build tridiagonal matrix |
---|
| 128 | IF( ll_zAimp ) THEN |
---|
| 129 | ALLOCATE(zwdia(jpi,jpj,jpk), zwinf(jpi,jpj,jpk),zwsup(jpi,jpj,jpk)) |
---|
| 130 | DO jk = 1, jpkm1 |
---|
| 131 | DO jj = 2, jpjm1 |
---|
| 132 | DO ji = fs_2, fs_jpim1 ! vector opt. (ensure same order of calculation as below if wi=0.) |
---|
| 133 | zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk ) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) / e3t_a(ji,jj,jk) |
---|
| 134 | zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t_a(ji,jj,jk) |
---|
| 135 | zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t_a(ji,jj,jk) |
---|
| 136 | END DO |
---|
| 137 | END DO |
---|
| 138 | END DO |
---|
| 139 | END IF |
---|
| 140 | ! |
---|
[6140] | 141 | DO jn = 1, kjpt !== loop over the tracers ==! |
---|
[5770] | 142 | ! |
---|
| 143 | ! !== upstream advection with initial mass fluxes & intermediate update ==! |
---|
| 144 | ! !* upstream tracer flux in the i and j direction |
---|
[2528] | 145 | DO jk = 1, jpkm1 |
---|
| 146 | DO jj = 1, jpjm1 |
---|
| 147 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 148 | ! upstream scheme |
---|
| 149 | zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) |
---|
| 150 | zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) |
---|
| 151 | zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) |
---|
| 152 | zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) |
---|
| 153 | zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) ) |
---|
| 154 | zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) ) |
---|
| 155 | END DO |
---|
[3] | 156 | END DO |
---|
| 157 | END DO |
---|
[5770] | 158 | ! !* upstream tracer flux in the k direction *! |
---|
[6140] | 159 | DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) |
---|
[4990] | 160 | DO jj = 1, jpj |
---|
| 161 | DO ji = 1, jpi |
---|
[2528] | 162 | zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) |
---|
| 163 | zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) |
---|
[5120] | 164 | zwz(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk) |
---|
[2528] | 165 | END DO |
---|
[3] | 166 | END DO |
---|
| 167 | END DO |
---|
[6140] | 168 | IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked) |
---|
[5770] | 169 | IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface |
---|
[5120] | 170 | DO jj = 1, jpj |
---|
| 171 | DO ji = 1, jpi |
---|
| 172 | zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface |
---|
| 173 | END DO |
---|
| 174 | END DO |
---|
[5770] | 175 | ELSE ! no cavities: only at the ocean surface |
---|
[7753] | 176 | zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) |
---|
[5770] | 177 | ENDIF |
---|
[5120] | 178 | ENDIF |
---|
[5770] | 179 | ! |
---|
| 180 | DO jk = 1, jpkm1 !* trend and after field with monotonic scheme |
---|
[216] | 181 | DO jj = 2, jpjm1 |
---|
| 182 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[6691] | 183 | ! ! total intermediate advective trends |
---|
[5770] | 184 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
---|
| 185 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
---|
[6691] | 186 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
---|
| 187 | ! ! update and guess with monotonic sheme |
---|
| 188 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk) |
---|
| 189 | zwi(ji,jj,jk) = ( e3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + p2dt * ztra ) / e3t_a(ji,jj,jk) * tmask(ji,jj,jk) |
---|
[216] | 190 | END DO |
---|
| 191 | END DO |
---|
| 192 | END DO |
---|
[11407] | 193 | |
---|
| 194 | IF ( ll_zAimp ) THEN |
---|
| 195 | CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 ) |
---|
| 196 | ! |
---|
[11411] | 197 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ; |
---|
[11407] | 198 | DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) |
---|
[11411] | 199 | DO jj = 2, jpjm1 |
---|
| 200 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[11407] | 201 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
---|
| 202 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
---|
[11411] | 203 | ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
---|
| 204 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes |
---|
[11407] | 205 | END DO |
---|
| 206 | END DO |
---|
| 207 | END DO |
---|
| 208 | DO jk = 1, jpkm1 |
---|
| 209 | DO jj = 2, jpjm1 |
---|
| 210 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[11411] | 211 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & |
---|
[11407] | 212 | & * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) |
---|
| 213 | END DO |
---|
| 214 | END DO |
---|
| 215 | END DO |
---|
| 216 | ! |
---|
| 217 | END IF |
---|
[5770] | 218 | ! |
---|
[7646] | 219 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes) |
---|
[7753] | 220 | ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) |
---|
[2528] | 221 | END IF |
---|
[5770] | 222 | ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) |
---|
[9019] | 223 | IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:) |
---|
[5770] | 224 | ! |
---|
| 225 | ! !== anti-diffusive flux : high order minus low order ==! |
---|
| 226 | ! |
---|
[6140] | 227 | SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes |
---|
[5770] | 228 | ! |
---|
[6140] | 229 | CASE( 2 ) !- 2nd order centered |
---|
[5770] | 230 | DO jk = 1, jpkm1 |
---|
| 231 | DO jj = 1, jpjm1 |
---|
| 232 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 233 | zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) - zwx(ji,jj,jk) |
---|
| 234 | zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) - zwy(ji,jj,jk) |
---|
| 235 | END DO |
---|
[503] | 236 | END DO |
---|
| 237 | END DO |
---|
[5770] | 238 | ! |
---|
[6140] | 239 | CASE( 4 ) !- 4th order centered |
---|
[7753] | 240 | zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
---|
| 241 | zltv(:,:,jpk) = 0._wp |
---|
[6140] | 242 | DO jk = 1, jpkm1 ! Laplacian |
---|
| 243 | DO jj = 1, jpjm1 ! 1st derivative (gradient) |
---|
[5770] | 244 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 245 | ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
---|
| 246 | ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
---|
| 247 | END DO |
---|
[503] | 248 | END DO |
---|
[6140] | 249 | DO jj = 2, jpjm1 ! 2nd derivative * 1/ 6 |
---|
[5770] | 250 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 251 | zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 |
---|
| 252 | zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 |
---|
| 253 | END DO |
---|
| 254 | END DO |
---|
[503] | 255 | END DO |
---|
[10425] | 256 | CALL lbc_lnk_multi( 'traadv_fct', zltu, 'T', 1. , zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) |
---|
[5770] | 257 | ! |
---|
[6140] | 258 | DO jk = 1, jpkm1 ! Horizontal advective fluxes |
---|
[5770] | 259 | DO jj = 1, jpjm1 |
---|
| 260 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 261 | zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points |
---|
| 262 | zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) |
---|
| 263 | ! ! C4 minus upstream advective fluxes |
---|
| 264 | zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk) |
---|
| 265 | zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk) |
---|
| 266 | END DO |
---|
[5120] | 267 | END DO |
---|
[5770] | 268 | END DO |
---|
| 269 | ! |
---|
[6140] | 270 | CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested |
---|
[7753] | 271 | ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero |
---|
| 272 | ztv(:,:,jpk) = 0._wp |
---|
[6140] | 273 | DO jk = 1, jpkm1 ! 1st derivative (gradient) |
---|
| 274 | DO jj = 1, jpjm1 |
---|
[5770] | 275 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 276 | ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) |
---|
| 277 | ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) |
---|
| 278 | END DO |
---|
| 279 | END DO |
---|
[5120] | 280 | END DO |
---|
[10425] | 281 | CALL lbc_lnk_multi( 'traadv_fct', ztu, 'U', -1. , ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn) |
---|
[5770] | 282 | ! |
---|
[6140] | 283 | DO jk = 1, jpkm1 ! Horizontal advective fluxes |
---|
[5770] | 284 | DO jj = 2, jpjm1 |
---|
| 285 | DO ji = 2, fs_jpim1 ! vector opt. |
---|
| 286 | zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2) |
---|
| 287 | zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) |
---|
| 288 | ! ! C4 interpolation of T at u- & v-points (x2) |
---|
| 289 | zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) ) |
---|
| 290 | zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) ) |
---|
| 291 | ! ! C4 minus upstream advective fluxes |
---|
| 292 | zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk) |
---|
| 293 | zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk) |
---|
| 294 | END DO |
---|
| 295 | END DO |
---|
| 296 | END DO |
---|
| 297 | ! |
---|
| 298 | END SELECT |
---|
[6140] | 299 | ! |
---|
| 300 | SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values) |
---|
[5770] | 301 | ! |
---|
[6140] | 302 | CASE( 2 ) !- 2nd order centered |
---|
[5770] | 303 | DO jk = 2, jpkm1 |
---|
| 304 | DO jj = 2, jpjm1 |
---|
| 305 | DO ji = fs_2, fs_jpim1 |
---|
[6140] | 306 | zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * 0.5_wp * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) & |
---|
| 307 | & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
---|
[5770] | 308 | END DO |
---|
| 309 | END DO |
---|
| 310 | END DO |
---|
| 311 | ! |
---|
[6140] | 312 | CASE( 4 ) !- 4th order COMPACT |
---|
| 313 | CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! zwt = COMPACT interpolation of T at w-point |
---|
[5770] | 314 | DO jk = 2, jpkm1 |
---|
| 315 | DO jj = 2, jpjm1 |
---|
| 316 | DO ji = fs_2, fs_jpim1 |
---|
| 317 | zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) |
---|
| 318 | END DO |
---|
| 319 | END DO |
---|
| 320 | END DO |
---|
| 321 | ! |
---|
| 322 | END SELECT |
---|
[6140] | 323 | IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0 |
---|
[7753] | 324 | zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked |
---|
[6140] | 325 | ENDIF |
---|
[11407] | 326 | ! |
---|
| 327 | IF ( ll_zAimp ) THEN |
---|
| 328 | DO jk = 1, jpkm1 !* trend and after field with monotonic scheme |
---|
| 329 | DO jj = 2, jpjm1 |
---|
| 330 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 331 | ! ! total intermediate advective trends |
---|
| 332 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
---|
| 333 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
---|
| 334 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
---|
[11411] | 335 | ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t_a(ji,jj,jk) * tmask(ji,jj,jk) |
---|
[11407] | 336 | END DO |
---|
| 337 | END DO |
---|
| 338 | END DO |
---|
| 339 | ! |
---|
[11411] | 340 | CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 ) |
---|
[11407] | 341 | ! |
---|
| 342 | DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) |
---|
| 343 | DO jj = 2, jpjm1 |
---|
| 344 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 345 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
---|
| 346 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
---|
[11411] | 347 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
---|
[11407] | 348 | END DO |
---|
| 349 | END DO |
---|
| 350 | END DO |
---|
| 351 | END IF |
---|
[11411] | 352 | ! |
---|
| 353 | CALL lbc_lnk_multi( 'traadv_fct', zwi, 'T', 1., zwx, 'U', -1. , zwy, 'V', -1., zwz, 'W', 1. ) |
---|
| 354 | ! |
---|
[5770] | 355 | ! !== monotonicity algorithm ==! |
---|
| 356 | ! |
---|
[2528] | 357 | CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) |
---|
[6140] | 358 | ! |
---|
[5770] | 359 | ! !== final trend with corrected fluxes ==! |
---|
| 360 | ! |
---|
[216] | 361 | DO jk = 1, jpkm1 |
---|
| 362 | DO jj = 2, jpjm1 |
---|
[2528] | 363 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[11407] | 364 | ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & |
---|
| 365 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & |
---|
| 366 | & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj) |
---|
| 367 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) |
---|
| 368 | zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t_a(ji,jj,jk) * tmask(ji,jj,jk) |
---|
[216] | 369 | END DO |
---|
| 370 | END DO |
---|
| 371 | END DO |
---|
[5770] | 372 | ! |
---|
[11407] | 373 | IF ( ll_zAimp ) THEN |
---|
| 374 | ! |
---|
[11411] | 375 | ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp |
---|
[11407] | 376 | DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) |
---|
| 377 | DO jj = 2, jpjm1 |
---|
| 378 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 379 | zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) ) |
---|
| 380 | zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) ) |
---|
[11411] | 381 | ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk) |
---|
| 382 | zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic |
---|
[11407] | 383 | END DO |
---|
| 384 | END DO |
---|
| 385 | END DO |
---|
| 386 | DO jk = 1, jpkm1 |
---|
| 387 | DO jj = 2, jpjm1 |
---|
| 388 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[11411] | 389 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) & |
---|
[11407] | 390 | & * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) |
---|
| 391 | END DO |
---|
| 392 | END DO |
---|
| 393 | END DO |
---|
| 394 | END IF |
---|
| 395 | ! |
---|
[9019] | 396 | IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport |
---|
| 397 | ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes |
---|
| 398 | ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes |
---|
| 399 | ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! |
---|
[5770] | 400 | ! |
---|
[9019] | 401 | IF( l_trd ) THEN ! trend diagnostics |
---|
| 402 | CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) |
---|
| 403 | CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) |
---|
| 404 | CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) |
---|
| 405 | ENDIF |
---|
| 406 | ! ! heat/salt transport |
---|
| 407 | IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) ) |
---|
[5770] | 408 | ! |
---|
[9019] | 409 | ENDIF |
---|
| 410 | IF( l_ptr ) THEN ! "Poleward" transports |
---|
| 411 | zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes |
---|
[7646] | 412 | CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) ) |
---|
[2528] | 413 | ENDIF |
---|
[503] | 414 | ! |
---|
[6140] | 415 | END DO ! end of tracer loop |
---|
[503] | 416 | ! |
---|
[11407] | 417 | IF ( ll_zAimp ) THEN |
---|
| 418 | DEALLOCATE( zwdia, zwinf, zwsup ) |
---|
| 419 | ENDIF |
---|
[10024] | 420 | IF( l_trd .OR. l_hst ) THEN |
---|
| 421 | DEALLOCATE( ztrdx, ztrdy, ztrdz ) |
---|
| 422 | ENDIF |
---|
| 423 | IF( l_ptr ) THEN |
---|
| 424 | DEALLOCATE( zptry ) |
---|
| 425 | ENDIF |
---|
| 426 | ! |
---|
[5770] | 427 | END SUBROUTINE tra_adv_fct |
---|
[3] | 428 | |
---|
[5737] | 429 | |
---|
[2528] | 430 | SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt ) |
---|
[3] | 431 | !!--------------------------------------------------------------------- |
---|
| 432 | !! *** ROUTINE nonosc *** |
---|
| 433 | !! |
---|
| 434 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
| 435 | !! scheme and the before field by a nonoscillatory algorithm |
---|
| 436 | !! |
---|
| 437 | !! ** Method : ... ??? |
---|
| 438 | !! warning : pbef and paft must be masked, but the boundaries |
---|
| 439 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
| 440 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
| 441 | !! in-space based differencing for fluid |
---|
| 442 | !!---------------------------------------------------------------------- |
---|
[6140] | 443 | REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step |
---|
[2528] | 444 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field |
---|
| 445 | REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions |
---|
[2715] | 446 | ! |
---|
[4990] | 447 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 448 | INTEGER :: ikm1 ! local integer |
---|
[6140] | 449 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars |
---|
[2715] | 450 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
[9019] | 451 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zbetup, zbetdo, zbup, zbdo |
---|
[3] | 452 | !!---------------------------------------------------------------------- |
---|
[3294] | 453 | ! |
---|
[2715] | 454 | zbig = 1.e+40_wp |
---|
| 455 | zrtrn = 1.e-15_wp |
---|
[7753] | 456 | zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp |
---|
[785] | 457 | |
---|
[3] | 458 | ! Search local extrema |
---|
| 459 | ! -------------------- |
---|
[785] | 460 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
[4990] | 461 | zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & |
---|
| 462 | & paft * tmask - zbig * ( 1._wp - tmask ) ) |
---|
| 463 | zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & |
---|
| 464 | & paft * tmask + zbig * ( 1._wp - tmask ) ) |
---|
[785] | 465 | |
---|
[5120] | 466 | DO jk = 1, jpkm1 |
---|
| 467 | ikm1 = MAX(jk-1,1) |
---|
| 468 | DO jj = 2, jpjm1 |
---|
| 469 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 470 | |
---|
[785] | 471 | ! search maximum in neighbourhood |
---|
| 472 | zup = MAX( zbup(ji ,jj ,jk ), & |
---|
| 473 | & zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), & |
---|
| 474 | & zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), & |
---|
| 475 | & zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) ) |
---|
[3] | 476 | |
---|
[785] | 477 | ! search minimum in neighbourhood |
---|
| 478 | zdo = MIN( zbdo(ji ,jj ,jk ), & |
---|
| 479 | & zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), & |
---|
| 480 | & zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), & |
---|
| 481 | & zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) ) |
---|
[3] | 482 | |
---|
[785] | 483 | ! positive part of the flux |
---|
[3] | 484 | zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) & |
---|
| 485 | & + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) & |
---|
| 486 | & + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) |
---|
[785] | 487 | |
---|
| 488 | ! negative part of the flux |
---|
[3] | 489 | zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) & |
---|
| 490 | & + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) & |
---|
| 491 | & + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) ) |
---|
[785] | 492 | |
---|
[3] | 493 | ! up & down beta terms |
---|
[6140] | 494 | zbt = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt |
---|
[785] | 495 | zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt |
---|
| 496 | zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt |
---|
[3] | 497 | END DO |
---|
| 498 | END DO |
---|
| 499 | END DO |
---|
[10425] | 500 | CALL lbc_lnk_multi( 'traadv_fct', zbetup, 'T', 1. , zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
[3] | 501 | |
---|
[237] | 502 | ! 3. monotonic flux in the i & j direction (paa & pbb) |
---|
| 503 | ! ---------------------------------------- |
---|
[3] | 504 | DO jk = 1, jpkm1 |
---|
| 505 | DO jj = 2, jpjm1 |
---|
| 506 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 507 | zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) |
---|
| 508 | zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) |
---|
[785] | 509 | zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) ) |
---|
[4990] | 510 | paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
---|
[3] | 511 | |
---|
[4990] | 512 | zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) |
---|
| 513 | zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) |
---|
[785] | 514 | zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) ) |
---|
[4990] | 515 | pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
---|
[3] | 516 | |
---|
| 517 | ! monotonic flux in the k direction, i.e. pcc |
---|
| 518 | ! ------------------------------------------- |
---|
[785] | 519 | za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) ) |
---|
| 520 | zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) ) |
---|
| 521 | zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) ) |
---|
[4990] | 522 | pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb ) |
---|
[3] | 523 | END DO |
---|
| 524 | END DO |
---|
| 525 | END DO |
---|
[10425] | 526 | CALL lbc_lnk_multi( 'traadv_fct', paa, 'U', -1. , pbb, 'V', -1. ) ! lateral boundary condition (changed sign) |
---|
[503] | 527 | ! |
---|
[3] | 528 | END SUBROUTINE nonosc |
---|
| 529 | |
---|
[5770] | 530 | |
---|
[7646] | 531 | SUBROUTINE interp_4th_cpt_org( pt_in, pt_out ) |
---|
[5770] | 532 | !!---------------------------------------------------------------------- |
---|
[7646] | 533 | !! *** ROUTINE interp_4th_cpt_org *** |
---|
[5770] | 534 | !! |
---|
| 535 | !! ** Purpose : Compute the interpolation of tracer at w-point |
---|
| 536 | !! |
---|
| 537 | !! ** Method : 4th order compact interpolation |
---|
| 538 | !!---------------------------------------------------------------------- |
---|
| 539 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields |
---|
| 540 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts |
---|
| 541 | ! |
---|
| 542 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
| 543 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt |
---|
| 544 | !!---------------------------------------------------------------------- |
---|
| 545 | |
---|
| 546 | DO jk = 3, jpkm1 !== build the three diagonal matrix ==! |
---|
| 547 | DO jj = 1, jpj |
---|
| 548 | DO ji = 1, jpi |
---|
| 549 | zwd (ji,jj,jk) = 4._wp |
---|
| 550 | zwi (ji,jj,jk) = 1._wp |
---|
| 551 | zws (ji,jj,jk) = 1._wp |
---|
| 552 | zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 553 | ! |
---|
| 554 | IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom |
---|
| 555 | zwd (ji,jj,jk) = 1._wp |
---|
| 556 | zwi (ji,jj,jk) = 0._wp |
---|
| 557 | zws (ji,jj,jk) = 0._wp |
---|
| 558 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 559 | ENDIF |
---|
| 560 | END DO |
---|
| 561 | END DO |
---|
| 562 | END DO |
---|
| 563 | ! |
---|
[7646] | 564 | jk = 2 ! Switch to second order centered at top |
---|
| 565 | DO jj = 1, jpj |
---|
| 566 | DO ji = 1, jpi |
---|
[5770] | 567 | zwd (ji,jj,jk) = 1._wp |
---|
| 568 | zwi (ji,jj,jk) = 0._wp |
---|
| 569 | zws (ji,jj,jk) = 0._wp |
---|
| 570 | zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) ) |
---|
| 571 | END DO |
---|
| 572 | END DO |
---|
| 573 | ! |
---|
| 574 | ! !== tridiagonal solve ==! |
---|
| 575 | DO jj = 1, jpj ! first recurrence |
---|
| 576 | DO ji = 1, jpi |
---|
| 577 | zwt(ji,jj,2) = zwd(ji,jj,2) |
---|
| 578 | END DO |
---|
| 579 | END DO |
---|
| 580 | DO jk = 3, jpkm1 |
---|
| 581 | DO jj = 1, jpj |
---|
| 582 | DO ji = 1, jpi |
---|
| 583 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
| 584 | END DO |
---|
| 585 | END DO |
---|
| 586 | END DO |
---|
| 587 | ! |
---|
| 588 | DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
---|
| 589 | DO ji = 1, jpi |
---|
| 590 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
---|
| 591 | END DO |
---|
| 592 | END DO |
---|
| 593 | DO jk = 3, jpkm1 |
---|
| 594 | DO jj = 1, jpj |
---|
| 595 | DO ji = 1, jpi |
---|
| 596 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
| 597 | END DO |
---|
| 598 | END DO |
---|
| 599 | END DO |
---|
| 600 | |
---|
| 601 | DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
---|
| 602 | DO ji = 1, jpi |
---|
| 603 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
| 604 | END DO |
---|
| 605 | END DO |
---|
| 606 | DO jk = jpk-2, 2, -1 |
---|
| 607 | DO jj = 1, jpj |
---|
| 608 | DO ji = 1, jpi |
---|
| 609 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
| 610 | END DO |
---|
| 611 | END DO |
---|
| 612 | END DO |
---|
| 613 | ! |
---|
[7646] | 614 | END SUBROUTINE interp_4th_cpt_org |
---|
| 615 | |
---|
| 616 | |
---|
| 617 | SUBROUTINE interp_4th_cpt( pt_in, pt_out ) |
---|
| 618 | !!---------------------------------------------------------------------- |
---|
| 619 | !! *** ROUTINE interp_4th_cpt *** |
---|
| 620 | !! |
---|
| 621 | !! ** Purpose : Compute the interpolation of tracer at w-point |
---|
| 622 | !! |
---|
| 623 | !! ** Method : 4th order compact interpolation |
---|
| 624 | !!---------------------------------------------------------------------- |
---|
| 625 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point |
---|
| 626 | REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! field interpolated at w-point |
---|
| 627 | ! |
---|
| 628 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
| 629 | INTEGER :: ikt, ikb ! local integers |
---|
| 630 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt |
---|
| 631 | !!---------------------------------------------------------------------- |
---|
| 632 | ! |
---|
| 633 | ! !== build the three diagonal matrix & the RHS ==! |
---|
| 634 | ! |
---|
| 635 | DO jk = 3, jpkm1 ! interior (from jk=3 to jpk-1) |
---|
| 636 | DO jj = 2, jpjm1 |
---|
| 637 | DO ji = fs_2, fs_jpim1 |
---|
| 638 | zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal |
---|
| 639 | zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal |
---|
| 640 | zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal |
---|
| 641 | zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS |
---|
| 642 | & * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) ) |
---|
| 643 | END DO |
---|
| 644 | END DO |
---|
| 645 | END DO |
---|
| 646 | ! |
---|
| 647 | !!gm |
---|
| 648 | ! SELECT CASE( kbc ) !* boundary condition |
---|
| 649 | ! CASE( np_NH ) ! Neumann homogeneous at top & bottom |
---|
| 650 | ! CASE( np_CEN2 ) ! 2nd order centered at top & bottom |
---|
| 651 | ! END SELECT |
---|
| 652 | !!gm |
---|
| 653 | ! |
---|
[9901] | 654 | IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case |
---|
| 655 | zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp |
---|
| 656 | END IF |
---|
| 657 | ! |
---|
[7646] | 658 | DO jj = 2, jpjm1 ! 2nd order centered at top & bottom |
---|
| 659 | DO ji = fs_2, fs_jpim1 |
---|
| 660 | ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point |
---|
| 661 | ikb = mbkt(ji,jj) ! - above the last wet point |
---|
| 662 | ! |
---|
| 663 | zwd (ji,jj,ikt) = 1._wp ! top |
---|
| 664 | zwi (ji,jj,ikt) = 0._wp |
---|
| 665 | zws (ji,jj,ikt) = 0._wp |
---|
[9901] | 666 | zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) ) |
---|
[7646] | 667 | ! |
---|
| 668 | zwd (ji,jj,ikb) = 1._wp ! bottom |
---|
| 669 | zwi (ji,jj,ikb) = 0._wp |
---|
| 670 | zws (ji,jj,ikb) = 0._wp |
---|
[9901] | 671 | zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) ) |
---|
[7646] | 672 | END DO |
---|
| 673 | END DO |
---|
| 674 | ! |
---|
| 675 | ! !== tridiagonal solver ==! |
---|
| 676 | ! |
---|
| 677 | DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1 |
---|
| 678 | DO ji = fs_2, fs_jpim1 |
---|
| 679 | zwt(ji,jj,2) = zwd(ji,jj,2) |
---|
| 680 | END DO |
---|
| 681 | END DO |
---|
| 682 | DO jk = 3, jpkm1 |
---|
| 683 | DO jj = 2, jpjm1 |
---|
| 684 | DO ji = fs_2, fs_jpim1 |
---|
| 685 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
| 686 | END DO |
---|
| 687 | END DO |
---|
| 688 | END DO |
---|
| 689 | ! |
---|
| 690 | DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
---|
| 691 | DO ji = fs_2, fs_jpim1 |
---|
| 692 | pt_out(ji,jj,2) = zwrm(ji,jj,2) |
---|
| 693 | END DO |
---|
| 694 | END DO |
---|
| 695 | DO jk = 3, jpkm1 |
---|
| 696 | DO jj = 2, jpjm1 |
---|
| 697 | DO ji = fs_2, fs_jpim1 |
---|
| 698 | pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
| 699 | END DO |
---|
| 700 | END DO |
---|
| 701 | END DO |
---|
| 702 | |
---|
| 703 | DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
---|
| 704 | DO ji = fs_2, fs_jpim1 |
---|
| 705 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
| 706 | END DO |
---|
| 707 | END DO |
---|
| 708 | DO jk = jpk-2, 2, -1 |
---|
| 709 | DO jj = 2, jpjm1 |
---|
| 710 | DO ji = fs_2, fs_jpim1 |
---|
| 711 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
| 712 | END DO |
---|
| 713 | END DO |
---|
| 714 | END DO |
---|
| 715 | ! |
---|
[5770] | 716 | END SUBROUTINE interp_4th_cpt |
---|
[7646] | 717 | |
---|
| 718 | |
---|
| 719 | SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev ) |
---|
| 720 | !!---------------------------------------------------------------------- |
---|
| 721 | !! *** ROUTINE tridia_solver *** |
---|
| 722 | !! |
---|
| 723 | !! ** Purpose : solve a symmetric 3diagonal system |
---|
| 724 | !! |
---|
| 725 | !! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk ) |
---|
| 726 | !! |
---|
| 727 | !! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 ) |
---|
| 728 | !! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 ) |
---|
| 729 | !! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 ) |
---|
| 730 | !! ( ... )( ... ) ( ... ) |
---|
| 731 | !! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k ) |
---|
| 732 | !! |
---|
| 733 | !! M is decomposed in the product of an upper and lower triangular matrix. |
---|
| 734 | !! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL |
---|
| 735 | !! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal). |
---|
| 736 | !! The solution is pta. |
---|
| 737 | !! The 3d array zwt is used as a work space array. |
---|
| 738 | !!---------------------------------------------------------------------- |
---|
| 739 | REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix |
---|
| 740 | REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pRHS ! Right-Hand-Side |
---|
| 741 | REAL(wp),DIMENSION(:,:,:), INTENT( out) :: pt_out !!gm field at level=F(klev) |
---|
| 742 | INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level |
---|
| 743 | ! ! =0 pt at t-level |
---|
| 744 | INTEGER :: ji, jj, jk ! dummy loop integers |
---|
| 745 | INTEGER :: kstart ! local indices |
---|
| 746 | REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwt ! 3D work array |
---|
| 747 | !!---------------------------------------------------------------------- |
---|
| 748 | ! |
---|
| 749 | kstart = 1 + klev |
---|
| 750 | ! |
---|
| 751 | DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1 |
---|
| 752 | DO ji = fs_2, fs_jpim1 |
---|
| 753 | zwt(ji,jj,kstart) = pD(ji,jj,kstart) |
---|
| 754 | END DO |
---|
| 755 | END DO |
---|
| 756 | DO jk = kstart+1, jpkm1 |
---|
| 757 | DO jj = 2, jpjm1 |
---|
| 758 | DO ji = fs_2, fs_jpim1 |
---|
| 759 | zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
---|
| 760 | END DO |
---|
| 761 | END DO |
---|
| 762 | END DO |
---|
| 763 | ! |
---|
| 764 | DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
---|
| 765 | DO ji = fs_2, fs_jpim1 |
---|
| 766 | pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart) |
---|
| 767 | END DO |
---|
| 768 | END DO |
---|
| 769 | DO jk = kstart+1, jpkm1 |
---|
| 770 | DO jj = 2, jpjm1 |
---|
| 771 | DO ji = fs_2, fs_jpim1 |
---|
| 772 | pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1) |
---|
| 773 | END DO |
---|
| 774 | END DO |
---|
| 775 | END DO |
---|
| 776 | |
---|
| 777 | DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
---|
| 778 | DO ji = fs_2, fs_jpim1 |
---|
| 779 | pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) |
---|
| 780 | END DO |
---|
| 781 | END DO |
---|
| 782 | DO jk = jpk-2, kstart, -1 |
---|
| 783 | DO jj = 2, jpjm1 |
---|
| 784 | DO ji = fs_2, fs_jpim1 |
---|
| 785 | pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk) |
---|
| 786 | END DO |
---|
| 787 | END DO |
---|
| 788 | END DO |
---|
| 789 | ! |
---|
| 790 | END SUBROUTINE tridia_solver |
---|
| 791 | |
---|
[3] | 792 | !!====================================================================== |
---|
[5770] | 793 | END MODULE traadv_fct |
---|