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limthd_dh.F90 in branches/2012/dev_r3385_NOCS04_HAMF/NEMOGCM/NEMO/LIM_SRC_3 – NEMO

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source: branches/2012/dev_r3385_NOCS04_HAMF/NEMOGCM/NEMO/LIM_SRC_3/limthd_dh.F90 @ 3524

Last change on this file since 3524 was 3524, checked in by gm, 12 years ago
Branch: dev_r3385_NOCS04_HAMF; #665. add USE lib_fortran when SIGN is used (TOP,OPA,LIM2&3) ; salt flux names start with sfx_ in LIM3
Property svn:keywords set to `Id`
File size: 34.7 KB

Rev	Line
[825]	1	MODULE limthd_dh
[1572]	2	!!======================================================================
	3	!! * MODULE limthd_dh *
	4	!! LIM-3 : thermodynamic growth and decay of the ice
	5	!!======================================================================
	6	!! History : LIM ! 2003-05 (M. Vancoppenolle) Original code in 1D
	7	!! ! 2005-06 (M. Vancoppenolle) 3D version
	8	!! 3.2 ! 2009-07 (M. Vancoppenolle, Y. Aksenov, G. Madec) bug correction in rdmsnif & rdmicif
[3517]	9	!! 3.4 ! 2011-02 (G. Madec) dynamical allocation
	10	!! 3.5 ! 2012-10 (G. Madec & co) salt flux + bug fixes
[1572]	11	!!----------------------------------------------------------------------
[825]	12	#if defined key_lim3
[834]	13	!!----------------------------------------------------------------------
	14	!! 'key_lim3' LIM3 sea-ice model
	15	!!----------------------------------------------------------------------
[3524]	16	!! lim_thd_dh : vertical accr./abl. and lateral ablation of sea ice
[825]	17	!!----------------------------------------------------------------------
[3524]	18	USE par_oce ! ocean parameters
	19	USE phycst ! physical constants (OCE directory)
	20	USE sbc_oce ! Surface boundary condition: ocean fields
	21	USE ice ! LIM variables
	22	USE par_ice ! LIM parameters
	23	USE thd_ice ! LIM thermodynamics
	24	USE in_out_manager ! I/O manager
	25	USE lib_mpp ! MPP library
	26	USE wrk_nemo ! work arrays
	27	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[921]	28
[825]	29	IMPLICIT NONE
	30	PRIVATE
	31
[1572]	32	PUBLIC lim_thd_dh ! called by lim_thd
[825]	33
[1572]	34	REAL(wp) :: epsi20 = 1e-20 ! constant values
	35	REAL(wp) :: epsi13 = 1e-13 !
	36	REAL(wp) :: epsi16 = 1e-16 !
	37	REAL(wp) :: zzero = 0.e0 !
	38	REAL(wp) :: zone = 1.e0 !
[825]	39
	40	!!----------------------------------------------------------------------
[3524]	41	!! NEMO/LIM3 3.4 , UCL - NEMO Consortium (2011)
[1156]	42	!! $Id$
[2715]	43	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[825]	44	!!----------------------------------------------------------------------
	45	CONTAINS
	46
[2715]	47	SUBROUTINE lim_thd_dh( kideb, kiut, jl )
[921]	48	!!------------------------------------------------------------------
	49	!! * ROUTINE lim_thd_dh *
	50	!!
[1572]	51	!! ** Purpose : determines variations of ice and snow thicknesses.
[921]	52	!!
[1572]	53	!! ** Method : Ice/Snow surface melting arises from imbalance in surface fluxes
	54	!! Bottom accretion/ablation arises from flux budget
	55	!! Snow thickness can increase by precipitation and decrease by sublimation
	56	!! If snow load excesses Archmiede limit, snow-ice is formed by
	57	!! the flooding of sea-water in the snow
[921]	58	!!
[1572]	59	!! 1) Compute available flux of heat for surface ablation
	60	!! 2) Compute snow and sea ice enthalpies
	61	!! 3) Surface ablation and sublimation
	62	!! 4) Bottom accretion/ablation
	63	!! 5) Case of Total ablation
	64	!! 6) Snow ice formation
[921]	65	!!
[1572]	66	!! References : Bitz and Lipscomb, 1999, J. Geophys. Res.
	67	!! Fichefet T. and M. Maqueda 1997, J. Geophys. Res., 102(C6), 12609-12646
	68	!! Vancoppenolle, Fichefet and Bitz, 2005, Geophys. Res. Let.
	69	!! Vancoppenolle et al.,2009, Ocean Modelling
[921]	70	!!------------------------------------------------------------------
[1572]	71	INTEGER , INTENT(in) :: kideb, kiut ! Start/End point on which the the computation is applied
	72	INTEGER , INTENT(in) :: jl ! Thickness cateogry number
	73	!!
	74	INTEGER :: ji , jk ! dummy loop indices
[3517]	75	INTEGER :: ii, ij ! 2D corresponding indices to ji
[1572]	76	INTEGER :: isnow ! switch for presence (1) or absence (0) of snow
	77	INTEGER :: isnowic ! snow ice formation not
	78	INTEGER :: i_ice_switch ! ice thickness above a certain treshold or not
	79	INTEGER :: iter
[825]	80
[2715]	81	REAL(wp) :: zzfmass_i, zihgnew ! local scalar
	82	REAL(wp) :: zzfmass_s, zhsnew, ztmelts ! local scalar
[1572]	83	REAL(wp) :: zhn, zdhcf, zdhbf, zhni, zhnfi, zihg !
[2715]	84	REAL(wp) :: zdhnm, zhnnew, zhisn, zihic, zzc !
[1572]	85	REAL(wp) :: zfracs ! fractionation coefficient for bottom salt entrapment
	86	REAL(wp) :: zds ! increment of bottom ice salinity
	87	REAL(wp) :: zcoeff ! dummy argument for snowfall partitioning over ice and leads
	88	REAL(wp) :: zsm_snowice ! snow-ice salinity
	89	REAL(wp) :: zswi1 ! switch for computation of bottom salinity
	90	REAL(wp) :: zswi12 ! switch for computation of bottom salinity
	91	REAL(wp) :: zswi2 ! switch for computation of bottom salinity
	92	REAL(wp) :: zgrr ! bottom growth rate
	93	REAL(wp) :: ztform ! bottom formation temperature
[2715]	94	!
[3294]	95	REAL(wp), POINTER, DIMENSION(:) :: zh_i ! ice layer thickness
	96	REAL(wp), POINTER, DIMENSION(:) :: zh_s ! snow layer thickness
	97	REAL(wp), POINTER, DIMENSION(:) :: ztfs ! melting point
	98	REAL(wp), POINTER, DIMENSION(:) :: zhsold ! old snow thickness
	99	REAL(wp), POINTER, DIMENSION(:) :: zqprec ! energy of fallen snow
	100	REAL(wp), POINTER, DIMENSION(:) :: zqfont_su ! incoming, remaining surface energy
	101	REAL(wp), POINTER, DIMENSION(:) :: zqfont_bo ! incoming, bottom energy
	102	REAL(wp), POINTER, DIMENSION(:) :: z_f_surf ! surface heat for ablation
	103	REAL(wp), POINTER, DIMENSION(:) :: zhgnew ! new ice thickness
	104	REAL(wp), POINTER, DIMENSION(:) :: zfmass_i !
	105
[3524]	106	REAL(wp), POINTER, DIMENSION(:) :: zdh_s_mel ! snow melt
	107	REAL(wp), POINTER, DIMENSION(:) :: zdh_s_pre ! snow precipitation
	108	REAL(wp), POINTER, DIMENSION(:) :: zdh_s_sub ! snow sublimation
	109	REAL(wp), POINTER, DIMENSION(:) :: zsfx_melt ! salt flux due to ice melt
[3294]	110
	111	REAL(wp), POINTER, DIMENSION(:,:) :: zdeltah
	112
	113	! Pathological cases
	114	REAL(wp), POINTER, DIMENSION(:) :: zfdt_init ! total incoming heat for ice melt
	115	REAL(wp), POINTER, DIMENSION(:) :: zfdt_final ! total remaing heat for ice melt
	116	REAL(wp), POINTER, DIMENSION(:) :: zqt_i ! total ice heat content
	117	REAL(wp), POINTER, DIMENSION(:) :: zqt_s ! total snow heat content
	118	REAL(wp), POINTER, DIMENSION(:) :: zqt_dummy ! dummy heat content
	119
	120	REAL(wp), POINTER, DIMENSION(:,:) :: zqt_i_lay ! total ice heat content
	121
	122	! Heat conservation
	123	INTEGER :: num_iter_max, numce_dh
	124	REAL(wp) :: meance_dh
	125	REAL(wp), POINTER, DIMENSION(:) :: zinnermelt
	126	REAL(wp), POINTER, DIMENSION(:) :: zfbase, zdq_i
[1572]	127	!!------------------------------------------------------------------
[825]	128
[3294]	129	CALL wrk_alloc( jpij, zh_i, zh_s, ztfs, zhsold, zqprec, zqfont_su, zqfont_bo, z_f_surf, zhgnew, zfmass_i )
[3524]	130	CALL wrk_alloc( jpij, zdh_s_mel, zdh_s_pre, zdh_s_sub, zsfx_melt, zfdt_init, zfdt_final, zqt_i, zqt_s, zqt_dummy )
[3294]	131	CALL wrk_alloc( jpij, zinnermelt, zfbase, zdq_i )
	132	CALL wrk_alloc( jpij, jkmax, zdeltah, zqt_i_lay )
[825]	133
[3524]	134	zsfx_melt (:) = 0._wp
	135	ftotal_fin(:) = 0._wp
	136	zfdt_init (:) = 0._wp
	137	zfdt_final(:) = 0._wp
[2715]	138
[825]	139	DO ji = kideb, kiut
	140	old_ht_i_b(ji) = ht_i_b(ji)
	141	old_ht_s_b(ji) = ht_s_b(ji)
	142	END DO
[921]	143	!
	144	!------------------------------------------------------------------------------!
	145	! 1) Calculate available heat for surface ablation !
	146	!------------------------------------------------------------------------------!
	147	!
[2715]	148	DO ji = kideb, kiut
[3517]	149	isnow = INT( 1.0 - MAX( 0.0 , SIGN( 1.0 , - ht_s_b(ji) ) ) )
	150	ztfs (ji) = isnow * rtt + ( 1.0 - isnow ) * rtt
	151	z_f_surf (ji) = qnsr_ice_1d(ji) + ( 1.0 - i0(ji) ) * qsr_ice_1d(ji) - fc_su(ji)
	152	z_f_surf (ji) = MAX( zzero , z_f_surf(ji) ) * MAX( zzero , SIGN( zone , t_su_b(ji) - ztfs(ji) ) )
[1572]	153	zfdt_init(ji) = ( z_f_surf(ji) + MAX( fbif_1d(ji) + qlbbq_1d(ji) + fc_bo_i(ji),0.0 ) ) * rdt_ice
[825]	154	END DO ! ji
	155
[2715]	156	zqfont_su (:) = 0._wp
	157	zqfont_bo (:) = 0._wp
	158	dsm_i_se_1d(:) = 0._wp
	159	dsm_i_si_1d(:) = 0._wp
[921]	160	!
	161	!------------------------------------------------------------------------------!
	162	! 2) Computing layer thicknesses and snow and sea-ice enthalpies. !
	163	!------------------------------------------------------------------------------!
	164	!
[2715]	165	DO ji = kideb, kiut ! Layer thickness
[825]	166	zh_i(ji) = ht_i_b(ji) / nlay_i
	167	zh_s(ji) = ht_s_b(ji) / nlay_s
	168	END DO
[2715]	169	!
	170	zqt_s(:) = 0._wp ! Total enthalpy of the snow
[825]	171	DO jk = 1, nlay_s
[2715]	172	DO ji = kideb, kiut
[1572]	173	zqt_s(ji) = zqt_s(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s
[825]	174	END DO
	175	END DO
[2715]	176	!
	177	zqt_i(:) = 0._wp ! Total enthalpy of the ice
[825]	178	DO jk = 1, nlay_i
[2715]	179	DO ji = kideb, kiut
	180	zzc = q_i_b(ji,jk) * ht_i_b(ji) / nlay_i
	181	zqt_i(ji) = zqt_i(ji) + zzc
	182	zqt_i_lay(ji,jk) = zzc
[825]	183	END DO
	184	END DO
[921]	185	!
	186	!------------------------------------------------------------------------------\|
	187	! 3) Surface ablation and sublimation \|
	188	!------------------------------------------------------------------------------\|
	189	!
[834]	190	!-------------------------
	191	! 3.1 Snow precips / melt
	192	!-------------------------
[825]	193	! Snow accumulation in one thermodynamic time step
	194	! snowfall is partitionned between leads and ice
	195	! if snow fall was uniform, a fraction (1-at_i) would fall into leads
	196	! but because of the winds, more snow falls on leads than on sea ice
	197	! and a greater fraction (1-at_i)^beta of the total mass of snow
[834]	198	! (beta < 1) falls in leads.
[825]	199	! In reality, beta depends on wind speed,
	200	! and should decrease with increasing wind speed but here, it is
[834]	201	! considered as a constant. an average value is 0.66
[825]	202	! Martin Vancoppenolle, December 2006
	203
	204	! Snow fall
	205	DO ji = kideb, kiut
	206	zcoeff = ( 1.0 - ( 1.0 - at_i_b(ji) )**betas ) / at_i_b(ji)
	207	zdh_s_pre(ji) = zcoeff * sprecip_1d(ji) * rdt_ice / rhosn
	208	END DO
[2715]	209	zdh_s_mel(:) = 0._wp
[825]	210
	211	! Melt of fallen snow
	212	DO ji = kideb, kiut
	213	! tatm_ice is now in K
[1572]	214	zqprec (ji) = rhosn * ( cpic * ( rtt - tatm_ice_1d(ji) ) + lfus )
	215	zqfont_su(ji) = z_f_surf(ji) * rdt_ice
	216	zdeltah (ji,1) = MIN( 0.e0 , - zqfont_su(ji) / MAX( zqprec(ji) , epsi13 ) )
	217	zqfont_su(ji) = MAX( 0.e0 , - zdh_s_pre(ji) - zdeltah(ji,1) ) * zqprec(ji)
	218	zdeltah (ji,1) = MAX( - zdh_s_pre(ji) , zdeltah(ji,1) )
	219	zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,1)
[825]	220	! heat conservation
[1572]	221	qt_s_in(ji,jl) = qt_s_in(ji,jl) + zqprec(ji) * zdh_s_pre(ji)
	222	zqt_s (ji) = zqt_s (ji) + zqprec(ji) * zdh_s_pre(ji)
	223	zqt_s (ji) = MAX( zqt_s(ji) - zqfont_su(ji) , 0.e0 )
[825]	224	END DO
	225
	226
	227	! Snow melt due to surface heat imbalance
	228	DO jk = 1, nlay_s
	229	DO ji = kideb, kiut
[1572]	230	zdeltah (ji,jk) = - zqfont_su(ji) / q_s_b(ji,jk)
	231	zqfont_su(ji) = MAX( 0.0 , - zh_s(ji) - zdeltah(ji,jk) ) * q_s_b(ji,jk)
	232	zdeltah (ji,jk) = MAX( zdeltah(ji,jk) , - zh_s(ji) )
	233	zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,jk) ! resulting melt of snow
[825]	234	END DO
	235	END DO
	236
	237	! Apply snow melt to snow depth
	238	DO ji = kideb, kiut
	239	dh_s_tot(ji) = zdh_s_mel(ji) + zdh_s_pre(ji)
	240	! Old and new snow depths
	241	zhsold(ji) = ht_s_b(ji)
	242	zhsnew = ht_s_b(ji) + dh_s_tot(ji)
	243	! If snow is still present zhn = 1, else zhn = 0
[3517]	244	zhn = 1.0 - MAX( zzero , SIGN( zone , - zhsnew ) )
[825]	245	ht_s_b(ji) = MAX( zzero , zhsnew )
	246	! Volume and mass variations of snow
[3517]	247	dvsbq_1d (ji) = a_i_b(ji) * ( ht_s_b(ji) - zhsold(ji) - zdh_s_pre(ji) )
[1572]	248	dvsbq_1d (ji) = MIN( zzero, dvsbq_1d(ji) )
[3517]	249	rdm_snw_1d(ji) = rdm_snw_1d(ji) + rhosn * dvsbq_1d(ji)
[825]	250	END DO ! ji
	251
[834]	252	!--------------------------
	253	! 3.2 Surface ice ablation
	254	!--------------------------
[825]	255	DO ji = kideb, kiut
[2715]	256	dh_i_surf(ji) = 0._wp
[3517]	257	z_f_surf (ji) = zqfont_su(ji) * r1_rdtice ! heat conservation test
[2715]	258	zdq_i (ji) = 0._wp
[825]	259	END DO ! ji
	260
	261	DO jk = 1, nlay_i
	262	DO ji = kideb, kiut
[1572]	263	! ! melt of layer jk
	264	zdeltah (ji,jk) = - zqfont_su(ji) / q_i_b(ji,jk)
	265	! ! recompute heat available
[3517]	266	zqfont_su(ji ) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
[1572]	267	! ! melt of layer jk cannot be higher than its thickness
	268	zdeltah (ji,jk) = MAX( zdeltah(ji,jk) , - zh_i(ji) )
	269	! ! update surface melt
[3517]	270	dh_i_surf(ji ) = dh_i_surf(ji) + zdeltah(ji,jk)
[1572]	271	! ! for energy conservation
[3517]	272	zdq_i (ji ) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) * r1_rdtice
[1572]	273	!
[3517]	274	! ! contribution to ice-ocean salt flux
[3524]	275	zsfx_melt(ji) = zsfx_melt(ji) - sm_i_b(ji) * a_i_b(ji) * MIN( zdeltah(ji,jk) , 0._wp ) * rhoic * r1_rdtice
[1572]	276	END DO
	277	END DO
[825]	278
[1572]	279	! !-------------------
	280	IF( con_i ) THEN ! Conservation test
	281	! !-------------------
	282	numce_dh = 0
[2715]	283	meance_dh = 0._wp
[921]	284	DO ji = kideb, kiut
	285	IF ( ( z_f_surf(ji) + zdq_i(ji) ) .GE. 1.0e-3 ) THEN
	286	numce_dh = numce_dh + 1
	287	meance_dh = meance_dh + z_f_surf(ji) + zdq_i(ji)
	288	ENDIF
[1572]	289	IF( z_f_surf(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN!
[921]	290	WRITE(numout,*) ' ALERTE heat loss for surface melt '
[3517]	291	WRITE(numout,*) ' ii, ij, jl :', ii, ij, jl
[2715]	292	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	293	WRITE(numout,*) ' z_f_surf : ', z_f_surf(ji)
	294	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	295	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	296	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	297	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	298	WRITE(numout,*) ' qlbbq_1d : ', qlbbq_1d(ji)
	299	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
[3517]	300	WRITE(numout,*) ' sss_m : ', sss_m(ii,ij)
[921]	301	ENDIF
[1572]	302	END DO
	303	!
	304	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	305	WRITE(numout,*) ' Error report - Category : ', jl
	306	WRITE(numout,*) ' ~~~~~~~~~~~~ '
	307	WRITE(numout,*) ' Number of points where there is sur. me. error : ', numce_dh
	308	WRITE(numout,*) ' Mean basal growth error on error points : ', meance_dh
[1572]	309	!
	310	ENDIF
[825]	311
[834]	312	!----------------------
	313	! 3.3 Snow sublimation
	314	!----------------------
[825]	315
	316	DO ji = kideb, kiut
	317	! if qla is positive (upwards), heat goes to the atmosphere, therefore
	318	! snow sublimates, if qla is negative (downwards), snow condensates
[1572]	319	zdh_s_sub(ji) = - parsub * qla_ice_1d(ji) / ( rhosn * lsub ) * rdt_ice
	320	dh_s_tot (ji) = dh_s_tot(ji) + zdh_s_sub(ji)
	321	zdhcf = ht_s_b(ji) + zdh_s_sub(ji)
	322	ht_s_b (ji) = MAX( zzero , zdhcf )
[825]	323	! we recompute dh_s_tot
[1572]	324	dh_s_tot (ji) = ht_s_b(ji) - zhsold(ji)
	325	qt_s_in (ji,jl) = qt_s_in(ji,jl) + zdh_s_sub(ji)*q_s_b(ji,1)
	326	END DO
[825]	327
[1572]	328	zqt_dummy(:) = 0.e0
[825]	329	DO jk = 1, nlay_s
	330	DO ji = kideb,kiut
[1572]	331	q_s_b (ji,jk) = rhosn * ( cpic * ( rtt - t_s_b(ji,jk) ) + lfus )
	332	zqt_dummy(ji) = zqt_dummy(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s ! heat conservation
[825]	333	END DO
	334	END DO
	335
[1572]	336	DO jk = 1, nlay_s
	337	DO ji = kideb, kiut
	338	! In case of disparition of the snow, we have to update the snow temperatures
[3517]	339	zhisn = MAX( zzero , SIGN( zone, - ht_s_b(ji) ) )
[825]	340	t_s_b(ji,jk) = ( 1.0 - zhisn ) * t_s_b(ji,jk) + zhisn * rtt
	341	q_s_b(ji,jk) = ( 1.0 - zhisn ) * q_s_b(ji,jk)
	342	END DO
[921]	343	END DO
[825]	344
[921]	345	!
	346	!------------------------------------------------------------------------------!
	347	! 4) Basal growth / melt !
	348	!------------------------------------------------------------------------------!
	349	!
[825]	350	! Ice basal growth / melt is given by the ratio of heat budget over basal
	351	! ice heat content. Basal heat budget is given by the difference between
	352	! the inner conductive flux (fc_bo_i), from the open water heat flux
	353	! (qlbbqb) and the turbulent ocean flux (fbif).
[834]	354	! fc_bo_i is positive downwards. fbif and qlbbq are positive to the ice
[825]	355
[834]	356	!-----------------------------------------------------
	357	! 4.1 Basal growth - (a) salinity not varying in time
	358	!-----------------------------------------------------
[3517]	359	IF( num_sal /= 2 ) THEN ! ice salinity constant in time
[825]	360	DO ji = kideb, kiut
[3517]	361	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) < 0._wp ) THEN
[825]	362	s_i_new(ji) = sm_i_b(ji)
	363	! Melting point in K
	364	ztmelts = - tmut * s_i_new(ji) + rtt
	365	! New ice heat content (Bitz and Lipscomb, 1999)
	366	ztform = t_i_b(ji,nlay_i) ! t_bo_b crashes in the
[921]	367	! Baltic
[1572]	368	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - ztform ) &
	369	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( ztform - rtt ) ) &
	370	& - rcp * ( ztmelts - rtt ) )
[825]	371	! Basal growth rate = - F*dt / q
[3517]	372	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[1572]	373	ENDIF
	374	END DO
	375	ENDIF
[825]	376
[834]	377	!-------------------------------------------------
	378	! 4.1 Basal growth - (b) salinity varying in time
	379	!-------------------------------------------------
[3517]	380	IF( num_sal == 2 ) THEN
	381	! the growth rate (dh_i_bott) is function of the new ice heat content (q_i_b(nlay_i+1)).
	382	! q_i_b depends on the new ice salinity (snewice).
	383	! snewice depends on dh_i_bott ; it converges quickly, so, no problem
[834]	384	! See Vancoppenolle et al., OM08 for more info on this
[825]	385
	386	! Initial value (tested 1D, can be anything between 1 and 20)
	387	num_iter_max = 4
[1572]	388	s_i_new(:) = 4.0
[825]	389
	390	! Iterative procedure
	391	DO iter = 1, num_iter_max
	392	DO ji = kideb, kiut
[1572]	393	IF( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) < 0.e0 ) THEN
[3517]	394	ii = MOD( npb(ji) - 1, jpi ) + 1
	395	ij = ( npb(ji) - 1 ) / jpi + 1
[825]	396	! Melting point in K
	397	ztmelts = - tmut * s_i_new(ji) + rtt
	398	! New ice heat content (Bitz and Lipscomb, 1999)
[1572]	399	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) &
	400	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( t_bo_b(ji) - rtt ) ) &
	401	& - rcp * ( ztmelts-rtt ) )
[825]	402	! Bottom growth rate = - F*dt / q
[1572]	403	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[825]	404	! New ice salinity ( Cox and Weeks, JGR, 1988 )
	405	! zswi2 (1) if dh_i_bott/rdt .GT. 3.6e-7
	406	! zswi12 (1) if dh_i_bott/rdt .LT. 3.6e-7 and .GT. 2.0e-8
	407	! zswi1 (1) if dh_i_bott/rdt .LT. 2.0e-8
[3517]	408	zgrr = MIN( 1.0e-3, MAX ( dh_i_bott(ji) * r1_rdtice , epsi13 ) )
[825]	409	zswi2 = MAX( zzero , SIGN( zone , zgrr - 3.6e-7 ) )
	410	zswi12 = MAX( zzero , SIGN( zone , zgrr - 2.0e-8 ) ) * ( 1.0 - zswi2 )
	411	zswi1 = 1. - zswi2 * zswi12
[1572]	412	zfracs = zswi1 * 0.12 + zswi12 * ( 0.8925 + 0.0568 * LOG( 100.0 * zgrr ) ) &
	413	& + zswi2 * 0.26 / ( 0.26 + 0.74 * EXP ( - 724300.0 * zgrr ) )
[3517]	414	zds = zfracs * sss_m(ii,ij) - s_i_new(ji)
	415	s_i_new(ji) = zfracs * sss_m(ii,ij)
[825]	416	ENDIF ! fc_bo_i
	417	END DO ! ji
	418	END DO ! iter
	419
	420	! Final values
	421	DO ji = kideb, kiut
[1572]	422	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .LT. 0.0 ) THEN
[825]	423	! New ice salinity must not exceed 15 psu
	424	s_i_new(ji) = MIN( s_i_new(ji), s_i_max )
	425	! Metling point in K
	426	ztmelts = - tmut * s_i_new(ji) + rtt
	427	! New ice heat content (Bitz and Lipscomb, 1999)
[1572]	428	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) &
	429	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( t_bo_b(ji) - rtt ) ) &
	430	& - rcp * ( ztmelts - rtt ) )
[825]	431	! Basal growth rate = - F*dt / q
[3517]	432	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[834]	433	! Salinity update
[825]	434	! entrapment during bottom growth
[1572]	435	dsm_i_se_1d(ji) = ( s_i_new(ji) * dh_i_bott(ji) + sm_i_b(ji) * ht_i_b(ji) ) &
	436	& / MAX( ht_i_b(ji) + dh_i_bott(ji) ,epsi13 ) - sm_i_b(ji)
[825]	437	ENDIF ! heat budget
[1572]	438	END DO
	439	ENDIF
[825]	440
[834]	441	!----------------
	442	! 4.2 Basal melt
	443	!----------------
[2715]	444	meance_dh = 0._wp
[1572]	445	numce_dh = 0
[2715]	446	zinnermelt(:) = 0._wp
[825]	447
	448	DO ji = kideb, kiut
	449	! heat convergence at the surface > 0
[2715]	450	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0._wp ) THEN
[825]	451	s_i_new(ji) = s_i_b(ji,nlay_i)
	452	zqfont_bo(ji) = rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) )
[3517]	453	zfbase(ji) = zqfont_bo(ji) * r1_rdtice ! heat conservation test
[2715]	454	zdq_i(ji) = 0._wp
	455	dh_i_bott(ji) = 0._wp
[825]	456	ENDIF
	457	END DO
	458
	459	DO jk = nlay_i, 1, -1
	460	DO ji = kideb, kiut
[3517]	461	IF( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) >= 0._wp ) THEN
	462	ztmelts = - tmut * s_i_b(ji,jk) + rtt
	463	IF( t_i_b(ji,jk) >= ztmelts ) THEN !!gm : a comment is needed
	464	zdeltah (ji,jk) = - zh_i(ji)
	465	dh_i_bott (ji ) = dh_i_bott(ji) + zdeltah(ji,jk)
	466	zinnermelt(ji ) = 1._wp
	467	ELSE ! normal ablation
	468	zdeltah (ji,jk) = - zqfont_bo(ji) / q_i_b(ji,jk)
	469	zqfont_bo(ji ) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
	470	zdeltah (ji,jk) = MAX(zdeltah(ji,jk), - zh_i(ji) )
	471	dh_i_bott(ji ) = dh_i_bott(ji) + zdeltah(ji,jk)
	472	zdq_i (ji ) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) * r1_rdtice
[825]	473	ENDIF
[3517]	474	! contribution to salt flux
[3524]	475	zsfx_melt(ji) = zsfx_melt(ji) - sm_i_b(ji) * a_i_b(ji) * MIN( zdeltah(ji,jk) , 0._wp ) * rhoic * r1_rdtice
[825]	476	ENDIF
	477	END DO ! ji
	478	END DO ! jk
	479
[1572]	480	! !-------------------
	481	IF( con_i ) THEN ! Conservation test
	482	! !-------------------
[921]	483	DO ji = kideb, kiut
[1572]	484	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0.e0 ) THEN
	485	IF( ( zfbase(ji) + zdq_i(ji) ) >= 1.e-3 ) THEN
	486	numce_dh = numce_dh + 1
[921]	487	meance_dh = meance_dh + zfbase(ji) + zdq_i(ji)
	488	ENDIF
	489	IF ( zfbase(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN
[3517]	490	WRITE(numout,*) ' ALERTE heat loss for basal melt : ii, ij, jl :', ii, ij, jl
[2715]	491	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	492	WRITE(numout,*) ' zfbase : ', zfbase(ji)
	493	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	494	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	495	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	496	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	497	WRITE(numout,*) ' qlbbq_1d : ', qlbbq_1d(ji)
	498	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
[3517]	499	WRITE(numout,*) ' sss_m : ', sss_m(ii,ij)
[921]	500	WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji)
[2715]	501	WRITE(numout,*) ' innermelt : ', INT( zinnermelt(ji) )
[921]	502	ENDIF
[1572]	503	ENDIF
	504	END DO
	505	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	506	WRITE(numout,*) ' Number of points where there is bas. me. error : ', numce_dh
	507	WRITE(numout,*) ' Mean basal melt error on error points : ', meance_dh
	508	WRITE(numout,*) ' Remaining bottom heat : ', zqfont_bo(jiindex_1d)
[1572]	509	!
	510	ENDIF
[825]	511
[921]	512	!
	513	!------------------------------------------------------------------------------!
	514	! 5) Pathological cases !
	515	!------------------------------------------------------------------------------!
	516	!
[834]	517	!----------------------------------------------
	518	! 5.1 Excessive ablation in a 1-category model
	519	!----------------------------------------------
[825]	520
	521	DO ji = kideb, kiut
[1572]	522	! ! in a 1-category sea ice model, bottom ablation must not exceed hmelt (-0.15)
	523	IF( jpl == 1 ) THEN ; zdhbf = MAX( hmelt , dh_i_bott(ji) )
	524	ELSE ; zdhbf = dh_i_bott(ji)
	525	ENDIF
	526	! ! excessive energy is sent to lateral ablation
	527	fsup (ji) = rhoic * lfus * at_i_b(ji) / MAX( 1.0 - at_i_b(ji) , epsi13 ) &
[3517]	528	& * ( zdhbf - dh_i_bott(ji) ) * r1_rdtice
[825]	529	dh_i_bott(ji) = zdhbf
[1572]	530	! !since ice volume is only used for outputs, we keep it global for all categories
	531	dvbbq_1d (ji) = a_i_b(ji) * dh_i_bott(ji)
	532	! !new ice thickness
	533	zhgnew (ji) = ht_i_b(ji) + dh_i_surf(ji) + dh_i_bott(ji)
	534	! ! diagnostic ( bottom ice growth )
[3517]	535	ii = MOD( npb(ji) - 1, jpi ) + 1
	536	ij = ( npb(ji) - 1 ) / jpi + 1
	537	diag_bot_gr(ii,ij) = diag_bot_gr(ii,ij) + MAX(dh_i_bott(ji),0.0)a_i_b(ji) r1_rdtice
	538	diag_sur_me(ii,ij) = diag_sur_me(ii,ij) + MIN(dh_i_surf(ji),0.0)a_i_b(ji) r1_rdtice
	539	diag_bot_me(ii,ij) = diag_bot_me(ii,ij) + MIN(dh_i_bott(ji),0.0)a_i_b(ji) r1_rdtice
[825]	540	END DO
	541
[834]	542	!-----------------------------------
	543	! 5.2 More than available ice melts
	544	!-----------------------------------
[3517]	545	! then heat applied minus heat content at previous time step should equal heat remaining
[825]	546	!
	547	DO ji = kideb, kiut
	548	! Adapt the remaining energy if too much ice melts
	549	!--------------------------------------------------
[3517]	550	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) ! =1 if ice
[825]	551	! 0 if no more ice
[1572]	552	zhgnew (ji) = zihgnew * zhgnew(ji) ! ice thickness is put to 0
[825]	553	! remaining heat
[834]	554	zfdt_final(ji) = ( 1.0 - zihgnew ) * ( zqfont_su(ji) + zqfont_bo(ji) )
[825]	555
	556	! If snow remains, energy is used to melt snow
[1572]	557	zhni = ht_s_b(ji) ! snow depth at previous time step
[3517]	558	zihg = MAX( zzero , SIGN ( zone , - ht_s_b(ji) ) ) ! =0 if snow
[825]	559
	560	! energy of melting of remaining snow
[1572]	561	zqt_s(ji) = ( 1. - zihg ) * zqt_s(ji) / MAX( zhni, epsi13 )
	562	zdhnm = - ( 1. - zihg ) * ( 1. - zihgnew ) * zfdt_final(ji) / MAX( zqt_s(ji) , epsi13 )
[3517]	563	zhnfi = zhni + zdhnm
[1572]	564	zfdt_final(ji) = MAX( zfdt_final(ji) + zqt_s(ji) * zdhnm , 0.0 )
[825]	565	ht_s_b(ji) = MAX( zzero , zhnfi )
	566	zqt_s(ji) = zqt_s(ji) * ht_s_b(ji)
	567
	568	! Mass variations of ice and snow
	569	!---------------------------------
[1572]	570	! ! mass variation of the jl category
[1571]	571	zzfmass_s = - a_i_b(ji) * ( zhni - ht_s_b(ji) ) * rhosn ! snow
	572	zzfmass_i = a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic ! ice
	573	!
	574	zfmass_i(ji) = zzfmass_i ! ice variation saved to compute salt flux (see below)
	575	!
	576	! ! mass variation cumulated over category
[3517]	577	rdm_snw_1d(ji) = rdm_snw_1d(ji) + zzfmass_s ! snow
	578	rdm_ice_1d(ji) = rdm_ice_1d(ji) + zzfmass_i ! ice
[825]	579
	580	! Remaining heat to the ocean
	581	!---------------------------------
[3517]	582	focea(ji) = - zfdt_final(ji) * r1_rdtice ! focea is in W.m-2 * dt
[825]	583
	584	END DO
	585
[3517]	586	ftotal_fin (:) = zfdt_final(:) * r1_rdtice
[825]	587
	588	!---------------------------
	589	! Salt flux and heat fluxes
	590	!---------------------------
	591	DO ji = kideb, kiut
[3517]	592	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) ! =1 if ice
	593	!
[825]	594	! Salt flux
[3524]	595	sfx_thd_1d(ji) = sfx_thd_1d(ji) + zihgnew * zsfx_melt(ji) &
	596	& - (1.0 - zihgnew) * zfmass_i (ji) * sm_i_b(ji) ) * r1_rdtice
[3517]	597	!
[825]	598	! Heat flux
	599	! excessive bottom ablation energy (fsup) - 0 except if jpl = 1
[3517]	600	! excessive total ablation energy (focea) sent to the ocean
[1572]	601	qfvbq_1d(ji) = qfvbq_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) * rdt_ice
[825]	602
[3517]	603	zihic = 1.0 - MAX( zzero , SIGN( zone , -ht_i_b(ji) ) ) ! equals 0 if ht_i = 0, 1 if ht_i gt 0
[825]	604	fscbq_1d(ji) = a_i_b(ji) * fstbif_1d(ji)
[3517]	605	qldif_1d(ji) = qldif_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea (ji) * a_i_b(ji) * rdt_ice &
[1572]	606	& + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice
[825]	607	END DO ! ji
	608
	609	!-------------------------------------------
	610	! Correct temperature, energy and thickness
	611	!-------------------------------------------
	612	DO ji = kideb, kiut
[1572]	613	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	614	t_su_b(ji) = zihgnew * t_su_b(ji) + ( 1.0 - zihgnew ) * rtt
[825]	615	END DO ! ji
	616
	617	DO jk = 1, nlay_i
	618	DO ji = kideb, kiut
[1572]	619	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	620	t_i_b(ji,jk) = zihgnew * t_i_b(ji,jk) + ( 1.0 - zihgnew ) * rtt
	621	q_i_b(ji,jk) = zihgnew * q_i_b(ji,jk)
[825]	622	END DO
	623	END DO ! ji
	624
	625	DO ji = kideb, kiut
	626	ht_i_b(ji) = zhgnew(ji)
	627	END DO ! ji
[921]	628	!
	629	!------------------------------------------------------------------------------\|
	630	! 6) Snow-Ice formation \|
	631	!------------------------------------------------------------------------------\|
[1572]	632	! When snow load excesses Archimede's limit, snow-ice interface goes down under sea-level,
	633	! flooding of seawater transforms snow into ice dh_snowice is positive for the ice
[825]	634	DO ji = kideb, kiut
[1572]	635	!
	636	dh_snowice(ji) = MAX( zzero , ( rhosn * ht_s_b(ji) + (rhoic-rau0) * ht_i_b(ji) ) / ( rhosn+rau0-rhoic ) )
	637	zhgnew(ji) = MAX( zhgnew(ji) , zhgnew(ji) + dh_snowice(ji) )
	638	zhnnew = MIN( ht_s_b(ji) , ht_s_b(ji) - dh_snowice(ji) )
[825]	639
[921]	640	! Changes in ice volume and ice mass.
[1572]	641	dvnbq_1d (ji) = a_i_b(ji) * ( zhgnew(ji)-ht_i_b(ji) )
	642	dmgwi_1d (ji) = dmgwi_1d(ji) + a_i_b(ji) * ( ht_s_b(ji) - zhnnew ) * rhosn
[825]	643
[3523]	644	! All snow is thrown in the ocean, and seawater is taken to replace the volume
	645	rdm_ice_1d(ji) = rdm_ice_1d(ji) + a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic * ( 1. - rhosn / rhoic )
[3517]	646	rdm_snw_1d(ji) = rdm_snw_1d(ji) + a_i_b(ji) * ( zhnnew - ht_s_b(ji) ) * rhosn
[825]	647
[921]	648	! Equivalent salt flux (1) Snow-ice formation component
	649	! -----------------------------------------------------
[3517]	650	ii = MOD( npb(ji) - 1, jpi ) + 1
	651	ij = ( npb(ji) - 1 ) / jpi + 1
[825]	652
[3517]	653	IF( num_sal == 2 ) THEN ; zsm_snowice = sss_m(ii,ij) * ( rhoic - rhosn ) / rhoic
	654	ELSE ; zsm_snowice = sm_i_b(ji)
[1572]	655	ENDIF
[3524]	656	sfx_thd_1d(ji) = sfx_thd_1d(ji) - zsm_snowice * a_i_b(ji) * dh_snowice(ji) * rhoic * r1_rdtice
[3517]	657	!
[825]	658	! entrapment during snow ice formation
[1572]	659	i_ice_switch = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - ht_i_b(ji) + 1.0e-6 ) )
	660	isnowic = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - dh_snowice(ji) ) ) * i_ice_switch
[3517]	661	IF( num_sal == 2 ) &
	662	dsm_i_si_1d(ji) = ( zsm_snowice * dh_snowice(ji) &
	663	& + sm_i_b(ji) * ht_i_b(ji) / MAX( ht_i_b(ji) + dh_snowice(ji), epsi13 ) &
	664	& - sm_i_b(ji) ) * isnowic
[825]	665
[921]	666	! Actualize new snow and ice thickness.
[825]	667	ht_s_b(ji) = zhnnew
	668	ht_i_b(ji) = zhgnew(ji)
	669
	670	! Total ablation ! new lines added to debug
[2715]	671	IF( ht_i_b(ji) <= 0._wp ) a_i_b(ji) = 0._wp
[825]	672
	673	! diagnostic ( snow ice growth )
[3517]	674	ii = MOD( npb(ji) - 1, jpi ) + 1
	675	ij = ( npb(ji) - 1 ) / jpi + 1
	676	diag_sni_gr(ii,ij) = diag_sni_gr(ii,ij) + dh_snowice(ji)a_i_b(ji) r1_rdtice
[1572]	677	!
[825]	678	END DO !ji
[2715]	679	!
[3294]	680	CALL wrk_dealloc( jpij, zh_i, zh_s, ztfs, zhsold, zqprec, zqfont_su, zqfont_bo, z_f_surf, zhgnew, zfmass_i )
[3524]	681	CALL wrk_dealloc( jpij, zdh_s_mel, zdh_s_pre, zdh_s_sub, zsfx_melt, zfdt_init, zfdt_final, zqt_i, zqt_s, zqt_dummy )
[3294]	682	CALL wrk_dealloc( jpij, zinnermelt, zfbase, zdq_i )
	683	CALL wrk_dealloc( jpij, jkmax, zdeltah, zqt_i_lay )
[2715]	684	!
[921]	685	END SUBROUTINE lim_thd_dh
[1572]	686
[825]	687	#else
[1572]	688	!!----------------------------------------------------------------------
	689	!! Default option NO LIM3 sea-ice model
	690	!!----------------------------------------------------------------------
[825]	691	CONTAINS
	692	SUBROUTINE lim_thd_dh ! Empty routine
	693	END SUBROUTINE lim_thd_dh
	694	#endif
[1572]	695
	696	!!======================================================================
[921]	697	END MODULE limthd_dh

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