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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 @ 3523

Last change on this file since 3523 was 3523, checked in by gm, 12 years ago
Branch: dev_r3385_NOCS04_HAMF; #665. LIM3 update: bug correction in limtrp and mass flux added in limthd_lac
Property svn:keywords set to `Id`
File size: 34.6 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	!!----------------------------------------------------------------------
[1572]	16	!! lim_thd_dh : vertical accr./abl. and lateral ablation of sea ice
[825]	17	!!----------------------------------------------------------------------
	18	USE par_oce ! ocean parameters
	19	USE phycst ! physical constants (OCE directory)
[888]	20	USE sbc_oce ! Surface boundary condition: ocean fields
[2715]	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
[3294]	26	USE wrk_nemo ! work arrays
[921]	27
[825]	28	IMPLICIT NONE
	29	PRIVATE
	30
[1572]	31	PUBLIC lim_thd_dh ! called by lim_thd
[825]	32
[1572]	33	REAL(wp) :: epsi20 = 1e-20 ! constant values
	34	REAL(wp) :: epsi13 = 1e-13 !
	35	REAL(wp) :: epsi16 = 1e-16 !
	36	REAL(wp) :: zzero = 0.e0 !
	37	REAL(wp) :: zone = 1.e0 !
[825]	38
	39	!!----------------------------------------------------------------------
[2715]	40	!! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2010)
[1156]	41	!! $Id$
[2715]	42	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[825]	43	!!----------------------------------------------------------------------
	44	CONTAINS
	45
[2715]	46	SUBROUTINE lim_thd_dh( kideb, kiut, jl )
[921]	47	!!------------------------------------------------------------------
	48	!! * ROUTINE lim_thd_dh *
	49	!!
[1572]	50	!! ** Purpose : determines variations of ice and snow thicknesses.
[921]	51	!!
[1572]	52	!! ** Method : Ice/Snow surface melting arises from imbalance in surface fluxes
	53	!! Bottom accretion/ablation arises from flux budget
	54	!! Snow thickness can increase by precipitation and decrease by sublimation
	55	!! If snow load excesses Archmiede limit, snow-ice is formed by
	56	!! the flooding of sea-water in the snow
[921]	57	!!
[1572]	58	!! 1) Compute available flux of heat for surface ablation
	59	!! 2) Compute snow and sea ice enthalpies
	60	!! 3) Surface ablation and sublimation
	61	!! 4) Bottom accretion/ablation
	62	!! 5) Case of Total ablation
	63	!! 6) Snow ice formation
[921]	64	!!
[1572]	65	!! References : Bitz and Lipscomb, 1999, J. Geophys. Res.
	66	!! Fichefet T. and M. Maqueda 1997, J. Geophys. Res., 102(C6), 12609-12646
	67	!! Vancoppenolle, Fichefet and Bitz, 2005, Geophys. Res. Let.
	68	!! Vancoppenolle et al.,2009, Ocean Modelling
[921]	69	!!------------------------------------------------------------------
[1572]	70	INTEGER , INTENT(in) :: kideb, kiut ! Start/End point on which the the computation is applied
	71	INTEGER , INTENT(in) :: jl ! Thickness cateogry number
	72	!!
	73	INTEGER :: ji , jk ! dummy loop indices
[3517]	74	INTEGER :: ii, ij ! 2D corresponding indices to ji
[1572]	75	INTEGER :: isnow ! switch for presence (1) or absence (0) of snow
	76	INTEGER :: isnowic ! snow ice formation not
	77	INTEGER :: i_ice_switch ! ice thickness above a certain treshold or not
	78	INTEGER :: iter
[825]	79
[2715]	80	REAL(wp) :: zzfmass_i, zihgnew ! local scalar
	81	REAL(wp) :: zzfmass_s, zhsnew, ztmelts ! local scalar
[1572]	82	REAL(wp) :: zhn, zdhcf, zdhbf, zhni, zhnfi, zihg !
[2715]	83	REAL(wp) :: zdhnm, zhnnew, zhisn, zihic, zzc !
[1572]	84	REAL(wp) :: zfracs ! fractionation coefficient for bottom salt entrapment
	85	REAL(wp) :: zds ! increment of bottom ice salinity
	86	REAL(wp) :: zcoeff ! dummy argument for snowfall partitioning over ice and leads
	87	REAL(wp) :: zsm_snowice ! snow-ice salinity
	88	REAL(wp) :: zswi1 ! switch for computation of bottom salinity
	89	REAL(wp) :: zswi12 ! switch for computation of bottom salinity
	90	REAL(wp) :: zswi2 ! switch for computation of bottom salinity
	91	REAL(wp) :: zgrr ! bottom growth rate
	92	REAL(wp) :: ztform ! bottom formation temperature
[2715]	93	!
[3294]	94	REAL(wp), POINTER, DIMENSION(:) :: zh_i ! ice layer thickness
	95	REAL(wp), POINTER, DIMENSION(:) :: zh_s ! snow layer thickness
	96	REAL(wp), POINTER, DIMENSION(:) :: ztfs ! melting point
	97	REAL(wp), POINTER, DIMENSION(:) :: zhsold ! old snow thickness
	98	REAL(wp), POINTER, DIMENSION(:) :: zqprec ! energy of fallen snow
	99	REAL(wp), POINTER, DIMENSION(:) :: zqfont_su ! incoming, remaining surface energy
	100	REAL(wp), POINTER, DIMENSION(:) :: zqfont_bo ! incoming, bottom energy
	101	REAL(wp), POINTER, DIMENSION(:) :: z_f_surf ! surface heat for ablation
	102	REAL(wp), POINTER, DIMENSION(:) :: zhgnew ! new ice thickness
	103	REAL(wp), POINTER, DIMENSION(:) :: zfmass_i !
	104
	105	REAL(wp), POINTER, DIMENSION(:) :: zdh_s_mel ! snow melt
	106	REAL(wp), POINTER, DIMENSION(:) :: zdh_s_pre ! snow precipitation
	107	REAL(wp), POINTER, DIMENSION(:) :: zdh_s_sub ! snow sublimation
	108	REAL(wp), POINTER, DIMENSION(:) :: zfsalt_melt ! salt flux due to ice melt
	109
	110	REAL(wp), POINTER, DIMENSION(:,:) :: zdeltah
	111
	112	! Pathological cases
	113	REAL(wp), POINTER, DIMENSION(:) :: zfdt_init ! total incoming heat for ice melt
	114	REAL(wp), POINTER, DIMENSION(:) :: zfdt_final ! total remaing heat for ice melt
	115	REAL(wp), POINTER, DIMENSION(:) :: zqt_i ! total ice heat content
	116	REAL(wp), POINTER, DIMENSION(:) :: zqt_s ! total snow heat content
	117	REAL(wp), POINTER, DIMENSION(:) :: zqt_dummy ! dummy heat content
	118
	119	REAL(wp), POINTER, DIMENSION(:,:) :: zqt_i_lay ! total ice heat content
	120
	121	! Heat conservation
	122	INTEGER :: num_iter_max, numce_dh
	123	REAL(wp) :: meance_dh
	124	REAL(wp), POINTER, DIMENSION(:) :: zinnermelt
	125	REAL(wp), POINTER, DIMENSION(:) :: zfbase, zdq_i
[1572]	126	!!------------------------------------------------------------------
[825]	127
[3294]	128	CALL wrk_alloc( jpij, zh_i, zh_s, ztfs, zhsold, zqprec, zqfont_su, zqfont_bo, z_f_surf, zhgnew, zfmass_i )
	129	CALL wrk_alloc( jpij, zdh_s_mel, zdh_s_pre, zdh_s_sub, zfsalt_melt, zfdt_init, zfdt_final, zqt_i, zqt_s, zqt_dummy )
	130	CALL wrk_alloc( jpij, zinnermelt, zfbase, zdq_i )
	131	CALL wrk_alloc( jpij, jkmax, zdeltah, zqt_i_lay )
[825]	132
[2715]	133	zfsalt_melt(:) = 0._wp
	134	ftotal_fin(:) = 0._wp
	135	zfdt_init(:) = 0._wp
	136	zfdt_final(:) = 0._wp
	137
[825]	138	DO ji = kideb, kiut
	139	old_ht_i_b(ji) = ht_i_b(ji)
	140	old_ht_s_b(ji) = ht_s_b(ji)
	141	END DO
[921]	142	!
	143	!------------------------------------------------------------------------------!
	144	! 1) Calculate available heat for surface ablation !
	145	!------------------------------------------------------------------------------!
	146	!
[2715]	147	DO ji = kideb, kiut
[3517]	148	isnow = INT( 1.0 - MAX( 0.0 , SIGN( 1.0 , - ht_s_b(ji) ) ) )
	149	ztfs (ji) = isnow * rtt + ( 1.0 - isnow ) * rtt
	150	z_f_surf (ji) = qnsr_ice_1d(ji) + ( 1.0 - i0(ji) ) * qsr_ice_1d(ji) - fc_su(ji)
	151	z_f_surf (ji) = MAX( zzero , z_f_surf(ji) ) * MAX( zzero , SIGN( zone , t_su_b(ji) - ztfs(ji) ) )
[1572]	152	zfdt_init(ji) = ( z_f_surf(ji) + MAX( fbif_1d(ji) + qlbbq_1d(ji) + fc_bo_i(ji),0.0 ) ) * rdt_ice
[825]	153	END DO ! ji
	154
[2715]	155	zqfont_su (:) = 0._wp
	156	zqfont_bo (:) = 0._wp
	157	dsm_i_se_1d(:) = 0._wp
	158	dsm_i_si_1d(:) = 0._wp
[921]	159	!
	160	!------------------------------------------------------------------------------!
	161	! 2) Computing layer thicknesses and snow and sea-ice enthalpies. !
	162	!------------------------------------------------------------------------------!
	163	!
[2715]	164	DO ji = kideb, kiut ! Layer thickness
[825]	165	zh_i(ji) = ht_i_b(ji) / nlay_i
	166	zh_s(ji) = ht_s_b(ji) / nlay_s
	167	END DO
[2715]	168	!
	169	zqt_s(:) = 0._wp ! Total enthalpy of the snow
[825]	170	DO jk = 1, nlay_s
[2715]	171	DO ji = kideb, kiut
[1572]	172	zqt_s(ji) = zqt_s(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s
[825]	173	END DO
	174	END DO
[2715]	175	!
	176	zqt_i(:) = 0._wp ! Total enthalpy of the ice
[825]	177	DO jk = 1, nlay_i
[2715]	178	DO ji = kideb, kiut
	179	zzc = q_i_b(ji,jk) * ht_i_b(ji) / nlay_i
	180	zqt_i(ji) = zqt_i(ji) + zzc
	181	zqt_i_lay(ji,jk) = zzc
[825]	182	END DO
	183	END DO
[921]	184	!
	185	!------------------------------------------------------------------------------\|
	186	! 3) Surface ablation and sublimation \|
	187	!------------------------------------------------------------------------------\|
	188	!
[834]	189	!-------------------------
	190	! 3.1 Snow precips / melt
	191	!-------------------------
[825]	192	! Snow accumulation in one thermodynamic time step
	193	! snowfall is partitionned between leads and ice
	194	! if snow fall was uniform, a fraction (1-at_i) would fall into leads
	195	! but because of the winds, more snow falls on leads than on sea ice
	196	! and a greater fraction (1-at_i)^beta of the total mass of snow
[834]	197	! (beta < 1) falls in leads.
[825]	198	! In reality, beta depends on wind speed,
	199	! and should decrease with increasing wind speed but here, it is
[834]	200	! considered as a constant. an average value is 0.66
[825]	201	! Martin Vancoppenolle, December 2006
	202
	203	! Snow fall
	204	DO ji = kideb, kiut
	205	zcoeff = ( 1.0 - ( 1.0 - at_i_b(ji) )**betas ) / at_i_b(ji)
	206	zdh_s_pre(ji) = zcoeff * sprecip_1d(ji) * rdt_ice / rhosn
	207	END DO
[2715]	208	zdh_s_mel(:) = 0._wp
[825]	209
	210	! Melt of fallen snow
	211	DO ji = kideb, kiut
	212	! tatm_ice is now in K
[1572]	213	zqprec (ji) = rhosn * ( cpic * ( rtt - tatm_ice_1d(ji) ) + lfus )
	214	zqfont_su(ji) = z_f_surf(ji) * rdt_ice
	215	zdeltah (ji,1) = MIN( 0.e0 , - zqfont_su(ji) / MAX( zqprec(ji) , epsi13 ) )
	216	zqfont_su(ji) = MAX( 0.e0 , - zdh_s_pre(ji) - zdeltah(ji,1) ) * zqprec(ji)
	217	zdeltah (ji,1) = MAX( - zdh_s_pre(ji) , zdeltah(ji,1) )
	218	zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,1)
[825]	219	! heat conservation
[1572]	220	qt_s_in(ji,jl) = qt_s_in(ji,jl) + zqprec(ji) * zdh_s_pre(ji)
	221	zqt_s (ji) = zqt_s (ji) + zqprec(ji) * zdh_s_pre(ji)
	222	zqt_s (ji) = MAX( zqt_s(ji) - zqfont_su(ji) , 0.e0 )
[825]	223	END DO
	224
	225
	226	! Snow melt due to surface heat imbalance
	227	DO jk = 1, nlay_s
	228	DO ji = kideb, kiut
[1572]	229	zdeltah (ji,jk) = - zqfont_su(ji) / q_s_b(ji,jk)
	230	zqfont_su(ji) = MAX( 0.0 , - zh_s(ji) - zdeltah(ji,jk) ) * q_s_b(ji,jk)
	231	zdeltah (ji,jk) = MAX( zdeltah(ji,jk) , - zh_s(ji) )
	232	zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,jk) ! resulting melt of snow
[825]	233	END DO
	234	END DO
	235
	236	! Apply snow melt to snow depth
	237	DO ji = kideb, kiut
	238	dh_s_tot(ji) = zdh_s_mel(ji) + zdh_s_pre(ji)
	239	! Old and new snow depths
	240	zhsold(ji) = ht_s_b(ji)
	241	zhsnew = ht_s_b(ji) + dh_s_tot(ji)
	242	! If snow is still present zhn = 1, else zhn = 0
[3517]	243	zhn = 1.0 - MAX( zzero , SIGN( zone , - zhsnew ) )
[825]	244	ht_s_b(ji) = MAX( zzero , zhsnew )
	245	! Volume and mass variations of snow
[3517]	246	dvsbq_1d (ji) = a_i_b(ji) * ( ht_s_b(ji) - zhsold(ji) - zdh_s_pre(ji) )
[1572]	247	dvsbq_1d (ji) = MIN( zzero, dvsbq_1d(ji) )
[3517]	248	rdm_snw_1d(ji) = rdm_snw_1d(ji) + rhosn * dvsbq_1d(ji)
[825]	249	END DO ! ji
	250
[834]	251	!--------------------------
	252	! 3.2 Surface ice ablation
	253	!--------------------------
[825]	254	DO ji = kideb, kiut
[2715]	255	dh_i_surf(ji) = 0._wp
[3517]	256	z_f_surf (ji) = zqfont_su(ji) * r1_rdtice ! heat conservation test
[2715]	257	zdq_i (ji) = 0._wp
[825]	258	END DO ! ji
	259
	260	DO jk = 1, nlay_i
	261	DO ji = kideb, kiut
[1572]	262	! ! melt of layer jk
	263	zdeltah (ji,jk) = - zqfont_su(ji) / q_i_b(ji,jk)
	264	! ! recompute heat available
[3517]	265	zqfont_su(ji ) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
[1572]	266	! ! melt of layer jk cannot be higher than its thickness
	267	zdeltah (ji,jk) = MAX( zdeltah(ji,jk) , - zh_i(ji) )
	268	! ! update surface melt
[3517]	269	dh_i_surf(ji ) = dh_i_surf(ji) + zdeltah(ji,jk)
[1572]	270	! ! for energy conservation
[3517]	271	zdq_i (ji ) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) * r1_rdtice
[1572]	272	!
[3517]	273	! ! contribution to ice-ocean salt flux
	274	zfsalt_melt(ji) = zfsalt_melt(ji) - sm_i_b(ji) * a_i_b(ji) * MIN( zdeltah(ji,jk) , 0._wp ) * rhoic * r1_rdtice
[1572]	275	END DO
	276	END DO
[825]	277
[1572]	278	! !-------------------
	279	IF( con_i ) THEN ! Conservation test
	280	! !-------------------
	281	numce_dh = 0
[2715]	282	meance_dh = 0._wp
[921]	283	DO ji = kideb, kiut
	284	IF ( ( z_f_surf(ji) + zdq_i(ji) ) .GE. 1.0e-3 ) THEN
	285	numce_dh = numce_dh + 1
	286	meance_dh = meance_dh + z_f_surf(ji) + zdq_i(ji)
	287	ENDIF
[1572]	288	IF( z_f_surf(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN!
[921]	289	WRITE(numout,*) ' ALERTE heat loss for surface melt '
[3517]	290	WRITE(numout,*) ' ii, ij, jl :', ii, ij, jl
[2715]	291	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	292	WRITE(numout,*) ' z_f_surf : ', z_f_surf(ji)
	293	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	294	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	295	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	296	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	297	WRITE(numout,*) ' qlbbq_1d : ', qlbbq_1d(ji)
	298	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
[3517]	299	WRITE(numout,*) ' sss_m : ', sss_m(ii,ij)
[921]	300	ENDIF
[1572]	301	END DO
	302	!
	303	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	304	WRITE(numout,*) ' Error report - Category : ', jl
	305	WRITE(numout,*) ' ~~~~~~~~~~~~ '
	306	WRITE(numout,*) ' Number of points where there is sur. me. error : ', numce_dh
	307	WRITE(numout,*) ' Mean basal growth error on error points : ', meance_dh
[1572]	308	!
	309	ENDIF
[825]	310
[834]	311	!----------------------
	312	! 3.3 Snow sublimation
	313	!----------------------
[825]	314
	315	DO ji = kideb, kiut
	316	! if qla is positive (upwards), heat goes to the atmosphere, therefore
	317	! snow sublimates, if qla is negative (downwards), snow condensates
[1572]	318	zdh_s_sub(ji) = - parsub * qla_ice_1d(ji) / ( rhosn * lsub ) * rdt_ice
	319	dh_s_tot (ji) = dh_s_tot(ji) + zdh_s_sub(ji)
	320	zdhcf = ht_s_b(ji) + zdh_s_sub(ji)
	321	ht_s_b (ji) = MAX( zzero , zdhcf )
[825]	322	! we recompute dh_s_tot
[1572]	323	dh_s_tot (ji) = ht_s_b(ji) - zhsold(ji)
	324	qt_s_in (ji,jl) = qt_s_in(ji,jl) + zdh_s_sub(ji)*q_s_b(ji,1)
	325	END DO
[825]	326
[1572]	327	zqt_dummy(:) = 0.e0
[825]	328	DO jk = 1, nlay_s
	329	DO ji = kideb,kiut
[1572]	330	q_s_b (ji,jk) = rhosn * ( cpic * ( rtt - t_s_b(ji,jk) ) + lfus )
	331	zqt_dummy(ji) = zqt_dummy(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s ! heat conservation
[825]	332	END DO
	333	END DO
	334
[1572]	335	DO jk = 1, nlay_s
	336	DO ji = kideb, kiut
	337	! In case of disparition of the snow, we have to update the snow temperatures
[3517]	338	zhisn = MAX( zzero , SIGN( zone, - ht_s_b(ji) ) )
[825]	339	t_s_b(ji,jk) = ( 1.0 - zhisn ) * t_s_b(ji,jk) + zhisn * rtt
	340	q_s_b(ji,jk) = ( 1.0 - zhisn ) * q_s_b(ji,jk)
	341	END DO
[921]	342	END DO
[825]	343
[921]	344	!
	345	!------------------------------------------------------------------------------!
	346	! 4) Basal growth / melt !
	347	!------------------------------------------------------------------------------!
	348	!
[825]	349	! Ice basal growth / melt is given by the ratio of heat budget over basal
	350	! ice heat content. Basal heat budget is given by the difference between
	351	! the inner conductive flux (fc_bo_i), from the open water heat flux
	352	! (qlbbqb) and the turbulent ocean flux (fbif).
[834]	353	! fc_bo_i is positive downwards. fbif and qlbbq are positive to the ice
[825]	354
[834]	355	!-----------------------------------------------------
	356	! 4.1 Basal growth - (a) salinity not varying in time
	357	!-----------------------------------------------------
[3517]	358	IF( num_sal /= 2 ) THEN ! ice salinity constant in time
[825]	359	DO ji = kideb, kiut
[3517]	360	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) < 0._wp ) THEN
[825]	361	s_i_new(ji) = sm_i_b(ji)
	362	! Melting point in K
	363	ztmelts = - tmut * s_i_new(ji) + rtt
	364	! New ice heat content (Bitz and Lipscomb, 1999)
	365	ztform = t_i_b(ji,nlay_i) ! t_bo_b crashes in the
[921]	366	! Baltic
[1572]	367	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - ztform ) &
	368	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( ztform - rtt ) ) &
	369	& - rcp * ( ztmelts - rtt ) )
[825]	370	! Basal growth rate = - F*dt / q
[3517]	371	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[1572]	372	ENDIF
	373	END DO
	374	ENDIF
[825]	375
[834]	376	!-------------------------------------------------
	377	! 4.1 Basal growth - (b) salinity varying in time
	378	!-------------------------------------------------
[3517]	379	IF( num_sal == 2 ) THEN
	380	! the growth rate (dh_i_bott) is function of the new ice heat content (q_i_b(nlay_i+1)).
	381	! q_i_b depends on the new ice salinity (snewice).
	382	! snewice depends on dh_i_bott ; it converges quickly, so, no problem
[834]	383	! See Vancoppenolle et al., OM08 for more info on this
[825]	384
	385	! Initial value (tested 1D, can be anything between 1 and 20)
	386	num_iter_max = 4
[1572]	387	s_i_new(:) = 4.0
[825]	388
	389	! Iterative procedure
	390	DO iter = 1, num_iter_max
	391	DO ji = kideb, kiut
[1572]	392	IF( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) < 0.e0 ) THEN
[3517]	393	ii = MOD( npb(ji) - 1, jpi ) + 1
	394	ij = ( npb(ji) - 1 ) / jpi + 1
[825]	395	! Melting point in K
	396	ztmelts = - tmut * s_i_new(ji) + rtt
	397	! New ice heat content (Bitz and Lipscomb, 1999)
[1572]	398	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) &
	399	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( t_bo_b(ji) - rtt ) ) &
	400	& - rcp * ( ztmelts-rtt ) )
[825]	401	! Bottom growth rate = - F*dt / q
[1572]	402	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[825]	403	! New ice salinity ( Cox and Weeks, JGR, 1988 )
	404	! zswi2 (1) if dh_i_bott/rdt .GT. 3.6e-7
	405	! zswi12 (1) if dh_i_bott/rdt .LT. 3.6e-7 and .GT. 2.0e-8
	406	! zswi1 (1) if dh_i_bott/rdt .LT. 2.0e-8
[3517]	407	zgrr = MIN( 1.0e-3, MAX ( dh_i_bott(ji) * r1_rdtice , epsi13 ) )
[825]	408	zswi2 = MAX( zzero , SIGN( zone , zgrr - 3.6e-7 ) )
	409	zswi12 = MAX( zzero , SIGN( zone , zgrr - 2.0e-8 ) ) * ( 1.0 - zswi2 )
	410	zswi1 = 1. - zswi2 * zswi12
[1572]	411	zfracs = zswi1 * 0.12 + zswi12 * ( 0.8925 + 0.0568 * LOG( 100.0 * zgrr ) ) &
	412	& + zswi2 * 0.26 / ( 0.26 + 0.74 * EXP ( - 724300.0 * zgrr ) )
[3517]	413	zds = zfracs * sss_m(ii,ij) - s_i_new(ji)
	414	s_i_new(ji) = zfracs * sss_m(ii,ij)
[825]	415	ENDIF ! fc_bo_i
	416	END DO ! ji
	417	END DO ! iter
	418
	419	! Final values
	420	DO ji = kideb, kiut
[1572]	421	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .LT. 0.0 ) THEN
[825]	422	! New ice salinity must not exceed 15 psu
	423	s_i_new(ji) = MIN( s_i_new(ji), s_i_max )
	424	! Metling point in K
	425	ztmelts = - tmut * s_i_new(ji) + rtt
	426	! New ice heat content (Bitz and Lipscomb, 1999)
[1572]	427	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) &
	428	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( t_bo_b(ji) - rtt ) ) &
	429	& - rcp * ( ztmelts - rtt ) )
[825]	430	! Basal growth rate = - F*dt / q
[3517]	431	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[834]	432	! Salinity update
[825]	433	! entrapment during bottom growth
[1572]	434	dsm_i_se_1d(ji) = ( s_i_new(ji) * dh_i_bott(ji) + sm_i_b(ji) * ht_i_b(ji) ) &
	435	& / MAX( ht_i_b(ji) + dh_i_bott(ji) ,epsi13 ) - sm_i_b(ji)
[825]	436	ENDIF ! heat budget
[1572]	437	END DO
	438	ENDIF
[825]	439
[834]	440	!----------------
	441	! 4.2 Basal melt
	442	!----------------
[2715]	443	meance_dh = 0._wp
[1572]	444	numce_dh = 0
[2715]	445	zinnermelt(:) = 0._wp
[825]	446
	447	DO ji = kideb, kiut
	448	! heat convergence at the surface > 0
[2715]	449	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0._wp ) THEN
[825]	450	s_i_new(ji) = s_i_b(ji,nlay_i)
	451	zqfont_bo(ji) = rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) )
[3517]	452	zfbase(ji) = zqfont_bo(ji) * r1_rdtice ! heat conservation test
[2715]	453	zdq_i(ji) = 0._wp
	454	dh_i_bott(ji) = 0._wp
[825]	455	ENDIF
	456	END DO
	457
	458	DO jk = nlay_i, 1, -1
	459	DO ji = kideb, kiut
[3517]	460	IF( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) >= 0._wp ) THEN
	461	ztmelts = - tmut * s_i_b(ji,jk) + rtt
	462	IF( t_i_b(ji,jk) >= ztmelts ) THEN !!gm : a comment is needed
	463	zdeltah (ji,jk) = - zh_i(ji)
	464	dh_i_bott (ji ) = dh_i_bott(ji) + zdeltah(ji,jk)
	465	zinnermelt(ji ) = 1._wp
	466	ELSE ! normal ablation
	467	zdeltah (ji,jk) = - zqfont_bo(ji) / q_i_b(ji,jk)
	468	zqfont_bo(ji ) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
	469	zdeltah (ji,jk) = MAX(zdeltah(ji,jk), - zh_i(ji) )
	470	dh_i_bott(ji ) = dh_i_bott(ji) + zdeltah(ji,jk)
	471	zdq_i (ji ) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) * r1_rdtice
[825]	472	ENDIF
[3517]	473	! contribution to salt flux
	474	zfsalt_melt(ji) = zfsalt_melt(ji) - sm_i_b(ji) * a_i_b(ji) * MIN( zdeltah(ji,jk) , 0._wp ) * rhoic * r1_rdtice
[825]	475	ENDIF
	476	END DO ! ji
	477	END DO ! jk
	478
[1572]	479	! !-------------------
	480	IF( con_i ) THEN ! Conservation test
	481	! !-------------------
[921]	482	DO ji = kideb, kiut
[1572]	483	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0.e0 ) THEN
	484	IF( ( zfbase(ji) + zdq_i(ji) ) >= 1.e-3 ) THEN
	485	numce_dh = numce_dh + 1
[921]	486	meance_dh = meance_dh + zfbase(ji) + zdq_i(ji)
	487	ENDIF
	488	IF ( zfbase(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN
[3517]	489	WRITE(numout,*) ' ALERTE heat loss for basal melt : ii, ij, jl :', ii, ij, jl
[2715]	490	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	491	WRITE(numout,*) ' zfbase : ', zfbase(ji)
	492	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	493	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	494	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	495	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	496	WRITE(numout,*) ' qlbbq_1d : ', qlbbq_1d(ji)
	497	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
[3517]	498	WRITE(numout,*) ' sss_m : ', sss_m(ii,ij)
[921]	499	WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji)
[2715]	500	WRITE(numout,*) ' innermelt : ', INT( zinnermelt(ji) )
[921]	501	ENDIF
[1572]	502	ENDIF
	503	END DO
	504	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	505	WRITE(numout,*) ' Number of points where there is bas. me. error : ', numce_dh
	506	WRITE(numout,*) ' Mean basal melt error on error points : ', meance_dh
	507	WRITE(numout,*) ' Remaining bottom heat : ', zqfont_bo(jiindex_1d)
[1572]	508	!
	509	ENDIF
[825]	510
[921]	511	!
	512	!------------------------------------------------------------------------------!
	513	! 5) Pathological cases !
	514	!------------------------------------------------------------------------------!
	515	!
[834]	516	!----------------------------------------------
	517	! 5.1 Excessive ablation in a 1-category model
	518	!----------------------------------------------
[825]	519
	520	DO ji = kideb, kiut
[1572]	521	! ! in a 1-category sea ice model, bottom ablation must not exceed hmelt (-0.15)
	522	IF( jpl == 1 ) THEN ; zdhbf = MAX( hmelt , dh_i_bott(ji) )
	523	ELSE ; zdhbf = dh_i_bott(ji)
	524	ENDIF
	525	! ! excessive energy is sent to lateral ablation
	526	fsup (ji) = rhoic * lfus * at_i_b(ji) / MAX( 1.0 - at_i_b(ji) , epsi13 ) &
[3517]	527	& * ( zdhbf - dh_i_bott(ji) ) * r1_rdtice
[825]	528	dh_i_bott(ji) = zdhbf
[1572]	529	! !since ice volume is only used for outputs, we keep it global for all categories
	530	dvbbq_1d (ji) = a_i_b(ji) * dh_i_bott(ji)
	531	! !new ice thickness
	532	zhgnew (ji) = ht_i_b(ji) + dh_i_surf(ji) + dh_i_bott(ji)
	533	! ! diagnostic ( bottom ice growth )
[3517]	534	ii = MOD( npb(ji) - 1, jpi ) + 1
	535	ij = ( npb(ji) - 1 ) / jpi + 1
	536	diag_bot_gr(ii,ij) = diag_bot_gr(ii,ij) + MAX(dh_i_bott(ji),0.0)a_i_b(ji) r1_rdtice
	537	diag_sur_me(ii,ij) = diag_sur_me(ii,ij) + MIN(dh_i_surf(ji),0.0)a_i_b(ji) r1_rdtice
	538	diag_bot_me(ii,ij) = diag_bot_me(ii,ij) + MIN(dh_i_bott(ji),0.0)a_i_b(ji) r1_rdtice
[825]	539	END DO
	540
[834]	541	!-----------------------------------
	542	! 5.2 More than available ice melts
	543	!-----------------------------------
[3517]	544	! then heat applied minus heat content at previous time step should equal heat remaining
[825]	545	!
	546	DO ji = kideb, kiut
	547	! Adapt the remaining energy if too much ice melts
	548	!--------------------------------------------------
[3517]	549	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) ! =1 if ice
[825]	550	! 0 if no more ice
[1572]	551	zhgnew (ji) = zihgnew * zhgnew(ji) ! ice thickness is put to 0
[825]	552	! remaining heat
[834]	553	zfdt_final(ji) = ( 1.0 - zihgnew ) * ( zqfont_su(ji) + zqfont_bo(ji) )
[825]	554
	555	! If snow remains, energy is used to melt snow
[1572]	556	zhni = ht_s_b(ji) ! snow depth at previous time step
[3517]	557	zihg = MAX( zzero , SIGN ( zone , - ht_s_b(ji) ) ) ! =0 if snow
[825]	558
	559	! energy of melting of remaining snow
[1572]	560	zqt_s(ji) = ( 1. - zihg ) * zqt_s(ji) / MAX( zhni, epsi13 )
	561	zdhnm = - ( 1. - zihg ) * ( 1. - zihgnew ) * zfdt_final(ji) / MAX( zqt_s(ji) , epsi13 )
[3517]	562	zhnfi = zhni + zdhnm
[1572]	563	zfdt_final(ji) = MAX( zfdt_final(ji) + zqt_s(ji) * zdhnm , 0.0 )
[825]	564	ht_s_b(ji) = MAX( zzero , zhnfi )
	565	zqt_s(ji) = zqt_s(ji) * ht_s_b(ji)
	566
	567	! Mass variations of ice and snow
	568	!---------------------------------
[1572]	569	! ! mass variation of the jl category
[1571]	570	zzfmass_s = - a_i_b(ji) * ( zhni - ht_s_b(ji) ) * rhosn ! snow
	571	zzfmass_i = a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic ! ice
	572	!
	573	zfmass_i(ji) = zzfmass_i ! ice variation saved to compute salt flux (see below)
	574	!
	575	! ! mass variation cumulated over category
[3517]	576	rdm_snw_1d(ji) = rdm_snw_1d(ji) + zzfmass_s ! snow
	577	rdm_ice_1d(ji) = rdm_ice_1d(ji) + zzfmass_i ! ice
[825]	578
	579	! Remaining heat to the ocean
	580	!---------------------------------
[3517]	581	focea(ji) = - zfdt_final(ji) * r1_rdtice ! focea is in W.m-2 * dt
[825]	582
	583	END DO
	584
[3517]	585	ftotal_fin (:) = zfdt_final(:) * r1_rdtice
[825]	586
	587	!---------------------------
	588	! Salt flux and heat fluxes
	589	!---------------------------
	590	DO ji = kideb, kiut
[3517]	591	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) ! =1 if ice
	592	!
[825]	593	! Salt flux
[3517]	594	fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) &
	595	& - (1.0 - zihgnew) * zfmass_i (ji) * sm_i_b(ji) ) * r1_rdtice
	596	!
[825]	597	! Heat flux
	598	! excessive bottom ablation energy (fsup) - 0 except if jpl = 1
[3517]	599	! excessive total ablation energy (focea) sent to the ocean
[1572]	600	qfvbq_1d(ji) = qfvbq_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) * rdt_ice
[825]	601
[3517]	602	zihic = 1.0 - MAX( zzero , SIGN( zone , -ht_i_b(ji) ) ) ! equals 0 if ht_i = 0, 1 if ht_i gt 0
[825]	603	fscbq_1d(ji) = a_i_b(ji) * fstbif_1d(ji)
[3517]	604	qldif_1d(ji) = qldif_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea (ji) * a_i_b(ji) * rdt_ice &
[1572]	605	& + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice
[825]	606	END DO ! ji
	607
	608	!-------------------------------------------
	609	! Correct temperature, energy and thickness
	610	!-------------------------------------------
	611	DO ji = kideb, kiut
[1572]	612	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	613	t_su_b(ji) = zihgnew * t_su_b(ji) + ( 1.0 - zihgnew ) * rtt
[825]	614	END DO ! ji
	615
	616	DO jk = 1, nlay_i
	617	DO ji = kideb, kiut
[1572]	618	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	619	t_i_b(ji,jk) = zihgnew * t_i_b(ji,jk) + ( 1.0 - zihgnew ) * rtt
	620	q_i_b(ji,jk) = zihgnew * q_i_b(ji,jk)
[825]	621	END DO
	622	END DO ! ji
	623
	624	DO ji = kideb, kiut
	625	ht_i_b(ji) = zhgnew(ji)
	626	END DO ! ji
[921]	627	!
	628	!------------------------------------------------------------------------------\|
	629	! 6) Snow-Ice formation \|
	630	!------------------------------------------------------------------------------\|
[1572]	631	! When snow load excesses Archimede's limit, snow-ice interface goes down under sea-level,
	632	! flooding of seawater transforms snow into ice dh_snowice is positive for the ice
[825]	633	DO ji = kideb, kiut
[1572]	634	!
	635	dh_snowice(ji) = MAX( zzero , ( rhosn * ht_s_b(ji) + (rhoic-rau0) * ht_i_b(ji) ) / ( rhosn+rau0-rhoic ) )
	636	zhgnew(ji) = MAX( zhgnew(ji) , zhgnew(ji) + dh_snowice(ji) )
	637	zhnnew = MIN( ht_s_b(ji) , ht_s_b(ji) - dh_snowice(ji) )
[825]	638
[921]	639	! Changes in ice volume and ice mass.
[1572]	640	dvnbq_1d (ji) = a_i_b(ji) * ( zhgnew(ji)-ht_i_b(ji) )
	641	dmgwi_1d (ji) = dmgwi_1d(ji) + a_i_b(ji) * ( ht_s_b(ji) - zhnnew ) * rhosn
[825]	642
[3523]	643	! All snow is thrown in the ocean, and seawater is taken to replace the volume
	644	rdm_ice_1d(ji) = rdm_ice_1d(ji) + a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic * ( 1. - rhosn / rhoic )
[3517]	645	rdm_snw_1d(ji) = rdm_snw_1d(ji) + a_i_b(ji) * ( zhnnew - ht_s_b(ji) ) * rhosn
[825]	646
[921]	647	! Equivalent salt flux (1) Snow-ice formation component
	648	! -----------------------------------------------------
[3517]	649	ii = MOD( npb(ji) - 1, jpi ) + 1
	650	ij = ( npb(ji) - 1 ) / jpi + 1
[825]	651
[3517]	652	IF( num_sal == 2 ) THEN ; zsm_snowice = sss_m(ii,ij) * ( rhoic - rhosn ) / rhoic
	653	ELSE ; zsm_snowice = sm_i_b(ji)
[1572]	654	ENDIF
[3517]	655	fseqv_1d(ji) = fseqv_1d(ji) - zsm_snowice * a_i_b(ji) * dh_snowice(ji) * rhoic * r1_rdtice
	656	!
[825]	657	! entrapment during snow ice formation
[1572]	658	i_ice_switch = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - ht_i_b(ji) + 1.0e-6 ) )
	659	isnowic = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - dh_snowice(ji) ) ) * i_ice_switch
[3517]	660	IF( num_sal == 2 ) &
	661	dsm_i_si_1d(ji) = ( zsm_snowice * dh_snowice(ji) &
	662	& + sm_i_b(ji) * ht_i_b(ji) / MAX( ht_i_b(ji) + dh_snowice(ji), epsi13 ) &
	663	& - sm_i_b(ji) ) * isnowic
[825]	664
[921]	665	! Actualize new snow and ice thickness.
[825]	666	ht_s_b(ji) = zhnnew
	667	ht_i_b(ji) = zhgnew(ji)
	668
	669	! Total ablation ! new lines added to debug
[2715]	670	IF( ht_i_b(ji) <= 0._wp ) a_i_b(ji) = 0._wp
[825]	671
	672	! diagnostic ( snow ice growth )
[3517]	673	ii = MOD( npb(ji) - 1, jpi ) + 1
	674	ij = ( npb(ji) - 1 ) / jpi + 1
	675	diag_sni_gr(ii,ij) = diag_sni_gr(ii,ij) + dh_snowice(ji)a_i_b(ji) r1_rdtice
[1572]	676	!
[825]	677	END DO !ji
[2715]	678	!
[3294]	679	CALL wrk_dealloc( jpij, zh_i, zh_s, ztfs, zhsold, zqprec, zqfont_su, zqfont_bo, z_f_surf, zhgnew, zfmass_i )
	680	CALL wrk_dealloc( jpij, zdh_s_mel, zdh_s_pre, zdh_s_sub, zfsalt_melt, zfdt_init, zfdt_final, zqt_i, zqt_s, zqt_dummy )
	681	CALL wrk_dealloc( jpij, zinnermelt, zfbase, zdq_i )
	682	CALL wrk_dealloc( jpij, jkmax, zdeltah, zqt_i_lay )
[2715]	683	!
[921]	684	END SUBROUTINE lim_thd_dh
[1572]	685
[825]	686	#else
[1572]	687	!!----------------------------------------------------------------------
	688	!! Default option NO LIM3 sea-ice model
	689	!!----------------------------------------------------------------------
[825]	690	CONTAINS
	691	SUBROUTINE lim_thd_dh ! Empty routine
	692	END SUBROUTINE lim_thd_dh
	693	#endif
[1572]	694
	695	!!======================================================================
[921]	696	END MODULE limthd_dh

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