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zdfkpp.F90 @ 2000

Last change on this file since 2000 was 2000, checked in by acc, 14 years ago
ticket #684 step 7: Add in changes between the head of the DEV_r1821_Rivers branch and the trunk@1821. Note untested changes were made to the Rivers branch before this merge see wiki ticket page for details
Property svn:eol-style set to `native` Property svn:keywords set to `Id`
File size: 73.2 KB

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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
[1537]	38	LOGICAL , PUBLIC, PARAMETER :: lk_zdfkpp = .TRUE. !: KPP vertical mixing flag
	39
[1601]	40	REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: ghats !: non-local scalar mixing term (gamma/<ws>o)
	41	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: wt0 !: surface temperature flux for non local flux
	42	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: ws0 !: surface salinity flux for non local flux
	43	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: hkpp !: boundary layer depht
[503]	44
[1601]	45	! !!* Namelist namzdf_kpp *
[1537]	46	REAL(wp) :: rn_difmiw = 1.2e-04_wp ! constant internal wave viscosity (m2/s)
	47	REAL(wp) :: rn_difsiw = 1.2e-05_wp ! constant internal wave diffusivity (m2/s)
	48	REAL(wp) :: rn_riinfty = 0.8_wp ! local Richardson Number limit for shear instability
	49	REAL(wp) :: rn_difri = 5.e-03_wp ! maximum shear mixing at Rig = 0 (m2/s)
	50	REAL(wp) :: rn_bvsqcon = -1.e-09_wp ! Brunt-Vaisala squared (1/s**2) for maximum convection
	51	REAL(wp) :: rn_difcon = 1._wp ! maximum mixing in interior convection (m2/s)
	52	INTEGER :: nn_ave = 1 ! = 0/1 flag for horizontal average on avt, avmu, avmv
[255]	53
	54	#if defined key_zdfddm
	55	REAL(wp) :: & !!! ** Double diffusion Mixing
	56	difssf = 1.e-03_wp , & ! maximum salt fingering mixing
	57	Rrho0 = 1.9_wp , & ! limit for salt fingering mixing
	58	difsdc = 1.5e-06_wp ! maximum diffusive convection mixing
	59	#endif
[1601]	60	LOGICAL :: ln_kpprimix = .TRUE. ! Shear instability mixing
[255]	61
	62	REAL(wp) :: & !!! General constants
	63	epsln = 1.0e-20_wp , & ! a small positive number
	64	pthird = 1._wp/3._wp , & ! 1/3
	65	pfourth = 1._wp/4._wp ! 1/4
	66
	67	REAL(wp) :: & !!! Boundary Layer Turbulence Parameters
	68	vonk = 0.4_wp , & ! von Karman's constant
	69	epsilon = 0.1_wp , & ! nondimensional extent of the surface layer
	70	rconc1 = 5.0_wp , & ! standard flux profile function parmaeters
	71	rconc2 = 16.0_wp , & ! " "
	72	rconcm = 8.38_wp , & ! momentum flux profile fit
	73	rconam = 1.26_wp , & ! " "
	74	rzetam = -.20_wp , & ! " "
	75	rconcs = 98.96_wp , & ! scalar flux profile fit
	76	rconas = -28.86_wp , & ! " "
	77	rzetas = -1.0_wp ! " "
	78	REAL(wp) :: & !!! Boundary Layer Depth Diagnostic
	79	Ricr = 0.3_wp , & ! critical bulk Richardson Number
	80	rcekman = 0.7_wp , & ! coefficient for ekman depth
	81	rcmonob = 1.0_wp , & ! coefficient for Monin-Obukhov depth
	82	rconcv = 1.7_wp , & ! ratio of interior buoyancy frequency to buoyancy frequency at entrainment depth
	83	hbf = 1.0_wp , & ! fraction of bound. layer depth to which absorbed solar
	84	! ! rad. and contributes to surf. buo. forcing
	85	Vtc ! function of rconcv,rconcs,epsilon,vonk,Ricr
	86	REAL(wp) :: & !!! Nonlocal Boundary Layer Mixing
	87	rcstar = 5.0_wp , & ! coefficient for convective nonlocal transport
	88	rcs = 1.0e-3_wp , & ! conversion: mm/s ==> m/s
	89	rcg ! non-dimensional coefficient for nonlocal transport
	90
	91	#if ! defined key_kppcustom
[1601]	92	REAL(wp), DIMENSION(jpk,jpk) :: del ! array for reference mean values of vertical integration
[255]	93	#endif
	94
	95	#if defined key_kpplktb
	96	INTEGER, PARAMETER :: & !!! Parameters for lookup table for turbulent velocity scales
	97	nilktb = 892 , & ! number of values for zehat in KPP lookup table
	98	njlktb = 482 , & ! number of values for ustar in KPP lookup table
	99	nilktbm1 = nilktb - 1 , & !
	100	njlktbm1 = njlktb - 1 !
	101
[1601]	102	REAL(wp), DIMENSION(nilktb,njlktb) :: wmlktb ! lookup table for the turbulent vertical velocity scale for momentum
	103	REAL(wp), DIMENSION(nilktb,njlktb) :: wslktb ! lookup table for the turbulent vertical velocity scale for tracers
[255]	104
	105	REAL(wp) :: &
	106	dehatmin = -4.e-7_wp , & ! minimum limit for zhat in lookup table (m3/s3)
	107	dehatmax = 0._wp , & ! maximum limit for zhat in lookup table (m3/s3)
	108	ustmin = 0._wp , & ! minimum limit for ustar in lookup table (m/s)
	109	ustmax = 0.04_wp , & ! maximum limit for ustar in lookup table (m/s)
	110	dezehat , & ! delta zhat in lookup table
	111	deustar ! delta ustar in lookup table
	112	#endif
[1601]	113	REAL(wp), DIMENSION(jpk) :: ratt ! attenuation coef (already defines in module traqsr,
	114	! ! but only if the solar radiation penetration is considered)
[255]	115	REAL(wp) :: & !!! * penetrative solar radiation coefficient *
	116	rabs = 0.58_wp , & ! fraction associated with xsi1
	117	xsi1 = 0.35_wp , & ! first depth of extinction
	118	xsi2 = 23.0_wp ! second depth of extinction
	119	! ! (default values: water type Ib)
	120
	121	REAL(wp), DIMENSION(jpi,jpj,jpk) :: &
	122	etmean , & ! coefficient used for horizontal smoothing
	123	eumean , & ! at t-, u- and v-points
	124	evmean
	125
[899]	126	#if defined key_c1d
[255]	127	REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: &
	128	rig , & ! gradient Richardson number
	129	rib , & ! bulk Richardson number
	130	buof , & ! buoyancy forcing
	131	mols ! moning-Obukhov length scale
[1601]	132	REAL(wp), PUBLIC, DIMENSION(jpi,jpj) :: ekdp ! Ekman depth
[255]	133	#endif
	134
[1601]	135	INTEGER :: jip = 62 , jjp = 111
[255]	136
	137	!! * Substitutions
	138	# include "domzgr_substitute.h90"
	139	# include "vectopt_loop_substitute.h90"
[896]	140	# include "zdfddm_substitute.h90"
[255]	141	!!----------------------------------------------------------------------
[1601]	142	!! NEMO/OPA 3.2 , LOCEAN-IPSL (2009)
[888]	143	!! $Id$
[503]	144	!! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt)
[255]	145	!!----------------------------------------------------------------------
	146
	147	CONTAINS
	148
	149	SUBROUTINE zdf_kpp ( kt )
	150	!!----------------------------------------------------------------------
	151	!! * ROUTINE zdf_kpp *
	152	!!
	153	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	154	!! coefficients and non local mixing using K-profile parameterization
	155	!!
	156	!! ** Method : The boundary layer depth hkpp is diagnosed at tracer points
	157	!! from profiles of buoyancy, and shear, and the surface forcing.
	158	!! Above hbl (sigma=-z/hbl <1) the mixing coefficients are computed from
	159	!!
	160	!! Kx = hkpp Wx(sigma) G(sigma)
	161	!!
	162	!! and the non local term ghat = Cs / Ws(sigma) / hkpp
	163	!! Below hkpp the coefficients are the sum of mixing due to internal waves
	164	!! shear instability and double diffusion.
	165	!!
	166	!! -1- Compute the now interior vertical mixing coefficients at all depths.
	167	!! -2- Diagnose the boundary layer depth.
	168	!! -3- Compute the now boundary layer vertical mixing coefficients.
	169	!! -4- Compute the now vertical eddy vicosity and diffusivity.
	170	!! -5- Smoothing
	171	!!
	172	!! N.B. The computation is done from jk=2 to jpkm1
	173	!! Surface value of avt avmu avmv are set once a time to zero
	174	!! in routine zdf_kpp_init.
	175	!!
	176	!! ** Action : update the non-local terms ghats
	177	!! update avt, avmu, avmv (before vertical eddy coef.)
	178	!!
[503]	179	!! References : Large W.G., Mc Williams J.C. and Doney S.C.
[255]	180	!! Reviews of Geophysics, 32, 4, November 1994
	181	!! Comments in the code refer to this paper, particularly
	182	!! the equation number. (LMD94, here after)
	183	!!----------------------------------------------------------------------
	184	#if defined key_zdfddm
	185	USE oce , zviscos => ua, & ! temp. array for viscosities use ua as workspace
	186	& zdiffut => ta, & ! temp. array for diffusivities use sa as workspace
	187	& zdiffus => sa ! temp. array for diffusivities use sa as workspace
	188	#else
	189	USE oce , zviscos => ua, & ! temp. array for viscosities use ua as workspace
	190	& zdiffut => ta ! temp. array for diffusivities use sa as workspace
	191	#endif
[503]	192	!!
	193	INTEGER, INTENT( in ) :: kt ! ocean time step
	194	!!
	195	INTEGER :: ji, jj, jk ! dummy loop indices
	196	INTEGER :: ikbot, jkmax, jkm1, jkp2 !
[255]	197
	198	REAL(wp), DIMENSION(jpi,jpj) :: & !!! Surface buoyancy forcing, friction velocity
	199	zBo, zBosol, zustar !
	200	!
	201	REAL(wp) :: & !
[1695]	202	ztx, zty, zflageos, & !
[255]	203	zstabl, zbuofdep,zucube, & !
	204	zrhos, zalbet, zbeta, & !
	205	zthermal, zhalin, zatt1 !
	206
	207	REAL(wp) :: & !!! Bulk richardson number
	208	zref, zt, zs, zh, & !
	209	zu, zv, zrh, & !
	210	zrib, zrinum, & !
	211	zdVsq, zVtsq !
	212
	213	REAL(wp) :: & !!! Velocity scales
	214	zehat, zeta, zhrib, zsig, & !
	215	zscale, zwst, zws, zwm
	216
	217	#if defined key_kpplktb
	218	INTEGER :: & !!! Lookup table or Analytical functions
	219	il, jl !
	220	REAL(wp) :: & !
	221	ud, zfrac, ufrac, & !
	222	zwam, zwbm, zwas, zwbs !
	223	#else
	224	REAL(wp) :: & !
	225	zwsun, zwmun, &
	226	zcons, zconm, zwcons, zwconm !
	227	#endif
	228
	229	REAL(wp) :: & !!! In situ density
	230	zsr, zbw, ze, & !
	231	zb, zd, zc, zaw, za, & !
	232	zb1, za1, zkw, zk0, & !
	233	zcomp , zrhd, zrhdr,zbvzed !
	234
	235	#if ! defined key_kppcustom
	236	!! * local declarations
	237	INTEGER :: &
	238	jm ! dummy loop indices
	239	REAL(wp) :: & !!! Compression terms
	240	zr1, zr2, zr3, zr4, & !
	241	zrhop !
	242	#endif
	243
	244	REAL(wp) :: & !
	245	zflag, ztemp, zrn2, & !
	246	zdep21, zdep32, zdep43
	247
	248	REAL(wp) :: & !!! Interior richardson mixing
	249	zdku2, zdkv2, ze3sqr, & !
	250	zsh2, zri, zfri !
	251
	252	REAL(wp), DIMENSION(jpi,0:2) :: & !!! Moning-Obukov limitation
	253	zmoek
	254	REAL(wp), DIMENSION(jpi) :: &
	255	zmoa, zekman
	256	REAL(wp) :: &
	257	zmob, zek
	258
	259	REAL(wp), DIMENSION(jpi,4) :: & !!! The pipe
	260	zdepw, zdift, zvisc
	261	REAL(wp), DIMENSION(jpi,3) :: &
	262	zdept
	263	REAL(wp), DIMENSION(jpi,2) :: &
	264	zriblk
	265	REAL(wp), DIMENSION(jpi,jpk) :: & !
	266	zmask
	267	REAL(wp), DIMENSION(jpi) :: & !
	268	zhmax, zria, zhbl
	269	REAL(wp) :: & !
	270	zflagri, zflagek, & !
	271	zflagmo, zflagh, zflagkb !
	272	REAL(wp), DIMENSION(jpi) :: & !!! Shape function (G)
	273	za2m, za3m, zkmpm, &
	274	za2t, za3t, zkmpt
	275	REAL(wp) :: & !
	276	zdelta, zdelta2, & !
	277	zdzup, zdzdn, zdzh, & !
	278	zvath, zgat1, zdat1, & !
	279	zkm1m, zkm1t
	280	REAL(wp), DIMENSION(jpi,jpk) :: & !!! Boundary layer diffusivities/viscosities
	281	zblcm, zblct
	282	#if defined key_zdfddm
	283	REAL(wp) :: & !!! double diffusion mixing
	284	zrrau, zds, &
	285	zavdds, zavddt,zinr
	286	REAL(wp), DIMENSION(jpi,4) :: &
	287	zdifs
	288	REAL(wp), DIMENSION(jpi) :: &
	289	za2s, za3s, zkmps
	290	REAL(wp) :: &
	291	zkm1s
	292	REAL(wp), DIMENSION(jpi,jpk) :: &
	293	zblcs
	294	#endif
	295	!!--------------------------------------------------------------------
	296
	297
	298	! Initialization (first time-step only)
	299	! --------------
	300	IF( kt == nit000 ) CALL zdf_kpp_init
	301
	302	zviscos(:,:,:) = 0.
	303	zblcm (:,: ) = 0.
	304	zdiffut(:,:,:) = 0.
	305	zblct (:,: ) = 0.
	306	#if defined key_zdfddm
	307	zdiffus(:,:,:) = 0.
	308	zblcs (:,: ) = 0.
	309	#endif
	310	ghats(:,:,:) = 0.
	311
	312	zBo (:,:) = 0.
	313	zBosol(:,:) = 0.
	314	zustar(:,:) = 0.
	315
	316
	317	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	318	! I. Interior diffusivity and viscosity at w points ( T interfaces)
	319	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	320	DO jk = 2, jpkm1
	321	DO jj = 2, jpjm1
	322	DO ji = fs_2, fs_jpim1
	323	! Mixing due to internal waves breaking
	324	! -------------------------------------
[1537]	325	avmu(ji,jj,jk) = rn_difmiw
	326	avt (ji,jj,jk) = rn_difsiw
[255]	327	! Mixing due to vertical shear instability
	328	! -------------------------------------
	329	IF( ln_kpprimix ) THEN
	330	! Compute the gradient Richardson number at interfaces (zri):
	331	! LMD94, eq. 27 (is vertical smoothing needed : Rig=N^2 / (dz(u))^2 + (dz(v))^2
	332	zdku2 = ( un(ji - 1,jj,jk - 1) - un(ji - 1,jj,jk) ) &
	333	& * ( un(ji - 1,jj,jk - 1) - un(ji - 1,jj,jk) ) &
	334	& + ( un(ji ,jj,jk - 1) - un(ji ,jj,jk) ) &
	335	& * ( un(ji ,jj,jk - 1) - un(ji ,jj,jk) )
	336
	337	zdkv2 = ( vn(ji,jj - 1,jk - 1) - vn(ji,jj - 1,jk) ) &
	338	& * ( vn(ji,jj - 1,jk - 1) - vn(ji,jj - 1,jk) ) &
	339	& + ( vn(ji, jj,jk - 1) - vn(ji, jj,jk) ) &
	340	& * ( vn(ji, jj,jk - 1) - vn(ji, jj,jk) )
	341
	342	ze3sqr = 1. / ( fse3w(ji,jj,jk) * fse3w(ji,jj,jk) )
	343	! Square of vertical shear at interfaces
[1082]	344	zsh2 = 0.5 * ( zdku2 + zdkv2 ) * ze3sqr
[255]	345	zri = MAX( rn2(ji,jj,jk), 0. ) / ( zsh2 + epsln )
[899]	346	#if defined key_c1d
[255]	347	! save the gradient richardson number
	348	rig(ji,jj,jk) = zri * tmask(ji,jj,jk)
	349	#endif
	350	! Evaluate f of Ri (zri) for shear instability store in zfri
	351	! LMD94, eq. 28a,b,c, figure 3 ; Rem: p1 is 3, hard coded
	352	zfri = MAX( zri , 0. )
[1537]	353	zfri = MIN( zfri / rn_riinfty , 1.0 )
[255]	354	zfri = ( 1.0 - zfri * zfri )
	355	zfri = zfri * zfri * zfri
	356	! add shear contribution to mixing coef.
[1537]	357	avmu(ji,jj,jk) = avmu(ji,jj,jk) + rn_difri * zfri
	358	avt (ji,jj,jk) = avt (ji,jj,jk) + rn_difri * zfri
[255]	359	ENDIF
	360	#if defined key_zdfddm
	361	avs (ji,jj,jk) = avt (ji,jj,jk)
	362	! Double diffusion mixing ; NOT IN ROUTINE ZDFDDM.F90
	363	! ------------------------------------------------------------------
	364	! only retains positive value of rrau
	365	zrrau = MAX( rrau(ji,jj,jk), epsln )
	366	zds = sn(ji,jj,jk-1) - sn(ji,jj,jk)
	367	IF( zrrau > 1. .AND. zds > 0.) THEN
	368	!
	369	! Salt fingering case.
	370	!---------------------
	371	! Compute interior diffusivity for double diffusive mixing of
	372	! salinity. Upper bound "zrrau" by "Rrho0"; (Rrho0=1.9, difcoefnuf=0.001).
	373	! After that set interior diffusivity for double diffusive mixing
	374	! of temperature
	375	zavdds = MIN( zrrau, Rrho0 )
	376	zavdds = ( zavdds - 1.0 ) / ( Rrho0 - 1.0 )
	377	zavdds = 1.0 - zavdds * zavdds
	378	zavdds = zavdds * zavdds * zavdds
	379	zavdds = difssf * zavdds
	380	zavddt = 0.7 * zavdds
	381	ELSEIF( zrrau < 1. .AND. zrrau > 0. .AND. zds < 0.) THEN
	382	!
	383	! Diffusive convection case.
	384	!---------------------------
	385	! Compute interior diffusivity for double diffusive mixing of
	386	! temperature (Marmorino and Caldwell, 1976);
	387	! Compute interior diffusivity for double diffusive mixing of salinity
	388	zinr = 1. / zrrau
	389	zavddt = 0.909 * EXP( 4.6 * EXP( -0.54* ( zinr - 1. ) ) )
	390	zavddt = difsdc * zavddt
	391	IF( zrrau < 0.5) THEN
	392	zavdds = zavddt * 0.15 * zrrau
	393	ELSE
	394	zavdds = zavddt * (1.85 * zrrau - 0.85 )
	395	ENDIF
	396	ELSE
	397	zavddt = 0.
	398	zavdds = 0.
	399	ENDIF
	400	! Add double diffusion contribution to temperature and salinity mixing coefficients.
	401	avt (ji,jj,jk) = avt (ji,jj,jk) + zavddt
	402	avs (ji,jj,jk) = avs (ji,jj,jk) + zavdds
	403	#endif
	404	END DO
	405	END DO
	406	END DO
	407
	408
	409	! Radiative (zBosol) and non radiative (zBo) surface buoyancy
	410	!JMM at the time zdfkpp is called, q still holds the sum q + qsr
	411	!---------------------------------------------------------------------
	412	DO jj = 2, jpjm1
	413	DO ji = fs_2, fs_jpim1
[1601]	414	IF( nn_eos < 1) THEN
[255]	415	zt = tn(ji,jj,1)
	416	zs = sn(ji,jj,1) - 35.0
	417	zh = fsdept(ji,jj,1)
	418	! potential volumic mass
	419	zrhos = rhop(ji,jj,1)
	420	zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta
	421	& - 0.203814e-03 ) * zt &
	422	& + 0.170907e-01 ) * zt &
	423	& + 0.665157e-01 &
	424	& + ( - 0.678662e-05 * zs &
	425	& - 0.846960e-04 * zt + 0.378110e-02 ) * zs &
	426	& + ( ( - 0.302285e-13 * zh &
	427	& - 0.251520e-11 * zs &
	428	& + 0.512857e-12 * zt * zt ) * zh &
	429	& - 0.164759e-06 * zs &
	430	& +( 0.791325e-08 * zt - 0.933746e-06 ) * zt &
	431	& + 0.380374e-04 ) * zh
	432
	433	zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta
	434	& - 0.301985e-05 ) * zt &
	435	& + 0.785567e-03 &
	436	& + ( 0.515032e-08 * zs &
	437	& + 0.788212e-08 * zt - 0.356603e-06 ) * zs &
	438	& +( ( 0.121551e-17 * zh &
	439	& - 0.602281e-15 * zs &
	440	& - 0.175379e-14 * zt + 0.176621e-12 ) * zh &
	441	& + 0.408195e-10 * zs &
	442	& + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt &
	443	& - 0.121555e-07 ) * zh
	444
	445	zthermal = zbeta * zalbet / ( rcp * zrhos + epsln )
	446	zhalin = zbeta * sn(ji,jj,1) * rcs
	447	ELSE
	448	zrhos = rhop(ji,jj,1) + rau0 * ( 1. - tmask(ji,jj,1) )
[1601]	449	zthermal = rn_alpha / ( rcp * zrhos + epsln )
	450	zhalin = rn_beta * sn(ji,jj,1) * rcs
[255]	451	ENDIF
	452	! Radiative surface buoyancy force
	453	zBosol(ji,jj) = grav * zthermal * qsr(ji,jj)
	454	! Non radiative surface buoyancy force
[2000]	455	zBo (ji,jj) = grav * zthermal * qns(ji,jj) - grav * zhalin * ( emps(ji,jj)-rnf(ji,jj) )
[255]	456	! Surface Temperature flux for non-local term
[888]	457	wt0(ji,jj) = - ( qsr(ji,jj) + qns(ji,jj) )* ro0cpr * tmask(ji,jj,1)
[255]	458	! Surface salinity flux for non-local term
[2000]	459	ws0(ji,jj) = - ( ( emps(ji,jj)-rnf(ji,jj) ) * sn(ji,jj,1) * rcs ) * tmask(ji,jj,1)
[255]	460	ENDDO
	461	ENDDO
	462
[1601]	463	zflageos = 0.5 + SIGN( 0.5, nn_eos - 1. )
[255]	464	! Compute surface buoyancy forcing, Monin Obukhov and Ekman depths
	465	!------------------------------------------------------------------
	466	DO jj = 2, jpjm1
	467	DO ji = fs_2, fs_jpim1
	468	! Reference surface density = density at first T point level
	469	zrhos = rhop(ji,jj,1) + zflageos * rau0 * ( 1. - tmask(ji,jj,1) )
	470	! Friction velocity (zustar), at T-point : LMD94 eq. 2
[1695]	471	zustar(ji,jj) = SQRT( taum(ji,jj) / ( zrhos + epsln ) )
[255]	472	ENDDO
	473	ENDDO
	474
	475	!CDIR NOVERRCHK
	476	! ! ===============
	477	DO jj = 2, jpjm1 ! Vertical slab
	478	! ! ===============
	479
	480	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	481	! II Compute Boundary layer mixing coef. and diagnose the new boundary layer depth
	482	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	483
	484	! Initialization
	485	jkmax = 0
	486	zdept (:,:) = 0.
	487	zdepw (:,:) = 0.
	488	zriblk(:,:) = 0.
	489	zmoek (:,:) = 0.
	490	zvisc (:,:) = 0.
	491	zdift (:,:) = 0.
	492	#if defined key_zdfddm
	493	zdifs (:,:) = 0.
	494	#endif
	495	zmask (:,:) = 0.
	496	DO ji = fs_2, fs_jpim1
	497	zria(ji ) = 0.
	498	! Maximum boundary layer depth
	499	ikbot = mbathy(ji,jj) - 1 ! ikbot is the last T point in the water
	500	zhmax(ji) = fsdept(ji,jj,ikbot) - 0.001
	501	! Compute Monin obukhov length scale at the surface and Ekman depth:
	502	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * ratt(1)
	503	zekman(ji) = rcekman * zustar(ji,jj) / ( ABS( ff(ji,jj) ) + epsln )
	504	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	505	zmoa(ji) = zucube / ( vonk * ( zbuofdep + epsln ) )
[899]	506	#if defined key_c1d
[255]	507	! store the surface buoyancy forcing
	508	zstabl = 0.5 + SIGN( 0.5, zbuofdep )
	509	buof(ji,jj,1) = zbuofdep * tmask(ji,jj,1)
	510	! store the moning-oboukov length scale at surface
	511	zmob = zstabl * zmoa(ji) + ( 1.0 - zstabl ) * fsdept(ji,jj,1)
	512	mols(ji,jj,1) = MIN( zmob , zhmax(ji) ) * tmask(ji,jj,1)
	513	! store Ekman depth
	514	zek = zstabl * zekman(ji) + ( 1.0 - zstabl ) * fsdept(ji,jj,1)
	515	ekdp(ji,jj ) = MIN( zek , zhmax(ji) ) * tmask(ji,jj,1)
	516	#endif
	517	END DO
	518	! Compute the pipe
	519	! ---------------------
	520	DO jk = 2, jpkm1
	521	DO ji = fs_2, fs_jpim1
	522	! Compute bfsfc = Bo + radiative contribution down to hbf*depht
	523	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * ratt(jk)
	524	! Flag (zstabl = 1) if positive forcing
	525	zstabl = 0.5 + SIGN( 0.5, zbuofdep)
	526
	527	! Compute bulk richardson number zrib at depht
	528	!-------------------------------------------------------
	529	! [Br - B(d)] * d zrinum
	530	! Rib(z) = ----------------------- = -------------
	531	! \|Vr - V(d)\|^2 + Vt(d)^2 zdVsq + zVtsq
	532	!
	533	! First compute zt,zs,zu,zv = means in the surface layer < epsilon*depht
	534	! Else surface values are taken at the first T level.
	535	! For stability, resolved vertical shear is computed with "before velocities".
	536	zref = epsilon * fsdept(ji,jj,jk)
	537	#if defined key_kppcustom
	538	! zref = gdept(1)
	539	zref = fsdept(ji,jj,1)
	540	zt = tn(ji,jj,1)
	541	zs = sn(ji,jj,1)
	542	zrh = rhop(ji,jj,1)
	543	zu = ( ub(ji,jj,1) + ub(ji - 1,jj ,1) ) / MAX( 1. , umask(ji,jj,1) + umask(ji - 1,jj ,1) )
	544	zv = ( vb(ji,jj,1) + vb(ji ,jj - 1,1) ) / MAX( 1. , vmask(ji,jj,1) + vmask(ji ,jj - 1,1) )
	545	#else
	546	zt = 0.
	547	zs = 0.
	548	zu = 0.
	549	zv = 0.
	550	zrh = 0.
	551	! vertically integration over the upper epsilon*gdept(jk) ; del () array is computed once in zdf_kpp_init
	552	DO jm = 1, jpkm1
	553	zt = zt + del(jk,jm) * tn(ji,jj,jm)
	554	zs = zs + del(jk,jm) * sn(ji,jj,jm)
	555	zu = zu + 0.5 * del(jk,jm) &
	556	& * ( ub(ji,jj,jm) + ub(ji - 1,jj,jm) ) &
	557	& / MAX( 1. , umask(ji,jj,jm) + umask(ji - 1,jj,jm) )
	558	zv = zv + 0.5 * del(jk,jm) &
	559	& * ( vb(ji,jj,jm) + vb(ji,jj - 1,jm) ) &
	560	& / MAX( 1. , vmask(ji,jj,jm) + vmask(ji,jj - 1,jm) )
	561	zrh = zrh + del(jk,jm) * rhop(ji,jj,jm)
	562	END DO
	563	#endif
	564	zsr = SQRT( ABS( sn(ji,jj,jk) ) )
	565	! depth
	566	zh = fsdept(ji,jj,jk)
	567	! compute compression terms on density
	568	ze = ( -3.508914e-8zt-1.248266e-8 ) zt-2.595994e-6
	569	zbw = ( 1.296821e-6zt-5.782165e-9 ) zt+1.045941e-4
	570	zb = zbw + ze * zs
	571
	572	zd = -2.042967e-2
	573	zc = (-7.267926e-5zt+2.598241e-3 ) zt+0.1571896
	574	zaw = ( ( 5.939910e-6zt+2.512549e-3 ) zt-0.1028859 ) *zt - 4.721788
	575	za = ( zdzsr + zc ) zs + zaw
	576
	577	zb1 = (-0.1909078zt+7.390729 ) zt-55.87545
	578	za1 = ( ( 2.326469e-3zt+1.553190)zt-65.00517 ) *zt+1044.077
	579	zkw = ( ( (-1.361629e-4zt-1.852732e-2 ) zt-30.41638 ) zt + 2098.925 ) zt+190925.6
	580	zk0 = ( zb1zsr + za1 )zs + zkw
	581	zcomp = 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) )
	582
	583	#if defined key_kppcustom
	584	! potential density of water(zrh = zt,zs at level jk):
	585	zrhdr = zrh / zcomp
	586	#else
	587	! potential density of water(ztref,zsref at level jk):
	588	! compute volumic mass pure water at atm pressure
[1601]	589	IF ( nn_eos < 1 ) THEN
[255]	590	zr1= ( ( ( ( 6.536332e-9zt-1.120083e-6 )zt+1.001685e-4)*zt &
	591	& -9.095290e-3 )zt+6.793952e-2 )zt+999.842594
	592	! seawater volumic mass atm pressure
	593	zr2= ( ( ( 5.3875e-9zt-8.2467e-7 ) zt+7.6438e-5 ) *zt &
	594	& -4.0899e-3 ) *zt+0.824493
	595	zr3= ( -1.6546e-6zt+1.0227e-4 ) zt-5.72466e-3
	596	zr4= 4.8314e-4
	597	! potential volumic mass (reference to the surface)
	598	zrhop= ( zr4zs + zr3zsr + zr2 ) *zs + zr1
	599	zrhdr = zrhop / zcomp
	600	ELSE
	601	zrhdr = zrh / zcomp
	602	ENDIF
	603	#endif
	604
	605	! potential density of ambiant water at level jk :
	606	zrhd = ( rhd(ji,jj,jk) * rau0 + rau0 )
	607
	608	! And now the Rib number numerator .
	609	zrinum = grav * ( zrhd - zrhdr ) / rau0
	610	zrinum = zrinum * ( fsdept(ji,jj,jk) - zref ) * tmask(ji,jj,jk)
	611
	612	! Resolved shear contribution to Rib at depth T-point (zdVsq)
	613	ztx = ( ub( ji , jj ,jk) + ub(ji - 1, jj ,jk) ) &
	614	& / MAX( 1. , umask( ji , jj ,jk) + umask(ji - 1, jj ,jk) )
	615	zty = ( vb( ji , jj ,jk) + vb(ji ,jj - 1,jk) ) &
	616	& / MAX( 1., vmask( ji , jj ,jk) + vmask(ji ,jj - 1,jk) )
	617
	618	zdVsq = ( zu - ztx ) * ( zu - ztx ) + ( zv - zty ) * ( zv - zty )
	619
	620	! Scalar turbulent velocity scale zws for hbl=gdept
	621	zscale = zstabl + ( 1.0 - zstabl ) * epsilon
	622	zehat = vonk * zscale * fsdept(ji,jj,jk) * zbuofdep
	623	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	624	zeta = zehat / ( zucube + epsln )
	625
	626	IF( zehat > 0. ) THEN
	627	! Stable case
	628	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	629	ELSE
	630	! Unstable case
	631	#if defined key_kpplktb
	632	! use lookup table
	633	zd = zehat - dehatmin
	634	il = INT( zd / dezehat )
	635	il = MIN( il, nilktbm1 )
	636	il = MAX( il, 1 )
	637
	638	ud = zustar(ji,jj) - ustmin
	639	jl = INT( ud / deustar )
	640	jl = MIN( jl, njlktbm1 )
	641	jl = MAX( jl, 1 )
	642
	643	zfrac = zd / dezehat - FLOAT( il )
	644	ufrac = ud / deustar - FLOAT( jl )
	645	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	646	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	647	!
	648	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	649	#else
	650	! use analytical functions:
	651	zcons = 0.5 + SIGN( 0.5 , ( rzetas - zeta ) )
	652	zwcons = vonk * zustar(ji,jj) * ( ( ABS( rconas - rconcs * zeta ) )**pthird )
	653	zwsun = vonk * zustar(ji,jj) * SQRT( ABS ( 1.0 - rconc2 * zeta ) )
	654	!
	655	zws = zcons * zwcons + ( 1.0 - zcons) * zwsun
	656	#endif
	657	ENDIF
	658
	659	! Turbulent shear contribution to Rib (zVtsq) bv frequency at levels ( ie T-point jk)
	660	zrn2 = 0.5 * ( rn2(ji,jj,jk) + rn2(ji,jj,jk+1) )
	661	zbvzed = SQRT( ABS( zrn2 ) )
	662	zVtsq = fsdept(ji,jj,jk) * zws * zbvzed * Vtc
	663
	664	! Finally, the bulk Richardson number at depth fsdept(i,j,k)
	665	zrib = zrinum / ( zdVsq + zVtsq + epsln )
	666
	667	! Find subscripts around the boundary layer depth, build the pipe
	668	! ----------------------------------------------------------------
	669
	670	! Flag (zflagri = 1) if zrib < Ricr
	671	zflagri = 0.5 + SIGN( 0.5, ( Ricr - zrib ) )
	672	! Flag (zflagh = 1) if still within overall boundary layer
	673	zflagh = 0.5 + SIGN( 0.5, ( fsdept(ji,jj,1) - zdept(ji,2) ) )
	674
	675	! Ekman layer depth
	676	zek = zstabl * zekman(ji) + ( 1.0 - zstabl ) * zhmax(ji)
	677	zflag = 0.5 + SIGN( 0.5, ( zek - fsdept(ji,jj,jk-1) ) )
	678	zek = zflag * zek + ( 1.0 - zflag ) * zhmax(ji)
	679	zflagek = 0.5 + SIGN( 0.5, ( zek - fsdept(ji,jj,jk) ) )
	680	! Flag (zflagmo = 1) if still within stable Monin-Obukhov and in water
	681	zmob = zucube / ( vonk * ( zbuofdep + epsln ) )
	682	ztemp = zstabl * zmob + ( 1.0 - zstabl) * zhmax(ji)
	683	ztemp = MIN( ztemp , zhmax(ji) )
	684	zflagmo = 0.5 + SIGN( 0.5, ( ztemp - fsdept(ji,jj,jk) ) )
	685
	686	! No limitation by Monin Obukhov or Ekman depths:
	687	! zflagek = 1.0
	688	! zflagmo = 0.5 + SIGN( 0.5, ( zhmax(ji) - fsdept(ji,jj,jk) ) )
	689
	690	! Load pipe via zflagkb for later calculations
	691	! Flag (zflagkb = 1) if zflagh = 1 and (zflagri = 0 or zflagek = 0 or zflagmo = 0)
	692	zflagkb = zflagh * ( 1.0 - ( zflagri * zflagek * zflagmo ) )
	693
	694	zmask(ji,jk) = zflagh
	695	jkp2 = MIN( jk+2 , ikbot )
	696	jkm1 = MAX( jk-1 , 2 )
	697	jkmax = MAX( jkmax, jk * INT( REAL( zflagh+epsln ) ) )
	698
	699	zdept(ji,1) = zdept(ji,1) + zflagkb * fsdept(ji,jj,jk-1)
	700	zdept(ji,2) = zdept(ji,2) + zflagkb * fsdept(ji,jj,jk )
	701	zdept(ji,3) = zdept(ji,3) + zflagkb * fsdept(ji,jj,jk+1)
	702
	703	zdepw(ji,1) = zdepw(ji,1) + zflagkb * fsdepw(ji,jj,jk-1)
	704	zdepw(ji,2) = zdepw(ji,2) + zflagkb * fsdepw(ji,jj,jk )
	705	zdepw(ji,3) = zdepw(ji,3) + zflagkb * fsdepw(ji,jj,jk+1)
	706	zdepw(ji,4) = zdepw(ji,4) + zflagkb * fsdepw(ji,jj,jkp2)
	707
	708	zriblk(ji,1) = zriblk(ji,1) + zflagkb * zria(ji)
	709	zriblk(ji,2) = zriblk(ji,2) + zflagkb * zrib
	710
	711	zmoek (ji,0) = zmoek (ji,0) + zflagkb * zek
	712	zmoek (ji,1) = zmoek (ji,1) + zflagkb * zmoa(ji)
	713	zmoek (ji,2) = zmoek (ji,2) + zflagkb * ztemp
	714	! Save Monin Obukhov depth
	715	zmoa (ji) = zmob
	716
	717	zvisc(ji,1) = zvisc(ji,1) + zflagkb * avmu(ji,jj,jkm1)
	718	zvisc(ji,2) = zvisc(ji,2) + zflagkb * avmu(ji,jj,jk )
	719	zvisc(ji,3) = zvisc(ji,3) + zflagkb * avmu(ji,jj,jk+1)
	720	zvisc(ji,4) = zvisc(ji,4) + zflagkb * avmu(ji,jj,jkp2)
	721
	722	zdift(ji,1) = zdift(ji,1) + zflagkb * avt (ji,jj,jkm1)
	723	zdift(ji,2) = zdift(ji,2) + zflagkb * avt (ji,jj,jk )
	724	zdift(ji,3) = zdift(ji,3) + zflagkb * avt (ji,jj,jk+1)
	725	zdift(ji,4) = zdift(ji,4) + zflagkb * avt (ji,jj,jkp2)
	726
	727	#if defined key_zdfddm
	728	zdifs(ji,1) = zdifs(ji,1) + zflagkb * avs (ji,jj,jkm1)
	729	zdifs(ji,2) = zdifs(ji,2) + zflagkb * avs (ji,jj,jk )
	730	zdifs(ji,3) = zdifs(ji,3) + zflagkb * avs (ji,jj,jk+1)
	731	zdifs(ji,4) = zdifs(ji,4) + zflagkb * avs (ji,jj,jkp2)
	732	#endif
	733	! Save the Richardson number
	734	zria (ji) = zrib
[899]	735	#if defined key_c1d
[255]	736	! store buoyancy length scale
	737	buof(ji,jj,jk) = zbuofdep * tmask(ji,jj,jk)
	738	! store Monin Obukhov
	739	zmob = zstabl * zmob + ( 1.0 - zstabl) * fsdept(ji,jj,1)
	740	mols(ji,jj,jk) = MIN( zmob , zhmax(ji) ) * tmask(ji,jj,jk)
	741	! Bulk Richardson number
	742	rib(ji,jj,jk) = zrib * tmask(ji,jj,jk)
	743	#endif
	744	END DO
	745	END DO
	746	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	747	! III PROCESS THE PIPE
	748	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	749
	750	DO ji = fs_2, fs_jpim1
	751
	752	! Find the boundary layer depth zhbl
	753	! ----------------------------------------
	754
	755	! Interpolate monin Obukhov and critical Ri mumber depths
	756	ztemp = zdept(ji,2) - zdept(ji,1)
	757	zflag = ( Ricr - zriblk(ji,1) ) / ( zriblk(ji,2) - zriblk(ji,1) + epsln )
	758	zhrib = zdept(ji,1) + zflag * ztemp
	759
	760	IF( zriblk(ji,2) < Ricr ) zhrib = zhmax(ji)
	761
	762	IF( zmoek(ji,2) < zdept(ji,2) ) THEN
	763	IF ( zmoek(ji,1) < 0. ) THEN
	764	zmob = zdept(ji,2) - epsln
	765	ELSE
	766	zmob = ztemp + zmoek(ji,1) - zmoek(ji,2)
	767	zmob = ( zmoek(ji,1) * zdept(ji,2) - zmoek(ji,2) * zdept(ji,1) ) / zmob
	768	zmob = MAX( zmob , zdept(ji,1) + epsln )
	769	ENDIF
	770	ELSE
	771	zmob = zhmax(ji)
	772	ENDIF
	773	ztemp = MIN( zmob , zmoek(ji,0) )
	774
	775	! Finally, the boundary layer depth, zhbl
	776	zhbl(ji) = MAX( fsdept(ji,jj,1) + epsln, MIN( zhrib , ztemp ) )
	777
	778	! Save hkpp for further diagnostics (optional)
	779	hkpp(ji,jj) = zhbl(ji) * tmask(ji,jj,1)
	780
	781	! Correct mask if zhbl < fsdepw(ji,jj,2) for no viscosity/diffusivity enhancement at fsdepw(ji,jj,2)
	782	! zflag = 1 if zhbl(ji) > fsdepw(ji,jj,2)
	783	IF( zhbl(ji) < fsdepw(ji,jj,2) ) zmask(ji,2) = 0.
	784
	785
	786	! Velocity scales at depth zhbl
	787	! -----------------------------------
	788
	789	! Compute bouyancy forcing down to zhbl
	790	ztemp = -hbf * zhbl(ji)
	791	zatt1 = 1.0 - ( rabs * EXP( ztemp / xsi1 ) + ( 1.0 - rabs ) * EXP( ztemp / xsi2 ) )
	792	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * zatt1
	793	zstabl = 0.5 + SIGN( 0.5 , zbuofdep )
	794
	795	zbuofdep = zbuofdep + zstabl * epsln
	796
	797	zscale = zstabl + ( 1.0 - zstabl ) * epsilon
	798	zehat = vonk * zscale * zhbl(ji) * zbuofdep
	799	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	800	zeta = zehat / ( zucube + epsln )
	801
	802	IF( zehat > 0. ) THEN
	803	! Stable case
	804	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	805	zwm = zws
	806	ELSE
	807	! Unstable case
	808	#if defined key_kpplktb
	809	! use lookup table
	810	zd = zehat - dehatmin
	811	il = INT( zd / dezehat )
	812	il = MIN( il, nilktbm1 )
	813	il = MAX( il, 1 )
	814
	815	ud = zustar(ji,jj) - ustmin
	816	jl = INT( ud / deustar )
	817	jl = MIN( jl, njlktbm1 )
	818	jl = MAX( jl, 1 )
	819
	820	zfrac = zd / dezehat - FLOAT( il )
	821	ufrac = ud / deustar - FLOAT( jl )
	822	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	823	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	824	zwam = ( 1. - zfrac ) * wmlktb(il,jl+1) + zfrac * wmlktb(il+1,jl+1)
	825	zwbm = ( 1. - zfrac ) * wmlktb(il,jl ) + zfrac * wmlktb(il+1,jl )
	826	!
	827	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	828	zwm = ( 1. - ufrac ) * zwbm + ufrac * zwam
	829	#else
	830	! use analytical functions
	831	zconm = 0.5 + SIGN( 0.5, ( rzetam - zeta) )
	832	zcons = 0.5 + SIGN( 0.5, ( rzetas - zeta) )
	833
	834	! Momentum : zeta < rzetam (zconm = 1)
	835	! Scalars : zeta < rzetas (zcons = 1)
	836	zwconm = zustar(ji,jj) * vonk * ( ( ABS( rconam - rconcm * zeta) )**pthird )
	837	zwcons = zustar(ji,jj) * vonk * ( ( ABS( rconas - rconcs * zeta) )**pthird )
	838
	839	! Momentum : rzetam <= zeta < 0 (zconm = 0)
	840	! Scalars : rzetas <= zeta < 0 (zcons = 0)
	841	zwmun = SQRT( ABS( 1.0 - rconc2 * zeta ) )
	842	zwsun = vonk * zustar(ji,jj) * zwmun
	843	zwmun = vonk * zustar(ji,jj) * SQRT(zwmun)
	844	!
	845	zwm = zconm * zwconm + ( 1.0 - zconm ) * zwmun
	846	zws = zcons * zwcons + ( 1.0 - zcons ) * zwsun
	847
	848	#endif
	849	ENDIF
	850
	851
	852	! Viscosity, diffusivity values and derivatives at h
	853	! --------------------------------------------------------
	854
	855	! check between at which interfaces is located zhbl(ji)
	856	! ztemp = 1, zdepw(ji,2) < zhbl < zdepw(ji,3)
	857	! ztemp = 0, zdepw(ji,1) < zhbl < zdepw(ji,2)
	858	ztemp = 0.5 + SIGN( 0.5, ( zhbl(ji) - zdepw(ji,2) ) )
	859	zdep21 = zdepw(ji,2) - zdepw(ji,1) + epsln
	860	zdep32 = zdepw(ji,3) - zdepw(ji,2) + epsln
	861	zdep43 = zdepw(ji,4) - zdepw(ji,3) + epsln
	862
	863	! Compute R as in LMD94, eq D5b
	864	zdelta = ( zhbl(ji) - zdepw(ji,2) ) * ztemp / zdep32 &
	865	& + ( zhbl(ji) - zdepw(ji,1) ) * ( 1.0 - ztemp ) / zdep21
	866
	867	! Compute the vertical derivative of viscosities (zdzh) at z=zhbl(ji)
	868	zdzup = ( zvisc(ji,2) - zvisc(ji,3) ) * ztemp / zdep32 &
	869	& + ( zvisc(ji,1) - zvisc(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	870
	871	zdzdn = ( zvisc(ji,3) - zvisc(ji,4) ) * ztemp / zdep43 &
	872	& + ( zvisc(ji,2) - zvisc(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	873
	874	! LMD94, eq D5b :
	875	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	876	zdzh = MAX( zdzh , 0. )
	877
	878	! Compute viscosities (zvath) at z=zhbl(ji), LMD94 eq D5a
	879	zvath = ztemp * ( zvisc(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	880	& + ( 1.0 - ztemp ) * ( zvisc(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	881
	882	! Compute G (zgat1) and its derivative (zdat1) at z=hbl(ji), LMD94 eq 18
	883
	884	! Vertical derivative of velocity scale divided by velocity scale squared at z=hbl(ji)
	885	! (non zero only in stable conditions)
	886	zflag = -zstabl * rconc1 * zbuofdep / ( zucube * zustar(ji,jj) + epsln )
	887
	888	! G at its derivative at z=hbl:
	889	zgat1 = zvath / ( zhbl(ji) * ( zwm + epsln ) )
	890	zdat1 = -zdzh / ( zwm + epsln ) - zflag * zvath / zhbl(ji)
	891
	892	! G coefficients, LMD94 eq 17
	893	za2m(ji) = -2.0 + 3.0 * zgat1 - zdat1
	894	za3m(ji) = 1.0 - 2.0 * zgat1 + zdat1
	895
	896
	897	! Compute the vertical derivative of temperature diffusivities (zdzh) at z=zhbl(ji)
	898	zdzup = ( zdift(ji,2) - zdift(ji,3) ) * ztemp / zdep32 &
	899	& + ( zdift(ji,1) - zdift(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	900
	901	zdzdn = ( zdift(ji,3) - zdift(ji,4) ) * ztemp / zdep43 &
	902	& + ( zdift(ji,2) - zdift(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	903
	904	! LMD94, eq D5b :
	905	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	906	zdzh = MAX( zdzh , 0. )
	907
	908
	909	! Compute diffusivities (zvath) at z=zhbl(ji), LMD94 eq D5a
	910	zvath = ztemp * ( zdift(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	911	& + ( 1.0 - ztemp ) * ( zdift(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	912
	913	! G at its derivative at z=hbl:
	914	zgat1 = zvath / ( zhbl(ji) * ( zws + epsln ) )
	915	zdat1 = -zdzh / ( zws + epsln ) - zflag * zvath / zhbl(ji)
	916
	917	! G coefficients, LMD94 eq 17
	918	za2t(ji) = -2.0 + 3.0 * zgat1 - zdat1
	919	za3t(ji) = 1.0 - 2.0 * zgat1 + zdat1
	920
	921	#if defined key_zdfddm
	922	! Compute the vertical derivative of salinities diffusivities (zdzh) at z=zhbl(ji)
	923	zdzup = ( zdifs(ji,2) - zdifs(ji,3) ) * ztemp / zdep32 &
	924	& + ( zdifs(ji,1) - zdifs(ji,2) ) * ( 1.0 - ztemp ) / zdep21
	925
	926	zdzdn = ( zdifs(ji,3) - zdifs(ji,4) ) * ztemp / zdep43 &
	927	& + ( zdifs(ji,2) - zdifs(ji,3) ) * ( 1.0 - ztemp ) / zdep32
	928
	929	! LMD94, eq D5b :
	930	zdzh = ( 1.0 - zdelta ) * zdzup + zdelta * zdzdn
	931	zdzh = MAX( zdzh , 0. )
	932
	933	! Compute diffusivities (zvath) at z=zhbl(ji), LMD94 eq D5a
	934	zvath = ztemp * ( zdifs(ji,3) + zdzh * ( zdepw(ji,3) - zhbl(ji) ) ) &
	935	& + ( 1.0 - ztemp ) * ( zdifs(ji,2) + zdzh * ( zdepw(ji,2) - zhbl(ji) ) )
	936
	937	! G at its derivative at z=hbl:
	938	zgat1 = zvath / ( zhbl(ji) * ( zws + epsln ) )
	939	zdat1 = -zdzh / ( zws + epsln ) - zflag * zvath / zhbl(ji)
	940
	941	! G coefficients, LMD94 eq 17
	942	za2s(ji) = -2.0 + 3.0 * zgat1 - zdat1
	943	za3s(ji) = 1.0 - 2.0 * zgat1 + zdat1
	944	#endif
	945
	946	!-------------------turn off interior matching here------
	947	! za2(ji,1) = -2.0
	948	! za3(ji,1) = 1.0
	949	! za2(ji,2) = -2.0
	950	! za3(ji,2) = 1.0
	951	!--------------------------------------------------------
	952
	953	! Compute Enhanced Mixing Coefficients (LMD94,eq D6)
	954	! ---------------------------------------------------------------
	955
	956	! Delta
	957	zdelta = ( zhbl(ji) - zdept(ji,1) ) / ( zdept(ji,2) - zdept(ji,1) + epsln )
	958	zdelta2 = zdelta * zdelta
	959
	960	! Mixing coefficients at first level above h (zdept(ji,1))
	961	! and at first interface in the pipe (zdepw(ji,2))
	962
	963	! At first T level above h (zdept(ji,1)) (always in the boundary layer)
	964	zsig = zdept(ji,1) / zhbl(ji)
	965	ztemp = zstabl * zsig + ( 1.0 - zstabl ) * MIN( zsig , epsilon )
	966	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	967	zeta = zehat / ( zucube + epsln)
	968	zwst = vonk * zustar(ji,jj) / ( ABS( 1.0 + rconc1 * zeta ) + epsln)
	969	zwm = zstabl * zwst + ( 1.0 - zstabl ) * zwm
	970	zws = zstabl * zwst + ( 1.0 - zstabl ) * zws
	971
	972	zkm1m = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	973	zkm1t = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	974	#if defined key_zdfddm
	975	zkm1s = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	976	#endif
	977	! At first W level in the pipe (zdepw(ji,2)) (not always in the boundary layer ):
	978	zsig = MIN( zdepw(ji,2) / zhbl(ji) , 1.0 )
	979	ztemp = zstabl * zsig + ( 1.0 - zstabl ) * MIN( zsig , epsilon )
	980	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	981	zeta = zehat / ( zucube + epsln )
	982	zwst = vonk * zustar(ji,jj) / ( ABS( 1.0 + rconc1 * zeta ) + epsln)
	983	zws = zstabl * zws + ( 1.0 - zstabl ) * zws
	984	zwm = zstabl * zws + ( 1.0 - zstabl ) * zwm
	985
	986	zkmpm(ji) = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	987	zkmpt(ji) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	988	#if defined key_zdfddm
	989	zkmps(ji) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	990	#endif
	991
	992	! check if this point is in the boundary layer,else take interior viscosity/diffusivity:
	993	zflag = 0.5 + SIGN( 0.5, ( zhbl(ji) - zdepw(ji,2) ) )
	994	zkmpm(ji) = zkmpm(ji) * zflag + ( 1.0 - zflag ) * zvisc(ji,2)
	995	zkmpt(ji) = zkmpt(ji) * zflag + ( 1.0 - zflag ) * zdift(ji,2)
	996	#if defined key_zdfddm
	997	zkmps(ji) = zkmps(ji) * zflag + ( 1.0 - zflag ) * zdifs(ji,2)
	998	#endif
	999
	1000	! Enhanced viscosity/diffusivity at zdepw(ji,2)
	1001	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1m + zdelta2 * zkmpm(ji)
	1002	zkmpm(ji) = ( 1.0 - zdelta ) * zvisc(ji,2) + zdelta * ztemp
	1003	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1t + zdelta2 * zkmpt(ji)
	1004	zkmpt(ji) = ( 1.0 - zdelta ) * zdift(ji,2) + zdelta * ztemp
	1005	#if defined key_zdfddm
	1006	ztemp = ( 1.0 - 2.0 * zdelta + zdelta2 ) * zkm1s + zdelta2 * zkmps(ji)
	1007	zkmps(ji) = ( 1.0 - zdelta ) * zdifs(ji,2) + zdelta * ztemp
	1008	#endif
	1009
	1010	END DO
	1011	!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
	1012	! IV. Compute vertical eddy viscosity and diffusivity coefficients
	1013	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	1014
	1015	DO jk = 2, jkmax
	1016
	1017	! Compute turbulent velocity scales on the interfaces
	1018	! --------------------------------------------------------
	1019	DO ji = fs_2, fs_jpim1
	1020	zbuofdep = zBo(ji,jj) + zBosol(ji,jj) * zatt1
	1021	zstabl = 0.5 + SIGN( 0.5 , zbuofdep )
	1022	zbuofdep = zbuofdep + zstabl * epsln
	1023	zsig = fsdepw(ji,jj,jk) / zhbl(ji)
	1024	ztemp = zstabl * zsig + ( 1. - zstabl ) * MIN( zsig , epsilon )
	1025	zehat = vonk * ztemp * zhbl(ji) * zbuofdep
	1026	zucube = zustar(ji,jj) * zustar(ji,jj) * zustar(ji,jj)
	1027	zeta = zehat / ( zucube + epsln )
	1028
	1029	IF( zehat > 0. ) THEN
	1030	! Stable case
	1031	zws = vonk * zustar(ji,jj) / ( 1.0 + rconc1 * zeta )
	1032	zwm = zws
	1033	ELSE
	1034	! Unstable case
	1035	#if defined key_kpplktb
	1036	! use lookup table
	1037	zd = zehat - dehatmin
	1038	il = INT( zd / dezehat )
	1039	il = MIN( il, nilktbm1 )
	1040	il = MAX( il, 1 )
	1041
	1042	ud = zustar(ji,jj) - ustmin
	1043	jl = INT( ud / deustar )
	1044	jl = MIN( jl, njlktbm1 )
	1045	jl = MAX( jl, 1 )
	1046
	1047	zfrac = zd / dezehat - FLOAT( il )
	1048	ufrac = ud / deustar - FLOAT( jl )
	1049	zwas = ( 1. - zfrac ) * wslktb(il,jl+1) + zfrac * wslktb(il+1,jl+1)
	1050	zwbs = ( 1. - zfrac ) * wslktb(il,jl ) + zfrac * wslktb(il+1,jl )
	1051	zwam = ( 1. - zfrac ) * wmlktb(il,jl+1) + zfrac * wmlktb(il+1,jl+1)
	1052	zwbm = ( 1. - zfrac ) * wmlktb(il,jl ) + zfrac * wmlktb(il+1,jl )
	1053	!
	1054	zws = ( 1. - ufrac ) * zwbs + ufrac * zwas
	1055	zwm = ( 1. - ufrac ) * zwbm + ufrac * zwam
	1056	#else
	1057	! use analytical functions
	1058	zconm = 0.5 + SIGN( 0.5, ( rzetam - zeta) )
	1059	zcons = 0.5 + SIGN( 0.5, ( rzetas - zeta) )
	1060
	1061	! Momentum : zeta < rzetam (zconm = 1)
	1062	! Scalars : zeta < rzetas (zcons = 1)
	1063	zwconm = zustar(ji,jj) * vonk * ( ( ABS( rconam - rconcm * zeta) )**pthird )
	1064	zwcons = zustar(ji,jj) * vonk * ( ( ABS( rconas - rconcs * zeta) )**pthird )
	1065
	1066	! Momentum : rzetam <= zeta < 0 (zconm = 0)
	1067	! Scalars : rzetas <= zeta < 0 (zcons = 0)
	1068	zwmun = SQRT( ABS( 1.0 - rconc2 * zeta ) )
	1069	zwsun = vonk * zustar(ji,jj) * zwmun
	1070	zwmun = vonk * zustar(ji,jj) * SQRT(zwmun)
	1071	!
	1072	zwm = zconm * zwconm + ( 1.0 - zconm ) * zwmun
	1073	zws = zcons * zwcons + ( 1.0 - zcons ) * zwsun
	1074
	1075	#endif
	1076	ENDIF
	1077
	1078	zblcm(ji,jk) = zhbl(ji) * zwm * zsig * ( 1.0 + zsig * ( za2m(ji) + zsig * za3m(ji) ) )
	1079	zblct(ji,jk) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2t(ji) + zsig * za3t(ji) ) )
	1080	#if defined key_zdfddm
	1081	zblcs(ji,jk) = zhbl(ji) * zws * zsig * ( 1.0 + zsig * ( za2s(ji) + zsig * za3s(ji) ) )
	1082	#endif
	1083	! Compute Nonlocal transport term = ghats * <ws>o
	1084	! ----------------------------------------------------
	1085	ghats(ji,jj,jk-1) = ( 1. - zstabl ) * rcg / ( zws * zhbl(ji) + epsln ) * tmask(ji,jj,jk)
	1086
	1087	END DO
	1088	END DO
	1089	! Combine interior and boundary layer coefficients and nonlocal term
	1090	! -----------------------------------------------------------------------
	1091	DO jk = 2, jpkm1
	1092	DO ji = fs_2, fs_jpim1
	1093	zflag = zmask(ji,jk) * zmask(ji,jk+1)
	1094	zviscos(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avmu (ji,jj,jk) & ! interior viscosities
	1095	& + zflag * zblcm(ji,jk ) & ! boundary layer viscosities
	1096	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmpm(ji ) ! viscosity enhancement at W_level near zhbl
	1097
	1098	zviscos(ji,jj,jk) = zviscos(ji,jj,jk) * tmask(ji,jj,jk)
	1099
	1100
	1101	zdiffut(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avt (ji,jj,jk) & ! interior diffusivities
	1102	& + zflag * zblct(ji,jk ) & ! boundary layer diffusivities
	1103	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmpt(ji ) ! diffusivity enhancement at W_level near zhbl
	1104
	1105	zdiffut(ji,jj,jk) = zdiffut(ji,jj,jk) * tmask(ji,jj,jk)
	1106	#if defined key_zdfddm
	1107	zdiffus(ji,jj,jk) = ( 1.0 - zmask(ji,jk) ) * avs (ji,jj,jk) & ! interior diffusivities
	1108	& + zflag * zblcs(ji,jk ) & ! boundary layer diffusivities
	1109	& + zmask(ji,jk) * ( 1.0 - zflag ) * zkmps(ji ) ! diffusivity enhancement at W_level near zhbl
	1110
	1111	zdiffus(ji,jj,jk) = zdiffus(ji,jj,jk) * tmask(ji,jj,jk)
	1112	#endif
	1113	! Non local flux in the boundary layer only
	1114	ghats(ji,jj,jk-1) = zmask(ji,jk) * ghats(ji,jj,jk-1)
	1115
	1116	ENDDO
	1117	END DO
	1118	! ! ===============
	1119	END DO ! End of slab
	1120	! ! ===============
	1121
	1122	! Lateral boundary conditions on zvicos and zdiffus (sign unchanged)
	1123	CALL lbc_lnk( zviscos(:,:,:), 'U', 1. ) ; CALL lbc_lnk( zdiffut(:,:,:), 'W', 1. )
	1124	#if defined key_zdfddm
	1125	CALL lbc_lnk( zdiffus(:,:,:), 'W', 1. )
	1126	#endif
	1127
[1537]	1128	SELECT CASE ( nn_ave )
[255]	1129	!
	1130	CASE ( 0 ) ! no viscosity and diffusivity smoothing
	1131
	1132	DO jk = 2, jpkm1
	1133	DO jj = 2, jpjm1
	1134	DO ji = fs_2, fs_jpim1
	1135	avmu(ji,jj,jk) = ( zviscos(ji,jj,jk) + zviscos(ji+1,jj,jk) ) &
	1136	& / MAX( 1., tmask(ji,jj,jk) + tmask (ji + 1,jj,jk) ) * umask(ji,jj,jk)
	1137
	1138	avmv(ji,jj,jk) = ( zviscos(ji,jj,jk) + zviscos(ji,jj+1,jk) ) &
	1139	& / MAX( 1., tmask(ji,jj,jk) + tmask (ji,jj+1,jk) ) * vmask(ji,jj,jk)
	1140
	1141	avt (ji,jj,jk) = zdiffut(ji,jj,jk) * tmask(ji,jj,jk)
	1142	#if defined key_zdfddm
	1143	avs (ji,jj,jk) = zdiffus(ji,jj,jk) * tmask(ji,jj,jk)
	1144	#endif
	1145	END DO
	1146	END DO
	1147	END DO
	1148
	1149	CASE ( 1 ) ! viscosity and diffusivity smoothing
	1150	!
	1151	! ( 1/2 1 1/2 ) ( 1/2 1/2 ) ( 1/2 1 1/2 )
	1152	! avt = 1/8 ( 1 2 1 ) avmu = 1/4 ( 1 1 ) avmv= 1/4 ( 1/2 1 1/2 )
	1153	! ( 1/2 1 1/2 ) ( 1/2 1/2 )
	1154
	1155	DO jk = 2, jpkm1
	1156	DO jj = 2, jpjm1
	1157	DO ji = fs_2, fs_jpim1
	1158
	1159	avmu(ji,jj,jk) = ( zviscos(ji ,jj ,jk) + zviscos(ji+1,jj ,jk) &
	1160	& +.5*( zviscos(ji ,jj-1,jk) + zviscos(ji+1,jj-1,jk) &
	1161	& +zviscos(ji ,jj+1,jk) + zviscos(ji+1,jj+1,jk) ) ) * eumean(ji,jj,jk)
	1162
	1163	avmv(ji,jj,jk) = ( zviscos(ji ,jj ,jk) + zviscos(ji ,jj+1,jk) &
	1164	& +.5*( zviscos(ji-1,jj ,jk) + zviscos(ji-1,jj+1,jk) &
	1165	& +zviscos(ji+1,jj ,jk) + zviscos(ji+1,jj+1,jk) ) ) * evmean(ji,jj,jk)
	1166
	1167	avt (ji,jj,jk) = ( .5*( zdiffut(ji-1,jj+1,jk) + zdiffut(ji-1,jj-1,jk) &
	1168	& +zdiffut(ji+1,jj+1,jk) + zdiffut(ji+1,jj-1,jk) ) &
	1169	& +1.*( zdiffut(ji-1,jj ,jk) + zdiffut(ji ,jj+1,jk) &
	1170	& +zdiffut(ji ,jj-1,jk) + zdiffut(ji+1,jj ,jk) ) &
	1171	& +2.* zdiffut(ji ,jj ,jk) ) * etmean(ji,jj,jk)
	1172	#if defined key_zdfddm
	1173	avs (ji,jj,jk) = ( .5*( zdiffus(ji-1,jj+1,jk) + zdiffus(ji-1,jj-1,jk) &
	1174	& +zdiffus(ji+1,jj+1,jk) + zdiffus(ji+1,jj-1,jk) ) &
	1175	& +1.*( zdiffus(ji-1,jj ,jk) + zdiffus(ji ,jj+1,jk) &
	1176	& +zdiffus(ji ,jj-1,jk) + zdiffus(ji+1,jj ,jk) ) &
	1177	& +2.* zdiffus(ji ,jj ,jk) ) * etmean(ji,jj,jk)
	1178	#endif
	1179	END DO
	1180	END DO
	1181	END DO
	1182
	1183	END SELECT
	1184
	1185	DO jk = 2, jpkm1 ! vertical slab
	1186	!
	1187	! Minimum value on the eddy diffusivity
	1188	! ----------------------------------------
	1189	DO jj = 2, jpjm1
	1190	DO ji = fs_2, fs_jpim1 ! vector opt.
	1191	avt(ji,jj,jk) = MAX( avt(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
	1192	#if defined key_zdfddm
	1193	avs(ji,jj,jk) = MAX( avs(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
	1194	#endif
	1195	END DO
	1196	END DO
	1197
	1198	!
	1199	! Minimum value on the eddy viscosity
	1200	! ----------------------------------------
	1201	DO jj = 1, jpj
	1202	DO ji = 1, jpi
	1203	avmu(ji,jj,jk) = MAX( avmu(ji,jj,jk), avmb(jk) ) * umask(ji,jj,jk)
	1204	avmv(ji,jj,jk) = MAX( avmv(ji,jj,jk), avmb(jk) ) * vmask(ji,jj,jk)
	1205	END DO
	1206	END DO
	1207	!
	1208	END DO
	1209
	1210	! Lateral boundary conditions on avt (sign unchanged)
	1211	CALL lbc_lnk( hkpp(:,:), 'T', 1. )
	1212
	1213	! Lateral boundary conditions on avt (sign unchanged)
	1214	CALL lbc_lnk( avt(:,:,:), 'W', 1. )
	1215	#if defined key_zdfddm
	1216	CALL lbc_lnk( avs(:,:,:), 'W', 1. )
	1217	#endif
	1218	! Lateral boundary conditions (avmu,avmv) (U- and V- points, sign unchanged)
	1219	CALL lbc_lnk( avmu(:,:,:), 'U', 1. ) ; CALL lbc_lnk( avmv(:,:,:), 'V', 1. )
	1220
[258]	1221	IF(ln_ctl) THEN
	1222	#if defined key_zdfddm
[516]	1223	CALL prt_ctl(tab3d_1=avt , clinfo1=' kpp - t: ', tab3d_2=avs , clinfo2=' s: ', ovlap=1, kdim=jpk)
[258]	1224	#else
[516]	1225	CALL prt_ctl(tab3d_1=avt , clinfo1=' kpp - t: ', ovlap=1, kdim=jpk)
[258]	1226	#endif
[516]	1227	CALL prt_ctl(tab3d_1=avmu, clinfo1=' kpp - u: ', mask1=umask, &
	1228	& tab3d_2=avmv, clinfo2= ' v: ', mask2=vmask, ovlap=1, kdim=jpk)
[258]	1229	ENDIF
	1230
[255]	1231	END SUBROUTINE zdf_kpp
	1232
	1233
[896]	1234	SUBROUTINE tra_kpp( kt )
[463]	1235	!!----------------------------------------------------------------------
	1236	!! * ROUTINE tra_kpp *
	1237	!!
	1238	!! ** Purpose : compute and add to the tracer trend the non-local
	1239	!! tracer flux
	1240	!!
	1241	!! ** Method : ???
	1242	!!
	1243	!! history :
	1244	!! 9.0 ! 05-11 (G. Madec) Original code
	1245	!!----------------------------------------------------------------------
	1246	!! * Modules used
	1247	USE oce, ONLY : ztrdt => ua, & ! use ua as 3D workspace
	1248	ztrds => va ! use va as 3D workspace
	1249	!!----------------------------------------------------------------------
[896]	1250	INTEGER, INTENT(in) :: kt
	1251	INTEGER :: ji, jj, jk
[255]	1252
[463]	1253	IF( kt == nit000 ) THEN
	1254	IF(lwp) WRITE(numout,*)
	1255	IF(lwp) WRITE(numout,*) 'tra_kpp : KPP non-local tracer fluxes'
	1256	IF(lwp) WRITE(numout,*) '~~~~~~~ '
	1257	ENDIF
	1258
	1259
	1260	! Save ta and sa trends
	1261	IF( l_trdtra ) THEN
	1262	ztrdt(:,:,:) = ta(:,:,:)
	1263	ztrds(:,:,:) = sa(:,:,:)
	1264	ENDIF
	1265
	1266	! add non-local temperature and salinity flux ( in convective case only)
	1267	DO jk = 1, jpkm1
	1268	DO jj = 2, jpjm1
	1269	DO ji = fs_2, fs_jpim1
	1270	ta(ji,jj,jk) = ta(ji,jj,jk) &
	1271	& - ( ghats(ji,jj,jk ) * avt(ji,jj,jk ) &
	1272	& - ghats(ji,jj,jk+1) * avt(ji,jj,jk+1) ) * wt0(ji,jj) / fse3t(ji,jj,jk)
	1273	sa(ji,jj,jk) = sa(ji,jj,jk) &
	1274	& - ( ghats(ji,jj,jk ) * fsavs(ji,jj,jk ) &
	1275	& - ghats(ji,jj,jk+1) * fsavs(ji,jj,jk+1) ) * ws0(ji,jj) / fse3t(ji,jj,jk)
	1276	END DO
	1277	END DO
	1278	END DO
	1279
	1280	! save the non-local tracer flux trends for diagnostic
	1281	IF( l_trdtra ) THEN
	1282	ztrdt(:,:,:) = ta(:,:,:) - ztrdt(:,:,:)
	1283	ztrds(:,:,:) = sa(:,:,:) - ztrds(:,:,:)
	1284	!!bug gm jpttdzdf ==> jpttkpp
[503]	1285	CALL trd_mod(ztrdt, ztrds, jptra_trd_zdf, 'TRA', kt)
[463]	1286	ENDIF
	1287
[896]	1288	IF(ln_ctl) THEN
	1289	CALL prt_ctl( tab3d_1=ta, clinfo1=' kpp - Ta: ', mask1=tmask, &
	1290	& tab3d_2=sa, clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' )
[463]	1291	ENDIF
	1292
	1293	END SUBROUTINE tra_kpp
	1294
	1295
[255]	1296	SUBROUTINE zdf_kpp_init
	1297	!!----------------------------------------------------------------------
	1298	!! * ROUTINE zdf_kpp_init *
	1299	!!
	1300	!! ** Purpose : Initialization of the vertical eddy diffivity and
	1301	!! viscosity when using a kpp turbulent closure scheme
	1302	!!
	1303	!! ** Method : Read the namkpp namelist and check the parameters
	1304	!! called at the first timestep (nit000)
	1305	!!
	1306	!! ** input : Namlist namkpp
	1307	!!
	1308	!!
	1309	!! history :
	1310	!! 8.1 ! 00-02 (J. Chanut) KPP Mixing
	1311	!! 9.0 ! 05-01 (C. Ethe) F90 : free form
	1312	!!----------------------------------------------------------------------
	1313	!! * local declarations
	1314
	1315	INTEGER :: &
	1316	ji, jj, jk ! dummy loop indices
	1317
	1318	#if ! defined key_kppcustom
	1319	INTEGER :: &
	1320	jm ! dummy loop indices
	1321	REAL(wp) :: & !!! tempory scalars
	1322	zref, zdist
	1323	#endif
	1324
	1325	#if defined key_kpplktb
	1326	REAL(wp) :: & !!! tempory scalars
	1327	zustar, &
	1328	zucube, zustvk, &
	1329	zeta, zehat
	1330	#endif
	1331	REAL(wp) :: & !!! tempory scalars
	1332	zhbf
	1333	LOGICAL :: &
	1334	ll_kppcustom, & ! 1st ocean level taken as surface layer
	1335	ll_kpplktb ! Lookup table for turbul. velocity scales
[1537]	1336	!!
[1601]	1337	NAMELIST/namzdf_kpp/ ln_kpprimix, rn_difmiw, rn_difsiw, rn_riinfty, rn_difri, rn_bvsqcon, rn_difcon, nn_ave
[255]	1338	!!----------------------------------------------------------------------
	1339
[1537]	1340	REWIND ( numnam ) ! Read Namelist namkpp : K-Profile Parameterisation
[1601]	1341	READ ( numnam, namzdf_kpp )
[255]	1342
[1537]	1343	IF(lwp) THEN ! Control print
[255]	1344	WRITE(numout,*)
[1537]	1345	WRITE(numout,*) 'zdf_kpp_init : K-Profile Parameterisation'
[255]	1346	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	1347	WRITE(numout,*) ' Namelist namzdf_kpp : set tke mixing parameters'
[1537]	1348	WRITE(numout,*) ' Shear instability mixing ln_kpprimix = ', ln_kpprimix
	1349	WRITE(numout,*) ' max. internal wave viscosity rn_difmiw = ', rn_difmiw
	1350	WRITE(numout,*) ' max. internal wave diffusivity rn_difsiw = ', rn_difsiw
	1351	WRITE(numout,*) ' Richardson Number limit for shear instability rn_riinfty = ', rn_riinfty
	1352	WRITE(numout,*) ' max. shear mixing at Rig = 0 rn_difri = ', rn_difri
	1353	WRITE(numout,*) ' Brunt-Vaisala squared for max. convection rn_bvsqcon = ', rn_bvsqcon
	1354	WRITE(numout,*) ' max. mix. in interior convec. rn_difcon = ', rn_difcon
	1355	WRITE(numout,*) ' horizontal average flag nn_ave = ', nn_ave
[255]	1356	ENDIF
	1357
	1358	ll_kppcustom = .FALSE.
	1359	ll_kpplktb = .FALSE.
	1360
	1361	#if defined key_kppcustom
	1362	ll_kppcustom = .TRUE.
	1363	#endif
	1364	#if defined key_kpplktb
	1365	ll_kpplktb = .TRUE.
	1366	#endif
	1367	IF(lwp) THEN
	1368	WRITE(numout,*) ' Lookup table for turbul. velocity scales ll_kpplktb = ', ll_kpplktb
	1369	WRITE(numout,*) ' 1st ocean level taken as surface layer ll_kppcustom = ', ll_kppcustom
	1370	ENDIF
	1371
	1372	IF( lk_zdfddm) THEN
	1373	IF(lwp) THEN
	1374	WRITE(numout,*)
	1375	WRITE(numout,*) ' Double diffusion mixing on temperature and salinity '
	1376	WRITE(numout,*) ' CAUTION : done in routine zdfkpp, not in routine zdfddm '
	1377	ENDIF
	1378	ENDIF
	1379
	1380
	1381
	1382	!set constants not in namelist
	1383	!-----------------------------
	1384	Vtc = rconcv * SQRT( 0.2 / ( rconcs * epsilon ) ) / ( vonk * vonk * Ricr )
	1385	rcg = rcstar * vonk * ( rconcs * vonk * epsilon )**pthird
	1386
	1387	IF(lwp) THEN
[1537]	1388	WRITE(numout,*)
[255]	1389	WRITE(numout,*) ' Constant value for unreso. turbul. velocity shear Vtc = ', Vtc
	1390	WRITE(numout,*) ' Non-dimensional coef. for nonlocal transport rcg = ', rcg
	1391	ENDIF
	1392
	1393	! ratt is the attenuation coefficient for solar flux
	1394	! Should be different is s_coordinate
	1395	DO jk = 1, jpk
	1396	zhbf = - fsdept(1,1,jk) * hbf
	1397	ratt(jk) = 1.0 - ( rabs * EXP( zhbf / xsi1 ) + ( 1.0 - rabs ) * EXP( zhbf / xsi2 ) )
	1398	ENDDO
	1399
	1400	! Horizontal average : initialization of weighting arrays
	1401	! -------------------
	1402
[1537]	1403	SELECT CASE ( nn_ave )
[255]	1404
	1405	CASE ( 0 ) ! no horizontal average
	1406	IF(lwp) WRITE(numout,*) ' no horizontal average on avt, avmu, avmv'
	1407	IF(lwp) WRITE(numout,*) ' only in very high horizontal resolution !'
	1408	! weighting mean arrays etmean, eumean and evmean
	1409	! ( 1 1 ) ( 1 )
	1410	! avt = 1/4 ( 1 1 ) avmu = 1/2 ( 1 1 ) avmv= 1/2 ( 1 )
	1411	!
	1412	etmean(:,:,:) = 0.e0
	1413	eumean(:,:,:) = 0.e0
	1414	evmean(:,:,:) = 0.e0
	1415
	1416	DO jk = 1, jpkm1
	1417	DO jj = 2, jpjm1
	1418	DO ji = 2, jpim1 ! vector opt.
	1419	etmean(ji,jj,jk) = tmask(ji,jj,jk) &
	1420	& / MAX( 1., umask(ji-1,jj ,jk) + umask(ji,jj,jk) &
	1421	& + vmask(ji ,jj-1,jk) + vmask(ji,jj,jk) )
	1422
	1423	eumean(ji,jj,jk) = umask(ji,jj,jk) &
	1424	& / MAX( 1., tmask(ji,jj,jk) + tmask(ji+1,jj ,jk) )
	1425
	1426	evmean(ji,jj,jk) = vmask(ji,jj,jk) &
	1427	& / MAX( 1., tmask(ji,jj,jk) + tmask(ji ,jj+1,jk) )
	1428	END DO
	1429	END DO
	1430	END DO
	1431
	1432	CASE ( 1 ) ! horizontal average
	1433	IF(lwp) WRITE(numout,*) ' horizontal average on avt, avmu, avmv'
	1434	! weighting mean arrays etmean, eumean and evmean
	1435	! ( 1/2 1 1/2 ) ( 1/2 1/2 ) ( 1/2 1 1/2 )
	1436	! avt = 1/8 ( 1 2 1 ) avmu = 1/4 ( 1 1 ) avmv= 1/4 ( 1/2 1 1/2 )
	1437	! ( 1/2 1 1/2 ) ( 1/2 1/2 )
	1438	etmean(:,:,:) = 0.e0
	1439	eumean(:,:,:) = 0.e0
	1440	evmean(:,:,:) = 0.e0
	1441
	1442	DO jk = 1, jpkm1
	1443	DO jj = 2, jpjm1
	1444	DO ji = fs_2, fs_jpim1 ! vector opt.
	1445	etmean(ji,jj,jk) = tmask(ji, jj,jk) &
	1446	& / MAX( 1., 2.* tmask(ji,jj,jk) &
	1447	& +.5 * ( tmask(ji-1,jj+1,jk) + tmask(ji-1,jj-1,jk) &
	1448	& +tmask(ji+1,jj+1,jk) + tmask(ji+1,jj-1,jk) ) &
	1449	& +1. * ( tmask(ji-1,jj ,jk) + tmask(ji ,jj+1,jk) &
	1450	& +tmask(ji ,jj-1,jk) + tmask(ji+1,jj ,jk) ) )
	1451
	1452	eumean(ji,jj,jk) = umask(ji,jj,jk) &
	1453	& / MAX( 1., tmask(ji,jj ,jk) + tmask(ji+1,jj ,jk) &
	1454	& +.5 * ( tmask(ji,jj-1,jk) + tmask(ji+1,jj-1,jk) &
	1455	& +tmask(ji,jj+1,jk) + tmask(ji+1,jj+1,jk) ) )
	1456
	1457	evmean(ji,jj,jk) = vmask(ji,jj,jk) &
	1458	& / MAX( 1., tmask(ji ,jj,jk) + tmask(ji ,jj+1,jk) &
	1459	& +.5 * ( tmask(ji-1,jj,jk) + tmask(ji-1,jj+1,jk) &
	1460	& +tmask(ji+1,jj,jk) + tmask(ji+1,jj+1,jk) ) )
	1461	END DO
	1462	END DO
	1463	END DO
	1464
	1465	CASE DEFAULT
[1537]	1466	WRITE(ctmp1,*) ' bad flag value for nn_ave = ', nn_ave
[896]	1467	CALL ctl_stop( ctmp1 )
[255]	1468
	1469	END SELECT
	1470
	1471	! Initialization of vertical eddy coef. to the background value
	1472	! -------------------------------------------------------------
	1473	DO jk = 1, jpk
	1474	avt (:,:,jk) = avtb(jk) * tmask(:,:,jk)
	1475	avmu(:,:,jk) = avmb(jk) * umask(:,:,jk)
	1476	avmv(:,:,jk) = avmb(jk) * vmask(:,:,jk)
	1477	END DO
	1478
	1479	! zero the surface flux for non local term and kpp mixed layer depth
	1480	! ------------------------------------------------------------------
	1481	ghats(:,:,:) = 0.
	1482	wt0 (:,: ) = 0.
	1483	ws0 (:,: ) = 0.
	1484	hkpp (:,: ) = 0. ! just a diagnostic (not essential)
	1485
	1486	#if ! defined key_kppcustom
	1487	! compute arrays (del, wz) for reference mean values
	1488	! (increase speed for vectorization key_kppcustom not defined)
	1489	del(1:jpk, 1:jpk) = 0.
	1490	DO jk = 1, jpk
	1491	zref = epsilon * fsdept(1,1,jk)
	1492	DO jm = 1 , jpk
	1493	zdist = zref - fsdepw(1,1,jm)
	1494	IF( zdist > 0. ) THEN
	1495	del(jk,jm) = MIN( zdist, fse3t(1,1,jm) ) / zref
	1496	ELSE
	1497	del(jk,jm) = 0.
	1498	ENDIF
	1499	ENDDO
	1500	ENDDO
	1501	#endif
	1502
	1503	#if defined key_kpplktb
	1504	! build lookup table for turbulent velocity scales
	1505	dezehat = ( dehatmax - dehatmin ) / nilktbm1
	1506	deustar = ( ustmax - ustmin ) / njlktbm1
	1507
	1508	DO jj = 1, njlktb
	1509	zustar = ( jj - 1) * deustar + ustmin
	1510	zustvk = vonk * zustar
	1511	zucube = zustar * zustar * zustar
	1512	DO ji = 1 , nilktb
	1513	zehat = ( ji - 1 ) * dezehat + dehatmin
	1514	zeta = zehat / ( zucube + epsln )
	1515	IF( zehat >= 0 ) THEN ! Stable case
	1516	wmlktb(ji,jj) = zustvk / ABS( 1.0 + rconc1 * zeta + epsln )
	1517	wslktb(ji,jj) = wmlktb(ji,jj)
	1518	ELSE ! Unstable case
	1519	IF( zeta > rzetam ) THEN
	1520	wmlktb(ji,jj) = zustvk * ABS( 1.0 - rconc2 * zeta )**pfourth
	1521	ELSE
	1522	wmlktb(ji,jj) = zustvk * ABS( rconam - rconcm * zeta )**pthird
	1523	ENDIF
	1524
	1525	IF( zeta > rzetas ) THEN
	1526	wslktb(ji,jj) = zustvk * SQRT( ABS( 1.0 - rconc2 * zeta ) )
	1527	ELSE
	1528	wslktb(ji,jj) = zustvk * ABS( rconas - rconcs * zeta )**pthird
	1529	ENDIF
	1530	ENDIF
	1531	END DO
	1532	END DO
	1533	#endif
	1534	END SUBROUTINE zdf_kpp_init
	1535
	1536	#else
	1537	!!----------------------------------------------------------------------
	1538	!! Dummy module : NO KPP scheme
	1539	!!----------------------------------------------------------------------
	1540	LOGICAL, PUBLIC, PARAMETER :: lk_zdfkpp = .FALSE. !: KPP flag
	1541	CONTAINS
	1542	SUBROUTINE zdf_kpp( kt ) ! Empty routine
	1543	WRITE(,) 'zdf_kpp: You should not have seen this print! error?', kt
	1544	END SUBROUTINE zdf_kpp
[463]	1545	SUBROUTINE tra_kpp( kt ) ! Empty routine
	1546	WRITE(,) 'tra_kpp: You should not have seen this print! error?', kt
	1547	END SUBROUTINE tra_kpp
[255]	1548	#endif
	1549
	1550	!!======================================================================
	1551	END MODULE zdfkpp

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source: branches/DEV_r1784_mid_year_merge_2010/NEMO/OPA_SRC/ZDF/zdfkpp.F90 @ 2000

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