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zdftke.F90 in branches/UKMO/dev_r5518_GO6_package_FOAMv14/NEMOGCM/NEMO/OPA_SRC/ZDF – NEMO

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source: branches/UKMO/dev_r5518_GO6_package_FOAMv14/NEMOGCM/NEMO/OPA_SRC/ZDF/zdftke.F90 @ 11442

Last change on this file since 11442 was 11442, checked in by mattmartin, 5 years ago
Introduction of stochastic physics in NEMO, based on Andrea Storto's code. For details, see ticket https://code.metoffice.gov.uk/trac/utils/ticket/251.
File size: 53.1 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)
[6487]	55	#if defined key_agrif
	56	USE agrif_opa_interp
	57	USE agrif_opa_update
	58	#endif
[11442]	59	USE stopack
[1239]	60
	61	IMPLICIT NONE
	62	PRIVATE
	63
[2528]	64	PUBLIC zdf_tke ! routine called in step module
	65	PUBLIC zdf_tke_init ! routine called in opa module
	66	PUBLIC tke_rst ! routine called in step module
[1239]	67
[2715]	68	LOGICAL , PUBLIC, PARAMETER :: lk_zdftke = .TRUE. !: TKE vertical mixing flag
[1239]	69
[4147]	70	! !! Namelist namzdf_tke
	71	LOGICAL :: ln_mxl0 ! mixing length scale surface value as function of wind stress or not
	72	INTEGER :: nn_mxl ! type of mixing length (=0/1/2/3)
	73	REAL(wp) :: rn_mxl0 ! surface min value of mixing length (kappaz_o=0.40.1 m) [m]
	74	INTEGER :: nn_pdl ! Prandtl number or not (ratio avt/avm) (=0/1)
	75	REAL(wp) :: rn_ediff ! coefficient for avt: avt=rn_ediffmxlsqrt(e)
	76	REAL(wp) :: rn_ediss ! coefficient of the Kolmogoroff dissipation
	77	REAL(wp) :: rn_ebb ! coefficient of the surface input of tke
	78	REAL(wp) :: rn_emin ! minimum value of tke [m2/s2]
	79	REAL(wp) :: rn_emin0 ! surface minimum value of tke [m2/s2]
	80	REAL(wp) :: rn_bshear ! background shear (>0) currently a numerical threshold (do not change it)
	81	INTEGER :: nn_etau ! type of depth penetration of surface tke (=0/1/2/3)
	82	INTEGER :: nn_htau ! type of tke profile of penetration (=0/1)
	83	REAL(wp) :: rn_efr ! fraction of TKE surface value which penetrates in the ocean
[6491]	84	REAL(wp) :: rn_c ! fraction of TKE added within the mixed layer by nn_etau
[4147]	85	LOGICAL :: ln_lc ! Langmuir cells (LC) as a source term of TKE or not
	86	REAL(wp) :: rn_lc ! coef to compute vertical velocity of Langmuir cells
[1239]	87
[4147]	88	REAL(wp) :: ri_cri ! critic Richardson number (deduced from rn_ediff and rn_ediss values)
	89	REAL(wp) :: rmxl_min ! minimum mixing length value (deduced from rn_ediff and rn_emin values) [m]
[6491]	90	REAL(wp) :: rhtau ! coefficient to relate MLD to htau when nn_htau == 2
[2528]	91	REAL(wp) :: rhftau_add = 1.e-3_wp ! add offset applied to HF part of taum (nn_etau=3)
	92	REAL(wp) :: rhftau_scl = 1.0_wp ! scale factor applied to HF part of taum (nn_etau=3)
[1239]	93
[2715]	94	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: htau ! depth of tke penetration (nn_htau)
	95	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dissl ! now mixing lenght of dissipation
	96	#if defined key_c1d
	97	! !! 1D cfg only ('key_c1d')
	98	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_dis, e_mix !: dissipation and mixing turbulent lengh scales
	99	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_pdl, e_ric !: prandl and local Richardson numbers
	100	#endif
[11442]	101	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: rn_lc0, rn_ediff0, rn_ediss0, rn_ebb0, rn_efr0
	102	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_niw !: TKE budget- near-inertial waves term
	103	REAL(wp) , ALLOCATABLE, SAVE, DIMENSION(:,:) :: efr ! surface boundary condition for nn_etau = 4
	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( &
[6491]	120	& efr (jpi,jpj) , e_niw(jpi,jpj,jpk) , &
[2715]	121	#if defined key_c1d
	122	& e_dis(jpi,jpj,jpk) , e_mix(jpi,jpj,jpk) , &
	123	& e_pdl(jpi,jpj,jpk) , e_ric(jpi,jpj,jpk) , &
	124	#endif
[6487]	125	& htau (jpi,jpj) , dissl(jpi,jpj,jpk) , STAT= zdf_tke_alloc )
[2715]	126	!
	127	IF( lk_mpp ) CALL mpp_sum ( zdf_tke_alloc )
	128	IF( zdf_tke_alloc /= 0 ) CALL ctl_warn('zdf_tke_alloc: failed to allocate arrays')
	129	!
	130	END FUNCTION zdf_tke_alloc
	131
	132
[1531]	133	SUBROUTINE zdf_tke( kt )
[1239]	134	!!----------------------------------------------------------------------
[1531]	135	!! * ROUTINE zdf_tke *
[1239]	136	!!
	137	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
[1492]	138	!! coefficients using a turbulent closure scheme (TKE).
[1239]	139	!!
[1492]	140	!! ** Method : The time evolution of the turbulent kinetic energy (tke)
	141	!! is computed from a prognostic equation :
	142	!! d(en)/dt = avm (d(u)/dz)**2 ! shear production
	143	!! + d( avm d(en)/dz )/dz ! diffusion of tke
	144	!! + avt N^2 ! stratif. destruc.
	145	!! - rn_ediss / emxl en**(2/3) ! Kolmogoroff dissipation
[1239]	146	!! with the boundary conditions:
[1695]	147	!! surface: en = max( rn_emin0, rn_ebb * taum )
[1239]	148	!! bottom : en = rn_emin
[1492]	149	!! The associated critical Richardson number is: ri_cri = 2/(2+rn_ediss/rn_ediff)
	150	!!
	151	!! The now Turbulent kinetic energy is computed using the following
	152	!! time stepping: implicit for vertical diffusion term, linearized semi
	153	!! implicit for kolmogoroff dissipation term, and explicit forward for
	154	!! both buoyancy and shear production terms. Therefore a tridiagonal
	155	!! linear system is solved. Note that buoyancy and shear terms are
	156	!! discretized in a energy conserving form (Bruchard 2002).
	157	!!
	158	!! The dissipative and mixing length scale are computed from en and
	159	!! the stratification (see tke_avn)
	160	!!
	161	!! The now vertical eddy vicosity and diffusivity coefficients are
	162	!! given by:
	163	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	164	!! avt = max( avmb, pdl * avm )
[1239]	165	!! eav = max( avmb, avm )
[1492]	166	!! where pdl, the inverse of the Prandtl number is 1 if nn_pdl=0 and
	167	!! given by an empirical funtion of the localRichardson number if nn_pdl=1
[1239]	168	!!
	169	!! ** Action : compute en (now turbulent kinetic energy)
	170	!! update avt, avmu, avmv (before vertical eddy coef.)
	171	!!
	172	!! References : Gaspar et al., JGR, 1990,
	173	!! Blanke and Delecluse, JPO, 1991
	174	!! Mellor and Blumberg, JPO 2004
	175	!! Axell, JGR, 2002
[1492]	176	!! Bruchard OM 2002
[1239]	177	!!----------------------------------------------------------------------
[1492]	178	INTEGER, INTENT(in) :: kt ! ocean time step
	179	!!----------------------------------------------------------------------
[1481]	180	!
[3632]	181	IF( kt /= nit000 ) THEN ! restore before value to compute tke
	182	avt (:,:,:) = avt_k (:,:,:)
	183	avm (:,:,:) = avm_k (:,:,:)
	184	avmu(:,:,:) = avmu_k(:,:,:)
	185	avmv(:,:,:) = avmv_k(:,:,:)
[11442]	186	ENDIF
[3632]	187	!
[11442]	188	IF( ln_stopack) THEN
	189	IF( nn_spp_tkelc > 0 ) THEN
	190	rn_lc0 = rn_lc
	191	CALL spp_gen( kt, rn_lc0, nn_spp_tkelc, rn_tkelc_sd, jk_spp_tkelc )
	192	ENDIF
	193	IF( nn_spp_tkedf > 0 ) THEN
	194	rn_ediff0 = rn_ediff
	195	CALL spp_gen( kt, rn_ediff0, nn_spp_tkedf, rn_tkedf_sd, jk_spp_tkedf )
	196	ENDIF
	197	IF( nn_spp_tkeds > 0 ) THEN
	198	rn_ediss0 = rn_ediss
	199	CALL spp_gen( kt, rn_ediss0, nn_spp_tkeds, rn_tkeds_sd, jk_spp_tkeds )
	200	ENDIF
	201	IF( nn_spp_tkebb > 0 ) THEN
	202	rn_ebb0 = rn_ebb
	203	CALL spp_gen( kt, rn_ebb0, nn_spp_tkebb, rn_tkebb_sd, jk_spp_tkebb )
	204	ENDIF
	205	IF( nn_spp_tkefr > 0 ) THEN
	206	rn_efr0 = rn_efr
	207	CALL spp_gen( kt, rn_efr0, nn_spp_tkefr, rn_tkefr_sd, jk_spp_tkefr )
	208	ENDIF
	209	ENDIF
	210	!
[2528]	211	CALL tke_tke ! now tke (en)
[1492]	212	!
[2528]	213	CALL tke_avn ! now avt, avm, avmu, avmv
	214	!
[3632]	215	avt_k (:,:,:) = avt (:,:,:)
	216	avm_k (:,:,:) = avm (:,:,:)
	217	avmu_k(:,:,:) = avmu(:,:,:)
	218	avmv_k(:,:,:) = avmv(:,:,:)
	219	!
[6487]	220	#if defined key_agrif
	221	! Update child grid f => parent grid
	222	IF( .NOT.Agrif_Root() ) CALL Agrif_Update_Tke( kt ) ! children only
	223	#endif
[11442]	224	IF ( kt == nitend ) THEN
	225	DEALLOCATE ( rn_lc0, rn_ediff0, rn_ediss0, rn_ebb0, rn_efr0 )
	226	ENDIF
	227	!
	228
[1531]	229	END SUBROUTINE zdf_tke
[1239]	230
[1492]	231
[1481]	232	SUBROUTINE tke_tke
[1239]	233	!!----------------------------------------------------------------------
[1492]	234	!! * ROUTINE tke_tke *
	235	!!
	236	!! ** Purpose : Compute the now Turbulente Kinetic Energy (TKE)
	237	!!
	238	!! ** Method : - TKE surface boundary condition
[2528]	239	!! - source term due to Langmuir cells (Axell JGR 2002) (ln_lc=T)
[1492]	240	!! - source term due to shear (saved in avmu, avmv arrays)
	241	!! - Now TKE : resolution of the TKE equation by inverting
	242	!! a tridiagonal linear system by a "methode de chasse"
	243	!! - increase TKE due to surface and internal wave breaking
	244	!!
	245	!! ** Action : - en : now turbulent kinetic energy)
	246	!! - avmu, avmv : production of TKE by shear at u and v-points
	247	!! (= Kz dz[Ub] * dz[Un] )
[1239]	248	!! ---------------------------------------------------------------------
[1705]	249	INTEGER :: ji, jj, jk ! dummy loop arguments
[2528]	250	!!bfr INTEGER :: ikbu, ikbv, ikbum1, ikbvm1 ! temporary scalar
	251	!!bfr INTEGER :: ikbt, ikbumm1, ikbvmm1 ! temporary scalar
[1705]	252	REAL(wp) :: zrhoa = 1.22 ! Air density kg/m3
	253	REAL(wp) :: zcdrag = 1.5e-3 ! drag coefficient
[11442]	254	REAL(wp) :: zesh2 ! temporary scalars
	255	REAL(wp) :: zfact1 ! - -
[1705]	256	REAL(wp) :: ztx2 , zty2 , zcof ! - -
	257	REAL(wp) :: ztau , zdif ! - -
	258	REAL(wp) :: zus , zwlc , zind ! - -
	259	REAL(wp) :: zzd_up, zzd_lw ! - -
[2528]	260	!!bfr REAL(wp) :: zebot ! - -
[3294]	261	INTEGER , POINTER, DIMENSION(:,: ) :: imlc
[11442]	262	REAL(wp), POINTER, DIMENSION(:,: ) :: zhlc, zbbrau,zfact2,zfact3
[3294]	263	REAL(wp), POINTER, DIMENSION(:,:,:) :: zpelc, zdiag, zd_up, zd_lw
[1239]	264	!!--------------------------------------------------------------------
[1492]	265	!
[3294]	266	IF( nn_timing == 1 ) CALL timing_start('tke_tke')
	267	!
	268	CALL wrk_alloc( jpi,jpj, imlc ) ! integer
[11442]	269	CALL wrk_alloc( jpi,jpj, zhlc )
	270	CALL wrk_alloc( jpi,jpj, zbbrau )
	271	CALL wrk_alloc( jpi,jpj, zfact2 )
	272	CALL wrk_alloc( jpi,jpj, zfact3 )
[3294]	273	CALL wrk_alloc( jpi,jpj,jpk, zpelc, zdiag, zd_up, zd_lw )
	274	!
[11442]	275	zbbrau = rn_ebb0 / rau0 ! Local constant initialisation
[2528]	276	zfact1 = -.5_wp * rdt
[11442]	277	zfact2 = 1.5_wp * rdt * rn_ediss0
	278	zfact3 = 0.5_wp * rn_ediss0
[1492]	279	!
[5120]	280	!
[1492]	281	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	282	! ! Surface boundary condition on tke
	283	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[5120]	284	IF ( ln_isfcav ) THEN
	285	DO jj = 2, jpjm1 ! en(mikt(ji,jj)) = rn_emin
	286	DO ji = fs_2, fs_jpim1 ! vector opt.
	287	en(ji,jj,mikt(ji,jj))=rn_emin * tmask(ji,jj,1)
	288	END DO
	289	END DO
	290	END IF
[1695]	291	DO jj = 2, jpjm1 ! en(1) = rn_ebb taum / rau0 (min value rn_emin0)
[1481]	292	DO ji = fs_2, fs_jpim1 ! vector opt.
[11442]	293	en(ji,jj,1) = MAX( rn_emin0, zbbrau(ji,jj) * taum(ji,jj) ) * tmask(ji,jj,1)
[1481]	294	END DO
	295	END DO
[2528]	296
	297	!!bfr - start commented area
[1492]	298	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	299	! ! Bottom boundary condition on tke
	300	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1719]	301	!
	302	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	303	! Tests to date have found the bottom boundary condition on tke to have very little effect.
	304	! The condition is coded here for completion but commented out until there is proof that the
	305	! computational cost is justified
	306	!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	307	! en(bot) = (rn_ebb0/rau0)0.5sqrt(u_botfr^2+v_botfr^2) (min value rn_emin)
[1662]	308	!CDIR NOVERRCHK
[1719]	309	!! DO jj = 2, jpjm1
[1662]	310	!CDIR NOVERRCHK
[1719]	311	!! DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	312	!! ztx2 = bfrua(ji-1,jj) * ub(ji-1,jj,mbku(ji-1,jj)) + &
	313	!! bfrua(ji ,jj) * ub(ji ,jj,mbku(ji ,jj) )
	314	!! zty2 = bfrva(ji,jj ) * vb(ji,jj ,mbkv(ji,jj )) + &
	315	!! bfrva(ji,jj-1) * vb(ji,jj-1,mbkv(ji,jj-1) )
[1719]	316	!! zebot = 0.001875_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) ! where 0.001875 = (rn_ebb0/rau0) * 0.5 = 3.75*0.5/1000.
[2528]	317	!! en (ji,jj,mbkt(ji,jj)+1) = MAX( zebot, rn_emin ) * tmask(ji,jj,1)
[1719]	318	!! END DO
	319	!! END DO
[2528]	320	!!bfr - end commented area
[1492]	321	!
	322	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[2528]	323	IF( ln_lc ) THEN ! Langmuir circulation source term added to tke (Axell JGR 2002)
[1492]	324	! !>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
[1239]	325	!
[1492]	326	! !* total energy produce by LC : cumulative sum over jk
[2528]	327	zpelc(:,:,1) = MAX( rn2b(:,:,1), 0._wp ) * fsdepw(:,:,1) * fse3w(:,:,1)
[1239]	328	DO jk = 2, jpk
[2528]	329	zpelc(:,:,jk) = zpelc(:,:,jk-1) + MAX( rn2b(:,:,jk), 0._wp ) * fsdepw(:,:,jk) * fse3w(:,:,jk)
[1239]	330	END DO
[1492]	331	! !* finite Langmuir Circulation depth
[1705]	332	zcof = 0.5 * 0.016 * 0.016 / ( zrhoa * zcdrag )
[2528]	333	imlc(:,:) = mbkt(:,:) + 1 ! Initialization to the number of w ocean point (=2 over land)
[1239]	334	DO jk = jpkm1, 2, -1
[1492]	335	DO jj = 1, jpj ! Last w-level at which zpelc>=0.5usus
	336	DO ji = 1, jpi ! with us=0.016*wind(starting from jpk-1)
[1705]	337	zus = zcof * taum(ji,jj)
[1239]	338	IF( zpelc(ji,jj,jk) > zus ) imlc(ji,jj) = jk
	339	END DO
	340	END DO
	341	END DO
[1492]	342	! ! finite LC depth
	343	DO jj = 1, jpj
[1239]	344	DO ji = 1, jpi
	345	zhlc(ji,jj) = fsdepw(ji,jj,imlc(ji,jj))
	346	END DO
	347	END DO
[1705]	348	zcof = 0.016 / SQRT( zrhoa * zcdrag )
[5120]	349	!CDIR NOVERRCHK
[1492]	350	DO jk = 2, jpkm1 !* TKE Langmuir circulation source term added to en
[5120]	351	!CDIR NOVERRCHK
[1239]	352	DO jj = 2, jpjm1
[5120]	353	!CDIR NOVERRCHK
[1239]	354	DO ji = fs_2, fs_jpim1 ! vector opt.
[1705]	355	zus = zcof * SQRT( taum(ji,jj) ) ! Stokes drift
[1492]	356	! ! vertical velocity due to LC
[1239]	357	zind = 0.5 - SIGN( 0.5, fsdepw(ji,jj,jk) - zhlc(ji,jj) )
[11442]	358	zwlc = zind * rn_lc0(ji,jj) * zus * SIN( rpi * fsdepw(ji,jj,jk) / zhlc(ji,jj) )
[1492]	359	! ! TKE Langmuir circulation source term
[11442]	360	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( 1._wp - fr_i(ji,jj) )* ( zwlc * zwlc * zwlc ) / &
[6487]	361	& zhlc(ji,jj) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[11442]	362
[1239]	363	END DO
	364	END DO
	365	END DO
	366	!
	367	ENDIF
[1492]	368	!
	369	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	370	! ! Now Turbulent kinetic energy (output in en)
	371	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	372	! ! Resolution of a tridiagonal linear system by a "methode de chasse"
	373	! ! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
	374	! ! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
	375	!
	376	DO jk = 2, jpkm1 !* Shear production at uw- and vw-points (energy conserving form)
	377	DO jj = 1, jpj ! here avmu, avmv used as workspace
	378	DO ji = 1, jpi
	379	avmu(ji,jj,jk) = avmu(ji,jj,jk) * ( un(ji,jj,jk-1) - un(ji,jj,jk) ) &
	380	& * ( ub(ji,jj,jk-1) - ub(ji,jj,jk) ) &
[5120]	381	& / ( fse3uw_n(ji,jj,jk) &
	382	& * fse3uw_b(ji,jj,jk) )
[1492]	383	avmv(ji,jj,jk) = avmv(ji,jj,jk) * ( vn(ji,jj,jk-1) - vn(ji,jj,jk) ) &
	384	& * ( vb(ji,jj,jk-1) - vb(ji,jj,jk) ) &
	385	& / ( fse3vw_n(ji,jj,jk) &
	386	& * fse3vw_b(ji,jj,jk) )
	387	END DO
	388	END DO
	389	END DO
	390	!
[5120]	391	DO jk = 2, jpkm1 !* Matrix and right hand side in en
	392	DO jj = 2, jpjm1
	393	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	394	zcof = zfact1 * tmask(ji,jj,jk)
[6498]	395	# if defined key_zdftmx_new
	396	! key_zdftmx_new: New internal wave-driven param: set a minimum value for Kz on TKE (ensure numerical stability)
	397	zzd_up = zcof * ( MAX( avm(ji,jj,jk+1) + avm(ji,jj,jk), 2.e-5_wp ) ) & ! upper diagonal
	398	& / ( fse3t(ji,jj,jk ) * fse3w(ji,jj,jk ) )
	399	zzd_lw = zcof * ( MAX( avm(ji,jj,jk) + avm(ji,jj,jk-1), 2.e-5_wp ) ) & ! lower diagonal
	400	& / ( fse3t(ji,jj,jk-1) * fse3w(ji,jj,jk ) )
	401	# else
[1492]	402	zzd_up = zcof * ( avm (ji,jj,jk+1) + avm (ji,jj,jk ) ) & ! upper diagonal
	403	& / ( fse3t(ji,jj,jk ) * fse3w(ji,jj,jk ) )
	404	zzd_lw = zcof * ( avm (ji,jj,jk ) + avm (ji,jj,jk-1) ) & ! lower diagonal
	405	& / ( fse3t(ji,jj,jk-1) * fse3w(ji,jj,jk ) )
[6498]	406	# endif
[1492]	407	! ! shear prod. at w-point weightened by mask
[2528]	408	zesh2 = ( avmu(ji-1,jj,jk) + avmu(ji,jj,jk) ) / MAX( 1._wp , umask(ji-1,jj,jk) + umask(ji,jj,jk) ) &
	409	& + ( avmv(ji,jj-1,jk) + avmv(ji,jj,jk) ) / MAX( 1._wp , vmask(ji,jj-1,jk) + vmask(ji,jj,jk) )
[1492]	410	!
	411	zd_up(ji,jj,jk) = zzd_up ! Matrix (zdiag, zd_up, zd_lw)
	412	zd_lw(ji,jj,jk) = zzd_lw
[11442]	413	zdiag(ji,jj,jk) = 1._wp - zzd_lw - zzd_up + zfact2(ji,jj) * dissl(ji,jj,jk) * tmask(ji,jj,jk)
[1239]	414	!
[1492]	415	! ! right hand side in en
[1481]	416	en(ji,jj,jk) = en(ji,jj,jk) + rdt * ( zesh2 - avt(ji,jj,jk) * rn2(ji,jj,jk) &
[11442]	417	& + zfact3(ji,jj) * dissl(ji,jj,jk) * en (ji,jj,jk) ) &
[5120]	418	& * wmask(ji,jj,jk)
[1239]	419	END DO
[5120]	420	END DO
	421	END DO
	422	! !* Matrix inversion from level 2 (tke prescribed at level 1)
	423	DO jk = 3, jpkm1 ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
	424	DO jj = 2, jpjm1
	425	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	426	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]	427	END DO
[5120]	428	END DO
	429	END DO
	430	!
	431	! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
	432	DO jj = 2, jpjm1
	433	DO ji = fs_2, fs_jpim1 ! vector opt.
	434	zd_lw(ji,jj,2) = en(ji,jj,2) - zd_lw(ji,jj,2) * en(ji,jj,1) ! Surface boudary conditions on tke
	435	END DO
	436	END DO
	437	DO jk = 3, jpkm1
	438	DO jj = 2, jpjm1
	439	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	440	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]	441	END DO
[5120]	442	END DO
	443	END DO
	444	!
	445	! thrid recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
	446	DO jj = 2, jpjm1
	447	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	448	en(ji,jj,jpkm1) = zd_lw(ji,jj,jpkm1) / zdiag(ji,jj,jpkm1)
[5120]	449	END DO
	450	END DO
	451	DO jk = jpk-2, 2, -1
	452	DO jj = 2, jpjm1
	453	DO ji = fs_2, fs_jpim1 ! vector opt.
[1492]	454	en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
[1239]	455	END DO
[5120]	456	END DO
	457	END DO
	458	DO jk = 2, jpkm1 ! set the minimum value of tke
	459	DO jj = 2, jpjm1
	460	DO ji = fs_2, fs_jpim1 ! vector opt.
	461	en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin ) * wmask(ji,jj,jk)
[1239]	462	END DO
	463	END DO
	464	END DO
	465
[6491]	466	! ! Save TKE prior to nn_etau addition
	467	e_niw(:,:,:) = en(:,:,:)
	468	!
[1492]	469	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	470	! ! TKE due to surface and internal wave breaking
	471	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[6491]	472	IF( nn_htau == 2 ) THEN !* mixed-layer depth dependant length scale
	473	DO jj = 2, jpjm1
	474	DO ji = fs_2, fs_jpim1 ! vector opt.
	475	htau(ji,jj) = rhtau * hmlp(ji,jj)
	476	END DO
	477	END DO
	478	ENDIF
	479	#if defined key_iomput
	480	!
	481	CALL iom_put( "htau", htau(:,:) ) ! Check htau (even if constant in time)
	482	#endif
	483	!
[2528]	484	IF( nn_etau == 1 ) THEN !* penetration below the mixed layer (rn_efr fraction)
[1492]	485	DO jk = 2, jpkm1
[1239]	486	DO jj = 2, jpjm1
	487	DO ji = fs_2, fs_jpim1 ! vector opt.
[11442]	488	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr0(ji,jj) * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	489	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	490	END DO
	491	END DO
[1492]	492	END DO
[2528]	493	ELSEIF( nn_etau == 2 ) THEN !* act only at the base of the mixed layer (jk=nmln) (rn_efr fraction)
[1492]	494	DO jj = 2, jpjm1
	495	DO ji = fs_2, fs_jpim1 ! vector opt.
	496	jk = nmln(ji,jj)
[11442]	497	en(ji,jj,jk) = en(ji,jj,jk) + rn_efr0(ji,jj) * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	498	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1239]	499	END DO
[1492]	500	END DO
[2528]	501	ELSEIF( nn_etau == 3 ) THEN !* penetration belox the mixed layer (HF variability)
[1705]	502	!CDIR NOVERRCHK
	503	DO jk = 2, jpkm1
	504	!CDIR NOVERRCHK
	505	DO jj = 2, jpjm1
	506	!CDIR NOVERRCHK
	507	DO ji = fs_2, fs_jpim1 ! vector opt.
	508	ztx2 = utau(ji-1,jj ) + utau(ji,jj)
	509	zty2 = vtau(ji ,jj-1) + vtau(ji,jj)
[4990]	510	ztau = 0.5_wp * SQRT( ztx2 * ztx2 + zty2 * zty2 ) * tmask(ji,jj,1) ! module of the mean stress
[2528]	511	zdif = taum(ji,jj) - ztau ! mean of modulus - modulus of the mean
	512	zdif = rhftau_scl * MAX( 0._wp, zdif + rhftau_add ) ! apply some modifications...
[11442]	513	en(ji,jj,jk) = en(ji,jj,jk) + zbbrau(ji,jj) * zdif * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
[5120]	514	& * ( 1._wp - fr_i(ji,jj) ) * wmask(ji,jj,jk) * tmask(ji,jj,1)
[1705]	515	END DO
	516	END DO
	517	END DO
[6491]	518	ELSEIF( nn_etau == 4 ) THEN !* column integral independant of htau (rn_efr must be scaled up)
	519	IF( nn_htau == 2 ) THEN ! efr dependant on time-varying htau
	520	DO jj = 2, jpjm1
	521	DO ji = fs_2, fs_jpim1 ! vector opt.
	522	efr(ji,jj) = rn_efr / ( htau(ji,jj) * ( 1._wp - EXP( -bathy(ji,jj) / htau(ji,jj) ) ) )
	523	END DO
	524	END DO
	525	ENDIF
	526	DO jk = 2, jpkm1
	527	DO jj = 2, jpjm1
	528	DO ji = fs_2, fs_jpim1 ! vector opt.
	529	en(ji,jj,jk) = en(ji,jj,jk) + efr(ji,jj) * en(ji,jj,1) * EXP( -fsdepw(ji,jj,jk) / htau(ji,jj) ) &
	530	& * ( 1._wp - fr_i(ji,jj) ) * tmask(ji,jj,jk)
	531	END DO
	532	END DO
	533	END DO
[1239]	534	ENDIF
[1492]	535	CALL lbc_lnk( en, 'W', 1. ) ! Lateral boundary conditions (sign unchanged)
	536	!
[6491]	537	DO jk = 2, jpkm1 ! TKE budget: near-inertial waves term
	538	DO jj = 2, jpjm1
	539	DO ji = fs_2, fs_jpim1 ! vector opt.
	540	e_niw(ji,jj,jk) = en(ji,jj,jk) - e_niw(ji,jj,jk)
	541	END DO
	542	END DO
	543	END DO
	544	!
	545	CALL lbc_lnk( e_niw, 'W', 1. )
	546	!
[3294]	547	CALL wrk_dealloc( jpi,jpj, imlc ) ! integer
	548	CALL wrk_dealloc( jpi,jpj, zhlc )
[11442]	549	CALL wrk_dealloc( jpi,jpj, zbbrau )
	550	CALL wrk_dealloc( jpi,jpj, zfact2 )
	551	CALL wrk_dealloc( jpi,jpj, zfact3 )
[3294]	552	CALL wrk_dealloc( jpi,jpj,jpk, zpelc, zdiag, zd_up, zd_lw )
[2715]	553	!
[3294]	554	IF( nn_timing == 1 ) CALL timing_stop('tke_tke')
	555	!
[1239]	556	END SUBROUTINE tke_tke
	557
[1492]	558
	559	SUBROUTINE tke_avn
[1239]	560	!!----------------------------------------------------------------------
[1492]	561	!! * ROUTINE tke_avn *
[1239]	562	!!
[1492]	563	!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
	564	!!
	565	!! ** Method : At this stage, en, the now TKE, is known (computed in
	566	!! the tke_tke routine). First, the now mixing lenth is
	567	!! computed from en and the strafification (N^2), then the mixings
	568	!! coefficients are computed.
	569	!! - Mixing length : a first evaluation of the mixing lengh
	570	!! scales is:
	571	!! mxl = sqrt(2*en) / N
	572	!! where N is the brunt-vaisala frequency, with a minimum value set
[2528]	573	!! to rmxl_min (rn_mxl0) in the interior (surface) ocean.
[1492]	574	!! The mixing and dissipative length scale are bound as follow :
	575	!! nn_mxl=0 : mxl bounded by the distance to surface and bottom.
	576	!! zmxld = zmxlm = mxl
	577	!! nn_mxl=1 : mxl bounded by the e3w and zmxld = zmxlm = mxl
	578	!! nn_mxl=2 : mxl bounded such that the vertical derivative of mxl is
	579	!! less than 1 (\|d/dz(mxl)\|<1) and zmxld = zmxlm = mxl
	580	!! nn_mxl=3 : mxl is bounded from the surface to the bottom usings
	581	!! \|d/dz(xml)\|<1 to obtain lup, and from the bottom to
	582	!! the surface to obtain ldown. the resulting length
	583	!! scales are:
	584	!! zmxld = sqrt( lup * ldown )
	585	!! zmxlm = min ( lup , ldown )
	586	!! - Vertical eddy viscosity and diffusivity:
	587	!! avm = max( avtb, rn_ediff * zmxlm * en^1/2 )
	588	!! avt = max( avmb, pdlr * avm )
	589	!! with pdlr=1 if nn_pdl=0, pdlr=1/pdl=F(Ri) otherwise.
	590	!!
	591	!! ** Action : - avt : now vertical eddy diffusivity (w-point)
	592	!! - avmu, avmv : now vertical eddy viscosity at uw- and vw-points
[1239]	593	!!----------------------------------------------------------------------
[2715]	594	INTEGER :: ji, jj, jk ! dummy loop indices
	595	REAL(wp) :: zrn2, zraug, zcoef, zav ! local scalars
	596	REAL(wp) :: zdku, zpdlr, zri, zsqen ! - -
	597	REAL(wp) :: zdkv, zemxl, zemlm, zemlp ! - -
[3294]	598	REAL(wp), POINTER, DIMENSION(:,:,:) :: zmpdl, zmxlm, zmxld
[1239]	599	!!--------------------------------------------------------------------
[3294]	600	!
	601	IF( nn_timing == 1 ) CALL timing_start('tke_avn')
[1239]	602
[3294]	603	CALL wrk_alloc( jpi,jpj,jpk, zmpdl, zmxlm, zmxld )
	604
[1492]	605	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	606	! ! Mixing length
	607	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	608	!
	609	! !* Buoyancy length scale: l=sqrt(2e/n*2)
	610	!
[5120]	611	! initialisation of interior minimum value (avoid a 2d loop with mikt)
	612	zmxlm(:,:,:) = rmxl_min
	613	zmxld(:,:,:) = rmxl_min
	614	!
[2528]	615	IF( ln_mxl0 ) THEN ! surface mixing length = F(stress) : l=vkarmn2.e5taum/(rau0*g)
[4990]	616	DO jj = 2, jpjm1
	617	DO ji = fs_2, fs_jpim1
[5120]	618	zraug = vkarmn * 2.e5_wp / ( rau0 * grav )
	619	zmxlm(ji,jj,1) = MAX( rn_mxl0, zraug * taum(ji,jj) * tmask(ji,jj,1) )
[4990]	620	END DO
	621	END DO
	622	ELSE
[5120]	623	zmxlm(:,:,1) = rn_mxl0
[1239]	624	ENDIF
	625	!
	626	!CDIR NOVERRCHK
[5120]	627	DO jk = 2, jpkm1 ! interior value : l=sqrt(2*e/n^2)
[1239]	628	!CDIR NOVERRCHK
[5120]	629	DO jj = 2, jpjm1
	630	!CDIR NOVERRCHK
	631	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	632	zrn2 = MAX( rn2(ji,jj,jk), rsmall )
[5120]	633	zmxlm(ji,jj,jk) = MAX( rmxl_min, SQRT( 2._wp * en(ji,jj,jk) / zrn2 ) )
[1239]	634	END DO
	635	END DO
	636	END DO
[1492]	637	!
	638	! !* Physical limits for the mixing length
	639	!
[5120]	640	zmxld(:,:,1 ) = zmxlm(:,:,1) ! surface set to the minimum value
[2528]	641	zmxld(:,:,jpk) = rmxl_min ! last level set to the minimum value
[1492]	642	!
[1239]	643	SELECT CASE ( nn_mxl )
	644	!
[5120]	645	! where wmask = 0 set zmxlm == fse3w
[1239]	646	CASE ( 0 ) ! bounded by the distance to surface and bottom
[5120]	647	DO jk = 2, jpkm1
	648	DO jj = 2, jpjm1
	649	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	650	zemxl = MIN( fsdepw(ji,jj,jk) - fsdepw(ji,jj,mikt(ji,jj)), zmxlm(ji,jj,jk), &
[2528]	651	& fsdepw(ji,jj,mbkt(ji,jj)+1) - fsdepw(ji,jj,jk) )
[5120]	652	! wmask prevent zmxlm = 0 if jk = mikt(ji,jj)
	653	zmxlm(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN(zmxlm(ji,jj,jk),fse3w(ji,jj,jk)) * (1 - wmask(ji,jj,jk))
	654	zmxld(ji,jj,jk) = zemxl * wmask(ji,jj,jk) + MIN(zmxlm(ji,jj,jk),fse3w(ji,jj,jk)) * (1 - wmask(ji,jj,jk))
[1239]	655	END DO
	656	END DO
	657	END DO
	658	!
	659	CASE ( 1 ) ! bounded by the vertical scale factor
[5120]	660	DO jk = 2, jpkm1
	661	DO jj = 2, jpjm1
	662	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	663	zemxl = MIN( fse3w(ji,jj,jk), zmxlm(ji,jj,jk) )
	664	zmxlm(ji,jj,jk) = zemxl
	665	zmxld(ji,jj,jk) = zemxl
	666	END DO
	667	END DO
	668	END DO
	669	!
	670	CASE ( 2 ) ! \|dk[xml]\| bounded by e3t :
[5120]	671	DO jk = 2, jpkm1 ! from the surface to the bottom :
	672	DO jj = 2, jpjm1
	673	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	674	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk-1) + fse3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
	675	END DO
[5120]	676	END DO
	677	END DO
	678	DO jk = jpkm1, 2, -1 ! from the bottom to the surface :
	679	DO jj = 2, jpjm1
	680	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	681	zemxl = MIN( zmxlm(ji,jj,jk+1) + fse3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
	682	zmxlm(ji,jj,jk) = zemxl
	683	zmxld(ji,jj,jk) = zemxl
	684	END DO
	685	END DO
	686	END DO
	687	!
	688	CASE ( 3 ) ! lup and ldown, \|dk[xml]\| bounded by e3t :
[5120]	689	DO jk = 2, jpkm1 ! from the surface to the bottom : lup
	690	DO jj = 2, jpjm1
	691	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	692	zmxld(ji,jj,jk) = MIN( zmxld(ji,jj,jk-1) + fse3t(ji,jj,jk-1), zmxlm(ji,jj,jk) )
	693	END DO
[5120]	694	END DO
	695	END DO
	696	DO jk = jpkm1, 2, -1 ! from the bottom to the surface : ldown
	697	DO jj = 2, jpjm1
	698	DO ji = fs_2, fs_jpim1 ! vector opt.
[1239]	699	zmxlm(ji,jj,jk) = MIN( zmxlm(ji,jj,jk+1) + fse3t(ji,jj,jk+1), zmxlm(ji,jj,jk) )
	700	END DO
	701	END DO
	702	END DO
	703	!CDIR NOVERRCHK
	704	DO jk = 2, jpkm1
	705	!CDIR NOVERRCHK
	706	DO jj = 2, jpjm1
	707	!CDIR NOVERRCHK
	708	DO ji = fs_2, fs_jpim1 ! vector opt.
	709	zemlm = MIN ( zmxld(ji,jj,jk), zmxlm(ji,jj,jk) )
	710	zemlp = SQRT( zmxld(ji,jj,jk) * zmxlm(ji,jj,jk) )
	711	zmxlm(ji,jj,jk) = zemlm
	712	zmxld(ji,jj,jk) = zemlp
	713	END DO
	714	END DO
	715	END DO
	716	!
	717	END SELECT
[1492]	718	!
[1239]	719	# if defined key_c1d
[1492]	720	e_dis(:,:,:) = zmxld(:,:,:) ! c1d configuration : save mixing and dissipation turbulent length scales
[1239]	721	e_mix(:,:,:) = zmxlm(:,:,:)
	722	# endif
	723
[1492]	724	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
	725	! ! Vertical eddy viscosity and diffusivity (avmu, avmv, avt)
	726	! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
[1239]	727	!CDIR NOVERRCHK
[1492]	728	DO jk = 1, jpkm1 !* vertical eddy viscosity & diffivity at w-points
[1239]	729	!CDIR NOVERRCHK
	730	DO jj = 2, jpjm1
	731	!CDIR NOVERRCHK
	732	DO ji = fs_2, fs_jpim1 ! vector opt.
	733	zsqen = SQRT( en(ji,jj,jk) )
[11442]	734	zav = rn_ediff0(ji,jj) * zmxlm(ji,jj,jk) * zsqen
[5120]	735	avm (ji,jj,jk) = MAX( zav, avmb(jk) ) * wmask(ji,jj,jk)
	736	avt (ji,jj,jk) = MAX( zav, avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1239]	737	dissl(ji,jj,jk) = zsqen / zmxld(ji,jj,jk)
	738	END DO
	739	END DO
[11442]	740	IF( ln_stopack) THEN
	741	IF(nn_spp_avt > 0 ) CALL spp_gen( 1, avt(:,:,jk), nn_spp_avt, rn_avt_sd, jk_spp_avt, jk)
	742	IF(nn_spp_avm > 0 ) CALL spp_gen( 1, avm(:,:,jk), nn_spp_avm, rn_avm_sd, jk_spp_avm, jk)
	743	ENDIF
[1239]	744	END DO
[1492]	745	CALL lbc_lnk( avm, 'W', 1. ) ! Lateral boundary conditions (sign unchanged)
	746	!
[5120]	747	DO jk = 2, jpkm1 !* vertical eddy viscosity at wu- and wv-points
	748	DO jj = 2, jpjm1
	749	DO ji = fs_2, fs_jpim1 ! vector opt.
	750	avmu(ji,jj,jk) = 0.5 * ( avm(ji,jj,jk) + avm(ji+1,jj ,jk) ) * wumask(ji,jj,jk)
	751	avmv(ji,jj,jk) = 0.5 * ( avm(ji,jj,jk) + avm(ji ,jj+1,jk) ) * wvmask(ji,jj,jk)
[4990]	752	END DO
[1239]	753	END DO
	754	END DO
	755	CALL lbc_lnk( avmu, 'U', 1. ) ; CALL lbc_lnk( avmv, 'V', 1. ) ! Lateral boundary conditions
[1492]	756	!
	757	IF( nn_pdl == 1 ) THEN !* Prandtl number case: update avt
[5120]	758	DO jk = 2, jpkm1
	759	DO jj = 2, jpjm1
	760	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	761	zcoef = avm(ji,jj,jk) * 2._wp * fse3w(ji,jj,jk) * fse3w(ji,jj,jk)
[1492]	762	! ! shear
	763	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) ) &
	764	& + avmu(ji ,jj,jk) * ( un(ji ,jj,jk-1) - un(ji ,jj,jk) ) * ( ub(ji ,jj,jk-1) - ub(ji ,jj,jk) )
	765	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) ) &
	766	& + avmv(ji,jj ,jk) * ( vn(ji,jj ,jk-1) - vn(ji,jj ,jk) ) * ( vb(ji,jj ,jk-1) - vb(ji,jj ,jk) )
	767	! ! local Richardson number
[2528]	768	zri = MAX( rn2b(ji,jj,jk), 0._wp ) * zcoef / (zdku + zdkv + rn_bshear )
	769	zpdlr = MAX( 0.1_wp, 0.2 / MAX( 0.2 , zri ) )
[1492]	770	!!gm and even better with the use of the "true" ri_crit=0.22222... (this change the results!)
[2528]	771	!!gm zpdlr = MAX( 0.1_wp, ri_crit / MAX( ri_crit , zri ) )
[5120]	772	avt(ji,jj,jk) = MAX( zpdlr * avt(ji,jj,jk), avtb_2d(ji,jj) * avtb(jk) ) * wmask(ji,jj,jk)
[1492]	773	# if defined key_c1d
[5120]	774	e_pdl(ji,jj,jk) = zpdlr * wmask(ji,jj,jk) ! c1d configuration : save masked Prandlt number
	775	e_ric(ji,jj,jk) = zri * wmask(ji,jj,jk) ! c1d config. : save Ri
[1239]	776	# endif
	777	END DO
	778	END DO
	779	END DO
	780	ENDIF
	781	CALL lbc_lnk( avt, 'W', 1. ) ! Lateral boundary conditions on avt (sign unchanged)
	782
	783	IF(ln_ctl) THEN
	784	CALL prt_ctl( tab3d_1=en , clinfo1=' tke - e: ', tab3d_2=avt, clinfo2=' t: ', ovlap=1, kdim=jpk)
	785	CALL prt_ctl( tab3d_1=avmu, clinfo1=' tke - u: ', mask1=umask, &
	786	& tab3d_2=avmv, clinfo2= ' v: ', mask2=vmask, ovlap=1, kdim=jpk )
	787	ENDIF
	788	!
[3294]	789	CALL wrk_dealloc( jpi,jpj,jpk, zmpdl, zmxlm, zmxld )
	790	!
	791	IF( nn_timing == 1 ) CALL timing_stop('tke_avn')
	792	!
[1492]	793	END SUBROUTINE tke_avn
[1239]	794
[1492]	795
[2528]	796	SUBROUTINE zdf_tke_init
[1239]	797	!!----------------------------------------------------------------------
[2528]	798	!! * ROUTINE zdf_tke_init *
[1239]	799	!!
	800	!! ** Purpose : Initialization of the vertical eddy diffivity and
[1492]	801	!! viscosity when using a tke turbulent closure scheme
[1239]	802	!!
[1601]	803	!! ** Method : Read the namzdf_tke namelist and check the parameters
[1492]	804	!! called at the first timestep (nit000)
[1239]	805	!!
[1601]	806	!! ** input : Namlist namzdf_tke
[1239]	807	!!
	808	!! ** Action : Increase by 1 the nstop flag is setting problem encounter
	809	!!----------------------------------------------------------------------
	810	INTEGER :: ji, jj, jk ! dummy loop indices
[6487]	811	INTEGER :: ios, ierr
[1239]	812	!!
[2528]	813	NAMELIST/namzdf_tke/ rn_ediff, rn_ediss , rn_ebb , rn_emin , &
	814	& rn_emin0, rn_bshear, nn_mxl , ln_mxl0 , &
	815	& rn_mxl0 , nn_pdl , ln_lc , rn_lc , &
[6491]	816	& nn_etau , nn_htau , rn_efr , rn_c
[1239]	817	!!----------------------------------------------------------------------
[6491]	818
[4147]	819	REWIND( numnam_ref ) ! Namelist namzdf_tke in reference namelist : Turbulent Kinetic Energy
	820	READ ( numnam_ref, namzdf_tke, IOSTAT = ios, ERR = 901)
	821	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in reference namelist', lwp )
	822
	823	REWIND( numnam_cfg ) ! Namelist namzdf_tke in configuration namelist : Turbulent Kinetic Energy
	824	READ ( numnam_cfg, namzdf_tke, IOSTAT = ios, ERR = 902 )
	825	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_tke in configuration namelist', lwp )
[4624]	826	IF(lwm) WRITE ( numond, namzdf_tke )
[2715]	827	!
[2528]	828	ri_cri = 2._wp / ( 2._wp + rn_ediss / rn_ediff ) ! resulting critical Richardson number
[6498]	829	# if defined key_zdftmx_new
	830	! key_zdftmx_new: New internal wave-driven param: specified value of rn_emin & rmxl_min are used
	831	rn_emin = 1.e-10_wp
	832	rmxl_min = 1.e-03_wp
	833	IF(lwp) THEN ! Control print
	834	WRITE(numout,*)
	835	WRITE(numout,*) 'zdf_tke_init : New tidal mixing case: force rn_emin = 1.e-10 and rmxl_min = 1.e-3 '
	836	WRITE(numout,*) '~~~~~~~~~~~~'
	837	ENDIF
	838	# else
[2528]	839	rmxl_min = 1.e-6_wp / ( rn_ediff * SQRT( rn_emin ) ) ! resulting minimum length to recover molecular viscosity
[6498]	840	# endif
[2715]	841	!
[1492]	842	IF(lwp) THEN !* Control print
[1239]	843	WRITE(numout,*)
[2528]	844	WRITE(numout,*) 'zdf_tke_init : tke turbulent closure scheme - initialisation'
	845	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	846	WRITE(numout,*) ' Namelist namzdf_tke : set tke mixing parameters'
[1705]	847	WRITE(numout,*) ' coef. to compute avt rn_ediff = ', rn_ediff
	848	WRITE(numout,*) ' Kolmogoroff dissipation coef. rn_ediss = ', rn_ediss
	849	WRITE(numout,*) ' tke surface input coef. rn_ebb = ', rn_ebb
	850	WRITE(numout,*) ' minimum value of tke rn_emin = ', rn_emin
	851	WRITE(numout,*) ' surface minimum value of tke rn_emin0 = ', rn_emin0
	852	WRITE(numout,*) ' background shear (>0) rn_bshear = ', rn_bshear
	853	WRITE(numout,*) ' mixing length type nn_mxl = ', nn_mxl
	854	WRITE(numout,*) ' prandl number flag nn_pdl = ', nn_pdl
	855	WRITE(numout,*) ' surface mixing length = F(stress) or not ln_mxl0 = ', ln_mxl0
[2528]	856	WRITE(numout,*) ' surface mixing length minimum value rn_mxl0 = ', rn_mxl0
	857	WRITE(numout,*) ' flag to take into acc. Langmuir circ. ln_lc = ', ln_lc
	858	WRITE(numout,*) ' coef to compute verticla velocity of LC rn_lc = ', rn_lc
[1705]	859	WRITE(numout,*) ' test param. to add tke induced by wind nn_etau = ', nn_etau
	860	WRITE(numout,*) ' flag for computation of exp. tke profile nn_htau = ', nn_htau
	861	WRITE(numout,*) ' fraction of en which pene. the thermocline rn_efr = ', rn_efr
[6491]	862	WRITE(numout,*) ' fraction of TKE added within the mixed layer by nn_etau rn_c = ', rn_c
[1239]	863	WRITE(numout,*)
[1601]	864	WRITE(numout,*) ' critical Richardson nb with your parameters ri_cri = ', ri_cri
[1239]	865	ENDIF
[2715]	866	!
	867	! ! allocate tke arrays
	868	IF( zdf_tke_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_tke_init : unable to allocate arrays' )
	869	!
[1492]	870	! !* Check of some namelist values
[4990]	871	IF( nn_mxl < 0 .OR. nn_mxl > 3 ) CALL ctl_stop( 'bad flag: nn_mxl is 0, 1 or 2 ' )
	872	IF( nn_pdl < 0 .OR. nn_pdl > 1 ) CALL ctl_stop( 'bad flag: nn_pdl is 0 or 1 ' )
[6491]	873	IF( nn_htau < 0 .OR. nn_htau > 5 ) CALL ctl_stop( 'bad flag: nn_htau is 0 to 5 ' )
[5407]	874	IF( nn_etau == 3 .AND. .NOT. ln_cpl ) CALL ctl_stop( 'nn_etau == 3 : HF taum only known in coupled mode' )
[1239]	875
[2528]	876	IF( ln_mxl0 ) THEN
	877	IF(lwp) WRITE(numout,*) ' use a surface mixing length = F(stress) : set rn_mxl0 = rmxl_min'
	878	rn_mxl0 = rmxl_min
	879	ENDIF
[11442]	880
	881	ALLOCATE( rn_lc0 (jpi,jpj) ) ; rn_lc0 = rn_lc
	882	ALLOCATE( rn_ediff0(jpi,jpj) ) ; rn_ediff0 = rn_ediff
	883	ALLOCATE( rn_ediss0(jpi,jpj) ) ; rn_ediss0 = rn_ediss
	884	ALLOCATE( rn_ebb0 (jpi,jpj) ) ; rn_ebb0 = rn_ebb
	885	ALLOCATE( rn_efr0 (jpi,jpj) ) ; rn_efr0 = rn_efr
[2528]	886
[6487]	887	IF( nn_etau == 2 ) THEN
	888	ierr = zdf_mxl_alloc()
	889	nmln(:,:) = nlb10 ! Initialization of nmln
	890	ENDIF
[1239]	891
[6491]	892	IF( nn_etau /= 0 .and. nn_htau == 2 ) THEN
	893	ierr = zdf_mxl_alloc()
	894	nmln(:,:) = nlb10 ! Initialization of nmln
	895	ENDIF
	896
[1492]	897	! !* depth of penetration of surface tke
	898	IF( nn_etau /= 0 ) THEN
[6491]	899	htau(:,:) = 0._wp
[1601]	900	SELECT CASE( nn_htau ) ! Choice of the depth of penetration
[2528]	901	CASE( 0 ) ! constant depth penetration (here 10 meters)
	902	htau(:,:) = 10._wp
	903	CASE( 1 ) ! F(latitude) : 0.5m to 30m poleward of 40 degrees
	904	htau(:,:) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
[6491]	905	CASE( 2 ) ! fraction of depth-integrated TKE within mixed-layer
	906	rhtau = -1._wp / LOG( 1._wp - rn_c )
	907	CASE( 3 ) ! F(latitude) : 0.5m to 15m poleward of 20 degrees
	908	htau(:,:) = MAX( 0.5_wp, MIN( 15._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(:,:) ) ) ) )
	909	CASE( 4 ) ! F(latitude) : 0.5m to 10m/30m poleward of 13/40 degrees north/south
	910	DO jj = 2, jpjm1
	911	DO ji = fs_2, fs_jpim1 ! vector opt.
	912	IF( gphit(ji,jj) <= 0._wp ) THEN
	913	htau(ji,jj) = MAX( 0.5_wp, MIN( 30._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	914	ELSE
	915	htau(ji,jj) = MAX( 0.5_wp, MIN( 10._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	916	ENDIF
	917	END DO
	918	END DO
	919	CASE ( 5 ) ! F(latitude) : 0.5m to 10m poleward of 13 degrees north/south,
	920	DO jj = 2, jpjm1 ! 10m to 30m between 30/45 degrees south
	921	DO ji = fs_2, fs_jpim1 ! vector opt.
	922	IF( gphit(ji,jj) <= -30._wp ) THEN
	923	htau(ji,jj) = MAX( 10._wp, MIN( 30._wp, 55._wp* ABS( SIN( rpi/120._wp * ( gphit(ji,jj) + 23._wp ) ) ) ) )
	924	ELSE
	925	htau(ji,jj) = MAX( 0.5_wp, MIN( 10._wp, 45._wp* ABS( SIN( rpi/180._wp * gphit(ji,jj) ) ) ) )
	926	ENDIF
	927	END DO
	928	END DO
[1492]	929	END SELECT
[6491]	930	!
	931	IF( nn_etau == 4 .AND. nn_htau /= 2 ) THEN ! efr dependant on constant htau
	932	DO jj = 2, jpjm1
	933	DO ji = fs_2, fs_jpim1 ! vector opt.
	934	efr(ji,jj) = rn_efr / ( htau(ji,jj) * ( 1._wp - EXP( -bathy(ji,jj) / htau(ji,jj) ) ) )
	935	END DO
	936	END DO
	937	ENDIF
[1492]	938	ENDIF
	939	! !* set vertical eddy coef. to the background value
[1239]	940	DO jk = 1, jpk
[5120]	941	avt (:,:,jk) = avtb(jk) * wmask (:,:,jk)
	942	avm (:,:,jk) = avmb(jk) * wmask (:,:,jk)
	943	avmu(:,:,jk) = avmb(jk) * wumask(:,:,jk)
	944	avmv(:,:,jk) = avmb(jk) * wvmask(:,:,jk)
[1239]	945	END DO
[2528]	946	dissl(:,:,:) = 1.e-12_wp
[2715]	947	!
	948	CALL tke_rst( nit000, 'READ' ) !* read or initialize all required files
[1239]	949	!
[2528]	950	END SUBROUTINE zdf_tke_init
[1239]	951
	952
[1531]	953	SUBROUTINE tke_rst( kt, cdrw )
[1239]	954	!!---------------------------------------------------------------------
[1531]	955	!! * ROUTINE tke_rst *
[1239]	956	!!
	957	!! ** Purpose : Read or write TKE file (en) in restart file
	958	!!
	959	!! ** Method : use of IOM library
	960	!! if the restart does not contain TKE, en is either
[1537]	961	!! set to rn_emin or recomputed
[1239]	962	!!----------------------------------------------------------------------
[2715]	963	INTEGER , INTENT(in) :: kt ! ocean time-step
	964	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
[1239]	965	!
[1481]	966	INTEGER :: jit, jk ! dummy loop indices
[2715]	967	INTEGER :: id1, id2, id3, id4, id5, id6 ! local integers
[1239]	968	!!----------------------------------------------------------------------
	969	!
[1481]	970	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
	971	! ! ---------------
	972	IF( ln_rstart ) THEN !* Read the restart file
	973	id1 = iom_varid( numror, 'en' , ldstop = .FALSE. )
	974	id2 = iom_varid( numror, 'avt' , ldstop = .FALSE. )
	975	id3 = iom_varid( numror, 'avm' , ldstop = .FALSE. )
	976	id4 = iom_varid( numror, 'avmu' , ldstop = .FALSE. )
	977	id5 = iom_varid( numror, 'avmv' , ldstop = .FALSE. )
	978	id6 = iom_varid( numror, 'dissl', ldstop = .FALSE. )
	979	!
	980	IF( id1 > 0 ) THEN ! 'en' exists
[1239]	981	CALL iom_get( numror, jpdom_autoglo, 'en', en )
[1481]	982	IF( MIN( id2, id3, id4, id5, id6 ) > 0 ) THEN ! all required arrays exist
[10302]	983	IF(nn_timing == 2) CALL timing_start('iom_rstget')
[1481]	984	CALL iom_get( numror, jpdom_autoglo, 'avt' , avt )
	985	CALL iom_get( numror, jpdom_autoglo, 'avm' , avm )
	986	CALL iom_get( numror, jpdom_autoglo, 'avmu' , avmu )
	987	CALL iom_get( numror, jpdom_autoglo, 'avmv' , avmv )
	988	CALL iom_get( numror, jpdom_autoglo, 'dissl', dissl )
[10302]	989	IF(nn_timing == 2) CALL timing_stop('iom_rstget')
[1492]	990	ELSE ! one at least array is missing
	991	CALL tke_avn ! compute avt, avm, avmu, avmv and dissl (approximation)
[1481]	992	ENDIF
	993	ELSE ! No TKE array found: initialisation
	994	IF(lwp) WRITE(numout,*) ' ===>>>> : previous run without tke scheme, en computed by iterative loop'
[1239]	995	en (:,:,:) = rn_emin * tmask(:,:,:)
[1492]	996	CALL tke_avn ! recompute avt, avm, avmu, avmv and dissl (approximation)
[5112]	997	!
[1531]	998	DO jit = nit000 + 1, nit000 + 10 ; CALL zdf_tke( jit ) ; END DO
[1239]	999	ENDIF
[1481]	1000	ELSE !* Start from rest
	1001	en(:,:,:) = rn_emin * tmask(:,:,:)
[1239]	1002	ENDIF
[1481]	1003	!
[11442]	1004	avt_k (:,:,:) = avt (:,:,:)
	1005	avm_k (:,:,:) = avm (:,:,:)
	1006	avmu_k(:,:,:) = avmu(:,:,:)
	1007	avmv_k(:,:,:) = avmv(:,:,:)
	1008
[1481]	1009	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
	1010	! ! -------------------
[1531]	1011	IF(lwp) WRITE(numout,*) '---- tke-rst ----'
[10302]	1012	IF(nn_timing == 2) CALL timing_start('iom_rstput')
[3632]	1013	CALL iom_rstput( kt, nitrst, numrow, 'en' , en )
	1014	CALL iom_rstput( kt, nitrst, numrow, 'avt' , avt_k )
	1015	CALL iom_rstput( kt, nitrst, numrow, 'avm' , avm_k )
	1016	CALL iom_rstput( kt, nitrst, numrow, 'avmu' , avmu_k )
	1017	CALL iom_rstput( kt, nitrst, numrow, 'avmv' , avmv_k )
	1018	CALL iom_rstput( kt, nitrst, numrow, 'dissl', dissl )
[10302]	1019	IF(nn_timing == 2) CALL timing_stop('iom_rstput')
[1481]	1020	!
[1239]	1021	ENDIF
	1022	!
[1531]	1023	END SUBROUTINE tke_rst
[1239]	1024
	1025	#else
	1026	!!----------------------------------------------------------------------
	1027	!! Dummy module : NO TKE scheme
	1028	!!----------------------------------------------------------------------
[1531]	1029	LOGICAL, PUBLIC, PARAMETER :: lk_zdftke = .FALSE. !: TKE flag
[1239]	1030	CONTAINS
[2528]	1031	SUBROUTINE zdf_tke_init ! Dummy routine
	1032	END SUBROUTINE zdf_tke_init
	1033	SUBROUTINE zdf_tke( kt ) ! Dummy routine
[1531]	1034	WRITE(,) 'zdf_tke: You should not have seen this print! error?', kt
	1035	END SUBROUTINE zdf_tke
	1036	SUBROUTINE tke_rst( kt, cdrw )
[1492]	1037	CHARACTER(len=*) :: cdrw
[1531]	1038	WRITE(,) 'tke_rst: You should not have seen this print! error?', kt, cdwr
	1039	END SUBROUTINE tke_rst
[1239]	1040	#endif
	1041
	1042	!!======================================================================
[1531]	1043	END MODULE zdftke

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