[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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[5836] | 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 ! local 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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[5120] | 100 | !!---------------------------------------------------------------------- |
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| 101 | ! |
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[5836] | 102 | IF( nn_timing == 1 ) CALL timing_start( 'zps_hde') |
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[5120] | 103 | ! |
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[5836] | 104 | pgtu(:,:,:)=0._wp ; zti (:,:,:)=0._wp ; zhi (:,: )=0._wp |
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| 105 | pgtv(:,:,:)=0._wp ; ztj (:,:,:)=0._wp ; zhj (:,: )=0._wp |
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[5120] | 106 | ! |
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| 107 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 108 | ! |
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| 109 | DO jj = 1, jpjm1 |
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| 110 | DO ji = 1, jpim1 |
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| 111 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 112 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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| 113 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 114 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 115 | ! |
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| 116 | ! i- direction |
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| 117 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 118 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 119 | ! interpolated values of tracers |
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| 120 | 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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| 121 | ! gradient of tracers |
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| 122 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 123 | ELSE ! case 2 |
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| 124 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
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| 125 | ! interpolated values of tracers |
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| 126 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
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| 127 | ! gradient of tracers |
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| 128 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 129 | ENDIF |
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| 130 | ! |
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| 131 | ! j- direction |
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| 132 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 133 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 134 | ! interpolated values of tracers |
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| 135 | 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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| 136 | ! gradient of tracers |
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| 137 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 138 | ELSE ! case 2 |
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| 139 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
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| 140 | ! interpolated values of tracers |
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| 141 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
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| 142 | ! gradient of tracers |
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| 143 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 144 | ENDIF |
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| 145 | END DO |
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| 146 | END DO |
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| 147 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
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| 148 | ! |
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| 149 | END DO |
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[5836] | 150 | ! |
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| 151 | IF( PRESENT( prd ) ) THEN !== horizontal derivative of density anomalies (rd) ==! (optional part) |
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| 152 | pgru(:,:) = 0._wp |
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| 153 | pgrv(:,:) = 0._wp ! depth of the partial step level |
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[5120] | 154 | DO jj = 1, jpjm1 |
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| 155 | DO ji = 1, jpim1 |
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| 156 | iku = mbku(ji,jj) |
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| 157 | ikv = mbkv(ji,jj) |
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| 158 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 159 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 160 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji ,jj,iku) ! i-direction: case 1 |
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| 161 | ELSE ; zhi(ji,jj) = fsdept(ji+1,jj,iku) ! - - case 2 |
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| 162 | ENDIF |
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| 163 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj ,ikv) ! j-direction: case 1 |
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| 164 | ELSE ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) ! - - case 2 |
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| 165 | ENDIF |
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| 166 | END DO |
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| 167 | END DO |
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[5836] | 168 | ! |
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| 169 | CALL eos( zti, zhi, zri ) ! interpolated density from zti, ztj |
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| 170 | CALL eos( ztj, zhj, zrj ) ! at the partial step depth output in zri, zrj |
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| 171 | ! |
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| 172 | DO jj = 1, jpjm1 ! Gradient of density at the last level |
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[5120] | 173 | DO ji = 1, jpim1 |
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| 174 | iku = mbku(ji,jj) |
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| 175 | ikv = mbkv(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._wp ) THEN ; pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji ,jj ) - prd(ji,jj,iku) ) ! i: 1 |
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| 179 | ELSE ; pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj ) ) ! i: 2 |
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| 180 | ENDIF |
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| 181 | 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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| 182 | ELSE ; pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj ) ) ! j: 2 |
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| 183 | ENDIF |
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| 184 | END DO |
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| 185 | END DO |
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| 186 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
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| 187 | ! |
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| 188 | END IF |
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| 189 | ! |
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[5836] | 190 | IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde') |
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[5120] | 191 | ! |
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| 192 | END SUBROUTINE zps_hde |
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[5836] | 193 | |
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| 194 | |
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| 195 | SUBROUTINE zps_hde_isf( kt, kjpt, pta, pgtu , pgtv , pgtui, pgtvi, & |
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| 196 | & prd, pgru , pgrv , pmru , pmrv , pgzu , pgzv , pge3ru , pge3rv , & |
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| 197 | & pgrui, pgrvi, pmrui, pmrvi, pgzui, pgzvi, pge3rui, pge3rvi ) |
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[3] | 198 | !!---------------------------------------------------------------------- |
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| 199 | !! *** ROUTINE zps_hde *** |
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| 200 | !! |
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[2528] | 201 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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[3] | 202 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 203 | !! with partial steps. |
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| 204 | !! |
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| 205 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 206 | !! levels are different for each grid point, so that T, S and rd |
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| 207 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 208 | !! gradients again, we interpolate T and S at the good depth : |
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| 209 | !! Linear interpolation of T, S |
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| 210 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 211 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 212 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 213 | !! This formulation computes the two cases: |
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| 214 | !! CASE 1 CASE 2 |
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| 215 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 216 | !! Ti T~ T~ Ti+1 |
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| 217 | !! _____ _____ |
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| 218 | !! k | |Ti+1 k Ti | | |
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| 219 | !! | |____ ____| | |
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| 220 | !! ___ | | | ___ | | | |
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| 221 | !! |
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| 222 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 223 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 224 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 225 | !! or |
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| 226 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 227 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 228 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 229 | !! Idem for di(s) and dj(s) |
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| 230 | !! |
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[4990] | 231 | !! For rho, we call eos which will compute rd~(t~,s~) at the right |
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| 232 | !! depth zh from interpolated T and S for the different formulations |
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| 233 | !! of the equation of state (eos). |
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[3] | 234 | !! Gradient formulation for rho : |
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[4990] | 235 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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[3] | 236 | !! |
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[4990] | 237 | !! ** Action : compute for top and bottom interfaces |
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[5120] | 238 | !! - pgtu, pgtv, pgtui, pgtvi: horizontal gradient of tracer at u- & v-points |
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| 239 | !! - pgru, pgrv, pgrui, pgtvi: horizontal gradient of rho (if present) at u- & v-points |
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| 240 | !! - pmru, pmrv, pmrui, pmrvi: horizontal sum of rho at u- & v- point (used in dynhpg with vvl) |
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| 241 | !! - pgzu, pgzv, pgzui, pgzvi: horizontal gradient of z at u- and v- point (used in dynhpg with vvl) |
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| 242 | !! - pge3ru, pge3rv, pge3rui, pge3rvi: horizontal gradient of rho weighted by local e3w at u- & v-points |
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[2528] | 243 | !!---------------------------------------------------------------------- |
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[5836] | 244 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 245 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 246 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
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| 247 | ! !! u-point ! v-point ! |
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| 248 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu , pgtv ! bottom GRADh( ptra ) |
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| 249 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtui , pgtvi ! top GRADh( ptra ) |
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| 250 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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| 251 | ! !! u-point ! v-point ! |
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| 252 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru , pgrv ! bottom GRADh( prd ) |
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| 253 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmru , pmrv ! bottom SUM ( prd ) |
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| 254 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzu , pgzv ! bottom GRADh( z ) |
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| 255 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pge3ru , pge3rv ! bottom GRADh( prd ) weighted by e3w |
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| 256 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgrui , pgrvi ! top GRADh( prd ) |
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| 257 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pmrui , pmrvi ! top SUM ( prd ) |
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| 258 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgzui , pgzvi ! top GRADh( z ) |
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| 259 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pge3rui , pge3rvi ! top GRADh( prd ) weighted by e3w |
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[2715] | 260 | ! |
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[2528] | 261 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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[4990] | 262 | INTEGER :: iku, ikv, ikum1, ikvm1,ikup1, ikvp1 ! partial step level (ocean bottom level) at u- and v-points |
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| 263 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv, zdzwu, zdzwv, zdzwuip1, zdzwvjp1 ! temporary scalars |
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| 264 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj, zhi, zhj ! NB: 3rd dim=1 to use eos |
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| 265 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! |
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[3] | 266 | !!---------------------------------------------------------------------- |
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[3294] | 267 | ! |
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[5120] | 268 | IF( nn_timing == 1 ) CALL timing_start( 'zps_hde_isf') |
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[3294] | 269 | ! |
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[5836] | 270 | pgtu (:,:,:) = 0._wp ; pgtv (:,:,:) =0._wp |
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| 271 | pgtui(:,:,:) = 0._wp ; pgtvi(:,:,:) =0._wp |
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| 272 | zti (:,:,:) = 0._wp ; ztj (:,:,:) =0._wp |
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| 273 | zhi (:,: ) = 0._wp ; zhj (:,: ) =0._wp |
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[3294] | 274 | ! |
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[2528] | 275 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 276 | ! |
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[3] | 277 | DO jj = 1, jpjm1 |
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[2528] | 278 | DO ji = 1, jpim1 |
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[2569] | 279 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 280 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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[4990] | 281 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
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| 282 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
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| 283 | ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj |
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| 284 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
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| 285 | 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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| 286 | 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] | 287 | ! |
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| 288 | ! i- direction |
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| 289 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 290 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 291 | ! interpolated values of tracers |
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[4990] | 292 | zti (ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) |
---|
[2528] | 293 | ! gradient of tracers |
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[4990] | 294 | pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
---|
[2528] | 295 | ELSE ! case 2 |
---|
| 296 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
---|
| 297 | ! interpolated values of tracers |
---|
[4990] | 298 | zti (ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
---|
[2528] | 299 | ! gradient of tracers |
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[4990] | 300 | pgtu(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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[2528] | 301 | ENDIF |
---|
| 302 | ! |
---|
| 303 | ! j- direction |
---|
| 304 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
---|
| 305 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 306 | ! interpolated values of tracers |
---|
[4990] | 307 | ztj (ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) |
---|
[2528] | 308 | ! gradient of tracers |
---|
[4990] | 309 | pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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[2528] | 310 | ELSE ! case 2 |
---|
| 311 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
---|
| 312 | ! interpolated values of tracers |
---|
[4990] | 313 | ztj (ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
---|
[2528] | 314 | ! gradient of tracers |
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[4990] | 315 | pgtv(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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[2528] | 316 | ENDIF |
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[3] | 317 | END DO |
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| 318 | END DO |
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[2528] | 319 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
---|
| 320 | ! |
---|
| 321 | END DO |
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[3] | 322 | |
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[5836] | 323 | IF( PRESENT( prd ) ) THEN !== horizontal derivative of density anomalies (rd) ==! (optional part) |
---|
| 324 | ! |
---|
| 325 | pgru (:,:)=0._wp ; pgrv (:,:) = 0._wp |
---|
| 326 | pgzu (:,:)=0._wp ; pgzv (:,:) = 0._wp |
---|
| 327 | pmru (:,:)=0._wp ; pmru (:,:) = 0._wp |
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| 328 | pge3ru(:,:)=0._wp ; pge3rv(:,:) = 0._wp |
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| 329 | ! |
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| 330 | DO jj = 1, jpjm1 ! depth of the partial step level |
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[2528] | 331 | DO ji = 1, jpim1 |
---|
| 332 | iku = mbku(ji,jj) |
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| 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)) |
---|
[5836] | 336 | ! |
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[4990] | 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 |
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| 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 |
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[5836] | 345 | ! |
---|
| 346 | CALL eos( zti, zhi, zri ) ! interpolated density from zti, ztj |
---|
| 347 | CALL eos( ztj, zhj, zrj ) ! at the partial step depth output in zri, zrj |
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[3] | 348 | |
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[5836] | 349 | DO jj = 1, jpjm1 ! Gradient of density at the last level |
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[4990] | 350 | DO ji = 1, jpim1 |
---|
| 351 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
---|
| 352 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! last and before last ocean level at u- & v-points |
---|
| 353 | ze3wu = (gdept_0(ji+1,jj,iku) - gdepw_0(ji+1,jj,iku)) - (gdept_0(ji,jj,iku) - gdepw_0(ji,jj,iku)) |
---|
| 354 | ze3wv = (gdept_0(ji,jj+1,ikv) - gdepw_0(ji,jj+1,ikv)) - (gdept_0(ji,jj,ikv) - gdepw_0(ji,jj,ikv)) |
---|
| 355 | IF( ze3wu >= 0._wp ) THEN |
---|
| 356 | pgzu(ji,jj) = (fsde3w(ji+1,jj,iku) - ze3wu) - fsde3w(ji,jj,iku) |
---|
| 357 | pgru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) - prd(ji,jj,iku) ) ! i: 1 |
---|
| 358 | pmru(ji,jj) = umask(ji,jj,iku) * ( zri(ji ,jj) + prd(ji,jj,iku) ) ! i: 1 |
---|
| 359 | pge3ru(ji,jj) = umask(ji,jj,iku) & |
---|
| 360 | * ( (fse3w(ji+1,jj,iku) - ze3wu )* ( zri(ji ,jj ) + prd(ji+1,jj,ikum1) + 2._wp) & |
---|
| 361 | - fse3w(ji ,jj,iku) * ( prd(ji ,jj,iku) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 |
---|
| 362 | ELSE |
---|
| 363 | pgzu(ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) + ze3wu) |
---|
| 364 | pgru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
---|
| 365 | pmru(ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 |
---|
| 366 | pge3ru(ji,jj) = umask(ji,jj,iku) & |
---|
| 367 | * ( fse3w(ji+1,jj,iku) * ( prd(ji+1,jj,iku) + prd(ji+1,jj,ikum1) + 2._wp) & |
---|
| 368 | -(fse3w(ji ,jj,iku) + ze3wu) * ( zri(ji ,jj ) + prd(ji ,jj,ikum1) + 2._wp) ) ! j: 2 |
---|
| 369 | ENDIF |
---|
| 370 | IF( ze3wv >= 0._wp ) THEN |
---|
| 371 | pgzv(ji,jj) = (fsde3w(ji,jj+1,ikv) - ze3wv) - fsde3w(ji,jj,ikv) |
---|
| 372 | pgrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
---|
| 373 | pmrv(ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 |
---|
| 374 | pge3rv(ji,jj) = vmask(ji,jj,ikv) & |
---|
| 375 | * ( (fse3w(ji,jj+1,ikv) - ze3wv )* ( zrj(ji,jj ) + prd(ji,jj+1,ikvm1) + 2._wp) & |
---|
| 376 | - fse3w(ji,jj ,ikv) * ( prd(ji,jj ,ikv) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 |
---|
| 377 | ELSE |
---|
| 378 | pgzv(ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) + ze3wv) |
---|
| 379 | pgrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
---|
| 380 | pmrv(ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 |
---|
| 381 | pge3rv(ji,jj) = vmask(ji,jj,ikv) & |
---|
| 382 | * ( fse3w(ji,jj+1,ikv) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikvm1) + 2._wp) & |
---|
| 383 | -(fse3w(ji,jj ,ikv) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikvm1) + 2._wp) ) ! j: 2 |
---|
| 384 | ENDIF |
---|
| 385 | END DO |
---|
| 386 | END DO |
---|
| 387 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
---|
| 388 | CALL lbc_lnk( pmru , 'U', 1. ) ; CALL lbc_lnk( pmrv , 'V', 1. ) ! Lateral boundary conditions |
---|
| 389 | CALL lbc_lnk( pgzu , 'U', -1. ) ; CALL lbc_lnk( pgzv , 'V', -1. ) ! Lateral boundary conditions |
---|
| 390 | CALL lbc_lnk( pge3ru , 'U', -1. ) ; CALL lbc_lnk( pge3rv , 'V', -1. ) ! Lateral boundary conditions |
---|
| 391 | ! |
---|
| 392 | END IF |
---|
[5836] | 393 | ! |
---|
| 394 | ! !== (ISH) compute grui and gruvi ==! |
---|
| 395 | ! |
---|
[4990] | 396 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! ! |
---|
| 397 | DO jj = 1, jpjm1 |
---|
| 398 | DO ji = 1, jpim1 |
---|
| 399 | iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 |
---|
| 400 | ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 |
---|
| 401 | ! |
---|
| 402 | ! (ISF) case partial step top and bottom in adjacent cell in vertical |
---|
| 403 | ! cannot used e3w because if 2 cell water column, we have ps at top and bottom |
---|
| 404 | ! in this case e3w(i,j) - e3w(i,j+1) is not the distance between Tj~ and Tj |
---|
| 405 | ! the only common depth between cells (i,j) and (i,j+1) is gdepw_0 |
---|
| 406 | 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)) |
---|
| 407 | 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)) |
---|
| 408 | ! i- direction |
---|
| 409 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
---|
| 410 | zmaxu = ze3wu / fse3w(ji+1,jj,iku+1) |
---|
| 411 | ! interpolated values of tracers |
---|
| 412 | zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,iku+1,jn) - pta(ji+1,jj,iku,jn) ) |
---|
| 413 | ! gradient of tracers |
---|
[5120] | 414 | pgtui(ji,jj,jn) = umask(ji,jj,iku) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
---|
[4990] | 415 | ELSE ! case 2 |
---|
| 416 | zmaxu = - ze3wu / fse3w(ji,jj,iku+1) |
---|
| 417 | ! interpolated values of tracers |
---|
| 418 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,iku+1,jn) - pta(ji,jj,iku,jn) ) |
---|
| 419 | ! gradient of tracers |
---|
[5120] | 420 | pgtui(ji,jj,jn) = umask(ji,jj,iku) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
---|
[4990] | 421 | ENDIF |
---|
| 422 | ! |
---|
| 423 | ! j- direction |
---|
| 424 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
---|
| 425 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv+1) |
---|
| 426 | ! interpolated values of tracers |
---|
| 427 | ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikv+1,jn) - pta(ji,jj+1,ikv,jn) ) |
---|
| 428 | ! gradient of tracers |
---|
[5120] | 429 | pgtvi(ji,jj,jn) = vmask(ji,jj,ikv) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
---|
[4990] | 430 | ELSE ! case 2 |
---|
| 431 | zmaxv = - ze3wv / fse3w(ji,jj,ikv+1) |
---|
| 432 | ! interpolated values of tracers |
---|
| 433 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikv+1,jn) - pta(ji,jj,ikv,jn) ) |
---|
| 434 | ! gradient of tracers |
---|
[5120] | 435 | pgtvi(ji,jj,jn) = vmask(ji,jj,ikv) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
---|
[4990] | 436 | ENDIF |
---|
| 437 | END DO!! |
---|
| 438 | END DO!! |
---|
[5120] | 439 | CALL lbc_lnk( pgtui(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtvi(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
---|
[4990] | 440 | ! |
---|
| 441 | END DO |
---|
| 442 | |
---|
[5836] | 443 | IF( PRESENT( prd ) ) THEN !== horizontal derivative of density anomalies (rd) ==! (optional part) |
---|
| 444 | ! |
---|
[5120] | 445 | pgrui(:,:) =0.0_wp ; pgrvi(:,:) =0.0_wp ; |
---|
| 446 | pgzui(:,:) =0.0_wp ; pgzvi(:,:) =0.0_wp ; |
---|
| 447 | pmrui(:,:) =0.0_wp ; pmrui(:,:) =0.0_wp ; |
---|
| 448 | pge3rui(:,:)=0.0_wp ; pge3rvi(:,:)=0.0_wp ; |
---|
[5836] | 449 | ! |
---|
| 450 | DO jj = 1, jpjm1 ! depth of the partial step level |
---|
[4990] | 451 | DO ji = 1, jpim1 |
---|
| 452 | iku = miku(ji,jj) |
---|
| 453 | ikv = mikv(ji,jj) |
---|
| 454 | 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)) |
---|
| 455 | 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)) |
---|
[5836] | 456 | ! |
---|
[4990] | 457 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji+1,jj,iku) + ze3wu ! i-direction: case 1 |
---|
| 458 | ELSE ; zhi(ji,jj) = fsdept(ji ,jj,iku) - ze3wu ! - - case 2 |
---|
| 459 | ENDIF |
---|
| 460 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) + ze3wv ! j-direction: case 1 |
---|
| 461 | ELSE ; zhj(ji,jj) = fsdept(ji,jj ,ikv) - ze3wv ! - - case 2 |
---|
| 462 | ENDIF |
---|
| 463 | END DO |
---|
| 464 | END DO |
---|
[5836] | 465 | ! |
---|
| 466 | CALL eos( zti, zhi, zri ) ! interpolated density from zti, ztj |
---|
| 467 | CALL eos( ztj, zhj, zrj ) ! at the partial step depth output in zri, zrj |
---|
| 468 | ! |
---|
| 469 | DO jj = 1, jpjm1 ! Gradient of density at the last level |
---|
[2528] | 470 | DO ji = 1, jpim1 |
---|
[4990] | 471 | iku = miku(ji,jj) ; ikup1 = miku(ji,jj) + 1 |
---|
| 472 | ikv = mikv(ji,jj) ; ikvp1 = mikv(ji,jj) + 1 |
---|
| 473 | 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)) |
---|
| 474 | 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)) |
---|
| 475 | IF( ze3wu >= 0._wp ) THEN |
---|
[5120] | 476 | pgzui (ji,jj) = (fsde3w(ji+1,jj,iku) + ze3wu) - fsde3w(ji,jj,iku) |
---|
| 477 | pgrui (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) - prd(ji,jj,iku) ) ! i: 1 |
---|
| 478 | pmrui (ji,jj) = umask(ji,jj,iku) * ( zri(ji,jj) + prd(ji,jj,iku) ) ! i: 1 |
---|
| 479 | pge3rui(ji,jj) = umask(ji,jj,iku+1) & |
---|
[5836] | 480 | & * ( (fse3w(ji+1,jj,iku+1) - ze3wu) * (zri(ji,jj ) + prd(ji+1,jj,iku+1) + 2._wp) & |
---|
| 481 | & - fse3w(ji ,jj,iku+1) * (prd(ji,jj,iku) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 1 |
---|
[4990] | 482 | ELSE |
---|
[5120] | 483 | pgzui (ji,jj) = fsde3w(ji+1,jj,iku) - (fsde3w(ji,jj,iku) - ze3wu) |
---|
| 484 | pgrui (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
---|
| 485 | pmrui (ji,jj) = umask(ji,jj,iku) * ( prd(ji+1,jj,iku) + zri(ji,jj) ) ! i: 2 |
---|
| 486 | pge3rui(ji,jj) = umask(ji,jj,iku+1) & |
---|
[5836] | 487 | & * ( fse3w(ji+1,jj,iku+1) * (prd(ji+1,jj,iku) + prd(ji+1,jj,iku+1) + 2._wp) & |
---|
| 488 | & -(fse3w(ji ,jj,iku+1) + ze3wu) * (zri(ji,jj ) + prd(ji ,jj,iku+1) + 2._wp) ) ! i: 2 |
---|
[2528] | 489 | ENDIF |
---|
[4990] | 490 | IF( ze3wv >= 0._wp ) THEN |
---|
[5120] | 491 | pgzvi (ji,jj) = (fsde3w(ji,jj+1,ikv) + ze3wv) - fsde3w(ji,jj,ikv) |
---|
| 492 | pgrvi (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
---|
| 493 | pmrvi (ji,jj) = vmask(ji,jj,ikv) * ( zrj(ji,jj ) + prd(ji,jj,ikv) ) ! j: 1 |
---|
| 494 | pge3rvi(ji,jj) = vmask(ji,jj,ikv+1) & |
---|
[5836] | 495 | & * ( (fse3w(ji,jj+1,ikv+1) - ze3wv) * ( zrj(ji,jj ) + prd(ji,jj+1,ikv+1) + 2._wp) & |
---|
| 496 | & - fse3w(ji,jj ,ikv+1) * ( prd(ji,jj,ikv) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 1 |
---|
[4990] | 497 | ! + 2 due to the formulation in density and not in anomalie in hpg sco |
---|
| 498 | ELSE |
---|
[5120] | 499 | pgzvi (ji,jj) = fsde3w(ji,jj+1,ikv) - (fsde3w(ji,jj,ikv) - ze3wv) |
---|
| 500 | pgrvi (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
---|
| 501 | pmrvi (ji,jj) = vmask(ji,jj,ikv) * ( prd(ji,jj+1,ikv) + zrj(ji,jj) ) ! j: 2 |
---|
| 502 | pge3rvi(ji,jj) = vmask(ji,jj,ikv+1) & |
---|
[5836] | 503 | & * ( fse3w(ji,jj+1,ikv+1) * ( prd(ji,jj+1,ikv) + prd(ji,jj+1,ikv+1) + 2._wp) & |
---|
| 504 | & -(fse3w(ji,jj ,ikv+1) + ze3wv) * ( zrj(ji,jj ) + prd(ji,jj ,ikv+1) + 2._wp) ) ! j: 2 |
---|
[2528] | 505 | ENDIF |
---|
| 506 | END DO |
---|
[3] | 507 | END DO |
---|
[5120] | 508 | CALL lbc_lnk( pgrui , 'U', -1. ) ; CALL lbc_lnk( pgrvi , 'V', -1. ) ! Lateral boundary conditions |
---|
| 509 | CALL lbc_lnk( pmrui , 'U', 1. ) ; CALL lbc_lnk( pmrvi , 'V', 1. ) ! Lateral boundary conditions |
---|
| 510 | CALL lbc_lnk( pgzui , 'U', -1. ) ; CALL lbc_lnk( pgzvi , 'V', -1. ) ! Lateral boundary conditions |
---|
| 511 | CALL lbc_lnk( pge3rui , 'U', -1. ) ; CALL lbc_lnk( pge3rvi , 'V', -1. ) ! Lateral boundary conditions |
---|
[2528] | 512 | ! |
---|
[4990] | 513 | END IF |
---|
[2528] | 514 | ! |
---|
[5836] | 515 | IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde_isf') |
---|
[2715] | 516 | ! |
---|
[5120] | 517 | END SUBROUTINE zps_hde_isf |
---|
[3] | 518 | !!====================================================================== |
---|
| 519 | END MODULE zpshde |
---|