[3] | 1 | MODULE traldf_bilapg |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE traldf_bilapg *** |
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[2528] | 4 | !! Ocean tracers: horizontal component of the lateral tracer mixing trend |
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[3] | 5 | !!============================================================================== |
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[2528] | 6 | !! History : 8.0 ! 1997-07 (G. Madec) Original code |
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| 7 | !! NEMO 1.0 ! 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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[2528] | 25 | USE trc_oce ! share passive tracers/Ocean variables |
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[2715] | 26 | USE lib_mpp ! MPP library |
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[3294] | 27 | USE wrk_nemo ! Memory Allocation |
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| 28 | USE timing ! Timing |
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[3] | 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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[2528] | 33 | PUBLIC tra_ldf_bilapg ! routine called by step.F90 |
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[3] | 34 | |
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| 35 | !! * Substitutions |
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| 36 | # include "domzgr_substitute.h90" |
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| 37 | # include "ldftra_substitute.h90" |
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| 38 | # include "ldfeiv_substitute.h90" |
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| 39 | !!---------------------------------------------------------------------- |
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[2528] | 40 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 41 | !! $Id$ |
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| 42 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 43 | !!---------------------------------------------------------------------- |
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| 44 | CONTAINS |
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| 45 | |
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[3294] | 46 | SUBROUTINE tra_ldf_bilapg( kt, kit000, cdtype, ptb, pta, kjpt ) |
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[3] | 47 | !!---------------------------------------------------------------------- |
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| 48 | !! *** ROUTINE tra_ldf_bilapg *** |
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| 49 | !! |
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[2528] | 50 | !! ** Purpose : Compute the before horizontal tracer diffusive |
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[3] | 51 | !! trend and add it to the general trend of tracer equation. |
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| 52 | !! |
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| 53 | !! ** Method : The lateral diffusive trends is provided by a 4th order |
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| 54 | !! operator rotated along geopotential surfaces. It is computed |
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| 55 | !! using before fields (forward in time) and geopotential slopes |
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| 56 | !! computed in routine inildf. |
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| 57 | !! -1- compute the geopotential harmonic operator applied to |
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[2528] | 58 | !! ptb and multiply it by the eddy diffusivity coefficient |
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| 59 | !! (done by a call to ldfght routine, result in wk1 arrays). |
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[3] | 60 | !! Applied the domain lateral boundary conditions by call to lbc_lnk |
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| 61 | !! -2- compute the geopotential harmonic operator applied to |
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[2528] | 62 | !! wk1 by a second call to ldfght routine (result in wk2) |
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[3] | 63 | !! arrays). |
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[2528] | 64 | !! -3- Add this trend to the general trend |
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| 65 | !! pta = pta + wk2 |
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[3] | 66 | !! |
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[2528] | 67 | !! ** Action : - Update pta arrays with the before geopotential |
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[3] | 68 | !! biharmonic mixing trend. |
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[2528] | 69 | !!---------------------------------------------------------------------- |
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[2715] | 70 | ! |
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[2528] | 71 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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[3294] | 72 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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[2528] | 73 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 74 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 75 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb ! before and now tracer fields |
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| 76 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend |
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[2715] | 77 | ! |
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| 78 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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[3294] | 79 | REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zwk1, zwk2 |
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[3] | 80 | !!---------------------------------------------------------------------- |
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[3294] | 81 | ! |
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| 82 | IF( nn_timing == 1 ) CALL timing_start('tra_ldf_bilapg') |
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| 83 | ! |
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| 84 | CALL wrk_alloc( jpi, jpj, jpk, kjpt, zwk1, zwk2 ) |
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| 85 | ! |
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| 86 | IF( kt == kit000 ) THEN |
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[3] | 87 | IF(lwp) WRITE(numout,*) |
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[2528] | 88 | IF(lwp) WRITE(numout,*) 'tra_ldf_bilapg : horizontal biharmonic operator in s-coordinate on ', cdtype |
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[3] | 89 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~' |
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| 90 | ENDIF |
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| 91 | |
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[2528] | 92 | ! 1. Laplacian of ptb * aht |
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[3] | 93 | ! ----------------------------- |
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[3294] | 94 | CALL ldfght( kt, cdtype, ptb, zwk1, kjpt, 1 ) ! rotated harmonic operator applied to ptb and multiply by aht |
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[2528] | 95 | ! ! output in wk1 |
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| 96 | ! |
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| 97 | DO jn = 1, kjpt |
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[3294] | 98 | CALL lbc_lnk( zwk1(:,:,:,jn) , 'T', 1. ) ! Lateral boundary conditions on wk1 (unchanged sign) |
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[2528] | 99 | END DO |
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[3] | 100 | |
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[2528] | 101 | ! 2. Bilaplacian of ptb |
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[3] | 102 | ! ------------------------- |
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[3294] | 103 | CALL ldfght( kt, cdtype, zwk1, zwk2, kjpt, 2 ) ! rotated harmonic operator applied to wk1 ; output in wk2 |
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[3] | 104 | |
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| 105 | |
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| 106 | ! 3. Update the tracer trends (j-slab : 2, jpj-1) |
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| 107 | ! --------------------------- |
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[2528] | 108 | DO jn = 1, kjpt |
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| 109 | DO jj = 2, jpjm1 |
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| 110 | DO jk = 1, jpkm1 |
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| 111 | DO ji = 2, jpim1 |
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| 112 | ! add it to the general tracer trends |
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[3294] | 113 | pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + zwk2(ji,jj,jk,jn) |
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[2528] | 114 | END DO |
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[3] | 115 | END DO |
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| 116 | END DO |
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[2528] | 117 | END DO |
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| 118 | ! |
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[3294] | 119 | CALL wrk_dealloc( jpi, jpj, jpk, kjpt, zwk1, zwk2 ) |
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[2715] | 120 | ! |
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[3294] | 121 | IF( nn_timing == 1 ) CALL timing_stop('tra_ldf_bilapg') |
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| 122 | ! |
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[3] | 123 | END SUBROUTINE tra_ldf_bilapg |
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| 124 | |
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| 125 | |
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[2528] | 126 | SUBROUTINE ldfght ( kt, cdtype, pt, plt, kjpt, kaht ) |
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[3] | 127 | !!---------------------------------------------------------------------- |
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| 128 | !! *** ROUTINE ldfght *** |
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| 129 | !! |
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[2528] | 130 | !! ** Purpose : Apply a geopotential harmonic operator to (pt) and |
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[3] | 131 | !! multiply it by the eddy diffusivity coefficient (if kaht=1). |
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| 132 | !! Routine only used in s-coordinates (l_sco=T) with bilaplacian |
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| 133 | !! operator (ln_traldf_bilap=T) acting along geopotential surfaces |
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| 134 | !! (ln_traldf_hor). |
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| 135 | !! |
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| 136 | !! ** Method : The harmonic operator rotated along geopotential |
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[2528] | 137 | !! surfaces is applied to (pt) using the slopes of geopotential |
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[3] | 138 | !! surfaces computed in inildf routine. The result is provided in |
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| 139 | !! (plt,pls) arrays. It is computed in 2 steps: |
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| 140 | !! |
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| 141 | !! First step: horizontal part of the operator. It is computed on |
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| 142 | !! ========== pt as follows (idem on ps) |
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| 143 | !! horizontal fluxes : |
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| 144 | !! zftu = e2u*e3u/e1u di[ pt ] - e2u*uslp dk[ mi(mk(pt)) ] |
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| 145 | !! zftv = e1v*e3v/e2v dj[ pt ] - e1v*vslp dk[ mj(mk(pt)) ] |
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| 146 | !! take the horizontal divergence of the fluxes (no divided by |
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| 147 | !! the volume element : |
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| 148 | !! plt = di-1[ zftu ] + dj-1[ zftv ] |
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| 149 | !! |
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| 150 | !! Second step: vertical part of the operator. It is computed on |
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| 151 | !! =========== pt as follows (idem on ps) |
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| 152 | !! vertical fluxes : |
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| 153 | !! zftw = e1t*e2t/e3w * (wslpi^2+wslpj^2) dk-1[ pt ] |
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| 154 | !! - e2t * wslpi di[ mi(mk(pt)) ] |
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| 155 | !! - e1t * wslpj dj[ mj(mk(pt)) ] |
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| 156 | !! take the vertical divergence of the fluxes add it to the hori- |
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| 157 | !! zontal component, divide the result by the volume element and |
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| 158 | !! if kaht=1, multiply by the eddy diffusivity coefficient: |
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| 159 | !! plt = aht / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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| 160 | !! else: |
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| 161 | !! plt = 1 / (e1t*e2t*e3t) { plt + dk[ zftw ] } |
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| 162 | !! |
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[2528] | 163 | !!---------------------------------------------------------------------- |
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[2715] | 164 | USE oce , ONLY: zftv => ua ! ua used as workspace |
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| 165 | ! |
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[2528] | 166 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 167 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 168 | INTEGER , INTENT(in ) :: kjpt !: dimension of |
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| 169 | REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,jpk,kjpt) :: pt ! tracer fields ( before for 1st call |
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| 170 | ! ! and laplacian of these fields for 2nd call. |
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| 171 | REAL(wp) , INTENT(out), DIMENSION(jpi,jpj,jpk,kjpt) :: plt !: partial harmonic operator applied to pt components except |
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| 172 | ! !: second order vertical derivative term |
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| 173 | INTEGER , INTENT(in ) :: kaht !: =1 multiply the laplacian by the eddy diffusivity coeff. |
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| 174 | ! !: =2 no multiplication |
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| 175 | !! |
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| 176 | INTEGER :: ji, jj, jk,jn ! dummy loop indices |
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| 177 | ! ! temporary scalars |
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| 178 | REAL(wp) :: zabe1, zabe2, zmku, zmkv |
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| 179 | REAL(wp) :: zbtr, ztah, ztav |
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| 180 | REAL(wp) :: zcof0, zcof1, zcof2, zcof3, zcof4 |
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[3294] | 181 | REAL(wp), POINTER, DIMENSION(:,:) :: zftu, zdkt, zdk1t |
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| 182 | REAL(wp), POINTER, DIMENSION(:,:) :: zftw, zdit, zdjt, zdj1t |
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[3] | 183 | !!---------------------------------------------------------------------- |
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[2528] | 184 | ! |
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[3294] | 185 | IF( nn_timing == 1 ) CALL timing_start('ldfght') |
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| 186 | ! |
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| 187 | CALL wrk_alloc( jpi, jpj, zftu, zdkt, zdk1t ) |
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| 188 | CALL wrk_alloc( jpi, jpk, zftw, zdit, zdjt, zdj1t ) |
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| 189 | ! |
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[2528] | 190 | DO jn = 1, kjpt |
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| 191 | ! ! ********** ! ! =============== |
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| 192 | DO jk = 1, jpkm1 ! First step ! ! Horizontal slab |
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| 193 | ! ! ********** ! ! =============== |
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| 194 | |
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| 195 | ! I.1 Vertical gradient of pt and ps at level jk and jk+1 |
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| 196 | ! ------------------------------------------------------- |
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| 197 | ! surface boundary condition: zdkt(jk=1)=zdkt(jk=2) |
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| 198 | |
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| 199 | zdk1t(:,:) = ( pt(:,:,jk,jn) - pt(:,:,jk+1,jn) ) * tmask(:,:,jk+1) |
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| 200 | IF( jk == 1 ) THEN |
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| 201 | zdkt(:,:) = zdk1t(:,:) |
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| 202 | ELSE |
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| 203 | zdkt(:,:) = ( pt(:,:,jk-1,jn) - pt(:,:,jk,jn) ) * tmask(:,:,jk) |
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| 204 | ENDIF |
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[3] | 205 | |
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| 206 | |
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[2528] | 207 | ! I.2 Horizontal fluxes |
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| 208 | ! --------------------- |
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| 209 | |
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| 210 | DO jj = 1, jpjm1 |
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| 211 | DO ji = 1, jpim1 |
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[4292] | 212 | zabe1 = re2u_e1u(ji,jj) * fse3u_n(ji,jj,jk) |
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| 213 | zabe2 = re1v_e2v(ji,jj) * fse3v_n(ji,jj,jk) |
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[2528] | 214 | |
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| 215 | zmku = 1./MAX( tmask(ji+1,jj,jk )+tmask(ji,jj,jk+1) & |
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| 216 | & +tmask(ji+1,jj,jk+1)+tmask(ji,jj,jk ),1. ) |
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| 217 | zmkv = 1./MAX( tmask(ji,jj+1,jk )+tmask(ji,jj,jk+1) & |
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| 218 | & +tmask(ji,jj+1,jk+1)+tmask(ji,jj,jk ),1. ) |
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| 219 | |
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| 220 | zcof1 = -e2u(ji,jj) * uslp(ji,jj,jk) * zmku |
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| 221 | zcof2 = -e1v(ji,jj) * vslp(ji,jj,jk) * zmkv |
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| 222 | |
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| 223 | zftu(ji,jj)= umask(ji,jj,jk) * & |
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| 224 | & ( zabe1 *( pt (ji+1,jj,jk,jn) - pt(ji,jj,jk,jn) ) & |
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| 225 | & + zcof1 *( zdkt (ji+1,jj) + zdk1t(ji,jj) & |
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| 226 | & +zdk1t(ji+1,jj) + zdkt (ji,jj) ) ) |
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| 227 | |
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| 228 | zftv(ji,jj,jk)= vmask(ji,jj,jk) * & |
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| 229 | & ( zabe2 *( pt(ji,jj+1,jk,jn) - pt(ji,jj,jk,jn) ) & |
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| 230 | & + zcof2 *( zdkt (ji,jj+1) + zdk1t(ji,jj) & |
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| 231 | & +zdk1t(ji,jj+1) + zdkt (ji,jj) ) ) |
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| 232 | END DO |
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[3] | 233 | END DO |
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| 234 | |
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| 235 | |
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[2528] | 236 | ! I.3 Second derivative (divergence) (not divided by the volume) |
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| 237 | ! --------------------- |
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| 238 | |
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| 239 | DO jj = 2 , jpjm1 |
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| 240 | DO ji = 2 , jpim1 |
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| 241 | ztah = zftu(ji,jj) - zftu(ji-1,jj) + zftv(ji,jj,jk) - zftv(ji,jj-1,jk) |
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| 242 | plt(ji,jj,jk,jn) = ztah |
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| 243 | END DO |
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[3] | 244 | END DO |
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[2528] | 245 | ! ! =============== |
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| 246 | END DO ! End of slab |
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| 247 | ! ! =============== |
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| 248 | ! "Poleward" diffusive heat or salt transport |
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[5147] | 249 | IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( kaht == 2 ) ) THEN |
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[3805] | 250 | ! note sign is reversed to give down-gradient diffusive transports (#1043) |
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[5147] | 251 | IF( jn == jp_tem) htr_ldf(:) = ptr_sj( -zftv(:,:,:) ) |
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| 252 | IF( jn == jp_sal) str_ldf(:) = ptr_sj( -zftv(:,:,:) ) |
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[2528] | 253 | ENDIF |
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[3] | 254 | |
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[2528] | 255 | ! ! ************ ! ! =============== |
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| 256 | DO jj = 2, jpjm1 ! Second step ! ! Horizontal slab |
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| 257 | ! ! ************ ! ! =============== |
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| 258 | |
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| 259 | ! II.1 horizontal tracer gradient |
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| 260 | ! ------------------------------- |
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| 261 | |
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| 262 | DO jk = 1, jpk |
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| 263 | DO ji = 1, jpim1 |
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| 264 | zdit (ji,jk) = ( pt(ji+1,jj ,jk,jn) - pt(ji,jj ,jk,jn) ) * umask(ji,jj ,jk) |
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| 265 | zdjt (ji,jk) = ( pt(ji ,jj+1,jk,jn) - pt(ji,jj ,jk,jn) ) * vmask(ji,jj ,jk) |
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| 266 | zdj1t(ji,jk) = ( pt(ji ,jj ,jk,jn) - pt(ji,jj-1,jk,jn) ) * vmask(ji,jj-1,jk) |
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| 267 | END DO |
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[3] | 268 | END DO |
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| 269 | |
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| 270 | |
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[2528] | 271 | ! II.2 Vertical fluxes |
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| 272 | ! -------------------- |
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| 273 | |
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| 274 | ! Surface and bottom vertical fluxes set to zero |
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| 275 | zftw(:, 1 ) = 0.e0 |
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| 276 | zftw(:,jpk) = 0.e0 |
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| 277 | |
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| 278 | ! interior (2=<jk=<jpk-1) |
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| 279 | DO jk = 2, jpkm1 |
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| 280 | DO ji = 2, jpim1 |
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[4292] | 281 | zcof0 = e12t(ji,jj) / fse3w_n(ji,jj,jk) & |
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[2528] | 282 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 283 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 284 | |
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| 285 | zmku = 1./MAX( umask(ji ,jj,jk-1)+umask(ji-1,jj,jk) & |
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| 286 | & +umask(ji-1,jj,jk-1)+umask(ji ,jj,jk), 1. ) |
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| 287 | |
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| 288 | zmkv = 1./MAX( vmask(ji,jj ,jk-1)+vmask(ji,jj-1,jk) & |
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| 289 | & +vmask(ji,jj-1,jk-1)+vmask(ji,jj ,jk), 1. ) |
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| 290 | |
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| 291 | zcof3 = - e2t(ji,jj) * wslpi (ji,jj,jk) * zmku |
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| 292 | zcof4 = - e1t(ji,jj) * wslpj (ji,jj,jk) * zmkv |
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| 293 | |
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| 294 | zftw(ji,jk) = tmask(ji,jj,jk) * & |
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| 295 | & ( zcof0 * ( pt (ji,jj,jk-1,jn) - pt (ji ,jj,jk,jn) ) & |
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| 296 | & + zcof3 * ( zdit (ji ,jk-1 ) + zdit (ji-1,jk ) & |
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| 297 | & +zdit (ji-1 ,jk-1 ) + zdit (ji ,jk ) ) & |
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| 298 | & + zcof4 * ( zdjt (ji ,jk-1 ) + zdj1t(ji ,jk) & |
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| 299 | & +zdj1t(ji ,jk-1 ) + zdjt (ji ,jk ) ) ) |
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| 300 | END DO |
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[3] | 301 | END DO |
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| 302 | |
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| 303 | |
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[2528] | 304 | ! II.3 Divergence of vertical fluxes added to the horizontal divergence |
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| 305 | ! --------------------------------------------------------------------- |
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| 306 | |
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| 307 | IF( kaht == 1 ) THEN |
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| 308 | ! multiply the laplacian by the eddy diffusivity coefficient |
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| 309 | DO jk = 1, jpkm1 |
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| 310 | DO ji = 2, jpim1 |
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| 311 | ! eddy coef. divided by the volume element |
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[4292] | 312 | zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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[2528] | 313 | ! vertical divergence |
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| 314 | ztav = fsahtt(ji,jj,jk) * ( zftw(ji,jk) - zftw(ji,jk+1) ) |
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| 315 | ! harmonic operator applied to (pt,ps) and multiply by aht |
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| 316 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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| 317 | END DO |
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[3] | 318 | END DO |
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[2528] | 319 | ELSEIF( kaht == 2 ) THEN |
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| 320 | ! second call, no multiplication |
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| 321 | DO jk = 1, jpkm1 |
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| 322 | DO ji = 2, jpim1 |
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| 323 | ! inverse of the volume element |
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[4292] | 324 | zbtr = 1.0 / ( e12t(ji,jj) * fse3t_n(ji,jj,jk) ) |
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[2528] | 325 | ! vertical divergence |
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| 326 | ztav = zftw(ji,jk) - zftw(ji,jk+1) |
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| 327 | ! harmonic operator applied to (pt,ps) |
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| 328 | plt(ji,jj,jk,jn) = ( plt(ji,jj,jk,jn) + ztav ) * zbtr |
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| 329 | END DO |
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[3] | 330 | END DO |
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[2528] | 331 | ELSE |
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| 332 | IF(lwp) WRITE(numout,*) ' ldfght: kaht= 1 or 2, here =', kaht |
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| 333 | IF(lwp) WRITE(numout,*) ' We stop' |
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| 334 | STOP 'ldfght' |
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| 335 | ENDIF |
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| 336 | ! ! =============== |
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| 337 | END DO ! End of slab |
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| 338 | ! ! =============== |
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| 339 | END DO |
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| 340 | ! |
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[3294] | 341 | CALL wrk_dealloc( jpi, jpj, zftu, zdkt, zdk1t ) |
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| 342 | CALL wrk_dealloc( jpi, jpk, zftw, zdit, zdjt, zdj1t ) |
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[2715] | 343 | ! |
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[3294] | 344 | IF( nn_timing == 1 ) CALL timing_stop('ldfght') |
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| 345 | ! |
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[3] | 346 | END SUBROUTINE ldfght |
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| 347 | |
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| 348 | #else |
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| 349 | !!---------------------------------------------------------------------- |
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| 350 | !! Dummy module : NO rotation of the lateral mixing tensor |
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| 351 | !!---------------------------------------------------------------------- |
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| 352 | CONTAINS |
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[3294] | 353 | SUBROUTINE tra_ldf_bilapg( kt, kit000, cdtype, ptb, pta, kjpt ) ! Empty routine |
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| 354 | INTEGER :: kt, kit000 |
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[2528] | 355 | CHARACTER(len=3) :: cdtype |
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| 356 | REAL, DIMENSION(:,:,:,:) :: ptb, pta |
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[3294] | 357 | WRITE(*,*) 'tra_ldf_iso: You should not have seen this print! error?', & |
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| 358 | & kt, kit000, cdtype, ptb(1,1,1,1), pta(1,1,1,1), kjpt |
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[3] | 359 | END SUBROUTINE tra_ldf_bilapg |
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| 360 | #endif |
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| 361 | |
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| 362 | !!============================================================================== |
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| 363 | END MODULE traldf_bilapg |
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