| 1 | MODULE ldfslp |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE ldfslp *** |
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| 4 | !! Ocean physics: slopes of neutral surfaces |
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| 5 | !!====================================================================== |
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| 6 | !! History : OPA ! 1994-12 (G. Madec, M. Imbard) Original code |
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| 7 | !! 8.0 ! 1997-06 (G. Madec) optimization, lbc |
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| 8 | !! 8.1 ! 1999-10 (A. Jouzeau) NEW profile in the mixed layer |
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| 9 | !! NEMO 1.0 ! 2002-10 (G. Madec) Free form, F90 |
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| 10 | !! - ! 2005-10 (A. Beckmann) correction for s-coordinates |
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| 11 | !! 3.3 ! 2010-10 (G. Nurser, C. Harris, G. Madec) add Griffies operator |
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| 12 | !! - ! 2010-11 (F. Dupond, G. Madec) bug correction in slopes just below the ML |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | #if defined key_ldfslp || defined key_esopa |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | !! 'key_ldfslp' Rotation of lateral mixing tensor |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | !! ldf_slp_grif : calculates the triads of isoneutral slopes (Griffies operator) |
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| 19 | !! ldf_slp : calculates the slopes of neutral surface (Madec operator) |
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| 20 | !! ldf_slp_mxl : calculates the slopes at the base of the mixed layer (Madec operator) |
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| 21 | !! ldf_slp_init : initialization of the slopes computation |
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| 22 | !!---------------------------------------------------------------------- |
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| 23 | USE oce ! ocean dynamics and tracers |
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| 24 | USE dom_oce ! ocean space and time domain |
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| 25 | USE ldftra_oce ! lateral diffusion: traceur |
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| 26 | USE ldfdyn_oce ! lateral diffusion: dynamics |
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| 27 | USE phycst ! physical constants |
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| 28 | USE zdfmxl ! mixed layer depth |
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| 29 | USE eosbn2 ! equation of states |
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| 30 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| 31 | USE in_out_manager ! I/O manager |
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| 32 | USE prtctl ! Print control |
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| 33 | |
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| 34 | IMPLICIT NONE |
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| 35 | PRIVATE |
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| 36 | |
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| 37 | PUBLIC ldf_slp ! routine called by step.F90 |
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| 38 | PUBLIC ldf_slp_grif ! routine called by step.F90 |
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| 39 | PUBLIC ldf_slp_init ! routine called by opa.F90 |
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| 40 | |
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| 41 | LOGICAL , PUBLIC, PARAMETER :: lk_ldfslp = .TRUE. !: slopes flag |
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| 42 | ! !! Madec operator |
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| 43 | REAL(wp), PUBLIC, DIMENSION(:,:,:) , ALLOCATABLE :: uslp, wslpi !: i_slope at U- and W-points |
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| 44 | REAL(wp), PUBLIC, DIMENSION(:,:,:) , ALLOCATABLE :: vslp, wslpj !: j-slope at V- and W-points |
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| 45 | ! !! Griffies operator |
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| 46 | REAL(wp), PUBLIC, DIMENSION(:,:,:) , ALLOCATABLE :: wslp2 !: wslp**2 from Griffies quarter cells |
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| 47 | REAL(wp), PUBLIC, DIMENSION(:,:,:,:,:), ALLOCATABLE :: triadi_g, triadj_g !: skew flux slopes relative to geopotentials |
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| 48 | REAL(wp), PUBLIC, DIMENSION(:,:,:,:,:), ALLOCATABLE :: triadi , triadj !: isoneutral slopes relative to model-coordinate |
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| 49 | |
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| 50 | ! !! Madec operator |
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| 51 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: omlmask ! mask of the surface mixed layer at T-pt |
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| 52 | REAL(wp), DIMENSION(:,:) , ALLOCATABLE :: uslpml, wslpiml ! i_slope at U- and W-points just below the mixed layer |
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| 53 | REAL(wp), DIMENSION(:,:) , ALLOCATABLE :: vslpml, wslpjml ! j_slope at V- and W-points just below the mixed layer |
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| 54 | |
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| 55 | REAL(wp) :: repsln = 1.e-25_wp ! tiny value used as minium of di(rho), dj(rho) and dk(rho) |
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| 56 | |
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| 57 | !! * Substitutions |
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| 58 | # include "domzgr_substitute.h90" |
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| 59 | # include "ldftra_substitute.h90" |
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| 60 | # include "ldfeiv_substitute.h90" |
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| 61 | # include "vectopt_loop_substitute.h90" |
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| 62 | !!---------------------------------------------------------------------- |
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| 63 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 64 | !! $Id$ |
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| 65 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 66 | !!---------------------------------------------------------------------- |
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| 67 | CONTAINS |
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| 68 | |
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| 69 | SUBROUTINE ldf_slp( kt, prd, pn2 ) |
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| 70 | !!---------------------------------------------------------------------- |
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| 71 | !! *** ROUTINE ldf_slp *** |
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| 72 | !! |
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| 73 | !! ** Purpose : Compute the slopes of neutral surface (slope of isopycnal |
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| 74 | !! surfaces referenced locally) (ln_traldf_iso=T). |
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| 75 | !! |
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| 76 | !! ** Method : The slope in the i-direction is computed at U- and |
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| 77 | !! W-points (uslp, wslpi) and the slope in the j-direction is |
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| 78 | !! computed at V- and W-points (vslp, wslpj). |
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| 79 | !! They are bounded by 1/100 over the whole ocean, and within the |
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| 80 | !! surface layer they are bounded by the distance to the surface |
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| 81 | !! ( slope<= depth/l where l is the length scale of horizontal |
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| 82 | !! diffusion (here, aht=2000m2/s ==> l=20km with a typical velocity |
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| 83 | !! of 10cm/s) |
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| 84 | !! A horizontal shapiro filter is applied to the slopes |
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| 85 | !! ln_sco=T, s-coordinate, add to the previously computed slopes |
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| 86 | !! the slope of the model level surface. |
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| 87 | !! macro-tasked on horizontal slab (jk-loop) (2, jpk-1) |
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| 88 | !! [slopes already set to zero at level 1, and to zero or the ocean |
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| 89 | !! bottom slope (ln_sco=T) at level jpk in inildf] |
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| 90 | !! |
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| 91 | !! ** Action : - uslp, wslpi, and vslp, wslpj, the i- and j-slopes |
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| 92 | !! of now neutral surfaces at u-, w- and v- w-points, resp. |
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| 93 | !!---------------------------------------------------------------------- |
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| 94 | USE oce , zgru => ua ! use ua as workspace |
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| 95 | USE oce , zgrv => va ! use va as workspace |
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| 96 | USE oce , zww => ta ! use ta as workspace |
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| 97 | USE oce , zwz => sa ! use sa as workspace |
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| 98 | !! |
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| 99 | INTEGER , INTENT(in) :: kt ! ocean time-step index |
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| 100 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: prd ! in situ density |
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| 101 | REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pn2 ! Brunt-Vaisala frequency (locally ref.) |
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| 102 | !! |
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| 103 | INTEGER :: ji , jj , jk ! dummy loop indices |
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| 104 | INTEGER :: ii0, ii1, iku ! temporary integer |
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| 105 | INTEGER :: ij0, ij1, ikv ! temporary integer |
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| 106 | REAL(wp) :: zeps, zm1_g, zm1_2g, z1_16 ! local scalars |
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| 107 | REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - |
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| 108 | REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - |
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| 109 | REAL(wp) :: zck, zfk, zbw ! - - |
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| 110 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdzr ! 3D workspace |
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| 111 | !!---------------------------------------------------------------------- |
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| 112 | |
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| 113 | zeps = 1.e-20_wp !== Local constant initialization ==! |
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| 114 | z1_16 = 1.0_wp / 16._wp |
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| 115 | zm1_g = -1.0_wp / grav |
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| 116 | zm1_2g = -0.5_wp / grav |
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| 117 | ! |
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| 118 | zww(:,:,:) = 0._wp |
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| 119 | zwz(:,:,:) = 0._wp |
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| 120 | ! |
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| 121 | DO jk = 1, jpk !== i- & j-gradient of density ==! |
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| 122 | DO jj = 1, jpjm1 |
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| 123 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 124 | zgru(ji,jj,jk) = umask(ji,jj,jk) * ( prd(ji+1,jj ,jk) - prd(ji,jj,jk) ) |
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| 125 | zgrv(ji,jj,jk) = vmask(ji,jj,jk) * ( prd(ji ,jj+1,jk) - prd(ji,jj,jk) ) |
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| 126 | END DO |
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| 127 | END DO |
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| 128 | END DO |
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| 129 | IF( ln_zps ) THEN ! partial steps correction at the bottom ocean level |
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| 130 | # if defined key_vectopt_loop |
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| 131 | DO jj = 1, 1 |
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| 132 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) |
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| 133 | # else |
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| 134 | DO jj = 1, jpjm1 |
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| 135 | DO ji = 1, jpim1 |
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| 136 | # endif |
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| 137 | zgru(ji,jj,mbku(ji,jj)) = gru(ji,jj) |
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| 138 | zgrv(ji,jj,mbkv(ji,jj)) = grv(ji,jj) |
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| 139 | END DO |
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| 140 | END DO |
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| 141 | ENDIF |
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| 142 | ! |
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| 143 | zdzr(:,:,1) = 0._wp !== Local vertical density gradient at T-point == ! (evaluated from N^2) |
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| 144 | DO jk = 2, jpkm1 |
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| 145 | ! ! zdzr = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point |
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| 146 | ! ! trick: tmask(ik ) = 0 => all pn2 = 0 => zdzr = 0 |
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| 147 | ! ! else tmask(ik+1) = 0 => pn2(ik+1) = 0 => zdzr divides by 1 |
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| 148 | ! ! umask(ik+1) /= 0 => all pn2 /= 0 => zdzr divides by 2 |
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| 149 | ! ! NB: 1/(tmask+1) = (1-.5*tmask) substitute a / by a * ==> faster |
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| 150 | zdzr(:,:,jk) = zm1_g * ( prd(:,:,jk) + 1._wp ) & |
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| 151 | & * ( pn2(:,:,jk) + pn2(:,:,jk+1) ) * ( 1._wp - 0.5_wp * tmask(:,:,jk+1) ) |
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| 152 | END DO |
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| 153 | ! |
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| 154 | ! !== Slopes just below the mixed layer ==! |
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| 155 | CALL ldf_slp_mxl( prd, pn2, zgru, zgrv, zdzr ) ! output: uslpml, vslpml, wslpiml, wslpjml |
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| 156 | |
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| 157 | |
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| 158 | ! I. slopes at u and v point | uslp = d/di( prd ) / d/dz( prd ) |
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| 159 | ! =========================== | vslp = d/dj( prd ) / d/dz( prd ) |
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| 160 | ! |
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| 161 | DO jk = 2, jpkm1 !* Slopes at u and v points |
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| 162 | DO jj = 2, jpjm1 |
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| 163 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 164 | ! ! horizontal and vertical density gradient at u- and v-points |
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| 165 | zau = zgru(ji,jj,jk) / e1u(ji,jj) |
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| 166 | zav = zgrv(ji,jj,jk) / e2v(ji,jj) |
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| 167 | zbu = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji+1,jj ,jk) ) |
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| 168 | zbv = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji ,jj+1,jk) ) |
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| 169 | ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 |
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| 170 | ! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) |
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| 171 | zbu = MIN( zbu, -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,jk)* ABS( zau ) ) |
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| 172 | zbv = MIN( zbv, -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,jk)* ABS( zav ) ) |
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| 173 | ! ! uslp and vslp output in zwz and zww, resp. |
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| 174 | zfi = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj,jk) ) |
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| 175 | zfj = MAX( omlmask(ji,jj,jk), omlmask(ji,jj+1,jk) ) |
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| 176 | zwz(ji,jj,jk) = ( ( 1. - zfi) * zau / ( zbu - zeps ) & |
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| 177 | & + zfi * uslpml(ji,jj) & |
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| 178 | & * 0.5_wp * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk)-fse3u(ji,jj,1) ) & |
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| 179 | & / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 5._wp ) ) * umask(ji,jj,jk) |
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| 180 | zww(ji,jj,jk) = ( ( 1. - zfj) * zav / ( zbv - zeps ) & |
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| 181 | & + zfj * vslpml(ji,jj) & |
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| 182 | & * 0.5_wp * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk)-fse3v(ji,jj,1) ) & |
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| 183 | & / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 5. ) ) * vmask(ji,jj,jk) |
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| 184 | !!gm modif to suppress omlmask.... (as in Griffies case) |
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| 185 | ! ! ! jk must be >= ML level for zf=1. otherwise zf=0. |
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| 186 | ! zfi = REAL( 1 - 1/(1 + jk / MAX( nmln(ji+1,jj), nmln(ji,jj) ) ), wp ) |
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| 187 | ! zfj = REAL( 1 - 1/(1 + jk / MAX( nmln(ji,jj+1), nmln(ji,jj) ) ), wp ) |
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| 188 | ! zci = 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) ) |
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| 189 | ! zcj = 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 10. ) ) |
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| 190 | ! zwz(ji,jj,jk) = ( zfi * zai / ( zbi - zeps ) + ( 1._wp - zfi ) * wslpiml(ji,jj) * zci ) * tmask(ji,jj,jk) |
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| 191 | ! zww(ji,jj,jk) = ( zfj * zaj / ( zbj - zeps ) + ( 1._wp - zfj ) * wslpjml(ji,jj) * zcj ) * tmask(ji,jj,jk) |
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| 192 | !!gm end modif |
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| 193 | END DO |
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| 194 | END DO |
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| 195 | END DO |
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| 196 | CALL lbc_lnk( zwz, 'U', -1. ) ; CALL lbc_lnk( zww, 'V', -1. ) ! lateral boundary conditions |
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| 197 | ! |
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| 198 | ! !* horizontal Shapiro filter |
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| 199 | DO jk = 2, jpkm1 |
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| 200 | DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only |
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| 201 | DO ji = 2, jpim1 |
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| 202 | uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & |
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| 203 | & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & |
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| 204 | & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & |
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| 205 | & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & |
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| 206 | & + 4.* zwz(ji ,jj ,jk) ) |
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| 207 | vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & |
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| 208 | & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & |
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| 209 | & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & |
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| 210 | & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & |
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| 211 | & + 4.* zww(ji,jj ,jk) ) |
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| 212 | END DO |
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| 213 | END DO |
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| 214 | DO jj = 3, jpj-2 ! other rows |
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| 215 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 216 | uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & |
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| 217 | & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & |
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| 218 | & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & |
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| 219 | & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & |
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| 220 | & + 4.* zwz(ji ,jj ,jk) ) |
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| 221 | vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & |
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| 222 | & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & |
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| 223 | & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & |
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| 224 | & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & |
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| 225 | & + 4.* zww(ji,jj ,jk) ) |
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| 226 | END DO |
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| 227 | END DO |
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| 228 | ! !* decrease along coastal boundaries |
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| 229 | DO jj = 2, jpjm1 |
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| 230 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 231 | uslp(ji,jj,jk) = uslp(ji,jj,jk) * ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk ) ) * 0.5_wp & |
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| 232 | & * ( umask(ji,jj ,jk) + umask(ji,jj ,jk+1) ) * 0.5_wp |
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| 233 | vslp(ji,jj,jk) = vslp(ji,jj,jk) * ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk ) ) * 0.5_wp & |
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| 234 | & * ( vmask(ji ,jj,jk) + vmask(ji ,jj,jk+1) ) * 0.5_wp |
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| 235 | END DO |
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| 236 | END DO |
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| 237 | END DO |
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| 238 | |
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| 239 | |
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| 240 | ! II. slopes at w point | wslpi = mij( d/di( prd ) / d/dz( prd ) |
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| 241 | ! =========================== | wslpj = mij( d/dj( prd ) / d/dz( prd ) |
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| 242 | ! |
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| 243 | DO jk = 2, jpkm1 |
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| 244 | DO jj = 2, jpjm1 |
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| 245 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 246 | ! !* Local vertical density gradient evaluated from N^2 |
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| 247 | zbw = zm1_2g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. ) |
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| 248 | ! !* Slopes at w point |
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| 249 | ! ! i- & j-gradient of density at w-points |
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| 250 | zci = MAX( umask(ji-1,jj,jk ) + umask(ji,jj,jk ) & |
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| 251 | & + umask(ji-1,jj,jk-1) + umask(ji,jj,jk-1) , zeps ) * e1t(ji,jj) |
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| 252 | zcj = MAX( vmask(ji,jj-1,jk ) + vmask(ji,jj,jk-1) & |
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| 253 | & + vmask(ji,jj-1,jk-1) + vmask(ji,jj,jk ) , zeps ) * e2t(ji,jj) |
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| 254 | zai = ( zgru (ji-1,jj,jk ) + zgru (ji,jj,jk-1) & |
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| 255 | & + zgru (ji-1,jj,jk-1) + zgru (ji,jj,jk ) ) / zci * tmask (ji,jj,jk) |
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| 256 | zaj = ( zgrv (ji,jj-1,jk ) + zgrv (ji,jj,jk-1) & |
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| 257 | & + zgrv (ji,jj-1,jk-1) + zgrv (ji,jj,jk ) ) / zcj * tmask (ji,jj,jk) |
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| 258 | ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0. |
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| 259 | ! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) |
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| 260 | zbi = MIN( zbw ,- 100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zai ) ) |
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| 261 | zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zaj ) ) |
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| 262 | ! ! wslpi and wslpj with ML flattening (output in zwz and zww, resp.) |
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| 263 | zfk = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) ! zfk=1 in the ML otherwise zfk=0 |
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| 264 | zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10._wp ) |
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| 265 | zwz(ji,jj,jk) = ( zai / ( zbi - zeps ) * ( 1._wp - zfk ) + zck * wslpiml(ji,jj) * zfk ) * tmask(ji,jj,jk) |
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| 266 | zww(ji,jj,jk) = ( zaj / ( zbj - zeps ) * ( 1._wp - zfk ) + zck * wslpjml(ji,jj) * zfk ) * tmask(ji,jj,jk) |
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| 267 | |
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| 268 | !!gm modif to suppress omlmask.... (as in Griffies operator) |
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| 269 | ! ! ! jk must be >= ML level for zfk=1. otherwise zfk=0. |
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| 270 | ! zfk = REAL( 1 - 1/(1 + jk / nmln(ji+1,jj)), wp ) |
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| 271 | ! zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. ) |
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| 272 | ! zwz(ji,jj,jk) = ( zfk * zai / ( zbi - zeps ) + ( 1._wp - zfk ) * wslpiml(ji,jj) * zck ) * tmask(ji,jj,jk) |
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| 273 | ! zww(ji,jj,jk) = ( zfk * zaj / ( zbj - zeps ) + ( 1._wp - zfk ) * wslpjml(ji,jj) * zck ) * tmask(ji,jj,jk) |
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| 274 | !!gm end modif |
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| 275 | END DO |
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| 276 | END DO |
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| 277 | END DO |
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| 278 | CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions |
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| 279 | ! |
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| 280 | ! !* horizontal Shapiro filter |
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| 281 | DO jk = 2, jpkm1 |
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| 282 | DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only |
|---|
| 283 | DO ji = 2, jpim1 |
|---|
| 284 | wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & |
|---|
| 285 | & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & |
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| 286 | & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & |
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| 287 | & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & |
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| 288 | & + 4.* zwz(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) |
|---|
| 289 | |
|---|
| 290 | wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & |
|---|
| 291 | & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & |
|---|
| 292 | & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & |
|---|
| 293 | & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & |
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| 294 | & + 4.* zww(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) |
|---|
| 295 | END DO |
|---|
| 296 | END DO |
|---|
| 297 | DO jj = 3, jpj-2 ! other rows |
|---|
| 298 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 299 | wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & |
|---|
| 300 | & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & |
|---|
| 301 | & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & |
|---|
| 302 | & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & |
|---|
| 303 | & + 4.* zwz(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) |
|---|
| 304 | |
|---|
| 305 | wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & |
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| 306 | & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & |
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| 307 | & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & |
|---|
| 308 | & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & |
|---|
| 309 | & + 4.* zww(ji ,jj ,jk) ) * z1_16 * tmask(ji,jj,jk) |
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| 310 | END DO |
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| 311 | END DO |
|---|
| 312 | ! !* decrease along coastal boundaries |
|---|
| 313 | DO jj = 2, jpjm1 |
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| 314 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 315 | zck = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) & |
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| 316 | & * ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) * 0.25 |
|---|
| 317 | wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * zck |
|---|
| 318 | wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * zck |
|---|
| 319 | END DO |
|---|
| 320 | END DO |
|---|
| 321 | END DO |
|---|
| 322 | |
|---|
| 323 | ! III. Specific grid points |
|---|
| 324 | ! =========================== |
|---|
| 325 | ! |
|---|
| 326 | IF( cp_cfg == "orca" .AND. jp_cfg == 4 ) THEN ! ORCA_R4 configuration: horizontal diffusion in specific area |
|---|
| 327 | ! ! Gibraltar Strait |
|---|
| 328 | ij0 = 50 ; ij1 = 53 |
|---|
| 329 | ii0 = 69 ; ii1 = 71 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 330 | ij0 = 51 ; ij1 = 53 |
|---|
| 331 | ii0 = 68 ; ii1 = 71 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 332 | ii0 = 69 ; ii1 = 71 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 333 | ii0 = 69 ; ii1 = 71 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 334 | ! |
|---|
| 335 | ! ! Mediterrannean Sea |
|---|
| 336 | ij0 = 49 ; ij1 = 56 |
|---|
| 337 | ii0 = 71 ; ii1 = 90 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 338 | ij0 = 50 ; ij1 = 56 |
|---|
| 339 | ii0 = 70 ; ii1 = 90 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 340 | ii0 = 71 ; ii1 = 90 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 341 | ii0 = 71 ; ii1 = 90 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp |
|---|
| 342 | ENDIF |
|---|
| 343 | |
|---|
| 344 | |
|---|
| 345 | ! IV. Lateral boundary conditions |
|---|
| 346 | ! =============================== |
|---|
| 347 | CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) |
|---|
| 348 | CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. ) |
|---|
| 349 | |
|---|
| 350 | |
|---|
| 351 | IF(ln_ctl) THEN |
|---|
| 352 | CALL prt_ctl(tab3d_1=uslp , clinfo1=' slp - u : ', tab3d_2=vslp, clinfo2=' v : ', kdim=jpk) |
|---|
| 353 | CALL prt_ctl(tab3d_1=wslpi, clinfo1=' slp - wi: ', tab3d_2=wslpj, clinfo2=' wj: ', kdim=jpk) |
|---|
| 354 | ENDIF |
|---|
| 355 | ! |
|---|
| 356 | END SUBROUTINE ldf_slp |
|---|
| 357 | |
|---|
| 358 | |
|---|
| 359 | SUBROUTINE ldf_slp_grif ( kt ) |
|---|
| 360 | !!---------------------------------------------------------------------- |
|---|
| 361 | !! *** ROUTINE ldf_slp_grif *** |
|---|
| 362 | !! |
|---|
| 363 | !! ** Purpose : Compute the squared slopes of neutral surfaces (slope |
|---|
| 364 | !! of iso-pycnal surfaces referenced locally) (ln_traldf_grif=T) |
|---|
| 365 | !! at W-points using the Griffies quarter-cells. |
|---|
| 366 | !! |
|---|
| 367 | !! ** Method : calculates alpha and beta at T-points |
|---|
| 368 | !! |
|---|
| 369 | !! ** Action : - triadi_g, triadj_g T-pts i- and j-slope triads relative to geopot. (used for eiv) |
|---|
| 370 | !! - triadi , triadj T-pts i- and j-slope triads relative to model-coordinate |
|---|
| 371 | !! - wslp2 squared slope of neutral surfaces at w-points. |
|---|
| 372 | !!---------------------------------------------------------------------- |
|---|
| 373 | USE oce, zdit => ua ! use ua as workspace |
|---|
| 374 | USE oce, zdis => va ! use va as workspace |
|---|
| 375 | USE oce, zdjt => ta ! use ta as workspace |
|---|
| 376 | USE oce, zdjs => sa ! use sa as workspace |
|---|
| 377 | !! |
|---|
| 378 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
|---|
| 379 | !! |
|---|
| 380 | INTEGER :: ji, jj, jk, jl, ip, jp, kp ! dummy loop indices |
|---|
| 381 | INTEGER :: iku, ikv ! temporary integer |
|---|
| 382 | REAL(wp) :: zfacti, zfactj, zatempw,zatempu,zatempv ! local scalars |
|---|
| 383 | REAL(wp) :: zbu, zbv, zbti, zbtj |
|---|
| 384 | REAL(wp) :: zdxrho_raw, zti_coord, zti_raw, zti_lim, zti_lim2, zti_g_raw, zti_g_lim |
|---|
| 385 | REAL(wp) :: zdyrho_raw, ztj_coord, ztj_raw, ztj_lim, ztj_lim2, ztj_g_raw, ztj_g_lim |
|---|
| 386 | REAL(wp) :: zdzrho_raw |
|---|
| 387 | REAL(wp), DIMENSION(jpi,jpj,jpk,0:1) :: zdzrho, zdyrho, zdxrho ! Horizontal and vertical density gradients |
|---|
| 388 | REAL(wp), DIMENSION(jpi,jpj,0:1,0:1) :: zti_mlb, ztj_mlb |
|---|
| 389 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdkt, zdks |
|---|
| 390 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zalpha, zbeta ! alpha, beta at T points, at depth fsgdept |
|---|
| 391 | REAL(wp), DIMENSION(jpi,jpj) :: z1_mlbw |
|---|
| 392 | !!---------------------------------------------------------------------- |
|---|
| 393 | |
|---|
| 394 | !--------------------------------! |
|---|
| 395 | ! Some preliminary calculation ! |
|---|
| 396 | !--------------------------------! |
|---|
| 397 | ! |
|---|
| 398 | CALL eos_alpbet( tsb, zalpha, zbeta ) !== before thermal and haline expension coeff. at T-points ==! |
|---|
| 399 | ! |
|---|
| 400 | DO jk = 1, jpkm1 !== before lateral T & S gradients at T-level jk ==! |
|---|
| 401 | DO jj = 1, jpjm1 |
|---|
| 402 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 403 | zdit(ji,jj,jk) = ( tb(ji+1,jj,jk) - tb(ji,jj,jk) ) * umask(ji,jj,jk) ! i-gradient of T and S at jj |
|---|
| 404 | zdis(ji,jj,jk) = ( sb(ji+1,jj,jk) - sb(ji,jj,jk) ) * umask(ji,jj,jk) |
|---|
| 405 | zdjt(ji,jj,jk) = ( tb(ji,jj+1,jk) - tb(ji,jj,jk) ) * vmask(ji,jj,jk) ! j-gradient of T and S at jj |
|---|
| 406 | zdjs(ji,jj,jk) = ( sb(ji,jj+1,jk) - sb(ji,jj,jk) ) * vmask(ji,jj,jk) |
|---|
| 407 | END DO |
|---|
| 408 | END DO |
|---|
| 409 | END DO |
|---|
| 410 | IF( ln_zps ) THEN ! partial steps: correction at the last level |
|---|
| 411 | # if defined key_vectopt_loop |
|---|
| 412 | DO jj = 1, 1 |
|---|
| 413 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) |
|---|
| 414 | # else |
|---|
| 415 | DO jj = 1, jpjm1 |
|---|
| 416 | DO ji = 1, jpim1 |
|---|
| 417 | # endif |
|---|
| 418 | zdit(ji,jj,mbku(ji,jj)) = gtsu(ji,jj,jp_tem) ! i-gradient of T and S |
|---|
| 419 | zdis(ji,jj,mbku(ji,jj)) = gtsu(ji,jj,jp_sal) |
|---|
| 420 | zdjt(ji,jj,mbkv(ji,jj)) = gtsv(ji,jj,jp_tem) ! j-gradient of T and S |
|---|
| 421 | zdjs(ji,jj,mbkv(ji,jj)) = gtsv(ji,jj,jp_sal) |
|---|
| 422 | END DO |
|---|
| 423 | END DO |
|---|
| 424 | ENDIF |
|---|
| 425 | ! |
|---|
| 426 | zdkt(:,:,1) = 0._wp !== before vertical T & S gradient at w-level ==! |
|---|
| 427 | zdks(:,:,1) = 0._wp |
|---|
| 428 | DO jk = 2, jpk |
|---|
| 429 | zdkt(:,:,jk) = ( tb(:,:,jk-1) - tb(:,:,jk) ) * tmask(:,:,jk) |
|---|
| 430 | zdks(:,:,jk) = ( sb(:,:,jk-1) - sb(:,:,jk) ) * tmask(:,:,jk) |
|---|
| 431 | END DO |
|---|
| 432 | ! |
|---|
| 433 | ! |
|---|
| 434 | DO jl = 0, 1 !== density i-, j-, and k-gradients ==! |
|---|
| 435 | ip = jl ; jp = jl ! guaranteed nonzero gradients ( absolute value larger than repsln) |
|---|
| 436 | DO jk = 1, jpkm1 ! done each pair of triad |
|---|
| 437 | DO jj = 1, jpjm1 ! NB: not masked due to the minimum value set |
|---|
| 438 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 439 | zdxrho_raw = ( zalpha(ji+ip,jj ,jk) * zdit(ji,jj,jk) + zbeta(ji+ip,jj ,jk) * zdis(ji,jj,jk) ) / e1u(ji,jj) |
|---|
| 440 | zdyrho_raw = ( zalpha(ji ,jj+jp,jk) * zdjt(ji,jj,jk) + zbeta(ji ,jj+jp,jk) * zdjs(ji,jj,jk) ) / e2v(ji,jj) |
|---|
| 441 | zdxrho(ji+ip,jj ,jk,1-ip) = SIGN( MAX( repsln, ABS( zdxrho_raw ) ), zdxrho_raw ) ! keep the sign |
|---|
| 442 | zdyrho(ji ,jj+jp,jk,1-jp) = SIGN( MAX( repsln, ABS( zdyrho_raw ) ), zdyrho_raw ) |
|---|
| 443 | END DO |
|---|
| 444 | END DO |
|---|
| 445 | END DO |
|---|
| 446 | END DO |
|---|
| 447 | DO kp = 0, 1 !== density i-, j-, and k-gradients ==! |
|---|
| 448 | DO jk = 1, jpkm1 ! done each pair of triad |
|---|
| 449 | DO jj = 1, jpj ! NB: not masked due to the minimum value set |
|---|
| 450 | DO ji = 1, jpi ! vector opt. |
|---|
| 451 | zdzrho_raw = ( zalpha(ji,jj,jk) * zdkt(ji,jj,jk+kp) + zbeta(ji,jj,jk) * zdks(ji,jj,jk+kp) ) & |
|---|
| 452 | & / fse3w(ji,jj,jk+kp) |
|---|
| 453 | zdzrho(ji ,jj ,jk, kp) = - MIN( - repsln, zdzrho_raw ) ! force zdzrho >= repsln |
|---|
| 454 | END DO |
|---|
| 455 | END DO |
|---|
| 456 | END DO |
|---|
| 457 | END DO |
|---|
| 458 | ! |
|---|
| 459 | DO jj = 1, jpj !== Reciprocal depth of the w-point below ML base ==! |
|---|
| 460 | DO ji = 1, jpi |
|---|
| 461 | jk = MIN( nmln(ji,jj), mbkt(ji,jj) ) + 1 ! MIN in case ML depth is the ocean depth |
|---|
| 462 | z1_mlbw(ji,jj) = 1._wp / fsdepw(ji,jj,jk) |
|---|
| 463 | END DO |
|---|
| 464 | END DO |
|---|
| 465 | ! |
|---|
| 466 | ! !== intialisations to zero ==! |
|---|
| 467 | ! |
|---|
| 468 | wslp2 (:,:,:) = 0._wp ! wslp2 will be cumulated 3D field set to zero |
|---|
| 469 | triadi_g(:,:,1,:,:) = 0._wp ; triadi_g(:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero |
|---|
| 470 | triadj_g(:,:,1,:,:) = 0._wp ; triadj_g(:,:,jpk,:,:) = 0._wp |
|---|
| 471 | !!gm _iso set to zero missing |
|---|
| 472 | triadi (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero |
|---|
| 473 | triadj (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp |
|---|
| 474 | |
|---|
| 475 | !-------------------------------------! |
|---|
| 476 | ! Triads just below the Mixed Layer ! |
|---|
| 477 | !-------------------------------------! |
|---|
| 478 | ! |
|---|
| 479 | DO jl = 0, 1 ! calculate slope of the 4 triads immediately ONE level below mixed-layer base |
|---|
| 480 | DO kp = 0, 1 ! with only the slope-max limit and MASKED |
|---|
| 481 | DO jj = 1, jpjm1 |
|---|
| 482 | DO ji = 1, fs_jpim1 |
|---|
| 483 | ip = jl ; jp = jl |
|---|
| 484 | jk = MIN( nmln(ji+ip,jj) , mbkt(ji+ip,jj) ) + 1 ! ML level+1 (MIN in case ML depth is the ocean depth) |
|---|
| 485 | zti_g_raw = ( zdxrho(ji+ip,jj,jk-kp,1-ip) / zdzrho(ji+ip,jj,jk-kp,kp) & |
|---|
| 486 | & + ( fsdept(ji+1,jj,jk-kp) - fsdept(ji,jj,jk-kp) ) / e1u(ji,jj) ) * umask(ji,jj,jk) |
|---|
| 487 | jk = MIN( nmln(ji,jj+jp) , mbkt(ji,jj+jp) ) + 1 |
|---|
| 488 | ztj_g_raw = ( zdyrho(ji,jj+jp,jk-kp,1-jp) / zdzrho(ji,jj+jp,jk-kp,kp) & |
|---|
| 489 | & + ( fsdept(ji,jj+1,jk-kp) - fsdept(ji,jj,jk-kp) ) / e2v(ji,jj) ) * vmask(ji,jj,jk) |
|---|
| 490 | zti_mlb(ji+ip,jj ,1-ip,kp) = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw ) |
|---|
| 491 | ztj_mlb(ji ,jj+jp,1-jp,kp) = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw ) |
|---|
| 492 | END DO |
|---|
| 493 | END DO |
|---|
| 494 | END DO |
|---|
| 495 | END DO |
|---|
| 496 | |
|---|
| 497 | !-------------------------------------! |
|---|
| 498 | ! Triads with surface limits ! |
|---|
| 499 | !-------------------------------------! |
|---|
| 500 | ! |
|---|
| 501 | DO kp = 0, 1 ! k-index of triads |
|---|
| 502 | DO jl = 0, 1 |
|---|
| 503 | ip = jl ; jp = jl ! i- and j-indices of triads (i-k and j-k planes) |
|---|
| 504 | DO jk = 1, jpkm1 |
|---|
| 505 | DO jj = 1, jpjm1 |
|---|
| 506 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 507 | ! |
|---|
| 508 | ! Calculate slope relative to geopotentials used for GM skew fluxes |
|---|
| 509 | ! For s-coordinate, subtract slope at t-points (equivalent to *adding* gradient of depth) |
|---|
| 510 | ! Limit by slope *relative to geopotentials* by rn_slpmax, and mask by psi-point |
|---|
| 511 | ! masked by umask taken at the level of dz(rho) |
|---|
| 512 | ! |
|---|
| 513 | ! raw slopes: unmasked unbounded slopes (relative to geopotential (zti_g) and model surface (zti) |
|---|
| 514 | ! |
|---|
| 515 | zti_raw = zdxrho(ji+ip,jj ,jk,1-ip) / zdzrho(ji+ip,jj ,jk,kp) ! unmasked |
|---|
| 516 | ztj_raw = zdyrho(ji ,jj+jp,jk,1-jp) / zdzrho(ji ,jj+jp,jk,kp) |
|---|
| 517 | zti_coord = ( fsdept(ji+1,jj ,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj) |
|---|
| 518 | ztj_coord = ( fsdept(ji ,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) |
|---|
| 519 | ! unmasked |
|---|
| 520 | zti_g_raw = zti_raw + zti_coord ! ref to geopot surfaces |
|---|
| 521 | ztj_g_raw = ztj_raw + ztj_coord |
|---|
| 522 | zti_g_lim = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw ) |
|---|
| 523 | ztj_g_lim = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw ) |
|---|
| 524 | ! |
|---|
| 525 | ! Below ML use limited zti_g as is |
|---|
| 526 | ! Inside ML replace by linearly reducing sx_mlb towards surface |
|---|
| 527 | ! |
|---|
| 528 | zfacti = REAL( 1 - 1/(1 + (jk+kp-1)/nmln(ji+ip,jj)), wp ) ! k index of uppermost point(s) of triad is jk+kp-1 |
|---|
| 529 | zfactj = REAL( 1 - 1/(1 + (jk+kp-1)/nmln(ji,jj+jp)), wp ) ! must be .ge. nmln(ji,jj) for zfact=1 |
|---|
| 530 | ! ! otherwise zfact=0 |
|---|
| 531 | zti_g_lim = zfacti * zti_g_lim & |
|---|
| 532 | & + ( 1._wp - zfacti ) * zti_mlb(ji+ip,jj,1-ip,kp) & |
|---|
| 533 | & * fsdepw(ji+ip,jj,jk+kp) * z1_mlbw(ji+ip,jj) |
|---|
| 534 | ztj_g_lim = zfactj * ztj_g_lim & |
|---|
| 535 | & + ( 1._wp - zfactj ) * ztj_mlb(ji,jj+jp,1-jp,kp) & |
|---|
| 536 | & * fsdepw(ji,jj+jp,jk+kp) * z1_mlbw(ji,jj+jp) ! masked |
|---|
| 537 | ! |
|---|
| 538 | triadi_g(ji+ip,jj ,jk,1-ip,kp) = zti_g_lim * umask(ji,jj,jk+kp) |
|---|
| 539 | triadj_g(ji ,jj+jp,jk,1-jp,kp) = ztj_g_lim * vmask(ji,jj,jk+kp) |
|---|
| 540 | ! |
|---|
| 541 | ! Get coefficients of isoneutral diffusion tensor |
|---|
| 542 | ! 1. Utilise gradients *relative* to s-coordinate, so add t-point slopes (*subtract* depth gradients) |
|---|
| 543 | ! 2. We require that isoneutral diffusion gives no vertical buoyancy flux |
|---|
| 544 | ! i.e. 33 term = (real slope* 31, 13 terms) |
|---|
| 545 | ! To do this, retain limited sx**2 in vertical flux, but divide by real slope for 13/31 terms |
|---|
| 546 | ! Equivalent to tapering A_iso = sx_limited**2/(real slope)**2 |
|---|
| 547 | ! |
|---|
| 548 | zti_lim = zti_g_lim - zti_coord ! remove the coordinate slope ==> relative to coordinate surfaces |
|---|
| 549 | ztj_lim = ztj_g_lim - ztj_coord |
|---|
| 550 | zti_lim2 = zti_lim * zti_lim * umask(ji,jj,jk+kp) ! square of limited slopes ! masked <<== |
|---|
| 551 | ztj_lim2 = ztj_lim * ztj_lim * vmask(ji,jj,jk+kp) |
|---|
| 552 | ! |
|---|
| 553 | zbu = e1u(ji ,jj) * e2u(ji ,jj) * fse3u(ji ,jj,jk ) |
|---|
| 554 | zbv = e1v(ji ,jj) * e2v(ji ,jj) * fse3v(ji ,jj,jk ) |
|---|
| 555 | zbti = e1t(ji+ip,jj) * e2t(ji+ip,jj) * fse3w(ji+ip,jj,jk+kp) |
|---|
| 556 | zbtj = e1t(ji,jj+jp) * e2t(ji,jj+jp) * fse3w(ji,jj+jp,jk+kp) |
|---|
| 557 | ! |
|---|
| 558 | triadi(ji+ip,jj ,jk,1-ip,kp) = zti_lim2 / zti_raw ! masked |
|---|
| 559 | triadj(ji ,jj+jp,jk,1-jp,kp) = ztj_lim2 / ztj_raw |
|---|
| 560 | ! |
|---|
| 561 | !!gm this may inhibit vectorization on Vect Computers, and even on scalar computers.... ==> to be checked |
|---|
| 562 | wslp2 (ji+ip,jj,jk+kp) = wslp2(ji+ip,jj,jk+kp) + 0.25_wp * zbu / zbti * zti_lim2 ! masked |
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| 563 | wslp2 (ji,jj+jp,jk+kp) = wslp2(ji,jj+jp,jk+kp) + 0.25_wp * zbv / zbtj * ztj_lim2 |
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| 564 | END DO |
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| 565 | END DO |
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| 566 | END DO |
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| 567 | END DO |
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| 568 | END DO |
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| 569 | ! |
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| 570 | wslp2(:,:,1) = 0._wp ! force the surface wslp to zero |
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| 571 | |
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| 572 | CALL lbc_lnk( wslp2, 'W', 1. ) ! lateral boundary confition on wslp2 only ==>>> gm : necessary ? to be checked |
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| 573 | ! |
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| 574 | END SUBROUTINE ldf_slp_grif |
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| 575 | |
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| 576 | |
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| 577 | SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr ) |
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| 578 | !!---------------------------------------------------------------------- |
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| 579 | !! *** ROUTINE ldf_slp_mxl *** |
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| 580 | !! |
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| 581 | !! ** Purpose : Compute the slopes of iso-neutral surface just below |
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| 582 | !! the mixed layer. |
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| 583 | !! |
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| 584 | !! ** Method : The slope in the i-direction is computed at u- & w-points |
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| 585 | !! (uslpml, wslpiml) and the slope in the j-direction is computed |
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| 586 | !! at v- and w-points (vslpml, wslpjml) with the same bounds as |
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| 587 | !! in ldf_slp. |
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| 588 | !! |
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| 589 | !! ** Action : uslpml, wslpiml : i- & j-slopes of neutral surfaces |
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| 590 | !! vslpml, wslpjml just below the mixed layer |
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| 591 | !! omlmask : mixed layer mask |
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| 592 | !!---------------------------------------------------------------------- |
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| 593 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: prd ! in situ density |
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| 594 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.) |
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| 595 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: p_gru, p_grv ! i- & j-gradient of density (u- & v-pts) |
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| 596 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: p_dzr ! z-gradient of density (T-point) |
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| 597 | !! |
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| 598 | INTEGER :: ji , jj , jk ! dummy loop indices |
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| 599 | INTEGER :: iku, ikv, ik, ikm1 ! local integers |
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| 600 | REAL(wp) :: zeps, zm1_g, zm1_2g ! local scalars |
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| 601 | REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - |
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| 602 | REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - |
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| 603 | REAL(wp) :: zck, zfk, zbw ! - - |
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| 604 | !!---------------------------------------------------------------------- |
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| 605 | |
|---|
| 606 | zeps = 1.e-20_wp !== Local constant initialization ==! |
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| 607 | zm1_g = -1.0_wp / grav |
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| 608 | zm1_2g = -0.5_wp / grav |
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| 609 | ! |
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| 610 | uslpml (1,:) = 0._wp ; uslpml (jpi,:) = 0._wp |
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| 611 | vslpml (1,:) = 0._wp ; vslpml (jpi,:) = 0._wp |
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| 612 | wslpiml(1,:) = 0._wp ; wslpiml(jpi,:) = 0._wp |
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| 613 | wslpjml(1,:) = 0._wp ; wslpjml(jpi,:) = 0._wp |
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| 614 | ! |
|---|
| 615 | ! !== surface mixed layer mask ! |
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| 616 | DO jk = 1, jpk ! =1 inside the mixed layer, =0 otherwise |
|---|
| 617 | # if defined key_vectopt_loop |
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| 618 | DO jj = 1, 1 |
|---|
| 619 | DO ji = 1, jpij ! vector opt. (forced unrolling) |
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| 620 | # else |
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| 621 | DO jj = 1, jpj |
|---|
| 622 | DO ji = 1, jpi |
|---|
| 623 | # endif |
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| 624 | ik = nmln(ji,jj) - 1 |
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| 625 | IF( jk <= ik ) THEN ; omlmask(ji,jj,jk) = 1._wp |
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| 626 | ELSE ; omlmask(ji,jj,jk) = 0._wp |
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| 627 | ENDIF |
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| 628 | END DO |
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| 629 | END DO |
|---|
| 630 | END DO |
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| 631 | |
|---|
| 632 | |
|---|
| 633 | ! Slopes of isopycnal surfaces just before bottom of mixed layer |
|---|
| 634 | ! -------------------------------------------------------------- |
|---|
| 635 | ! The slope are computed as in the 3D case. |
|---|
| 636 | ! A key point here is the definition of the mixed layer at u- and v-points. |
|---|
| 637 | ! It is assumed to be the maximum of the two neighbouring T-point mixed layer depth. |
|---|
| 638 | ! Otherwise, a n2 value inside the mixed layer can be involved in the computation |
|---|
| 639 | ! of the slope, resulting in a too steep diagnosed slope and thus a spurious eddy |
|---|
| 640 | ! induce velocity field near the base of the mixed layer. |
|---|
| 641 | !----------------------------------------------------------------------- |
|---|
| 642 | ! |
|---|
| 643 | # if defined key_vectopt_loop |
|---|
| 644 | DO jj = 1, 1 |
|---|
| 645 | DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) |
|---|
| 646 | # else |
|---|
| 647 | DO jj = 2, jpjm1 |
|---|
| 648 | DO ji = 2, jpim1 |
|---|
| 649 | # endif |
|---|
| 650 | ! !== Slope at u- & v-points just below the Mixed Layer ==! |
|---|
| 651 | ! |
|---|
| 652 | ! !- vertical density gradient for u- and v-slopes (from dzr at T-point) |
|---|
| 653 | iku = MIN( MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) , jpkm1 ) ! ML (MAX of T-pts, bound by jpkm1) |
|---|
| 654 | ikv = MIN( MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) , jpkm1 ) ! |
|---|
| 655 | zbu = 0.5_wp * ( p_dzr(ji,jj,iku) + p_dzr(ji+1,jj ,iku) ) |
|---|
| 656 | zbv = 0.5_wp * ( p_dzr(ji,jj,ikv) + p_dzr(ji ,jj+1,ikv) ) |
|---|
| 657 | ! !- horizontal density gradient at u- & v-points |
|---|
| 658 | zau = p_gru(ji,jj,iku) / e1u(ji,jj) |
|---|
| 659 | zav = p_grv(ji,jj,ikv) / e2v(ji,jj) |
|---|
| 660 | ! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0 |
|---|
| 661 | ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) |
|---|
| 662 | zbu = MIN( zbu , -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,ik)* ABS( zau ) ) |
|---|
| 663 | zbv = MIN( zbv , -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,ik)* ABS( zav ) ) |
|---|
| 664 | ! !- Slope at u- & v-points (uslpml, vslpml) |
|---|
| 665 | uslpml(ji,jj) = zau / ( zbu - zeps ) * umask(ji,jj,ik) |
|---|
| 666 | vslpml(ji,jj) = zav / ( zbv - zeps ) * vmask(ji,jj,ik) |
|---|
| 667 | ! |
|---|
| 668 | ! !== i- & j-slopes at w-points just below the Mixed Layer ==! |
|---|
| 669 | ! |
|---|
| 670 | ik = MIN( nmln(ji,jj) + 1, jpk ) |
|---|
| 671 | ikm1 = MAX( 1, ik-1 ) |
|---|
| 672 | ! !- vertical density gradient for w-slope (from N^2) |
|---|
| 673 | zbw = zm1_2g * pn2 (ji,jj,ik) * ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. ) |
|---|
| 674 | ! !- horizontal density i- & j-gradient at w-points |
|---|
| 675 | zci = MAX( umask(ji-1,jj,ik ) + umask(ji,jj,ik ) & |
|---|
| 676 | & + umask(ji-1,jj,ikm1) + umask(ji,jj,ikm1) , zeps ) * e1t(ji,jj) |
|---|
| 677 | zcj = MAX( vmask(ji,jj-1,ik ) + vmask(ji,jj,ik ) & |
|---|
| 678 | & + vmask(ji,jj-1,ikm1) + vmask(ji,jj,ikm1) , zeps ) * e2t(ji,jj) |
|---|
| 679 | zai = ( p_gru(ji-1,jj,ik ) + p_gru(ji,jj,ik) & |
|---|
| 680 | & + p_gru(ji-1,jj,ikm1) + p_gru(ji,jj,ikm1 ) ) / zci * tmask(ji,jj,ik) |
|---|
| 681 | zaj = ( p_grv(ji,jj-1,ik ) + p_grv(ji,jj,ik ) & |
|---|
| 682 | & + p_grv(ji,jj-1,ikm1) + p_grv(ji,jj,ikm1) ) / zcj * tmask(ji,jj,ik) |
|---|
| 683 | ! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0. |
|---|
| 684 | ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) |
|---|
| 685 | zbi = MIN( zbw , -100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zai ) ) |
|---|
| 686 | zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zaj ) ) |
|---|
| 687 | ! !- i- & j-slope at w-points (wslpiml, wslpjml) |
|---|
| 688 | wslpiml(ji,jj) = zai / ( zbi - zeps ) * tmask (ji,jj,ik) |
|---|
| 689 | wslpjml(ji,jj) = zaj / ( zbj - zeps ) * tmask (ji,jj,ik) |
|---|
| 690 | END DO |
|---|
| 691 | END DO |
|---|
| 692 | !!gm this lbc_lnk should be useless.... |
|---|
| 693 | CALL lbc_lnk( uslpml , 'U', -1. ) ; CALL lbc_lnk( vslpml , 'V', -1. ) ! lateral boundary cond. (sign change) |
|---|
| 694 | CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions |
|---|
| 695 | ! |
|---|
| 696 | END SUBROUTINE ldf_slp_mxl |
|---|
| 697 | |
|---|
| 698 | |
|---|
| 699 | SUBROUTINE ldf_slp_init |
|---|
| 700 | !!---------------------------------------------------------------------- |
|---|
| 701 | !! *** ROUTINE ldf_slp_init *** |
|---|
| 702 | !! |
|---|
| 703 | !! ** Purpose : Initialization for the isopycnal slopes computation |
|---|
| 704 | !! |
|---|
| 705 | !! ** Method : read the nammbf namelist and check the parameter |
|---|
| 706 | !! values called by tra_dmp at the first timestep (nit000) |
|---|
| 707 | !!---------------------------------------------------------------------- |
|---|
| 708 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 709 | INTEGER :: ierr ! local integer |
|---|
| 710 | !!---------------------------------------------------------------------- |
|---|
| 711 | |
|---|
| 712 | IF(lwp) THEN |
|---|
| 713 | WRITE(numout,*) |
|---|
| 714 | WRITE(numout,*) 'ldf_slp_init : direction of lateral mixing' |
|---|
| 715 | WRITE(numout,*) '~~~~~~~~~~~~' |
|---|
| 716 | ENDIF |
|---|
| 717 | |
|---|
| 718 | IF( ln_traldf_grif ) THEN ! Griffies operator : triad of slopes |
|---|
| 719 | ALLOCATE( triadi_g(jpi,jpj,jpk,0:1,0:1) , triadj_g(jpi,jpj,jpk,0:1,0:1) , wslp2(jpi,jpj,jpk) , STAT=ierr ) |
|---|
| 720 | ALLOCATE( triadi (jpi,jpj,jpk,0:1,0:1) , triadj (jpi,jpj,jpk,0:1,0:1) , STAT=ierr ) |
|---|
| 721 | IF( ierr > 0 ) THEN |
|---|
| 722 | CALL ctl_stop( 'ldf_slp_init : unable to allocate Griffies operator slope ' ) ; RETURN |
|---|
| 723 | ENDIF |
|---|
| 724 | ! |
|---|
| 725 | IF( ln_dynldf_iso ) CALL ctl_stop( 'ldf_slp_init: Griffies operator on momentum not supported' ) |
|---|
| 726 | ! |
|---|
| 727 | IF( ( ln_traldf_hor .AND. ln_dynldf_hor ) .AND. ln_sco ) & |
|---|
| 728 | & CALL ctl_stop( 'ldf_slp_init: horizontal Griffies operator ', & |
|---|
| 729 | & 'in s-coordinate not supported' ) |
|---|
| 730 | ! |
|---|
| 731 | ELSE ! Madec operator : slopes at u-, v-, and w-points |
|---|
| 732 | ALLOCATE( uslp(jpi,jpj,jpk) , vslp(jpi,jpj,jpk) , wslpi(jpi,jpj,jpk) , wslpj(jpi,jpj,jpk) , & |
|---|
| 733 | & omlmask(jpi,jpj,jpk) , uslpml(jpi,jpj) , vslpml(jpi,jpj) , wslpiml(jpi,jpj) , wslpjml(jpi,jpj) , STAT=ierr ) |
|---|
| 734 | IF( ierr > 0 ) THEN |
|---|
| 735 | CALL ctl_stop( 'ldf_slp_init : unable to allocate Madec operator slope ' ) ; RETURN |
|---|
| 736 | ENDIF |
|---|
| 737 | |
|---|
| 738 | ! Direction of lateral diffusion (tracers and/or momentum) |
|---|
| 739 | ! ------------------------------ |
|---|
| 740 | uslp (:,:,:) = 0._wp ; uslpml (:,:) = 0._wp ! set the slope to zero (even in s-coordinates) |
|---|
| 741 | vslp (:,:,:) = 0._wp ; vslpml (:,:) = 0._wp |
|---|
| 742 | wslpi(:,:,:) = 0._wp ; wslpiml(:,:) = 0._wp |
|---|
| 743 | wslpj(:,:,:) = 0._wp ; wslpjml(:,:) = 0._wp |
|---|
| 744 | |
|---|
| 745 | !!gm I no longer understand this..... |
|---|
| 746 | IF( (ln_traldf_hor .OR. ln_dynldf_hor) .AND. .NOT. (lk_vvl .AND. ln_rstart) ) THEN |
|---|
| 747 | IF(lwp) THEN |
|---|
| 748 | WRITE(numout,*) ' Horizontal mixing in s-coordinate: slope = slope of s-surfaces' |
|---|
| 749 | ENDIF |
|---|
| 750 | |
|---|
| 751 | ! geopotential diffusion in s-coordinates on tracers and/or momentum |
|---|
| 752 | ! The slopes of s-surfaces are computed once (no call to ldfslp in step) |
|---|
| 753 | ! The slopes for momentum diffusion are i- or j- averaged of those on tracers |
|---|
| 754 | |
|---|
| 755 | ! set the slope of diffusion to the slope of s-surfaces |
|---|
| 756 | ! ( c a u t i o n : minus sign as fsdep has positive value ) |
|---|
| 757 | DO jk = 1, jpk |
|---|
| 758 | DO jj = 2, jpjm1 |
|---|
| 759 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 760 | uslp (ji,jj,jk) = -1./e1u(ji,jj) * ( fsdept(ji+1,jj,jk) - fsdept(ji ,jj ,jk) ) * umask(ji,jj,jk) |
|---|
| 761 | vslp (ji,jj,jk) = -1./e2v(ji,jj) * ( fsdept(ji,jj+1,jk) - fsdept(ji ,jj ,jk) ) * vmask(ji,jj,jk) |
|---|
| 762 | wslpi(ji,jj,jk) = -1./e1t(ji,jj) * ( fsdepw(ji+1,jj,jk) - fsdepw(ji-1,jj,jk) ) * tmask(ji,jj,jk) * 0.5 |
|---|
| 763 | wslpj(ji,jj,jk) = -1./e2t(ji,jj) * ( fsdepw(ji,jj+1,jk) - fsdepw(ji,jj-1,jk) ) * tmask(ji,jj,jk) * 0.5 |
|---|
| 764 | END DO |
|---|
| 765 | END DO |
|---|
| 766 | END DO |
|---|
| 767 | ! Lateral boundary conditions on the slopes |
|---|
| 768 | CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) |
|---|
| 769 | CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. ) |
|---|
| 770 | ENDIF |
|---|
| 771 | ENDIF ! |
|---|
| 772 | END SUBROUTINE ldf_slp_init |
|---|
| 773 | |
|---|
| 774 | #else |
|---|
| 775 | !!------------------------------------------------------------------------ |
|---|
| 776 | !! Dummy module : NO Rotation of lateral mixing tensor |
|---|
| 777 | !!------------------------------------------------------------------------ |
|---|
| 778 | LOGICAL, PUBLIC, PARAMETER :: lk_ldfslp = .FALSE. !: slopes flag |
|---|
| 779 | CONTAINS |
|---|
| 780 | SUBROUTINE ldf_slp( kt, prd, pn2 ) ! Dummy routine |
|---|
| 781 | INTEGER, INTENT(in) :: kt |
|---|
| 782 | REAL, DIMENSION(:,:,:), INTENT(in) :: prd, pn2 |
|---|
| 783 | WRITE(*,*) 'ldf_slp: You should not have seen this print! error?', kt, prd(1,1,1), pn2(1,1,1) |
|---|
| 784 | END SUBROUTINE ldf_slp |
|---|
| 785 | SUBROUTINE ldf_slp_init ! Dummy routine |
|---|
| 786 | END SUBROUTINE ldf_slp_init |
|---|
| 787 | #endif |
|---|
| 788 | |
|---|
| 789 | !!====================================================================== |
|---|
| 790 | END MODULE ldfslp |
|---|
