SNTHERM could be added to SNAP. The model,
3
d = 23
Vav
(26)
developed and tested at the lysimeter at Sleepers
4π
River Research Watershed near Danville, Ver-
mont, would benefit from additional validations.
where Vav is the average crystal volume. Then, the
The model is fairly new and has had little use to
absolute permeability of snow (k, cm2) is
date.
k = 0.077d2 exp (-7.8ρs )
(27)
Strengths
The model provides a quasi-analytical solution
where d is snow grain diameter (cm), and ρs is
for routing meltwater and rainfall through a snow-
density of water (g cm3).
pack. This model is based more on physics than
current operational models, yet takes less compu-
Snow depth and effective porosity
tation time than a complete numerical solution.
The model will use either user-supplied snow
depths or will predict snow depth from the rate
of densification over time due to metamorphism
SYNOPSIS
and overburden (Albert and Krajeski 1999). Snow
Current operational models
densification due to metamorphism is determined
The operational algorithms reviewed have a
as a function of temperature, dry snow density,
common basis in early snowmelt investigations of
and fraction of the snowpack that is wet. Densifi-
the North Pacific Division (NPD), U.S. Army
cation due to overburden is determined as a func-
Corps of Engineers and U.S. Weather Bureau (U.S.
tion of temperature and bulk density of the snow.
Army Corps of Engineers 1956, 1960), and the
Effective porosity changes are updated, accord-
National Weather Service (Anderson 1968, 1973,
ingly.
1976). These initial model developments were
energy balance approaches simplified for opera-
Refreezing within the snowpack
tional use that defaulted to a temperature index
SNAP uses an analytical solution of the
method when only temperature and precipitation
Neumann equation (Carslaw and Jaegar 1959) to
data were available. SSARR and HEC-1 are based
predict the depth of refreezing in the pack,
directly on the NPD snow investigations in the
Sierras. The SSARR generalized energy balance
(
)
2k1 Tf - Ts t
equations allow use of coefficients for forest cover,
X=
(28)
solar exposure, and wind speed, where HEC-1
ρl
fixes these coefficients at midrange values. Rain
and non-rain periods in the meteorological record
where X = depth of the freezing front,
are used to distinguish heavily overcast condi-
tions, since these have specific energy balance
snow (0.0045 J s1 cm1 C 1),
characteristics. A temperature index method is
Tf = temperature of fusiom (taken as 0C),
used in both SSARR and HEC-1 when only tem-
Ts = surface temperature (taken as ambi-
perature and precipitation data are available.
ent air temperature),
Snowmelt in HEC-1 is simply a surface energy
t = time,
balance with no consideration of internal snow-
ρ = density of the snow medium,
pack processes.
l = latent heat of fusion (333.05 J g1).
In later versions of SSARR, NPD adopted
Thermal conductivity of the snow medium is
some of the internal snowpack processes used in
determined using a depth averaged value of satu-
NWSRFS for "ripening" the snowpack. NWSRFS
ration, and Ts is a time averaged value over the
snow algorithms are based on Anderson's (1973,
most recent period in which the snowpack is pre-
1976) work in the Sierras and in Vermont, which
dicted by the model to be less than isothermal
drew from the work of Anderson and Crawford
(<0C).
(1964) and the U.S. Army Corps of Engineers
(1956). In contrast to SSARR and HEC-1, Ander-
Limitations
son's NWSRFS operational algorithm computes
SNAP currently does not estimate radiation
snowmelt using a simplified energy budget for
with cloud cover nor adjust for slope and aspect,
rainy periods rather than a temperature index
t h o u g h these additional subroutines from
method, but similarly defaults to a temperature
11
Back to contents
Previous Page
