[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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| 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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[2528] | 16 | USE oce ! ocean: dynamics and tracers variables |
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| 17 | USE dom_oce ! domain: ocean variables |
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[3] | 18 | USE phycst ! physical constants |
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[2528] | 19 | USE eosbn2 ! ocean equation of state |
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[3] | 20 | USE in_out_manager ! I/O manager |
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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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[2528] | 26 | PUBLIC zps_hde ! routine called by step.F90 |
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[3] | 27 | |
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| 28 | !! * Substitutions |
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| 29 | # include "domzgr_substitute.h90" |
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| 30 | # include "vectopt_loop_substitute.h90" |
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| 31 | !!---------------------------------------------------------------------- |
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[2528] | 32 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 33 | !! $Id$ |
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| 34 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[247] | 35 | !!---------------------------------------------------------------------- |
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[3] | 36 | CONTAINS |
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| 37 | |
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[2528] | 38 | SUBROUTINE zps_hde( kt, kjpt, pta, pgtu, pgtv, & |
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| 39 | prd, pgru, pgrv ) |
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[3] | 40 | !!---------------------------------------------------------------------- |
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| 41 | !! *** ROUTINE zps_hde *** |
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| 42 | !! |
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[2528] | 43 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
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[3] | 44 | !! at u- and v-points with a linear interpolation for z-coordinate |
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| 45 | !! with partial steps. |
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| 46 | !! |
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| 47 | !! ** Method : In z-coord with partial steps, scale factors on last |
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| 48 | !! levels are different for each grid point, so that T, S and rd |
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| 49 | !! points are not at the same depth as in z-coord. To have horizontal |
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| 50 | !! gradients again, we interpolate T and S at the good depth : |
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| 51 | !! Linear interpolation of T, S |
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| 52 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
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| 53 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
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| 54 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
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| 55 | !! This formulation computes the two cases: |
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| 56 | !! CASE 1 CASE 2 |
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| 57 | !! k-1 ___ ___________ k-1 ___ ___________ |
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| 58 | !! Ti T~ T~ Ti+1 |
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| 59 | !! _____ _____ |
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| 60 | !! k | |Ti+1 k Ti | | |
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| 61 | !! | |____ ____| | |
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| 62 | !! ___ | | | ___ | | | |
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| 63 | !! |
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| 64 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
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| 65 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
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| 66 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
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| 67 | !! or |
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| 68 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
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| 69 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
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| 70 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
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| 71 | !! Idem for di(s) and dj(s) |
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| 72 | !! |
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[87] | 73 | !! For rho, we call eos_insitu_2d which will compute rd~(t~,s~) at |
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[3] | 74 | !! the good depth zh from interpolated T and S for the different |
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| 75 | !! formulation of the equation of state (eos). |
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| 76 | !! Gradient formulation for rho : |
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[2528] | 77 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
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[3] | 78 | !! |
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[2528] | 79 | !! ** Action : - pgtu, pgtv: horizontal gradient of tracer at u- & v-points |
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| 80 | !! - pgru, pgrv: horizontal gradient of rho (if present) at u- & v-points |
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| 81 | !!---------------------------------------------------------------------- |
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| 82 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 83 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 84 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
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| 85 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
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| 86 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
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| 87 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad. of prd at u- & v-pts |
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[3] | 88 | !! |
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[2528] | 89 | INTEGER :: ji, jj, jn ! Dummy loop indices |
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| 90 | INTEGER :: iku, ikv, ikum1, ikvm1 ! partial step level (ocean bottom level) at u- and v-points |
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| 91 | REAL(wp), DIMENSION(jpi,jpj,kjpt) :: zti, ztj ! interpolated value of tracer |
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| 92 | REAL(wp), DIMENSION(jpi,jpj) :: zri, zrj ! interpolated value of rd |
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| 93 | REAL(wp), DIMENSION(jpi,jpj) :: zhi, zhj ! depth of interpolation for eos2d |
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| 94 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars |
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[3] | 95 | !!---------------------------------------------------------------------- |
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| 96 | |
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[2528] | 97 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
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| 98 | ! |
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| 99 | # if defined key_vectopt_loop |
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| 100 | jj = 1 |
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| 101 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 102 | # else |
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[3] | 103 | DO jj = 1, jpjm1 |
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[2528] | 104 | DO ji = 1, jpim1 |
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| 105 | # endif |
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[2569] | 106 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
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| 107 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
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[2528] | 108 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 109 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 110 | ! |
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| 111 | ! i- direction |
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| 112 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
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| 113 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
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| 114 | ! interpolated values of tracers |
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| 115 | 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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| 116 | ! gradient of tracers |
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| 117 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
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| 118 | ELSE ! case 2 |
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| 119 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
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| 120 | ! interpolated values of tracers |
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| 121 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
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| 122 | ! gradient of tracers |
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| 123 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
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| 124 | ENDIF |
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| 125 | ! |
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| 126 | ! j- direction |
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| 127 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
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| 128 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
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| 129 | ! interpolated values of tracers |
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| 130 | 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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| 131 | ! gradient of tracers |
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| 132 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
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| 133 | ELSE ! case 2 |
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| 134 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
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| 135 | ! interpolated values of tracers |
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| 136 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
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| 137 | ! gradient of tracers |
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| 138 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
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| 139 | ENDIF |
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| 140 | # if ! defined key_vectopt_loop |
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[3] | 141 | END DO |
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[2528] | 142 | # endif |
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[3] | 143 | END DO |
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[2528] | 144 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
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| 145 | ! |
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| 146 | END DO |
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[3] | 147 | |
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[2528] | 148 | ! horizontal derivative of density anomalies (rd) |
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| 149 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
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[789] | 150 | # if defined key_vectopt_loop |
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[3] | 151 | jj = 1 |
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| 152 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 153 | # else |
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[2528] | 154 | DO jj = 1, jpjm1 |
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| 155 | DO ji = 1, jpim1 |
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[3] | 156 | # endif |
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[2528] | 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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[789] | 167 | # if ! defined key_vectopt_loop |
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[2528] | 168 | END DO |
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| 169 | # endif |
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[3] | 170 | END DO |
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| 171 | |
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[2528] | 172 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
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| 173 | ! step and store it in zri, zrj for each case |
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| 174 | CALL eos( zti, zhi, zri ) ; CALL eos( ztj, zhj, zrj ) |
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[3] | 175 | |
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[2528] | 176 | ! Gradient of density at the last level |
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[789] | 177 | # if defined key_vectopt_loop |
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[3] | 178 | jj = 1 |
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| 179 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
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| 180 | # else |
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[2528] | 181 | DO jj = 1, jpjm1 |
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| 182 | DO ji = 1, jpim1 |
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[3] | 183 | # endif |
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[2528] | 184 | iku = mbku(ji,jj) |
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| 185 | ikv = mbkv(ji,jj) |
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| 186 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
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| 187 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
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| 188 | 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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| 189 | ELSE ; pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
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| 190 | ENDIF |
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| 191 | 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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| 192 | ELSE ; pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
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| 193 | ENDIF |
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[789] | 194 | # if ! defined key_vectopt_loop |
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[2528] | 195 | END DO |
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| 196 | # endif |
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[3] | 197 | END DO |
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[2528] | 198 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
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| 199 | ! |
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| 200 | END IF |
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| 201 | ! |
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[3] | 202 | END SUBROUTINE zps_hde |
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| 203 | |
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| 204 | !!====================================================================== |
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| 205 | END MODULE zpshde |
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