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traadv_fct.F90 in NEMO/trunk/src/OCE/TRA – NEMO

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source: NEMO/trunk/src/OCE/TRA/traadv_fct.F90 @ 10068

Last change on this file since 10068 was 10068, checked in by nicolasmartin, 6 years ago
First part of modifications to have a common default header : fix typos and SVN keywords properties
Property svn:keywords set to `Id`
File size: 33.2 KB

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[5770]	1	MODULE traadv_fct
[3]	2	!!==============================================================================
[5770]	3	!! * MODULE traadv_fct *
	4	!! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method)
[3]	5	!!==============================================================================
[5770]	6	!! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90)
[503]	7	!!----------------------------------------------------------------------
[3]	8
	9	!!----------------------------------------------------------------------
[5770]	10	!! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme
	11	!! with sub-time-stepping in the vertical direction
	12	!! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm
	13	!! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection
[3]	14	!!----------------------------------------------------------------------
[3625]	15	USE oce ! ocean dynamics and active tracers
	16	USE dom_oce ! ocean space and time domain
[4990]	17	USE trc_oce ! share passive tracers/Ocean variables
	18	USE trd_oce ! trends: ocean variables
[3625]	19	USE trdtra ! tracers trends
[4990]	20	USE diaptr ! poleward transport diagnostics
[7646]	21	USE diaar5 ! AR5 diagnostics
[9019]	22	USE phycst , ONLY : rau0_rcp
[4990]	23	!
[5770]	24	USE in_out_manager ! I/O manager
[9019]	25	USE iom !
[3625]	26	USE lib_mpp ! MPP library
	27	USE lbclnk ! ocean lateral boundary condition (or mpp link)
[5770]	28	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[3]	29
	30	IMPLICIT NONE
	31	PRIVATE
	32
[9019]	33	PUBLIC tra_adv_fct ! called by traadv.F90
	34	PUBLIC interp_4th_cpt ! called by traadv_cen.F90
[3]	35
[5770]	36	LOGICAL :: l_trd ! flag to compute trends
[7646]	37	LOGICAL :: l_ptr ! flag to compute poleward transport
	38	LOGICAL :: l_hst ! flag to compute heat/salt transport
[5770]	39	REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6
[2528]	40
[7646]	41	! ! tridiag solver associated indices:
	42	INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition
	43	INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition
	44
[3]	45	!! * Substitutions
	46	# include "vectopt_loop_substitute.h90"
	47	!!----------------------------------------------------------------------
[9598]	48	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1152]	49	!! $Id$
[10068]	50	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	51	!!----------------------------------------------------------------------
	52	CONTAINS
	53
[5770]	54	SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, &
	55	& ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v )
[3]	56	!!----------------------------------------------------------------------
[5770]	57	!! * ROUTINE tra_adv_fct *
[3]	58	!!
[6140]	59	!! ** Purpose : Compute the now trend due to total advection of tracers
	60	!! and add it to the general trend of tracer equations
[3]	61	!!
[5770]	62	!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
	63	!! (choice through the value of kn_fct)
[6140]	64	!! - on the vertical the 4th order is a compact scheme
[5770]	65	!! - corrected flux (monotonic correction)
[3]	66	!!
[6140]	67	!! ** Action : - update pta with the now advective tracer trends
[9019]	68	!! - send trends to trdtra module for further diagnostics (l_trdtra=T)
[6140]	69	!! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T)
[503]	70	!!----------------------------------------------------------------------
[2528]	71	INTEGER , INTENT(in ) :: kt ! ocean time-step index
[3294]	72	INTEGER , INTENT(in ) :: kit000 ! first time step index
[2528]	73	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	74	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[5770]	75	INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
	76	INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
[6140]	77	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	78	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	79	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	80	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[2715]	81	!
[5770]	82	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	83	REAL(wp) :: ztra ! local scalar
[5770]	84	REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - -
	85	REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - -
[9019]	86	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
	87	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
[3]	88	!!----------------------------------------------------------------------
[3294]	89	!
	90	IF( kt == kit000 ) THEN
[2528]	91	IF(lwp) WRITE(numout,*)
[5770]	92	IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype
[2528]	93	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
[3]	94	ENDIF
[2528]	95	!
[9019]	96	l_trd = .FALSE. ! set local switches
[7646]	97	l_hst = .FALSE.
	98	l_ptr = .FALSE.
[9019]	99	IF( ( cdtype =='TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	100	IF( cdtype =='TRA' .AND. ln_diaptr ) l_ptr = .TRUE.
	101	IF( cdtype =='TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. &
	102	& iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE.
[5770]	103	!
[7646]	104	IF( l_trd .OR. l_hst ) THEN
[9019]	105	ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) )
[7753]	106	ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
[3294]	107	ENDIF
[2528]	108	!
[7646]	109	IF( l_ptr ) THEN
[9019]	110	ALLOCATE( zptry(jpi,jpj,jpk) )
[7753]	111	zptry(:,:,:) = 0._wp
[7646]	112	ENDIF
[6140]	113	! ! surface & bottom value : flux set to zero one for all
[7753]	114	zwz(:,:, 1 ) = 0._wp
	115	zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp
[2528]	116	!
[7753]	117	zwi(:,:,:) = 0._wp
	118	!
[6140]	119	DO jn = 1, kjpt !== loop over the tracers ==!
[5770]	120	!
	121	! !== upstream advection with initial mass fluxes & intermediate update ==!
	122	! !* upstream tracer flux in the i and j direction
[2528]	123	DO jk = 1, jpkm1
	124	DO jj = 1, jpjm1
	125	DO ji = 1, fs_jpim1 ! vector opt.
	126	! upstream scheme
	127	zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) )
	128	zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) )
	129	zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) )
	130	zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) )
	131	zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) )
	132	zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) )
	133	END DO
[3]	134	END DO
	135	END DO
[5770]	136	! !* upstream tracer flux in the k direction *!
[6140]	137	DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask)
[4990]	138	DO jj = 1, jpj
	139	DO ji = 1, jpi
[2528]	140	zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) )
	141	zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) )
[5120]	142	zwz(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk)
[2528]	143	END DO
[3]	144	END DO
	145	END DO
[6140]	146	IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
[5770]	147	IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
[5120]	148	DO jj = 1, jpj
	149	DO ji = 1, jpi
	150	zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface
	151	END DO
	152	END DO
[5770]	153	ELSE ! no cavities: only at the ocean surface
[7753]	154	zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn)
[5770]	155	ENDIF
[5120]	156	ENDIF
[5770]	157	!
	158	DO jk = 1, jpkm1 !* trend and after field with monotonic scheme
[216]	159	DO jj = 2, jpjm1
	160	DO ji = fs_2, fs_jpim1 ! vector opt.
[6691]	161	! ! total intermediate advective trends
[5770]	162	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	163	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
[6691]	164	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
	165	! ! update and guess with monotonic sheme
	166	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk)
	167	zwi(ji,jj,jk) = ( e3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + p2dt * ztra ) / e3t_a(ji,jj,jk) * tmask(ji,jj,jk)
[216]	168	END DO
	169	END DO
	170	END DO
[5770]	171	CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign)
	172	!
[7646]	173	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes)
[7753]	174	ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
[2528]	175	END IF
[5770]	176	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[9019]	177	IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:)
[5770]	178	!
	179	! !== anti-diffusive flux : high order minus low order ==!
	180	!
[6140]	181	SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
[5770]	182	!
[6140]	183	CASE( 2 ) !- 2nd order centered
[5770]	184	DO jk = 1, jpkm1
	185	DO jj = 1, jpjm1
	186	DO ji = 1, fs_jpim1 ! vector opt.
	187	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) - zwx(ji,jj,jk)
	188	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) - zwy(ji,jj,jk)
	189	END DO
[503]	190	END DO
	191	END DO
[5770]	192	!
[6140]	193	CASE( 4 ) !- 4th order centered
[7753]	194	zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	195	zltv(:,:,jpk) = 0._wp
[6140]	196	DO jk = 1, jpkm1 ! Laplacian
	197	DO jj = 1, jpjm1 ! 1st derivative (gradient)
[5770]	198	DO ji = 1, fs_jpim1 ! vector opt.
	199	ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk)
	200	ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk)
	201	END DO
[503]	202	END DO
[6140]	203	DO jj = 2, jpjm1 ! 2nd derivative * 1/ 6
[5770]	204	DO ji = fs_2, fs_jpim1 ! vector opt.
	205	zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6
	206	zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6
	207	END DO
	208	END DO
[503]	209	END DO
[9094]	210	CALL lbc_lnk_multi( zltu, 'T', 1. , zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn)
[5770]	211	!
[6140]	212	DO jk = 1, jpkm1 ! Horizontal advective fluxes
[5770]	213	DO jj = 1, jpjm1
	214	DO ji = 1, fs_jpim1 ! vector opt.
	215	zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points
	216	zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn)
	217	! ! C4 minus upstream advective fluxes
	218	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk)
	219	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk)
	220	END DO
[5120]	221	END DO
[5770]	222	END DO
	223	!
[6140]	224	CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
[7753]	225	ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	226	ztv(:,:,jpk) = 0._wp
[6140]	227	DO jk = 1, jpkm1 ! 1st derivative (gradient)
	228	DO jj = 1, jpjm1
[5770]	229	DO ji = 1, fs_jpim1 ! vector opt.
	230	ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk)
	231	ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk)
	232	END DO
	233	END DO
[5120]	234	END DO
[9094]	235	CALL lbc_lnk_multi( ztu, 'U', -1. , ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn)
[5770]	236	!
[6140]	237	DO jk = 1, jpkm1 ! Horizontal advective fluxes
[5770]	238	DO jj = 2, jpjm1
	239	DO ji = 2, fs_jpim1 ! vector opt.
	240	zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2)
	241	zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn)
	242	! ! C4 interpolation of T at u- & v-points (x2)
	243	zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) )
	244	zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) )
	245	! ! C4 minus upstream advective fluxes
	246	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk)
	247	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk)
	248	END DO
	249	END DO
	250	END DO
	251	!
	252	END SELECT
[6140]	253	!
	254	SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
[5770]	255	!
[6140]	256	CASE( 2 ) !- 2nd order centered
[5770]	257	DO jk = 2, jpkm1
	258	DO jj = 2, jpjm1
	259	DO ji = fs_2, fs_jpim1
[6140]	260	zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * 0.5_wp * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) &
	261	& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
[5770]	262	END DO
	263	END DO
	264	END DO
	265	!
[6140]	266	CASE( 4 ) !- 4th order COMPACT
	267	CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! zwt = COMPACT interpolation of T at w-point
[5770]	268	DO jk = 2, jpkm1
	269	DO jj = 2, jpjm1
	270	DO ji = fs_2, fs_jpim1
	271	zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	272	END DO
	273	END DO
	274	END DO
	275	!
	276	END SELECT
[6140]	277	IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
[7753]	278	zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
[6140]	279	ENDIF
[5770]	280	!
[9094]	281	CALL lbc_lnk_multi( zwx, 'U', -1. , zwy, 'V', -1., zwz, 'W', 1. )
[6140]	282	!
[5770]	283	! !== monotonicity algorithm ==!
	284	!
[2528]	285	CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt )
[6140]	286	!
[5770]	287	! !== final trend with corrected fluxes ==!
	288	!
[216]	289	DO jk = 1, jpkm1
	290	DO jj = 2, jpjm1
[2528]	291	DO ji = fs_2, fs_jpim1 ! vector opt.
[5770]	292	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	293	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	294	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) &
[6140]	295	& * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[216]	296	END DO
	297	END DO
	298	END DO
[5770]	299	!
[9019]	300	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
	301	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes
	302	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes
	303	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
[5770]	304	!
[9019]	305	IF( l_trd ) THEN ! trend diagnostics
	306	CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) )
	307	CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) )
	308	CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) )
	309	ENDIF
	310	! ! heat/salt transport
	311	IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
[5770]	312	!
[9019]	313	ENDIF
	314	IF( l_ptr ) THEN ! "Poleward" transports
	315	zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes
[7646]	316	CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
[2528]	317	ENDIF
[503]	318	!
[6140]	319	END DO ! end of tracer loop
[503]	320	!
[10024]	321	IF( l_trd .OR. l_hst ) THEN
	322	DEALLOCATE( ztrdx, ztrdy, ztrdz )
	323	ENDIF
	324	IF( l_ptr ) THEN
	325	DEALLOCATE( zptry )
	326	ENDIF
	327	!
[5770]	328	END SUBROUTINE tra_adv_fct
[3]	329
[5737]	330
[2528]	331	SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt )
[3]	332	!!---------------------------------------------------------------------
	333	!! * ROUTINE nonosc *
	334	!!
	335	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	336	!! scheme and the before field by a nonoscillatory algorithm
	337	!!
	338	!! ** Method : ... ???
	339	!! warning : pbef and paft must be masked, but the boundaries
	340	!! conditions on the fluxes are not necessary zalezak (1979)
	341	!! drange (1995) multi-dimensional forward-in-time and upstream-
	342	!! in-space based differencing for fluid
	343	!!----------------------------------------------------------------------
[6140]	344	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	345	REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field
	346	REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
[2715]	347	!
[4990]	348	INTEGER :: ji, jj, jk ! dummy loop indices
	349	INTEGER :: ikm1 ! local integer
[6140]	350	REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
[2715]	351	REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
[9019]	352	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zbetup, zbetdo, zbup, zbdo
[3]	353	!!----------------------------------------------------------------------
[3294]	354	!
[2715]	355	zbig = 1.e+40_wp
	356	zrtrn = 1.e-15_wp
[7753]	357	zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp
[785]	358
[3]	359	! Search local extrema
	360	! --------------------
[785]	361	! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
[4990]	362	zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), &
	363	& paft * tmask - zbig * ( 1._wp - tmask ) )
	364	zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), &
	365	& paft * tmask + zbig * ( 1._wp - tmask ) )
[785]	366
[5120]	367	DO jk = 1, jpkm1
	368	ikm1 = MAX(jk-1,1)
	369	DO jj = 2, jpjm1
	370	DO ji = fs_2, fs_jpim1 ! vector opt.
	371
[785]	372	! search maximum in neighbourhood
	373	zup = MAX( zbup(ji ,jj ,jk ), &
	374	& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
	375	& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
	376	& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
[3]	377
[785]	378	! search minimum in neighbourhood
	379	zdo = MIN( zbdo(ji ,jj ,jk ), &
	380	& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
	381	& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
	382	& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
[3]	383
[785]	384	! positive part of the flux
[3]	385	zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
	386	& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
	387	& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
[785]	388
	389	! negative part of the flux
[3]	390	zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
	391	& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
	392	& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
[785]	393
[3]	394	! up & down beta terms
[6140]	395	zbt = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt
[785]	396	zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
	397	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
[3]	398	END DO
	399	END DO
	400	END DO
[9094]	401	CALL lbc_lnk_multi( zbetup, 'T', 1. , zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign)
[3]	402
[237]	403	! 3. monotonic flux in the i & j direction (paa & pbb)
	404	! ----------------------------------------
[3]	405	DO jk = 1, jpkm1
	406	DO jj = 2, jpjm1
	407	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	408	zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
	409	zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
[785]	410	zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) )
[4990]	411	paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
[3]	412
[4990]	413	zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
	414	zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
[785]	415	zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) )
[4990]	416	pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
[3]	417
	418	! monotonic flux in the k direction, i.e. pcc
	419	! -------------------------------------------
[785]	420	za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
	421	zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
	422	zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) )
[4990]	423	pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
[3]	424	END DO
	425	END DO
	426	END DO
[9094]	427	CALL lbc_lnk_multi( paa, 'U', -1. , pbb, 'V', -1. ) ! lateral boundary condition (changed sign)
[503]	428	!
[3]	429	END SUBROUTINE nonosc
	430
[5770]	431
[7646]	432	SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
[5770]	433	!!----------------------------------------------------------------------
[7646]	434	!! * ROUTINE interp_4th_cpt_org *
[5770]	435	!!
	436	!! ** Purpose : Compute the interpolation of tracer at w-point
	437	!!
	438	!! ** Method : 4th order compact interpolation
	439	!!----------------------------------------------------------------------
	440	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
	441	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
	442	!
	443	INTEGER :: ji, jj, jk ! dummy loop integers
	444	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	445	!!----------------------------------------------------------------------
	446
	447	DO jk = 3, jpkm1 !== build the three diagonal matrix ==!
	448	DO jj = 1, jpj
	449	DO ji = 1, jpi
	450	zwd (ji,jj,jk) = 4._wp
	451	zwi (ji,jj,jk) = 1._wp
	452	zws (ji,jj,jk) = 1._wp
	453	zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	454	!
	455	IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
	456	zwd (ji,jj,jk) = 1._wp
	457	zwi (ji,jj,jk) = 0._wp
	458	zws (ji,jj,jk) = 0._wp
	459	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	460	ENDIF
	461	END DO
	462	END DO
	463	END DO
	464	!
[7646]	465	jk = 2 ! Switch to second order centered at top
	466	DO jj = 1, jpj
	467	DO ji = 1, jpi
[5770]	468	zwd (ji,jj,jk) = 1._wp
	469	zwi (ji,jj,jk) = 0._wp
	470	zws (ji,jj,jk) = 0._wp
	471	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	472	END DO
	473	END DO
	474	!
	475	! !== tridiagonal solve ==!
	476	DO jj = 1, jpj ! first recurrence
	477	DO ji = 1, jpi
	478	zwt(ji,jj,2) = zwd(ji,jj,2)
	479	END DO
	480	END DO
	481	DO jk = 3, jpkm1
	482	DO jj = 1, jpj
	483	DO ji = 1, jpi
	484	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	485	END DO
	486	END DO
	487	END DO
	488	!
	489	DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	490	DO ji = 1, jpi
	491	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	492	END DO
	493	END DO
	494	DO jk = 3, jpkm1
	495	DO jj = 1, jpj
	496	DO ji = 1, jpi
	497	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	498	END DO
	499	END DO
	500	END DO
	501
	502	DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	503	DO ji = 1, jpi
	504	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	505	END DO
	506	END DO
	507	DO jk = jpk-2, 2, -1
	508	DO jj = 1, jpj
	509	DO ji = 1, jpi
	510	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	511	END DO
	512	END DO
	513	END DO
	514	!
[7646]	515	END SUBROUTINE interp_4th_cpt_org
	516
	517
	518	SUBROUTINE interp_4th_cpt( pt_in, pt_out )
	519	!!----------------------------------------------------------------------
	520	!! * ROUTINE interp_4th_cpt *
	521	!!
	522	!! ** Purpose : Compute the interpolation of tracer at w-point
	523	!!
	524	!! ** Method : 4th order compact interpolation
	525	!!----------------------------------------------------------------------
	526	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
	527	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
	528	!
	529	INTEGER :: ji, jj, jk ! dummy loop integers
	530	INTEGER :: ikt, ikb ! local integers
	531	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	532	!!----------------------------------------------------------------------
	533	!
	534	! !== build the three diagonal matrix & the RHS ==!
	535	!
	536	DO jk = 3, jpkm1 ! interior (from jk=3 to jpk-1)
	537	DO jj = 2, jpjm1
	538	DO ji = fs_2, fs_jpim1
	539	zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
	540	zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
	541	zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
	542	zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
	543	& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
	544	END DO
	545	END DO
	546	END DO
	547	!
	548	!!gm
	549	! SELECT CASE( kbc ) !* boundary condition
	550	! CASE( np_NH ) ! Neumann homogeneous at top & bottom
	551	! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
	552	! END SELECT
	553	!!gm
	554	!
[9901]	555	IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case
	556	zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp
	557	END IF
	558	!
[7646]	559	DO jj = 2, jpjm1 ! 2nd order centered at top & bottom
	560	DO ji = fs_2, fs_jpim1
	561	ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
	562	ikb = mbkt(ji,jj) ! - above the last wet point
	563	!
	564	zwd (ji,jj,ikt) = 1._wp ! top
	565	zwi (ji,jj,ikt) = 0._wp
	566	zws (ji,jj,ikt) = 0._wp
[9901]	567	zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) )
[7646]	568	!
	569	zwd (ji,jj,ikb) = 1._wp ! bottom
	570	zwi (ji,jj,ikb) = 0._wp
	571	zws (ji,jj,ikb) = 0._wp
[9901]	572	zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) )
[7646]	573	END DO
	574	END DO
	575	!
	576	! !== tridiagonal solver ==!
	577	!
	578	DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
	579	DO ji = fs_2, fs_jpim1
	580	zwt(ji,jj,2) = zwd(ji,jj,2)
	581	END DO
	582	END DO
	583	DO jk = 3, jpkm1
	584	DO jj = 2, jpjm1
	585	DO ji = fs_2, fs_jpim1
	586	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	587	END DO
	588	END DO
	589	END DO
	590	!
	591	DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	592	DO ji = fs_2, fs_jpim1
	593	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	594	END DO
	595	END DO
	596	DO jk = 3, jpkm1
	597	DO jj = 2, jpjm1
	598	DO ji = fs_2, fs_jpim1
	599	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	600	END DO
	601	END DO
	602	END DO
	603
	604	DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	605	DO ji = fs_2, fs_jpim1
	606	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	607	END DO
	608	END DO
	609	DO jk = jpk-2, 2, -1
	610	DO jj = 2, jpjm1
	611	DO ji = fs_2, fs_jpim1
	612	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	613	END DO
	614	END DO
	615	END DO
	616	!
[5770]	617	END SUBROUTINE interp_4th_cpt
[7646]	618
	619
	620	SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
	621	!!----------------------------------------------------------------------
	622	!! * ROUTINE tridia_solver *
	623	!!
	624	!! ** Purpose : solve a symmetric 3diagonal system
	625	!!
	626	!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
	627	!!
	628	!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
	629	!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
	630	!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
	631	!! ( ... )( ... ) ( ... )
	632	!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
	633	!!
	634	!! M is decomposed in the product of an upper and lower triangular matrix.
	635	!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
	636	!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
	637	!! The solution is pta.
	638	!! The 3d array zwt is used as a work space array.
	639	!!----------------------------------------------------------------------
	640	REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix
	641	REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pRHS ! Right-Hand-Side
	642	REAL(wp),DIMENSION(:,:,:), INTENT( out) :: pt_out !!gm field at level=F(klev)
	643	INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
	644	! ! =0 pt at t-level
	645	INTEGER :: ji, jj, jk ! dummy loop integers
	646	INTEGER :: kstart ! local indices
	647	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwt ! 3D work array
	648	!!----------------------------------------------------------------------
	649	!
	650	kstart = 1 + klev
	651	!
	652	DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
	653	DO ji = fs_2, fs_jpim1
	654	zwt(ji,jj,kstart) = pD(ji,jj,kstart)
	655	END DO
	656	END DO
	657	DO jk = kstart+1, jpkm1
	658	DO jj = 2, jpjm1
	659	DO ji = fs_2, fs_jpim1
	660	zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	661	END DO
	662	END DO
	663	END DO
	664	!
	665	DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	666	DO ji = fs_2, fs_jpim1
	667	pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
	668	END DO
	669	END DO
	670	DO jk = kstart+1, jpkm1
	671	DO jj = 2, jpjm1
	672	DO ji = fs_2, fs_jpim1
	673	pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	674	END DO
	675	END DO
	676	END DO
	677
	678	DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	679	DO ji = fs_2, fs_jpim1
	680	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	681	END DO
	682	END DO
	683	DO jk = jpk-2, kstart, -1
	684	DO jj = 2, jpjm1
	685	DO ji = fs_2, fs_jpim1
	686	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	687	END DO
	688	END DO
	689	END DO
	690	!
	691	END SUBROUTINE tridia_solver
	692
[3]	693	!!======================================================================
[5770]	694	END MODULE traadv_fct

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