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dynzdf_imp.F90 @ 12555

Last change on this file since 12555 was 12555, checked in by charris, 4 years ago

Changes from GO6 package branch (GMED ticket 450):

svn merge -r 11035:11101 svn+ssh://charris@forge.ipsl.jussieu.fr/ipsl/forge/projets/nemo/svn/branches/UKMO/dev_r5518_GO6_package

File size: 17.4 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
[3294]	72	REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwd, zws
	73	!!----------------------------------------------------------------------
	74	!
	75	IF( nn_timing == 1 ) CALL timing_start('dyn_zdf_imp')
	76	!
	77	CALL wrk_alloc( jpi,jpj,jpk, zwi, zwd, zws )
	78	!
[3]	79	IF( kt == nit000 ) THEN
	80	IF(lwp) WRITE(numout,*)
	81	IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator'
	82	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ '
[12555]	83	IF(lwp .AND. lflush) CALL flush(numout)
[4292]	84	!
	85	IF( lk_vvl ) THEN ; r_vvl = 1._wp ! Variable volume indicator
	86	ELSE ; r_vvl = 0._wp
	87	ENDIF
[3]	88	ENDIF
	89
	90	! 0. Local constant initialization
	91	! --------------------------------
[2528]	92	z1_p2dt = 1._wp / p2dt ! inverse of the timestep
[455]	93
[3294]	94	! 1. Apply semi-implicit bottom friction
	95	! --------------------------------------
	96	! Only needed for semi-implicit bottom friction setup. The explicit
	97	! bottom friction has been included in "u(v)a" which act as the R.H.S
	98	! column vector of the tri-diagonal matrix equation
	99	!
	100
	101	IF( ln_bfrimp ) THEN
[4292]	102	DO jj = 2, jpjm1
	103	DO ji = 2, jpim1
	104	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	105	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	106	avmu(ji,jj,ikbu+1) = -bfrua(ji,jj) * fse3uw(ji,jj,ikbu+1)
	107	avmv(ji,jj,ikbv+1) = -bfrva(ji,jj) * fse3vw(ji,jj,ikbv+1)
	108	END DO
[3294]	109	END DO
[5120]	110	IF ( ln_isfcav ) THEN
	111	DO jj = 2, jpjm1
	112	DO ji = 2, jpim1
	113	ikbu = miku(ji,jj) ! ocean top level at u- and v-points
	114	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	115	IF (ikbu .GE. 2) avmu(ji,jj,ikbu) = -tfrua(ji,jj) * fse3uw(ji,jj,ikbu)
	116	IF (ikbv .GE. 2) avmv(ji,jj,ikbv) = -tfrva(ji,jj) * fse3vw(ji,jj,ikbv)
	117	END DO
	118	END DO
	119	END IF
[3294]	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)
[4990]	144	END DO
	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
	154	END DO
	155	END DO
[5120]	156	IF ( ln_isfcav ) THEN
	157	DO jj = 2, jpjm1
	158	DO ji = fs_2, fs_jpim1 ! vector opt.
	159	ikbu = miku(ji,jj) ! top ocean level at u- and v-points
	160	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	161	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,ikbu) + r_vvl * fse3u_a(ji,jj,ikbu)
	162	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,ikbv) + r_vvl * fse3v_a(ji,jj,ikbv)
	163	ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * tfrua(ji,jj) * ua_b(ji,jj) / ze3ua
	164	va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * tfrva(ji,jj) * va_b(ji,jj) / ze3va
	165	END DO
	166	END DO
	167	END IF
[4292]	168	ENDIF
	169	#endif
	170
[3294]	171	! 2. Vertical diffusion on u
[3]	172	! ---------------------------
	173	! Matrix and second member construction
[1662]	174	! bottom boundary condition: both zwi and zws must be masked as avmu can take
[3294]	175	! non zero value at the ocean bottom depending on the bottom friction used.
[2528]	176	!
	177	DO jk = 1, jpkm1 ! Matrix
[3]	178	DO jj = 2, jpjm1
	179	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	180	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,jk) + r_vvl * fse3u_a(ji,jj,jk) ! after scale factor at T-point
	181	zcoef = - p2dt / ze3ua
[5120]	182	zzwi = zcoef * avmu (ji,jj,jk ) / fse3uw(ji,jj,jk )
	183	zwi(ji,jj,jk) = zzwi * wumask(ji,jj,jk )
	184	zzws = zcoef * avmu (ji,jj,jk+1) / fse3uw(ji,jj,jk+1)
	185	zws(ji,jj,jk) = zzws * wumask(ji,jj,jk+1)
	186	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
[3]	187	END DO
	188	END DO
	189	END DO
[4292]	190	DO jj = 2, jpjm1 ! Surface boundary conditions
[3]	191	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	192	zwi(ji,jj,1) = 0._wp
	193	zwd(ji,jj,1) = 1._wp - zws(ji,jj,1)
[3]	194	END DO
	195	END DO
	196
	197	! Matrix inversion starting from the first level
	198	!-----------------------------------------------------------------------
	199	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	200	!
	201	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	202	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	203	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	204	! ( ... )( ... ) ( ... )
	205	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	206	!
	207	! m is decomposed in the product of an upper and a lower triangular matrix
	208	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	209	! The solution (the after velocity) is in ua
	210	!-----------------------------------------------------------------------
[2528]	211	!
[4990]	212	!== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
[5120]	213	DO jk = 2, jpkm1
	214	DO jj = 2, jpjm1
	215	DO ji = fs_2, fs_jpim1 ! vector opt.
[3]	216	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	217	END DO
	218	END DO
	219	END DO
[2528]	220	!
	221	DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==
[3]	222	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	223	#if defined key_dynspg_ts
[5120]	224	ze3ua = ( 1._wp - r_vvl ) * fse3u_n(ji,jj,1) + r_vvl * fse3u_a(ji,jj,1)
	225	ua(ji,jj,1) = ua(ji,jj,1) + p2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) &
	226	& / ( ze3ua * rau0 ) * umask(ji,jj,1)
[4292]	227	#else
[5120]	228	ua(ji,jj,1) = ub(ji,jj,1) &
	229	& + p2dt (ua(ji,jj,1) + 0.5_wp ( utau_b(ji,jj) + utau(ji,jj) ) &
	230	& / ( fse3u(ji,jj,1) * rau0 ) * umask(ji,jj,1) )
[4292]	231	#endif
[5120]	232	END DO
	233	END DO
	234	DO jk = 2, jpkm1
	235	DO jj = 2, jpjm1
	236	DO ji = fs_2, fs_jpim1
[4292]	237	#if defined key_dynspg_ts
	238	zrhs = ua(ji,jj,jk) ! zrhs=right hand side
	239	#else
	240	zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk)
	241	#endif
[3]	242	ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1)
	243	END DO
	244	END DO
	245	END DO
[2528]	246	!
	247	DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==
[3]	248	DO ji = fs_2, fs_jpim1 ! vector opt.
	249	ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1)
[5120]	250	END DO
	251	END DO
	252	DO jk = jpk-2, 1, -1
	253	DO jj = 2, jpjm1
	254	DO ji = fs_2, fs_jpim1
[2528]	255	ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk)
[3]	256	END DO
	257	END DO
	258	END DO
	259
[4292]	260	#if ! defined key_dynspg_ts
[3]	261	! Normalization to obtain the general momentum trend ua
	262	DO jk = 1, jpkm1
	263	DO jj = 2, jpjm1
	264	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	265	ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) * z1_p2dt
[3]	266	END DO
	267	END DO
	268	END DO
[4292]	269	#endif
[3]	270
[3294]	271	! 3. Vertical diffusion on v
[3]	272	! ---------------------------
	273	! Matrix and second member construction
[1662]	274	! bottom boundary condition: both zwi and zws must be masked as avmv can take
[3294]	275	! non zero value at the ocean bottom depending on the bottom friction used
[2528]	276	!
	277	DO jk = 1, jpkm1 ! Matrix
[3]	278	DO jj = 2, jpjm1
	279	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	280	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,jk) + r_vvl * fse3v_a(ji,jj,jk) ! after scale factor at T-point
	281	zcoef = - p2dt / ze3va
[2528]	282	zzwi = zcoef * avmv (ji,jj,jk ) / fse3vw(ji,jj,jk )
[5120]	283	zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk)
[2528]	284	zzws = zcoef * avmv (ji,jj,jk+1) / fse3vw(ji,jj,jk+1)
[5120]	285	zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1)
	286	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
[3]	287	END DO
	288	END DO
	289	END DO
[4292]	290	DO jj = 2, jpjm1 ! Surface boundary conditions
[3]	291	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	292	zwi(ji,jj,1) = 0._wp
	293	zwd(ji,jj,1) = 1._wp - zws(ji,jj,1)
[3]	294	END DO
	295	END DO
	296
	297	! Matrix inversion
	298	!-----------------------------------------------------------------------
	299	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	300	!
	301	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	302	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	303	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	304	! ( ... )( ... ) ( ... )
	305	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	306	!
[2528]	307	! m is decomposed in the product of an upper and lower triangular matrix
[3]	308	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	309	! The solution (after velocity) is in 2d array va
	310	!-----------------------------------------------------------------------
[2528]	311	!
[4990]	312	!== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
[5120]	313	DO jk = 2, jpkm1
	314	DO jj = 2, jpjm1
	315	DO ji = fs_2, fs_jpim1 ! vector opt.
[3]	316	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	317	END DO
	318	END DO
	319	END DO
[2528]	320	!
	321	DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==
[3]	322	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	323	#if defined key_dynspg_ts
[5120]	324	ze3va = ( 1._wp - r_vvl ) * fse3v_n(ji,jj,1) + r_vvl * fse3v_a(ji,jj,1)
	325	va(ji,jj,1) = va(ji,jj,1) + p2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) &
[6795]	326	& / ( ze3va * rau0 ) * vmask(ji,jj,1)
[4292]	327	#else
[5120]	328	va(ji,jj,1) = vb(ji,jj,1) &
	329	& + p2dt (va(ji,jj,1) + 0.5_wp ( vtau_b(ji,jj) + vtau(ji,jj) ) &
[6795]	330	& / ( fse3v(ji,jj,1) * rau0 ) * vmask(ji,jj,1) )
[4292]	331	#endif
[5120]	332	END DO
	333	END DO
	334	DO jk = 2, jpkm1
	335	DO jj = 2, jpjm1
	336	DO ji = fs_2, fs_jpim1 ! vector opt.
[4292]	337	#if defined key_dynspg_ts
	338	zrhs = va(ji,jj,jk) ! zrhs=right hand side
	339	#else
	340	zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk)
	341	#endif
[3]	342	va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1)
	343	END DO
	344	END DO
	345	END DO
[2528]	346	!
[4292]	347	DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==
[3]	348	DO ji = fs_2, fs_jpim1 ! vector opt.
	349	va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1)
[5120]	350	END DO
	351	END DO
	352	DO jk = jpk-2, 1, -1
	353	DO jj = 2, jpjm1
	354	DO ji = fs_2, fs_jpim1
[2528]	355	va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk)
[3]	356	END DO
	357	END DO
	358	END DO
	359
	360	! Normalization to obtain the general momentum trend va
[4292]	361	#if ! defined key_dynspg_ts
[3]	362	DO jk = 1, jpkm1
	363	DO jj = 2, jpjm1
	364	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	365	va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) * z1_p2dt
[3]	366	END DO
	367	END DO
	368	END DO
[4292]	369	#endif
[3294]	370
[4292]	371	! J. Chanut: Lines below are useless ?
[3294]	372	!! restore bottom layer avmu(v)
	373	IF( ln_bfrimp ) THEN
[4990]	374	DO jj = 2, jpjm1
	375	DO ji = 2, jpim1
	376	ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points
	377	ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
	378	avmu(ji,jj,ikbu+1) = 0.e0
	379	avmv(ji,jj,ikbv+1) = 0.e0
	380	END DO
	381	END DO
[5120]	382	IF (ln_isfcav) THEN
	383	DO jj = 2, jpjm1
	384	DO ji = 2, jpim1
	385	ikbu = miku(ji,jj) ! ocean top level at u- and v-points
	386	ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points)
	387	IF (ikbu > 1) avmu(ji,jj,ikbu) = 0.e0
	388	IF (ikbv > 1) avmv(ji,jj,ikbv) = 0.e0
	389	END DO
	390	END DO
	391	END IF
[3294]	392	ENDIF
[2528]	393	!
[3294]	394	CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwd, zws)
[2715]	395	!
[3294]	396	IF( nn_timing == 1 ) CALL timing_stop('dyn_zdf_imp')
	397	!
[3]	398	END SUBROUTINE dyn_zdf_imp
	399
	400	!!==============================================================================
	401	END MODULE dynzdf_imp

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