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

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source: branches/UKMO/test_moci_test_suite_namelist_read/NEMOGCM/NEMO/OPA_SRC/ZDF/zdftke.F90 @ 9366

Last change on this file since 9366 was 9366, checked in by andmirek, 6 years ago
#2050 first version. Compiled OK in moci test suite
File size: 52.7 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
[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)
[8243]	55	USE iom_def, ONLY : lwxios
[6487]	56	#if defined key_agrif
	57	USE agrif_opa_interp
	58	USE agrif_opa_update
	59	#endif
[7924]	60	USE iom_def, ONLY : lxios_read
[1239]	61
[6487]	62
	63
[1239]	64	IMPLICIT NONE
	65	PRIVATE
	66
[2528]	67	PUBLIC zdf_tke ! routine called in step module
	68	PUBLIC zdf_tke_init ! routine called in opa module
	69	PUBLIC tke_rst ! routine called in step module
[9366]	70	PRIVATE tke_namelist
[1239]	71
[2715]	72	LOGICAL , PUBLIC, PARAMETER :: lk_zdftke = .TRUE. !: TKE vertical mixing flag
[1239]	73
[4147]	74	! !! Namelist namzdf_tke
	75	LOGICAL :: ln_mxl0 ! mixing length scale surface value as function of wind stress or not
	76	INTEGER :: nn_mxl ! type of mixing length (=0/1/2/3)
	77	REAL(wp) :: rn_mxl0 ! surface min value of mixing length (kappaz_o=0.40.1 m) [m]
	78	INTEGER :: nn_pdl ! Prandtl number or not (ratio avt/avm) (=0/1)
	79	REAL(wp) :: rn_ediff ! coefficient for avt: avt=rn_ediffmxlsqrt(e)
	80	REAL(wp) :: rn_ediss ! coefficient of the Kolmogoroff dissipation
	81	REAL(wp) :: rn_ebb ! coefficient of the surface input of tke
	82	REAL(wp) :: rn_emin ! minimum value of tke [m2/s2]
	83	REAL(wp) :: rn_emin0 ! surface minimum value of tke [m2/s2]
	84	REAL(wp) :: rn_bshear ! background shear (>0) currently a numerical threshold (do not change it)
	85	INTEGER :: nn_etau ! type of depth penetration of surface tke (=0/1/2/3)
	86	INTEGER :: nn_htau ! type of tke profile of penetration (=0/1)
	87	REAL(wp) :: rn_efr ! fraction of TKE surface value which penetrates in the ocean
[6491]	88	REAL(wp) :: rn_c ! fraction of TKE added within the mixed layer by nn_etau
[4147]	89	LOGICAL :: ln_lc ! Langmuir cells (LC) as a source term of TKE or not
	90	REAL(wp) :: rn_lc ! coef to compute vertical velocity of Langmuir cells
[1239]	91
[4147]	92	REAL(wp) :: ri_cri ! critic Richardson number (deduced from rn_ediff and rn_ediss values)
	93	REAL(wp) :: rmxl_min ! minimum mixing length value (deduced from rn_ediff and rn_emin values) [m]
[6491]	94	REAL(wp) :: rhtau ! coefficient to relate MLD to htau when nn_htau == 2
[2528]	95	REAL(wp) :: rhftau_add = 1.e-3_wp ! add offset applied to HF part of taum (nn_etau=3)
	96	REAL(wp) :: rhftau_scl = 1.0_wp ! scale factor applied to HF part of taum (nn_etau=3)
[1239]	97
[2715]	98	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: htau ! depth of tke penetration (nn_htau)
[6491]	99	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_niw !: TKE budget- near-inertial waves term
	100	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: efr ! surface boundary condition for nn_etau = 4
[2715]	101	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dissl ! now mixing lenght of dissipation
	102	#if defined key_c1d
	103	! !! 1D cfg only ('key_c1d')
	104	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_dis, e_mix !: dissipation and mixing turbulent lengh scales
	105	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_pdl, e_ric !: prandl and local Richardson numbers
	106	#endif
[1492]	107
[1239]	108	!! * Substitutions
	109	# include "domzgr_substitute.h90"
	110	# include "vectopt_loop_substitute.h90"
	111	!!----------------------------------------------------------------------
[2715]	112	!! NEMO/OPA 4.0 , NEMO Consortium (2011)
[2528]	113	!! $Id$
	114	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[1239]	115	!!----------------------------------------------------------------------
	116	CONTAINS
	117
[2715]	118	INTEGER FUNCTION zdf_tke_alloc()
	119	!!----------------------------------------------------------------------
	120	!! * FUNCTION zdf_tke_alloc *
	121	!!----------------------------------------------------------------------
	122	ALLOCATE( &
[6491]	123	& efr (jpi,jpj) , e_niw(jpi,jpj,jpk) , &
[2715]	124	#if defined key_c1d
	125	& e_dis(jpi,jpj,jpk) , e_mix(jpi,jpj,jpk) , &
	126	& e_pdl(jpi,jpj,jpk) , e_ric(jpi,jpj,jpk) , &
	127	#endif
[6487]	128	& htau (jpi,jpj) , dissl(jpi,jpj,jpk) , STAT= zdf_tke_alloc )
[2715]	129	!
	130	IF( lk_mpp ) CALL mpp_sum ( zdf_tke_alloc )
	131	IF( zdf_tke_alloc /= 0 ) CALL ctl_warn('zdf_tke_alloc: failed to allocate arrays')
	132	!
	133	END FUNCTION zdf_tke_alloc
	134
	135
[1531]	136	SUBROUTINE zdf_tke( kt )
[1239]	137	!!----------------------------------------------------------------------
[1531]	138	!! * ROUTINE zdf_tke *
[1239]	139	!!
	140	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
[1492]	141	!! coefficients using a turbulent closure scheme (TKE).
[1239]	142	!!
[1492]	143	!! ** Method : The time evolution of the turbulent kinetic energy (tke)
	144	!! is computed from a prognostic equation :
	145	!! d(en)/dt = avm (d(u)/dz)**2 ! shear production
	146	!! + d( avm d(en)/dz )/dz ! diffusion of tke
	147	!! + avt N^2 ! stratif. destruc.
	148	!! - rn_ediss / emxl en**(2/3) ! Kolmogoroff dissipation
[1239]	149	!! with the boundary conditions:
[1695]	150	!! surface: en = max( rn_emin0, rn_ebb * taum )
[1239]	151	!! bottom : en = rn_emin
[1492]	152	!! The associated critical Richardson number is: ri_cri = 2/(2+rn_ediss/rn_ediff)
	153	!!
	154	!! The now Turbulent kinetic energy is computed using the following
	155	!! time stepping: implicit for vertical diffusion term, linearized semi
	156	!! implicit for kolmogoroff dissipation term, and explicit forward for
	157	!! both buoyancy and shear production terms. Therefore a tridiagonal
	158	!! linear system is solved. Note that buoyancy and shear terms are
	159	!! discretized in a energy conserving form (Bruchard 2002).
	160	!!
	161	!! The dissipative and mixing length scale are computed from en and
	162	!! the stratification (see tke_avn)
	163	!!
	164	!! The now vertical eddy vicosity and diffusivity coefficients are
	165	!! given by:
	166	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	167	!! avt = max( avmb, pdl * avm )
[1239]	168	!! eav = max( avmb, avm )
[1492]	169	!! where pdl, the inverse of the Prandtl number is 1 if nn_pdl=0 and
	170	!! given by an empirical funtion of the localRichardson number if nn_pdl=1
[1239]	171	!!
	172	!! ** Action : compute en (now turbulent kinetic energy)
	173	!! update avt, avmu, avmv (before vertical eddy coef.)
	174	!!
	175	!! References : Gaspar et al., JGR, 1990,
	176	!! Blanke and Delecluse, JPO, 1991
	177	!! Mellor and Blumberg, JPO 2004
	178	!! Axell, JGR, 2002
[1492]	179	!! Bruchard OM 2002
[1239]	180	!!----------------------------------------------------------------------
[1492]	181	INTEGER, INTENT(in) :: kt ! ocean time step
	182	!!----------------------------------------------------------------------
[1481]	183	!
[3632]	184	IF( kt /= nit000 ) THEN ! restore before value to compute tke
	185	avt (:,:,:) = avt_k (:,:,:)
	186	avm (:,:,:) = avm_k (:,:,:)
	187	avmu(:,:,:) = avmu_k(:,:,:)
	188	avmv(:,:,:) = avmv_k(:,:,:)
	189	ENDIF
	190	!
[2528]	191	CALL tke_tke ! now tke (en)
[1492]	192	!
[2528]	193	CALL tke_avn ! now avt, avm, avmu, avmv
	194	!
[3632]	195	avt_k (:,:,:) = avt (:,:,:)
	196	avm_k (:,:,:) = avm (:,:,:)
	197	avmu_k(:,:,:) = avmu(:,:,:)
	198	avmv_k(:,:,:) = avmv(:,:,:)
	199	!
[6487]	200	#if defined key_agrif
	201	! Update child grid f => parent grid
	202	IF( .NOT.Agrif_Root() ) CALL Agrif_Update_Tke( kt ) ! children only
	203	#endif
	204	!
[1531]	205	END SUBROUTINE zdf_tke
[1239]	206
[1492]	207
[1481]	208	SUBROUTINE tke_tke
[1239]	209	!!----------------------------------------------------------------------
[1492]	210	!! * ROUTINE tke_tke *
	211	!!
	212	!! ** Purpose : Compute the now Turbulente Kinetic Energy (TKE)
	213	!!
	214	!! ** Method : - TKE surface boundary condition
[2528]	215	!! - source term due to Langmuir cells (Axell JGR 2002) (ln_lc=T)
[1492]	216	!! - source term due to shear (saved in avmu, avmv arrays)
	217	!! - Now TKE : resolution of the TKE equation by inverting
	218	!! a tridiagonal linear system by a "methode de chasse"
	219	!! - increase TKE due to surface and internal wave breaking
	220	!!
	221	!! ** Action : - en : now turbulent kinetic energy)
	222	!! - avmu, avmv : production of TKE by shear at u and v-points
	223	!! (= Kz dz[Ub] * dz[Un] )
[1239]	224	!! ---------------------------------------------------------------------
[1705]	225	INTEGER :: ji, jj, jk ! dummy loop arguments
[2528]	226	!!bfr INTEGER :: ikbu, ikbv, ikbum1, ikbvm1 ! temporary scalar
	227	!!bfr INTEGER :: ikbt, ikbumm1, ikbvmm1 ! temporary scalar
[1705]	228	REAL(wp) :: zrhoa = 1.22 ! Air density kg/m3
	229	REAL(wp) :: zcdrag = 1.5e-3 ! drag coefficient
	230	REAL(wp) :: zbbrau, zesh2 ! temporary scalars
	231	REAL(wp) :: zfact1, zfact2, zfact3 ! - -
	232	REAL(wp) :: ztx2 , zty2 , zcof ! - -
	233	REAL(wp) :: ztau , zdif ! - -
	234	REAL(wp) :: zus , zwlc , zind ! - -
	235	REAL(wp) :: zzd_up, zzd_lw ! - -
[2528]	236	!!bfr REAL(wp) :: zebot ! - -
[3294]	237	INTEGER , POINTER, DIMENSION(:,: ) :: imlc
	238	REAL(wp), POINTER, DIMENSION(:,: ) :: zhlc
	239	REAL(wp), POINTER, DIMENSION(:,:,:) :: zpelc, zdiag, zd_up, zd_lw
[1239]	240	!!--------------------------------------------------------------------
[1492]	241	!
[3294]	242	IF( nn_timing == 1 ) CALL timing_start('tke_tke')
	243	!
	244	CALL wrk_alloc( jpi,jpj, imlc ) ! integer
	245	CALL wrk_alloc( jpi,jpj, zhlc )
	246	CALL wrk_alloc( jpi,jpj,jpk, zpelc, zdiag, zd_up, zd_lw )
	247	!
[1695]	248	zbbrau = rn_ebb / rau0 ! Local constant initialisation
[2528]	249	zfact1 = -.5_wp * rdt
	250	zfact2 = 1.5_wp * rdt * rn_ediss
	251	zfact3 = 0.5_wp * rn_ediss
[1492]	252	!
[5120]	253	!
[1492]	254	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	255	! ! Surface boundary condition on tke
	256	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[5120]	257	IF ( ln_isfcav ) THEN
	258	DO jj = 2, jpjm1 ! en(mikt(ji,jj)) = rn_emin
	259	DO ji = fs_2, fs_jpim1 ! vector opt.
	260	en(ji,jj,mikt(ji,jj))=rn_emin * tmask(ji,jj,1)
	261	END DO
	262	END DO
	263	END IF
[1695]	264	DO jj = 2, jpjm1 ! en(1) = rn_ebb taum / rau0 (min value rn_emin0)
[1481]	265	DO ji = fs_2, fs_jpim1 ! vector opt.
[5120]	266	en(ji,jj,1) = MAX( rn_emin0, zbbrau * taum(ji,jj) ) * tmask(ji,jj,1)
[1481]	267	END DO
	268	END DO
[2528]	269
	270	!!bfr - start commented area
[1492]	271	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	272	! ! Bottom boundary condition on tke
	273	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1719]	274	!
	275	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	276	! Tests to date have found the bottom boundary condition on tke to have very little effect.
	277	! The condition is coded here for completion but commented out until there is proof that the
	278	! computational cost is justified
	279	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	280	! en(bot) = (rn_ebb0/rau0)0.5sqrt(u_botfr^2+v_botfr^2) (min value rn_emin)
[1662]	281	!CDIR NOVERRCHK
[1719]	282	!! DO jj = 2, jpjm1
[1662]	283	!CDIR NOVERRCHK
[1719]	284	!! DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	285	!! ztx2 = bfrua(ji-1,jj) * ub(ji-1,jj,mbku(ji-1,jj)) + &
	286	!! bfrua(ji ,jj) * ub(ji ,jj,mbku(ji ,jj) )
	287	!! zty2 = bfrva(ji,jj ) * vb(ji,jj ,mbkv(ji,jj )) + &
	288	!! bfrva(ji,jj-1) * vb(ji,jj-1,mbkv(ji,jj-1) )
[1719]	289	!! zebot = 0.001875_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000.
[2528]	290	!! en (ji,jj,mbkt(ji,jj)+1) = MAX( zebot, rn_emin ) * tmask(ji,jj,1)
[1719]	291	!! END DO
	292	!! END DO
[2528]	293	!!bfr - end commented area
[1492]	294	!
	295	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[2528]	296	IF( ln_lc ) THEN ! Langmuir circulation source term added to tke (Axell JGR 2002)
[1492]	297	! !>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
[1239]	298	!
[1492]	299	! !* total energy produce by LC : cumulative sum over jk
[2528]	300	zpelc(:,:,1) = MAX( rn2b(:,:,1), 0._wp ) * fsdepw(:,:,1) * fse3w(:,:,1)
[1239]	301	DO jk = 2, jpk
[2528]	302	zpelc(:,:,jk) = zpelc(:,:,jk-1) + MAX( rn2b(:,:,jk), 0._wp ) * fsdepw(:,:,jk) * fse3w(:,:,jk)
[1239]	303	END DO
[1492]	304	! !* finite Langmuir Circulation depth
[1705]	305	zcof = 0.5 * 0.016 * 0.016 / ( zrhoa * zcdrag )
[2528]	306	imlc(:,:) = mbkt(:,:) + 1 ! Initialization to the number of w ocean point (=2 over land)
[1239]	307	DO jk = jpkm1, 2, -1
[1492]	308	DO jj = 1, jpj ! Last w-level at which zpelc>=0.5usus
	309	DO ji = 1, jpi ! with us=0.016*wind(starting from jpk-1)
[1705]	310	zus = zcof * taum(ji,jj)
[1239]	311	IF( zpelc(ji,jj,jk) > zus ) imlc(ji,jj) = jk
	312	END DO
	313	END DO
	314	END DO
[1492]	315	! ! finite LC depth
	316	DO jj = 1, jpj
[1239]	317	DO ji = 1, jpi
	318	zhlc(ji,jj) = fsdepw(ji,jj,imlc(ji,jj))
	319	END DO
	320	END DO
[1705]	321	zcof = 0.016 / SQRT( zrhoa * zcdrag )
[5120]	322	!CDIR NOVERRCHK
[1492]	323	DO jk = 2, jpkm1 !* TKE Langmuir circulation source term added to en
[5120]	324	!CDIR NOVERRCHK
[1239]	325	DO jj = 2, jpjm1
[5120]	326	!CDIR NOVERRCHK
[1239]	327	DO ji = fs_2, fs_jpim1 ! vector opt.
[1705]	328	zus = zcof * SQRT( taum(ji,jj) ) ! Stokes drift
[1492]	329	! ! vertical velocity due to LC
[1239]	330	zind = 0.5 - SIGN( 0.5, fsdepw(ji,jj,jk) - zhlc(ji,jj) )
	331	zwlc = zind * rn_lc * zus * SIN( rpi * fsdepw(ji,jj,jk) / zhlc(ji,jj) )
[1492]	332	! ! TKE Langmuir circulation source term
[6487]	333	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( 1._wp - fr_i(ji,jj) ) * ( zwlc * zwlc * zwlc ) / &
	334	& zhlc(ji,jj) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	335	END DO
	336	END DO
	337	END DO
	338	!
	339	ENDIF
[1492]	340	!
	341	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	342	! ! Now Turbulent kinetic energy (output in en)
	343	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	344	! ! Resolution of a tridiagonal linear system by a "methode de chasse"
	345	! ! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
	346	! ! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
	347	!
	348	DO jk = 2, jpkm1 !* Shear production at uw- and vw-points (energy conserving form)
	349	DO jj = 1, jpj ! here avmu, avmv used as workspace
	350	DO ji = 1, jpi
	351	avmu(ji,jj,jk) = avmu(ji,jj,jk) * ( un(ji,jj,jk-1) - un(ji,jj,jk) ) &
	352	& * ( ub(ji,jj,jk-1) - ub(ji,jj,jk) ) &
[5120]	353	& / ( fse3uw_n(ji,jj,jk) &
	354	& * fse3uw_b(ji,jj,jk) )
[1492]	355	avmv(ji,jj,jk) = avmv(ji,jj,jk) * ( vn(ji,jj,jk-1) - vn(ji,jj,jk) ) &
	356	& * ( vb(ji,jj,jk-1) - vb(ji,jj,jk) ) &
	357	& / ( fse3vw_n(ji,jj,jk) &
	358	& * fse3vw_b(ji,jj,jk) )
	359	END DO
	360	END DO
	361	END DO
	362	!
[5120]	363	DO jk = 2, jpkm1 !* Matrix and right hand side in en
	364	DO jj = 2, jpjm1
	365	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	366	zcof = zfact1 * tmask(ji,jj,jk)
[6498]	367	# if defined key_zdftmx_new
	368	! key_zdftmx_new: New internal wave-driven param: set a minimum value for Kz on TKE (ensure numerical stability)
	369	zzd_up = zcof * ( MAX( avm(ji,jj,jk+1) + avm(ji,jj,jk), 2.e-5_wp ) ) & ! upper diagonal
	370	& / ( fse3t(ji,jj,jk ) * fse3w(ji,jj,jk ) )
	371	zzd_lw = zcof * ( MAX( avm(ji,jj,jk) + avm(ji,jj,jk-1), 2.e-5_wp ) ) & ! lower diagonal
	372	& / ( fse3t(ji,jj,jk-1) * fse3w(ji,jj,jk ) )
	373	# else
[1492]	374	zzd_up = zcof * ( avm (ji,jj,jk+1) + avm (ji,jj,jk ) ) & ! upper diagonal
	375	& / ( fse3t(ji,jj,jk ) * fse3w(ji,jj,jk ) )
	376	zzd_lw = zcof * ( avm (ji,jj,jk ) + avm (ji,jj,jk-1) ) & ! lower diagonal
	377	& / ( fse3t(ji,jj,jk-1) * fse3w(ji,jj,jk ) )
[6498]	378	# endif
[1492]	379	! ! shear prod. at w-point weightened by mask
[2528]	380	zesh2 = ( avmu(ji-1,jj,jk) + avmu(ji,jj,jk) ) / MAX( 1._wp , umask(ji-1,jj,jk) + umask(ji,jj,jk) ) &
	381	& + ( avmv(ji,jj-1,jk) + avmv(ji,jj,jk) ) / MAX( 1._wp , vmask(ji,jj-1,jk) + vmask(ji,jj,jk) )
[1492]	382	!
	383	zd_up(ji,jj,jk) = zzd_up ! Matrix (zdiag, zd_up, zd_lw)
	384	zd_lw(ji,jj,jk) = zzd_lw
[2528]	385	zdiag(ji,jj,jk) = 1._wp - zzd_lw - zzd_up + zfact2 * dissl(ji,jj,jk) * tmask(ji,jj,jk)
[1239]	386	!
[1492]	387	! ! right hand side in en
[1481]	388	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( zesh2 - avt(ji,jj,jk) * rn2(ji,jj,jk) &
[4990]	389	& + zfact3 * dissl(ji,jj,jk) * en (ji,jj,jk) ) &
[5120]	390	& * wmask(ji,jj,jk)
[1239]	391	END DO
[5120]	392	END DO
	393	END DO
	394	! !* Matrix inversion from level 2 (tke prescribed at level 1)
	395	DO jk = 3, jpkm1 ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
	396	DO jj = 2, jpjm1
	397	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	398	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]	399	END DO
[5120]	400	END DO
	401	END DO
	402	!
	403	! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
	404	DO jj = 2, jpjm1
	405	DO ji = fs_2, fs_jpim1 ! vector opt.
	406	zd_lw(ji,jj,2) = en(ji,jj,2) - zd_lw(ji,jj,2) * en(ji,jj,1) ! Surface boudary conditions on tke
	407	END DO
	408	END DO
	409	DO jk = 3, jpkm1
	410	DO jj = 2, jpjm1
	411	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	412	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]	413	END DO
[5120]	414	END DO
	415	END DO
	416	!
	417	! thrid recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
	418	DO jj = 2, jpjm1
	419	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	420	en(ji,jj,jpkm1) = zd_lw(ji,jj,jpkm1) / zdiag(ji,jj,jpkm1)
[5120]	421	END DO
	422	END DO
	423	DO jk = jpk-2, 2, -1
	424	DO jj = 2, jpjm1
	425	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	426	en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
[1239]	427	END DO
[5120]	428	END DO
	429	END DO
	430	DO jk = 2, jpkm1 ! set the minimum value of tke
	431	DO jj = 2, jpjm1
	432	DO ji = fs_2, fs_jpim1 ! vector opt.
	433	en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin ) * wmask(ji,jj,jk)
[1239]	434	END DO
	435	END DO
	436	END DO
	437
[6491]	438	! ! Save TKE prior to nn_etau addition
	439	e_niw(:,:,:) = en(:,:,:)
	440	!
[1492]	441	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	442	! ! TKE due to surface and internal wave breaking
	443	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[6491]	444	IF( nn_htau == 2 ) THEN !* mixed-layer depth dependant length scale
	445	DO jj = 2, jpjm1
	446	DO ji = fs_2, fs_jpim1 ! vector opt.
	447	htau(ji,jj) = rhtau * hmlp(ji,jj)
	448	END DO
	449	END DO
	450	ENDIF
	451	#if defined key_iomput
	452	!
	453	CALL iom_put( "htau", htau(:,:) ) ! Check htau (even if constant in time)
	454	#endif
	455	!
[2528]	456	IF( nn_etau == 1 ) THEN !* penetration below the mixed layer (rn_efr fraction)
[1492]	457	DO jk = 2, jpkm1
[1239]	458	DO jj = 2, jpjm1
	459	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	460	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	461	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	462	END DO
	463	END DO
[1492]	464	END DO
[2528]	465	ELSEIF( nn_etau == 2 ) THEN !* act only at the base of the mixed layer (jk=nmln) (rn_efr fraction)
[1492]	466	DO jj = 2, jpjm1
	467	DO ji = fs_2, fs_jpim1 ! vector opt.
	468	jk = nmln(ji,jj)
	469	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	470	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	471	END DO
[1492]	472	END DO
[2528]	473	ELSEIF( nn_etau == 3 ) THEN !* penetration belox the mixed layer (HF variability)
[1705]	474	!CDIR NOVERRCHK
	475	DO jk = 2, jpkm1
	476	!CDIR NOVERRCHK
	477	DO jj = 2, jpjm1
	478	!CDIR NOVERRCHK
	479	DO ji = fs_2, fs_jpim1 ! vector opt.
	480	ztx2 = utau(ji-1,jj ) + utau(ji,jj)
	481	zty2 = vtau(ji ,jj-1) + vtau(ji,jj)
[4990]	482	ztau = 0.5_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) * tmask(ji,jj,1) ! module of the mean stress
[2528]	483	zdif = taum(ji,jj) - ztau ! mean of modulus - modulus of the mean
	484	zdif = rhftau_scl * MAX( 0._wp, zdif + rhftau_add ) ! apply some modifications...
[1705]	485	en(ji,jj,jk) = en(ji,jj,jk) + zbbrau * zdif * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	486	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1705]	487	END DO
	488	END DO
	489	END DO
[6491]	490	ELSEIF( nn_etau == 4 ) THEN !* column integral independant of htau (rn_efr must be scaled up)
	491	IF( nn_htau == 2 ) THEN ! efr dependant on time-varying htau
	492	DO jj = 2, jpjm1
	493	DO ji = fs_2, fs_jpim1 ! vector opt.
	494	efr(ji,jj) = rn_efr / ( htau(ji,jj) * ( 1._wp - EXP( -bathy(ji,jj) / htau(ji,jj) ) ) )
	495	END DO
	496	END DO
	497	ENDIF
	498	DO jk = 2, jpkm1
	499	DO jj = 2, jpjm1
	500	DO ji = fs_2, fs_jpim1 ! vector opt.
	501	en(ji,jj,jk) = en(ji,jj,jk) + efr(ji,jj) * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
	502	& * ( 1._wp - fr_i(ji,jj) ) * tmask(ji,jj,jk)
	503	END DO
	504	END DO
	505	END DO
[1239]	506	ENDIF
[1492]	507	CALL lbc_lnk( en, 'W', 1. ) ! Lateral boundary conditions (sign unchanged)
	508	!
[6491]	509	DO jk = 2, jpkm1 ! TKE budget: near-inertial waves term
	510	DO jj = 2, jpjm1
	511	DO ji = fs_2, fs_jpim1 ! vector opt.
	512	e_niw(ji,jj,jk) = en(ji,jj,jk) - e_niw(ji,jj,jk)
	513	END DO
	514	END DO
	515	END DO
	516	!
	517	CALL lbc_lnk( e_niw, 'W', 1. )
	518	!
[3294]	519	CALL wrk_dealloc( jpi,jpj, imlc ) ! integer
	520	CALL wrk_dealloc( jpi,jpj, zhlc )
	521	CALL wrk_dealloc( jpi,jpj,jpk, zpelc, zdiag, zd_up, zd_lw )
[2715]	522	!
[3294]	523	IF( nn_timing == 1 ) CALL timing_stop('tke_tke')
	524	!
[1239]	525	END SUBROUTINE tke_tke
	526
[1492]	527
	528	SUBROUTINE tke_avn
[1239]	529	!!----------------------------------------------------------------------
[1492]	530	!! * ROUTINE tke_avn *
[1239]	531	!!
[1492]	532	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	533	!!
	534	!! ** Method : At this stage, en, the now TKE, is known (computed in
	535	!! the tke_tke routine). First, the now mixing lenth is
	536	!! computed from en and the strafification (N^2), then the mixings
	537	!! coefficients are computed.
	538	!! - Mixing length : a first evaluation of the mixing lengh
	539	!! scales is:
	540	!! mxl = sqrt(2*en) / N
	541	!! where N is the brunt-vaisala frequency, with a minimum value set
[2528]	542	!! to rmxl_min (rn_mxl0) in the interior (surface) ocean.
[1492]	543	!! The mixing and dissipative length scale are bound as follow :
	544	!! nn_mxl=0 : mxl bounded by the distance to surface and bottom.
	545	!! zmxld = zmxlm = mxl
	546	!! nn_mxl=1 : mxl bounded by the e3w and zmxld = zmxlm = mxl
	547	!! nn_mxl=2 : mxl bounded such that the vertical derivative of mxl is
	548	!! less than 1 (\|d/dz(mxl)\|<1) and zmxld = zmxlm = mxl
	549	!! nn_mxl=3 : mxl is bounded from the surface to the bottom usings
	550	!! \|d/dz(xml)\|<1 to obtain lup, and from the bottom to
	551	!! the surface to obtain ldown. the resulting length
	552	!! scales are:
	553	!! zmxld = sqrt( lup * ldown )
	554	!! zmxlm = min ( lup , ldown )
	555	!! - Vertical eddy viscosity and diffusivity:
	556	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	557	!! avt = max( avmb, pdlr * avm )
	558	!! with pdlr=1 if nn_pdl=0, pdlr=1/pdl=F(Ri) otherwise.
	559	!!
	560	!! ** Action : - avt : now vertical eddy diffusivity (w-point)
	561	!! - avmu, avmv : now vertical eddy viscosity at uw- and vw-points
[1239]	562	!!----------------------------------------------------------------------
[2715]	563	INTEGER :: ji, jj, jk ! dummy loop indices
	564	REAL(wp) :: zrn2, zraug, zcoef, zav ! local scalars
	565	REAL(wp) :: zdku, zpdlr, zri, zsqen ! - -
	566	REAL(wp) :: zdkv, zemxl, zemlm, zemlp ! - -
[3294]	567	REAL(wp), POINTER, DIMENSION(:,:,:) :: zmpdl, zmxlm, zmxld
[1239]	568	!!--------------------------------------------------------------------
[3294]	569	!
	570	IF( nn_timing == 1 ) CALL timing_start('tke_avn')
[1239]	571
[3294]	572	CALL wrk_alloc( jpi,jpj,jpk, zmpdl, zmxlm, zmxld )
	573
[1492]	574	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	575	! ! Mixing length
	576	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	577	!
	578	! !* Buoyancy length scale: l=sqrt(2e/n*2)
	579	!
[5120]	580	! initialisation of interior minimum value (avoid a 2d loop with mikt)
	581	zmxlm(:,:,:) = rmxl_min
	582	zmxld(:,:,:) = rmxl_min
	583	!
[2528]	584	IF( ln_mxl0 ) THEN ! surface mixing length = F(stress) : l=vkarmn2.e5taum/(rau0*g)
[4990]	585	DO jj = 2, jpjm1
	586	DO ji = fs_2, fs_jpim1
[5120]	587	zraug = vkarmn * 2.e5_wp / ( rau0 * grav )
	588	zmxlm(ji,jj,1) = MAX( rn_mxl0, zraug * taum(ji,jj) * tmask(ji,jj,1) )
[4990]	589	END DO
	590	END DO
	591	ELSE
[5120]	592	zmxlm(:,:,1) = rn_mxl0
[1239]	593	ENDIF
	594	!
	595	!CDIR NOVERRCHK
[5120]	596	DO jk = 2, jpkm1 ! interior value : l=sqrt(2*e/n^2)
[1239]	597	!CDIR NOVERRCHK
[5120]	598	DO jj = 2, jpjm1
	599	!CDIR NOVERRCHK
	600	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	601	zrn2 = MAX( rn2(ji,jj,jk), rsmall )
[5120]	602	zmxlm(ji,jj,jk) = MAX( rmxl_min, SQRT( 2._wp * en(ji,jj,jk) / zrn2 ) )
[1239]	603	END DO
	604	END DO
	605	END DO
[1492]	606	!
	607	! !* Physical limits for the mixing length
	608	!
[5120]	609	zmxld(:,:,1 ) = zmxlm(:,:,1) ! surface set to the minimum value
[2528]	610	zmxld(:,:,jpk) = rmxl_min ! last level set to the minimum value
[1492]	611	!
[1239]	612	SELECT CASE ( nn_mxl )
	613	!
[5120]	614	! where wmask = 0 set zmxlm == fse3w
[1239]	615	CASE ( 0 ) ! bounded by the distance to surface and bottom
[5120]	616	DO jk = 2, jpkm1
	617	DO jj = 2, jpjm1
	618	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	619	zemxl = MIN( fsdepw(ji,jj,jk) - fsdepw(ji,jj,mikt(ji,jj)), zmxlm(ji,jj,jk), &
[2528]	620	& fsdepw(ji,jj,mbkt(ji,jj)+1) - fsdepw(ji,jj,jk) )
[5120]	621	! wmask prevent zmxlm = 0 if jk = mikt(ji,jj)
	622	zmxlm(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN(zmxlm(ji,jj,jk),fse3w(ji,jj,jk)) * (1 - wmask(ji,jj,jk))
	623	zmxld(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN(zmxlm(ji,jj,jk),fse3w(ji,jj,jk)) * (1 - wmask(ji,jj,jk))
[1239]	624	END DO
	625	END DO
	626	END DO
	627	!
	628	CASE ( 1 ) ! bounded by the vertical scale factor
[5120]	629	DO jk = 2, jpkm1
	630	DO jj = 2, jpjm1
	631	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	632	zemxl = MIN( fse3w(ji,jj,jk), zmxlm(ji,jj,jk) )
	633	zmxlm(ji,jj,jk) = zemxl
	634	zmxld(ji,jj,jk) = zemxl
	635	END DO
	636	END DO
	637	END DO
	638	!
	639	CASE ( 2 ) ! \|dk[xml]\| bounded by e3t :
[5120]	640	DO jk = 2, jpkm1 ! from the surface to the bottom :
	641	DO jj = 2, jpjm1
	642	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	643	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk-1) + fse3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
	644	END DO
[5120]	645	END DO
	646	END DO
	647	DO jk = jpkm1, 2, -1 ! from the bottom to the surface :
	648	DO jj = 2, jpjm1
	649	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	650	zemxl = MIN( zmxlm(ji,jj,jk+1) + fse3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
	651	zmxlm(ji,jj,jk) = zemxl
	652	zmxld(ji,jj,jk) = zemxl
	653	END DO
	654	END DO
	655	END DO
	656	!
	657	CASE ( 3 ) ! lup and ldown, \|dk[xml]\| bounded by e3t :
[5120]	658	DO jk = 2, jpkm1 ! from the surface to the bottom : lup
	659	DO jj = 2, jpjm1
	660	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	661	zmxld(ji,jj,jk) = MIN( zmxld(ji,jj,jk-1) + fse3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
	662	END DO
[5120]	663	END DO
	664	END DO
	665	DO jk = jpkm1, 2, -1 ! from the bottom to the surface : ldown
	666	DO jj = 2, jpjm1
	667	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	668	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk+1) + fse3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
	669	END DO
	670	END DO
	671	END DO
	672	!CDIR NOVERRCHK
	673	DO jk = 2, jpkm1
	674	!CDIR NOVERRCHK
	675	DO jj = 2, jpjm1
	676	!CDIR NOVERRCHK
	677	DO ji = fs_2, fs_jpim1 ! vector opt.
	678	zemlm = MIN ( zmxld(ji,jj,jk), zmxlm(ji,jj,jk) )
	679	zemlp = SQRT( zmxld(ji,jj,jk) * zmxlm(ji,jj,jk) )
	680	zmxlm(ji,jj,jk) = zemlm
	681	zmxld(ji,jj,jk) = zemlp
	682	END DO
	683	END DO
	684	END DO
	685	!
	686	END SELECT
[1492]	687	!
[1239]	688	# if defined key_c1d
[1492]	689	e_dis(:,:,:) = zmxld(:,:,:) ! c1d configuration : save mixing and dissipation turbulent length scales
[1239]	690	e_mix(:,:,:) = zmxlm(:,:,:)
	691	# endif
	692
[1492]	693	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	694	! ! Vertical eddy viscosity and diffusivity (avmu, avmv, avt)
	695	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1239]	696	!CDIR NOVERRCHK
[1492]	697	DO jk = 1, jpkm1 !* vertical eddy viscosity & diffivity at w-points
[1239]	698	!CDIR NOVERRCHK
	699	DO jj = 2, jpjm1
	700	!CDIR NOVERRCHK
	701	DO ji = fs_2, fs_jpim1 ! vector opt.
	702	zsqen = SQRT( en(ji,jj,jk) )
	703	zav = rn_ediff * zmxlm(ji,jj,jk) * zsqen
[5120]	704	avm (ji,jj,jk) = MAX( zav, avmb(jk) ) * wmask(ji,jj,jk)
	705	avt (ji,jj,jk) = MAX( zav, avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1239]	706	dissl(ji,jj,jk) = zsqen / zmxld(ji,jj,jk)
	707	END DO
	708	END DO
	709	END DO
[1492]	710	CALL lbc_lnk( avm, 'W', 1. ) ! Lateral boundary conditions (sign unchanged)
	711	!
[5120]	712	DO jk = 2, jpkm1 !* vertical eddy viscosity at wu- and wv-points
	713	DO jj = 2, jpjm1
	714	DO ji = fs_2, fs_jpim1 ! vector opt.
	715	avmu(ji,jj,jk) = 0.5 * ( avm(ji,jj,jk) + avm(ji+1,jj ,jk) ) * wumask(ji,jj,jk)
	716	avmv(ji,jj,jk) = 0.5 * ( avm(ji,jj,jk) + avm(ji ,jj+1,jk) ) * wvmask(ji,jj,jk)
[4990]	717	END DO
[1239]	718	END DO
	719	END DO
	720	CALL lbc_lnk( avmu, 'U', 1. ) ; CALL lbc_lnk( avmv, 'V', 1. ) ! Lateral boundary conditions
[1492]	721	!
	722	IF( nn_pdl == 1 ) THEN !* Prandtl number case: update avt
[5120]	723	DO jk = 2, jpkm1
	724	DO jj = 2, jpjm1
	725	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	726	zcoef = avm(ji,jj,jk) * 2._wp * fse3w(ji,jj,jk) * fse3w(ji,jj,jk)
[1492]	727	! ! shear
	728	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) ) &
	729	& + avmu(ji ,jj,jk) * ( un(ji ,jj,jk-1) - un(ji ,jj,jk) ) * ( ub(ji ,jj,jk-1) - ub(ji ,jj,jk) )
	730	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) ) &
	731	& + avmv(ji,jj ,jk) * ( vn(ji,jj ,jk-1) - vn(ji,jj ,jk) ) * ( vb(ji,jj ,jk-1) - vb(ji,jj ,jk) )
	732	! ! local Richardson number
[2528]	733	zri = MAX( rn2b(ji,jj,jk), 0._wp ) * zcoef / (zdku + zdkv + rn_bshear )
	734	zpdlr = MAX( 0.1_wp, 0.2 / MAX( 0.2 , zri ) )
[1492]	735	!!gm and even better with the use of the "true" ri_crit=0.22222... (this change the results!)
[2528]	736	!!gm zpdlr = MAX( 0.1_wp, ri_crit / MAX( ri_crit , zri ) )
[5120]	737	avt(ji,jj,jk) = MAX( zpdlr * avt(ji,jj,jk), avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1492]	738	# if defined key_c1d
[5120]	739	e_pdl(ji,jj,jk) = zpdlr * wmask(ji,jj,jk) ! c1d configuration : save masked Prandlt number
	740	e_ric(ji,jj,jk) = zri * wmask(ji,jj,jk) ! c1d config. : save Ri
[1239]	741	# endif
	742	END DO
	743	END DO
	744	END DO
	745	ENDIF
	746	CALL lbc_lnk( avt, 'W', 1. ) ! Lateral boundary conditions on avt (sign unchanged)
	747
	748	IF(ln_ctl) THEN
	749	CALL prt_ctl( tab3d_1=en , clinfo1=' tke - e: ', tab3d_2=avt, clinfo2=' t: ', ovlap=1, kdim=jpk)
	750	CALL prt_ctl( tab3d_1=avmu, clinfo1=' tke - u: ', mask1=umask, &
	751	& tab3d_2=avmv, clinfo2= ' v: ', mask2=vmask, ovlap=1, kdim=jpk )
	752	ENDIF
	753	!
[3294]	754	CALL wrk_dealloc( jpi,jpj,jpk, zmpdl, zmxlm, zmxld )
	755	!
	756	IF( nn_timing == 1 ) CALL timing_stop('tke_avn')
	757	!
[1492]	758	END SUBROUTINE tke_avn
[1239]	759
[1492]	760
[2528]	761	SUBROUTINE zdf_tke_init
[1239]	762	!!----------------------------------------------------------------------
[2528]	763	!! * ROUTINE zdf_tke_init *
[1239]	764	!!
	765	!! ** Purpose : Initialization of the vertical eddy diffivity and
[1492]	766	!! viscosity when using a tke turbulent closure scheme
[1239]	767	!!
[1601]	768	!! ** Method : Read the namzdf_tke namelist and check the parameters
[1492]	769	!! called at the first timestep (nit000)
[1239]	770	!!
[1601]	771	!! ** input : Namlist namzdf_tke
[1239]	772	!!
	773	!! ** Action : Increase by 1 the nstop flag is setting problem encounter
	774	!!----------------------------------------------------------------------
	775	INTEGER :: ji, jj, jk ! dummy loop indices
[6487]	776	INTEGER :: ios, ierr
[1239]	777	!!
[2528]	778	NAMELIST/namzdf_tke/ rn_ediff, rn_ediss , rn_ebb , rn_emin , &
	779	& rn_emin0, rn_bshear, nn_mxl , ln_mxl0 , &
	780	& rn_mxl0 , nn_pdl , ln_lc , rn_lc , &
[6491]	781	& nn_etau , nn_htau , rn_efr , rn_c
[1239]	782	!!----------------------------------------------------------------------
[9366]	783	IF(lwm) THEN
	784	REWIND( numnam_ref ) ! Namelist namzdf_tke in reference namelist : Turbulent Kinetic Energy
	785	READ ( numnam_ref, namzdf_tke, IOSTAT = ios, ERR = 901)
	786	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in reference namelist', lwm )
	787	REWIND( numnam_cfg ) ! Namelist namzdf_tke in configuration namelist : Turbulent Kinetic Energy
	788	READ ( numnam_cfg, namzdf_tke, IOSTAT = ios, ERR = 902 )
	789	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in configuration namelist', lwm )
	790	ENDIF
[6491]	791
[4624]	792	IF(lwm) WRITE ( numond, namzdf_tke )
[9366]	793	! Broadcast namelist
	794	CALL tke_namelist()
[2715]	795	!
[2528]	796	ri_cri = 2._wp / ( 2._wp + rn_ediss / rn_ediff ) ! resulting critical Richardson number
[6498]	797	# if defined key_zdftmx_new
	798	! key_zdftmx_new: New internal wave-driven param: specified value of rn_emin & rmxl_min are used
	799	rn_emin = 1.e-10_wp
	800	rmxl_min = 1.e-03_wp
	801	IF(lwp) THEN ! Control print
	802	WRITE(numout,*)
	803	WRITE(numout,*) 'zdf_tke_init : New tidal mixing case: force rn_emin = 1.e-10 and rmxl_min = 1.e-3 '
	804	WRITE(numout,*) '~~~~~~~~~~~~'
	805	ENDIF
	806	# else
[2528]	807	rmxl_min = 1.e-6_wp / ( rn_ediff * SQRT( rn_emin ) ) ! resulting minimum length to recover molecular viscosity
[6498]	808	# endif
[2715]	809	!
[1492]	810	IF(lwp) THEN !* Control print
[1239]	811	WRITE(numout,*)
[2528]	812	WRITE(numout,*) 'zdf_tke_init : tke turbulent closure scheme - initialisation'
	813	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	814	WRITE(numout,*) ' Namelist namzdf_tke : set tke mixing parameters'
[1705]	815	WRITE(numout,*) ' coef. to compute avt rn_ediff = ', rn_ediff
	816	WRITE(numout,*) ' Kolmogoroff dissipation coef. rn_ediss = ', rn_ediss
	817	WRITE(numout,*) ' tke surface input coef. rn_ebb = ', rn_ebb
	818	WRITE(numout,*) ' minimum value of tke rn_emin = ', rn_emin
	819	WRITE(numout,*) ' surface minimum value of tke rn_emin0 = ', rn_emin0
	820	WRITE(numout,*) ' background shear (>0) rn_bshear = ', rn_bshear
	821	WRITE(numout,*) ' mixing length type nn_mxl = ', nn_mxl
	822	WRITE(numout,*) ' prandl number flag nn_pdl = ', nn_pdl
	823	WRITE(numout,*) ' surface mixing length = F(stress) or not ln_mxl0 = ', ln_mxl0
[2528]	824	WRITE(numout,*) ' surface mixing length minimum value rn_mxl0 = ', rn_mxl0
	825	WRITE(numout,*) ' flag to take into acc. Langmuir circ. ln_lc = ', ln_lc
	826	WRITE(numout,*) ' coef to compute verticla velocity of LC rn_lc = ', rn_lc
[1705]	827	WRITE(numout,*) ' test param. to add tke induced by wind nn_etau = ', nn_etau
	828	WRITE(numout,*) ' flag for computation of exp. tke profile nn_htau = ', nn_htau
	829	WRITE(numout,*) ' fraction of en which pene. the thermocline rn_efr = ', rn_efr
[6491]	830	WRITE(numout,*) ' fraction of TKE added within the mixed layer by nn_etau rn_c = ', rn_c
[1239]	831	WRITE(numout,*)
[1601]	832	WRITE(numout,*) ' critical Richardson nb with your parameters ri_cri = ', ri_cri
[1239]	833	ENDIF
[2715]	834	!
	835	! ! allocate tke arrays
	836	IF( zdf_tke_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_tke_init : unable to allocate arrays' )
	837	!
[1492]	838	! !* Check of some namelist values
[4990]	839	IF( nn_mxl < 0 .OR. nn_mxl > 3 ) CALL ctl_stop( 'bad flag: nn_mxl is 0, 1 or 2 ' )
	840	IF( nn_pdl < 0 .OR. nn_pdl > 1 ) CALL ctl_stop( 'bad flag: nn_pdl is 0 or 1 ' )
[6491]	841	IF( nn_htau < 0 .OR. nn_htau > 5 ) CALL ctl_stop( 'bad flag: nn_htau is 0 to 5 ' )
[5407]	842	IF( nn_etau == 3 .AND. .NOT. ln_cpl ) CALL ctl_stop( 'nn_etau == 3 : HF taum only known in coupled mode' )
[1239]	843
[2528]	844	IF( ln_mxl0 ) THEN
	845	IF(lwp) WRITE(numout,*) ' use a surface mixing length = F(stress) : set rn_mxl0 = rmxl_min'
	846	rn_mxl0 = rmxl_min
	847	ENDIF
	848
[6487]	849	IF( nn_etau == 2 ) THEN
	850	ierr = zdf_mxl_alloc()
	851	nmln(:,:) = nlb10 ! Initialization of nmln
	852	ENDIF
[1239]	853
[6491]	854	IF( nn_etau /= 0 .and. nn_htau == 2 ) THEN
	855	ierr = zdf_mxl_alloc()
	856	nmln(:,:) = nlb10 ! Initialization of nmln
	857	ENDIF
	858
[1492]	859	! !* depth of penetration of surface tke
	860	IF( nn_etau /= 0 ) THEN
[6491]	861	htau(:,:) = 0._wp
[1601]	862	SELECT CASE( nn_htau ) ! Choice of the depth of penetration
[2528]	863	CASE( 0 ) ! constant depth penetration (here 10 meters)
	864	htau(:,:) = 10._wp
	865	CASE( 1 ) ! F(latitude) : 0.5m to 30m poleward of 40 degrees
	866	htau(:,:) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
[6491]	867	CASE( 2 ) ! fraction of depth-integrated TKE within mixed-layer
	868	rhtau = -1._wp / LOG( 1._wp - rn_c )
	869	CASE( 3 ) ! F(latitude) : 0.5m to 15m poleward of 20 degrees
	870	htau(:,:) = MAX( 0.5_wp, MIN( 15._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
	871	CASE( 4 ) ! F(latitude) : 0.5m to 10m/30m poleward of 13/40 degrees north/south
	872	DO jj = 2, jpjm1
	873	DO ji = fs_2, fs_jpim1 ! vector opt.
	874	IF( gphit(ji,jj) <= 0._wp ) THEN
	875	htau(ji,jj) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	876	ELSE
	877	htau(ji,jj) = MAX( 0.5_wp, MIN( 10._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	878	ENDIF
	879	END DO
	880	END DO
	881	CASE ( 5 ) ! F(latitude) : 0.5m to 10m poleward of 13 degrees north/south,
	882	DO jj = 2, jpjm1 ! 10m to 30m between 30/45 degrees south
	883	DO ji = fs_2, fs_jpim1 ! vector opt.
	884	IF( gphit(ji,jj) <= -30._wp ) THEN
	885	htau(ji,jj) = MAX( 10._wp, MIN( 30._wp, 55._wp* ABS( SIN( rpi/120._wp * ( gphit(ji,jj) + 23._wp ) ) ) ) )
	886	ELSE
	887	htau(ji,jj) = MAX( 0.5_wp, MIN( 10._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	888	ENDIF
	889	END DO
	890	END DO
[1492]	891	END SELECT
[6491]	892	!
	893	IF( nn_etau == 4 .AND. nn_htau /= 2 ) THEN ! efr dependant on constant htau
	894	DO jj = 2, jpjm1
	895	DO ji = fs_2, fs_jpim1 ! vector opt.
	896	efr(ji,jj) = rn_efr / ( htau(ji,jj) * ( 1._wp - EXP( -bathy(ji,jj) / htau(ji,jj) ) ) )
	897	END DO
	898	END DO
	899	ENDIF
[1492]	900	ENDIF
	901	! !* set vertical eddy coef. to the background value
[1239]	902	DO jk = 1, jpk
[5120]	903	avt (:,:,jk) = avtb(jk) * wmask (:,:,jk)
	904	avm (:,:,jk) = avmb(jk) * wmask (:,:,jk)
	905	avmu(:,:,jk) = avmb(jk) * wumask(:,:,jk)
	906	avmv(:,:,jk) = avmb(jk) * wvmask(:,:,jk)
[1239]	907	END DO
[2528]	908	dissl(:,:,:) = 1.e-12_wp
[2715]	909	!
	910	CALL tke_rst( nit000, 'READ' ) !* read or initialize all required files
[1239]	911	!
[2528]	912	END SUBROUTINE zdf_tke_init
[1239]	913
	914
[1531]	915	SUBROUTINE tke_rst( kt, cdrw )
[1239]	916	!!---------------------------------------------------------------------
[1531]	917	!! * ROUTINE tke_rst *
[1239]	918	!!
	919	!! ** Purpose : Read or write TKE file (en) in restart file
	920	!!
	921	!! ** Method : use of IOM library
	922	!! if the restart does not contain TKE, en is either
[1537]	923	!! set to rn_emin or recomputed
[1239]	924	!!----------------------------------------------------------------------
[2715]	925	INTEGER , INTENT(in) :: kt ! ocean time-step
	926	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
[1239]	927	!
[1481]	928	INTEGER :: jit, jk ! dummy loop indices
[2715]	929	INTEGER :: id1, id2, id3, id4, id5, id6 ! local integers
[1239]	930	!!----------------------------------------------------------------------
	931	!
[1481]	932	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
	933	! ! ---------------
	934	IF( ln_rstart ) THEN !* Read the restart file
	935	id1 = iom_varid( numror, 'en' , ldstop = .FALSE. )
	936	id2 = iom_varid( numror, 'avt' , ldstop = .FALSE. )
	937	id3 = iom_varid( numror, 'avm' , ldstop = .FALSE. )
	938	id4 = iom_varid( numror, 'avmu' , ldstop = .FALSE. )
	939	id5 = iom_varid( numror, 'avmv' , ldstop = .FALSE. )
	940	id6 = iom_varid( numror, 'dissl', ldstop = .FALSE. )
	941	!
	942	IF( id1 > 0 ) THEN ! 'en' exists
[7924]	943	CALL iom_get( numror, jpdom_autoglo, 'en', en, lrxios = lxios_read )
[1481]	944	IF( MIN( id2, id3, id4, id5, id6 ) > 0 ) THEN ! all required arrays exist
[7924]	945	CALL iom_get( numror, jpdom_autoglo, 'avt' , avt, lrxios = lxios_read )
	946	CALL iom_get( numror, jpdom_autoglo, 'avm' , avm, lrxios = lxios_read )
	947	CALL iom_get( numror, jpdom_autoglo, 'avmu' , avmu, lrxios = lxios_read )
	948	CALL iom_get( numror, jpdom_autoglo, 'avmv' , avmv, lrxios = lxios_read )
	949	CALL iom_get( numror, jpdom_autoglo, 'dissl', dissl, lrxios = lxios_read )
[1492]	950	ELSE ! one at least array is missing
	951	CALL tke_avn ! compute avt, avm, avmu, avmv and dissl (approximation)
[1481]	952	ENDIF
	953	ELSE ! No TKE array found: initialisation
	954	IF(lwp) WRITE(numout,*) ' ===>>>> : previous run without tke scheme, en computed by iterative loop'
[1239]	955	en (:,:,:) = rn_emin * tmask(:,:,:)
[1492]	956	CALL tke_avn ! recompute avt, avm, avmu, avmv and dissl (approximation)
[5112]	957	!
	958	avt_k (:,:,:) = avt (:,:,:)
	959	avm_k (:,:,:) = avm (:,:,:)
	960	avmu_k(:,:,:) = avmu(:,:,:)
	961	avmv_k(:,:,:) = avmv(:,:,:)
	962	!
[1531]	963	DO jit = nit000 + 1, nit000 + 10 ; CALL zdf_tke( jit ) ; END DO
[1239]	964	ENDIF
[1481]	965	ELSE !* Start from rest
	966	en(:,:,:) = rn_emin * tmask(:,:,:)
	967	DO jk = 1, jpk ! set the Kz to the background value
[5120]	968	avt (:,:,jk) = avtb(jk) * wmask (:,:,jk)
	969	avm (:,:,jk) = avmb(jk) * wmask (:,:,jk)
	970	avmu(:,:,jk) = avmb(jk) * wumask(:,:,jk)
	971	avmv(:,:,jk) = avmb(jk) * wvmask(:,:,jk)
[1481]	972	END DO
[1239]	973	ENDIF
[1481]	974	!
	975	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
	976	! ! -------------------
[1531]	977	IF(lwp) WRITE(numout,*) '---- tke-rst ----'
[8243]	978	IF( lwxios ) CALL iom_swap( wxios_context )
	979	CALL iom_rstput( kt, nitrst, numrow, 'en' , en , lxios = lwxios )
	980	CALL iom_rstput( kt, nitrst, numrow, 'avt' , avt_k , lxios = lwxios )
	981	CALL iom_rstput( kt, nitrst, numrow, 'avm' , avm_k , lxios = lwxios )
	982	CALL iom_rstput( kt, nitrst, numrow, 'avmu' , avmu_k, lxios = lwxios )
	983	CALL iom_rstput( kt, nitrst, numrow, 'avmv' , avmv_k, lxios = lwxios )
	984	CALL iom_rstput( kt, nitrst, numrow, 'dissl', dissl , lxios = lwxios )
	985	IF( lwxios ) CALL iom_swap( cxios_context )
[1481]	986	!
[1239]	987	ENDIF
	988	!
[1531]	989	END SUBROUTINE tke_rst
[1239]	990
[9366]	991	SUBROUTINE tke_namelist()
	992	!!---------------------------------------------------------------------
	993	!! * ROUTINE tke_namelist *
	994	!!
	995	!! ** Purpose : Broadcast namelist variables read by procesor lwp
	996	!!
	997	!! ** Method : use lib_mpp
	998	!!----------------------------------------------------------------------
	999	#if defined key_mpp_mpi
	1000	call mpp_bcast(rn_ediff)
	1001	call mpp_bcast(rn_ediss)
	1002	call mpp_bcast(rn_ebb)
	1003	call mpp_bcast(rn_emin)
	1004	call mpp_bcast(rn_emin0)
	1005	call mpp_bcast(rn_bshear)
	1006	call mpp_bcast(nn_mxl)
	1007	call mpp_bcast(ln_mxl0)
	1008	call mpp_bcast(rn_mxl0)
	1009	call mpp_bcast(nn_pdl)
	1010	call mpp_bcast(ln_lc)
	1011	call mpp_bcast(rn_lc)
	1012	call mpp_bcast(nn_etau)
	1013	call mpp_bcast(nn_htau)
	1014	call mpp_bcast(rn_efr)
	1015	call mpp_bcast(rn_c)
	1016	#endif
	1017	END SUBROUTINE tke_namelist
[1239]	1018	#else
	1019	!!----------------------------------------------------------------------
	1020	!! Dummy module : NO TKE scheme
	1021	!!----------------------------------------------------------------------
[1531]	1022	LOGICAL, PUBLIC, PARAMETER :: lk_zdftke = .FALSE. !: TKE flag
[1239]	1023	CONTAINS
[2528]	1024	SUBROUTINE zdf_tke_init ! Dummy routine
	1025	END SUBROUTINE zdf_tke_init
	1026	SUBROUTINE zdf_tke( kt ) ! Dummy routine
[1531]	1027	WRITE(,) 'zdf_tke: You should not have seen this print! error?', kt
	1028	END SUBROUTINE zdf_tke
	1029	SUBROUTINE tke_rst( kt, cdrw )
[1492]	1030	CHARACTER(len=*) :: cdrw
[1531]	1031	WRITE(,) 'tke_rst: You should not have seen this print! error?', kt, cdwr
	1032	END SUBROUTINE tke_rst
[1239]	1033	#endif
	1034
	1035	!!======================================================================
[1531]	1036	END MODULE zdftke

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