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zdftke.F90 in branches/2017/dev_r7881_HPC09_ZDF/NEMOGCM/NEMO/OPA_SRC/ZDF – NEMO

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source: branches/2017/dev_r7881_HPC09_ZDF/NEMOGCM/NEMO/OPA_SRC/ZDF/zdftke.F90 @ 8143

Last change on this file since 8143 was 8143, checked in by gm, 7 years ago
#1880 (HPC-09) - step-7: top/bottom drag computed at T-points, zdfbfr.F90 replaced by zdfdrg.F90 + changes in namelist
Property svn:keywords set to `Id`
File size: 42.8 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
[7990]	29	!! 4.0 ! 2017-04 (G. Madec) remove CPP ddm key & avm at t-point only
[8143]	30	!! - ! 2017-05 (G. Madec) add top/bottom friction as boundary condition (ln_drg)
[1239]	31	!!----------------------------------------------------------------------
[7953]	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
[8093]	46	USE zdfdrg ! vertical physics: top/bottom drag coef.
[2528]	47	USE zdfmxl ! vertical physics: mixed layer
[8093]	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
[8093]	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)
[8143]	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)
[8143]	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
[8143]	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
[8093]	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	!!----------------------------------------------------------------------
[7991]	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
[8093]	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)
[7990]	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	!!----------------------------------------------------------------------
[8093]	161	INTEGER , INTENT(in ) :: kt ! ocean time step
	162	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: p_sh2 ! shear production term
	163	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: p_avm, p_avt ! momentum and tracer Kz (w-points)
[1492]	164	!!----------------------------------------------------------------------
[1481]	165	!
[5656]	166	#if defined key_agrif
	167	! interpolation parent grid => child grid for avm_k ( ex : at west border: update column 1 and 2)
	168	IF( .NOT.Agrif_Root() ) CALL Agrif_Tke
	169	#endif
	170	!
[8093]	171	CALL tke_tke( gdepw_n, e3t_n, e3w_n, p_sh2, p_avm, p_avt ) ! now tke (en)
[3632]	172	!
[8093]	173	CALL tke_avn( gdepw_n, e3t_n, e3w_n, p_avm, p_avt ) ! now avt, avm, dissl
[1492]	174	!
[5656]	175	#if defined key_agrif
	176	! Update child grid f => parent grid
	177	IF( .NOT.Agrif_Root() ) CALL Agrif_Update_Tke( kt ) ! children only
	178	#endif
[7990]	179	!
[5656]	180	END SUBROUTINE zdf_tke
[1239]	181
[1492]	182
[8093]	183	SUBROUTINE tke_tke( pdepw, p_e3t, p_e3w, p_sh2 &
	184	& , p_avm, p_avt )
[1239]	185	!!----------------------------------------------------------------------
[1492]	186	!! * ROUTINE tke_tke *
	187	!!
	188	!! ** Purpose : Compute the now Turbulente Kinetic Energy (TKE)
	189	!!
	190	!! ** Method : - TKE surface boundary condition
[2528]	191	!! - source term due to Langmuir cells (Axell JGR 2002) (ln_lc=T)
[7990]	192	!! - source term due to shear (= Kz dz[Ub] * dz[Un] )
[1492]	193	!! - Now TKE : resolution of the TKE equation by inverting
	194	!! a tridiagonal linear system by a "methode de chasse"
	195	!! - increase TKE due to surface and internal wave breaking
	196	!!
	197	!! ** Action : - en : now turbulent kinetic energy)
[1239]	198	!! ---------------------------------------------------------------------
[8093]	199	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdepw ! depth of w-points
	200	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_e3t, p_e3w ! level thickness (t- & w-points)
	201	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_sh2 ! shear production term
	202	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: p_avm, p_avt ! vertical eddy viscosity & diffusivity (w-points)
	203	!
	204	INTEGER :: ji, jj, jk ! dummy loop arguments
[8143]	205	REAL(wp) :: zetop, zebot, zmsku, zmskv ! local scalars
	206	REAL(wp) :: zrhoa = 1.22 ! Air density kg/m3
	207	REAL(wp) :: zcdrag = 1.5e-3 ! drag coefficient
	208	REAL(wp) :: zbbrau, zri ! local scalars
	209	REAL(wp) :: zfact1, zfact2, zfact3 ! - -
	210	REAL(wp) :: ztx2 , zty2 , zcof ! - -
	211	REAL(wp) :: ztau , zdif ! - -
	212	REAL(wp) :: zus , zwlc , zind ! - -
	213	REAL(wp) :: zzd_up, zzd_lw ! - -
[8093]	214	INTEGER , DIMENSION(jpi,jpj) :: imlc
	215	REAL(wp), DIMENSION(jpi,jpj) :: zhlc
	216	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zpelc, zdiag, zd_up, zd_lw
[1239]	217	!!--------------------------------------------------------------------
[1492]	218	!
[3294]	219	IF( nn_timing == 1 ) CALL timing_start('tke_tke')
	220	!
[1695]	221	zbbrau = rn_ebb / rau0 ! Local constant initialisation
[2528]	222	zfact1 = -.5_wp * rdt
	223	zfact2 = 1.5_wp * rdt * rn_ediss
	224	zfact3 = 0.5_wp * rn_ediss
[1492]	225	!
[5120]	226	!
[1492]	227	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8143]	228	! ! Surface/top/bottom boundary condition on tke
[1492]	229	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8143]	230
	231	DO jj = 2, jpjm1 ! en(1) = rn_ebb taum / rau0 (min value rn_emin0)
	232	DO ji = fs_2, fs_jpim1 ! vector opt.
	233	en(ji,jj,1) = MAX( rn_emin0, zbbrau * taum(ji,jj) ) * tmask(ji,jj,1)
	234	END DO
	235	END DO
[5120]	236	IF ( ln_isfcav ) THEN
	237	DO jj = 2, jpjm1 ! en(mikt(ji,jj)) = rn_emin
	238	DO ji = fs_2, fs_jpim1 ! vector opt.
[5836]	239	en(ji,jj,mikt(ji,jj)) = rn_emin * tmask(ji,jj,1)
[5120]	240	END DO
	241	END DO
[8143]	242	ENDIF
[2528]	243
[1492]	244	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	245	! ! Bottom boundary condition on tke
	246	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1719]	247	!
[8143]	248	! en(bot) = (ebb0/rau0)0.5sqrt(u_botfr^2+v_botfr^2) (min value rn_emin)
	249	! where ebb0 does not includes surface wave enhancement (i.e. ebb0=3.75)
	250	! Note that stress averaged is done using an wet-only calculation of u and v at t-point like in zdfsh2
[1492]	251	!
[8143]	252	IF( ln_drg ) THEN !== friction used as top/bottom boundary condition on TKE
	253	!
	254	DO jj = 2, jpjm1 ! bottom friction
	255	DO ji = fs_2, fs_jpim1 ! vector opt.
	256	zmsku = ( 2. - umask(ji-1,jj,mbkt(ji,jj)) * umask(ji,jj,mbkt(ji,jj)) )
	257	zmskv = ( 2. - vmask(ji,jj-1,mbkt(ji,jj)) * vmask(ji,jj,mbkt(ji,jj)) )
	258	! ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000. (CAUTION CdU<0)
	259	zebot = - 0.001875_wp * rCdU_bot(ji,jj) * SQRT( ( zmsku( ub(ji,jj,mbkt(ji,jj))+ub(ji-1,jj,mbkt(ji,jj)) ) )*2 &
	260	& + ( zmskv( vb(ji,jj,mbkt(ji,jj))+vb(ji,jj-1,mbkt(ji,jj)) ) )*2 )
	261	en(ji,jj,mbkt(ji,jj)+1) = MAX( zebot, rn_emin ) * ssmask(ji,jj)
	262	END DO
	263	END DO
	264	IF( ln_isfcav ) THEN ! top friction
	265	DO jj = 2, jpjm1
	266	DO ji = fs_2, fs_jpim1 ! vector opt.
	267	zmsku = ( 2. - umask(ji-1,jj,mikt(ji,jj)) * umask(ji,jj,mikt(ji,jj)) )
	268	zmskv = ( 2. - vmask(ji,jj-1,mikt(ji,jj)) * vmask(ji,jj,mikt(ji,jj)) )
	269	! ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000. (CAUTION CdU<0)
	270	zetop = - 0.001875_wp * rCdU_top(ji,jj) * SQRT( ( zmsku( ub(ji,jj,mikt(ji,jj))+ub(ji-1,jj,mikt(ji,jj)) ) )*2 &
	271	& + ( zmskv( vb(ji,jj,mikt(ji,jj))+vb(ji,jj-1,mikt(ji,jj)) ) )*2 )
	272	en(ji,jj,mikt(ji,jj)) = MAX( zetop, rn_emin ) * (1._wp - tmask(ji,jj,1)) ! masked at ocean surface
	273	END DO
	274	END DO
	275	ENDIF
	276	!
	277	ENDIF
	278	!
[1492]	279	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[8093]	280	IF( ln_lc ) THEN ! Langmuir circulation source term added to tke ! (Axell JGR 2002)
[1492]	281	! !>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
[1239]	282	!
[1492]	283	! !* total energy produce by LC : cumulative sum over jk
[8093]	284	zpelc(:,:,1) = MAX( rn2b(:,:,1), 0._wp ) * pdepw(:,:,1) * p_e3w(:,:,1)
[1239]	285	DO jk = 2, jpk
[8093]	286	zpelc(:,:,jk) = zpelc(:,:,jk-1) + MAX( rn2b(:,:,jk), 0._wp ) * pdepw(:,:,jk) * p_e3w(:,:,jk)
[1239]	287	END DO
[1492]	288	! !* finite Langmuir Circulation depth
[1705]	289	zcof = 0.5 * 0.016 * 0.016 / ( zrhoa * zcdrag )
[7753]	290	imlc(:,:) = mbkt(:,:) + 1 ! Initialization to the number of w ocean point (=2 over land)
[1239]	291	DO jk = jpkm1, 2, -1
[1492]	292	DO jj = 1, jpj ! Last w-level at which zpelc>=0.5usus
	293	DO ji = 1, jpi ! with us=0.016*wind(starting from jpk-1)
[1705]	294	zus = zcof * taum(ji,jj)
[1239]	295	IF( zpelc(ji,jj,jk) > zus ) imlc(ji,jj) = jk
	296	END DO
	297	END DO
	298	END DO
[1492]	299	! ! finite LC depth
	300	DO jj = 1, jpj
[1239]	301	DO ji = 1, jpi
[8093]	302	zhlc(ji,jj) = pdepw(ji,jj,imlc(ji,jj))
[1239]	303	END DO
	304	END DO
[1705]	305	zcof = 0.016 / SQRT( zrhoa * zcdrag )
[1492]	306	DO jk = 2, jpkm1 !* TKE Langmuir circulation source term added to en
[1239]	307	DO jj = 2, jpjm1
	308	DO ji = fs_2, fs_jpim1 ! vector opt.
[1705]	309	zus = zcof * SQRT( taum(ji,jj) ) ! Stokes drift
[1492]	310	! ! vertical velocity due to LC
[8093]	311	zind = 0.5 - SIGN( 0.5, pdepw(ji,jj,jk) - zhlc(ji,jj) )
	312	zwlc = zind * rn_lc * zus * SIN( rpi * pdepw(ji,jj,jk) / zhlc(ji,jj) )
[1492]	313	! ! TKE Langmuir circulation source term
[7813]	314	en(ji,jj,jk) = en(ji,jj,jk) + rdt * MAX(0.,1._wp - 2.fr_i(ji,jj) ) ( zwlc * zwlc * zwlc ) &
[6497]	315	& / zhlc(ji,jj) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	316	END DO
	317	END DO
	318	END DO
	319	!
	320	ENDIF
[1492]	321	!
	322	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	323	! ! Now Turbulent kinetic energy (output in en)
	324	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	325	! ! Resolution of a tridiagonal linear system by a "methode de chasse"
	326	! ! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
	327	! ! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
	328	!
[7991]	329	IF( nn_pdl == 1 ) THEN !* Prandtl number = F( Ri )
[5656]	330	DO jk = 2, jpkm1
	331	DO jj = 2, jpjm1
[7991]	332	DO ji = 2, jpim1
	333	! ! local Richardson number
[8093]	334	zri = MAX( rn2b(ji,jj,jk), 0._wp ) * p_avm(ji,jj,jk) / ( p_sh2(ji,jj,jk) + rn_bshear )
[7991]	335	! ! inverse of Prandtl number
[5656]	336	apdlr(ji,jj,jk) = MAX( 0.1_wp, ri_cri / MAX( ri_cri , zri ) )
	337	END DO
	338	END DO
	339	END DO
	340	ENDIF
[5836]	341	!
[5120]	342	DO jk = 2, jpkm1 !* Matrix and right hand side in en
	343	DO jj = 2, jpjm1
	344	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	345	zcof = zfact1 * tmask(ji,jj,jk)
[7953]	346	! ! A minimum of 2.e-5 m2/s is imposed on TKE vertical
	347	! ! eddy coefficient (ensure numerical stability)
[8093]	348	zzd_up = zcof * MAX( p_avm(ji,jj,jk+1) + p_avm(ji,jj,jk ) , 2.e-5_wp ) & ! upper diagonal
	349	& / ( p_e3t(ji,jj,jk ) * p_e3w(ji,jj,jk ) )
	350	zzd_lw = zcof * MAX( p_avm(ji,jj,jk ) + p_avm(ji,jj,jk-1) , 2.e-5_wp ) & ! lower diagonal
	351	& / ( p_e3t(ji,jj,jk-1) * p_e3w(ji,jj,jk ) )
[7953]	352	!
[1492]	353	zd_up(ji,jj,jk) = zzd_up ! Matrix (zdiag, zd_up, zd_lw)
	354	zd_lw(ji,jj,jk) = zzd_lw
[7991]	355	zdiag(ji,jj,jk) = 1._wp - zzd_lw - zzd_up + zfact2 * dissl(ji,jj,jk) * wmask(ji,jj,jk)
[1239]	356	!
[1492]	357	! ! right hand side in en
[8093]	358	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( p_sh2(ji,jj,jk) & ! shear
	359	& - p_avt(ji,jj,jk) * rn2(ji,jj,jk) & ! stratification
[7991]	360	& + zfact3 * dissl(ji,jj,jk) * en(ji,jj,jk) & ! dissipation
	361	& ) * wmask(ji,jj,jk)
[1239]	362	END DO
[5120]	363	END DO
	364	END DO
	365	! !* Matrix inversion from level 2 (tke prescribed at level 1)
	366	DO jk = 3, jpkm1 ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
	367	DO jj = 2, jpjm1
	368	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	369	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]	370	END DO
[5120]	371	END DO
	372	END DO
[5836]	373	DO jj = 2, jpjm1 ! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
[5120]	374	DO ji = fs_2, fs_jpim1 ! vector opt.
	375	zd_lw(ji,jj,2) = en(ji,jj,2) - zd_lw(ji,jj,2) * en(ji,jj,1) ! Surface boudary conditions on tke
	376	END DO
	377	END DO
	378	DO jk = 3, jpkm1
	379	DO jj = 2, jpjm1
	380	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	381	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]	382	END DO
[5120]	383	END DO
	384	END DO
[5836]	385	DO jj = 2, jpjm1 ! thrid recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
[5120]	386	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	387	en(ji,jj,jpkm1) = zd_lw(ji,jj,jpkm1) / zdiag(ji,jj,jpkm1)
[5120]	388	END DO
	389	END DO
	390	DO jk = jpk-2, 2, -1
	391	DO jj = 2, jpjm1
	392	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	393	en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
[1239]	394	END DO
[5120]	395	END DO
	396	END DO
	397	DO jk = 2, jpkm1 ! set the minimum value of tke
	398	DO jj = 2, jpjm1
	399	DO ji = fs_2, fs_jpim1 ! vector opt.
	400	en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin ) * wmask(ji,jj,jk)
[1239]	401	END DO
	402	END DO
	403	END DO
	404
[1492]	405	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	406	! ! TKE due to surface and internal wave breaking
	407	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[6140]	408	!!gm BUG : in the exp remove the depth of ssh !!!
[8143]	409	!!gm i.e. use gde3w in argument (pdepw)
[6140]	410
	411
[2528]	412	IF( nn_etau == 1 ) THEN !* penetration below the mixed layer (rn_efr fraction)
[1492]	413	DO jk = 2, jpkm1
[1239]	414	DO jj = 2, jpjm1
	415	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	416	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
[7813]	417	& * MAX(0.,1._wp - 2.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	418	END DO
	419	END DO
[1492]	420	END DO
[2528]	421	ELSEIF( nn_etau == 2 ) THEN !* act only at the base of the mixed layer (jk=nmln) (rn_efr fraction)
[1492]	422	DO jj = 2, jpjm1
	423	DO ji = fs_2, fs_jpim1 ! vector opt.
	424	jk = nmln(ji,jj)
[8093]	425	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
[7813]	426	& * MAX(0.,1._wp - 2.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	427	END DO
[1492]	428	END DO
[2528]	429	ELSEIF( nn_etau == 3 ) THEN !* penetration belox the mixed layer (HF variability)
[1705]	430	DO jk = 2, jpkm1
	431	DO jj = 2, jpjm1
	432	DO ji = fs_2, fs_jpim1 ! vector opt.
	433	ztx2 = utau(ji-1,jj ) + utau(ji,jj)
	434	zty2 = vtau(ji ,jj-1) + vtau(ji,jj)
[4990]	435	ztau = 0.5_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) * tmask(ji,jj,1) ! module of the mean stress
[2528]	436	zdif = taum(ji,jj) - ztau ! mean of modulus - modulus of the mean
	437	zdif = rhftau_scl * MAX( 0._wp, zdif + rhftau_add ) ! apply some modifications...
[8093]	438	en(ji,jj,jk) = en(ji,jj,jk) + zbbrau * zdif * EXP( -pdepw(ji,jj,jk) / htau(ji,jj) ) &
[7813]	439	& * MAX(0.,1._wp - 2.fr_i(ji,jj) ) wmask(ji,jj,jk) * tmask(ji,jj,1)
[1705]	440	END DO
	441	END DO
	442	END DO
[1239]	443	ENDIF
[1492]	444	!
[3294]	445	IF( nn_timing == 1 ) CALL timing_stop('tke_tke')
	446	!
[1239]	447	END SUBROUTINE tke_tke
	448
[1492]	449
[8093]	450	SUBROUTINE tke_avn( pdepw, p_e3t, p_e3w, p_avm, p_avt )
[1239]	451	!!----------------------------------------------------------------------
[1492]	452	!! * ROUTINE tke_avn *
[1239]	453	!!
[1492]	454	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	455	!!
	456	!! ** Method : At this stage, en, the now TKE, is known (computed in
	457	!! the tke_tke routine). First, the now mixing lenth is
	458	!! computed from en and the strafification (N^2), then the mixings
	459	!! coefficients are computed.
	460	!! - Mixing length : a first evaluation of the mixing lengh
	461	!! scales is:
	462	!! mxl = sqrt(2*en) / N
	463	!! where N is the brunt-vaisala frequency, with a minimum value set
[2528]	464	!! to rmxl_min (rn_mxl0) in the interior (surface) ocean.
[1492]	465	!! The mixing and dissipative length scale are bound as follow :
	466	!! nn_mxl=0 : mxl bounded by the distance to surface and bottom.
	467	!! zmxld = zmxlm = mxl
	468	!! nn_mxl=1 : mxl bounded by the e3w and zmxld = zmxlm = mxl
	469	!! nn_mxl=2 : mxl bounded such that the vertical derivative of mxl is
	470	!! less than 1 (\|d/dz(mxl)\|<1) and zmxld = zmxlm = mxl
	471	!! nn_mxl=3 : mxl is bounded from the surface to the bottom usings
	472	!! \|d/dz(xml)\|<1 to obtain lup, and from the bottom to
	473	!! the surface to obtain ldown. the resulting length
	474	!! scales are:
	475	!! zmxld = sqrt( lup * ldown )
	476	!! zmxlm = min ( lup , ldown )
	477	!! - Vertical eddy viscosity and diffusivity:
	478	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	479	!! avt = max( avmb, pdlr * avm )
	480	!! with pdlr=1 if nn_pdl=0, pdlr=1/pdl=F(Ri) otherwise.
	481	!!
[7990]	482	!! ** Action : - avt, avm : now vertical eddy diffusivity and viscosity (w-point)
[1239]	483	!!----------------------------------------------------------------------
[8093]	484	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pdepw ! depth (w-points)
	485	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: p_e3t, p_e3w ! level thickness (t- & w-points)
	486	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: p_avm, p_avt ! vertical eddy viscosity & diffusivity (w-points)
	487	!
[2715]	488	INTEGER :: ji, jj, jk ! dummy loop indices
[7990]	489	REAL(wp) :: zrn2, zraug, zcoef, zav ! local scalars
	490	REAL(wp) :: zdku, zdkv, zsqen ! - -
	491	REAL(wp) :: zemxl, zemlm, zemlp ! - -
[8093]	492	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zmxlm, zmxld
[1239]	493	!!--------------------------------------------------------------------
[3294]	494	!
	495	IF( nn_timing == 1 ) CALL timing_start('tke_avn')
[1239]	496
[1492]	497	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	498	! ! Mixing length
	499	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	500	!
	501	! !* Buoyancy length scale: l=sqrt(2e/n*2)
	502	!
[5120]	503	! initialisation of interior minimum value (avoid a 2d loop with mikt)
[7753]	504	zmxlm(:,:,:) = rmxl_min
	505	zmxld(:,:,:) = rmxl_min
[5120]	506	!
[2528]	507	IF( ln_mxl0 ) THEN ! surface mixing length = F(stress) : l=vkarmn2.e5taum/(rau0*g)
[8093]	508	zraug = vkarmn * 2.e5_wp / ( rau0 * grav )
[4990]	509	DO jj = 2, jpjm1
	510	DO ji = fs_2, fs_jpim1
[5120]	511	zmxlm(ji,jj,1) = MAX( rn_mxl0, zraug * taum(ji,jj) * tmask(ji,jj,1) )
[4990]	512	END DO
	513	END DO
	514	ELSE
[7753]	515	zmxlm(:,:,1) = rn_mxl0
[1239]	516	ENDIF
	517	!
[5120]	518	DO jk = 2, jpkm1 ! interior value : l=sqrt(2*e/n^2)
	519	DO jj = 2, jpjm1
	520	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	521	zrn2 = MAX( rn2(ji,jj,jk), rsmall )
[5836]	522	zmxlm(ji,jj,jk) = MAX( rmxl_min, SQRT( 2._wp * en(ji,jj,jk) / zrn2 ) )
[1239]	523	END DO
	524	END DO
	525	END DO
[1492]	526	!
	527	! !* Physical limits for the mixing length
	528	!
[7753]	529	zmxld(:,:, 1 ) = zmxlm(:,:,1) ! surface set to the minimum value
	530	zmxld(:,:,jpk) = rmxl_min ! last level set to the minimum value
[1492]	531	!
[1239]	532	SELECT CASE ( nn_mxl )
	533	!
[5836]	534	!!gm Not sure of that coding for ISF....
[8093]	535	! where wmask = 0 set zmxlm == p_e3w
[1239]	536	CASE ( 0 ) ! bounded by the distance to surface and bottom
[5120]	537	DO jk = 2, jpkm1
	538	DO jj = 2, jpjm1
	539	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	540	zemxl = MIN( pdepw(ji,jj,jk) - pdepw(ji,jj,mikt(ji,jj)), zmxlm(ji,jj,jk), &
	541	& pdepw(ji,jj,mbkt(ji,jj)+1) - pdepw(ji,jj,jk) )
[5120]	542	! wmask prevent zmxlm = 0 if jk = mikt(ji,jj)
[8093]	543	zmxlm(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN( zmxlm(ji,jj,jk) , p_e3w(ji,jj,jk) ) * (1 - wmask(ji,jj,jk))
	544	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]	545	END DO
	546	END DO
	547	END DO
	548	!
	549	CASE ( 1 ) ! bounded by the vertical scale factor
[5120]	550	DO jk = 2, jpkm1
	551	DO jj = 2, jpjm1
	552	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	553	zemxl = MIN( p_e3w(ji,jj,jk), zmxlm(ji,jj,jk) )
[1239]	554	zmxlm(ji,jj,jk) = zemxl
	555	zmxld(ji,jj,jk) = zemxl
	556	END DO
	557	END DO
	558	END DO
	559	!
	560	CASE ( 2 ) ! \|dk[xml]\| bounded by e3t :
[5120]	561	DO jk = 2, jpkm1 ! from the surface to the bottom :
	562	DO jj = 2, jpjm1
	563	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	564	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk-1) + p_e3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
[1239]	565	END DO
[5120]	566	END DO
	567	END DO
	568	DO jk = jpkm1, 2, -1 ! from the bottom to the surface :
	569	DO jj = 2, jpjm1
	570	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	571	zemxl = MIN( zmxlm(ji,jj,jk+1) + p_e3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
[1239]	572	zmxlm(ji,jj,jk) = zemxl
	573	zmxld(ji,jj,jk) = zemxl
	574	END DO
	575	END DO
	576	END DO
	577	!
	578	CASE ( 3 ) ! lup and ldown, \|dk[xml]\| bounded by e3t :
[5120]	579	DO jk = 2, jpkm1 ! from the surface to the bottom : lup
	580	DO jj = 2, jpjm1
	581	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	582	zmxld(ji,jj,jk) = MIN( zmxld(ji,jj,jk-1) + p_e3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
[1239]	583	END DO
[5120]	584	END DO
	585	END DO
	586	DO jk = jpkm1, 2, -1 ! from the bottom to the surface : ldown
	587	DO jj = 2, jpjm1
	588	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	589	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk+1) + p_e3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
[1239]	590	END DO
	591	END DO
	592	END DO
	593	DO jk = 2, jpkm1
	594	DO jj = 2, jpjm1
	595	DO ji = fs_2, fs_jpim1 ! vector opt.
	596	zemlm = MIN ( zmxld(ji,jj,jk), zmxlm(ji,jj,jk) )
	597	zemlp = SQRT( zmxld(ji,jj,jk) * zmxlm(ji,jj,jk) )
	598	zmxlm(ji,jj,jk) = zemlm
	599	zmxld(ji,jj,jk) = zemlp
	600	END DO
	601	END DO
	602	END DO
	603	!
	604	END SELECT
[1492]	605	!
[1239]	606
[1492]	607	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[7990]	608	! ! Vertical eddy viscosity and diffusivity (avm and avt)
[1492]	609	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	610	DO jk = 1, jpkm1 !* vertical eddy viscosity & diffivity at w-points
[1239]	611	DO jj = 2, jpjm1
	612	DO ji = fs_2, fs_jpim1 ! vector opt.
	613	zsqen = SQRT( en(ji,jj,jk) )
	614	zav = rn_ediff * zmxlm(ji,jj,jk) * zsqen
[8093]	615	p_avm(ji,jj,jk) = MAX( zav, avmb(jk) ) * wmask(ji,jj,jk)
	616	p_avt(ji,jj,jk) = MAX( zav, avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1239]	617	dissl(ji,jj,jk) = zsqen / zmxld(ji,jj,jk)
	618	END DO
	619	END DO
	620	END DO
[1492]	621	!
	622	!
	623	IF( nn_pdl == 1 ) THEN !* Prandtl number case: update avt
[5120]	624	DO jk = 2, jpkm1
	625	DO jj = 2, jpjm1
	626	DO ji = fs_2, fs_jpim1 ! vector opt.
[8093]	627	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]	628	END DO
	629	END DO
	630	END DO
	631	ENDIF
	632
	633	IF(ln_ctl) THEN
[7990]	634	CALL prt_ctl( tab3d_1=en , clinfo1=' tke - e: ', tab3d_2=avt, clinfo2=' t: ', ovlap=1, kdim=jpk)
	635	CALL prt_ctl( tab3d_1=avm, clinfo1=' tke - m: ', ovlap=1, kdim=jpk )
[1239]	636	ENDIF
	637	!
[3294]	638	IF( nn_timing == 1 ) CALL timing_stop('tke_avn')
	639	!
[1492]	640	END SUBROUTINE tke_avn
[1239]	641
[1492]	642
[2528]	643	SUBROUTINE zdf_tke_init
[1239]	644	!!----------------------------------------------------------------------
[2528]	645	!! * ROUTINE zdf_tke_init *
[1239]	646	!!
	647	!! ** Purpose : Initialization of the vertical eddy diffivity and
[1492]	648	!! viscosity when using a tke turbulent closure scheme
[1239]	649	!!
[1601]	650	!! ** Method : Read the namzdf_tke namelist and check the parameters
[1492]	651	!! called at the first timestep (nit000)
[1239]	652	!!
[1601]	653	!! ** input : Namlist namzdf_tke
[1239]	654	!!
	655	!! ** Action : Increase by 1 the nstop flag is setting problem encounter
	656	!!----------------------------------------------------------------------
	657	INTEGER :: ji, jj, jk ! dummy loop indices
[4147]	658	INTEGER :: ios
[1239]	659	!!
[2528]	660	NAMELIST/namzdf_tke/ rn_ediff, rn_ediss , rn_ebb , rn_emin , &
	661	& rn_emin0, rn_bshear, nn_mxl , ln_mxl0 , &
[8143]	662	& rn_mxl0 , nn_pdl , ln_drg , ln_lc , rn_lc , &
[2528]	663	& nn_etau , nn_htau , rn_efr
[1239]	664	!!----------------------------------------------------------------------
[2715]	665	!
[4147]	666	REWIND( numnam_ref ) ! Namelist namzdf_tke in reference namelist : Turbulent Kinetic Energy
	667	READ ( numnam_ref, namzdf_tke, IOSTAT = ios, ERR = 901)
	668	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in reference namelist', lwp )
	669
	670	REWIND( numnam_cfg ) ! Namelist namzdf_tke in configuration namelist : Turbulent Kinetic Energy
	671	READ ( numnam_cfg, namzdf_tke, IOSTAT = ios, ERR = 902 )
	672	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in configuration namelist', lwp )
[4624]	673	IF(lwm) WRITE ( numond, namzdf_tke )
[2715]	674	!
[2528]	675	ri_cri = 2._wp / ( 2._wp + rn_ediss / rn_ediff ) ! resulting critical Richardson number
[2715]	676	!
[1492]	677	IF(lwp) THEN !* Control print
[1239]	678	WRITE(numout,*)
[2528]	679	WRITE(numout,*) 'zdf_tke_init : tke turbulent closure scheme - initialisation'
	680	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	681	WRITE(numout,*) ' Namelist namzdf_tke : set tke mixing parameters'
[1705]	682	WRITE(numout,*) ' coef. to compute avt rn_ediff = ', rn_ediff
	683	WRITE(numout,*) ' Kolmogoroff dissipation coef. rn_ediss = ', rn_ediss
	684	WRITE(numout,*) ' tke surface input coef. rn_ebb = ', rn_ebb
	685	WRITE(numout,*) ' minimum value of tke rn_emin = ', rn_emin
	686	WRITE(numout,*) ' surface minimum value of tke rn_emin0 = ', rn_emin0
[8143]	687	WRITE(numout,*) ' prandl number flag nn_pdl = ', nn_pdl
[1705]	688	WRITE(numout,*) ' background shear (>0) rn_bshear = ', rn_bshear
	689	WRITE(numout,*) ' mixing length type nn_mxl = ', nn_mxl
[8143]	690	WRITE(numout,*) ' surface mixing length = F(stress) or not ln_mxl0 = ', ln_mxl0
	691	WRITE(numout,*) ' surface mixing length minimum value rn_mxl0 = ', rn_mxl0
	692	WRITE(numout,*) ' top/bottom friction forcing flag ln_drg = ', ln_drg
	693	WRITE(numout,*) ' Langmuir cells parametrization ln_lc = ', ln_lc
	694	WRITE(numout,*) ' coef to compute vertical velocity of LC rn_lc = ', rn_lc
[1705]	695	WRITE(numout,*) ' test param. to add tke induced by wind nn_etau = ', nn_etau
[8143]	696	WRITE(numout,*) ' type of tke penetration profile nn_htau = ', nn_htau
	697	WRITE(numout,*) ' fraction of TKE that penetrates rn_efr = ', rn_efr
[1239]	698	WRITE(numout,*)
[8143]	699	IF( ln_drg ) THEN
	700	WRITE(numout,*) ' Namelist namdrg_top/_bot: used values:'
	701	WRITE(numout,*) ' top ocean cavity roughness (m) rn_z0(_top)= ', r_z0_top
	702	WRITE(numout,*) ' Bottom seafloor roughness (m) rn_z0(_bot)= ', r_z0_bot
	703	ENDIF
[7953]	704	WRITE(numout,*)
[8143]	705	WRITE(numout,*)
	706	WRITE(numout,*) ' ==>> critical Richardson nb with your parameters ri_cri = ', ri_cri
	707	WRITE(numout,*)
[1239]	708	ENDIF
[2715]	709	!
[7990]	710	IF( ln_zdfiwm ) THEN ! Internal wave-driven mixing
	711	rn_emin = 1.e-10_wp ! specific values of rn_emin & rmxl_min are used
	712	rmxl_min = 1.e-03_wp ! associated avt minimum = molecular salt diffusivity (10^-9 m2/s)
[7953]	713	IF(lwp) WRITE(numout,*) ' Internal wave-driven mixing case: force rn_emin = 1.e-10 and rmxl_min = 1.e-3 '
[7990]	714	ELSE ! standard case : associated avt minimum = molecular viscosity (10^-6 m2/s)
[7953]	715	rmxl_min = 1.e-6_wp / ( rn_ediff * SQRT( rn_emin ) ) ! resulting minimum length to recover molecular viscosity
	716	IF(lwp) WRITE(numout,*) ' minimum mixing length with your parameters rmxl_min = ', rmxl_min
	717	ENDIF
	718	!
[2715]	719	! ! allocate tke arrays
	720	IF( zdf_tke_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_tke_init : unable to allocate arrays' )
	721	!
[1492]	722	! !* Check of some namelist values
[4990]	723	IF( nn_mxl < 0 .OR. nn_mxl > 3 ) CALL ctl_stop( 'bad flag: nn_mxl is 0, 1 or 2 ' )
	724	IF( nn_pdl < 0 .OR. nn_pdl > 1 ) CALL ctl_stop( 'bad flag: nn_pdl is 0 or 1 ' )
	725	IF( nn_htau < 0 .OR. nn_htau > 1 ) CALL ctl_stop( 'bad flag: nn_htau is 0, 1 or 2 ' )
[5407]	726	IF( nn_etau == 3 .AND. .NOT. ln_cpl ) CALL ctl_stop( 'nn_etau == 3 : HF taum only known in coupled mode' )
[1239]	727
[2528]	728	IF( ln_mxl0 ) THEN
	729	IF(lwp) WRITE(numout,*) ' use a surface mixing length = F(stress) : set rn_mxl0 = rmxl_min'
	730	rn_mxl0 = rmxl_min
	731	ENDIF
	732
[1492]	733	IF( nn_etau == 2 ) CALL zdf_mxl( nit000 ) ! Initialization of nmln
[1239]	734
[1492]	735	! !* depth of penetration of surface tke
	736	IF( nn_etau /= 0 ) THEN
[1601]	737	SELECT CASE( nn_htau ) ! Choice of the depth of penetration
[2528]	738	CASE( 0 ) ! constant depth penetration (here 10 meters)
[7753]	739	htau(:,:) = 10._wp
[2528]	740	CASE( 1 ) ! F(latitude) : 0.5m to 30m poleward of 40 degrees
[7753]	741	htau(:,:) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
[1492]	742	END SELECT
	743	ENDIF
	744	! !* set vertical eddy coef. to the background value
[1239]	745	DO jk = 1, jpk
[8093]	746	avt(:,:,jk) = avtb(jk) * wmask(:,:,jk)
	747	avm(:,:,jk) = avmb(jk) * wmask(:,:,jk)
[1239]	748	END DO
[7753]	749	dissl(:,:,:) = 1.e-12_wp
[2715]	750	!
	751	CALL tke_rst( nit000, 'READ' ) !* read or initialize all required files
[1239]	752	!
[2528]	753	END SUBROUTINE zdf_tke_init
[1239]	754
	755
[1531]	756	SUBROUTINE tke_rst( kt, cdrw )
[8093]	757	!!---------------------------------------------------------------------
	758	!! * ROUTINE tke_rst *
	759	!!
	760	!! ** Purpose : Read or write TKE file (en) in restart file
	761	!!
	762	!! ** Method : use of IOM library
	763	!! if the restart does not contain TKE, en is either
	764	!! set to rn_emin or recomputed
	765	!!----------------------------------------------------------------------
	766	INTEGER , INTENT(in) :: kt ! ocean time-step
	767	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
	768	!
	769	INTEGER :: jit, jk ! dummy loop indices
	770	INTEGER :: id1, id2, id3, id4 ! local integers
	771	!!----------------------------------------------------------------------
	772	!
	773	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
	774	! ! ---------------
	775	IF( ln_rstart ) THEN !* Read the restart file
	776	id1 = iom_varid( numror, 'en' , ldstop = .FALSE. )
	777	id2 = iom_varid( numror, 'avt_k', ldstop = .FALSE. )
	778	id3 = iom_varid( numror, 'avm_k', ldstop = .FALSE. )
	779	id4 = iom_varid( numror, 'dissl', ldstop = .FALSE. )
	780	!
	781	IF( MIN( id1, id2, id3, id4 ) > 0 ) THEN ! fields exist
	782	CALL iom_get( numror, jpdom_autoglo, 'en', en )
	783	CALL iom_get( numror, jpdom_autoglo, 'avt_k', avt_k )
	784	CALL iom_get( numror, jpdom_autoglo, 'avm_k', avm_k )
	785	CALL iom_get( numror, jpdom_autoglo, 'dissl', dissl )
	786	ELSE ! start TKE from rest
	787	IF(lwp) WRITE(numout,*) ' ==>> previous run without TKE scheme, set en to background values'
	788	en(:,:,:) = rn_emin * wmask(:,:,:)
	789	! avt_k, avm_k already set to the background value in zdf_phy_init
	790	ENDIF
	791	ELSE !* Start from rest
	792	IF(lwp) WRITE(numout,*) ' ==>> start from rest: set en to the background value'
	793	en(:,:,:) = rn_emin * wmask(:,:,:)
	794	! avt_k, avm_k already set to the background value in zdf_phy_init
	795	ENDIF
	796	!
	797	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
	798	! ! -------------------
	799	IF(lwp) WRITE(numout,*) '---- tke-rst ----'
	800	CALL iom_rstput( kt, nitrst, numrow, 'en' , en )
	801	CALL iom_rstput( kt, nitrst, numrow, 'avt_k', avt_k )
	802	CALL iom_rstput( kt, nitrst, numrow, 'avm_k', avm_k )
	803	CALL iom_rstput( kt, nitrst, numrow, 'dissl', dissl )
	804	!
	805	ENDIF
	806	!
[1531]	807	END SUBROUTINE tke_rst
[1239]	808
	809	!!======================================================================
[1531]	810	END MODULE zdftke

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