Context Navigation

limitd_me.F90 @ 7753

Last change on this file since 7753 was 7753, checked in by mocavero, 7 years ago
Reverting trunk to remove OpenMP
Property svn:keywords set to `Id`
File size: 47.0 KB

Rev	Line
[825]	1	MODULE limitd_me
	2	!!======================================================================
	3	!! * MODULE limitd_me *
[2715]	4	!! LIM-3 : Mechanical impact on ice thickness distribution
[825]	5	!!======================================================================
[1572]	6	!! History : LIM ! 2006-02 (M. Vancoppenolle) Original code
[4688]	7	!! 3.2 ! 2009-07 (M. Vancoppenolle, Y. Aksenov, G. Madec) bug correction in smsw & sfx_dyn
[2715]	8	!! 4.0 ! 2011-02 (G. Madec) dynamical allocation
[825]	9	!!----------------------------------------------------------------------
[1572]	10	#if defined key_lim3
	11	!!----------------------------------------------------------------------
[3625]	12	!! 'key_lim3' LIM-3 sea-ice model
[1572]	13	!!----------------------------------------------------------------------
[4161]	14	USE par_oce ! ocean parameters
	15	USE dom_oce ! ocean domain
	16	USE phycst ! physical constants (ocean directory)
	17	USE sbc_oce ! surface boundary condition: ocean fields
	18	USE thd_ice ! LIM thermodynamics
	19	USE ice ! LIM variables
	20	USE limvar ! LIM
	21	USE lbclnk ! lateral boundary condition - MPP exchanges
	22	USE lib_mpp ! MPP library
	23	USE wrk_nemo ! work arrays
[5123]	24
[5134]	25	USE in_out_manager ! I/O manager
[4161]	26	USE iom ! I/O manager
[4688]	27	USE lib_fortran ! glob_sum
	28	USE timing ! Timing
	29	USE limcons ! conservation tests
[7646]	30	USE limctl ! control prints
[921]	31
[825]	32	IMPLICIT NONE
	33	PRIVATE
	34
[2715]	35	PUBLIC lim_itd_me ! called by ice_stp
	36	PUBLIC lim_itd_me_icestrength
	37	PUBLIC lim_itd_me_init
[5123]	38	PUBLIC lim_itd_me_alloc ! called by sbc_lim_init
[825]	39
[921]	40	!-----------------------------------------------------------------------
	41	! Variables shared among ridging subroutines
	42	!-----------------------------------------------------------------------
[4333]	43	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area
	44	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged
[6416]	45	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/closing associated w/ category n
[4333]	46	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness
	47	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness
	48	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice
[6416]	49	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! thickness of ridging ice / mean ridge thickness
[4333]	50	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging
	51	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting
[825]	52
[2715]	53	REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier
[6416]	54	REAL(wp), PARAMETER :: kraft = 0.5_wp ! rafting multipliyer
[825]	55
[2715]	56	REAL(wp) :: Cp !
[921]	57	!
[3625]	58	!
[825]	59	!!----------------------------------------------------------------------
[2528]	60	!! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010)
[1156]	61	!! $Id$
[2715]	62	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[825]	63	!!----------------------------------------------------------------------
[2715]	64	CONTAINS
[825]	65
[2715]	66	INTEGER FUNCTION lim_itd_me_alloc()
	67	!!---------------------------------------------------------------------!
	68	!! * ROUTINE lim_itd_me_alloc *
	69	!!---------------------------------------------------------------------!
[7646]	70	ALLOCATE( &
[2715]	71	!* Variables shared among ridging subroutines
[7646]	72	& asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , aksum (jpi,jpj) , &
	73	& hrmin(jpi,jpj,jpl) , hraft(jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , &
	74	& hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , STAT=lim_itd_me_alloc )
[2715]	75	!
	76	IF( lim_itd_me_alloc /= 0 ) CALL ctl_warn( 'lim_itd_me_alloc: failed to allocate arrays' )
	77	!
	78	END FUNCTION lim_itd_me_alloc
[1156]	79
[825]	80
[2715]	81	SUBROUTINE lim_itd_me
[921]	82	!!---------------------------------------------------------------------!
	83	!! * ROUTINE lim_itd_me *
	84	!!
[2715]	85	!! ** Purpose : computes the mechanical redistribution of ice thickness
[921]	86	!!
[2715]	87	!! ** Method : Steps :
	88	!! 1) Thickness categories boundaries, ice / o.w. concentrations
	89	!! Ridge preparation
	90	!! 2) Dynamical inputs (closing rate, divu_adv, opning)
	91	!! 3) Ridging iteration
	92	!! 4) Ridging diagnostics
	93	!! 5) Heat, salt and freshwater fluxes
	94	!! 6) Compute increments of tate variables and come back to old values
[921]	95	!!
[2715]	96	!! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626.
	97	!! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980.
	98	!! Rothrock, D. A., 1975: JGR, 80, 4514-4519.
	99	!! Thorndike et al., 1975, JGR, 80, 4501-4513.
	100	!! Bitz et al., JGR, 2001
	101	!! Amundrud and Melling, JGR 2005
	102	!! Babko et al., JGR 2002
[921]	103	!!
[1572]	104	!! This routine is based on CICE code and authors William H. Lipscomb,
	105	!! and Elizabeth C. Hunke, LANL are gratefully acknowledged
[921]	106	!!--------------------------------------------------------------------!
[5123]	107	INTEGER :: ji, jj, jk, jl ! dummy loop index
	108	INTEGER :: niter ! local integer
[3625]	109	INTEGER :: iterate_ridging ! if true, repeat the ridging
[5123]	110	REAL(wp) :: za, zfac ! local scalar
[2715]	111	CHARACTER (len = 15) :: fieldid
[5202]	112	REAL(wp), POINTER, DIMENSION(:,:) :: closing_net ! net rate at which area is removed (1/s)
	113	! (ridging ice area - area of new ridges) / dt
	114	REAL(wp), POINTER, DIMENSION(:,:) :: divu_adv ! divu as implied by transport scheme (1/s)
	115	REAL(wp), POINTER, DIMENSION(:,:) :: opning ! rate of opening due to divergence/shear
	116	REAL(wp), POINTER, DIMENSION(:,:) :: closing_gross ! rate at which area removed, not counting area of new ridges
[4688]	117	!
[5123]	118	INTEGER, PARAMETER :: nitermax = 20
	119	!
[4688]	120	REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b
[2715]	121	!!-----------------------------------------------------------------------------
[4161]	122	IF( nn_timing == 1 ) CALL timing_start('limitd_me')
[825]	123
[7753]	124	CALL wrk_alloc( jpi,jpj, closing_net, divu_adv, opning, closing_gross )
[825]	125
[4688]	126	! conservation test
[7646]	127	IF( ln_limdiachk ) CALL lim_cons_hsm(0, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b)
[4161]	128
[921]	129	!-----------------------------------------------------------------------------!
	130	! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons
	131	!-----------------------------------------------------------------------------!
[5134]	132	Cp = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE
[3625]	133	!
	134	CALL lim_itd_me_ridgeprep ! prepare ridging
	135	!
[825]	136
[2715]	137	DO jj = 1, jpj ! Initialize arrays.
[825]	138	DO ji = 1, jpi
	139
[921]	140	!-----------------------------------------------------------------------------!
	141	! 2) Dynamical inputs (closing rate, divu_adv, opning)
	142	!-----------------------------------------------------------------------------!
	143	!
	144	! 2.1 closing_net
	145	!-----------------
	146	! Compute the net rate of closing due to convergence
	147	! and shear, based on Flato and Hibler (1995).
	148	!
	149	! The energy dissipation rate is equal to the net closing rate
	150	! times the ice strength.
	151	!
	152	! NOTE: The NET closing rate is equal to the rate that open water
	153	! area is removed, plus the rate at which ice area is removed by
	154	! ridging, minus the rate at which area is added in new ridges.
	155	! The GROSS closing rate is equal to the first two terms (open
	156	! water closing and thin ice ridging) without the third term
	157	! (thick, newly ridged ice).
[825]	158
[5123]	159	closing_net(ji,jj) = rn_cs * 0.5 * ( delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp )
[825]	160
[921]	161	! 2.2 divu_adv
	162	!--------------
	163	! Compute divu_adv, the divergence rate given by the transport/
	164	! advection scheme, which may not be equal to divu as computed
	165	! from the velocity field.
	166	!
	167	! If divu_adv < 0, make sure the closing rate is large enough
	168	! to give asum = 1.0 after ridging.
[6416]	169
	170	divu_adv(ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep
[825]	171
[2715]	172	IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) )
[825]	173
[921]	174	! 2.3 opning
	175	!------------
[3625]	176	! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging.
[921]	177	opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj)
[825]	178	END DO
	179	END DO
	180
[921]	181	!-----------------------------------------------------------------------------!
	182	! 3) Ridging iteration
	183	!-----------------------------------------------------------------------------!
[2715]	184	niter = 1 ! iteration counter
[869]	185	iterate_ridging = 1
[825]	186
[869]	187	DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax )
[825]	188
[6416]	189	! 3.2 closing_gross
	190	!-----------------------------------------------------------------------------!
	191	! Based on the ITD of ridging and ridged ice, convert the net
	192	! closing rate to a gross closing rate.
	193	! NOTE: 0 < aksum <= 1
[7753]	194	closing_gross(:,:) = closing_net(:,:) / aksum(:,:)
[6416]	195
	196	! correction to closing rate and opening if closing rate is excessive
	197	!---------------------------------------------------------------------
	198	! Reduce the closing rate if more than 100% of the open water
	199	! would be removed. Reduce the opening rate proportionately.
[921]	200	DO jj = 1, jpj
	201	DO ji = 1, jpi
[6416]	202	za = ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice
[7646]	203	IF ( za < 0._wp .AND. za > - ato_i(ji,jj) ) THEN ! would lead to negative ato_i
	204	zfac = - ato_i(ji,jj) / za
[6416]	205	opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) - ato_i(ji,jj) * r1_rdtice
	206	ELSEIF( za > 0._wp .AND. za > ( asum(ji,jj) - ato_i(ji,jj) ) ) THEN ! would lead to ato_i > asum
[7646]	207	zfac = ( asum(ji,jj) - ato_i(ji,jj) ) / za
[6416]	208	opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) + ( asum(ji,jj) - ato_i(ji,jj) ) * r1_rdtice
[5123]	209	ENDIF
	210	END DO
	211	END DO
[825]	212
[921]	213	! correction to closing rate / opening if excessive ice removal
	214	!---------------------------------------------------------------
	215	! Reduce the closing rate if more than 100% of any ice category
	216	! would be removed. Reduce the opening rate proportionately.
	217	DO jl = 1, jpl
	218	DO jj = 1, jpj
	219	DO ji = 1, jpi
[5167]	220	za = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice
[6416]	221	IF( za > a_i(ji,jj,jl) ) THEN
	222	zfac = a_i(ji,jj,jl) / za
[5167]	223	closing_gross(ji,jj) = closing_gross(ji,jj) * zfac
[825]	224	ENDIF
[5123]	225	END DO
	226	END DO
	227	END DO
[825]	228
[921]	229	! 3.3 Redistribute area, volume, and energy.
	230	!-----------------------------------------------------------------------------!
[825]	231
[6416]	232	CALL lim_itd_me_ridgeshift( opning, closing_gross )
[825]	233
[6416]	234
[921]	235	! 3.4 Compute total area of ice plus open water after ridging.
	236	!-----------------------------------------------------------------------------!
[5134]	237	! This is in general not equal to one because of divergence during transport
[7753]	238	asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 )
[825]	239
[921]	240	! 3.5 Do we keep on iterating ???
	241	!-----------------------------------------------------------------------------!
	242	! Check whether asum = 1. If not (because the closing and opening
	243	! rates were reduced above), ridge again with new rates.
[825]	244
[921]	245	iterate_ridging = 0
	246	DO jj = 1, jpj
	247	DO ji = 1, jpi
[6416]	248	IF( ABS( asum(ji,jj) - 1._wp ) < epsi10 ) THEN
[2715]	249	closing_net(ji,jj) = 0._wp
	250	opning (ji,jj) = 0._wp
[7646]	251	ato_i (ji,jj) = MAX( 0._wp, 1._wp - SUM( a_i(ji,jj,:) ) )
[921]	252	ELSE
	253	iterate_ridging = 1
[6416]	254	divu_adv (ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice
[2715]	255	closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) )
	256	opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) )
[921]	257	ENDIF
	258	END DO
[825]	259	END DO
	260
[2715]	261	IF( lk_mpp ) CALL mpp_max( iterate_ridging )
[869]	262
[921]	263	! Repeat if necessary.
	264	! NOTE: If strength smoothing is turned on, the ridging must be
	265	! iterated globally because of the boundary update in the
	266	! smoothing.
[825]	267
[921]	268	niter = niter + 1
[825]	269
[2715]	270	IF( iterate_ridging == 1 ) THEN
[6416]	271	CALL lim_itd_me_ridgeprep
[3625]	272	IF( niter > nitermax ) THEN
[921]	273	WRITE(numout,*) ' ALERTE : non-converging ridging scheme '
	274	WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging
	275	ENDIF
[825]	276	ENDIF
	277
	278	END DO !! on the do while over iter
	279
[5123]	280	CALL lim_var_agg( 1 )
[825]	281
[5134]	282	!-----------------------------------------------------------------------------!
	283	! control prints
	284	!-----------------------------------------------------------------------------!
[7646]	285	! conservation test
	286	IF( ln_limdiachk ) CALL lim_cons_hsm(1, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b)
[5167]	287
[7646]	288	! control prints
	289	IF( ln_ctl ) CALL lim_prt3D( 'limitd_me' )
[825]	290
[7753]	291	CALL wrk_dealloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross )
[2715]	292	!
[4161]	293	IF( nn_timing == 1 ) CALL timing_stop('limitd_me')
[825]	294	END SUBROUTINE lim_itd_me
	295
[2715]	296	SUBROUTINE lim_itd_me_ridgeprep
[921]	297	!!---------------------------------------------------------------------!
	298	!! * ROUTINE lim_itd_me_ridgeprep *
	299	!!
[2715]	300	!! ** Purpose : preparation for ridging and strength calculations
[921]	301	!!
[2715]	302	!! ** Method : Compute the thickness distribution of the ice and open water
	303	!! participating in ridging and of the resulting ridges.
[921]	304	!!---------------------------------------------------------------------!
[2715]	305	INTEGER :: ji,jj, jl ! dummy loop indices
[6416]	306	REAL(wp) :: Gstari, astari, hrmean, zdummy ! local scalar
[3294]	307	REAL(wp), POINTER, DIMENSION(:,:,:) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n
	308	!------------------------------------------------------------------------------!
[825]	309
[3294]	310	CALL wrk_alloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 )
[825]	311
[5123]	312	Gstari = 1.0/rn_gstar
	313	astari = 1.0/rn_astar
[7753]	314	aksum(:,:) = 0.0
	315	athorn(:,:,:) = 0.0
	316	aridge(:,:,:) = 0.0
	317	araft (:,:,:) = 0.0
[825]	318
[6416]	319	! Zero out categories with very small areas
[5123]	320	CALL lim_var_zapsmall
[825]	321
[6416]	322	! Ice thickness needed for rafting
	323	DO jl = 1, jpl
	324	DO jj = 1, jpj
	325	DO ji = 1, jpi
	326	rswitch = MAX( 0._wp , SIGN( 1._wp, a_i(ji,jj,jl) - epsi20 ) )
	327	ht_i(ji,jj,jl) = v_i (ji,jj,jl) / MAX( a_i(ji,jj,jl) , epsi20 ) * rswitch
[7646]	328	END DO
[6416]	329	END DO
	330	END DO
	331
[921]	332	!------------------------------------------------------------------------------!
	333	! 1) Participation function
	334	!------------------------------------------------------------------------------!
[825]	335
	336	! Compute total area of ice plus open water.
[5134]	337	! This is in general not equal to one because of divergence during transport
[7753]	338	asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 )
[825]	339
	340	! Compute cumulative thickness distribution function
	341	! Compute the cumulative thickness distribution function Gsum,
	342	! where Gsum(n) is the fractional area in categories 0 to n.
	343	! initial value (in h = 0) equals open water area
[7753]	344	Gsum(:,:,-1) = 0._wp
	345	Gsum(:,:,0 ) = ato_i(:,:)
[825]	346	! for each value of h, you have to add ice concentration then
	347	DO jl = 1, jpl
[7753]	348	Gsum(:,:,jl) = Gsum(:,:,jl-1) + a_i(:,:,jl)
[825]	349	END DO
	350
	351	! Normalize the cumulative distribution to 1
	352	DO jl = 0, jpl
[7753]	353	Gsum(:,:,jl) = Gsum(:,:,jl) / asum(:,:)
[825]	354	END DO
	355
[921]	356	! 1.3 Compute participation function a(h) = b(h).g(h) (athorn)
	357	!--------------------------------------------------------------------------------------------------
	358	! Compute the participation function athorn; this is analogous to
	359	! a(h) = b(h)g(h) as defined in Thorndike et al. (1975).
	360	! area lost from category n due to ridging/closing
	361	! athorn(n) = total area lost due to ridging/closing
	362	! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar).
	363	!
	364	! The expressions for athorn are found by integrating b(h)g(h) between
	365	! the category boundaries.
[6416]	366	! athorn is always >= 0 and SUM(athorn(0:jpl))=1
[921]	367	!-----------------------------------------------------------------
[825]	368
[5123]	369	IF( nn_partfun == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975)
[4869]	370	DO jl = 0, jpl
[921]	371	DO jj = 1, jpj
	372	DO ji = 1, jpi
[6416]	373	IF ( Gsum(ji,jj,jl) < rn_gstar ) THEN
[5134]	374	athorn(ji,jj,jl) = Gstari * ( Gsum(ji,jj,jl) - Gsum(ji,jj,jl-1) ) * &
[6416]	375	& ( 2._wp - ( Gsum(ji,jj,jl-1) + Gsum(ji,jj,jl) ) * Gstari )
	376	ELSEIF( Gsum(ji,jj,jl-1) < rn_gstar ) THEN
	377	athorn(ji,jj,jl) = Gstari * ( rn_gstar - Gsum(ji,jj,jl-1) ) * &
	378	& ( 2._wp - ( Gsum(ji,jj,jl-1) + rn_gstar ) * Gstari )
[921]	379	ELSE
[6416]	380	athorn(ji,jj,jl) = 0._wp
[921]	381	ENDIF
[5123]	382	END DO
	383	END DO
	384	END DO
[825]	385
[2715]	386	ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007)
	387	!
	388	zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array
[921]	389	DO jl = -1, jpl
[7753]	390	Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy
[5134]	391	END DO
[4869]	392	DO jl = 0, jpl
[7753]	393	athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl)
[2715]	394	END DO
	395	!
[5134]	396	ENDIF
[825]	397
[7646]	398	! --- Ridging and rafting participation concentrations --- !
	399	IF( ln_rafting .AND. ln_ridging ) THEN
[2715]	400	!
[825]	401	DO jl = 1, jpl
	402	DO jj = 1, jpj
	403	DO ji = 1, jpi
[6416]	404	zdummy = TANH ( rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) )
	405	aridge(ji,jj,jl) = ( 1._wp + zdummy ) * 0.5_wp * athorn(ji,jj,jl)
[7646]	406	araft (ji,jj,jl) = athorn(ji,jj,jl) - aridge(ji,jj,jl)
[5123]	407	END DO
	408	END DO
	409	END DO
[2715]	410	!
[7646]	411	ELSEIF( ln_ridging .AND. .NOT. ln_rafting ) THEN
	412	!
[825]	413	DO jl = 1, jpl
[7753]	414	aridge(:,:,jl) = athorn(:,:,jl)
[825]	415	END DO
[2715]	416	!
[7646]	417	ELSEIF( ln_rafting .AND. .NOT. ln_ridging ) THEN
	418	!
	419	DO jl = 1, jpl
[7753]	420	araft(:,:,jl) = athorn(:,:,jl)
[7646]	421	END DO
	422	!
[825]	423	ENDIF
	424
[921]	425	!-----------------------------------------------------------------
	426	! 2) Transfer function
	427	!-----------------------------------------------------------------
	428	! Compute max and min ridged ice thickness for each ridging category.
	429	! Assume ridged ice is uniformly distributed between hrmin and hrmax.
	430	!
	431	! This parameterization is a modified version of Hibler (1980).
	432	! The mean ridging thickness, hrmean, is proportional to hi^(0.5)
	433	! and for very thick ridging ice must be >= krdgmin*hi
	434	!
	435	! The minimum ridging thickness, hrmin, is equal to 2*hi
	436	! (i.e., rafting) and for very thick ridging ice is
	437	! constrained by hrmin <= (hrmean + hi)/2.
	438	!
	439	! The maximum ridging thickness, hrmax, is determined by
	440	! hrmean and hrmin.
	441	!
	442	! These modifications have the effect of reducing the ice strength
	443	! (relative to the Hibler formulation) when very thick ice is
	444	! ridging.
	445	!
	446	! aksum = net area removed/ total area removed
	447	! where total area removed = area of ice that ridges
	448	! net area removed = total area removed - area of new ridges
	449	!-----------------------------------------------------------------
[825]	450
[7753]	451	aksum(:,:) = athorn(:,:,0)
[825]	452	! Transfer function
	453	DO jl = 1, jpl !all categories have a specific transfer function
	454	DO jj = 1, jpj
	455	DO ji = 1, jpi
[6416]	456
	457	IF( athorn(ji,jj,jl) > 0._wp ) THEN
	458	hrmean = MAX( SQRT( rn_hstar * ht_i(ji,jj,jl) ), ht_i(ji,jj,jl) * krdgmin )
	459	hrmin(ji,jj,jl) = MIN( 2._wp * ht_i(ji,jj,jl), 0.5_wp * ( hrmean + ht_i(ji,jj,jl) ) )
	460	hrmax(ji,jj,jl) = 2._wp * hrmean - hrmin(ji,jj,jl)
	461	hraft(ji,jj,jl) = ht_i(ji,jj,jl) / kraft
	462	krdg(ji,jj,jl) = ht_i(ji,jj,jl) / MAX( hrmean, epsi20 )
[825]	463
[6416]	464	! Normalization factor : aksum, ensures mass conservation
	465	aksum(ji,jj) = aksum(ji,jj) + aridge(ji,jj,jl) * ( 1._wp - krdg(ji,jj,jl) ) &
	466	& + araft (ji,jj,jl) * ( 1._wp - kraft )
	467
[825]	468	ELSE
[6416]	469	hrmin(ji,jj,jl) = 0._wp
	470	hrmax(ji,jj,jl) = 0._wp
	471	hraft(ji,jj,jl) = 0._wp
	472	krdg (ji,jj,jl) = 1._wp
[825]	473	ENDIF
	474
[5134]	475	END DO
	476	END DO
	477	END DO
[2715]	478	!
[3294]	479	CALL wrk_dealloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 )
	480	!
[921]	481	END SUBROUTINE lim_itd_me_ridgeprep
[825]	482
	483
[6416]	484	SUBROUTINE lim_itd_me_ridgeshift( opning, closing_gross )
[2715]	485	!!----------------------------------------------------------------------
[921]	486	!! * ROUTINE lim_itd_me_icestrength *
	487	!!
[2715]	488	!! ** Purpose : shift ridging ice among thickness categories of ice thickness
[921]	489	!!
[2715]	490	!! ** Method : Remove area, volume, and energy from each ridging category
	491	!! and add to thicker ice categories.
	492	!!----------------------------------------------------------------------
	493	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear
	494	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges
	495	!
	496	CHARACTER (len=80) :: fieldid ! field identifier
	497	!
	498	INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices
	499	INTEGER :: ij ! horizontal index, combines i and j loops
[6416]	500	INTEGER :: icells ! number of cells with a_i > puny
	501	REAL(wp) :: hL, hR, farea ! left and right limits of integration
[825]	502
[3294]	503	INTEGER , POINTER, DIMENSION(:) :: indxi, indxj ! compressed indices
[6416]	504	REAL(wp), POINTER, DIMENSION(:) :: zswitch, fvol ! new ridge volume going to n2
[825]	505
[6416]	506	REAL(wp), POINTER, DIMENSION(:) :: afrac ! fraction of category area ridged
	507	REAL(wp), POINTER, DIMENSION(:) :: ardg1 , ardg2 ! area of ice ridged & new ridges
	508	REAL(wp), POINTER, DIMENSION(:) :: vsrdg , esrdg ! snow volume & energy of ridging ice
	509	REAL(wp), POINTER, DIMENSION(:) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2
[825]	510
[6416]	511	REAL(wp), POINTER, DIMENSION(:) :: vrdg1 ! volume of ice ridged
	512	REAL(wp), POINTER, DIMENSION(:) :: vrdg2 ! volume of new ridges
	513	REAL(wp), POINTER, DIMENSION(:) :: vsw ! volume of seawater trapped into ridges
	514	REAL(wp), POINTER, DIMENSION(:) :: srdg1 ! sal*volume of ice ridged
	515	REAL(wp), POINTER, DIMENSION(:) :: srdg2 ! sal*volume of new ridges
	516	REAL(wp), POINTER, DIMENSION(:) :: smsw ! sal*volume of water trapped into ridges
	517	REAL(wp), POINTER, DIMENSION(:) :: oirdg1, oirdg2 ! ice age of ice ridged
[825]	518
[6416]	519	REAL(wp), POINTER, DIMENSION(:) :: afrft ! fraction of category area rafted
	520	REAL(wp), POINTER, DIMENSION(:) :: arft1 , arft2 ! area of ice rafted and new rafted zone
	521	REAL(wp), POINTER, DIMENSION(:) :: virft , vsrft ! ice & snow volume of rafting ice
	522	REAL(wp), POINTER, DIMENSION(:) :: esrft , smrft ! snow energy & salinity of rafting ice
	523	REAL(wp), POINTER, DIMENSION(:) :: oirft1, oirft2 ! ice age of ice rafted
[825]	524
[6416]	525	REAL(wp), POINTER, DIMENSION(:,:) :: eirft ! ice energy of rafting ice
	526	REAL(wp), POINTER, DIMENSION(:,:) :: erdg1 ! enth*volume of ice ridged
	527	REAL(wp), POINTER, DIMENSION(:,:) :: erdg2 ! enth*volume of new ridges
	528	REAL(wp), POINTER, DIMENSION(:,:) :: ersw ! enth of water trapped into ridges
[3294]	529	!!----------------------------------------------------------------------
[825]	530
[6416]	531	CALL wrk_alloc( jpij, indxi, indxj )
	532	CALL wrk_alloc( jpij, zswitch, fvol )
	533	CALL wrk_alloc( jpij, afrac, ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 )
	534	CALL wrk_alloc( jpij, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 )
	535	CALL wrk_alloc( jpij, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 )
	536	CALL wrk_alloc( jpij,nlay_i, eirft, erdg1, erdg2, ersw )
[3294]	537
[921]	538	!-------------------------------------------------------------------------------
	539	! 1) Compute change in open water area due to closing and opening.
	540	!-------------------------------------------------------------------------------
[825]	541	DO jj = 1, jpj
	542	DO ji = 1, jpi
[6416]	543	ato_i(ji,jj) = MAX( 0._wp, ato_i(ji,jj) + &
	544	& ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice )
[5134]	545	END DO
	546	END DO
[825]	547
[921]	548	!-----------------------------------------------------------------
	549	! 3) Pump everything from ice which is being ridged / rafted
	550	!-----------------------------------------------------------------
	551	! Compute the area, volume, and energy of ice ridging in each
	552	! category, along with the area of the resulting ridge.
[825]	553
	554	DO jl1 = 1, jpl !jl1 describes the ridging category
	555
[921]	556	!------------------------------------------------
	557	! 3.1) Identify grid cells with nonzero ridging
	558	!------------------------------------------------
[825]	559	icells = 0
	560	DO jj = 1, jpj
	561	DO ji = 1, jpi
[6416]	562	IF( athorn(ji,jj,jl1) > 0._wp .AND. closing_gross(ji,jj) > 0._wp ) THEN
[825]	563	icells = icells + 1
	564	indxi(icells) = ji
	565	indxj(icells) = jj
[5134]	566	ENDIF
	567	END DO
	568	END DO
[825]	569
	570	DO ij = 1, icells
[6416]	571	ji = indxi(ij) ; jj = indxj(ij)
[825]	572
[921]	573	!--------------------------------------------------------------------
	574	! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2)
	575	!--------------------------------------------------------------------
[6416]	576	ardg1(ij) = aridge(ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice
	577	arft1(ij) = araft (ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice
[825]	578
[921]	579	!---------------------------------------------------------------
	580	! 3.3) Compute ridging /rafting fractions, make sure afrac <=1
	581	!---------------------------------------------------------------
[6416]	582	afrac(ij) = ardg1(ij) / a_i(ji,jj,jl1) !ridging
	583	afrft(ij) = arft1(ij) / a_i(ji,jj,jl1) !rafting
	584	ardg2(ij) = ardg1(ij) * krdg(ji,jj,jl1)
	585	arft2(ij) = arft1(ij) * kraft
[825]	586
[921]	587	!--------------------------------------------------------------------------
	588	! 3.4) Subtract area, volume, and energy from ridging
	589	! / rafting category n1.
	590	!--------------------------------------------------------------------------
[6416]	591	vrdg1(ij) = v_i(ji,jj,jl1) * afrac(ij)
	592	vrdg2(ij) = vrdg1(ij) * ( 1. + rn_por_rdg )
	593	vsw (ij) = vrdg1(ij) * rn_por_rdg
[825]	594
[6416]	595	vsrdg (ij) = v_s (ji,jj, jl1) * afrac(ij)
	596	esrdg (ij) = e_s (ji,jj,1,jl1) * afrac(ij)
	597	srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij)
	598	oirdg1(ij) = oa_i (ji,jj, jl1) * afrac(ij)
	599	oirdg2(ij) = oa_i (ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1)
[825]	600
	601	! rafting volumes, heat contents ...
[6416]	602	virft (ij) = v_i (ji,jj, jl1) * afrft(ij)
	603	vsrft (ij) = v_s (ji,jj, jl1) * afrft(ij)
	604	esrft (ij) = e_s (ji,jj,1,jl1) * afrft(ij)
	605	smrft (ij) = smv_i(ji,jj, jl1) * afrft(ij)
	606	oirft1(ij) = oa_i (ji,jj, jl1) * afrft(ij)
	607	oirft2(ij) = oa_i (ji,jj, jl1) * afrft(ij) * kraft
[825]	608
[921]	609	!-----------------------------------------------------------------
	610	! 3.5) Compute properties of new ridges
	611	!-----------------------------------------------------------------
[6416]	612	smsw(ij) = vsw(ij) * sss_m(ji,jj) ! salt content of seawater frozen in voids
	613	srdg2(ij) = srdg1(ij) + smsw(ij) ! salt content of new ridge
[1572]	614
[6416]	615	sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ij) * rhoic * r1_rdtice
	616	wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ij) * rhoic * r1_rdtice ! increase in ice volume due to seawater frozen in voids
[6470]	617
	618	! virtual salt flux to keep salinity constant
	619	IF( nn_icesal == 1 .OR. nn_icesal == 3 ) THEN
	620	srdg2(ij) = srdg2(ij) - vsw(ij) * ( sss_m(ji,jj) - sm_i(ji,jj,jl1) ) ! ridge salinity = sm_i
	621	sfx_bri(ji,jj) = sfx_bri(ji,jj) + sss_m(ji,jj) * vsw(ij) * rhoic * r1_rdtice & ! put back sss_m into the ocean
	622	& - sm_i(ji,jj,jl1) * vsw(ij) * rhoic * r1_rdtice ! and get sm_i from the ocean
	623	ENDIF
[7646]	624
[921]	625	!------------------------------------------
	626	! 3.7 Put the snow somewhere in the ocean
	627	!------------------------------------------
	628	! Place part of the snow lost by ridging into the ocean.
[6416]	629	! Note that esrdg > 0; the ocean must cool to melt snow.
[921]	630	! If the ocean temp = Tf already, new ice must grow.
	631	! During the next time step, thermo_rates will determine whether
	632	! the ocean cools or new ice grows.
[6416]	633	wfx_snw(ji,jj) = wfx_snw(ji,jj) + ( rhosn * vsrdg(ij) * ( 1._wp - rn_fsnowrdg ) &
	634	& + rhosn * vsrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! fresh water source for ocean
[921]	635
[6416]	636	hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ( - esrdg(ij) * ( 1._wp - rn_fsnowrdg ) &
	637	& - esrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! heat sink for ocean (<0, W.m-2)
[825]	638
[921]	639	!-----------------------------------------------------------------
	640	! 3.8 Compute quantities used to apportion ice among categories
	641	! in the n2 loop below
	642	!-----------------------------------------------------------------
[6416]	643	dhr (ij) = 1._wp / ( hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) )
	644	dhr2(ij) = 1._wp / ( hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) )
[825]	645
	646
[6416]	647	! update jl1 (removing ridged/rafted area)
	648	a_i (ji,jj, jl1) = a_i (ji,jj, jl1) - ardg1 (ij) - arft1 (ij)
	649	v_i (ji,jj, jl1) = v_i (ji,jj, jl1) - vrdg1 (ij) - virft (ij)
	650	v_s (ji,jj, jl1) = v_s (ji,jj, jl1) - vsrdg (ij) - vsrft (ij)
	651	e_s (ji,jj,1,jl1) = e_s (ji,jj,1,jl1) - esrdg (ij) - esrft (ij)
	652	smv_i(ji,jj, jl1) = smv_i(ji,jj, jl1) - srdg1 (ij) - smrft (ij)
	653	oa_i (ji,jj, jl1) = oa_i (ji,jj, jl1) - oirdg1(ij) - oirft1(ij)
[825]	654
[5134]	655	END DO
[825]	656
[921]	657	!--------------------------------------------------------------------
	658	! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and
	659	! compute ridged ice enthalpy
	660	!--------------------------------------------------------------------
[825]	661	DO jk = 1, nlay_i
	662	DO ij = 1, icells
[6416]	663	ji = indxi(ij) ; jj = indxj(ij)
[921]	664	! heat content of ridged ice
[6416]	665	erdg1(ij,jk) = e_i(ji,jj,jk,jl1) * afrac(ij)
	666	eirft(ij,jk) = e_i(ji,jj,jk,jl1) * afrft(ij)
[4688]	667
	668	! enthalpy of the trapped seawater (J/m2, >0)
	669	! clem: if sst>0, then ersw <0 (is that possible?)
[6416]	670	ersw(ij,jk) = - rhoic * vsw(ij) * rcp * sst_m(ji,jj) * r1_nlay_i
[825]	671
[4688]	672	! heat flux to the ocean
[6416]	673	hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ij,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux
[825]	674
[5123]	675	! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean
[6416]	676	erdg2(ij,jk) = erdg1(ij,jk) + ersw(ij,jk)
[4688]	677
[6416]	678	! update jl1
	679	e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ij,jk) - eirft(ij,jk)
	680
[5134]	681	END DO
	682	END DO
[825]	683
[921]	684	!-------------------------------------------------------------------------------
	685	! 4) Add area, volume, and energy of new ridge to each category jl2
	686	!-------------------------------------------------------------------------------
[4869]	687	DO jl2 = 1, jpl
[6416]	688	! over categories to which ridged/rafted ice is transferred
[825]	689	DO ij = 1, icells
[6416]	690	ji = indxi(ij) ; jj = indxj(ij)
[825]	691
[6416]	692	! Compute the fraction of ridged ice area and volume going to thickness category jl2.
	693	IF( hrmin(ji,jj,jl1) <= hi_max(jl2) .AND. hrmax(ji,jj,jl1) > hi_max(jl2-1) ) THEN
[3625]	694	hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) )
	695	hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) )
[6416]	696	farea = ( hR - hL ) * dhr(ij)
	697	fvol(ij) = ( hR * hR - hL * hL ) * dhr2(ij)
	698	ELSE
	699	farea = 0._wp
	700	fvol(ij) = 0._wp
[825]	701	ENDIF
	702
[6416]	703	! Compute the fraction of rafted ice area and volume going to thickness category jl2
	704	IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN
	705	zswitch(ij) = 1._wp
	706	ELSE
	707	zswitch(ij) = 0._wp
	708	ENDIF
[825]	709
[6416]	710	a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ( ardg2 (ij) * farea + arft2 (ij) * zswitch(ij) )
	711	oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + ( oirdg2(ij) * farea + oirft2(ij) * zswitch(ij) )
	712	v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + ( vrdg2 (ij) * fvol(ij) + virft (ij) * zswitch(ij) )
	713	smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + ( srdg2 (ij) * fvol(ij) + smrft (ij) * zswitch(ij) )
	714	v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + ( vsrdg (ij) * rn_fsnowrdg * fvol(ij) + &
	715	& vsrft (ij) * rn_fsnowrft * zswitch(ij) )
	716	e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + ( esrdg (ij) * rn_fsnowrdg * fvol(ij) + &
	717	& esrft (ij) * rn_fsnowrft * zswitch(ij) )
[825]	718
[5202]	719	END DO
[825]	720
	721	! Transfer ice energy to category jl2 by ridging
	722	DO jk = 1, nlay_i
	723	DO ij = 1, icells
[6416]	724	ji = indxi(ij) ; jj = indxj(ij)
	725	e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + erdg2(ij,jk) * fvol(ij) + eirft(ij,jk) * zswitch(ij)
[2715]	726	END DO
	727	END DO
	728	!
[6416]	729	END DO ! jl2
	730
	731	END DO ! jl1 (deforming categories)
[7753]	732
[6416]	733	!
	734	CALL wrk_dealloc( jpij, indxi, indxj )
	735	CALL wrk_dealloc( jpij, zswitch, fvol )
	736	CALL wrk_dealloc( jpij, afrac, ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 )
	737	CALL wrk_dealloc( jpij, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 )
	738	CALL wrk_dealloc( jpij, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 )
	739	CALL wrk_dealloc( jpij,nlay_i, eirft, erdg1, erdg2, ersw )
	740	!
	741	END SUBROUTINE lim_itd_me_ridgeshift
[825]	742
[6416]	743	SUBROUTINE lim_itd_me_icestrength( kstrngth )
	744	!!----------------------------------------------------------------------
	745	!! * ROUTINE lim_itd_me_icestrength *
	746	!!
	747	!! ** Purpose : computes ice strength used in dynamics routines of ice thickness
	748	!!
	749	!! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2)
	750	!! dissipated per unit area removed from the ice pack under compression,
	751	!! and assumed proportional to the change in potential energy caused
	752	!! by ridging. Note that only Hibler's formulation is stable and that
	753	!! ice strength has to be smoothed
	754	!!
	755	!! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using)
	756	!!----------------------------------------------------------------------
	757	INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979)
	758	INTEGER :: ji,jj, jl ! dummy loop indices
	759	INTEGER :: ksmooth ! smoothing the resistance to deformation
	760	INTEGER :: numts_rm ! number of time steps for the P smoothing
	761	REAL(wp) :: zp, z1_3 ! local scalars
[7646]	762	REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here
	763	REAL(wp), POINTER, DIMENSION(:,:) :: zstrp1, zstrp2 ! strength at previous time steps
[6416]	764	!!----------------------------------------------------------------------
[825]	765
[7646]	766	CALL wrk_alloc( jpi,jpj, zworka, zstrp1, zstrp2 )
[6416]	767
	768	!------------------------------------------------------------------------------!
	769	! 1) Initialize
	770	!------------------------------------------------------------------------------!
[7753]	771	strength(:,:) = 0._wp
[6416]	772
	773	!------------------------------------------------------------------------------!
	774	! 2) Compute thickness distribution of ridging and ridged ice
	775	!------------------------------------------------------------------------------!
	776	CALL lim_itd_me_ridgeprep
	777
	778	!------------------------------------------------------------------------------!
	779	! 3) Rothrock(1975)'s method
	780	!------------------------------------------------------------------------------!
	781	IF( kstrngth == 1 ) THEN
	782	z1_3 = 1._wp / 3._wp
	783	DO jl = 1, jpl
	784	DO jj= 1, jpj
	785	DO ji = 1, jpi
	786	!
	787	IF( athorn(ji,jj,jl) > 0._wp ) THEN
	788	!----------------------------
	789	! PE loss from deforming ice
	790	!----------------------------
	791	strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl)
	792
	793	!--------------------------
	794	! PE gain from rafting ice
	795	!--------------------------
	796	strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl)
	797
	798	!----------------------------
	799	! PE gain from ridging ice
	800	!----------------------------
	801	strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl) * krdg(ji,jj,jl) * z1_3 * &
	802	& ( hrmax(ji,jj,jl) * hrmax(ji,jj,jl) + &
	803	& hrmin(ji,jj,jl) * hrmin(ji,jj,jl) + &
	804	& hrmax(ji,jj,jl) * hrmin(ji,jj,jl) )
	805	!!(a3-b3)/(a-b) = aa+ab+bb
[825]	806	ENDIF
[6416]	807	!
[5123]	808	END DO
	809	END DO
[6416]	810	END DO
	811
[7753]	812	strength(:,:) = rn_pe_rdg * Cp * strength(:,:) / aksum(:,:) * tmask(:,:,1)
[6416]	813	! where Cp = (g/2)(rhow-rhoi)(rhoi/rhow) and rn_pe_rdg accounts for frictional dissipation
	814	ksmooth = 1
[825]	815
[7646]	816	!------------------------------------------------------------------------------!
	817	! 4) Hibler (1979)' method
	818	!------------------------------------------------------------------------------!
[6416]	819	ELSE ! kstrngth ne 1: Hibler (1979) form
	820	!
[7753]	821	strength(:,:) = rn_pstar * vt_i(:,:) * EXP( - rn_crhg * ( 1._wp - at_i(:,:) ) ) * tmask(:,:,1)
	822	!
[6416]	823	ksmooth = 1
	824	!
	825	ENDIF ! kstrngth
	826	!
	827	!------------------------------------------------------------------------------!
	828	! 5) Impact of brine volume
	829	!------------------------------------------------------------------------------!
	830	! CAN BE REMOVED
	831	IF( ln_icestr_bvf ) THEN
	832	DO jj = 1, jpj
	833	DO ji = 1, jpi
[7646]	834	strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bvm_i(ji,jj),0.0)))
[6416]	835	END DO
[5123]	836	END DO
[6416]	837	ENDIF
	838	!
	839	!------------------------------------------------------------------------------!
	840	! 6) Smoothing ice strength
	841	!------------------------------------------------------------------------------!
	842	!
	843	!-------------------
	844	! Spatial smoothing
	845	!-------------------
	846	IF ( ksmooth == 1 ) THEN
[825]	847
[6416]	848	DO jj = 2, jpjm1
	849	DO ji = 2, jpim1
[7646]	850	IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN
[6416]	851	zworka(ji,jj) = ( 4.0 * strength(ji,jj) &
	852	& + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) &
	853	& + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) &
	854	& ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) )
	855	ELSE
	856	zworka(ji,jj) = 0._wp
	857	ENDIF
	858	END DO
	859	END DO
[825]	860
[6416]	861	DO jj = 2, jpjm1
	862	DO ji = 2, jpim1
	863	strength(ji,jj) = zworka(ji,jj)
	864	END DO
	865	END DO
	866	CALL lbc_lnk( strength, 'T', 1. )
[4333]	867
[6416]	868	ENDIF
	869
	870	!--------------------
	871	! Temporal smoothing
	872	!--------------------
	873	IF ( ksmooth == 2 ) THEN
	874
[7646]	875	IF ( numit == nit000 + nn_fsbc - 1 ) THEN
[7753]	876	zstrp1(:,:) = 0._wp
	877	zstrp2(:,:) = 0._wp
[7646]	878	ENDIF
[6416]	879
[7646]	880	DO jj = 2, jpjm1
	881	DO ji = 2, jpim1
	882	IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN
[6416]	883	numts_rm = 1 ! number of time steps for the running mean
[7646]	884	IF ( zstrp1(ji,jj) > 0._wp ) numts_rm = numts_rm + 1
	885	IF ( zstrp2(ji,jj) > 0._wp ) numts_rm = numts_rm + 1
	886	zp = ( strength(ji,jj) + zstrp1(ji,jj) + zstrp2(ji,jj) ) / numts_rm
	887	zstrp2(ji,jj) = zstrp1(ji,jj)
	888	zstrp1(ji,jj) = strength(ji,jj)
[6416]	889	strength(ji,jj) = zp
	890	ENDIF
[4333]	891	END DO
	892	END DO
[6416]	893
[7646]	894	CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions
	895
[6416]	896	ENDIF ! ksmooth
	897
[7646]	898	CALL wrk_dealloc( jpi,jpj, zworka, zstrp1, zstrp2 )
[2715]	899	!
[6416]	900	END SUBROUTINE lim_itd_me_icestrength
[825]	901
[2715]	902	SUBROUTINE lim_itd_me_init
[825]	903	!!-------------------------------------------------------------------
	904	!! * ROUTINE lim_itd_me_init *
	905	!!
	906	!! ** Purpose : Physical constants and parameters linked
	907	!! to the mechanical ice redistribution
	908	!!
	909	!! ** Method : Read the namiceitdme namelist
	910	!! and check the parameters values
	911	!! called at the first timestep (nit000)
	912	!!
	913	!! ** input : Namelist namiceitdme
	914	!!-------------------------------------------------------------------
[4298]	915	INTEGER :: ios ! Local integer output status for namelist read
[7646]	916	NAMELIST/namiceitdme/ rn_cs, nn_partfun, rn_gstar, rn_astar, &
	917	& ln_ridging, rn_hstar, rn_por_rdg, rn_fsnowrdg, ln_rafting, rn_hraft, rn_craft, rn_fsnowrft
[825]	918	!!-------------------------------------------------------------------
[2715]	919	!
[4298]	920	REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution
	921	READ ( numnam_ice_ref, namiceitdme, IOSTAT = ios, ERR = 901)
	922	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in reference namelist', lwp )
	923
	924	REWIND( numnam_ice_cfg ) ! Namelist namiceitdme in configuration namelist : Ice mechanical ice redistribution
	925	READ ( numnam_ice_cfg, namiceitdme, IOSTAT = ios, ERR = 902 )
	926	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in configuration namelist', lwp )
[4624]	927	IF(lwm) WRITE ( numoni, namiceitdme )
[2715]	928	!
	929	IF (lwp) THEN ! control print
[825]	930	WRITE(numout,*)
[7646]	931	WRITE(numout,*)'lim_itd_me_init : ice parameters for mechanical ice redistribution '
	932	WRITE(numout,*)'~~~~~~~~~~~~~~~'
[5123]	933	WRITE(numout,*)' Fraction of shear energy contributing to ridging rn_cs = ', rn_cs
[7646]	934	WRITE(numout,*)' Switch for part. function (0) linear (1) exponential nn_partfun = ', nn_partfun
[5123]	935	WRITE(numout,*)' Fraction of total ice coverage contributing to ridging rn_gstar = ', rn_gstar
	936	WRITE(numout,)' Equivalent to G for an exponential part function rn_astar = ', rn_astar
[7646]	937	WRITE(numout,*)' Ridging of ice sheets or not ln_ridging = ', ln_ridging
[5123]	938	WRITE(numout,*)' Quantity playing a role in max ridged ice thickness rn_hstar = ', rn_hstar
[7646]	939	WRITE(numout,*)' Initial porosity of ridges rn_por_rdg = ', rn_por_rdg
	940	WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrdg = ', rn_fsnowrdg
[5123]	941	WRITE(numout,*)' Rafting of ice sheets or not ln_rafting = ', ln_rafting
	942	WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft
	943	WRITE(numout,*)' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft
[7646]	944	WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrft = ', rn_fsnowrft
[825]	945	ENDIF
[2715]	946	!
[825]	947	END SUBROUTINE lim_itd_me_init
	948
	949	#else
[2715]	950	!!----------------------------------------------------------------------
	951	!! Default option Empty module NO LIM-3 sea-ice model
	952	!!----------------------------------------------------------------------
[825]	953	CONTAINS
	954	SUBROUTINE lim_itd_me ! Empty routines
	955	END SUBROUTINE lim_itd_me
	956	SUBROUTINE lim_itd_me_icestrength
	957	END SUBROUTINE lim_itd_me_icestrength
	958	SUBROUTINE lim_itd_me_init
	959	END SUBROUTINE lim_itd_me_init
	960	#endif
[2715]	961	!!======================================================================
[825]	962	END MODULE limitd_me

Note: See TracBrowser for help on using the repository browser.

New URL for NEMO forge! http://forge.nemo-ocean.eu

Context Navigation

source: trunk/NEMOGCM/NEMO/LIM_SRC_3/limitd_me.F90 @ 7753

Download in other formats: