| [3] | 1 | MODULE zpshde |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE zpshde *** |
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| [457] | 4 | !! z-coordinate - partial step : Horizontal Derivative |
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| [3] | 5 | !!============================================================================== |
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| [2104] | 6 | !! History : OPA ! 2002-04 (A. Bozec) Original code |
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| 7 | !! 8.5 ! 2002-08 (G. Madec E. Durand) Optimization and Free form |
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| 8 | !! NEMO 1.0 ! 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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| [2024] | 10 | !!============================================================================== |
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| [457] | 11 | |
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| [3] | 12 | !!---------------------------------------------------------------------- |
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| 13 | !! zps_hde : Horizontal DErivative of T, S and rd at the last |
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| 14 | !! ocean level (Z-coord. with Partial Steps) |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | USE dom_oce ! ocean space domain variables |
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| 17 | USE oce ! ocean dynamics and tracers variables |
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| 18 | USE phycst ! physical constants |
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| 19 | USE in_out_manager ! I/O manager |
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| 20 | USE eosbn2 ! ocean equation of state |
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| 21 | USE lbclnk ! lateral boundary conditions (or mpp link) |
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| 22 | |
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| 23 | IMPLICIT NONE |
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| 24 | PRIVATE |
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| 25 | |
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| [2104] | 26 | PUBLIC zps_hde ! routine called by step.F90 |
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| 27 | PUBLIC zps_hde_init ! routine called by opa.F90 |
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| [3] | 28 | |
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| [2104] | 29 | INTEGER, DIMENSION(jpi,jpj) :: mbatu, mbatv ! bottom ocean level index at U- and V-points |
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| [3] | 30 | |
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| 31 | !! * Substitutions |
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| 32 | # include "domzgr_substitute.h90" |
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| 33 | # include "vectopt_loop_substitute.h90" |
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| 34 | !!---------------------------------------------------------------------- |
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| [2104] | 35 | !! NEMO/OPA 3.3 , LOCEAN-IPSL (2010) |
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| 36 | !! $Id$ |
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| 37 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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| [247] | 38 | !!---------------------------------------------------------------------- |
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| [3] | 39 | CONTAINS |
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| [2082] | 40 | |
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| 41 | SUBROUTINE zps_hde( kt, kjpt, pta, pgtu, pgtv, & |
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| 42 | prd, pgru, pgrv ) |
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| [3] | 43 | !!---------------------------------------------------------------------- |
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| 44 | !! *** ROUTINE zps_hde *** |
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| 45 | !! |
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| 46 | !! ** Purpose : Compute the horizontal derivative of T, S and rd |
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| 47 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 48 | !! with partial steps. |
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| 49 | !! |
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| 50 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 51 | !! levels are different for each grid point, so that T, S and rd |
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| 52 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 53 | !! gradients again, we interpolate T and S at the good depth : |
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| 54 | !! Linear interpolation of T, S |
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| 55 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 56 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 57 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 58 | !! This formulation computes the two cases: |
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| 59 | !! CASE 1 CASE 2 |
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| 60 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 61 | !! Ti T~ T~ Ti+1 |
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| 62 | !! _____ _____ |
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| 63 | !! k | |Ti+1 k Ti | | |
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| 64 | !! | |____ ____| | |
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| 65 | !! ___ | | | ___ | | | |
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| 66 | !! |
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| 67 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 68 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 69 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 70 | !! or |
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| 71 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 72 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 73 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 74 | !! Idem for di(s) and dj(s) |
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| 75 | !! |
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| [87] | 76 | !! For rho, we call eos_insitu_2d which will compute rd~(t~,s~) at |
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| [3] | 77 | !! the good depth zh from interpolated T and S for the different |
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| 78 | !! formulation of the equation of state (eos). |
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| 79 | !! Gradient formulation for rho : |
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| 80 | !! di(rho) = rd~ - rd(i,j,k) or rd (i+1,j,k) - rd~ |
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| 81 | !! |
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| [2082] | 82 | !! ** Action : - pgtu, pgtv: horizontal gradient of tracer at U/V-points |
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| 83 | !! - pgru, pgrv: horizontal gradient of rd if present at U/V-points |
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| [3] | 84 | !! and rd at V-points |
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| 85 | !!---------------------------------------------------------------------- |
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| [2104] | 86 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 87 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 88 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
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| 89 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 90 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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| 91 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad. of prd at u- & v-pts |
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| 92 | !! |
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| [2082] | 93 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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| 94 | INTEGER :: iku, ikv ! partial step level at u- and v-points |
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| 95 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! interpolated value of tracer |
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| 96 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj ! interpolated value of rd |
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| 97 | REAL(wp), DIMENSION(jpi,jpj) :: zhi, zhj ! depth of interpolation for eos2d |
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| 98 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars |
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| 99 | !!---------------------------------------------------------------------- |
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| [3] | 100 | |
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| 101 | |
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| [2082] | 102 | ! Interpolation of tracers at the last ocean level |
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| 103 | DO jn = 1, kjpt |
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| [2104] | 104 | ! |
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| [789] | 105 | # if defined key_vectopt_loop |
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| [3] | 106 | jj = 1 |
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| 107 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 108 | # else |
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| [2082] | 109 | DO jj = 1, jpjm1 |
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| 110 | DO ji = 1, jpim1 |
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| [3] | 111 | # endif |
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| [2082] | 112 | ! last level |
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| 113 | iku = mbatu(ji,jj) |
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| 114 | ikv = mbatv(ji,jj) |
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| 115 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 116 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| [3] | 117 | |
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| [2082] | 118 | ! i- direction |
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| 119 | IF( ze3wu >= 0. ) THEN ! case 1 |
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| 120 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 121 | ! interpolated values of tracers |
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| 122 | zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,iku-1,jn) - pta(ji+1,jj,iku,jn) ) |
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| 123 | ! gradient of tracers |
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| 124 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 125 | ELSE ! case 2 |
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| 126 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
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| 127 | ! interpolated values of tracers |
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| 128 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,iku-1,jn) - pta(ji,jj,iku,jn) ) |
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| 129 | ! gradient of tracers |
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| 130 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 131 | ENDIF |
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| [3] | 132 | |
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| [2082] | 133 | ! j- direction |
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| 134 | IF( ze3wv >= 0. ) THEN ! case 1 |
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| 135 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 136 | ! interpolated values of tracers |
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| 137 | ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikv-1,jn) - pta(ji,jj+1,ikv,jn) ) |
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| 138 | ! gradient of tracers |
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| 139 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 140 | ELSE ! case 2 |
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| 141 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
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| 142 | ! interpolated values of tracers |
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| 143 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikv-1,jn) - pta(ji,jj,ikv,jn) ) |
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| 144 | ! gradient of tracers |
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| 145 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 146 | ENDIF |
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| [789] | 147 | # if ! defined key_vectopt_loop |
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| [2082] | 148 | END DO |
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| 149 | # endif |
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| [3] | 150 | END DO |
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| [2104] | 151 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
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| 152 | ! |
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| [2082] | 153 | END DO |
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| [3] | 154 | |
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| [2104] | 155 | ! horizontal derivative of density anomalies (rd) |
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| 156 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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| [789] | 157 | # if defined key_vectopt_loop |
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| [3] | 158 | jj = 1 |
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| 159 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 160 | # else |
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| [2082] | 161 | DO jj = 1, jpjm1 |
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| 162 | DO ji = 1, jpim1 |
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| [3] | 163 | # endif |
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| [2082] | 164 | iku = mbatu(ji,jj) |
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| 165 | ikv = mbatv(ji,jj) |
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| 166 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 167 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 168 | IF( ze3wu >= 0. ) THEN |
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| 169 | zhi(ji,jj) = fsdept(ji ,jj,iku) |
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| 170 | ELSE |
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| 171 | zhi(ji,jj) = fsdept(ji+1,jj,iku) |
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| 172 | ENDIF |
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| 173 | IF( ze3wv >= 0. ) THEN |
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| 174 | zhj(ji,jj) = fsdept(ji,jj ,ikv) |
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| 175 | ELSE |
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| 176 | zhj(ji,jj) = fsdept(ji,jj+1,ikv) |
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| 177 | ENDIF |
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| [789] | 178 | # if ! defined key_vectopt_loop |
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| [2082] | 179 | END DO |
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| 180 | # endif |
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| [3] | 181 | END DO |
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| 182 | |
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| [2082] | 183 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 184 | ! step and store it in zri, zrj for each case |
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| [2104] | 185 | CALL eos( zti, zhi, zri ) ; CALL eos( ztj, zhj, zrj ) |
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| [3] | 186 | |
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| [2082] | 187 | ! Gradient of density at the last level |
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| [2024] | 188 | # if defined key_vectopt_loop |
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| 189 | jj = 1 |
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| 190 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 191 | # else |
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| 192 | DO jj = 1, jpjm1 |
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| 193 | DO ji = 1, jpim1 |
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| 194 | # endif |
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| 195 | iku = mbatu(ji,jj) |
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| 196 | ikv = mbatv(ji,jj) |
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| 197 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 198 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| [2082] | 199 | IF( ze3wu >= 0. ) THEN ! i-direction: case 1 |
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| 200 | pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji,jj) - prd(ji,jj,iku) ) |
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| 201 | ELSE ! i-direction: case 2 |
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| 202 | pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) |
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| [2024] | 203 | ENDIF |
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| [2082] | 204 | IF( ze3wv >= 0. ) THEN ! j-direction: case 1 |
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| 205 | pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj) - prd(ji,jj,ikv) ) |
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| 206 | ELSE ! j-direction: case 2 |
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| 207 | pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) |
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| [2024] | 208 | ENDIF |
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| 209 | # if ! defined key_vectopt_loop |
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| 210 | END DO |
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| 211 | # endif |
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| 212 | END DO |
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| [2104] | 213 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
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| [2082] | 214 | ! |
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| 215 | END IF |
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| 216 | ! |
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| 217 | END SUBROUTINE zps_hde |
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| [2024] | 218 | |
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| [2104] | 219 | |
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| [2024] | 220 | SUBROUTINE zps_hde_init |
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| 221 | !!---------------------------------------------------------------------- |
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| 222 | !! *** ROUTINE zps_hde_init *** |
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| 223 | !! |
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| 224 | !! ** Purpose : Computation of bottom ocean level index at U- and V-points |
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| 225 | !! |
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| 226 | !!---------------------------------------------------------------------- |
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| [2104] | 227 | INTEGER :: ji, jj ! Dummy loop indices |
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| 228 | REAL(wp), DIMENSION(jpi,jpj) :: zti, ztj ! 2D workspace |
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| [2024] | 229 | !!---------------------------------------------------------------------- |
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| [2104] | 230 | ! |
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| [2024] | 231 | mbatu(:,:) = 0 |
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| 232 | mbatv(:,:) = 0 |
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| 233 | DO jj = 1, jpjm1 |
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| 234 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 235 | mbatu(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1, 2 ) |
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| 236 | mbatv(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1, 2 ) |
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| 237 | END DO |
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| 238 | END DO |
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| 239 | zti(:,:) = FLOAT( mbatu(:,:) ) |
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| 240 | ztj(:,:) = FLOAT( mbatv(:,:) ) |
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| 241 | ! lateral boundary conditions: T-point, sign unchanged |
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| [2104] | 242 | CALL lbc_lnk( zti , 'U', 1. ) ; CALL lbc_lnk( ztj , 'V', 1. ) |
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| [2024] | 243 | mbatu(:,:) = MAX( INT( zti(:,:) ), 2 ) |
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| 244 | mbatv(:,:) = MAX( INT( ztj(:,:) ), 2 ) |
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| [2104] | 245 | ! |
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| [2024] | 246 | END SUBROUTINE zps_hde_init |
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| [3] | 247 | !!====================================================================== |
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| 248 | END MODULE zpshde |
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