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traadv_ubs.F90 in branches/2012/dev_MERGE_2012/NEMOGCM/NEMO/OPA_SRC/TRA – NEMO

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source: branches/2012/dev_MERGE_2012/NEMOGCM/NEMO/OPA_SRC/TRA/traadv_ubs.F90 @ 3787

Last change on this file since 3787 was 3787, checked in by gm, 11 years ago
dev_MERGE_2012: #1049 & #1053 : bug corrections in traadv_eiv.F90 (AR5 diag) and in traadv_ubs.F90 (UBS scheme), resp.
Property svn:keywords set to `Id`
File size: 19.0 KB

Rev	Line
[503]	1	MODULE traadv_ubs
	2	!!==============================================================================
	3	!! * MODULE traadv_ubs *
	4	!! Ocean active tracers: horizontal & vertical advective trend
	5	!!==============================================================================
[2528]	6	!! History : 1.0 ! 2006-08 (L. Debreu, R. Benshila) Original code
	7	!! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport
[503]	8	!!----------------------------------------------------------------------
	9
	10	!!----------------------------------------------------------------------
	11	!! tra_adv_ubs : update the tracer trend with the horizontal
	12	!! advection trends using a third order biaised scheme
	13	!!----------------------------------------------------------------------
[3625]	14	USE oce ! ocean dynamics and active tracers
	15	USE dom_oce ! ocean space and time domain
	16	USE trdmod_oce ! ocean space and time domain
[2528]	17	USE trdtra
[503]	18	USE lib_mpp
[3625]	19	USE lbclnk ! ocean lateral boundary condition (or mpp link)
	20	USE in_out_manager ! I/O manager
	21	USE diaptr ! poleward transport diagnostics
	22	USE dynspg_oce ! choice/control of key cpp for surface pressure gradient
	23	USE trc_oce ! share passive tracers/Ocean variables
	24	USE wrk_nemo ! Memory Allocation
	25	USE timing ! Timing
	26	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[503]	27
	28	IMPLICIT NONE
	29	PRIVATE
	30
	31	PUBLIC tra_adv_ubs ! routine called by traadv module
	32
[2528]	33	LOGICAL :: l_trd ! flag to compute trends or not
[503]	34
	35	!! * Substitutions
	36	# include "domzgr_substitute.h90"
	37	# include "vectopt_loop_substitute.h90"
	38	!!----------------------------------------------------------------------
[2528]	39	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
[1152]	40	!! $Id$
[2528]	41	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[503]	42	!!----------------------------------------------------------------------
	43	CONTAINS
	44
[3294]	45	SUBROUTINE tra_adv_ubs ( kt, kit000, cdtype, p2dt, pun, pvn, pwn, &
[2528]	46	& ptb, ptn, pta, kjpt )
[503]	47	!!----------------------------------------------------------------------
	48	!! * ROUTINE tra_adv_ubs *
	49	!!
	50	!! ** Purpose : Compute the now trend due to the advection of tracers
	51	!! and add it to the general trend of passive tracer equations.
	52	!!
[3787]	53	!! ** Method : The upstream biased 3rd order scheme (UBS) is based on an
	54	!! upstream-biased parabolic interpolation (Shchepetkin and McWilliams 2005)
[519]	55	!! It is only used in the horizontal direction.
	56	!! For example the i-component of the advective fluxes are given by :
[3787]	57	!! ! e2u e3u un ( mi(Tn) - zltu(i ) ) if un(i) >= 0
[519]	58	!! zwx = ! or
[3787]	59	!! ! e2u e3u un ( mi(Tn) - zltu(i+1) ) if un(i) < 0
[519]	60	!! where zltu is the second derivative of the before temperature field:
	61	!! zltu = 1/e3t di[ e2u e3u / e1u di[Tb] ]
	62	!! This results in a dissipatively dominant (i.e. hyper-diffusive)
	63	!! truncation error. The overall performance of the advection scheme
	64	!! is similar to that reported in (Farrow and Stevens, 1995).
	65	!! For stability reasons, the first term of the fluxes which corresponds
	66	!! to a second order centered scheme is evaluated using the now velocity
	67	!! (centered in time) while the second term which is the diffusive part
	68	!! of the scheme, is evaluated using the before velocity (forward in time).
	69	!! Note that UBS is not positive. Do not use it on passive tracers.
[3787]	70	!! On the vertical, the advection is evaluated using a TVD scheme,
	71	!! as the UBS have been found to be too diffusive.
[503]	72	!!
[2528]	73	!! ** Action : - update (pta) with the now advective tracer trends
[519]	74	!!
	75	!! Reference : Shchepetkin, A. F., J. C. McWilliams, 2005, Ocean Modelling, 9, 347-404.
	76	!! Farrow, D.E., Stevens, D.P., 1995, J. Phys. Ocean. 25, 1731Ð1741.
[503]	77	!!----------------------------------------------------------------------
[2715]	78	USE oce , ONLY: zwx => ua , zwy => va ! (ua,va) used as workspace
	79	!
[2528]	80	INTEGER , INTENT(in ) :: kt ! ocean time-step index
[3294]	81	INTEGER , INTENT(in ) :: kit000 ! first time step index
[2528]	82	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	83	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	84	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
[3787]	85	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean transport components
[2528]	86	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	87	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[2715]	88	!
	89	INTEGER :: ji, jj, jk, jn ! dummy loop indices
	90	REAL(wp) :: ztra, zbtr, zcoef, z2dtt ! local scalars
	91	REAL(wp) :: zfp_ui, zfm_ui, zcenut, ztak, zfp_wk, zfm_wk ! - -
	92	REAL(wp) :: zfp_vj, zfm_vj, zcenvt, zeeu, zeev, z_hdivn ! - -
[3294]	93	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztu, ztv, zltu, zltv, zti, ztw
[503]	94	!!----------------------------------------------------------------------
[3294]	95	!
	96	IF( nn_timing == 1 ) CALL timing_start('tra_adv_ubs')
	97	!
	98	CALL wrk_alloc( jpi, jpj, jpk, ztu, ztv, zltu, zltv, zti, ztw )
	99	!
[503]	100
[3294]	101	IF( kt == kit000 ) THEN
[503]	102	IF(lwp) WRITE(numout,*)
[2528]	103	IF(lwp) WRITE(numout,*) 'tra_adv_ubs : horizontal UBS advection scheme on ', cdtype
[503]	104	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
	105	!
[2528]	106	l_trd = .FALSE.
	107	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
[503]	108	ENDIF
[2528]	109	!
	110	! ! ===========
	111	DO jn = 1, kjpt ! tracer loop
	112	! ! ===========
	113	! 1. Bottom value : flux set to zero
	114	! ----------------------------------
	115	zltu(:,:,jpk) = 0.e0 ; zltv(:,:,jpk) = 0.e0
	116	!
	117	DO jk = 1, jpkm1 ! Horizontal slab
	118	!
	119	! Laplacian
	120	DO jj = 1, jpjm1 ! First derivative (gradient)
	121	DO ji = 1, fs_jpim1 ! vector opt.
	122	zeeu = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk)
	123	zeev = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk)
	124	ztu(ji,jj,jk) = zeeu * ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) )
	125	ztv(ji,jj,jk) = zeev * ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) )
	126	END DO
[503]	127	END DO
[2528]	128	DO jj = 2, jpjm1 ! Second derivative (divergence)
	129	DO ji = fs_2, fs_jpim1 ! vector opt.
	130	zcoef = 1. / ( 6. * fse3t(ji,jj,jk) )
	131	zltu(ji,jj,jk) = ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zcoef
	132	zltv(ji,jj,jk) = ( ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) * zcoef
	133	END DO
[503]	134	END DO
[2528]	135	!
	136	END DO ! End of slab
	137	CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn)
[503]	138
[2528]	139	!
	140	! Horizontal advective fluxes
	141	DO jk = 1, jpkm1 ! Horizontal slab
	142	DO jj = 1, jpjm1
	143	DO ji = 1, fs_jpim1 ! vector opt.
[3787]	144	! upstream transport (x2)
[2528]	145	zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) )
	146	zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) )
	147	zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) )
	148	zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) )
[3787]	149	! 2nd order centered advective fluxes (x2)
	150	zcenut = pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) )
	151	zcenvt = pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) )
	152	! UBS advective fluxes
	153	zwx(ji,jj,jk) = 0.5 * ( zcenut - zfp_ui * zltu(ji,jj,jk) - zfm_ui * zltu(ji+1,jj,jk) )
	154	zwy(ji,jj,jk) = 0.5 * ( zcenvt - zfp_vj * zltv(ji,jj,jk) - zfm_vj * zltv(ji,jj+1,jk) )
[2528]	155	END DO
[503]	156	END DO
[2528]	157	END DO ! End of slab
[503]	158
[2528]	159	zltu(:,:,:) = pta(:,:,:,jn) ! store pta trends
[503]	160
[2528]	161	! Horizontal advective trends
[503]	162	DO jk = 1, jpkm1
[2528]	163	! Tracer flux divergence at t-point added to the general trend
[503]	164	DO jj = 2, jpjm1
	165	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	166	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	167	! horizontal advective
	168	ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) &
	169	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) )
	170	! add it to the general tracer trends
	171	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
[503]	172	END DO
	173	END DO
[2528]	174	!
	175	END DO ! End of slab
[503]	176
[2528]	177	! Horizontal trend used in tra_adv_ztvd subroutine
	178	zltu(:,:,:) = pta(:,:,:,jn) - zltu(:,:,:)
[503]	179
[2528]	180	! 3. Save the horizontal advective trends for diagnostic
	181	! ------------------------------------------------------
	182	! ! trend diagnostics (contribution of upstream fluxes)
	183	IF( l_trd ) THEN
	184	CALL trd_tra( kt, cdtype, jn, jptra_trd_xad, zwx, pun, ptn(:,:,:,jn) )
	185	CALL trd_tra( kt, cdtype, jn, jptra_trd_yad, zwy, pvn, ptn(:,:,:,jn) )
	186	END IF
	187	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
	188	IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nn_fptr ) == 0 ) ) THEN
	189	IF( jn == jp_tem ) htr_adv(:) = ptr_vj( zwy(:,:,:) )
	190	IF( jn == jp_sal ) str_adv(:) = ptr_vj( zwy(:,:,:) )
[503]	191	ENDIF
[2528]	192
	193	! TVD scheme for the vertical direction
	194	! ----------------------
	195	IF( l_trd ) zltv(:,:,:) = pta(:,:,:,jn) ! store pta if trend diag.
[503]	196
[2528]	197	! Bottom value : flux set to zero
	198	ztw(:,:,jpk) = 0.e0 ; zti(:,:,jpk) = 0.e0
[503]	199
[2528]	200	! Surface value
	201	IF( lk_vvl ) THEN ; ztw(:,:,1) = 0.e0 ! variable volume : flux set to zero
	202	ELSE ; ztw(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ! free constant surface
	203	ENDIF
	204	! upstream advection with initial mass fluxes & intermediate update
	205	! -------------------------------------------------------------------
	206	! Interior value
	207	DO jk = 2, jpkm1
	208	DO jj = 1, jpj
	209	DO ji = 1, jpi
	210	zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) )
	211	zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) )
	212	ztw(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) )
	213	END DO
	214	END DO
	215	END DO
	216	! update and guess with monotonic sheme
[503]	217	DO jk = 1, jpkm1
[2528]	218	z2dtt = p2dt(jk)
[503]	219	DO jj = 2, jpjm1
	220	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	221	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	222	ztak = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr
	223	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztak
	224	zti(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ( ztak + zltu(ji,jj,jk) ) ) * tmask(ji,jj,jk)
[503]	225	END DO
	226	END DO
	227	END DO
	228	!
[2528]	229	CALL lbc_lnk( zti, 'T', 1. ) ! Lateral boundary conditions on zti, zsi (unchanged sign)
[503]	230
[2528]	231	! antidiffusive flux : high order minus low order
	232	ztw(:,:,1) = 0.e0 ! Surface value
	233	DO jk = 2, jpkm1 ! Interior value
	234	DO jj = 1, jpj
	235	DO ji = 1, jpi
	236	ztw(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) - ztw(ji,jj,jk)
	237	END DO
[503]	238	END DO
	239	END DO
[2528]	240	!
	241	CALL nonosc_z( ptb(:,:,:,jn), ztw, zti, p2dt ) ! monotonicity algorithm
[503]	242
[2528]	243	! final trend with corrected fluxes
	244	DO jk = 1, jpkm1
	245	DO jj = 2, jpjm1
	246	DO ji = fs_2, fs_jpim1 ! vector opt.
	247	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	248	! k- vertical advective trends
	249	ztra = - zbtr * ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) )
	250	! added to the general tracer trends
	251	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
	252	END DO
[503]	253	END DO
	254	END DO
	255
[2528]	256	! Save the final vertical advective trends
	257	IF( l_trd ) THEN ! vertical advective trend diagnostics
	258	DO jk = 1, jpkm1 ! (compute -w.dk[ptn]= -dk[w.ptn] + ptn.dk[w])
	259	DO jj = 2, jpjm1
	260	DO ji = fs_2, fs_jpim1 ! vector opt.
	261	zbtr = 1.e0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	262	z_hdivn = ( pwn(ji,jj,jk) - pwn(ji,jj,jk+1) ) * zbtr
	263	zltv(ji,jj,jk) = pta(ji,jj,jk,jn) - zltv(ji,jj,jk) + ptn(ji,jj,jk,jn) * z_hdivn
	264	END DO
	265	END DO
[503]	266	END DO
[2528]	267	CALL trd_tra( kt, cdtype, jn, jptra_trd_zad, zltv )
	268	ENDIF
	269	!
	270	ENDDO
[503]	271	!
[3294]	272	CALL wrk_dealloc( jpi, jpj, jpk, ztu, ztv, zltu, zltv, zti, ztw )
[2715]	273	!
[3294]	274	IF( nn_timing == 1 ) CALL timing_stop('tra_adv_ubs')
	275	!
[2528]	276	END SUBROUTINE tra_adv_ubs
[503]	277
	278
[2528]	279	SUBROUTINE nonosc_z( pbef, pcc, paft, p2dt )
[503]	280	!!---------------------------------------------------------------------
	281	!! * ROUTINE nonosc_z *
	282	!!
	283	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	284	!! scheme and the before field by a nonoscillatory algorithm
	285	!!
	286	!! ** Method : ... ???
	287	!! warning : pbef and paft must be masked, but the boundaries
	288	!! conditions on the fluxes are not necessary zalezak (1979)
	289	!! drange (1995) multi-dimensional forward-in-time and upstream-
	290	!! in-space based differencing for fluid
	291	!!----------------------------------------------------------------------
[2715]	292	!
[2528]	293	REAL(wp), INTENT(in ), DIMENSION(jpk) :: p2dt ! vertical profile of tracer time-step
	294	REAL(wp), DIMENSION (jpi,jpj,jpk) :: pbef ! before field
[503]	295	REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: paft ! after field
	296	REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pcc ! monotonic flux in the k direction
[2715]	297	!
	298	INTEGER :: ji, jj, jk ! dummy loop indices
	299	INTEGER :: ikm1 ! local integer
	300	REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt ! local scalars
[3294]	301	REAL(wp), POINTER, DIMENSION(:,:,:) :: zbetup, zbetdo
[503]	302	!!----------------------------------------------------------------------
[3294]	303	!
	304	IF( nn_timing == 1 ) CALL timing_start('nonosc_z')
	305	!
	306	CALL wrk_alloc( jpi, jpj, jpk, zbetup, zbetdo )
	307	!
[503]	308
[2715]	309	zbig = 1.e+40_wp
	310	zrtrn = 1.e-15_wp
	311	zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp
	312
[503]	313	! Search local extrema
	314	! --------------------
	315	! large negative value (-zbig) inside land
	316	pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) )
	317	paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) )
	318	! search maximum in neighbourhood
	319	DO jk = 1, jpkm1
	320	ikm1 = MAX(jk-1,1)
	321	DO jj = 2, jpjm1
	322	DO ji = fs_2, fs_jpim1 ! vector opt.
	323	zbetup(ji,jj,jk) = MAX( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), &
	324	& pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), &
	325	& paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) )
	326	END DO
	327	END DO
	328	END DO
	329	! large positive value (+zbig) inside land
	330	pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) )
	331	paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) )
	332	! search minimum in neighbourhood
	333	DO jk = 1, jpkm1
	334	ikm1 = MAX(jk-1,1)
	335	DO jj = 2, jpjm1
	336	DO ji = fs_2, fs_jpim1 ! vector opt.
	337	zbetdo(ji,jj,jk) = MIN( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), &
	338	& pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), &
	339	& paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) )
	340	END DO
	341	END DO
	342	END DO
	343
	344	! restore masked values to zero
	345	pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:)
	346	paft(:,:,:) = paft(:,:,:) * tmask(:,:,:)
	347
[2528]	348
[503]	349	! 2. Positive and negative part of fluxes and beta terms
	350	! ------------------------------------------------------
	351
	352	DO jk = 1, jpkm1
[2528]	353	z2dtt = p2dt(jk)
[503]	354	DO jj = 2, jpjm1
	355	DO ji = fs_2, fs_jpim1 ! vector opt.
	356	! positive & negative part of the flux
	357	zpos = MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
	358	zneg = MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
	359	! up & down beta terms
	360	zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) / z2dtt
	361	zbetup(ji,jj,jk) = ( zbetup(ji,jj,jk) - paft(ji,jj,jk) ) / (zpos+zrtrn) * zbt
	362	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zbetdo(ji,jj,jk) ) / (zneg+zrtrn) * zbt
	363	END DO
	364	END DO
	365	END DO
	366	! monotonic flux in the k direction, i.e. pcc
	367	! -------------------------------------------
	368	DO jk = 2, jpkm1
	369	DO jj = 2, jpjm1
	370	DO ji = fs_2, fs_jpim1 ! vector opt.
	371	za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj,jk-1) )
	372	zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj,jk-1) )
	373	zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pcc(ji,jj,jk) ) )
	374	pcc(ji,jj,jk) = pcc(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb )
	375	END DO
	376	END DO
	377	END DO
	378	!
[3294]	379	CALL wrk_dealloc( jpi, jpj, jpk, zbetup, zbetdo )
[2715]	380	!
[3294]	381	IF( nn_timing == 1 ) CALL timing_stop('nonosc_z')
	382	!
[503]	383	END SUBROUTINE nonosc_z
	384
	385	!!======================================================================
	386	END MODULE traadv_ubs

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