[3] | 1 | MODULE zpshde |
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[2528] | 2 | !!====================================================================== |
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[3] | 3 | !! *** MODULE zpshde *** |
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[2528] | 4 | !! z-coordinate + partial step : Horizontal Derivative at ocean bottom level |
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| 5 | !!====================================================================== |
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| 6 | !! History : OPA ! 2002-04 (A. Bozec) Original code |
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| 7 | !! NEMO 1.0 ! 2002-08 (G. Madec E. Durand) Optimization and Free form |
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| 8 | !! - ! 2004-03 (C. Ethe) adapted for passive tracers |
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| 9 | !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA |
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[5120] | 10 | !! 3.6 ! 2014-11 (P. Mathiot) Add zps_hde_isf (needed to open a cavity) |
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[2528] | 11 | !!====================================================================== |
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[457] | 12 | |
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[3] | 13 | !!---------------------------------------------------------------------- |
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| 14 | !! zps_hde : Horizontal DErivative of T, S and rd at the last |
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| 15 | !! ocean level (Z-coord. with Partial Steps) |
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| 16 | !!---------------------------------------------------------------------- |
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[2528] | 17 | USE oce ! ocean: dynamics and tracers variables |
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| 18 | USE dom_oce ! domain: ocean variables |
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[13515] | 19 | USE domutl, ONLY : is_tile |
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[3] | 20 | USE phycst ! physical constants |
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[2528] | 21 | USE eosbn2 ! ocean equation of state |
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[3] | 22 | USE in_out_manager ! I/O manager |
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| 23 | USE lbclnk ! lateral boundary conditions (or mpp link) |
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[2715] | 24 | USE lib_mpp ! MPP library |
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[3294] | 25 | USE timing ! Timing |
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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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[5120] | 30 | PUBLIC zps_hde ! routine called by step.F90 |
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| 31 | PUBLIC zps_hde_isf ! routine called by step.F90 |
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[3] | 32 | |
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| 33 | !! * Substitutions |
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[12377] | 34 | # include "do_loop_substitute.h90" |
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[13237] | 35 | # include "domzgr_substitute.h90" |
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[3] | 36 | !!---------------------------------------------------------------------- |
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[9598] | 37 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[2528] | 38 | !! $Id$ |
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[10068] | 39 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[247] | 40 | !!---------------------------------------------------------------------- |
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[3] | 41 | CONTAINS |
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| 42 | |
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[13515] | 43 | ! TODO: NOT TESTED- requires zps |
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| 44 | SUBROUTINE zps_hde( kt, Kmm, kjpt, pta, pgtu, pgtv, & |
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| 45 | & prd, pgru, pgrv ) |
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| 46 | !! |
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| 47 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 48 | INTEGER , INTENT(in ) :: Kmm ! ocean time level index |
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| 49 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 50 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pta ! 4D tracers fields |
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| 51 | REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 52 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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| 53 | REAL(wp), DIMENSION(:,:) , INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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| 54 | ! |
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| 55 | INTEGER :: itrd, itgr |
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| 56 | !! |
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| 57 | IF( PRESENT(prd) ) THEN ; itrd = is_tile(prd) ; ELSE ; itrd = 0 ; ENDIF |
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| 58 | IF( PRESENT(pgru) ) THEN ; itgr = is_tile(pgru) ; ELSE ; itgr = 0 ; ENDIF |
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| 59 | |
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| 60 | CALL zps_hde_t( kt, Kmm, kjpt, pta, is_tile(pta), pgtu, pgtv, is_tile(pgtu), & |
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| 61 | & prd, itrd, pgru, pgrv, itgr ) |
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| 62 | END SUBROUTINE zps_hde |
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| 63 | |
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| 64 | |
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| 65 | SUBROUTINE zps_hde_t( kt, Kmm, kjpt, pta, ktta, pgtu, pgtv, ktgt, & |
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| 66 | & prd, ktrd, pgru, pgrv, ktgr ) |
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[5120] | 67 | !!---------------------------------------------------------------------- |
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| 68 | !! *** ROUTINE zps_hde *** |
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| 69 | !! |
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| 70 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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| 71 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 72 | !! with partial steps. |
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| 73 | !! |
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| 74 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 75 | !! levels are different for each grid point, so that T, S and rd |
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| 76 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 77 | !! gradients again, we interpolate T and S at the good depth : |
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| 78 | !! Linear interpolation of T, S |
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| 79 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 80 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 81 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 82 | !! This formulation computes the two cases: |
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| 83 | !! CASE 1 CASE 2 |
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| 84 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 85 | !! Ti T~ T~ Ti+1 |
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| 86 | !! _____ _____ |
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| 87 | !! k | |Ti+1 k Ti | | |
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| 88 | !! | |____ ____| | |
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| 89 | !! ___ | | | ___ | | | |
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| 90 | !! |
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[13237] | 91 | !! case 1-> e3w(i+1,:,:,Kmm) >= e3w(i,:,:,Kmm) ( and e3w(:,j+1,:,Kmm) >= e3w(:,j,:,Kmm) ) then |
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| 92 | !! t~ = t(i+1,j ,k) + (e3w(i+1,j,k,Kmm) - e3w(i,j,k,Kmm)) * dk(Ti+1)/e3w(i+1,j,k,Kmm) |
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| 93 | !! ( t~ = t(i ,j+1,k) + (e3w(i,j+1,k,Kmm) - e3w(i,j,k,Kmm)) * dk(Tj+1)/e3w(i,j+1,k,Kmm) ) |
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[5120] | 94 | !! or |
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[13237] | 95 | !! case 2-> e3w(i+1,:,:,Kmm) <= e3w(i,:,:,Kmm) ( and e3w(:,j+1,:,Kmm) <= e3w(:,j,:,Kmm) ) then |
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| 96 | !! t~ = t(i,j,k) + (e3w(i,j,k,Kmm) - e3w(i+1,j,k,Kmm)) * dk(Ti)/e3w(i,j,k,Kmm) |
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| 97 | !! ( t~ = t(i,j,k) + (e3w(i,j,k,Kmm) - e3w(i,j+1,k,Kmm)) * dk(Tj)/e3w(i,j,k,Kmm) ) |
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[5120] | 98 | !! Idem for di(s) and dj(s) |
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| 99 | !! |
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| 100 | !! For rho, we call eos which will compute rd~(t~,s~) at the right |
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| 101 | !! depth zh from interpolated T and S for the different formulations |
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| 102 | !! of the equation of state (eos). |
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| 103 | !! Gradient formulation for rho : |
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| 104 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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| 105 | !! |
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| 106 | !! ** Action : compute for top interfaces |
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| 107 | !! - pgtu, pgtv: horizontal gradient of tracer at u- & v-points |
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| 108 | !! - pgru, pgrv: horizontal gradient of rho (if present) at u- & v-points |
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| 109 | !!---------------------------------------------------------------------- |
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[13515] | 110 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 111 | INTEGER , INTENT(in ) :: Kmm ! ocean time level index |
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| 112 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 113 | INTEGER , INTENT(in ) :: ktta, ktgt, ktrd, ktgr |
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[13539] | 114 | REAL(wp), DIMENSION(ST_2DT(ktta),JPK,KJPT), INTENT(in ) :: pta ! 4D tracers fields |
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| 115 | REAL(wp), DIMENSION(ST_2DT(ktgt) ,KJPT), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 116 | REAL(wp), DIMENSION(ST_2DT(ktrd),JPK ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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[13515] | 117 | REAL(wp), DIMENSION(ST_2DT(ktgr) ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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[5120] | 118 | ! |
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[5836] | 119 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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| 120 | INTEGER :: iku, ikv, ikum1, ikvm1 ! partial step level (ocean bottom level) at u- and v-points |
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| 121 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! local scalars |
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[13515] | 122 | REAL(wp), DIMENSION(ST_2D(nn_hls)) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos |
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| 123 | REAL(wp), DIMENSION(ST_2D(nn_hls),kjpt) :: zti, ztj ! |
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[5120] | 124 | !!---------------------------------------------------------------------- |
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| 125 | ! |
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[9019] | 126 | IF( ln_timing ) CALL timing_start( 'zps_hde') |
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[5120] | 127 | ! |
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[9019] | 128 | pgtu(:,:,:) = 0._wp ; zti (:,:,:) = 0._wp ; zhi (:,:) = 0._wp |
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| 129 | pgtv(:,:,:) = 0._wp ; ztj (:,:,:) = 0._wp ; zhj (:,:) = 0._wp |
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[5120] | 130 | ! |
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| 131 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 132 | ! |
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[13295] | 133 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 134 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 135 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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[13237] | 136 | !!gm BUG ? when applied to before fields, e3w(:,:,k,Kbb) should be used.... |
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[12377] | 137 | ze3wu = e3w(ji+1,jj ,iku,Kmm) - e3w(ji,jj,iku,Kmm) |
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| 138 | ze3wv = e3w(ji ,jj+1,ikv,Kmm) - e3w(ji,jj,ikv,Kmm) |
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| 139 | ! |
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| 140 | ! i- direction |
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| 141 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 142 | zmaxu = ze3wu / e3w(ji+1,jj,iku,Kmm) |
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| 143 | ! interpolated values of tracers |
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| 144 | zti (ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) |
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| 145 | ! gradient of tracers |
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| 146 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 147 | ELSE ! case 2 |
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| 148 | zmaxu = -ze3wu / e3w(ji,jj,iku,Kmm) |
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| 149 | ! interpolated values of tracers |
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| 150 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
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| 151 | ! gradient of tracers |
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| 152 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 153 | ENDIF |
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| 154 | ! |
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| 155 | ! j- direction |
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| 156 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 157 | zmaxv = ze3wv / e3w(ji,jj+1,ikv,Kmm) |
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| 158 | ! interpolated values of tracers |
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| 159 | ztj (ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) |
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| 160 | ! gradient of tracers |
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| 161 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 162 | ELSE ! case 2 |
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| 163 | zmaxv = -ze3wv / e3w(ji,jj,ikv,Kmm) |
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| 164 | ! interpolated values of tracers |
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| 165 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
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| 166 | ! gradient of tracers |
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| 167 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 168 | ENDIF |
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| 169 | END_2D |
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[5120] | 170 | END DO |
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[10425] | 171 | ! |
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[13226] | 172 | CALL lbc_lnk_multi( 'zpshde', pgtu(:,:,:), 'U', -1.0_wp , pgtv(:,:,:), 'V', -1.0_wp ) ! Lateral boundary cond. |
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[5836] | 173 | ! |
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| 174 | IF( PRESENT( prd ) ) THEN !== horizontal derivative of density anomalies (rd) ==! (optional part) |
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[7753] | 175 | pgru(:,:) = 0._wp |
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| 176 | pgrv(:,:) = 0._wp ! depth of the partial step level |
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[13295] | 177 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 178 | iku = mbku(ji,jj) |
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| 179 | ikv = mbkv(ji,jj) |
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| 180 | ze3wu = e3w(ji+1,jj ,iku,Kmm) - e3w(ji,jj,iku,Kmm) |
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| 181 | ze3wv = e3w(ji ,jj+1,ikv,Kmm) - e3w(ji,jj,ikv,Kmm) |
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| 182 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = gdept(ji ,jj,iku,Kmm) ! i-direction: case 1 |
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| 183 | ELSE ; zhi(ji,jj) = gdept(ji+1,jj,iku,Kmm) ! - - case 2 |
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| 184 | ENDIF |
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| 185 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = gdept(ji,jj ,ikv,Kmm) ! j-direction: case 1 |
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| 186 | ELSE ; zhj(ji,jj) = gdept(ji,jj+1,ikv,Kmm) ! - - case 2 |
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| 187 | ENDIF |
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| 188 | END_2D |
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[5836] | 189 | ! |
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| 190 | CALL eos( zti, zhi, zri ) ! interpolated density from zti, ztj |
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| 191 | CALL eos( ztj, zhj, zrj ) ! at the partial step depth output in zri, zrj |
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| 192 | ! |
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[13295] | 193 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 194 | iku = mbku(ji,jj) |
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| 195 | ikv = mbkv(ji,jj) |
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| 196 | ze3wu = e3w(ji+1,jj ,iku,Kmm) - e3w(ji,jj,iku,Kmm) |
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| 197 | ze3wv = e3w(ji ,jj+1,ikv,Kmm) - e3w(ji,jj,ikv,Kmm) |
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| 198 | IF( ze3wu >= 0._wp ) THEN ; pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji ,jj ) - prd(ji,jj,iku) ) ! i: 1 |
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| 199 | ELSE ; pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj ) ) ! i: 2 |
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| 200 | ENDIF |
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| 201 | IF( ze3wv >= 0._wp ) THEN ; pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
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| 202 | ELSE ; pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj ) ) ! j: 2 |
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| 203 | ENDIF |
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| 204 | END_2D |
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[13226] | 205 | CALL lbc_lnk_multi( 'zpshde', pgru , 'U', -1.0_wp , pgrv , 'V', -1.0_wp ) ! Lateral boundary conditions |
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[5120] | 206 | ! |
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| 207 | END IF |
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| 208 | ! |
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[9019] | 209 | IF( ln_timing ) CALL timing_stop( 'zps_hde') |
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[5120] | 210 | ! |
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[13515] | 211 | END SUBROUTINE zps_hde_t |
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[9019] | 212 | |
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| 213 | |
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[13515] | 214 | ! TODO: NOT TESTED- requires zps |
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[12377] | 215 | SUBROUTINE zps_hde_isf( kt, Kmm, kjpt, pta, pgtu, pgtv, pgtui, pgtvi, & |
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[13515] | 216 | & prd, pgru, pgrv, pgrui, pgrvi ) |
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| 217 | !! |
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| 218 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 219 | INTEGER , INTENT(in ) :: Kmm ! ocean time level index |
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| 220 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 221 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pta ! 4D tracers fields |
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| 222 | REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 223 | REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pgtui, pgtvi ! hor. grad. of stra at u- & v-pts (ISF) |
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| 224 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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| 225 | REAL(wp), DIMENSION(:,:) , INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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| 226 | REAL(wp), DIMENSION(:,:) , INTENT( out), OPTIONAL :: pgrui, pgrvi ! hor. grad of prd at u- & v-pts (top) |
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| 227 | ! |
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| 228 | INTEGER :: itrd, itgr, itgri |
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| 229 | !! |
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| 230 | IF( PRESENT(prd) ) THEN ; itrd = is_tile(prd) ; ELSE ; itrd = 0 ; ENDIF |
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| 231 | IF( PRESENT(pgru) ) THEN ; itgr = is_tile(pgru) ; ELSE ; itgr = 0 ; ENDIF |
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| 232 | IF( PRESENT(pgrui) ) THEN ; itgri = is_tile(pgrui) ; ELSE ; itgri = 0 ; ENDIF |
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| 233 | |
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| 234 | CALL zps_hde_isf_t( kt, Kmm, kjpt, pta, is_tile(pta), pgtu, pgtv, is_tile(pgtu), pgtui, pgtvi, is_tile(pgtui), & |
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| 235 | & prd, itrd, pgru, pgrv, itgr, pgrui, pgrvi, itgri ) |
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| 236 | END SUBROUTINE zps_hde_isf |
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| 237 | |
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| 238 | |
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| 239 | SUBROUTINE zps_hde_isf_t( kt, Kmm, kjpt, pta, ktta, pgtu, pgtv, ktgt, pgtui, pgtvi, ktgti, & |
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| 240 | & prd, ktrd, pgru, pgrv, ktgr, pgrui, pgrvi, ktgri ) |
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[3] | 241 | !!---------------------------------------------------------------------- |
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[6140] | 242 | !! *** ROUTINE zps_hde_isf *** |
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[3] | 243 | !! |
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[2528] | 244 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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[3] | 245 | !! at u- and v-points with a linear interpolation for z-coordinate |
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[6140] | 246 | !! with partial steps for top (ice shelf) and bottom. |
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[3] | 247 | !! |
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| 248 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 249 | !! levels are different for each grid point, so that T, S and rd |
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| 250 | !! points are not at the same depth as in z-coord. To have horizontal |
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[6140] | 251 | !! gradients again, we interpolate T and S at the good depth : |
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| 252 | !! For the bottom case: |
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[3] | 253 | !! Linear interpolation of T, S |
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| 254 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 255 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 256 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 257 | !! This formulation computes the two cases: |
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| 258 | !! CASE 1 CASE 2 |
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| 259 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 260 | !! Ti T~ T~ Ti+1 |
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| 261 | !! _____ _____ |
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| 262 | !! k | |Ti+1 k Ti | | |
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| 263 | !! | |____ ____| | |
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| 264 | !! ___ | | | ___ | | | |
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| 265 | !! |
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[13237] | 266 | !! case 1-> e3w(i+1,j,k,Kmm) >= e3w(i,j,k,Kmm) ( and e3w(i,j+1,k,Kmm) >= e3w(i,j,k,Kmm) ) then |
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| 267 | !! t~ = t(i+1,j ,k) + (e3w(i+1,j ,k,Kmm) - e3w(i,j,k,Kmm)) * dk(Ti+1)/e3w(i+1,j ,k,Kmm) |
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| 268 | !! ( t~ = t(i ,j+1,k) + (e3w(i ,j+1,k,Kmm) - e3w(i,j,k,Kmm)) * dk(Tj+1)/e3w(i ,j+1,k,Kmm) ) |
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[3] | 269 | !! or |
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[13237] | 270 | !! case 2-> e3w(i+1,j,k,Kmm) <= e3w(i,j,k,Kmm) ( and e3w(i,j+1,k,Kmm) <= e3w(i,j,k,Kmm) ) then |
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| 271 | !! t~ = t(i,j,k) + (e3w(i,j,k,Kmm) - e3w(i+1,j ,k,Kmm)) * dk(Ti)/e3w(i,j,k,Kmm) |
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| 272 | !! ( t~ = t(i,j,k) + (e3w(i,j,k,Kmm) - e3w(i ,j+1,k,Kmm)) * dk(Tj)/e3w(i,j,k,Kmm) ) |
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[3] | 273 | !! Idem for di(s) and dj(s) |
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| 274 | !! |
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[4990] | 275 | !! For rho, we call eos which will compute rd~(t~,s~) at the right |
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| 276 | !! depth zh from interpolated T and S for the different formulations |
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| 277 | !! of the equation of state (eos). |
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[3] | 278 | !! Gradient formulation for rho : |
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[4990] | 279 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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[3] | 280 | !! |
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[6140] | 281 | !! For the top case (ice shelf): As for the bottom case but upside down |
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| 282 | !! |
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[4990] | 283 | !! ** Action : compute for top and bottom interfaces |
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[5120] | 284 | !! - pgtu, pgtv, pgtui, pgtvi: horizontal gradient of tracer at u- & v-points |
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| 285 | !! - pgru, pgrv, pgrui, pgtvi: horizontal gradient of rho (if present) at u- & v-points |
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[2528] | 286 | !!---------------------------------------------------------------------- |
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[13515] | 287 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 288 | INTEGER , INTENT(in ) :: Kmm ! ocean time level index |
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| 289 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 290 | INTEGER , INTENT(in ) :: ktta, ktgt, ktgti, ktrd, ktgr, ktgri |
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[13539] | 291 | REAL(wp), DIMENSION(ST_2DT(ktta),JPK,KJPT), INTENT(in ) :: pta ! 4D tracers fields |
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| 292 | REAL(wp), DIMENSION(ST_2DT(ktgt) ,KJPT), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 293 | REAL(wp), DIMENSION(ST_2DT(ktgti) ,KJPT), INTENT( out) :: pgtui, pgtvi ! hor. grad. of stra at u- & v-pts (ISF) |
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| 294 | REAL(wp), DIMENSION(ST_2DT(ktrd),JPK ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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[13515] | 295 | REAL(wp), DIMENSION(ST_2DT(ktgr) ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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| 296 | REAL(wp), DIMENSION(ST_2DT(ktgri) ), INTENT( out), OPTIONAL :: pgrui, pgrvi ! hor. grad of prd at u- & v-pts (top) |
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[2715] | 297 | ! |
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[2528] | 298 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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[4990] | 299 | INTEGER :: iku, ikv, ikum1, ikvm1,ikup1, ikvp1 ! partial step level (ocean bottom level) at u- and v-points |
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[6140] | 300 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars |
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[13515] | 301 | REAL(wp), DIMENSION(ST_2D(nn_hls)) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos |
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| 302 | REAL(wp), DIMENSION(ST_2D(nn_hls),kjpt) :: zti, ztj ! |
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[3] | 303 | !!---------------------------------------------------------------------- |
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[3294] | 304 | ! |
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[9019] | 305 | IF( ln_timing ) CALL timing_start( 'zps_hde_isf') |
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[3294] | 306 | ! |
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[5836] | 307 | pgtu (:,:,:) = 0._wp ; pgtv (:,:,:) =0._wp |
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| 308 | pgtui(:,:,:) = 0._wp ; pgtvi(:,:,:) =0._wp |
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| 309 | zti (:,:,:) = 0._wp ; ztj (:,:,:) =0._wp |
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| 310 | zhi (:,: ) = 0._wp ; zhj (:,: ) =0._wp |
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[3294] | 311 | ! |
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[2528] | 312 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 313 | ! |
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[13295] | 314 | DO_2D( 1, 0, 1, 0 ) |
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[6140] | 315 | |
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[12377] | 316 | iku = mbku(ji,jj); ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 317 | ikv = mbkv(ji,jj); ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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| 318 | ze3wu = gdept(ji+1,jj,iku,Kmm) - gdept(ji,jj,iku,Kmm) |
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| 319 | ze3wv = gdept(ji,jj+1,ikv,Kmm) - gdept(ji,jj,ikv,Kmm) |
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| 320 | ! |
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| 321 | ! i- direction |
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| 322 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 323 | zmaxu = ze3wu / e3w(ji+1,jj,iku,Kmm) |
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| 324 | ! interpolated values of tracers |
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| 325 | zti (ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) |
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| 326 | ! gradient of tracers |
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| 327 | pgtu(ji,jj,jn) = ssumask(ji,jj) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 328 | ELSE ! case 2 |
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| 329 | zmaxu = -ze3wu / e3w(ji,jj,iku,Kmm) |
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| 330 | ! interpolated values of tracers |
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| 331 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
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| 332 | ! gradient of tracers |
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| 333 | pgtu(ji,jj,jn) = ssumask(ji,jj) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 334 | ENDIF |
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| 335 | ! |
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| 336 | ! j- direction |
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| 337 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 338 | zmaxv = ze3wv / e3w(ji,jj+1,ikv,Kmm) |
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| 339 | ! interpolated values of tracers |
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| 340 | ztj (ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) |
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| 341 | ! gradient of tracers |
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| 342 | pgtv(ji,jj,jn) = ssvmask(ji,jj) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 343 | ELSE ! case 2 |
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| 344 | zmaxv = -ze3wv / e3w(ji,jj,ikv,Kmm) |
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| 345 | ! interpolated values of tracers |
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| 346 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
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| 347 | ! gradient of tracers |
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| 348 | pgtv(ji,jj,jn) = ssvmask(ji,jj) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 349 | ENDIF |
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[6140] | 350 | |
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[12377] | 351 | END_2D |
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[2528] | 352 | END DO |
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[10425] | 353 | ! |
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[13226] | 354 | CALL lbc_lnk_multi( 'zpshde', pgtu(:,:,:), 'U', -1.0_wp , pgtv(:,:,:), 'V', -1.0_wp ) ! Lateral boundary cond. |
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[3] | 355 | |
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[6140] | 356 | ! horizontal derivative of density anomalies (rd) |
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| 357 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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| 358 | pgru(:,:)=0.0_wp ; pgrv(:,:)=0.0_wp ; |
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[5836] | 359 | ! |
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[13295] | 360 | DO_2D( 1, 0, 1, 0 ) |
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[6140] | 361 | |
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[12377] | 362 | iku = mbku(ji,jj) |
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| 363 | ikv = mbkv(ji,jj) |
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| 364 | ze3wu = gdept(ji+1,jj,iku,Kmm) - gdept(ji,jj,iku,Kmm) |
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| 365 | ze3wv = gdept(ji,jj+1,ikv,Kmm) - gdept(ji,jj,ikv,Kmm) |
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| 366 | ! |
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| 367 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = gdept(ji ,jj,iku,Kmm) ! i-direction: case 1 |
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| 368 | ELSE ; zhi(ji,jj) = gdept(ji+1,jj,iku,Kmm) ! - - case 2 |
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| 369 | ENDIF |
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| 370 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = gdept(ji,jj ,ikv,Kmm) ! j-direction: case 1 |
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| 371 | ELSE ; zhj(ji,jj) = gdept(ji,jj+1,ikv,Kmm) ! - - case 2 |
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| 372 | ENDIF |
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[6140] | 373 | |
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[12377] | 374 | END_2D |
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[3] | 375 | |
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[6140] | 376 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 377 | ! step and store it in zri, zrj for each case |
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| 378 | CALL eos( zti, zhi, zri ) |
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| 379 | CALL eos( ztj, zhj, zrj ) |
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| 380 | |
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[13295] | 381 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 382 | iku = mbku(ji,jj) |
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| 383 | ikv = mbkv(ji,jj) |
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| 384 | ze3wu = gdept(ji+1,jj,iku,Kmm) - gdept(ji,jj,iku,Kmm) |
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| 385 | ze3wv = gdept(ji,jj+1,ikv,Kmm) - gdept(ji,jj,ikv,Kmm) |
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[6140] | 386 | |
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[12377] | 387 | IF( ze3wu >= 0._wp ) THEN ; pgru(ji,jj) = ssumask(ji,jj) * ( zri(ji ,jj ) - prd(ji,jj,iku) ) ! i: 1 |
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| 388 | ELSE ; pgru(ji,jj) = ssumask(ji,jj) * ( prd(ji+1,jj,iku) - zri(ji,jj ) ) ! i: 2 |
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| 389 | ENDIF |
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| 390 | IF( ze3wv >= 0._wp ) THEN ; pgrv(ji,jj) = ssvmask(ji,jj) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
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| 391 | ELSE ; pgrv(ji,jj) = ssvmask(ji,jj) * ( prd(ji,jj+1,ikv) - zrj(ji,jj ) ) ! j: 2 |
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| 392 | ENDIF |
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[6140] | 393 | |
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[12377] | 394 | END_2D |
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[6140] | 395 | |
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[13226] | 396 | CALL lbc_lnk_multi( 'zpshde', pgru , 'U', -1.0_wp , pgrv , 'V', -1.0_wp ) ! Lateral boundary conditions |
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[4990] | 397 | ! |
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| 398 | END IF |
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[5836] | 399 | ! |
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| 400 | ! !== (ISH) compute grui and gruvi ==! |
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| 401 | ! |
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[4990] | 402 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! |
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[13295] | 403 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 404 | iku = miku(ji,jj); ikup1 = miku(ji,jj) + 1 |
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| 405 | ikv = mikv(ji,jj); ikvp1 = mikv(ji,jj) + 1 |
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| 406 | ! |
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| 407 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
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| 408 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
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[13237] | 409 | ! in this case e3w(i,j,k,Kmm) - e3w(i,j+1,k,Kmm) is not the distance between Tj~ and Tj |
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[12377] | 410 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
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| 411 | ze3wu = gdept(ji,jj,iku,Kmm) - gdept(ji+1,jj,iku,Kmm) |
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| 412 | ze3wv = gdept(ji,jj,ikv,Kmm) - gdept(ji,jj+1,ikv,Kmm) |
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[6140] | 413 | |
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[12377] | 414 | ! i- direction |
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| 415 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 416 | zmaxu = ze3wu / e3w(ji+1,jj,ikup1,Kmm) |
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| 417 | ! interpolated values of tracers |
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| 418 | zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikup1,jn) - pta(ji+1,jj,iku,jn) ) |
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| 419 | ! gradient of tracers |
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| 420 | pgtui(ji,jj,jn) = ssumask(ji,jj) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 421 | ELSE ! case 2 |
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| 422 | zmaxu = - ze3wu / e3w(ji,jj,ikup1,Kmm) |
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| 423 | ! interpolated values of tracers |
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| 424 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikup1,jn) - pta(ji,jj,iku,jn) ) |
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| 425 | ! gradient of tracers |
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| 426 | pgtui(ji,jj,jn) = ssumask(ji,jj) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 427 | ENDIF |
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| 428 | ! |
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| 429 | ! j- direction |
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| 430 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 431 | zmaxv = ze3wv / e3w(ji,jj+1,ikvp1,Kmm) |
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| 432 | ! interpolated values of tracers |
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| 433 | ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvp1,jn) - pta(ji,jj+1,ikv,jn) ) |
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| 434 | ! gradient of tracers |
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| 435 | pgtvi(ji,jj,jn) = ssvmask(ji,jj) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 436 | ELSE ! case 2 |
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| 437 | zmaxv = - ze3wv / e3w(ji,jj,ikvp1,Kmm) |
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| 438 | ! interpolated values of tracers |
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| 439 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvp1,jn) - pta(ji,jj,ikv,jn) ) |
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| 440 | ! gradient of tracers |
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| 441 | pgtvi(ji,jj,jn) = ssvmask(ji,jj) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 442 | ENDIF |
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[6140] | 443 | |
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[12377] | 444 | END_2D |
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[4990] | 445 | ! |
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| 446 | END DO |
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[13226] | 447 | CALL lbc_lnk_multi( 'zpshde', pgtui(:,:,:), 'U', -1.0_wp , pgtvi(:,:,:), 'V', -1.0_wp ) ! Lateral boundary cond. |
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[4990] | 448 | |
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[5836] | 449 | IF( PRESENT( prd ) ) THEN !== horizontal derivative of density anomalies (rd) ==! (optional part) |
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| 450 | ! |
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[6140] | 451 | pgrui(:,:) =0.0_wp; pgrvi(:,:) =0.0_wp; |
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[13295] | 452 | DO_2D( 1, 0, 1, 0 ) |
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[6140] | 453 | |
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[12377] | 454 | iku = miku(ji,jj) |
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| 455 | ikv = mikv(ji,jj) |
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| 456 | ze3wu = gdept(ji,jj,iku,Kmm) - gdept(ji+1,jj,iku,Kmm) |
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| 457 | ze3wv = gdept(ji,jj,ikv,Kmm) - gdept(ji,jj+1,ikv,Kmm) |
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| 458 | ! |
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| 459 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = gdept(ji ,jj,iku,Kmm) ! i-direction: case 1 |
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| 460 | ELSE ; zhi(ji,jj) = gdept(ji+1,jj,iku,Kmm) ! - - case 2 |
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| 461 | ENDIF |
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[6140] | 462 | |
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[12377] | 463 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = gdept(ji,jj ,ikv,Kmm) ! j-direction: case 1 |
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| 464 | ELSE ; zhj(ji,jj) = gdept(ji,jj+1,ikv,Kmm) ! - - case 2 |
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| 465 | ENDIF |
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[6140] | 466 | |
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[12377] | 467 | END_2D |
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[5836] | 468 | ! |
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| 469 | CALL eos( zti, zhi, zri ) ! interpolated density from zti, ztj |
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| 470 | CALL eos( ztj, zhj, zrj ) ! at the partial step depth output in zri, zrj |
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| 471 | ! |
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[13295] | 472 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 473 | iku = miku(ji,jj) |
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| 474 | ikv = mikv(ji,jj) |
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| 475 | ze3wu = gdept(ji,jj,iku,Kmm) - gdept(ji+1,jj,iku,Kmm) |
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| 476 | ze3wv = gdept(ji,jj,ikv,Kmm) - gdept(ji,jj+1,ikv,Kmm) |
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[6140] | 477 | |
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[12377] | 478 | IF( ze3wu >= 0._wp ) THEN ; pgrui(ji,jj) = ssumask(ji,jj) * ( zri(ji ,jj ) - prd(ji,jj,iku) ) ! i: 1 |
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| 479 | ELSE ; pgrui(ji,jj) = ssumask(ji,jj) * ( prd(ji+1,jj ,iku) - zri(ji,jj ) ) ! i: 2 |
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| 480 | ENDIF |
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| 481 | IF( ze3wv >= 0._wp ) THEN ; pgrvi(ji,jj) = ssvmask(ji,jj) * ( zrj(ji ,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
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| 482 | ELSE ; pgrvi(ji,jj) = ssvmask(ji,jj) * ( prd(ji ,jj+1,ikv) - zrj(ji,jj ) ) ! j: 2 |
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| 483 | ENDIF |
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[6140] | 484 | |
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[12377] | 485 | END_2D |
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[13226] | 486 | CALL lbc_lnk_multi( 'zpshde', pgrui, 'U', -1.0_wp , pgrvi, 'V', -1.0_wp ) ! Lateral boundary conditions |
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[2528] | 487 | ! |
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[4990] | 488 | END IF |
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[2528] | 489 | ! |
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[9019] | 490 | IF( ln_timing ) CALL timing_stop( 'zps_hde_isf') |
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[2715] | 491 | ! |
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[13515] | 492 | END SUBROUTINE zps_hde_isf_t |
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[9019] | 493 | |
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[3] | 494 | !!====================================================================== |
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| 495 | END MODULE zpshde |
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