[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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[3] | 19 | USE phycst ! physical constants |
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[2528] | 20 | USE eosbn2 ! ocean equation of state |
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[3] | 21 | USE in_out_manager ! I/O manager |
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| 22 | USE lbclnk ! lateral boundary conditions (or mpp link) |
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[2715] | 23 | USE lib_mpp ! MPP library |
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[3294] | 24 | USE wrk_nemo ! Memory allocation |
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| 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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| 34 | # include "domzgr_substitute.h90" |
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| 35 | # include "vectopt_loop_substitute.h90" |
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| 36 | !!---------------------------------------------------------------------- |
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[2528] | 37 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 38 | !! $Id$ |
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| 39 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[247] | 40 | !!---------------------------------------------------------------------- |
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[3] | 41 | CONTAINS |
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| 42 | |
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[2528] | 43 | SUBROUTINE zps_hde( kt, kjpt, pta, pgtu, pgtv, & |
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[5120] | 44 | & prd, pgru, pgrv ) |
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| 45 | !!---------------------------------------------------------------------- |
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| 46 | !! *** ROUTINE zps_hde *** |
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| 47 | !! |
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| 48 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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| 49 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 50 | !! with partial steps. |
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| 51 | !! |
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| 52 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 53 | !! levels are different for each grid point, so that T, S and rd |
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| 54 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 55 | !! gradients again, we interpolate T and S at the good depth : |
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| 56 | !! Linear interpolation of T, S |
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| 57 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 58 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 59 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 60 | !! This formulation computes the two cases: |
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| 61 | !! CASE 1 CASE 2 |
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| 62 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 63 | !! Ti T~ T~ Ti+1 |
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| 64 | !! _____ _____ |
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| 65 | !! k | |Ti+1 k Ti | | |
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| 66 | !! | |____ ____| | |
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| 67 | !! ___ | | | ___ | | | |
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| 68 | !! |
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| 69 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 70 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 71 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 72 | !! or |
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| 73 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 74 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 75 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 76 | !! Idem for di(s) and dj(s) |
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| 77 | !! |
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| 78 | !! For rho, we call eos which will compute rd~(t~,s~) at the right |
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| 79 | !! depth zh from interpolated T and S for the different formulations |
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| 80 | !! of the equation of state (eos). |
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| 81 | !! Gradient formulation for rho : |
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| 82 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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| 83 | !! |
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| 84 | !! ** Action : compute for top interfaces |
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| 85 | !! - pgtu, pgtv: horizontal gradient of tracer at u- & v-points |
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| 86 | !! - pgru, pgrv: horizontal gradient of rho (if present) at u- & v-points |
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| 87 | !!---------------------------------------------------------------------- |
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| 88 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 89 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 90 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
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| 91 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 92 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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| 93 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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| 94 | ! |
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| 95 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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| 96 | INTEGER :: iku, ikv, ikum1, ikvm1 ! partial step level (ocean bottom level) at u- and v-points |
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| 97 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars |
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| 98 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos |
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| 99 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! |
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| 100 | !!---------------------------------------------------------------------- |
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| 101 | ! |
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| 102 | IF( nn_timing == 1 ) CALL timing_start( 'zps_hde') |
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| 103 | ! |
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| 104 | pgtu(:,:,:)=0.0_wp ; pgtv(:,:,:)=0.0_wp ; |
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| 105 | zti (:,:,:)=0.0_wp ; ztj (:,:,:)=0.0_wp ; |
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| 106 | zhi (:,: )=0.0_wp ; zhj (:,: )=0.0_wp ; |
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| 107 | ! |
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| 108 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 109 | ! |
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| 110 | DO jj = 1, jpjm1 |
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| 111 | DO ji = 1, jpim1 |
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| 112 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 113 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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| 114 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 115 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 116 | ! |
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| 117 | ! i- direction |
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| 118 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 119 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 120 | ! interpolated values of tracers |
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| 121 | 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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| 122 | ! gradient of tracers |
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| 123 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 124 | ELSE ! case 2 |
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| 125 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
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| 126 | ! interpolated values of tracers |
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| 127 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
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| 128 | ! gradient of tracers |
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| 129 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 130 | ENDIF |
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| 131 | ! |
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| 132 | ! j- direction |
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| 133 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 134 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 135 | ! interpolated values of tracers |
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| 136 | 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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| 137 | ! gradient of tracers |
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| 138 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 139 | ELSE ! case 2 |
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| 140 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
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| 141 | ! interpolated values of tracers |
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| 142 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
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| 143 | ! gradient of tracers |
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| 144 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 145 | ENDIF |
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| 146 | END DO |
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| 147 | END DO |
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| 148 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
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| 149 | ! |
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| 150 | END DO |
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| 151 | |
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| 152 | ! horizontal derivative of density anomalies (rd) |
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| 153 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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| 154 | pgru(:,:)=0.0_wp ; pgrv(:,:)=0.0_wp ; |
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| 155 | DO jj = 1, jpjm1 |
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| 156 | DO ji = 1, jpim1 |
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| 157 | iku = mbku(ji,jj) |
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| 158 | ikv = mbkv(ji,jj) |
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| 159 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 160 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 161 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji ,jj,iku) ! i-direction: case 1 |
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| 162 | ELSE ; zhi(ji,jj) = fsdept(ji+1,jj,iku) ! - - case 2 |
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| 163 | ENDIF |
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| 164 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj ,ikv) ! j-direction: case 1 |
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| 165 | ELSE ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) ! - - case 2 |
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| 166 | ENDIF |
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| 167 | END DO |
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| 168 | END DO |
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| 169 | |
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| 170 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 171 | ! step and store it in zri, zrj for each case |
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| 172 | CALL eos( zti, zhi, zri ) |
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| 173 | CALL eos( ztj, zhj, zrj ) |
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| 174 | |
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| 175 | ! Gradient of density at the last level |
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| 176 | DO jj = 1, jpjm1 |
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| 177 | DO ji = 1, jpim1 |
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| 178 | iku = mbku(ji,jj) |
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| 179 | ikv = mbkv(ji,jj) |
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| 180 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 181 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 182 | 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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| 183 | ELSE ; pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj ) ) ! i: 2 |
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| 184 | ENDIF |
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| 185 | 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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| 186 | ELSE ; pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj ) ) ! j: 2 |
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| 187 | ENDIF |
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| 188 | END DO |
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| 189 | END DO |
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| 190 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
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| 191 | ! |
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| 192 | END IF |
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| 193 | ! |
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| 194 | IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde') |
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| 195 | ! |
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| 196 | END SUBROUTINE zps_hde |
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| 197 | ! |
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| 198 | SUBROUTINE zps_hde_isf( kt, kjpt, pta, pgtu, pgtv, & |
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[4990] | 199 | & prd, pgru, pgrv, pmru, pmrv, pgzu, pgzv, pge3ru, pge3rv, & |
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[5120] | 200 | & pgtui, pgtvi, pgrui, pgrvi, pmrui, pmrvi, pgzui, pgzvi, pge3rui, pge3rvi ) |
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[3] | 201 | !!---------------------------------------------------------------------- |
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| 202 | !! *** ROUTINE zps_hde *** |
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| 203 | !! |
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[2528] | 204 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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[3] | 205 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 206 | !! with partial steps. |
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| 207 | !! |
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| 208 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 209 | !! levels are different for each grid point, so that T, S and rd |
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| 210 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 211 | !! gradients again, we interpolate T and S at the good depth : |
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| 212 | !! Linear interpolation of T, S |
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| 213 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 214 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 215 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 216 | !! This formulation computes the two cases: |
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| 217 | !! CASE 1 CASE 2 |
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| 218 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 219 | !! Ti T~ T~ Ti+1 |
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| 220 | !! _____ _____ |
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| 221 | !! k | |Ti+1 k Ti | | |
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| 222 | !! | |____ ____| | |
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| 223 | !! ___ | | | ___ | | | |
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| 224 | !! |
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| 225 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 226 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 227 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 228 | !! or |
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| 229 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 230 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 231 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 232 | !! Idem for di(s) and dj(s) |
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| 233 | !! |
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[4990] | 234 | !! For rho, we call eos which will compute rd~(t~,s~) at the right |
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| 235 | !! depth zh from interpolated T and S for the different formulations |
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| 236 | !! of the equation of state (eos). |
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[3] | 237 | !! Gradient formulation for rho : |
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[4990] | 238 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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[3] | 239 | !! |
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[4990] | 240 | !! ** Action : compute for top and bottom interfaces |
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[5120] | 241 | !! - pgtu, pgtv, pgtui, pgtvi: horizontal gradient of tracer at u- & v-points |
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| 242 | !! - pgru, pgrv, pgrui, pgtvi: horizontal gradient of rho (if present) at u- & v-points |
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| 243 | !! - pmru, pmrv, pmrui, pmrvi: horizontal sum of rho at u- & v- point (used in dynhpg with vvl) |
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| 244 | !! - pgzu, pgzv, pgzui, pgzvi: horizontal gradient of z at u- and v- point (used in dynhpg with vvl) |
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| 245 | !! - pge3ru, pge3rv, pge3rui, pge3rvi: horizontal gradient of rho weighted by local e3w at u- & v-points |
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[2528] | 246 | !!---------------------------------------------------------------------- |
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| 247 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 248 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 249 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
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| 250 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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[5120] | 251 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtui, pgtvi ! hor. grad. of stra at u- & v-pts (ISF) |
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[2528] | 252 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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[4990] | 253 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad of prd at u- & v-pts (bottom) |
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| 254 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmru, pmrv ! hor. sum of prd at u- & v-pts (bottom) |
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| 255 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzu, pgzv ! hor. grad of z at u- & v-pts (bottom) |
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| 256 | 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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[5120] | 257 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgrui, pgrvi ! hor. grad of prd at u- & v-pts (top) |
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| 258 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmrui, pmrvi ! hor. sum of prd at u- & v-pts (top) |
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| 259 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzui, pgzvi ! hor. grad of z at u- & v-pts (top) |
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| 260 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pge3rui, pge3rvi ! hor. grad of prd weighted by local e3w at u- & v-pts (top) |
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[2715] | 261 | ! |
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[2528] | 262 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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[4990] | 263 | INTEGER :: iku, ikv, ikum1, ikvm1,ikup1, ikvp1 ! partial step level (ocean bottom level) at u- and v-points |
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| 264 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv, zdzwu, zdzwv, zdzwuip1, zdzwvjp1 ! temporary scalars |
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| 265 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos |
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| 266 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! |
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[3] | 267 | !!---------------------------------------------------------------------- |
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[3294] | 268 | ! |
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[5120] | 269 | IF( nn_timing == 1 ) CALL timing_start( 'zps_hde_isf') |
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[3294] | 270 | ! |
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[4990] | 271 | pgtu(:,:,:)=0.0_wp ; pgtv(:,:,:)=0.0_wp ; |
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[5120] | 272 | pgtui(:,:,:)=0.0_wp ; pgtvi(:,:,:)=0.0_wp ; |
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[4990] | 273 | zti (:,:,:)=0.0_wp ; ztj (:,:,:)=0.0_wp ; |
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| 274 | zhi (:,: )=0.0_wp ; zhj (:,: )=0.0_wp ; |
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[3294] | 275 | ! |
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[2528] | 276 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 277 | ! |
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[3] | 278 | DO jj = 1, jpjm1 |
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[2528] | 279 | DO ji = 1, jpim1 |
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[2569] | 280 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 281 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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[4990] | 282 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
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| 283 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
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| 284 | ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj |
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| 285 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
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| 286 | 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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| 287 | 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] | 288 | ! |
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| 289 | ! i- direction |
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| 290 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
---|
| 291 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
---|
| 292 | ! interpolated values of tracers |
---|
[4990] | 293 | zti (ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) |
---|
[2528] | 294 | ! gradient of tracers |
---|
[4990] | 295 | pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
---|
[2528] | 296 | ELSE ! case 2 |
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| 297 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
---|
| 298 | ! interpolated values of tracers |
---|
[4990] | 299 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
---|
[2528] | 300 | ! gradient of tracers |
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[4990] | 301 | pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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[2528] | 302 | ENDIF |
---|
| 303 | ! |
---|
| 304 | ! j- direction |
---|
| 305 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
---|
| 306 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
---|
| 307 | ! interpolated values of tracers |
---|
[4990] | 308 | ztj (ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) |
---|
[2528] | 309 | ! gradient of tracers |
---|
[4990] | 310 | pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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[2528] | 311 | ELSE ! case 2 |
---|
| 312 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
---|
| 313 | ! interpolated values of tracers |
---|
[4990] | 314 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
---|
[2528] | 315 | ! gradient of tracers |
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[4990] | 316 | pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
---|
[2528] | 317 | ENDIF |
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[3] | 318 | END DO |
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| 319 | END DO |
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[2528] | 320 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
---|
| 321 | ! |
---|
| 322 | END DO |
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[3] | 323 | |
---|
[2528] | 324 | ! horizontal derivative of density anomalies (rd) |
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| 325 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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[4990] | 326 | pgru(:,:)=0.0_wp ; pgrv(:,:)=0.0_wp ; |
---|
| 327 | pgzu(:,:)=0.0_wp ; pgzv(:,:)=0.0_wp ; |
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| 328 | pmru(:,:)=0.0_wp ; pmru(:,:)=0.0_wp ; |
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| 329 | pge3ru(:,:)=0.0_wp ; pge3rv(:,:)=0.0_wp ; |
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[2528] | 330 | DO jj = 1, jpjm1 |
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| 331 | DO ji = 1, jpim1 |
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| 332 | iku = mbku(ji,jj) |
---|
| 333 | ikv = mbkv(ji,jj) |
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[4990] | 334 | ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) |
---|
| 335 | ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) |
---|
| 336 | |
---|
| 337 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) - ze3wu ! i-direction: case 1 |
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| 338 | ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) + ze3wu ! - - case 2 |
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[2528] | 339 | ENDIF |
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[4990] | 340 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) - ze3wv ! j-direction: case 1 |
---|
| 341 | ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) + ze3wv ! - - case 2 |
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[2528] | 342 | ENDIF |
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| 343 | END DO |
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[3] | 344 | END DO |
---|
[4990] | 345 | |
---|
| 346 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
---|
| 347 | ! step and store it in zri, zrj for each case |
---|
| 348 | CALL eos( zti, zhi, zri ) |
---|
| 349 | CALL eos( ztj, zhj, zrj ) |
---|
[3] | 350 | |
---|
[4990] | 351 | ! Gradient of density at the last level |
---|
| 352 | DO jj = 1, jpjm1 |
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| 353 | DO ji = 1, jpim1 |
---|
| 354 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
---|
| 355 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! last and before last ocean level at u- & v-points |
---|
| 356 | ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) |
---|
| 357 | ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) |
---|
| 358 | IF( ze3wu >= 0._wp ) THEN |
---|
| 359 | pgzu(ji,jj) = (fsde3w(ji+1,jj,iku) - ze3wu) - fsde3w(ji,jj,iku) |
---|
| 360 | pgru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) - prd(ji,jj,iku) ) ! i: 1 |
---|
| 361 | pmru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) + prd(ji,jj,iku) ) ! i: 1 |
---|
| 362 | pge3ru(ji,jj) = umask(ji,jj,iku) & |
---|
| 363 | * ( (fse3w(ji+1,jj,iku) - ze3wu )* ( zri(ji ,jj ) + prd(ji+1,jj,ikum1) + 2._wp) & |
---|
| 364 | - fse3w(ji ,jj,iku) * ( prd(ji ,jj,iku) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 |
---|
| 365 | ELSE |
---|
| 366 | pgzu(ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) + ze3wu) |
---|
| 367 | pgru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
---|
| 368 | pmru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 |
---|
| 369 | pge3ru(ji,jj) = umask(ji,jj,iku) & |
---|
| 370 | * ( fse3w(ji+1,jj,iku) * ( prd(ji+1,jj,iku) + prd(ji+1,jj,ikum1) + 2._wp) & |
---|
| 371 | -(fse3w(ji ,jj,iku) + ze3wu) * ( zri(ji ,jj ) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 |
---|
| 372 | ENDIF |
---|
| 373 | IF( ze3wv >= 0._wp ) THEN |
---|
| 374 | pgzv(ji,jj) = (fsde3w(ji,jj+1,ikv) - ze3wv) - fsde3w(ji,jj,ikv) |
---|
| 375 | pgrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
---|
| 376 | pmrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 |
---|
| 377 | pge3rv(ji,jj) = vmask(ji,jj,ikv) & |
---|
| 378 | * ( (fse3w(ji,jj+1,ikv) - ze3wv )* ( zrj(ji,jj ) + prd(ji,jj+1,ikvm1) + 2._wp) & |
---|
| 379 | - fse3w(ji,jj ,ikv) * ( prd(ji,jj ,ikv) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 |
---|
| 380 | ELSE |
---|
| 381 | pgzv(ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) + ze3wv) |
---|
| 382 | pgrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
---|
| 383 | pmrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 |
---|
| 384 | pge3rv(ji,jj) = vmask(ji,jj,ikv) & |
---|
| 385 | * ( fse3w(ji,jj+1,ikv) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikvm1) + 2._wp) & |
---|
| 386 | -(fse3w(ji,jj ,ikv) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 |
---|
| 387 | ENDIF |
---|
| 388 | END DO |
---|
| 389 | END DO |
---|
| 390 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
---|
| 391 | CALL lbc_lnk( pmru , 'U', 1. ) ; CALL lbc_lnk( pmrv , 'V', 1. ) ! Lateral boundary conditions |
---|
| 392 | CALL lbc_lnk( pgzu , 'U', -1. ) ; CALL lbc_lnk( pgzv , 'V', -1. ) ! Lateral boundary conditions |
---|
| 393 | CALL lbc_lnk( pge3ru , 'U', -1. ) ; CALL lbc_lnk( pge3rv , 'V', -1. ) ! Lateral boundary conditions |
---|
| 394 | ! |
---|
| 395 | END IF |
---|
| 396 | ! (ISH) compute grui and gruvi |
---|
| 397 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! |
---|
| 398 | DO jj = 1, jpjm1 |
---|
| 399 | DO ji = 1, jpim1 |
---|
| 400 | iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 |
---|
| 401 | ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 |
---|
| 402 | ! |
---|
| 403 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
---|
| 404 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
---|
| 405 | ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj |
---|
| 406 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
---|
| 407 | 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)) |
---|
| 408 | 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)) |
---|
| 409 | ! i- direction |
---|
| 410 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
---|
| 411 | zmaxu = ze3wu / fse3w(ji+1,jj,iku+1) |
---|
| 412 | ! interpolated values of tracers |
---|
| 413 | zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,iku+1,jn) - pta(ji+1,jj,iku,jn) ) |
---|
| 414 | ! gradient of tracers |
---|
[5120] | 415 | pgtui(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
---|
[4990] | 416 | ELSE ! case 2 |
---|
| 417 | zmaxu = - ze3wu / fse3w(ji,jj,iku+1) |
---|
| 418 | ! interpolated values of tracers |
---|
| 419 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,iku+1,jn) - pta(ji,jj,iku,jn) ) |
---|
| 420 | ! gradient of tracers |
---|
[5120] | 421 | pgtui(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
---|
[4990] | 422 | ENDIF |
---|
| 423 | ! |
---|
| 424 | ! j- direction |
---|
| 425 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
---|
| 426 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv+1) |
---|
| 427 | ! interpolated values of tracers |
---|
| 428 | ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikv+1,jn) - pta(ji,jj+1,ikv,jn) ) |
---|
| 429 | ! gradient of tracers |
---|
[5120] | 430 | pgtvi(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
---|
[4990] | 431 | ELSE ! case 2 |
---|
| 432 | zmaxv = - ze3wv / fse3w(ji,jj,ikv+1) |
---|
| 433 | ! interpolated values of tracers |
---|
| 434 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikv+1,jn) - pta(ji,jj,ikv,jn) ) |
---|
| 435 | ! gradient of tracers |
---|
[5120] | 436 | pgtvi(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
---|
[4990] | 437 | ENDIF |
---|
| 438 | END DO!! |
---|
| 439 | END DO!! |
---|
[5120] | 440 | CALL lbc_lnk( pgtui(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtvi(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
---|
[4990] | 441 | ! |
---|
| 442 | END DO |
---|
| 443 | |
---|
| 444 | ! horizontal derivative of density anomalies (rd) |
---|
| 445 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
---|
[5120] | 446 | pgrui(:,:) =0.0_wp ; pgrvi(:,:) =0.0_wp ; |
---|
| 447 | pgzui(:,:) =0.0_wp ; pgzvi(:,:) =0.0_wp ; |
---|
| 448 | pmrui(:,:) =0.0_wp ; pmrui(:,:) =0.0_wp ; |
---|
| 449 | pge3rui(:,:)=0.0_wp ; pge3rvi(:,:)=0.0_wp ; |
---|
[4990] | 450 | |
---|
| 451 | DO jj = 1, jpjm1 |
---|
| 452 | DO ji = 1, jpim1 |
---|
| 453 | iku = miku(ji,jj) |
---|
| 454 | ikv = mikv(ji,jj) |
---|
| 455 | 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)) |
---|
| 456 | 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)) |
---|
| 457 | |
---|
| 458 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) + ze3wu ! i-direction: case 1 |
---|
| 459 | ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) - ze3wu ! - - case 2 |
---|
| 460 | ENDIF |
---|
| 461 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) + ze3wv ! j-direction: case 1 |
---|
| 462 | ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) - ze3wv ! - - case 2 |
---|
| 463 | ENDIF |
---|
| 464 | END DO |
---|
| 465 | END DO |
---|
| 466 | |
---|
[2528] | 467 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
---|
| 468 | ! step and store it in zri, zrj for each case |
---|
[3294] | 469 | CALL eos( zti, zhi, zri ) |
---|
| 470 | CALL eos( ztj, zhj, zrj ) |
---|
[3] | 471 | |
---|
[2528] | 472 | ! Gradient of density at the last level |
---|
| 473 | DO jj = 1, jpjm1 |
---|
| 474 | DO ji = 1, jpim1 |
---|
[4990] | 475 | iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 |
---|
| 476 | ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 |
---|
| 477 | 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)) |
---|
| 478 | 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)) |
---|
| 479 | IF( ze3wu >= 0._wp ) THEN |
---|
[5120] | 480 | pgzui (ji,jj) = (fsde3w(ji+1,jj,iku) + ze3wu) - fsde3w(ji,jj,iku) |
---|
| 481 | pgrui (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) - prd(ji,jj,iku) ) ! i: 1 |
---|
| 482 | pmrui (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) + prd(ji,jj,iku) ) ! i: 1 |
---|
| 483 | pge3rui(ji,jj) = umask(ji,jj,iku+1) & |
---|
[4990] | 484 | * ( (fse3w(ji+1,jj,iku+1) - ze3wu) * (zri(ji,jj ) + prd(ji+1,jj,iku+1) + 2._wp) & |
---|
| 485 | - fse3w(ji ,jj,iku+1) * (prd(ji,jj,iku) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 1 |
---|
| 486 | ELSE |
---|
[5120] | 487 | pgzui (ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) - ze3wu) |
---|
| 488 | pgrui (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
---|
| 489 | pmrui (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 |
---|
| 490 | pge3rui(ji,jj) = umask(ji,jj,iku+1) & |
---|
[4990] | 491 | * ( fse3w(ji+1,jj,iku+1) * (prd(ji+1,jj,iku) + prd(ji+1,jj,iku+1) + 2._wp) & |
---|
| 492 | -(fse3w(ji ,jj,iku+1) + ze3wu) * (zri(ji,jj ) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 2 |
---|
[2528] | 493 | ENDIF |
---|
[4990] | 494 | IF( ze3wv >= 0._wp ) THEN |
---|
[5120] | 495 | pgzvi (ji,jj) = (fsde3w(ji,jj+1,ikv) + ze3wv) - fsde3w(ji,jj,ikv) |
---|
| 496 | pgrvi (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
---|
| 497 | pmrvi (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 |
---|
| 498 | pge3rvi(ji,jj) = vmask(ji,jj,ikv+1) & |
---|
[4990] | 499 | * ( (fse3w(ji,jj+1,ikv+1) - ze3wv) * ( zrj(ji,jj ) + prd(ji,jj+1,ikv+1) + 2._wp) & |
---|
| 500 | - fse3w(ji,jj ,ikv+1) * ( prd(ji,jj,ikv) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 1 |
---|
| 501 | ! + 2 due to the formulation in density and not in anomalie in hpg sco |
---|
| 502 | ELSE |
---|
[5120] | 503 | pgzvi (ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) - ze3wv) |
---|
| 504 | pgrvi (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
---|
| 505 | pmrvi (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 |
---|
| 506 | pge3rvi(ji,jj) = vmask(ji,jj,ikv+1) & |
---|
[4990] | 507 | * ( fse3w(ji,jj+1,ikv+1) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikv+1) + 2._wp) & |
---|
| 508 | -(fse3w(ji,jj ,ikv+1) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 2 |
---|
[2528] | 509 | ENDIF |
---|
| 510 | END DO |
---|
[3] | 511 | END DO |
---|
[5120] | 512 | CALL lbc_lnk( pgrui , 'U', -1. ) ; CALL lbc_lnk( pgrvi , 'V', -1. ) ! Lateral boundary conditions |
---|
| 513 | CALL lbc_lnk( pmrui , 'U', 1. ) ; CALL lbc_lnk( pmrvi , 'V', 1. ) ! Lateral boundary conditions |
---|
| 514 | CALL lbc_lnk( pgzui , 'U', -1. ) ; CALL lbc_lnk( pgzvi , 'V', -1. ) ! Lateral boundary conditions |
---|
| 515 | CALL lbc_lnk( pge3rui , 'U', -1. ) ; CALL lbc_lnk( pge3rvi , 'V', -1. ) ! Lateral boundary conditions |
---|
[2528] | 516 | ! |
---|
[4990] | 517 | END IF |
---|
[2528] | 518 | ! |
---|
[5120] | 519 | IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde_isf') |
---|
[2715] | 520 | ! |
---|
[5120] | 521 | END SUBROUTINE zps_hde_isf |
---|
[3] | 522 | !!====================================================================== |
---|
| 523 | END MODULE zpshde |
---|