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zdftke.F90 in branches/2017/dev_merge_2017/NEMOGCM/NEMO/OPA_SRC/ZDF – NEMO

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source: branches/2017/dev_merge_2017/NEMOGCM/NEMO/OPA_SRC/ZDF/zdftke.F90 @ 9090

Last change on this file since 9090 was 9019, checked in by timgraham, 6 years ago
Merge of dev_CNRS_2017 into branch
Property svn:keywords set to `Id`
File size: 42.7 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
[9019]	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	!!----------------------------------------------------------------------
[9019]	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
[9019]	45	USE zdfdrg ! vertical physics: top/bottom drag coef.
[2528]	46	USE zdfmxl ! vertical physics: mixed layer
[9019]	47	!
[1492]	48	USE in_out_manager ! I/O manager
	49	USE iom ! I/O manager library
[2715]	50	USE lib_mpp ! MPP library
[9019]	51	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
	52	USE prtctl ! Print control
[3294]	53	USE timing ! Timing
[3625]	54	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[1239]	55
	56	IMPLICIT NONE
	57	PRIVATE
	58
[2528]	59	PUBLIC zdf_tke ! routine called in step module
	60	PUBLIC zdf_tke_init ! routine called in opa module
	61	PUBLIC tke_rst ! routine called in step module
[1239]	62
[4147]	63	! !! Namelist namzdf_tke
	64	LOGICAL :: ln_mxl0 ! mixing length scale surface value as function of wind stress or not
	65	INTEGER :: nn_mxl ! type of mixing length (=0/1/2/3)
	66	REAL(wp) :: rn_mxl0 ! surface min value of mixing length (kappaz_o=0.40.1 m) [m]
	67	INTEGER :: nn_pdl ! Prandtl number or not (ratio avt/avm) (=0/1)
	68	REAL(wp) :: rn_ediff ! coefficient for avt: avt=rn_ediffmxlsqrt(e)
	69	REAL(wp) :: rn_ediss ! coefficient of the Kolmogoroff dissipation
	70	REAL(wp) :: rn_ebb ! coefficient of the surface input of tke
	71	REAL(wp) :: rn_emin ! minimum value of tke [m2/s2]
	72	REAL(wp) :: rn_emin0 ! surface minimum value of tke [m2/s2]
	73	REAL(wp) :: rn_bshear ! background shear (>0) currently a numerical threshold (do not change it)
[9019]	74	LOGICAL :: ln_drg ! top/bottom friction forcing flag
[4147]	75	INTEGER :: nn_etau ! type of depth penetration of surface tke (=0/1/2/3)
[9019]	76	INTEGER :: nn_htau ! type of tke profile of penetration (=0/1)
	77	REAL(wp) :: rn_efr ! fraction of TKE surface value which penetrates in the ocean
[4147]	78	LOGICAL :: ln_lc ! Langmuir cells (LC) as a source term of TKE or not
[9019]	79	REAL(wp) :: rn_lc ! coef to compute vertical velocity of Langmuir cells
[1239]	80
[4147]	81	REAL(wp) :: ri_cri ! critic Richardson number (deduced from rn_ediff and rn_ediss values)
	82	REAL(wp) :: rmxl_min ! minimum mixing length value (deduced from rn_ediff and rn_emin values) [m]
[2528]	83	REAL(wp) :: rhftau_add = 1.e-3_wp ! add offset applied to HF part of taum (nn_etau=3)
	84	REAL(wp) :: rhftau_scl = 1.0_wp ! scale factor applied to HF part of taum (nn_etau=3)
[1239]	85
[9019]	86	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: htau ! depth of tke penetration (nn_htau)
	87	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dissl ! now mixing lenght of dissipation
	88	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: apdlr ! now mixing lenght of dissipation
[1492]	89
[1239]	90	!! * Substitutions
	91	# include "vectopt_loop_substitute.h90"
	92	!!----------------------------------------------------------------------
[5836]	93	!! NEMO/OPA 3.7 , NEMO Consortium (2015)
[2528]	94	!! $Id$
	95	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[1239]	96	!!----------------------------------------------------------------------
	97	CONTAINS
	98
[2715]	99	INTEGER FUNCTION zdf_tke_alloc()
	100	!!----------------------------------------------------------------------
	101	!! * FUNCTION zdf_tke_alloc *
	102	!!----------------------------------------------------------------------
[9019]	103	ALLOCATE( htau(jpi,jpj) , dissl(jpi,jpj,jpk) , apdlr(jpi,jpj,jpk) , STAT= zdf_tke_alloc )
	104	!
[2715]	105	IF( lk_mpp ) CALL mpp_sum ( zdf_tke_alloc )
	106	IF( zdf_tke_alloc /= 0 ) CALL ctl_warn('zdf_tke_alloc: failed to allocate arrays')
	107	!
	108	END FUNCTION zdf_tke_alloc
	109
	110
[9019]	111	SUBROUTINE zdf_tke( kt, p_sh2, p_avm, p_avt )
[1239]	112	!!----------------------------------------------------------------------
[1531]	113	!! * ROUTINE zdf_tke *
[1239]	114	!!
	115	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
[1492]	116	!! coefficients using a turbulent closure scheme (TKE).
[1239]	117	!!
[1492]	118	!! ** Method : The time evolution of the turbulent kinetic energy (tke)
	119	!! is computed from a prognostic equation :
	120	!! d(en)/dt = avm (d(u)/dz)**2 ! shear production
	121	!! + d( avm d(en)/dz )/dz ! diffusion of tke
	122	!! + avt N^2 ! stratif. destruc.
	123	!! - rn_ediss / emxl en**(2/3) ! Kolmogoroff dissipation
[1239]	124	!! with the boundary conditions:
[1695]	125	!! surface: en = max( rn_emin0, rn_ebb * taum )
[1239]	126	!! bottom : en = rn_emin
[1492]	127	!! The associated critical Richardson number is: ri_cri = 2/(2+rn_ediss/rn_ediff)
	128	!!
	129	!! The now Turbulent kinetic energy is computed using the following
	130	!! time stepping: implicit for vertical diffusion term, linearized semi
	131	!! implicit for kolmogoroff dissipation term, and explicit forward for
	132	!! both buoyancy and shear production terms. Therefore a tridiagonal
	133	!! linear system is solved. Note that buoyancy and shear terms are
	134	!! discretized in a energy conserving form (Bruchard 2002).
	135	!!
	136	!! The dissipative and mixing length scale are computed from en and
	137	!! the stratification (see tke_avn)
	138	!!
	139	!! The now vertical eddy vicosity and diffusivity coefficients are
	140	!! given by:
	141	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	142	!! avt = max( avmb, pdl * avm )
[1239]	143	!! eav = max( avmb, avm )
[1492]	144	!! where pdl, the inverse of the Prandtl number is 1 if nn_pdl=0 and
	145	!! given by an empirical funtion of the localRichardson number if nn_pdl=1
[1239]	146	!!
	147	!! ** Action : compute en (now turbulent kinetic energy)
[9019]	148	!! update avt, avm (before vertical eddy coef.)
[1239]	149	!!
	150	!! References : Gaspar et al., JGR, 1990,
	151	!! Blanke and Delecluse, JPO, 1991
	152	!! Mellor and Blumberg, JPO 2004
	153	!! Axell, JGR, 2002
[1492]	154	!! Bruchard OM 2002
[1239]	155	!!----------------------------------------------------------------------
[9019]	156	INTEGER , INTENT(in ) :: kt ! ocean time step
	157	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: p_sh2 ! shear production term
	158	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: p_avm, p_avt ! momentum and tracer Kz (w-points)
[1492]	159	!!----------------------------------------------------------------------
[1481]	160	!
[9019]	161	CALL tke_tke( gdepw_n, e3t_n, e3w_n, p_sh2, p_avm, p_avt ) ! now tke (en)
[5656]	162	!
[9019]	163	CALL tke_avn( gdepw_n, e3t_n, e3w_n, p_avm, p_avt ) ! now avt, avm, dissl
[3632]	164	!
[5656]	165	END SUBROUTINE zdf_tke
[1239]	166
[1492]	167
[9019]	168	SUBROUTINE tke_tke( pdepw, p_e3t, p_e3w, p_sh2, p_avm, p_avt )
[1239]	169	!!----------------------------------------------------------------------
[1492]	170	!! * ROUTINE tke_tke *
	171	!!
	172	!! ** Purpose : Compute the now Turbulente Kinetic Energy (TKE)
	173	!!
	174	!! ** Method : - TKE surface boundary condition
[2528]	175	!! - source term due to Langmuir cells (Axell JGR 2002) (ln_lc=T)
[9019]	176	!! - source term due to shear (= Kz dz[Ub] * dz[Un] )
[1492]	177	!! - Now TKE : resolution of the TKE equation by inverting
	178	!! a tridiagonal linear system by a "methode de chasse"
	179	!! - increase TKE due to surface and internal wave breaking
[9019]	180	!! NB: when sea-ice is present, both LC parameterization
	181	!! and TKE penetration are turned off when the ice fraction
	182	!! is smaller than 0.25
[1492]	183	!!
	184	!! ** Action : - en : now turbulent kinetic energy)
[1239]	185	!! ---------------------------------------------------------------------
[9019]	186	USE zdf_oce , ONLY : en ! ocean vertical physics
	187	!!
	188	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdepw ! depth of w-points
	189	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_e3t, p_e3w ! level thickness (t- & w-points)
	190	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_sh2 ! shear production term
	191	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_avm, p_avt ! vertical eddy viscosity & diffusivity (w-points)
	192	!
	193	INTEGER :: ji, jj, jk ! dummy loop arguments
	194	REAL(wp) :: zetop, zebot, zmsku, zmskv ! local scalars
	195	REAL(wp) :: zrhoa = 1.22 ! Air density kg/m3
	196	REAL(wp) :: zcdrag = 1.5e-3 ! drag coefficient
	197	REAL(wp) :: zbbrau, zri ! local scalars
	198	REAL(wp) :: zfact1, zfact2, zfact3 ! - -
	199	REAL(wp) :: ztx2 , zty2 , zcof ! - -
	200	REAL(wp) :: ztau , zdif ! - -
	201	REAL(wp) :: zus , zwlc , zind ! - -
	202	REAL(wp) :: zzd_up, zzd_lw ! - -
	203	INTEGER , DIMENSION(jpi,jpj) :: imlc
	204	REAL(wp), DIMENSION(jpi,jpj) :: zhlc
	205	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zpelc, zdiag, zd_up, zd_lw
[1239]	206	!!--------------------------------------------------------------------
[1492]	207	!
[9019]	208	IF( ln_timing ) CALL timing_start('tke_tke')
[3294]	209	!
[1695]	210	zbbrau = rn_ebb / rau0 ! Local constant initialisation
[2528]	211	zfact1 = -.5_wp * rdt
	212	zfact2 = 1.5_wp * rdt * rn_ediss
	213	zfact3 = 0.5_wp * rn_ediss
[1492]	214	!
	215	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[9019]	216	! ! Surface/top/bottom boundary condition on tke
[1492]	217	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[9019]	218
	219	DO jj = 2, jpjm1 ! en(1) = rn_ebb taum / rau0 (min value rn_emin0)
	220	DO ji = fs_2, fs_jpim1 ! vector opt.
	221	en(ji,jj,1) = MAX( rn_emin0, zbbrau * taum(ji,jj) ) * tmask(ji,jj,1)
	222	END DO
	223	END DO
[5120]	224	IF ( ln_isfcav ) THEN
	225	DO jj = 2, jpjm1 ! en(mikt(ji,jj)) = rn_emin
	226	DO ji = fs_2, fs_jpim1 ! vector opt.
[5836]	227	en(ji,jj,mikt(ji,jj)) = rn_emin * tmask(ji,jj,1)
[5120]	228	END DO
	229	END DO
[9019]	230	ENDIF
	231	!
[1492]	232	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	233	! ! Bottom boundary condition on tke
	234	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1719]	235	!
[9019]	236	! en(bot) = (ebb0/rau0)0.5sqrt(u_botfr^2+v_botfr^2) (min value rn_emin)
	237	! where ebb0 does not includes surface wave enhancement (i.e. ebb0=3.75)
	238	! Note that stress averaged is done using an wet-only calculation of u and v at t-point like in zdfsh2
[1492]	239	!
[9019]	240	IF( ln_drg ) THEN !== friction used as top/bottom boundary condition on TKE
	241	!
	242	DO jj = 2, jpjm1 ! bottom friction
	243	DO ji = fs_2, fs_jpim1 ! vector opt.
	244	zmsku = ( 2. - umask(ji-1,jj,mbkt(ji,jj)) * umask(ji,jj,mbkt(ji,jj)) )
	245	zmskv = ( 2. - vmask(ji,jj-1,mbkt(ji,jj)) * vmask(ji,jj,mbkt(ji,jj)) )
	246	! ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000. (CAUTION CdU<0)
	247	zebot = - 0.001875_wp * rCdU_bot(ji,jj) * SQRT( ( zmsku( ub(ji,jj,mbkt(ji,jj))+ub(ji-1,jj,mbkt(ji,jj)) ) )*2 &
	248	& + ( zmskv( vb(ji,jj,mbkt(ji,jj))+vb(ji,jj-1,mbkt(ji,jj)) ) )*2 )
	249	en(ji,jj,mbkt(ji,jj)+1) = MAX( zebot, rn_emin ) * ssmask(ji,jj)
	250	END DO
	251	END DO
	252	IF( ln_isfcav ) THEN ! top friction
	253	DO jj = 2, jpjm1
	254	DO ji = fs_2, fs_jpim1 ! vector opt.
	255	zmsku = ( 2. - umask(ji-1,jj,mikt(ji,jj)) * umask(ji,jj,mikt(ji,jj)) )
	256	zmskv = ( 2. - vmask(ji,jj-1,mikt(ji,jj)) * vmask(ji,jj,mikt(ji,jj)) )
	257	! ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000. (CAUTION CdU<0)
	258	zetop = - 0.001875_wp * rCdU_top(ji,jj) * SQRT( ( zmsku( ub(ji,jj,mikt(ji,jj))+ub(ji-1,jj,mikt(ji,jj)) ) )*2 &
	259	& + ( zmskv( vb(ji,jj,mikt(ji,jj))+vb(ji,jj-1,mikt(ji,jj)) ) )*2 )
	260	en(ji,jj,mikt(ji,jj)) = MAX( zetop, rn_emin ) * (1._wp - tmask(ji,jj,1)) ! masked at ocean surface
	261	END DO
	262	END DO
	263	ENDIF
	264	!
	265	ENDIF
	266	!
[1492]	267	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[9019]	268	IF( ln_lc ) THEN ! Langmuir circulation source term added to tke ! (Axell JGR 2002)
[1492]	269	! !>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
[1239]	270	!
[1492]	271	! !* total energy produce by LC : cumulative sum over jk
[9019]	272	zpelc(:,:,1) = MAX( rn2b(:,:,1), 0._wp ) * pdepw(:,:,1) * p_e3w(:,:,1)
[1239]	273	DO jk = 2, jpk
[9019]	274	zpelc(:,:,jk) = zpelc(:,:,jk-1) + MAX( rn2b(:,:,jk), 0._wp ) * pdepw(:,:,jk) * p_e3w(:,:,jk)
[1239]	275	END DO
[1492]	276	! !* finite Langmuir Circulation depth
[1705]	277	zcof = 0.5 * 0.016 * 0.016 / ( zrhoa * zcdrag )
[7753]	278	imlc(:,:) = mbkt(:,:) + 1 ! Initialization to the number of w ocean point (=2 over land)
[1239]	279	DO jk = jpkm1, 2, -1
[1492]	280	DO jj = 1, jpj ! Last w-level at which zpelc>=0.5usus
	281	DO ji = 1, jpi ! with us=0.016*wind(starting from jpk-1)
[1705]	282	zus = zcof * taum(ji,jj)
[1239]	283	IF( zpelc(ji,jj,jk) > zus ) imlc(ji,jj) = jk
	284	END DO
	285	END DO
	286	END DO
[1492]	287	! ! finite LC depth
	288	DO jj = 1, jpj
[1239]	289	DO ji = 1, jpi
[9019]	290	zhlc(ji,jj) = pdepw(ji,jj,imlc(ji,jj))
[1239]	291	END DO
	292	END DO
[1705]	293	zcof = 0.016 / SQRT( zrhoa * zcdrag )
[1492]	294	DO jk = 2, jpkm1 !* TKE Langmuir circulation source term added to en
[1239]	295	DO jj = 2, jpjm1
	296	DO ji = fs_2, fs_jpim1 ! vector opt.
[1705]	297	zus = zcof * SQRT( taum(ji,jj) ) ! Stokes drift
[1492]	298	! ! vertical velocity due to LC
[9019]	299	zind = 0.5 - SIGN( 0.5, pdepw(ji,jj,jk) - zhlc(ji,jj) )
	300	zwlc = zind * rn_lc * zus * SIN( rpi * pdepw(ji,jj,jk) / zhlc(ji,jj) )
[1492]	301	! ! TKE Langmuir circulation source term
[9019]	302	en(ji,jj,jk) = en(ji,jj,jk) + rdt * MAX(0.,1._wp - 4.fr_i(ji,jj) ) ( zwlc * zwlc * zwlc ) &
[6497]	303	& / zhlc(ji,jj) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	304	END DO
	305	END DO
	306	END DO
	307	!
	308	ENDIF
[1492]	309	!
	310	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	311	! ! Now Turbulent kinetic energy (output in en)
	312	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	313	! ! Resolution of a tridiagonal linear system by a "methode de chasse"
	314	! ! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
	315	! ! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
	316	!
[9019]	317	IF( nn_pdl == 1 ) THEN !* Prandtl number = F( Ri )
[5656]	318	DO jk = 2, jpkm1
	319	DO jj = 2, jpjm1
[9019]	320	DO ji = 2, jpim1
	321	! ! local Richardson number
	322	zri = MAX( rn2b(ji,jj,jk), 0._wp ) * p_avm(ji,jj,jk) / ( p_sh2(ji,jj,jk) + rn_bshear )
	323	! ! inverse of Prandtl number
[5656]	324	apdlr(ji,jj,jk) = MAX( 0.1_wp, ri_cri / MAX( ri_cri , zri ) )
	325	END DO
	326	END DO
	327	END DO
	328	ENDIF
[5836]	329	!
[5120]	330	DO jk = 2, jpkm1 !* Matrix and right hand side in en
	331	DO jj = 2, jpjm1
	332	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	333	zcof = zfact1 * tmask(ji,jj,jk)
[9019]	334	! ! A minimum of 2.e-5 m2/s is imposed on TKE vertical
	335	! ! eddy coefficient (ensure numerical stability)
	336	zzd_up = zcof * MAX( p_avm(ji,jj,jk+1) + p_avm(ji,jj,jk ) , 2.e-5_wp ) & ! upper diagonal
	337	& / ( p_e3t(ji,jj,jk ) * p_e3w(ji,jj,jk ) )
	338	zzd_lw = zcof * MAX( p_avm(ji,jj,jk ) + p_avm(ji,jj,jk-1) , 2.e-5_wp ) & ! lower diagonal
	339	& / ( p_e3t(ji,jj,jk-1) * p_e3w(ji,jj,jk ) )
[5656]	340	!
[1492]	341	zd_up(ji,jj,jk) = zzd_up ! Matrix (zdiag, zd_up, zd_lw)
	342	zd_lw(ji,jj,jk) = zzd_lw
[9019]	343	zdiag(ji,jj,jk) = 1._wp - zzd_lw - zzd_up + zfact2 * dissl(ji,jj,jk) * wmask(ji,jj,jk)
[1239]	344	!
[1492]	345	! ! right hand side in en
[9019]	346	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( p_sh2(ji,jj,jk) & ! shear
	347	& - p_avt(ji,jj,jk) * rn2(ji,jj,jk) & ! stratification
	348	& + zfact3 * dissl(ji,jj,jk) * en(ji,jj,jk) & ! dissipation
	349	& ) * wmask(ji,jj,jk)
[1239]	350	END DO
[5120]	351	END DO
	352	END DO
	353	! !* Matrix inversion from level 2 (tke prescribed at level 1)
	354	DO jk = 3, jpkm1 ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
	355	DO jj = 2, jpjm1
	356	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	357	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]	358	END DO
[5120]	359	END DO
	360	END DO
[5836]	361	DO jj = 2, jpjm1 ! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
[5120]	362	DO ji = fs_2, fs_jpim1 ! vector opt.
	363	zd_lw(ji,jj,2) = en(ji,jj,2) - zd_lw(ji,jj,2) * en(ji,jj,1) ! Surface boudary conditions on tke
	364	END DO
	365	END DO
	366	DO jk = 3, jpkm1
	367	DO jj = 2, jpjm1
	368	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	369	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]	370	END DO
[5120]	371	END DO
	372	END DO
[5836]	373	DO jj = 2, jpjm1 ! thrid recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
[5120]	374	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	375	en(ji,jj,jpkm1) = zd_lw(ji,jj,jpkm1) / zdiag(ji,jj,jpkm1)
[5120]	376	END DO
	377	END DO
	378	DO jk = jpk-2, 2, -1
	379	DO jj = 2, jpjm1
	380	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	381	en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
[1239]	382	END DO
[5120]	383	END DO
	384	END DO
	385	DO jk = 2, jpkm1 ! set the minimum value of tke
	386	DO jj = 2, jpjm1
	387	DO ji = fs_2, fs_jpim1 ! vector opt.
	388	en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin ) * wmask(ji,jj,jk)
[1239]	389	END DO
	390	END DO
	391	END DO
[9019]	392	!
[1492]	393	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	394	! ! TKE due to surface and internal wave breaking
	395	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[6140]	396	!!gm BUG : in the exp remove the depth of ssh !!!
[9019]	397	!!gm i.e. use gde3w in argument (pdepw)
[6140]	398
	399
[2528]	400	IF( nn_etau == 1 ) THEN !* penetration below the mixed layer (rn_efr fraction)
[1492]	401	DO jk = 2, jpkm1
[1239]	402	DO jj = 2, jpjm1
	403	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	404	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
	405	& * MAX(0.,1._wp - 4.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	406	END DO
	407	END DO
[1492]	408	END DO
[2528]	409	ELSEIF( nn_etau == 2 ) THEN !* act only at the base of the mixed layer (jk=nmln) (rn_efr fraction)
[1492]	410	DO jj = 2, jpjm1
	411	DO ji = fs_2, fs_jpim1 ! vector opt.
	412	jk = nmln(ji,jj)
[9019]	413	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
	414	& * MAX(0.,1._wp - 4.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	415	END DO
[1492]	416	END DO
[2528]	417	ELSEIF( nn_etau == 3 ) THEN !* penetration belox the mixed layer (HF variability)
[1705]	418	DO jk = 2, jpkm1
	419	DO jj = 2, jpjm1
	420	DO ji = fs_2, fs_jpim1 ! vector opt.
	421	ztx2 = utau(ji-1,jj ) + utau(ji,jj)
	422	zty2 = vtau(ji ,jj-1) + vtau(ji,jj)
[4990]	423	ztau = 0.5_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) * tmask(ji,jj,1) ! module of the mean stress
[2528]	424	zdif = taum(ji,jj) - ztau ! mean of modulus - modulus of the mean
	425	zdif = rhftau_scl * MAX( 0._wp, zdif + rhftau_add ) ! apply some modifications...
[9019]	426	en(ji,jj,jk) = en(ji,jj,jk) + zbbrau * zdif * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
	427	& * MAX(0.,1._wp - 4.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1705]	428	END DO
	429	END DO
	430	END DO
[1239]	431	ENDIF
[1492]	432	!
[9019]	433	IF( ln_timing ) CALL timing_stop('tke_tke')
[2715]	434	!
[1239]	435	END SUBROUTINE tke_tke
	436
[1492]	437
[9019]	438	SUBROUTINE tke_avn( pdepw, p_e3t, p_e3w, p_avm, p_avt )
[1239]	439	!!----------------------------------------------------------------------
[1492]	440	!! * ROUTINE tke_avn *
[1239]	441	!!
[1492]	442	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	443	!!
	444	!! ** Method : At this stage, en, the now TKE, is known (computed in
	445	!! the tke_tke routine). First, the now mixing lenth is
	446	!! computed from en and the strafification (N^2), then the mixings
	447	!! coefficients are computed.
	448	!! - Mixing length : a first evaluation of the mixing lengh
	449	!! scales is:
	450	!! mxl = sqrt(2*en) / N
	451	!! where N is the brunt-vaisala frequency, with a minimum value set
[2528]	452	!! to rmxl_min (rn_mxl0) in the interior (surface) ocean.
[1492]	453	!! The mixing and dissipative length scale are bound as follow :
	454	!! nn_mxl=0 : mxl bounded by the distance to surface and bottom.
	455	!! zmxld = zmxlm = mxl
	456	!! nn_mxl=1 : mxl bounded by the e3w and zmxld = zmxlm = mxl
	457	!! nn_mxl=2 : mxl bounded such that the vertical derivative of mxl is
	458	!! less than 1 (\|d/dz(mxl)\|<1) and zmxld = zmxlm = mxl
	459	!! nn_mxl=3 : mxl is bounded from the surface to the bottom usings
	460	!! \|d/dz(xml)\|<1 to obtain lup, and from the bottom to
	461	!! the surface to obtain ldown. the resulting length
	462	!! scales are:
	463	!! zmxld = sqrt( lup * ldown )
	464	!! zmxlm = min ( lup , ldown )
	465	!! - Vertical eddy viscosity and diffusivity:
	466	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	467	!! avt = max( avmb, pdlr * avm )
	468	!! with pdlr=1 if nn_pdl=0, pdlr=1/pdl=F(Ri) otherwise.
	469	!!
[9019]	470	!! ** Action : - avt, avm : now vertical eddy diffusivity and viscosity (w-point)
[1239]	471	!!----------------------------------------------------------------------
[9019]	472	USE zdf_oce , ONLY : en, avtb, avmb, avtb_2d ! ocean vertical physics
	473	!!
	474	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pdepw ! depth (w-points)
	475	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: p_e3t, p_e3w ! level thickness (t- & w-points)
	476	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: p_avm, p_avt ! vertical eddy viscosity & diffusivity (w-points)
	477	!
[2715]	478	INTEGER :: ji, jj, jk ! dummy loop indices
[9019]	479	REAL(wp) :: zrn2, zraug, zcoef, zav ! local scalars
	480	REAL(wp) :: zdku, zdkv, zsqen ! - -
	481	REAL(wp) :: zemxl, zemlm, zemlp ! - -
	482	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zmxlm, zmxld ! 3D workspace
[1239]	483	!!--------------------------------------------------------------------
[3294]	484	!
[9019]	485	IF( ln_timing ) CALL timing_start('tke_avn')
	486	!
[1492]	487	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	488	! ! Mixing length
	489	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	490	!
	491	! !* Buoyancy length scale: l=sqrt(2e/n*2)
	492	!
[5120]	493	! initialisation of interior minimum value (avoid a 2d loop with mikt)
[7753]	494	zmxlm(:,:,:) = rmxl_min
	495	zmxld(:,:,:) = rmxl_min
[5120]	496	!
[2528]	497	IF( ln_mxl0 ) THEN ! surface mixing length = F(stress) : l=vkarmn2.e5taum/(rau0*g)
[9019]	498	zraug = vkarmn * 2.e5_wp / ( rau0 * grav )
[4990]	499	DO jj = 2, jpjm1
	500	DO ji = fs_2, fs_jpim1
[5120]	501	zmxlm(ji,jj,1) = MAX( rn_mxl0, zraug * taum(ji,jj) * tmask(ji,jj,1) )
[4990]	502	END DO
	503	END DO
	504	ELSE
[7753]	505	zmxlm(:,:,1) = rn_mxl0
[1239]	506	ENDIF
	507	!
[5120]	508	DO jk = 2, jpkm1 ! interior value : l=sqrt(2*e/n^2)
	509	DO jj = 2, jpjm1
	510	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	511	zrn2 = MAX( rn2(ji,jj,jk), rsmall )
[5836]	512	zmxlm(ji,jj,jk) = MAX( rmxl_min, SQRT( 2._wp * en(ji,jj,jk) / zrn2 ) )
[1239]	513	END DO
	514	END DO
	515	END DO
[1492]	516	!
	517	! !* Physical limits for the mixing length
	518	!
[7753]	519	zmxld(:,:, 1 ) = zmxlm(:,:,1) ! surface set to the minimum value
	520	zmxld(:,:,jpk) = rmxl_min ! last level set to the minimum value
[1492]	521	!
[1239]	522	SELECT CASE ( nn_mxl )
	523	!
[5836]	524	!!gm Not sure of that coding for ISF....
[9019]	525	! where wmask = 0 set zmxlm == p_e3w
[1239]	526	CASE ( 0 ) ! bounded by the distance to surface and bottom
[5120]	527	DO jk = 2, jpkm1
	528	DO jj = 2, jpjm1
	529	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	530	zemxl = MIN( pdepw(ji,jj,jk) - pdepw(ji,jj,mikt(ji,jj)), zmxlm(ji,jj,jk), &
	531	& pdepw(ji,jj,mbkt(ji,jj)+1) - pdepw(ji,jj,jk) )
[5120]	532	! wmask prevent zmxlm = 0 if jk = mikt(ji,jj)
[9019]	533	zmxlm(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN( zmxlm(ji,jj,jk) , p_e3w(ji,jj,jk) ) * (1 - wmask(ji,jj,jk))
	534	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]	535	END DO
	536	END DO
	537	END DO
	538	!
	539	CASE ( 1 ) ! bounded by the vertical scale factor
[5120]	540	DO jk = 2, jpkm1
	541	DO jj = 2, jpjm1
	542	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	543	zemxl = MIN( p_e3w(ji,jj,jk), zmxlm(ji,jj,jk) )
[1239]	544	zmxlm(ji,jj,jk) = zemxl
	545	zmxld(ji,jj,jk) = zemxl
	546	END DO
	547	END DO
	548	END DO
	549	!
	550	CASE ( 2 ) ! \|dk[xml]\| bounded by e3t :
[5120]	551	DO jk = 2, jpkm1 ! from the surface to the bottom :
	552	DO jj = 2, jpjm1
	553	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	554	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk-1) + p_e3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
[1239]	555	END DO
[5120]	556	END DO
	557	END DO
	558	DO jk = jpkm1, 2, -1 ! from the bottom to the surface :
	559	DO jj = 2, jpjm1
	560	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	561	zemxl = MIN( zmxlm(ji,jj,jk+1) + p_e3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
[1239]	562	zmxlm(ji,jj,jk) = zemxl
	563	zmxld(ji,jj,jk) = zemxl
	564	END DO
	565	END DO
	566	END DO
	567	!
	568	CASE ( 3 ) ! lup and ldown, \|dk[xml]\| bounded by e3t :
[5120]	569	DO jk = 2, jpkm1 ! from the surface to the bottom : lup
	570	DO jj = 2, jpjm1
	571	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	572	zmxld(ji,jj,jk) = MIN( zmxld(ji,jj,jk-1) + p_e3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
[1239]	573	END DO
[5120]	574	END DO
	575	END DO
	576	DO jk = jpkm1, 2, -1 ! from the bottom to the surface : ldown
	577	DO jj = 2, jpjm1
	578	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	579	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk+1) + p_e3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
[1239]	580	END DO
	581	END DO
	582	END DO
	583	DO jk = 2, jpkm1
	584	DO jj = 2, jpjm1
	585	DO ji = fs_2, fs_jpim1 ! vector opt.
	586	zemlm = MIN ( zmxld(ji,jj,jk), zmxlm(ji,jj,jk) )
	587	zemlp = SQRT( zmxld(ji,jj,jk) * zmxlm(ji,jj,jk) )
	588	zmxlm(ji,jj,jk) = zemlm
	589	zmxld(ji,jj,jk) = zemlp
	590	END DO
	591	END DO
	592	END DO
	593	!
	594	END SELECT
[1492]	595	!
	596	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[9019]	597	! ! Vertical eddy viscosity and diffusivity (avm and avt)
[1492]	598	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	599	DO jk = 1, jpkm1 !* vertical eddy viscosity & diffivity at w-points
[1239]	600	DO jj = 2, jpjm1
	601	DO ji = fs_2, fs_jpim1 ! vector opt.
	602	zsqen = SQRT( en(ji,jj,jk) )
	603	zav = rn_ediff * zmxlm(ji,jj,jk) * zsqen
[9019]	604	p_avm(ji,jj,jk) = MAX( zav, avmb(jk) ) * wmask(ji,jj,jk)
	605	p_avt(ji,jj,jk) = MAX( zav, avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1239]	606	dissl(ji,jj,jk) = zsqen / zmxld(ji,jj,jk)
	607	END DO
	608	END DO
	609	END DO
[1492]	610	!
	611	!
	612	IF( nn_pdl == 1 ) THEN !* Prandtl number case: update avt
[5120]	613	DO jk = 2, jpkm1
	614	DO jj = 2, jpjm1
	615	DO ji = fs_2, fs_jpim1 ! vector opt.
[9019]	616	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]	617	END DO
	618	END DO
	619	END DO
	620	ENDIF
[9019]	621	!
[1239]	622	IF(ln_ctl) THEN
[9019]	623	CALL prt_ctl( tab3d_1=en , clinfo1=' tke - e: ', tab3d_2=p_avt, clinfo2=' t: ', ovlap=1, kdim=jpk)
	624	CALL prt_ctl( tab3d_1=p_avm, clinfo1=' tke - m: ', ovlap=1, kdim=jpk )
[1239]	625	ENDIF
	626	!
[9019]	627	IF( ln_timing ) CALL timing_stop('tke_avn')
[3294]	628	!
[1492]	629	END SUBROUTINE tke_avn
[1239]	630
[1492]	631
[2528]	632	SUBROUTINE zdf_tke_init
[1239]	633	!!----------------------------------------------------------------------
[2528]	634	!! * ROUTINE zdf_tke_init *
[1239]	635	!!
	636	!! ** Purpose : Initialization of the vertical eddy diffivity and
[1492]	637	!! viscosity when using a tke turbulent closure scheme
[1239]	638	!!
[1601]	639	!! ** Method : Read the namzdf_tke namelist and check the parameters
[1492]	640	!! called at the first timestep (nit000)
[1239]	641	!!
[1601]	642	!! ** input : Namlist namzdf_tke
[1239]	643	!!
	644	!! ** Action : Increase by 1 the nstop flag is setting problem encounter
	645	!!----------------------------------------------------------------------
[9019]	646	USE zdf_oce , ONLY : ln_zdfiwm ! Internal Wave Mixing flag
	647	!!
[1239]	648	INTEGER :: ji, jj, jk ! dummy loop indices
[4147]	649	INTEGER :: ios
[1239]	650	!!
[9019]	651	NAMELIST/namzdf_tke/ rn_ediff, rn_ediss , rn_ebb , rn_emin , &
	652	& rn_emin0, rn_bshear, nn_mxl , ln_mxl0 , &
	653	& rn_mxl0 , nn_pdl , ln_drg , ln_lc , rn_lc, &
[2528]	654	& nn_etau , nn_htau , rn_efr
[1239]	655	!!----------------------------------------------------------------------
[2715]	656	!
[4147]	657	REWIND( numnam_ref ) ! Namelist namzdf_tke in reference namelist : Turbulent Kinetic Energy
	658	READ ( numnam_ref, namzdf_tke, IOSTAT = ios, ERR = 901)
	659	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in reference namelist', lwp )
	660
	661	REWIND( numnam_cfg ) ! Namelist namzdf_tke in configuration namelist : Turbulent Kinetic Energy
	662	READ ( numnam_cfg, namzdf_tke, IOSTAT = ios, ERR = 902 )
	663	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in configuration namelist', lwp )
[4624]	664	IF(lwm) WRITE ( numond, namzdf_tke )
[2715]	665	!
[2528]	666	ri_cri = 2._wp / ( 2._wp + rn_ediss / rn_ediff ) ! resulting critical Richardson number
[2715]	667	!
[1492]	668	IF(lwp) THEN !* Control print
[1239]	669	WRITE(numout,*)
[2528]	670	WRITE(numout,*) 'zdf_tke_init : tke turbulent closure scheme - initialisation'
	671	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	672	WRITE(numout,*) ' Namelist namzdf_tke : set tke mixing parameters'
[1705]	673	WRITE(numout,*) ' coef. to compute avt rn_ediff = ', rn_ediff
	674	WRITE(numout,*) ' Kolmogoroff dissipation coef. rn_ediss = ', rn_ediss
	675	WRITE(numout,*) ' tke surface input coef. rn_ebb = ', rn_ebb
	676	WRITE(numout,*) ' minimum value of tke rn_emin = ', rn_emin
	677	WRITE(numout,*) ' surface minimum value of tke rn_emin0 = ', rn_emin0
[9019]	678	WRITE(numout,*) ' prandl number flag nn_pdl = ', nn_pdl
[1705]	679	WRITE(numout,*) ' background shear (>0) rn_bshear = ', rn_bshear
	680	WRITE(numout,*) ' mixing length type nn_mxl = ', nn_mxl
[9019]	681	WRITE(numout,*) ' surface mixing length = F(stress) or not ln_mxl0 = ', ln_mxl0
	682	WRITE(numout,*) ' surface mixing length minimum value rn_mxl0 = ', rn_mxl0
	683	WRITE(numout,*) ' top/bottom friction forcing flag ln_drg = ', ln_drg
	684	WRITE(numout,*) ' Langmuir cells parametrization ln_lc = ', ln_lc
	685	WRITE(numout,*) ' coef to compute vertical velocity of LC rn_lc = ', rn_lc
[1705]	686	WRITE(numout,*) ' test param. to add tke induced by wind nn_etau = ', nn_etau
[9019]	687	WRITE(numout,*) ' type of tke penetration profile nn_htau = ', nn_htau
	688	WRITE(numout,*) ' fraction of TKE that penetrates rn_efr = ', rn_efr
[1239]	689	WRITE(numout,*)
[9019]	690	IF( ln_drg ) THEN
	691	WRITE(numout,*) ' Namelist namdrg_top/_bot: used values:'
	692	WRITE(numout,*) ' top ocean cavity roughness (m) rn_z0(_top)= ', r_z0_top
	693	WRITE(numout,*) ' Bottom seafloor roughness (m) rn_z0(_bot)= ', r_z0_bot
	694	ENDIF
	695	WRITE(numout,*)
	696	WRITE(numout,*)
	697	WRITE(numout,*) ' ==>> critical Richardson nb with your parameters ri_cri = ', ri_cri
	698	WRITE(numout,*)
[1239]	699	ENDIF
[2715]	700	!
[9019]	701	IF( ln_zdfiwm ) THEN ! Internal wave-driven mixing
	702	rn_emin = 1.e-10_wp ! specific values of rn_emin & rmxl_min are used
	703	rmxl_min = 1.e-03_wp ! associated avt minimum = molecular salt diffusivity (10^-9 m2/s)
	704	IF(lwp) WRITE(numout,*) ' Internal wave-driven mixing case: force rn_emin = 1.e-10 and rmxl_min = 1.e-3 '
	705	ELSE ! standard case : associated avt minimum = molecular viscosity (10^-6 m2/s)
	706	rmxl_min = 1.e-6_wp / ( rn_ediff * SQRT( rn_emin ) ) ! resulting minimum length to recover molecular viscosity
	707	IF(lwp) WRITE(numout,*) ' minimum mixing length with your parameters rmxl_min = ', rmxl_min
	708	ENDIF
	709	!
[2715]	710	! ! allocate tke arrays
	711	IF( zdf_tke_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_tke_init : unable to allocate arrays' )
	712	!
[1492]	713	! !* Check of some namelist values
[4990]	714	IF( nn_mxl < 0 .OR. nn_mxl > 3 ) CALL ctl_stop( 'bad flag: nn_mxl is 0, 1 or 2 ' )
	715	IF( nn_pdl < 0 .OR. nn_pdl > 1 ) CALL ctl_stop( 'bad flag: nn_pdl is 0 or 1 ' )
	716	IF( nn_htau < 0 .OR. nn_htau > 1 ) CALL ctl_stop( 'bad flag: nn_htau is 0, 1 or 2 ' )
[5407]	717	IF( nn_etau == 3 .AND. .NOT. ln_cpl ) CALL ctl_stop( 'nn_etau == 3 : HF taum only known in coupled mode' )
[9019]	718	!
[2528]	719	IF( ln_mxl0 ) THEN
	720	IF(lwp) WRITE(numout,*) ' use a surface mixing length = F(stress) : set rn_mxl0 = rmxl_min'
	721	rn_mxl0 = rmxl_min
	722	ENDIF
	723
[1492]	724	IF( nn_etau == 2 ) CALL zdf_mxl( nit000 ) ! Initialization of nmln
[1239]	725
[1492]	726	! !* depth of penetration of surface tke
	727	IF( nn_etau /= 0 ) THEN
[1601]	728	SELECT CASE( nn_htau ) ! Choice of the depth of penetration
[2528]	729	CASE( 0 ) ! constant depth penetration (here 10 meters)
[7753]	730	htau(:,:) = 10._wp
[2528]	731	CASE( 1 ) ! F(latitude) : 0.5m to 30m poleward of 40 degrees
[7753]	732	htau(:,:) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
[1492]	733	END SELECT
	734	ENDIF
[9019]	735	! !* read or initialize all required files
	736	CALL tke_rst( nit000, 'READ' ) ! (en, avt_k, avm_k, dissl)
[1239]	737	!
[2528]	738	END SUBROUTINE zdf_tke_init
[1239]	739
	740
[1531]	741	SUBROUTINE tke_rst( kt, cdrw )
[9019]	742	!!---------------------------------------------------------------------
	743	!! * ROUTINE tke_rst *
	744	!!
	745	!! ** Purpose : Read or write TKE file (en) in restart file
	746	!!
	747	!! ** Method : use of IOM library
	748	!! if the restart does not contain TKE, en is either
	749	!! set to rn_emin or recomputed
	750	!!----------------------------------------------------------------------
	751	USE zdf_oce , ONLY : en, avt_k, avm_k ! ocean vertical physics
	752	!!
	753	INTEGER , INTENT(in) :: kt ! ocean time-step
	754	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
	755	!
	756	INTEGER :: jit, jk ! dummy loop indices
	757	INTEGER :: id1, id2, id3, id4 ! local integers
	758	!!----------------------------------------------------------------------
	759	!
	760	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
	761	! ! ---------------
	762	IF( ln_rstart ) THEN !* Read the restart file
	763	id1 = iom_varid( numror, 'en' , ldstop = .FALSE. )
	764	id2 = iom_varid( numror, 'avt_k', ldstop = .FALSE. )
	765	id3 = iom_varid( numror, 'avm_k', ldstop = .FALSE. )
	766	id4 = iom_varid( numror, 'dissl', ldstop = .FALSE. )
	767	!
	768	IF( MIN( id1, id2, id3, id4 ) > 0 ) THEN ! fields exist
	769	CALL iom_get( numror, jpdom_autoglo, 'en', en )
	770	CALL iom_get( numror, jpdom_autoglo, 'avt_k', avt_k )
	771	CALL iom_get( numror, jpdom_autoglo, 'avm_k', avm_k )
	772	CALL iom_get( numror, jpdom_autoglo, 'dissl', dissl )
	773	ELSE ! start TKE from rest
	774	IF(lwp) WRITE(numout,*) ' ==>> previous run without TKE scheme, set en to background values'
	775	en (:,:,:) = rn_emin * wmask(:,:,:)
	776	dissl(:,:,:) = 1.e-12_wp
	777	! avt_k, avm_k already set to the background value in zdf_phy_init
	778	ENDIF
	779	ELSE !* Start from rest
	780	IF(lwp) WRITE(numout,*) ' ==>> start from rest: set en to the background value'
	781	en (:,:,:) = rn_emin * wmask(:,:,:)
	782	dissl(:,:,:) = 1.e-12_wp
	783	! avt_k, avm_k already set to the background value in zdf_phy_init
	784	ENDIF
	785	!
	786	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
	787	! ! -------------------
	788	IF(lwp) WRITE(numout,*) '---- tke-rst ----'
	789	CALL iom_rstput( kt, nitrst, numrow, 'en' , en )
	790	CALL iom_rstput( kt, nitrst, numrow, 'avt_k', avt_k )
	791	CALL iom_rstput( kt, nitrst, numrow, 'avm_k', avm_k )
	792	CALL iom_rstput( kt, nitrst, numrow, 'dissl', dissl )
	793	!
	794	ENDIF
	795	!
[1531]	796	END SUBROUTINE tke_rst
[1239]	797
	798	!!======================================================================
[1531]	799	END MODULE zdftke

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