Chapter 7
Snow Accretion, Depletion, and Meltwater Outflow Model
7.0 Introduction
The Snow Accretion-Depletion Module uses the Snowmelt Numerical Analysis Package
(SNAP) developed by Albert and Krajeski (1998). It is a physically based approach to
modeling snowmelt, where the physics of flow through snow are considered and the melt
is driven by an energy budget at the snow surface. Snow accretion occurs when a
snowfall amount is given in the input or when precipitation is given in the input and the
input air temperature is below freezing. In the latter case, the precipitation amount is
converted to a snowfall amount. Sections 7.1 and 7.2 are from Albert and Krajeski
(1998).
7.1 Governing Equations of Flow within the Snow
For modeling the movement of water through the snow, the effects of capilarity are taken
as negligibly small compared to the effects of gravity (Colbeck 1972), yielding the
simplified form of Darcy's equation:
ρkg
U= w w
(7.1)
ηw
where U is the volume flux of water, ρw is the density of water, kw is the relative
Under some circumstances this will be applicable to the entire snowpack, while
modifications will be necessary under some conditions of layering. The effective
permeability of the water phase is taken to be proportional to a power (nc) of the effective
water saturation (Morel-Saytoux 1969, Colbeck 1972):
kw = kw0 Senc
(7.2)
where the effective water saturation, Se, is defined by
S - Swi
Se = wa
(7.3)
1 - Swi
where Swa is the absolute water saturation and Swi is the irreducible water saturation. The
general applicability of the relationship kw ∝ Senc is discussed in Maulem (1978). Here, nc
is taken as a constant with a default value of 3.3.
The flux in terms of absolute water saturation is defined as
ρk g
U = w w0 Senc .
(7.4)
ηw
The water volume conservation equation (Colbeck 1972) used states that the change in
water volume flux with depth, U (where the z axis is positive downwards), is equal to the
change in water saturation with time:
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