∆t = time interval (s),
where VDEN = winter vegetation cover density
TS = temperature of the surface snow
above the snowpack,
layer (C),
Em LIR↓ = longwave radiation emitted from
TP = temperature of the lower layer of the
snowpack (C).
the atmosphere, calculated at the
surface air temperature (cal),
Density of the snow (ρs) is computed daily
LIR↑ = longwave energy emitted from the
using the procedure of Riley et al. (1973). TP is cal-
snowpack surface for the 12-hr
culated as a function of the modeled snow water
period (cal).
equivalent and the calories needed to bring the
snow to an isothermal state of 0C. Heat transfer
Emissivities varying from 0.757 to 1.0 are cal-
due to rain occurs as mass transfer using the aver-
culated as a function of air moisture content
age 24-hr air temperature as the rain temperature.
(U.S. Army 1956). If humidity data are unavail-
When TP is < 0C, the meltwater or rain is refro-
able, Em is estimated. On days with precipitation
zen in the pack and decreases the cold content of
due to frontal storms, Em is assumed equal to 1.0.
the snowpack. When the snowpack becomes iso-
During convective storms, Em is computed sepa-
thermal, the meltwater is first used to satisfy the
rately for each 12-hr period as a function of pre-
irreducible water content of the pack, and the
cipitation and ratio of observed to potential solar
remainder leaves the bottom of the snowpack.
The energy balance (I, cal) for 12-hour periods
to the Stefan-Boltzmann law using the tempera-
is computed as
ture of the snowpack surface, and air temperature,
respectively.
I = INs + INir + (ICOND,CONV)
(19)
The latent and sensible heat loss (cal) is com-
puted using a temperature-index approach,
where
I = energy balance at the air/snow
interface (cal)
ICOND,CONV =CMTAVG
(22)
where TAVG is the mean air temperature for
the 12-hr period (C), and CM is a monthly
ICOND,CONV = approximation of latent and sen-
convectioncondensation parameter (cal C1).
sible heat (cal).
ICOND,CONV is computed only on rainy days, or
Net shortwave radiation, INs (cal), is computed
when clouds cause observed solar radiation to be
as
less than one-third of potential. Forested areas
INs= IS↓ (1.0α) VT
assume a value of ICOND,CONV = 0.5 on these days.
(20)
A limitation of the PRMS is that heat conduc-
tion from the soil to the snowpack is always
assumed negligible.
VT = transmission coefficient for winter
cover density of the vegetation
SNTHERM
canopy,
α = albedo of the snowpack surface.
SNTHERM (Jordan 1990, 1991) is a one-dimen-
sional mass and energy balance model that con-
Incoming shortwave radiation (IS↓) is measured
siders, in more detail, the processes that occur
or estimated from cloud cover.
within a multi-layered snowpack. These include
The vegetation transmission coefficient (VT ) is
snow accumulation, compaction, grain growth,
based on relations presented by Miller (1959) and
melt, condensation melt, advection, pore water
Vezina and Pech (1964). Albedo (α) is computed
retention, and water flow through the pack. In
as a function of the number of days since the last
addition to being the most comprehensive of the
snowfall, and whether the snowpack is accumu-
models reviewed, SNTHERM has the most
lating or melting.
diverse scientific validation. Originally written to
Net longwave radiation (cal) is computed as
predict snow surface temperatures (Jordan 1991),
SNTHERM has been applied to a range of snow
INir = (1.0 VDEN) (Εm LIR↓ LIR↑)
types and scientific inquiries, including prediction
of the spectral signature of snow at an alpine site
+ VDEN (LIR↓ LIR↑)
(21)
in California (Davis et al. 1993), snow layer evo-
8
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