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icedyn_adv_umx.F90 @ 11083

Last change on this file since 11083 was 11083, checked in by davestorkey, 5 years ago
UKMO/NEMO_4.0_GO6_mixing : Update to be relative to rev 11081 of NEMO_4.0_mirror.
File size: 84.2 KB

Rev	Line
[8586]	1	MODULE icedyn_adv_umx
	2	!!==============================================================================
	3	!! * MODULE icedyn_adv_umx *
	4	!! sea-ice : advection using the ULTIMATE-MACHO scheme
	5	!!==============================================================================
	6	!! History : 3.6 ! 2014-11 (C. Rousset, G. Madec) Original code
[9604]	7	!! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube]
[8586]	8	!!----------------------------------------------------------------------
[9570]	9	#if defined key_si3
[8586]	10	!!----------------------------------------------------------------------
[9570]	11	!! 'key_si3' SI3 sea-ice model
[8586]	12	!!----------------------------------------------------------------------
[11083]	13	!! ice_dyn_adv_umx : update the tracer fields
[8586]	14	!! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders
[11083]	15	!! macho : compute the fluxes
	16	!! nonosc_ice : limit the fluxes using a non-oscillatory algorithm
[8586]	17	!!----------------------------------------------------------------------
	18	USE phycst ! physical constant
	19	USE dom_oce ! ocean domain
	20	USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition
	21	USE ice ! sea-ice variables
[10413]	22	USE icevar ! sea-ice: operations
[8586]	23	!
	24	USE in_out_manager ! I/O manager
[10785]	25	USE iom ! I/O manager library
[8586]	26	USE lib_mpp ! MPP library
	27	USE lib_fortran ! fortran utilities (glob_sum + no signed zero)
	28	USE lbclnk ! lateral boundary conditions (or mpp links)
	29
	30	IMPLICIT NONE
	31	PRIVATE
	32
	33	PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90
[11083]	34	!
	35	INTEGER, PARAMETER :: np_advS = 1 ! advection for S and T: dVS/dt = -div( uVS ) => np_advS = 1
	36	! or dVS/dt = -div( uA * uHS / u ) => np_advS = 2
	37	! or dVS/dt = -div( uV * uS / u ) => np_advS = 3
	38	INTEGER, PARAMETER :: np_limiter = 1 ! limiter: 1 = nonosc
	39	! 2 = superbee
	40	! 3 = h3
	41	LOGICAL :: ll_upsxy = .TRUE. ! alternate directions for upstream
	42	LOGICAL :: ll_hoxy = .TRUE. ! alternate directions for high order
	43	LOGICAL :: ll_neg = .TRUE. ! if T interpolated at u/v points is negative or v_i < 1.e-6
	44	! then interpolate T at u/v points using the upstream scheme
	45	LOGICAL :: ll_prelim = .FALSE. ! prelimiter from: Zalesak(1979) eq. 14 => not well defined in 2D
	46	!
	47	REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6
	48	REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120
	49	!
	50	INTEGER, ALLOCATABLE, DIMENSION(:,:,:) :: imsk_small, jmsk_small
	51	!
[8586]	52	!! * Substitutions
	53	# include "vectopt_loop_substitute.h90"
	54	!!----------------------------------------------------------------------
[9598]	55	!! NEMO/ICE 4.0 , NEMO Consortium (2018)
[10069]	56	!! $Id$
[10413]	57	!! Software governed by the CeCILL licence (./LICENSE)
[8586]	58	!!----------------------------------------------------------------------
	59	CONTAINS
	60
[11083]	61	SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, ph_i, ph_s, ph_ip, &
[10413]	62	& pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i )
[8586]	63	!!----------------------------------------------------------------------
	64	!! * ROUTINE ice_dyn_adv_umx *
	65	!!
	66	!! ** Purpose : Compute the now trend due to total advection of
	67	!! tracers and add it to the general trend of tracer equations
	68	!! using an "Ultimate-Macho" scheme
	69	!!
	70	!! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74.
	71	!!----------------------------------------------------------------------
[10413]	72	INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2)
[8586]	73	INTEGER , INTENT(in ) :: kt ! time step
	74	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity
	75	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity
[11083]	76	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_i ! ice thickness
	77	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_s ! snw thickness
	78	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_ip ! ice pond thickness
[8586]	79	REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area
	80	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume
	81	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume
	82	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content
	83	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content
	84	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration
	85	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction
	86	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume
	87	REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content
	88	REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content
	89	!
	90	INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices
[10413]	91	INTEGER :: icycle ! number of sub-timestep for the advection
	92	REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers
[11083]	93	REAL(wp) :: zdt, zvi_cen
	94	REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! for global communication
	95	REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box
[10439]	96	REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2
[11083]	97	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zu_cat, zv_cat
	98	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho, zua_ups, zva_ups
	99	REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai , z1_aip, zhvar
	100	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhi_max, zhs_max, zhip_max
	101	!
	102	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs
[8586]	103	!!----------------------------------------------------------------------
	104	!
	105	IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme'
	106	!
[11083]	107	! --- Record max of the surrounding 9-pts ice thick. (for call Hbig) --- !
	108	DO jl = 1, jpl
	109	DO jj = 2, jpjm1
	110	DO ji = fs_2, fs_jpim1
	111	zhip_max(ji,jj,jl) = MAX( epsi20, ph_ip(ji,jj,jl), ph_ip(ji+1,jj ,jl), ph_ip(ji ,jj+1,jl), &
	112	& ph_ip(ji-1,jj ,jl), ph_ip(ji ,jj-1,jl), &
	113	& ph_ip(ji+1,jj+1,jl), ph_ip(ji-1,jj-1,jl), &
	114	& ph_ip(ji+1,jj-1,jl), ph_ip(ji-1,jj+1,jl) )
	115	zhi_max (ji,jj,jl) = MAX( epsi20, ph_i (ji,jj,jl), ph_i (ji+1,jj ,jl), ph_i (ji ,jj+1,jl), &
	116	& ph_i (ji-1,jj ,jl), ph_i (ji ,jj-1,jl), &
	117	& ph_i (ji+1,jj+1,jl), ph_i (ji-1,jj-1,jl), &
	118	& ph_i (ji+1,jj-1,jl), ph_i (ji-1,jj+1,jl) )
	119	zhs_max (ji,jj,jl) = MAX( epsi20, ph_s (ji,jj,jl), ph_s (ji+1,jj ,jl), ph_s (ji ,jj+1,jl), &
	120	& ph_s (ji-1,jj ,jl), ph_s (ji ,jj-1,jl), &
	121	& ph_s (ji+1,jj+1,jl), ph_s (ji-1,jj-1,jl), &
	122	& ph_s (ji+1,jj-1,jl), ph_s (ji-1,jj+1,jl) )
	123	END DO
	124	END DO
	125	END DO
	126	CALL lbc_lnk_multi( 'icedyn_adv_umx', zhi_max, 'T', 1., zhs_max, 'T', 1., zhip_max, 'T', 1. )
	127	!
	128	!
	129	! --- If ice drift is too fast, use subtime steps for advection (CFL test for stability) --- !
	130	! Note: the advection split is applied at the next time-step in order to avoid blocking global comm.
	131	! this should not affect too much the stability
[10425]	132	zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) )
	133	zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) )
	134
	135	! non-blocking global communication send zcflnow and receive zcflprv
	136	CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 )
[8586]	137
[10425]	138	IF( zcflprv(1) > .5 ) THEN ; icycle = 2
	139	ELSE ; icycle = 1
[8586]	140	ENDIF
[10413]	141	zdt = rdt_ice / REAL(icycle)
[8586]	142
	143	! --- transport --- !
	144	zudy(:,:) = pu_ice(:,:) * e2u(:,:)
	145	zvdx(:,:) = pv_ice(:,:) * e1v(:,:)
[11083]	146	!
	147	! setup transport for each ice cat
	148	DO jl = 1, jpl
	149	zu_cat(:,:,jl) = zudy(:,:)
	150	zv_cat(:,:,jl) = zvdx(:,:)
	151	END DO
	152	!
[8586]	153	! --- define velocity for advection: u*grad(H) --- !
	154	DO jj = 2, jpjm1
	155	DO ji = fs_2, fs_jpim1
	156	IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp
	157	ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj)
	158	ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj)
	159	ENDIF
	160
	161	IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp
	162	ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1)
	163	ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj )
	164	ENDIF
	165	END DO
	166	END DO
	167
	168	!---------------!
	169	!== advection ==!
	170	!---------------!
[10413]	171	DO jt = 1, icycle
	172
[10439]	173	! record at_i before advection (for open water)
	174	zati1(:,:) = SUM( pa_i(:,:,:), dim=3 )
[10413]	175
[10439]	176	! inverse of A and Ap
[10425]	177	WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:)
	178	ELSEWHERE ; z1_ai(:,:,:) = 0.
	179	END WHERE
	180	WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:)
	181	ELSEWHERE ; z1_aip(:,:,:) = 0.
	182	END WHERE
	183	!
[11083]	184	! setup a mask where advection will be upstream
	185	IF( ll_neg ) THEN
	186	IF( .NOT. ALLOCATED(imsk_small) ) ALLOCATE( imsk_small(jpi,jpj,jpl) )
	187	IF( .NOT. ALLOCATED(jmsk_small) ) ALLOCATE( jmsk_small(jpi,jpj,jpl) )
	188	DO jl = 1, jpl
	189	DO jj = 1, jpjm1
	190	DO ji = 1, jpim1
	191	zvi_cen = 0.5_wp * ( pv_i(ji+1,jj,jl) + pv_i(ji,jj,jl) )
	192	IF( zvi_cen < epsi06) THEN ; imsk_small(ji,jj,jl) = 0
	193	ELSE ; imsk_small(ji,jj,jl) = 1 ; ENDIF
	194	zvi_cen = 0.5_wp * ( pv_i(ji,jj+1,jl) + pv_i(ji,jj,jl) )
	195	IF( zvi_cen < epsi06) THEN ; jmsk_small(ji,jj,jl) = 0
	196	ELSE ; jmsk_small(ji,jj,jl) = 1 ; ENDIF
	197	END DO
	198	END DO
	199	END DO
	200	ENDIF
[10425]	201	!
[11083]	202	! ----------------------- !
	203	! ==> start advection <== !
	204	! ----------------------- !
[10425]	205	!
[11083]	206	!== Ice area ==!
	207	zamsk = 1._wp
	208	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zu_cat , zv_cat , zcu_box, zcv_box, &
	209	& pa_i, pa_i, zua_ups, zva_ups, zua_ho , zva_ho )
[10425]	210	!
[11083]	211	! ! --------------------------------- !
	212	IF( np_advS == 1 ) THEN ! -- advection form: -div( uVS ) -- !
	213	! ! --------------------------------- !
	214	zamsk = 0._wp
	215	!== Ice volume ==!
	216	zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:)
	217	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, &
	218	& zhvar, pv_i, zua_ups, zva_ups )
	219	!== Snw volume ==!
	220	zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:)
	221	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, &
	222	& zhvar, pv_s, zua_ups, zva_ups )
	223	!
	224	zamsk = 1._wp
	225	!== Salt content ==!
	226	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, &
	227	& psv_i, psv_i )
	228	!== Ice heat content ==!
	229	DO jk = 1, nlay_i
	230	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, &
	231	& pe_i(:,:,jk,:), pe_i(:,:,jk,:) )
[10785]	232	END DO
[11083]	233	!== Snw heat content ==!
	234	DO jk = 1, nlay_s
	235	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, &
	236	& pe_s(:,:,jk,:), pe_s(:,:,jk,:) )
	237	END DO
	238	!
	239	! ! ------------------------------------------ !
	240	ELSEIF( np_advS == 2 ) THEN ! -- advection form: -div( uA * uHS / u ) -- !
	241	! ! ------------------------------------------ !
[10785]	242	zamsk = 0._wp
[11083]	243	!== Ice volume ==!
	244	zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:)
	245	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, &
	246	& zhvar, pv_i, zua_ups, zva_ups )
	247	!== Snw volume ==!
	248	zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:)
	249	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, &
	250	& zhvar, pv_s, zua_ups, zva_ups )
	251	!== Salt content ==!
	252	zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:)
	253	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, &
	254	& zhvar, psv_i, zua_ups, zva_ups )
	255	!== Ice heat content ==!
	256	DO jk = 1, nlay_i
	257	zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:)
	258	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, &
	259	& zhvar, pe_i(:,:,jk,:), zua_ups, zva_ups )
	260	END DO
	261	!== Snw heat content ==!
	262	DO jk = 1, nlay_s
	263	zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:)
	264	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, &
	265	& zhvar, pe_s(:,:,jk,:), zua_ups, zva_ups )
	266	END DO
	267	!
	268	! ! ----------------------------------------- !
	269	ELSEIF( np_advS == 3 ) THEN ! -- advection form: -div( uV * uS / u ) -- !
	270	! ! ----------------------------------------- !
	271	zamsk = 0._wp
	272	!
	273	ALLOCATE( zuv_ho (jpi,jpj,jpl), zvv_ho (jpi,jpj,jpl), &
	274	& zuv_ups(jpi,jpj,jpl), zvv_ups(jpi,jpj,jpl), z1_vi(jpi,jpj,jpl), z1_vs(jpi,jpj,jpl) )
	275	!
	276	! inverse of Vi
	277	WHERE( pv_i(:,:,:) >= epsi20 ) ; z1_vi(:,:,:) = 1._wp / pv_i(:,:,:)
	278	ELSEWHERE ; z1_vi(:,:,:) = 0.
	279	END WHERE
	280	! inverse of Vs
	281	WHERE( pv_s(:,:,:) >= epsi20 ) ; z1_vs(:,:,:) = 1._wp / pv_s(:,:,:)
	282	ELSEWHERE ; z1_vs(:,:,:) = 0.
	283	END WHERE
	284	!
	285	! It is important to first calculate the ice fields and then the snow fields (because we use the same arrays)
	286	!
	287	!== Ice volume ==!
	288	zuv_ups = zua_ups
	289	zvv_ups = zva_ups
	290	zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:)
	291	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, &
	292	& zhvar, pv_i, zuv_ups, zvv_ups, zuv_ho , zvv_ho )
	293	!== Salt content ==!
	294	zhvar(:,:,:) = psv_i(:,:,:) * z1_vi(:,:,:)
	295	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zuv_ho , zvv_ho , zcu_box, zcv_box, &
	296	& zhvar, psv_i, zuv_ups, zvv_ups )
	297	!== Ice heat content ==!
	298	DO jk = 1, nlay_i
	299	zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_vi(:,:,:)
	300	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, &
	301	& zhvar, pe_i(:,:,jk,:), zuv_ups, zvv_ups )
	302	END DO
	303	!== Snow volume ==!
	304	zuv_ups = zua_ups
	305	zvv_ups = zva_ups
	306	zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:)
	307	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, &
	308	& zhvar, pv_s, zuv_ups, zvv_ups, zuv_ho , zvv_ho )
	309	!== Snw heat content ==!
	310	DO jk = 1, nlay_s
	311	zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_vs(:,:,:)
	312	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, &
	313	& zhvar, pe_s(:,:,jk,:), zuv_ups, zvv_ups )
	314	END DO
	315	!
	316	DEALLOCATE( zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs )
	317	!
[10785]	318	ENDIF
	319	!
[11083]	320	!== Ice age ==!
	321	IF( iom_use('iceage') .OR. iom_use('iceage_cat') ) THEN
[10425]	322	zamsk = 1._wp
[11083]	323	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, &
	324	& poa_i, poa_i )
	325	ENDIF
	326	!
	327	!== melt ponds ==!
	328	IF ( ln_pnd_H12 ) THEN
	329	! fraction
	330	zamsk = 1._wp
	331	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat , zv_cat , zcu_box, zcv_box, &
	332	& pa_ip, pa_ip, zua_ups, zva_ups, zua_ho , zva_ho )
	333	! volume
[10425]	334	zamsk = 0._wp
[10475]	335	zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:)
[11083]	336	CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, &
	337	& zhvar, pv_ip, zua_ups, zva_ups )
[10425]	338	ENDIF
[10418]	339	!
[11083]	340	!== Open water area ==!
[10439]	341	zati2(:,:) = SUM( pa_i(:,:,:), dim=3 )
	342	DO jj = 2, jpjm1
	343	DO ji = fs_2, fs_jpim1
[11083]	344	pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) &
[10439]	345	& - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt
[10413]	346	END DO
[10439]	347	END DO
[11083]	348	CALL lbc_lnk( 'icedyn_adv_umx', pato_i, 'T', 1. )
[10418]	349	!
[11083]	350	!
	351	! --- Ensure non-negative fields and in-bound thicknesses --- !
	352	! Remove negative values (conservation is ensured)
	353	! (because advected fields are not perfectly bounded and tiny negative values can occur, e.g. -1.e-20)
	354	CALL ice_var_zapneg( zdt, pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i )
	355	!
	356	! Make sure ice thickness is not too big
	357	! (because ice thickness can be too large where ice concentration is very small)
	358	CALL Hbig( zdt, zhi_max, zhs_max, zhip_max, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i )
	359
[8586]	360	END DO
	361	!
	362	END SUBROUTINE ice_dyn_adv_umx
[9929]	363
[8586]	364
[11083]	365	SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, &
	366	& pt, ptc, pua_ups, pva_ups, pua_ho, pva_ho )
[8586]	367	!!----------------------------------------------------------------------
	368	!! * ROUTINE adv_umx *
	369	!!
	370	!! ** Purpose : Compute the now trend due to total advection of
[10446]	371	!! tracers and add it to the general trend of tracer equations
[8586]	372	!!
[11083]	373	!! ** Method : - calculate upstream fluxes and upstream solution for tracers V/A(=H) etc
[10446]	374	!! - calculate tracer H at u and v points (Ultimate)
[11083]	375	!! - calculate the high order fluxes using alterning directions (Macho)
[10519]	376	!! - apply a limiter on the fluxes (nonosc_ice)
[11083]	377	!! - convert this tracer flux to a "volume" flux (uH -> uV)
	378	!! - apply a limiter a second time on the volumes fluxes (nonosc_ice)
	379	!! - calculate the high order solution for V
[8586]	380	!!
[11083]	381	!! ** Action : solve 3 equations => a) dA/dt = -div(uA)
	382	!! b) dV/dt = -div(uV) using dH/dt = -u.grad(H)
	383	!! c) dVS/dt = -div(uVS) using either dHS/dt = -u.grad(HS) or dS/dt = -u.grad(S)
[10446]	384	!!
[11083]	385	!! in eq. b), - fluxes uH are evaluated (with UMx) and limited with nonosc_ice. This step is necessary to get a good H.
	386	!! - then we convert this flux to a "volume" flux this way => uH * uA / u
	387	!! where uA is the flux from eq. a)
	388	!! this "volume" flux is also limited with nonosc_ice (otherwise overshoots can occur)
	389	!! - at last we estimate dV/dt = -div(uH * uA / u)
	390	!!
	391	!! in eq. c), one can solve the equation for S (ln_advS=T), then dVS/dt = -div(uV * uS / u)
	392	!! or for HS (ln_advS=F), then dVS/dt = -div(uA * uHS / u)
	393	!!
	394	!! ** Note : - this method can lead to tiny negative V (-1.e-20) => set it to 0 while conserving mass etc.
	395	!! - At the ice edge, Ultimate scheme can lead to:
	396	!! 1) negative interpolated tracers at u-v points
	397	!! 2) non-zero interpolated tracers at u-v points eventhough there is no ice and velocity is outward
	398	!! Solution for 1): apply an upstream scheme when it occurs. A better solution would be to degrade the order of
	399	!! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done).
	400	!! Solution for 2): we set it to 0 in this case
[10446]	401	!! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good.
	402	!! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we
[11083]	403	!! work on H (and not V). It is partly related to the multi-category approach
[10446]	404	!! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice
[11083]	405	!! concentration is small). Since we do not limit S and T, large values can occur at the edge but it does not really matter
	406	!! since sv_i and e_i are still good.
[8586]	407	!!----------------------------------------------------------------------
[11083]	408	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
	409	INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2)
	410	INTEGER , INTENT(in ) :: jt ! number of sub-iteration
	411	INTEGER , INTENT(in ) :: kt ! number of iteration
	412	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	413	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2
	414	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => ue2 or ua*e2u
	415	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity
	416	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field
	417	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field
	418	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT(inout), OPTIONAL :: pua_ups, pva_ups ! upstream u*a fluxes
	419	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes
[8586]	420	!
[10425]	421	INTEGER :: ji, jj, jl ! dummy loop indices
[8586]	422	REAL(wp) :: ztra ! local scalar
[10446]	423	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt
[10439]	424	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups
[8586]	425	!!----------------------------------------------------------------------
	426	!
[10446]	427	! Upstream (_ups) fluxes
	428	! -----------------------
	429	CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups )
	430
	431	! High order (_ho) fluxes
	432	! -----------------------
	433	SELECT CASE( kn_umx )
	434	!
	435	CASE ( 20 ) !== centered second order ==!
	436	!
[10475]	437	CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho )
[10446]	438	!
	439	CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==!
	440	!
[10475]	441	CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho )
[10446]	442	!
	443	END SELECT
[10439]	444	!
[10446]	445	! --ho --ho
	446	! new fluxes = uH u*a / u
	447	! ----------------------------
[10475]	448	IF( pamsk == 0._wp ) THEN
[10446]	449	DO jl = 1, jpl
	450	DO jj = 1, jpjm1
	451	DO ji = 1, fs_jpim1
[11083]	452	IF( ABS( pu(ji,jj) ) > epsi10 ) THEN
	453	zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc (ji,jj,jl) / pu(ji,jj)
	454	zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * pua_ups(ji,jj,jl) / pu(ji,jj)
[10446]	455	ELSE
	456	zfu_ho (ji,jj,jl) = 0._wp
	457	zfu_ups(ji,jj,jl) = 0._wp
	458	ENDIF
	459	!
[11083]	460	IF( ABS( pv(ji,jj) ) > epsi10 ) THEN
	461	zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc (ji,jj,jl) / pv(ji,jj)
	462	zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pva_ups(ji,jj,jl) / pv(ji,jj)
[10446]	463	ELSE
	464	zfv_ho (ji,jj,jl) = 0._wp
	465	zfv_ups(ji,jj,jl) = 0._wp
	466	ENDIF
	467	END DO
	468	END DO
	469	END DO
[11083]	470
	471	! the new "volume" fluxes must also be "flux corrected"
	472	! thus we calculate the upstream solution and apply a limiter again
	473	DO jl = 1, jpl
	474	DO jj = 2, jpjm1
	475	DO ji = fs_2, fs_jpim1
	476	ztra = - ( zfu_ups(ji,jj,jl) - zfu_ups(ji-1,jj,jl) + zfv_ups(ji,jj,jl) - zfv_ups(ji,jj-1,jl) )
	477	!
	478	zt_ups(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1)
	479	END DO
	480	END DO
	481	END DO
	482	CALL lbc_lnk( 'icedyn_adv_umx', zt_ups, 'T', 1. )
	483	!
	484	IF ( np_limiter == 1 ) THEN
	485	CALL nonosc_ice( 1._wp, pdt, pu, pv, ptc, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho )
	486	ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN
	487	CALL limiter_x( pdt, pu, ptc, zfu_ups, zfu_ho )
	488	CALL limiter_y( pdt, pv, ptc, zfv_ups, zfv_ho )
	489	ENDIF
	490	!
[10446]	491	ENDIF
[11083]	492	! --ho --ups
	493	! in case of advection of A: output ua and ua
	494	! -----------------------------------------------
[10446]	495	IF( PRESENT( pua_ho ) ) THEN
	496	DO jl = 1, jpl
	497	DO jj = 1, jpjm1
	498	DO ji = 1, fs_jpim1
[11083]	499	pua_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) ; pva_ho (ji,jj,jl) = zfv_ho (ji,jj,jl)
	500	pua_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) ; pva_ups(ji,jj,jl) = zfv_ups(ji,jj,jl)
	501	END DO
[10446]	502	END DO
	503	END DO
	504	ENDIF
	505	!
	506	! final trend with corrected fluxes
	507	! ---------------------------------
	508	DO jl = 1, jpl
	509	DO jj = 2, jpjm1
	510	DO ji = fs_2, fs_jpim1
	511	ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) )
	512	!
	513	ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1)
	514	END DO
	515	END DO
	516	END DO
	517	CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1. )
	518	!
	519	END SUBROUTINE adv_umx
	520
	521
	522	SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups )
	523	!!---------------------------------------------------------------------
	524	!! * ROUTINE upstream *
	525	!!
	526	!! ** Purpose : compute the upstream fluxes and upstream guess of tracer
	527	!!----------------------------------------------------------------------
	528	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
	529	INTEGER , INTENT(in ) :: jt ! number of sub-iteration
	530	INTEGER , INTENT(in ) :: kt ! number of iteration
	531	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	532	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields
	533	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components
	534	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer
	535	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes
	536	!
	537	INTEGER :: ji, jj, jl ! dummy loop indices
	538	REAL(wp) :: ztra ! local scalar
	539	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt
	540	!!----------------------------------------------------------------------
	541
[10439]	542	IF( .NOT. ll_upsxy ) THEN ! no alternate directions !
[10446]	543	!
[10425]	544	DO jl = 1, jpl
	545	DO jj = 1, jpjm1
	546	DO ji = 1, fs_jpim1
[10446]	547	pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl)
	548	pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl)
[10425]	549	END DO
[10413]	550	END DO
	551	END DO
[10446]	552	!
[10439]	553	ELSE ! alternate directions !
[10413]	554	!
	555	IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==!
[10439]	556	!
	557	DO jl = 1, jpl !-- flux in x-direction
[10425]	558	DO jj = 1, jpjm1
	559	DO ji = 1, fs_jpim1
[10446]	560	pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl)
[10425]	561	END DO
[10413]	562	END DO
	563	END DO
[10439]	564	!
	565	DO jl = 1, jpl !-- first guess of tracer from u-flux
[10425]	566	DO jj = 2, jpjm1
[10439]	567	DO ji = fs_2, fs_jpim1
[10446]	568	ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) &
	569	& + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk)
	570	!
	571	zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1)
[10425]	572	END DO
[10413]	573	END DO
	574	END DO
[10425]	575	CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. )
[8586]	576	!
[10439]	577	DO jl = 1, jpl !-- flux in y-direction
[10425]	578	DO jj = 1, jpjm1
	579	DO ji = 1, fs_jpim1
[10446]	580	pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * zpt(ji,jj+1,jl)
[10425]	581	END DO
[10413]	582	END DO
	583	END DO
[10439]	584	!
[10413]	585	ELSE !== even ice time step: adv_y then adv_x ==!
[10439]	586	!
	587	DO jl = 1, jpl !-- flux in y-direction
[10425]	588	DO jj = 1, jpjm1
	589	DO ji = 1, fs_jpim1
[10446]	590	pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl)
[10425]	591	END DO
[10413]	592	END DO
	593	END DO
[10439]	594	!
	595	DO jl = 1, jpl !-- first guess of tracer from v-flux
[10425]	596	DO jj = 2, jpjm1
[10439]	597	DO ji = fs_2, fs_jpim1
[10446]	598	ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) &
	599	& + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk)
	600	!
	601	zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1)
[10425]	602	END DO
	603	END DO
[10413]	604	END DO
[10425]	605	CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. )
[10413]	606	!
[10439]	607	DO jl = 1, jpl !-- flux in x-direction
[10425]	608	DO jj = 1, jpjm1
	609	DO ji = 1, fs_jpim1
[10446]	610	pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * zpt(ji+1,jj,jl)
[10425]	611	END DO
[10413]	612	END DO
	613	END DO
	614	!
	615	ENDIF
	616
	617	ENDIF
[10439]	618	!
	619	DO jl = 1, jpl !-- after tracer with upstream scheme
[10425]	620	DO jj = 2, jpjm1
	621	DO ji = fs_2, fs_jpim1
[10446]	622	ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) &
	623	& + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) &
	624	& + ( pu (ji,jj ) - pu (ji-1,jj ) &
	625	& + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk)
	626	!
[10475]	627	pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1)
[10425]	628	END DO
[10413]	629	END DO
[8586]	630	END DO
[10446]	631	CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1. )
[10413]	632
[10446]	633	END SUBROUTINE upstream
[8586]	634
[10446]	635
[10475]	636	SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
[8586]	637	!!---------------------------------------------------------------------
[10446]	638	!! * ROUTINE cen2 *
[8586]	639	!!
[10446]	640	!! ** Purpose : compute the high order fluxes using a centered
	641	!! second order scheme
[8586]	642	!!----------------------------------------------------------------------
[10439]	643	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
	644	INTEGER , INTENT(in ) :: jt ! number of sub-iteration
	645	INTEGER , INTENT(in ) :: kt ! number of iteration
	646	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	647	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields
	648	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components
[10446]	649	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer
	650	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes
[10425]	651	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes
[8586]	652	!
[10425]	653	INTEGER :: ji, jj, jl ! dummy loop indices
[10446]	654	REAL(wp) :: ztra ! local scalar
	655	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt
[8586]	656	!!----------------------------------------------------------------------
	657	!
[10439]	658	IF( .NOT.ll_hoxy ) THEN ! no alternate directions !
[8586]	659	!
[10425]	660	DO jl = 1, jpl
	661	DO jj = 1, jpjm1
	662	DO ji = 1, fs_jpim1
[10475]	663	pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) )
	664	pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) )
[10425]	665	END DO
[8586]	666	END DO
	667	END DO
[10475]	668	!
[11083]	669	IF ( np_limiter == 1 ) THEN
[10519]	670	CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
[11083]	671	ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN
[10446]	672	CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
	673	CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
[10413]	674	ENDIF
[8586]	675	!
[10439]	676	ELSE ! alternate directions !
[8586]	677	!
[10413]	678	IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==!
	679	!
[10439]	680	DO jl = 1, jpl !-- flux in x-direction
[10425]	681	DO jj = 1, jpjm1
	682	DO ji = 1, fs_jpim1
[10475]	683	pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) )
[10425]	684	END DO
[10413]	685	END DO
	686	END DO
[11083]	687	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
[10413]	688
[10439]	689	DO jl = 1, jpl !-- first guess of tracer from u-flux
[10425]	690	DO jj = 2, jpjm1
[10439]	691	DO ji = fs_2, fs_jpim1
[10446]	692	ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) &
	693	& + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk)
	694	!
	695	zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1)
[10425]	696	END DO
[10413]	697	END DO
	698	END DO
[10446]	699	CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. )
[10413]	700
[10439]	701	DO jl = 1, jpl !-- flux in y-direction
[10425]	702	DO jj = 1, jpjm1
	703	DO ji = 1, fs_jpim1
[10475]	704	pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) )
[10425]	705	END DO
[10413]	706	END DO
	707	END DO
[11083]	708	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
[10413]	709
	710	ELSE !== even ice time step: adv_y then adv_x ==!
	711	!
[10439]	712	DO jl = 1, jpl !-- flux in y-direction
[10425]	713	DO jj = 1, jpjm1
	714	DO ji = 1, fs_jpim1
[10475]	715	pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) )
[10425]	716	END DO
[10413]	717	END DO
	718	END DO
[11083]	719	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
[10413]	720	!
[10439]	721	DO jl = 1, jpl !-- first guess of tracer from v-flux
[10425]	722	DO jj = 2, jpjm1
[10439]	723	DO ji = fs_2, fs_jpim1
[10446]	724	ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) &
	725	& + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk)
	726	!
	727	zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1)
[10425]	728	END DO
[10413]	729	END DO
	730	END DO
[10446]	731	CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. )
[10413]	732	!
[10439]	733	DO jl = 1, jpl !-- flux in x-direction
[10425]	734	DO jj = 1, jpjm1
	735	DO ji = 1, fs_jpim1
[10475]	736	pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) )
[10425]	737	END DO
[10413]	738	END DO
	739	END DO
[11083]	740	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
[10413]	741
	742	ENDIF
[11083]	743	IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
[10413]	744
	745	ENDIF
	746
	747	END SUBROUTINE cen2
	748
	749
[10475]	750	SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
[10413]	751	!!---------------------------------------------------------------------
	752	!! * ROUTINE macho *
	753	!!
[10446]	754	!! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme
[10413]	755	!!
[10446]	756	!! ** Method : ...
[10413]	757	!!
	758	!! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74.
	759	!!----------------------------------------------------------------------
[10439]	760	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
	761	INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2)
	762	INTEGER , INTENT(in ) :: jt ! number of sub-iteration
	763	INTEGER , INTENT(in ) :: kt ! number of iteration
	764	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	765	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields
	766	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components
	767	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity
[10446]	768	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer
	769	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes
[10425]	770	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes
[10413]	771	!
[10425]	772	INTEGER :: ji, jj, jl ! dummy loop indices
[10446]	773	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt
[10413]	774	!!----------------------------------------------------------------------
	775	!
	776	IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==!
[8586]	777	!
[10413]	778	! !-- ultimate interpolation of pt at u-point --!
[11083]	779	CALL ultimate_x( pamsk, kn_umx, pdt, pt, pu, zt_u, pfu_ho )
[10413]	780	! !-- limiter in x --!
[11083]	781	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
[10446]	782	! !-- advective form update in zpt --!
[10439]	783	DO jl = 1, jpl
	784	DO jj = 2, jpjm1
	785	DO ji = fs_2, fs_jpim1
[10446]	786	zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pubox(ji,jj ) * ( zt_u(ji,jj,jl) - zt_u(ji-1,jj,jl) ) * r1_e1t (ji,jj) &
	787	& + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) &
	788	& * pamsk &
[11083]	789	& ) * pdt ) * tmask(ji,jj,1)
[10413]	790	END DO
[8586]	791	END DO
[10439]	792	END DO
[10446]	793	CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. )
[8586]	794	!
[10413]	795	! !-- ultimate interpolation of pt at v-point --!
	796	IF( ll_hoxy ) THEN
[11083]	797	CALL ultimate_y( pamsk, kn_umx, pdt, zpt, pv, zt_v, pfv_ho )
[10413]	798	ELSE
[11083]	799	CALL ultimate_y( pamsk, kn_umx, pdt, pt , pv, zt_v, pfv_ho )
[10413]	800	ENDIF
	801	! !-- limiter in y --!
[11083]	802	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
[10413]	803	!
	804	!
	805	ELSE !== even ice time step: adv_y then adv_x ==!
	806	!
	807	! !-- ultimate interpolation of pt at v-point --!
[11083]	808	CALL ultimate_y( pamsk, kn_umx, pdt, pt, pv, zt_v, pfv_ho )
[10413]	809	! !-- limiter in y --!
[11083]	810	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
[10446]	811	! !-- advective form update in zpt --!
[10439]	812	DO jl = 1, jpl
	813	DO jj = 2, jpjm1
	814	DO ji = fs_2, fs_jpim1
[10446]	815	zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pvbox(ji,jj ) * ( zt_v(ji,jj,jl) - zt_v(ji,jj-1,jl) ) * r1_e2t (ji,jj) &
	816	& + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) &
	817	& * pamsk &
	818	& ) * pdt ) * tmask(ji,jj,1)
[10425]	819	END DO
[10413]	820	END DO
[10439]	821	END DO
[10446]	822	CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. )
[10413]	823	!
	824	! !-- ultimate interpolation of pt at u-point --!
	825	IF( ll_hoxy ) THEN
[11083]	826	CALL ultimate_x( pamsk, kn_umx, pdt, zpt, pu, zt_u, pfu_ho )
[10413]	827	ELSE
[11083]	828	CALL ultimate_x( pamsk, kn_umx, pdt, pt , pu, zt_u, pfu_ho )
[10413]	829	ENDIF
	830	! !-- limiter in x --!
[11083]	831	IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
[10413]	832	!
	833	ENDIF
	834
[11083]	835	IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
[8586]	836	!
	837	END SUBROUTINE macho
	838
	839
[11083]	840	SUBROUTINE ultimate_x( pamsk, kn_umx, pdt, pt, pu, pt_u, pfu_ho )
[8586]	841	!!---------------------------------------------------------------------
	842	!! * ROUTINE ultimate_x *
	843	!!
[10446]	844	!! ** Purpose : compute tracer at u-points
[8586]	845	!!
[10446]	846	!! ** Method : ...
[8586]	847	!!
	848	!! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74.
	849	!!----------------------------------------------------------------------
[11083]	850	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
[10439]	851	INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2)
	852	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	853	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component
	854	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields
[10425]	855	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point
	856	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux
[8586]	857	!
[10425]	858	INTEGER :: ji, jj, jl ! dummy loop indices
[10439]	859	REAL(wp) :: zcu, zdx2, zdx4 ! - -
[10425]	860	REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4
[8586]	861	!!----------------------------------------------------------------------
	862	!
	863	! !-- Laplacian in i-direction --!
[10425]	864	DO jl = 1, jpl
	865	DO jj = 2, jpjm1 ! First derivative (gradient)
	866	DO ji = 1, fs_jpim1
	867	ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1)
	868	END DO
	869	! ! Second derivative (Laplacian)
	870	DO ji = fs_2, fs_jpim1
	871	ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj)
	872	END DO
[8586]	873	END DO
	874	END DO
[10425]	875	CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1. )
[8586]	876	!
	877	! !-- BiLaplacian in i-direction --!
[10425]	878	DO jl = 1, jpl
	879	DO jj = 2, jpjm1 ! Third derivative
	880	DO ji = 1, fs_jpim1
	881	ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1)
	882	END DO
	883	! ! Fourth derivative
	884	DO ji = fs_2, fs_jpim1
	885	ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj)
	886	END DO
[8586]	887	END DO
	888	END DO
[10425]	889	CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1. )
[8586]	890	!
	891	!
[10413]	892	SELECT CASE (kn_umx )
[8586]	893	!
	894	CASE( 1 ) !== 1st order central TIM ==! (Eq. 21)
	895	!
[10425]	896	DO jl = 1, jpl
	897	DO jj = 1, jpjm1
	898	DO ji = 1, fs_jpim1 ! vector opt.
[10475]	899	pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) &
	900	& - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) )
[10425]	901	END DO
[8586]	902	END DO
	903	END DO
	904	!
	905	CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23)
	906	!
[10425]	907	DO jl = 1, jpl
	908	DO jj = 1, jpjm1
	909	DO ji = 1, fs_jpim1 ! vector opt.
	910	zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj)
	911	pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) &
[10475]	912	& - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) )
[10425]	913	END DO
[8586]	914	END DO
	915	END DO
	916	!
	917	CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24)
	918	!
[10425]	919	DO jl = 1, jpl
	920	DO jj = 1, jpjm1
	921	DO ji = 1, fs_jpim1 ! vector opt.
	922	zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj)
	923	zdx2 = e1u(ji,jj) * e1u(ji,jj)
[10439]	924	!!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj)
[10446]	925	pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) &
[10475]	926	& - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) &
	927	& + z1_6 * zdx2 * ( zcuzcu - 1._wp ) ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) &
[10446]	928	& - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) )
[10425]	929	END DO
[8586]	930	END DO
	931	END DO
	932	!
	933	CASE( 4 ) !== 4th order central TIM ==! (Eq. 27)
	934	!
[10425]	935	DO jl = 1, jpl
	936	DO jj = 1, jpjm1
	937	DO ji = 1, fs_jpim1 ! vector opt.
	938	zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj)
	939	zdx2 = e1u(ji,jj) * e1u(ji,jj)
[10439]	940	!!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj)
[10475]	941	pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) &
	942	& - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) &
	943	& + z1_6 * zdx2 * ( zcuzcu - 1._wp ) ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) &
	944	& - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) )
[10425]	945	END DO
[8586]	946	END DO
	947	END DO
	948	!
	949	CASE( 5 ) !== 5th order central TIM ==! (Eq. 29)
	950	!
[10425]	951	DO jl = 1, jpl
	952	DO jj = 1, jpjm1
	953	DO ji = 1, fs_jpim1 ! vector opt.
	954	zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj)
	955	zdx2 = e1u(ji,jj) * e1u(ji,jj)
[10439]	956	!!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj)
[10425]	957	zdx4 = zdx2 * zdx2
[10475]	958	pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) &
	959	& - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) &
	960	& + z1_6 * zdx2 * ( zcuzcu - 1._wp ) ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) &
	961	& - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) &
[10446]	962	& + z1_120 * zdx4 * ( zcuzcu - 1._wp ) ( zcuzcu - 4._wp ) ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) &
[10425]	963	& - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) )
	964	END DO
[8586]	965	END DO
	966	END DO
	967	!
	968	END SELECT
[10439]	969	!
	970	! if pt at u-point is negative then use the upstream value
	971	! this should not be necessary if a proper sea-ice mask is set in Ultimate
	972	! to degrade the order of the scheme when necessary (for ex. at the ice edge)
[10413]	973	IF( ll_neg ) THEN
[10425]	974	DO jl = 1, jpl
	975	DO jj = 1, jpjm1
	976	DO ji = 1, fs_jpim1
[11083]	977	IF( pt_u(ji,jj,jl) < 0._wp .OR. ( imsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN
[10475]	978	pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) &
	979	& - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) )
[10425]	980	ENDIF
	981	END DO
[10413]	982	END DO
	983	END DO
	984	ENDIF
[10439]	985	! !-- High order flux in i-direction --!
[10425]	986	DO jl = 1, jpl
	987	DO jj = 1, jpjm1
	988	DO ji = 1, fs_jpim1 ! vector opt.
[10439]	989	pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl)
[10425]	990	END DO
[10413]	991	END DO
	992	END DO
[8586]	993	!
	994	END SUBROUTINE ultimate_x
	995
	996
[11083]	997	SUBROUTINE ultimate_y( pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho )
[8586]	998	!!---------------------------------------------------------------------
	999	!! * ROUTINE ultimate_y *
	1000	!!
[10446]	1001	!! ** Purpose : compute tracer at v-points
[8586]	1002	!!
[10446]	1003	!! ** Method : ...
[8586]	1004	!!
	1005	!! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74.
	1006	!!----------------------------------------------------------------------
[11083]	1007	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
[10439]	1008	INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2)
	1009	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	1010	REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component
	1011	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields
[10425]	1012	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point
	1013	REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux
[8586]	1014	!
[10439]	1015	INTEGER :: ji, jj, jl ! dummy loop indices
[8586]	1016	REAL(wp) :: zcv, zdy2, zdy4 ! - -
[10425]	1017	REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4
[8586]	1018	!!----------------------------------------------------------------------
	1019	!
	1020	! !-- Laplacian in j-direction --!
[10425]	1021	DO jl = 1, jpl
	1022	DO jj = 1, jpjm1 ! First derivative (gradient)
	1023	DO ji = fs_2, fs_jpim1
	1024	ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1)
	1025	END DO
[8586]	1026	END DO
[10425]	1027	DO jj = 2, jpjm1 ! Second derivative (Laplacian)
	1028	DO ji = fs_2, fs_jpim1
	1029	ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj)
	1030	END DO
[8586]	1031	END DO
	1032	END DO
[10425]	1033	CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1. )
[8586]	1034	!
	1035	! !-- BiLaplacian in j-direction --!
[10425]	1036	DO jl = 1, jpl
	1037	DO jj = 1, jpjm1 ! First derivative
	1038	DO ji = fs_2, fs_jpim1
	1039	ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1)
	1040	END DO
[8586]	1041	END DO
[10425]	1042	DO jj = 2, jpjm1 ! Second derivative
	1043	DO ji = fs_2, fs_jpim1
	1044	ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj)
	1045	END DO
[8586]	1046	END DO
	1047	END DO
[10425]	1048	CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1. )
[8586]	1049	!
	1050	!
[10413]	1051	SELECT CASE (kn_umx )
[10425]	1052	!
[8586]	1053	CASE( 1 ) !== 1st order central TIM ==! (Eq. 21)
[10425]	1054	DO jl = 1, jpl
	1055	DO jj = 1, jpjm1
	1056	DO ji = 1, fs_jpim1
[10475]	1057	pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) &
	1058	& - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) )
[10425]	1059	END DO
[8586]	1060	END DO
	1061	END DO
	1062	!
	1063	CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23)
[10425]	1064	DO jl = 1, jpl
	1065	DO jj = 1, jpjm1
	1066	DO ji = 1, fs_jpim1
	1067	zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
[10475]	1068	pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) &
	1069	& - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) )
[10425]	1070	END DO
[8586]	1071	END DO
	1072	END DO
	1073	!
	1074	CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24)
[10425]	1075	DO jl = 1, jpl
	1076	DO jj = 1, jpjm1
	1077	DO ji = 1, fs_jpim1
	1078	zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
	1079	zdy2 = e2v(ji,jj) * e2v(ji,jj)
[10439]	1080	!!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj)
[10475]	1081	pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) &
	1082	& - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) &
[10446]	1083	& + z1_6 * zdy2 * ( zcvzcv - 1._wp ) ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) &
[10425]	1084	& - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) )
	1085	END DO
[8586]	1086	END DO
	1087	END DO
	1088	!
	1089	CASE( 4 ) !== 4th order central TIM ==! (Eq. 27)
[10425]	1090	DO jl = 1, jpl
	1091	DO jj = 1, jpjm1
	1092	DO ji = 1, fs_jpim1
	1093	zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
	1094	zdy2 = e2v(ji,jj) * e2v(ji,jj)
[10439]	1095	!!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj)
[10475]	1096	pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) &
	1097	& - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) &
	1098	& + z1_6 * zdy2 * ( zcvzcv - 1._wp ) ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) &
	1099	& - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) )
[10425]	1100	END DO
[8586]	1101	END DO
	1102	END DO
	1103	!
	1104	CASE( 5 ) !== 5th order central TIM ==! (Eq. 29)
[10425]	1105	DO jl = 1, jpl
	1106	DO jj = 1, jpjm1
	1107	DO ji = 1, fs_jpim1
	1108	zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
	1109	zdy2 = e2v(ji,jj) * e2v(ji,jj)
[10439]	1110	!!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj)
[10425]	1111	zdy4 = zdy2 * zdy2
[10446]	1112	pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) &
[10475]	1113	& - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) &
	1114	& + z1_6 * zdy2 * ( zcvzcv - 1._wp ) ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) &
	1115	& - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) &
[10446]	1116	& + z1_120 * zdy4 * ( zcvzcv - 1._wp ) ( zcvzcv - 4._wp ) ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) &
[10425]	1117	& - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) )
	1118	END DO
[8586]	1119	END DO
	1120	END DO
	1121	!
	1122	END SELECT
[10439]	1123	!
	1124	! if pt at v-point is negative then use the upstream value
	1125	! this should not be necessary if a proper sea-ice mask is set in Ultimate
	1126	! to degrade the order of the scheme when necessary (for ex. at the ice edge)
[10413]	1127	IF( ll_neg ) THEN
[10425]	1128	DO jl = 1, jpl
	1129	DO jj = 1, jpjm1
	1130	DO ji = 1, fs_jpim1
[11083]	1131	IF( pt_v(ji,jj,jl) < 0._wp .OR. ( jmsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN
[10475]	1132	pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) &
	1133	& - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) )
[10425]	1134	ENDIF
	1135	END DO
[10413]	1136	END DO
	1137	END DO
	1138	ENDIF
[10439]	1139	! !-- High order flux in j-direction --!
[10425]	1140	DO jl = 1, jpl
	1141	DO jj = 1, jpjm1
	1142	DO ji = 1, fs_jpim1 ! vector opt.
[10439]	1143	pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl)
[10425]	1144	END DO
[10413]	1145	END DO
	1146	END DO
[8586]	1147	!
	1148	END SUBROUTINE ultimate_y
[10413]	1149
	1150
[10519]	1151	SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
[8586]	1152	!!---------------------------------------------------------------------
[10519]	1153	!! * ROUTINE nonosc_ice *
[8586]	1154	!!
[10446]	1155	!! ** Purpose : compute monotonic tracer fluxes from the upstream
[10519]	1156	!! scheme and the before field by a non-oscillatory algorithm
[8586]	1157	!!
[10446]	1158	!! ** Method : ...
[8586]	1159	!!----------------------------------------------------------------------
[10439]	1160	REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
	1161	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
[10425]	1162	REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2
	1163	REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1
[10446]	1164	REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field
	1165	REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux
[10425]	1166	REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux
[8586]	1167	!
[10425]	1168	INTEGER :: ji, jj, jl ! dummy loop indices
[10475]	1169	REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars
	1170	REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - -
[10425]	1171	REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo
[10439]	1172	REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups
[8586]	1173	!!----------------------------------------------------------------------
	1174	zbig = 1.e+40_wp
[10425]	1175
[10413]	1176	! antidiffusive flux : high order minus low order
	1177	! --------------------------------------------------
[10425]	1178	DO jl = 1, jpl
	1179	DO jj = 1, jpjm1
	1180	DO ji = 1, fs_jpim1 ! vector opt.
[10439]	1181	pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl)
	1182	pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl)
[10425]	1183	END DO
	1184	END DO
[8586]	1185	END DO
	1186
[10413]	1187	! extreme case where pfu_ho has to be zero
	1188	! ----------------------------------------
	1189	! pfu_ho
	1190	! * --->
	1191	! \| \| * \| \|
	1192	! \| \| \| * \|
	1193	! \| \| \| \| *
[10439]	1194	! t_ups : i-1 i i+1 i+2
[11083]	1195	IF( ll_prelim ) THEN
[10413]	1196
[10425]	1197	DO jl = 1, jpl
	1198	DO jj = 2, jpjm1
	1199	DO ji = fs_2, fs_jpim1
[10439]	1200	zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl)
	1201	ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl)
[10425]	1202	END DO
[10413]	1203	END DO
	1204	END DO
[10439]	1205	CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1., ztj_ups, 'T', 1. )
[8586]	1206
[10425]	1207	DO jl = 1, jpl
	1208	DO jj = 2, jpjm1
	1209	DO ji = fs_2, fs_jpim1
[10475]	1210	IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. &
	1211	& pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN
[10425]	1212	!
[10475]	1213	IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. &
	1214	& pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN
	1215	pfu_ho(ji,jj,jl)=0._wp
	1216	pfv_ho(ji,jj,jl)=0._wp
[10439]	1217	ENDIF
[10425]	1218	!
[10475]	1219	IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. &
	1220	& pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN
	1221	pfu_ho(ji,jj,jl)=0._wp
	1222	pfv_ho(ji,jj,jl)=0._wp
[10439]	1223	ENDIF
[10425]	1224	!
	1225	ENDIF
	1226	END DO
[10413]	1227	END DO
	1228	END DO
[10425]	1229	CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond.
[10413]	1230
	1231	ENDIF
[10425]	1232
[8586]	1233	! Search local extrema
	1234	! --------------------
[10439]	1235	! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover
[10425]	1236	z1_dt = 1._wp / pdt
	1237	DO jl = 1, jpl
	1238
	1239	DO jj = 1, jpj
	1240	DO ji = 1, jpi
[10439]	1241	IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN
[10425]	1242	zbup(ji,jj) = -zbig
	1243	zbdo(ji,jj) = zbig
[10439]	1244	ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN
	1245	zbup(ji,jj) = pt_ups(ji,jj,jl)
	1246	zbdo(ji,jj) = pt_ups(ji,jj,jl)
	1247	ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN
[10425]	1248	zbup(ji,jj) = pt(ji,jj,jl)
	1249	zbdo(ji,jj) = pt(ji,jj,jl)
	1250	ELSE
[10439]	1251	zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) )
	1252	zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) )
[10425]	1253	ENDIF
	1254	END DO
[10413]	1255	END DO
[8586]	1256
[10425]	1257	DO jj = 2, jpjm1
	1258	DO ji = fs_2, fs_jpim1 ! vector opt.
	1259	!
[10475]	1260	zup = MAX( zbup(ji,jj), zbup(ji-1,jj), zbup(ji+1,jj), zbup(ji,jj-1), zbup(ji,jj+1) ) ! search max/min in neighbourhood
	1261	zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) )
[10425]	1262	!
[10475]	1263	zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux
	1264	& + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) )
	1265	zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) &
	1266	& + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) )
[10425]	1267	!
[10475]	1268	zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) &
[10439]	1269	& ) * ( 1. - pamsk )
[10475]	1270	zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) &
[10439]	1271	& ) * ( 1. - pamsk )
[10425]	1272	!
	1273	! ! up & down beta terms
[11083]	1274	! clem: zbetup and zbetdo must be 0 for zpos>1.e-10 & zneg>1.e-10 (do not put 0 instead of 1.e-10 !!!)
	1275	IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt
	1276	ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig
[10425]	1277	ENDIF
	1278	!
[11083]	1279	IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt
	1280	ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig
[10425]	1281	ENDIF
	1282	!
	1283	! if all the points are outside ice cover
[10475]	1284	IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig
	1285	IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig
[10425]	1286	!
	1287	END DO
[8586]	1288	END DO
	1289	END DO
[10425]	1290	CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign)
[8586]	1291
[10413]	1292
	1293	! monotonic flux in the y direction
	1294	! ---------------------------------
[10425]	1295	DO jl = 1, jpl
	1296	DO jj = 1, jpjm1
	1297	DO ji = 1, fs_jpim1 ! vector opt.
	1298	zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) )
	1299	zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) )
[10475]	1300	zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) )
[10425]	1301	!
	1302	zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu )
[10439]	1303	!
	1304	pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl)
	1305	!
[10425]	1306	END DO
[8637]	1307	END DO
[10413]	1308
[10425]	1309	DO jj = 1, jpjm1
	1310	DO ji = 1, fs_jpim1 ! vector opt.
	1311	zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) )
	1312	zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) )
[10475]	1313	zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) )
[10425]	1314	!
	1315	zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv )
[10439]	1316	!
	1317	pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl)
	1318	!
[10425]	1319	END DO
[8586]	1320	END DO
[10413]	1321
	1322	END DO
[8586]	1323	!
[10519]	1324	END SUBROUTINE nonosc_ice
[8586]	1325
[10446]	1326
	1327	SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
[10413]	1328	!!---------------------------------------------------------------------
	1329	!! * ROUTINE limiter_x *
	1330	!!
	1331	!! ** Purpose : compute flux limiter
	1332	!!----------------------------------------------------------------------
[10446]	1333	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	1334	REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2
	1335	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer
	1336	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux
	1337	REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux
[10413]	1338	!
	1339	REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr
[10425]	1340	INTEGER :: ji, jj, jl ! dummy loop indices
	1341	REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes
[10413]	1342	!!----------------------------------------------------------------------
	1343	!
[10425]	1344	DO jl = 1, jpl
	1345	DO jj = 2, jpjm1
	1346	DO ji = fs_2, fs_jpim1 ! vector opt.
	1347	zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1)
	1348	END DO
[10413]	1349	END DO
	1350	END DO
[10425]	1351	CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.) ! lateral boundary cond.
[10413]	1352
[10425]	1353	DO jl = 1, jpl
	1354	DO jj = 2, jpjm1
	1355	DO ji = fs_2, fs_jpim1 ! vector opt.
	1356	uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj)
	1357
	1358	Rjm = zslpx(ji-1,jj,jl)
	1359	Rj = zslpx(ji ,jj,jl)
	1360	Rjp = zslpx(ji+1,jj,jl)
[10413]	1361
[11083]	1362	IF( np_limiter == 3 ) THEN
[10413]	1363
[10425]	1364	IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm
	1365	ELSE ; Rr = Rjp
	1366	ENDIF
[10413]	1367
[10425]	1368	zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl)
	1369	IF( Rj > 0. ) THEN
	1370	zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), &
	1371	& MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) )
	1372	ELSE
	1373	zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), &
	1374	& MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) )
	1375	ENDIF
	1376	pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter
[10413]	1377
[11083]	1378	ELSEIF( np_limiter == 2 ) THEN
[10425]	1379	IF( Rj /= 0. ) THEN
	1380	IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj
	1381	ELSE ; Cr = Rjp / Rj
	1382	ENDIF
	1383	ELSE
	1384	Cr = 0.
[10413]	1385	ENDIF
[10425]	1386
	1387	! -- superbee --
	1388	zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) )
	1389	! -- van albada 2 --
	1390	!!zpsi = 2.Cr / (CrCr+1.)
	1391	! -- sweby (with beta=1) --
	1392	!!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) )
	1393	! -- van Leer --
	1394	!!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) )
	1395	! -- ospre --
	1396	!!zpsi = 1.5 * ( CrCr + Cr ) / ( CrCr + Cr + 1. )
	1397	! -- koren --
	1398	!!zpsi = MAX( 0., MIN( 2.Cr, MIN( (1.+2Cr)/3., 2. ) ) )
	1399	! -- charm --
	1400	!IF( Cr > 0. ) THEN ; zpsi = Cr * (3.Cr + 1.) / ( (Cr + 1.) (Cr + 1.) )
	1401	!ELSE ; zpsi = 0.
[10413]	1402	!ENDIF
[10425]	1403	! -- van albada 1 --
	1404	!!zpsi = (CrCr + Cr) / (CrCr +1)
	1405	! -- smart --
	1406	!!zpsi = MAX( 0., MIN( 2.Cr, MIN( 0.25+0.75Cr, 4. ) ) )
	1407	! -- umist --
	1408	!!zpsi = MAX( 0., MIN( 2.Cr, MIN( 0.25+0.75Cr, MIN(0.75+0.25*Cr, 2. ) ) ) )
[10413]	1409
[10425]	1410	! high order flux corrected by the limiter
	1411	pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFLzpsi ) Rj * 0.5
[10413]	1412
[10425]	1413	ENDIF
	1414	END DO
[10413]	1415	END DO
	1416	END DO
[10425]	1417	CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.) ! lateral boundary cond.
[10413]	1418	!
	1419	END SUBROUTINE limiter_x
	1420
[10446]	1421
	1422	SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
[10413]	1423	!!---------------------------------------------------------------------
	1424	!! * ROUTINE limiter_y *
	1425	!!
	1426	!! ** Purpose : compute flux limiter
	1427	!!----------------------------------------------------------------------
[10446]	1428	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	1429	REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2
	1430	REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer
	1431	REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux
	1432	REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux
[10413]	1433	!
	1434	REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr
[10425]	1435	INTEGER :: ji, jj, jl ! dummy loop indices
	1436	REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes
[10413]	1437	!!----------------------------------------------------------------------
	1438	!
[10425]	1439	DO jl = 1, jpl
	1440	DO jj = 2, jpjm1
	1441	DO ji = fs_2, fs_jpim1 ! vector opt.
	1442	zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1)
	1443	END DO
[10413]	1444	END DO
	1445	END DO
[10425]	1446	CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.) ! lateral boundary cond.
[10413]	1447
[10425]	1448	DO jl = 1, jpl
	1449	DO jj = 2, jpjm1
	1450	DO ji = fs_2, fs_jpim1 ! vector opt.
	1451	vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj)
[10413]	1452
[10425]	1453	Rjm = zslpy(ji,jj-1,jl)
	1454	Rj = zslpy(ji,jj ,jl)
	1455	Rjp = zslpy(ji,jj+1,jl)
[10413]	1456
[11083]	1457	IF( np_limiter == 3 ) THEN
[10413]	1458
[10425]	1459	IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm
	1460	ELSE ; Rr = Rjp
	1461	ENDIF
[10413]	1462
[10425]	1463	zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl)
	1464	IF( Rj > 0. ) THEN
	1465	zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), &
	1466	& MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) )
	1467	ELSE
	1468	zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), &
	1469	& MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) )
	1470	ENDIF
	1471	pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter
[10413]	1472
[11083]	1473	ELSEIF( np_limiter == 2 ) THEN
[10413]	1474
[10425]	1475	IF( Rj /= 0. ) THEN
	1476	IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj
	1477	ELSE ; Cr = Rjp / Rj
	1478	ENDIF
	1479	ELSE
	1480	Cr = 0.
	1481	ENDIF
[10413]	1482
[10425]	1483	! -- superbee --
	1484	zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) )
	1485	! -- van albada 2 --
	1486	!!zpsi = 2.Cr / (CrCr+1.)
	1487	! -- sweby (with beta=1) --
	1488	!!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) )
	1489	! -- van Leer --
	1490	!!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) )
	1491	! -- ospre --
	1492	!!zpsi = 1.5 * ( CrCr + Cr ) / ( CrCr + Cr + 1. )
	1493	! -- koren --
	1494	!!zpsi = MAX( 0., MIN( 2.Cr, MIN( (1.+2Cr)/3., 2. ) ) )
	1495	! -- charm --
	1496	!IF( Cr > 0. ) THEN ; zpsi = Cr * (3.Cr + 1.) / ( (Cr + 1.) (Cr + 1.) )
	1497	!ELSE ; zpsi = 0.
	1498	!ENDIF
	1499	! -- van albada 1 --
	1500	!!zpsi = (CrCr + Cr) / (CrCr +1)
	1501	! -- smart --
	1502	!!zpsi = MAX( 0., MIN( 2.Cr, MIN( 0.25+0.75Cr, 4. ) ) )
	1503	! -- umist --
	1504	!!zpsi = MAX( 0., MIN( 2.Cr, MIN( 0.25+0.75Cr, MIN(0.75+0.25*Cr, 2. ) ) ) )
[10413]	1505
[10425]	1506	! high order flux corrected by the limiter
	1507	pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFLzpsi ) Rj * 0.5
	1508
	1509	ENDIF
	1510	END DO
[10413]	1511	END DO
	1512	END DO
[10425]	1513	CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.) ! lateral boundary cond.
[10413]	1514	!
	1515	END SUBROUTINE limiter_y
	1516
[11083]	1517
	1518	SUBROUTINE Hbig( pdt, phi_max, phs_max, phip_max, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i )
	1519	!!-------------------------------------------------------------------
	1520	!! * ROUTINE Hbig *
	1521	!!
	1522	!! ** Purpose : Thickness correction in case advection scheme creates
	1523	!! abnormally tick ice or snow
	1524	!!
	1525	!! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points
	1526	!! (before advection) and reduce it by adapting ice concentration
	1527	!! 2- check whether snow thickness is larger than the surrounding 9-points
	1528	!! (before advection) and reduce it by sending the excess in the ocean
	1529	!! 3- check whether snow load deplets the snow-ice interface below sea level$
	1530	!! and reduce it by sending the excess in the ocean
	1531	!! 4- correct pond fraction to avoid a_ip > a_i
	1532	!!
	1533	!! ** input : Max thickness of the surrounding 9-points
	1534	!!-------------------------------------------------------------------
	1535	REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
	1536	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max ! max ice thick from surrounding 9-pts
	1537	REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip
	1538	REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s
	1539	REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i
	1540	!
	1541	INTEGER :: ji, jj, jk, jl ! dummy loop indices
	1542	REAL(wp) :: z1_dt, zhip, zhi, zhs, zvs_excess, zfra
	1543	REAL(wp), DIMENSION(jpi,jpj) :: zswitch
	1544	!!-------------------------------------------------------------------
	1545	!
	1546	z1_dt = 1._wp / pdt
	1547	!
	1548	DO jl = 1, jpl
	1549
	1550	DO jj = 1, jpj
	1551	DO ji = 1, jpi
	1552	IF ( pv_i(ji,jj,jl) > 0._wp ) THEN
	1553	!
	1554	! ! -- check h_ip -- !
	1555	! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip
	1556	IF( ln_pnd_H12 .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN
	1557	zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) )
	1558	IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN
	1559	pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl)
	1560	ENDIF
	1561	ENDIF
	1562	!
	1563	! ! -- check h_i -- !
	1564	! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i
	1565	zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl)
	1566	IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
	1567	pa_i(ji,jj,jl) = pv_i(ji,jj,jl) / MIN( phi_max(ji,jj,jl), hi_max(jpl) ) !-- bound h_i to hi_max (99 m)
	1568	ENDIF
	1569	!
	1570	! ! -- check h_s -- !
	1571	! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean
	1572	zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl)
	1573	IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
	1574	zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 )
	1575	!
	1576	wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * z1_dt
	1577	hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0
	1578	!
	1579	pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra
	1580	pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl)
	1581	ENDIF
	1582	!
	1583	! ! -- check snow load -- !
	1584	! if snow load makes snow-ice interface to deplet below the ocean surface => put the snow excess in the ocean
	1585	! this correction is crucial because of the call to routine icecor afterwards which imposes a mini of ice thick. (rn_himin)
	1586	! this imposed mini can artificially make the snow very thick (if concentration decreases drastically)
	1587	zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rau0-rhoi) * r1_rhos )
	1588	IF( zvs_excess > 0._wp ) THEN
	1589	zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 )
	1590	wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * z1_dt
	1591	hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0
	1592	!
	1593	pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra
	1594	pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess
	1595	ENDIF
	1596
	1597	ENDIF
	1598	END DO
	1599	END DO
	1600	END DO
	1601	! !-- correct pond fraction to avoid a_ip > a_i
	1602	WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:)
	1603	!
	1604	!
	1605	END SUBROUTINE Hbig
	1606
[8586]	1607	#else
	1608	!!----------------------------------------------------------------------
[9570]	1609	!! Default option Dummy module NO SI3 sea-ice model
[8586]	1610	!!----------------------------------------------------------------------
	1611	#endif
	1612
	1613	!!======================================================================
	1614	END MODULE icedyn_adv_umx

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source: NEMO/branches/UKMO/NEMO_4.0_GO6_mixing/src/ICE/icedyn_adv_umx.F90 @ 11083

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