On Dielectric Properties of Dry and Wet Snow
Anatoly D. Frolov1 and Yury Ya. Macheret2
Density and moisture content in snow cover are the important parameters for snow hydrology as
they determine practically all physical and mechanical properties of this medium. One of the
most sensitive properties relative to these parameters is a complex dielectric permittivity of snow,
which is indispensable for interpretation of high-frequency electromagnetic remote-sensing data.
There are many experimental data on real and imaginary parts of complex dielectric permittivity
at high (from 1 MHz to 10 GHz) frequency, but the results obtained by different authors are not
in good quantitative agreement. There are no convincing reasons to prefer something from them.
Therefore we decided to consider in detail all available data in order to find their satisfactory ap-
proximation appropriate for practical aims.
In literature there are many attempts to model the snow dielectric properties (especially for wet
snow) by various mixture formulae, but the authors frequently did not take into account that this
is physically justified only at small concentrations of inclusions in a matrix medium. Usually this
is not the case for snow. Because of this we used the statistical approach for experimental data
approximations, applying the structure-independent mixture formulae only as a version of de-
scribing the resulting correlations. It is commonly supposed that a real part of dielectric permit-
tivity of wet snow may be expressed by linear relation [εw = εd + ∆ εw], which was taken by us,
too.
Firstly, we defined more precisely approximation for dry snow matrix dielectric permittivity as
the function of density in the state near melting point: [εd = (1 + 0.857 ρ) ]. Secondly, the expres-
2
sion for incremental dielectric permittivity due to water content [∆ εw] was found by statistical
averaging of published experimental data in the form of the following regression expression: [∆ ε
2
= 16.7 W + 42.5 W ] (R = 0.915). The comparison with statistical mixture formulae has shown
that it is quite possible to use Looenga's formula for description of the above-mentioned depen-
dencies with the deviations about 2%. Corresponding forms of this formula for [εd] and [∆ εw] are
presented and discussed in this paper. All obtained relations reflect well enough the main avail-
able experimental data and are quite useable for practical implementation in snow hydrology and
radio-echo sounding data interpretation concerning the moisture content and hydrothermal re-
gime of snow cover.
1 Consolidated Scientific Council on Earth Cryology of the Russian Academy of Sciences, Fersman Street 11,
Moscow, 117312, Russia
2
Institute of Geography, Russian Academy of Sciences, Staromonetny per., 29, 109017, Moscow, Russia
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