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zdftke.F90 in branches/UKMO/dev_r5518_GC3p0_package/NEMOGCM/NEMO/OPA_SRC/ZDF – NEMO

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source: branches/UKMO/dev_r5518_GC3p0_package/NEMOGCM/NEMO/OPA_SRC/ZDF/zdftke.F90 @ 6450

Last change on this file since 6450 was 6450, checked in by dancopsey, 8 years ago
Merged in changeset 5242 of dev_r5021_nn_etau_revision
File size: 51.1 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
[1239]	29	!!----------------------------------------------------------------------
[1531]	30	#if defined key_zdftke \|\| defined key_esopa
[1239]	31	!!----------------------------------------------------------------------
[1531]	32	!! 'key_zdftke' TKE vertical physics
[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
	46	USE zdfmxl ! vertical physics: mixed layer
[1492]	47	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
	48	USE prtctl ! Print control
	49	USE in_out_manager ! I/O manager
	50	USE iom ! I/O manager library
[2715]	51	USE lib_mpp ! MPP library
[3294]	52	USE wrk_nemo ! work arrays
	53	USE timing ! Timing
[3625]	54	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[6440]	55	#if defined key_agrif
	56	USE agrif_opa_interp
	57	USE agrif_opa_update
	58	#endif
[1239]	59
[6440]	60
	61
[1239]	62	IMPLICIT NONE
	63	PRIVATE
	64
[2528]	65	PUBLIC zdf_tke ! routine called in step module
	66	PUBLIC zdf_tke_init ! routine called in opa module
	67	PUBLIC tke_rst ! routine called in step module
[1239]	68
[2715]	69	LOGICAL , PUBLIC, PARAMETER :: lk_zdftke = .TRUE. !: TKE vertical mixing flag
[1239]	70
[4147]	71	! !! Namelist namzdf_tke
	72	LOGICAL :: ln_mxl0 ! mixing length scale surface value as function of wind stress or not
	73	INTEGER :: nn_mxl ! type of mixing length (=0/1/2/3)
	74	REAL(wp) :: rn_mxl0 ! surface min value of mixing length (kappaz_o=0.40.1 m) [m]
	75	INTEGER :: nn_pdl ! Prandtl number or not (ratio avt/avm) (=0/1)
	76	REAL(wp) :: rn_ediff ! coefficient for avt: avt=rn_ediffmxlsqrt(e)
	77	REAL(wp) :: rn_ediss ! coefficient of the Kolmogoroff dissipation
	78	REAL(wp) :: rn_ebb ! coefficient of the surface input of tke
	79	REAL(wp) :: rn_emin ! minimum value of tke [m2/s2]
	80	REAL(wp) :: rn_emin0 ! surface minimum value of tke [m2/s2]
	81	REAL(wp) :: rn_bshear ! background shear (>0) currently a numerical threshold (do not change it)
	82	INTEGER :: nn_etau ! type of depth penetration of surface tke (=0/1/2/3)
	83	INTEGER :: nn_htau ! type of tke profile of penetration (=0/1)
	84	REAL(wp) :: rn_efr ! fraction of TKE surface value which penetrates in the ocean
[6448]	85	REAL(wp) :: rn_c ! fraction of TKE added within the mixed layer by nn_etau
[4147]	86	LOGICAL :: ln_lc ! Langmuir cells (LC) as a source term of TKE or not
	87	REAL(wp) :: rn_lc ! coef to compute vertical velocity of Langmuir cells
[1239]	88
[4147]	89	REAL(wp) :: ri_cri ! critic Richardson number (deduced from rn_ediff and rn_ediss values)
	90	REAL(wp) :: rmxl_min ! minimum mixing length value (deduced from rn_ediff and rn_emin values) [m]
[6448]	91	REAL(wp) :: rhtau ! coefficient to relate MLD to htau when nn_htau == 2
[2528]	92	REAL(wp) :: rhftau_add = 1.e-3_wp ! add offset applied to HF part of taum (nn_etau=3)
	93	REAL(wp) :: rhftau_scl = 1.0_wp ! scale factor applied to HF part of taum (nn_etau=3)
[1239]	94
[6448]	95	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_niw !: TKE budget- near-inertial waves term
[2715]	96	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: htau ! depth of tke penetration (nn_htau)
[6448]	97	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: efr ! surface boundary condition for nn_etau = 4
[2715]	98	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dissl ! now mixing lenght of dissipation
	99	#if defined key_c1d
	100	! !! 1D cfg only ('key_c1d')
	101	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_dis, e_mix !: dissipation and mixing turbulent lengh scales
	102	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_pdl, e_ric !: prandl and local Richardson numbers
	103	#endif
[1492]	104
[1239]	105	!! * Substitutions
	106	# include "domzgr_substitute.h90"
	107	# include "vectopt_loop_substitute.h90"
	108	!!----------------------------------------------------------------------
[2715]	109	!! NEMO/OPA 4.0 , NEMO Consortium (2011)
[2528]	110	!! $Id$
	111	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[1239]	112	!!----------------------------------------------------------------------
	113	CONTAINS
	114
[2715]	115	INTEGER FUNCTION zdf_tke_alloc()
	116	!!----------------------------------------------------------------------
	117	!! * FUNCTION zdf_tke_alloc *
	118	!!----------------------------------------------------------------------
	119	ALLOCATE( &
	120	#if defined key_c1d
	121	& e_dis(jpi,jpj,jpk) , e_mix(jpi,jpj,jpk) , &
	122	& e_pdl(jpi,jpj,jpk) , e_ric(jpi,jpj,jpk) , &
	123	#endif
[6448]	124	& htau (jpi,jpj) , dissl(jpi,jpj,jpk) , &
	125	& efr (jpi,jpj) , e_niw(jpi,jpj,jpk) , &
	126	& STAT= zdf_tke_alloc )
[2715]	127	!
	128	IF( lk_mpp ) CALL mpp_sum ( zdf_tke_alloc )
	129	IF( zdf_tke_alloc /= 0 ) CALL ctl_warn('zdf_tke_alloc: failed to allocate arrays')
	130	!
	131	END FUNCTION zdf_tke_alloc
	132
	133
[1531]	134	SUBROUTINE zdf_tke( kt )
[1239]	135	!!----------------------------------------------------------------------
[1531]	136	!! * ROUTINE zdf_tke *
[1239]	137	!!
	138	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
[1492]	139	!! coefficients using a turbulent closure scheme (TKE).
[1239]	140	!!
[1492]	141	!! ** Method : The time evolution of the turbulent kinetic energy (tke)
	142	!! is computed from a prognostic equation :
	143	!! d(en)/dt = avm (d(u)/dz)**2 ! shear production
	144	!! + d( avm d(en)/dz )/dz ! diffusion of tke
	145	!! + avt N^2 ! stratif. destruc.
	146	!! - rn_ediss / emxl en**(2/3) ! Kolmogoroff dissipation
[1239]	147	!! with the boundary conditions:
[1695]	148	!! surface: en = max( rn_emin0, rn_ebb * taum )
[1239]	149	!! bottom : en = rn_emin
[1492]	150	!! The associated critical Richardson number is: ri_cri = 2/(2+rn_ediss/rn_ediff)
	151	!!
	152	!! The now Turbulent kinetic energy is computed using the following
	153	!! time stepping: implicit for vertical diffusion term, linearized semi
	154	!! implicit for kolmogoroff dissipation term, and explicit forward for
	155	!! both buoyancy and shear production terms. Therefore a tridiagonal
	156	!! linear system is solved. Note that buoyancy and shear terms are
	157	!! discretized in a energy conserving form (Bruchard 2002).
	158	!!
	159	!! The dissipative and mixing length scale are computed from en and
	160	!! the stratification (see tke_avn)
	161	!!
	162	!! The now vertical eddy vicosity and diffusivity coefficients are
	163	!! given by:
	164	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	165	!! avt = max( avmb, pdl * avm )
[1239]	166	!! eav = max( avmb, avm )
[1492]	167	!! where pdl, the inverse of the Prandtl number is 1 if nn_pdl=0 and
	168	!! given by an empirical funtion of the localRichardson number if nn_pdl=1
[1239]	169	!!
	170	!! ** Action : compute en (now turbulent kinetic energy)
	171	!! update avt, avmu, avmv (before vertical eddy coef.)
	172	!!
	173	!! References : Gaspar et al., JGR, 1990,
	174	!! Blanke and Delecluse, JPO, 1991
	175	!! Mellor and Blumberg, JPO 2004
	176	!! Axell, JGR, 2002
[1492]	177	!! Bruchard OM 2002
[1239]	178	!!----------------------------------------------------------------------
[1492]	179	INTEGER, INTENT(in) :: kt ! ocean time step
	180	!!----------------------------------------------------------------------
[1481]	181	!
[3632]	182	IF( kt /= nit000 ) THEN ! restore before value to compute tke
	183	avt (:,:,:) = avt_k (:,:,:)
	184	avm (:,:,:) = avm_k (:,:,:)
	185	avmu(:,:,:) = avmu_k(:,:,:)
	186	avmv(:,:,:) = avmv_k(:,:,:)
	187	ENDIF
	188	!
[2528]	189	CALL tke_tke ! now tke (en)
[1492]	190	!
[2528]	191	CALL tke_avn ! now avt, avm, avmu, avmv
	192	!
[3632]	193	avt_k (:,:,:) = avt (:,:,:)
	194	avm_k (:,:,:) = avm (:,:,:)
	195	avmu_k(:,:,:) = avmu(:,:,:)
	196	avmv_k(:,:,:) = avmv(:,:,:)
	197	!
[6440]	198	#if defined key_agrif
	199	! Update child grid f => parent grid
	200	IF( .NOT.Agrif_Root() ) CALL Agrif_Update_Tke( kt ) ! children only
	201	#endif
	202	!
[1531]	203	END SUBROUTINE zdf_tke
[1239]	204
[1492]	205
[1481]	206	SUBROUTINE tke_tke
[1239]	207	!!----------------------------------------------------------------------
[1492]	208	!! * ROUTINE tke_tke *
	209	!!
	210	!! ** Purpose : Compute the now Turbulente Kinetic Energy (TKE)
	211	!!
	212	!! ** Method : - TKE surface boundary condition
[2528]	213	!! - source term due to Langmuir cells (Axell JGR 2002) (ln_lc=T)
[1492]	214	!! - source term due to shear (saved in avmu, avmv arrays)
	215	!! - Now TKE : resolution of the TKE equation by inverting
	216	!! a tridiagonal linear system by a "methode de chasse"
	217	!! - increase TKE due to surface and internal wave breaking
	218	!!
	219	!! ** Action : - en : now turbulent kinetic energy)
	220	!! - avmu, avmv : production of TKE by shear at u and v-points
	221	!! (= Kz dz[Ub] * dz[Un] )
[1239]	222	!! ---------------------------------------------------------------------
[1705]	223	INTEGER :: ji, jj, jk ! dummy loop arguments
[2528]	224	!!bfr INTEGER :: ikbu, ikbv, ikbum1, ikbvm1 ! temporary scalar
	225	!!bfr INTEGER :: ikbt, ikbumm1, ikbvmm1 ! temporary scalar
[1705]	226	REAL(wp) :: zrhoa = 1.22 ! Air density kg/m3
	227	REAL(wp) :: zcdrag = 1.5e-3 ! drag coefficient
	228	REAL(wp) :: zbbrau, zesh2 ! temporary scalars
	229	REAL(wp) :: zfact1, zfact2, zfact3 ! - -
	230	REAL(wp) :: ztx2 , zty2 , zcof ! - -
	231	REAL(wp) :: ztau , zdif ! - -
	232	REAL(wp) :: zus , zwlc , zind ! - -
	233	REAL(wp) :: zzd_up, zzd_lw ! - -
[2528]	234	!!bfr REAL(wp) :: zebot ! - -
[3294]	235	INTEGER , POINTER, DIMENSION(:,: ) :: imlc
	236	REAL(wp), POINTER, DIMENSION(:,: ) :: zhlc
	237	REAL(wp), POINTER, DIMENSION(:,:,:) :: zpelc, zdiag, zd_up, zd_lw
[1239]	238	!!--------------------------------------------------------------------
[1492]	239	!
[3294]	240	IF( nn_timing == 1 ) CALL timing_start('tke_tke')
	241	!
	242	CALL wrk_alloc( jpi,jpj, imlc ) ! integer
	243	CALL wrk_alloc( jpi,jpj, zhlc )
	244	CALL wrk_alloc( jpi,jpj,jpk, zpelc, zdiag, zd_up, zd_lw )
	245	!
[1695]	246	zbbrau = rn_ebb / rau0 ! Local constant initialisation
[2528]	247	zfact1 = -.5_wp * rdt
	248	zfact2 = 1.5_wp * rdt * rn_ediss
	249	zfact3 = 0.5_wp * rn_ediss
[1492]	250	!
[5120]	251	!
[1492]	252	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	253	! ! Surface boundary condition on tke
	254	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[5120]	255	IF ( ln_isfcav ) THEN
	256	DO jj = 2, jpjm1 ! en(mikt(ji,jj)) = rn_emin
	257	DO ji = fs_2, fs_jpim1 ! vector opt.
	258	en(ji,jj,mikt(ji,jj))=rn_emin * tmask(ji,jj,1)
	259	END DO
	260	END DO
	261	END IF
[1695]	262	DO jj = 2, jpjm1 ! en(1) = rn_ebb taum / rau0 (min value rn_emin0)
[1481]	263	DO ji = fs_2, fs_jpim1 ! vector opt.
[5120]	264	en(ji,jj,1) = MAX( rn_emin0, zbbrau * taum(ji,jj) ) * tmask(ji,jj,1)
[1481]	265	END DO
	266	END DO
[2528]	267
	268	!!bfr - start commented area
[1492]	269	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	270	! ! Bottom boundary condition on tke
	271	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1719]	272	!
	273	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	274	! Tests to date have found the bottom boundary condition on tke to have very little effect.
	275	! The condition is coded here for completion but commented out until there is proof that the
	276	! computational cost is justified
	277	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	278	! en(bot) = (rn_ebb0/rau0)0.5sqrt(u_botfr^2+v_botfr^2) (min value rn_emin)
[1662]	279	!CDIR NOVERRCHK
[1719]	280	!! DO jj = 2, jpjm1
[1662]	281	!CDIR NOVERRCHK
[1719]	282	!! DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	283	!! ztx2 = bfrua(ji-1,jj) * ub(ji-1,jj,mbku(ji-1,jj)) + &
	284	!! bfrua(ji ,jj) * ub(ji ,jj,mbku(ji ,jj) )
	285	!! zty2 = bfrva(ji,jj ) * vb(ji,jj ,mbkv(ji,jj )) + &
	286	!! bfrva(ji,jj-1) * vb(ji,jj-1,mbkv(ji,jj-1) )
[1719]	287	!! zebot = 0.001875_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000.
[2528]	288	!! en (ji,jj,mbkt(ji,jj)+1) = MAX( zebot, rn_emin ) * tmask(ji,jj,1)
[1719]	289	!! END DO
	290	!! END DO
[2528]	291	!!bfr - end commented area
[1492]	292	!
	293	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[2528]	294	IF( ln_lc ) THEN ! Langmuir circulation source term added to tke (Axell JGR 2002)
[1492]	295	! !>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
[1239]	296	!
[1492]	297	! !* total energy produce by LC : cumulative sum over jk
[2528]	298	zpelc(:,:,1) = MAX( rn2b(:,:,1), 0._wp ) * fsdepw(:,:,1) * fse3w(:,:,1)
[1239]	299	DO jk = 2, jpk
[2528]	300	zpelc(:,:,jk) = zpelc(:,:,jk-1) + MAX( rn2b(:,:,jk), 0._wp ) * fsdepw(:,:,jk) * fse3w(:,:,jk)
[1239]	301	END DO
[1492]	302	! !* finite Langmuir Circulation depth
[1705]	303	zcof = 0.5 * 0.016 * 0.016 / ( zrhoa * zcdrag )
[2528]	304	imlc(:,:) = mbkt(:,:) + 1 ! Initialization to the number of w ocean point (=2 over land)
[1239]	305	DO jk = jpkm1, 2, -1
[1492]	306	DO jj = 1, jpj ! Last w-level at which zpelc>=0.5usus
	307	DO ji = 1, jpi ! with us=0.016*wind(starting from jpk-1)
[1705]	308	zus = zcof * taum(ji,jj)
[1239]	309	IF( zpelc(ji,jj,jk) > zus ) imlc(ji,jj) = jk
	310	END DO
	311	END DO
	312	END DO
[1492]	313	! ! finite LC depth
	314	DO jj = 1, jpj
[1239]	315	DO ji = 1, jpi
	316	zhlc(ji,jj) = fsdepw(ji,jj,imlc(ji,jj))
	317	END DO
	318	END DO
[1705]	319	zcof = 0.016 / SQRT( zrhoa * zcdrag )
[5120]	320	!CDIR NOVERRCHK
[1492]	321	DO jk = 2, jpkm1 !* TKE Langmuir circulation source term added to en
[5120]	322	!CDIR NOVERRCHK
[1239]	323	DO jj = 2, jpjm1
[5120]	324	!CDIR NOVERRCHK
[1239]	325	DO ji = fs_2, fs_jpim1 ! vector opt.
[1705]	326	zus = zcof * SQRT( taum(ji,jj) ) ! Stokes drift
[1492]	327	! ! vertical velocity due to LC
[1239]	328	zind = 0.5 - SIGN( 0.5, fsdepw(ji,jj,jk) - zhlc(ji,jj) )
	329	zwlc = zind * rn_lc * zus * SIN( rpi * fsdepw(ji,jj,jk) / zhlc(ji,jj) )
[1492]	330	! ! TKE Langmuir circulation source term
[6440]	331	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( 1._wp - fr_i(ji,jj) ) * ( zwlc * zwlc * zwlc ) / &
	332	& zhlc(ji,jj) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	333	END DO
	334	END DO
	335	END DO
	336	!
	337	ENDIF
[1492]	338	!
	339	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	340	! ! Now Turbulent kinetic energy (output in en)
	341	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	342	! ! Resolution of a tridiagonal linear system by a "methode de chasse"
	343	! ! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
	344	! ! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
	345	!
	346	DO jk = 2, jpkm1 !* Shear production at uw- and vw-points (energy conserving form)
	347	DO jj = 1, jpj ! here avmu, avmv used as workspace
	348	DO ji = 1, jpi
	349	avmu(ji,jj,jk) = avmu(ji,jj,jk) * ( un(ji,jj,jk-1) - un(ji,jj,jk) ) &
	350	& * ( ub(ji,jj,jk-1) - ub(ji,jj,jk) ) &
[5120]	351	& / ( fse3uw_n(ji,jj,jk) &
	352	& * fse3uw_b(ji,jj,jk) )
[1492]	353	avmv(ji,jj,jk) = avmv(ji,jj,jk) * ( vn(ji,jj,jk-1) - vn(ji,jj,jk) ) &
	354	& * ( vb(ji,jj,jk-1) - vb(ji,jj,jk) ) &
	355	& / ( fse3vw_n(ji,jj,jk) &
	356	& * fse3vw_b(ji,jj,jk) )
	357	END DO
	358	END DO
	359	END DO
	360	!
[5120]	361	DO jk = 2, jpkm1 !* Matrix and right hand side in en
	362	DO jj = 2, jpjm1
	363	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	364	zcof = zfact1 * tmask(ji,jj,jk)
[6440]	365	# if defined key_zdftmx_new
	366	! key_zdftmx_new: New internal wave-driven param: set a minimum value for Kz on TKE (ensure numerical stability)
	367	zzd_up = zcof * ( MAX( avm(ji,jj,jk+1) + avm(ji,jj,jk), 2.e-5_wp ) ) & ! upper diagonal
	368	& / ( fse3t(ji,jj,jk ) * fse3w(ji,jj,jk ) )
	369	zzd_lw = zcof * ( MAX( avm(ji,jj,jk) + avm(ji,jj,jk-1), 2.e-5_wp ) ) & ! lower diagonal
	370	& / ( fse3t(ji,jj,jk-1) * fse3w(ji,jj,jk ) )
	371	# else
[1492]	372	zzd_up = zcof * ( avm (ji,jj,jk+1) + avm (ji,jj,jk ) ) & ! upper diagonal
	373	& / ( fse3t(ji,jj,jk ) * fse3w(ji,jj,jk ) )
	374	zzd_lw = zcof * ( avm (ji,jj,jk ) + avm (ji,jj,jk-1) ) & ! lower diagonal
	375	& / ( fse3t(ji,jj,jk-1) * fse3w(ji,jj,jk ) )
[6440]	376	# endif
[1492]	377	! ! shear prod. at w-point weightened by mask
[2528]	378	zesh2 = ( avmu(ji-1,jj,jk) + avmu(ji,jj,jk) ) / MAX( 1._wp , umask(ji-1,jj,jk) + umask(ji,jj,jk) ) &
	379	& + ( avmv(ji,jj-1,jk) + avmv(ji,jj,jk) ) / MAX( 1._wp , vmask(ji,jj-1,jk) + vmask(ji,jj,jk) )
[1492]	380	!
	381	zd_up(ji,jj,jk) = zzd_up ! Matrix (zdiag, zd_up, zd_lw)
	382	zd_lw(ji,jj,jk) = zzd_lw
[2528]	383	zdiag(ji,jj,jk) = 1._wp - zzd_lw - zzd_up + zfact2 * dissl(ji,jj,jk) * tmask(ji,jj,jk)
[1239]	384	!
[1492]	385	! ! right hand side in en
[1481]	386	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( zesh2 - avt(ji,jj,jk) * rn2(ji,jj,jk) &
[4990]	387	& + zfact3 * dissl(ji,jj,jk) * en (ji,jj,jk) ) &
[5120]	388	& * wmask(ji,jj,jk)
[1239]	389	END DO
[5120]	390	END DO
	391	END DO
	392	! !* Matrix inversion from level 2 (tke prescribed at level 1)
	393	DO jk = 3, jpkm1 ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
	394	DO jj = 2, jpjm1
	395	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	396	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]	397	END DO
[5120]	398	END DO
	399	END DO
	400	!
	401	! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
	402	DO jj = 2, jpjm1
	403	DO ji = fs_2, fs_jpim1 ! vector opt.
	404	zd_lw(ji,jj,2) = en(ji,jj,2) - zd_lw(ji,jj,2) * en(ji,jj,1) ! Surface boudary conditions on tke
	405	END DO
	406	END DO
	407	DO jk = 3, jpkm1
	408	DO jj = 2, jpjm1
	409	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	410	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]	411	END DO
[5120]	412	END DO
	413	END DO
	414	!
	415	! thrid recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
	416	DO jj = 2, jpjm1
	417	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	418	en(ji,jj,jpkm1) = zd_lw(ji,jj,jpkm1) / zdiag(ji,jj,jpkm1)
[5120]	419	END DO
	420	END DO
	421	DO jk = jpk-2, 2, -1
	422	DO jj = 2, jpjm1
	423	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	424	en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
[1239]	425	END DO
[5120]	426	END DO
	427	END DO
	428	DO jk = 2, jpkm1 ! set the minimum value of tke
	429	DO jj = 2, jpjm1
	430	DO ji = fs_2, fs_jpim1 ! vector opt.
	431	en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin ) * wmask(ji,jj,jk)
[1239]	432	END DO
	433	END DO
	434	END DO
	435
[6448]	436	! ! Save TKE prior to nn_etau addition
	437	e_niw(:,:,:) = en(:,:,:)
	438	!
[1492]	439	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	440	! ! TKE due to surface and internal wave breaking
	441	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[6448]	442	IF( nn_htau == 2 ) THEN !* mixed-layer depth dependant length scale
	443	DO jj = 2, jpjm1
	444	DO ji = fs_2, fs_jpim1 ! vector opt.
	445	htau(ji,jj) = rhtau * hmlp(ji,jj)
	446	END DO
	447	END DO
	448	ENDIF
	449	#if defined key_iomput
	450	!
	451	CALL iom_put( "htau", htau(:,:) ) ! Check htau (even if constant in time)
	452	#endif
	453	!
[2528]	454	IF( nn_etau == 1 ) THEN !* penetration below the mixed layer (rn_efr fraction)
[1492]	455	DO jk = 2, jpkm1
[1239]	456	DO jj = 2, jpjm1
	457	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	458	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	459	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	460	END DO
	461	END DO
[1492]	462	END DO
[2528]	463	ELSEIF( nn_etau == 2 ) THEN !* act only at the base of the mixed layer (jk=nmln) (rn_efr fraction)
[1492]	464	DO jj = 2, jpjm1
	465	DO ji = fs_2, fs_jpim1 ! vector opt.
	466	jk = nmln(ji,jj)
	467	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	468	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	469	END DO
[1492]	470	END DO
[2528]	471	ELSEIF( nn_etau == 3 ) THEN !* penetration belox the mixed layer (HF variability)
[1705]	472	!CDIR NOVERRCHK
	473	DO jk = 2, jpkm1
	474	!CDIR NOVERRCHK
	475	DO jj = 2, jpjm1
	476	!CDIR NOVERRCHK
	477	DO ji = fs_2, fs_jpim1 ! vector opt.
	478	ztx2 = utau(ji-1,jj ) + utau(ji,jj)
	479	zty2 = vtau(ji ,jj-1) + vtau(ji,jj)
[4990]	480	ztau = 0.5_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) * tmask(ji,jj,1) ! module of the mean stress
[2528]	481	zdif = taum(ji,jj) - ztau ! mean of modulus - modulus of the mean
	482	zdif = rhftau_scl * MAX( 0._wp, zdif + rhftau_add ) ! apply some modifications...
[1705]	483	en(ji,jj,jk) = en(ji,jj,jk) + zbbrau * zdif * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	484	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1705]	485	END DO
	486	END DO
	487	END DO
[6448]	488	ELSEIF( nn_etau == 4 ) THEN !* column integral independant of htau (rn_efr must be scaled up)
	489	IF( nn_htau == 2 ) THEN ! efr dependant on time-varying htau
	490	DO jj = 2, jpjm1
	491	DO ji = fs_2, fs_jpim1 ! vector opt.
	492	efr(ji,jj) = rn_efr / ( htau(ji,jj) * ( 1._wp - EXP( -bathy(ji,jj) / htau(ji,jj) ) ) )
	493	END DO
	494	END DO
	495	ENDIF
	496	DO jk = 2, jpkm1
	497	DO jj = 2, jpjm1
	498	DO ji = fs_2, fs_jpim1 ! vector opt.
	499	en(ji,jj,jk) = en(ji,jj,jk) + efr(ji,jj) * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
	500	& * ( 1._wp - fr_i(ji,jj) ) * tmask(ji,jj,jk)
	501	END DO
	502	END DO
	503	END DO
[1239]	504	ENDIF
[1492]	505	CALL lbc_lnk( en, 'W', 1. ) ! Lateral boundary conditions (sign unchanged)
	506	!
[6448]	507	DO jk = 2, jpkm1 ! TKE budget: near-inertial waves term
	508	DO jj = 2, jpjm1
	509	DO ji = fs_2, fs_jpim1 ! vector opt.
	510	e_niw(ji,jj,jk) = en(ji,jj,jk) - e_niw(ji,jj,jk)
	511	END DO
	512	END DO
	513	END DO
	514	!
	515	CALL lbc_lnk( e_niw, 'W', 1. )
	516	!
[3294]	517	CALL wrk_dealloc( jpi,jpj, imlc ) ! integer
	518	CALL wrk_dealloc( jpi,jpj, zhlc )
	519	CALL wrk_dealloc( jpi,jpj,jpk, zpelc, zdiag, zd_up, zd_lw )
[2715]	520	!
[3294]	521	IF( nn_timing == 1 ) CALL timing_stop('tke_tke')
	522	!
[1239]	523	END SUBROUTINE tke_tke
	524
[1492]	525
	526	SUBROUTINE tke_avn
[1239]	527	!!----------------------------------------------------------------------
[1492]	528	!! * ROUTINE tke_avn *
[1239]	529	!!
[1492]	530	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	531	!!
	532	!! ** Method : At this stage, en, the now TKE, is known (computed in
	533	!! the tke_tke routine). First, the now mixing lenth is
	534	!! computed from en and the strafification (N^2), then the mixings
	535	!! coefficients are computed.
	536	!! - Mixing length : a first evaluation of the mixing lengh
	537	!! scales is:
	538	!! mxl = sqrt(2*en) / N
	539	!! where N is the brunt-vaisala frequency, with a minimum value set
[2528]	540	!! to rmxl_min (rn_mxl0) in the interior (surface) ocean.
[1492]	541	!! The mixing and dissipative length scale are bound as follow :
	542	!! nn_mxl=0 : mxl bounded by the distance to surface and bottom.
	543	!! zmxld = zmxlm = mxl
	544	!! nn_mxl=1 : mxl bounded by the e3w and zmxld = zmxlm = mxl
	545	!! nn_mxl=2 : mxl bounded such that the vertical derivative of mxl is
	546	!! less than 1 (\|d/dz(mxl)\|<1) and zmxld = zmxlm = mxl
	547	!! nn_mxl=3 : mxl is bounded from the surface to the bottom usings
	548	!! \|d/dz(xml)\|<1 to obtain lup, and from the bottom to
	549	!! the surface to obtain ldown. the resulting length
	550	!! scales are:
	551	!! zmxld = sqrt( lup * ldown )
	552	!! zmxlm = min ( lup , ldown )
	553	!! - Vertical eddy viscosity and diffusivity:
	554	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	555	!! avt = max( avmb, pdlr * avm )
	556	!! with pdlr=1 if nn_pdl=0, pdlr=1/pdl=F(Ri) otherwise.
	557	!!
	558	!! ** Action : - avt : now vertical eddy diffusivity (w-point)
	559	!! - avmu, avmv : now vertical eddy viscosity at uw- and vw-points
[1239]	560	!!----------------------------------------------------------------------
[2715]	561	INTEGER :: ji, jj, jk ! dummy loop indices
	562	REAL(wp) :: zrn2, zraug, zcoef, zav ! local scalars
	563	REAL(wp) :: zdku, zpdlr, zri, zsqen ! - -
	564	REAL(wp) :: zdkv, zemxl, zemlm, zemlp ! - -
[3294]	565	REAL(wp), POINTER, DIMENSION(:,:,:) :: zmpdl, zmxlm, zmxld
[1239]	566	!!--------------------------------------------------------------------
[3294]	567	!
	568	IF( nn_timing == 1 ) CALL timing_start('tke_avn')
[1239]	569
[3294]	570	CALL wrk_alloc( jpi,jpj,jpk, zmpdl, zmxlm, zmxld )
	571
[1492]	572	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	573	! ! Mixing length
	574	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	575	!
	576	! !* Buoyancy length scale: l=sqrt(2e/n*2)
	577	!
[5120]	578	! initialisation of interior minimum value (avoid a 2d loop with mikt)
	579	zmxlm(:,:,:) = rmxl_min
	580	zmxld(:,:,:) = rmxl_min
	581	!
[2528]	582	IF( ln_mxl0 ) THEN ! surface mixing length = F(stress) : l=vkarmn2.e5taum/(rau0*g)
[4990]	583	DO jj = 2, jpjm1
	584	DO ji = fs_2, fs_jpim1
[5120]	585	zraug = vkarmn * 2.e5_wp / ( rau0 * grav )
	586	zmxlm(ji,jj,1) = MAX( rn_mxl0, zraug * taum(ji,jj) * tmask(ji,jj,1) )
[4990]	587	END DO
	588	END DO
	589	ELSE
[5120]	590	zmxlm(:,:,1) = rn_mxl0
[1239]	591	ENDIF
	592	!
	593	!CDIR NOVERRCHK
[5120]	594	DO jk = 2, jpkm1 ! interior value : l=sqrt(2*e/n^2)
[1239]	595	!CDIR NOVERRCHK
[5120]	596	DO jj = 2, jpjm1
	597	!CDIR NOVERRCHK
	598	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	599	zrn2 = MAX( rn2(ji,jj,jk), rsmall )
[5120]	600	zmxlm(ji,jj,jk) = MAX( rmxl_min, SQRT( 2._wp * en(ji,jj,jk) / zrn2 ) )
[1239]	601	END DO
	602	END DO
	603	END DO
[1492]	604	!
	605	! !* Physical limits for the mixing length
	606	!
[5120]	607	zmxld(:,:,1 ) = zmxlm(:,:,1) ! surface set to the minimum value
[2528]	608	zmxld(:,:,jpk) = rmxl_min ! last level set to the minimum value
[1492]	609	!
[1239]	610	SELECT CASE ( nn_mxl )
	611	!
[5120]	612	! where wmask = 0 set zmxlm == fse3w
[1239]	613	CASE ( 0 ) ! bounded by the distance to surface and bottom
[5120]	614	DO jk = 2, jpkm1
	615	DO jj = 2, jpjm1
	616	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	617	zemxl = MIN( fsdepw(ji,jj,jk) - fsdepw(ji,jj,mikt(ji,jj)), zmxlm(ji,jj,jk), &
[2528]	618	& fsdepw(ji,jj,mbkt(ji,jj)+1) - fsdepw(ji,jj,jk) )
[5120]	619	! wmask prevent zmxlm = 0 if jk = mikt(ji,jj)
	620	zmxlm(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN(zmxlm(ji,jj,jk),fse3w(ji,jj,jk)) * (1 - wmask(ji,jj,jk))
	621	zmxld(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN(zmxlm(ji,jj,jk),fse3w(ji,jj,jk)) * (1 - wmask(ji,jj,jk))
[1239]	622	END DO
	623	END DO
	624	END DO
	625	!
	626	CASE ( 1 ) ! bounded by the vertical scale factor
[5120]	627	DO jk = 2, jpkm1
	628	DO jj = 2, jpjm1
	629	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	630	zemxl = MIN( fse3w(ji,jj,jk), zmxlm(ji,jj,jk) )
	631	zmxlm(ji,jj,jk) = zemxl
	632	zmxld(ji,jj,jk) = zemxl
	633	END DO
	634	END DO
	635	END DO
	636	!
	637	CASE ( 2 ) ! \|dk[xml]\| bounded by e3t :
[5120]	638	DO jk = 2, jpkm1 ! from the surface to the bottom :
	639	DO jj = 2, jpjm1
	640	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	641	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk-1) + fse3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
	642	END DO
[5120]	643	END DO
	644	END DO
	645	DO jk = jpkm1, 2, -1 ! from the bottom to the surface :
	646	DO jj = 2, jpjm1
	647	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	648	zemxl = MIN( zmxlm(ji,jj,jk+1) + fse3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
	649	zmxlm(ji,jj,jk) = zemxl
	650	zmxld(ji,jj,jk) = zemxl
	651	END DO
	652	END DO
	653	END DO
	654	!
	655	CASE ( 3 ) ! lup and ldown, \|dk[xml]\| bounded by e3t :
[5120]	656	DO jk = 2, jpkm1 ! from the surface to the bottom : lup
	657	DO jj = 2, jpjm1
	658	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	659	zmxld(ji,jj,jk) = MIN( zmxld(ji,jj,jk-1) + fse3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
	660	END DO
[5120]	661	END DO
	662	END DO
	663	DO jk = jpkm1, 2, -1 ! from the bottom to the surface : ldown
	664	DO jj = 2, jpjm1
	665	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	666	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk+1) + fse3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
	667	END DO
	668	END DO
	669	END DO
	670	!CDIR NOVERRCHK
	671	DO jk = 2, jpkm1
	672	!CDIR NOVERRCHK
	673	DO jj = 2, jpjm1
	674	!CDIR NOVERRCHK
	675	DO ji = fs_2, fs_jpim1 ! vector opt.
	676	zemlm = MIN ( zmxld(ji,jj,jk), zmxlm(ji,jj,jk) )
	677	zemlp = SQRT( zmxld(ji,jj,jk) * zmxlm(ji,jj,jk) )
	678	zmxlm(ji,jj,jk) = zemlm
	679	zmxld(ji,jj,jk) = zemlp
	680	END DO
	681	END DO
	682	END DO
	683	!
	684	END SELECT
[1492]	685	!
[1239]	686	# if defined key_c1d
[1492]	687	e_dis(:,:,:) = zmxld(:,:,:) ! c1d configuration : save mixing and dissipation turbulent length scales
[1239]	688	e_mix(:,:,:) = zmxlm(:,:,:)
	689	# endif
	690
[1492]	691	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	692	! ! Vertical eddy viscosity and diffusivity (avmu, avmv, avt)
	693	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1239]	694	!CDIR NOVERRCHK
[1492]	695	DO jk = 1, jpkm1 !* vertical eddy viscosity & diffivity at w-points
[1239]	696	!CDIR NOVERRCHK
	697	DO jj = 2, jpjm1
	698	!CDIR NOVERRCHK
	699	DO ji = fs_2, fs_jpim1 ! vector opt.
	700	zsqen = SQRT( en(ji,jj,jk) )
	701	zav = rn_ediff * zmxlm(ji,jj,jk) * zsqen
[5120]	702	avm (ji,jj,jk) = MAX( zav, avmb(jk) ) * wmask(ji,jj,jk)
	703	avt (ji,jj,jk) = MAX( zav, avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1239]	704	dissl(ji,jj,jk) = zsqen / zmxld(ji,jj,jk)
	705	END DO
	706	END DO
	707	END DO
[1492]	708	CALL lbc_lnk( avm, 'W', 1. ) ! Lateral boundary conditions (sign unchanged)
	709	!
[5120]	710	DO jk = 2, jpkm1 !* vertical eddy viscosity at wu- and wv-points
	711	DO jj = 2, jpjm1
	712	DO ji = fs_2, fs_jpim1 ! vector opt.
	713	avmu(ji,jj,jk) = 0.5 * ( avm(ji,jj,jk) + avm(ji+1,jj ,jk) ) * wumask(ji,jj,jk)
	714	avmv(ji,jj,jk) = 0.5 * ( avm(ji,jj,jk) + avm(ji ,jj+1,jk) ) * wvmask(ji,jj,jk)
[4990]	715	END DO
[1239]	716	END DO
	717	END DO
	718	CALL lbc_lnk( avmu, 'U', 1. ) ; CALL lbc_lnk( avmv, 'V', 1. ) ! Lateral boundary conditions
[1492]	719	!
	720	IF( nn_pdl == 1 ) THEN !* Prandtl number case: update avt
[5120]	721	DO jk = 2, jpkm1
	722	DO jj = 2, jpjm1
	723	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	724	zcoef = avm(ji,jj,jk) * 2._wp * fse3w(ji,jj,jk) * fse3w(ji,jj,jk)
[1492]	725	! ! shear
	726	zdku = avmu(ji-1,jj,jk) * ( un(ji-1,jj,jk-1) - un(ji-1,jj,jk) ) * ( ub(ji-1,jj,jk-1) - ub(ji-1,jj,jk) ) &
	727	& + avmu(ji ,jj,jk) * ( un(ji ,jj,jk-1) - un(ji ,jj,jk) ) * ( ub(ji ,jj,jk-1) - ub(ji ,jj,jk) )
	728	zdkv = avmv(ji,jj-1,jk) * ( vn(ji,jj-1,jk-1) - vn(ji,jj-1,jk) ) * ( vb(ji,jj-1,jk-1) - vb(ji,jj-1,jk) ) &
	729	& + avmv(ji,jj ,jk) * ( vn(ji,jj ,jk-1) - vn(ji,jj ,jk) ) * ( vb(ji,jj ,jk-1) - vb(ji,jj ,jk) )
	730	! ! local Richardson number
[2528]	731	zri = MAX( rn2b(ji,jj,jk), 0._wp ) * zcoef / (zdku + zdkv + rn_bshear )
	732	zpdlr = MAX( 0.1_wp, 0.2 / MAX( 0.2 , zri ) )
[1492]	733	!!gm and even better with the use of the "true" ri_crit=0.22222... (this change the results!)
[2528]	734	!!gm zpdlr = MAX( 0.1_wp, ri_crit / MAX( ri_crit , zri ) )
[5120]	735	avt(ji,jj,jk) = MAX( zpdlr * avt(ji,jj,jk), avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1492]	736	# if defined key_c1d
[5120]	737	e_pdl(ji,jj,jk) = zpdlr * wmask(ji,jj,jk) ! c1d configuration : save masked Prandlt number
	738	e_ric(ji,jj,jk) = zri * wmask(ji,jj,jk) ! c1d config. : save Ri
[1239]	739	# endif
	740	END DO
	741	END DO
	742	END DO
	743	ENDIF
	744	CALL lbc_lnk( avt, 'W', 1. ) ! Lateral boundary conditions on avt (sign unchanged)
	745
	746	IF(ln_ctl) THEN
	747	CALL prt_ctl( tab3d_1=en , clinfo1=' tke - e: ', tab3d_2=avt, clinfo2=' t: ', ovlap=1, kdim=jpk)
	748	CALL prt_ctl( tab3d_1=avmu, clinfo1=' tke - u: ', mask1=umask, &
	749	& tab3d_2=avmv, clinfo2= ' v: ', mask2=vmask, ovlap=1, kdim=jpk )
	750	ENDIF
	751	!
[3294]	752	CALL wrk_dealloc( jpi,jpj,jpk, zmpdl, zmxlm, zmxld )
	753	!
	754	IF( nn_timing == 1 ) CALL timing_stop('tke_avn')
	755	!
[1492]	756	END SUBROUTINE tke_avn
[1239]	757
[1492]	758
[2528]	759	SUBROUTINE zdf_tke_init
[1239]	760	!!----------------------------------------------------------------------
[2528]	761	!! * ROUTINE zdf_tke_init *
[1239]	762	!!
	763	!! ** Purpose : Initialization of the vertical eddy diffivity and
[1492]	764	!! viscosity when using a tke turbulent closure scheme
[1239]	765	!!
[1601]	766	!! ** Method : Read the namzdf_tke namelist and check the parameters
[1492]	767	!! called at the first timestep (nit000)
[1239]	768	!!
[1601]	769	!! ** input : Namlist namzdf_tke
[1239]	770	!!
	771	!! ** Action : Increase by 1 the nstop flag is setting problem encounter
	772	!!----------------------------------------------------------------------
	773	INTEGER :: ji, jj, jk ! dummy loop indices
[6440]	774	INTEGER :: ios, ierr
[1239]	775	!!
[2528]	776	NAMELIST/namzdf_tke/ rn_ediff, rn_ediss , rn_ebb , rn_emin , &
	777	& rn_emin0, rn_bshear, nn_mxl , ln_mxl0 , &
	778	& rn_mxl0 , nn_pdl , ln_lc , rn_lc , &
[6448]	779	& nn_etau , nn_htau , rn_efr , rn_c
[1239]	780	!!----------------------------------------------------------------------
[6448]	781
[4147]	782	REWIND( numnam_ref ) ! Namelist namzdf_tke in reference namelist : Turbulent Kinetic Energy
	783	READ ( numnam_ref, namzdf_tke, IOSTAT = ios, ERR = 901)
	784	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in reference namelist', lwp )
	785
	786	REWIND( numnam_cfg ) ! Namelist namzdf_tke in configuration namelist : Turbulent Kinetic Energy
	787	READ ( numnam_cfg, namzdf_tke, IOSTAT = ios, ERR = 902 )
	788	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in configuration namelist', lwp )
[4624]	789	IF(lwm) WRITE ( numond, namzdf_tke )
[2715]	790	!
[2528]	791	ri_cri = 2._wp / ( 2._wp + rn_ediss / rn_ediff ) ! resulting critical Richardson number
[6440]	792	# if defined key_zdftmx_new
	793	! key_zdftmx_new: New internal wave-driven param: specified value of rn_emin & rmxl_min are used
	794	rn_emin = 1.e-10_wp
	795	rmxl_min = 1.e-03_wp
	796	IF(lwp) THEN ! Control print
	797	WRITE(numout,*)
	798	WRITE(numout,*) 'zdf_tke_init : New tidal mixing case: force rn_emin = 1.e-10 and rmxl_min = 1.e-3 '
	799	WRITE(numout,*) '~~~~~~~~~~~~'
	800	ENDIF
	801	# else
[2528]	802	rmxl_min = 1.e-6_wp / ( rn_ediff * SQRT( rn_emin ) ) ! resulting minimum length to recover molecular viscosity
[6440]	803	# endif
[2715]	804	!
[1492]	805	IF(lwp) THEN !* Control print
[1239]	806	WRITE(numout,*)
[2528]	807	WRITE(numout,*) 'zdf_tke_init : tke turbulent closure scheme - initialisation'
	808	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	809	WRITE(numout,*) ' Namelist namzdf_tke : set tke mixing parameters'
[1705]	810	WRITE(numout,*) ' coef. to compute avt rn_ediff = ', rn_ediff
	811	WRITE(numout,*) ' Kolmogoroff dissipation coef. rn_ediss = ', rn_ediss
	812	WRITE(numout,*) ' tke surface input coef. rn_ebb = ', rn_ebb
	813	WRITE(numout,*) ' minimum value of tke rn_emin = ', rn_emin
	814	WRITE(numout,*) ' surface minimum value of tke rn_emin0 = ', rn_emin0
	815	WRITE(numout,*) ' background shear (>0) rn_bshear = ', rn_bshear
	816	WRITE(numout,*) ' mixing length type nn_mxl = ', nn_mxl
	817	WRITE(numout,*) ' prandl number flag nn_pdl = ', nn_pdl
	818	WRITE(numout,*) ' surface mixing length = F(stress) or not ln_mxl0 = ', ln_mxl0
[2528]	819	WRITE(numout,*) ' surface mixing length minimum value rn_mxl0 = ', rn_mxl0
	820	WRITE(numout,*) ' flag to take into acc. Langmuir circ. ln_lc = ', ln_lc
	821	WRITE(numout,*) ' coef to compute verticla velocity of LC rn_lc = ', rn_lc
[1705]	822	WRITE(numout,*) ' test param. to add tke induced by wind nn_etau = ', nn_etau
	823	WRITE(numout,*) ' flag for computation of exp. tke profile nn_htau = ', nn_htau
	824	WRITE(numout,*) ' fraction of en which pene. the thermocline rn_efr = ', rn_efr
[6448]	825	WRITE(numout,*) ' fraction of TKE added within the mixed layer by nn_etau rn_c = ', rn_c
[1239]	826	WRITE(numout,*)
[1601]	827	WRITE(numout,*) ' critical Richardson nb with your parameters ri_cri = ', ri_cri
[1239]	828	ENDIF
[2715]	829	!
	830	! ! allocate tke arrays
	831	IF( zdf_tke_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_tke_init : unable to allocate arrays' )
	832	!
[1492]	833	! !* Check of some namelist values
[4990]	834	IF( nn_mxl < 0 .OR. nn_mxl > 3 ) CALL ctl_stop( 'bad flag: nn_mxl is 0, 1 or 2 ' )
	835	IF( nn_pdl < 0 .OR. nn_pdl > 1 ) CALL ctl_stop( 'bad flag: nn_pdl is 0 or 1 ' )
[6448]	836	IF( nn_htau < 0 .OR. nn_htau > 5 ) CALL ctl_stop( 'bad flag: nn_htau is 0 to 5 ' )
[5407]	837	IF( nn_etau == 3 .AND. .NOT. ln_cpl ) CALL ctl_stop( 'nn_etau == 3 : HF taum only known in coupled mode' )
[1239]	838
[2528]	839	IF( ln_mxl0 ) THEN
	840	IF(lwp) WRITE(numout,*) ' use a surface mixing length = F(stress) : set rn_mxl0 = rmxl_min'
	841	rn_mxl0 = rmxl_min
	842	ENDIF
	843
[6448]	844	IF( nn_etau == 2 .OR. ( nn_etau /= 0 .AND. nn_htau == 2 ) ) CALL zdf_mxl( nit000 - 1 ) ! Initialization of nmln and hmlp
[1239]	845
[1492]	846	! !* depth of penetration of surface tke
	847	IF( nn_etau /= 0 ) THEN
[6448]	848	htau(:,:) = 0._wp
[1601]	849	SELECT CASE( nn_htau ) ! Choice of the depth of penetration
[2528]	850	CASE( 0 ) ! constant depth penetration (here 10 meters)
	851	htau(:,:) = 10._wp
	852	CASE( 1 ) ! F(latitude) : 0.5m to 30m poleward of 40 degrees
	853	htau(:,:) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
[6448]	854	CASE( 2 ) ! fraction of depth-integrated TKE within mixed-layer
	855	rhtau = -1._wp / LOG( 1._wp - rn_c )
	856	CASE( 3 ) ! F(latitude) : 0.5m to 15m poleward of 20 degrees
	857	htau(:,:) = MAX( 0.5_wp, MIN( 15._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
	858	CASE( 4 ) ! F(latitude) : 0.5m to 10m/30m poleward of 13/40 degrees north/south
	859	DO jj = 2, jpjm1
	860	DO ji = fs_2, fs_jpim1 ! vector opt.
	861	IF( gphit(ji,jj) <= 0._wp ) THEN
	862	htau(ji,jj) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	863	ELSE
	864	htau(ji,jj) = MAX( 0.5_wp, MIN( 10._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	865	ENDIF
	866	END DO
	867	END DO
	868	CASE ( 5 ) ! F(latitude) : 0.5m to 10m poleward of 13 degrees north/south,
	869	DO jj = 2, jpjm1 ! 10m to 30m between 30/45 degrees south
	870	DO ji = fs_2, fs_jpim1 ! vector opt.
	871	IF( gphit(ji,jj) <= -30._wp ) THEN
	872	htau(ji,jj) = MAX( 10._wp, MIN( 30._wp, 55._wp* ABS( SIN( rpi/120._wp * ( gphit(ji,jj) + 23._wp ) ) ) ) )
	873	ELSE
	874	htau(ji,jj) = MAX( 0.5_wp, MIN( 10._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	875	ENDIF
	876	END DO
	877	END DO
[1492]	878	END SELECT
[6448]	879	!
	880	IF( nn_etau == 4 .AND. nn_htau /= 2 ) THEN ! efr dependant on constant htau
	881	DO jj = 2, jpjm1
	882	DO ji = fs_2, fs_jpim1 ! vector opt.
	883	efr(ji,jj) = rn_efr / ( htau(ji,jj) * ( 1._wp - EXP( -bathy(ji,jj) / htau(ji,jj) ) ) )
	884	END DO
	885	END DO
	886	ENDIF
[1492]	887	ENDIF
	888	! !* set vertical eddy coef. to the background value
[1239]	889	DO jk = 1, jpk
[5120]	890	avt (:,:,jk) = avtb(jk) * wmask (:,:,jk)
	891	avm (:,:,jk) = avmb(jk) * wmask (:,:,jk)
	892	avmu(:,:,jk) = avmb(jk) * wumask(:,:,jk)
	893	avmv(:,:,jk) = avmb(jk) * wvmask(:,:,jk)
[1239]	894	END DO
[2528]	895	dissl(:,:,:) = 1.e-12_wp
[2715]	896	!
	897	CALL tke_rst( nit000, 'READ' ) !* read or initialize all required files
[1239]	898	!
[2528]	899	END SUBROUTINE zdf_tke_init
[1239]	900
	901
[1531]	902	SUBROUTINE tke_rst( kt, cdrw )
[1239]	903	!!---------------------------------------------------------------------
[1531]	904	!! * ROUTINE tke_rst *
[1239]	905	!!
	906	!! ** Purpose : Read or write TKE file (en) in restart file
	907	!!
	908	!! ** Method : use of IOM library
	909	!! if the restart does not contain TKE, en is either
[1537]	910	!! set to rn_emin or recomputed
[1239]	911	!!----------------------------------------------------------------------
[2715]	912	INTEGER , INTENT(in) :: kt ! ocean time-step
	913	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
[1239]	914	!
[1481]	915	INTEGER :: jit, jk ! dummy loop indices
[2715]	916	INTEGER :: id1, id2, id3, id4, id5, id6 ! local integers
[1239]	917	!!----------------------------------------------------------------------
	918	!
[1481]	919	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
	920	! ! ---------------
	921	IF( ln_rstart ) THEN !* Read the restart file
	922	id1 = iom_varid( numror, 'en' , ldstop = .FALSE. )
	923	id2 = iom_varid( numror, 'avt' , ldstop = .FALSE. )
	924	id3 = iom_varid( numror, 'avm' , ldstop = .FALSE. )
	925	id4 = iom_varid( numror, 'avmu' , ldstop = .FALSE. )
	926	id5 = iom_varid( numror, 'avmv' , ldstop = .FALSE. )
	927	id6 = iom_varid( numror, 'dissl', ldstop = .FALSE. )
	928	!
	929	IF( id1 > 0 ) THEN ! 'en' exists
[1239]	930	CALL iom_get( numror, jpdom_autoglo, 'en', en )
[1481]	931	IF( MIN( id2, id3, id4, id5, id6 ) > 0 ) THEN ! all required arrays exist
	932	CALL iom_get( numror, jpdom_autoglo, 'avt' , avt )
	933	CALL iom_get( numror, jpdom_autoglo, 'avm' , avm )
	934	CALL iom_get( numror, jpdom_autoglo, 'avmu' , avmu )
	935	CALL iom_get( numror, jpdom_autoglo, 'avmv' , avmv )
	936	CALL iom_get( numror, jpdom_autoglo, 'dissl', dissl )
[1492]	937	ELSE ! one at least array is missing
	938	CALL tke_avn ! compute avt, avm, avmu, avmv and dissl (approximation)
[1481]	939	ENDIF
	940	ELSE ! No TKE array found: initialisation
	941	IF(lwp) WRITE(numout,*) ' ===>>>> : previous run without tke scheme, en computed by iterative loop'
[1239]	942	en (:,:,:) = rn_emin * tmask(:,:,:)
[1492]	943	CALL tke_avn ! recompute avt, avm, avmu, avmv and dissl (approximation)
[5112]	944	!
	945	avt_k (:,:,:) = avt (:,:,:)
	946	avm_k (:,:,:) = avm (:,:,:)
	947	avmu_k(:,:,:) = avmu(:,:,:)
	948	avmv_k(:,:,:) = avmv(:,:,:)
	949	!
[1531]	950	DO jit = nit000 + 1, nit000 + 10 ; CALL zdf_tke( jit ) ; END DO
[1239]	951	ENDIF
[1481]	952	ELSE !* Start from rest
	953	en(:,:,:) = rn_emin * tmask(:,:,:)
	954	DO jk = 1, jpk ! set the Kz to the background value
[5120]	955	avt (:,:,jk) = avtb(jk) * wmask (:,:,jk)
	956	avm (:,:,jk) = avmb(jk) * wmask (:,:,jk)
	957	avmu(:,:,jk) = avmb(jk) * wumask(:,:,jk)
	958	avmv(:,:,jk) = avmb(jk) * wvmask(:,:,jk)
[1481]	959	END DO
[1239]	960	ENDIF
[1481]	961	!
	962	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
	963	! ! -------------------
[1531]	964	IF(lwp) WRITE(numout,*) '---- tke-rst ----'
[3632]	965	CALL iom_rstput( kt, nitrst, numrow, 'en' , en )
	966	CALL iom_rstput( kt, nitrst, numrow, 'avt' , avt_k )
	967	CALL iom_rstput( kt, nitrst, numrow, 'avm' , avm_k )
	968	CALL iom_rstput( kt, nitrst, numrow, 'avmu' , avmu_k )
	969	CALL iom_rstput( kt, nitrst, numrow, 'avmv' , avmv_k )
	970	CALL iom_rstput( kt, nitrst, numrow, 'dissl', dissl )
[1481]	971	!
[1239]	972	ENDIF
	973	!
[1531]	974	END SUBROUTINE tke_rst
[1239]	975
	976	#else
	977	!!----------------------------------------------------------------------
	978	!! Dummy module : NO TKE scheme
	979	!!----------------------------------------------------------------------
[1531]	980	LOGICAL, PUBLIC, PARAMETER :: lk_zdftke = .FALSE. !: TKE flag
[1239]	981	CONTAINS
[2528]	982	SUBROUTINE zdf_tke_init ! Dummy routine
	983	END SUBROUTINE zdf_tke_init
	984	SUBROUTINE zdf_tke( kt ) ! Dummy routine
[1531]	985	WRITE(,) 'zdf_tke: You should not have seen this print! error?', kt
	986	END SUBROUTINE zdf_tke
	987	SUBROUTINE tke_rst( kt, cdrw )
[1492]	988	CHARACTER(len=*) :: cdrw
[1531]	989	WRITE(,) 'tke_rst: You should not have seen this print! error?', kt, cdwr
	990	END SUBROUTINE tke_rst
[1239]	991	#endif
	992
	993	!!======================================================================
[1531]	994	END MODULE zdftke

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