[3] | 1 | MODULE traldf_bilap |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE traldf_bilap *** |
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| 4 | !! Ocean active tracers: horizontal component of the lateral tracer mixing trend |
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| 5 | !!============================================================================== |
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| 6 | |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! tra_ldf_bilap : update the tracer trend with the horizontal diffusion |
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| 9 | !! using a iso-level biharmonic operator |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! * Modules used |
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| 12 | USE oce ! ocean dynamics and active tracers |
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| 13 | USE dom_oce ! ocean space and time domain |
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[74] | 14 | USE ldftra_oce ! ocean tracer lateral physics |
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[216] | 15 | USE trdmod ! ocean active tracers trends |
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| 16 | USE trdmod_oce ! ocean variables trends |
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[3] | 17 | USE in_out_manager ! I/O manager |
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| 18 | USE ldfslp ! iso-neutral slopes |
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| 19 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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[132] | 20 | USE diaptr ! poleward transport diagnostics |
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[258] | 21 | USE prtctl ! Print control |
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[3] | 22 | |
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| 23 | IMPLICIT NONE |
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| 24 | PRIVATE |
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| 25 | |
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| 26 | !! * Routine accessibility |
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| 27 | PUBLIC tra_ldf_bilap ! routine called by step.F90 |
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| 28 | |
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| 29 | !! * Substitutions |
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| 30 | # include "domzgr_substitute.h90" |
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| 31 | # include "ldftra_substitute.h90" |
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| 32 | # include "ldfeiv_substitute.h90" |
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| 33 | # include "vectopt_loop_substitute.h90" |
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| 34 | !!---------------------------------------------------------------------- |
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[247] | 35 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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[699] | 36 | !! $Id$ |
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[247] | 37 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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[3] | 38 | !!---------------------------------------------------------------------- |
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| 39 | |
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| 40 | CONTAINS |
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| 41 | |
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| 42 | SUBROUTINE tra_ldf_bilap( kt ) |
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| 43 | !!---------------------------------------------------------------------- |
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| 44 | !! *** ROUTINE tra_ldf_bilap *** |
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| 45 | !! |
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| 46 | !! ** Purpose : Compute the before horizontal tracer (t & s) diffusive |
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| 47 | !! trend and add it to the general trend of tracer equation. |
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| 48 | !! |
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| 49 | !! ** Method : 4th order diffusive operator along model level surfaces |
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| 50 | !! evaluated using before fields (forward time scheme). The hor. |
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| 51 | !! diffusive trends of temperature (idem for salinity) is given by: |
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| 52 | !! Laplacian of tb: |
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| 53 | !! zlt = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(tb) ] |
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| 54 | !! + dj-1[ e1v*e3v/e2v dj(tb) ] } |
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| 55 | !! Multiply by the eddy diffusivity coef. and insure lateral bc: |
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| 56 | !! zlt = ahtt * zlt |
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| 57 | !! call to lbc_lnk |
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| 58 | !! Bilaplacian (laplacian of zlt): |
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| 59 | !! difft = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(zlt) ] |
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| 60 | !! + dj-1[ e1v*e3v/e2v dj(zlt) ] } |
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[457] | 61 | !! Note: if key_zco defined, e3t=e3u=e3v, they are simplified. |
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[3] | 62 | !! |
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| 63 | !! Add this trend to the general trend (ta,sa): |
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| 64 | !! (ta,sa) = (ta,sa) + ( difft , diffs ) |
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| 65 | !! |
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| 66 | !! ** Action : - Update (ta,sa) arrays with the before iso-level |
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| 67 | !! biharmonic mixing trend. |
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| 68 | !! |
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| 69 | !! History : |
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| 70 | !! ! 91-11 (G. Madec) Original code |
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| 71 | !! ! 93-03 (M. Guyon) symetrical conditions |
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| 72 | !! ! 95-11 (G. Madec) suppress volumetric scale factors |
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| 73 | !! ! 96-01 (G. Madec) statement function for e3 |
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| 74 | !! ! 96-01 (M. Imbard) mpp exchange |
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| 75 | !! ! 97-07 (G. Madec) optimization, and ahtt |
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| 76 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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[216] | 77 | !! 9.0 ! 04-08 (C. Talandier) New trends organization |
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[457] | 78 | !! ! 05-11 (G. Madec) zps or sco as default option |
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[3] | 79 | !!---------------------------------------------------------------------- |
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[132] | 80 | !! * Modules used |
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| 81 | USE oce , ztu => ua, & ! use ua as workspace |
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| 82 | & ztv => va ! use va as workspace |
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| 83 | |
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[3] | 84 | !! * Arguments |
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| 85 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 86 | |
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| 87 | !! * Local declarations |
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| 88 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 89 | INTEGER :: iku, ikv ! temporary integers |
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[216] | 90 | REAL(wp) :: zta, zsa ! temporary scalars |
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[3] | 91 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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[589] | 92 | zeeu, zeev, zbtr, & ! 2D workspace |
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| 93 | zlt, zls |
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[132] | 94 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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[589] | 95 | zsu, zsv ! 3D workspace |
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[3] | 96 | !!---------------------------------------------------------------------- |
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| 97 | |
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| 98 | IF( kt == nit000 ) THEN |
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| 99 | IF(lwp) WRITE(numout,*) |
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| 100 | IF(lwp) WRITE(numout,*) 'tra_ldf_bilap : iso-level biharmonic operator' |
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| 101 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' |
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| 102 | ENDIF |
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[216] | 103 | |
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[589] | 104 | |
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[3] | 105 | ! ! =============== |
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| 106 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 107 | ! ! =============== |
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| 108 | |
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| 109 | ! 0. Initialization of metric arrays (for z- or s-coordinates) |
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| 110 | ! ---------------------------------- |
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| 111 | |
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[457] | 112 | IF( lk_zco ) THEN ! z-coordinate (1D arrays): no vertical scale factors |
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| 113 | DO jj = 1, jpjm1 |
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| 114 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 115 | zbtr(ji,jj) = 1. / ( e1t(ji,jj)*e2t(ji,jj) ) |
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| 116 | zeeu(ji,jj) = e2u(ji,jj) / e1u(ji,jj) * umask(ji,jj,jk) |
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| 117 | zeev(ji,jj) = e1v(ji,jj) / e2v(ji,jj) * vmask(ji,jj,jk) |
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| 118 | END DO |
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[3] | 119 | END DO |
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[457] | 120 | ELSE ! All coordinates (3D arrays): vertical scale factor are used |
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| 121 | DO jj = 1, jpjm1 |
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| 122 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 123 | zbtr(ji,jj) = 1. / ( e1t(ji,jj)*e2t(ji,jj)*fse3t(ji,jj,jk) ) |
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| 124 | zeeu(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) |
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| 125 | zeev(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) |
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| 126 | END DO |
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| 127 | END DO |
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| 128 | ENDIF |
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[3] | 129 | |
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| 130 | |
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| 131 | ! 1. Laplacian |
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| 132 | ! ------------ |
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| 133 | |
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| 134 | ! First derivative (gradient) |
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| 135 | DO jj = 1, jpjm1 |
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| 136 | DO ji = 1, fs_jpim1 ! vector opt. |
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[132] | 137 | ztu(ji,jj,jk) = zeeu(ji,jj) * ( tb(ji+1,jj ,jk) - tb(ji,jj,jk) ) |
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| 138 | zsu(ji,jj,jk) = zeeu(ji,jj) * ( sb(ji+1,jj ,jk) - sb(ji,jj,jk) ) |
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| 139 | ztv(ji,jj,jk) = zeev(ji,jj) * ( tb(ji ,jj+1,jk) - tb(ji,jj,jk) ) |
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| 140 | zsv(ji,jj,jk) = zeev(ji,jj) * ( sb(ji ,jj+1,jk) - sb(ji,jj,jk) ) |
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[3] | 141 | END DO |
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| 142 | END DO |
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[457] | 143 | IF( ln_zps ) THEN ! set gradient at partial step level |
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| 144 | DO jj = 1, jpjm1 |
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| 145 | DO ji = 1, jpim1 |
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| 146 | ! last level |
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| 147 | iku = MIN ( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1 |
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| 148 | ikv = MIN ( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1 |
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| 149 | IF( iku == jk ) THEN |
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| 150 | ztu(ji,jj,jk) = zeeu(ji,jj) * gtu(ji,jj) |
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| 151 | zsu(ji,jj,jk) = zeeu(ji,jj) * gsu(ji,jj) |
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| 152 | ENDIF |
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| 153 | IF( ikv == jk ) THEN |
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| 154 | ztv(ji,jj,jk) = zeev(ji,jj) * gtv(ji,jj) |
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| 155 | zsv(ji,jj,jk) = zeev(ji,jj) * gsv(ji,jj) |
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| 156 | ENDIF |
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| 157 | END DO |
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[3] | 158 | END DO |
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[457] | 159 | ENDIF |
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[3] | 160 | |
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| 161 | ! Second derivative (divergence) |
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| 162 | DO jj = 2, jpjm1 |
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| 163 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[589] | 164 | zlt(ji,jj) = zbtr(ji,jj) * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) |
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| 165 | zls(ji,jj) = zbtr(ji,jj) * ( zsu(ji,jj,jk) - zsu(ji-1,jj,jk) + zsv(ji,jj,jk) - zsv(ji,jj-1,jk) ) |
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[3] | 166 | END DO |
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| 167 | END DO |
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| 168 | |
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| 169 | ! Multiply by the eddy diffusivity coefficient |
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| 170 | DO jj = 2, jpjm1 |
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| 171 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[589] | 172 | zlt(ji,jj) = fsahtt(ji,jj,jk) * zlt(ji,jj) |
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| 173 | zls(ji,jj) = fsahtt(ji,jj,jk) * zls(ji,jj) |
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[3] | 174 | END DO |
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| 175 | END DO |
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| 176 | |
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[589] | 177 | ! Lateral boundary conditions on the laplacian (zlt,zls) (unchanged sgn) |
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| 178 | CALL lbc_lnk( zlt, 'T', 1. ) ; CALL lbc_lnk( zls, 'T', 1. ) |
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[3] | 179 | |
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| 180 | ! 2. Bilaplacian |
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| 181 | ! -------------- |
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| 182 | |
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| 183 | ! third derivative (gradient) |
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| 184 | DO jj = 1, jpjm1 |
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| 185 | DO ji = 1, fs_jpim1 ! vector opt. |
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[589] | 186 | ztu(ji,jj,jk) = zeeu(ji,jj) * ( zlt(ji+1,jj ) - zlt(ji,jj) ) |
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| 187 | zsu(ji,jj,jk) = zeeu(ji,jj) * ( zls(ji+1,jj ) - zls(ji,jj) ) |
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| 188 | ztv(ji,jj,jk) = zeev(ji,jj) * ( zlt(ji ,jj+1) - zlt(ji,jj) ) |
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| 189 | zsv(ji,jj,jk) = zeev(ji,jj) * ( zls(ji ,jj+1) - zls(ji,jj) ) |
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[3] | 190 | END DO |
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| 191 | END DO |
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| 192 | |
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| 193 | ! fourth derivative (divergence) and add to the general tracer trend |
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| 194 | DO jj = 2, jpjm1 |
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| 195 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 196 | ! horizontal diffusive trends |
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[132] | 197 | zta = zbtr(ji,jj) * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) |
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| 198 | zsa = zbtr(ji,jj) * ( zsu(ji,jj,jk) - zsu(ji-1,jj,jk) + zsv(ji,jj,jk) - zsv(ji,jj-1,jk) ) |
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[3] | 199 | ! add it to the general tracer trends |
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| 200 | ta(ji,jj,jk) = ta(ji,jj,jk) + zta |
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| 201 | sa(ji,jj,jk) = sa(ji,jj,jk) + zsa |
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| 202 | END DO |
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| 203 | END DO |
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| 204 | ! ! =============== |
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| 205 | END DO ! Horizontal slab |
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| 206 | ! ! =============== |
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| 207 | |
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| 208 | ! "zonal" mean lateral diffusive heat and salt transport |
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[132] | 209 | IF( ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN |
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[457] | 210 | IF( lk_zco ) THEN ! z-coordinate (1D arrays): multiply by the vertical scale factor |
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| 211 | DO jk = 1, jpkm1 |
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| 212 | DO jj = 2, jpjm1 |
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| 213 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 214 | ztv(ji,jj,jk) = ztv(ji,jj,jk) * fse3v(ji,jj,jk) |
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| 215 | zsv(ji,jj,jk) = zsv(ji,jj,jk) * fse3v(ji,jj,jk) |
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| 216 | END DO |
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[132] | 217 | END DO |
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[3] | 218 | END DO |
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[457] | 219 | ENDIF |
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[132] | 220 | pht_ldf(:) = ptr_vj( ztv(:,:,:) ) |
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| 221 | pst_ldf(:) = ptr_vj( zsv(:,:,:) ) |
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[3] | 222 | ENDIF |
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| 223 | |
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| 224 | END SUBROUTINE tra_ldf_bilap |
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| 225 | |
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| 226 | !!============================================================================== |
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| 227 | END MODULE traldf_bilap |
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