FSM

The Factorial Snow Model (FSM) is a multi-physics energy balance model of accumulation and melt of snow on the ground. The model includes 5 parameterizations that can be switched on or off independently, giving 32 possible model configurations identified by decimal numbers between 0 and 31. The corresponding 5 digit binary number n_an_cn_dn_en_w has digits n_a for prognostic snow albedo, n_c for variable thermal conductivity, n_d for prognostic snow density, n_e for stability adjustment of the turbulent exchange coefficient and n_w for prognostic liquid water content; the digits are 0 if a parametrization is switched off and 1 if it is switched on. FSM uses a four-layer soil model extending to 1.5 m depth and one snow layer for snow depths up to 0.2 m, two layers for depths up to 0.5 m or three layers for greater depths. A full description is given by Essery (2015).

Building the model

FSM is coded in Fortran. A linux executable FSM or a Windows executable FSM.exe is produced by running the script compil.sh or the batch file compil.bat. Both use the gfortran compiler but could be edited to use other compilers. The bin directory holds precompiled executables.

Running the model

FSM requires meteorological driving data and namelists to set options and parameters. The model is run with the command

./FSM < nlst.txt

or

FSM.exe < nlst.txt

where nlst.txt is a text file containing five namelists described below; nlst_CdP_0506.txt gives an example to run FSM for the winter of 2005-2006 at Col de Porte (Morin et al. 2011). All of the namelists have to be present in the same order as in the example, but any or all of the namelist variables listed in the tables below can be omitted; defaults are then used.

The executable runs a single configuration of FSM, but a Python script is provided to run an ensemble of simulations. For example,

python FSMens.py nlst_CdP_0506.txt

will run all configurations of FSM for Col de Porte and write output files tagged with the binary configuration numbers to directory output.

Driving data

Meteorological driving data are read from a text file named in namelist &drive. A driving data file has 12 columns containing the variables listed in the table below. Each row of the file corresponds with a timestep. Driving data for the Col de Porte example are given in file data/met_CdP_0506.txt.

Variable	Units	Description
year	years	Year
month	months	Month of the year
day	days	Day of the month
hour	hours	Hour of the day
SW	W m-2	Incoming shortwave radiation
LW	W m-2	Incoming longwave radiation
Sf	kg m-2 s-1	Snowfall rate
Rf	kg m-2 s-1	Rainfall rate
Ta	K	Air temperature
RH	RH	Relative humidity
Ua	m s-1	Wind speed
Ps	Pa	Surface air pressure

Model configuration namelist

&config

Variable	Range	Default	Description
nconfig	0 - 31	31	Configuration number

Driving data namelist

&drive

Variable	Default	Units	Description
met_file	'met.txt'	string	Driving file name
dt	3600	s	Time step
SnowMIP	.FALSE.	logical	Read driving data in ESM-SnowMIP format
zT	2	m	Temperature measurement height
zU	10	m	Wind speed measurement height
zvar	.TRUE.	logical	Subtract snow depth from measurement height

SnowMIP = .TRUE. is required for driving data files from ESM-SnowMIP (Krinner et al. 2018). These files can be downloaded from https://www.geos.ed.ac.uk/~ressery/ESM-SnowMIP.html.

Switch zvar is provided because the temperature and relative humidity sensors at Col de Porte are moved during site visits to maintain a constant height above the snow surface (zvar = .FALSE.). This will not be the case at sites that are not regularly attended.

Parameter namelist

&params

Variable	Default	Units	Description
alb0	0.2	-	Snow-free ground albedo
asmx	0.8	-	Maximum albedo for fresh snow
asmn	0.5	-	Minimum albedo for melting snow
bstb	5	-	Atmospheric stability adjustment parameter (if ne=1)
bthr	2	-	Thermal conductivity exponent (if nc=1)
fcly	0.3	-	Soil clay fraction
fsnd	0.6	-	Soil sand fraction
gsat	0.01	m s-1	Surface conductance for saturated soil
hfsn	0.1	m	Snow cover fraction depth scale
kfix	0.24	W m-1 K-1	Fixed thermal conductivity (if nc=0)
rho0	300	kg m-3	Fixed snow density (if nd=0)
rhof	100	kg m-3	Fresh snow density (if nd=1)
rcld	300	kg m-3	Maximum density for cold snow (if nd=1)
rmlt	500	kg m-3	Maximum density for melting snow (if nd=1)
Salb	10	kg m-2	Snowfall to refresh albedo (if na=1)
Talb	-2	°C	Albedo decay temperature threshold (if na=0)
tcld	1000	h	Cold snow albedo decay timescale (if na=1)
tmlt	100	h	Melting snow albedo decay timescale (if na=1)
trho	200	h	Compaction time scale (if nd=1)
Wirr	0.03	-	Irreducible liquid water content (if nw=1)
z0sf	0.1	m	Snow-free roughness length
z0sn	0.01	m	Snow roughness length

Initial values namelist

&initial

Variable	Default	Units	Description
start_file	'none'	string	Start file
fsat	4 * 0.5	-	Initial moisture content of soil layers as fractions of saturation
Tsoil	4 * 285	K	Initial temperatures of soil layers

Soil temperature and moisture content are taken from the namelist and FSM is initialized in a snow-free state by default. If a start file is named, it should be a text file containing initial values for each of the state variables in order:

Variable	Units	Description
albs	-	Snow albedo
Ds(1:3)	m	Snow layer thicknesses
Nsnow	-	Number of snow layers
Sice(1:3)	kg m-2	Ice content of snow layers
Sliq(1:3)	kg m-2	Liquid content of snow layers
theta(1:4)	-	Volumetric moisture content of soil layers
Tsnow(1:3)	K	Snow layer temperatures
Tsoil(1:4)	K	Soil layer temperatures
Tsurf	K	Surface skin temperature

Snow and soil layers are numbered from the top downwards. File data/dump.txt is an example of a dump file produced at the end of a run which could be used to restart the model.

Output namelist

&outputs

Variable	Default	Description
Nave	24	Number of timesteps in averaged outputs
out_file	'out.txt'	Output file name
dump_file	'dump.txt'	Dump file name

At present a simple fixed output format is used. The output text file has 10 columns:

Variable	Units	Description
year	years	Year
month	months	Month of the year
day	days	Day of the month
hour	hours	Hour of the day
alb	-	Effective albedo
Rof	kg m-2	Cumulated runoff from snow
snd	m	Average snow depth
SWE	kg m-2	Average snow water equivalent
Tsf	°C	Average surface temperature
Tsl	°C	Average soil temperature at 20 cm depth

Example file data/out_CdP_0506.txt contains output from a run of FSM configuration 31; data/obs_CdP_0506.txt contains daily observations of the same variables, with -99 indicating missing data.

At the end of a run, the state variables are written to a dump file with the same format as the start file.

Model configurations

Configuration	na	nc	nd	ne	nw
0	0	0	0	0	0
1	0	0	0	0	1
2	0	0	0	1	0
3	0	0	0	1	1
4	0	0	1	0	0
5	0	0	1	0	1
6	0	0	1	1	0
7	0	0	1	1	1
8	0	1	0	0	0
9	0	1	0	0	1
10	0	1	0	1	0
11	0	1	0	1	1
12	0	1	1	0	0
13	0	1	1	0	1
14	0	1	1	1	0
15	0	1	1	1	1
16	1	0	0	0	0
17	1	0	0	0	1
18	1	0	0	1	0
19	1	0	0	1	1
20	1	0	1	0	0
21	1	0	1	0	1
22	1	0	1	1	0
23	1	0	1	1	1
24	1	1	0	0	0
25	1	1	0	0	1
26	1	1	0	1	0
27	1	1	0	1	1
28	1	1	1	0	0
29	1	1	1	0	1
30	1	1	1	1	0
31	1	1	1	1	1

References

Essery (2015). A Factorial Snowpack Model (FSM 1.0). Geoscientific Model Development, 8, 3867-3876, doi:10.5194/gmd-8-3867-2015

Krinner et al. (2018). ESM-SnowMIP: assessing snow models and quantifying snow-related climate feedbacks. Geoscientific Model Development, 11, 5027-5049, doi:10.5194/gmd-11-5027-2018

Morin et al. (2012). A 18-yr long (1993-2011) snow and meteorological dataset from a mid-altitude mountain site (Col de Porte, France, 1325 m alt.) for driving and evaluating snowpack models. Earth System Science Data, 4(1), 13-21, doi:10.5194/essd-4-13-2012