[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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[457] | 6 | |
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[3] | 7 | !!---------------------------------------------------------------------- |
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| 8 | !! zps_hde : Horizontal DErivative of T, S and rd at the last |
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| 9 | !! ocean level (Z-coord. with Partial Steps) |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! * Modules used |
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| 12 | USE dom_oce ! ocean space domain variables |
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| 13 | USE oce ! ocean dynamics and tracers variables |
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| 14 | USE phycst ! physical constants |
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| 15 | USE in_out_manager ! I/O manager |
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| 16 | USE eosbn2 ! ocean equation of state |
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| 17 | USE lbclnk ! lateral boundary conditions (or mpp link) |
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| 18 | |
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| 19 | IMPLICIT NONE |
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| 20 | PRIVATE |
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| 21 | |
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| 22 | !! * Routine accessibility |
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| 23 | PUBLIC zps_hde ! routine called by step.F90 |
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| 24 | |
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| 25 | !! * module variables |
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| 26 | INTEGER, DIMENSION(jpi,jpj) :: & |
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| 27 | mbatu, mbatv ! bottom ocean level index at U- and V-points |
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| 28 | |
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| 29 | !! * Substitutions |
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| 30 | # include "domzgr_substitute.h90" |
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| 31 | # include "vectopt_loop_substitute.h90" |
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| 32 | !!---------------------------------------------------------------------- |
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[247] | 33 | !!---------------------------------------------------------------------- |
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| 34 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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[1152] | 35 | !! $Id$ |
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[247] | 36 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 37 | !!---------------------------------------------------------------------- |
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[3] | 38 | CONTAINS |
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| 39 | |
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| 40 | SUBROUTINE zps_hde ( kt, ptem, psal, prd , & |
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| 41 | pgtu, pgsu, pgru, & |
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| 42 | pgtv, pgsv, pgrv ) |
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| 43 | !!---------------------------------------------------------------------- |
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| 44 | !! *** ROUTINE zps_hde *** |
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| 45 | !! |
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| 46 | !! ** Purpose : Compute the horizontal derivative of T, S and rd |
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| 47 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 48 | !! with partial steps. |
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| 49 | !! |
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| 50 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 51 | !! levels are different for each grid point, so that T, S and rd |
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| 52 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 53 | !! gradients again, we interpolate T and S at the good depth : |
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| 54 | !! Linear interpolation of T, S |
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| 55 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 56 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 57 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 58 | !! This formulation computes the two cases: |
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| 59 | !! CASE 1 CASE 2 |
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| 60 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 61 | !! Ti T~ T~ Ti+1 |
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| 62 | !! _____ _____ |
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| 63 | !! k | |Ti+1 k Ti | | |
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| 64 | !! | |____ ____| | |
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| 65 | !! ___ | | | ___ | | | |
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| 66 | !! |
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| 67 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 68 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 69 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 70 | !! or |
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| 71 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 72 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 73 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 74 | !! Idem for di(s) and dj(s) |
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| 75 | !! |
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[87] | 76 | !! For rho, we call eos_insitu_2d which will compute rd~(t~,s~) at |
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[3] | 77 | !! the good depth zh from interpolated T and S for the different |
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| 78 | !! formulation of the equation of state (eos). |
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| 79 | !! Gradient formulation for rho : |
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| 80 | !! di(rho) = rd~ - rd(i,j,k) or rd (i+1,j,k) - rd~ |
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| 81 | !! |
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| 82 | !! ** Action : - pgtu, pgsu, pgru: horizontal gradient of T, S |
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| 83 | !! and rd at U-points |
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| 84 | !! - pgtv, pgsv, pgrv: horizontal gradient of T, S |
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| 85 | !! and rd at V-points |
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| 86 | !! |
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| 87 | !! History : |
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| 88 | !! 8.5 ! 02-04 (A. Bozec) Original code |
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| 89 | !! 8.5 ! 02-08 (G. Madec E. Durand) Optimization and Free form |
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| 90 | !!---------------------------------------------------------------------- |
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| 91 | !! * Arguments |
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| 92 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 93 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
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| 94 | ptem, psal, prd ! 3D T, S and rd fields |
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| 95 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out ) :: & |
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| 96 | pgtu, pgsu, pgru, & ! horizontal grad. of T, S and rd at u- |
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| 97 | pgtv, pgsv, pgrv ! and v-points of the partial step level |
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| 98 | |
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| 99 | !! * Local declarations |
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| 100 | INTEGER :: ji, jj, & ! Dummy loop indices |
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| 101 | iku,ikv ! partial step level at u- and v-points |
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| 102 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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| 103 | zti, ztj, zsi, zsj, & ! interpolated value of T, S |
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| 104 | zri, zrj, & ! and rd |
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| 105 | zhgi, zhgj ! depth of interpolation for eos2d |
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| 106 | REAL(wp) :: & |
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| 107 | ze3wu, ze3wv, & ! temporary scalars |
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| 108 | zmaxu1, zmaxu2, & ! " " |
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| 109 | zmaxv1, zmaxv2 ! " " |
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| 110 | |
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| 111 | ! Initialization (first time-step only): compute mbatu and mbatv |
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| 112 | IF( kt == nit000 ) THEN |
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| 113 | mbatu(:,:) = 0 |
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| 114 | mbatv(:,:) = 0 |
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| 115 | DO jj = 1, jpjm1 |
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| 116 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 117 | mbatu(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1, 2 ) |
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| 118 | mbatv(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1, 2 ) |
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| 119 | END DO |
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| 120 | END DO |
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| 121 | zti(:,:) = FLOAT( mbatu(:,:) ) |
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| 122 | ztj(:,:) = FLOAT( mbatv(:,:) ) |
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| 123 | ! lateral boundary conditions: T-point, sign unchanged |
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| 124 | CALL lbc_lnk( zti , 'U', 1. ) |
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| 125 | CALL lbc_lnk( ztj , 'V', 1. ) |
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| 126 | mbatu(:,:) = MAX( INT( zti(:,:) ), 2 ) |
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| 127 | mbatv(:,:) = MAX( INT( ztj(:,:) ), 2 ) |
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| 128 | ENDIF |
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| 129 | |
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| 130 | |
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| 131 | ! Interpolation of T and S at the last ocean level |
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[789] | 132 | # if defined key_vectopt_loop |
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[3] | 133 | jj = 1 |
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| 134 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 135 | # else |
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| 136 | DO jj = 1, jpjm1 |
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| 137 | DO ji = 1, jpim1 |
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| 138 | # endif |
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| 139 | ! last level |
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| 140 | iku = mbatu(ji,jj) |
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| 141 | ikv = mbatv(ji,jj) |
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| 142 | |
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| 143 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 144 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 145 | zmaxu1 = ze3wu / fse3w(ji+1,jj ,iku) |
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| 146 | zmaxu2 = -ze3wu / fse3w(ji ,jj ,iku) |
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| 147 | zmaxv1 = ze3wv / fse3w(ji ,jj+1,ikv) |
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| 148 | zmaxv2 = -ze3wv / fse3w(ji ,jj ,ikv) |
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| 149 | |
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| 150 | ! i- direction |
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| 151 | |
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| 152 | IF( ze3wu >= 0. ) THEN ! case 1 |
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| 153 | ! interpolated values of T and S |
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| 154 | zti(ji,jj) = ptem(ji+1,jj,iku) + zmaxu1 * ( ptem(ji+1,jj,iku-1) - ptem(ji+1,jj,iku) ) |
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| 155 | zsi(ji,jj) = psal(ji+1,jj,iku) + zmaxu1 * ( psal(ji+1,jj,iku-1) - psal(ji+1,jj,iku) ) |
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| 156 | ! depth of the partial step level |
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| 157 | zhgi(ji,jj) = fsdept(ji,jj,iku) |
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| 158 | ! gradient of T and S |
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| 159 | pgtu(ji,jj) = umask(ji,jj,1) * ( zti(ji,jj) - ptem(ji,jj,iku) ) |
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| 160 | pgsu(ji,jj) = umask(ji,jj,1) * ( zsi(ji,jj) - psal(ji,jj,iku) ) |
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| 161 | |
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| 162 | ELSE ! case 2 |
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| 163 | ! interpolated values of T and S |
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| 164 | zti(ji,jj) = ptem(ji,jj,iku) + zmaxu2 * ( ptem(ji,jj,iku-1) - ptem(ji,jj,iku) ) |
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| 165 | zsi(ji,jj) = psal(ji,jj,iku) + zmaxu2 * ( psal(ji,jj,iku-1) - psal(ji,jj,iku) ) |
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| 166 | ! depth of the partial step level |
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| 167 | zhgi(ji,jj) = fsdept(ji+1,jj,iku) |
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| 168 | ! gradient of T and S |
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| 169 | pgtu(ji,jj) = umask(ji,jj,1) * ( ptem(ji+1,jj,iku) - zti (ji,jj) ) |
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| 170 | pgsu(ji,jj) = umask(ji,jj,1) * ( psal(ji+1,jj,iku) - zsi (ji,jj) ) |
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| 171 | ENDIF |
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| 172 | |
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| 173 | ! j- direction |
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| 174 | |
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| 175 | IF( ze3wv >= 0. ) THEN ! case 1 |
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| 176 | ! interpolated values of T and S |
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| 177 | ztj(ji,jj) = ptem(ji,jj+1,ikv) + zmaxv1 * ( ptem(ji,jj+1,ikv-1) - ptem(ji,jj+1,ikv) ) |
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| 178 | zsj(ji,jj) = psal(ji,jj+1,ikv) + zmaxv1 * ( psal(ji,jj+1,ikv-1) - psal(ji,jj+1,ikv) ) |
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| 179 | ! depth of the partial step level |
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| 180 | zhgj(ji,jj) = fsdept(ji,jj,ikv) |
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| 181 | ! gradient of T and S |
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| 182 | pgtv(ji,jj) = vmask(ji,jj,1) * ( ztj(ji,jj) - ptem(ji,jj,ikv) ) |
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| 183 | pgsv(ji,jj) = vmask(ji,jj,1) * ( zsj(ji,jj) - psal(ji,jj,ikv) ) |
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| 184 | |
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| 185 | ELSE ! case 2 |
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| 186 | ! interpolated values of T and S |
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| 187 | ztj(ji,jj) = ptem(ji,jj,ikv) + zmaxv2 * ( ptem(ji,jj,ikv-1) - ptem(ji,jj,ikv) ) |
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| 188 | zsj(ji,jj) = psal(ji,jj,ikv) + zmaxv2 * ( psal(ji,jj,ikv-1) - psal(ji,jj,ikv) ) |
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| 189 | ! depth of the partial step level |
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| 190 | zhgj(ji,jj) = fsdept(ji,jj+1,ikv) |
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| 191 | ! gradient of T and S |
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| 192 | pgtv(ji,jj) = vmask(ji,jj,1) * ( ptem(ji,jj+1,ikv) - ztj(ji,jj) ) |
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| 193 | pgsv(ji,jj) = vmask(ji,jj,1) * ( psal(ji,jj+1,ikv) - zsj(ji,jj) ) |
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| 194 | ENDIF |
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[789] | 195 | # if ! defined key_vectopt_loop |
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[3] | 196 | END DO |
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| 197 | # endif |
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| 198 | END DO |
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| 199 | |
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| 200 | ! Compute interpolated rd from zti, zsi, ztj, zsj for the 2 cases at the depth of the partial |
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| 201 | ! step and store it in zri, zrj for each case |
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| 202 | CALL eos( zti, zsi, zhgi, zri ) |
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| 203 | CALL eos( ztj, zsj, zhgj, zrj ) |
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| 204 | |
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| 205 | |
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| 206 | ! Gradient of density at the last level |
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[789] | 207 | # if defined key_vectopt_loop |
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[3] | 208 | jj = 1 |
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| 209 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 210 | # else |
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| 211 | DO jj = 1, jpjm1 |
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| 212 | DO ji = 1, jpim1 |
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| 213 | # endif |
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| 214 | iku = mbatu(ji,jj) |
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| 215 | ikv = mbatv(ji,jj) |
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| 216 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 217 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 218 | IF( ze3wu >= 0. ) THEN ! i-direction: case 1 |
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| 219 | pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji,jj) - prd(ji,jj,iku) ) |
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| 220 | ELSE ! i-direction: case 2 |
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| 221 | pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) |
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| 222 | ENDIF |
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| 223 | IF( ze3wv >= 0. ) THEN ! j-direction: case 1 |
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| 224 | pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj) - prd(ji,jj,ikv) ) |
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| 225 | ELSE ! j-direction: case 2 |
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| 226 | pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) |
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| 227 | ENDIF |
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[789] | 228 | # if ! defined key_vectopt_loop |
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[3] | 229 | END DO |
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| 230 | # endif |
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| 231 | END DO |
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| 232 | |
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| 233 | ! Lateral boundary conditions on each gradient |
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| 234 | CALL lbc_lnk( pgtu , 'U', -1. ) ; CALL lbc_lnk( pgtv , 'V', -1. ) |
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| 235 | CALL lbc_lnk( pgsu , 'U', -1. ) ; CALL lbc_lnk( pgsv , 'V', -1. ) |
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| 236 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) |
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| 237 | |
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| 238 | END SUBROUTINE zps_hde |
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| 239 | |
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| 240 | !!====================================================================== |
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| 241 | END MODULE zpshde |
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