Improving snow water equivalent estimates with ground
penetrating radar: laboratory test of snow wetness influence
on electrical conductivity of snow

Abstract: Snow water equivalent (SWE) of annual snowpacks is of major importance for
Scandinavian hydropower industry, since reliable predictions of snowmelt
are needed for an efficient energy production. SWE over large areas can be
estimated using ground penetrating radar operated from helicopters or
snowmobiles from the two-way travel time of radar wave propagation through
a snowpack. Radar estimates of SWE can either be based directly on
empirical relationships with the two-way travel time, or calculated from
snow density and snowpack depth, which can be measured manually at selected
locations or estimated from the radar wave two-way travel time and
propagation velocity in snow. However, it is known that presence of liquid
water in a snowpack creates uncertainties, which for a typical snowpack
with 5% (by volume) liquid water can lead to an overestimation of snow
water equivalent by about 20%. It would therefore be beneficial if radar
data could also be used to determine snow wetness.

Radar wave amplitude is reduced when the wave passes through a snowpack.
This attenuation depends on electrical properties of snow: permittivity and
electrical conductivity, which in turn depend on snow wetness. The
relationship between wave attenuation and these electrical properties can
be derived theoretically from Maxwell’s equations. The connection between
snow permittivity and snow wetness and density follows an empirical formula
known to be highly accurate. However, to be able to determine snow wetness
from wave attenuation the relationship between electrical conductivity and
snow wetness also has to be known. The present work attempts to establish
this relationship experimentally.

A laboratory test was set up to study the relationship between snow wetness
and electrical conductivity of snow. Three sets of radar amplitude
measurements, two with “old” and one with new-fallen snow, were made on
initially dry one-meter thick snow samples contained in a plywood box with
cross-section area about 0.5 m2. Snow wetness was controlled by stepwise
adding water to the snow in between radar measurements. Permittivity of
snow was obtained in two different ways: estimated using Looyenga’s
empirical formula for mixtures, and calculated from the radar wave one-way
travel time and path length (both methods produced similar results).
Electrical conductivity of snow was calculated from snow permittivity,
snowpack depth, and radar wave attenuation.

A tentative relationship between electrical conductivity and snow wetness
was found, but further tests including studies of the effect of variations
of salt content in snow are needed to assess the generality of the result.