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

Since March 2022 along with NEMO 4.2 release, the code development moved to a self-hosted GitLab.
This present forge is now archived and remained online for history.

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

Context Navigation

source: trunk/NEMOGCM/NEMO/LIM_SRC_3/ice.F90 @ 4765

Last change on this file since 4765 was 4765, checked in by rblod, 10 years ago
Compilation issue, see ticket #1379
Property svn:keywords set to `Id`
File size: 39.5 KB

Rev	Line
[825]	1	MODULE ice
[2528]	2	!!======================================================================
	3	!! * MODULE ice *
	4	!! LIM-3 Sea Ice physics: diagnostics variables of ice defined in memory
	5	!!=====================================================================
[2715]	6	!! History : 3.0 ! 2008-03 (M. Vancoppenolle) original code LIM-3
	7	!! 4.0 ! 2011-02 (G. Madec) dynamical allocation
[2528]	8	!!----------------------------------------------------------------------
[825]	9	#if defined key_lim3
	10	!!----------------------------------------------------------------------
[3625]	11	!! 'key_lim3' LIM-3 sea-ice model
[825]	12	!!----------------------------------------------------------------------
[3625]	13	USE par_ice ! LIM sea-ice parameters
	14	USE in_out_manager ! I/O manager
	15	USE lib_mpp ! MPP library
[825]	16
	17	IMPLICIT NONE
	18	PRIVATE
[2528]	19
[2715]	20	PUBLIC ice_alloc ! Called in iceini.F90
	21
[834]	22	!!======================================================================
	23	!! LIM3 by the use of sweat, agile fingers and sometimes brain juice,
	24	!! was developed in Louvain-la-Neuve by :
	25	!! * Martin Vancoppenolle (UCL-ASTR, Belgium)
	26	!! * Sylvain Bouillon (UCL-ASTR, Belgium)
[2715]	27	!! * Miguel Angel Morales Maqueda (NOC-L, UK)
[834]	28	!!
	29	!! Based on extremely valuable earlier work by
	30	!! * Thierry Fichefet
	31	!! * Hugues Goosse
	32	!!
	33	!! The following persons also contributed to the code in various ways
[2715]	34	!! * Gurvan Madec, Claude Talandier, Christian Ethe (LOCEAN, France)
[834]	35	!! * Xavier Fettweis (UCL-ASTR), Ralph Timmermann (AWI, Germany)
	36	!! * Bill Lipscomb (LANL), Cecilia Bitz (UWa)
	37	!! and Elisabeth Hunke (LANL), USA.
	38	!!
[2715]	39	!! For more info, the interested user is kindly invited to consult the following references
[834]	40	!! For model description and validation :
	41	!! * Vancoppenolle et al., Ocean Modelling, 2008a.
	42	!! * Vancoppenolle et al., Ocean Modelling, 2008b.
	43	!! For a specific description of EVP :
[2715]	44	!! * Bouillon et al., Ocean Modelling 2009.
[834]	45	!!
[2715]	46	!! Or the reference manual, that should be available by 2011
[834]	47	!!======================================================================
	48	!! \|
[2528]	49	!! I C E S T A T E V A R I A B L E S \|
[834]	50	!! \|
	51	!! Introduction : \|
	52	!! -------------- \|
	53	!! Every ice-covered grid cell is characterized by a series of state \|
	54	!! variables. To account for unresolved spatial variability in ice \|
	55	!! thickness, the ice cover in divided in ice thickness categories. \|
	56	!! \|
	57	!! Sea ice state variables depend on the ice thickness category \|
	58	!! \|
	59	!! Those variables are divided into two groups \|
	60	!! * Extensive (or global) variables. \|
	61	!! These are the variables that are transported by all means \|
	62	!! * Intensive (or equivalent) variables. \|
	63	!! These are the variables that are either physically more \|
	64	!! meaningful and/or used in ice thermodynamics \|
	65	!! \|
	66	!! Routines in limvar.F90 perform conversions \|
	67	!! - lim_var_glo2eqv : from global to equivalent variables \|
	68	!! - lim_var_eqv2glo : from equivalent to global variables \|
	69	!! \|
	70	!! For various purposes, the sea ice state variables have sometimes \|
	71	!! to be aggregated over all ice thickness categories. This operation \|
	72	!! is done in : \|
	73	!! - lim_var_agg \|
	74	!! \|
	75	!! in icestp.F90, the routines that compute the changes in the ice \|
	76	!! state variables are called \|
	77	!! - lim_dyn : ice dynamics \|
	78	!! - lim_trp : ice transport \|
	79	!! - lim_itd_me : mechanical redistribution (ridging and rafting) \|
	80	!! - lim_thd : ice halo-thermodynamics \|
	81	!! - lim_itd_th : thermodynamic changes in ice thickness distribution \|
	82	!! and creation of new ice \|
	83	!! \|
	84	!! See the associated routines for more information \|
	85	!! \|
	86	!! List of ice state variables : \|
	87	!! ----------------------------- \|
	88	!! \|
	89	!!-------------\|-------------\|---------------------------------\|-------\|
	90	!! name in \| name in \| meaning \| units \|
	91	!! 2D routines \| 1D routines \| \| \|
	92	!!-------------\|-------------\|---------------------------------\|-------\|
	93	!! \|
	94	!! ******************************************************************* \|
	95	!! * Dynamical variables (prognostic) * \|
	96	!! ******************************************************************* \|
	97	!! \|
	98	!! u_ice \| - \| Comp. U of the ice velocity \| m/s \|
	99	!! v_ice \| - \| Comp. V of the ice velocity \| m/s \|
	100	!! \|
	101	!! ******************************************************************* \|
	102	!! * Category dependent state variables (prognostic) * \|
	103	!! ******************************************************************* \|
	104	!! \|
	105	!! ** Global variables \|
	106	!!-------------\|-------------\|---------------------------------\|-------\|
	107	!! a_i \| a_i_b \| Ice concentration \| \|
	108	!! v_i \| - \| Ice volume per unit area \| m \|
	109	!! v_s \| - \| Snow volume per unit area \| m \|
	110	!! smv_i \| - \| Sea ice salt content \| ppt.m \|
	111	!! oa_i ! - ! Sea ice areal age content \| day \|
	112	!! e_i ! - ! Ice enthalpy \| 10^9 J\|
	113	!! - ! q_i_b ! Ice enthalpy per unit vol. \| J/m3 \|
	114	!! e_s ! - ! Snow enthalpy \| 10^9 J\|
	115	!! - ! q_s_b ! Snow enthalpy per unit vol. \| J/m3 \|
	116	!! \|
	117	!!-------------\|-------------\|---------------------------------\|-------\|
	118	!! \|
	119	!! ** Equivalent variables \|
	120	!!-------------\|-------------\|---------------------------------\|-------\|
	121	!! \|
	122	!! ht_i \| ht_i_b \| Ice thickness \| m \|
	123	!! ht_s ! ht_s_b \| Snow depth \| m \|
	124	!! sm_i ! sm_i_b \| Sea ice bulk salinity ! ppt \|
	125	!! s_i ! s_i_b \| Sea ice salinity profile ! ppt \|
	126	!! o_i ! - \| Sea ice Age ! days \|
	127	!! t_i ! t_i_b \| Sea ice temperature ! K \|
	128	!! t_s ! t_s_b \| Snow temperature ! K \|
	129	!! t_su ! t_su_b \| Sea ice surface temperature ! K \|
	130	!! \|
	131	!! notes: the ice model only sees a bulk (i.e., vertically averaged) \|
	132	!! salinity, except in thermodynamic computations, for which \|
	133	!! the salinity profile is computed as a function of bulk \|
	134	!! salinity \|
	135	!! \|
	136	!! the sea ice surface temperature is not associated to any \|
	137	!! heat content. Therefore, it is not a state variable and \|
	138	!! does not have to be advected. Nevertheless, it has to be \|
	139	!! computed to determine whether the ice is melting or not \|
	140	!! \|
	141	!! ******************************************************************* \|
	142	!! * Category-summed state variables (diagnostic) * \|
	143	!! ******************************************************************* \|
	144	!! at_i \| at_i_b \| Total ice concentration \| \|
	145	!! vt_i \| - \| Total ice vol. per unit area \| m \|
	146	!! vt_s \| - \| Total snow vol. per unit ar. \| m \|
	147	!! smt_i \| - \| Mean sea ice salinity \| ppt \|
	148	!! tm_i \| - \| Mean sea ice temperature \| K \|
	149	!! ot_i ! - ! Sea ice areal age content \| day \|
	150	!! et_i ! - ! Total ice enthalpy \| 10^9 J\|
	151	!! et_s ! - ! Total snow enthalpy \| 10^9 J\|
	152	!! bv_i ! - ! Mean relative brine volume \| ??? \|
	153	!!=====================================================================
[825]	154
[2528]	155	LOGICAL, PUBLIC :: con_i = .false. ! switch for conservation test
[825]	156
[834]	157	!!--------------------------------------------------------------------------
[825]	158	!! * Share Module variables
[834]	159	!!--------------------------------------------------------------------------
[4147]	160	INTEGER , PUBLIC :: nstart !: iteration number of the begining of the run
	161	INTEGER , PUBLIC :: nlast !: iteration number of the end of the run
	162	INTEGER , PUBLIC :: nitrun !: number of iteration
	163	INTEGER , PUBLIC :: numit !: iteration number
	164	REAL(wp), PUBLIC :: rdt_ice !: ice time step
	165	REAL(wp), PUBLIC :: r1_rdtice !: = 1. / rdt_ice
[1465]	166
[4147]	167	! !! ice-dynamic namelist (namicedyn)
	168	INTEGER , PUBLIC :: nevp !: number of iterations for subcycling
	169	REAL(wp), PUBLIC :: epsd !: tolerance parameter for dynamic
	170	REAL(wp), PUBLIC :: om !: relaxation constant
	171	REAL(wp), PUBLIC :: cw !: drag coefficient for oceanic stress
	172	REAL(wp), PUBLIC :: angvg !: turning angle for oceanic stress
	173	REAL(wp), PUBLIC :: pstar !: determines ice strength (N/M), Hibler JPO79
	174	REAL(wp), PUBLIC :: c_rhg !: determines changes in ice strength
	175	REAL(wp), PUBLIC :: creepl !: creep limit : has to be under 1.0e-9
	176	REAL(wp), PUBLIC :: ecc !: eccentricity of the elliptical yield curve
	177	REAL(wp), PUBLIC :: ahi0 !: sea-ice hor. eddy diffusivity coeff. (m2/s)
	178	REAL(wp), PUBLIC :: telast !: timescale for elastic waves (s) !SB
	179	REAL(wp), PUBLIC :: alphaevp !: coeficient of the internal stresses !SB
[2715]	180	REAL(wp), PUBLIC :: unit_fac = 1.e+09_wp !: conversion factor for ice / snow enthalpy
[4688]	181	REAL(wp), PUBLIC :: hminrhg !: ice volume (a*h, in m) below which ice velocity is set to ocean velocity
[825]	182
[4147]	183	! !! ice-salinity namelist (namicesal)
	184	REAL(wp), PUBLIC :: s_i_max !: maximum ice salinity [PSU]
	185	REAL(wp), PUBLIC :: s_i_min !: minimum ice salinity [PSU]
	186	REAL(wp), PUBLIC :: s_i_0 !: 1st sal. value for the computation of sal .prof. [PSU]
	187	REAL(wp), PUBLIC :: s_i_1 !: 2nd sal. value for the computation of sal .prof. [PSU]
	188	REAL(wp), PUBLIC :: sal_G !: restoring salinity for gravity drainage [PSU]
	189	REAL(wp), PUBLIC :: sal_F !: restoring salinity for flushing [PSU]
	190	REAL(wp), PUBLIC :: time_G !: restoring time constant for gravity drainage (= 20 days) [s]
	191	REAL(wp), PUBLIC :: time_F !: restoring time constant for gravity drainage (= 10 days) [s]
	192	REAL(wp), PUBLIC :: bulk_sal !: bulk salinity (ppt) in case of constant salinity
[825]	193
[4147]	194	! !! ice-salinity namelist (namicesal)
[4688]	195	INTEGER , PUBLIC :: num_sal !: salinity configuration used in the model
[4147]	196	! ! 1 - constant salinity in both space and time
	197	! ! 2 - prognostic salinity (s(z,t))
	198	! ! 3 - salinity profile, constant in time
[4688]	199	INTEGER , PUBLIC :: thcon_i_swi !: thermal conductivity: =0 Untersteiner (1964) ; =1 Pringle et al (2007)
[825]	200
[4147]	201	! !!** ice-mechanical redistribution namelist (namiceitdme)
	202	REAL(wp), PUBLIC :: Cs !: fraction of shearing energy contributing to ridging
	203	REAL(wp), PUBLIC :: Cf !: ratio of ridging work to PE loss
	204	REAL(wp), PUBLIC :: fsnowrdg !: fractional snow loss to the ocean during ridging
	205	REAL(wp), PUBLIC :: fsnowrft !: fractional snow loss to the ocean during ridging
	206	REAL(wp), PUBLIC :: Gstar !: fractional area of young ice contributing to ridging
	207	REAL(wp), PUBLIC :: astar !: equivalent of G* for an exponential participation function
	208	REAL(wp), PUBLIC :: Hstar !: thickness that determines the maximal thickness of ridged ice
	209	REAL(wp), PUBLIC :: hparmeter !: threshold thickness (m) for rafting / ridging
	210	REAL(wp), PUBLIC :: Craft !: coefficient for smoothness of the hyperbolic tangent in rafting
	211	REAL(wp), PUBLIC :: ridge_por !: initial porosity of ridges (0.3 regular value)
	212	REAL(wp), PUBLIC :: betas !: coef. for partitioning of snowfall between leads and sea ice
	213	REAL(wp), PUBLIC :: kappa_i !: coef. for the extinction of radiation Grenfell et al. (2006) [1/m]
	214	REAL(wp), PUBLIC :: nconv_i_thd !: maximal number of iterations for heat diffusion
	215	REAL(wp), PUBLIC :: maxer_i_thd !: maximal tolerated error (C) for heat diffusion
[825]	216
[4147]	217	! !!** ice-mechanical redistribution namelist (namiceitdme)
	218	INTEGER , PUBLIC :: ridge_scheme_swi !: scheme used for ice ridging
[4688]	219	INTEGER , PUBLIC :: raft_swi !: rafting of ice or not
[4147]	220	INTEGER , PUBLIC :: partfun_swi !: participation function: =0 Thorndike et al. (1975), =1 Lipscomb et al. (2007)
	221	INTEGER , PUBLIC :: brinstren_swi !: use brine volume to diminish ice strength
[825]	222
[2715]	223	REAL(wp), PUBLIC :: usecc2 !: = 1.0 / ( ecc * ecc )
	224	REAL(wp), PUBLIC :: rhoco !: = rau0 * cw
	225	REAL(wp), PUBLIC :: sangvg, cangvg !: sin and cos of the turning angle for ocean stress
	226	REAL(wp), PUBLIC :: pstarh !: pstar / 2.0
[825]	227
[2715]	228	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: u_oce, v_oce !: surface ocean velocity used in ice dynamics
	229	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ahiu , ahiv !: hor. diffusivity coeff. at U- and V-points [m2/s]
	230	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: pahu , pahv !: ice hor. eddy diffusivity coef. at U- and V-points
	231	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ust2s, hicol !: friction velocity, ice collection thickness accreted in leads
	232	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: strp1, strp2 !: strength at previous time steps
	233	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: strength !: ice strength
	234	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: stress1_i, stress2_i, stress12_i !: 1st, 2nd & diagonal stress tensor element
	235	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: delta_i !: ice rheology elta factor (Flato & Hibler 95) [s-1]
	236	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: divu_i !: Divergence of the velocity field [s-1]
	237	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: shear_i !: Shear of the velocity field [s-1]
	238	!
	239	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sist !: Average Sea-Ice Surface Temperature [Kelvin]
	240	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: icethi !: total ice thickness (for all categories) (diag only)
	241	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: t_bo !: Sea-Ice bottom temperature [Kelvin]
	242	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: frld !: Leads fraction = 1 - ice fraction
	243	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: pfrld !: Leads fraction at previous time
	244	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: phicif !: Old ice thickness
[4688]	245	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: qlead !: heat balance of the lead (or of the open ocean)
	246	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: fhtur !: net downward heat flux from the ice to the ocean
	247	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: fhld !: heat flux from the lead used for bottom melting
	248
	249	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_snw !: Variation of snow mass over 1 time step [Kg/m2]
	250	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_ice !: Variation of ice mass over 1 time step [Kg/m2]
	251	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_sub !: Variation of snow mass over 1 time step due to sublimation [Kg/m2]
	252
	253	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_sni !: snow ice growth
	254	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_opw !: lateral ice growth
	255	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_bog !: bottom ice growth
	256	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_dyn !: dynamical ice growth
	257	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_bom !: vertical bottom melt
	258	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_sum !: vertical surface melt
	259	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_res !: production (growth+melt) due to limupdate
	260	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: wfx_spr !: snow precipitation on ice
	261
	262	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_bog !: salt flux due to ice growth/melt [PSU/m2/s]
	263	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_bom !: salt flux due to ice growth/melt [PSU/m2/s]
	264	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_sum !: salt flux due to ice growth/melt [PSU/m2/s]
	265	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_sni !: salt flux due to ice growth/melt [PSU/m2/s]
	266	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_opw !: salt flux due to ice growth/melt [PSU/m2/s]
[3625]	267	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_bri !: salt flux due to brine rejection [PSU/m2/s]
[4688]	268	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_dyn !: salt flux due to porous ridged ice formation [PSU/m2/s]
[3625]	269	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sfx_res !: residual salt flux due to correction of ice thickness [PSU/m2/s]
[825]	270
[4688]	271	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_bog !: total heat flux causing bottom ice growth
	272	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_bom !: total heat flux causing bottom ice melt
	273	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_sum !: total heat flux causing surface ice melt
	274	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_opw !: total heat flux causing open water ice formation
	275	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_dif !: total heat flux causing Temp change in the ice
	276	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_snw !: heat flux for snow melt
	277	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_err !: heat flux error after heat diffusion
	278	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_err_rem !: heat flux error after heat remapping
	279	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_in !: heat flux available for thermo transformations
	280	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_out !: heat flux remaining at the end of thermo transformations
	281
	282	! heat flux associated with ice-atmosphere mass exchange
	283	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_sub !: heat flux for sublimation
	284	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_spr !: heat flux of the snow precipitation
	285
	286	! heat flux associated with ice-ocean mass exchange
	287	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_thd !: ice-ocean heat flux from thermo processes (limthd_dh)
	288	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_dyn !: ice-ocean heat flux from mecanical processes (limitd_me)
	289	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hfx_res !: residual heat flux due to correction of ice thickness
	290
	291	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ftr_ice !: transmitted solar radiation under ice
	292
[921]	293	! temporary arrays for dummy version of the code
[4688]	294	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: dh_i_surf2D, dh_i_bott2D, q_s
[825]	295
[834]	296	!!--------------------------------------------------------------------------
	297	!! * Ice global state variables
	298	!!--------------------------------------------------------------------------
	299	!! Variables defined for each ice category
[2715]	300	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ht_i !: Ice thickness (m)
	301	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: a_i !: Ice fractional areas (concentration)
	302	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: v_i !: Ice volume per unit area (m)
	303	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: v_s !: Snow volume per unit area(m)
	304	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ht_s !: Snow thickness (m)
	305	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: t_su !: Sea-Ice Surface Temperature (K)
	306	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sm_i !: Sea-Ice Bulk salinity (ppt)
	307	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: smv_i !: Sea-Ice Bulk salinity times volume per area (ppt.m)
	308	! ! this is an extensive variable that has to be transported
	309	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: o_i !: Sea-Ice Age (days)
	310	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ov_i !: Sea-Ice Age times volume per area (days.m)
	311	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: oa_i !: Sea-Ice Age times ice area (days)
[825]	312
[2715]	313	!! Variables summed over all categories, or associated to all the ice in a single grid cell
	314	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: u_ice, v_ice !: components of the ice velocity (m/s)
	315	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: tio_u, tio_v !: components of the ice-ocean stress (N/m2)
	316	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: vt_i , vt_s !: ice and snow total volume per unit area (m)
	317	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: at_i !: ice total fractional area (ice concentration)
	318	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ato_i !: =1-at_i ; total open water fractional area
	319	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: et_i , et_s !: ice and snow total heat content
	320	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ot_i !: mean age over all categories
	321	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: tm_i !: mean ice temperature over all categories
	322	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: bv_i !: brine volume averaged over all categories
	323	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: smt_i !: mean sea ice salinity averaged over all categories [PSU]
[825]	324
[2715]	325	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: at_i_typ !: total area contained in each ice type [m^2]
	326	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: vt_i_typ !: total volume contained in each ice type [m^3]
[825]	327
[2715]	328	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: t_s !: Snow temperatures [K]
	329	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: e_s !: Snow ...
[825]	330
[2715]	331	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: e_i_cat !: ! go to trash
	332
	333	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: t_i !: ice temperatures [K]
	334	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: e_i !: ice thermal contents [Giga J]
	335	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: s_i !: ice salinities [PSU]
[825]	336
[834]	337	!!--------------------------------------------------------------------------
	338	!! * Moments for advection
	339	!!--------------------------------------------------------------------------
[2715]	340	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: sxopw, syopw, sxxopw, syyopw, sxyopw !: open water in sea ice
	341	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sxice, syice, sxxice, syyice, sxyice !: ice thickness
	342	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sxsn , sysn , sxxsn , syysn , sxysn !: snow thickness
	343	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sxa , sya , sxxa , syya , sxya !: lead fraction
	344	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sxc0 , syc0 , sxxc0 , syyc0 , sxyc0 !: snow thermal content
	345	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sxsal, sysal, sxxsal, syysal, sxysal !: ice salinity
	346	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sxage, syage, sxxage, syyage, sxyage !: ice age
	347	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: sxe , sye , sxxe , syye , sxye !: ice layers heat content
[825]	348
[834]	349	!!--------------------------------------------------------------------------
	350	!! * Old values of global variables
	351	!!--------------------------------------------------------------------------
[2715]	352	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: old_v_s, old_v_i !: snow and ice volumes
	353	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: old_a_i, old_smv_i, old_oa_i !: ???
	354	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: old_e_s !: snow heat content
	355	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: old_e_i !: ice temperatures
	356	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: old_u_ice, old_v_ice !: ice velocity (gv6 and gv7)
	357
[825]	358
[834]	359	!!--------------------------------------------------------------------------
	360	!! * Increment of global variables
	361	!!--------------------------------------------------------------------------
	362	! thd refers to changes induced by thermodynamics
	363	! trp '' '' '' advection (transport of ice)
[2715]	364	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_a_i_thd , d_a_i_trp !: icefractions
	365	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_v_s_thd , d_v_s_trp !: snow volume
	366	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_v_i_thd , d_v_i_trp !: ice volume
	367	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_smv_i_thd, d_smv_i_trp !:
	368	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_sm_i_fl , d_sm_i_gd !:
	369	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_sm_i_se , d_sm_i_si , d_sm_i_la !:
	370	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: d_oa_i_thd , d_oa_i_trp , s_i_newice !:
[825]	371
[2715]	372	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: d_e_s_thd , d_e_s_trp !:
	373	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: d_e_i_thd , d_e_i_trp !:
	374	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: d_u_ice_dyn, d_v_ice_dyn !: ice velocity
	375
[834]	376	!!--------------------------------------------------------------------------
	377	!! * Ice thickness distribution variables
	378	!!--------------------------------------------------------------------------
	379	! REMOVE
[2715]	380	INTEGER , PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:) :: ice_types !: Vector connecting types and categories
	381	INTEGER , PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ice_cat_bounds !: Matrix containing the integer upper and
	382	! ! lower boundaries of ice thickness categories
[834]	383	! REMOVE
[2715]	384	INTEGER , PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:) :: ice_ncat_types !: nb of thickness categories in each ice type
	385	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:) :: hi_max !: Boundary of ice thickness categories in thickness space
	386	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:) :: hi_mean !: Mean ice thickness in catgories
[834]	387	! REMOVE
[2715]	388	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hi_max_typ !: Boundary of ice thickness categories in thickness space
[825]	389
[834]	390	!!--------------------------------------------------------------------------
[921]	391	!! * Ice Run
	392	!!--------------------------------------------------------------------------
[4147]	393	! !!: Namelist namicerun read in iceini
	394	CHARACTER(len=32) , PUBLIC :: cn_icerst_in !: suffix of ice restart name (input)
	395	CHARACTER(len=32) , PUBLIC :: cn_icerst_out !: suffix of ice restart name (output)
	396	LOGICAL , PUBLIC :: ln_limdyn !: flag for ice dynamics (T) or not (F)
	397	LOGICAL , PUBLIC :: ln_nicep !: flag for sea-ice points output (T) or not (F)
	398	REAL(wp) , PUBLIC :: cai !: atmospheric drag over sea ice
	399	REAL(wp) , PUBLIC :: cao !: atmospheric drag over ocean
[4205]	400	REAL(wp) , PUBLIC :: amax !: maximum ice concentration
[4147]	401	!
[921]	402	!!--------------------------------------------------------------------------
[834]	403	!! * Ice diagnostics
	404	!!--------------------------------------------------------------------------
	405	!! Check if everything down here is necessary
[4161]	406	LOGICAL , PUBLIC :: ln_limdiahsb !: flag for ice diag (T) or not (F)
	407	LOGICAL , PUBLIC :: ln_limdiaout !: flag for ice diag (T) or not (F)
[4688]	408	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: dv_dt_thd !: thermodynamic growth rates
	409	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: izero
	410	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: diag_trp_vi !: transport of ice volume
	411	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: diag_trp_vs !: transport of snw volume
	412	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: diag_trp_ei !: transport of ice enthalpy (W/m2)
	413	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: diag_trp_es !: transport of snw enthalpy (W/m2)
	414	!
	415	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: diag_heat_dhc !: snw/ice heat content variation [W/m2]
	416	!
[888]	417	INTEGER , PUBLIC :: jiindx, jjindx !: indexes of the debugging point
[825]	418
[2715]	419	!!----------------------------------------------------------------------
[4161]	420	!! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2010)
[2715]	421	!! $Id$
	422	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
	423	!!----------------------------------------------------------------------
	424	CONTAINS
	425
	426	FUNCTION ice_alloc()
	427	!!-----------------------------------------------------------------
	428	!! * Routine ice_alloc_2 *
	429	!!-----------------------------------------------------------------
	430	INTEGER :: ice_alloc
	431	!
	432	INTEGER :: ierr(20), ii
	433	!!-----------------------------------------------------------------
	434
	435	ierr(:) = 0
	436
	437	! What could be one huge allocate statement is broken-up to try to
	438	! stay within Fortran's max-line length limit.
	439	ii = 1
	440	ALLOCATE( u_oce (jpi,jpj) , v_oce (jpi,jpj) , &
	441	& ahiu (jpi,jpj) , ahiv (jpi,jpj) , &
	442	& pahu (jpi,jpj) , pahv (jpi,jpj) , &
	443	& ust2s (jpi,jpj) , hicol (jpi,jpj) , &
	444	& strp1 (jpi,jpj) , strp2 (jpi,jpj) , strength (jpi,jpj) , &
	445	& stress1_i(jpi,jpj) , stress2_i(jpi,jpj) , stress12_i(jpi,jpj) , &
	446	& delta_i (jpi,jpj) , divu_i (jpi,jpj) , shear_i (jpi,jpj) , STAT=ierr(ii) )
	447
	448	ii = ii + 1
[4688]	449	ALLOCATE( sist (jpi,jpj) , icethi (jpi,jpj) , t_bo (jpi,jpj) , &
	450	& frld (jpi,jpj) , pfrld (jpi,jpj) , phicif (jpi,jpj) , &
	451	& wfx_snw(jpi,jpj) , wfx_ice(jpi,jpj) , wfx_sub(jpi,jpj) , &
	452	& wfx_bog(jpi,jpj) , wfx_dyn(jpi,jpj) , wfx_bom(jpi,jpj) , wfx_sum(jpi,jpj) , &
	453	& wfx_res(jpi,jpj) , wfx_sni(jpi,jpj) , wfx_opw(jpi,jpj) , wfx_spr(jpi,jpj) , qlead (jpi,jpj) , &
	454	& fhtur (jpi,jpj) , ftr_ice(jpi,jpj,jpl) , &
	455	& sfx_res(jpi,jpj) , sfx_bri(jpi,jpj) , sfx_dyn(jpi,jpj) , &
	456	& sfx_bog(jpi,jpj) , sfx_bom(jpi,jpj) , sfx_sum(jpi,jpj) , sfx_sni(jpi,jpj) , sfx_opw(jpi,jpj) , &
	457	& hfx_res(jpi,jpj) , hfx_snw(jpi,jpj) , hfx_sub(jpi,jpj) , hfx_err(jpi,jpj) , hfx_err_rem(jpi,jpj), &
	458	& hfx_in (jpi,jpj) , hfx_out(jpi,jpj) , fhld(jpi,jpj) , &
	459	& hfx_sum(jpi,jpj) , hfx_bom(jpi,jpj) , hfx_bog(jpi,jpj) , hfx_dif(jpi,jpj) , hfx_opw(jpi,jpj) , &
	460	& hfx_thd(jpi,jpj) , hfx_dyn(jpi,jpj) , hfx_spr(jpi,jpj) , STAT=ierr(ii) )
[2715]	461
	462	ii = ii + 1
[4688]	463	ALLOCATE( dh_i_surf2D(jpi,jpj) , dh_i_bott2D(jpi,jpj) , q_s(jpi,jpj) , STAT=ierr(ii) )
[2715]	464
	465	! * Ice global state variables
	466	ii = ii + 1
	467	ALLOCATE( ht_i (jpi,jpj,jpl) , a_i (jpi,jpj,jpl) , v_i (jpi,jpj,jpl) , &
	468	& v_s (jpi,jpj,jpl) , ht_s (jpi,jpj,jpl) , t_su (jpi,jpj,jpl) , &
	469	& sm_i (jpi,jpj,jpl) , smv_i(jpi,jpj,jpl) , o_i (jpi,jpj,jpl) , &
	470	& ov_i (jpi,jpj,jpl) , oa_i (jpi,jpj,jpl) , STAT=ierr(ii) )
	471	ii = ii + 1
	472	ALLOCATE( u_ice(jpi,jpj) , v_ice(jpi,jpj) , tio_u(jpi,jpj) , tio_v(jpi,jpj) , &
	473	& vt_i (jpi,jpj) , vt_s (jpi,jpj) , at_i (jpi,jpj) , ato_i(jpi,jpj) , &
	474	& et_i (jpi,jpj) , et_s (jpi,jpj) , ot_i (jpi,jpj) , tm_i (jpi,jpj) , &
	475	& bv_i (jpi,jpj) , smt_i(jpi,jpj) , STAT=ierr(ii) )
	476	ii = ii + 1
	477	ALLOCATE( t_s(jpi,jpj,nlay_s,jpl) , at_i_typ(jpi,jpj,jpm) , &
	478	& e_s(jpi,jpj,nlay_s,jpl) , vt_i_typ(jpi,jpj,jpm) , e_i_cat(jpi,jpj,jpl) , STAT=ierr(ii) )
	479	ii = ii + 1
	480	ALLOCATE( t_i(jpi,jpj,jkmax,jpl) , e_i(jpi,jpj,jkmax,jpl) , s_i(jpi,jpj,jkmax,jpl) , STAT=ierr(ii) )
	481
	482	! * Moments for advection
	483	ii = ii + 1
	484	ALLOCATE( sxopw(jpi,jpj) , syopw(jpi,jpj) , sxxopw(jpi,jpj) , syyopw(jpi,jpj) , sxyopw(jpi,jpj) , STAT=ierr(ii) )
	485	ii = ii + 1
	486	ALLOCATE( sxice(jpi,jpj,jpl) , syice(jpi,jpj,jpl) , sxxice(jpi,jpj,jpl) , syyice(jpi,jpj,jpl) , sxyice(jpi,jpj,jpl) , &
	487	& sxsn (jpi,jpj,jpl) , sysn (jpi,jpj,jpl) , sxxsn (jpi,jpj,jpl) , syysn (jpi,jpj,jpl) , sxysn (jpi,jpj,jpl) , &
	488	& STAT=ierr(ii) )
	489	ii = ii + 1
	490	ALLOCATE( sxa (jpi,jpj,jpl) , sya (jpi,jpj,jpl) , sxxa (jpi,jpj,jpl) , syya (jpi,jpj,jpl) , sxya (jpi,jpj,jpl) , &
	491	& sxc0 (jpi,jpj,jpl) , syc0 (jpi,jpj,jpl) , sxxc0 (jpi,jpj,jpl) , syyc0 (jpi,jpj,jpl) , sxyc0 (jpi,jpj,jpl) , &
	492	& sxsal(jpi,jpj,jpl) , sysal(jpi,jpj,jpl) , sxxsal(jpi,jpj,jpl) , syysal(jpi,jpj,jpl) , sxysal(jpi,jpj,jpl) , &
	493	& sxage(jpi,jpj,jpl) , syage(jpi,jpj,jpl) , sxxage(jpi,jpj,jpl) , syyage(jpi,jpj,jpl) , sxyage(jpi,jpj,jpl) , &
	494	& STAT=ierr(ii) )
	495	ii = ii + 1
	496	ALLOCATE( sxe (jpi,jpj,jkmax,jpl) , sye (jpi,jpj,jkmax,jpl) , sxxe(jpi,jpj,jkmax,jpl) , &
	497	& syye(jpi,jpj,jkmax,jpl) , sxye(jpi,jpj,jkmax,jpl) , STAT=ierr(ii) )
	498
	499	! * Old values of global variables
	500	ii = ii + 1
	501	ALLOCATE( old_v_s (jpi,jpj,jpl) , old_v_i (jpi,jpj,jpl) , old_e_s(jpi,jpj,nlay_s,jpl) , &
	502	& old_a_i (jpi,jpj,jpl) , old_smv_i(jpi,jpj,jpl) , old_e_i(jpi,jpj,jkmax ,jpl) , &
	503	& old_oa_i (jpi,jpj,jpl) , &
	504	& old_u_ice(jpi,jpj) , old_v_ice(jpi,jpj) , STAT=ierr(ii) )
	505
	506	! * Increment of global variables
	507	ii = ii + 1
	508	ALLOCATE( d_a_i_thd(jpi,jpj,jpl) , d_a_i_trp (jpi,jpj,jpl) , d_v_s_thd (jpi,jpj,jpl) , d_v_s_trp (jpi,jpj,jpl) , &
	509	& d_v_i_thd(jpi,jpj,jpl) , d_v_i_trp (jpi,jpj,jpl) , d_smv_i_thd(jpi,jpj,jpl) , d_smv_i_trp(jpi,jpj,jpl) , &
	510	& d_sm_i_fl(jpi,jpj,jpl) , d_sm_i_gd (jpi,jpj,jpl) , d_sm_i_se (jpi,jpj,jpl) , d_sm_i_si (jpi,jpj,jpl) , &
	511	& d_sm_i_la(jpi,jpj,jpl) , d_oa_i_thd(jpi,jpj,jpl) , d_oa_i_trp (jpi,jpj,jpl) , s_i_newice (jpi,jpj,jpl) , &
	512	& STAT=ierr(ii) )
	513	ii = ii + 1
	514	ALLOCATE( d_e_s_thd(jpi,jpj,nlay_s,jpl) , d_e_i_thd(jpi,jpj,jkmax,jpl) , d_u_ice_dyn(jpi,jpj) , &
	515	& d_e_s_trp(jpi,jpj,nlay_s,jpl) , d_e_i_trp(jpi,jpj,jkmax,jpl) , d_v_ice_dyn(jpi,jpj) , STAT=ierr(ii) )
	516
	517	! * Ice thickness distribution variables
	518	ii = ii + 1
	519	ALLOCATE( ice_types(jpl) , ice_cat_bounds(jpm,2) , ice_ncat_types (jpm) , &
	520	& hi_max (0:jpl) , hi_mean(jpl) , hi_max_typ(0:jpl,jpm) , STAT=ierr(ii) )
	521
	522	! * Ice diagnostics
	523	ii = ii + 1
[4765]	524	ALLOCATE( dv_dt_thd(jpi,jpj,jpl), izero (jpi,jpj,jpl), &
	525	& diag_trp_vi(jpi,jpj), diag_trp_vs (jpi,jpj), diag_trp_ei(jpi,jpj), &
	526	& diag_trp_es(jpi,jpj), diag_heat_dhc(jpi,jpj), STAT=ierr(ii) )
[2715]	527
	528	ice_alloc = MAXVAL( ierr(:) )
	529	IF( ice_alloc /= 0 ) CALL ctl_warn('ice_alloc_2: failed to allocate arrays.')
	530	!
	531	END FUNCTION ice_alloc
	532
[825]	533	#else
	534	!!----------------------------------------------------------------------
	535	!! Default option Empty module NO LIM sea-ice model
	536	!!----------------------------------------------------------------------
	537	#endif
	538
	539	!!======================================================================
	540	END MODULE ice

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

Download in other formats: