Chapter 8
Ice Thickness Model
8.0 Introduction
Of great hindrance to mobility is the presence of ice on the ground. This can happen
when the ground is at or below freezing and any precipitation is in the form of rain
instead of snow.
8.1 Theory
8.1.1 Growth
The formation of an ice cover on the surface is allowed only if there is no snow. If snow
is present, any rain that falls is assumed to percolate into the snowpack instead of forming
an ice cover on the snow surface. Following Jones (1996), the fraction of precipitation
that freezes is
∑ heat fluxes - latent heat flux .
f=
(8.1)
latent heat flux
The sum of the heat fluxes is fully described in Chapter 6, Section 6.1. The resulting ice
thickness, hi (m) per unit area is
∆t ρw
hi = fP
(8.2)
3600 ρi
of water, and ρi (kg/m3) is the ice density.
8.1.2 Decay
Decay of an ice layer can occur from both the top and bottom, but only if enough energy
is present at the corresponding interface. Once this condition is met, the resulting melt
depths, ∆hi,top (m) and ∆hi,bottom (m), are
∆t
∆hi,top = qnet
ρil f
(8.3)
∂t ∆t
∆hi,bottom = κ
∂z ρil f
where qnet (W/m2) is the net surface heat flux, lf (J/kg) is the latent heat of fusion,
ci (J/kg⋅K) is the specific heat of ice, Ts (K) is the surface temperature, and κ is the
soil thermal conductivity (W/mK). This is the same procedure used by the snow
accretion and depletion model described in Chapter 9.
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