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ldfslp.F90 in trunk/NEMOGCM/NEMO/OPA_SRC/LDF – NEMO

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source: trunk/NEMOGCM/NEMO/OPA_SRC/LDF/ldfslp.F90 @ 3393

Last change on this file since 3393 was 3294, checked in by rblod, 12 years ago
Merge of 3.4beta into the trunk
Property svn:keywords set to `Id`
File size: 48.8 KB

Rev	Line
[3]	1	MODULE ldfslp
	2	!!======================================================================
	3	!! * MODULE ldfslp *
	4	!! Ocean physics: slopes of neutral surfaces
	5	!!======================================================================
[1515]	6	!! History : OPA ! 1994-12 (G. Madec, M. Imbard) Original code
	7	!! 8.0 ! 1997-06 (G. Madec) optimization, lbc
	8	!! 8.1 ! 1999-10 (A. Jouzeau) NEW profile in the mixed layer
[2528]	9	!! NEMO 1.0 ! 2002-10 (G. Madec) Free form, F90
	10	!! - ! 2005-10 (A. Beckmann) correction for s-coordinates
	11	!! 3.3 ! 2010-10 (G. Nurser, C. Harris, G. Madec) add Griffies operator
	12	!! - ! 2010-11 (F. Dupond, G. Madec) bug correction in slopes just below the ML
[1515]	13	!!----------------------------------------------------------------------
[3]	14	#if defined key_ldfslp \|\| defined key_esopa
	15	!!----------------------------------------------------------------------
	16	!! 'key_ldfslp' Rotation of lateral mixing tensor
	17	!!----------------------------------------------------------------------
[2528]	18	!! ldf_slp_grif : calculates the triads of isoneutral slopes (Griffies operator)
	19	!! ldf_slp : calculates the slopes of neutral surface (Madec operator)
	20	!! ldf_slp_mxl : calculates the slopes at the base of the mixed layer (Madec operator)
[3]	21	!! ldf_slp_init : initialization of the slopes computation
	22	!!----------------------------------------------------------------------
	23	USE oce ! ocean dynamics and tracers
	24	USE dom_oce ! ocean space and time domain
[2528]	25	USE ldftra_oce ! lateral diffusion: traceur
	26	USE ldfdyn_oce ! lateral diffusion: dynamics
[3]	27	USE phycst ! physical constants
	28	USE zdfmxl ! mixed layer depth
[2528]	29	USE eosbn2 ! equation of states
[3]	30	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
	31	USE in_out_manager ! I/O manager
[258]	32	USE prtctl ! Print control
[3294]	33	USE wrk_nemo ! work arrays
	34	USE timing ! Timing
[3]	35
	36	IMPLICIT NONE
	37	PRIVATE
	38
[2528]	39	PUBLIC ldf_slp ! routine called by step.F90
	40	PUBLIC ldf_slp_grif ! routine called by step.F90
	41	PUBLIC ldf_slp_init ! routine called by opa.F90
[3]	42
[2528]	43	LOGICAL , PUBLIC, PARAMETER :: lk_ldfslp = .TRUE. !: slopes flag
	44	! !! Madec operator
[2715]	45	! Arrays allocated in ldf_slp_init() routine once we know whether we're using the Griffies or Madec operator
	46	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: uslp, wslpi !: i_slope at U- and W-points
	47	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: vslp, wslpj !: j-slope at V- and W-points
	48	! !! Griffies operator
	49	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: wslp2 !: wslp**2 from Griffies quarter cells
[3294]	50	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:,:) :: triadi_g, triadj_g !: skew flux slopes relative to geopotentials
[2715]	51	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:,:) :: triadi , triadj !: isoneutral slopes relative to model-coordinate
[3]	52
[2528]	53	! !! Madec operator
[2715]	54	! Arrays allocated in ldf_slp_init() routine once we know whether we're using the Griffies or Madec operator
	55	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: omlmask ! mask of the surface mixed layer at T-pt
	56	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: uslpml, wslpiml ! i_slope at U- and W-points just below the mixed layer
	57	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: vslpml, wslpjml ! j_slope at V- and W-points just below the mixed layer
[2528]	58
	59	REAL(wp) :: repsln = 1.e-25_wp ! tiny value used as minium of di(rho), dj(rho) and dk(rho)
	60
[3]	61	!! * Substitutions
	62	# include "domzgr_substitute.h90"
[2528]	63	# include "ldftra_substitute.h90"
	64	# include "ldfeiv_substitute.h90"
[3]	65	# include "vectopt_loop_substitute.h90"
	66	!!----------------------------------------------------------------------
[2715]	67	!! NEMO/OPA 4.0 , NEMO Consortium (2011)
[1156]	68	!! $Id$
[2528]	69	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	70	!!----------------------------------------------------------------------
	71	CONTAINS
	72
	73	SUBROUTINE ldf_slp( kt, prd, pn2 )
	74	!!----------------------------------------------------------------------
	75	!! * ROUTINE ldf_slp *
[3294]	76	!!
[1515]	77	!! ** Purpose : Compute the slopes of neutral surface (slope of isopycnal
[2528]	78	!! surfaces referenced locally) (ln_traldf_iso=T).
[3294]	79	!!
	80	!! ** Method : The slope in the i-direction is computed at U- and
	81	!! W-points (uslp, wslpi) and the slope in the j-direction is
[3]	82	!! computed at V- and W-points (vslp, wslpj).
	83	!! They are bounded by 1/100 over the whole ocean, and within the
	84	!! surface layer they are bounded by the distance to the surface
	85	!! ( slope<= depth/l where l is the length scale of horizontal
	86	!! diffusion (here, aht=2000m2/s ==> l=20km with a typical velocity
	87	!! of 10cm/s)
	88	!! A horizontal shapiro filter is applied to the slopes
[461]	89	!! ln_sco=T, s-coordinate, add to the previously computed slopes
[3]	90	!! the slope of the model level surface.
	91	!! macro-tasked on horizontal slab (jk-loop) (2, jpk-1)
	92	!! [slopes already set to zero at level 1, and to zero or the ocean
[461]	93	!! bottom slope (ln_sco=T) at level jpk in inildf]
[3]	94	!!
[3294]	95	!! ** Action : - uslp, wslpi, and vslp, wslpj, the i- and j-slopes
[3]	96	!! of now neutral surfaces at u-, w- and v- w-points, resp.
[1515]	97	!!----------------------------------------------------------------------
[2715]	98	INTEGER , INTENT(in) :: kt ! ocean time-step index
	99	REAL(wp), INTENT(in), DIMENSION(:,:,:) :: prd ! in situ density
	100	REAL(wp), INTENT(in), DIMENSION(:,:,:) :: pn2 ! Brunt-Vaisala frequency (locally ref.)
[1515]	101	!!
	102	INTEGER :: ji , jj , jk ! dummy loop indices
	103	INTEGER :: ii0, ii1, iku ! temporary integer
	104	INTEGER :: ij0, ij1, ikv ! temporary integer
[3294]	105	REAL(wp) :: zeps, zm1_g, zm1_2g, z1_16, zcofw ! local scalars
[2528]	106	REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - -
	107	REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - -
	108	REAL(wp) :: zck, zfk, zbw ! - -
[3294]	109	REAL(wp), POINTER, DIMENSION(:,:,:) :: zwz, zww
	110	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdzr
	111	REAL(wp), POINTER, DIMENSION(:,:,:) :: zgru, zgrv
[3]	112	!!----------------------------------------------------------------------
[3294]	113	!
	114	IF( nn_timing == 1 ) CALL timing_start('ldf_slp')
	115	!
	116	CALL wrk_alloc( jpi,jpj,jpk, zwz, zww, zdzr, zgru, zgrv )
[2715]	117
[2528]	118	zeps = 1.e-20_wp !== Local constant initialization ==!
	119	z1_16 = 1.0_wp / 16._wp
	120	zm1_g = -1.0_wp / grav
	121	zm1_2g = -0.5_wp / grav
[1515]	122	!
[2528]	123	zww(:,:,:) = 0._wp
	124	zwz(:,:,:) = 0._wp
	125	!
	126	DO jk = 1, jpk !== i- & j-gradient of density ==!
[3]	127	DO jj = 1, jpjm1
	128	DO ji = 1, fs_jpim1 ! vector opt.
[3294]	129	zgru(ji,jj,jk) = umask(ji,jj,jk) * ( prd(ji+1,jj ,jk) - prd(ji,jj,jk) )
	130	zgrv(ji,jj,jk) = vmask(ji,jj,jk) * ( prd(ji ,jj+1,jk) - prd(ji,jj,jk) )
[3]	131	END DO
	132	END DO
	133	END DO
[1515]	134	IF( ln_zps ) THEN ! partial steps correction at the bottom ocean level
[3294]	135	# if defined key_vectopt_loop
[1515]	136	DO jj = 1, 1
	137	DO ji = 1, jpij-jpi ! vector opt. (forced unrolling)
[3]	138	# else
[461]	139	DO jj = 1, jpjm1
	140	DO ji = 1, jpim1
[3]	141	# endif
[3294]	142	zgru(ji,jj,mbku(ji,jj)) = gru(ji,jj)
	143	zgrv(ji,jj,mbkv(ji,jj)) = grv(ji,jj)
[461]	144	END DO
[3]	145	END DO
[461]	146	ENDIF
[2528]	147	!
	148	zdzr(:,:,1) = 0._wp !== Local vertical density gradient at T-point == ! (evaluated from N^2)
	149	DO jk = 2, jpkm1
	150	! ! zdzr = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point
	151	! ! trick: tmask(ik ) = 0 => all pn2 = 0 => zdzr = 0
	152	! ! else tmask(ik+1) = 0 => pn2(ik+1) = 0 => zdzr divides by 1
	153	! ! umask(ik+1) /= 0 => all pn2 /= 0 => zdzr divides by 2
	154	! ! NB: 1/(tmask+1) = (1-.5tmask) substitute a / by a ==> faster
	155	zdzr(:,:,jk) = zm1_g * ( prd(:,:,jk) + 1._wp ) &
	156	& * ( pn2(:,:,jk) + pn2(:,:,jk+1) ) * ( 1._wp - 0.5_wp * tmask(:,:,jk+1) )
[2389]	157	END DO
[2528]	158	!
	159	! !== Slopes just below the mixed layer ==!
	160	CALL ldf_slp_mxl( prd, pn2, zgru, zgrv, zdzr ) ! output: uslpml, vslpml, wslpiml, wslpjml
[2389]	161
[3294]	162
[1515]	163	! I. slopes at u and v point \| uslp = d/di( prd ) / d/dz( prd )
	164	! =========================== \| vslp = d/dj( prd ) / d/dz( prd )
[3294]	165	!
[1515]	166	DO jk = 2, jpkm1 !* Slopes at u and v points
[3]	167	DO jj = 2, jpjm1
	168	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	169	! ! horizontal and vertical density gradient at u- and v-points
	170	zau = zgru(ji,jj,jk) / e1u(ji,jj)
	171	zav = zgrv(ji,jj,jk) / e2v(ji,jj)
	172	zbu = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji+1,jj ,jk) )
	173	zbv = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji ,jj+1,jk) )
	174	! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0
	175	! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
	176	zbu = MIN( zbu, -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,jk)* ABS( zau ) )
	177	zbv = MIN( zbv, -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,jk)* ABS( zav ) )
	178	! ! uslp and vslp output in zwz and zww, resp.
	179	zfi = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj,jk) )
	180	zfj = MAX( omlmask(ji,jj,jk), omlmask(ji,jj+1,jk) )
	181	zwz(ji,jj,jk) = ( ( 1. - zfi) * zau / ( zbu - zeps ) &
	182	& + zfi * uslpml(ji,jj) &
	183	& * 0.5_wp * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk)-fse3u(ji,jj,1) ) &
	184	& / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 5._wp ) ) * umask(ji,jj,jk)
	185	zww(ji,jj,jk) = ( ( 1. - zfj) * zav / ( zbv - zeps ) &
	186	& + zfj * vslpml(ji,jj) &
	187	& * 0.5_wp * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk)-fse3v(ji,jj,1) ) &
	188	& / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 5. ) ) * vmask(ji,jj,jk)
	189	!!gm modif to suppress omlmask.... (as in Griffies case)
	190	! ! ! jk must be >= ML level for zf=1. otherwise zf=0.
	191	! zfi = REAL( 1 - 1/(1 + jk / MAX( nmln(ji+1,jj), nmln(ji,jj) ) ), wp )
	192	! zfj = REAL( 1 - 1/(1 + jk / MAX( nmln(ji,jj+1), nmln(ji,jj) ) ), wp )
	193	! zci = 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) )
	194	! zcj = 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 10. ) )
	195	! zwz(ji,jj,jk) = ( zfi * zai / ( zbi - zeps ) + ( 1._wp - zfi ) * wslpiml(ji,jj) * zci ) * tmask(ji,jj,jk)
	196	! zww(ji,jj,jk) = ( zfj * zaj / ( zbj - zeps ) + ( 1._wp - zfj ) * wslpjml(ji,jj) * zcj ) * tmask(ji,jj,jk)
	197	!!gm end modif
[3]	198	END DO
	199	END DO
[1515]	200	END DO
	201	CALL lbc_lnk( zwz, 'U', -1. ) ; CALL lbc_lnk( zww, 'V', -1. ) ! lateral boundary conditions
	202	!
[2528]	203	! !* horizontal Shapiro filter
[1515]	204	DO jk = 2, jpkm1
[2528]	205	DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only
[3294]	206	DO ji = 2, jpim1
[2528]	207	uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[1515]	208	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	209	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	210	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	211	& + 4.* zwz(ji ,jj ,jk) )
[2528]	212	vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[1515]	213	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	214	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	215	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	216	& + 4.* zww(ji,jj ,jk) )
[3]	217	END DO
	218	END DO
[1515]	219	DO jj = 3, jpj-2 ! other rows
[3]	220	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	221	uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[3]	222	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	223	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	224	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	225	& + 4.* zwz(ji ,jj ,jk) )
[2528]	226	vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[3]	227	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	228	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	229	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	230	& + 4.* zww(ji,jj ,jk) )
	231	END DO
	232	END DO
[1515]	233	! !* decrease along coastal boundaries
[3]	234	DO jj = 2, jpjm1
	235	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	236	uslp(ji,jj,jk) = uslp(ji,jj,jk) * ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk ) ) * 0.5_wp &
	237	& * ( umask(ji,jj ,jk) + umask(ji,jj ,jk+1) ) * 0.5_wp
	238	vslp(ji,jj,jk) = vslp(ji,jj,jk) * ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk ) ) * 0.5_wp &
	239	& * ( vmask(ji ,jj,jk) + vmask(ji ,jj,jk+1) ) * 0.5_wp
[3]	240	END DO
	241	END DO
[1515]	242	END DO
[3]	243
	244
[1515]	245	! II. slopes at w point \| wslpi = mij( d/di( prd ) / d/dz( prd )
	246	! =========================== \| wslpj = mij( d/dj( prd ) / d/dz( prd )
[3294]	247	!
[2528]	248	DO jk = 2, jpkm1
[3]	249	DO jj = 2, jpjm1
	250	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	251	! !* Local vertical density gradient evaluated from N^2
	252	zbw = zm1_2g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. )
	253	! !* Slopes at w point
	254	! ! i- & j-gradient of density at w-points
	255	zci = MAX( umask(ji-1,jj,jk ) + umask(ji,jj,jk ) &
	256	& + umask(ji-1,jj,jk-1) + umask(ji,jj,jk-1) , zeps ) * e1t(ji,jj)
	257	zcj = MAX( vmask(ji,jj-1,jk ) + vmask(ji,jj,jk-1) &
	258	& + vmask(ji,jj-1,jk-1) + vmask(ji,jj,jk ) , zeps ) * e2t(ji,jj)
	259	zai = ( zgru (ji-1,jj,jk ) + zgru (ji,jj,jk-1) &
	260	& + zgru (ji-1,jj,jk-1) + zgru (ji,jj,jk ) ) / zci * tmask (ji,jj,jk)
	261	zaj = ( zgrv (ji,jj-1,jk ) + zgrv (ji,jj,jk-1) &
	262	& + zgrv (ji,jj-1,jk-1) + zgrv (ji,jj,jk ) ) / zcj * tmask (ji,jj,jk)
[1515]	263	! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0.
[2528]	264	! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
	265	zbi = MIN( zbw ,- 100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zai ) )
	266	zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zaj ) )
	267	! ! wslpi and wslpj with ML flattening (output in zwz and zww, resp.)
	268	zfk = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) ! zfk=1 in the ML otherwise zfk=0
	269	zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10._wp )
	270	zwz(ji,jj,jk) = ( zai / ( zbi - zeps ) * ( 1._wp - zfk ) + zck * wslpiml(ji,jj) * zfk ) * tmask(ji,jj,jk)
	271	zww(ji,jj,jk) = ( zaj / ( zbj - zeps ) * ( 1._wp - zfk ) + zck * wslpjml(ji,jj) * zfk ) * tmask(ji,jj,jk)
	272
	273	!!gm modif to suppress omlmask.... (as in Griffies operator)
	274	! ! ! jk must be >= ML level for zfk=1. otherwise zfk=0.
	275	! zfk = REAL( 1 - 1/(1 + jk / nmln(ji+1,jj)), wp )
	276	! zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. )
	277	! zwz(ji,jj,jk) = ( zfk * zai / ( zbi - zeps ) + ( 1._wp - zfk ) * wslpiml(ji,jj) * zck ) * tmask(ji,jj,jk)
	278	! zww(ji,jj,jk) = ( zfk * zaj / ( zbj - zeps ) + ( 1._wp - zfk ) * wslpjml(ji,jj) * zck ) * tmask(ji,jj,jk)
	279	!!gm end modif
[3]	280	END DO
	281	END DO
[1515]	282	END DO
[2528]	283	CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions
[1515]	284	!
	285	! !* horizontal Shapiro filter
	286	DO jk = 2, jpkm1
[2528]	287	DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only
[3]	288	DO ji = 2, jpim1
[3294]	289	zcofw = tmask(ji,jj,jk) * z1_16
[3]	290	wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[3294]	291	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	292	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	293	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	294	& + 4.* zwz(ji ,jj ,jk) ) * zcofw
[3]	295
	296	wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[3294]	297	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	298	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	299	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	300	& + 4.* zww(ji ,jj ,jk) ) * zcofw
[3]	301	END DO
[3294]	302	END DO
[1515]	303	DO jj = 3, jpj-2 ! other rows
[3]	304	DO ji = fs_2, fs_jpim1 ! vector opt.
[3294]	305	zcofw = tmask(ji,jj,jk) * z1_16
[3]	306	wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[3294]	307	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	308	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	309	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	310	& + 4.* zwz(ji ,jj ,jk) ) * zcofw
[3]	311
	312	wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[3294]	313	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	314	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	315	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	316	& + 4.* zww(ji ,jj ,jk) ) * zcofw
[3]	317	END DO
	318	END DO
[1515]	319	! !* decrease along coastal boundaries
[3]	320	DO jj = 2, jpjm1
	321	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	322	zck = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) &
	323	& * ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) * 0.25
	324	wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * zck
	325	wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * zck
[3]	326	END DO
	327	END DO
[1515]	328	END DO
[3294]	329
	330	! III. Specific grid points
	331	! ===========================
	332	!
[1515]	333	IF( cp_cfg == "orca" .AND. jp_cfg == 4 ) THEN ! ORCA_R4 configuration: horizontal diffusion in specific area
	334	! ! Gibraltar Strait
	335	ij0 = 50 ; ij1 = 53
[2528]	336	ii0 = 69 ; ii1 = 71 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	337	ij0 = 51 ; ij1 = 53
[2528]	338	ii0 = 68 ; ii1 = 71 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	339	ii0 = 69 ; ii1 = 71 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	340	ii0 = 69 ; ii1 = 71 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	341	!
	342	! ! Mediterrannean Sea
	343	ij0 = 49 ; ij1 = 56
[2528]	344	ii0 = 71 ; ii1 = 90 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	345	ij0 = 50 ; ij1 = 56
[2528]	346	ii0 = 70 ; ii1 = 90 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	347	ii0 = 71 ; ii1 = 90 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	348	ii0 = 71 ; ii1 = 90 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	349	ENDIF
[3]	350
[3294]	351
	352	! IV. Lateral boundary conditions
[1515]	353	! ===============================
[461]	354	CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. )
	355	CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. )
[3]	356
[1515]	357
[258]	358	IF(ln_ctl) THEN
	359	CALL prt_ctl(tab3d_1=uslp , clinfo1=' slp - u : ', tab3d_2=vslp, clinfo2=' v : ', kdim=jpk)
	360	CALL prt_ctl(tab3d_1=wslpi, clinfo1=' slp - wi: ', tab3d_2=wslpj, clinfo2=' wj: ', kdim=jpk)
[49]	361	ENDIF
[1515]	362	!
[3294]	363	CALL wrk_dealloc( jpi,jpj,jpk, zwz, zww, zdzr, zgru, zgrv )
[2715]	364	!
[3294]	365	IF( nn_timing == 1 ) CALL timing_stop('ldf_slp')
	366	!
[3]	367	END SUBROUTINE ldf_slp
	368
[3294]	369
[2528]	370	SUBROUTINE ldf_slp_grif ( kt )
	371	!!----------------------------------------------------------------------
	372	!! * ROUTINE ldf_slp_grif *
	373	!!
	374	!! ** Purpose : Compute the squared slopes of neutral surfaces (slope
	375	!! of iso-pycnal surfaces referenced locally) (ln_traldf_grif=T)
[3294]	376	!! at W-points using the Griffies quarter-cells.
[2528]	377	!!
[3294]	378	!! ** Method : calculates alpha and beta at T-points
[2528]	379	!!
	380	!! ** Action : - triadi_g, triadj_g T-pts i- and j-slope triads relative to geopot. (used for eiv)
	381	!! - triadi , triadj T-pts i- and j-slope triads relative to model-coordinate
	382	!! - wslp2 squared slope of neutral surfaces at w-points.
	383	!!----------------------------------------------------------------------
[3294]	384	INTEGER, INTENT( in ) :: kt ! ocean time-step index
	385	!!
[2528]	386	INTEGER :: ji, jj, jk, jl, ip, jp, kp ! dummy loop indices
[3294]	387	INTEGER :: iku, ikv ! local integer
	388	REAL(wp) :: zfacti, zfactj ! local scalars
	389	REAL(wp) :: znot_thru_surface ! local scalars
	390	REAL(wp) :: zdit, zdis, zdjt, zdjs, zdkt, zdks, zbu, zbv, zbti, zbtj
	391	REAL(wp) :: zdxrho_raw, zti_coord, zti_raw, zti_lim, zti_g_raw, zti_g_lim
	392	REAL(wp) :: zdyrho_raw, ztj_coord, ztj_raw, ztj_lim, ztj_g_raw, ztj_g_lim
[2528]	393	REAL(wp) :: zdzrho_raw
[3294]	394	REAL(wp) :: zbeta0
	395	REAL(wp), POINTER, DIMENSION(:,:) :: z1_mlbw
	396	REAL(wp), POINTER, DIMENSION(:,:,:) :: zalbet
	397	REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zdxrho , zdyrho, zdzrho ! Horizontal and vertical density gradients
	398	REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zti_mlb, ztj_mlb ! for Griffies operator only
[2528]	399	!!----------------------------------------------------------------------
[3294]	400	!
	401	IF( nn_timing == 1 ) CALL timing_start('ldf_slp_grif')
	402	!
	403	CALL wrk_alloc( jpi,jpj, z1_mlbw )
	404	CALL wrk_alloc( jpi,jpj,jpk, zalbet )
	405	CALL wrk_alloc( jpi,jpj,jpk,2, zdxrho , zdyrho, zdzrho, klstart = 0 )
	406	CALL wrk_alloc( jpi,jpj, 2,2, zti_mlb, ztj_mlb, kkstart = 0, klstart = 0 )
	407	!
[2528]	408	!--------------------------------!
	409	! Some preliminary calculation !
	410	!--------------------------------!
	411	!
[3294]	412	CALL eos_alpbet( tsb, zalbet, zbeta0 ) !== before local thermal/haline expension ratio at T-points ==!
[2528]	413	!
[3294]	414	DO jl = 0, 1 !== unmasked before density i- j-, k-gradients ==!
	415	!
	416	ip = jl ; jp = jl ! guaranteed nonzero gradients ( absolute value larger than repsln)
	417	DO jk = 1, jpkm1 ! done each pair of triad
	418	DO jj = 1, jpjm1 ! NB: not masked ==> a minimum value is set
	419	DO ji = 1, fs_jpim1 ! vector opt.
	420	zdit = ( tsb(ji+1,jj,jk,jp_tem) - tsb(ji,jj,jk,jp_tem) ) ! i-gradient of T & S at u-point
	421	zdis = ( tsb(ji+1,jj,jk,jp_sal) - tsb(ji,jj,jk,jp_sal) )
	422	zdjt = ( tsb(ji,jj+1,jk,jp_tem) - tsb(ji,jj,jk,jp_tem) ) ! j-gradient of T & S at v-point
	423	zdjs = ( tsb(ji,jj+1,jk,jp_sal) - tsb(ji,jj,jk,jp_sal) )
	424	zdxrho_raw = ( - zalbet(ji+ip,jj ,jk) * zdit + zbeta0*zdis ) / e1u(ji,jj)
	425	zdyrho_raw = ( - zalbet(ji ,jj+jp,jk) * zdjt + zbeta0*zdjs ) / e2v(ji,jj)
	426	zdxrho(ji+ip,jj ,jk,1-ip) = SIGN( MAX( repsln, ABS( zdxrho_raw ) ), zdxrho_raw ) ! keep the sign
	427	zdyrho(ji ,jj+jp,jk,1-jp) = SIGN( MAX( repsln, ABS( zdyrho_raw ) ), zdyrho_raw )
	428	END DO
[2528]	429	END DO
	430	END DO
[3294]	431	!
	432	IF( ln_zps.and.l_grad_zps ) THEN ! partial steps: correction of i- & j-grad on bottom
[2528]	433	# if defined key_vectopt_loop
[3294]	434	DO jj = 1, 1
	435	DO ji = 1, jpij-jpi ! vector opt. (forced unrolling)
[2528]	436	# else
[3294]	437	DO jj = 1, jpjm1
	438	DO ji = 1, jpim1
[2528]	439	# endif
[3294]	440	iku = mbku(ji,jj) ; ikv = mbkv(ji,jj) ! last ocean level (u- & v-points)
	441	zdit = gtsu(ji,jj,jp_tem) ; zdjt = gtsv(ji,jj,jp_tem) ! i- & j-gradient of Temperature
	442	zdis = gtsu(ji,jj,jp_sal) ; zdjs = gtsv(ji,jj,jp_sal) ! i- & j-gradient of Salinity
	443	zdxrho_raw = ( - zalbet(ji+ip,jj ,iku) * zdit + zbeta0*zdis ) / e1u(ji,jj)
	444	zdyrho_raw = ( - zalbet(ji ,jj+jp,ikv) * zdjt + zbeta0*zdjs ) / e2v(ji,jj)
	445	zdxrho(ji+ip,jj ,iku,1-ip) = SIGN( MAX( repsln, ABS( zdxrho_raw ) ), zdxrho_raw ) ! keep the sign
	446	zdyrho(ji ,jj+jp,ikv,1-jp) = SIGN( MAX( repsln, ABS( zdyrho_raw ) ), zdyrho_raw )
[2528]	447	END DO
	448	END DO
[3294]	449	ENDIF
	450	!
[2528]	451	END DO
[3294]	452
	453	DO kp = 0, 1 !== unmasked before density i- j-, k-gradients ==!
	454	DO jk = 1, jpkm1 ! done each pair of triad
	455	DO jj = 1, jpj ! NB: not masked ==> a minimum value is set
	456	DO ji = 1, jpi ! vector opt.
	457	IF( jk+kp > 1 ) THEN ! k-gradient of T & S a jk+kp
	458	zdkt = ( tsb(ji,jj,jk+kp-1,jp_tem) - tsb(ji,jj,jk+kp,jp_tem) )
	459	zdks = ( tsb(ji,jj,jk+kp-1,jp_sal) - tsb(ji,jj,jk+kp,jp_sal) )
	460	ELSE
	461	zdkt = 0._wp ! 1st level gradient set to zero
	462	zdks = 0._wp
	463	ENDIF
	464	zdzrho_raw = ( - zalbet(ji ,jj ,jk) * zdkt + zbeta0*zdks ) / fse3w(ji,jj,jk+kp)
	465	zdzrho(ji ,jj ,jk, kp) = - MIN( - repsln, zdzrho_raw ) ! force zdzrho >= repsln
	466	END DO
[2528]	467	END DO
	468	END DO
	469	END DO
	470	!
[3294]	471	DO jj = 1, jpj !== Reciprocal depth of the w-point below ML base ==!
[2528]	472	DO ji = 1, jpi
	473	jk = MIN( nmln(ji,jj), mbkt(ji,jj) ) + 1 ! MIN in case ML depth is the ocean depth
	474	z1_mlbw(ji,jj) = 1._wp / fsdepw(ji,jj,jk)
	475	END DO
	476	END DO
	477	!
[3294]	478	! !== intialisations to zero ==!
[2528]	479	!
[3294]	480	wslp2 (:,:,:) = 0._wp ! wslp2 will be cumulated 3D field set to zero
	481	triadi_g(:,:,1,:,:) = 0._wp ; triadi_g(:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero
[2528]	482	triadj_g(:,:,1,:,:) = 0._wp ; triadj_g(:,:,jpk,:,:) = 0._wp
[3294]	483	!!gm _iso set to zero missing
	484	triadi (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero
	485	triadj (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp
	486
[2528]	487	!-------------------------------------!
	488	! Triads just below the Mixed Layer !
	489	!-------------------------------------!
	490	!
[3294]	491	DO jl = 0, 1 ! calculate slope of the 4 triads immediately ONE level below mixed-layer base
	492	DO kp = 0, 1 ! with only the slope-max limit and MASKED
[2528]	493	DO jj = 1, jpjm1
	494	DO ji = 1, fs_jpim1
	495	ip = jl ; jp = jl
	496	jk = MIN( nmln(ji+ip,jj) , mbkt(ji+ip,jj) ) + 1 ! ML level+1 (MIN in case ML depth is the ocean depth)
[3294]	497	! Add s-coordinate slope at t-points (do this by subtracting gradient of depth)
[2528]	498	zti_g_raw = ( zdxrho(ji+ip,jj,jk-kp,1-ip) / zdzrho(ji+ip,jj,jk-kp,kp) &
[3294]	499	& - ( fsdept(ji+1,jj,jk-kp) - fsdept(ji,jj,jk-kp) ) / e1u(ji,jj) ) * umask(ji,jj,jk)
[2528]	500	jk = MIN( nmln(ji,jj+jp) , mbkt(ji,jj+jp) ) + 1
	501	ztj_g_raw = ( zdyrho(ji,jj+jp,jk-kp,1-jp) / zdzrho(ji,jj+jp,jk-kp,kp) &
[3294]	502	& - ( fsdept(ji,jj+1,jk-kp) - fsdept(ji,jj,jk-kp) ) / e2v(ji,jj) ) * vmask(ji,jj,jk)
[2528]	503	zti_mlb(ji+ip,jj ,1-ip,kp) = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw )
	504	ztj_mlb(ji ,jj+jp,1-jp,kp) = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw )
	505	END DO
	506	END DO
	507	END DO
	508	END DO
	509
	510	!-------------------------------------!
	511	! Triads with surface limits !
	512	!-------------------------------------!
	513	!
[3294]	514	DO kp = 0, 1 ! k-index of triads
[2528]	515	DO jl = 0, 1
[3294]	516	ip = jl ; jp = jl ! i- and j-indices of triads (i-k and j-k planes)
[2528]	517	DO jk = 1, jpkm1
[3294]	518	! Must mask contribution to slope from dz/dx at constant s for triads jk=1,kp=0 that poke up though ocean surface
	519	znot_thru_surface = REAL( 1-1/(jk+kp), wp ) !jk+kp=1,=0.; otherwise=1.0
[2528]	520	DO jj = 1, jpjm1
[3294]	521	DO ji = 1, fs_jpim1 ! vector opt.
[2528]	522	!
	523	! Calculate slope relative to geopotentials used for GM skew fluxes
[3294]	524	! Add s-coordinate slope at t-points (do this by subtracting gradient of depth)
[2528]	525	! Limit by slope relative to geopotentials by rn_slpmax, and mask by psi-point
	526	! masked by umask taken at the level of dz(rho)
	527	!
	528	! raw slopes: unmasked unbounded slopes (relative to geopotential (zti_g) and model surface (zti)
	529	!
	530	zti_raw = zdxrho(ji+ip,jj ,jk,1-ip) / zdzrho(ji+ip,jj ,jk,kp) ! unmasked
	531	ztj_raw = zdyrho(ji ,jj+jp,jk,1-jp) / zdzrho(ji ,jj+jp,jk,kp)
[3294]	532
	533	! Must mask contribution to slope for triad jk=1,kp=0 that poke up though ocean surface
	534	zti_coord = znot_thru_surface * ( fsdept(ji+1,jj ,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj)
	535	ztj_coord = znot_thru_surface * ( fsdept(ji ,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) ! unmasked
	536	zti_g_raw = zti_raw - zti_coord ! ref to geopot surfaces
	537	ztj_g_raw = ztj_raw - ztj_coord
[2528]	538	zti_g_lim = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw )
	539	ztj_g_lim = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw )
	540	!
[3294]	541	! Below ML use limited zti_g as is & mask
	542	! Inside ML replace by linearly reducing sx_mlb towards surface & mask
[2528]	543	!
	544	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
	545	zfactj = REAL( 1 - 1/(1 + (jk+kp-1)/nmln(ji,jj+jp)), wp ) ! must be .ge. nmln(ji,jj) for zfact=1
	546	! ! otherwise zfact=0
[3294]	547	zti_g_lim = ( zfacti * zti_g_lim &
[2528]	548	& + ( 1._wp - zfacti ) * zti_mlb(ji+ip,jj,1-ip,kp) &
[3294]	549	& * fsdepw(ji+ip,jj,jk+kp) * z1_mlbw(ji+ip,jj) ) * umask(ji,jj,jk+kp)
	550	ztj_g_lim = ( zfactj * ztj_g_lim &
[2528]	551	& + ( 1._wp - zfactj ) * ztj_mlb(ji,jj+jp,1-jp,kp) &
[3294]	552	& * fsdepw(ji,jj+jp,jk+kp) * z1_mlbw(ji,jj+jp) ) * vmask(ji,jj,jk+kp)
[2528]	553	!
[3294]	554	triadi_g(ji+ip,jj ,jk,1-ip,kp) = zti_g_lim
	555	triadj_g(ji ,jj+jp,jk,1-jp,kp) = ztj_g_lim
[2528]	556	!
	557	! Get coefficients of isoneutral diffusion tensor
	558	! 1. Utilise gradients relative to s-coordinate, so add t-point slopes (subtract depth gradients)
	559	! 2. We require that isoneutral diffusion gives no vertical buoyancy flux
	560	! i.e. 33 term = (real slope* 31, 13 terms)
	561	! To do this, retain limited sx**2 in vertical flux, but divide by real slope for 13/31 terms
	562	! Equivalent to tapering A_iso = sx_limited2/(real slope)2
	563	!
[3294]	564	zti_lim = ( zti_g_lim + zti_coord ) * umask(ji,jj,jk+kp) ! remove coordinate slope => relative to coordinate surfaces
	565	ztj_lim = ( ztj_g_lim + ztj_coord ) * vmask(ji,jj,jk+kp)
[2528]	566	!
[3294]	567	IF( ln_triad_iso ) THEN
	568	zti_raw = zti_lim**2 / zti_raw
	569	ztj_raw = ztj_lim**2 / ztj_raw
	570	zti_raw = SIGN( MIN( ABS(zti_lim), ABS( zti_raw ) ), zti_raw )
	571	ztj_raw = SIGN( MIN( ABS(ztj_lim), ABS( ztj_raw ) ), ztj_raw )
	572	zti_lim = zfacti * zti_lim &
	573	& + ( 1._wp - zfacti ) * zti_raw
	574	ztj_lim = zfactj * ztj_lim &
	575	& + ( 1._wp - zfactj ) * ztj_raw
	576	ENDIF
	577	triadi(ji+ip,jj ,jk,1-ip,kp) = zti_lim
	578	triadj(ji ,jj+jp,jk,1-jp,kp) = ztj_lim
	579	!
[2528]	580	zbu = e1u(ji ,jj) * e2u(ji ,jj) * fse3u(ji ,jj,jk )
	581	zbv = e1v(ji ,jj) * e2v(ji ,jj) * fse3v(ji ,jj,jk )
	582	zbti = e1t(ji+ip,jj) * e2t(ji+ip,jj) * fse3w(ji+ip,jj,jk+kp)
	583	zbtj = e1t(ji,jj+jp) * e2t(ji,jj+jp) * fse3w(ji,jj+jp,jk+kp)
	584	!
[3294]	585	!!gm this may inhibit vectorization on Vect Computers, and even on scalar computers.... ==> to be checked
	586	wslp2 (ji+ip,jj,jk+kp) = wslp2(ji+ip,jj,jk+kp) + 0.25_wp * zbu / zbti * zti_g_lim**2 ! masked
	587	wslp2 (ji,jj+jp,jk+kp) = wslp2(ji,jj+jp,jk+kp) + 0.25_wp * zbv / zbtj * ztj_g_lim**2
[2528]	588	END DO
	589	END DO
	590	END DO
	591	END DO
	592	END DO
	593	!
	594	wslp2(:,:,1) = 0._wp ! force the surface wslp to zero
[3294]	595
[2528]	596	CALL lbc_lnk( wslp2, 'W', 1. ) ! lateral boundary confition on wslp2 only ==>>> gm : necessary ? to be checked
	597	!
[3294]	598	CALL wrk_dealloc( jpi,jpj, z1_mlbw )
	599	CALL wrk_dealloc( jpi,jpj,jpk, zalbet )
	600	CALL wrk_dealloc( jpi,jpj,jpk,2, zdxrho , zdyrho, zdzrho, klstart = 0 )
	601	CALL wrk_dealloc( jpi,jpj, 2,2, zti_mlb, ztj_mlb, kkstart = 0, klstart = 0 )
[2715]	602	!
[3294]	603	IF( nn_timing == 1 ) CALL timing_stop('ldf_slp_grif')
	604	!
[2528]	605	END SUBROUTINE ldf_slp_grif
	606
	607
	608	SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr )
[3]	609	!!----------------------------------------------------------------------
	610	!! * ROUTINE ldf_slp_mxl *
	611	!!
[3294]	612	!! ** Purpose : Compute the slopes of iso-neutral surface just below
[1515]	613	!! the mixed layer.
	614	!!
[2528]	615	!! ** Method : The slope in the i-direction is computed at u- & w-points
	616	!! (uslpml, wslpiml) and the slope in the j-direction is computed
	617	!! at v- and w-points (vslpml, wslpjml) with the same bounds as
	618	!! in ldf_slp.
[3]	619	!!
[2389]	620	!! ** Action : uslpml, wslpiml : i- & j-slopes of neutral surfaces
[3294]	621	!! vslpml, wslpjml just below the mixed layer
[2389]	622	!! omlmask : mixed layer mask
[1515]	623	!!----------------------------------------------------------------------
[2715]	624	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: prd ! in situ density
	625	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.)
	626	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: p_gru, p_grv ! i- & j-gradient of density (u- & v-pts)
	627	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: p_dzr ! z-gradient of density (T-point)
[3]	628	!!
[3294]	629	INTEGER :: ji , jj , jk ! dummy loop indices
	630	INTEGER :: iku, ikv, ik, ikm1 ! local integers
[2528]	631	REAL(wp) :: zeps, zm1_g, zm1_2g ! local scalars
	632	REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - -
	633	REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - -
	634	REAL(wp) :: zck, zfk, zbw ! - -
[3]	635	!!----------------------------------------------------------------------
[3294]	636	!
	637	IF( nn_timing == 1 ) CALL timing_start('ldf_slp_mxl')
	638	!
[2528]	639	zeps = 1.e-20_wp !== Local constant initialization ==!
	640	zm1_g = -1.0_wp / grav
	641	zm1_2g = -0.5_wp / grav
[1515]	642	!
[2528]	643	uslpml (1,:) = 0._wp ; uslpml (jpi,:) = 0._wp
	644	vslpml (1,:) = 0._wp ; vslpml (jpi,:) = 0._wp
	645	wslpiml(1,:) = 0._wp ; wslpiml(jpi,:) = 0._wp
	646	wslpjml(1,:) = 0._wp ; wslpjml(jpi,:) = 0._wp
	647	!
[3294]	648	! !== surface mixed layer mask !
	649	DO jk = 1, jpk ! =1 inside the mixed layer, =0 otherwise
[789]	650	# if defined key_vectopt_loop
[1515]	651	DO jj = 1, 1
[3294]	652	DO ji = 1, jpij ! vector opt. (forced unrolling)
[3]	653	# else
	654	DO jj = 1, jpj
	655	DO ji = 1, jpi
	656	# endif
	657	ik = nmln(ji,jj) - 1
[2528]	658	IF( jk <= ik ) THEN ; omlmask(ji,jj,jk) = 1._wp
	659	ELSE ; omlmask(ji,jj,jk) = 0._wp
[3]	660	ENDIF
	661	END DO
	662	END DO
	663	END DO
	664
	665
	666	! Slopes of isopycnal surfaces just before bottom of mixed layer
	667	! --------------------------------------------------------------
[1515]	668	! The slope are computed as in the 3D case.
	669	! A key point here is the definition of the mixed layer at u- and v-points.
	670	! It is assumed to be the maximum of the two neighbouring T-point mixed layer depth.
	671	! Otherwise, a n2 value inside the mixed layer can be involved in the computation
	672	! of the slope, resulting in a too steep diagnosed slope and thus a spurious eddy
	673	! induce velocity field near the base of the mixed layer.
[3]	674	!-----------------------------------------------------------------------
[1515]	675	!
[789]	676	# if defined key_vectopt_loop
[1515]	677	DO jj = 1, 1
	678	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
[3]	679	# else
	680	DO jj = 2, jpjm1
	681	DO ji = 2, jpim1
	682	# endif
[3294]	683	! !== Slope at u- & v-points just below the Mixed Layer ==!
[2528]	684	!
[3294]	685	! !- vertical density gradient for u- and v-slopes (from dzr at T-point)
[2528]	686	iku = MIN( MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) , jpkm1 ) ! ML (MAX of T-pts, bound by jpkm1)
[3294]	687	ikv = MIN( MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) , jpkm1 ) !
[2528]	688	zbu = 0.5_wp * ( p_dzr(ji,jj,iku) + p_dzr(ji+1,jj ,iku) )
	689	zbv = 0.5_wp * ( p_dzr(ji,jj,ikv) + p_dzr(ji ,jj+1,ikv) )
[3294]	690	! !- horizontal density gradient at u- & v-points
[2528]	691	zau = p_gru(ji,jj,iku) / e1u(ji,jj)
	692	zav = p_grv(ji,jj,ikv) / e2v(ji,jj)
[3294]	693	! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0
	694	! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
[2772]	695	zbu = MIN( zbu , -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,iku)* ABS( zau ) )
	696	zbv = MIN( zbv , -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,ikv)* ABS( zav ) )
[3294]	697	! !- Slope at u- & v-points (uslpml, vslpml)
[2772]	698	uslpml(ji,jj) = zau / ( zbu - zeps ) * umask(ji,jj,iku)
	699	vslpml(ji,jj) = zav / ( zbv - zeps ) * vmask(ji,jj,ikv)
[2528]	700	!
[3294]	701	! !== i- & j-slopes at w-points just below the Mixed Layer ==!
[2528]	702	!
	703	ik = MIN( nmln(ji,jj) + 1, jpk )
	704	ikm1 = MAX( 1, ik-1 )
[3294]	705	! !- vertical density gradient for w-slope (from N^2)
[2528]	706	zbw = zm1_2g * pn2 (ji,jj,ik) * ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. )
[3294]	707	! !- horizontal density i- & j-gradient at w-points
[2528]	708	zci = MAX( umask(ji-1,jj,ik ) + umask(ji,jj,ik ) &
[3294]	709	& + umask(ji-1,jj,ikm1) + umask(ji,jj,ikm1) , zeps ) * e1t(ji,jj)
[2528]	710	zcj = MAX( vmask(ji,jj-1,ik ) + vmask(ji,jj,ik ) &
	711	& + vmask(ji,jj-1,ikm1) + vmask(ji,jj,ikm1) , zeps ) * e2t(ji,jj)
	712	zai = ( p_gru(ji-1,jj,ik ) + p_gru(ji,jj,ik) &
	713	& + p_gru(ji-1,jj,ikm1) + p_gru(ji,jj,ikm1 ) ) / zci * tmask(ji,jj,ik)
	714	zaj = ( p_grv(ji,jj-1,ik ) + p_grv(ji,jj,ik ) &
	715	& + p_grv(ji,jj-1,ikm1) + p_grv(ji,jj,ikm1) ) / zcj * tmask(ji,jj,ik)
[3294]	716	! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0.
	717	! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
[2528]	718	zbi = MIN( zbw , -100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zai ) )
	719	zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zaj ) )
[3294]	720	! !- i- & j-slope at w-points (wslpiml, wslpjml)
[2528]	721	wslpiml(ji,jj) = zai / ( zbi - zeps ) * tmask (ji,jj,ik)
	722	wslpjml(ji,jj) = zaj / ( zbj - zeps ) * tmask (ji,jj,ik)
[3]	723	END DO
	724	END DO
[3294]	725	!!gm this lbc_lnk should be useless....
[2528]	726	CALL lbc_lnk( uslpml , 'U', -1. ) ; CALL lbc_lnk( vslpml , 'V', -1. ) ! lateral boundary cond. (sign change)
	727	CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions
[1515]	728	!
[3294]	729	IF( nn_timing == 1 ) CALL timing_stop('ldf_slp_mxl')
	730	!
[3]	731	END SUBROUTINE ldf_slp_mxl
	732
	733
	734	SUBROUTINE ldf_slp_init
	735	!!----------------------------------------------------------------------
	736	!! * ROUTINE ldf_slp_init *
	737	!!
	738	!! ** Purpose : Initialization for the isopycnal slopes computation
	739	!!
[3294]	740	!! ** Method : read the nammbf namelist and check the parameter
	741	!! values called by tra_dmp at the first timestep (nit000)
[3]	742	!!----------------------------------------------------------------------
	743	INTEGER :: ji, jj, jk ! dummy loop indices
[2528]	744	INTEGER :: ierr ! local integer
[3]	745	!!----------------------------------------------------------------------
[3294]	746	!
	747	IF( nn_timing == 1 ) CALL timing_start('ldf_slp_init')
	748	!
	749	IF(lwp) THEN
[3]	750	WRITE(numout,*)
[2528]	751	WRITE(numout,*) 'ldf_slp_init : direction of lateral mixing'
	752	WRITE(numout,*) '~~~~~~~~~~~~'
[3]	753	ENDIF
[3294]	754
[2528]	755	IF( ln_traldf_grif ) THEN ! Griffies operator : triad of slopes
	756	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 )
	757	ALLOCATE( triadi (jpi,jpj,jpk,0:1,0:1) , triadj (jpi,jpj,jpk,0:1,0:1) , STAT=ierr )
[2715]	758	IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate Griffies operator slope' )
[2528]	759	!
	760	IF( ln_dynldf_iso ) CALL ctl_stop( 'ldf_slp_init: Griffies operator on momentum not supported' )
	761	!
	762	ELSE ! Madec operator : slopes at u-, v-, and w-points
	763	ALLOCATE( uslp(jpi,jpj,jpk) , vslp(jpi,jpj,jpk) , wslpi(jpi,jpj,jpk) , wslpj(jpi,jpj,jpk) , &
	764	& omlmask(jpi,jpj,jpk) , uslpml(jpi,jpj) , vslpml(jpi,jpj) , wslpiml(jpi,jpj) , wslpjml(jpi,jpj) , STAT=ierr )
[2715]	765	IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate Madec operator slope ' )
[3]	766
[2528]	767	! Direction of lateral diffusion (tracers and/or momentum)
	768	! ------------------------------
	769	uslp (:,:,:) = 0._wp ; uslpml (:,:) = 0._wp ! set the slope to zero (even in s-coordinates)
	770	vslp (:,:,:) = 0._wp ; vslpml (:,:) = 0._wp
	771	wslpi(:,:,:) = 0._wp ; wslpiml(:,:) = 0._wp
	772	wslpj(:,:,:) = 0._wp ; wslpjml(:,:) = 0._wp
[3]	773
[3294]	774	!!gm I no longer understand this.....
[2528]	775	IF( (ln_traldf_hor .OR. ln_dynldf_hor) .AND. .NOT. (lk_vvl .AND. ln_rstart) ) THEN
[2715]	776	IF(lwp) WRITE(numout,*) ' Horizontal mixing in s-coordinate: slope = slope of s-surfaces'
[3]	777
[2528]	778	! geopotential diffusion in s-coordinates on tracers and/or momentum
	779	! The slopes of s-surfaces are computed once (no call to ldfslp in step)
	780	! The slopes for momentum diffusion are i- or j- averaged of those on tracers
[3]	781
[2528]	782	! set the slope of diffusion to the slope of s-surfaces
	783	! ( c a u t i o n : minus sign as fsdep has positive value )
	784	DO jk = 1, jpk
	785	DO jj = 2, jpjm1
	786	DO ji = fs_2, fs_jpim1 ! vector opt.
	787	uslp (ji,jj,jk) = -1./e1u(ji,jj) * ( fsdept(ji+1,jj,jk) - fsdept(ji ,jj ,jk) ) * umask(ji,jj,jk)
	788	vslp (ji,jj,jk) = -1./e2v(ji,jj) * ( fsdept(ji,jj+1,jk) - fsdept(ji ,jj ,jk) ) * vmask(ji,jj,jk)
	789	wslpi(ji,jj,jk) = -1./e1t(ji,jj) * ( fsdepw(ji+1,jj,jk) - fsdepw(ji-1,jj,jk) ) * tmask(ji,jj,jk) * 0.5
	790	wslpj(ji,jj,jk) = -1./e2t(ji,jj) * ( fsdepw(ji,jj+1,jk) - fsdepw(ji,jj-1,jk) ) * tmask(ji,jj,jk) * 0.5
	791	END DO
[3]	792	END DO
	793	END DO
[2715]	794	CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) ! Lateral boundary conditions
	795	CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. )
[2528]	796	ENDIF
[2715]	797	ENDIF
	798	!
[3294]	799	IF( nn_timing == 1 ) CALL timing_stop('ldf_slp_init')
	800	!
[3]	801	END SUBROUTINE ldf_slp_init
	802
	803	#else
	804	!!------------------------------------------------------------------------
	805	!! Dummy module : NO Rotation of lateral mixing tensor
	806	!!------------------------------------------------------------------------
[32]	807	LOGICAL, PUBLIC, PARAMETER :: lk_ldfslp = .FALSE. !: slopes flag
[3]	808	CONTAINS
[3294]	809	SUBROUTINE ldf_slp( kt, prd, pn2 ) ! Dummy routine
	810	INTEGER, INTENT(in) :: kt
[1515]	811	REAL, DIMENSION(:,:,:), INTENT(in) :: prd, pn2
[32]	812	WRITE(,) 'ldf_slp: You should not have seen this print! error?', kt, prd(1,1,1), pn2(1,1,1)
[3]	813	END SUBROUTINE ldf_slp
[2605]	814	SUBROUTINE ldf_slp_grif( kt ) ! Dummy routine
	815	INTEGER, INTENT(in) :: kt
	816	WRITE(,) 'ldf_slp_grif: You should not have seen this print! error?', kt
	817	END SUBROUTINE ldf_slp_grif
[3294]	818	SUBROUTINE ldf_slp_init ! Dummy routine
[2528]	819	END SUBROUTINE ldf_slp_init
[3]	820	#endif
	821
	822	!!======================================================================
	823	END MODULE ldfslp

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