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dynzdf_imp.F90 in branches/2014/dev_r4650_UKMO2_ice_shelves/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2014/dev_r4650_UKMO2_ice_shelves/NEMOGCM/NEMO/OPA_SRC/DYN/dynzdf_imp.F90 @ 4704

Last change on this file since 4704 was 4704, checked in by mathiot, 10 years ago
Ice Shelf: correction of minor bugs if running without ice shelf
Property svn:keywords set to `Id`
File size: 17.0 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
	30	IMPLICIT NONE
	31	PRIVATE
	32
[2528]	33	PUBLIC dyn_zdf_imp ! called by step.F90
[3]	34
[4292]	35	REAL(wp) :: r_vvl ! variable volume indicator, =1 if lk_vvl=T, =0 otherwise
	36
[3]	37	!! * Substitutions
	38	# include "domzgr_substitute.h90"
	39	# include "vectopt_loop_substitute.h90"
	40	!!----------------------------------------------------------------------
[2528]	41	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
[888]	42	!! $Id$
[2528]	43	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	44	!!----------------------------------------------------------------------
	45	CONTAINS
	46
[503]	47	SUBROUTINE dyn_zdf_imp( kt, p2dt )
[3]	48	!!----------------------------------------------------------------------
	49	!! * ROUTINE dyn_zdf_imp *
	50	!!
	51	!! ** Purpose : Compute the trend due to the vert. momentum diffusion
	52	!! and the surface forcing, and add it to the general trend of
	53	!! the momentum equations.
	54	!!
	55	!! ** Method : The vertical momentum mixing trend is given by :
	56	!! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) )
	57	!! backward time stepping
[2528]	58	!! Surface boundary conditions: wind stress input (averaged over kt-1/2 & kt+1/2)
[3]	59	!! Bottom boundary conditions : bottom stress (cf zdfbfr.F)
	60	!! Add this trend to the general trend ua :
	61	!! ua = ua + dz( avmu dz(u) )
	62	!!
[2528]	63	!! ** Action : - Update (ua,va) arrays with the after vertical diffusive mixing trend.
[3]	64	!!---------------------------------------------------------------------
[3294]	65	INTEGER , INTENT(in) :: kt ! ocean time-step index
[2715]	66	REAL(wp), INTENT(in) :: p2dt ! vertical profile of tracer time-step
[2528]	67	!!
[2715]	68	INTEGER :: ji, jj, jk ! dummy loop indices
[3294]	69	INTEGER :: ikbu, ikbv ! local integers
[2715]	70	REAL(wp) :: z1_p2dt, zcoef, zzwi, zzws, zrhs ! local scalars
[4292]	71	REAL(wp) :: ze3ua, ze3va
[3]	72	!!----------------------------------------------------------------------
	73
[3294]	74	REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwd, zws
	75	!!----------------------------------------------------------------------
	76	!
	77	IF( nn_timing == 1 ) CALL timing_start('dyn_zdf_imp')
	78	!
	79	CALL wrk_alloc( jpi,jpj,jpk, zwi, zwd, zws )
	80	!
[3]	81	IF( kt == nit000 ) THEN
	82	IF(lwp) WRITE(numout,*)
	83	IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator'
	84	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ '
[4292]	85	!
	86	IF( lk_vvl ) THEN ; r_vvl = 1._wp ! Variable volume indicator
	87	ELSE ; r_vvl = 0._wp
	88	ENDIF
[3]	89	ENDIF
	90
	91	! 0. Local constant initialization
	92	! --------------------------------
[2528]	93	z1_p2dt = 1._wp / p2dt ! inverse of the timestep
[455]	94
[3294]	95	! 1. Apply semi-implicit bottom friction
	96	! --------------------------------------
	97	! Only needed for semi-implicit bottom friction setup. The explicit
	98	! bottom friction has been included in "u(v)a" which act as the R.H.S
	99	! column vector of the tri-diagonal matrix equation
	100	!
	101
	102	IF( ln_bfrimp ) THEN
	103	# if defined key_vectopt_loop
[4292]	104	DO jj = 1, 1
	105	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
[3294]	106	# else
[4292]	107	DO jj = 2, jpjm1
	108	DO ji = 2, jpim1
[3294]	109	# endif
[4292]	110	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	111	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	112	avmu(ji,jj,ikbu+1) = -bfrua(ji,jj) * fse3uw(ji,jj,ikbu+1)
	113	avmv(ji,jj,ikbv+1) = -bfrva(ji,jj) * fse3vw(ji,jj,ikbv+1)
[4666]	114	ikbu = miku(ji,jj) ! ocean top level at u- and v-points
	115	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
[4704]	116	IF (ikbu .GE. 2) avmu(ji,jj,ikbu-1) = -tfrua(ji,jj) * fse3uw(ji,jj,ikbu-1)
	117	IF (ikbv .GE. 2) avmv(ji,jj,ikbv-1) = -tfrva(ji,jj) * fse3vw(ji,jj,ikbv-1)
[4292]	118	END DO
[3294]	119	END DO
	120	ENDIF
	121
[4292]	122	#if defined key_dynspg_ts
	123	IF( ln_dynadv_vec .OR. .NOT. lk_vvl ) THEN ! applied on velocity
	124	DO jk = 1, jpkm1
	125	ua(:,:,jk) = ( ub(:,:,jk) + p2dt * ua(:,:,jk) ) * umask(:,:,jk)
	126	va(:,:,jk) = ( vb(:,:,jk) + p2dt * va(:,:,jk) ) * vmask(:,:,jk)
	127	END DO
	128	ELSE ! applied on thickness weighted velocity
	129	DO jk = 1, jpkm1
	130	ua(:,:,jk) = ( ub(:,:,jk) * fse3u_b(:,:,jk) &
	131	& + p2dt * ua(:,:,jk) * fse3u_n(:,:,jk) ) &
	132	& / fse3u_a(:,:,jk) * umask(:,:,jk)
	133	va(:,:,jk) = ( vb(:,:,jk) * fse3v_b(:,:,jk) &
	134	& + p2dt * va(:,:,jk) * fse3v_n(:,:,jk) ) &
	135	& / fse3v_a(:,:,jk) * vmask(:,:,jk)
	136	END DO
	137	ENDIF
	138
	139	IF ( ln_bfrimp .AND.lk_dynspg_ts ) THEN
	140	! remove barotropic velocities:
	141	DO jk = 1, jpkm1
	142	ua(:,:,jk) = (ua(:,:,jk) - ua_b(:,:)) * umask(:,:,jk)
	143	va(:,:,jk) = (va(:,:,jk) - va_b(:,:)) * vmask(:,:,jk)
	144	ENDDO
[4666]	145	! Add bottom/top stress due to barotropic component only:
[4292]	146	DO jj = 2, jpjm1
	147	DO ji = fs_2, fs_jpim1 ! vector opt.
	148	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	149	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	150	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,ikbu) + r_vvl * fse3u_a(ji,jj,ikbu)
	151	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,ikbv) + r_vvl * fse3v_a(ji,jj,ikbv)
	152	ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * bfrua(ji,jj) * ua_b(ji,jj) / ze3ua
	153	va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * bfrva(ji,jj) * va_b(ji,jj) / ze3va
[4704]	154	ikbu = miku(ji,jj) ! top ocean level at u- and v-points
	155	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
[4666]	156	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,ikbu) + r_vvl * fse3u_a(ji,jj,ikbu)
	157	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,ikbv) + r_vvl * fse3v_a(ji,jj,ikbv)
	158	ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * tfrua(ji,jj) * ua_b(ji,jj) / ze3ua
	159	va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * tfrva(ji,jj) * va_b(ji,jj) / ze3va
[4292]	160	END DO
	161	END DO
	162	ENDIF
	163	#endif
	164
[3294]	165	! 2. Vertical diffusion on u
[3]	166	! ---------------------------
	167	! Matrix and second member construction
[1662]	168	! bottom boundary condition: both zwi and zws must be masked as avmu can take
[3294]	169	! non zero value at the ocean bottom depending on the bottom friction used.
[2528]	170	!
	171	DO jk = 1, jpkm1 ! Matrix
[3]	172	DO jj = 2, jpjm1
	173	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	174	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,jk) + r_vvl * fse3u_a(ji,jj,jk) ! after scale factor at T-point
	175	zcoef = - p2dt / ze3ua
[2528]	176	zzwi = zcoef * avmu (ji,jj,jk ) / fse3uw(ji,jj,jk )
	177	zwi(ji,jj,jk) = zzwi * umask(ji,jj,jk)
	178	zzws = zcoef * avmu (ji,jj,jk+1) / fse3uw(ji,jj,jk+1)
	179	zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1)
	180	zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws
[3]	181	END DO
	182	END DO
	183	END DO
[4292]	184	DO jj = 2, jpjm1 ! Surface boundary conditions
[3]	185	DO ji = fs_2, fs_jpim1 ! vector opt.
[4666]	186	zwi(ji,jj,miku(ji,jj)) = 0._wp
	187	zwd(ji,jj,miku(ji,jj)) = 1._wp - zws(ji,jj,miku(ji,jj))
[3]	188	END DO
	189	END DO
	190
	191	! Matrix inversion starting from the first level
	192	!-----------------------------------------------------------------------
	193	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	194	!
	195	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	196	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	197	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	198	! ( ... )( ... ) ( ... )
	199	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	200	!
	201	! m is decomposed in the product of an upper and a lower triangular matrix
	202	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	203	! The solution (the after velocity) is in ua
	204	!-----------------------------------------------------------------------
[2528]	205	!
[4666]	206	!== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
	207	DO jj = 2, jpjm1
	208	DO ji = fs_2, fs_jpim1 ! vector opt.
	209	DO jk = miku(ji,jj)+1, jpkm1
[3]	210	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	211	END DO
	212	END DO
	213	END DO
[2528]	214	!
	215	DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==
[3]	216	DO ji = fs_2, fs_jpim1 ! vector opt.
[4666]	217	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,miku(ji,jj)) + r_vvl * fse3u_a(ji,jj,miku(ji,jj))
[4292]	218	#if defined key_dynspg_ts
[4666]	219	ua(ji,jj,miku(ji,jj)) = ua(ji,jj,miku(ji,jj)) + p2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) &
[4292]	220	& / ( ze3ua * rau0 )
	221	#else
[4666]	222	ua(ji,jj,miku(ji,jj)) = ub(ji,jj,miku(ji,jj)) + p2dt (ua(ji,jj,miku(ji,jj)) + 0.5_wp ( utau_b(ji,jj) + utau(ji,jj) ) &
	223	& / ( fse3u(ji,jj,miku(ji,jj)) * rau0 ) )
[4292]	224	#endif
[4666]	225	DO jk = miku(ji,jj)+1, jpkm1
[4292]	226	#if defined key_dynspg_ts
	227	zrhs = ua(ji,jj,jk) ! zrhs=right hand side
	228	#else
	229	zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk)
	230	#endif
[3]	231	ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1)
	232	END DO
	233	END DO
	234	END DO
[2528]	235	!
	236	DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==
[3]	237	DO ji = fs_2, fs_jpim1 ! vector opt.
	238	ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1)
[4666]	239	DO jk = jpk-2, miku(ji,jj), -1
[2528]	240	ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk)
[3]	241	END DO
	242	END DO
	243	END DO
	244
[4292]	245	#if ! defined key_dynspg_ts
[3]	246	! Normalization to obtain the general momentum trend ua
	247	DO jk = 1, jpkm1
	248	DO jj = 2, jpjm1
	249	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	250	ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) * z1_p2dt
[3]	251	END DO
	252	END DO
	253	END DO
[4292]	254	#endif
[3]	255
[3294]	256	! 3. Vertical diffusion on v
[3]	257	! ---------------------------
	258	! Matrix and second member construction
[1662]	259	! bottom boundary condition: both zwi and zws must be masked as avmv can take
[3294]	260	! non zero value at the ocean bottom depending on the bottom friction used
[2528]	261	!
	262	DO jk = 1, jpkm1 ! Matrix
[3]	263	DO jj = 2, jpjm1
	264	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	265	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,jk) + r_vvl * fse3v_a(ji,jj,jk) ! after scale factor at T-point
	266	zcoef = - p2dt / ze3va
[2528]	267	zzwi = zcoef * avmv (ji,jj,jk ) / fse3vw(ji,jj,jk )
[1662]	268	zwi(ji,jj,jk) = zzwi * vmask(ji,jj,jk)
[2528]	269	zzws = zcoef * avmv (ji,jj,jk+1) / fse3vw(ji,jj,jk+1)
[3]	270	zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1)
[2528]	271	zwd(ji,jj,jk) = 1._wp - zwi(ji,jj,jk) - zzws
[3]	272	END DO
	273	END DO
	274	END DO
[4292]	275	DO jj = 2, jpjm1 ! Surface boundary conditions
[3]	276	DO ji = fs_2, fs_jpim1 ! vector opt.
[4666]	277	zwi(ji,jj,mikv(ji,jj)) = 0._wp
	278	zwd(ji,jj,mikv(ji,jj)) = 1._wp - zws(ji,jj,mikv(ji,jj))
[3]	279	END DO
	280	END DO
	281
	282	! Matrix inversion
	283	!-----------------------------------------------------------------------
	284	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	285	!
	286	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	287	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	288	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	289	! ( ... )( ... ) ( ... )
	290	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	291	!
[2528]	292	! m is decomposed in the product of an upper and lower triangular matrix
[3]	293	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	294	! The solution (after velocity) is in 2d array va
	295	!-----------------------------------------------------------------------
[2528]	296	!
[4666]	297	!== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
	298	DO jj = 2, jpjm1
	299	DO ji = fs_2, fs_jpim1 ! vector opt.
	300	DO jk = mikv(ji,jj)+1, jpkm1
[3]	301	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	302	END DO
	303	END DO
	304	END DO
[2528]	305	!
	306	DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==
[3]	307	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	308	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,1) + r_vvl * fse3v_a(ji,jj,1)
	309	#if defined key_dynspg_ts
[4666]	310	va(ji,jj,mikv(ji,jj)) = va(ji,jj,mikv(ji,jj)) + p2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) &
[4292]	311	& / ( ze3va * rau0 )
	312	#else
[4666]	313	va(ji,jj,mikv(ji,jj)) = vb(ji,jj,mikv(ji,jj)) + p2dt (va(ji,jj,mikv(ji,jj)) + 0.5_wp ( vtau_b(ji,jj) + vtau(ji,jj) ) &
	314	& / ( fse3v(ji,jj,mikv(ji,jj)) * rau0 ) )
[4292]	315	#endif
[4666]	316	DO jk = mikv(ji,jj)+1, jpkm1
[4292]	317	#if defined key_dynspg_ts
	318	zrhs = va(ji,jj,jk) ! zrhs=right hand side
	319	#else
	320	zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk)
	321	#endif
[3]	322	va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1)
	323	END DO
	324	END DO
	325	END DO
[2528]	326	!
[4292]	327	DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==
[3]	328	DO ji = fs_2, fs_jpim1 ! vector opt.
	329	va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1)
[4666]	330	DO jk = jpk-2, mikv(ji,jj), -1
[2528]	331	va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk)
[3]	332	END DO
	333	END DO
	334	END DO
	335
	336	! Normalization to obtain the general momentum trend va
[4292]	337	#if ! defined key_dynspg_ts
[3]	338	DO jk = 1, jpkm1
	339	DO jj = 2, jpjm1
	340	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	341	va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) * z1_p2dt
[3]	342	END DO
	343	END DO
	344	END DO
[4292]	345	#endif
[3294]	346
[4292]	347	! J. Chanut: Lines below are useless ?
[3294]	348	!! restore bottom layer avmu(v)
	349	IF( ln_bfrimp ) THEN
	350	# if defined key_vectopt_loop
	351	DO jj = 1, 1
	352	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
	353	# else
	354	DO jj = 2, jpjm1
	355	DO ji = 2, jpim1
	356	# endif
	357	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	358	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
[4292]	359	avmu(ji,jj,ikbu+1) = 0.e0
	360	avmv(ji,jj,ikbv+1) = 0.e0
[4666]	361	ikbu = miku(ji,jj) ! ocean top level at u- and v-points
	362	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	363	avmu(ji,jj,ikbu-1) = 0.e0
	364	avmv(ji,jj,ikbv-1) = 0.e0
[3294]	365	END DO
	366	END DO
	367	ENDIF
[2528]	368	!
[3294]	369	CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwd, zws)
[2715]	370	!
[3294]	371	IF( nn_timing == 1 ) CALL timing_stop('dyn_zdf_imp')
	372	!
[3]	373	END SUBROUTINE dyn_zdf_imp
	374
	375	!!==============================================================================
	376	END MODULE dynzdf_imp

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