[3] | 1 | MODULE zpshde |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE zpshde *** |
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[457] | 4 | !! z-coordinate - partial step : Horizontal Derivative |
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[3] | 5 | !!============================================================================== |
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[2024] | 6 | !! History : |
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| 7 | !! OPA 8.5 ! 2002-04 (A. Bozec) Original code |
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| 8 | !! 8.5 ! 2002-08 (G. Madec E. Durand) Optimization and Free form |
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| 9 | !! 9.0 ! 2004-03 (C. Ethe) adapted for passive tracers |
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| 10 | !! NEMO 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA |
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| 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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| 17 | !! * Modules used |
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| 18 | USE dom_oce ! ocean space domain variables |
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| 19 | USE oce ! ocean dynamics and tracers variables |
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| 20 | USE phycst ! physical constants |
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| 21 | USE in_out_manager ! I/O manager |
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| 22 | USE eosbn2 ! ocean equation of state |
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| 23 | USE lbclnk ! lateral boundary conditions (or mpp link) |
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| 24 | |
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| 25 | IMPLICIT NONE |
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| 26 | PRIVATE |
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| 27 | |
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| 28 | !! * Routine accessibility |
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| 29 | PUBLIC zps_hde ! routine called by step.F90 |
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[2024] | 30 | PUBLIC zps_hde_init ! routine called by opa.F90 |
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[3] | 31 | |
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| 32 | !! * module variables |
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| 33 | INTEGER, DIMENSION(jpi,jpj) :: & |
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| 34 | mbatu, mbatv ! bottom ocean level index at U- and V-points |
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| 35 | |
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| 36 | !! * Substitutions |
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| 37 | # include "domzgr_substitute.h90" |
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| 38 | # include "vectopt_loop_substitute.h90" |
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| 39 | !!---------------------------------------------------------------------- |
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[247] | 40 | !!---------------------------------------------------------------------- |
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| 41 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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[1152] | 42 | !! $Id$ |
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[247] | 43 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 44 | !!---------------------------------------------------------------------- |
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[3] | 45 | CONTAINS |
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[2082] | 46 | |
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| 47 | SUBROUTINE zps_hde( kt, kjpt, pta, pgtu, pgtv, & |
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| 48 | prd, pgru, pgrv ) |
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[3] | 49 | !!---------------------------------------------------------------------- |
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| 50 | !! *** ROUTINE zps_hde *** |
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| 51 | !! |
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| 52 | !! ** Purpose : Compute the horizontal derivative of T, S and rd |
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| 53 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 54 | !! with partial steps. |
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| 55 | !! |
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| 56 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 57 | !! levels are different for each grid point, so that T, S and rd |
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| 58 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 59 | !! gradients again, we interpolate T and S at the good depth : |
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| 60 | !! Linear interpolation of T, S |
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| 61 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 62 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 63 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 64 | !! This formulation computes the two cases: |
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| 65 | !! CASE 1 CASE 2 |
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| 66 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 67 | !! Ti T~ T~ Ti+1 |
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| 68 | !! _____ _____ |
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| 69 | !! k | |Ti+1 k Ti | | |
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| 70 | !! | |____ ____| | |
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| 71 | !! ___ | | | ___ | | | |
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| 72 | !! |
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| 73 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 74 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 75 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 76 | !! or |
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| 77 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 78 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 79 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 80 | !! Idem for di(s) and dj(s) |
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| 81 | !! |
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[87] | 82 | !! For rho, we call eos_insitu_2d which will compute rd~(t~,s~) at |
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[3] | 83 | !! the good depth zh from interpolated T and S for the different |
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| 84 | !! formulation of the equation of state (eos). |
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| 85 | !! Gradient formulation for rho : |
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| 86 | !! di(rho) = rd~ - rd(i,j,k) or rd (i+1,j,k) - rd~ |
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| 87 | !! |
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[2082] | 88 | !! ** Action : - pgtu, pgtv: horizontal gradient of tracer at U/V-points |
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| 89 | !! - pgru, pgrv: horizontal gradient of rd if present at U/V-points |
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[3] | 90 | !! and rd at V-points |
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| 91 | !!---------------------------------------------------------------------- |
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| 92 | !! * Arguments |
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[2082] | 93 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 94 | INTEGER , INTENT( in ) :: kjpt ! number of tracers |
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| 95 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT( in ) :: pta ! 4D active or passive tracers fields |
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| 96 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! horizontal grad. of ptra u- and v-points |
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| 97 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( in ), OPTIONAL :: prd ! 3D rd fields |
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| 98 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! horizontal grad. of prd u- and v-points |
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[3] | 99 | !! * Local declarations |
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[2082] | 100 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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| 101 | INTEGER :: iku, ikv ! partial step level at u- and v-points |
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| 102 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! interpolated value of tracer |
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| 103 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj ! interpolated value of rd |
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| 104 | REAL(wp), DIMENSION(jpi,jpj) :: zhi, zhj ! depth of interpolation for eos2d |
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| 105 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars |
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| 106 | !!---------------------------------------------------------------------- |
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[3] | 107 | |
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| 108 | |
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[2082] | 109 | ! Interpolation of tracers at the last ocean level |
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| 110 | DO jn = 1, kjpt |
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[789] | 111 | # if defined key_vectopt_loop |
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[3] | 112 | jj = 1 |
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| 113 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 114 | # else |
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[2082] | 115 | DO jj = 1, jpjm1 |
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| 116 | DO ji = 1, jpim1 |
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[3] | 117 | # endif |
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[2082] | 118 | ! last level |
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| 119 | iku = mbatu(ji,jj) |
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| 120 | ikv = mbatv(ji,jj) |
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| 121 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 122 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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[3] | 123 | |
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[2082] | 124 | ! i- direction |
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| 125 | IF( ze3wu >= 0. ) THEN ! case 1 |
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| 126 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 127 | ! interpolated values of tracers |
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| 128 | 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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| 129 | ! gradient of tracers |
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| 130 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 131 | ELSE ! case 2 |
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| 132 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
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| 133 | ! interpolated values of tracers |
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| 134 | 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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| 135 | ! gradient of tracers |
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| 136 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 137 | ENDIF |
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[3] | 138 | |
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[2082] | 139 | ! j- direction |
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| 140 | IF( ze3wv >= 0. ) THEN ! case 1 |
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| 141 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 142 | ! interpolated values of tracers |
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| 143 | 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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| 144 | ! gradient of tracers |
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| 145 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 146 | ELSE ! case 2 |
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| 147 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
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| 148 | ! interpolated values of tracers |
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| 149 | 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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| 150 | ! gradient of tracers |
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| 151 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 152 | ENDIF |
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[789] | 153 | # if ! defined key_vectopt_loop |
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[2082] | 154 | END DO |
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| 155 | # endif |
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[3] | 156 | END DO |
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| 157 | |
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[2082] | 158 | ! Lateral boundary conditions on each gradient |
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| 159 | CALL lbc_lnk( pgtu(:,:,jn) , 'U', -1. ) |
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| 160 | CALL lbc_lnk( pgtv(:,:,jn) , 'V', -1. ) |
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[3] | 161 | |
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[2082] | 162 | END DO |
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[3] | 163 | |
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[2082] | 164 | ! horizontal derivative of rd |
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| 165 | IF( PRESENT( prd ) ) THEN |
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| 166 | ! depth of the partial step level |
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[789] | 167 | # if defined key_vectopt_loop |
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[3] | 168 | jj = 1 |
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| 169 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 170 | # else |
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[2082] | 171 | DO jj = 1, jpjm1 |
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| 172 | DO ji = 1, jpim1 |
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[3] | 173 | # endif |
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[2082] | 174 | iku = mbatu(ji,jj) |
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| 175 | ikv = mbatv(ji,jj) |
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| 176 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 177 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 178 | IF( ze3wu >= 0. ) THEN |
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| 179 | zhi(ji,jj) = fsdept(ji ,jj,iku) |
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| 180 | ELSE |
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| 181 | zhi(ji,jj) = fsdept(ji+1,jj,iku) |
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| 182 | ENDIF |
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| 183 | IF( ze3wv >= 0. ) THEN |
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| 184 | zhj(ji,jj) = fsdept(ji,jj ,ikv) |
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| 185 | ELSE |
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| 186 | zhj(ji,jj) = fsdept(ji,jj+1,ikv) |
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| 187 | ENDIF |
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[789] | 188 | # if ! defined key_vectopt_loop |
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[2082] | 189 | END DO |
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| 190 | # endif |
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[3] | 191 | END DO |
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| 192 | |
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[2082] | 193 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 194 | ! step and store it in zri, zrj for each case |
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| 195 | CALL eos( zti, zhi, zri ) |
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| 196 | CALL eos( ztj, zhj, zrj ) |
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[3] | 197 | |
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[2082] | 198 | ! Gradient of density at the last level |
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[2024] | 199 | # if defined key_vectopt_loop |
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| 200 | jj = 1 |
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| 201 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 202 | # else |
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| 203 | DO jj = 1, jpjm1 |
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| 204 | DO ji = 1, jpim1 |
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| 205 | # endif |
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| 206 | iku = mbatu(ji,jj) |
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| 207 | ikv = mbatv(ji,jj) |
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| 208 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 209 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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[2082] | 210 | IF( ze3wu >= 0. ) THEN ! i-direction: case 1 |
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| 211 | pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji,jj) - prd(ji,jj,iku) ) |
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| 212 | ELSE ! i-direction: case 2 |
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| 213 | pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) |
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[2024] | 214 | ENDIF |
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[2082] | 215 | IF( ze3wv >= 0. ) THEN ! j-direction: case 1 |
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| 216 | pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj) - prd(ji,jj,ikv) ) |
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| 217 | ELSE ! j-direction: case 2 |
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| 218 | pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) |
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[2024] | 219 | ENDIF |
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| 220 | # if ! defined key_vectopt_loop |
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| 221 | END DO |
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| 222 | # endif |
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| 223 | END DO |
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| 224 | |
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| 225 | ! Lateral boundary conditions on each gradient |
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[2082] | 226 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) |
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| 227 | ! |
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| 228 | END IF |
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| 229 | ! |
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| 230 | END SUBROUTINE zps_hde |
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[2024] | 231 | |
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| 232 | SUBROUTINE zps_hde_init |
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| 233 | !!---------------------------------------------------------------------- |
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| 234 | !! *** ROUTINE zps_hde_init *** |
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| 235 | !! |
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| 236 | !! ** Purpose : Computation of bottom ocean level index at U- and V-points |
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| 237 | !! |
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| 238 | !!---------------------------------------------------------------------- |
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| 239 | !! * Local declarations |
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| 240 | INTEGER :: ji, jj ! Dummy loop indices |
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| 241 | REAL(wp), DIMENSION(jpi,jpj) :: zti, ztj ! temporary arrays |
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| 242 | !!---------------------------------------------------------------------- |
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| 243 | |
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| 244 | mbatu(:,:) = 0 |
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| 245 | mbatv(:,:) = 0 |
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| 246 | DO jj = 1, jpjm1 |
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| 247 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 248 | mbatu(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1, 2 ) |
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| 249 | mbatv(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1, 2 ) |
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| 250 | END DO |
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| 251 | END DO |
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| 252 | zti(:,:) = FLOAT( mbatu(:,:) ) |
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| 253 | ztj(:,:) = FLOAT( mbatv(:,:) ) |
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| 254 | ! lateral boundary conditions: T-point, sign unchanged |
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| 255 | CALL lbc_lnk( zti , 'U', 1. ) |
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| 256 | CALL lbc_lnk( ztj , 'V', 1. ) |
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| 257 | mbatu(:,:) = MAX( INT( zti(:,:) ), 2 ) |
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| 258 | mbatv(:,:) = MAX( INT( ztj(:,:) ), 2 ) |
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| 259 | |
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| 260 | END SUBROUTINE zps_hde_init |
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[3] | 261 | !!====================================================================== |
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| 262 | END MODULE zpshde |
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