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zdfkpp.F90 in trunk/NEMO/OPA_SRC/ZDF – NEMO

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source: trunk/NEMO/OPA_SRC/ZDF/zdfkpp.F90 @ 888

Last change on this file since 888 was 888, checked in by ctlod, 16 years ago
merge dev_001_SBC branche with the trunk to include the New Surface Module package, see ticket: #113
Property svn:eol-style set to `native` Property svn:keywords set to `Author Date Id Revision`
File size: 74.2 KB

Rev	Line
[255]	1	MODULE zdfkpp
	2	!!======================================================================
	3	!! * MODULE zdfkpp *
	4	!! Ocean physics: vertical mixing coefficient compute from the KPP
	5	!! turbulent closure parameterization
	6	!!=====================================================================
[503]	7	!! History : 8.1 ! 00-03 (W.G. Large, J. Chanut) Original code
	8	!! 8.1 ! 02-06 (J.M. Molines) for real case CLIPPER
	9	!! 8.2 ! 03-10 (Chanut J.) re-writting
	10	!! 9.0 ! 05-01 (C. Ethe) Free form, F90
	11	!!----------------------------------------------------------------------
[255]	12	#if defined key_zdfkpp \|\| defined key_esopa
	13	!!----------------------------------------------------------------------
	14	!! 'key_zdfkpp' KPP scheme
	15	!!----------------------------------------------------------------------
[503]	16	!!----------------------------------------------------------------------
[255]	17	!! zdf_kpp : update momentum and tracer Kz from a kpp scheme
	18	!! zdf_kpp_init : initialization, namelist read, and parameters control
	19	!!----------------------------------------------------------------------
	20	USE oce ! ocean dynamics and active tracers
	21	USE dom_oce ! ocean space and time domain
	22	USE zdf_oce ! ocean vertical physics
[888]	23	USE sbc_oce ! surface boundary condition: ocean
[255]	24	USE phycst ! physical constants
	25	USE eosbn2 ! equation of state
	26	USE zdfddm ! double diffusion mixing
[463]	27	USE in_out_manager ! I/O manager
	28	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
[258]	29	USE prtctl ! Print control
[255]	30
	31	IMPLICIT NONE
	32	PRIVATE
	33
[503]	34	PUBLIC zdf_kpp ! routine called by step.F90
	35	PUBLIC tra_kpp ! routine called by step.F90
[255]	36
[503]	37	LOGICAL, PUBLIC, PARAMETER :: lk_zdfkpp = .TRUE. !: KPP vertical mixing flag
	38	REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: ghats !: non-local scalar mixing term (gamma/<ws>o)
[255]	39	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: &
[503]	40	wt0 , & !: surface temperature flux for non local flux
	41	ws0 , & !: surface salinity flux for non local flux
	42	hkpp !: boundary layer depht
	43
[255]	44	INTEGER :: & !!! kpp namelist (namkpp)
	45	nave = 1 , & ! = 0/1 flag for horizontal average on avt, avmu, avmv
	46	navb = 0 ! = 0/1 flag for constant or profile background avt
	47
	48	REAL(wp) :: & !!! ** Interior Mixing
	49	difmiw = 1.2e-04_wp , & ! constant internal wave viscosity (m2/s)
	50	difsiw = 1.2e-05_wp , & ! constant internal wave diffusivity (m2/s)
	51	Riinfty = 0.8_wp , & ! local Richardson Number limit for shear instability
	52	difri = 5.e-03_wp , & ! maximum shear mixing at Rig = 0 (m2/s)
	53	bvsqcon = -1.e-09_wp , & ! Brunt-Vaisala squared (1/s**2) for maximum convection
	54	difcon = 1._wp ! maximum mixing in interior convection (m2/s)
	55	#if defined key_zdfddm
	56	REAL(wp) :: & !!! ** Double diffusion Mixing
	57	difssf = 1.e-03_wp , & ! maximum salt fingering mixing
	58	Rrho0 = 1.9_wp , & ! limit for salt fingering mixing
	59	difsdc = 1.5e-06_wp ! maximum diffusive convection mixing
	60	#endif
	61	LOGICAL :: &
	62	ln_kpprimix = .TRUE. ! Shear instability mixing
	63
	64	REAL(wp) :: & !!! General constants
	65	epsln = 1.0e-20_wp , & ! a small positive number
	66	pthird = 1._wp/3._wp , & ! 1/3
	67	pfourth = 1._wp/4._wp ! 1/4
	68
	69	REAL(wp) :: & !!! Boundary Layer Turbulence Parameters
	70	vonk = 0.4_wp , & ! von Karman's constant
	71	epsilon = 0.1_wp , & ! nondimensional extent of the surface layer
	72	rconc1 = 5.0_wp , & ! standard flux profile function parmaeters
	73	rconc2 = 16.0_wp , & ! " "
	74	rconcm = 8.38_wp , & ! momentum flux profile fit
	75	rconam = 1.26_wp , & ! " "
	76	rzetam = -.20_wp , & ! " "
	77	rconcs = 98.96_wp , & ! scalar flux profile fit
	78	rconas = -28.86_wp , & ! " "
	79	rzetas = -1.0_wp ! " "
	80	REAL(wp) :: & !!! Boundary Layer Depth Diagnostic
	81	Ricr = 0.3_wp , & ! critical bulk Richardson Number
	82	rcekman = 0.7_wp , & ! coefficient for ekman depth
	83	rcmonob = 1.0_wp , & ! coefficient for Monin-Obukhov depth
	84	rconcv = 1.7_wp , & ! ratio of interior buoyancy frequency to buoyancy frequency at entrainment depth
	85	hbf = 1.0_wp , & ! fraction of bound. layer depth to which absorbed solar
	86	! ! rad. and contributes to surf. buo. forcing
	87	Vtc ! function of rconcv,rconcs,epsilon,vonk,Ricr
	88	REAL(wp) :: & !!! Nonlocal Boundary Layer Mixing
	89	rcstar = 5.0_wp , & ! coefficient for convective nonlocal transport
	90	rcs = 1.0e-3_wp , & ! conversion: mm/s ==> m/s
	91	rcg ! non-dimensional coefficient for nonlocal transport
	92
	93	#if ! defined key_kppcustom
	94	REAL(wp), DIMENSION(jpk,jpk) :: &
	95	del ! array for reference mean values of vertical integration
	96	#endif
	97
	98	#if defined key_kpplktb
	99	INTEGER, PARAMETER :: & !!! Parameters for lookup table for turbulent velocity scales
	100	nilktb = 892 , & ! number of values for zehat in KPP lookup table
	101	njlktb = 482 , & ! number of values for ustar in KPP lookup table
	102	nilktbm1 = nilktb - 1 , & !
	103	njlktbm1 = njlktb - 1 !
	104
	105	REAL(wp), DIMENSION(nilktb,njlktb) :: &
	106	wmlktb , & ! lookup table for the turbulent vertical velocity scale for momentum
	107	wslktb ! lookup table for the turbulent vertical velocity scale for tracers
	108
	109	REAL(wp) :: &
	110	dehatmin = -4.e-7_wp , & ! minimum limit for zhat in lookup table (m3/s3)
	111	dehatmax = 0._wp , & ! maximum limit for zhat in lookup table (m3/s3)
	112	ustmin = 0._wp , & ! minimum limit for ustar in lookup table (m/s)
	113	ustmax = 0.04_wp , & ! maximum limit for ustar in lookup table (m/s)
	114	dezehat , & ! delta zhat in lookup table
	115	deustar ! delta ustar in lookup table
	116	#endif
	117	REAL(wp), DIMENSION(jpk) :: & !!! attenuation coef
	118	ratt
	119	!! already defines in module traqsr, but only if the solar radiation penetration is considered
	120	REAL(wp) :: & !!! * penetrative solar radiation coefficient *
	121	rabs = 0.58_wp , & ! fraction associated with xsi1
	122	xsi1 = 0.35_wp , & ! first depth of extinction
	123	xsi2 = 23.0_wp ! second depth of extinction
	124	! ! (default values: water type Ib)
	125
	126	REAL(wp), DIMENSION(jpi,jpj,jpk) :: &
	127	etmean , & ! coefficient used for horizontal smoothing
	128	eumean , & ! at t-, u- and v-points
	129	evmean
	130
	131	#if defined key_cfg_1d
	132	REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: &
	133	rig , & ! gradient Richardson number
	134	rib , & ! bulk Richardson number
	135	buof , & ! buoyancy forcing
	136	mols ! moning-Obukhov length scale
	137	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: &
	138	ekdp ! Ekman depth
	139	#endif
	140
	141	INTEGER :: & !
	142	jip = 62 , jjp = 111
	143
	144	!! * Substitutions
	145	# include "domzgr_substitute.h90"
	146	# include "vectopt_loop_substitute.h90"
	147	!!----------------------------------------------------------------------
	148	!! OPA 9.0 , LOCEAN-IPSL (2005)
[888]	149	!! $Id$
[503]	150	!! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt)
[255]	151	!!----------------------------------------------------------------------
	152
	153	CONTAINS
	154
	155	SUBROUTINE zdf_kpp ( kt )
	156	!!----------------------------------------------------------------------
	157	!! * ROUTINE zdf_kpp *
	158	!!
	159	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	160	!! coefficients and non local mixing using K-profile parameterization
	161	!!
	162	!! ** Method : The boundary layer depth hkpp is diagnosed at tracer points
	163	!! from profiles of buoyancy, and shear, and the surface forcing.
	164	!! Above hbl (sigma=-z/hbl <1) the mixing coefficients are computed from
	165	!!
	166	!! Kx = hkpp Wx(sigma) G(sigma)
	167	!!
	168	!! and the non local term ghat = Cs / Ws(sigma) / hkpp
	169	!! Below hkpp the coefficients are the sum of mixing due to internal waves
	170	!! shear instability and double diffusion.
	171	!!
	172	!! -1- Compute the now interior vertical mixing coefficients at all depths.
	173	!! -2- Diagnose the boundary layer depth.
	174	!! -3- Compute the now boundary layer vertical mixing coefficients.
	175	!! -4- Compute the now vertical eddy vicosity and diffusivity.
	176	!! -5- Smoothing
	177	!!
	178	!! N.B. The computation is done from jk=2 to jpkm1
	179	!! Surface value of avt avmu avmv are set once a time to zero
	180	!! in routine zdf_kpp_init.
	181	!!
	182	!! ** Action : update the non-local terms ghats
	183	!! update avt, avmu, avmv (before vertical eddy coef.)
	184	!!
[503]	185	!! References : Large W.G., Mc Williams J.C. and Doney S.C.
[255]	186	!! Reviews of Geophysics, 32, 4, November 1994
	187	!! Comments in the code refer to this paper, particularly
	188	!! the equation number. (LMD94, here after)
	189	!!----------------------------------------------------------------------
	190	#if defined key_zdfddm
	191	USE oce , zviscos => ua, & ! temp. array for viscosities use ua as workspace
	192	& zdiffut => ta, & ! temp. array for diffusivities use sa as workspace
	193	& zdiffus => sa ! temp. array for diffusivities use sa as workspace
	194	#else
	195	USE oce , zviscos => ua, & ! temp. array for viscosities use ua as workspace
	196	& zdiffut => ta ! temp. array for diffusivities use sa as workspace
	197	#endif
[503]	198	!!
	199	INTEGER, INTENT( in ) :: kt ! ocean time step
	200	!!
	201	INTEGER :: ji, jj, jk ! dummy loop indices
	202	INTEGER :: ikbot, jkmax, jkm1, jkp2 !
[255]	203
	204	REAL(wp), DIMENSION(jpi,jpj) :: & !!! Surface buoyancy forcing, friction velocity
	205	zBo, zBosol, zustar !
	206	!
	207	REAL(wp) :: & !
	208	ztx, zty, ztau, zflageos, & !
	209	zstabl, zbuofdep,zucube, & !
	210	zrhos, zalbet, zbeta, & !
	211	zthermal, zhalin, zatt1 !
	212
	213	REAL(wp) :: & !!! Bulk richardson number
	214	zref, zt, zs, zh, & !
	215	zu, zv, zrh, & !
	216	zrib, zrinum, & !
	217	zdVsq, zVtsq !
	218
	219	REAL(wp) :: & !!! Velocity scales
	220	zehat, zeta, zhrib, zsig, & !
	221	zscale, zwst, zws, zwm
	222
	223	#if defined key_kpplktb
	224	INTEGER :: & !!! Lookup table or Analytical functions
	225	il, jl !
	226	REAL(wp) :: & !
	227	ud, zfrac, ufrac, & !
	228	zwam, zwbm, zwas, zwbs !
	229	#else
	230	REAL(wp) :: & !
	231	zwsun, zwmun, &
	232	zcons, zconm, zwcons, zwconm !
	233	#endif
	234
	235	REAL(wp) :: & !!! In situ density
	236	zsr, zbw, ze, & !
	237	zb, zd, zc, zaw, za, & !
	238	zb1, za1, zkw, zk0, & !
	239	zcomp , zrhd, zrhdr,zbvzed !
	240
	241	#if ! defined key_kppcustom
	242	!! * local declarations
	243	INTEGER :: &
	244	jm ! dummy loop indices
	245	REAL(wp) :: & !!! Compression terms
	246	zr1, zr2, zr3, zr4, & !
	247	zrhop !
	248	#endif
	249
	250	REAL(wp) :: & !
	251	zflag, ztemp, zrn2, & !
	252	zdep21, zdep32, zdep43
	253
	254	REAL(wp) :: & !!! Interior richardson mixing
	255	zdku2, zdkv2, ze3sqr, & !
	256	zsh2, zri, zfri !
	257
	258	REAL(wp), DIMENSION(jpi,0:2) :: & !!! Moning-Obukov limitation
	259	zmoek
	260	REAL(wp), DIMENSION(jpi) :: &
	261	zmoa, zekman
	262	REAL(wp) :: &
	263	zmob, zek
	264
	265	REAL(wp), DIMENSION(jpi,4) :: & !!! The pipe
	266	zdepw, zdift, zvisc
	267	REAL(wp), DIMENSION(jpi,3) :: &
	268	zdept
	269	REAL(wp), DIMENSION(jpi,2) :: &
	270	zriblk
	271	REAL(wp), DIMENSION(jpi,jpk) :: & !
	272	zmask
	273	REAL(wp), DIMENSION(jpi) :: & !
	274	zhmax, zria, zhbl
	275	REAL(wp) :: & !
	276	zflagri, zflagek, & !
	277	zflagmo, zflagh, zflagkb !
	278	REAL(wp), DIMENSION(jpi) :: & !!! Shape function (G)
	279	za2m, za3m, zkmpm, &
	280	za2t, za3t, zkmpt
	281	REAL(wp) :: & !
	282	zdelta, zdelta2, & !
	283	zdzup, zdzdn, zdzh, & !
	284	zvath, zgat1, zdat1, & !
	285	zkm1m, zkm1t
	286	REAL(wp), DIMENSION(jpi,jpk) :: & !!! Boundary layer diffusivities/viscosities
	287	zblcm, zblct
	288	#if defined key_zdfddm
	289	REAL(wp) :: & !!! double diffusion mixing
	290	zrrau, zds, &
	291	zavdds, zavddt,zinr
	292	REAL(wp), DIMENSION(jpi,4) :: &
	293	zdifs
	294	REAL(wp), DIMENSION(jpi) :: &
	295	za2s, za3s, zkmps
	296	REAL(wp) :: &
	297	zkm1s
	298	REAL(wp), DIMENSION(jpi,jpk) :: &
	299	zblcs
	300	#endif
	301	!!--------------------------------------------------------------------
	302
	303
	304	! Initialization (first time-step only)
	305	! --------------
	306	IF( kt == nit000 ) CALL zdf_kpp_init
	307
	308	zviscos(:,:,:) = 0.
	309	zblcm (:,: ) = 0.
	310	zdiffut(:,:,:) = 0.
	311	zblct (:,: ) = 0.
	312	#if defined key_zdfddm
	313	zdiffus(:,:,:) = 0.
	314	zblcs (:,: ) = 0.
	315	#endif
	316	ghats(:,:,:) = 0.
	317
	318	zBo (:,:) = 0.
	319	zBosol(:,:) = 0.
	320	zustar(:,:) = 0.
	321
	322
	323	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	324	! I. Interior diffusivity and viscosity at w points ( T interfaces)
	325	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	326	DO jk = 2, jpkm1
	327	DO jj = 2, jpjm1
	328	DO ji = fs_2, fs_jpim1
	329	! Mixing due to internal waves breaking
	330	! -------------------------------------
	331	avmu(ji,jj,jk) = difmiw
	332	avt (ji,jj,jk) = difsiw
	333	! Mixing due to vertical shear instability
	334	! -------------------------------------
	335	IF( ln_kpprimix ) THEN
	336	! Compute the gradient Richardson number at interfaces (zri):
	337	! LMD94, eq. 27 (is vertical smoothing needed : Rig=N^2 / (dz(u))^2 + (dz(v))^2
	338	zdku2 = ( un(ji - 1,jj,jk - 1) - un(ji - 1,jj,jk) ) &
	339	& * ( un(ji - 1,jj,jk - 1) - un(ji - 1,jj,jk) ) &
	340	& + ( un(ji ,jj,jk - 1) - un(ji ,jj,jk) ) &
	341	& * ( un(ji ,jj,jk - 1) - un(ji ,jj,jk) )
	342
	343	zdkv2 = ( vn(ji,jj - 1,jk - 1) - vn(ji,jj - 1,jk) ) &
	344	& * ( vn(ji,jj - 1,jk - 1) - vn(ji,jj - 1,jk) ) &
	345	& + ( vn(ji, jj,jk - 1) - vn(ji, jj,jk) ) &
	346	& * ( vn(ji, jj,jk - 1) - vn(ji, jj,jk) )
	347
	348	ze3sqr = 1. / ( fse3w(ji,jj,jk) * fse3w(ji,jj,jk) )
	349	! Square of vertical shear at interfaces
	350	zsh2 = 0.5 * 0.5 * ( zdku2 + zdkv2 ) * ze3sqr
	351	zri = MAX( rn2(ji,jj,jk), 0. ) / ( zsh2 + epsln )
	352	#if defined key_cfg_1d
	353	! save the gradient richardson number
	354	rig(ji,jj,jk) = zri * tmask(ji,jj,jk)
	355	#endif
	356	! Evaluate f of Ri (zri) for shear instability store in zfri
	357	! LMD94, eq. 28a,b,c, figure 3 ; Rem: p1 is 3, hard coded
	358	zfri = MAX( zri , 0. )
	359	zfri = MIN( zfri / Riinfty , 1.0 )
	360	zfri = ( 1.0 - zfri * zfri )
	361	zfri = zfri * zfri * zfri
	362	! add shear contribution to mixing coef.
	363	avmu(ji,jj,jk) = avmu(ji,jj,jk) + difri * zfri
	364	avt (ji,jj,jk) = avt (ji,jj,jk) + difri * zfri
	365	ENDIF
	366	#if defined key_zdfddm
	367	avs (ji,jj,jk) = avt (ji,jj,jk)
	368	! Double diffusion mixing ; NOT IN ROUTINE ZDFDDM.F90
	369	! ------------------------------------------------------------------
	370	! only retains positive value of rrau
	371	zrrau = MAX( rrau(ji,jj,jk), epsln )
	372	zds = sn(ji,jj,jk-1) - sn(ji,jj,jk)
	373	IF( zrrau > 1. .AND. zds > 0.) THEN
	374	!
	375	! Salt fingering case.
	376	!---------------------
	377	! Compute interior diffusivity for double diffusive mixing of
	378	! salinity. Upper bound "zrrau" by "Rrho0"; (Rrho0=1.9, difcoefnuf=0.001).
	379	! After that set interior diffusivity for double diffusive mixing
	380	! of temperature
	381	zavdds = MIN( zrrau, Rrho0 )
	382	zavdds = ( zavdds - 1.0 ) / ( Rrho0 - 1.0 )
	383	zavdds = 1.0 - zavdds * zavdds
	384	zavdds = zavdds * zavdds * zavdds
	385	zavdds = difssf * zavdds
	386	zavddt = 0.7 * zavdds
	387	ELSEIF( zrrau < 1. .AND. zrrau > 0. .AND. zds < 0.) THEN
	388	!
	389	! Diffusive convection case.
	390	!---------------------------
	391	! Compute interior diffusivity for double diffusive mixing of
	392	! temperature (Marmorino and Caldwell, 1976);
	393	! Compute interior diffusivity for double diffusive mixing of salinity
	394	zinr = 1. / zrrau
	395	zavddt = 0.909 * EXP( 4.6 * EXP( -0.54* ( zinr - 1. ) ) )
	396	zavddt = difsdc * zavddt
	397	IF( zrrau < 0.5) THEN
	398	zavdds = zavddt * 0.15 * zrrau
	399	ELSE
	400	zavdds = zavddt * (1.85 * zrrau - 0.85 )
	401	ENDIF
	402	ELSE
	403	zavddt = 0.
	404	zavdds = 0.
	405	ENDIF
	406	! Add double diffusion contribution to temperature and salinity mixing coefficients.
	407	avt (ji,jj,jk) = avt (ji,jj,jk) + zavddt
	408	avs (ji,jj,jk) = avs (ji,jj,jk) + zavdds
	409	#endif
	410	END DO
	411	END DO
	412	END DO
	413
	414
	415	! Radiative (zBosol) and non radiative (zBo) surface buoyancy
	416	!JMM at the time zdfkpp is called, q still holds the sum q + qsr
	417	!---------------------------------------------------------------------
	418	DO jj = 2, jpjm1
	419	DO ji = fs_2, fs_jpim1
	420	IF( neos < 1) THEN
	421	zt = tn(ji,jj,1)
	422	zs = sn(ji,jj,1) - 35.0
	423	zh = fsdept(ji,jj,1)
	424	! potential volumic mass
	425	zrhos = rhop(ji,jj,1)
	426	zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta
	427	& - 0.203814e-03 ) * zt &
	428	& + 0.170907e-01 ) * zt &
	429	& + 0.665157e-01 &
	430	& + ( - 0.678662e-05 * zs &
	431	& - 0.846960e-04 * zt + 0.378110e-02 ) * zs &
	432	& + ( ( - 0.302285e-13 * zh &
	433	& - 0.251520e-11 * zs &
	434	& + 0.512857e-12 * zt * zt ) * zh &
	435	& - 0.164759e-06 * zs &
	436	& +( 0.791325e-08 * zt - 0.933746e-06 ) * zt &
	437	& + 0.380374e-04 ) * zh
	438
	439	zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta
	440	& - 0.301985e-05 ) * zt &
	441	& + 0.785567e-03 &
	442	& + ( 0.515032e-08 * zs &
	443	& + 0.788212e-08 * zt - 0.356603e-06 ) * zs &
	444	& +( ( 0.121551e-17 * zh &
	445	& - 0.602281e-15 * zs &
	446	& - 0.175379e-14 * zt + 0.176621e-12 ) * zh &
	447	& + 0.408195e-10 * zs &
	448	& + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt &
	449	& - 0.121555e-07 ) * zh
	450
	451	zthermal = zbeta * zalbet / ( rcp * zrhos + epsln )
	452	zhalin = zbeta * sn(ji,jj,1) * rcs
	453	ELSE
	454	zrhos = rhop(ji,jj,1) + rau0 * ( 1. - tmask(ji,jj,1) )
	455	zthermal = ralpha / ( rcp * zrhos + epsln )
	456	zhalin = rbeta * sn(ji,jj,1) * rcs
	457	ENDIF
	458	! Radiative surface buoyancy force
	459	zBosol(ji,jj) = grav * zthermal * qsr(ji,jj)
	460	! Non radiative surface buoyancy force
[888]	461	zBo (ji,jj) = grav * zthermal * qns(ji,jj) - grav * zhalin * emp(ji,jj)
[255]	462	! Surface Temperature flux for non-local term
[888]	463	wt0(ji,jj) = - ( qsr(ji,jj) + qns(ji,jj) )* ro0cpr * tmask(ji,jj,1)
[255]	464	! Surface salinity flux for non-local term
	465	ws0(ji,jj) = - ( emp(ji,jj) * sn(ji,jj,1) * rcs ) * tmask(ji,jj,1)
	466	ENDDO
	467	ENDDO
	468
	469	zflageos = 0.5 + SIGN( 0.5, neos - 1. )
	470	! Compute surface buoyancy forcing, Monin Obukhov and Ekman depths
	471	!------------------------------------------------------------------
	472	DO jj = 2, jpjm1
	473	DO ji = fs_2, fs_jpim1
	474	! Reference surface density = density at first T point level
	475	zrhos = rhop(ji,jj,1) + zflageos * rau0 * ( 1. - tmask(ji,jj,1) )
	476	! Friction velocity (zustar), at T-point : LMD94 eq. 2
[888]	477	ztx = 0.5 * ( utau(ji,jj) + utau(ji - 1, jj ) )
	478	zty = 0.5 * ( vtau(ji,jj) + vtau(ji , jj - 1) )
[255]	479	ztau = SQRT( ztx * ztx + zty * zty )
	480	zustar(ji,jj) = SQRT( ztau / ( zrhos + epsln ) )
	481	ENDDO
	482	ENDDO
	483
	484	!CDIR NOVERRCHK
	485	! ! ===============
	486	DO jj = 2, jpjm1 ! Vertical slab
	487	! ! ===============
	488
	489	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	490	! II Compute Boundary layer mixing coef. and diagnose the new boundary layer depth
	491	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	492
	493	! Initialization
	494	jkmax = 0
	495	zdept (:,:) = 0.
	496	zdepw (:,:) = 0.
	497	zriblk(:,:) = 0.
	498	zmoek (:,:) = 0.
	499	zvisc (:,:) = 0.
	500	zdift (:,:) = 0.
	501	#if defined key_zdfddm
	502	zdifs (:,:) = 0.
	503	#endif
	504	zmask (:,:) = 0.
	505	DO ji = fs_2, fs_jpim1
	506	zria(ji ) = 0.
	507	! Maximum boundary layer depth
	508	ikbot = mbathy(ji,jj) - 1 ! ikbot is the last T point in the water
	509	zhmax(ji) = fsdept(ji,jj,ikbot) - 0.001
	510	! Compute Monin obukhov length scale at the surface and Ekman depth:
	511	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * ratt(1)
	512	zekman(ji) = rcekman * zustar(ji,jj) / ( ABS( ff(ji,jj) ) + epsln )
	513	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	514	zmoa(ji) = zucube / ( vonk * ( zbuofdep + epsln ) )
	515	#if defined key_cfg_1d
	516	! store the surface buoyancy forcing
	517	zstabl = 0.5 + SIGN( 0.5, zbuofdep )
	518	buof(ji,jj,1) = zbuofdep * tmask(ji,jj,1)
	519	! store the moning-oboukov length scale at surface
	520	zmob = zstabl * zmoa(ji) + ( 1.0 - zstabl ) * fsdept(ji,jj,1)
	521	mols(ji,jj,1) = MIN( zmob , zhmax(ji) ) * tmask(ji,jj,1)
	522	! store Ekman depth
	523	zek = zstabl * zekman(ji) + ( 1.0 - zstabl ) * fsdept(ji,jj,1)
	524	ekdp(ji,jj ) = MIN( zek , zhmax(ji) ) * tmask(ji,jj,1)
	525	#endif
	526	END DO
	527	! Compute the pipe
	528	! ---------------------
	529	DO jk = 2, jpkm1
	530	DO ji = fs_2, fs_jpim1
	531	! Compute bfsfc = Bo + radiative contribution down to hbf*depht
	532	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * ratt(jk)
	533	! Flag (zstabl = 1) if positive forcing
	534	zstabl = 0.5 + SIGN( 0.5, zbuofdep)
	535
	536	! Compute bulk richardson number zrib at depht
	537	!-------------------------------------------------------
	538	! [Br - B(d)] * d zrinum
	539	! Rib(z) = ----------------------- = -------------
	540	! \|Vr - V(d)\|^2 + Vt(d)^2 zdVsq + zVtsq
	541	!
	542	! First compute zt,zs,zu,zv = means in the surface layer < epsilon*depht
	543	! Else surface values are taken at the first T level.
	544	! For stability, resolved vertical shear is computed with "before velocities".
	545	zref = epsilon * fsdept(ji,jj,jk)
	546	#if defined key_kppcustom
	547	! zref = gdept(1)
	548	zref = fsdept(ji,jj,1)
	549	zt = tn(ji,jj,1)
	550	zs = sn(ji,jj,1)
	551	zrh = rhop(ji,jj,1)
	552	zu = ( ub(ji,jj,1) + ub(ji - 1,jj ,1) ) / MAX( 1. , umask(ji,jj,1) + umask(ji - 1,jj ,1) )
	553	zv = ( vb(ji,jj,1) + vb(ji ,jj - 1,1) ) / MAX( 1. , vmask(ji,jj,1) + vmask(ji ,jj - 1,1) )
	554	#else
	555	zt = 0.
	556	zs = 0.
	557	zu = 0.
	558	zv = 0.
	559	zrh = 0.
	560	! vertically integration over the upper epsilon*gdept(jk) ; del () array is computed once in zdf_kpp_init
	561	DO jm = 1, jpkm1
	562	zt = zt + del(jk,jm) * tn(ji,jj,jm)
	563	zs = zs + del(jk,jm) * sn(ji,jj,jm)
	564	zu = zu + 0.5 * del(jk,jm) &
	565	& * ( ub(ji,jj,jm) + ub(ji - 1,jj,jm) ) &
	566	& / MAX( 1. , umask(ji,jj,jm) + umask(ji - 1,jj,jm) )
	567	zv = zv + 0.5 * del(jk,jm) &
	568	& * ( vb(ji,jj,jm) + vb(ji,jj - 1,jm) ) &
	569	& / MAX( 1. , vmask(ji,jj,jm) + vmask(ji,jj - 1,jm) )
	570	zrh = zrh + del(jk,jm) * rhop(ji,jj,jm)
	571	END DO
	572	#endif
	573	zsr = SQRT( ABS( sn(ji,jj,jk) ) )
	574	! depth
	575	zh = fsdept(ji,jj,jk)
	576	! compute compression terms on density
	577	ze = ( -3.508914e-8zt-1.248266e-8 ) zt-2.595994e-6
	578	zbw = ( 1.296821e-6zt-5.782165e-9 ) zt+1.045941e-4
	579	zb = zbw + ze * zs
	580
	581	zd = -2.042967e-2
	582	zc = (-7.267926e-5zt+2.598241e-3 ) zt+0.1571896
	583	zaw = ( ( 5.939910e-6zt+2.512549e-3 ) zt-0.1028859 ) *zt - 4.721788
	584	za = ( zdzsr + zc ) zs + zaw
	585
	586	zb1 = (-0.1909078zt+7.390729 ) zt-55.87545
	587	za1 = ( ( 2.326469e-3zt+1.553190)zt-65.00517 ) *zt+1044.077
	588	zkw = ( ( (-1.361629e-4zt-1.852732e-2 ) zt-30.41638 ) zt + 2098.925 ) zt+190925.6
	589	zk0 = ( zb1zsr + za1 )zs + zkw
	590	zcomp = 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) )
	591
	592	#if defined key_kppcustom
	593	! potential density of water(zrh = zt,zs at level jk):
	594	zrhdr = zrh / zcomp
	595	#else
	596	! potential density of water(ztref,zsref at level jk):
	597	! compute volumic mass pure water at atm pressure
	598	IF ( neos < 1 ) THEN
	599	zr1= ( ( ( ( 6.536332e-9zt-1.120083e-6 )zt+1.001685e-4)*zt &
	600	& -9.095290e-3 )zt+6.793952e-2 )zt+999.842594
	601	! seawater volumic mass atm pressure
	602	zr2= ( ( ( 5.3875e-9zt-8.2467e-7 ) zt+7.6438e-5 ) *zt &
	603	& -4.0899e-3 ) *zt+0.824493
	604	zr3= ( -1.6546e-6zt+1.0227e-4 ) zt-5.72466e-3
	605	zr4= 4.8314e-4
	606	! potential volumic mass (reference to the surface)
	607	zrhop= ( zr4zs + zr3zsr + zr2 ) *zs + zr1
	608	zrhdr = zrhop / zcomp
	609	ELSE
	610	zrhdr = zrh / zcomp
	611	ENDIF
	612	#endif
	613
	614	! potential density of ambiant water at level jk :
	615	zrhd = ( rhd(ji,jj,jk) * rau0 + rau0 )
	616
	617	! And now the Rib number numerator .
	618	zrinum = grav * ( zrhd - zrhdr ) / rau0
	619	zrinum = zrinum * ( fsdept(ji,jj,jk) - zref ) * tmask(ji,jj,jk)
	620
	621	! Resolved shear contribution to Rib at depth T-point (zdVsq)
	622	ztx = ( ub( ji , jj ,jk) + ub(ji - 1, jj ,jk) ) &
	623	& / MAX( 1. , umask( ji , jj ,jk) + umask(ji - 1, jj ,jk) )
	624	zty = ( vb( ji , jj ,jk) + vb(ji ,jj - 1,jk) ) &
	625	& / MAX( 1., vmask( ji , jj ,jk) + vmask(ji ,jj - 1,jk) )
	626
	627	zdVsq = ( zu - ztx ) * ( zu - ztx ) + ( zv - zty ) * ( zv - zty )
	628
	629	! Scalar turbulent velocity scale zws for hbl=gdept
	630	zscale = zstabl + ( 1.0 - zstabl ) * epsilon
	631	zehat = vonk * zscale * fsdept(ji,jj,jk) * zbuofdep
	632	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	633	zeta = zehat / ( zucube + epsln )
	634
	635	IF( zehat > 0. ) THEN
	636	! Stable case
	637	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	638	ELSE
	639	! Unstable case
	640	#if defined key_kpplktb
	641	! use lookup table
	642	zd = zehat - dehatmin
	643	il = INT( zd / dezehat )
	644	il = MIN( il, nilktbm1 )
	645	il = MAX( il, 1 )
	646
	647	ud = zustar(ji,jj) - ustmin
	648	jl = INT( ud / deustar )
	649	jl = MIN( jl, njlktbm1 )
	650	jl = MAX( jl, 1 )
	651
	652	zfrac = zd / dezehat - FLOAT( il )
	653	ufrac = ud / deustar - FLOAT( jl )
	654	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	655	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	656	!
	657	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	658	#else
	659	! use analytical functions:
	660	zcons = 0.5 + SIGN( 0.5 , ( rzetas - zeta ) )
	661	zwcons = vonk * zustar(ji,jj) * ( ( ABS( rconas - rconcs * zeta ) )**pthird )
	662	zwsun = vonk * zustar(ji,jj) * SQRT( ABS ( 1.0 - rconc2 * zeta ) )
	663	!
	664	zws = zcons * zwcons + ( 1.0 - zcons) * zwsun
	665	#endif
	666	ENDIF
	667
	668	! Turbulent shear contribution to Rib (zVtsq) bv frequency at levels ( ie T-point jk)
	669	zrn2 = 0.5 * ( rn2(ji,jj,jk) + rn2(ji,jj,jk+1) )
	670	zbvzed = SQRT( ABS( zrn2 ) )
	671	zVtsq = fsdept(ji,jj,jk) * zws * zbvzed * Vtc
	672
	673	! Finally, the bulk Richardson number at depth fsdept(i,j,k)
	674	zrib = zrinum / ( zdVsq + zVtsq + epsln )
	675
	676	! Find subscripts around the boundary layer depth, build the pipe
	677	! ----------------------------------------------------------------
	678
	679	! Flag (zflagri = 1) if zrib < Ricr
	680	zflagri = 0.5 + SIGN( 0.5, ( Ricr - zrib ) )
	681	! Flag (zflagh = 1) if still within overall boundary layer
	682	zflagh = 0.5 + SIGN( 0.5, ( fsdept(ji,jj,1) - zdept(ji,2) ) )
	683
	684	! Ekman layer depth
	685	zek = zstabl * zekman(ji) + ( 1.0 - zstabl ) * zhmax(ji)
	686	zflag = 0.5 + SIGN( 0.5, ( zek - fsdept(ji,jj,jk-1) ) )
	687	zek = zflag * zek + ( 1.0 - zflag ) * zhmax(ji)
	688	zflagek = 0.5 + SIGN( 0.5, ( zek - fsdept(ji,jj,jk) ) )
	689	! Flag (zflagmo = 1) if still within stable Monin-Obukhov and in water
	690	zmob = zucube / ( vonk * ( zbuofdep + epsln ) )
	691	ztemp = zstabl * zmob + ( 1.0 - zstabl) * zhmax(ji)
	692	ztemp = MIN( ztemp , zhmax(ji) )
	693	zflagmo = 0.5 + SIGN( 0.5, ( ztemp - fsdept(ji,jj,jk) ) )
	694
	695	! No limitation by Monin Obukhov or Ekman depths:
	696	! zflagek = 1.0
	697	! zflagmo = 0.5 + SIGN( 0.5, ( zhmax(ji) - fsdept(ji,jj,jk) ) )
	698
	699	! Load pipe via zflagkb for later calculations
	700	! Flag (zflagkb = 1) if zflagh = 1 and (zflagri = 0 or zflagek = 0 or zflagmo = 0)
	701	zflagkb = zflagh * ( 1.0 - ( zflagri * zflagek * zflagmo ) )
	702
	703	zmask(ji,jk) = zflagh
	704	jkp2 = MIN( jk+2 , ikbot )
	705	jkm1 = MAX( jk-1 , 2 )
	706	jkmax = MAX( jkmax, jk * INT( REAL( zflagh+epsln ) ) )
	707
	708	zdept(ji,1) = zdept(ji,1) + zflagkb * fsdept(ji,jj,jk-1)
	709	zdept(ji,2) = zdept(ji,2) + zflagkb * fsdept(ji,jj,jk )
	710	zdept(ji,3) = zdept(ji,3) + zflagkb * fsdept(ji,jj,jk+1)
	711
	712	zdepw(ji,1) = zdepw(ji,1) + zflagkb * fsdepw(ji,jj,jk-1)
	713	zdepw(ji,2) = zdepw(ji,2) + zflagkb * fsdepw(ji,jj,jk )
	714	zdepw(ji,3) = zdepw(ji,3) + zflagkb * fsdepw(ji,jj,jk+1)
	715	zdepw(ji,4) = zdepw(ji,4) + zflagkb * fsdepw(ji,jj,jkp2)
	716
	717	zriblk(ji,1) = zriblk(ji,1) + zflagkb * zria(ji)
	718	zriblk(ji,2) = zriblk(ji,2) + zflagkb * zrib
	719
	720	zmoek (ji,0) = zmoek (ji,0) + zflagkb * zek
	721	zmoek (ji,1) = zmoek (ji,1) + zflagkb * zmoa(ji)
	722	zmoek (ji,2) = zmoek (ji,2) + zflagkb * ztemp
	723	! Save Monin Obukhov depth
	724	zmoa (ji) = zmob
	725
	726	zvisc(ji,1) = zvisc(ji,1) + zflagkb * avmu(ji,jj,jkm1)
	727	zvisc(ji,2) = zvisc(ji,2) + zflagkb * avmu(ji,jj,jk )
	728	zvisc(ji,3) = zvisc(ji,3) + zflagkb * avmu(ji,jj,jk+1)
	729	zvisc(ji,4) = zvisc(ji,4) + zflagkb * avmu(ji,jj,jkp2)
	730
	731	zdift(ji,1) = zdift(ji,1) + zflagkb * avt (ji,jj,jkm1)
	732	zdift(ji,2) = zdift(ji,2) + zflagkb * avt (ji,jj,jk )
	733	zdift(ji,3) = zdift(ji,3) + zflagkb * avt (ji,jj,jk+1)
	734	zdift(ji,4) = zdift(ji,4) + zflagkb * avt (ji,jj,jkp2)
	735
	736	#if defined key_zdfddm
	737	zdifs(ji,1) = zdifs(ji,1) + zflagkb * avs (ji,jj,jkm1)
	738	zdifs(ji,2) = zdifs(ji,2) + zflagkb * avs (ji,jj,jk )
	739	zdifs(ji,3) = zdifs(ji,3) + zflagkb * avs (ji,jj,jk+1)
	740	zdifs(ji,4) = zdifs(ji,4) + zflagkb * avs (ji,jj,jkp2)
	741	#endif
	742	! Save the Richardson number
	743	zria (ji) = zrib
	744	#if defined key_cfg_1d
	745	! store buoyancy length scale
	746	buof(ji,jj,jk) = zbuofdep * tmask(ji,jj,jk)
	747	! store Monin Obukhov
	748	zmob = zstabl * zmob + ( 1.0 - zstabl) * fsdept(ji,jj,1)
	749	mols(ji,jj,jk) = MIN( zmob , zhmax(ji) ) * tmask(ji,jj,jk)
	750	! Bulk Richardson number
	751	rib(ji,jj,jk) = zrib * tmask(ji,jj,jk)
	752	#endif
	753	END DO
	754	END DO
	755	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	756	! III PROCESS THE PIPE
	757	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	758
	759	DO ji = fs_2, fs_jpim1
	760
	761	! Find the boundary layer depth zhbl
	762	! ----------------------------------------
	763
	764	! Interpolate monin Obukhov and critical Ri mumber depths
	765	ztemp = zdept(ji,2) - zdept(ji,1)
	766	zflag = ( Ricr - zriblk(ji,1) ) / ( zriblk(ji,2) - zriblk(ji,1) + epsln )
	767	zhrib = zdept(ji,1) + zflag * ztemp
	768
	769	IF( zriblk(ji,2) < Ricr ) zhrib = zhmax(ji)
	770
	771	IF( zmoek(ji,2) < zdept(ji,2) ) THEN
	772	IF ( zmoek(ji,1) < 0. ) THEN
	773	zmob = zdept(ji,2) - epsln
	774	ELSE
	775	zmob = ztemp + zmoek(ji,1) - zmoek(ji,2)
	776	zmob = ( zmoek(ji,1) * zdept(ji,2) - zmoek(ji,2) * zdept(ji,1) ) / zmob
	777	zmob = MAX( zmob , zdept(ji,1) + epsln )
	778	ENDIF
	779	ELSE
	780	zmob = zhmax(ji)
	781	ENDIF
	782	ztemp = MIN( zmob , zmoek(ji,0) )
	783
	784	! Finally, the boundary layer depth, zhbl
	785	zhbl(ji) = MAX( fsdept(ji,jj,1) + epsln, MIN( zhrib , ztemp ) )
	786
	787	! Save hkpp for further diagnostics (optional)
	788	hkpp(ji,jj) = zhbl(ji) * tmask(ji,jj,1)
	789
	790	! Correct mask if zhbl < fsdepw(ji,jj,2) for no viscosity/diffusivity enhancement at fsdepw(ji,jj,2)
	791	! zflag = 1 if zhbl(ji) > fsdepw(ji,jj,2)
	792	IF( zhbl(ji) < fsdepw(ji,jj,2) ) zmask(ji,2) = 0.
	793
	794
	795	! Velocity scales at depth zhbl
	796	! -----------------------------------
	797
	798	! Compute bouyancy forcing down to zhbl
	799	ztemp = -hbf * zhbl(ji)
	800	zatt1 = 1.0 - ( rabs * EXP( ztemp / xsi1 ) + ( 1.0 - rabs ) * EXP( ztemp / xsi2 ) )
	801	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * zatt1
	802	zstabl = 0.5 + SIGN( 0.5 , zbuofdep )
	803
	804	zbuofdep = zbuofdep + zstabl * epsln
	805
	806	zscale = zstabl + ( 1.0 - zstabl ) * epsilon
	807	zehat = vonk * zscale * zhbl(ji) * zbuofdep
	808	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	809	zeta = zehat / ( zucube + epsln )
	810
	811	IF( zehat > 0. ) THEN
	812	! Stable case
	813	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	814	zwm = zws
	815	ELSE
	816	! Unstable case
	817	#if defined key_kpplktb
	818	! use lookup table
	819	zd = zehat - dehatmin
	820	il = INT( zd / dezehat )
	821	il = MIN( il, nilktbm1 )
	822	il = MAX( il, 1 )
	823
	824	ud = zustar(ji,jj) - ustmin
	825	jl = INT( ud / deustar )
	826	jl = MIN( jl, njlktbm1 )
	827	jl = MAX( jl, 1 )
	828
	829	zfrac = zd / dezehat - FLOAT( il )
	830	ufrac = ud / deustar - FLOAT( jl )
	831	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	832	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	833	zwam = ( 1. - zfrac ) * wmlktb(il,jl+1) + zfrac * wmlktb(il+1,jl+1)
	834	zwbm = ( 1. - zfrac ) * wmlktb(il,jl ) + zfrac * wmlktb(il+1,jl )
	835	!
	836	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	837	zwm = ( 1. - ufrac ) * zwbm + ufrac * zwam
	838	#else
	839	! use analytical functions
	840	zconm = 0.5 + SIGN( 0.5, ( rzetam - zeta) )
	841	zcons = 0.5 + SIGN( 0.5, ( rzetas - zeta) )
	842
	843	! Momentum : zeta < rzetam (zconm = 1)
	844	! Scalars : zeta < rzetas (zcons = 1)
	845	zwconm = zustar(ji,jj) * vonk * ( ( ABS( rconam - rconcm * zeta) )**pthird )
	846	zwcons = zustar(ji,jj) * vonk * ( ( ABS( rconas - rconcs * zeta) )**pthird )
	847
	848	! Momentum : rzetam <= zeta < 0 (zconm = 0)
	849	! Scalars : rzetas <= zeta < 0 (zcons = 0)
	850	zwmun = SQRT( ABS( 1.0 - rconc2 * zeta ) )
	851	zwsun = vonk * zustar(ji,jj) * zwmun
	852	zwmun = vonk * zustar(ji,jj) * SQRT(zwmun)
	853	!
	854	zwm = zconm * zwconm + ( 1.0 - zconm ) * zwmun
	855	zws = zcons * zwcons + ( 1.0 - zcons ) * zwsun
	856
	857	#endif
	858	ENDIF
	859
	860
	861	! Viscosity, diffusivity values and derivatives at h
	862	! --------------------------------------------------------
	863
	864	! check between at which interfaces is located zhbl(ji)
	865	! ztemp = 1, zdepw(ji,2) < zhbl < zdepw(ji,3)
	866	! ztemp = 0, zdepw(ji,1) < zhbl < zdepw(ji,2)
	867	ztemp = 0.5 + SIGN( 0.5, ( zhbl(ji) - zdepw(ji,2) ) )
	868	zdep21 = zdepw(ji,2) - zdepw(ji,1) + epsln
	869	zdep32 = zdepw(ji,3) - zdepw(ji,2) + epsln
	870	zdep43 = zdepw(ji,4) - zdepw(ji,3) + epsln
	871
	872	! Compute R as in LMD94, eq D5b
	873	zdelta = ( zhbl(ji) - zdepw(ji,2) ) * ztemp / zdep32 &
	874	& + ( zhbl(ji) - zdepw(ji,1) ) * ( 1.0 - ztemp ) / zdep21
	875
	876	! Compute the vertical derivative of viscosities (zdzh) at z=zhbl(ji)
	877	zdzup = ( zvisc(ji,2) - zvisc(ji,3) ) * ztemp / zdep32 &
	878	& + ( zvisc(ji,1) - zvisc(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	879
	880	zdzdn = ( zvisc(ji,3) - zvisc(ji,4) ) * ztemp / zdep43 &
	881	& + ( zvisc(ji,2) - zvisc(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	882
	883	! LMD94, eq D5b :
	884	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	885	zdzh = MAX( zdzh , 0. )
	886
	887	! Compute viscosities (zvath) at z=zhbl(ji), LMD94 eq D5a
	888	zvath = ztemp * ( zvisc(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	889	& + ( 1.0 - ztemp ) * ( zvisc(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	890
	891	! Compute G (zgat1) and its derivative (zdat1) at z=hbl(ji), LMD94 eq 18
	892
	893	! Vertical derivative of velocity scale divided by velocity scale squared at z=hbl(ji)
	894	! (non zero only in stable conditions)
	895	zflag = -zstabl * rconc1 * zbuofdep / ( zucube * zustar(ji,jj) + epsln )
	896
	897	! G at its derivative at z=hbl:
	898	zgat1 = zvath / ( zhbl(ji) * ( zwm + epsln ) )
	899	zdat1 = -zdzh / ( zwm + epsln ) - zflag * zvath / zhbl(ji)
	900
	901	! G coefficients, LMD94 eq 17
	902	za2m(ji) = -2.0 + 3.0 * zgat1 - zdat1
	903	za3m(ji) = 1.0 - 2.0 * zgat1 + zdat1
	904
	905
	906	! Compute the vertical derivative of temperature diffusivities (zdzh) at z=zhbl(ji)
	907	zdzup = ( zdift(ji,2) - zdift(ji,3) ) * ztemp / zdep32 &
	908	& + ( zdift(ji,1) - zdift(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	909
	910	zdzdn = ( zdift(ji,3) - zdift(ji,4) ) * ztemp / zdep43 &
	911	& + ( zdift(ji,2) - zdift(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	912
	913	! LMD94, eq D5b :
	914	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	915	zdzh = MAX( zdzh , 0. )
	916
	917
	918	! Compute diffusivities (zvath) at z=zhbl(ji), LMD94 eq D5a
	919	zvath = ztemp * ( zdift(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	920	& + ( 1.0 - ztemp ) * ( zdift(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	921
	922	! G at its derivative at z=hbl:
	923	zgat1 = zvath / ( zhbl(ji) * ( zws + epsln ) )
	924	zdat1 = -zdzh / ( zws + epsln ) - zflag * zvath / zhbl(ji)
	925
	926	! G coefficients, LMD94 eq 17
	927	za2t(ji) = -2.0 + 3.0 * zgat1 - zdat1
	928	za3t(ji) = 1.0 - 2.0 * zgat1 + zdat1
	929
	930	#if defined key_zdfddm
	931	! Compute the vertical derivative of salinities diffusivities (zdzh) at z=zhbl(ji)
	932	zdzup = ( zdifs(ji,2) - zdifs(ji,3) ) * ztemp / zdep32 &
	933	& + ( zdifs(ji,1) - zdifs(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	934
	935	zdzdn = ( zdifs(ji,3) - zdifs(ji,4) ) * ztemp / zdep43 &
	936	& + ( zdifs(ji,2) - zdifs(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	937
	938	! LMD94, eq D5b :
	939	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	940	zdzh = MAX( zdzh , 0. )
	941
	942	! Compute diffusivities (zvath) at z=zhbl(ji), LMD94 eq D5a
	943	zvath = ztemp * ( zdifs(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	944	& + ( 1.0 - ztemp ) * ( zdifs(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	945
	946	! G at its derivative at z=hbl:
	947	zgat1 = zvath / ( zhbl(ji) * ( zws + epsln ) )
	948	zdat1 = -zdzh / ( zws + epsln ) - zflag * zvath / zhbl(ji)
	949
	950	! G coefficients, LMD94 eq 17
	951	za2s(ji) = -2.0 + 3.0 * zgat1 - zdat1
	952	za3s(ji) = 1.0 - 2.0 * zgat1 + zdat1
	953	#endif
	954
	955	!-------------------turn off interior matching here------
	956	! za2(ji,1) = -2.0
	957	! za3(ji,1) = 1.0
	958	! za2(ji,2) = -2.0
	959	! za3(ji,2) = 1.0
	960	!--------------------------------------------------------
	961
	962	! Compute Enhanced Mixing Coefficients (LMD94,eq D6)
	963	! ---------------------------------------------------------------
	964
	965	! Delta
	966	zdelta = ( zhbl(ji) - zdept(ji,1) ) / ( zdept(ji,2) - zdept(ji,1) + epsln )
	967	zdelta2 = zdelta * zdelta
	968
	969	! Mixing coefficients at first level above h (zdept(ji,1))
	970	! and at first interface in the pipe (zdepw(ji,2))
	971
	972	! At first T level above h (zdept(ji,1)) (always in the boundary layer)
	973	zsig = zdept(ji,1) / zhbl(ji)
	974	ztemp = zstabl * zsig + ( 1.0 - zstabl ) * MIN( zsig , epsilon )
	975	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	976	zeta = zehat / ( zucube + epsln)
	977	zwst = vonk * zustar(ji,jj) / ( ABS( 1.0 + rconc1 * zeta ) + epsln)
	978	zwm = zstabl * zwst + ( 1.0 - zstabl ) * zwm
	979	zws = zstabl * zwst + ( 1.0 - zstabl ) * zws
	980
	981	zkm1m = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	982	zkm1t = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	983	#if defined key_zdfddm
	984	zkm1s = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	985	#endif
	986	! At first W level in the pipe (zdepw(ji,2)) (not always in the boundary layer ):
	987	zsig = MIN( zdepw(ji,2) / zhbl(ji) , 1.0 )
	988	ztemp = zstabl * zsig + ( 1.0 - zstabl ) * MIN( zsig , epsilon )
	989	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	990	zeta = zehat / ( zucube + epsln )
	991	zwst = vonk * zustar(ji,jj) / ( ABS( 1.0 + rconc1 * zeta ) + epsln)
	992	zws = zstabl * zws + ( 1.0 - zstabl ) * zws
	993	zwm = zstabl * zws + ( 1.0 - zstabl ) * zwm
	994
	995	zkmpm(ji) = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	996	zkmpt(ji) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	997	#if defined key_zdfddm
	998	zkmps(ji) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	999	#endif
	1000
	1001	! check if this point is in the boundary layer,else take interior viscosity/diffusivity:
	1002	zflag = 0.5 + SIGN( 0.5, ( zhbl(ji) - zdepw(ji,2) ) )
	1003	zkmpm(ji) = zkmpm(ji) * zflag + ( 1.0 - zflag ) * zvisc(ji,2)
	1004	zkmpt(ji) = zkmpt(ji) * zflag + ( 1.0 - zflag ) * zdift(ji,2)
	1005	#if defined key_zdfddm
	1006	zkmps(ji) = zkmps(ji) * zflag + ( 1.0 - zflag ) * zdifs(ji,2)
	1007	#endif
	1008
	1009	! Enhanced viscosity/diffusivity at zdepw(ji,2)
	1010	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1m + zdelta2 * zkmpm(ji)
	1011	zkmpm(ji) = ( 1.0 - zdelta ) * zvisc(ji,2) + zdelta * ztemp
	1012	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1t + zdelta2 * zkmpt(ji)
	1013	zkmpt(ji) = ( 1.0 - zdelta ) * zdift(ji,2) + zdelta * ztemp
	1014	#if defined key_zdfddm
	1015	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1s + zdelta2 * zkmps(ji)
	1016	zkmps(ji) = ( 1.0 - zdelta ) * zdifs(ji,2) + zdelta * ztemp
	1017	#endif
	1018
	1019	END DO
	1020	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	1021	! IV. Compute vertical eddy viscosity and diffusivity coefficients
	1022	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	1023
	1024	DO jk = 2, jkmax
	1025
	1026	! Compute turbulent velocity scales on the interfaces
	1027	! --------------------------------------------------------
	1028	DO ji = fs_2, fs_jpim1
	1029	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * zatt1
	1030	zstabl = 0.5 + SIGN( 0.5 , zbuofdep )
	1031	zbuofdep = zbuofdep + zstabl * epsln
	1032	zsig = fsdepw(ji,jj,jk) / zhbl(ji)
	1033	ztemp = zstabl * zsig + ( 1. - zstabl ) * MIN( zsig , epsilon )
	1034	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	1035	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	1036	zeta = zehat / ( zucube + epsln )
	1037
	1038	IF( zehat > 0. ) THEN
	1039	! Stable case
	1040	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	1041	zwm = zws
	1042	ELSE
	1043	! Unstable case
	1044	#if defined key_kpplktb
	1045	! use lookup table
	1046	zd = zehat - dehatmin
	1047	il = INT( zd / dezehat )
	1048	il = MIN( il, nilktbm1 )
	1049	il = MAX( il, 1 )
	1050
	1051	ud = zustar(ji,jj) - ustmin
	1052	jl = INT( ud / deustar )
	1053	jl = MIN( jl, njlktbm1 )
	1054	jl = MAX( jl, 1 )
	1055
	1056	zfrac = zd / dezehat - FLOAT( il )
	1057	ufrac = ud / deustar - FLOAT( jl )
	1058	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	1059	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	1060	zwam = ( 1. - zfrac ) * wmlktb(il,jl+1) + zfrac * wmlktb(il+1,jl+1)
	1061	zwbm = ( 1. - zfrac ) * wmlktb(il,jl ) + zfrac * wmlktb(il+1,jl )
	1062	!
	1063	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	1064	zwm = ( 1. - ufrac ) * zwbm + ufrac * zwam
	1065	#else
	1066	! use analytical functions
	1067	zconm = 0.5 + SIGN( 0.5, ( rzetam - zeta) )
	1068	zcons = 0.5 + SIGN( 0.5, ( rzetas - zeta) )
	1069
	1070	! Momentum : zeta < rzetam (zconm = 1)
	1071	! Scalars : zeta < rzetas (zcons = 1)
	1072	zwconm = zustar(ji,jj) * vonk * ( ( ABS( rconam - rconcm * zeta) )**pthird )
	1073	zwcons = zustar(ji,jj) * vonk * ( ( ABS( rconas - rconcs * zeta) )**pthird )
	1074
	1075	! Momentum : rzetam <= zeta < 0 (zconm = 0)
	1076	! Scalars : rzetas <= zeta < 0 (zcons = 0)
	1077	zwmun = SQRT( ABS( 1.0 - rconc2 * zeta ) )
	1078	zwsun = vonk * zustar(ji,jj) * zwmun
	1079	zwmun = vonk * zustar(ji,jj) * SQRT(zwmun)
	1080	!
	1081	zwm = zconm * zwconm + ( 1.0 - zconm ) * zwmun
	1082	zws = zcons * zwcons + ( 1.0 - zcons ) * zwsun
	1083
	1084	#endif
	1085	ENDIF
	1086
	1087	zblcm(ji,jk) = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	1088	zblct(ji,jk) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	1089	#if defined key_zdfddm
	1090	zblcs(ji,jk) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	1091	#endif
	1092	! Compute Nonlocal transport term = ghats * <ws>o
	1093	! ----------------------------------------------------
	1094	ghats(ji,jj,jk-1) = ( 1. - zstabl ) * rcg / ( zws * zhbl(ji) + epsln ) * tmask(ji,jj,jk)
	1095
	1096	END DO
	1097	END DO
	1098	! Combine interior and boundary layer coefficients and nonlocal term
	1099	! -----------------------------------------------------------------------
	1100	DO jk = 2, jpkm1
	1101	DO ji = fs_2, fs_jpim1
	1102	zflag = zmask(ji,jk) * zmask(ji,jk+1)
	1103	zviscos(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avmu (ji,jj,jk) & ! interior viscosities
	1104	& + zflag * zblcm(ji,jk ) & ! boundary layer viscosities
	1105	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmpm(ji ) ! viscosity enhancement at W_level near zhbl
	1106
	1107	zviscos(ji,jj,jk) = zviscos(ji,jj,jk) * tmask(ji,jj,jk)
	1108
	1109
	1110	zdiffut(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avt (ji,jj,jk) & ! interior diffusivities
	1111	& + zflag * zblct(ji,jk ) & ! boundary layer diffusivities
	1112	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmpt(ji ) ! diffusivity enhancement at W_level near zhbl
	1113
	1114	zdiffut(ji,jj,jk) = zdiffut(ji,jj,jk) * tmask(ji,jj,jk)
	1115	#if defined key_zdfddm
	1116	zdiffus(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avs (ji,jj,jk) & ! interior diffusivities
	1117	& + zflag * zblcs(ji,jk ) & ! boundary layer diffusivities
	1118	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmps(ji ) ! diffusivity enhancement at W_level near zhbl
	1119
	1120	zdiffus(ji,jj,jk) = zdiffus(ji,jj,jk) * tmask(ji,jj,jk)
	1121	#endif
	1122	! Non local flux in the boundary layer only
	1123	ghats(ji,jj,jk-1) = zmask(ji,jk) * ghats(ji,jj,jk-1)
	1124
	1125	ENDDO
	1126	END DO
	1127	! ! ===============
	1128	END DO ! End of slab
	1129	! ! ===============
	1130
	1131	! Lateral boundary conditions on zvicos and zdiffus (sign unchanged)
	1132	CALL lbc_lnk( zviscos(:,:,:), 'U', 1. ) ; CALL lbc_lnk( zdiffut(:,:,:), 'W', 1. )
	1133	#if defined key_zdfddm
	1134	CALL lbc_lnk( zdiffus(:,:,:), 'W', 1. )
	1135	#endif
	1136
	1137	SELECT CASE ( nave )
	1138	!
	1139	CASE ( 0 ) ! no viscosity and diffusivity smoothing
	1140
	1141	DO jk = 2, jpkm1
	1142	DO jj = 2, jpjm1
	1143	DO ji = fs_2, fs_jpim1
	1144	avmu(ji,jj,jk) = ( zviscos(ji,jj,jk) + zviscos(ji+1,jj,jk) ) &
	1145	& / MAX( 1., tmask(ji,jj,jk) + tmask (ji + 1,jj,jk) ) * umask(ji,jj,jk)
	1146
	1147	avmv(ji,jj,jk) = ( zviscos(ji,jj,jk) + zviscos(ji,jj+1,jk) ) &
	1148	& / MAX( 1., tmask(ji,jj,jk) + tmask (ji,jj+1,jk) ) * vmask(ji,jj,jk)
	1149
	1150	avt (ji,jj,jk) = zdiffut(ji,jj,jk) * tmask(ji,jj,jk)
	1151	#if defined key_zdfddm
	1152	avs (ji,jj,jk) = zdiffus(ji,jj,jk) * tmask(ji,jj,jk)
	1153	#endif
	1154	END DO
	1155	END DO
	1156	END DO
	1157
	1158	CASE ( 1 ) ! viscosity and diffusivity smoothing
	1159	!
	1160	! ( 1/2 1 1/2 ) ( 1/2 1/2 ) ( 1/2 1 1/2 )
	1161	! avt = 1/8 ( 1 2 1 ) avmu = 1/4 ( 1 1 ) avmv= 1/4 ( 1/2 1 1/2 )
	1162	! ( 1/2 1 1/2 ) ( 1/2 1/2 )
	1163
	1164	DO jk = 2, jpkm1
	1165	DO jj = 2, jpjm1
	1166	DO ji = fs_2, fs_jpim1
	1167
	1168	avmu(ji,jj,jk) = ( zviscos(ji ,jj ,jk) + zviscos(ji+1,jj ,jk) &
	1169	& +.5*( zviscos(ji ,jj-1,jk) + zviscos(ji+1,jj-1,jk) &
	1170	& +zviscos(ji ,jj+1,jk) + zviscos(ji+1,jj+1,jk) ) ) * eumean(ji,jj,jk)
	1171
	1172	avmv(ji,jj,jk) = ( zviscos(ji ,jj ,jk) + zviscos(ji ,jj+1,jk) &
	1173	& +.5*( zviscos(ji-1,jj ,jk) + zviscos(ji-1,jj+1,jk) &
	1174	& +zviscos(ji+1,jj ,jk) + zviscos(ji+1,jj+1,jk) ) ) * evmean(ji,jj,jk)
	1175
	1176	avt (ji,jj,jk) = ( .5*( zdiffut(ji-1,jj+1,jk) + zdiffut(ji-1,jj-1,jk) &
	1177	& +zdiffut(ji+1,jj+1,jk) + zdiffut(ji+1,jj-1,jk) ) &
	1178	& +1.*( zdiffut(ji-1,jj ,jk) + zdiffut(ji ,jj+1,jk) &
	1179	& +zdiffut(ji ,jj-1,jk) + zdiffut(ji+1,jj ,jk) ) &
	1180	& +2.* zdiffut(ji ,jj ,jk) ) * etmean(ji,jj,jk)
	1181	#if defined key_zdfddm
	1182	avs (ji,jj,jk) = ( .5*( zdiffus(ji-1,jj+1,jk) + zdiffus(ji-1,jj-1,jk) &
	1183	& +zdiffus(ji+1,jj+1,jk) + zdiffus(ji+1,jj-1,jk) ) &
	1184	& +1.*( zdiffus(ji-1,jj ,jk) + zdiffus(ji ,jj+1,jk) &
	1185	& +zdiffus(ji ,jj-1,jk) + zdiffus(ji+1,jj ,jk) ) &
	1186	& +2.* zdiffus(ji ,jj ,jk) ) * etmean(ji,jj,jk)
	1187	#endif
	1188	END DO
	1189	END DO
	1190	END DO
	1191
	1192	END SELECT
	1193
	1194	DO jk = 2, jpkm1 ! vertical slab
	1195	!
	1196	! Minimum value on the eddy diffusivity
	1197	! ----------------------------------------
	1198	DO jj = 2, jpjm1
	1199	DO ji = fs_2, fs_jpim1 ! vector opt.
	1200	avt(ji,jj,jk) = MAX( avt(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
	1201	#if defined key_zdfddm
	1202	avs(ji,jj,jk) = MAX( avs(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
	1203	#endif
	1204	END DO
	1205	END DO
	1206
	1207	!
	1208	! Minimum value on the eddy viscosity
	1209	! ----------------------------------------
	1210	DO jj = 1, jpj
	1211	DO ji = 1, jpi
	1212	avmu(ji,jj,jk) = MAX( avmu(ji,jj,jk), avmb(jk) ) * umask(ji,jj,jk)
	1213	avmv(ji,jj,jk) = MAX( avmv(ji,jj,jk), avmb(jk) ) * vmask(ji,jj,jk)
	1214	END DO
	1215	END DO
	1216	!
	1217	END DO
	1218
	1219	! Lateral boundary conditions on avt (sign unchanged)
	1220	CALL lbc_lnk( hkpp(:,:), 'T', 1. )
	1221
	1222	! Lateral boundary conditions on avt (sign unchanged)
	1223	CALL lbc_lnk( avt(:,:,:), 'W', 1. )
	1224	#if defined key_zdfddm
	1225	CALL lbc_lnk( avs(:,:,:), 'W', 1. )
	1226	#endif
	1227	! Lateral boundary conditions (avmu,avmv) (U- and V- points, sign unchanged)
	1228	CALL lbc_lnk( avmu(:,:,:), 'U', 1. ) ; CALL lbc_lnk( avmv(:,:,:), 'V', 1. )
	1229
[258]	1230	IF(ln_ctl) THEN
	1231	#if defined key_zdfddm
[516]	1232	CALL prt_ctl(tab3d_1=avt , clinfo1=' kpp - t: ', tab3d_2=avs , clinfo2=' s: ', ovlap=1, kdim=jpk)
[258]	1233	#else
[516]	1234	CALL prt_ctl(tab3d_1=avt , clinfo1=' kpp - t: ', ovlap=1, kdim=jpk)
[258]	1235	#endif
[516]	1236	CALL prt_ctl(tab3d_1=avmu, clinfo1=' kpp - u: ', mask1=umask, &
	1237	& tab3d_2=avmv, clinfo2= ' v: ', mask2=vmask, ovlap=1, kdim=jpk)
[258]	1238	ENDIF
	1239
[255]	1240	END SUBROUTINE zdf_kpp
	1241
	1242
[463]	1243	SUBROUTINE tra_kpp
	1244	!!----------------------------------------------------------------------
	1245	!! * ROUTINE tra_kpp *
	1246	!!
	1247	!! ** Purpose : compute and add to the tracer trend the non-local
	1248	!! tracer flux
	1249	!!
	1250	!! ** Method : ???
	1251	!!
	1252	!! history :
	1253	!! 9.0 ! 05-11 (G. Madec) Original code
	1254	!!----------------------------------------------------------------------
	1255	!! * Modules used
	1256	USE oce, ONLY : ztrdt => ua, & ! use ua as 3D workspace
	1257	ztrds => va ! use va as 3D workspace
	1258	!!----------------------------------------------------------------------
[255]	1259
[463]	1260	IF( kt == nit000 ) THEN
	1261	IF(lwp) WRITE(numout,*)
	1262	IF(lwp) WRITE(numout,*) 'tra_kpp : KPP non-local tracer fluxes'
	1263	IF(lwp) WRITE(numout,*) '~~~~~~~ '
	1264	ENDIF
	1265
	1266
	1267	! Save ta and sa trends
	1268	IF( l_trdtra ) THEN
	1269	ztrdt(:,:,:) = ta(:,:,:)
	1270	ztrds(:,:,:) = sa(:,:,:)
	1271	ENDIF
	1272
	1273	! add non-local temperature and salinity flux ( in convective case only)
	1274	DO jk = 1, jpkm1
	1275	DO jj = 2, jpjm1
	1276	DO ji = fs_2, fs_jpim1
	1277	ta(ji,jj,jk) = ta(ji,jj,jk) &
	1278	& - ( ghats(ji,jj,jk ) * avt(ji,jj,jk ) &
	1279	& - ghats(ji,jj,jk+1) * avt(ji,jj,jk+1) ) * wt0(ji,jj) / fse3t(ji,jj,jk)
	1280	sa(ji,jj,jk) = sa(ji,jj,jk) &
	1281	& - ( ghats(ji,jj,jk ) * fsavs(ji,jj,jk ) &
	1282	& - ghats(ji,jj,jk+1) * fsavs(ji,jj,jk+1) ) * ws0(ji,jj) / fse3t(ji,jj,jk)
	1283	END DO
	1284	END DO
	1285	END DO
	1286
	1287	! save the non-local tracer flux trends for diagnostic
	1288	IF( l_trdtra ) THEN
	1289	ztrdt(:,:,:) = ta(:,:,:) - ztrdt(:,:,:)
	1290	ztrds(:,:,:) = sa(:,:,:) - ztrds(:,:,:)
	1291	!!bug gm jpttdzdf ==> jpttkpp
[503]	1292	CALL trd_mod(ztrdt, ztrds, jptra_trd_zdf, 'TRA', kt)
[463]	1293	ENDIF
	1294
[503]	1295	IF(ln_ctl) CALL prt_ctl( tab3d_1=ta, clinfo1=' kpp - Ta: ', mask1=tmask, &
	1296	& tab3d_2=sa, clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' )
[463]	1297	ENDIF
	1298
	1299	END SUBROUTINE tra_kpp
	1300
	1301
[255]	1302	SUBROUTINE zdf_kpp_init
	1303	!!----------------------------------------------------------------------
	1304	!! * ROUTINE zdf_kpp_init *
	1305	!!
	1306	!! ** Purpose : Initialization of the vertical eddy diffivity and
	1307	!! viscosity when using a kpp turbulent closure scheme
	1308	!!
	1309	!! ** Method : Read the namkpp namelist and check the parameters
	1310	!! called at the first timestep (nit000)
	1311	!!
	1312	!! ** input : Namlist namkpp
	1313	!!
	1314	!!
	1315	!! history :
	1316	!! 8.1 ! 00-02 (J. Chanut) KPP Mixing
	1317	!! 9.0 ! 05-01 (C. Ethe) F90 : free form
	1318	!!----------------------------------------------------------------------
	1319	!! * local declarations
	1320
	1321	INTEGER :: &
	1322	ji, jj, jk ! dummy loop indices
	1323
	1324	#if ! defined key_kppcustom
	1325	INTEGER :: &
	1326	jm ! dummy loop indices
	1327	REAL(wp) :: & !!! tempory scalars
	1328	zref, zdist
	1329	#endif
	1330
	1331	#if defined key_kpplktb
	1332	REAL(wp) :: & !!! tempory scalars
	1333	zustar, &
	1334	zucube, zustvk, &
	1335	zeta, zehat
	1336	#endif
	1337	REAL(wp) :: & !!! tempory scalars
	1338	zhbf
	1339	LOGICAL :: &
	1340	ll_kppcustom, & ! 1st ocean level taken as surface layer
	1341	ll_kpplktb ! Lookup table for turbul. velocity scales
	1342
	1343	NAMELIST/namkpp/ ln_kpprimix, difmiw, difsiw, Riinfty, difri, bvsqcon, difcon, nave, navb
	1344
	1345	!!----------------------------------------------------------------------
	1346
	1347	! Read Namelist namtke : Turbulente Kinetic Energy
	1348	! --------------------
	1349	REWIND ( numnam )
	1350	READ ( numnam, namkpp )
	1351
	1352	! Parameter control and print
	1353	! ---------------------------
	1354	REWIND( numnam )
	1355	READ ( numnam, namkpp )
	1356
	1357	! Control print
	1358	IF(lwp) THEN
	1359	WRITE(numout,*)
	1360	WRITE(numout,*) 'zdf_kpp_init : kpp turbulent closure scheme'
	1361	WRITE(numout,*) '~~~~~~~~~~~~'
	1362	WRITE(numout,*) ' Namelist namkpp : set tke mixing parameters'
	1363	WRITE(numout,*) ' Shear instability mixing ln_kpprimix = ', ln_kpprimix
	1364	WRITE(numout,*) ' max. internal wave viscosity difmiw = ', difmiw
	1365	WRITE(numout,*) ' max. internal wave diffusivity difsiw = ', difsiw
	1366	WRITE(numout,*) ' Richardson Number limit for shear instability Riinfty = ', Riinfty
	1367	WRITE(numout,*) ' max. shear mixing at Rig = 0 difri = ', difri
	1368	WRITE(numout,*) ' Brunt-Vaisala squared for max. convection bvsqcon = ', bvsqcon
	1369	WRITE(numout,*) ' max. mix. in interior convec. difcon = ', difcon
	1370	WRITE(numout,*) ' horizontal average flag nave = ', nave
	1371	WRITE(numout,*) ' constant background or profile navb = ', navb
	1372	ENDIF
	1373
	1374	ll_kppcustom = .FALSE.
	1375	ll_kpplktb = .FALSE.
	1376
	1377	#if defined key_kppcustom
	1378	ll_kppcustom = .TRUE.
	1379	#endif
	1380	#if defined key_kpplktb
	1381	ll_kpplktb = .TRUE.
	1382	#endif
	1383	IF(lwp) THEN
	1384	WRITE(numout,*) ' Lookup table for turbul. velocity scales ll_kpplktb = ', ll_kpplktb
	1385	WRITE(numout,*) ' 1st ocean level taken as surface layer ll_kppcustom = ', ll_kppcustom
	1386	WRITE(numout,*) ' '
	1387	ENDIF
	1388
	1389	IF( lk_zdfddm) THEN
	1390	IF(lwp) THEN
	1391	WRITE(numout,*)
	1392	WRITE(numout,*) ' Double diffusion mixing on temperature and salinity '
	1393	WRITE(numout,*) ' CAUTION : done in routine zdfkpp, not in routine zdfddm '
	1394	WRITE(numout,*) ' '
	1395	ENDIF
	1396	ENDIF
	1397
	1398
	1399
	1400	!set constants not in namelist
	1401	!-----------------------------
	1402	Vtc = rconcv * SQRT( 0.2 / ( rconcs * epsilon ) ) / ( vonk * vonk * Ricr )
	1403	rcg = rcstar * vonk * ( rconcs * vonk * epsilon )**pthird
	1404
	1405	IF(lwp) THEN
	1406	WRITE(numout,*) ' Constant value for unreso. turbul. velocity shear Vtc = ', Vtc
	1407	WRITE(numout,*) ' Non-dimensional coef. for nonlocal transport rcg = ', rcg
	1408	WRITE(numout,*) ' '
	1409	ENDIF
	1410
	1411	! ratt is the attenuation coefficient for solar flux
	1412	! Should be different is s_coordinate
	1413	DO jk = 1, jpk
	1414	zhbf = - fsdept(1,1,jk) * hbf
	1415	ratt(jk) = 1.0 - ( rabs * EXP( zhbf / xsi1 ) + ( 1.0 - rabs ) * EXP( zhbf / xsi2 ) )
	1416	ENDDO
	1417
	1418	! Horizontal average : initialization of weighting arrays
	1419	! -------------------
	1420
	1421	SELECT CASE ( nave )
	1422
	1423	CASE ( 0 ) ! no horizontal average
	1424	IF(lwp) WRITE(numout,*) ' no horizontal average on avt, avmu, avmv'
	1425	IF(lwp) WRITE(numout,*) ' only in very high horizontal resolution !'
	1426	! weighting mean arrays etmean, eumean and evmean
	1427	! ( 1 1 ) ( 1 )
	1428	! avt = 1/4 ( 1 1 ) avmu = 1/2 ( 1 1 ) avmv= 1/2 ( 1 )
	1429	!
	1430	etmean(:,:,:) = 0.e0
	1431	eumean(:,:,:) = 0.e0
	1432	evmean(:,:,:) = 0.e0
	1433
	1434	DO jk = 1, jpkm1
	1435	DO jj = 2, jpjm1
	1436	DO ji = 2, jpim1 ! vector opt.
	1437	etmean(ji,jj,jk) = tmask(ji,jj,jk) &
	1438	& / MAX( 1., umask(ji-1,jj ,jk) + umask(ji,jj,jk) &
	1439	& + vmask(ji ,jj-1,jk) + vmask(ji,jj,jk) )
	1440
	1441	eumean(ji,jj,jk) = umask(ji,jj,jk) &
	1442	& / MAX( 1., tmask(ji,jj,jk) + tmask(ji+1,jj ,jk) )
	1443
	1444	evmean(ji,jj,jk) = vmask(ji,jj,jk) &
	1445	& / MAX( 1., tmask(ji,jj,jk) + tmask(ji ,jj+1,jk) )
	1446	END DO
	1447	END DO
	1448	END DO
	1449
	1450	CASE ( 1 ) ! horizontal average
	1451	IF(lwp) WRITE(numout,*) ' horizontal average on avt, avmu, avmv'
	1452	! weighting mean arrays etmean, eumean and evmean
	1453	! ( 1/2 1 1/2 ) ( 1/2 1/2 ) ( 1/2 1 1/2 )
	1454	! avt = 1/8 ( 1 2 1 ) avmu = 1/4 ( 1 1 ) avmv= 1/4 ( 1/2 1 1/2 )
	1455	! ( 1/2 1 1/2 ) ( 1/2 1/2 )
	1456	etmean(:,:,:) = 0.e0
	1457	eumean(:,:,:) = 0.e0
	1458	evmean(:,:,:) = 0.e0
	1459
	1460	DO jk = 1, jpkm1
	1461	DO jj = 2, jpjm1
	1462	DO ji = fs_2, fs_jpim1 ! vector opt.
	1463	etmean(ji,jj,jk) = tmask(ji, jj,jk) &
	1464	& / MAX( 1., 2.* tmask(ji,jj,jk) &
	1465	& +.5 * ( tmask(ji-1,jj+1,jk) + tmask(ji-1,jj-1,jk) &
	1466	& +tmask(ji+1,jj+1,jk) + tmask(ji+1,jj-1,jk) ) &
	1467	& +1. * ( tmask(ji-1,jj ,jk) + tmask(ji ,jj+1,jk) &
	1468	& +tmask(ji ,jj-1,jk) + tmask(ji+1,jj ,jk) ) )
	1469
	1470	eumean(ji,jj,jk) = umask(ji,jj,jk) &
	1471	& / MAX( 1., tmask(ji,jj ,jk) + tmask(ji+1,jj ,jk) &
	1472	& +.5 * ( tmask(ji,jj-1,jk) + tmask(ji+1,jj-1,jk) &
	1473	& +tmask(ji,jj+1,jk) + tmask(ji+1,jj+1,jk) ) )
	1474
	1475	evmean(ji,jj,jk) = vmask(ji,jj,jk) &
	1476	& / MAX( 1., tmask(ji ,jj,jk) + tmask(ji ,jj+1,jk) &
	1477	& +.5 * ( tmask(ji-1,jj,jk) + tmask(ji-1,jj+1,jk) &
	1478	& +tmask(ji+1,jj,jk) + tmask(ji+1,jj+1,jk) ) )
	1479	END DO
	1480	END DO
	1481	END DO
	1482
	1483	CASE DEFAULT
[474]	1484	WRITE(ctmp1,*) ' bad flag value for nave = ', nave
	1485	CALL ctl_opa( ctmp1 )
[255]	1486
	1487	END SELECT
	1488
	1489
	1490
	1491	! Background eddy viscosity and diffusivity profil
	1492	! ------------------------------------------------
	1493	IF( navb == 0 ) THEN
	1494	! Define avmb, avtb from namelist parameter
	1495	avmb(:) = avm0
	1496	avtb(:) = avt0
	1497	ELSE
	1498	! Background profile of avt (fit a theoretical/observational profile (Krauss 1990)
	1499	avmb(:) = avm0
	1500	avtb(:) = 1.e-5 + 2.8e-8 * gdepw(:) ! m2/s
	1501	ENDIF
	1502
	1503	! Increase the background in the surface layers
	1504	!! avmb(1) = 1. * avmb(1) ; avtb(1) = 1. * avtb(1)
	1505	!! avmb(2) = 1. * avmb(2) ; avtb(2) = 1. * avtb(2)
	1506	!! avmb(3) = 1. * avmb(3) ; avtb(3) = 1. * avtb(3)
	1507	!! avmb(4) = 1. * avmb(4) ; avtb(4) = 1. * avtb(4)
	1508
	1509
	1510	! Initialization of vertical eddy coef. to the background value
	1511	! -------------------------------------------------------------
	1512	DO jk = 1, jpk
	1513	avt (:,:,jk) = avtb(jk) * tmask(:,:,jk)
	1514	avmu(:,:,jk) = avmb(jk) * umask(:,:,jk)
	1515	avmv(:,:,jk) = avmb(jk) * vmask(:,:,jk)
	1516	END DO
	1517
	1518	! zero the surface flux for non local term and kpp mixed layer depth
	1519	! ------------------------------------------------------------------
	1520	ghats(:,:,:) = 0.
	1521	wt0 (:,: ) = 0.
	1522	ws0 (:,: ) = 0.
	1523	hkpp (:,: ) = 0. ! just a diagnostic (not essential)
	1524
	1525	#if ! defined key_kppcustom
	1526	! compute arrays (del, wz) for reference mean values
	1527	! (increase speed for vectorization key_kppcustom not defined)
	1528	del(1:jpk, 1:jpk) = 0.
	1529	DO jk = 1, jpk
	1530	zref = epsilon * fsdept(1,1,jk)
	1531	DO jm = 1 , jpk
	1532	zdist = zref - fsdepw(1,1,jm)
	1533	IF( zdist > 0. ) THEN
	1534	del(jk,jm) = MIN( zdist, fse3t(1,1,jm) ) / zref
	1535	ELSE
	1536	del(jk,jm) = 0.
	1537	ENDIF
	1538	ENDDO
	1539	ENDDO
	1540	#endif
	1541
	1542	#if defined key_kpplktb
	1543	! build lookup table for turbulent velocity scales
	1544	dezehat = ( dehatmax - dehatmin ) / nilktbm1
	1545	deustar = ( ustmax - ustmin ) / njlktbm1
	1546
	1547	DO jj = 1, njlktb
	1548	zustar = ( jj - 1) * deustar + ustmin
	1549	zustvk = vonk * zustar
	1550	zucube = zustar * zustar * zustar
	1551	DO ji = 1 , nilktb
	1552	zehat = ( ji - 1 ) * dezehat + dehatmin
	1553	zeta = zehat / ( zucube + epsln )
	1554	IF( zehat >= 0 ) THEN ! Stable case
	1555	wmlktb(ji,jj) = zustvk / ABS( 1.0 + rconc1 * zeta + epsln )
	1556	wslktb(ji,jj) = wmlktb(ji,jj)
	1557	ELSE ! Unstable case
	1558	IF( zeta > rzetam ) THEN
	1559	wmlktb(ji,jj) = zustvk * ABS( 1.0 - rconc2 * zeta )**pfourth
	1560	ELSE
	1561	wmlktb(ji,jj) = zustvk * ABS( rconam - rconcm * zeta )**pthird
	1562	ENDIF
	1563
	1564	IF( zeta > rzetas ) THEN
	1565	wslktb(ji,jj) = zustvk * SQRT( ABS( 1.0 - rconc2 * zeta ) )
	1566	ELSE
	1567	wslktb(ji,jj) = zustvk * ABS( rconas - rconcs * zeta )**pthird
	1568	ENDIF
	1569	ENDIF
	1570	END DO
	1571	END DO
	1572	#endif
	1573	END SUBROUTINE zdf_kpp_init
	1574
	1575	#else
	1576	!!----------------------------------------------------------------------
	1577	!! Dummy module : NO KPP scheme
	1578	!!----------------------------------------------------------------------
	1579	LOGICAL, PUBLIC, PARAMETER :: lk_zdfkpp = .FALSE. !: KPP flag
	1580	CONTAINS
	1581	SUBROUTINE zdf_kpp( kt ) ! Empty routine
	1582	WRITE(,) 'zdf_kpp: You should not have seen this print! error?', kt
	1583	END SUBROUTINE zdf_kpp
[463]	1584	SUBROUTINE tra_kpp( kt ) ! Empty routine
	1585	WRITE(,) 'tra_kpp: You should not have seen this print! error?', kt
	1586	END SUBROUTINE tra_kpp
[255]	1587	#endif
	1588
	1589	!!======================================================================
	1590	END MODULE zdfkpp

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