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limthd_dh.F90 in branches/DEV_r2191_3partymerge2010/NEMO/LIM_SRC_3 – NEMO

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source: branches/DEV_r2191_3partymerge2010/NEMO/LIM_SRC_3/limthd_dh.F90 @ 2208

Last change on this file since 2208 was 2208, checked in by rblod, 14 years ago
Put FCM NEMO code changes in DEV_r2191_3partymerge2010 branch
Property svn:keywords set to `Id`
File size: 34.3 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
	9	!!----------------------------------------------------------------------
[825]	10	#if defined key_lim3
[834]	11	!!----------------------------------------------------------------------
	12	!! 'key_lim3' LIM3 sea-ice model
	13	!!----------------------------------------------------------------------
[1572]	14	!! lim_thd_dh : vertical accr./abl. and lateral ablation of sea ice
[825]	15	!!----------------------------------------------------------------------
	16	USE par_oce ! ocean parameters
	17	USE phycst ! physical constants (OCE directory)
[888]	18	USE sbc_oce ! Surface boundary condition: ocean fields
[825]	19	USE thd_ice
	20	USE iceini
	21	USE limistate
	22	USE in_out_manager
	23	USE ice
	24	USE par_ice
[869]	25	USE lib_mpp
[921]	26
[825]	27	IMPLICIT NONE
	28	PRIVATE
	29
[1572]	30	PUBLIC lim_thd_dh ! called by lim_thd
[825]	31
[1572]	32	REAL(wp) :: epsi20 = 1e-20 ! constant values
	33	REAL(wp) :: epsi13 = 1e-13 !
	34	REAL(wp) :: epsi16 = 1e-16 !
	35	REAL(wp) :: zzero = 0.e0 !
	36	REAL(wp) :: zone = 1.e0 !
[825]	37
	38	!!----------------------------------------------------------------------
[1572]	39	!! NEMO/LIM 3.2, UCL-LOCEAN-IPSL (2009)
[1156]	40	!! $Id$
[2208]	41	!! Software governed by the CeCILL licence (NEMOGCM/License_CeCILL.txt)
[825]	42	!!----------------------------------------------------------------------
	43
	44	CONTAINS
	45
	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
[1572]	80	REAL(wp) :: zzfmass_i, zzfmass_s ! temporary scalar
	81	REAL(wp) :: zhsnew, zihgnew, ztmelts ! temporary scalar
	82	REAL(wp) :: zhn, zdhcf, zdhbf, zhni, zhnfi, zihg !
	83	REAL(wp) :: zdhnm, zhnnew, zhisn, zihic !
	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
[825]	93
[1572]	94	REAL(wp), DIMENSION(jpij) :: zh_i ! ice layer thickness
	95	REAL(wp), DIMENSION(jpij) :: zh_s ! snow layer thickness
	96	REAL(wp), DIMENSION(jpij) :: ztfs ! melting point
	97	REAL(wp), DIMENSION(jpij) :: zhsold ! old snow thickness
	98	REAL(wp), DIMENSION(jpij) :: zqprec ! energy of fallen snow
	99	REAL(wp), DIMENSION(jpij) :: zqfont_su ! incoming, remaining surface energy
	100	REAL(wp), DIMENSION(jpij) :: zqfont_bo ! incoming, bottom energy
	101	REAL(wp), DIMENSION(jpij) :: z_f_surf ! surface heat for ablation
	102	REAL(wp), DIMENSION(jpij) :: zhgnew ! new ice thickness
	103	REAL(wp), DIMENSION(jpij) :: zfmass_i !
[825]	104
[1572]	105	REAL(wp), DIMENSION(jpij) :: zdh_s_mel ! snow melt
	106	REAL(wp), DIMENSION(jpij) :: zdh_s_pre ! snow precipitation
	107	REAL(wp), DIMENSION(jpij) :: zdh_s_sub ! snow sublimation
	108	REAL(wp), DIMENSION(jpij) :: zfsalt_melt ! salt flux due to ice melt
[825]	109
[1572]	110	REAL(wp) , DIMENSION(jpij,jkmax) :: zdeltah
[825]	111
[921]	112	! Pathological cases
[1572]	113	REAL(wp), DIMENSION(jpij) :: zfdt_init ! total incoming heat for ice melt
	114	REAL(wp), DIMENSION(jpij) :: zfdt_final ! total remaing heat for ice melt
	115	REAL(wp), DIMENSION(jpij) :: zqt_i ! total ice heat content
	116	REAL(wp), DIMENSION(jpij) :: zqt_s ! total snow heat content
	117	REAL(wp), DIMENSION(jpij) :: zqt_dummy ! dummy heat content
[825]	118
[1572]	119	REAL(wp), DIMENSION(jpij,jkmax) :: zqt_i_lay ! total ice heat content
[825]	120
[921]	121	! Heat conservation
[1572]	122	INTEGER :: num_iter_max, numce_dh
	123	REAL(wp) :: meance_dh
	124	INTEGER , DIMENSION(jpij) :: innermelt
	125	REAL(wp), DIMENSION(jpij) :: zfbase, zdq_i
	126	!!------------------------------------------------------------------
[825]	127
	128	zfsalt_melt(:) = 0.0
	129	ftotal_fin(:) = 0.0
	130	zfdt_init(:) = 0.0
	131	zfdt_final(:) = 0.0
	132
	133	DO ji = kideb, kiut
	134	old_ht_i_b(ji) = ht_i_b(ji)
	135	old_ht_s_b(ji) = ht_s_b(ji)
	136	END DO
[921]	137	!
	138	!------------------------------------------------------------------------------!
	139	! 1) Calculate available heat for surface ablation !
	140	!------------------------------------------------------------------------------!
	141	!
[825]	142	DO ji = kideb,kiut
	143	isnow = INT( 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - ht_s_b(ji) ) ) )
	144	ztfs(ji) = isnow * rtt + ( 1.0 - isnow ) * rtt
[1572]	145	z_f_surf(ji) = qnsr_ice_1d(ji) + ( 1.0 - i0(ji) ) * qsr_ice_1d(ji) - fc_su(ji)
	146	z_f_surf(ji) = MAX( zzero , z_f_surf(ji) ) * MAX( zzero , SIGN( zone , t_su_b(ji) - ztfs(ji) ) )
	147	zfdt_init(ji) = ( z_f_surf(ji) + MAX( fbif_1d(ji) + qlbbq_1d(ji) + fc_bo_i(ji),0.0 ) ) * rdt_ice
[825]	148	END DO ! ji
	149
	150	zqfont_su(:) = 0.0
	151	zqfont_bo(:) = 0.0
	152	dsm_i_se_1d(:) = 0.0
	153	dsm_i_si_1d(:) = 0.0
[921]	154	!
	155	!------------------------------------------------------------------------------!
	156	! 2) Computing layer thicknesses and snow and sea-ice enthalpies. !
	157	!------------------------------------------------------------------------------!
	158	!
[825]	159	! Layer thickness
	160	DO ji = kideb,kiut
	161	zh_i(ji) = ht_i_b(ji) / nlay_i
	162	zh_s(ji) = ht_s_b(ji) / nlay_s
	163	END DO
	164
[834]	165	! Total enthalpy of the snow
[825]	166	zqt_s(:) = 0.0
	167	DO jk = 1, nlay_s
	168	DO ji = kideb,kiut
[1572]	169	zqt_s(ji) = zqt_s(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s
[825]	170	END DO
	171	END DO
	172
[834]	173	! Total enthalpy of the ice
[825]	174	zqt_i(:) = 0.0
	175	DO jk = 1, nlay_i
	176	DO ji = kideb,kiut
	177	zqt_i(ji) = zqt_i(ji) + q_i_b(ji,jk) * ht_i_b(ji) / nlay_i
[1572]	178	zqt_i_lay(ji,jk) = q_i_b(ji,jk) * ht_i_b(ji) / nlay_i
[825]	179	END DO
	180	END DO
[921]	181	!
	182	!------------------------------------------------------------------------------\|
	183	! 3) Surface ablation and sublimation \|
	184	!------------------------------------------------------------------------------\|
	185	!
[834]	186	!-------------------------
	187	! 3.1 Snow precips / melt
	188	!-------------------------
[825]	189	! Snow accumulation in one thermodynamic time step
	190	! snowfall is partitionned between leads and ice
	191	! if snow fall was uniform, a fraction (1-at_i) would fall into leads
	192	! but because of the winds, more snow falls on leads than on sea ice
	193	! and a greater fraction (1-at_i)^beta of the total mass of snow
[834]	194	! (beta < 1) falls in leads.
[825]	195	! In reality, beta depends on wind speed,
	196	! and should decrease with increasing wind speed but here, it is
[834]	197	! considered as a constant. an average value is 0.66
[825]	198	! Martin Vancoppenolle, December 2006
	199
	200	! Snow fall
	201	DO ji = kideb, kiut
	202	zcoeff = ( 1.0 - ( 1.0 - at_i_b(ji) )**betas ) / at_i_b(ji)
	203	zdh_s_pre(ji) = zcoeff * sprecip_1d(ji) * rdt_ice / rhosn
	204	END DO
	205	zdh_s_mel(:) = 0.0
	206
	207	! Melt of fallen snow
	208	DO ji = kideb, kiut
	209	! tatm_ice is now in K
[1572]	210	zqprec (ji) = rhosn * ( cpic * ( rtt - tatm_ice_1d(ji) ) + lfus )
	211	zqfont_su(ji) = z_f_surf(ji) * rdt_ice
	212	zdeltah (ji,1) = MIN( 0.e0 , - zqfont_su(ji) / MAX( zqprec(ji) , epsi13 ) )
	213	zqfont_su(ji) = MAX( 0.e0 , - zdh_s_pre(ji) - zdeltah(ji,1) ) * zqprec(ji)
	214	zdeltah (ji,1) = MAX( - zdh_s_pre(ji) , zdeltah(ji,1) )
	215	zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,1)
[825]	216	! heat conservation
[1572]	217	qt_s_in(ji,jl) = qt_s_in(ji,jl) + zqprec(ji) * zdh_s_pre(ji)
	218	zqt_s (ji) = zqt_s (ji) + zqprec(ji) * zdh_s_pre(ji)
	219	zqt_s (ji) = MAX( zqt_s(ji) - zqfont_su(ji) , 0.e0 )
[825]	220	END DO
	221
	222
	223	! Snow melt due to surface heat imbalance
	224	DO jk = 1, nlay_s
	225	DO ji = kideb, kiut
[1572]	226	zdeltah (ji,jk) = - zqfont_su(ji) / q_s_b(ji,jk)
	227	zqfont_su(ji) = MAX( 0.0 , - zh_s(ji) - zdeltah(ji,jk) ) * q_s_b(ji,jk)
	228	zdeltah (ji,jk) = MAX( zdeltah(ji,jk) , - zh_s(ji) )
	229	zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,jk) ! resulting melt of snow
[825]	230	END DO
	231	END DO
	232
	233	! Apply snow melt to snow depth
	234	DO ji = kideb, kiut
	235	dh_s_tot(ji) = zdh_s_mel(ji) + zdh_s_pre(ji)
	236	! Old and new snow depths
	237	zhsold(ji) = ht_s_b(ji)
	238	zhsnew = ht_s_b(ji) + dh_s_tot(ji)
	239	! If snow is still present zhn = 1, else zhn = 0
	240	zhn = 1.0 - MAX( zzero , SIGN( zone , - zhsnew ) )
	241	ht_s_b(ji) = MAX( zzero , zhsnew )
	242	! Volume and mass variations of snow
[1572]	243	dvsbq_1d (ji) = a_i_b(ji) * ( ht_s_b(ji) - zhsold(ji) - zdh_s_mel(ji) )
	244	dvsbq_1d (ji) = MIN( zzero, dvsbq_1d(ji) )
[1571]	245	rdmsnif_1d(ji) = rdmsnif_1d(ji) + rhosn * dvsbq_1d(ji)
[825]	246	END DO ! ji
	247
[834]	248	!--------------------------
	249	! 3.2 Surface ice ablation
	250	!--------------------------
[825]	251	DO ji = kideb, kiut
[1572]	252	dh_i_surf(ji) = 0.e0
	253	z_f_surf (ji) = zqfont_su(ji) / rdt_ice ! heat conservation test
	254	zdq_i (ji) = 0.e0
[825]	255	END DO ! ji
	256
	257	DO jk = 1, nlay_i
	258	DO ji = kideb, kiut
[1572]	259	! ! melt of layer jk
	260	zdeltah (ji,jk) = - zqfont_su(ji) / q_i_b(ji,jk)
	261	! ! recompute heat available
	262	zqfont_su(ji) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * q_i_b(ji,jk)
	263	! ! melt of layer jk cannot be higher than its thickness
	264	zdeltah (ji,jk) = MAX( zdeltah(ji,jk) , - zh_i(ji) )
	265	! ! update surface melt
	266	dh_i_surf(ji) = dh_i_surf(ji) + zdeltah(ji,jk)
	267	! ! for energy conservation
	268	zdq_i (ji) = zdq_i(ji) + zdeltah(ji,jk) * q_i_b(ji,jk) / rdt_ice
	269	!
[834]	270	! contribution to ice-ocean salt flux
[1572]	271	zji = MOD( npb(ji) - 1, jpi ) + 1
	272	zjj = ( npb(ji) - 1 ) / jpi + 1
	273	zfsalt_melt(ji) = zfsalt_melt(ji) + ( sss_m(zji,zjj) - sm_i_b(ji) ) * a_i_b(ji) &
	274	& * MIN( zdeltah(ji,jk) , 0.e0 ) * rhoic / rdt_ice
	275	END DO
	276	END DO
[825]	277
[1572]	278	! !-------------------
	279	IF( con_i ) THEN ! Conservation test
	280	! !-------------------
	281	numce_dh = 0
	282	meance_dh = 0.e0
[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 '
	290	WRITE(numout,*) ' zji, zjj, jl :', zji, zjj, jl
	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)
	299	WRITE(numout,*) ' sss_m : ', sss_m(zji,zjj)
	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
[825]	338	zhisn = MAX( zzero , SIGN( zone, - ht_s_b(ji) ) )
	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	!-----------------------------------------------------
[1572]	358	IF( num_sal /= 2 .AND. num_sal /= 4 ) THEN
[825]	359	DO ji = kideb, kiut
[1572]	360	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) < 0.0 ) 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
[1572]	371	dh_i_bott(ji) = - rdt_ice*( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1)
	372	ENDIF
	373	END DO
	374	ENDIF
[825]	375
[834]	376	!-------------------------------------------------
	377	! 4.1 Basal growth - (b) salinity varying in time
	378	!-------------------------------------------------
[1572]	379	IF( num_sal == 2 .OR. num_sal == 4 ) THEN
[825]	380	! the growth rate (dh_i_bott) is function of the new ice
	381	! heat content (q_i_b(nlay_i+1)). q_i_b depends on the new ice
	382	! salinity (snewice). snewice depends on dh_i_bott
	383	! 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
[825]	394	zji = MOD( npb(ji) - 1, jpi ) + 1
	395	zjj = ( npb(ji) - 1 ) / jpi + 1
	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
[1572]	408	zgrr = MIN( 1.0e-3, MAX ( dh_i_bott(ji) / rdt_ice , 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 ) )
	414	zds = zfracs * sss_m(zji,zjj) - s_i_new(ji)
[888]	415	s_i_new(ji) = zfracs * sss_m(zji,zjj)
[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
[1572]	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	!----------------
[825]	444	meance_dh = 0.0
[1572]	445	numce_dh = 0
[825]	446	innermelt(:) = 0
	447
	448	DO ji = kideb, kiut
	449	! heat convergence at the surface > 0
[1572]	450	IF( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) >= 0.e0 ) THEN
[921]	451
[825]	452	s_i_new(ji) = s_i_b(ji,nlay_i)
	453	zqfont_bo(ji) = rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) )
	454
	455	zfbase(ji) = zqfont_bo(ji) / rdt_ice ! heat conservation test
[1572]	456	zdq_i(ji) = 0.e0
[825]	457
[1572]	458	dh_i_bott(ji) = 0.e0
[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
	465	ztmelts = - tmut * s_i_b(ji,jk) + rtt
	466	IF ( t_i_b(ji,jk) .GE. ztmelts ) THEN
	467	zdeltah(ji,jk) = - zh_i(ji)
	468	dh_i_bott(ji) = dh_i_bott(ji) + zdeltah(ji,jk)
	469	innermelt(ji) = 1
	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
	496	WRITE(numout,*) ' ALERTE heat loss for basal melt '
	497	WRITE(numout,*) ' zji, zjj, jl :', zji, zjj, jl
	498	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	499	WRITE(numout,*) ' zfbase : ', zfbase(ji)
	500	WRITE(numout,*) ' zdq_i : ', zdq_i(ji)
	501	WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji)
	502	WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji)
	503	WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji)
	504	WRITE(numout,*) ' qlbbq_1d: ', qlbbq_1d(ji)
	505	WRITE(numout,*) ' s_i_new : ', s_i_new(ji)
	506	WRITE(numout,*) ' sss_m : ', sss_m(zji,zjj)
	507	WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji)
	508	WRITE(numout,*) ' innermelt : ', innermelt(ji)
	509	ENDIF
[1572]	510	ENDIF
	511	END DO
	512	IF( numce_dh > 0 ) meance_dh = meance_dh / numce_dh
[921]	513	WRITE(numout,*) ' Number of points where there is bas. me. error : ', numce_dh
	514	WRITE(numout,*) ' Mean basal melt error on error points : ', meance_dh
	515	WRITE(numout,*) ' Remaining bottom heat : ', zqfont_bo(jiindex_1d)
[1572]	516	!
	517	ENDIF
[825]	518
[921]	519	!
	520	!------------------------------------------------------------------------------!
	521	! 5) Pathological cases !
	522	!------------------------------------------------------------------------------!
	523	!
[834]	524	!----------------------------------------------
	525	! 5.1 Excessive ablation in a 1-category model
	526	!----------------------------------------------
[825]	527
	528	DO ji = kideb, kiut
[1572]	529	! ! in a 1-category sea ice model, bottom ablation must not exceed hmelt (-0.15)
	530	IF( jpl == 1 ) THEN ; zdhbf = MAX( hmelt , dh_i_bott(ji) )
	531	ELSE ; zdhbf = dh_i_bott(ji)
	532	ENDIF
	533	! ! excessive energy is sent to lateral ablation
	534	fsup (ji) = rhoic * lfus * at_i_b(ji) / MAX( 1.0 - at_i_b(ji) , epsi13 ) &
	535	& * ( zdhbf - dh_i_bott(ji) ) / rdt_ice
[825]	536	dh_i_bott(ji) = zdhbf
[1572]	537	! !since ice volume is only used for outputs, we keep it global for all categories
	538	dvbbq_1d (ji) = a_i_b(ji) * dh_i_bott(ji)
	539	! !new ice thickness
	540	zhgnew (ji) = ht_i_b(ji) + dh_i_surf(ji) + dh_i_bott(ji)
	541	! ! diagnostic ( bottom ice growth )
	542	zji = MOD( npb(ji) - 1, jpi ) + 1
	543	zjj = ( npb(ji) - 1 ) / jpi + 1
	544	diag_bot_gr(zji,zjj) = diag_bot_gr(zji,zjj) + MAX(dh_i_bott(ji),0.0)*a_i_b(ji) / rdt_ice
	545	diag_sur_me(zji,zjj) = diag_sur_me(zji,zjj) + MIN(dh_i_surf(ji),0.0)*a_i_b(ji) / rdt_ice
	546	diag_bot_me(zji,zjj) = diag_bot_me(zji,zjj) + MIN(dh_i_bott(ji),0.0)*a_i_b(ji) / rdt_ice
[825]	547	END DO
	548
[834]	549	!-----------------------------------
	550	! 5.2 More than available ice melts
	551	!-----------------------------------
[825]	552	! then heat applied minus heat content at previous time step
	553	! should equal heat remaining
	554	!
	555	DO ji = kideb, kiut
	556	! Adapt the remaining energy if too much ice melts
	557	!--------------------------------------------------
	558	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) !1 if ice
	559	! 0 if no more ice
[1572]	560	zhgnew (ji) = zihgnew * zhgnew(ji) ! ice thickness is put to 0
[825]	561	! remaining heat
[834]	562	zfdt_final(ji) = ( 1.0 - zihgnew ) * ( zqfont_su(ji) + zqfont_bo(ji) )
[825]	563
	564	! If snow remains, energy is used to melt snow
[1572]	565	zhni = ht_s_b(ji) ! snow depth at previous time step
	566	zihg = MAX( zzero , SIGN ( zone , - ht_s_b(ji) ) ) ! 0 if snow
[825]	567
	568	! energy of melting of remaining snow
[1572]	569	zqt_s(ji) = ( 1. - zihg ) * zqt_s(ji) / MAX( zhni, epsi13 )
	570	zdhnm = - ( 1. - zihg ) * ( 1. - zihgnew ) * zfdt_final(ji) / MAX( zqt_s(ji) , epsi13 )
[825]	571	zhnfi = zhni + zdhnm
[1572]	572	zfdt_final(ji) = MAX( zfdt_final(ji) + zqt_s(ji) * zdhnm , 0.0 )
[825]	573	ht_s_b(ji) = MAX( zzero , zhnfi )
	574	zqt_s(ji) = zqt_s(ji) * ht_s_b(ji)
	575
	576	! Mass variations of ice and snow
	577	!---------------------------------
[1572]	578	! ! mass variation of the jl category
[1571]	579	zzfmass_s = - a_i_b(ji) * ( zhni - ht_s_b(ji) ) * rhosn ! snow
	580	zzfmass_i = a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic ! ice
	581	!
	582	zfmass_i(ji) = zzfmass_i ! ice variation saved to compute salt flux (see below)
	583	!
	584	! ! mass variation cumulated over category
	585	rdmsnif_1d(ji) = rdmsnif_1d(ji) + zzfmass_s ! snow
	586	rdmicif_1d(ji) = rdmicif_1d(ji) + zzfmass_i ! ice
[825]	587
	588	! Remaining heat to the ocean
	589	!---------------------------------
[1572]	590	focea(ji) = - zfdt_final(ji) / rdt_ice ! focea is in W.m-2 * dt
[825]	591
	592	END DO
	593
	594	ftotal_fin (:) = zfdt_final(:) / rdt_ice
	595
	596	!---------------------------
	597	! Salt flux and heat fluxes
	598	!---------------------------
	599	DO ji = kideb, kiut
[1572]	600	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) !1 if ice
[825]	601
	602	! Salt flux
[1572]	603	zji = MOD( npb(ji) - 1, jpi ) + 1
	604	zjj = ( npb(ji) - 1 ) / jpi + 1
[825]	605	! new lines
[1572]	606	IF( num_sal == 4 ) THEN
	607	fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) &
	608	& + (1.0 - zihgnew) * zfmass_i(ji) * ( sss_m(zji,zjj) - bulk_sal ) / rdt_ice
	609	ELSE
	610	fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) &
	611	& + (1.0 - zihgnew) * zfmass_i(ji) * ( sss_m(zji,zjj) - sm_i_b(ji) ) / rdt_ice
	612	ENDIF
[825]	613	! Heat flux
	614	! excessive bottom ablation energy (fsup) - 0 except if jpl = 1
	615	! excessive total ablation energy (focea) sent to the ocean
[1572]	616	qfvbq_1d(ji) = qfvbq_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) * rdt_ice
[825]	617
	618	zihic = 1.0 - MAX( zzero , SIGN( zone , -ht_i_b(ji) ) )
	619	! equals 0 if ht_i = 0, 1 if ht_i gt 0
	620	fscbq_1d(ji) = a_i_b(ji) * fstbif_1d(ji)
[1572]	621	qldif_1d(ji) = qldif_1d(ji) + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) * rdt_ice &
	622	& + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice
[825]	623	END DO ! ji
	624
	625	!-------------------------------------------
	626	! Correct temperature, energy and thickness
	627	!-------------------------------------------
	628	DO ji = kideb, kiut
[1572]	629	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	630	t_su_b(ji) = zihgnew * t_su_b(ji) + ( 1.0 - zihgnew ) * rtt
[825]	631	END DO ! ji
	632
	633	DO jk = 1, nlay_i
	634	DO ji = kideb, kiut
[1572]	635	zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) )
	636	t_i_b(ji,jk) = zihgnew * t_i_b(ji,jk) + ( 1.0 - zihgnew ) * rtt
	637	q_i_b(ji,jk) = zihgnew * q_i_b(ji,jk)
[825]	638	END DO
	639	END DO ! ji
	640
	641	DO ji = kideb, kiut
	642	ht_i_b(ji) = zhgnew(ji)
	643	END DO ! ji
[921]	644	!
	645	!------------------------------------------------------------------------------\|
	646	! 6) Snow-Ice formation \|
	647	!------------------------------------------------------------------------------\|
[1572]	648	! When snow load excesses Archimede's limit, snow-ice interface goes down under sea-level,
	649	! flooding of seawater transforms snow into ice dh_snowice is positive for the ice
[825]	650	DO ji = kideb, kiut
[1572]	651	!
	652	dh_snowice(ji) = MAX( zzero , ( rhosn * ht_s_b(ji) + (rhoic-rau0) * ht_i_b(ji) ) / ( rhosn+rau0-rhoic ) )
	653	zhgnew(ji) = MAX( zhgnew(ji) , zhgnew(ji) + dh_snowice(ji) )
	654	zhnnew = MIN( ht_s_b(ji) , ht_s_b(ji) - dh_snowice(ji) )
[825]	655
[921]	656	! Changes in ice volume and ice mass.
[1572]	657	dvnbq_1d (ji) = a_i_b(ji) * ( zhgnew(ji)-ht_i_b(ji) )
	658	dmgwi_1d (ji) = dmgwi_1d(ji) + a_i_b(ji) * ( ht_s_b(ji) - zhnnew ) * rhosn
[825]	659
[1572]	660	rdmicif_1d(ji) = rdmicif_1d(ji) + a_i_b(ji) * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic
	661	rdmsnif_1d(ji) = rdmsnif_1d(ji) + a_i_b(ji) * ( zhnnew - ht_s_b(ji) ) * rhosn
[825]	662
[921]	663	! Equivalent salt flux (1) Snow-ice formation component
	664	! -----------------------------------------------------
[1572]	665	zji = MOD( npb(ji) - 1, jpi ) + 1
	666	zjj = ( npb(ji) - 1 ) / jpi + 1
[825]	667
[1572]	668	IF( num_sal /= 2 ) THEN ; zsm_snowice = sm_i_b(ji)
	669	ELSE ; zsm_snowice = ( rhoic - rhosn ) / rhoic * sss_m(zji,zjj)
	670	ENDIF
	671	IF( num_sal == 4 ) THEN
	672	fseqv_1d(ji) = fseqv_1d(ji) + ( sss_m(zji,zjj) - bulk_sal ) * a_i_b(ji) &
	673	& * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic / rdt_ice
	674	ELSE
	675	fseqv_1d(ji) = fseqv_1d(ji) + ( sss_m(zji,zjj) - zsm_snowice ) * a_i_b(ji) &
	676	& * ( zhgnew(ji) - ht_i_b(ji) ) * rhoic / rdt_ice
	677	ENDIF
[825]	678	! entrapment during snow ice formation
[1572]	679	i_ice_switch = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - ht_i_b(ji) + 1.0e-6 ) )
	680	isnowic = 1.0 - MAX( 0.e0 , SIGN( 1.0 , - dh_snowice(ji) ) ) * i_ice_switch
	681	IF( num_sal == 2 .OR. num_sal == 4 ) &
	682	dsm_i_si_1d(ji) = ( zsm_snowice*dh_snowice(ji) &
	683	& + sm_i_b(ji) * ht_i_b(ji) / MAX( ht_i_b(ji) + dh_snowice(ji), epsi13) &
	684	& - sm_i_b(ji) ) * isnowic
[825]	685
[921]	686	! Actualize new snow and ice thickness.
[825]	687	ht_s_b(ji) = zhnnew
	688	ht_i_b(ji) = zhgnew(ji)
	689
	690	! Total ablation ! new lines added to debug
[1572]	691	IF( ht_i_b(ji) <= 0.e0 ) a_i_b(ji) = 0.0
[825]	692
	693	! diagnostic ( snow ice growth )
[1572]	694	zji = MOD( npb(ji) - 1, jpi ) + 1
	695	zjj = ( npb(ji) - 1 ) / jpi + 1
	696	diag_sni_gr(zji,zjj) = diag_sni_gr(zji,zjj) + dh_snowice(ji)*a_i_b(ji) / rdt_ice
	697	!
[825]	698	END DO !ji
	699
[921]	700	END SUBROUTINE lim_thd_dh
[1572]	701
[825]	702	#else
[1572]	703	!!----------------------------------------------------------------------
	704	!! Default option NO LIM3 sea-ice model
	705	!!----------------------------------------------------------------------
[825]	706	CONTAINS
	707	SUBROUTINE lim_thd_dh ! Empty routine
	708	END SUBROUTINE lim_thd_dh
	709	#endif
[1572]	710
	711	!!======================================================================
[921]	712	END MODULE limthd_dh

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