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zdftke.F90 in branches/2017/dev_r7881_ENHANCE09_RK3/NEMOGCM/NEMO/OPA_SRC/ZDF – NEMO

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source: branches/2017/dev_r7881_ENHANCE09_RK3/NEMOGCM/NEMO/OPA_SRC/ZDF/zdftke.F90 @ 8863

Last change on this file since 8863 was 8863, checked in by flavoni, 6 years ago
(ENHANCE-09): fix AGRIF reproducibility problem
Property svn:keywords set to `Id`
File size: 42.6 KB

Rev	Line
[1531]	1	MODULE zdftke
[1239]	2	!!======================================================================
[1531]	3	!! * MODULE zdftke *
[1239]	4	!! Ocean physics: vertical mixing coefficient computed from the tke
	5	!! turbulent closure parameterization
	6	!!=====================================================================
[1492]	7	!! History : OPA ! 1991-03 (b. blanke) Original code
	8	!! 7.0 ! 1991-11 (G. Madec) bug fix
	9	!! 7.1 ! 1992-10 (G. Madec) new mixing length and eav
	10	!! 7.2 ! 1993-03 (M. Guyon) symetrical conditions
	11	!! 7.3 ! 1994-08 (G. Madec, M. Imbard) nn_pdl flag
	12	!! 7.5 ! 1996-01 (G. Madec) s-coordinates
	13	!! 8.0 ! 1997-07 (G. Madec) lbc
	14	!! 8.1 ! 1999-01 (E. Stretta) new option for the mixing length
	15	!! NEMO 1.0 ! 2002-06 (G. Madec) add tke_init routine
	16	!! - ! 2004-10 (C. Ethe ) 1D configuration
	17	!! 2.0 ! 2006-07 (S. Masson) distributed restart using iom
	18	!! 3.0 ! 2008-05 (C. Ethe, G.Madec) : update TKE physics:
	19	!! ! - tke penetration (wind steering)
	20	!! ! - suface condition for tke & mixing length
	21	!! ! - Langmuir cells
	22	!! - ! 2008-05 (J.-M. Molines, G. Madec) 2D form of avtb
	23	!! - ! 2008-06 (G. Madec) style + DOCTOR name for namelist parameters
	24	!! - ! 2008-12 (G. Reffray) stable discretization of the production term
	25	!! 3.2 ! 2009-06 (G. Madec, S. Masson) TKE restart compatible with key_cpl
	26	!! ! + cleaning of the parameters + bugs correction
[2528]	27	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[5120]	28	!! 3.6 ! 2014-11 (P. Mathiot) add ice shelf capability
[8215]	29	!! 4.0 ! 2017-04 (G. Madec) remove CPP ddm key & avm at t-point only
	30	!! - ! 2017-05 (G. Madec) add top/bottom friction as boundary condition (ln_drg)
[1239]	31	!!----------------------------------------------------------------------
[8215]	32
[1239]	33	!!----------------------------------------------------------------------
[3625]	34	!! zdf_tke : update momentum and tracer Kz from a tke scheme
	35	!! tke_tke : tke time stepping: update tke at now time step (en)
	36	!! tke_avn : compute mixing length scale and deduce avm and avt
	37	!! zdf_tke_init : initialization, namelist read, and parameters control
	38	!! tke_rst : read/write tke restart in ocean restart file
[1239]	39	!!----------------------------------------------------------------------
[2528]	40	USE oce ! ocean: dynamics and active tracers variables
	41	USE phycst ! physical constants
	42	USE dom_oce ! domain: ocean
	43	USE domvvl ! domain: variable volume layer
[1492]	44	USE sbc_oce ! surface boundary condition: ocean
[2528]	45	USE zdf_oce ! vertical physics: ocean variables
[8215]	46	USE zdfdrg ! vertical physics: top/bottom drag coef.
[2528]	47	USE zdfmxl ! vertical physics: mixed layer
[8215]	48	#if defined key_agrif
	49	USE agrif_opa_interp
	50	USE agrif_opa_update
	51	#endif
	52	!
[1492]	53	USE in_out_manager ! I/O manager
	54	USE iom ! I/O manager library
[2715]	55	USE lib_mpp ! MPP library
[8215]	56	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
	57	USE prtctl ! Print control
[3294]	58	USE timing ! Timing
[3625]	59	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[1239]	60
	61	IMPLICIT NONE
	62	PRIVATE
	63
[2528]	64	PUBLIC zdf_tke ! routine called in step module
	65	PUBLIC zdf_tke_init ! routine called in opa module
	66	PUBLIC tke_rst ! routine called in step module
[1239]	67
[4147]	68	! !! Namelist namzdf_tke
	69	LOGICAL :: ln_mxl0 ! mixing length scale surface value as function of wind stress or not
	70	INTEGER :: nn_mxl ! type of mixing length (=0/1/2/3)
	71	REAL(wp) :: rn_mxl0 ! surface min value of mixing length (kappaz_o=0.40.1 m) [m]
	72	INTEGER :: nn_pdl ! Prandtl number or not (ratio avt/avm) (=0/1)
	73	REAL(wp) :: rn_ediff ! coefficient for avt: avt=rn_ediffmxlsqrt(e)
	74	REAL(wp) :: rn_ediss ! coefficient of the Kolmogoroff dissipation
	75	REAL(wp) :: rn_ebb ! coefficient of the surface input of tke
	76	REAL(wp) :: rn_emin ! minimum value of tke [m2/s2]
	77	REAL(wp) :: rn_emin0 ! surface minimum value of tke [m2/s2]
	78	REAL(wp) :: rn_bshear ! background shear (>0) currently a numerical threshold (do not change it)
[8215]	79	LOGICAL :: ln_drg ! top/bottom friction forcing flag
[4147]	80	INTEGER :: nn_etau ! type of depth penetration of surface tke (=0/1/2/3)
[8215]	81	INTEGER :: nn_htau ! type of tke profile of penetration (=0/1)
	82	REAL(wp) :: rn_efr ! fraction of TKE surface value which penetrates in the ocean
[4147]	83	LOGICAL :: ln_lc ! Langmuir cells (LC) as a source term of TKE or not
[8215]	84	REAL(wp) :: rn_lc ! coef to compute vertical velocity of Langmuir cells
[1239]	85
[4147]	86	REAL(wp) :: ri_cri ! critic Richardson number (deduced from rn_ediff and rn_ediss values)
	87	REAL(wp) :: rmxl_min ! minimum mixing length value (deduced from rn_ediff and rn_emin values) [m]
[2528]	88	REAL(wp) :: rhftau_add = 1.e-3_wp ! add offset applied to HF part of taum (nn_etau=3)
	89	REAL(wp) :: rhftau_scl = 1.0_wp ! scale factor applied to HF part of taum (nn_etau=3)
[1239]	90
[8215]	91	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: htau ! depth of tke penetration (nn_htau)
	92	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dissl ! now mixing lenght of dissipation
	93	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: apdlr ! now mixing lenght of dissipation
[1492]	94
[1239]	95	!! * Substitutions
	96	# include "vectopt_loop_substitute.h90"
	97	!!----------------------------------------------------------------------
[5836]	98	!! NEMO/OPA 3.7 , NEMO Consortium (2015)
[2528]	99	!! $Id$
	100	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[1239]	101	!!----------------------------------------------------------------------
	102	CONTAINS
	103
[2715]	104	INTEGER FUNCTION zdf_tke_alloc()
	105	!!----------------------------------------------------------------------
	106	!! * FUNCTION zdf_tke_alloc *
	107	!!----------------------------------------------------------------------
[8215]	108	ALLOCATE( htau(jpi,jpj) , dissl(jpi,jpj,jpk) , apdlr(jpi,jpj,jpk) , STAT= zdf_tke_alloc )
[2715]	109	!
	110	IF( lk_mpp ) CALL mpp_sum ( zdf_tke_alloc )
	111	IF( zdf_tke_alloc /= 0 ) CALL ctl_warn('zdf_tke_alloc: failed to allocate arrays')
	112	!
	113	END FUNCTION zdf_tke_alloc
	114
	115
[8215]	116	SUBROUTINE zdf_tke( kt, p_sh2, p_avm, p_avt )
[1239]	117	!!----------------------------------------------------------------------
[1531]	118	!! * ROUTINE zdf_tke *
[1239]	119	!!
	120	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
[1492]	121	!! coefficients using a turbulent closure scheme (TKE).
[1239]	122	!!
[1492]	123	!! ** Method : The time evolution of the turbulent kinetic energy (tke)
	124	!! is computed from a prognostic equation :
	125	!! d(en)/dt = avm (d(u)/dz)**2 ! shear production
	126	!! + d( avm d(en)/dz )/dz ! diffusion of tke
	127	!! + avt N^2 ! stratif. destruc.
	128	!! - rn_ediss / emxl en**(2/3) ! Kolmogoroff dissipation
[1239]	129	!! with the boundary conditions:
[1695]	130	!! surface: en = max( rn_emin0, rn_ebb * taum )
[1239]	131	!! bottom : en = rn_emin
[1492]	132	!! The associated critical Richardson number is: ri_cri = 2/(2+rn_ediss/rn_ediff)
	133	!!
	134	!! The now Turbulent kinetic energy is computed using the following
	135	!! time stepping: implicit for vertical diffusion term, linearized semi
	136	!! implicit for kolmogoroff dissipation term, and explicit forward for
	137	!! both buoyancy and shear production terms. Therefore a tridiagonal
	138	!! linear system is solved. Note that buoyancy and shear terms are
	139	!! discretized in a energy conserving form (Bruchard 2002).
	140	!!
	141	!! The dissipative and mixing length scale are computed from en and
	142	!! the stratification (see tke_avn)
	143	!!
	144	!! The now vertical eddy vicosity and diffusivity coefficients are
	145	!! given by:
	146	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	147	!! avt = max( avmb, pdl * avm )
[1239]	148	!! eav = max( avmb, avm )
[1492]	149	!! where pdl, the inverse of the Prandtl number is 1 if nn_pdl=0 and
	150	!! given by an empirical funtion of the localRichardson number if nn_pdl=1
[1239]	151	!!
	152	!! ** Action : compute en (now turbulent kinetic energy)
[8215]	153	!! update avt, avm (before vertical eddy coef.)
[1239]	154	!!
	155	!! References : Gaspar et al., JGR, 1990,
	156	!! Blanke and Delecluse, JPO, 1991
	157	!! Mellor and Blumberg, JPO 2004
	158	!! Axell, JGR, 2002
[1492]	159	!! Bruchard OM 2002
[1239]	160	!!----------------------------------------------------------------------
[8568]	161	INTEGER , INTENT(in ) :: kt ! ocean time step
[8215]	162	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: p_sh2 ! shear production term
[8568]	163	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: p_avm, p_avt ! momentum and tracer Kz (w-points)
[1492]	164	!!----------------------------------------------------------------------
[1481]	165	!
[8215]	166	CALL tke_tke( gdepw_n, e3t_n, e3w_n, p_sh2, p_avm, p_avt ) ! now tke (en)
[3632]	167	!
[8215]	168	CALL tke_avn( gdepw_n, e3t_n, e3w_n, p_avm, p_avt ) ! now avt, avm, dissl
[1492]	169	!
[5656]	170	END SUBROUTINE zdf_tke
[1239]	171
[1492]	172
[8215]	173	SUBROUTINE tke_tke( pdepw, p_e3t, p_e3w, p_sh2 &
	174	& , p_avm, p_avt )
[1239]	175	!!----------------------------------------------------------------------
[1492]	176	!! * ROUTINE tke_tke *
	177	!!
	178	!! ** Purpose : Compute the now Turbulente Kinetic Energy (TKE)
	179	!!
	180	!! ** Method : - TKE surface boundary condition
[2528]	181	!! - source term due to Langmuir cells (Axell JGR 2002) (ln_lc=T)
[8215]	182	!! - source term due to shear (= Kz dz[Ub] * dz[Un] )
[1492]	183	!! - Now TKE : resolution of the TKE equation by inverting
	184	!! a tridiagonal linear system by a "methode de chasse"
	185	!! - increase TKE due to surface and internal wave breaking
[8568]	186	!! NB: when sea-ice is present, both LC parameterization
	187	!! and TKE penetration are turned off when the ice fraction
	188	!! is smaller than 0.25
[1492]	189	!!
	190	!! ** Action : - en : now turbulent kinetic energy)
[1239]	191	!! ---------------------------------------------------------------------
[8215]	192	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdepw ! depth of w-points
	193	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_e3t, p_e3w ! level thickness (t- & w-points)
	194	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_sh2 ! shear production term
	195	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_avm, p_avt ! vertical eddy viscosity & diffusivity (w-points)
	196	!
	197	INTEGER :: ji, jj, jk ! dummy loop arguments
	198	REAL(wp) :: zetop, zebot, zmsku, zmskv ! local scalars
	199	REAL(wp) :: zrhoa = 1.22 ! Air density kg/m3
	200	REAL(wp) :: zcdrag = 1.5e-3 ! drag coefficient
	201	REAL(wp) :: zbbrau, zri ! local scalars
	202	REAL(wp) :: zfact1, zfact2, zfact3 ! - -
	203	REAL(wp) :: ztx2 , zty2 , zcof ! - -
	204	REAL(wp) :: ztau , zdif ! - -
	205	REAL(wp) :: zus , zwlc , zind ! - -
	206	REAL(wp) :: zzd_up, zzd_lw ! - -
	207	INTEGER , DIMENSION(jpi,jpj) :: imlc
	208	REAL(wp), DIMENSION(jpi,jpj) :: zhlc
	209	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zpelc, zdiag, zd_up, zd_lw
[1239]	210	!!--------------------------------------------------------------------
[1492]	211	!
[8568]	212	IF( ln_timing ) CALL timing_start('tke_tke')
[3294]	213	!
[1695]	214	zbbrau = rn_ebb / rau0 ! Local constant initialisation
[2528]	215	zfact1 = -.5_wp * rdt
	216	zfact2 = 1.5_wp * rdt * rn_ediss
	217	zfact3 = 0.5_wp * rn_ediss
[1492]	218	!
[5120]	219	!
[1492]	220	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8215]	221	! ! Surface/top/bottom boundary condition on tke
[1492]	222	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8215]	223
	224	DO jj = 2, jpjm1 ! en(1) = rn_ebb taum / rau0 (min value rn_emin0)
	225	DO ji = fs_2, fs_jpim1 ! vector opt.
	226	en(ji,jj,1) = MAX( rn_emin0, zbbrau * taum(ji,jj) ) * tmask(ji,jj,1)
	227	END DO
	228	END DO
[5120]	229	IF ( ln_isfcav ) THEN
	230	DO jj = 2, jpjm1 ! en(mikt(ji,jj)) = rn_emin
	231	DO ji = fs_2, fs_jpim1 ! vector opt.
[5836]	232	en(ji,jj,mikt(ji,jj)) = rn_emin * tmask(ji,jj,1)
[5120]	233	END DO
	234	END DO
[8215]	235	ENDIF
[2528]	236
[1492]	237	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	238	! ! Bottom boundary condition on tke
	239	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1719]	240	!
[8215]	241	! en(bot) = (ebb0/rau0)0.5sqrt(u_botfr^2+v_botfr^2) (min value rn_emin)
	242	! where ebb0 does not includes surface wave enhancement (i.e. ebb0=3.75)
	243	! Note that stress averaged is done using an wet-only calculation of u and v at t-point like in zdfsh2
[1492]	244	!
[8215]	245	IF( ln_drg ) THEN !== friction used as top/bottom boundary condition on TKE
	246	!
	247	DO jj = 2, jpjm1 ! bottom friction
	248	DO ji = fs_2, fs_jpim1 ! vector opt.
	249	zmsku = ( 2. - umask(ji-1,jj,mbkt(ji,jj)) * umask(ji,jj,mbkt(ji,jj)) )
	250	zmskv = ( 2. - vmask(ji,jj-1,mbkt(ji,jj)) * vmask(ji,jj,mbkt(ji,jj)) )
	251	! ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000. (CAUTION CdU<0)
	252	zebot = - 0.001875_wp * rCdU_bot(ji,jj) * SQRT( ( zmsku( ub(ji,jj,mbkt(ji,jj))+ub(ji-1,jj,mbkt(ji,jj)) ) )*2 &
	253	& + ( zmskv( vb(ji,jj,mbkt(ji,jj))+vb(ji,jj-1,mbkt(ji,jj)) ) )*2 )
	254	en(ji,jj,mbkt(ji,jj)+1) = MAX( zebot, rn_emin ) * ssmask(ji,jj)
	255	END DO
	256	END DO
	257	IF( ln_isfcav ) THEN ! top friction
	258	DO jj = 2, jpjm1
	259	DO ji = fs_2, fs_jpim1 ! vector opt.
	260	zmsku = ( 2. - umask(ji-1,jj,mikt(ji,jj)) * umask(ji,jj,mikt(ji,jj)) )
	261	zmskv = ( 2. - vmask(ji,jj-1,mikt(ji,jj)) * vmask(ji,jj,mikt(ji,jj)) )
	262	! ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000. (CAUTION CdU<0)
	263	zetop = - 0.001875_wp * rCdU_top(ji,jj) * SQRT( ( zmsku( ub(ji,jj,mikt(ji,jj))+ub(ji-1,jj,mikt(ji,jj)) ) )*2 &
	264	& + ( zmskv( vb(ji,jj,mikt(ji,jj))+vb(ji,jj-1,mikt(ji,jj)) ) )*2 )
	265	en(ji,jj,mikt(ji,jj)) = MAX( zetop, rn_emin ) * (1._wp - tmask(ji,jj,1)) ! masked at ocean surface
	266	END DO
	267	END DO
	268	ENDIF
	269	!
	270	ENDIF
	271	!
[1492]	272	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8215]	273	IF( ln_lc ) THEN ! Langmuir circulation source term added to tke ! (Axell JGR 2002)
[1492]	274	! !>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
[1239]	275	!
[1492]	276	! !* total energy produce by LC : cumulative sum over jk
[8215]	277	zpelc(:,:,1) = MAX( rn2b(:,:,1), 0._wp ) * pdepw(:,:,1) * p_e3w(:,:,1)
[1239]	278	DO jk = 2, jpk
[8215]	279	zpelc(:,:,jk) = zpelc(:,:,jk-1) + MAX( rn2b(:,:,jk), 0._wp ) * pdepw(:,:,jk) * p_e3w(:,:,jk)
[1239]	280	END DO
[1492]	281	! !* finite Langmuir Circulation depth
[1705]	282	zcof = 0.5 * 0.016 * 0.016 / ( zrhoa * zcdrag )
[7753]	283	imlc(:,:) = mbkt(:,:) + 1 ! Initialization to the number of w ocean point (=2 over land)
[1239]	284	DO jk = jpkm1, 2, -1
[1492]	285	DO jj = 1, jpj ! Last w-level at which zpelc>=0.5usus
	286	DO ji = 1, jpi ! with us=0.016*wind(starting from jpk-1)
[1705]	287	zus = zcof * taum(ji,jj)
[1239]	288	IF( zpelc(ji,jj,jk) > zus ) imlc(ji,jj) = jk
	289	END DO
	290	END DO
	291	END DO
[1492]	292	! ! finite LC depth
	293	DO jj = 1, jpj
[1239]	294	DO ji = 1, jpi
[8215]	295	zhlc(ji,jj) = pdepw(ji,jj,imlc(ji,jj))
[1239]	296	END DO
	297	END DO
[1705]	298	zcof = 0.016 / SQRT( zrhoa * zcdrag )
[1492]	299	DO jk = 2, jpkm1 !* TKE Langmuir circulation source term added to en
[1239]	300	DO jj = 2, jpjm1
	301	DO ji = fs_2, fs_jpim1 ! vector opt.
[1705]	302	zus = zcof * SQRT( taum(ji,jj) ) ! Stokes drift
[1492]	303	! ! vertical velocity due to LC
[8215]	304	zind = 0.5 - SIGN( 0.5, pdepw(ji,jj,jk) - zhlc(ji,jj) )
	305	zwlc = zind * rn_lc * zus * SIN( rpi * pdepw(ji,jj,jk) / zhlc(ji,jj) )
[1492]	306	! ! TKE Langmuir circulation source term
[8568]	307	en(ji,jj,jk) = en(ji,jj,jk) + rdt * MAX(0.,1._wp - 4.fr_i(ji,jj) ) ( zwlc * zwlc * zwlc ) &
[6497]	308	& / zhlc(ji,jj) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	309	END DO
	310	END DO
	311	END DO
	312	!
	313	ENDIF
[1492]	314	!
	315	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	316	! ! Now Turbulent kinetic energy (output in en)
	317	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	318	! ! Resolution of a tridiagonal linear system by a "methode de chasse"
	319	! ! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
	320	! ! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
	321	!
[8215]	322	IF( nn_pdl == 1 ) THEN !* Prandtl number = F( Ri )
[5656]	323	DO jk = 2, jpkm1
	324	DO jj = 2, jpjm1
[8215]	325	DO ji = 2, jpim1
	326	! ! local Richardson number
	327	zri = MAX( rn2b(ji,jj,jk), 0._wp ) * p_avm(ji,jj,jk) / ( p_sh2(ji,jj,jk) + rn_bshear )
	328	! ! inverse of Prandtl number
[5656]	329	apdlr(ji,jj,jk) = MAX( 0.1_wp, ri_cri / MAX( ri_cri , zri ) )
	330	END DO
	331	END DO
	332	END DO
	333	ENDIF
[5836]	334	!
[5120]	335	DO jk = 2, jpkm1 !* Matrix and right hand side in en
	336	DO jj = 2, jpjm1
	337	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	338	zcof = zfact1 * tmask(ji,jj,jk)
[8215]	339	! ! A minimum of 2.e-5 m2/s is imposed on TKE vertical
	340	! ! eddy coefficient (ensure numerical stability)
	341	zzd_up = zcof * MAX( p_avm(ji,jj,jk+1) + p_avm(ji,jj,jk ) , 2.e-5_wp ) & ! upper diagonal
	342	& / ( p_e3t(ji,jj,jk ) * p_e3w(ji,jj,jk ) )
	343	zzd_lw = zcof * MAX( p_avm(ji,jj,jk ) + p_avm(ji,jj,jk-1) , 2.e-5_wp ) & ! lower diagonal
	344	& / ( p_e3t(ji,jj,jk-1) * p_e3w(ji,jj,jk ) )
[5656]	345	!
[1492]	346	zd_up(ji,jj,jk) = zzd_up ! Matrix (zdiag, zd_up, zd_lw)
	347	zd_lw(ji,jj,jk) = zzd_lw
[8215]	348	zdiag(ji,jj,jk) = 1._wp - zzd_lw - zzd_up + zfact2 * dissl(ji,jj,jk) * wmask(ji,jj,jk)
[1239]	349	!
[1492]	350	! ! right hand side in en
[8215]	351	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( p_sh2(ji,jj,jk) & ! shear
	352	& - p_avt(ji,jj,jk) * rn2(ji,jj,jk) & ! stratification
	353	& + zfact3 * dissl(ji,jj,jk) * en(ji,jj,jk) & ! dissipation
	354	& ) * wmask(ji,jj,jk)
[1239]	355	END DO
[5120]	356	END DO
	357	END DO
	358	! !* Matrix inversion from level 2 (tke prescribed at level 1)
	359	DO jk = 3, jpkm1 ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
	360	DO jj = 2, jpjm1
	361	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	362	zdiag(ji,jj,jk) = zdiag(ji,jj,jk) - zd_lw(ji,jj,jk) * zd_up(ji,jj,jk-1) / zdiag(ji,jj,jk-1)
[1239]	363	END DO
[5120]	364	END DO
	365	END DO
[5836]	366	DO jj = 2, jpjm1 ! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
[5120]	367	DO ji = fs_2, fs_jpim1 ! vector opt.
	368	zd_lw(ji,jj,2) = en(ji,jj,2) - zd_lw(ji,jj,2) * en(ji,jj,1) ! Surface boudary conditions on tke
	369	END DO
	370	END DO
	371	DO jk = 3, jpkm1
	372	DO jj = 2, jpjm1
	373	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	374	zd_lw(ji,jj,jk) = en(ji,jj,jk) - zd_lw(ji,jj,jk) / zdiag(ji,jj,jk-1) *zd_lw(ji,jj,jk-1)
[1239]	375	END DO
[5120]	376	END DO
	377	END DO
[5836]	378	DO jj = 2, jpjm1 ! thrid recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
[5120]	379	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	380	en(ji,jj,jpkm1) = zd_lw(ji,jj,jpkm1) / zdiag(ji,jj,jpkm1)
[5120]	381	END DO
	382	END DO
	383	DO jk = jpk-2, 2, -1
	384	DO jj = 2, jpjm1
	385	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	386	en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
[1239]	387	END DO
[5120]	388	END DO
	389	END DO
	390	DO jk = 2, jpkm1 ! set the minimum value of tke
	391	DO jj = 2, jpjm1
	392	DO ji = fs_2, fs_jpim1 ! vector opt.
	393	en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin ) * wmask(ji,jj,jk)
[1239]	394	END DO
	395	END DO
	396	END DO
	397
[1492]	398	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	399	! ! TKE due to surface and internal wave breaking
	400	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[6140]	401	!!gm BUG : in the exp remove the depth of ssh !!!
[8215]	402	!!gm i.e. use gde3w in argument (pdepw)
[6140]	403
	404
[2528]	405	IF( nn_etau == 1 ) THEN !* penetration below the mixed layer (rn_efr fraction)
[1492]	406	DO jk = 2, jpkm1
[1239]	407	DO jj = 2, jpjm1
	408	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	409	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
[8568]	410	& * MAX(0.,1._wp - 4.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	411	END DO
	412	END DO
[1492]	413	END DO
[2528]	414	ELSEIF( nn_etau == 2 ) THEN !* act only at the base of the mixed layer (jk=nmln) (rn_efr fraction)
[1492]	415	DO jj = 2, jpjm1
	416	DO ji = fs_2, fs_jpim1 ! vector opt.
	417	jk = nmln(ji,jj)
[8215]	418	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
[8568]	419	& * MAX(0.,1._wp - 4.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	420	END DO
[1492]	421	END DO
[2528]	422	ELSEIF( nn_etau == 3 ) THEN !* penetration belox the mixed layer (HF variability)
[1705]	423	DO jk = 2, jpkm1
	424	DO jj = 2, jpjm1
	425	DO ji = fs_2, fs_jpim1 ! vector opt.
	426	ztx2 = utau(ji-1,jj ) + utau(ji,jj)
	427	zty2 = vtau(ji ,jj-1) + vtau(ji,jj)
[4990]	428	ztau = 0.5_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) * tmask(ji,jj,1) ! module of the mean stress
[2528]	429	zdif = taum(ji,jj) - ztau ! mean of modulus - modulus of the mean
	430	zdif = rhftau_scl * MAX( 0._wp, zdif + rhftau_add ) ! apply some modifications...
[8215]	431	en(ji,jj,jk) = en(ji,jj,jk) + zbbrau * zdif * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
[8568]	432	& * MAX(0.,1._wp - 4.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1705]	433	END DO
	434	END DO
	435	END DO
[1239]	436	ENDIF
[1492]	437	!
[8568]	438	IF( ln_timing ) CALL timing_stop('tke_tke')
[3294]	439	!
[1239]	440	END SUBROUTINE tke_tke
	441
[1492]	442
[8215]	443	SUBROUTINE tke_avn( pdepw, p_e3t, p_e3w, p_avm, p_avt )
[1239]	444	!!----------------------------------------------------------------------
[1492]	445	!! * ROUTINE tke_avn *
[1239]	446	!!
[1492]	447	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	448	!!
	449	!! ** Method : At this stage, en, the now TKE, is known (computed in
	450	!! the tke_tke routine). First, the now mixing lenth is
	451	!! computed from en and the strafification (N^2), then the mixings
	452	!! coefficients are computed.
	453	!! - Mixing length : a first evaluation of the mixing lengh
	454	!! scales is:
	455	!! mxl = sqrt(2*en) / N
	456	!! where N is the brunt-vaisala frequency, with a minimum value set
[2528]	457	!! to rmxl_min (rn_mxl0) in the interior (surface) ocean.
[1492]	458	!! The mixing and dissipative length scale are bound as follow :
	459	!! nn_mxl=0 : mxl bounded by the distance to surface and bottom.
	460	!! zmxld = zmxlm = mxl
	461	!! nn_mxl=1 : mxl bounded by the e3w and zmxld = zmxlm = mxl
	462	!! nn_mxl=2 : mxl bounded such that the vertical derivative of mxl is
	463	!! less than 1 (\|d/dz(mxl)\|<1) and zmxld = zmxlm = mxl
	464	!! nn_mxl=3 : mxl is bounded from the surface to the bottom usings
	465	!! \|d/dz(xml)\|<1 to obtain lup, and from the bottom to
	466	!! the surface to obtain ldown. the resulting length
	467	!! scales are:
	468	!! zmxld = sqrt( lup * ldown )
	469	!! zmxlm = min ( lup , ldown )
	470	!! - Vertical eddy viscosity and diffusivity:
	471	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	472	!! avt = max( avmb, pdlr * avm )
	473	!! with pdlr=1 if nn_pdl=0, pdlr=1/pdl=F(Ri) otherwise.
	474	!!
[8215]	475	!! ** Action : - avt, avm : now vertical eddy diffusivity and viscosity (w-point)
[1239]	476	!!----------------------------------------------------------------------
[8215]	477	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pdepw ! depth (w-points)
	478	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: p_e3t, p_e3w ! level thickness (t- & w-points)
	479	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: p_avm, p_avt ! vertical eddy viscosity & diffusivity (w-points)
	480	!
[2715]	481	INTEGER :: ji, jj, jk ! dummy loop indices
[8215]	482	REAL(wp) :: zrn2, zraug, zcoef, zav ! local scalars
	483	REAL(wp) :: zdku, zdkv, zsqen ! - -
	484	REAL(wp) :: zemxl, zemlm, zemlp ! - -
	485	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zmxlm, zmxld
[1239]	486	!!--------------------------------------------------------------------
[3294]	487	!
[8568]	488	IF( ln_timing ) CALL timing_start('tke_avn')
[1239]	489
[1492]	490	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	491	! ! Mixing length
	492	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	493	!
	494	! !* Buoyancy length scale: l=sqrt(2e/n*2)
	495	!
[5120]	496	! initialisation of interior minimum value (avoid a 2d loop with mikt)
[7753]	497	zmxlm(:,:,:) = rmxl_min
	498	zmxld(:,:,:) = rmxl_min
[5120]	499	!
[2528]	500	IF( ln_mxl0 ) THEN ! surface mixing length = F(stress) : l=vkarmn2.e5taum/(rau0*g)
[8215]	501	zraug = vkarmn * 2.e5_wp / ( rau0 * grav )
[4990]	502	DO jj = 2, jpjm1
	503	DO ji = fs_2, fs_jpim1
[5120]	504	zmxlm(ji,jj,1) = MAX( rn_mxl0, zraug * taum(ji,jj) * tmask(ji,jj,1) )
[4990]	505	END DO
	506	END DO
	507	ELSE
[7753]	508	zmxlm(:,:,1) = rn_mxl0
[1239]	509	ENDIF
	510	!
[5120]	511	DO jk = 2, jpkm1 ! interior value : l=sqrt(2*e/n^2)
	512	DO jj = 2, jpjm1
	513	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	514	zrn2 = MAX( rn2(ji,jj,jk), rsmall )
[5836]	515	zmxlm(ji,jj,jk) = MAX( rmxl_min, SQRT( 2._wp * en(ji,jj,jk) / zrn2 ) )
[1239]	516	END DO
	517	END DO
	518	END DO
[1492]	519	!
	520	! !* Physical limits for the mixing length
	521	!
[7753]	522	zmxld(:,:, 1 ) = zmxlm(:,:,1) ! surface set to the minimum value
	523	zmxld(:,:,jpk) = rmxl_min ! last level set to the minimum value
[1492]	524	!
[1239]	525	SELECT CASE ( nn_mxl )
	526	!
[5836]	527	!!gm Not sure of that coding for ISF....
[8215]	528	! where wmask = 0 set zmxlm == p_e3w
[1239]	529	CASE ( 0 ) ! bounded by the distance to surface and bottom
[5120]	530	DO jk = 2, jpkm1
	531	DO jj = 2, jpjm1
	532	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	533	zemxl = MIN( pdepw(ji,jj,jk) - pdepw(ji,jj,mikt(ji,jj)), zmxlm(ji,jj,jk), &
	534	& pdepw(ji,jj,mbkt(ji,jj)+1) - pdepw(ji,jj,jk) )
[5120]	535	! wmask prevent zmxlm = 0 if jk = mikt(ji,jj)
[8215]	536	zmxlm(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN( zmxlm(ji,jj,jk) , p_e3w(ji,jj,jk) ) * (1 - wmask(ji,jj,jk))
	537	zmxld(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN( zmxlm(ji,jj,jk) , p_e3w(ji,jj,jk) ) * (1 - wmask(ji,jj,jk))
[1239]	538	END DO
	539	END DO
	540	END DO
	541	!
	542	CASE ( 1 ) ! bounded by the vertical scale factor
[5120]	543	DO jk = 2, jpkm1
	544	DO jj = 2, jpjm1
	545	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	546	zemxl = MIN( p_e3w(ji,jj,jk), zmxlm(ji,jj,jk) )
[1239]	547	zmxlm(ji,jj,jk) = zemxl
	548	zmxld(ji,jj,jk) = zemxl
	549	END DO
	550	END DO
	551	END DO
	552	!
	553	CASE ( 2 ) ! \|dk[xml]\| bounded by e3t :
[5120]	554	DO jk = 2, jpkm1 ! from the surface to the bottom :
	555	DO jj = 2, jpjm1
	556	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	557	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk-1) + p_e3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
[1239]	558	END DO
[5120]	559	END DO
	560	END DO
	561	DO jk = jpkm1, 2, -1 ! from the bottom to the surface :
	562	DO jj = 2, jpjm1
	563	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	564	zemxl = MIN( zmxlm(ji,jj,jk+1) + p_e3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
[1239]	565	zmxlm(ji,jj,jk) = zemxl
	566	zmxld(ji,jj,jk) = zemxl
	567	END DO
	568	END DO
	569	END DO
	570	!
	571	CASE ( 3 ) ! lup and ldown, \|dk[xml]\| bounded by e3t :
[5120]	572	DO jk = 2, jpkm1 ! from the surface to the bottom : lup
	573	DO jj = 2, jpjm1
	574	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	575	zmxld(ji,jj,jk) = MIN( zmxld(ji,jj,jk-1) + p_e3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
[1239]	576	END DO
[5120]	577	END DO
	578	END DO
	579	DO jk = jpkm1, 2, -1 ! from the bottom to the surface : ldown
	580	DO jj = 2, jpjm1
	581	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	582	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk+1) + p_e3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
[1239]	583	END DO
	584	END DO
	585	END DO
	586	DO jk = 2, jpkm1
	587	DO jj = 2, jpjm1
	588	DO ji = fs_2, fs_jpim1 ! vector opt.
	589	zemlm = MIN ( zmxld(ji,jj,jk), zmxlm(ji,jj,jk) )
	590	zemlp = SQRT( zmxld(ji,jj,jk) * zmxlm(ji,jj,jk) )
	591	zmxlm(ji,jj,jk) = zemlm
	592	zmxld(ji,jj,jk) = zemlp
	593	END DO
	594	END DO
	595	END DO
	596	!
	597	END SELECT
[1492]	598	!
[1239]	599
[1492]	600	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8215]	601	! ! Vertical eddy viscosity and diffusivity (avm and avt)
[1492]	602	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	603	DO jk = 1, jpkm1 !* vertical eddy viscosity & diffivity at w-points
[1239]	604	DO jj = 2, jpjm1
	605	DO ji = fs_2, fs_jpim1 ! vector opt.
	606	zsqen = SQRT( en(ji,jj,jk) )
	607	zav = rn_ediff * zmxlm(ji,jj,jk) * zsqen
[8215]	608	p_avm(ji,jj,jk) = MAX( zav, avmb(jk) ) * wmask(ji,jj,jk)
	609	p_avt(ji,jj,jk) = MAX( zav, avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1239]	610	dissl(ji,jj,jk) = zsqen / zmxld(ji,jj,jk)
	611	END DO
	612	END DO
	613	END DO
[1492]	614	!
	615	!
	616	IF( nn_pdl == 1 ) THEN !* Prandtl number case: update avt
[5120]	617	DO jk = 2, jpkm1
	618	DO jj = 2, jpjm1
	619	DO ji = fs_2, fs_jpim1 ! vector opt.
[8215]	620	p_avt(ji,jj,jk) = MAX( apdlr(ji,jj,jk) * p_avt(ji,jj,jk), avtb_2d(ji,jj) * avtb(jk) ) * tmask(ji,jj,jk)
[1239]	621	END DO
	622	END DO
	623	END DO
	624	ENDIF
	625
	626	IF(ln_ctl) THEN
[8215]	627	CALL prt_ctl( tab3d_1=en , clinfo1=' tke - e: ', tab3d_2=avt, clinfo2=' t: ', ovlap=1, kdim=jpk)
	628	CALL prt_ctl( tab3d_1=avm, clinfo1=' tke - m: ', ovlap=1, kdim=jpk )
[1239]	629	ENDIF
	630	!
[8568]	631	IF( ln_timing ) CALL timing_stop('tke_avn')
[3294]	632	!
[1492]	633	END SUBROUTINE tke_avn
[1239]	634
[1492]	635
[2528]	636	SUBROUTINE zdf_tke_init
[1239]	637	!!----------------------------------------------------------------------
[2528]	638	!! * ROUTINE zdf_tke_init *
[1239]	639	!!
	640	!! ** Purpose : Initialization of the vertical eddy diffivity and
[1492]	641	!! viscosity when using a tke turbulent closure scheme
[1239]	642	!!
[1601]	643	!! ** Method : Read the namzdf_tke namelist and check the parameters
[1492]	644	!! called at the first timestep (nit000)
[1239]	645	!!
[1601]	646	!! ** input : Namlist namzdf_tke
[1239]	647	!!
	648	!! ** Action : Increase by 1 the nstop flag is setting problem encounter
	649	!!----------------------------------------------------------------------
	650	INTEGER :: ji, jj, jk ! dummy loop indices
[4147]	651	INTEGER :: ios
[1239]	652	!!
[2528]	653	NAMELIST/namzdf_tke/ rn_ediff, rn_ediss , rn_ebb , rn_emin , &
	654	& rn_emin0, rn_bshear, nn_mxl , ln_mxl0 , &
[8215]	655	& rn_mxl0 , nn_pdl , ln_drg , ln_lc , rn_lc , &
[2528]	656	& nn_etau , nn_htau , rn_efr
[1239]	657	!!----------------------------------------------------------------------
[2715]	658	!
[4147]	659	REWIND( numnam_ref ) ! Namelist namzdf_tke in reference namelist : Turbulent Kinetic Energy
	660	READ ( numnam_ref, namzdf_tke, IOSTAT = ios, ERR = 901)
	661	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in reference namelist', lwp )
	662
	663	REWIND( numnam_cfg ) ! Namelist namzdf_tke in configuration namelist : Turbulent Kinetic Energy
	664	READ ( numnam_cfg, namzdf_tke, IOSTAT = ios, ERR = 902 )
	665	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in configuration namelist', lwp )
[4624]	666	IF(lwm) WRITE ( numond, namzdf_tke )
[2715]	667	!
[2528]	668	ri_cri = 2._wp / ( 2._wp + rn_ediss / rn_ediff ) ! resulting critical Richardson number
[2715]	669	!
[1492]	670	IF(lwp) THEN !* Control print
[1239]	671	WRITE(numout,*)
[2528]	672	WRITE(numout,*) 'zdf_tke_init : tke turbulent closure scheme - initialisation'
	673	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	674	WRITE(numout,*) ' Namelist namzdf_tke : set tke mixing parameters'
[1705]	675	WRITE(numout,*) ' coef. to compute avt rn_ediff = ', rn_ediff
	676	WRITE(numout,*) ' Kolmogoroff dissipation coef. rn_ediss = ', rn_ediss
	677	WRITE(numout,*) ' tke surface input coef. rn_ebb = ', rn_ebb
	678	WRITE(numout,*) ' minimum value of tke rn_emin = ', rn_emin
	679	WRITE(numout,*) ' surface minimum value of tke rn_emin0 = ', rn_emin0
[8215]	680	WRITE(numout,*) ' prandl number flag nn_pdl = ', nn_pdl
[1705]	681	WRITE(numout,*) ' background shear (>0) rn_bshear = ', rn_bshear
	682	WRITE(numout,*) ' mixing length type nn_mxl = ', nn_mxl
[8215]	683	WRITE(numout,*) ' surface mixing length = F(stress) or not ln_mxl0 = ', ln_mxl0
	684	WRITE(numout,*) ' surface mixing length minimum value rn_mxl0 = ', rn_mxl0
	685	WRITE(numout,*) ' top/bottom friction forcing flag ln_drg = ', ln_drg
	686	WRITE(numout,*) ' Langmuir cells parametrization ln_lc = ', ln_lc
	687	WRITE(numout,*) ' coef to compute vertical velocity of LC rn_lc = ', rn_lc
[1705]	688	WRITE(numout,*) ' test param. to add tke induced by wind nn_etau = ', nn_etau
[8215]	689	WRITE(numout,*) ' type of tke penetration profile nn_htau = ', nn_htau
	690	WRITE(numout,*) ' fraction of TKE that penetrates rn_efr = ', rn_efr
[1239]	691	WRITE(numout,*)
[8215]	692	IF( ln_drg ) THEN
	693	WRITE(numout,*) ' Namelist namdrg_top/_bot: used values:'
	694	WRITE(numout,*) ' top ocean cavity roughness (m) rn_z0(_top)= ', r_z0_top
	695	WRITE(numout,*) ' Bottom seafloor roughness (m) rn_z0(_bot)= ', r_z0_bot
	696	ENDIF
	697	WRITE(numout,*)
	698	WRITE(numout,*)
	699	WRITE(numout,*) ' ==>> critical Richardson nb with your parameters ri_cri = ', ri_cri
	700	WRITE(numout,*)
[1239]	701	ENDIF
[2715]	702	!
[8215]	703	IF( ln_zdfiwm ) THEN ! Internal wave-driven mixing
	704	rn_emin = 1.e-10_wp ! specific values of rn_emin & rmxl_min are used
	705	rmxl_min = 1.e-03_wp ! associated avt minimum = molecular salt diffusivity (10^-9 m2/s)
	706	IF(lwp) WRITE(numout,*) ' Internal wave-driven mixing case: force rn_emin = 1.e-10 and rmxl_min = 1.e-3 '
	707	ELSE ! standard case : associated avt minimum = molecular viscosity (10^-6 m2/s)
	708	rmxl_min = 1.e-6_wp / ( rn_ediff * SQRT( rn_emin ) ) ! resulting minimum length to recover molecular viscosity
	709	IF(lwp) WRITE(numout,*) ' minimum mixing length with your parameters rmxl_min = ', rmxl_min
	710	ENDIF
	711	!
[2715]	712	! ! allocate tke arrays
	713	IF( zdf_tke_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_tke_init : unable to allocate arrays' )
	714	!
[1492]	715	! !* Check of some namelist values
[4990]	716	IF( nn_mxl < 0 .OR. nn_mxl > 3 ) CALL ctl_stop( 'bad flag: nn_mxl is 0, 1 or 2 ' )
	717	IF( nn_pdl < 0 .OR. nn_pdl > 1 ) CALL ctl_stop( 'bad flag: nn_pdl is 0 or 1 ' )
	718	IF( nn_htau < 0 .OR. nn_htau > 1 ) CALL ctl_stop( 'bad flag: nn_htau is 0, 1 or 2 ' )
[5407]	719	IF( nn_etau == 3 .AND. .NOT. ln_cpl ) CALL ctl_stop( 'nn_etau == 3 : HF taum only known in coupled mode' )
[1239]	720
[2528]	721	IF( ln_mxl0 ) THEN
	722	IF(lwp) WRITE(numout,*) ' use a surface mixing length = F(stress) : set rn_mxl0 = rmxl_min'
	723	rn_mxl0 = rmxl_min
	724	ENDIF
	725
[1492]	726	IF( nn_etau == 2 ) CALL zdf_mxl( nit000 ) ! Initialization of nmln
[1239]	727
[1492]	728	! !* depth of penetration of surface tke
	729	IF( nn_etau /= 0 ) THEN
[1601]	730	SELECT CASE( nn_htau ) ! Choice of the depth of penetration
[2528]	731	CASE( 0 ) ! constant depth penetration (here 10 meters)
[7753]	732	htau(:,:) = 10._wp
[2528]	733	CASE( 1 ) ! F(latitude) : 0.5m to 30m poleward of 40 degrees
[7753]	734	htau(:,:) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
[1492]	735	END SELECT
	736	ENDIF
	737	! !* set vertical eddy coef. to the background value
[1239]	738	DO jk = 1, jpk
[8215]	739	avt(:,:,jk) = avtb(jk) * wmask(:,:,jk)
	740	avm(:,:,jk) = avmb(jk) * wmask(:,:,jk)
[1239]	741	END DO
[7753]	742	dissl(:,:,:) = 1.e-12_wp
[2715]	743	!
	744	CALL tke_rst( nit000, 'READ' ) !* read or initialize all required files
[1239]	745	!
[2528]	746	END SUBROUTINE zdf_tke_init
[1239]	747
	748
[1531]	749	SUBROUTINE tke_rst( kt, cdrw )
[8215]	750	!!---------------------------------------------------------------------
	751	!! * ROUTINE tke_rst *
	752	!!
	753	!! ** Purpose : Read or write TKE file (en) in restart file
	754	!!
	755	!! ** Method : use of IOM library
	756	!! if the restart does not contain TKE, en is either
	757	!! set to rn_emin or recomputed
	758	!!----------------------------------------------------------------------
	759	INTEGER , INTENT(in) :: kt ! ocean time-step
	760	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
	761	!
	762	INTEGER :: jit, jk ! dummy loop indices
	763	INTEGER :: id1, id2, id3, id4 ! local integers
	764	!!----------------------------------------------------------------------
	765	!
	766	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
	767	! ! ---------------
	768	IF( ln_rstart ) THEN !* Read the restart file
	769	id1 = iom_varid( numror, 'en' , ldstop = .FALSE. )
	770	id2 = iom_varid( numror, 'avt_k', ldstop = .FALSE. )
	771	id3 = iom_varid( numror, 'avm_k', ldstop = .FALSE. )
	772	id4 = iom_varid( numror, 'dissl', ldstop = .FALSE. )
	773	!
	774	IF( MIN( id1, id2, id3, id4 ) > 0 ) THEN ! fields exist
	775	CALL iom_get( numror, jpdom_autoglo, 'en', en )
	776	CALL iom_get( numror, jpdom_autoglo, 'avt_k', avt_k )
	777	CALL iom_get( numror, jpdom_autoglo, 'avm_k', avm_k )
	778	CALL iom_get( numror, jpdom_autoglo, 'dissl', dissl )
	779	ELSE ! start TKE from rest
	780	IF(lwp) WRITE(numout,*) ' ==>> previous run without TKE scheme, set en to background values'
	781	en(:,:,:) = rn_emin * wmask(:,:,:)
	782	! avt_k, avm_k already set to the background value in zdf_phy_init
	783	ENDIF
	784	ELSE !* Start from rest
	785	IF(lwp) WRITE(numout,*) ' ==>> start from rest: set en to the background value'
	786	en(:,:,:) = rn_emin * wmask(:,:,:)
	787	! avt_k, avm_k already set to the background value in zdf_phy_init
	788	ENDIF
	789	!
	790	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
	791	! ! -------------------
	792	IF(lwp) WRITE(numout,*) '---- tke-rst ----'
	793	CALL iom_rstput( kt, nitrst, numrow, 'en' , en )
	794	CALL iom_rstput( kt, nitrst, numrow, 'avt_k', avt_k )
	795	CALL iom_rstput( kt, nitrst, numrow, 'avm_k', avm_k )
	796	CALL iom_rstput( kt, nitrst, numrow, 'dissl', dissl )
	797	!
	798	ENDIF
	799	!
[1531]	800	END SUBROUTINE tke_rst
[1239]	801
	802	!!======================================================================
[1531]	803	END MODULE zdftke

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