[3] | 1 | MODULE traldf_bilapg |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE traldf_bilapg *** |
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[2024] | 4 | !! Ocean tracers: horizontal component of the lateral tracer mixing trend |
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[3] | 5 | !!============================================================================== |
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[2024] | 6 | !! History : 8.0 ! 1997-07 (G. Madec) Original code |
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| 7 | !! NEMO ! 2002-08 (G. Madec) F90: Free form and module |
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| 8 | !! 3.3 ! 2010-06 (C. Ethe, G. Madec) Merge TRA-TRC |
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| 9 | !!============================================================================== |
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[3] | 10 | #if defined key_ldfslp || defined key_esopa |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! 'key_ldfslp' rotation of the lateral mixing tensor |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | !! tra_ldf_bilapg : update the tracer trend with the horizontal diffusion |
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| 15 | !! using an horizontal biharmonic operator in s-coordinate |
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| 16 | !! ldfght : ??? |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | USE oce ! ocean dynamics and tracers variables |
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| 19 | USE dom_oce ! ocean space and time domain variables |
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[74] | 20 | USE ldftra_oce ! ocean active tracers: lateral physics |
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[3] | 21 | USE in_out_manager ! I/O manager |
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| 22 | USE ldfslp ! iso-neutral slopes available |
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| 23 | USE lbclnk ! ocean lateral boundary condition (or mpp link) |
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[132] | 24 | USE diaptr ! poleward transport diagnostics |
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[2082] | 25 | USE trc_oce ! share passive tracers/Ocean variables |
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[3] | 26 | |
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| 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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[2104] | 30 | PUBLIC tra_ldf_bilapg ! routine called by step.F90 |
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[3] | 31 | |
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| 32 | !! * Substitutions |
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| 33 | # include "domzgr_substitute.h90" |
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| 34 | # include "ldftra_substitute.h90" |
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| 35 | # include "ldfeiv_substitute.h90" |
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| 36 | !!---------------------------------------------------------------------- |
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[2287] | 37 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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[2104] | 38 | !! $Id$ |
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[2287] | 39 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 40 | !!---------------------------------------------------------------------- |
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| 41 | |
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| 42 | CONTAINS |
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| 43 | |
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[2034] | 44 | SUBROUTINE tra_ldf_bilapg( kt, cdtype, ptb, pta, kjpt ) |
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[3] | 45 | !!---------------------------------------------------------------------- |
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| 46 | !! *** ROUTINE tra_ldf_bilapg *** |
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| 47 | !! |
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[2024] | 48 | !! ** Purpose : Compute the before horizontal tracer diffusive |
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[3] | 49 | !! trend and add it to the general trend of tracer equation. |
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| 50 | !! |
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| 51 | !! ** Method : The lateral diffusive trends is provided by a 4th order |
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| 52 | !! operator rotated along geopotential surfaces. It is computed |
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| 53 | !! using before fields (forward in time) and geopotential slopes |
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| 54 | !! computed in routine inildf. |
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| 55 | !! -1- compute the geopotential harmonic operator applied to |
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[2034] | 56 | !! ptb and multiply it by the eddy diffusivity coefficient |
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[2024] | 57 | !! (done by a call to ldfght routine, result in wk1 arrays). |
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[3] | 58 | !! Applied the domain lateral boundary conditions by call to lbc_lnk |
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| 59 | !! -2- compute the geopotential harmonic operator applied to |
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[2024] | 60 | !! wk1 by a second call to ldfght routine (result in wk2) |
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[3] | 61 | !! arrays). |
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[2024] | 62 | !! -3- Add this trend to the general trend |
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[2034] | 63 | !! pta = pta + wk2 |
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[3] | 64 | !! |
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[2034] | 65 | !! ** Action : - Update pta arrays with the before geopotential |
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[3] | 66 | !! biharmonic mixing trend. |
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| 67 | !!---------------------------------------------------------------------- |
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[2024] | 68 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 69 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 70 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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[2104] | 71 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields |
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| 72 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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| 73 | !! |
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[2024] | 74 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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[2104] | 75 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt) :: wk1, wk2 ! 4D workspace |
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[3] | 76 | !!---------------------------------------------------------------------- |
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| 77 | |
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[2104] | 78 | IF( kt == nit000 ) THEN |
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[3] | 79 | IF(lwp) WRITE(numout,*) |
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[2082] | 80 | IF(lwp) WRITE(numout,*) 'tra_ldf_bilapg : horizontal biharmonic operator in s-coordinate on ', cdtype |
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[3] | 81 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~' |
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| 82 | ENDIF |
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[2024] | 83 | ! |
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| 84 | ! |
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[3] | 85 | |
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[2034] | 86 | ! 1. Laplacian of ptb * aht |
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[3] | 87 | ! ----------------------------- |
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[2104] | 88 | CALL ldfght( kt, cdtype, ptb, wk1, kjpt, 1 ) ! rotated harmonic operator applied to ptb and multiply by aht |
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| 89 | ! ! output in wk1 |
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[2024] | 90 | ! |
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| 91 | DO jn = 1, kjpt |
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[2104] | 92 | CALL lbc_lnk( wk1(:,:,:,jn) , 'T', 1. ) ! Lateral boundary conditions on wk1 (unchanged sign) |
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[2024] | 93 | END DO |
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[3] | 94 | |
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[2034] | 95 | ! 2. Bilaplacian of ptb |
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[3] | 96 | ! ------------------------- |
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[2104] | 97 | CALL ldfght( kt, cdtype, wk1, wk2, kjpt, 2 ) ! rotated harmonic operator applied to wk1 ; output in wk2 |
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[3] | 98 | |
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| 99 | |
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| 100 | ! 3. Update the tracer trends (j-slab : 2, jpj-1) |
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| 101 | ! --------------------------- |
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[2024] | 102 | ! |
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| 103 | DO jn = 1, kjpt |
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| 104 | ! ! =============== |
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| 105 | DO jj = 2, jpjm1 ! Vertical slab |
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| 106 | ! ! =============== |
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| 107 | DO jk = 1, jpkm1 |
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| 108 | DO ji = 2, jpim1 |
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| 109 | ! add it to the general tracer trends |
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[2034] | 110 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + wk2(ji,jj,jk,jn) |
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[2024] | 111 | END DO |
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[3] | 112 | END DO |
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[2024] | 113 | ! ! =============== |
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| 114 | END DO ! End of slab |
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| 115 | ! ! =============== |
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| 116 | END DO |
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[216] | 117 | |
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[3] | 118 | END SUBROUTINE tra_ldf_bilapg |
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| 119 | |
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| 120 | |
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[2024] | 121 | SUBROUTINE ldfght ( kt, cdtype, pt, plt, kjpt, kaht ) |
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[3] | 122 | !!---------------------------------------------------------------------- |
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| 123 | !! *** ROUTINE ldfght *** |
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| 124 | !! |
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[2024] | 125 | !! ** Purpose : Apply a geopotential harmonic operator to (pt) and |
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[3] | 126 | !! multiply it by the eddy diffusivity coefficient (if kaht=1). |
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| 127 | !! Routine only used in s-coordinates (l_sco=T) with bilaplacian |
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| 128 | !! operator (ln_traldf_bilap=T) acting along geopotential surfaces |
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| 129 | !! (ln_traldf_hor). |
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| 130 | !! |
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| 131 | !! ** Method : The harmonic operator rotated along geopotential |
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[2024] | 132 | !! surfaces is applied to (pt) using the slopes of geopotential |
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[3] | 133 | !! surfaces computed in inildf routine. The result is provided in |
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| 134 | !! (plt,pls) arrays. It is computed in 2 steps: |
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| 135 | !! |
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| 136 | !! First step: horizontal part of the operator. It is computed on |
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| 137 | !! ========== pt as follows (idem on ps) |
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| 138 | !! horizontal fluxes : |
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| 139 | !! zftu = e2u*e3u/e1u di[ pt ] - e2u*uslp dk[ mi(mk(pt)) ] |
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| 140 | !! zftv = e1v*e3v/e2v dj[ pt ] - e1v*vslp dk[ mj(mk(pt)) ] |
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| 141 | !! take the horizontal divergence of the fluxes (no divided by |
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| 142 | !! the volume element : |
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| 143 | !! plt = di-1[ zftu ] + dj-1[ zftv ] |
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| 144 | !! |
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| 145 | !! Second step: vertical part of the operator. It is computed on |
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| 146 | !! =========== pt as follows (idem on ps) |
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| 147 | !! vertical fluxes : |
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| 148 | !! zftw = e1t*e2t/e3w * (wslpi^2+wslpj^2) dk-1[ pt ] |
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| 149 | !! - e2t * wslpi di[ mi(mk(pt)) ] |
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| 150 | !! - e1t * wslpj dj[ mj(mk(pt)) ] |
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| 151 | !! take the vertical divergence of the fluxes add it to the hori- |
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| 152 | !! zontal component, divide the result by the volume element and |
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| 153 | !! if kaht=1, multiply by the eddy diffusivity coefficient: |
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| 154 | !! plt = aht / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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| 155 | !! else: |
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| 156 | !! plt = 1 / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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| 157 | !! |
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| 158 | !!---------------------------------------------------------------------- |
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[2024] | 159 | USE oce , zftv => ua ! use ua as workspace |
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[2034] | 160 | !! |
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[2024] | 161 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 162 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 163 | INTEGER , INTENT(in ) :: kjpt !: dimension of |
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| 164 | REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,jpk,kjpt) :: pt ! tracer fields ( before for 1st call |
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| 165 | ! ! and laplacian of these fields for 2nd call. |
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| 166 | REAL(wp) , INTENT(out), DIMENSION(jpi,jpj,jpk,kjpt) :: plt !: partial harmonic operator applied to pt components except |
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| 167 | ! !: second order vertical derivative term |
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| 168 | INTEGER , INTENT(in ) :: kaht !: =1 multiply the laplacian by the eddy diffusivity coeff. |
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| 169 | ! !: =2 no multiplication |
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[2034] | 170 | !! |
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[2024] | 171 | INTEGER :: ji, jj, jk,jn ! dummy loop indices |
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| 172 | ! ! temporary scalars |
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| 173 | REAL(wp) :: zabe1, zabe2, zmku, zmkv |
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| 174 | REAL(wp) :: zbtr, ztah, ztav |
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| 175 | REAL(wp) :: zcof0, zcof1, zcof2, zcof3, zcof4 |
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| 176 | REAL(wp), DIMENSION(jpi,jpj) :: zftu, zdkt, zdk1t ! workspace |
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| 177 | REAL(wp), DIMENSION(jpi,jpk) :: zftw, zdit, zdjt, zdj1t ! |
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[3] | 178 | !!---------------------------------------------------------------------- |
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| 179 | |
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[2024] | 180 | ! |
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| 181 | DO jn = 1, kjpt |
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| 182 | ! ! ********** ! ! =============== |
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| 183 | DO jk = 1, jpkm1 ! First step ! ! Horizontal slab |
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| 184 | ! ! ********** ! ! =============== |
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| 185 | |
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| 186 | ! I.1 Vertical gradient of pt and ps at level jk and jk+1 |
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| 187 | ! ------------------------------------------------------- |
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| 188 | ! surface boundary condition: zdkt(jk=1)=zdkt(jk=2) |
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| 189 | |
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| 190 | zdk1t(:,:) = ( pt(:,:,jk,jn) - pt(:,:,jk+1,jn) ) * tmask(:,:,jk+1) |
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| 191 | IF( jk == 1 ) THEN |
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| 192 | zdkt(:,:) = zdk1t(:,:) |
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| 193 | ELSE |
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| 194 | zdkt(:,:) = ( pt(:,:,jk-1,jn) - pt(:,:,jk,jn) ) * tmask(:,:,jk) |
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| 195 | ENDIF |
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[3] | 196 | |
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| 197 | |
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[2024] | 198 | ! I.2 Horizontal fluxes |
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| 199 | ! --------------------- |
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| 200 | |
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| 201 | DO jj = 1, jpjm1 |
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| 202 | DO ji = 1, jpim1 |
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| 203 | zabe1 = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) |
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| 204 | zabe2 = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) |
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| 205 | |
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| 206 | zmku = 1./MAX( tmask(ji+1,jj,jk )+tmask(ji,jj,jk+1) & |
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| 207 | & +tmask(ji+1,jj,jk+1)+tmask(ji,jj,jk ),1. ) |
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| 208 | zmkv = 1./MAX( tmask(ji,jj+1,jk )+tmask(ji,jj,jk+1) & |
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| 209 | & +tmask(ji,jj+1,jk+1)+tmask(ji,jj,jk ),1. ) |
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| 210 | |
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| 211 | zcof1 = -e2u(ji,jj) * uslp(ji,jj,jk) * zmku |
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| 212 | zcof2 = -e1v(ji,jj) * vslp(ji,jj,jk) * zmkv |
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| 213 | |
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| 214 | zftu(ji,jj)= umask(ji,jj,jk) * & |
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| 215 | & ( zabe1 *( pt (ji+1,jj,jk,jn) - pt(ji,jj,jk,jn) ) & |
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| 216 | & + zcof1 *( zdkt (ji+1,jj) + zdk1t(ji,jj) & |
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| 217 | & +zdk1t(ji+1,jj) + zdkt (ji,jj) ) ) |
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| 218 | |
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| 219 | zftv(ji,jj,jk)= vmask(ji,jj,jk) * & |
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| 220 | & ( zabe2 *( pt(ji,jj+1,jk,jn) - pt(ji,jj,jk,jn) ) & |
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| 221 | & + zcof2 *( zdkt (ji,jj+1) + zdk1t(ji,jj) & |
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| 222 | & +zdk1t(ji,jj+1) + zdkt (ji,jj) ) ) |
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| 223 | END DO |
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[3] | 224 | END DO |
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| 225 | |
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| 226 | |
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[2024] | 227 | ! I.3 Second derivative (divergence) (not divided by the volume) |
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| 228 | ! --------------------- |
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| 229 | |
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| 230 | DO jj = 2 , jpjm1 |
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| 231 | DO ji = 2 , jpim1 |
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| 232 | ztah = zftu(ji,jj) - zftu(ji-1,jj) + zftv(ji,jj,jk) - zftv(ji,jj-1,jk) |
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| 233 | plt(ji,jj,jk,jn) = ztah |
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| 234 | END DO |
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[3] | 235 | END DO |
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[2024] | 236 | ! ! =============== |
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| 237 | END DO ! End of slab |
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| 238 | ! ! =============== |
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| 239 | ! "Poleward" diffusive heat or salt transport |
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| 240 | IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( kaht == 2 ) .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN |
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| 241 | IF( jn == jp_tem) pht_ldf(:) = ptr_vj( zftv(:,:,:) ) |
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| 242 | IF( jn == jp_sal) pst_ldf(:) = ptr_vj( zftv(:,:,:) ) |
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| 243 | ENDIF |
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[3] | 244 | |
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[2024] | 245 | ! ! ************ ! ! =============== |
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| 246 | DO jj = 2, jpjm1 ! Second step ! ! Horizontal slab |
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| 247 | ! ! ************ ! ! =============== |
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| 248 | |
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| 249 | ! II.1 horizontal tracer gradient |
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| 250 | ! ------------------------------- |
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| 251 | |
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| 252 | DO jk = 1, jpk |
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| 253 | DO ji = 1, jpim1 |
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| 254 | zdit (ji,jk) = ( pt(ji+1,jj ,jk,jn) - pt(ji,jj ,jk,jn) ) * umask(ji,jj ,jk) |
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| 255 | zdjt (ji,jk) = ( pt(ji ,jj+1,jk,jn) - pt(ji,jj ,jk,jn) ) * vmask(ji,jj ,jk) |
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| 256 | zdj1t(ji,jk) = ( pt(ji ,jj ,jk,jn) - pt(ji,jj-1,jk,jn) ) * vmask(ji,jj-1,jk) |
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| 257 | END DO |
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[3] | 258 | END DO |
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| 259 | |
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| 260 | |
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[2024] | 261 | ! II.2 Vertical fluxes |
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| 262 | ! -------------------- |
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| 263 | |
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| 264 | ! Surface and bottom vertical fluxes set to zero |
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| 265 | zftw(:, 1 ) = 0.e0 |
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| 266 | zftw(:,jpk) = 0.e0 |
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| 267 | |
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| 268 | ! interior (2=<jk=<jpk-1) |
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| 269 | DO jk = 2, jpkm1 |
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| 270 | DO ji = 2, jpim1 |
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| 271 | zcof0 = e1t(ji,jj) * e2t(ji,jj) / fse3w(ji,jj,jk) & |
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| 272 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 273 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 274 | |
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| 275 | zmku = 1./MAX( umask(ji ,jj,jk-1)+umask(ji-1,jj,jk) & |
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| 276 | & +umask(ji-1,jj,jk-1)+umask(ji ,jj,jk), 1. ) |
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| 277 | |
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| 278 | zmkv = 1./MAX( vmask(ji,jj ,jk-1)+vmask(ji,jj-1,jk) & |
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| 279 | & +vmask(ji,jj-1,jk-1)+vmask(ji,jj ,jk), 1. ) |
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| 280 | |
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| 281 | zcof3 = - e2t(ji,jj) * wslpi (ji,jj,jk) * zmku |
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| 282 | zcof4 = - e1t(ji,jj) * wslpj (ji,jj,jk) * zmkv |
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| 283 | |
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| 284 | zftw(ji,jk) = tmask(ji,jj,jk) * & |
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| 285 | & ( zcof0 * ( pt (ji,jj,jk-1,jn) - pt (ji ,jj,jk,jn) ) & |
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| 286 | & + zcof3 * ( zdit (ji ,jk-1 ) + zdit (ji-1,jk ) & |
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| 287 | & +zdit (ji-1 ,jk-1 ) + zdit (ji ,jk ) ) & |
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| 288 | & + zcof4 * ( zdjt (ji ,jk-1 ) + zdj1t(ji ,jk) & |
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| 289 | & +zdj1t(ji ,jk-1 ) + zdjt (ji ,jk ) ) ) |
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| 290 | END DO |
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[3] | 291 | END DO |
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| 292 | |
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| 293 | |
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[2024] | 294 | ! II.3 Divergence of vertical fluxes added to the horizontal divergence |
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| 295 | ! --------------------------------------------------------------------- |
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| 296 | |
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| 297 | IF( kaht == 1 ) THEN |
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| 298 | ! multiply the laplacian by the eddy diffusivity coefficient |
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| 299 | DO jk = 1, jpkm1 |
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| 300 | DO ji = 2, jpim1 |
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| 301 | ! eddy coef. divided by the volume element |
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| 302 | zbtr = 1.0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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| 303 | ! vertical divergence |
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| 304 | ztav = fsahtt(ji,jj,jk) * ( zftw(ji,jk) - zftw(ji,jk+1) ) |
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| 305 | ! harmonic operator applied to (pt,ps) and multiply by aht |
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| 306 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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| 307 | END DO |
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[3] | 308 | END DO |
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[2024] | 309 | ELSEIF( kaht == 2 ) THEN |
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| 310 | ! second call, no multiplication |
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| 311 | DO jk = 1, jpkm1 |
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| 312 | DO ji = 2, jpim1 |
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| 313 | ! inverse of the volume element |
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| 314 | zbtr = 1.0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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| 315 | ! vertical divergence |
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| 316 | ztav = zftw(ji,jk) - zftw(ji,jk+1) |
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| 317 | ! harmonic operator applied to (pt,ps) |
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| 318 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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| 319 | END DO |
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[3] | 320 | END DO |
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[2024] | 321 | ELSE |
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| 322 | IF(lwp) WRITE(numout,*) ' ldfght: kaht= 1 or 2, here =', kaht |
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| 323 | IF(lwp) WRITE(numout,*) ' We stop' |
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| 324 | STOP 'ldfght' |
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| 325 | ENDIF |
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| 326 | ! ! =============== |
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| 327 | END DO ! End of slab |
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| 328 | ! ! =============== |
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| 329 | END DO |
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| 330 | ! |
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[3] | 331 | END SUBROUTINE ldfght |
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| 332 | |
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| 333 | #else |
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| 334 | !!---------------------------------------------------------------------- |
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| 335 | !! Dummy module : NO rotation of the lateral mixing tensor |
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| 336 | !!---------------------------------------------------------------------- |
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| 337 | CONTAINS |
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| 338 | SUBROUTINE tra_ldf_bilapg( kt ) ! Dummy routine |
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[32] | 339 | WRITE(*,*) 'tra_ldf_bilapg: You should not have seen this print! error?', kt |
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[3] | 340 | END SUBROUTINE tra_ldf_bilapg |
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| 341 | #endif |
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| 342 | |
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| 343 | !!============================================================================== |
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| 344 | END MODULE traldf_bilapg |
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