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limthd_dh.F90 in trunk/NEMOGCM/NEMO/LIM_SRC_3 – NEMO

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source: trunk/NEMOGCM/NEMO/LIM_SRC_3/limthd_dh.F90 @ 3584

Last change on this file since 3584 was 3558, checked in by rblod, 12 years ago
Fix issues when using key_nosignedzeo, see ticket #996
Property svn:keywords set to `Id`
File size: 35.5 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
[2715]	9	!! 4.0 ! 2011-02 (G. Madec) dynamical allocation
[1572]	10	!!----------------------------------------------------------------------
[825]	11	#if defined key_lim3
[834]	12	!!----------------------------------------------------------------------
	13	!! 'key_lim3' LIM3 sea-ice model
	14	!!----------------------------------------------------------------------
[1572]	15	!! lim_thd_dh : vertical accr./abl. and lateral ablation of sea ice
[825]	16	!!----------------------------------------------------------------------
	17	USE par_oce ! ocean parameters
	18	USE phycst ! physical constants (OCE directory)
[888]	19	USE sbc_oce ! Surface boundary condition: ocean fields
[2715]	20	USE ice ! LIM variables
	21	USE par_ice ! LIM parameters
	22	USE thd_ice ! LIM thermodynamics
	23	USE in_out_manager ! I/O manager
	24	USE lib_mpp ! MPP library
[3294]	25	USE wrk_nemo ! work arrays
[3558]	26	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[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
	74	INTEGER :: zji, zjj ! 2D corresponding indices to ji
	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
[825]	148	isnow = INT( 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - ht_s_b(ji) ) ) )
	149	ztfs(ji) = isnow * rtt + ( 1.0 - isnow ) * rtt
[1572]	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) ) )
	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
	243	zhn = 1.0 - MAX( zzero , SIGN( zone , - zhsnew ) )
	244	ht_s_b(ji) = MAX( zzero , zhsnew )
	245	! Volume and mass variations of snow
[1572]	246	dvsbq_1d (ji) = a_i_b(ji) * ( ht_s_b(ji) - zhsold(ji) - zdh_s_mel(ji) )
	247	dvsbq_1d (ji) = MIN( zzero, dvsbq_1d(ji) )
[1571]	248	rdmsnif_1d(ji) = rdmsnif_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
[1572]	256	z_f_surf (ji) = zqfont_su(ji) / rdt_ice ! 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
	265	zqfont_su(ji) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
	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
	269	dh_i_surf(ji) = dh_i_surf(ji) + zdeltah(ji,jk)
	270	! ! for energy conservation
	271	zdq_i (ji) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) / rdt_ice
	272	!
[834]	273	! contribution to ice-ocean salt flux
[2715]	274	zji = MOD( npb(ji) - 1 , jpi ) + 1
	275	zjj = ( npb(ji) - 1 ) / jpi + 1
[1572]	276	zfsalt_melt(ji) = zfsalt_melt(ji) + ( sss_m(zji,zjj) - sm_i_b(ji) ) * a_i_b(ji) &
	277	& * MIN( zdeltah(ji,jk) , 0.e0 ) * rhoic / rdt_ice
	278	END DO
	279	END DO
[825]	280
[1572]	281	! !-------------------
	282	IF( con_i ) THEN ! Conservation test
	283	! !-------------------
	284	numce_dh = 0
[2715]	285	meance_dh = 0._wp
[921]	286	DO ji = kideb, kiut
	287	IF ( ( z_f_surf(ji) + zdq_i(ji) ) .GE. 1.0e-3 ) THEN
	288	numce_dh = numce_dh + 1
	289	meance_dh = meance_dh + z_f_surf(ji) + zdq_i(ji)
	290	ENDIF
[1572]	291	IF( z_f_surf(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN!
[921]	292	WRITE(numout,*) ' ALERTE heat loss for surface melt '
	293	WRITE(numout,*) ' zji, zjj, jl :', zji, zjj, jl
[2715]	294	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	295	WRITE(numout,*) ' z_f_surf : ', z_f_surf(ji)
	296	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	297	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	298	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	299	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	300	WRITE(numout,*) ' qlbbq_1d : ', qlbbq_1d(ji)
	301	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
	302	WRITE(numout,*) ' sss_m : ', sss_m(zji,zjj)
[921]	303	ENDIF
[1572]	304	END DO
	305	!
	306	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	307	WRITE(numout,*) ' Error report - Category : ', jl
	308	WRITE(numout,*) ' ~~~~~~~~~~~~ '
	309	WRITE(numout,*) ' Number of points where there is sur. me. error : ', numce_dh
	310	WRITE(numout,*) ' Mean basal growth error on error points : ', meance_dh
[1572]	311	!
	312	ENDIF
[825]	313
[834]	314	!----------------------
	315	! 3.3 Snow sublimation
	316	!----------------------
[825]	317
	318	DO ji = kideb, kiut
	319	! if qla is positive (upwards), heat goes to the atmosphere, therefore
	320	! snow sublimates, if qla is negative (downwards), snow condensates
[1572]	321	zdh_s_sub(ji) = - parsub * qla_ice_1d(ji) / ( rhosn * lsub ) * rdt_ice
	322	dh_s_tot (ji) = dh_s_tot(ji) + zdh_s_sub(ji)
	323	zdhcf = ht_s_b(ji) + zdh_s_sub(ji)
	324	ht_s_b (ji) = MAX( zzero , zdhcf )
[825]	325	! we recompute dh_s_tot
[1572]	326	dh_s_tot (ji) = ht_s_b(ji) - zhsold(ji)
	327	qt_s_in (ji,jl) = qt_s_in(ji,jl) + zdh_s_sub(ji)*q_s_b(ji,1)
	328	END DO
[825]	329
[1572]	330	zqt_dummy(:) = 0.e0
[825]	331	DO jk = 1, nlay_s
	332	DO ji = kideb,kiut
[1572]	333	q_s_b (ji,jk) = rhosn * ( cpic * ( rtt - t_s_b(ji,jk) ) + lfus )
	334	zqt_dummy(ji) = zqt_dummy(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s ! heat conservation
[825]	335	END DO
	336	END DO
	337
[1572]	338	DO jk = 1, nlay_s
	339	DO ji = kideb, kiut
	340	! In case of disparition of the snow, we have to update the snow temperatures
[825]	341	zhisn = MAX( zzero , SIGN( zone, - ht_s_b(ji) ) )
	342	t_s_b(ji,jk) = ( 1.0 - zhisn ) * t_s_b(ji,jk) + zhisn * rtt
	343	q_s_b(ji,jk) = ( 1.0 - zhisn ) * q_s_b(ji,jk)
	344	END DO
[921]	345	END DO
[825]	346
[921]	347	!
	348	!------------------------------------------------------------------------------!
	349	! 4) Basal growth / melt !
	350	!------------------------------------------------------------------------------!
	351	!
[825]	352	! Ice basal growth / melt is given by the ratio of heat budget over basal
	353	! ice heat content. Basal heat budget is given by the difference between
	354	! the inner conductive flux (fc_bo_i), from the open water heat flux
	355	! (qlbbqb) and the turbulent ocean flux (fbif).
[834]	356	! fc_bo_i is positive downwards. fbif and qlbbq are positive to the ice
[825]	357
[834]	358	!-----------------------------------------------------
	359	! 4.1 Basal growth - (a) salinity not varying in time
	360	!-----------------------------------------------------
[1572]	361	IF( num_sal /= 2 .AND. num_sal /= 4 ) THEN
[825]	362	DO ji = kideb, kiut
[1572]	363	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) < 0.0 ) THEN
[825]	364	s_i_new(ji) = sm_i_b(ji)
	365	! Melting point in K
	366	ztmelts = - tmut * s_i_new(ji) + rtt
	367	! New ice heat content (Bitz and Lipscomb, 1999)
	368	ztform = t_i_b(ji,nlay_i) ! t_bo_b crashes in the
[921]	369	! Baltic
[1572]	370	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - ztform ) &
	371	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( ztform - rtt ) ) &
	372	& - rcp * ( ztmelts - rtt ) )
[825]	373	! Basal growth rate = - F*dt / q
[1572]	374	dh_i_bott(ji) = - rdt_ice*( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
	375	ENDIF
	376	END DO
	377	ENDIF
[825]	378
[834]	379	!-------------------------------------------------
	380	! 4.1 Basal growth - (b) salinity varying in time
	381	!-------------------------------------------------
[1572]	382	IF( num_sal == 2 .OR. num_sal == 4 ) THEN
[825]	383	! the growth rate (dh_i_bott) is function of the new ice
	384	! heat content (q_i_b(nlay_i+1)). q_i_b depends on the new ice
	385	! salinity (snewice). snewice depends on dh_i_bott
	386	! it converges quickly, so, no problem
[834]	387	! See Vancoppenolle et al., OM08 for more info on this
[825]	388
	389	! Initial value (tested 1D, can be anything between 1 and 20)
	390	num_iter_max = 4
[1572]	391	s_i_new(:) = 4.0
[825]	392
	393	! Iterative procedure
	394	DO iter = 1, num_iter_max
	395	DO ji = kideb, kiut
[1572]	396	IF( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) < 0.e0 ) THEN
[825]	397	zji = MOD( npb(ji) - 1, jpi ) + 1
	398	zjj = ( npb(ji) - 1 ) / jpi + 1
	399	! Melting point in K
	400	ztmelts = - tmut * s_i_new(ji) + rtt
	401	! New ice heat content (Bitz and Lipscomb, 1999)
[1572]	402	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) &
	403	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( t_bo_b(ji) - rtt ) ) &
	404	& - rcp * ( ztmelts-rtt ) )
[825]	405	! Bottom growth rate = - F*dt / q
[1572]	406	dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[825]	407	! New ice salinity ( Cox and Weeks, JGR, 1988 )
	408	! zswi2 (1) if dh_i_bott/rdt .GT. 3.6e-7
	409	! zswi12 (1) if dh_i_bott/rdt .LT. 3.6e-7 and .GT. 2.0e-8
	410	! zswi1 (1) if dh_i_bott/rdt .LT. 2.0e-8
[1572]	411	zgrr = MIN( 1.0e-3, MAX ( dh_i_bott(ji) / rdt_ice , epsi13 ) )
[825]	412	zswi2 = MAX( zzero , SIGN( zone , zgrr - 3.6e-7 ) )
	413	zswi12 = MAX( zzero , SIGN( zone , zgrr - 2.0e-8 ) ) * ( 1.0 - zswi2 )
	414	zswi1 = 1. - zswi2 * zswi12
[1572]	415	zfracs = zswi1 * 0.12 + zswi12 * ( 0.8925 + 0.0568 * LOG( 100.0 * zgrr ) ) &
	416	& + zswi2 * 0.26 / ( 0.26 + 0.74 * EXP ( - 724300.0 * zgrr ) )
	417	zds = zfracs * sss_m(zji,zjj) - s_i_new(ji)
[888]	418	s_i_new(ji) = zfracs * sss_m(zji,zjj)
[825]	419	ENDIF ! fc_bo_i
	420	END DO ! ji
	421	END DO ! iter
	422
	423	! Final values
	424	DO ji = kideb, kiut
[1572]	425	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .LT. 0.0 ) THEN
[825]	426	! New ice salinity must not exceed 15 psu
	427	s_i_new(ji) = MIN( s_i_new(ji), s_i_max )
	428	! Metling point in K
	429	ztmelts = - tmut * s_i_new(ji) + rtt
	430	! New ice heat content (Bitz and Lipscomb, 1999)
[1572]	431	q_i_b(ji,nlay_i+1) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) &
	432	& + lfus * ( 1.0 - ( ztmelts - rtt ) / ( t_bo_b(ji) - rtt ) ) &
	433	& - rcp * ( ztmelts - rtt ) )
[825]	434	! Basal growth rate = - F*dt / q
[1572]	435	dh_i_bott(ji) = - rdt_ice*( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
[834]	436	! Salinity update
[825]	437	! entrapment during bottom growth
[1572]	438	dsm_i_se_1d(ji) = ( s_i_new(ji) * dh_i_bott(ji) + sm_i_b(ji) * ht_i_b(ji) ) &
	439	& / MAX( ht_i_b(ji) + dh_i_bott(ji) ,epsi13 ) - sm_i_b(ji)
[825]	440	ENDIF ! heat budget
[1572]	441	END DO
	442	ENDIF
[825]	443
[834]	444	!----------------
	445	! 4.2 Basal melt
	446	!----------------
[2715]	447	meance_dh = 0._wp
[1572]	448	numce_dh = 0
[2715]	449	zinnermelt(:) = 0._wp
[825]	450
	451	DO ji = kideb, kiut
	452	! heat convergence at the surface > 0
[2715]	453	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0._wp ) THEN
[825]	454	s_i_new(ji) = s_i_b(ji,nlay_i)
	455	zqfont_bo(ji) = rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) )
[2715]	456	zfbase(ji) = zqfont_bo(ji) / rdt_ice ! heat conservation test
	457	zdq_i(ji) = 0._wp
	458	dh_i_bott(ji) = 0._wp
[825]	459	ENDIF
	460	END DO
	461
	462	DO jk = nlay_i, 1, -1
	463	DO ji = kideb, kiut
	464	IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .GE. 0.0 ) THEN
[2715]	465	ztmelts = - tmut * s_i_b(ji,jk) + rtt
	466	IF( t_i_b(ji,jk) >= ztmelts ) THEN
[825]	467	zdeltah(ji,jk) = - zh_i(ji)
	468	dh_i_bott(ji) = dh_i_bott(ji) + zdeltah(ji,jk)
[2715]	469	zinnermelt(ji) = 1._wp
[825]	470	ELSE ! normal ablation
	471	zdeltah(ji,jk) = - zqfont_bo(ji) / q_i_b(ji,jk)
[1572]	472	zqfont_bo(ji) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
[825]	473	zdeltah(ji,jk) = MAX(zdeltah(ji,jk), - zh_i(ji) )
	474	dh_i_bott(ji) = dh_i_bott(ji) + zdeltah(ji,jk)
[1572]	475	zdq_i(ji) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) / rdt_ice
[921]	476	! contribution to salt flux
[825]	477	zji = MOD( npb(ji) - 1, jpi ) + 1
	478	zjj = ( npb(ji) - 1 ) / jpi + 1
[1572]	479	zfsalt_melt(ji) = zfsalt_melt(ji) + ( sss_m(zji,zjj) - sm_i_b(ji) ) * a_i_b(ji) &
	480	& * MIN( zdeltah(ji,jk) , 0.0 ) * rhoic / rdt_ice
[825]	481	ENDIF
	482	ENDIF
	483	END DO ! ji
	484	END DO ! jk
	485
[1572]	486	! !-------------------
	487	IF( con_i ) THEN ! Conservation test
	488	! !-------------------
[921]	489	DO ji = kideb, kiut
[1572]	490	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0.e0 ) THEN
	491	IF( ( zfbase(ji) + zdq_i(ji) ) >= 1.e-3 ) THEN
	492	numce_dh = numce_dh + 1
[921]	493	meance_dh = meance_dh + zfbase(ji) + zdq_i(ji)
	494	ENDIF
	495	IF ( zfbase(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN
[2715]	496	WRITE(numout,*) ' ALERTE heat loss for basal melt : zji, zjj, jl :', zji, zjj, jl
	497	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	498	WRITE(numout,*) ' zfbase : ', zfbase(ji)
	499	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	500	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	501	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	502	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	503	WRITE(numout,*) ' qlbbq_1d : ', qlbbq_1d(ji)
	504	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
	505	WRITE(numout,*) ' sss_m : ', sss_m(zji,zjj)
[921]	506	WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji)
[2715]	507	WRITE(numout,*) ' innermelt : ', INT( zinnermelt(ji) )
[921]	508	ENDIF
[1572]	509	ENDIF
	510	END DO
	511	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	512	WRITE(numout,*) ' Number of points where there is bas. me. error : ', numce_dh
	513	WRITE(numout,*) ' Mean basal melt error on error points : ', meance_dh
	514	WRITE(numout,*) ' Remaining bottom heat : ', zqfont_bo(jiindex_1d)
[1572]	515	!
	516	ENDIF
[825]	517
[921]	518	!
	519	!------------------------------------------------------------------------------!
	520	! 5) Pathological cases !
	521	!------------------------------------------------------------------------------!
	522	!
[834]	523	!----------------------------------------------
	524	! 5.1 Excessive ablation in a 1-category model
	525	!----------------------------------------------
[825]	526
	527	DO ji = kideb, kiut
[1572]	528	! ! in a 1-category sea ice model, bottom ablation must not exceed hmelt (-0.15)
	529	IF( jpl == 1 ) THEN ; zdhbf = MAX( hmelt , dh_i_bott(ji) )
	530	ELSE ; zdhbf = dh_i_bott(ji)
	531	ENDIF
	532	! ! excessive energy is sent to lateral ablation
	533	fsup (ji) = rhoic * lfus * at_i_b(ji) / MAX( 1.0 - at_i_b(ji) , epsi13 ) &
	534	& * ( zdhbf - dh_i_bott(ji) ) / rdt_ice
[825]	535	dh_i_bott(ji) = zdhbf
[1572]	536	! !since ice volume is only used for outputs, we keep it global for all categories
	537	dvbbq_1d (ji) = a_i_b(ji) * dh_i_bott(ji)
	538	! !new ice thickness
	539	zhgnew (ji) = ht_i_b(ji) + dh_i_surf(ji) + dh_i_bott(ji)
	540	! ! diagnostic ( bottom ice growth )
	541	zji = MOD( npb(ji) - 1, jpi ) + 1
	542	zjj = ( npb(ji) - 1 ) / jpi + 1
	543	diag_bot_gr(zji,zjj) = diag_bot_gr(zji,zjj) + MAX(dh_i_bott(ji),0.0)*a_i_b(ji) / rdt_ice
	544	diag_sur_me(zji,zjj) = diag_sur_me(zji,zjj) + MIN(dh_i_surf(ji),0.0)*a_i_b(ji) / rdt_ice
	545	diag_bot_me(zji,zjj) = diag_bot_me(zji,zjj) + MIN(dh_i_bott(ji),0.0)*a_i_b(ji) / rdt_ice
[825]	546	END DO
	547
[834]	548	!-----------------------------------
	549	! 5.2 More than available ice melts
	550	!-----------------------------------
[825]	551	! then heat applied minus heat content at previous time step
	552	! should equal heat remaining
	553	!
	554	DO ji = kideb, kiut
	555	! Adapt the remaining energy if too much ice melts
	556	!--------------------------------------------------
	557	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) !1 if ice
	558	! 0 if no more ice
[1572]	559	zhgnew (ji) = zihgnew * zhgnew(ji) ! ice thickness is put to 0
[825]	560	! remaining heat
[834]	561	zfdt_final(ji) = ( 1.0 - zihgnew ) * ( zqfont_su(ji) + zqfont_bo(ji) )
[825]	562
	563	! If snow remains, energy is used to melt snow
[1572]	564	zhni = ht_s_b(ji) ! snow depth at previous time step
	565	zihg = MAX( zzero , SIGN ( zone , - ht_s_b(ji) ) ) ! 0 if snow
[825]	566
	567	! energy of melting of remaining snow
[1572]	568	zqt_s(ji) = ( 1. - zihg ) * zqt_s(ji) / MAX( zhni, epsi13 )
	569	zdhnm = - ( 1. - zihg ) * ( 1. - zihgnew ) * zfdt_final(ji) / MAX( zqt_s(ji) , epsi13 )
[825]	570	zhnfi = zhni + zdhnm
[1572]	571	zfdt_final(ji) = MAX( zfdt_final(ji) + zqt_s(ji) * zdhnm , 0.0 )
[825]	572	ht_s_b(ji) = MAX( zzero , zhnfi )
	573	zqt_s(ji) = zqt_s(ji) * ht_s_b(ji)
	574
	575	! Mass variations of ice and snow
	576	!---------------------------------
[1572]	577	! ! mass variation of the jl category
[1571]	578	zzfmass_s = - a_i_b(ji) * ( zhni - ht_s_b(ji) ) * rhosn ! snow
	579	zzfmass_i = a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic ! ice
	580	!
	581	zfmass_i(ji) = zzfmass_i ! ice variation saved to compute salt flux (see below)
	582	!
	583	! ! mass variation cumulated over category
	584	rdmsnif_1d(ji) = rdmsnif_1d(ji) + zzfmass_s ! snow
	585	rdmicif_1d(ji) = rdmicif_1d(ji) + zzfmass_i ! ice
[825]	586
	587	! Remaining heat to the ocean
	588	!---------------------------------
[1572]	589	focea(ji) = - zfdt_final(ji) / rdt_ice ! focea is in W.m-2 * dt
[825]	590
	591	END DO
	592
	593	ftotal_fin (:) = zfdt_final(:) / rdt_ice
	594
	595	!---------------------------
	596	! Salt flux and heat fluxes
	597	!---------------------------
	598	DO ji = kideb, kiut
[1572]	599	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) !1 if ice
[825]	600
	601	! Salt flux
[1572]	602	zji = MOD( npb(ji) - 1, jpi ) + 1
	603	zjj = ( npb(ji) - 1 ) / jpi + 1
[825]	604	! new lines
[1572]	605	IF( num_sal == 4 ) THEN
	606	fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) &
	607	& + (1.0 - zihgnew) * zfmass_i(ji) * ( sss_m(zji,zjj) - bulk_sal ) / rdt_ice
	608	ELSE
	609	fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) &
	610	& + (1.0 - zihgnew) * zfmass_i(ji) * ( sss_m(zji,zjj) - sm_i_b(ji) ) / rdt_ice
	611	ENDIF
[825]	612	! Heat flux
	613	! excessive bottom ablation energy (fsup) - 0 except if jpl = 1
	614	! excessive total ablation energy (focea) sent to the ocean
[1572]	615	qfvbq_1d(ji) = qfvbq_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) * rdt_ice
[825]	616
	617	zihic = 1.0 - MAX( zzero , SIGN( zone , -ht_i_b(ji) ) )
	618	! equals 0 if ht_i = 0, 1 if ht_i gt 0
	619	fscbq_1d(ji) = a_i_b(ji) * fstbif_1d(ji)
[1572]	620	qldif_1d(ji) = qldif_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) * rdt_ice &
	621	& + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice
[825]	622	END DO ! ji
	623
	624	!-------------------------------------------
	625	! Correct temperature, energy and thickness
	626	!-------------------------------------------
	627	DO ji = kideb, kiut
[1572]	628	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	629	t_su_b(ji) = zihgnew * t_su_b(ji) + ( 1.0 - zihgnew ) * rtt
[825]	630	END DO ! ji
	631
	632	DO jk = 1, nlay_i
	633	DO ji = kideb, kiut
[1572]	634	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	635	t_i_b(ji,jk) = zihgnew * t_i_b(ji,jk) + ( 1.0 - zihgnew ) * rtt
	636	q_i_b(ji,jk) = zihgnew * q_i_b(ji,jk)
[825]	637	END DO
	638	END DO ! ji
	639
	640	DO ji = kideb, kiut
	641	ht_i_b(ji) = zhgnew(ji)
	642	END DO ! ji
[921]	643	!
	644	!------------------------------------------------------------------------------\|
	645	! 6) Snow-Ice formation \|
	646	!------------------------------------------------------------------------------\|
[1572]	647	! When snow load excesses Archimede's limit, snow-ice interface goes down under sea-level,
	648	! flooding of seawater transforms snow into ice dh_snowice is positive for the ice
[825]	649	DO ji = kideb, kiut
[1572]	650	!
	651	dh_snowice(ji) = MAX( zzero , ( rhosn * ht_s_b(ji) + (rhoic-rau0) * ht_i_b(ji) ) / ( rhosn+rau0-rhoic ) )
	652	zhgnew(ji) = MAX( zhgnew(ji) , zhgnew(ji) + dh_snowice(ji) )
	653	zhnnew = MIN( ht_s_b(ji) , ht_s_b(ji) - dh_snowice(ji) )
[825]	654
[921]	655	! Changes in ice volume and ice mass.
[1572]	656	dvnbq_1d (ji) = a_i_b(ji) * ( zhgnew(ji)-ht_i_b(ji) )
	657	dmgwi_1d (ji) = dmgwi_1d(ji) + a_i_b(ji) * ( ht_s_b(ji) - zhnnew ) * rhosn
[825]	658
[1572]	659	rdmicif_1d(ji) = rdmicif_1d(ji) + a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic
	660	rdmsnif_1d(ji) = rdmsnif_1d(ji) + a_i_b(ji) * ( zhnnew - ht_s_b(ji) ) * rhosn
[825]	661
[921]	662	! Equivalent salt flux (1) Snow-ice formation component
	663	! -----------------------------------------------------
[1572]	664	zji = MOD( npb(ji) - 1, jpi ) + 1
	665	zjj = ( npb(ji) - 1 ) / jpi + 1
[825]	666
[1572]	667	IF( num_sal /= 2 ) THEN ; zsm_snowice = sm_i_b(ji)
	668	ELSE ; zsm_snowice = ( rhoic - rhosn ) / rhoic * sss_m(zji,zjj)
	669	ENDIF
	670	IF( num_sal == 4 ) THEN
	671	fseqv_1d(ji) = fseqv_1d(ji) + ( sss_m(zji,zjj) - bulk_sal ) * a_i_b(ji) &
	672	& * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic / rdt_ice
	673	ELSE
	674	fseqv_1d(ji) = fseqv_1d(ji) + ( sss_m(zji,zjj) - zsm_snowice ) * a_i_b(ji) &
	675	& * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic / rdt_ice
	676	ENDIF
[825]	677	! entrapment during snow ice formation
[1572]	678	i_ice_switch = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - ht_i_b(ji) + 1.0e-6 ) )
	679	isnowic = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - dh_snowice(ji) ) ) * i_ice_switch
	680	IF( num_sal == 2 .OR. num_sal == 4 ) &
	681	dsm_i_si_1d(ji) = ( zsm_snowice*dh_snowice(ji) &
	682	& + sm_i_b(ji) * ht_i_b(ji) / MAX( ht_i_b(ji) + dh_snowice(ji), epsi13) &
	683	& - sm_i_b(ji) ) * isnowic
[825]	684
[921]	685	! Actualize new snow and ice thickness.
[825]	686	ht_s_b(ji) = zhnnew
	687	ht_i_b(ji) = zhgnew(ji)
	688
	689	! Total ablation ! new lines added to debug
[2715]	690	IF( ht_i_b(ji) <= 0._wp ) a_i_b(ji) = 0._wp
[825]	691
	692	! diagnostic ( snow ice growth )
[1572]	693	zji = MOD( npb(ji) - 1, jpi ) + 1
	694	zjj = ( npb(ji) - 1 ) / jpi + 1
	695	diag_sni_gr(zji,zjj) = diag_sni_gr(zji,zjj) + dh_snowice(ji)*a_i_b(ji) / rdt_ice
	696	!
[825]	697	END DO !ji
[2715]	698	!
[3294]	699	CALL wrk_dealloc( jpij, zh_i, zh_s, ztfs, zhsold, zqprec, zqfont_su, zqfont_bo, z_f_surf, zhgnew, zfmass_i )
	700	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 )
	701	CALL wrk_dealloc( jpij, zinnermelt, zfbase, zdq_i )
	702	CALL wrk_dealloc( jpij, jkmax, zdeltah, zqt_i_lay )
[2715]	703	!
[921]	704	END SUBROUTINE lim_thd_dh
[1572]	705
[825]	706	#else
[1572]	707	!!----------------------------------------------------------------------
	708	!! Default option NO LIM3 sea-ice model
	709	!!----------------------------------------------------------------------
[825]	710	CONTAINS
	711	SUBROUTINE lim_thd_dh ! Empty routine
	712	END SUBROUTINE lim_thd_dh
	713	#endif
[1572]	714
	715	!!======================================================================
[921]	716	END MODULE limthd_dh

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