  A method to estimate phase velocity and attenuation of acoustic waves in the
presence of liquid water in a snowpack is presented. The method is based on
Biot's theory of wave propagation in porous materials. Empirical relations and
a priori information is used to characterize snow as a porous material as a
function of porosity. Plane wave theory and an equivalent pore fluid are used
to solve Biot's differential equations and to asses the impact of the air and
water in the pore space. The liquid water in the pore space of a snow pack
reduces the velocity of the first compressional wave by roughly 300 m/s for
every 0.1 increase in liquid water saturation. Also the attenuation of the
compressional waves is increased with increasing liquid water content. Two end
member models for compaction are evaluated to asses the importance of an
independent density measurement for an estimate of liquid pore water saturation
in snow with acoustic waves. The two end members correspond to no compaction at
all and to a melting sphere packing where the grains remain in contact. The
change of velocity for the first compressional wave was found to strongly
depend on the compaction model, while the velocity of the second compressional
wave mainly depends on liquid water saturation. Also the attenuation for both
compressional waves depends mainly on the liquid water saturation and only
little on the compaction model. Finally, a simple field experiment illustrates
the potential use of the method to estimate the liquid water content of snow
with acoustic sensors.
