water flow scheme is coupled to the equilibrium
lution during summer snowmelt on the Greenland
temperature in frozen strata using thermody-
ice sheet (Rowe et al. 1995), an energy balance
namically derived freezing curves for typical
study of a continental, midlatitude alpine snow-
sand, silt, and clay soils. This conceptualization
pack at Niwot Ridge, Colorado (Cline 1997), and
of water infiltration through the snow is one of
beneath canopy energy balance studies in the
an even, horizontal wetting front proceeding
boreal forest in Saskatchewan, Canada (Hardy et
downward. In reality, finger flow occurs and
al. 1997). The model is currently being applied to
tends to accelerate the arrival of melt to the bot-
snow cover mapping in the boreal forest of Canada
tom of the snowpack (Colbeck 1979, Marsh and
(Davis et al. 1997), snowmelt forecasting in Bosnia
Woo 1984), while capillary tension draws water
(Melloh et al. 1997), integration with mesoscale
along finer grained snow layers. Deformation of
meteorological data (Melloh et al., in prep), and in
the snow cover over time takes into account set-
distributed snow model studies in Sleepers River
tling due to metamorphism, and compaction due
Research Watershed in northern Vermont (Melloh
to overburden, melt, or sublimation. Vapor flux
and Jordan, in prep.). SNTHERM is applicable to
through snow is assumed driven by diffusion of
a full range of meteorological conditions such as
saturated air and is computed by Fick's law. The
snowfall, rainfall, freeze-thaw cycles and transi-
residual water content of snow (irreducible
tions between bare and snow-covered ground.
water saturation) is assumed to be 4% of the snow
The meteorological boundary conditions in
pore volume.
SNTHERM require air temperature, dew point
The numerical solution is obtained by sub-
temperature, wind speed, precipitation, and
dividing into snow layers, each represented by the
either incoming values of solar and infrared radi-
governing equations for heat and mass balance.
ation, or cloud cover and site information (solar
SNTHERM uses a control volume numerical pro-
aspect and inclination of the surface). The surface
cedure (Patankar 1980) for spatial discretization
energy balance is
that allows for compaction of the snow cover. Use
(
)
of the control-volume technique conserves the
Itop = Is↓ 1 - α top + Iir↓ - Iir↑
quantities over a finite control volume (∆V) rather
than at an infinitesimal point as with a finite-
+ Isen + Ilat + Iconv
(23)
difference scheme. The rate of change of these
quantities within a control volume ∆V must equal
where Is↓(1αtop) = downwelling shortwave radi-
their net flow across the boundary surface plus
ation,
their rate of internal production. As snow com-
α = albedo or shortwave reflec-
pacts over time, the one-dimensional grid is
tance
allowed to compress, so that volume elements
Iir↓ = downwelling longwave radi-
continue to correspond with the original element
ation,
of snow. The rate of flux is taken with respect to
Iir↑ = upwelling longwave radia-
the deforming grid. A Crank-Nicholson central
tion,
difference scheme is used to solve partial differ-
Isen = turbulent sensible heat flux,
ential equations in the time domain. A new hydro-
Ilat = turbulent latent heat flux,
logic version of SNTHERM limits the number of
Iconv = heat convected by rain or
nodes in the bottom two-thirds of the snowpack
falling snow.
while maintaining detail near the surface to gain
efficiency for water resource applications.
Ground heat flux and soil temperature profiles are
The sum of the constituent bulk densities is the
modeled, but soil moisture is kept constant. The
total density (ρt) written as
steady-state bottom boundary condition is set by
the initial soil temperature and moisture profile
ρt = ∑ θkρk = ∑ γ k
specified by the user.
(24)
k
k
SNTHERM was based initially on the mass and
where θk = individual volume fractions of k con-
energy-balance snow model of Anderson (1976);
it incorporates the mixture theory approach
stituents,
espoused by Morris and Godfrey (1979), Morris
k = ice (i), liquid water (l), water vapor
(1987) and Morland et al. (1990), and the tech-
(v), and air (a),
ρk = density of each i, l, v, and a constitu-
nique for gravitational flow of water through the
snowpack of Colbeck (1971, 1972, 1976, 1979). The
ent,
9
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