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dynzdf_imp.F90

Last change on this file was 11738, checked in by marc, 5 years ago
The Dr Hook changes from my perl code.
File size: 17.8 KB

Rev	Line
[3]	1	MODULE dynzdf_imp
[2715]	2	!!======================================================================
[3]	3	!! * MODULE dynzdf_imp *
	4	!! Ocean dynamics: vertical component(s) of the momentum mixing trend
[2715]	5	!!======================================================================
[2528]	6	!! History : OPA ! 1990-10 (B. Blanke) Original code
	7	!! 8.0 ! 1997-05 (G. Madec) vertical component of isopycnal
[2715]	8	!! NEMO 0.5 ! 2002-08 (G. Madec) F90: Free form and module
[2528]	9	!! 3.3 ! 2010-04 (M. Leclair, G. Madec) Forcing averaged over 2 time steps
[3294]	10	!! 3.4 ! 2012-01 (H. Liu) Semi-implicit bottom friction
[503]	11	!!----------------------------------------------------------------------
[3]	12
	13	!!----------------------------------------------------------------------
[2715]	14	!! dyn_zdf_imp : update the momentum trend with the vertical diffusion using a implicit time-stepping
[3]	15	!!----------------------------------------------------------------------
	16	USE oce ! ocean dynamics and tracers
	17	USE dom_oce ! ocean space and time domain
[4292]	18	USE domvvl ! variable volume
[888]	19	USE sbc_oce ! surface boundary condition: ocean
	20	USE zdf_oce ! ocean vertical physics
[719]	21	USE phycst ! physical constants
[3]	22	USE in_out_manager ! I/O manager
[2715]	23	USE lib_mpp ! MPP library
[3294]	24	USE zdfbfr ! Bottom friction setup
	25	USE wrk_nemo ! Memory Allocation
	26	USE timing ! Timing
[4292]	27	USE dynadv ! dynamics: vector invariant versus flux form
[4354]	28	USE dynspg_oce, ONLY: lk_dynspg_ts
[3]	29
[11738]	30	USE yomhook, ONLY: lhook, dr_hook
	31	USE parkind1, ONLY: jprb, jpim
	32
[3]	33	IMPLICIT NONE
	34	PRIVATE
	35
[2528]	36	PUBLIC dyn_zdf_imp ! called by step.F90
[3]	37
[4292]	38	REAL(wp) :: r_vvl ! variable volume indicator, =1 if lk_vvl=T, =0 otherwise
	39
[3]	40	!! * Substitutions
	41	# include "domzgr_substitute.h90"
	42	# include "vectopt_loop_substitute.h90"
	43	!!----------------------------------------------------------------------
[2528]	44	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
[888]	45	!! $Id$
[2528]	46	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	47	!!----------------------------------------------------------------------
	48	CONTAINS
	49
[503]	50	SUBROUTINE dyn_zdf_imp( kt, p2dt )
[3]	51	!!----------------------------------------------------------------------
	52	!! * ROUTINE dyn_zdf_imp *
	53	!!
	54	!! ** Purpose : Compute the trend due to the vert. momentum diffusion
	55	!! and the surface forcing, and add it to the general trend of
	56	!! the momentum equations.
	57	!!
	58	!! ** Method : The vertical momentum mixing trend is given by :
	59	!! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) )
	60	!! backward time stepping
[2528]	61	!! Surface boundary conditions: wind stress input (averaged over kt-1/2 & kt+1/2)
[3]	62	!! Bottom boundary conditions : bottom stress (cf zdfbfr.F)
	63	!! Add this trend to the general trend ua :
	64	!! ua = ua + dz( avmu dz(u) )
	65	!!
[2528]	66	!! ** Action : - Update (ua,va) arrays with the after vertical diffusive mixing trend.
[3]	67	!!---------------------------------------------------------------------
[3294]	68	INTEGER , INTENT(in) :: kt ! ocean time-step index
[2715]	69	REAL(wp), INTENT(in) :: p2dt ! vertical profile of tracer time-step
[2528]	70	!!
[2715]	71	INTEGER :: ji, jj, jk ! dummy loop indices
[3294]	72	INTEGER :: ikbu, ikbv ! local integers
[2715]	73	REAL(wp) :: z1_p2dt, zcoef, zzwi, zzws, zrhs ! local scalars
[4292]	74	REAL(wp) :: ze3ua, ze3va
[3294]	75	REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwd, zws
[11738]	76	INTEGER(KIND=jpim), PARAMETER :: zhook_in = 0
	77	INTEGER(KIND=jpim), PARAMETER :: zhook_out = 1
	78	REAL(KIND=jprb) :: zhook_handle
	79
	80	CHARACTER(LEN=*), PARAMETER :: RoutineName='DYN_ZDF_IMP'
	81
	82	IF (lhook) CALL dr_hook(RoutineName,zhook_in,zhook_handle)
	83
[3294]	84	!!----------------------------------------------------------------------
	85	!
	86	IF( nn_timing == 1 ) CALL timing_start('dyn_zdf_imp')
	87	!
	88	CALL wrk_alloc( jpi,jpj,jpk, zwi, zwd, zws )
	89	!
[3]	90	IF( kt == nit000 ) THEN
	91	IF(lwp) WRITE(numout,*)
	92	IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator'
	93	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ '
[4292]	94	!
	95	IF( lk_vvl ) THEN ; r_vvl = 1._wp ! Variable volume indicator
	96	ELSE ; r_vvl = 0._wp
	97	ENDIF
[3]	98	ENDIF
	99
	100	! 0. Local constant initialization
	101	! --------------------------------
[2528]	102	z1_p2dt = 1._wp / p2dt ! inverse of the timestep
[455]	103
[3294]	104	! 1. Apply semi-implicit bottom friction
	105	! --------------------------------------
	106	! Only needed for semi-implicit bottom friction setup. The explicit
	107	! bottom friction has been included in "u(v)a" which act as the R.H.S
	108	! column vector of the tri-diagonal matrix equation
	109	!
	110
	111	IF( ln_bfrimp ) THEN
[4292]	112	DO jj = 2, jpjm1
	113	DO ji = 2, jpim1
	114	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	115	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	116	avmu(ji,jj,ikbu+1) = -bfrua(ji,jj) * fse3uw(ji,jj,ikbu+1)
	117	avmv(ji,jj,ikbv+1) = -bfrva(ji,jj) * fse3vw(ji,jj,ikbv+1)
	118	END DO
[3294]	119	END DO
[5120]	120	IF ( ln_isfcav ) THEN
	121	DO jj = 2, jpjm1
	122	DO ji = 2, jpim1
	123	ikbu = miku(ji,jj) ! ocean top level at u- and v-points
	124	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	125	IF (ikbu .GE. 2) avmu(ji,jj,ikbu) = -tfrua(ji,jj) * fse3uw(ji,jj,ikbu)
	126	IF (ikbv .GE. 2) avmv(ji,jj,ikbv) = -tfrva(ji,jj) * fse3vw(ji,jj,ikbv)
	127	END DO
	128	END DO
	129	END IF
[3294]	130	ENDIF
	131
[4292]	132	#if defined key_dynspg_ts
	133	IF( ln_dynadv_vec .OR. .NOT. lk_vvl ) THEN ! applied on velocity
	134	DO jk = 1, jpkm1
	135	ua(:,:,jk) = ( ub(:,:,jk) + p2dt * ua(:,:,jk) ) * umask(:,:,jk)
	136	va(:,:,jk) = ( vb(:,:,jk) + p2dt * va(:,:,jk) ) * vmask(:,:,jk)
	137	END DO
	138	ELSE ! applied on thickness weighted velocity
	139	DO jk = 1, jpkm1
	140	ua(:,:,jk) = ( ub(:,:,jk) * fse3u_b(:,:,jk) &
	141	& + p2dt * ua(:,:,jk) * fse3u_n(:,:,jk) ) &
	142	& / fse3u_a(:,:,jk) * umask(:,:,jk)
	143	va(:,:,jk) = ( vb(:,:,jk) * fse3v_b(:,:,jk) &
	144	& + p2dt * va(:,:,jk) * fse3v_n(:,:,jk) ) &
	145	& / fse3v_a(:,:,jk) * vmask(:,:,jk)
	146	END DO
	147	ENDIF
	148
	149	IF ( ln_bfrimp .AND.lk_dynspg_ts ) THEN
	150	! remove barotropic velocities:
	151	DO jk = 1, jpkm1
	152	ua(:,:,jk) = (ua(:,:,jk) - ua_b(:,:)) * umask(:,:,jk)
	153	va(:,:,jk) = (va(:,:,jk) - va_b(:,:)) * vmask(:,:,jk)
[4990]	154	END DO
	155	! Add bottom/top stress due to barotropic component only:
[4292]	156	DO jj = 2, jpjm1
	157	DO ji = fs_2, fs_jpim1 ! vector opt.
	158	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	159	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	160	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,ikbu) + r_vvl * fse3u_a(ji,jj,ikbu)
	161	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,ikbv) + r_vvl * fse3v_a(ji,jj,ikbv)
	162	ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * bfrua(ji,jj) * ua_b(ji,jj) / ze3ua
	163	va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * bfrva(ji,jj) * va_b(ji,jj) / ze3va
	164	END DO
	165	END DO
[5120]	166	IF ( ln_isfcav ) THEN
	167	DO jj = 2, jpjm1
	168	DO ji = fs_2, fs_jpim1 ! vector opt.
	169	ikbu = miku(ji,jj) ! top ocean level at u- and v-points
	170	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	171	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,ikbu) + r_vvl * fse3u_a(ji,jj,ikbu)
	172	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,ikbv) + r_vvl * fse3v_a(ji,jj,ikbv)
	173	ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * tfrua(ji,jj) * ua_b(ji,jj) / ze3ua
	174	va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * tfrva(ji,jj) * va_b(ji,jj) / ze3va
	175	END DO
	176	END DO
	177	END IF
[4292]	178	ENDIF
	179	#endif
	180
[3294]	181	! 2. Vertical diffusion on u
[3]	182	! ---------------------------
	183	! Matrix and second member construction
[1662]	184	! bottom boundary condition: both zwi and zws must be masked as avmu can take
[3294]	185	! non zero value at the ocean bottom depending on the bottom friction used.
[2528]	186	!
	187	DO jk = 1, jpkm1 ! Matrix
[3]	188	DO jj = 2, jpjm1
	189	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	190	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,jk) + r_vvl * fse3u_a(ji,jj,jk) ! after scale factor at T-point
	191	zcoef = - p2dt / ze3ua
[5120]	192	zzwi = zcoef * avmu (ji,jj,jk ) / fse3uw(ji,jj,jk )
	193	zwi(ji,jj,jk) = zzwi * wumask(ji,jj,jk )
	194	zzws = zcoef * avmu (ji,jj,jk+1) / fse3uw(ji,jj,jk+1)
	195	zws(ji,jj,jk) = zzws * wumask(ji,jj,jk+1)
	196	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
[3]	197	END DO
	198	END DO
	199	END DO
[4292]	200	DO jj = 2, jpjm1 ! Surface boundary conditions
[3]	201	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	202	zwi(ji,jj,1) = 0._wp
	203	zwd(ji,jj,1) = 1._wp - zws(ji,jj,1)
[3]	204	END DO
	205	END DO
	206
	207	! Matrix inversion starting from the first level
	208	!-----------------------------------------------------------------------
	209	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	210	!
	211	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	212	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	213	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	214	! ( ... )( ... ) ( ... )
	215	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	216	!
	217	! m is decomposed in the product of an upper and a lower triangular matrix
	218	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	219	! The solution (the after velocity) is in ua
	220	!-----------------------------------------------------------------------
[2528]	221	!
[4990]	222	!== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
[5120]	223	DO jk = 2, jpkm1
	224	DO jj = 2, jpjm1
	225	DO ji = fs_2, fs_jpim1 ! vector opt.
[3]	226	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	227	END DO
	228	END DO
	229	END DO
[2528]	230	!
	231	DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==
[3]	232	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	233	#if defined key_dynspg_ts
[5120]	234	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,1) + r_vvl * fse3u_a(ji,jj,1)
	235	ua(ji,jj,1) = ua(ji,jj,1) + p2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) &
	236	& / ( ze3ua * rau0 ) * umask(ji,jj,1)
[4292]	237	#else
[5120]	238	ua(ji,jj,1) = ub(ji,jj,1) &
	239	& + p2dt (ua(ji,jj,1) + 0.5_wp ( utau_b(ji,jj) + utau(ji,jj) ) &
	240	& / ( fse3u(ji,jj,1) * rau0 ) * umask(ji,jj,1) )
[4292]	241	#endif
[5120]	242	END DO
	243	END DO
	244	DO jk = 2, jpkm1
	245	DO jj = 2, jpjm1
	246	DO ji = fs_2, fs_jpim1
[4292]	247	#if defined key_dynspg_ts
	248	zrhs = ua(ji,jj,jk) ! zrhs=right hand side
	249	#else
	250	zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk)
	251	#endif
[3]	252	ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1)
	253	END DO
	254	END DO
	255	END DO
[2528]	256	!
	257	DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==
[3]	258	DO ji = fs_2, fs_jpim1 ! vector opt.
	259	ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1)
[5120]	260	END DO
	261	END DO
	262	DO jk = jpk-2, 1, -1
	263	DO jj = 2, jpjm1
	264	DO ji = fs_2, fs_jpim1
[2528]	265	ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk)
[3]	266	END DO
	267	END DO
	268	END DO
	269
[4292]	270	#if ! defined key_dynspg_ts
[3]	271	! Normalization to obtain the general momentum trend ua
	272	DO jk = 1, jpkm1
	273	DO jj = 2, jpjm1
	274	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	275	ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) * z1_p2dt
[3]	276	END DO
	277	END DO
	278	END DO
[4292]	279	#endif
[3]	280
[3294]	281	! 3. Vertical diffusion on v
[3]	282	! ---------------------------
	283	! Matrix and second member construction
[1662]	284	! bottom boundary condition: both zwi and zws must be masked as avmv can take
[3294]	285	! non zero value at the ocean bottom depending on the bottom friction used
[2528]	286	!
	287	DO jk = 1, jpkm1 ! Matrix
[3]	288	DO jj = 2, jpjm1
	289	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	290	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,jk) + r_vvl * fse3v_a(ji,jj,jk) ! after scale factor at T-point
	291	zcoef = - p2dt / ze3va
[2528]	292	zzwi = zcoef * avmv (ji,jj,jk ) / fse3vw(ji,jj,jk )
[5120]	293	zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk)
[2528]	294	zzws = zcoef * avmv (ji,jj,jk+1) / fse3vw(ji,jj,jk+1)
[5120]	295	zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1)
	296	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
[3]	297	END DO
	298	END DO
	299	END DO
[4292]	300	DO jj = 2, jpjm1 ! Surface boundary conditions
[3]	301	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	302	zwi(ji,jj,1) = 0._wp
	303	zwd(ji,jj,1) = 1._wp - zws(ji,jj,1)
[3]	304	END DO
	305	END DO
	306
	307	! Matrix inversion
	308	!-----------------------------------------------------------------------
	309	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	310	!
	311	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	312	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	313	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	314	! ( ... )( ... ) ( ... )
	315	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	316	!
[2528]	317	! m is decomposed in the product of an upper and lower triangular matrix
[3]	318	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	319	! The solution (after velocity) is in 2d array va
	320	!-----------------------------------------------------------------------
[2528]	321	!
[4990]	322	!== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
[5120]	323	DO jk = 2, jpkm1
	324	DO jj = 2, jpjm1
	325	DO ji = fs_2, fs_jpim1 ! vector opt.
[3]	326	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	327	END DO
	328	END DO
	329	END DO
[2528]	330	!
	331	DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==
[3]	332	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	333	#if defined key_dynspg_ts
[5120]	334	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,1) + r_vvl * fse3v_a(ji,jj,1)
	335	va(ji,jj,1) = va(ji,jj,1) + p2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) &
[6795]	336	& / ( ze3va * rau0 ) * vmask(ji,jj,1)
[4292]	337	#else
[5120]	338	va(ji,jj,1) = vb(ji,jj,1) &
	339	& + p2dt (va(ji,jj,1) + 0.5_wp ( vtau_b(ji,jj) + vtau(ji,jj) ) &
[6795]	340	& / ( fse3v(ji,jj,1) * rau0 ) * vmask(ji,jj,1) )
[4292]	341	#endif
[5120]	342	END DO
	343	END DO
	344	DO jk = 2, jpkm1
	345	DO jj = 2, jpjm1
	346	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	347	#if defined key_dynspg_ts
	348	zrhs = va(ji,jj,jk) ! zrhs=right hand side
	349	#else
	350	zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk)
	351	#endif
[3]	352	va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1)
	353	END DO
	354	END DO
	355	END DO
[2528]	356	!
[4292]	357	DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==
[3]	358	DO ji = fs_2, fs_jpim1 ! vector opt.
	359	va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1)
[5120]	360	END DO
	361	END DO
	362	DO jk = jpk-2, 1, -1
	363	DO jj = 2, jpjm1
	364	DO ji = fs_2, fs_jpim1
[2528]	365	va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk)
[3]	366	END DO
	367	END DO
	368	END DO
	369
	370	! Normalization to obtain the general momentum trend va
[4292]	371	#if ! defined key_dynspg_ts
[3]	372	DO jk = 1, jpkm1
	373	DO jj = 2, jpjm1
	374	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	375	va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) * z1_p2dt
[3]	376	END DO
	377	END DO
	378	END DO
[4292]	379	#endif
[3294]	380
[4292]	381	! J. Chanut: Lines below are useless ?
[3294]	382	!! restore bottom layer avmu(v)
	383	IF( ln_bfrimp ) THEN
[4990]	384	DO jj = 2, jpjm1
	385	DO ji = 2, jpim1
	386	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	387	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	388	avmu(ji,jj,ikbu+1) = 0.e0
	389	avmv(ji,jj,ikbv+1) = 0.e0
	390	END DO
	391	END DO
[5120]	392	IF (ln_isfcav) THEN
	393	DO jj = 2, jpjm1
	394	DO ji = 2, jpim1
	395	ikbu = miku(ji,jj) ! ocean top level at u- and v-points
	396	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	397	IF (ikbu > 1) avmu(ji,jj,ikbu) = 0.e0
	398	IF (ikbv > 1) avmv(ji,jj,ikbv) = 0.e0
	399	END DO
	400	END DO
	401	END IF
[3294]	402	ENDIF
[2528]	403	!
[3294]	404	CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwd, zws)
[2715]	405	!
[3294]	406	IF( nn_timing == 1 ) CALL timing_stop('dyn_zdf_imp')
	407	!
[11738]	408	IF (lhook) CALL dr_hook(RoutineName,zhook_out,zhook_handle)
[3]	409	END SUBROUTINE dyn_zdf_imp
	410
	411	!!==============================================================================
	412	END MODULE dynzdf_imp

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