Snow Attenuation Research Articles

The response of a seasonal snow cover to explosive loading

An explosive detonation in snow produces high intensity shock waves that are rapidly attenuated by momentum spreading as the snow is compacted. Our experimental measurements and numerical calculations indicate that the maximum shock-wave attenuation in seasonal snow (250 kgm−3) is proportional to betweenx−1.6andx−3for plane waves andx−3for spherical waves (xis the propagation distance). Outside the region of shock-compacted snow or in air over snow, stresses are transmitted as acoustic/seismic waves. Attenuation of these waves depends on snow permeability and the effective modulus of the ice frame and is proportional to aboutx−0.7for plane waves in seasonal snow and to aboutx−1for spherical waves in air over seasonal snow. Increasing the scaled detonation height of an explosive up to 2mkgf−1/3above a snow cover increases the far field (scaled distances greater than about 8m kgf−1/3snow surface pressures. Scaled detonation heights greater than about 2mkgf−1/3have little additional effect.

Simple model of shock-wave attenuation in snow

AbstractA simple momentum model, assuming that snow compacts along a prescribed pressure–density curve, is used to calculate the pressure attenuation of shock waves in snow. Four shock-loading situations are examined: instantaneously applied pressure impulses for one-dimensional, cylindrical and spherical shock-wave geometries, and a one-dimensional pressure impulse of finite duration. Calculations show that for an instantaneously applied impulse the pressure attenuation for one-dimensional, cylindrical and spherical shock waves is determined by the pressure density (P–ρ) compaction curve of snow. The maximum attenuation for a one-dimensional shock wave is proportional to (Xf–X0)−1.5 for the multi-stage (P–ρ) curve and (Xf–X0)−2 when compaction occurs in a single step (single-stage compaction), where (Xf–X0) is the shock-wave propagation distance. Cylindrical waves have a maximum attenutation that varies from (R–R0)−2 for single-stage compaction and (R–R0)−1.5 for multi-stage compaction, when (R – R0) ≪ R0, where R is the propagation radius and R0 is the interior radius over which a pressure impulse is applied, to R−4 when (R – R0) ≫ R0 Spherical waves have a maximum attenuation that varies from (R – R0)−2 for single-stage compaction and (R – R0)−1.5 for multi-stage compaction to R−6 when 〈R – R0〉 ≫ R0.The shock-wave pressure in snow for a finite-duration pressure impulse is determined by the pressure impulse versus time profile during the time interval of the impulse. After the pressure impulse ends, shock-wave pressure attenuation is the same as for an instantaneously applied pressure impulse containing the same total momentum. Pressure attenuation near a shock-wave source, where the duration of the shock wave is relatively short, is greater than for a shock wave farther from a source where the shock wave has a relatively long duration. Shock-wave attenuation in snow can be delayed or reduced by increasing the duration of a finite-duration pressure impulse. A sufficiently long-duration impulse may result in no shock-wave pressure attenuation in a shallow snow cover.

Simple model of shock-wave attenuation in snow

AbstractA simple momentum model, assuming that snow compacts along a prescribed pressure–density curve, is used to calculate the pressure attenuation of shock waves in snow. Four shock-loading situations are examined: instantaneously applied pressure impulses for one-dimensional, cylindrical and spherical shock-wave geometries, and a one-dimensional pressure impulse of finite duration. Calculations show that for an instantaneously applied impulse the pressure attenuation for one-dimensional, cylindrical and spherical shock waves is determined by the pressure density (P–ρ) compaction curve of snow. The maximum attenuation for a one-dimensional shock wave is proportional to (Xf–X0)−1.5for the multi-stage (P–ρ) curve and (Xf–X0)−2when compaction occurs in a single step (single-stage compaction), where (Xf–X0) is the shock-wave propagation distance. Cylindrical waves have a maximum attenutation that varies from (R–R0)−2for single-stage compaction and (R–R0)−1.5for multi-stage compaction, when (R–R0) ≪R0, whereRis the propagation radius andR0is the interior radius over which a pressure impulse is applied, toR−4when (R–R0) ≫R0Spherical waves have a maximum attenuation that varies from (R–R0)−2for single-stage compaction and (R–R0)−1.5for multi-stage compaction toR−6when 〈R–R0〉 ≫R0.The shock-wave pressure in snow for a finite-duration pressure impulse is determined by the pressure impulse versus time profile during the time interval of the impulse. After the pressure impulse ends, shock-wave pressure attenuation is the same as for an instantaneously applied pressure impulse containing the same total momentum. Pressure attenuation near a shock-wave source, where the duration of the shock wave is relatively short, is greater than for a shock wave farther from a source where the shock wave has a relatively long duration. Shock-wave attenuation in snow can be delayed or reduced by increasing the duration of a finite-duration pressure impulse. A sufficiently long-duration impulse may result in no shock-wave pressure attenuation in a shallow snow cover.

Attenuation and reflection of radio waves by a melting layer of precipitation

Attenuation and reflection of a melting layer are calculated using a meteorological model. The model employs a new scheme for the calculation of the dielectric properties of melting ice particles with densities ranging from those of loose snow to hail, and a new scheme for calculating the melting rate is employed. The input parameters are derived from high resolution Doppler radar data and provide a data set for statistical analysis. Statistical relations were derived for attenuation in the melting layer based on measurements made with a surface rain gauge, a radar (with and without a polarisation facility), and a lower frequency satellite link. It was found that the specific attenuation of melting snow surpasses the value of rain because of the larger size and particle number density during melting, the attenuation within the melting layer increasing with its reflection. In stratiform precipitation, the attenuation in the melting layer is found to increase only slightly with frequency. The reflection in the melting layer decreases with the frequency of the radio waves in such a way that a bright band is only observed for frequencies below 20 GHz.

Extinction Behavior of Dry Snow in the 18-to 90-GHz Range

The extinction properties of several dry snow types were examined in the 18-to 90-GHz range. The snow types ranged from newly fallen snow to refrozen snow, and the density and mean grain size varied from 0.17 to 0.39 g/cm3 and from 0.2 to 1.6 mm, respectively. From measurements of the transmission loss as a function of sample thickness at a temperature of -15°C, the extinction coefficient and the surface scattering loss (due to surface roughness at the front and back surfaces of the snow slab) were determined for each snow type. The experimental values were compared against theoretical results computed according to the strong fluctuation theory. In general, good agreement with the experimental data was obtained at 18, 35, and 60 GHz when the grain size used in the theoretical calculations was chosen to be slightly smaller than the observed snow-particle size. However, the extinction coefficient of large-grained refrozen snow as predicted by the strong fluctuation theory is much larger at 90 GHz than the values determined experimentally. The attenuation in snow was observed to increase only slightly with increasing temperature in the -35 to -1°C range.

A 500 m experimental range for propagation studies at millimetre, infrared and optical wavelengths

A 500 m experimental range which has been constructed to carry out propagation studies at millimetre, infra-red and optical wavelengths is described. The range is a well- instrumented open-air laboratory where the transmissions are monitored simultaneously with a comprehensive set of meteorological measurements to obtain propagation data required to develop prediction models of use in the design of future communications systems. Some examples are given of studies of attenuation in rain, snow and fog, and of the effects of scintillation.

Attenuation in melting snow on microwave- and millimetre-wave terrestrial radio links

The scattering properties of melting snow on microwave and millimetre-wave terrestrial radio links are predicted using a new model for melting which includes coalescence. Attenuation, differential attenuation and differential phase are calculated for a horizontal path, with results at 36.25 GHz presented. Peak specific attenuation in the range 8–13 dB/km is expected for underspread rain with 10–15 mm/h rain rates.

Permittivity and attenuation of wet snow between 4 and 12 GHz

The permittivity and attenuation of prepared samples of wet snow are measured and curves presented showing the dependence of these quantities on snow wetness and frequency. Equations are given that express the experimentally determined relation between attenuation per unit length and volume-percent wetness at any frequency between 4 and 12 GHz. Additional equations are given for the calculation of permittivity from the snow density, attenuation per unit length, and frequency. Water retention characteristics of snow are described. Some applications of the techniques, such as runoff forecasting from mountain snowpacks, are proposed.

Visibility and Light Attenuation in Falling Snow

Abstract The attenuation of visible light by failing snow was studied by making simultaneous determinations of attenuation coefficients and snow concentration. The attenuation coefficient was calculated from photo-metric measurements and from visual observations. Snow concentration in the air was evaluated by two methods. Formvar replicas collected during the snowfall, and mass accumulation of snow in collecting pans. The snowflakes were arbitrarily classified by crystal types according to their estimated fall velocity. It was found that the correlation between extinction coefficient and snow concentration was generally much higher by types than when all snowflakes were considered together regardless of crystal components and degree of riming. When no fog is present during the snowfall, the experimental results for some snow types coincide well with attenuation theory if a reasonable correction is applied to the values obtained in the measurement of snow-flake diameters. Measurements of mass flux indicate...