[186] | 1 | MODULE trcldf_bilapg |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE trcldf_bilapg *** |
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| 4 | !! Ocean passive tracers: horizontal component of the lateral tracer mixing trend |
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| 5 | !!============================================================================== |
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| 6 | #if key_passivetrc && defined key_ldfslp |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! 'key_ldfslp' rotation of the lateral mixing tensor |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! trc_ldf_bilapg : update the tracer trend with the horizontal diffusion |
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| 11 | !! using an horizontal biharmonic operator in s-coordinate |
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| 12 | !! ldfght : ??? |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | !! * Modules used |
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| 15 | USE oce_trc ! ocean dynamics and tracers variables |
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[202] | 16 | USE trc ! ocean passive tracers variables |
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| 17 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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[334] | 18 | USE prtctl_trc ! Print control for debbuging |
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[186] | 19 | |
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| 20 | IMPLICIT NONE |
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| 21 | PRIVATE |
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| 22 | |
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| 23 | !! * Routine accessibility |
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| 24 | PUBLIC trc_ldf_bilapg ! routine called by step.F90 |
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| 25 | |
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| 26 | !! * Substitutions |
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| 27 | # include "passivetrc_substitute.h90" |
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| 28 | !!---------------------------------------------------------------------- |
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[349] | 29 | !! TOP 1.0 , LOCEAN-IPSL (2005) |
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[342] | 30 | !! $Header$ |
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| 31 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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[186] | 32 | !!---------------------------------------------------------------------- |
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| 33 | |
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| 34 | CONTAINS |
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| 35 | |
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| 36 | SUBROUTINE trc_ldf_bilapg( kt ) |
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| 37 | !!---------------------------------------------------------------------- |
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| 38 | !! *** ROUTINE trc_ldf_bilapg *** |
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| 39 | !! |
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| 40 | !! ** Purpose : Compute the before horizontal passive tracer diffusive |
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| 41 | !! trend and add it to the general trend of tracer equation. |
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| 42 | !! |
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| 43 | !! ** Method : The lateral diffusive trends is provided by a 4th order |
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| 44 | !! operator rotated along geopotential surfaces. It is computed |
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| 45 | !! using before fields (forward in time) and geopotential slopes |
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| 46 | !! computed in routine inildf. |
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| 47 | !! -1- compute the geopotential harmonic operator applied to |
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| 48 | !! trb and multiply it by the eddy diffusivity coefficient |
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| 49 | !! (done by a call to ldfght routine, result in wk1 array). |
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| 50 | !! Applied the domain lateral boundary conditions by call to lbc_lnk |
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| 51 | !! -2- compute the geopotential harmonic operator applied to |
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| 52 | !! wk1 by a second call to ldfght routine (result in wk3 array). |
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| 53 | !! -3- Add this trend to the general trend (ta,sa): |
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| 54 | !! tra = tra + wk3 |
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| 55 | !! |
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| 56 | !! ** Action : - Update tra arrays with the before geopotential |
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| 57 | !! biharmonic mixing trend. |
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| 58 | !! - Save the trends in trtrd ('key_trc_diatrd') |
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| 59 | !! |
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| 60 | !! History : |
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| 61 | !! 8.0 ! 97-07 (G. Madec) Original code |
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| 62 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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| 63 | !! 9.0 ! 04-03 (C. Ethe) adapted for passive tracers |
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| 64 | !!---------------------------------------------------------------------- |
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| 65 | !! * Arguments |
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| 66 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 67 | |
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| 68 | !! * Local declarations |
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[202] | 69 | INTEGER :: ji, jj, jk,jn ! dummy loop indices |
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| 70 | REAL(wp) :: ztra ! workspace |
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[186] | 71 | REAL(wp), DIMENSION(jpi,jpj,jpk,jptra) :: & |
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| 72 | wk1, wk2 ! work array used for rotated biharmonic |
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| 73 | ! operator on tracers and/or momentum |
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[334] | 74 | CHARACTER (len=22) :: charout |
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[186] | 75 | !!---------------------------------------------------------------------- |
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| 76 | |
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| 77 | IF( kt == nittrc000 ) THEN |
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| 78 | IF(lwp) WRITE(numout,*) |
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| 79 | IF(lwp) WRITE(numout,*) 'trc_ldf_bilapg : horizontal biharmonic operator in s-coordinate' |
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| 80 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~' |
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| 81 | ENDIF |
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| 82 | |
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| 83 | ! 1. Laplacian of passive tracers trb * aht |
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| 84 | ! ----------------------------- |
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| 85 | ! rotated harmonic operator applied to trb |
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| 86 | ! and multiply by aht (output in wk1 ) |
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| 87 | |
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| 88 | CALL ldfght ( trb, wk1, 1 ) |
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| 89 | |
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| 90 | DO jn = 1, jptra |
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| 91 | ! Lateral boundary conditions on wk1 (unchanged sign) |
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| 92 | CALL lbc_lnk( wk1(:,:,:,jn) , 'T', 1. ) |
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| 93 | END DO |
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| 94 | |
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| 95 | ! 2. Bilaplacian of trb |
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| 96 | ! ------------------------- |
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| 97 | ! rotated harmonic operator applied to wk1 (output in wk2 ) |
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| 98 | |
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| 99 | CALL ldfght ( wk1, wk2, 2 ) |
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| 100 | |
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| 101 | |
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| 102 | DO jn = 1, jptra |
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| 103 | ! 3. Update the tracer trends (j-slab : 2, jpj-1) |
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| 104 | ! --------------------------- |
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| 105 | ! ! =============== |
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| 106 | DO jj = 2, jpjm1 ! Vertical slab |
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| 107 | ! ! =============== |
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| 108 | DO jk = 1, jpkm1 |
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| 109 | DO ji = 2, jpim1 |
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| 110 | ! add it to the general tracer trends |
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| 111 | tra(ji,jj,jk,jn) = tra(ji,jj,jk,jn) + wk2(ji,jj,jk,jn) |
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| 112 | #if defined key_trc_diatrd |
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| 113 | ! save the horizontal diffusive trends |
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[433] | 114 | IF (luttrd(jn)) trtrd(ji,jj,jk,ikeep(jn),3) = wk2(ji,jj,jk,jn) |
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[186] | 115 | #endif |
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| 116 | END DO |
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| 117 | END DO |
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| 118 | ! ! =============== |
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| 119 | END DO ! End of slab |
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| 120 | ! ! =============== |
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[202] | 121 | |
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[186] | 122 | END DO |
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| 123 | |
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[334] | 124 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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| 125 | WRITE(charout, FMT="('ldf - bilapg')") |
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| 126 | CALL prt_ctl_trc_info(charout) |
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| 127 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm,clinfo2='trd') |
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| 128 | ENDIF |
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| 129 | |
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[186] | 130 | END SUBROUTINE trc_ldf_bilapg |
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| 131 | |
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| 132 | |
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| 133 | SUBROUTINE ldfght ( pt, plt, kaht ) |
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| 134 | !!---------------------------------------------------------------------- |
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| 135 | !! *** ROUTINE ldfght *** |
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| 136 | !! |
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| 137 | !! ** Purpose : Apply a geopotential harmonic operator to pt and |
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| 138 | !! multiply it by the eddy diffusivity coefficient (if kaht=1). |
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| 139 | !! Routine only used in s-coordinates (l_sco=T) with bilaplacian |
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| 140 | !! operator (ln_traldf_bilap=T) acting along geopotential surfaces |
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| 141 | !! (ln_traldf_hor). |
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| 142 | !! |
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| 143 | !! ** Method : The harmonic operator rotated along geopotential |
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| 144 | !! surfaces is applied to pt using the slopes of geopotential |
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| 145 | !! surfaces computed in inildf routine. The result is provided in |
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| 146 | !! plt arrays. It is computed in 2 steps: |
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| 147 | !! |
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| 148 | !! First step: horizontal part of the operator. It is computed on |
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| 149 | !! ========== pt as follows (idem on ps) |
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| 150 | !! horizontal fluxes : |
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| 151 | !! zftu = e2u*e3u/e1u di[ pt ] - e2u*uslp dk[ mi(mk(pt)) ] |
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| 152 | !! zftv = e1v*e3v/e2v dj[ pt ] - e1v*vslp dk[ mj(mk(pt)) ] |
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| 153 | !! take the horizontal divergence of the fluxes (no divided by |
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| 154 | !! the volume element : |
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| 155 | !! plt = di-1[ zftu ] + dj-1[ zftv ] |
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| 156 | !! |
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| 157 | !! Second step: vertical part of the operator. It is computed on |
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| 158 | !! =========== pt as follows (idem on ps) |
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| 159 | !! vertical fluxes : |
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| 160 | !! zftw = e1t*e2t/e3w * (wslpi^2+wslpj^2) dk-1[ pt ] |
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| 161 | !! - e2t * wslpi di[ mi(mk(pt)) ] |
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| 162 | !! - e1t * wslpj dj[ mj(mk(pt)) ] |
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| 163 | !! take the vertical divergence of the fluxes add it to the hori- |
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| 164 | !! zontal component, divide the result by the volume element and |
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| 165 | !! if kaht=1, multiply by the eddy diffusivity coefficient: |
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| 166 | !! plt = aht / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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| 167 | !! else: |
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| 168 | !! plt = 1 / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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| 169 | !! |
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| 170 | !! * Action : |
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| 171 | !! 'key_trdtra' defined: the trend is saved for diagnostics. |
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| 172 | !! |
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| 173 | !! History : |
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| 174 | !! 8.0 ! 97-07 (G. Madec) Original code |
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| 175 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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| 176 | !! 9.0 ! 04-03 (C. Ethe) adapted for passive tracers |
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| 177 | !!---------------------------------------------------------------------- |
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| 178 | !! * Arguments |
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| 179 | REAL(wp), DIMENSION(jpi,jpj,jpk,jptra), INTENT( in ) :: & |
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| 180 | pt ! tracer fields before for 1st call |
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| 181 | ! ! and laplacian of these fields for 2nd call. |
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| 182 | REAL(wp), DIMENSION(jpi,jpj,jpk,jptra), INTENT( out ) :: & |
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| 183 | plt ! partial harmonic operator applied to |
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| 184 | ! ! pt components except |
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| 185 | ! ! second order vertical derivative term) |
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| 186 | INTEGER, INTENT( in ) :: & |
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| 187 | kaht ! =1 multiply the laplacian by the eddy diffusivity coeff. |
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| 188 | ! ! =2 no multiplication |
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| 189 | |
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| 190 | !! * Local declarations |
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| 191 | INTEGER :: ji, jj, jk,jn ! dummy loop indices |
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| 192 | REAL(wp) :: & |
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| 193 | zabe1, zabe2, zmku, zmkv, & ! temporary scalars |
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| 194 | zbtr, ztah, ztav, & |
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| 195 | zcof0, zcof1, zcof2, & |
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| 196 | zcof3, zcof4 |
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| 197 | |
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| 198 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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[202] | 199 | zftu, zftv , & ! workspace |
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[186] | 200 | zdkt, zdk1t |
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| 201 | |
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| 202 | REAL(wp), DIMENSION(jpi,jpk) :: & |
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[202] | 203 | zftw, & ! workspace |
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[186] | 204 | zdit, zdjt, zdj1t |
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| 205 | |
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| 206 | !!---------------------------------------------------------------------- |
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| 207 | |
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| 208 | |
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| 209 | DO jn = 1, jptra |
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| 210 | ! ! ********** ! ! =============== |
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| 211 | DO jk = 1, jpkm1 ! First step ! ! Horizontal slab |
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| 212 | ! ! ********** ! ! =============== |
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| 213 | |
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| 214 | ! I.1 Vertical gradient of pt and ps at level jk and jk+1 |
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| 215 | ! ------------------------------------------------------- |
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| 216 | ! surface boundary condition: zdkt(jk=1)=zdkt(jk=2) |
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| 217 | |
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| 218 | zdk1t(:,:) = ( pt(:,:,jk,jn) - pt(:,:,jk+1,jn) ) * tmask(:,:,jk+1) |
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| 219 | |
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| 220 | IF( jk == 1 ) THEN |
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| 221 | zdkt(:,:) = zdk1t(:,:) |
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| 222 | ELSE |
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| 223 | zdkt(:,:) = ( pt(:,:,jk-1,jn) - pt(:,:,jk,jn) ) * tmask(:,:,jk) |
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| 224 | ENDIF |
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| 225 | |
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| 226 | |
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| 227 | ! I.2 Horizontal fluxes |
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| 228 | ! --------------------- |
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| 229 | |
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| 230 | DO jj = 1, jpjm1 |
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| 231 | DO ji = 1, jpim1 |
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| 232 | zabe1 = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) |
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| 233 | zabe2 = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) |
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| 234 | |
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| 235 | zmku=1./MAX( tmask(ji+1,jj,jk )+tmask(ji,jj,jk+1) & |
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[202] | 236 | +tmask(ji+1,jj,jk+1)+tmask(ji,jj,jk ),1. ) |
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[186] | 237 | zmkv=1./MAX( tmask(ji,jj+1,jk )+tmask(ji,jj,jk+1) & |
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[202] | 238 | +tmask(ji,jj+1,jk+1)+tmask(ji,jj,jk ),1. ) |
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[186] | 239 | |
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| 240 | zcof1= -e2u(ji,jj) * uslp(ji,jj,jk) * zmku |
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| 241 | zcof2= -e1v(ji,jj) * vslp(ji,jj,jk) * zmkv |
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| 242 | |
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| 243 | zftu(ji,jj)= umask(ji,jj,jk) * & |
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| 244 | ( zabe1 *( pt(ji+1,jj,jk,jn) - pt(ji,jj,jk,jn) ) & |
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[202] | 245 | + zcof1 *( zdkt (ji+1,jj) + zdk1t(ji,jj) & |
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| 246 | +zdk1t(ji+1,jj) + zdkt (ji,jj) ) ) |
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[186] | 247 | |
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| 248 | zftv(ji,jj)= vmask(ji,jj,jk) * & |
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| 249 | ( zabe2 *( pt(ji,jj+1,jk,jn) - pt(ji,jj,jk,jn) ) & |
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[202] | 250 | + zcof2 *( zdkt (ji,jj+1) + zdk1t(ji,jj) & |
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| 251 | +zdk1t(ji,jj+1) + zdkt (ji,jj) ) ) |
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[186] | 252 | END DO |
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| 253 | END DO |
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| 254 | |
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| 255 | |
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| 256 | ! I.3 Second derivative (divergence) (not divided by the volume) |
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| 257 | ! --------------------- |
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| 258 | |
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| 259 | DO jj = 2 , jpjm1 |
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| 260 | DO ji = 2 , jpim1 |
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| 261 | ztah = zftu(ji,jj) - zftu(ji-1,jj) + zftv(ji,jj) - zftv(ji,jj-1) |
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| 262 | plt(ji,jj,jk,jn) = ztah |
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| 263 | END DO |
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| 264 | END DO |
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| 265 | ! ! =============== |
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| 266 | END DO ! End of slab |
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| 267 | ! ! =============== |
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| 268 | |
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| 269 | |
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| 270 | ! ! ************ ! ! =============== |
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| 271 | DO jj = 2, jpjm1 ! Second step ! ! Horizontal slab |
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| 272 | ! ! ************ ! ! =============== |
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| 273 | |
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| 274 | ! II.1 horizontal tracer gradient |
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| 275 | ! ------------------------------- |
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| 276 | |
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| 277 | DO jk = 1, jpk |
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| 278 | DO ji = 1, jpim1 |
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| 279 | zdit (ji,jk) = ( pt(ji+1,jj ,jk,jn) - pt(ji,jj ,jk,jn) ) * umask(ji,jj ,jk) |
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| 280 | zdjt (ji,jk) = ( pt(ji ,jj+1,jk,jn) - pt(ji,jj ,jk,jn) ) * vmask(ji,jj ,jk) |
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| 281 | zdj1t(ji,jk) = ( pt(ji ,jj ,jk,jn) - pt(ji,jj-1,jk,jn) ) * vmask(ji,jj-1,jk) |
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| 282 | END DO |
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| 283 | END DO |
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| 284 | |
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| 285 | |
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| 286 | ! II.2 Vertical fluxes |
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| 287 | ! -------------------- |
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| 288 | |
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| 289 | ! Surface and bottom vertical fluxes set to zero |
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| 290 | zftw(:, 1 ) = 0.e0 |
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| 291 | zftw(:,jpk) = 0.e0 |
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| 292 | |
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| 293 | ! interior (2=<jk=<jpk-1) |
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| 294 | DO jk = 2, jpkm1 |
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| 295 | DO ji = 2, jpim1 |
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| 296 | zcof0 = e1t(ji,jj) * e2t(ji,jj) / fse3w(ji,jj,jk) & |
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| 297 | * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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[202] | 298 | + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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[186] | 299 | |
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| 300 | zmku =1./MAX( umask(ji ,jj,jk-1)+umask(ji-1,jj,jk) & |
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[202] | 301 | +umask(ji-1,jj,jk-1)+umask(ji ,jj,jk), 1. ) |
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[186] | 302 | |
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| 303 | zmkv =1./MAX( vmask(ji,jj ,jk-1)+vmask(ji,jj-1,jk) & |
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[202] | 304 | +vmask(ji,jj-1,jk-1)+vmask(ji,jj ,jk), 1. ) |
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[186] | 305 | |
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| 306 | zcof3 = - e2t(ji,jj) * wslpi (ji,jj,jk) * zmku |
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| 307 | zcof4 = - e1t(ji,jj) * wslpj (ji,jj,jk) * zmkv |
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| 308 | |
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| 309 | zftw(ji,jk) = tmask(ji,jj,jk) * & |
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| 310 | ( zcof0 * ( pt (ji,jj,jk-1,jn) - pt (ji,jj,jk,jn) ) & |
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[202] | 311 | + zcof3 * ( zdit (ji ,jk-1) + zdit (ji-1,jk) & |
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| 312 | +zdit (ji-1,jk-1) + zdit (ji ,jk) ) & |
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| 313 | + zcof4 * ( zdjt (ji ,jk-1) + zdj1t(ji ,jk) & |
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| 314 | +zdj1t(ji ,jk-1) + zdjt (ji ,jk) ) ) |
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[186] | 315 | END DO |
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| 316 | END DO |
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| 317 | |
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| 318 | |
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| 319 | ! II.3 Divergence of vertical fluxes added to the horizontal divergence |
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| 320 | ! --------------------------------------------------------------------- |
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| 321 | |
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| 322 | IF( kaht == 1 ) THEN |
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| 323 | ! multiply the laplacian by the eddy diffusivity coefficient |
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| 324 | DO jk = 1, jpkm1 |
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| 325 | DO ji = 2, jpim1 |
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| 326 | ! eddy coef. divided by the volume element |
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| 327 | zbtr = fsahtrt(ji,jj,jk) / ( e1t(ji,jj)*e2t(ji,jj)*fse3t(ji,jj,jk) ) |
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| 328 | ! vertical divergence |
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| 329 | ztav = zftw(ji,jk) - zftw(ji,jk+1) |
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| 330 | ! harmonic operator applied to (pt,ps) and multiply by aht |
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| 331 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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| 332 | END DO |
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| 333 | END DO |
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| 334 | ELSEIF( kaht == 2 ) THEN |
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| 335 | ! second call, no multiplication |
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| 336 | DO jk = 1, jpkm1 |
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| 337 | DO ji = 2, jpim1 |
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| 338 | ! inverse of the volume element |
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| 339 | zbtr = 1. / ( e1t(ji,jj)*e2t(ji,jj)*fse3t(ji,jj,jk) ) |
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| 340 | ! vertical divergence |
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| 341 | ztav = zftw(ji,jk) - zftw(ji,jk+1) |
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| 342 | ! harmonic operator applied to (pt,ps) |
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| 343 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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| 344 | END DO |
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| 345 | END DO |
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| 346 | ELSE |
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| 347 | IF(lwp) WRITE(numout,*) ' ldfght: kaht= 1 or 2, here =', kaht |
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| 348 | IF(lwp) WRITE(numout,*) ' We stop' |
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| 349 | STOP 'ldfght' |
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| 350 | ENDIF |
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| 351 | ! ! =============== |
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| 352 | END DO ! End of slab |
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| 353 | ! ! =============== |
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| 354 | |
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| 355 | END DO |
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| 356 | |
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| 357 | END SUBROUTINE ldfght |
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| 358 | |
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| 359 | #else |
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| 360 | !!---------------------------------------------------------------------- |
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| 361 | !! Dummy module : NO rotation of the lateral mixing tensor |
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| 362 | !!---------------------------------------------------------------------- |
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| 363 | CONTAINS |
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| 364 | SUBROUTINE trc_ldf_bilapg( kt ) ! Dummy routine |
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| 365 | INTEGER, INTENT(in) :: kt |
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| 366 | WRITE(*,*) 'trc_ldf_bilapg: You should not have seen this print! error?', kt |
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| 367 | END SUBROUTINE trc_ldf_bilapg |
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| 368 | #endif |
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| 369 | |
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| 370 | !!============================================================================== |
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| 371 | END MODULE trcldf_bilapg |
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