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ldfslp.F90 in branches/2011/dev_NOC_2011_MERGE/NEMOGCM/NEMO/OPA_SRC/LDF – NEMO

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source: branches/2011/dev_NOC_2011_MERGE/NEMOGCM/NEMO/OPA_SRC/LDF/ldfslp.F90 @ 2980

Last change on this file since 2980 was 2980, checked in by acc, 13 years ago
Branch dev_NOC_2011_MERGE. #874. Step 2: Add changes from the 2011/dev_r2782_NOCS_Griffies branch
Property svn:keywords set to `Id`
File size: 49.3 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
[3]	33
	34	IMPLICIT NONE
	35	PRIVATE
	36
[2528]	37	PUBLIC ldf_slp ! routine called by step.F90
	38	PUBLIC ldf_slp_grif ! routine called by step.F90
	39	PUBLIC ldf_slp_init ! routine called by opa.F90
[3]	40
[2528]	41	LOGICAL , PUBLIC, PARAMETER :: lk_ldfslp = .TRUE. !: slopes flag
	42	! !! Madec operator
[2715]	43	! Arrays allocated in ldf_slp_init() routine once we know whether we're using the Griffies or Madec operator
	44	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: uslp, wslpi !: i_slope at U- and W-points
	45	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: vslp, wslpj !: j-slope at V- and W-points
	46	! !! Griffies operator
	47	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: wslp2 !: wslp**2 from Griffies quarter cells
[2980]	48	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:,:) :: triadi_g, triadj_g !: skew flux slopes relative to geopotentials
[2715]	49	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:,:) :: triadi , triadj !: isoneutral slopes relative to model-coordinate
[3]	50
[2528]	51	! !! Madec operator
[2715]	52	! Arrays allocated in ldf_slp_init() routine once we know whether we're using the Griffies or Madec operator
	53	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: omlmask ! mask of the surface mixed layer at T-pt
	54	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: uslpml, wslpiml ! i_slope at U- and W-points just below the mixed layer
	55	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: vslpml, wslpjml ! j_slope at V- and W-points just below the mixed layer
[2528]	56
	57	REAL(wp) :: repsln = 1.e-25_wp ! tiny value used as minium of di(rho), dj(rho) and dk(rho)
	58
[2715]	59	! Workspace arrays for ldf_slp_grif. These could be replaced by several 3D and 2D workspace
[2980]	60	! arrays from the wrk_nemo module with a bit of code re-writing. The 4D workspace
[2715]	61	! arrays can't be used here because of the zero-indexing of some of the ranks. ARPDBG.
	62	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: zdzrho , zdyrho, zdxrho ! Horizontal and vertical density gradients
	63	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: zti_mlb, ztj_mlb ! for Griffies operator only
	64
[3]	65	!! * Substitutions
	66	# include "domzgr_substitute.h90"
[2528]	67	# include "ldftra_substitute.h90"
	68	# include "ldfeiv_substitute.h90"
[3]	69	# include "vectopt_loop_substitute.h90"
	70	!!----------------------------------------------------------------------
[2715]	71	!! NEMO/OPA 4.0 , NEMO Consortium (2011)
[1156]	72	!! $Id$
[2528]	73	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	74	!!----------------------------------------------------------------------
	75	CONTAINS
	76
[2715]	77	INTEGER FUNCTION ldf_slp_alloc()
	78	!!----------------------------------------------------------------------
	79	!! * FUNCTION ldf_slp_alloc *
	80	!!----------------------------------------------------------------------
	81	!
	82	ALLOCATE( zdxrho (jpi,jpj,jpk,0:1) , zti_mlb(jpi,jpj,0:1,0:1) , &
	83	& zdyrho (jpi,jpj,jpk,0:1) , ztj_mlb(jpi,jpj,0:1,0:1) , &
	84	& zdzrho (jpi,jpj,jpk,0:1) , STAT=ldf_slp_alloc )
	85	!
	86	IF( lk_mpp ) CALL mpp_sum ( ldf_slp_alloc )
	87	IF( ldf_slp_alloc /= 0 ) CALL ctl_warn('ldf_slp_alloc : failed to allocate arrays.')
	88	!
	89	END FUNCTION ldf_slp_alloc
	90
	91
[3]	92	SUBROUTINE ldf_slp( kt, prd, pn2 )
	93	!!----------------------------------------------------------------------
	94	!! * ROUTINE ldf_slp *
[2980]	95	!!
[1515]	96	!! ** Purpose : Compute the slopes of neutral surface (slope of isopycnal
[2528]	97	!! surfaces referenced locally) (ln_traldf_iso=T).
[2980]	98	!!
	99	!! ** Method : The slope in the i-direction is computed at U- and
	100	!! W-points (uslp, wslpi) and the slope in the j-direction is
[3]	101	!! computed at V- and W-points (vslp, wslpj).
	102	!! They are bounded by 1/100 over the whole ocean, and within the
	103	!! surface layer they are bounded by the distance to the surface
	104	!! ( slope<= depth/l where l is the length scale of horizontal
	105	!! diffusion (here, aht=2000m2/s ==> l=20km with a typical velocity
	106	!! of 10cm/s)
	107	!! A horizontal shapiro filter is applied to the slopes
[461]	108	!! ln_sco=T, s-coordinate, add to the previously computed slopes
[3]	109	!! the slope of the model level surface.
	110	!! macro-tasked on horizontal slab (jk-loop) (2, jpk-1)
	111	!! [slopes already set to zero at level 1, and to zero or the ocean
[461]	112	!! bottom slope (ln_sco=T) at level jpk in inildf]
[3]	113	!!
[2980]	114	!! ** Action : - uslp, wslpi, and vslp, wslpj, the i- and j-slopes
[3]	115	!! of now neutral surfaces at u-, w- and v- w-points, resp.
[1515]	116	!!----------------------------------------------------------------------
[2715]	117	USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released
	118	USE oce , ONLY: zgru => ua , zww => va ! (ua,va) used as workspace
	119	USE oce , ONLY: zgrv => ta , zwz => sa ! (ta,sa) used as workspace
	120	USE wrk_nemo, ONLY: zdzr => wrk_3d_1 ! 3D workspace
[3]	121	!!
[2715]	122	INTEGER , INTENT(in) :: kt ! ocean time-step index
	123	REAL(wp), INTENT(in), DIMENSION(:,:,:) :: prd ! in situ density
	124	REAL(wp), INTENT(in), DIMENSION(:,:,:) :: pn2 ! Brunt-Vaisala frequency (locally ref.)
[1515]	125	!!
	126	INTEGER :: ji , jj , jk ! dummy loop indices
	127	INTEGER :: ii0, ii1, iku ! temporary integer
	128	INTEGER :: ij0, ij1, ikv ! temporary integer
[2980]	129	REAL(wp) :: zeps, zm1_g, zm1_2g, z1_16, zcofw ! local scalars
[2528]	130	REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - -
	131	REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - -
	132	REAL(wp) :: zck, zfk, zbw ! - -
[3]	133	!!----------------------------------------------------------------------
[2715]	134
	135	IF( wrk_in_use(3, 1) ) THEN
	136	CALL ctl_stop('ldf_slp: requested workspace arrays are unavailable') ; RETURN
	137	ENDIF
	138
[2528]	139	zeps = 1.e-20_wp !== Local constant initialization ==!
	140	z1_16 = 1.0_wp / 16._wp
	141	zm1_g = -1.0_wp / grav
	142	zm1_2g = -0.5_wp / grav
[1515]	143	!
[2528]	144	zww(:,:,:) = 0._wp
	145	zwz(:,:,:) = 0._wp
	146	!
	147	DO jk = 1, jpk !== i- & j-gradient of density ==!
[3]	148	DO jj = 1, jpjm1
	149	DO ji = 1, fs_jpim1 ! vector opt.
[2980]	150	zgru(ji,jj,jk) = umask(ji,jj,jk) * ( prd(ji+1,jj ,jk) - prd(ji,jj,jk) )
	151	zgrv(ji,jj,jk) = vmask(ji,jj,jk) * ( prd(ji ,jj+1,jk) - prd(ji,jj,jk) )
[3]	152	END DO
	153	END DO
	154	END DO
[1515]	155	IF( ln_zps ) THEN ! partial steps correction at the bottom ocean level
[2980]	156	# if defined key_vectopt_loop
[1515]	157	DO jj = 1, 1
	158	DO ji = 1, jpij-jpi ! vector opt. (forced unrolling)
[3]	159	# else
[461]	160	DO jj = 1, jpjm1
	161	DO ji = 1, jpim1
[3]	162	# endif
[2980]	163	zgru(ji,jj,mbku(ji,jj)) = gru(ji,jj)
	164	zgrv(ji,jj,mbkv(ji,jj)) = grv(ji,jj)
[461]	165	END DO
[3]	166	END DO
[461]	167	ENDIF
[2528]	168	!
	169	zdzr(:,:,1) = 0._wp !== Local vertical density gradient at T-point == ! (evaluated from N^2)
	170	DO jk = 2, jpkm1
	171	! ! zdzr = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point
	172	! ! trick: tmask(ik ) = 0 => all pn2 = 0 => zdzr = 0
	173	! ! else tmask(ik+1) = 0 => pn2(ik+1) = 0 => zdzr divides by 1
	174	! ! umask(ik+1) /= 0 => all pn2 /= 0 => zdzr divides by 2
	175	! ! NB: 1/(tmask+1) = (1-.5tmask) substitute a / by a ==> faster
	176	zdzr(:,:,jk) = zm1_g * ( prd(:,:,jk) + 1._wp ) &
	177	& * ( pn2(:,:,jk) + pn2(:,:,jk+1) ) * ( 1._wp - 0.5_wp * tmask(:,:,jk+1) )
[2389]	178	END DO
[2528]	179	!
	180	! !== Slopes just below the mixed layer ==!
	181	CALL ldf_slp_mxl( prd, pn2, zgru, zgrv, zdzr ) ! output: uslpml, vslpml, wslpiml, wslpjml
[2389]	182
[2980]	183
[1515]	184	! I. slopes at u and v point \| uslp = d/di( prd ) / d/dz( prd )
	185	! =========================== \| vslp = d/dj( prd ) / d/dz( prd )
[2980]	186	!
[1515]	187	DO jk = 2, jpkm1 !* Slopes at u and v points
[3]	188	DO jj = 2, jpjm1
	189	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	190	! ! horizontal and vertical density gradient at u- and v-points
	191	zau = zgru(ji,jj,jk) / e1u(ji,jj)
	192	zav = zgrv(ji,jj,jk) / e2v(ji,jj)
	193	zbu = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji+1,jj ,jk) )
	194	zbv = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji ,jj+1,jk) )
	195	! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0
	196	! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
	197	zbu = MIN( zbu, -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,jk)* ABS( zau ) )
	198	zbv = MIN( zbv, -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,jk)* ABS( zav ) )
	199	! ! uslp and vslp output in zwz and zww, resp.
	200	zfi = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj,jk) )
	201	zfj = MAX( omlmask(ji,jj,jk), omlmask(ji,jj+1,jk) )
	202	zwz(ji,jj,jk) = ( ( 1. - zfi) * zau / ( zbu - zeps ) &
	203	& + zfi * uslpml(ji,jj) &
	204	& * 0.5_wp * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk)-fse3u(ji,jj,1) ) &
	205	& / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 5._wp ) ) * umask(ji,jj,jk)
	206	zww(ji,jj,jk) = ( ( 1. - zfj) * zav / ( zbv - zeps ) &
	207	& + zfj * vslpml(ji,jj) &
	208	& * 0.5_wp * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk)-fse3v(ji,jj,1) ) &
	209	& / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 5. ) ) * vmask(ji,jj,jk)
	210	!!gm modif to suppress omlmask.... (as in Griffies case)
	211	! ! ! jk must be >= ML level for zf=1. otherwise zf=0.
	212	! zfi = REAL( 1 - 1/(1 + jk / MAX( nmln(ji+1,jj), nmln(ji,jj) ) ), wp )
	213	! zfj = REAL( 1 - 1/(1 + jk / MAX( nmln(ji,jj+1), nmln(ji,jj) ) ), wp )
	214	! zci = 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) )
	215	! zcj = 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 10. ) )
	216	! zwz(ji,jj,jk) = ( zfi * zai / ( zbi - zeps ) + ( 1._wp - zfi ) * wslpiml(ji,jj) * zci ) * tmask(ji,jj,jk)
	217	! zww(ji,jj,jk) = ( zfj * zaj / ( zbj - zeps ) + ( 1._wp - zfj ) * wslpjml(ji,jj) * zcj ) * tmask(ji,jj,jk)
	218	!!gm end modif
[3]	219	END DO
	220	END DO
[1515]	221	END DO
	222	CALL lbc_lnk( zwz, 'U', -1. ) ; CALL lbc_lnk( zww, 'V', -1. ) ! lateral boundary conditions
	223	!
[2528]	224	! !* horizontal Shapiro filter
[1515]	225	DO jk = 2, jpkm1
[2528]	226	DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only
[2980]	227	DO ji = 2, jpim1
[2528]	228	uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[1515]	229	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	230	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	231	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	232	& + 4.* zwz(ji ,jj ,jk) )
[2528]	233	vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[1515]	234	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	235	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	236	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	237	& + 4.* zww(ji,jj ,jk) )
[3]	238	END DO
	239	END DO
[1515]	240	DO jj = 3, jpj-2 ! other rows
[3]	241	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	242	uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[3]	243	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	244	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	245	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	246	& + 4.* zwz(ji ,jj ,jk) )
[2528]	247	vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[3]	248	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	249	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	250	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	251	& + 4.* zww(ji,jj ,jk) )
	252	END DO
	253	END DO
[1515]	254	! !* decrease along coastal boundaries
[3]	255	DO jj = 2, jpjm1
	256	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	257	uslp(ji,jj,jk) = uslp(ji,jj,jk) * ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk ) ) * 0.5_wp &
	258	& * ( umask(ji,jj ,jk) + umask(ji,jj ,jk+1) ) * 0.5_wp
	259	vslp(ji,jj,jk) = vslp(ji,jj,jk) * ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk ) ) * 0.5_wp &
	260	& * ( vmask(ji ,jj,jk) + vmask(ji ,jj,jk+1) ) * 0.5_wp
[3]	261	END DO
	262	END DO
[1515]	263	END DO
[3]	264
	265
[1515]	266	! II. slopes at w point \| wslpi = mij( d/di( prd ) / d/dz( prd )
	267	! =========================== \| wslpj = mij( d/dj( prd ) / d/dz( prd )
[2980]	268	!
[2528]	269	DO jk = 2, jpkm1
[3]	270	DO jj = 2, jpjm1
	271	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	272	! !* Local vertical density gradient evaluated from N^2
	273	zbw = zm1_2g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. )
	274	! !* Slopes at w point
	275	! ! i- & j-gradient of density at w-points
	276	zci = MAX( umask(ji-1,jj,jk ) + umask(ji,jj,jk ) &
	277	& + umask(ji-1,jj,jk-1) + umask(ji,jj,jk-1) , zeps ) * e1t(ji,jj)
	278	zcj = MAX( vmask(ji,jj-1,jk ) + vmask(ji,jj,jk-1) &
	279	& + vmask(ji,jj-1,jk-1) + vmask(ji,jj,jk ) , zeps ) * e2t(ji,jj)
	280	zai = ( zgru (ji-1,jj,jk ) + zgru (ji,jj,jk-1) &
	281	& + zgru (ji-1,jj,jk-1) + zgru (ji,jj,jk ) ) / zci * tmask (ji,jj,jk)
	282	zaj = ( zgrv (ji,jj-1,jk ) + zgrv (ji,jj,jk-1) &
	283	& + zgrv (ji,jj-1,jk-1) + zgrv (ji,jj,jk ) ) / zcj * tmask (ji,jj,jk)
[1515]	284	! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0.
[2528]	285	! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
	286	zbi = MIN( zbw ,- 100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zai ) )
	287	zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zaj ) )
	288	! ! wslpi and wslpj with ML flattening (output in zwz and zww, resp.)
	289	zfk = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) ! zfk=1 in the ML otherwise zfk=0
	290	zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10._wp )
	291	zwz(ji,jj,jk) = ( zai / ( zbi - zeps ) * ( 1._wp - zfk ) + zck * wslpiml(ji,jj) * zfk ) * tmask(ji,jj,jk)
	292	zww(ji,jj,jk) = ( zaj / ( zbj - zeps ) * ( 1._wp - zfk ) + zck * wslpjml(ji,jj) * zfk ) * tmask(ji,jj,jk)
	293
	294	!!gm modif to suppress omlmask.... (as in Griffies operator)
	295	! ! ! jk must be >= ML level for zfk=1. otherwise zfk=0.
	296	! zfk = REAL( 1 - 1/(1 + jk / nmln(ji+1,jj)), wp )
	297	! zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. )
	298	! zwz(ji,jj,jk) = ( zfk * zai / ( zbi - zeps ) + ( 1._wp - zfk ) * wslpiml(ji,jj) * zck ) * tmask(ji,jj,jk)
	299	! zww(ji,jj,jk) = ( zfk * zaj / ( zbj - zeps ) + ( 1._wp - zfk ) * wslpjml(ji,jj) * zck ) * tmask(ji,jj,jk)
	300	!!gm end modif
[3]	301	END DO
	302	END DO
[1515]	303	END DO
[2528]	304	CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions
[1515]	305	!
	306	! !* horizontal Shapiro filter
	307	DO jk = 2, jpkm1
[2528]	308	DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only
[3]	309	DO ji = 2, jpim1
[2980]	310	zcofw = tmask(ji,jj,jk) * z1_16
[3]	311	wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[2980]	312	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	313	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	314	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	315	& + 4.* zwz(ji ,jj ,jk) ) * zcofw
[3]	316
	317	wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[2980]	318	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	319	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	320	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	321	& + 4.* zww(ji ,jj ,jk) ) * zcofw
[3]	322	END DO
[2980]	323	END DO
[1515]	324	DO jj = 3, jpj-2 ! other rows
[3]	325	DO ji = fs_2, fs_jpim1 ! vector opt.
[2980]	326	zcofw = tmask(ji,jj,jk) * z1_16
[3]	327	wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) &
[2980]	328	& + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) &
	329	& + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) &
	330	& + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) &
	331	& + 4.* zwz(ji ,jj ,jk) ) * zcofw
[3]	332
	333	wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) &
[2980]	334	& + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) &
	335	& + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) &
	336	& + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) &
	337	& + 4.* zww(ji ,jj ,jk) ) * zcofw
[3]	338	END DO
	339	END DO
[1515]	340	! !* decrease along coastal boundaries
[3]	341	DO jj = 2, jpjm1
	342	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	343	zck = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) &
	344	& * ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) * 0.25
	345	wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * zck
	346	wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * zck
[3]	347	END DO
	348	END DO
[1515]	349	END DO
[2980]	350
	351	! III. Specific grid points
	352	! ===========================
	353	!
[1515]	354	IF( cp_cfg == "orca" .AND. jp_cfg == 4 ) THEN ! ORCA_R4 configuration: horizontal diffusion in specific area
	355	! ! Gibraltar Strait
	356	ij0 = 50 ; ij1 = 53
[2528]	357	ii0 = 69 ; ii1 = 71 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	358	ij0 = 51 ; ij1 = 53
[2528]	359	ii0 = 68 ; ii1 = 71 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	360	ii0 = 69 ; ii1 = 71 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	361	ii0 = 69 ; ii1 = 71 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	362	!
	363	! ! Mediterrannean Sea
	364	ij0 = 49 ; ij1 = 56
[2528]	365	ii0 = 71 ; ii1 = 90 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	366	ij0 = 50 ; ij1 = 56
[2528]	367	ii0 = 70 ; ii1 = 90 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	368	ii0 = 71 ; ii1 = 90 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
	369	ii0 = 71 ; ii1 = 90 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp
[1515]	370	ENDIF
[3]	371
[2980]	372
	373	! IV. Lateral boundary conditions
[1515]	374	! ===============================
[461]	375	CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. )
	376	CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. )
[3]	377
[1515]	378
[258]	379	IF(ln_ctl) THEN
	380	CALL prt_ctl(tab3d_1=uslp , clinfo1=' slp - u : ', tab3d_2=vslp, clinfo2=' v : ', kdim=jpk)
	381	CALL prt_ctl(tab3d_1=wslpi, clinfo1=' slp - wi: ', tab3d_2=wslpj, clinfo2=' wj: ', kdim=jpk)
[49]	382	ENDIF
[1515]	383	!
[2715]	384	IF( wrk_not_released(3, 1) ) CALL ctl_stop('ldf_slp: failed to release workspace arrays')
	385	!
[3]	386	END SUBROUTINE ldf_slp
	387
[2980]	388
[2528]	389	SUBROUTINE ldf_slp_grif ( kt )
	390	!!----------------------------------------------------------------------
	391	!! * ROUTINE ldf_slp_grif *
	392	!!
	393	!! ** Purpose : Compute the squared slopes of neutral surfaces (slope
	394	!! of iso-pycnal surfaces referenced locally) (ln_traldf_grif=T)
[2980]	395	!! at W-points using the Griffies quarter-cells.
[2528]	396	!!
[2980]	397	!! ** Method : calculates alpha and beta at T-points
[2528]	398	!!
	399	!! ** Action : - triadi_g, triadj_g T-pts i- and j-slope triads relative to geopot. (used for eiv)
	400	!! - triadi , triadj T-pts i- and j-slope triads relative to model-coordinate
	401	!! - wslp2 squared slope of neutral surfaces at w-points.
	402	!!----------------------------------------------------------------------
[2715]	403	USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released
[2980]	404	USE oce , ONLY: zalbet => ua ! use ua as workspace
[2715]	405	USE wrk_nemo, ONLY: z1_mlbw => wrk_2d_1
[2980]	406	!!
	407	INTEGER, INTENT( in ) :: kt ! ocean time-step index
	408	!!
[2528]	409	INTEGER :: ji, jj, jk, jl, ip, jp, kp ! dummy loop indices
[2980]	410	INTEGER :: iku, ikv ! local integer
	411	REAL(wp) :: zfacti, zfactj ! local scalars
	412	REAL(wp) :: zdit, zdis, zdjt, zdjs, zdkt, zdks, zbu, zbv, zbti, zbtj
[2528]	413	REAL(wp) :: zdxrho_raw, zti_coord, zti_raw, zti_lim, zti_lim2, zti_g_raw, zti_g_lim
	414	REAL(wp) :: zdyrho_raw, ztj_coord, ztj_raw, ztj_lim, ztj_lim2, ztj_g_raw, ztj_g_lim
	415	REAL(wp) :: zdzrho_raw
[2980]	416	REAL(wp) :: zbeta0
[2528]	417	!!----------------------------------------------------------------------
[3]	418
[2715]	419	IF( wrk_in_use(3, 2,3,4,5) .OR. wrk_in_use(2, 1) )THEN
	420	CALL ctl_stop('ldf_slp_grif: requested workspace arrays are unavailable') ; RETURN
	421	ENDIF
	422
[2528]	423	!--------------------------------!
	424	! Some preliminary calculation !
	425	!--------------------------------!
	426	!
[2980]	427	CALL eos_alpbet( tsb, zalbet, zbeta0 ) !== before local thermal/haline expension ratio at T-points ==!
[2528]	428	!
[2980]	429	DO jl = 0, 1 !== unmasked before density i- j-, k-gradients ==!
	430	!
	431	ip = jl ; jp = jl ! guaranteed nonzero gradients ( absolute value larger than repsln)
	432	DO jk = 1, jpkm1 ! done each pair of triad
	433	DO jj = 1, jpjm1 ! NB: not masked ==> a minimum value is set
	434	DO ji = 1, fs_jpim1 ! vector opt.
	435	zdit = ( tsb(ji+1,jj,jk,jp_tem) - tsb(ji,jj,jk,jp_tem) ) ! i-gradient of T & S at u-point
	436	zdis = ( tsb(ji+1,jj,jk,jp_sal) - tsb(ji,jj,jk,jp_sal) )
	437	zdjt = ( tsb(ji,jj+1,jk,jp_tem) - tsb(ji,jj,jk,jp_tem) ) ! j-gradient of T & S at v-point
	438	zdjs = ( tsb(ji,jj+1,jk,jp_sal) - tsb(ji,jj,jk,jp_sal) )
	439	zdxrho_raw = ( - zalbet(ji+ip,jj ,jk) * zdit + zbeta0*zdis ) / e1u(ji,jj)
	440	zdyrho_raw = ( - zalbet(ji ,jj+jp,jk) * zdjt + zbeta0*zdjs ) / 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
[2528]	444	END DO
	445	END DO
[2980]	446	!
	447	IF( ln_zps.and.l_grad_zps ) THEN ! partial steps: correction of i- & j-grad on bottom
[2528]	448	# if defined key_vectopt_loop
[2980]	449	DO jj = 1, 1
	450	DO ji = 1, jpij-jpi ! vector opt. (forced unrolling)
[2528]	451	# else
[2980]	452	DO jj = 1, jpjm1
	453	DO ji = 1, jpim1
[2528]	454	# endif
[2980]	455	iku = mbku(ji,jj) ; ikv = mbkv(ji,jj) ! last ocean level (u- & v-points)
	456	zdit = gtsu(ji,jj,jp_tem) ; zdjt = gtsv(ji,jj,jp_tem) ! i- & j-gradient of Temperature
	457	zdis = gtsu(ji,jj,jp_sal) ; zdjs = gtsv(ji,jj,jp_sal) ! i- & j-gradient of Salinity
	458	zdxrho_raw = ( - zalbet(ji+ip,jj ,iku) * zdit + zbeta0*zdis ) / e1u(ji,jj)
	459	zdyrho_raw = ( - zalbet(ji ,jj+jp,ikv) * zdjt + zbeta0*zdjs ) / e2v(ji,jj)
	460	zdxrho(ji+ip,jj ,iku,1-ip) = SIGN( MAX( repsln, ABS( zdxrho_raw ) ), zdxrho_raw ) ! keep the sign
	461	zdyrho(ji ,jj+jp,ikv,1-jp) = SIGN( MAX( repsln, ABS( zdyrho_raw ) ), zdyrho_raw )
[2528]	462	END DO
	463	END DO
[2980]	464	ENDIF
	465	!
[2528]	466	END DO
[2980]	467
	468	DO kp = 0, 1 !== unmasked before density i- j-, k-gradients ==!
	469	DO jk = 1, jpkm1 ! done each pair of triad
	470	DO jj = 1, jpj ! NB: not masked ==> a minimum value is set
	471	DO ji = 1, jpi ! vector opt.
	472	IF( jk+kp > 1 ) THEN ! k-gradient of T & S a jk+kp
	473	zdkt = ( tsb(ji,jj,jk+kp-1,jp_tem) - tsb(ji,jj,jk+kp,jp_tem) )
	474	zdks = ( tsb(ji,jj,jk+kp-1,jp_sal) - tsb(ji,jj,jk+kp,jp_sal) )
	475	ELSE
	476	zdkt = 0._wp ! 1st level gradient set to zero
	477	zdks = 0._wp
	478	ENDIF
	479	zdzrho_raw = ( - zalbet(ji ,jj ,jk) * zdkt + zbeta0*zdks ) / fse3w(ji,jj,jk+kp)
	480	zdzrho(ji ,jj ,jk, kp) = - MIN( - repsln, zdzrho_raw ) ! force zdzrho >= repsln
	481	END DO
[2528]	482	END DO
	483	END DO
	484	END DO
	485	!
[2980]	486	DO jj = 1, jpj !== Reciprocal depth of the w-point below ML base ==!
[2528]	487	DO ji = 1, jpi
	488	jk = MIN( nmln(ji,jj), mbkt(ji,jj) ) + 1 ! MIN in case ML depth is the ocean depth
	489	z1_mlbw(ji,jj) = 1._wp / fsdepw(ji,jj,jk)
	490	END DO
	491	END DO
	492	!
[2980]	493	! !== intialisations to zero ==!
[2528]	494	!
[2980]	495	wslp2 (:,:,:) = 0._wp ! wslp2 will be cumulated 3D field set to zero
	496	triadi_g(:,:,1,:,:) = 0._wp ; triadi_g(:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero
[2528]	497	triadj_g(:,:,1,:,:) = 0._wp ; triadj_g(:,:,jpk,:,:) = 0._wp
[2980]	498	!!gm _iso set to zero missing
	499	triadi (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero
	500	triadj (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp
	501
[2528]	502	!-------------------------------------!
	503	! Triads just below the Mixed Layer !
	504	!-------------------------------------!
	505	!
[2980]	506	DO jl = 0, 1 ! calculate slope of the 4 triads immediately ONE level below mixed-layer base
	507	DO kp = 0, 1 ! with only the slope-max limit and MASKED
[2528]	508	DO jj = 1, jpjm1
	509	DO ji = 1, fs_jpim1
	510	ip = jl ; jp = jl
	511	jk = MIN( nmln(ji+ip,jj) , mbkt(ji+ip,jj) ) + 1 ! ML level+1 (MIN in case ML depth is the ocean depth)
[2980]	512	! Add s-coordinate slope at t-points (do this by subtracting gradient of depth)
[2528]	513	zti_g_raw = ( zdxrho(ji+ip,jj,jk-kp,1-ip) / zdzrho(ji+ip,jj,jk-kp,kp) &
[2980]	514	& - ( fsdept(ji+1,jj,jk-kp) - fsdept(ji,jj,jk-kp) ) / e1u(ji,jj) ) * umask(ji,jj,jk)
[2528]	515	jk = MIN( nmln(ji,jj+jp) , mbkt(ji,jj+jp) ) + 1
	516	ztj_g_raw = ( zdyrho(ji,jj+jp,jk-kp,1-jp) / zdzrho(ji,jj+jp,jk-kp,kp) &
[2980]	517	& - ( fsdept(ji,jj+1,jk-kp) - fsdept(ji,jj,jk-kp) ) / e2v(ji,jj) ) * vmask(ji,jj,jk)
[2528]	518	zti_mlb(ji+ip,jj ,1-ip,kp) = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw )
	519	ztj_mlb(ji ,jj+jp,1-jp,kp) = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw )
	520	END DO
	521	END DO
	522	END DO
	523	END DO
	524
	525	!-------------------------------------!
	526	! Triads with surface limits !
	527	!-------------------------------------!
	528	!
[2980]	529	DO kp = 0, 1 ! k-index of triads
[2528]	530	DO jl = 0, 1
[2980]	531	ip = jl ; jp = jl ! i- and j-indices of triads (i-k and j-k planes)
[2528]	532	DO jk = 1, jpkm1
	533	DO jj = 1, jpjm1
[2980]	534	DO ji = 1, fs_jpim1 ! vector opt.
[2528]	535	!
	536	! Calculate slope relative to geopotentials used for GM skew fluxes
[2980]	537	! Add s-coordinate slope at t-points (do this by subtracting gradient of depth)
[2528]	538	! Limit by slope relative to geopotentials by rn_slpmax, and mask by psi-point
	539	! masked by umask taken at the level of dz(rho)
	540	!
	541	! raw slopes: unmasked unbounded slopes (relative to geopotential (zti_g) and model surface (zti)
	542	!
	543	zti_raw = zdxrho(ji+ip,jj ,jk,1-ip) / zdzrho(ji+ip,jj ,jk,kp) ! unmasked
	544	ztj_raw = zdyrho(ji ,jj+jp,jk,1-jp) / zdzrho(ji ,jj+jp,jk,kp)
	545	zti_coord = ( fsdept(ji+1,jj ,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj)
[2980]	546	ztj_coord = ( fsdept(ji ,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) ! unmasked
	547	zti_g_raw = zti_raw - zti_coord ! ref to geopot surfaces
	548	ztj_g_raw = ztj_raw - ztj_coord
[2528]	549	zti_g_lim = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw )
	550	ztj_g_lim = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw )
	551	!
	552	! Below ML use limited zti_g as is
	553	! Inside ML replace by linearly reducing sx_mlb towards surface
	554	!
	555	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
	556	zfactj = REAL( 1 - 1/(1 + (jk+kp-1)/nmln(ji,jj+jp)), wp ) ! must be .ge. nmln(ji,jj) for zfact=1
	557	! ! otherwise zfact=0
	558	zti_g_lim = zfacti * zti_g_lim &
	559	& + ( 1._wp - zfacti ) * zti_mlb(ji+ip,jj,1-ip,kp) &
	560	& * fsdepw(ji+ip,jj,jk+kp) * z1_mlbw(ji+ip,jj)
	561	ztj_g_lim = zfactj * ztj_g_lim &
	562	& + ( 1._wp - zfactj ) * ztj_mlb(ji,jj+jp,1-jp,kp) &
[2980]	563	& * fsdepw(ji,jj+jp,jk+kp) * z1_mlbw(ji,jj+jp)
[2528]	564	!
[2980]	565	triadi_g(ji+ip,jj ,jk,1-ip,kp) = zti_g_lim * umask(ji,jj,jk+kp) ! masked
[2528]	566	triadj_g(ji ,jj+jp,jk,1-jp,kp) = ztj_g_lim * vmask(ji,jj,jk+kp)
	567	!
	568	! Get coefficients of isoneutral diffusion tensor
	569	! 1. Utilise gradients relative to s-coordinate, so add t-point slopes (subtract depth gradients)
	570	! 2. We require that isoneutral diffusion gives no vertical buoyancy flux
	571	! i.e. 33 term = (real slope* 31, 13 terms)
	572	! To do this, retain limited sx**2 in vertical flux, but divide by real slope for 13/31 terms
	573	! Equivalent to tapering A_iso = sx_limited2/(real slope)2
	574	!
[2980]	575	zti_lim = ( zti_g_lim + zti_coord ) * umask(ji,jj,jk+kp) ! remove coordinate slope => relative to coordinate surfaces
	576	ztj_lim = ( ztj_g_lim + ztj_coord ) * vmask(ji,jj,jk+kp)
	577	zti_lim2 = zti_lim * zti_lim ! square of limited slopes ! masked <<==
	578	ztj_lim2 = ztj_lim * ztj_lim
[2528]	579	!
[2980]	580	IF( ln_triad_iso ) THEN
	581	zti_raw = zti_lim2 / zti_raw
	582	ztj_raw = ztj_lim2 / ztj_raw
	583	zti_raw = SIGN( MIN( ABS(zti_lim), ABS( zti_raw ) ), zti_raw )
	584	ztj_raw = SIGN( MIN( ABS(ztj_lim), ABS( ztj_raw ) ), ztj_raw )
	585	zti_lim = zfacti * zti_lim &
	586	& + ( 1._wp - zfacti ) * zti_raw
	587	ztj_lim = zfactj * ztj_lim &
	588	& + ( 1._wp - zfactj ) * ztj_raw
	589	ENDIF
	590	triadi(ji+ip,jj ,jk,1-ip,kp) = zti_lim
	591	triadj(ji ,jj+jp,jk,1-jp,kp) = ztj_lim
	592	!
[2528]	593	zbu = e1u(ji ,jj) * e2u(ji ,jj) * fse3u(ji ,jj,jk )
	594	zbv = e1v(ji ,jj) * e2v(ji ,jj) * fse3v(ji ,jj,jk )
	595	zbti = e1t(ji+ip,jj) * e2t(ji+ip,jj) * fse3w(ji+ip,jj,jk+kp)
	596	zbtj = e1t(ji,jj+jp) * e2t(ji,jj+jp) * fse3w(ji,jj+jp,jk+kp)
	597	!
[2980]	598	!!gm this may inhibit vectorization on Vect Computers, and even on scalar computers.... ==> to be checked
	599	! agn may need to change to using ztj_g_lim*2, as wslp2 just used for eddy growth rate, needs real* slope
	600	wslp2 (ji+ip,jj,jk+kp) = wslp2(ji+ip,jj,jk+kp) + 0.25_wp * zbu / zbti * zti_lim2 ! masked
[2528]	601	wslp2 (ji,jj+jp,jk+kp) = wslp2(ji,jj+jp,jk+kp) + 0.25_wp * zbv / zbtj * ztj_lim2
	602	END DO
	603	END DO
	604	END DO
	605	END DO
	606	END DO
	607	!
	608	wslp2(:,:,1) = 0._wp ! force the surface wslp to zero
[2980]	609
[2528]	610	CALL lbc_lnk( wslp2, 'W', 1. ) ! lateral boundary confition on wslp2 only ==>>> gm : necessary ? to be checked
	611	!
[2715]	612	IF( wrk_not_released(3, 2,3,4,5) .OR. &
	613	wrk_not_released(2, 1) ) CALL ctl_stop('ldf_slp_grif: failed to release workspace arrays')
	614	!
[2528]	615	END SUBROUTINE ldf_slp_grif
	616
	617
	618	SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr )
[3]	619	!!----------------------------------------------------------------------
	620	!! * ROUTINE ldf_slp_mxl *
	621	!!
[2980]	622	!! ** Purpose : Compute the slopes of iso-neutral surface just below
[1515]	623	!! the mixed layer.
	624	!!
[2528]	625	!! ** Method : The slope in the i-direction is computed at u- & w-points
	626	!! (uslpml, wslpiml) and the slope in the j-direction is computed
	627	!! at v- and w-points (vslpml, wslpjml) with the same bounds as
	628	!! in ldf_slp.
[3]	629	!!
[2389]	630	!! ** Action : uslpml, wslpiml : i- & j-slopes of neutral surfaces
[2980]	631	!! vslpml, wslpjml just below the mixed layer
[2389]	632	!! omlmask : mixed layer mask
[1515]	633	!!----------------------------------------------------------------------
[2715]	634	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: prd ! in situ density
	635	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.)
	636	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: p_gru, p_grv ! i- & j-gradient of density (u- & v-pts)
	637	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: p_dzr ! z-gradient of density (T-point)
[3]	638	!!
[2980]	639	INTEGER :: ji , jj , jk ! dummy loop indices
	640	INTEGER :: iku, ikv, ik, ikm1 ! local integers
[2528]	641	REAL(wp) :: zeps, zm1_g, zm1_2g ! local scalars
	642	REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - -
	643	REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - -
	644	REAL(wp) :: zck, zfk, zbw ! - -
[3]	645	!!----------------------------------------------------------------------
	646
[2528]	647	zeps = 1.e-20_wp !== Local constant initialization ==!
	648	zm1_g = -1.0_wp / grav
	649	zm1_2g = -0.5_wp / grav
[1515]	650	!
[2528]	651	uslpml (1,:) = 0._wp ; uslpml (jpi,:) = 0._wp
	652	vslpml (1,:) = 0._wp ; vslpml (jpi,:) = 0._wp
	653	wslpiml(1,:) = 0._wp ; wslpiml(jpi,:) = 0._wp
	654	wslpjml(1,:) = 0._wp ; wslpjml(jpi,:) = 0._wp
	655	!
[2980]	656	! !== surface mixed layer mask !
	657	DO jk = 1, jpk ! =1 inside the mixed layer, =0 otherwise
[789]	658	# if defined key_vectopt_loop
[1515]	659	DO jj = 1, 1
[2980]	660	DO ji = 1, jpij ! vector opt. (forced unrolling)
[3]	661	# else
	662	DO jj = 1, jpj
	663	DO ji = 1, jpi
	664	# endif
	665	ik = nmln(ji,jj) - 1
[2528]	666	IF( jk <= ik ) THEN ; omlmask(ji,jj,jk) = 1._wp
	667	ELSE ; omlmask(ji,jj,jk) = 0._wp
[3]	668	ENDIF
	669	END DO
	670	END DO
	671	END DO
	672
	673
	674	! Slopes of isopycnal surfaces just before bottom of mixed layer
	675	! --------------------------------------------------------------
[1515]	676	! The slope are computed as in the 3D case.
	677	! A key point here is the definition of the mixed layer at u- and v-points.
	678	! It is assumed to be the maximum of the two neighbouring T-point mixed layer depth.
	679	! Otherwise, a n2 value inside the mixed layer can be involved in the computation
	680	! of the slope, resulting in a too steep diagnosed slope and thus a spurious eddy
	681	! induce velocity field near the base of the mixed layer.
[3]	682	!-----------------------------------------------------------------------
[1515]	683	!
[789]	684	# if defined key_vectopt_loop
[1515]	685	DO jj = 1, 1
	686	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
[3]	687	# else
	688	DO jj = 2, jpjm1
	689	DO ji = 2, jpim1
	690	# endif
[2980]	691	! !== Slope at u- & v-points just below the Mixed Layer ==!
[2528]	692	!
[2980]	693	! !- vertical density gradient for u- and v-slopes (from dzr at T-point)
[2528]	694	iku = MIN( MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) , jpkm1 ) ! ML (MAX of T-pts, bound by jpkm1)
[2980]	695	ikv = MIN( MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) , jpkm1 ) !
[2528]	696	zbu = 0.5_wp * ( p_dzr(ji,jj,iku) + p_dzr(ji+1,jj ,iku) )
	697	zbv = 0.5_wp * ( p_dzr(ji,jj,ikv) + p_dzr(ji ,jj+1,ikv) )
[2980]	698	! !- horizontal density gradient at u- & v-points
[2528]	699	zau = p_gru(ji,jj,iku) / e1u(ji,jj)
	700	zav = p_grv(ji,jj,ikv) / e2v(ji,jj)
[2980]	701	! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0
	702	! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
[2772]	703	zbu = MIN( zbu , -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,iku)* ABS( zau ) )
	704	zbv = MIN( zbv , -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,ikv)* ABS( zav ) )
[2980]	705	! !- Slope at u- & v-points (uslpml, vslpml)
[2772]	706	uslpml(ji,jj) = zau / ( zbu - zeps ) * umask(ji,jj,iku)
	707	vslpml(ji,jj) = zav / ( zbv - zeps ) * vmask(ji,jj,ikv)
[2528]	708	!
[2980]	709	! !== i- & j-slopes at w-points just below the Mixed Layer ==!
[2528]	710	!
	711	ik = MIN( nmln(ji,jj) + 1, jpk )
	712	ikm1 = MAX( 1, ik-1 )
[2980]	713	! !- vertical density gradient for w-slope (from N^2)
[2528]	714	zbw = zm1_2g * pn2 (ji,jj,ik) * ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. )
[2980]	715	! !- horizontal density i- & j-gradient at w-points
[2528]	716	zci = MAX( umask(ji-1,jj,ik ) + umask(ji,jj,ik ) &
[2980]	717	& + umask(ji-1,jj,ikm1) + umask(ji,jj,ikm1) , zeps ) * e1t(ji,jj)
[2528]	718	zcj = MAX( vmask(ji,jj-1,ik ) + vmask(ji,jj,ik ) &
	719	& + vmask(ji,jj-1,ikm1) + vmask(ji,jj,ikm1) , zeps ) * e2t(ji,jj)
	720	zai = ( p_gru(ji-1,jj,ik ) + p_gru(ji,jj,ik) &
	721	& + p_gru(ji-1,jj,ikm1) + p_gru(ji,jj,ikm1 ) ) / zci * tmask(ji,jj,ik)
	722	zaj = ( p_grv(ji,jj-1,ik ) + p_grv(ji,jj,ik ) &
	723	& + p_grv(ji,jj-1,ikm1) + p_grv(ji,jj,ikm1) ) / zcj * tmask(ji,jj,ik)
[2980]	724	! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0.
	725	! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt)
[2528]	726	zbi = MIN( zbw , -100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zai ) )
	727	zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zaj ) )
[2980]	728	! !- i- & j-slope at w-points (wslpiml, wslpjml)
[2528]	729	wslpiml(ji,jj) = zai / ( zbi - zeps ) * tmask (ji,jj,ik)
	730	wslpjml(ji,jj) = zaj / ( zbj - zeps ) * tmask (ji,jj,ik)
[3]	731	END DO
	732	END DO
[2980]	733	!!gm this lbc_lnk should be useless....
[2528]	734	CALL lbc_lnk( uslpml , 'U', -1. ) ; CALL lbc_lnk( vslpml , 'V', -1. ) ! lateral boundary cond. (sign change)
	735	CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions
[1515]	736	!
[3]	737	END SUBROUTINE ldf_slp_mxl
	738
	739
	740	SUBROUTINE ldf_slp_init
	741	!!----------------------------------------------------------------------
	742	!! * ROUTINE ldf_slp_init *
	743	!!
	744	!! ** Purpose : Initialization for the isopycnal slopes computation
	745	!!
[2980]	746	!! ** Method : read the nammbf namelist and check the parameter
	747	!! values called by tra_dmp at the first timestep (nit000)
[3]	748	!!----------------------------------------------------------------------
	749	INTEGER :: ji, jj, jk ! dummy loop indices
[2528]	750	INTEGER :: ierr ! local integer
[3]	751	!!----------------------------------------------------------------------
[2980]	752
	753	IF(lwp) THEN
[3]	754	WRITE(numout,*)
[2528]	755	WRITE(numout,*) 'ldf_slp_init : direction of lateral mixing'
	756	WRITE(numout,*) '~~~~~~~~~~~~'
[3]	757	ENDIF
[2980]	758
[2528]	759	IF( ln_traldf_grif ) THEN ! Griffies operator : triad of slopes
	760	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 )
	761	ALLOCATE( triadi (jpi,jpj,jpk,0:1,0:1) , triadj (jpi,jpj,jpk,0:1,0:1) , STAT=ierr )
[2715]	762	IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate Griffies operator slope' )
	763	IF( ldf_slp_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate workspace arrays' )
[2528]	764	!
	765	IF( ln_dynldf_iso ) CALL ctl_stop( 'ldf_slp_init: Griffies operator on momentum not supported' )
	766	!
	767	ELSE ! Madec operator : slopes at u-, v-, and w-points
	768	ALLOCATE( uslp(jpi,jpj,jpk) , vslp(jpi,jpj,jpk) , wslpi(jpi,jpj,jpk) , wslpj(jpi,jpj,jpk) , &
	769	& omlmask(jpi,jpj,jpk) , uslpml(jpi,jpj) , vslpml(jpi,jpj) , wslpiml(jpi,jpj) , wslpjml(jpi,jpj) , STAT=ierr )
[2715]	770	IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate Madec operator slope ' )
[3]	771
[2528]	772	! Direction of lateral diffusion (tracers and/or momentum)
	773	! ------------------------------
	774	uslp (:,:,:) = 0._wp ; uslpml (:,:) = 0._wp ! set the slope to zero (even in s-coordinates)
	775	vslp (:,:,:) = 0._wp ; vslpml (:,:) = 0._wp
	776	wslpi(:,:,:) = 0._wp ; wslpiml(:,:) = 0._wp
	777	wslpj(:,:,:) = 0._wp ; wslpjml(:,:) = 0._wp
[3]	778
[2980]	779	!!gm I no longer understand this.....
[2528]	780	IF( (ln_traldf_hor .OR. ln_dynldf_hor) .AND. .NOT. (lk_vvl .AND. ln_rstart) ) THEN
[2715]	781	IF(lwp) WRITE(numout,*) ' Horizontal mixing in s-coordinate: slope = slope of s-surfaces'
[3]	782
[2528]	783	! geopotential diffusion in s-coordinates on tracers and/or momentum
	784	! The slopes of s-surfaces are computed once (no call to ldfslp in step)
	785	! The slopes for momentum diffusion are i- or j- averaged of those on tracers
[3]	786
[2528]	787	! set the slope of diffusion to the slope of s-surfaces
	788	! ( c a u t i o n : minus sign as fsdep has positive value )
	789	DO jk = 1, jpk
	790	DO jj = 2, jpjm1
	791	DO ji = fs_2, fs_jpim1 ! vector opt.
	792	uslp (ji,jj,jk) = -1./e1u(ji,jj) * ( fsdept(ji+1,jj,jk) - fsdept(ji ,jj ,jk) ) * umask(ji,jj,jk)
	793	vslp (ji,jj,jk) = -1./e2v(ji,jj) * ( fsdept(ji,jj+1,jk) - fsdept(ji ,jj ,jk) ) * vmask(ji,jj,jk)
	794	wslpi(ji,jj,jk) = -1./e1t(ji,jj) * ( fsdepw(ji+1,jj,jk) - fsdepw(ji-1,jj,jk) ) * tmask(ji,jj,jk) * 0.5
	795	wslpj(ji,jj,jk) = -1./e2t(ji,jj) * ( fsdepw(ji,jj+1,jk) - fsdepw(ji,jj-1,jk) ) * tmask(ji,jj,jk) * 0.5
	796	END DO
[3]	797	END DO
	798	END DO
[2715]	799	CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) ! Lateral boundary conditions
	800	CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. )
[2528]	801	ENDIF
[2715]	802	ENDIF
	803	!
[3]	804	END SUBROUTINE ldf_slp_init
	805
	806	#else
	807	!!------------------------------------------------------------------------
	808	!! Dummy module : NO Rotation of lateral mixing tensor
	809	!!------------------------------------------------------------------------
[32]	810	LOGICAL, PUBLIC, PARAMETER :: lk_ldfslp = .FALSE. !: slopes flag
[3]	811	CONTAINS
[2980]	812	SUBROUTINE ldf_slp( kt, prd, pn2 ) ! Dummy routine
	813	INTEGER, INTENT(in) :: kt
[1515]	814	REAL, DIMENSION(:,:,:), INTENT(in) :: prd, pn2
[32]	815	WRITE(,) 'ldf_slp: You should not have seen this print! error?', kt, prd(1,1,1), pn2(1,1,1)
[3]	816	END SUBROUTINE ldf_slp
[2605]	817	SUBROUTINE ldf_slp_grif( kt ) ! Dummy routine
	818	INTEGER, INTENT(in) :: kt
	819	WRITE(,) 'ldf_slp_grif: You should not have seen this print! error?', kt
	820	END SUBROUTINE ldf_slp_grif
[2980]	821	SUBROUTINE ldf_slp_init ! Dummy routine
[2528]	822	END SUBROUTINE ldf_slp_init
[3]	823	#endif
	824
	825	!!======================================================================
	826	END MODULE ldfslp

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