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dynzdf.F90 in NEMO/branches/2021/dev_r14318_RK3_stage1/src/OCE/DYN – NEMO

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source: NEMO/branches/2021/dev_r14318_RK3_stage1/src/OCE/DYN/dynzdf.F90 @ 14618

Last change on this file since 14618 was 14547, checked in by techene, 3 years ago
#2605 RK3 time-stepping on OCE only (run on GYRE_PISCES without key_top)
Property svn:keywords set to `Id`
File size: 25.2 KB

Rev	Line
[456]	1	MODULE dynzdf
	2	!!==============================================================================
	3	!! * MODULE dynzdf *
	4	!! Ocean dynamics : vertical component of the momentum mixing trend
	5	!!==============================================================================
[2528]	6	!! History : 1.0 ! 2005-11 (G. Madec) Original code
	7	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[9019]	8	!! 4.0 ! 2017-06 (G. Madec) remove the explicit time-stepping option + avm at t-point
[456]	9	!!----------------------------------------------------------------------
[503]	10
	11	!!----------------------------------------------------------------------
[9019]	12	!! dyn_zdf : compute the after velocity through implicit calculation of vertical mixing
[456]	13	!!----------------------------------------------------------------------
[5836]	14	USE oce ! ocean dynamics and tracers variables
[9019]	15	USE phycst ! physical constants
[5836]	16	USE dom_oce ! ocean space and time domain variables
[9019]	17	USE sbc_oce ! surface boundary condition: ocean
[5836]	18	USE zdf_oce ! ocean vertical physics variables
[9019]	19	USE zdfdrg ! vertical physics: top/bottom drag coef.
	20	USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form
	21	USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing
[9490]	22	USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator
[5836]	23	USE trd_oce ! trends: ocean variables
	24	USE trddyn ! trend manager: dynamics
	25	!
	26	USE in_out_manager ! I/O manager
	27	USE lib_mpp ! MPP library
	28	USE prtctl ! Print control
	29	USE timing ! Timing
[456]	30
	31	IMPLICIT NONE
	32	PRIVATE
	33
[9019]	34	PUBLIC dyn_zdf ! routine called by step.F90
[456]	35
[9019]	36	REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise
[456]	37
	38	!! * Substitutions
[12377]	39	# include "do_loop_substitute.h90"
[13237]	40	# include "domzgr_substitute.h90"
[456]	41	!!----------------------------------------------------------------------
[9598]	42	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1152]	43	!! $Id$
[10068]	44	!! Software governed by the CeCILL license (see ./LICENSE)
[456]	45	!!----------------------------------------------------------------------
	46	CONTAINS
	47
[12377]	48	SUBROUTINE dyn_zdf( kt, Kbb, Kmm, Krhs, puu, pvv, Kaa )
[456]	49	!!----------------------------------------------------------------------
	50	!! * ROUTINE dyn_zdf *
	51	!!
[9019]	52	!! ** Purpose : compute the trend due to the vert. momentum diffusion
	53	!! together with the Leap-Frog time stepping using an
	54	!! implicit scheme.
	55	!!
	56	!! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing
[12377]	57	!! u(after) = u(before) + 2dt u(rhs) vector form or linear free surf.
[13237]	58	!! u(after) = ( e3u_bu(before) + 2dt * e3u_n*u(rhs) ) / e3u_after otherwise
[9019]	59	!! - update the after velocity with the implicit vertical mixing.
	60	!! This requires to solver the following system:
[13237]	61	!! u(after) = u(after) + 1/e3u_after dk+1[ mi(avm) / e3uw_after dk[ua] ]
[9019]	62	!! with the following surface/top/bottom boundary condition:
	63	!! surface: wind stress input (averaged over kt-1/2 & kt+1/2)
	64	!! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90)
	65	!!
[12377]	66	!! ** Action : (puu(:,:,:,Kaa),pvv(:,:,:,Kaa)) after velocity
[456]	67	!!---------------------------------------------------------------------
[12377]	68	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	69	INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices
	70	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[3294]	71	!
[14547]	72	INTEGER :: ji, jj, jk ! dummy loop indices
	73	INTEGER :: iku, ikv ! local integers
	74	REAL(wp) :: zzwi, ze3ua, zDt_2 ! local scalars
	75	REAL(wp) :: zzws, ze3va ! - -
	76	REAL(wp) :: z1_e3ua, z1_e3va ! - -
	77	REAL(wp) :: zWu , zWv ! - -
	78	REAL(wp) :: zWui, zWvi ! - -
	79	REAL(wp) :: zWus, zWvs ! - -
[9019]	80	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace
	81	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - -
[456]	82	!!---------------------------------------------------------------------
[3294]	83	!
[9019]	84	IF( ln_timing ) CALL timing_start('dyn_zdf')
[3294]	85	!
[9019]	86	IF( kt == nit000 ) THEN !* initialization
	87	IF(lwp) WRITE(numout,*)
	88	IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator'
	89	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ '
	90	!
	91	If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator
	92	ELSE ; r_vvl = 1._wp
	93	ENDIF
	94	ENDIF
[14547]	95	!
	96	zDt_2 = rDt * 0.5_wp
	97	!
[9250]	98	! !* explicit top/bottom drag case
[12377]	99	IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, Kmm, puu(:,:,:,Kbb), pvv(:,:,:,Kbb), puu(:,:,:,Krhs), pvv(:,:,:,Krhs) ) ! add top/bottom friction trend to (puu(Kaa),pvv(Kaa))
[9250]	100	!
	101	!
[9019]	102	IF( l_trddyn ) THEN !* temporary save of ta and sa trends
	103	ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) )
[12377]	104	ztrdu(:,:,:) = puu(:,:,:,Krhs)
	105	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
[456]	106	ENDIF
[9019]	107	!
[12377]	108	! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in puu(:,:,:,Kaa),pvv(:,:,:,Kaa))
[9019]	109	!
	110	! ! time stepping except vertical diffusion
	111	IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity
[13295]	112	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13286]	113	puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kbb) + rDt * puu(ji,jj,jk,Krhs) ) * umask(ji,jj,jk)
	114	pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kbb) + rDt * pvv(ji,jj,jk,Krhs) ) * vmask(ji,jj,jk)
	115	END_3D
[9019]	116	ELSE ! applied on thickness weighted velocity
[13295]	117	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13286]	118	puu(ji,jj,jk,Kaa) = ( e3u(ji,jj,jk,Kbb) * puu(ji,jj,jk,Kbb ) &
	119	& + rDt * e3u(ji,jj,jk,Kmm) * puu(ji,jj,jk,Krhs) ) &
	120	& / e3u(ji,jj,jk,Kaa) * umask(ji,jj,jk)
	121	pvv(ji,jj,jk,Kaa) = ( e3v(ji,jj,jk,Kbb) * pvv(ji,jj,jk,Kbb ) &
	122	& + rDt * e3v(ji,jj,jk,Kmm) * pvv(ji,jj,jk,Krhs) ) &
	123	& / e3v(ji,jj,jk,Kaa) * vmask(ji,jj,jk)
	124	END_3D
[9019]	125	ENDIF
	126	! ! add top/bottom friction
	127	! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom.
	128	! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does
	129	! not lead to the effective stress seen over the whole barotropic loop.
[12377]	130	! G. Madec : in linear free surface, e3u(:,:,:,Kaa) = e3u(:,:,:,Kmm) = e3u_0, so systematic use of e3u(:,:,:,Kaa)
[9019]	131	IF( ln_drgimp .AND. ln_dynspg_ts ) THEN
[13295]	132	DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! remove barotropic velocities
[13286]	133	puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - uu_b(ji,jj,Kaa) ) * umask(ji,jj,jk)
	134	pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - vv_b(ji,jj,Kaa) ) * vmask(ji,jj,jk)
	135	END_3D
[13497]	136	DO_2D( 0, 0, 0, 0 ) ! Add bottom/top stress due to barotropic component only
[12377]	137	iku = mbku(ji,jj) ! ocean bottom level at u- and v-points
	138	ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
[13237]	139	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) &
	140	& + r_vvl * e3u(ji,jj,iku,Kaa)
	141	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) &
	142	& + r_vvl * e3v(ji,jj,ikv,Kaa)
[14547]	143	puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + zDt_2 ( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) uu_b(ji,jj,Kaa) / ze3ua
	144	pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + zDt_2 ( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) vv_b(ji,jj,Kaa) / ze3va
[12377]	145	END_2D
[13472]	146	IF( ln_isfcav.OR.ln_drgice_imp ) THEN ! Ocean cavities (ISF)
[13295]	147	DO_2D( 0, 0, 0, 0 )
[12377]	148	iku = miku(ji,jj) ! top ocean level at u- and v-points
	149	ikv = mikv(ji,jj) ! (first wet ocean u- and v-points)
[13237]	150	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) &
	151	& + r_vvl * e3u(ji,jj,iku,Kaa)
	152	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) &
	153	& + r_vvl * e3v(ji,jj,ikv,Kaa)
[14547]	154	puu(ji,jj,iku,Kaa) = puu(ji,jj,iku,Kaa) + zDt_2 ( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) uu_b(ji,jj,Kaa) / ze3ua
	155	pvv(ji,jj,ikv,Kaa) = pvv(ji,jj,ikv,Kaa) + zDt_2 ( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) vv_b(ji,jj,Kaa) / ze3va
[12377]	156	END_2D
[9019]	157	END IF
	158	ENDIF
	159	!
	160	! !== Vertical diffusion on u ==!
	161	!
	162	! !* Matrix construction
[10364]	163	IF( ln_zad_Aimp ) THEN !!
	164	SELECT CASE( nldf_dyn )
	165	CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu)
[13295]	166	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	167	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) &
	168	& + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point
[14547]	169	zzwi = - zDt_2 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) &
[12377]	170	& / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk )
[14547]	171	zzws = - zDt_2 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) &
[12377]	172	& / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1)
	173	zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua
	174	zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua
[14547]	175	zwi(ji,jj,jk) = zzwi + zDt_2 * MIN( zWui, 0._wp )
	176	zws(ji,jj,jk) = zzws - zDt_2 * MAX( zWus, 0._wp )
	177	zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zDt_2 * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) )
[12377]	178	END_3D
[10364]	179	CASE DEFAULT ! iso-level lateral mixing
[13295]	180	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	181	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) & ! after scale factor at U-point
	182	& + r_vvl * e3u(ji,jj,jk,Kaa)
[14547]	183	zzwi = - zDt_2 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) &
[13237]	184	& / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk )
[14547]	185	zzws = - zDt_2 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) &
[13237]	186	& / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1)
[12377]	187	zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua
	188	zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua
[14547]	189	zwi(ji,jj,jk) = zzwi + zDt_2 * MIN( zWui, 0._wp )
	190	zws(ji,jj,jk) = zzws - zDt_2 * MAX( zWus, 0._wp )
	191	zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zDt_2 * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) )
[12377]	192	END_3D
[10364]	193	END SELECT
[13497]	194	DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions
[12377]	195	zwi(ji,jj,1) = 0._wp
[13237]	196	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) &
	197	& + r_vvl * e3u(ji,jj,1,Kaa)
[14547]	198	zzws = - zDt_2 * ( avm(ji+1,jj,2) + avm(ji ,jj,2) ) &
[13237]	199	& / ( ze3ua * e3uw(ji,jj,2,Kmm) ) * wumask(ji,jj,2)
[12377]	200	zWus = ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) / ze3ua
[14547]	201	zws(ji,jj,1 ) = zzws - zDt_2 * MAX( zWus, 0._wp )
	202	zwd(ji,jj,1 ) = 1._wp - zzws - zDt_2 * ( MIN( zWus, 0._wp ) )
[12377]	203	END_2D
[10364]	204	ELSE
	205	SELECT CASE( nldf_dyn )
	206	CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu)
[13295]	207	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	208	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) &
	209	& + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point
[14547]	210	zzwi = - zDt_2 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) &
[12377]	211	& / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk )
[14547]	212	zzws = - zDt_2 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) &
[12377]	213	& / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1)
	214	zwi(ji,jj,jk) = zzwi
	215	zws(ji,jj,jk) = zzws
	216	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
	217	END_3D
[10364]	218	CASE DEFAULT ! iso-level lateral mixing
[13295]	219	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	220	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,jk,Kmm) &
	221	& + r_vvl * e3u(ji,jj,jk,Kaa) ! after scale factor at U-point
[14547]	222	zzwi = - zDt_2 * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) &
[13237]	223	& / ( ze3ua * e3uw(ji,jj,jk ,Kmm) ) * wumask(ji,jj,jk )
[14547]	224	zzws = - zDt_2 * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) &
[13237]	225	& / ( ze3ua * e3uw(ji,jj,jk+1,Kmm) ) * wumask(ji,jj,jk+1)
[12377]	226	zwi(ji,jj,jk) = zzwi
	227	zws(ji,jj,jk) = zzws
	228	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
	229	END_3D
[10364]	230	END SELECT
[13497]	231	DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions
[12377]	232	zwi(ji,jj,1) = 0._wp
	233	zwd(ji,jj,1) = 1._wp - zws(ji,jj,1)
	234	END_2D
[10364]	235	ENDIF
[9019]	236	!
	237	!
	238	! !== Apply semi-implicit bottom friction ==!
	239	!
	240	! Only needed for semi-implicit bottom friction setup. The explicit
	241	! bottom friction has been included in "u(v)a" which act as the R.H.S
	242	! column vector of the tri-diagonal matrix equation
	243	!
	244	IF ( ln_drgimp ) THEN ! implicit bottom friction
[13295]	245	DO_2D( 0, 0, 0, 0 )
[12377]	246	iku = mbku(ji,jj) ! ocean bottom level at u- and v-points
[13237]	247	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) &
	248	& + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point
[14547]	249	zwd(ji,jj,iku) = zwd(ji,jj,iku) - zDt_2 *( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua
[12377]	250	END_2D
[13472]	251	IF ( ln_isfcav.OR.ln_drgice_imp ) THEN ! top friction (always implicit)
[13295]	252	DO_2D( 0, 0, 0, 0 )
[12377]	253	!!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed
	254	iku = miku(ji,jj) ! ocean top level at u- and v-points
[13237]	255	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,iku,Kmm) &
	256	& + r_vvl * e3u(ji,jj,iku,Kaa) ! after scale factor at T-point
[14547]	257	zwd(ji,jj,iku) = zwd(ji,jj,iku) - zDt_2 *( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua
[12377]	258	END_2D
[9019]	259	END IF
	260	ENDIF
	261	!
	262	! Matrix inversion starting from the first level
	263	!-----------------------------------------------------------------------
	264	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
	265	!
	266	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	267	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	268	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	269	! ( ... )( ... ) ( ... )
	270	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
	271	!
	272	! m is decomposed in the product of an upper and a lower triangular matrix
	273	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
[12377]	274	! The solution (the after velocity) is in puu(:,:,:,Kaa)
[9019]	275	!-----------------------------------------------------------------------
	276	!
[13472]	277	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
[12377]	278	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	279	END_3D
[9019]	280	!
[13472]	281	DO_2D( 0, 0, 0, 0 ) !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==!
[13237]	282	ze3ua = ( 1._wp - r_vvl ) * e3u(ji,jj,1,Kmm) &
	283	& + r_vvl * e3u(ji,jj,1,Kaa)
[14547]	284	puu(ji,jj,1,Kaa) = puu(ji,jj,1,Kaa) + zDt_2 * ( utau_b(ji,jj) + utau(ji,jj) ) &
[12489]	285	& / ( ze3ua * rho0 ) * umask(ji,jj,1)
[12377]	286	END_2D
[13295]	287	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	288	puu(ji,jj,jk,Kaa) = puu(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * puu(ji,jj,jk-1,Kaa)
	289	END_3D
[9019]	290	!
[13472]	291	DO_2D( 0, 0, 0, 0 ) !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==!
[12377]	292	puu(ji,jj,jpkm1,Kaa) = puu(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1)
	293	END_2D
[13295]	294	DO_3DS( 0, 0, 0, 0, jpk-2, 1, -1 )
[12377]	295	puu(ji,jj,jk,Kaa) = ( puu(ji,jj,jk,Kaa) - zws(ji,jj,jk) * puu(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk)
	296	END_3D
[9019]	297	!
	298	! !== Vertical diffusion on v ==!
	299	!
	300	! !* Matrix construction
[10364]	301	IF( ln_zad_Aimp ) THEN !!
	302	SELECT CASE( nldf_dyn )
	303	CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv)
[13295]	304	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	305	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) &
	306	& + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point
[14547]	307	zzwi = - zDt_2 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) &
[12377]	308	& / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk )
[14547]	309	zzws = - zDt_2 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) &
[12377]	310	& / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1)
	311	zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va
	312	zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va
[14547]	313	zwi(ji,jj,jk) = zzwi + zDt_2 * MIN( zWvi, 0._wp )
	314	zws(ji,jj,jk) = zzws - zDt_2 * MAX( zWvs, 0._wp )
	315	zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zDt_2 * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) )
[12377]	316	END_3D
[10364]	317	CASE DEFAULT ! iso-level lateral mixing
[13295]	318	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	319	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) &
	320	& + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point
[14547]	321	zzwi = - zDt_2 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) &
[13237]	322	& / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk )
[14547]	323	zzws = - zDt_2 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) &
[13237]	324	& / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1)
[12377]	325	zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va
	326	zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va
[14547]	327	zwi(ji,jj,jk) = zzwi + zDt_2 * MIN( zWvi, 0._wp )
	328	zws(ji,jj,jk) = zzws - zDt_2 * MAX( zWvs, 0._wp )
	329	zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zDt_2 * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) )
[12377]	330	END_3D
[10364]	331	END SELECT
[13472]	332	DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions
[12377]	333	zwi(ji,jj,1) = 0._wp
[13237]	334	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) &
	335	& + r_vvl * e3v(ji,jj,1,Kaa)
[14547]	336	zzws = - zDt_2 * ( avm(ji,jj+1,2) + avm(ji,jj,2) ) &
[13237]	337	& / ( ze3va * e3vw(ji,jj,2,Kmm) ) * wvmask(ji,jj,2)
[12377]	338	zWvs = ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) / ze3va
[14547]	339	zws(ji,jj,1 ) = zzws - zDt_2 * MAX( zWvs, 0._wp )
	340	zwd(ji,jj,1 ) = 1._wp - zzws - zDt_2 * ( MIN( zWvs, 0._wp ) )
[12377]	341	END_2D
[10364]	342	ELSE
	343	SELECT CASE( nldf_dyn )
	344	CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu)
[13295]	345	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	346	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) &
	347	& + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point
[14547]	348	zzwi = - zDt_2 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) &
[12377]	349	& / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk )
[14547]	350	zzws = - zDt_2 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) &
[12377]	351	& / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1)
	352	zwi(ji,jj,jk) = zzwi
	353	zws(ji,jj,jk) = zzws
	354	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
	355	END_3D
[10364]	356	CASE DEFAULT ! iso-level lateral mixing
[13295]	357	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[13237]	358	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,jk,Kmm) &
	359	& + r_vvl * e3v(ji,jj,jk,Kaa) ! after scale factor at V-point
[14547]	360	zzwi = - zDt_2 * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) &
[13237]	361	& / ( ze3va * e3vw(ji,jj,jk ,Kmm) ) * wvmask(ji,jj,jk )
[14547]	362	zzws = - zDt_2 * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) &
[13237]	363	& / ( ze3va * e3vw(ji,jj,jk+1,Kmm) ) * wvmask(ji,jj,jk+1)
[12377]	364	zwi(ji,jj,jk) = zzwi
	365	zws(ji,jj,jk) = zzws
	366	zwd(ji,jj,jk) = 1._wp - zzwi - zzws
	367	END_3D
[10364]	368	END SELECT
[13497]	369	DO_2D( 0, 0, 0, 0 ) !* Surface boundary conditions
[12377]	370	zwi(ji,jj,1) = 0._wp
	371	zwd(ji,jj,1) = 1._wp - zws(ji,jj,1)
	372	END_2D
[10364]	373	ENDIF
[9019]	374	!
	375	! !== Apply semi-implicit top/bottom friction ==!
	376	!
	377	! Only needed for semi-implicit bottom friction setup. The explicit
	378	! bottom friction has been included in "u(v)a" which act as the R.H.S
	379	! column vector of the tri-diagonal matrix equation
	380	!
	381	IF( ln_drgimp ) THEN
[13295]	382	DO_2D( 0, 0, 0, 0 )
[12377]	383	ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points)
[13237]	384	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) &
	385	& + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point
[14547]	386	zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - zDt_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va
[12377]	387	END_2D
[13472]	388	IF ( ln_isfcav.OR.ln_drgice_imp ) THEN
[13295]	389	DO_2D( 0, 0, 0, 0 )
[12377]	390	ikv = mikv(ji,jj) ! (first wet ocean u- and v-points)
[13237]	391	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,ikv,Kmm) &
	392	& + r_vvl * e3v(ji,jj,ikv,Kaa) ! after scale factor at T-point
[14547]	393	zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - zDt_2*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) / ze3va
[12377]	394	END_2D
[9019]	395	ENDIF
	396	ENDIF
[456]	397
[9019]	398	! Matrix inversion
	399	!-----------------------------------------------------------------------
	400	! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk )
[503]	401	!
[9019]	402	! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 )
	403	! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 )
	404	! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 )
	405	! ( ... )( ... ) ( ... )
	406	! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk )
[503]	407	!
[9019]	408	! m is decomposed in the product of an upper and lower triangular matrix
	409	! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi
	410	! The solution (after velocity) is in 2d array va
	411	!-----------------------------------------------------------------------
	412	!
[13472]	413	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) ==
[12377]	414	zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1)
	415	END_3D
[9019]	416	!
[13472]	417	DO_2D( 0, 0, 0, 0 ) !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==!
[13237]	418	ze3va = ( 1._wp - r_vvl ) * e3v(ji,jj,1,Kmm) &
	419	& + r_vvl * e3v(ji,jj,1,Kaa)
[14547]	420	pvv(ji,jj,1,Kaa) = pvv(ji,jj,1,Kaa) + zDt_2*( vtau_b(ji,jj) + vtau(ji,jj) ) &
[12489]	421	& / ( ze3va * rho0 ) * vmask(ji,jj,1)
[12377]	422	END_2D
[13295]	423	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	424	pvv(ji,jj,jk,Kaa) = pvv(ji,jj,jk,Kaa) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * pvv(ji,jj,jk-1,Kaa)
	425	END_3D
[9019]	426	!
[13472]	427	DO_2D( 0, 0, 0, 0 ) !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==!
[12377]	428	pvv(ji,jj,jpkm1,Kaa) = pvv(ji,jj,jpkm1,Kaa) / zwd(ji,jj,jpkm1)
	429	END_2D
[13295]	430	DO_3DS( 0, 0, 0, 0, jpk-2, 1, -1 )
[12377]	431	pvv(ji,jj,jk,Kaa) = ( pvv(ji,jj,jk,Kaa) - zws(ji,jj,jk) * pvv(ji,jj,jk+1,Kaa) ) / zwd(ji,jj,jk)
	432	END_3D
[9019]	433	!
[503]	434	IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics
[14547]	435	ztrdu(:,:,:) = ( puu(:,:,:,Kaa) - puu(:,:,:,Kbb) )*r1_Dt - ztrdu(:,:,:)
	436	ztrdv(:,:,:) = ( pvv(:,:,:,Kaa) - pvv(:,:,:,Kbb) )*r1_Dt - ztrdv(:,:,:)
[12377]	437	CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt, Kmm )
[9019]	438	DEALLOCATE( ztrdu, ztrdv )
[456]	439	ENDIF
	440	! ! print mean trends (used for debugging)
[12377]	441	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Kaa), clinfo1=' zdf - Ua: ', mask1=umask, &
	442	& tab3d_2=pvv(:,:,:,Kaa), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
[5836]	443	!
[9019]	444	IF( ln_timing ) CALL timing_stop('dyn_zdf')
[503]	445	!
[456]	446	END SUBROUTINE dyn_zdf
	447
	448	!!==============================================================================
	449	END MODULE dynzdf

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