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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 @ 1146

Last change on this file since 1146 was 1146, checked in by rblod, 16 years ago
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[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
[896]	30	USE trdmod ! momentum/tracers trends
[255]	31
	32	IMPLICIT NONE
	33	PRIVATE
	34
[503]	35	PUBLIC zdf_kpp ! routine called by step.F90
	36	PUBLIC tra_kpp ! routine called by step.F90
[255]	37
[503]	38	LOGICAL, PUBLIC, PARAMETER :: lk_zdfkpp = .TRUE. !: KPP vertical mixing flag
	39	REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: ghats !: non-local scalar mixing term (gamma/<ws>o)
[255]	40	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: &
[503]	41	wt0 , & !: surface temperature flux for non local flux
	42	ws0 , & !: surface salinity flux for non local flux
	43	hkpp !: boundary layer depht
	44
[255]	45	INTEGER :: & !!! kpp namelist (namkpp)
	46	nave = 1 , & ! = 0/1 flag for horizontal average on avt, avmu, avmv
	47	navb = 0 ! = 0/1 flag for constant or profile background avt
	48
	49	REAL(wp) :: & !!! ** Interior Mixing
	50	difmiw = 1.2e-04_wp , & ! constant internal wave viscosity (m2/s)
	51	difsiw = 1.2e-05_wp , & ! constant internal wave diffusivity (m2/s)
	52	Riinfty = 0.8_wp , & ! local Richardson Number limit for shear instability
	53	difri = 5.e-03_wp , & ! maximum shear mixing at Rig = 0 (m2/s)
	54	bvsqcon = -1.e-09_wp , & ! Brunt-Vaisala squared (1/s**2) for maximum convection
	55	difcon = 1._wp ! maximum mixing in interior convection (m2/s)
	56	#if defined key_zdfddm
	57	REAL(wp) :: & !!! ** Double diffusion Mixing
	58	difssf = 1.e-03_wp , & ! maximum salt fingering mixing
	59	Rrho0 = 1.9_wp , & ! limit for salt fingering mixing
	60	difsdc = 1.5e-06_wp ! maximum diffusive convection mixing
	61	#endif
	62	LOGICAL :: &
	63	ln_kpprimix = .TRUE. ! Shear instability mixing
	64
	65	REAL(wp) :: & !!! General constants
	66	epsln = 1.0e-20_wp , & ! a small positive number
	67	pthird = 1._wp/3._wp , & ! 1/3
	68	pfourth = 1._wp/4._wp ! 1/4
	69
	70	REAL(wp) :: & !!! Boundary Layer Turbulence Parameters
	71	vonk = 0.4_wp , & ! von Karman's constant
	72	epsilon = 0.1_wp , & ! nondimensional extent of the surface layer
	73	rconc1 = 5.0_wp , & ! standard flux profile function parmaeters
	74	rconc2 = 16.0_wp , & ! " "
	75	rconcm = 8.38_wp , & ! momentum flux profile fit
	76	rconam = 1.26_wp , & ! " "
	77	rzetam = -.20_wp , & ! " "
	78	rconcs = 98.96_wp , & ! scalar flux profile fit
	79	rconas = -28.86_wp , & ! " "
	80	rzetas = -1.0_wp ! " "
	81	REAL(wp) :: & !!! Boundary Layer Depth Diagnostic
	82	Ricr = 0.3_wp , & ! critical bulk Richardson Number
	83	rcekman = 0.7_wp , & ! coefficient for ekman depth
	84	rcmonob = 1.0_wp , & ! coefficient for Monin-Obukhov depth
	85	rconcv = 1.7_wp , & ! ratio of interior buoyancy frequency to buoyancy frequency at entrainment depth
	86	hbf = 1.0_wp , & ! fraction of bound. layer depth to which absorbed solar
	87	! ! rad. and contributes to surf. buo. forcing
	88	Vtc ! function of rconcv,rconcs,epsilon,vonk,Ricr
	89	REAL(wp) :: & !!! Nonlocal Boundary Layer Mixing
	90	rcstar = 5.0_wp , & ! coefficient for convective nonlocal transport
	91	rcs = 1.0e-3_wp , & ! conversion: mm/s ==> m/s
	92	rcg ! non-dimensional coefficient for nonlocal transport
	93
	94	#if ! defined key_kppcustom
	95	REAL(wp), DIMENSION(jpk,jpk) :: &
	96	del ! array for reference mean values of vertical integration
	97	#endif
	98
	99	#if defined key_kpplktb
	100	INTEGER, PARAMETER :: & !!! Parameters for lookup table for turbulent velocity scales
	101	nilktb = 892 , & ! number of values for zehat in KPP lookup table
	102	njlktb = 482 , & ! number of values for ustar in KPP lookup table
	103	nilktbm1 = nilktb - 1 , & !
	104	njlktbm1 = njlktb - 1 !
	105
	106	REAL(wp), DIMENSION(nilktb,njlktb) :: &
	107	wmlktb , & ! lookup table for the turbulent vertical velocity scale for momentum
	108	wslktb ! lookup table for the turbulent vertical velocity scale for tracers
	109
	110	REAL(wp) :: &
	111	dehatmin = -4.e-7_wp , & ! minimum limit for zhat in lookup table (m3/s3)
	112	dehatmax = 0._wp , & ! maximum limit for zhat in lookup table (m3/s3)
	113	ustmin = 0._wp , & ! minimum limit for ustar in lookup table (m/s)
	114	ustmax = 0.04_wp , & ! maximum limit for ustar in lookup table (m/s)
	115	dezehat , & ! delta zhat in lookup table
	116	deustar ! delta ustar in lookup table
	117	#endif
	118	REAL(wp), DIMENSION(jpk) :: & !!! attenuation coef
	119	ratt
	120	!! already defines in module traqsr, but only if the solar radiation penetration is considered
	121	REAL(wp) :: & !!! * penetrative solar radiation coefficient *
	122	rabs = 0.58_wp , & ! fraction associated with xsi1
	123	xsi1 = 0.35_wp , & ! first depth of extinction
	124	xsi2 = 23.0_wp ! second depth of extinction
	125	! ! (default values: water type Ib)
	126
	127	REAL(wp), DIMENSION(jpi,jpj,jpk) :: &
	128	etmean , & ! coefficient used for horizontal smoothing
	129	eumean , & ! at t-, u- and v-points
	130	evmean
	131
[899]	132	#if defined key_c1d
[255]	133	REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: &
	134	rig , & ! gradient Richardson number
	135	rib , & ! bulk Richardson number
	136	buof , & ! buoyancy forcing
	137	mols ! moning-Obukhov length scale
	138	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: &
	139	ekdp ! Ekman depth
	140	#endif
	141
	142	INTEGER :: & !
	143	jip = 62 , jjp = 111
	144
	145	!! * Substitutions
	146	# include "domzgr_substitute.h90"
	147	# include "vectopt_loop_substitute.h90"
[896]	148	# include "zdfddm_substitute.h90"
[255]	149	!!----------------------------------------------------------------------
	150	!! OPA 9.0 , LOCEAN-IPSL (2005)
[888]	151	!! $Id$
[503]	152	!! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt)
[255]	153	!!----------------------------------------------------------------------
	154
	155	CONTAINS
	156
	157	SUBROUTINE zdf_kpp ( kt )
	158	!!----------------------------------------------------------------------
	159	!! * ROUTINE zdf_kpp *
	160	!!
	161	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	162	!! coefficients and non local mixing using K-profile parameterization
	163	!!
	164	!! ** Method : The boundary layer depth hkpp is diagnosed at tracer points
	165	!! from profiles of buoyancy, and shear, and the surface forcing.
	166	!! Above hbl (sigma=-z/hbl <1) the mixing coefficients are computed from
	167	!!
	168	!! Kx = hkpp Wx(sigma) G(sigma)
	169	!!
	170	!! and the non local term ghat = Cs / Ws(sigma) / hkpp
	171	!! Below hkpp the coefficients are the sum of mixing due to internal waves
	172	!! shear instability and double diffusion.
	173	!!
	174	!! -1- Compute the now interior vertical mixing coefficients at all depths.
	175	!! -2- Diagnose the boundary layer depth.
	176	!! -3- Compute the now boundary layer vertical mixing coefficients.
	177	!! -4- Compute the now vertical eddy vicosity and diffusivity.
	178	!! -5- Smoothing
	179	!!
	180	!! N.B. The computation is done from jk=2 to jpkm1
	181	!! Surface value of avt avmu avmv are set once a time to zero
	182	!! in routine zdf_kpp_init.
	183	!!
	184	!! ** Action : update the non-local terms ghats
	185	!! update avt, avmu, avmv (before vertical eddy coef.)
	186	!!
[503]	187	!! References : Large W.G., Mc Williams J.C. and Doney S.C.
[255]	188	!! Reviews of Geophysics, 32, 4, November 1994
	189	!! Comments in the code refer to this paper, particularly
	190	!! the equation number. (LMD94, here after)
	191	!!----------------------------------------------------------------------
	192	#if defined key_zdfddm
	193	USE oce , zviscos => ua, & ! temp. array for viscosities use ua as workspace
	194	& zdiffut => ta, & ! temp. array for diffusivities use sa as workspace
	195	& zdiffus => sa ! temp. array for diffusivities use sa as workspace
	196	#else
	197	USE oce , zviscos => ua, & ! temp. array for viscosities use ua as workspace
	198	& zdiffut => ta ! temp. array for diffusivities use sa as workspace
	199	#endif
[503]	200	!!
	201	INTEGER, INTENT( in ) :: kt ! ocean time step
	202	!!
	203	INTEGER :: ji, jj, jk ! dummy loop indices
	204	INTEGER :: ikbot, jkmax, jkm1, jkp2 !
[255]	205
	206	REAL(wp), DIMENSION(jpi,jpj) :: & !!! Surface buoyancy forcing, friction velocity
	207	zBo, zBosol, zustar !
	208	!
	209	REAL(wp) :: & !
	210	ztx, zty, ztau, zflageos, & !
	211	zstabl, zbuofdep,zucube, & !
	212	zrhos, zalbet, zbeta, & !
	213	zthermal, zhalin, zatt1 !
	214
	215	REAL(wp) :: & !!! Bulk richardson number
	216	zref, zt, zs, zh, & !
	217	zu, zv, zrh, & !
	218	zrib, zrinum, & !
	219	zdVsq, zVtsq !
	220
	221	REAL(wp) :: & !!! Velocity scales
	222	zehat, zeta, zhrib, zsig, & !
	223	zscale, zwst, zws, zwm
	224
	225	#if defined key_kpplktb
	226	INTEGER :: & !!! Lookup table or Analytical functions
	227	il, jl !
	228	REAL(wp) :: & !
	229	ud, zfrac, ufrac, & !
	230	zwam, zwbm, zwas, zwbs !
	231	#else
	232	REAL(wp) :: & !
	233	zwsun, zwmun, &
	234	zcons, zconm, zwcons, zwconm !
	235	#endif
	236
	237	REAL(wp) :: & !!! In situ density
	238	zsr, zbw, ze, & !
	239	zb, zd, zc, zaw, za, & !
	240	zb1, za1, zkw, zk0, & !
	241	zcomp , zrhd, zrhdr,zbvzed !
	242
	243	#if ! defined key_kppcustom
	244	!! * local declarations
	245	INTEGER :: &
	246	jm ! dummy loop indices
	247	REAL(wp) :: & !!! Compression terms
	248	zr1, zr2, zr3, zr4, & !
	249	zrhop !
	250	#endif
	251
	252	REAL(wp) :: & !
	253	zflag, ztemp, zrn2, & !
	254	zdep21, zdep32, zdep43
	255
	256	REAL(wp) :: & !!! Interior richardson mixing
	257	zdku2, zdkv2, ze3sqr, & !
	258	zsh2, zri, zfri !
	259
	260	REAL(wp), DIMENSION(jpi,0:2) :: & !!! Moning-Obukov limitation
	261	zmoek
	262	REAL(wp), DIMENSION(jpi) :: &
	263	zmoa, zekman
	264	REAL(wp) :: &
	265	zmob, zek
	266
	267	REAL(wp), DIMENSION(jpi,4) :: & !!! The pipe
	268	zdepw, zdift, zvisc
	269	REAL(wp), DIMENSION(jpi,3) :: &
	270	zdept
	271	REAL(wp), DIMENSION(jpi,2) :: &
	272	zriblk
	273	REAL(wp), DIMENSION(jpi,jpk) :: & !
	274	zmask
	275	REAL(wp), DIMENSION(jpi) :: & !
	276	zhmax, zria, zhbl
	277	REAL(wp) :: & !
	278	zflagri, zflagek, & !
	279	zflagmo, zflagh, zflagkb !
	280	REAL(wp), DIMENSION(jpi) :: & !!! Shape function (G)
	281	za2m, za3m, zkmpm, &
	282	za2t, za3t, zkmpt
	283	REAL(wp) :: & !
	284	zdelta, zdelta2, & !
	285	zdzup, zdzdn, zdzh, & !
	286	zvath, zgat1, zdat1, & !
	287	zkm1m, zkm1t
	288	REAL(wp), DIMENSION(jpi,jpk) :: & !!! Boundary layer diffusivities/viscosities
	289	zblcm, zblct
	290	#if defined key_zdfddm
	291	REAL(wp) :: & !!! double diffusion mixing
	292	zrrau, zds, &
	293	zavdds, zavddt,zinr
	294	REAL(wp), DIMENSION(jpi,4) :: &
	295	zdifs
	296	REAL(wp), DIMENSION(jpi) :: &
	297	za2s, za3s, zkmps
	298	REAL(wp) :: &
	299	zkm1s
	300	REAL(wp), DIMENSION(jpi,jpk) :: &
	301	zblcs
	302	#endif
	303	!!--------------------------------------------------------------------
	304
	305
	306	! Initialization (first time-step only)
	307	! --------------
	308	IF( kt == nit000 ) CALL zdf_kpp_init
	309
	310	zviscos(:,:,:) = 0.
	311	zblcm (:,: ) = 0.
	312	zdiffut(:,:,:) = 0.
	313	zblct (:,: ) = 0.
	314	#if defined key_zdfddm
	315	zdiffus(:,:,:) = 0.
	316	zblcs (:,: ) = 0.
	317	#endif
	318	ghats(:,:,:) = 0.
	319
	320	zBo (:,:) = 0.
	321	zBosol(:,:) = 0.
	322	zustar(:,:) = 0.
	323
	324
	325	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	326	! I. Interior diffusivity and viscosity at w points ( T interfaces)
	327	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	328	DO jk = 2, jpkm1
	329	DO jj = 2, jpjm1
	330	DO ji = fs_2, fs_jpim1
	331	! Mixing due to internal waves breaking
	332	! -------------------------------------
	333	avmu(ji,jj,jk) = difmiw
	334	avt (ji,jj,jk) = difsiw
	335	! Mixing due to vertical shear instability
	336	! -------------------------------------
	337	IF( ln_kpprimix ) THEN
	338	! Compute the gradient Richardson number at interfaces (zri):
	339	! LMD94, eq. 27 (is vertical smoothing needed : Rig=N^2 / (dz(u))^2 + (dz(v))^2
	340	zdku2 = ( un(ji - 1,jj,jk - 1) - un(ji - 1,jj,jk) ) &
	341	& * ( un(ji - 1,jj,jk - 1) - un(ji - 1,jj,jk) ) &
	342	& + ( un(ji ,jj,jk - 1) - un(ji ,jj,jk) ) &
	343	& * ( un(ji ,jj,jk - 1) - un(ji ,jj,jk) )
	344
	345	zdkv2 = ( vn(ji,jj - 1,jk - 1) - vn(ji,jj - 1,jk) ) &
	346	& * ( vn(ji,jj - 1,jk - 1) - vn(ji,jj - 1,jk) ) &
	347	& + ( vn(ji, jj,jk - 1) - vn(ji, jj,jk) ) &
	348	& * ( vn(ji, jj,jk - 1) - vn(ji, jj,jk) )
	349
	350	ze3sqr = 1. / ( fse3w(ji,jj,jk) * fse3w(ji,jj,jk) )
	351	! Square of vertical shear at interfaces
[1082]	352	zsh2 = 0.5 * ( zdku2 + zdkv2 ) * ze3sqr
[255]	353	zri = MAX( rn2(ji,jj,jk), 0. ) / ( zsh2 + epsln )
[899]	354	#if defined key_c1d
[255]	355	! save the gradient richardson number
	356	rig(ji,jj,jk) = zri * tmask(ji,jj,jk)
	357	#endif
	358	! Evaluate f of Ri (zri) for shear instability store in zfri
	359	! LMD94, eq. 28a,b,c, figure 3 ; Rem: p1 is 3, hard coded
	360	zfri = MAX( zri , 0. )
	361	zfri = MIN( zfri / Riinfty , 1.0 )
	362	zfri = ( 1.0 - zfri * zfri )
	363	zfri = zfri * zfri * zfri
	364	! add shear contribution to mixing coef.
	365	avmu(ji,jj,jk) = avmu(ji,jj,jk) + difri * zfri
	366	avt (ji,jj,jk) = avt (ji,jj,jk) + difri * zfri
	367	ENDIF
	368	#if defined key_zdfddm
	369	avs (ji,jj,jk) = avt (ji,jj,jk)
	370	! Double diffusion mixing ; NOT IN ROUTINE ZDFDDM.F90
	371	! ------------------------------------------------------------------
	372	! only retains positive value of rrau
	373	zrrau = MAX( rrau(ji,jj,jk), epsln )
	374	zds = sn(ji,jj,jk-1) - sn(ji,jj,jk)
	375	IF( zrrau > 1. .AND. zds > 0.) THEN
	376	!
	377	! Salt fingering case.
	378	!---------------------
	379	! Compute interior diffusivity for double diffusive mixing of
	380	! salinity. Upper bound "zrrau" by "Rrho0"; (Rrho0=1.9, difcoefnuf=0.001).
	381	! After that set interior diffusivity for double diffusive mixing
	382	! of temperature
	383	zavdds = MIN( zrrau, Rrho0 )
	384	zavdds = ( zavdds - 1.0 ) / ( Rrho0 - 1.0 )
	385	zavdds = 1.0 - zavdds * zavdds
	386	zavdds = zavdds * zavdds * zavdds
	387	zavdds = difssf * zavdds
	388	zavddt = 0.7 * zavdds
	389	ELSEIF( zrrau < 1. .AND. zrrau > 0. .AND. zds < 0.) THEN
	390	!
	391	! Diffusive convection case.
	392	!---------------------------
	393	! Compute interior diffusivity for double diffusive mixing of
	394	! temperature (Marmorino and Caldwell, 1976);
	395	! Compute interior diffusivity for double diffusive mixing of salinity
	396	zinr = 1. / zrrau
	397	zavddt = 0.909 * EXP( 4.6 * EXP( -0.54* ( zinr - 1. ) ) )
	398	zavddt = difsdc * zavddt
	399	IF( zrrau < 0.5) THEN
	400	zavdds = zavddt * 0.15 * zrrau
	401	ELSE
	402	zavdds = zavddt * (1.85 * zrrau - 0.85 )
	403	ENDIF
	404	ELSE
	405	zavddt = 0.
	406	zavdds = 0.
	407	ENDIF
	408	! Add double diffusion contribution to temperature and salinity mixing coefficients.
	409	avt (ji,jj,jk) = avt (ji,jj,jk) + zavddt
	410	avs (ji,jj,jk) = avs (ji,jj,jk) + zavdds
	411	#endif
	412	END DO
	413	END DO
	414	END DO
	415
	416
	417	! Radiative (zBosol) and non radiative (zBo) surface buoyancy
	418	!JMM at the time zdfkpp is called, q still holds the sum q + qsr
	419	!---------------------------------------------------------------------
	420	DO jj = 2, jpjm1
	421	DO ji = fs_2, fs_jpim1
	422	IF( neos < 1) THEN
	423	zt = tn(ji,jj,1)
	424	zs = sn(ji,jj,1) - 35.0
	425	zh = fsdept(ji,jj,1)
	426	! potential volumic mass
	427	zrhos = rhop(ji,jj,1)
	428	zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta
	429	& - 0.203814e-03 ) * zt &
	430	& + 0.170907e-01 ) * zt &
	431	& + 0.665157e-01 &
	432	& + ( - 0.678662e-05 * zs &
	433	& - 0.846960e-04 * zt + 0.378110e-02 ) * zs &
	434	& + ( ( - 0.302285e-13 * zh &
	435	& - 0.251520e-11 * zs &
	436	& + 0.512857e-12 * zt * zt ) * zh &
	437	& - 0.164759e-06 * zs &
	438	& +( 0.791325e-08 * zt - 0.933746e-06 ) * zt &
	439	& + 0.380374e-04 ) * zh
	440
	441	zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta
	442	& - 0.301985e-05 ) * zt &
	443	& + 0.785567e-03 &
	444	& + ( 0.515032e-08 * zs &
	445	& + 0.788212e-08 * zt - 0.356603e-06 ) * zs &
	446	& +( ( 0.121551e-17 * zh &
	447	& - 0.602281e-15 * zs &
	448	& - 0.175379e-14 * zt + 0.176621e-12 ) * zh &
	449	& + 0.408195e-10 * zs &
	450	& + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt &
	451	& - 0.121555e-07 ) * zh
	452
	453	zthermal = zbeta * zalbet / ( rcp * zrhos + epsln )
	454	zhalin = zbeta * sn(ji,jj,1) * rcs
	455	ELSE
	456	zrhos = rhop(ji,jj,1) + rau0 * ( 1. - tmask(ji,jj,1) )
	457	zthermal = ralpha / ( rcp * zrhos + epsln )
	458	zhalin = rbeta * sn(ji,jj,1) * rcs
	459	ENDIF
	460	! Radiative surface buoyancy force
	461	zBosol(ji,jj) = grav * zthermal * qsr(ji,jj)
	462	! Non radiative surface buoyancy force
[1082]	463	zBo (ji,jj) = grav * zthermal * qns(ji,jj) - grav * zhalin * emps(ji,jj)
[255]	464	! Surface Temperature flux for non-local term
[888]	465	wt0(ji,jj) = - ( qsr(ji,jj) + qns(ji,jj) )* ro0cpr * tmask(ji,jj,1)
[255]	466	! Surface salinity flux for non-local term
[1082]	467	ws0(ji,jj) = - ( emps(ji,jj) * sn(ji,jj,1) * rcs ) * tmask(ji,jj,1)
[255]	468	ENDDO
	469	ENDDO
	470
	471	zflageos = 0.5 + SIGN( 0.5, neos - 1. )
	472	! Compute surface buoyancy forcing, Monin Obukhov and Ekman depths
	473	!------------------------------------------------------------------
	474	DO jj = 2, jpjm1
	475	DO ji = fs_2, fs_jpim1
	476	! Reference surface density = density at first T point level
	477	zrhos = rhop(ji,jj,1) + zflageos * rau0 * ( 1. - tmask(ji,jj,1) )
	478	! Friction velocity (zustar), at T-point : LMD94 eq. 2
[888]	479	ztx = 0.5 * ( utau(ji,jj) + utau(ji - 1, jj ) )
	480	zty = 0.5 * ( vtau(ji,jj) + vtau(ji , jj - 1) )
[255]	481	ztau = SQRT( ztx * ztx + zty * zty )
	482	zustar(ji,jj) = SQRT( ztau / ( zrhos + epsln ) )
	483	ENDDO
	484	ENDDO
	485
	486	!CDIR NOVERRCHK
	487	! ! ===============
	488	DO jj = 2, jpjm1 ! Vertical slab
	489	! ! ===============
	490
	491	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	492	! II Compute Boundary layer mixing coef. and diagnose the new boundary layer depth
	493	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	494
	495	! Initialization
	496	jkmax = 0
	497	zdept (:,:) = 0.
	498	zdepw (:,:) = 0.
	499	zriblk(:,:) = 0.
	500	zmoek (:,:) = 0.
	501	zvisc (:,:) = 0.
	502	zdift (:,:) = 0.
	503	#if defined key_zdfddm
	504	zdifs (:,:) = 0.
	505	#endif
	506	zmask (:,:) = 0.
	507	DO ji = fs_2, fs_jpim1
	508	zria(ji ) = 0.
	509	! Maximum boundary layer depth
	510	ikbot = mbathy(ji,jj) - 1 ! ikbot is the last T point in the water
	511	zhmax(ji) = fsdept(ji,jj,ikbot) - 0.001
	512	! Compute Monin obukhov length scale at the surface and Ekman depth:
	513	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * ratt(1)
	514	zekman(ji) = rcekman * zustar(ji,jj) / ( ABS( ff(ji,jj) ) + epsln )
	515	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	516	zmoa(ji) = zucube / ( vonk * ( zbuofdep + epsln ) )
[899]	517	#if defined key_c1d
[255]	518	! store the surface buoyancy forcing
	519	zstabl = 0.5 + SIGN( 0.5, zbuofdep )
	520	buof(ji,jj,1) = zbuofdep * tmask(ji,jj,1)
	521	! store the moning-oboukov length scale at surface
	522	zmob = zstabl * zmoa(ji) + ( 1.0 - zstabl ) * fsdept(ji,jj,1)
	523	mols(ji,jj,1) = MIN( zmob , zhmax(ji) ) * tmask(ji,jj,1)
	524	! store Ekman depth
	525	zek = zstabl * zekman(ji) + ( 1.0 - zstabl ) * fsdept(ji,jj,1)
	526	ekdp(ji,jj ) = MIN( zek , zhmax(ji) ) * tmask(ji,jj,1)
	527	#endif
	528	END DO
	529	! Compute the pipe
	530	! ---------------------
	531	DO jk = 2, jpkm1
	532	DO ji = fs_2, fs_jpim1
	533	! Compute bfsfc = Bo + radiative contribution down to hbf*depht
	534	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * ratt(jk)
	535	! Flag (zstabl = 1) if positive forcing
	536	zstabl = 0.5 + SIGN( 0.5, zbuofdep)
	537
	538	! Compute bulk richardson number zrib at depht
	539	!-------------------------------------------------------
	540	! [Br - B(d)] * d zrinum
	541	! Rib(z) = ----------------------- = -------------
	542	! \|Vr - V(d)\|^2 + Vt(d)^2 zdVsq + zVtsq
	543	!
	544	! First compute zt,zs,zu,zv = means in the surface layer < epsilon*depht
	545	! Else surface values are taken at the first T level.
	546	! For stability, resolved vertical shear is computed with "before velocities".
	547	zref = epsilon * fsdept(ji,jj,jk)
	548	#if defined key_kppcustom
	549	! zref = gdept(1)
	550	zref = fsdept(ji,jj,1)
	551	zt = tn(ji,jj,1)
	552	zs = sn(ji,jj,1)
	553	zrh = rhop(ji,jj,1)
	554	zu = ( ub(ji,jj,1) + ub(ji - 1,jj ,1) ) / MAX( 1. , umask(ji,jj,1) + umask(ji - 1,jj ,1) )
	555	zv = ( vb(ji,jj,1) + vb(ji ,jj - 1,1) ) / MAX( 1. , vmask(ji,jj,1) + vmask(ji ,jj - 1,1) )
	556	#else
	557	zt = 0.
	558	zs = 0.
	559	zu = 0.
	560	zv = 0.
	561	zrh = 0.
	562	! vertically integration over the upper epsilon*gdept(jk) ; del () array is computed once in zdf_kpp_init
	563	DO jm = 1, jpkm1
	564	zt = zt + del(jk,jm) * tn(ji,jj,jm)
	565	zs = zs + del(jk,jm) * sn(ji,jj,jm)
	566	zu = zu + 0.5 * del(jk,jm) &
	567	& * ( ub(ji,jj,jm) + ub(ji - 1,jj,jm) ) &
	568	& / MAX( 1. , umask(ji,jj,jm) + umask(ji - 1,jj,jm) )
	569	zv = zv + 0.5 * del(jk,jm) &
	570	& * ( vb(ji,jj,jm) + vb(ji,jj - 1,jm) ) &
	571	& / MAX( 1. , vmask(ji,jj,jm) + vmask(ji,jj - 1,jm) )
	572	zrh = zrh + del(jk,jm) * rhop(ji,jj,jm)
	573	END DO
	574	#endif
	575	zsr = SQRT( ABS( sn(ji,jj,jk) ) )
	576	! depth
	577	zh = fsdept(ji,jj,jk)
	578	! compute compression terms on density
	579	ze = ( -3.508914e-8zt-1.248266e-8 ) zt-2.595994e-6
	580	zbw = ( 1.296821e-6zt-5.782165e-9 ) zt+1.045941e-4
	581	zb = zbw + ze * zs
	582
	583	zd = -2.042967e-2
	584	zc = (-7.267926e-5zt+2.598241e-3 ) zt+0.1571896
	585	zaw = ( ( 5.939910e-6zt+2.512549e-3 ) zt-0.1028859 ) *zt - 4.721788
	586	za = ( zdzsr + zc ) zs + zaw
	587
	588	zb1 = (-0.1909078zt+7.390729 ) zt-55.87545
	589	za1 = ( ( 2.326469e-3zt+1.553190)zt-65.00517 ) *zt+1044.077
	590	zkw = ( ( (-1.361629e-4zt-1.852732e-2 ) zt-30.41638 ) zt + 2098.925 ) zt+190925.6
	591	zk0 = ( zb1zsr + za1 )zs + zkw
	592	zcomp = 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) )
	593
	594	#if defined key_kppcustom
	595	! potential density of water(zrh = zt,zs at level jk):
	596	zrhdr = zrh / zcomp
	597	#else
	598	! potential density of water(ztref,zsref at level jk):
	599	! compute volumic mass pure water at atm pressure
	600	IF ( neos < 1 ) THEN
	601	zr1= ( ( ( ( 6.536332e-9zt-1.120083e-6 )zt+1.001685e-4)*zt &
	602	& -9.095290e-3 )zt+6.793952e-2 )zt+999.842594
	603	! seawater volumic mass atm pressure
	604	zr2= ( ( ( 5.3875e-9zt-8.2467e-7 ) zt+7.6438e-5 ) *zt &
	605	& -4.0899e-3 ) *zt+0.824493
	606	zr3= ( -1.6546e-6zt+1.0227e-4 ) zt-5.72466e-3
	607	zr4= 4.8314e-4
	608	! potential volumic mass (reference to the surface)
	609	zrhop= ( zr4zs + zr3zsr + zr2 ) *zs + zr1
	610	zrhdr = zrhop / zcomp
	611	ELSE
	612	zrhdr = zrh / zcomp
	613	ENDIF
	614	#endif
	615
	616	! potential density of ambiant water at level jk :
	617	zrhd = ( rhd(ji,jj,jk) * rau0 + rau0 )
	618
	619	! And now the Rib number numerator .
	620	zrinum = grav * ( zrhd - zrhdr ) / rau0
	621	zrinum = zrinum * ( fsdept(ji,jj,jk) - zref ) * tmask(ji,jj,jk)
	622
	623	! Resolved shear contribution to Rib at depth T-point (zdVsq)
	624	ztx = ( ub( ji , jj ,jk) + ub(ji - 1, jj ,jk) ) &
	625	& / MAX( 1. , umask( ji , jj ,jk) + umask(ji - 1, jj ,jk) )
	626	zty = ( vb( ji , jj ,jk) + vb(ji ,jj - 1,jk) ) &
	627	& / MAX( 1., vmask( ji , jj ,jk) + vmask(ji ,jj - 1,jk) )
	628
	629	zdVsq = ( zu - ztx ) * ( zu - ztx ) + ( zv - zty ) * ( zv - zty )
	630
	631	! Scalar turbulent velocity scale zws for hbl=gdept
	632	zscale = zstabl + ( 1.0 - zstabl ) * epsilon
	633	zehat = vonk * zscale * fsdept(ji,jj,jk) * zbuofdep
	634	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	635	zeta = zehat / ( zucube + epsln )
	636
	637	IF( zehat > 0. ) THEN
	638	! Stable case
	639	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	640	ELSE
	641	! Unstable case
	642	#if defined key_kpplktb
	643	! use lookup table
	644	zd = zehat - dehatmin
	645	il = INT( zd / dezehat )
	646	il = MIN( il, nilktbm1 )
	647	il = MAX( il, 1 )
	648
	649	ud = zustar(ji,jj) - ustmin
	650	jl = INT( ud / deustar )
	651	jl = MIN( jl, njlktbm1 )
	652	jl = MAX( jl, 1 )
	653
	654	zfrac = zd / dezehat - FLOAT( il )
	655	ufrac = ud / deustar - FLOAT( jl )
	656	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	657	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	658	!
	659	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	660	#else
	661	! use analytical functions:
	662	zcons = 0.5 + SIGN( 0.5 , ( rzetas - zeta ) )
	663	zwcons = vonk * zustar(ji,jj) * ( ( ABS( rconas - rconcs * zeta ) )**pthird )
	664	zwsun = vonk * zustar(ji,jj) * SQRT( ABS ( 1.0 - rconc2 * zeta ) )
	665	!
	666	zws = zcons * zwcons + ( 1.0 - zcons) * zwsun
	667	#endif
	668	ENDIF
	669
	670	! Turbulent shear contribution to Rib (zVtsq) bv frequency at levels ( ie T-point jk)
	671	zrn2 = 0.5 * ( rn2(ji,jj,jk) + rn2(ji,jj,jk+1) )
	672	zbvzed = SQRT( ABS( zrn2 ) )
	673	zVtsq = fsdept(ji,jj,jk) * zws * zbvzed * Vtc
	674
	675	! Finally, the bulk Richardson number at depth fsdept(i,j,k)
	676	zrib = zrinum / ( zdVsq + zVtsq + epsln )
	677
	678	! Find subscripts around the boundary layer depth, build the pipe
	679	! ----------------------------------------------------------------
	680
	681	! Flag (zflagri = 1) if zrib < Ricr
	682	zflagri = 0.5 + SIGN( 0.5, ( Ricr - zrib ) )
	683	! Flag (zflagh = 1) if still within overall boundary layer
	684	zflagh = 0.5 + SIGN( 0.5, ( fsdept(ji,jj,1) - zdept(ji,2) ) )
	685
	686	! Ekman layer depth
	687	zek = zstabl * zekman(ji) + ( 1.0 - zstabl ) * zhmax(ji)
	688	zflag = 0.5 + SIGN( 0.5, ( zek - fsdept(ji,jj,jk-1) ) )
	689	zek = zflag * zek + ( 1.0 - zflag ) * zhmax(ji)
	690	zflagek = 0.5 + SIGN( 0.5, ( zek - fsdept(ji,jj,jk) ) )
	691	! Flag (zflagmo = 1) if still within stable Monin-Obukhov and in water
	692	zmob = zucube / ( vonk * ( zbuofdep + epsln ) )
	693	ztemp = zstabl * zmob + ( 1.0 - zstabl) * zhmax(ji)
	694	ztemp = MIN( ztemp , zhmax(ji) )
	695	zflagmo = 0.5 + SIGN( 0.5, ( ztemp - fsdept(ji,jj,jk) ) )
	696
	697	! No limitation by Monin Obukhov or Ekman depths:
	698	! zflagek = 1.0
	699	! zflagmo = 0.5 + SIGN( 0.5, ( zhmax(ji) - fsdept(ji,jj,jk) ) )
	700
	701	! Load pipe via zflagkb for later calculations
	702	! Flag (zflagkb = 1) if zflagh = 1 and (zflagri = 0 or zflagek = 0 or zflagmo = 0)
	703	zflagkb = zflagh * ( 1.0 - ( zflagri * zflagek * zflagmo ) )
	704
	705	zmask(ji,jk) = zflagh
	706	jkp2 = MIN( jk+2 , ikbot )
	707	jkm1 = MAX( jk-1 , 2 )
	708	jkmax = MAX( jkmax, jk * INT( REAL( zflagh+epsln ) ) )
	709
	710	zdept(ji,1) = zdept(ji,1) + zflagkb * fsdept(ji,jj,jk-1)
	711	zdept(ji,2) = zdept(ji,2) + zflagkb * fsdept(ji,jj,jk )
	712	zdept(ji,3) = zdept(ji,3) + zflagkb * fsdept(ji,jj,jk+1)
	713
	714	zdepw(ji,1) = zdepw(ji,1) + zflagkb * fsdepw(ji,jj,jk-1)
	715	zdepw(ji,2) = zdepw(ji,2) + zflagkb * fsdepw(ji,jj,jk )
	716	zdepw(ji,3) = zdepw(ji,3) + zflagkb * fsdepw(ji,jj,jk+1)
	717	zdepw(ji,4) = zdepw(ji,4) + zflagkb * fsdepw(ji,jj,jkp2)
	718
	719	zriblk(ji,1) = zriblk(ji,1) + zflagkb * zria(ji)
	720	zriblk(ji,2) = zriblk(ji,2) + zflagkb * zrib
	721
	722	zmoek (ji,0) = zmoek (ji,0) + zflagkb * zek
	723	zmoek (ji,1) = zmoek (ji,1) + zflagkb * zmoa(ji)
	724	zmoek (ji,2) = zmoek (ji,2) + zflagkb * ztemp
	725	! Save Monin Obukhov depth
	726	zmoa (ji) = zmob
	727
	728	zvisc(ji,1) = zvisc(ji,1) + zflagkb * avmu(ji,jj,jkm1)
	729	zvisc(ji,2) = zvisc(ji,2) + zflagkb * avmu(ji,jj,jk )
	730	zvisc(ji,3) = zvisc(ji,3) + zflagkb * avmu(ji,jj,jk+1)
	731	zvisc(ji,4) = zvisc(ji,4) + zflagkb * avmu(ji,jj,jkp2)
	732
	733	zdift(ji,1) = zdift(ji,1) + zflagkb * avt (ji,jj,jkm1)
	734	zdift(ji,2) = zdift(ji,2) + zflagkb * avt (ji,jj,jk )
	735	zdift(ji,3) = zdift(ji,3) + zflagkb * avt (ji,jj,jk+1)
	736	zdift(ji,4) = zdift(ji,4) + zflagkb * avt (ji,jj,jkp2)
	737
	738	#if defined key_zdfddm
	739	zdifs(ji,1) = zdifs(ji,1) + zflagkb * avs (ji,jj,jkm1)
	740	zdifs(ji,2) = zdifs(ji,2) + zflagkb * avs (ji,jj,jk )
	741	zdifs(ji,3) = zdifs(ji,3) + zflagkb * avs (ji,jj,jk+1)
	742	zdifs(ji,4) = zdifs(ji,4) + zflagkb * avs (ji,jj,jkp2)
	743	#endif
	744	! Save the Richardson number
	745	zria (ji) = zrib
[899]	746	#if defined key_c1d
[255]	747	! store buoyancy length scale
	748	buof(ji,jj,jk) = zbuofdep * tmask(ji,jj,jk)
	749	! store Monin Obukhov
	750	zmob = zstabl * zmob + ( 1.0 - zstabl) * fsdept(ji,jj,1)
	751	mols(ji,jj,jk) = MIN( zmob , zhmax(ji) ) * tmask(ji,jj,jk)
	752	! Bulk Richardson number
	753	rib(ji,jj,jk) = zrib * tmask(ji,jj,jk)
	754	#endif
	755	END DO
	756	END DO
	757	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	758	! III PROCESS THE PIPE
	759	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	760
	761	DO ji = fs_2, fs_jpim1
	762
	763	! Find the boundary layer depth zhbl
	764	! ----------------------------------------
	765
	766	! Interpolate monin Obukhov and critical Ri mumber depths
	767	ztemp = zdept(ji,2) - zdept(ji,1)
	768	zflag = ( Ricr - zriblk(ji,1) ) / ( zriblk(ji,2) - zriblk(ji,1) + epsln )
	769	zhrib = zdept(ji,1) + zflag * ztemp
	770
	771	IF( zriblk(ji,2) < Ricr ) zhrib = zhmax(ji)
	772
	773	IF( zmoek(ji,2) < zdept(ji,2) ) THEN
	774	IF ( zmoek(ji,1) < 0. ) THEN
	775	zmob = zdept(ji,2) - epsln
	776	ELSE
	777	zmob = ztemp + zmoek(ji,1) - zmoek(ji,2)
	778	zmob = ( zmoek(ji,1) * zdept(ji,2) - zmoek(ji,2) * zdept(ji,1) ) / zmob
	779	zmob = MAX( zmob , zdept(ji,1) + epsln )
	780	ENDIF
	781	ELSE
	782	zmob = zhmax(ji)
	783	ENDIF
	784	ztemp = MIN( zmob , zmoek(ji,0) )
	785
	786	! Finally, the boundary layer depth, zhbl
	787	zhbl(ji) = MAX( fsdept(ji,jj,1) + epsln, MIN( zhrib , ztemp ) )
	788
	789	! Save hkpp for further diagnostics (optional)
	790	hkpp(ji,jj) = zhbl(ji) * tmask(ji,jj,1)
	791
	792	! Correct mask if zhbl < fsdepw(ji,jj,2) for no viscosity/diffusivity enhancement at fsdepw(ji,jj,2)
	793	! zflag = 1 if zhbl(ji) > fsdepw(ji,jj,2)
	794	IF( zhbl(ji) < fsdepw(ji,jj,2) ) zmask(ji,2) = 0.
	795
	796
	797	! Velocity scales at depth zhbl
	798	! -----------------------------------
	799
	800	! Compute bouyancy forcing down to zhbl
	801	ztemp = -hbf * zhbl(ji)
	802	zatt1 = 1.0 - ( rabs * EXP( ztemp / xsi1 ) + ( 1.0 - rabs ) * EXP( ztemp / xsi2 ) )
	803	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * zatt1
	804	zstabl = 0.5 + SIGN( 0.5 , zbuofdep )
	805
	806	zbuofdep = zbuofdep + zstabl * epsln
	807
	808	zscale = zstabl + ( 1.0 - zstabl ) * epsilon
	809	zehat = vonk * zscale * zhbl(ji) * zbuofdep
	810	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	811	zeta = zehat / ( zucube + epsln )
	812
	813	IF( zehat > 0. ) THEN
	814	! Stable case
	815	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	816	zwm = zws
	817	ELSE
	818	! Unstable case
	819	#if defined key_kpplktb
	820	! use lookup table
	821	zd = zehat - dehatmin
	822	il = INT( zd / dezehat )
	823	il = MIN( il, nilktbm1 )
	824	il = MAX( il, 1 )
	825
	826	ud = zustar(ji,jj) - ustmin
	827	jl = INT( ud / deustar )
	828	jl = MIN( jl, njlktbm1 )
	829	jl = MAX( jl, 1 )
	830
	831	zfrac = zd / dezehat - FLOAT( il )
	832	ufrac = ud / deustar - FLOAT( jl )
	833	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	834	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	835	zwam = ( 1. - zfrac ) * wmlktb(il,jl+1) + zfrac * wmlktb(il+1,jl+1)
	836	zwbm = ( 1. - zfrac ) * wmlktb(il,jl ) + zfrac * wmlktb(il+1,jl )
	837	!
	838	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	839	zwm = ( 1. - ufrac ) * zwbm + ufrac * zwam
	840	#else
	841	! use analytical functions
	842	zconm = 0.5 + SIGN( 0.5, ( rzetam - zeta) )
	843	zcons = 0.5 + SIGN( 0.5, ( rzetas - zeta) )
	844
	845	! Momentum : zeta < rzetam (zconm = 1)
	846	! Scalars : zeta < rzetas (zcons = 1)
	847	zwconm = zustar(ji,jj) * vonk * ( ( ABS( rconam - rconcm * zeta) )**pthird )
	848	zwcons = zustar(ji,jj) * vonk * ( ( ABS( rconas - rconcs * zeta) )**pthird )
	849
	850	! Momentum : rzetam <= zeta < 0 (zconm = 0)
	851	! Scalars : rzetas <= zeta < 0 (zcons = 0)
	852	zwmun = SQRT( ABS( 1.0 - rconc2 * zeta ) )
	853	zwsun = vonk * zustar(ji,jj) * zwmun
	854	zwmun = vonk * zustar(ji,jj) * SQRT(zwmun)
	855	!
	856	zwm = zconm * zwconm + ( 1.0 - zconm ) * zwmun
	857	zws = zcons * zwcons + ( 1.0 - zcons ) * zwsun
	858
	859	#endif
	860	ENDIF
	861
	862
	863	! Viscosity, diffusivity values and derivatives at h
	864	! --------------------------------------------------------
	865
	866	! check between at which interfaces is located zhbl(ji)
	867	! ztemp = 1, zdepw(ji,2) < zhbl < zdepw(ji,3)
	868	! ztemp = 0, zdepw(ji,1) < zhbl < zdepw(ji,2)
	869	ztemp = 0.5 + SIGN( 0.5, ( zhbl(ji) - zdepw(ji,2) ) )
	870	zdep21 = zdepw(ji,2) - zdepw(ji,1) + epsln
	871	zdep32 = zdepw(ji,3) - zdepw(ji,2) + epsln
	872	zdep43 = zdepw(ji,4) - zdepw(ji,3) + epsln
	873
	874	! Compute R as in LMD94, eq D5b
	875	zdelta = ( zhbl(ji) - zdepw(ji,2) ) * ztemp / zdep32 &
	876	& + ( zhbl(ji) - zdepw(ji,1) ) * ( 1.0 - ztemp ) / zdep21
	877
	878	! Compute the vertical derivative of viscosities (zdzh) at z=zhbl(ji)
	879	zdzup = ( zvisc(ji,2) - zvisc(ji,3) ) * ztemp / zdep32 &
	880	& + ( zvisc(ji,1) - zvisc(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	881
	882	zdzdn = ( zvisc(ji,3) - zvisc(ji,4) ) * ztemp / zdep43 &
	883	& + ( zvisc(ji,2) - zvisc(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	884
	885	! LMD94, eq D5b :
	886	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	887	zdzh = MAX( zdzh , 0. )
	888
	889	! Compute viscosities (zvath) at z=zhbl(ji), LMD94 eq D5a
	890	zvath = ztemp * ( zvisc(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	891	& + ( 1.0 - ztemp ) * ( zvisc(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	892
	893	! Compute G (zgat1) and its derivative (zdat1) at z=hbl(ji), LMD94 eq 18
	894
	895	! Vertical derivative of velocity scale divided by velocity scale squared at z=hbl(ji)
	896	! (non zero only in stable conditions)
	897	zflag = -zstabl * rconc1 * zbuofdep / ( zucube * zustar(ji,jj) + epsln )
	898
	899	! G at its derivative at z=hbl:
	900	zgat1 = zvath / ( zhbl(ji) * ( zwm + epsln ) )
	901	zdat1 = -zdzh / ( zwm + epsln ) - zflag * zvath / zhbl(ji)
	902
	903	! G coefficients, LMD94 eq 17
	904	za2m(ji) = -2.0 + 3.0 * zgat1 - zdat1
	905	za3m(ji) = 1.0 - 2.0 * zgat1 + zdat1
	906
	907
	908	! Compute the vertical derivative of temperature diffusivities (zdzh) at z=zhbl(ji)
	909	zdzup = ( zdift(ji,2) - zdift(ji,3) ) * ztemp / zdep32 &
	910	& + ( zdift(ji,1) - zdift(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	911
	912	zdzdn = ( zdift(ji,3) - zdift(ji,4) ) * ztemp / zdep43 &
	913	& + ( zdift(ji,2) - zdift(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	914
	915	! LMD94, eq D5b :
	916	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	917	zdzh = MAX( zdzh , 0. )
	918
	919
	920	! Compute diffusivities (zvath) at z=zhbl(ji), LMD94 eq D5a
	921	zvath = ztemp * ( zdift(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	922	& + ( 1.0 - ztemp ) * ( zdift(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	923
	924	! G at its derivative at z=hbl:
	925	zgat1 = zvath / ( zhbl(ji) * ( zws + epsln ) )
	926	zdat1 = -zdzh / ( zws + epsln ) - zflag * zvath / zhbl(ji)
	927
	928	! G coefficients, LMD94 eq 17
	929	za2t(ji) = -2.0 + 3.0 * zgat1 - zdat1
	930	za3t(ji) = 1.0 - 2.0 * zgat1 + zdat1
	931
	932	#if defined key_zdfddm
	933	! Compute the vertical derivative of salinities diffusivities (zdzh) at z=zhbl(ji)
	934	zdzup = ( zdifs(ji,2) - zdifs(ji,3) ) * ztemp / zdep32 &
	935	& + ( zdifs(ji,1) - zdifs(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	936
	937	zdzdn = ( zdifs(ji,3) - zdifs(ji,4) ) * ztemp / zdep43 &
	938	& + ( zdifs(ji,2) - zdifs(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	939
	940	! LMD94, eq D5b :
	941	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	942	zdzh = MAX( zdzh , 0. )
	943
	944	! Compute diffusivities (zvath) at z=zhbl(ji), LMD94 eq D5a
	945	zvath = ztemp * ( zdifs(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	946	& + ( 1.0 - ztemp ) * ( zdifs(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	947
	948	! G at its derivative at z=hbl:
	949	zgat1 = zvath / ( zhbl(ji) * ( zws + epsln ) )
	950	zdat1 = -zdzh / ( zws + epsln ) - zflag * zvath / zhbl(ji)
	951
	952	! G coefficients, LMD94 eq 17
	953	za2s(ji) = -2.0 + 3.0 * zgat1 - zdat1
	954	za3s(ji) = 1.0 - 2.0 * zgat1 + zdat1
	955	#endif
	956
	957	!-------------------turn off interior matching here------
	958	! za2(ji,1) = -2.0
	959	! za3(ji,1) = 1.0
	960	! za2(ji,2) = -2.0
	961	! za3(ji,2) = 1.0
	962	!--------------------------------------------------------
	963
	964	! Compute Enhanced Mixing Coefficients (LMD94,eq D6)
	965	! ---------------------------------------------------------------
	966
	967	! Delta
	968	zdelta = ( zhbl(ji) - zdept(ji,1) ) / ( zdept(ji,2) - zdept(ji,1) + epsln )
	969	zdelta2 = zdelta * zdelta
	970
	971	! Mixing coefficients at first level above h (zdept(ji,1))
	972	! and at first interface in the pipe (zdepw(ji,2))
	973
	974	! At first T level above h (zdept(ji,1)) (always in the boundary layer)
	975	zsig = zdept(ji,1) / zhbl(ji)
	976	ztemp = zstabl * zsig + ( 1.0 - zstabl ) * MIN( zsig , epsilon )
	977	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	978	zeta = zehat / ( zucube + epsln)
	979	zwst = vonk * zustar(ji,jj) / ( ABS( 1.0 + rconc1 * zeta ) + epsln)
	980	zwm = zstabl * zwst + ( 1.0 - zstabl ) * zwm
	981	zws = zstabl * zwst + ( 1.0 - zstabl ) * zws
	982
	983	zkm1m = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	984	zkm1t = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	985	#if defined key_zdfddm
	986	zkm1s = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	987	#endif
	988	! At first W level in the pipe (zdepw(ji,2)) (not always in the boundary layer ):
	989	zsig = MIN( zdepw(ji,2) / zhbl(ji) , 1.0 )
	990	ztemp = zstabl * zsig + ( 1.0 - zstabl ) * MIN( zsig , epsilon )
	991	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	992	zeta = zehat / ( zucube + epsln )
	993	zwst = vonk * zustar(ji,jj) / ( ABS( 1.0 + rconc1 * zeta ) + epsln)
	994	zws = zstabl * zws + ( 1.0 - zstabl ) * zws
	995	zwm = zstabl * zws + ( 1.0 - zstabl ) * zwm
	996
	997	zkmpm(ji) = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	998	zkmpt(ji) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	999	#if defined key_zdfddm
	1000	zkmps(ji) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	1001	#endif
	1002
	1003	! check if this point is in the boundary layer,else take interior viscosity/diffusivity:
	1004	zflag = 0.5 + SIGN( 0.5, ( zhbl(ji) - zdepw(ji,2) ) )
	1005	zkmpm(ji) = zkmpm(ji) * zflag + ( 1.0 - zflag ) * zvisc(ji,2)
	1006	zkmpt(ji) = zkmpt(ji) * zflag + ( 1.0 - zflag ) * zdift(ji,2)
	1007	#if defined key_zdfddm
	1008	zkmps(ji) = zkmps(ji) * zflag + ( 1.0 - zflag ) * zdifs(ji,2)
	1009	#endif
	1010
	1011	! Enhanced viscosity/diffusivity at zdepw(ji,2)
	1012	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1m + zdelta2 * zkmpm(ji)
	1013	zkmpm(ji) = ( 1.0 - zdelta ) * zvisc(ji,2) + zdelta * ztemp
	1014	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1t + zdelta2 * zkmpt(ji)
	1015	zkmpt(ji) = ( 1.0 - zdelta ) * zdift(ji,2) + zdelta * ztemp
	1016	#if defined key_zdfddm
	1017	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1s + zdelta2 * zkmps(ji)
	1018	zkmps(ji) = ( 1.0 - zdelta ) * zdifs(ji,2) + zdelta * ztemp
	1019	#endif
	1020
	1021	END DO
	1022	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	1023	! IV. Compute vertical eddy viscosity and diffusivity coefficients
	1024	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	1025
	1026	DO jk = 2, jkmax
	1027
	1028	! Compute turbulent velocity scales on the interfaces
	1029	! --------------------------------------------------------
	1030	DO ji = fs_2, fs_jpim1
	1031	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * zatt1
	1032	zstabl = 0.5 + SIGN( 0.5 , zbuofdep )
	1033	zbuofdep = zbuofdep + zstabl * epsln
	1034	zsig = fsdepw(ji,jj,jk) / zhbl(ji)
	1035	ztemp = zstabl * zsig + ( 1. - zstabl ) * MIN( zsig , epsilon )
	1036	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	1037	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	1038	zeta = zehat / ( zucube + epsln )
	1039
	1040	IF( zehat > 0. ) THEN
	1041	! Stable case
	1042	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	1043	zwm = zws
	1044	ELSE
	1045	! Unstable case
	1046	#if defined key_kpplktb
	1047	! use lookup table
	1048	zd = zehat - dehatmin
	1049	il = INT( zd / dezehat )
	1050	il = MIN( il, nilktbm1 )
	1051	il = MAX( il, 1 )
	1052
	1053	ud = zustar(ji,jj) - ustmin
	1054	jl = INT( ud / deustar )
	1055	jl = MIN( jl, njlktbm1 )
	1056	jl = MAX( jl, 1 )
	1057
	1058	zfrac = zd / dezehat - FLOAT( il )
	1059	ufrac = ud / deustar - FLOAT( jl )
	1060	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	1061	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	1062	zwam = ( 1. - zfrac ) * wmlktb(il,jl+1) + zfrac * wmlktb(il+1,jl+1)
	1063	zwbm = ( 1. - zfrac ) * wmlktb(il,jl ) + zfrac * wmlktb(il+1,jl )
	1064	!
	1065	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	1066	zwm = ( 1. - ufrac ) * zwbm + ufrac * zwam
	1067	#else
	1068	! use analytical functions
	1069	zconm = 0.5 + SIGN( 0.5, ( rzetam - zeta) )
	1070	zcons = 0.5 + SIGN( 0.5, ( rzetas - zeta) )
	1071
	1072	! Momentum : zeta < rzetam (zconm = 1)
	1073	! Scalars : zeta < rzetas (zcons = 1)
	1074	zwconm = zustar(ji,jj) * vonk * ( ( ABS( rconam - rconcm * zeta) )**pthird )
	1075	zwcons = zustar(ji,jj) * vonk * ( ( ABS( rconas - rconcs * zeta) )**pthird )
	1076
	1077	! Momentum : rzetam <= zeta < 0 (zconm = 0)
	1078	! Scalars : rzetas <= zeta < 0 (zcons = 0)
	1079	zwmun = SQRT( ABS( 1.0 - rconc2 * zeta ) )
	1080	zwsun = vonk * zustar(ji,jj) * zwmun
	1081	zwmun = vonk * zustar(ji,jj) * SQRT(zwmun)
	1082	!
	1083	zwm = zconm * zwconm + ( 1.0 - zconm ) * zwmun
	1084	zws = zcons * zwcons + ( 1.0 - zcons ) * zwsun
	1085
	1086	#endif
	1087	ENDIF
	1088
	1089	zblcm(ji,jk) = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	1090	zblct(ji,jk) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	1091	#if defined key_zdfddm
	1092	zblcs(ji,jk) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	1093	#endif
	1094	! Compute Nonlocal transport term = ghats * <ws>o
	1095	! ----------------------------------------------------
	1096	ghats(ji,jj,jk-1) = ( 1. - zstabl ) * rcg / ( zws * zhbl(ji) + epsln ) * tmask(ji,jj,jk)
	1097
	1098	END DO
	1099	END DO
	1100	! Combine interior and boundary layer coefficients and nonlocal term
	1101	! -----------------------------------------------------------------------
	1102	DO jk = 2, jpkm1
	1103	DO ji = fs_2, fs_jpim1
	1104	zflag = zmask(ji,jk) * zmask(ji,jk+1)
	1105	zviscos(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avmu (ji,jj,jk) & ! interior viscosities
	1106	& + zflag * zblcm(ji,jk ) & ! boundary layer viscosities
	1107	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmpm(ji ) ! viscosity enhancement at W_level near zhbl
	1108
	1109	zviscos(ji,jj,jk) = zviscos(ji,jj,jk) * tmask(ji,jj,jk)
	1110
	1111
	1112	zdiffut(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avt (ji,jj,jk) & ! interior diffusivities
	1113	& + zflag * zblct(ji,jk ) & ! boundary layer diffusivities
	1114	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmpt(ji ) ! diffusivity enhancement at W_level near zhbl
	1115
	1116	zdiffut(ji,jj,jk) = zdiffut(ji,jj,jk) * tmask(ji,jj,jk)
	1117	#if defined key_zdfddm
	1118	zdiffus(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avs (ji,jj,jk) & ! interior diffusivities
	1119	& + zflag * zblcs(ji,jk ) & ! boundary layer diffusivities
	1120	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmps(ji ) ! diffusivity enhancement at W_level near zhbl
	1121
	1122	zdiffus(ji,jj,jk) = zdiffus(ji,jj,jk) * tmask(ji,jj,jk)
	1123	#endif
	1124	! Non local flux in the boundary layer only
	1125	ghats(ji,jj,jk-1) = zmask(ji,jk) * ghats(ji,jj,jk-1)
	1126
	1127	ENDDO
	1128	END DO
	1129	! ! ===============
	1130	END DO ! End of slab
	1131	! ! ===============
	1132
	1133	! Lateral boundary conditions on zvicos and zdiffus (sign unchanged)
	1134	CALL lbc_lnk( zviscos(:,:,:), 'U', 1. ) ; CALL lbc_lnk( zdiffut(:,:,:), 'W', 1. )
	1135	#if defined key_zdfddm
	1136	CALL lbc_lnk( zdiffus(:,:,:), 'W', 1. )
	1137	#endif
	1138
	1139	SELECT CASE ( nave )
	1140	!
	1141	CASE ( 0 ) ! no viscosity and diffusivity smoothing
	1142
	1143	DO jk = 2, jpkm1
	1144	DO jj = 2, jpjm1
	1145	DO ji = fs_2, fs_jpim1
	1146	avmu(ji,jj,jk) = ( zviscos(ji,jj,jk) + zviscos(ji+1,jj,jk) ) &
	1147	& / MAX( 1., tmask(ji,jj,jk) + tmask (ji + 1,jj,jk) ) * umask(ji,jj,jk)
	1148
	1149	avmv(ji,jj,jk) = ( zviscos(ji,jj,jk) + zviscos(ji,jj+1,jk) ) &
	1150	& / MAX( 1., tmask(ji,jj,jk) + tmask (ji,jj+1,jk) ) * vmask(ji,jj,jk)
	1151
	1152	avt (ji,jj,jk) = zdiffut(ji,jj,jk) * tmask(ji,jj,jk)
	1153	#if defined key_zdfddm
	1154	avs (ji,jj,jk) = zdiffus(ji,jj,jk) * tmask(ji,jj,jk)
	1155	#endif
	1156	END DO
	1157	END DO
	1158	END DO
	1159
	1160	CASE ( 1 ) ! viscosity and diffusivity smoothing
	1161	!
	1162	! ( 1/2 1 1/2 ) ( 1/2 1/2 ) ( 1/2 1 1/2 )
	1163	! avt = 1/8 ( 1 2 1 ) avmu = 1/4 ( 1 1 ) avmv= 1/4 ( 1/2 1 1/2 )
	1164	! ( 1/2 1 1/2 ) ( 1/2 1/2 )
	1165
	1166	DO jk = 2, jpkm1
	1167	DO jj = 2, jpjm1
	1168	DO ji = fs_2, fs_jpim1
	1169
	1170	avmu(ji,jj,jk) = ( zviscos(ji ,jj ,jk) + zviscos(ji+1,jj ,jk) &
	1171	& +.5*( zviscos(ji ,jj-1,jk) + zviscos(ji+1,jj-1,jk) &
	1172	& +zviscos(ji ,jj+1,jk) + zviscos(ji+1,jj+1,jk) ) ) * eumean(ji,jj,jk)
	1173
	1174	avmv(ji,jj,jk) = ( zviscos(ji ,jj ,jk) + zviscos(ji ,jj+1,jk) &
	1175	& +.5*( zviscos(ji-1,jj ,jk) + zviscos(ji-1,jj+1,jk) &
	1176	& +zviscos(ji+1,jj ,jk) + zviscos(ji+1,jj+1,jk) ) ) * evmean(ji,jj,jk)
	1177
	1178	avt (ji,jj,jk) = ( .5*( zdiffut(ji-1,jj+1,jk) + zdiffut(ji-1,jj-1,jk) &
	1179	& +zdiffut(ji+1,jj+1,jk) + zdiffut(ji+1,jj-1,jk) ) &
	1180	& +1.*( zdiffut(ji-1,jj ,jk) + zdiffut(ji ,jj+1,jk) &
	1181	& +zdiffut(ji ,jj-1,jk) + zdiffut(ji+1,jj ,jk) ) &
	1182	& +2.* zdiffut(ji ,jj ,jk) ) * etmean(ji,jj,jk)
	1183	#if defined key_zdfddm
	1184	avs (ji,jj,jk) = ( .5*( zdiffus(ji-1,jj+1,jk) + zdiffus(ji-1,jj-1,jk) &
	1185	& +zdiffus(ji+1,jj+1,jk) + zdiffus(ji+1,jj-1,jk) ) &
	1186	& +1.*( zdiffus(ji-1,jj ,jk) + zdiffus(ji ,jj+1,jk) &
	1187	& +zdiffus(ji ,jj-1,jk) + zdiffus(ji+1,jj ,jk) ) &
	1188	& +2.* zdiffus(ji ,jj ,jk) ) * etmean(ji,jj,jk)
	1189	#endif
	1190	END DO
	1191	END DO
	1192	END DO
	1193
	1194	END SELECT
	1195
	1196	DO jk = 2, jpkm1 ! vertical slab
	1197	!
	1198	! Minimum value on the eddy diffusivity
	1199	! ----------------------------------------
	1200	DO jj = 2, jpjm1
	1201	DO ji = fs_2, fs_jpim1 ! vector opt.
	1202	avt(ji,jj,jk) = MAX( avt(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
	1203	#if defined key_zdfddm
	1204	avs(ji,jj,jk) = MAX( avs(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
	1205	#endif
	1206	END DO
	1207	END DO
	1208
	1209	!
	1210	! Minimum value on the eddy viscosity
	1211	! ----------------------------------------
	1212	DO jj = 1, jpj
	1213	DO ji = 1, jpi
	1214	avmu(ji,jj,jk) = MAX( avmu(ji,jj,jk), avmb(jk) ) * umask(ji,jj,jk)
	1215	avmv(ji,jj,jk) = MAX( avmv(ji,jj,jk), avmb(jk) ) * vmask(ji,jj,jk)
	1216	END DO
	1217	END DO
	1218	!
	1219	END DO
	1220
	1221	! Lateral boundary conditions on avt (sign unchanged)
	1222	CALL lbc_lnk( hkpp(:,:), 'T', 1. )
	1223
	1224	! Lateral boundary conditions on avt (sign unchanged)
	1225	CALL lbc_lnk( avt(:,:,:), 'W', 1. )
	1226	#if defined key_zdfddm
	1227	CALL lbc_lnk( avs(:,:,:), 'W', 1. )
	1228	#endif
	1229	! Lateral boundary conditions (avmu,avmv) (U- and V- points, sign unchanged)
	1230	CALL lbc_lnk( avmu(:,:,:), 'U', 1. ) ; CALL lbc_lnk( avmv(:,:,:), 'V', 1. )
	1231
[258]	1232	IF(ln_ctl) THEN
	1233	#if defined key_zdfddm
[516]	1234	CALL prt_ctl(tab3d_1=avt , clinfo1=' kpp - t: ', tab3d_2=avs , clinfo2=' s: ', ovlap=1, kdim=jpk)
[258]	1235	#else
[516]	1236	CALL prt_ctl(tab3d_1=avt , clinfo1=' kpp - t: ', ovlap=1, kdim=jpk)
[258]	1237	#endif
[516]	1238	CALL prt_ctl(tab3d_1=avmu, clinfo1=' kpp - u: ', mask1=umask, &
	1239	& tab3d_2=avmv, clinfo2= ' v: ', mask2=vmask, ovlap=1, kdim=jpk)
[258]	1240	ENDIF
	1241
[255]	1242	END SUBROUTINE zdf_kpp
	1243
	1244
[896]	1245	SUBROUTINE tra_kpp( kt )
[463]	1246	!!----------------------------------------------------------------------
	1247	!! * ROUTINE tra_kpp *
	1248	!!
	1249	!! ** Purpose : compute and add to the tracer trend the non-local
	1250	!! tracer flux
	1251	!!
	1252	!! ** Method : ???
	1253	!!
	1254	!! history :
	1255	!! 9.0 ! 05-11 (G. Madec) Original code
	1256	!!----------------------------------------------------------------------
	1257	!! * Modules used
	1258	USE oce, ONLY : ztrdt => ua, & ! use ua as 3D workspace
	1259	ztrds => va ! use va as 3D workspace
	1260	!!----------------------------------------------------------------------
[896]	1261	INTEGER, INTENT(in) :: kt
	1262	INTEGER :: ji, jj, jk
[255]	1263
[463]	1264	IF( kt == nit000 ) THEN
	1265	IF(lwp) WRITE(numout,*)
	1266	IF(lwp) WRITE(numout,*) 'tra_kpp : KPP non-local tracer fluxes'
	1267	IF(lwp) WRITE(numout,*) '~~~~~~~ '
	1268	ENDIF
	1269
	1270
	1271	! Save ta and sa trends
	1272	IF( l_trdtra ) THEN
	1273	ztrdt(:,:,:) = ta(:,:,:)
	1274	ztrds(:,:,:) = sa(:,:,:)
	1275	ENDIF
	1276
	1277	! add non-local temperature and salinity flux ( in convective case only)
	1278	DO jk = 1, jpkm1
	1279	DO jj = 2, jpjm1
	1280	DO ji = fs_2, fs_jpim1
	1281	ta(ji,jj,jk) = ta(ji,jj,jk) &
	1282	& - ( ghats(ji,jj,jk ) * avt(ji,jj,jk ) &
	1283	& - ghats(ji,jj,jk+1) * avt(ji,jj,jk+1) ) * wt0(ji,jj) / fse3t(ji,jj,jk)
	1284	sa(ji,jj,jk) = sa(ji,jj,jk) &
	1285	& - ( ghats(ji,jj,jk ) * fsavs(ji,jj,jk ) &
	1286	& - ghats(ji,jj,jk+1) * fsavs(ji,jj,jk+1) ) * ws0(ji,jj) / fse3t(ji,jj,jk)
	1287	END DO
	1288	END DO
	1289	END DO
	1290
	1291	! save the non-local tracer flux trends for diagnostic
	1292	IF( l_trdtra ) THEN
	1293	ztrdt(:,:,:) = ta(:,:,:) - ztrdt(:,:,:)
	1294	ztrds(:,:,:) = sa(:,:,:) - ztrds(:,:,:)
	1295	!!bug gm jpttdzdf ==> jpttkpp
[503]	1296	CALL trd_mod(ztrdt, ztrds, jptra_trd_zdf, 'TRA', kt)
[463]	1297	ENDIF
	1298
[896]	1299	IF(ln_ctl) THEN
	1300	CALL prt_ctl( tab3d_1=ta, clinfo1=' kpp - Ta: ', mask1=tmask, &
	1301	& tab3d_2=sa, clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' )
[463]	1302	ENDIF
	1303
	1304	END SUBROUTINE tra_kpp
	1305
	1306
[255]	1307	SUBROUTINE zdf_kpp_init
	1308	!!----------------------------------------------------------------------
	1309	!! * ROUTINE zdf_kpp_init *
	1310	!!
	1311	!! ** Purpose : Initialization of the vertical eddy diffivity and
	1312	!! viscosity when using a kpp turbulent closure scheme
	1313	!!
	1314	!! ** Method : Read the namkpp namelist and check the parameters
	1315	!! called at the first timestep (nit000)
	1316	!!
	1317	!! ** input : Namlist namkpp
	1318	!!
	1319	!!
	1320	!! history :
	1321	!! 8.1 ! 00-02 (J. Chanut) KPP Mixing
	1322	!! 9.0 ! 05-01 (C. Ethe) F90 : free form
	1323	!!----------------------------------------------------------------------
	1324	!! * local declarations
	1325
	1326	INTEGER :: &
	1327	ji, jj, jk ! dummy loop indices
	1328
	1329	#if ! defined key_kppcustom
	1330	INTEGER :: &
	1331	jm ! dummy loop indices
	1332	REAL(wp) :: & !!! tempory scalars
	1333	zref, zdist
	1334	#endif
	1335
	1336	#if defined key_kpplktb
	1337	REAL(wp) :: & !!! tempory scalars
	1338	zustar, &
	1339	zucube, zustvk, &
	1340	zeta, zehat
	1341	#endif
	1342	REAL(wp) :: & !!! tempory scalars
	1343	zhbf
	1344	LOGICAL :: &
	1345	ll_kppcustom, & ! 1st ocean level taken as surface layer
	1346	ll_kpplktb ! Lookup table for turbul. velocity scales
	1347
	1348	NAMELIST/namkpp/ ln_kpprimix, difmiw, difsiw, Riinfty, difri, bvsqcon, difcon, nave, navb
	1349
	1350	!!----------------------------------------------------------------------
	1351
	1352	! Read Namelist namtke : Turbulente Kinetic Energy
	1353	! --------------------
	1354	REWIND ( numnam )
	1355	READ ( numnam, namkpp )
	1356
	1357	! Parameter control and print
	1358	! ---------------------------
	1359	REWIND( numnam )
	1360	READ ( numnam, namkpp )
	1361
	1362	! Control print
	1363	IF(lwp) THEN
	1364	WRITE(numout,*)
	1365	WRITE(numout,*) 'zdf_kpp_init : kpp turbulent closure scheme'
	1366	WRITE(numout,*) '~~~~~~~~~~~~'
	1367	WRITE(numout,*) ' Namelist namkpp : set tke mixing parameters'
	1368	WRITE(numout,*) ' Shear instability mixing ln_kpprimix = ', ln_kpprimix
	1369	WRITE(numout,*) ' max. internal wave viscosity difmiw = ', difmiw
	1370	WRITE(numout,*) ' max. internal wave diffusivity difsiw = ', difsiw
	1371	WRITE(numout,*) ' Richardson Number limit for shear instability Riinfty = ', Riinfty
	1372	WRITE(numout,*) ' max. shear mixing at Rig = 0 difri = ', difri
	1373	WRITE(numout,*) ' Brunt-Vaisala squared for max. convection bvsqcon = ', bvsqcon
	1374	WRITE(numout,*) ' max. mix. in interior convec. difcon = ', difcon
	1375	WRITE(numout,*) ' horizontal average flag nave = ', nave
	1376	WRITE(numout,*) ' constant background or profile navb = ', navb
	1377	ENDIF
	1378
	1379	ll_kppcustom = .FALSE.
	1380	ll_kpplktb = .FALSE.
	1381
	1382	#if defined key_kppcustom
	1383	ll_kppcustom = .TRUE.
	1384	#endif
	1385	#if defined key_kpplktb
	1386	ll_kpplktb = .TRUE.
	1387	#endif
	1388	IF(lwp) THEN
	1389	WRITE(numout,*) ' Lookup table for turbul. velocity scales ll_kpplktb = ', ll_kpplktb
	1390	WRITE(numout,*) ' 1st ocean level taken as surface layer ll_kppcustom = ', ll_kppcustom
	1391	WRITE(numout,*) ' '
	1392	ENDIF
	1393
	1394	IF( lk_zdfddm) THEN
	1395	IF(lwp) THEN
	1396	WRITE(numout,*)
	1397	WRITE(numout,*) ' Double diffusion mixing on temperature and salinity '
	1398	WRITE(numout,*) ' CAUTION : done in routine zdfkpp, not in routine zdfddm '
	1399	WRITE(numout,*) ' '
	1400	ENDIF
	1401	ENDIF
	1402
	1403
	1404
	1405	!set constants not in namelist
	1406	!-----------------------------
	1407	Vtc = rconcv * SQRT( 0.2 / ( rconcs * epsilon ) ) / ( vonk * vonk * Ricr )
	1408	rcg = rcstar * vonk * ( rconcs * vonk * epsilon )**pthird
	1409
	1410	IF(lwp) THEN
	1411	WRITE(numout,*) ' Constant value for unreso. turbul. velocity shear Vtc = ', Vtc
	1412	WRITE(numout,*) ' Non-dimensional coef. for nonlocal transport rcg = ', rcg
	1413	WRITE(numout,*) ' '
	1414	ENDIF
	1415
	1416	! ratt is the attenuation coefficient for solar flux
	1417	! Should be different is s_coordinate
	1418	DO jk = 1, jpk
	1419	zhbf = - fsdept(1,1,jk) * hbf
	1420	ratt(jk) = 1.0 - ( rabs * EXP( zhbf / xsi1 ) + ( 1.0 - rabs ) * EXP( zhbf / xsi2 ) )
	1421	ENDDO
	1422
	1423	! Horizontal average : initialization of weighting arrays
	1424	! -------------------
	1425
	1426	SELECT CASE ( nave )
	1427
	1428	CASE ( 0 ) ! no horizontal average
	1429	IF(lwp) WRITE(numout,*) ' no horizontal average on avt, avmu, avmv'
	1430	IF(lwp) WRITE(numout,*) ' only in very high horizontal resolution !'
	1431	! weighting mean arrays etmean, eumean and evmean
	1432	! ( 1 1 ) ( 1 )
	1433	! avt = 1/4 ( 1 1 ) avmu = 1/2 ( 1 1 ) avmv= 1/2 ( 1 )
	1434	!
	1435	etmean(:,:,:) = 0.e0
	1436	eumean(:,:,:) = 0.e0
	1437	evmean(:,:,:) = 0.e0
	1438
	1439	DO jk = 1, jpkm1
	1440	DO jj = 2, jpjm1
	1441	DO ji = 2, jpim1 ! vector opt.
	1442	etmean(ji,jj,jk) = tmask(ji,jj,jk) &
	1443	& / MAX( 1., umask(ji-1,jj ,jk) + umask(ji,jj,jk) &
	1444	& + vmask(ji ,jj-1,jk) + vmask(ji,jj,jk) )
	1445
	1446	eumean(ji,jj,jk) = umask(ji,jj,jk) &
	1447	& / MAX( 1., tmask(ji,jj,jk) + tmask(ji+1,jj ,jk) )
	1448
	1449	evmean(ji,jj,jk) = vmask(ji,jj,jk) &
	1450	& / MAX( 1., tmask(ji,jj,jk) + tmask(ji ,jj+1,jk) )
	1451	END DO
	1452	END DO
	1453	END DO
	1454
	1455	CASE ( 1 ) ! horizontal average
	1456	IF(lwp) WRITE(numout,*) ' horizontal average on avt, avmu, avmv'
	1457	! weighting mean arrays etmean, eumean and evmean
	1458	! ( 1/2 1 1/2 ) ( 1/2 1/2 ) ( 1/2 1 1/2 )
	1459	! avt = 1/8 ( 1 2 1 ) avmu = 1/4 ( 1 1 ) avmv= 1/4 ( 1/2 1 1/2 )
	1460	! ( 1/2 1 1/2 ) ( 1/2 1/2 )
	1461	etmean(:,:,:) = 0.e0
	1462	eumean(:,:,:) = 0.e0
	1463	evmean(:,:,:) = 0.e0
	1464
	1465	DO jk = 1, jpkm1
	1466	DO jj = 2, jpjm1
	1467	DO ji = fs_2, fs_jpim1 ! vector opt.
	1468	etmean(ji,jj,jk) = tmask(ji, jj,jk) &
	1469	& / MAX( 1., 2.* tmask(ji,jj,jk) &
	1470	& +.5 * ( tmask(ji-1,jj+1,jk) + tmask(ji-1,jj-1,jk) &
	1471	& +tmask(ji+1,jj+1,jk) + tmask(ji+1,jj-1,jk) ) &
	1472	& +1. * ( tmask(ji-1,jj ,jk) + tmask(ji ,jj+1,jk) &
	1473	& +tmask(ji ,jj-1,jk) + tmask(ji+1,jj ,jk) ) )
	1474
	1475	eumean(ji,jj,jk) = umask(ji,jj,jk) &
	1476	& / MAX( 1., tmask(ji,jj ,jk) + tmask(ji+1,jj ,jk) &
	1477	& +.5 * ( tmask(ji,jj-1,jk) + tmask(ji+1,jj-1,jk) &
	1478	& +tmask(ji,jj+1,jk) + tmask(ji+1,jj+1,jk) ) )
	1479
	1480	evmean(ji,jj,jk) = vmask(ji,jj,jk) &
	1481	& / MAX( 1., tmask(ji ,jj,jk) + tmask(ji ,jj+1,jk) &
	1482	& +.5 * ( tmask(ji-1,jj,jk) + tmask(ji-1,jj+1,jk) &
	1483	& +tmask(ji+1,jj,jk) + tmask(ji+1,jj+1,jk) ) )
	1484	END DO
	1485	END DO
	1486	END DO
	1487
	1488	CASE DEFAULT
[474]	1489	WRITE(ctmp1,*) ' bad flag value for nave = ', nave
[896]	1490	CALL ctl_stop( ctmp1 )
[255]	1491
	1492	END SELECT
	1493
	1494
	1495
	1496	! Background eddy viscosity and diffusivity profil
	1497	! ------------------------------------------------
	1498	IF( navb == 0 ) THEN
	1499	! Define avmb, avtb from namelist parameter
	1500	avmb(:) = avm0
	1501	avtb(:) = avt0
	1502	ELSE
	1503	! Background profile of avt (fit a theoretical/observational profile (Krauss 1990)
	1504	avmb(:) = avm0
[896]	1505	avtb(:) = 1.e-5 + 2.8e-8 * gdepw_0(:) ! m2/s
[255]	1506	ENDIF
	1507
	1508	! Increase the background in the surface layers
	1509	!! avmb(1) = 1. * avmb(1) ; avtb(1) = 1. * avtb(1)
	1510	!! avmb(2) = 1. * avmb(2) ; avtb(2) = 1. * avtb(2)
	1511	!! avmb(3) = 1. * avmb(3) ; avtb(3) = 1. * avtb(3)
	1512	!! avmb(4) = 1. * avmb(4) ; avtb(4) = 1. * avtb(4)
	1513
	1514
	1515	! Initialization of vertical eddy coef. to the background value
	1516	! -------------------------------------------------------------
	1517	DO jk = 1, jpk
	1518	avt (:,:,jk) = avtb(jk) * tmask(:,:,jk)
	1519	avmu(:,:,jk) = avmb(jk) * umask(:,:,jk)
	1520	avmv(:,:,jk) = avmb(jk) * vmask(:,:,jk)
	1521	END DO
	1522
	1523	! zero the surface flux for non local term and kpp mixed layer depth
	1524	! ------------------------------------------------------------------
	1525	ghats(:,:,:) = 0.
	1526	wt0 (:,: ) = 0.
	1527	ws0 (:,: ) = 0.
	1528	hkpp (:,: ) = 0. ! just a diagnostic (not essential)
	1529
	1530	#if ! defined key_kppcustom
	1531	! compute arrays (del, wz) for reference mean values
	1532	! (increase speed for vectorization key_kppcustom not defined)
	1533	del(1:jpk, 1:jpk) = 0.
	1534	DO jk = 1, jpk
	1535	zref = epsilon * fsdept(1,1,jk)
	1536	DO jm = 1 , jpk
	1537	zdist = zref - fsdepw(1,1,jm)
	1538	IF( zdist > 0. ) THEN
	1539	del(jk,jm) = MIN( zdist, fse3t(1,1,jm) ) / zref
	1540	ELSE
	1541	del(jk,jm) = 0.
	1542	ENDIF
	1543	ENDDO
	1544	ENDDO
	1545	#endif
	1546
	1547	#if defined key_kpplktb
	1548	! build lookup table for turbulent velocity scales
	1549	dezehat = ( dehatmax - dehatmin ) / nilktbm1
	1550	deustar = ( ustmax - ustmin ) / njlktbm1
	1551
	1552	DO jj = 1, njlktb
	1553	zustar = ( jj - 1) * deustar + ustmin
	1554	zustvk = vonk * zustar
	1555	zucube = zustar * zustar * zustar
	1556	DO ji = 1 , nilktb
	1557	zehat = ( ji - 1 ) * dezehat + dehatmin
	1558	zeta = zehat / ( zucube + epsln )
	1559	IF( zehat >= 0 ) THEN ! Stable case
	1560	wmlktb(ji,jj) = zustvk / ABS( 1.0 + rconc1 * zeta + epsln )
	1561	wslktb(ji,jj) = wmlktb(ji,jj)
	1562	ELSE ! Unstable case
	1563	IF( zeta > rzetam ) THEN
	1564	wmlktb(ji,jj) = zustvk * ABS( 1.0 - rconc2 * zeta )**pfourth
	1565	ELSE
	1566	wmlktb(ji,jj) = zustvk * ABS( rconam - rconcm * zeta )**pthird
	1567	ENDIF
	1568
	1569	IF( zeta > rzetas ) THEN
	1570	wslktb(ji,jj) = zustvk * SQRT( ABS( 1.0 - rconc2 * zeta ) )
	1571	ELSE
	1572	wslktb(ji,jj) = zustvk * ABS( rconas - rconcs * zeta )**pthird
	1573	ENDIF
	1574	ENDIF
	1575	END DO
	1576	END DO
	1577	#endif
	1578	END SUBROUTINE zdf_kpp_init
	1579
	1580	#else
	1581	!!----------------------------------------------------------------------
	1582	!! Dummy module : NO KPP scheme
	1583	!!----------------------------------------------------------------------
	1584	LOGICAL, PUBLIC, PARAMETER :: lk_zdfkpp = .FALSE. !: KPP flag
	1585	CONTAINS
	1586	SUBROUTINE zdf_kpp( kt ) ! Empty routine
	1587	WRITE(,) 'zdf_kpp: You should not have seen this print! error?', kt
	1588	END SUBROUTINE zdf_kpp
[463]	1589	SUBROUTINE tra_kpp( kt ) ! Empty routine
	1590	WRITE(,) 'tra_kpp: You should not have seen this print! error?', kt
	1591	END SUBROUTINE tra_kpp
[255]	1592	#endif
	1593
	1594	!!======================================================================
	1595	END MODULE zdfkpp

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