[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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| 10 | !!====================================================================== |
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[457] | 11 | |
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[3] | 12 | !!---------------------------------------------------------------------- |
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| 13 | !! zps_hde : Horizontal DErivative of T, S and rd at the last |
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| 14 | !! ocean level (Z-coord. with Partial Steps) |
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| 15 | !!---------------------------------------------------------------------- |
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[2528] | 16 | USE oce ! ocean: dynamics and tracers variables |
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| 17 | USE dom_oce ! domain: ocean variables |
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[3] | 18 | USE phycst ! physical constants |
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[2528] | 19 | USE eosbn2 ! ocean equation of state |
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[3] | 20 | USE in_out_manager ! I/O manager |
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| 21 | USE lbclnk ! lateral boundary conditions (or mpp link) |
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[2715] | 22 | USE lib_mpp ! MPP library |
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[3294] | 23 | USE wrk_nemo ! Memory allocation |
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| 24 | USE timing ! Timing |
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[3] | 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | PRIVATE |
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| 28 | |
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[2528] | 29 | PUBLIC zps_hde ! routine called by step.F90 |
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[3] | 30 | |
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| 31 | !! * Substitutions |
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| 32 | # include "domzgr_substitute.h90" |
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| 33 | # include "vectopt_loop_substitute.h90" |
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| 34 | !!---------------------------------------------------------------------- |
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[2528] | 35 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 36 | !! $Id$ |
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| 37 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[247] | 38 | !!---------------------------------------------------------------------- |
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[3] | 39 | CONTAINS |
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| 40 | |
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[2528] | 41 | SUBROUTINE zps_hde( kt, kjpt, pta, pgtu, pgtv, & |
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[4990] | 42 | & prd, pgru, pgrv, pmru, pmrv, pgzu, pgzv, pge3ru, pge3rv, & |
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| 43 | & sgtu, sgtv, sgru, sgrv, smru, smrv, sgzu, sgzv, sge3ru, sge3rv ) |
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[3] | 44 | !!---------------------------------------------------------------------- |
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| 45 | !! *** ROUTINE zps_hde *** |
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| 46 | !! |
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[2528] | 47 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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[3] | 48 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 49 | !! with partial steps. |
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| 50 | !! |
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| 51 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 52 | !! levels are different for each grid point, so that T, S and rd |
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| 53 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 54 | !! gradients again, we interpolate T and S at the good depth : |
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| 55 | !! Linear interpolation of T, S |
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| 56 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 57 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 58 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 59 | !! This formulation computes the two cases: |
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| 60 | !! CASE 1 CASE 2 |
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| 61 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 62 | !! Ti T~ T~ Ti+1 |
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| 63 | !! _____ _____ |
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| 64 | !! k | |Ti+1 k Ti | | |
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| 65 | !! | |____ ____| | |
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| 66 | !! ___ | | | ___ | | | |
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| 67 | !! |
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| 68 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 69 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 70 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 71 | !! or |
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| 72 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 73 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 74 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 75 | !! Idem for di(s) and dj(s) |
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| 76 | !! |
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[4990] | 77 | !! For rho, we call eos which will compute rd~(t~,s~) at the right |
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| 78 | !! depth zh from interpolated T and S for the different formulations |
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| 79 | !! of the equation of state (eos). |
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[3] | 80 | !! Gradient formulation for rho : |
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[4990] | 81 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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[3] | 82 | !! |
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[4990] | 83 | !! ** Action : compute for top and bottom interfaces |
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| 84 | !! - pgtu, pgtv, sgtu, sgtv: horizontal gradient of tracer at u- & v-points |
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| 85 | !! - pgru, pgrv, sgru, sgtv: horizontal gradient of rho (if present) at u- & v-points |
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| 86 | !! - pmru, pmrv, smru, smrv: horizontal sum of rho at u- & v- point (used in dynhpg with vvl) |
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| 87 | !! - pgzu, pgzv, sgzu, sgzv: horizontal gradient of z at u- and v- point (used in dynhpg with vvl) |
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| 88 | !! - pge3ru, pge3rv, sge3ru, sge3rv: horizontal gradient of rho weighted by local e3w at u- & v-points |
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[2528] | 89 | !!---------------------------------------------------------------------- |
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| 90 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 91 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 92 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
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| 93 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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[4990] | 94 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: sgtu, sgtv ! hor. grad. of stra at u- & v-pts (ISF) |
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[2528] | 95 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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[4990] | 96 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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| 97 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmru, pmrv ! hor. sum of prd at u- & v-pts (bottom) |
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| 98 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzu, pgzv ! hor. grad of z at u- & v-pts (bottom) |
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| 99 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pge3ru, pge3rv ! hor. grad of prd weighted by local e3w at u- & v-pts (bottom) |
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| 100 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: sgru, sgrv ! hor. grad of prd at u- & v-pts (top) |
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| 101 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: smru, smrv ! hor. sum of prd at u- & v-pts (top) |
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| 102 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: sgzu, sgzv ! hor. grad of z at u- & v-pts (top) |
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| 103 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: sge3ru, sge3rv ! hor. grad of prd weighted by local e3w at u- & v-pts (top) |
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[2715] | 104 | ! |
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[2528] | 105 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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[4990] | 106 | INTEGER :: iku, ikv, ikum1, ikvm1,ikup1, ikvp1 ! partial step level (ocean bottom level) at u- and v-points |
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| 107 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv, zdzwu, zdzwv, zdzwuip1, zdzwvjp1 ! temporary scalars |
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| 108 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos |
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| 109 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! |
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[3] | 110 | !!---------------------------------------------------------------------- |
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[3294] | 111 | ! |
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| 112 | IF( nn_timing == 1 ) CALL timing_start( 'zps_hde') |
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| 113 | ! |
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[4990] | 114 | pgtu(:,:,:)=0.0_wp ; pgtv(:,:,:)=0.0_wp ; |
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| 115 | sgtu(:,:,:)=0.0_wp ; sgtv(:,:,:)=0.0_wp ; |
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| 116 | zti (:,:,:)=0.0_wp ; ztj (:,:,:)=0.0_wp ; |
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| 117 | zhi (:,: )=0.0_wp ; zhj (:,: )=0.0_wp ; |
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[3294] | 118 | ! |
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[2528] | 119 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 120 | ! |
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[3] | 121 | DO jj = 1, jpjm1 |
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[2528] | 122 | DO ji = 1, jpim1 |
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[2569] | 123 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 124 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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[4990] | 125 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
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| 126 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
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| 127 | ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj |
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| 128 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
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| 129 | ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) |
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| 130 | ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) |
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[2528] | 131 | ! |
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| 132 | ! i- direction |
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| 133 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 134 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 135 | ! interpolated values of tracers |
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[4990] | 136 | 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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[2528] | 137 | ! gradient of tracers |
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[4990] | 138 | pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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[2528] | 139 | ELSE ! case 2 |
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| 140 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
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| 141 | ! interpolated values of tracers |
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[4990] | 142 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
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[2528] | 143 | ! gradient of tracers |
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[4990] | 144 | pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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[2528] | 145 | ENDIF |
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| 146 | ! |
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| 147 | ! j- direction |
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| 148 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 149 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 150 | ! interpolated values of tracers |
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[4990] | 151 | 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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[2528] | 152 | ! gradient of tracers |
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[4990] | 153 | pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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[2528] | 154 | ELSE ! case 2 |
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| 155 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
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| 156 | ! interpolated values of tracers |
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[4990] | 157 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
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[2528] | 158 | ! gradient of tracers |
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[4990] | 159 | pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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[2528] | 160 | ENDIF |
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[3] | 161 | END DO |
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| 162 | END DO |
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[2528] | 163 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
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| 164 | ! |
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| 165 | END DO |
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[3] | 166 | |
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[2528] | 167 | ! horizontal derivative of density anomalies (rd) |
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| 168 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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[4990] | 169 | pgru(:,:)=0.0_wp ; pgrv(:,:)=0.0_wp ; |
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| 170 | pgzu(:,:)=0.0_wp ; pgzv(:,:)=0.0_wp ; |
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| 171 | pmru(:,:)=0.0_wp ; pmru(:,:)=0.0_wp ; |
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| 172 | pge3ru(:,:)=0.0_wp ; pge3rv(:,:)=0.0_wp ; |
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[2528] | 173 | DO jj = 1, jpjm1 |
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| 174 | DO ji = 1, jpim1 |
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| 175 | iku = mbku(ji,jj) |
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| 176 | ikv = mbkv(ji,jj) |
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[4990] | 177 | ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) |
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| 178 | ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) |
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| 179 | |
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| 180 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) - ze3wu ! i-direction: case 1 |
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| 181 | ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) + ze3wu ! - - case 2 |
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[2528] | 182 | ENDIF |
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[4990] | 183 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) - ze3wv ! j-direction: case 1 |
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| 184 | ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) + ze3wv ! - - case 2 |
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[2528] | 185 | ENDIF |
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| 186 | END DO |
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[3] | 187 | END DO |
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[4990] | 188 | |
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| 189 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 190 | ! step and store it in zri, zrj for each case |
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| 191 | CALL eos( zti, zhi, zri ) |
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| 192 | CALL eos( ztj, zhj, zrj ) |
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[3] | 193 | |
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[4990] | 194 | ! Gradient of density at the last level |
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| 195 | DO jj = 1, jpjm1 |
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| 196 | DO ji = 1, jpim1 |
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| 197 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 198 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 199 | ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) |
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| 200 | ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) |
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| 201 | IF( ze3wu >= 0._wp ) THEN |
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| 202 | pgzu(ji,jj) = (fsde3w(ji+1,jj,iku) - ze3wu) - fsde3w(ji,jj,iku) |
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| 203 | pgru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) - prd(ji,jj,iku) ) ! i: 1 |
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| 204 | pmru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) + prd(ji,jj,iku) ) ! i: 1 |
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| 205 | pge3ru(ji,jj) = umask(ji,jj,iku) & |
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| 206 | * ( (fse3w(ji+1,jj,iku) - ze3wu )* ( zri(ji ,jj ) + prd(ji+1,jj,ikum1) + 2._wp) & |
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| 207 | - fse3w(ji ,jj,iku) * ( prd(ji ,jj,iku) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 |
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| 208 | ELSE |
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| 209 | pgzu(ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) + ze3wu) |
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| 210 | pgru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
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| 211 | pmru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 |
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| 212 | pge3ru(ji,jj) = umask(ji,jj,iku) & |
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| 213 | * ( fse3w(ji+1,jj,iku) * ( prd(ji+1,jj,iku) + prd(ji+1,jj,ikum1) + 2._wp) & |
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| 214 | -(fse3w(ji ,jj,iku) + ze3wu) * ( zri(ji ,jj ) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 |
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| 215 | ENDIF |
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| 216 | IF( ze3wv >= 0._wp ) THEN |
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| 217 | pgzv(ji,jj) = (fsde3w(ji,jj+1,ikv) - ze3wv) - fsde3w(ji,jj,ikv) |
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| 218 | pgrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
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| 219 | pmrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 |
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| 220 | pge3rv(ji,jj) = vmask(ji,jj,ikv) & |
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| 221 | * ( (fse3w(ji,jj+1,ikv) - ze3wv )* ( zrj(ji,jj ) + prd(ji,jj+1,ikvm1) + 2._wp) & |
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| 222 | - fse3w(ji,jj ,ikv) * ( prd(ji,jj ,ikv) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 |
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| 223 | ELSE |
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| 224 | pgzv(ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) + ze3wv) |
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| 225 | pgrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
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| 226 | pmrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 |
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| 227 | pge3rv(ji,jj) = vmask(ji,jj,ikv) & |
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| 228 | * ( fse3w(ji,jj+1,ikv) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikvm1) + 2._wp) & |
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| 229 | -(fse3w(ji,jj ,ikv) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 |
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| 230 | ENDIF |
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| 231 | END DO |
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| 232 | END DO |
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| 233 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
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| 234 | CALL lbc_lnk( pmru , 'U', 1. ) ; CALL lbc_lnk( pmrv , 'V', 1. ) ! Lateral boundary conditions |
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| 235 | CALL lbc_lnk( pgzu , 'U', -1. ) ; CALL lbc_lnk( pgzv , 'V', -1. ) ! Lateral boundary conditions |
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| 236 | CALL lbc_lnk( pge3ru , 'U', -1. ) ; CALL lbc_lnk( pge3rv , 'V', -1. ) ! Lateral boundary conditions |
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| 237 | ! |
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| 238 | END IF |
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| 239 | ! (ISH) compute grui and gruvi |
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| 240 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! |
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| 241 | DO jj = 1, jpjm1 |
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| 242 | DO ji = 1, jpim1 |
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| 243 | iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 |
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| 244 | ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 |
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| 245 | ! |
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| 246 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
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| 247 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
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| 248 | ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj |
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| 249 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
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| 250 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
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| 251 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
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| 252 | ! i- direction |
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| 253 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 254 | zmaxu = ze3wu / fse3w(ji+1,jj,iku+1) |
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| 255 | ! interpolated values of tracers |
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| 256 | zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,iku+1,jn) - pta(ji+1,jj,iku,jn) ) |
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| 257 | ! gradient of tracers |
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| 258 | sgtu(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 259 | ELSE ! case 2 |
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| 260 | zmaxu = - ze3wu / fse3w(ji,jj,iku+1) |
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| 261 | ! interpolated values of tracers |
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| 262 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,iku+1,jn) - pta(ji,jj,iku,jn) ) |
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| 263 | ! gradient of tracers |
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| 264 | sgtu(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 265 | ENDIF |
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| 266 | ! |
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| 267 | ! j- direction |
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| 268 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 269 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv+1) |
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| 270 | ! interpolated values of tracers |
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| 271 | ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikv+1,jn) - pta(ji,jj+1,ikv,jn) ) |
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| 272 | ! gradient of tracers |
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| 273 | sgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 274 | ELSE ! case 2 |
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| 275 | zmaxv = - ze3wv / fse3w(ji,jj,ikv+1) |
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| 276 | ! interpolated values of tracers |
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| 277 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikv+1,jn) - pta(ji,jj,ikv,jn) ) |
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| 278 | ! gradient of tracers |
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| 279 | sgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 280 | ENDIF |
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| 281 | END DO!! |
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| 282 | END DO!! |
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| 283 | CALL lbc_lnk( sgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( sgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
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| 284 | ! |
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| 285 | END DO |
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| 286 | |
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| 287 | ! horizontal derivative of density anomalies (rd) |
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| 288 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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| 289 | sgru(:,:) =0.0_wp ; sgrv(:,:) =0.0_wp ; |
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| 290 | sgzu(:,:) =0.0_wp ; sgzv(:,:) =0.0_wp ; |
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| 291 | smru(:,:) =0.0_wp ; smru(:,:) =0.0_wp ; |
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| 292 | sge3ru(:,:)=0.0_wp ; sge3rv(:,:)=0.0_wp ; |
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| 293 | |
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| 294 | DO jj = 1, jpjm1 |
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| 295 | DO ji = 1, jpim1 |
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| 296 | iku = miku(ji,jj) |
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| 297 | ikv = mikv(ji,jj) |
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| 298 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
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| 299 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
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| 300 | |
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| 301 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) + ze3wu ! i-direction: case 1 |
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| 302 | ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) - ze3wu ! - - case 2 |
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| 303 | ENDIF |
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| 304 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) + ze3wv ! j-direction: case 1 |
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| 305 | ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) - ze3wv ! - - case 2 |
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| 306 | ENDIF |
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| 307 | END DO |
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| 308 | END DO |
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| 309 | |
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[2528] | 310 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 311 | ! step and store it in zri, zrj for each case |
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[3294] | 312 | CALL eos( zti, zhi, zri ) |
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| 313 | CALL eos( ztj, zhj, zrj ) |
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[3] | 314 | |
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[2528] | 315 | ! Gradient of density at the last level |
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| 316 | DO jj = 1, jpjm1 |
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| 317 | DO ji = 1, jpim1 |
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[4990] | 318 | iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 |
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| 319 | ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 |
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| 320 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
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| 321 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
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| 322 | IF( ze3wu >= 0._wp ) THEN |
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| 323 | sgzu (ji,jj) = (fsde3w(ji+1,jj,iku) + ze3wu) - fsde3w(ji,jj,iku) |
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| 324 | sgru (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) - prd(ji,jj,iku) ) ! i: 1 |
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| 325 | smru (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) + prd(ji,jj,iku) ) ! i: 1 |
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| 326 | sge3ru(ji,jj) = umask(ji,jj,iku+1) & |
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| 327 | * ( (fse3w(ji+1,jj,iku+1) - ze3wu) * (zri(ji,jj ) + prd(ji+1,jj,iku+1) + 2._wp) & |
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| 328 | - fse3w(ji ,jj,iku+1) * (prd(ji,jj,iku) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 1 |
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| 329 | ELSE |
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| 330 | sgzu (ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) - ze3wu) |
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| 331 | sgru (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
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| 332 | smru (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 |
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| 333 | sge3ru(ji,jj) = umask(ji,jj,iku+1) & |
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| 334 | * ( fse3w(ji+1,jj,iku+1) * (prd(ji+1,jj,iku) + prd(ji+1,jj,iku+1) + 2._wp) & |
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| 335 | -(fse3w(ji ,jj,iku+1) + ze3wu) * (zri(ji,jj ) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 2 |
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[2528] | 336 | ENDIF |
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[4990] | 337 | IF( ze3wv >= 0._wp ) THEN |
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| 338 | sgzv (ji,jj) = (fsde3w(ji,jj+1,ikv) + ze3wv) - fsde3w(ji,jj,ikv) |
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| 339 | sgrv (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
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| 340 | smrv (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 |
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| 341 | sge3rv(ji,jj) = vmask(ji,jj,ikv+1) & |
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| 342 | * ( (fse3w(ji,jj+1,ikv+1) - ze3wv) * ( zrj(ji,jj ) + prd(ji,jj+1,ikv+1) + 2._wp) & |
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| 343 | - fse3w(ji,jj ,ikv+1) * ( prd(ji,jj,ikv) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 1 |
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| 344 | ! + 2 due to the formulation in density and not in anomalie in hpg sco |
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| 345 | ELSE |
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| 346 | sgzv (ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) - ze3wv) |
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| 347 | sgrv (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
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| 348 | smrv (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 |
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| 349 | sge3rv(ji,jj) = vmask(ji,jj,ikv+1) & |
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| 350 | * ( fse3w(ji,jj+1,ikv+1) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikv+1) + 2._wp) & |
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| 351 | -(fse3w(ji,jj ,ikv+1) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 2 |
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[2528] | 352 | ENDIF |
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| 353 | END DO |
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[3] | 354 | END DO |
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[4990] | 355 | CALL lbc_lnk( sgru , 'U', -1. ) ; CALL lbc_lnk( sgrv , 'V', -1. ) ! Lateral boundary conditions |
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| 356 | CALL lbc_lnk( smru , 'U', 1. ) ; CALL lbc_lnk( smrv , 'V', 1. ) ! Lateral boundary conditions |
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| 357 | CALL lbc_lnk( sgzu , 'U', -1. ) ; CALL lbc_lnk( sgzv , 'V', -1. ) ! Lateral boundary conditions |
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| 358 | CALL lbc_lnk( sge3ru , 'U', -1. ) ; CALL lbc_lnk( sge3rv , 'V', -1. ) ! Lateral boundary conditions |
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[2528] | 359 | ! |
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[4990] | 360 | END IF |
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[2528] | 361 | ! |
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[3294] | 362 | IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde') |
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[2715] | 363 | ! |
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[3] | 364 | END SUBROUTINE zps_hde |
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| 365 | |
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| 366 | !!====================================================================== |
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| 367 | END MODULE zpshde |
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