Snow cover effects on acoustic sensors

Available online at www.sciencedirect.com

Cold Regions Science and Technology 52 (2008) 132 – 145 www.elsevier.com/locate/coldregions

Snow cover effects on acoustic sensors Donald G. Albert ⁎, Stephen N. Decato, David L. Carbee Engineer Research and Development Center, Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, NH 03755, USA Received 14 March 2007; accepted 21 May 2007

Abstract Measurements were conducted to determine the effect of a snow cover on acoustic wave propagation during a 50 day period in Alaska. Acoustic waveforms produced by a blank pistol shot were recorded after propagating horizontally over various snowcovered propagation paths and were used to determine the snow cover parameters by comparison with theoretically calculated waveforms. This automatic comparison procedure was successful in determining the average snow cover permeability and depth even when the snow cover depth varied greatly across the propagation path. Although the snow cover properties remained relatively constant during the measurement period, the acoustic measurements were able to determine the changes caused by wind events and new snowfall. Acoustic measurements can provide a rapid, accurate method for determining and monitoring snow cover characteristics. The excess attenuation produced by the snow cover was generally about − 30 dB for 100 m distance and frequencies above 100 Hz. Theoretical calculations also show that even a thin snow cover only 0.02 m thick will affect acoustic pulse propagation. The attenuation and distortion caused by a snow cover can degrade passive acoustic sensor identification and distance estimation, but these detrimental effects can be mitigated by proper design of signal processing algorithms. Published by Elsevier B.V. Keywords: Snow; Acoustics; Wave propagation; Outdoor sound; Porous media; Snow permeability; Snow cover

1. Introduction The propagation of sound through the atmosphere is controlled by a number of factors, including meteorological conditions, source characteristics, air absorption, and ground conditions. For low frequency, horizontally propagating acoustic waves traveling short distances, ground impedance is usually the most important parameter, and it has been studied extensively (Attenborough, 1988; Attenborough, 1992; Embleton et al., 1983; Embleton et al., 1976) because of its importance in practical appli-

⁎ Corresponding author. Tel.: +1 603 646 4459; fax: +1 603 646 4644. E-mail address: [email protected] (D.G. Albert). 0165-232X/$ - see front matter. Published by Elsevier B.V. doi:10.1016/j.coldregions.2007.05.009

cations such as predicting sound levels produced by traffic or industrial noise, artillery firing, construction blasting, and other sources. Snow represents an extreme case in ground impedance, because it is by far the most absorptive naturally occurring ground cover. Acoustic propagation above snow has been studied rather infrequently (Attenborough and Buser, 1988; Embleton et al., 1976; Gubler, 1977; Ishida, 1965; Moore et al., 1991; Nicolas et al., 1985). Most studies used continuously emitting sources (e.g., tones from loudspeakers) at high frequencies and short ranges, which provide transmission loss estimates but do not allow the details of the waveforms to be observed. Because of the high frequencies used in these experiments, the propagation ranges were less than 15 m, and usually 1–2 m.

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

Acoustic pulse measurements over a snow cover at distances of a few hundred meters were reported by Albert and Orcutt (1989, 1990). Using blank pistol shots, they showed that the snow cover significantly reduced the peak pressure amplitudes and distorted the measured waveforms compared to measurements over grass. Albert (2001) reported additional measurements over seasonal snow covers in New England, and showed that the acoustic responses varied over short periods of time as a result of changes in snow cover properties driven by meteorological effects including storms, melt periods, and snow metamorphism. A method of automatically determining the snow depth and acoustic flow resistivity from the measured pulse waveform shape was also presented. In this paper, acoustic pulse measurements conducted in central Alaska for a 50 day period during a test of Army sensor systems are described. Because there were fewer storms and the temperatures were always well below 0 °C, the Alaskan snow cover properties were more constant than what is normally observed in New England over a similar period of time. Acoustic pulse measurements are used to monitor the snow cover depth and snow permeability over time, and snow cover effects on the performance of acoustic sensor systems are discussed. 2. Theory of wave propagation above a porous ground The calculation of acoustic propagation in a homogeneous atmosphere above a finite impedance ground has been treated by many authors (Chandler-Wilde and Hothersall, 1995; Chien and Soroka, 1975; Habault and Filippi, 1981). The pressure P at a receiver produced by a monofrequency source can be expressed as P ¼ P0



 eikr1 eikr2 ixt þQ e kr1 kr2

ð1Þ

where P0 is the source level, ω the angular frequency, k the wavenumber, r1 the direct ray path length, and r2 the reflected ray path length. Q is called the image source strength and represents the result of the wave interaction with the ground surface, and in the far field it can be approximated by (Rudnick, 1947; Ingard, 1951; Attenborough et al., 1980) Q ¼ Rp þ ð1  RP ÞF

ð2Þ

where Rp is the plane wave reflection coefficient and F is the boundary loss factor. All of the terms in Eq. (2) are

133

functions of the ground impedance and the frequency. If the ground impedance is known, the pressure for a given receiver location and propagation distance can be determined using Eqs. (1) and (2). An acoustic pulse can be constructed for the receiver by repeatedly applying these equations over the frequencies in the source emission band, and then transforming the result into the time domain using an inverse Fourier transform, with corrections for the source spectrum, instrument response, and air attenuation. This procedure has been previously used to model acoustic pulse propagation over soil (Don and Cramond, 1987; Raspet et al., 1983; Raspet et al., 1985) and snow (Albert, 2001; Albert and Hole, 2001). There are various methods available to theoretically calculate the ground impedance as a function of frequency. The empirical model of Delany and Bazley (1970) is often used because it is easy to compute and works well for many situations. However when a snow cover is present, the Delany and Bazley model does not work well, especially at frequencies below 200 Hz (Albert and Orcutt, 1990; Nicolas et al., 1985). Attenborough (1985, 1988, 1992) has produced improved ground impedance models based on theoretical treatment of the ground as a rigid porous medium that are accurate at low frequencies. Recently, a waveform inversion method has been developed to determine the acoustic parameters of a snow cover from horizontally propagating acoustic pulses (Albert, 2001). In this method, Attenborough's (1985) four-parameter model of ground impedance is used to describe the effect of the porous snow cover. The four parameters in the ground impedance model are the porosity Ω, effective flow resistivity σe, pore shape factor ratio sf, and grain shape factor n′. For the calculations in Albert (2001) the porosity used in the impedance model was determined from the measured snow density, and the grain shape factor was set to 0.5, corresponding to spherically shaped grains. Then σe, sf, and the snow cover depth d were determined by comparing the measured waveforms to waveforms calculated theoretically using Attenborough's ground impedance model. While this procedure gave excellent agreement with the measured waveforms, the solutions are not unique. In Attenborough's model the specific impedance Z2 and wavenumber k2 of the snow cover are functions of a parameter λ, defined as k¼

1 sf

 1=2  1=2 8q0 q2 x 8q0 q2 x ¼ Xre Xs2f re

ð3Þ

134

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

where ρ0 is the density of the air, q the tortuosity (actual path length through the pores divided by the straight line distance), and ω the angular frequency. The tortuosity is estimated using Bruggemann's relation (Attenborough 1983, 1985) 0

q2 ¼ Xn :

ð4Þ

Because σe and sf appear in Attenborough's impedance model only in terms of λ, the method can only determine the combination sf2σe uniquely (Sabatier et al., 1993). Theoretical waveforms have been calculated to confirm that the same waveform shape is produced for identical values of sf2σe when the factors sf2 and σe are varied. Because of this dependence, we fix the value of sf at 1.0 and recommend that this value be used in future work. Also note that Attenborough and Buser (1988) found sf = 1.0 ± 20% in their laboratory measurements on natural snow samples. The actual macroscopic DC flow resistivity σ of a porous material is defined as the ratio of an applied pressure difference ▵P [Pa] through a material of thickness d [m] that induces a flow per unit area V [m s− 1] r¼

DP=d V

ð5Þ

where the flow resistivity σ has units of [Pa s m− 2]. Allard (1993, p. 106) has shown that the actual DC flow resistivity σ is related to Attenborough's impedance model parameters by r ¼ s2f re :

ð6Þ

This equation can be used to determine the actual macroscopic flow resistivity from acoustic measurements. In studies of physical and chemical processes occurring in natural snow covers, the snow permeability K is an important parameter controlling, for example, heat flow within the snow and chemical exchange with the atmosphere (Sumner and Shepson, 1999; Waddington et al., 1996; Albert et al., 1996). However, permeability is difficult to measure accurately because of the fragility of the ice frame. The permeability is given by K¼

l r

ð7Þ

where σ is the DC flow resistivity and μ is the dynamic viscosity of the air [Pa s] with temperature dependence l ¼ 1:708  105 þ ðT  15Þ  5:61  108 :

ð8Þ

Here, T is the temperature in degrees C. Eqs. (4) and (5) can be used to estimate the snow cover permeability from the acoustic pulse measurements.
1:708  105 þ 5:61  108 ðT  15Þ l K¼ ¼ r s2f re ð9Þ To summarize the theoretical approach, Attenborough's “four parameter” model of ground impedance (Attenborough, 1985) is used to describe the acoustic properties of the porous snow cover. For this model, the snow cover porosity is determined from density measurements in a snow pit, the grain shape factor n′ is set to 0.5 corresponding to spherical grains, and the pore shape factor ratio sf is set to 1.0 (Sabatier et al., 1993). An automatic procedure to match the measured acoustic pulse waveforms with those calculated using this impedance model (Albert, 2001) is then used to determine the effective flow resistivity σe and the depth d of the snow layer. These parameters can then be used to determine the snow cover permeability from Eq. (9) and to calculate the acoustic attenuation as a function of frequency produced by the snow cover. 3. Experimental measurements 3.1. Site description and methods A series of acoustic measurements were conducted to characterize the acoustic and physical properties of the snow cover during an engineering test of an autonomous Army acoustic sensor system. The measurements were conducted at the Cold Regions Test Center, located in the interior of Alaska near the town of Delta Junction, from 18 January through 11 March 1998 (Julian days 11–70). The test site (Fig. 1) is a relatively flat open field covered with scrub brush and underlain by permafrost. The area was snow-covered during the entire test period, and the air temperature was always well below 0 °C so no melting occurred. Typical daytime temperatures during the measurements ranged from − 10 °C to − 25 °C. A large herd of moose was wintering nearby, and occasionally moved through the test location. Although detailed snow pit measurements were conducted during the winter, it is difficult to relate the physical snow cover characteristics to acoustic effects. The effect of the snow cover on acoustic wave propagation was determined by recording the waveforms produced by a simple, known source (a blank pistol shot) after propagating horizontally over various propagation

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

Fig. 1. Photographs of the test site in Alaska. Despite the flat topography, the interaction of the wind and scrub brush produces a spatially nonuniform snow cover at this location.

135

For the acoustic measurements, three Globe low frequency microphones were installed on the snow surface a distance of 25, 50, and 75 m from a gravel road. These locations were close to the Army sensor systems that were also being tested. Each day during the test period, recordings were made of.45 caliber blank pistol shots fired from a height of 1 m above the snow surface. The microphone signals were digitally recorded using a Bison Model 9048 seismograph at a sampling rate of 5 kHz. Two different shot locations were used to measure the acoustic propagation along different paths and for different distances across the snow cover. The primary shot location was at the road perpendicular to the microphones. Another shot point located along the gravel road 100 m from the sensor line was also used; this location provided propagation lengths of 103, 112, and 125 m across a different snow path. In this paper the discussion focuses on the measurements for the 75-mlong path perpendicular to the road. In addition to the acoustic measurements, continuous surface meteorological measurements were also made. Measurements of snow cover stratigraphy, density, temperature, grain size, and crystal type were made in a daily snow pit following standard procedures (Colbeck et al., 1990). Snow depth measurements were also made daily at selected locations. Occasionally, snow permeability measurements were made on 0.1 m diameter samples removed from the snow cover using the apparatus described by Albert et al. (2000). 3.2. Monitoring snow conditions

paths. A wave propagation model that treats the snow as a rigid porous medium was used to calculate theoretical waveforms, and an inversion procedure automatically varied the model snow cover parameters until the calculated waveforms matched the measured waveforms. The model snow parameters determined in this procedure could then be used to calculate the frequency dependence of the sound attenuation caused by the snow cover and other acoustic parameters of interest.

Because the temperatures remained well below freezing and there were few storms in Alaska in the winter, the snow cover remained stable over long periods of time. On any given day, the stratigraphy and other snow properties were consistently observed at locations anywhere in the area, but the snow depth varied significantly from one location to another as will be discussed below. The measurements reveal that the

Table 1 Meteorological conditions and snow cover properties during the measurements Dates (1998)

Julian days

High temperatures (°C)

Wind speeds

Snow cover (letters refer to snow pit in Table 2)

10 Jan–27 Jan 27, 30 Jan 28 Jan–12 Feb 13 Feb–16 Feb 13 Feb–18 Feb 23 Feb–24 Feb 26 Feb–11 Mar

10–27 27, 30 28–43 44–47 44–49 54–55 57–70

−17.5 −7.5 −6.5 −12.0 −7.0 −5.0 −5.0

Low High Low Low Low High Low

A — “Loose grains” Formation and thickening of surface wind crust B 3 cm of new snow C New snow removed, thickening of wind crust D

136

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

Table 2 Summary of snow cover properties during the measurements Snow cover A: 10 Jan–27 Jan 1998 (Julian days 10–27) Layer number

Layer thickness (cm)

Density (kg m− 3)

Grain type

1 2 3 4

1–2 6–7 5–6 7–11

100–120 130–150 150–185 140–190

2B Fragmented particles 4A Solid faceted 5A Depth hoar 5B Columnar depth hoar

Snow cover B: 28 Jan–12 Feb 1998 (28–43) 1 2–3 2 7–10

320–430 125–170

9D Wind crust 5B Columnar depth hoar

Snow cover C: 13 Feb–18 Feb 1998 (44–49) 1 2–3

40–90

1 2

350–420 140–190

1C,D,E, 2A, B Precipitation and fragmented particles 9D Wind crust 5B Columnar depth hoar

1–3 8–14

Snow cover D: 26 Feb–11 Mar 1998 (57–70) 1 2–5 350–420 2 9–16 140–190

snow cover properties could be divided into four distinctive time periods, divided by two high wind speed events (storms) and one light snowfall (See Tables 1 and 2 for details). • Period A, 18–27 January (Julian days 18–27): A snow cover consisting of loose, unsintered grains with low strength. Air temperatures were cold and wind speeds were low during this period. • Period B, 28 January–12 February (Julian days 28– 43): High winds on 27 January formed a wind crust at top of snow cover. Snow depths were uneven with some bare ground patches present. Cold temperatures and low wind speed during this time. High winds on 30 January led to additional thickening of wind crust. • Period C, 13–18 February (Julian days 44–49): New snow fell gradually reaching a total of 3 cm on top of the wind crust over four days. • Period D, 26 February–11 March (Julian days 49–70): High winds on 23–24 February removed the upper snow layer, exposing the wind crust at the surface again. Low air temperatures and low wind speeds for the rest of the period after this high wind event. After the first episode of high winds on 27 January, the snow cover depth varied from 0 cm to approximately 30 cm at the test site. Bare ground spots were usually at local topographic high points. The snow cover was also affected by the short bushes (bare of leaves). This vegetation tended to trap the snow as it was drifting during high winds, so that a deeper snow cover with a

Direct snow permeability (x 10- 10 m2)

3.6, 4.7, 5.4, 4.7 99

5.9

9D Wind crust 5B Columnar depth hoar

thicker wind crust was often found near these bushes. Because of the topographic and vegetative influence, the snow cover often varied from bare ground to its deepest depth over just a few horizontal meters. This large variation in snow depth at the site made an estimation of the average depth from point measurements difficult. A typical example of snow cover stratigraphy is shown in Fig. 2. The relatively stable weather conditions during the measurements, with only two storms occurring in 50 days, produced few changes in the snow cover.

Fig. 2. Photograph of typical snow cover stratigraphy during the winter. In this case two similar wind crust layers are present, underlain by a large-grained hoar layer near the surface. Note that the vegetation at the ground surface extends up into the lower part of the snow cover.

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

137

4. Acoustic results 4.1. Comparison of grass and snow cover

Fig. 3. Blank pistol shot waveforms recorded at a distance of 79 m, with and without a snow cover. The pistol was 1 m high, and the microphone was on the surface. The snow waveform has been shifted by 15 ms to align with the grass waveform.

After the formation of the wind crust at the surface, the main metamorphic changes were the growth of depth hoar crystals near the ground surface and the sintering (strengthening) of the wind crust, both driven by temperature gradients in the snow cover. The air temperature always remained well below 0 °C, so no melting occurred.

Before discussing the Alaska snow cover results, propagation over a temperate ground condition will be compared to propagation over a snow cover. The acoustic pulse measured by a microphone at the ground or snow cover surface produced by a blank pistol shot 1 m high and 79 m away is shown in Fig. 3. A comparison of the two waveforms shows that when a snow cover is present the peak pressure is lower and the waveform is elongated, even for this relatively short propagation distance. These effects are caused by interaction of the acoustic pulse with the porous snow cover. The two waveforms also sound very different to a human listener. For the temperate case, the sound is sharp and loud, similar to a handclap or a “normal” gunshot. When snow is present, however, the human listener hears a sound that seems dampened, and more like a “whoomp” than a sharp clap. Fig. 4 displays the power spectra of the two waveforms in Fig. 3. This figure shows that frequencies above about 100 Hz are strongly attenuated by up to 30 dB and that the lower frequencies enhanced when snow is present. The low frequency enhancement is caused by an acoustic surface wave that is only present at small distances for propagation over a snow cover (Albert, 2003). Some power line harmonics contaminating the waveform recorded over grass are

Fig. 4. Power spectral density (PSD) calculated for the waveforms shown in Fig. 3. The peak frequency was 180 Hz for propagation over grass and 50 Hz for propagation over snow.

138

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

Fig. 5. Selected acoustic waveforms recorded by a microphone 75 m away from a blank pistol shot for the different snow conditions during the measurement period in Alaska. The waveforms are labeled with the Julian day of the measurement and with the snow parameters determined by the waveform inversion procedure. The positive peak pressure amplitude in Pa is given to the left of each waveform. These waveforms have been normalized and time aligned. The letters A–D refer to the different snow cover conditions listed in Table 2.

visible in the figure (despite the use of a 60 Hz notch filter). The waveform shape and frequency content changes shown in Figs. 3 and 4 are typical of those observed when a seasonal snow cover is present.

analysis of these measurements was presented in Albert (1998). As described previously, theoretical acoustic waveforms were calculated using a rigid-porous model of ground impedance (Attenborough, 1985). The propagation distance and snow density were fixed for the calculations, and an automatic procedure varied the effective flow resistivity σe and the depth d of the snow layer until the acoustic pulse waveforms calculated using this impedance model matched the measured waveform (Albert, 2001). These parameters were then be used to determine the snow cover permeability from Eq. (9) and to calculate the acoustic attenuation as a function of frequency produced by the snow cover. Fig. 6 shows examples of the good agreement usually found between the observed and calculated waveforms derived by the automatic waveform inversion procedure. The acoustic parameters derived from the waveforms shown in the figure are listed in Table 3, and a summary of the waveform inversion results for the entire measurement period are listed in Table 4. The waveform analysis shows that at the beginning of the experiment during period A, the effective flow resistivity of the snow was found to be σe = 21 kPa s m− 2, with the snow depth about 16 cm. This flow resistivity value is typical for seasonal snow covers, and is low enough to cause significant acoustic attenuation. After a period of strong winds on 27–28 January, the

4.2. Measured acoustic waveforms in Alaska Fig. 5 shows examples of the pressure waveforms produced by blank pistol shots and recorded after 75 m of propagation on different selected days during the Alaskan measurements. These waveforms show the variation in acoustic response during the entire measurement period. From the bottom to the top of the figure, the dates correspond to Julian days 21, 28, 37, 43, 44, 49, 57, and 70. The waveforms have different shapes because the snow cover conditions changed as discussed earlier and listed in Table 2. While the measured positive peak pressure also varies from day to day, this parameter may be controlled primarily by the instantaneous atmospheric conditions (for example temperature and wind gradients that refract the acoustic waves upwards or downwards) rather than the snow cover conditions. These acoustic waveforms are analyzed below to determine the physical and acoustical properties of the snow cover. A preliminary

Fig. 6. Comparison of measured (solid lines) and calculated (dashed lines) acoustic waveforms for a propagation distance of 75 m during different snow cover conditions A–D during the winter. The simple blank pistol source waveform used in all of the calculations is shown at the bottom left. The details for the four cases shown here are given in Table 3.

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

139

Table 3 Snow parameters determined from the particular acoustic waveforms shown in Fig. 6 Snow cover condition (in Table 2)

Julian day

Air temperature (°C)

Average snow cover density (kg m− 3)

Acoustic snow depth (cm)

Effective flow resistivity σe (kPa s m− 2)

Acoustic snow permeability (x10− 10 m2)

A B C D

26 38 46 60

−17.5 −14.5 −12.5 −12.0

125 230 215 215

15 11 13 13

20.6 34.0 24.1 32.6

7.4 4.5 6.4 4.8

snow was redistributed and a very hard wind crust a few cm thick formed at the snow cover surface (See Table 2). The effective flow resistivity values during period B increased to about σe = 34 kPa s m− 2, and the snow depths decreased as a result of the redistribution of the snow by these winds. These parameters indicate less acoustic attenuation than normally found for seasonal snow covers, and these snow conditions persisted until about 3 cm of new snow fell on 13 February. The effective flow resistivity after this snowfall again fell to about σe = 24 kPa s m− 2, indicating higher acoustic attenuation. On 26 February, an additional wind event blew away and reworked the new snow and the acoustic attenuation decreased once again, where it remained until the end of the tests on 11 March. The effective flow resistivities determined during these measurements range from 19 to 43 kPa s m− 2. In the past, other measurements of effective flow resistivities (corrected to sf = 1.0) for seasonal snow covers range from 7–23 kPa s m− 2, with a single measurement at 56 kPa s m− 2 (e.g., Attenborough and Buser, 1988; Hess et al., 1990; Nicolas et al., 1985; Albert, 2001). The Alaskan values found here of σe = 30 kPa s m− 2 are higher than most previous measurements on seasonal snow covers. Because the reciprocal value of effective flow resistivity is proportional to the amount of interaction of the acoustic pulses with the snow cover, the higher values indicate that lower acoustic attenuation will occur. Thus the acoustic waveform distortion and acoustic attenuation was generally less than is often encountered over typical seasonal snow covers. In addition, because only two storms occurred and the air

temperature was well below freezing during the measurement period, the snow cover remained relatively unchanged compared to common winter conditions in temperate regions, where more frequent storms and melting periods produce dramatic changes in snow cover properties, often over periods of a few hours or less. Fig. 7 compares the acoustic and directly-measured parameters of the snow cover during the winter. The acoustic permeability was determined from the waveform inversion using Eq. (9) and represents a spatial average over the 75 m propagation path. These measurements are compared to flow and pressure drop measurements made on small surface wind crust samples using the method of Albert et al. (2000). While the surface permeability values using the two methods agree well with each other, the snow permeability values changed very little during the measurement period because of the constant presence of the wind crust at the surface. In addition, much higher values were obtained by direct measurements on snow samples from the depth hoar layer (approximately 100 × 10− 10 m2), but these high values were not detected by the acoustic method which produced values that ranged from 4.5 to 7.5 × 10− 10 m2. A simple calculation of the normal surface impedance (Allard, 1993, Chapter 2) shows that the higher permeability material beneath the wind crust has only a very slight influence on the normal surface acoustic impedance. Previous acoustically estimated values of seasonal snow cover permeability determined from the measurements reported in (Albert, 2001) vary from

Table 4 Snow parameters from the acoustic waveform inversion analysis for the 75-m propagation distance during the winter Snow cover condition (in Table 2)

Julian days

Number of acoustic measurement days

Average snow cover density (kg m− 3)

Acoustic snow depth (cm)

Effective flow resistivity σe (kPa s m− 2)

Acoustic snow permeability (x10− 10 m2)

A B C D

18–27 28–43 44–49 57–70

5 14 4 14

125 230 215 215

16.1 ± 1.4 12.2 ± 1.9 13.7 ± 1.3 11.8 ± 1.5

21.3 ± 1.5 34.1 ± 2.7 23.6 ± 1.5 31.9 ± 5.9

7.1 ± 0.5 4.6 ± 0.4 6.6 ± 0.4 5.1 ± 1.0

(The snow density was determined from a snow pit. Means and standard deviations are given for acoustic parameters.)

140

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

Fig. 7. Comparison of acoustically- vs. directly-measured snow cover parameters during the measurement period. The acoustic parameters were derived from waveforms measured over a 75 m propagation path, while the direct measurements were obtained at a single location near the microphone. (Top) Acoustic (circles) snow depths compared to point direct snow depth measurements (triangles) made with a probe. The error bars are the minimum and maximum snow depths measured at the site on that day. (Bottom) Acoustic (circles) snow permeability compared to direct flow measurements (triangles) on small snow samples using the method of Albert et al. (2000). The direct measurements were conducted on surface wind crust samples.

1–25 × 10− 10 m−2 and agree with the range of permeability values found in previous laboratory measurements (e.g., Shimizu, 1970; Chacho and Johnson, 1987; Jordan et al., 1999, Albert et al. 2000). The acoustic method of estimating snow permeability has some advantages over the laboratory method, including not requiring the removal and handling of fragile snow samples and also of providing a measurement averaged over the propagation path length, typically tens of meters, instead of a 10-cm sample size. Previously reported methods of acoustically estimating soil permeability have either relied on laboratory-sized samples (Dai and Young, 1996; Attenborough and Buser, 1988) or have been used to deduce relative or effective values (Don and Cramond, 1985; Moore and Attenborough, 1992). The acoustic snow depths shown in Fig. 7 represent a spatial average over the 75 m propagation path. The direct measurements were obtained by averaging five probe measurements over a 30 × 30 cm area. The figure plots the direct measurement obtained near the microphone (75 m from the road) as well as the deepest and shallowest depth measurement in the area near the acoustic measurement path. Because of the very high spatial variation in the snow depth at this location, the acoustically-determined snow depth provides a very

useful estimate of the average snow cover depth over the acoustic propagation path. On the final day of the measurements, when disurbing the snow cover was no longer of concern, a series of direct snow depth profiles were measured. The point measurements were spaced two meters apart along the acoustic propagation paths. These values are compared to the acoustic depth estimates for the different acoustic propagation paths in Fig. 8. The large changes in the directly-measured snow depths over short distances are real and are caused by the vegetation and topographic effects discussed earlier. This figure shows that an average snow depth may be difficult to determine using standard probe measurements, so the acoustic technique provides a rapid method to obtain the average snow cover depth in these situations. In locations with more uniform snow covers, the acoustic method usually provides an average snow depth accuracy within 2–5 cm of direct probe measurements (Albert, 2001). 5. Snow cover effects on acoustic sensor performance Autonomous passive acoustic sensor systems have the potential to detect, classify, and track various objects that emit sounds like vehicles or animals. However, to operate reliably, sensor systems must properly account for environmental effects that may vary at different locations or over time. Some of the possible effects of

Fig. 8. Direct measurements of snow cover depth at 2 m intervals in the undisturbed snow cover along different acoustic propagation paths used during the measurements. These measurements were obtained on Julian day 70 after the acoustic measurements were completed to avoid disturbing the snow cover. This figure illustrates that the “average snow cover depth” can be a difficult parameter to estimate because of the large variability in the snow depth at this site. Much of the variation of the snow depth is caused by wind and vegetation effects that are discussed in the text.

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

a snow cover on the performance of acoustic sensor systems are discussed in this section. As shown in Fig. 3, a simple acoustic pulse can become distorted after propagating only a short distance over a snow cover. A signal processing description of acoustic propagation can be formulated as the convolution of the emission signature of an object (whether a blank pistol shot or vehicle engine noise) with the impulse response of the environment during propagation over some distance to produce the waveform recorded by a microphone. This description illustrates that complex signals like continuously emitting vehicles will also be subjected to the same distortion shown more clearly for simple sources like pistol shots. If the sensor is located below the snow cover (from a snow fall occurring after the sensor emplacement) then the distortion effect can be even more dramatic (Albert, 1987). If the sensor system algorithms do not include these effects, their performance will degrade and may fail when a snow cover is present. The signature distortion shown in Fig. 3 is caused by the interaction of the acoustic pulse with the porous snow cover. This interaction tends to attenuate higher frequencies (above 100 Hz as shown in Fig. 4) compared to temperate conditions, and can be accurately modeled and predicted using the rigid porous medium model discussed earlier to represent the snow cover. This type of filtering and distortion effect can be quantified by calculating a parameter known as excess attenuation. 5.1. Calculations of excess attenuation

141

ground surface located 100 m from the source. The calculations assumed a homogeneous atmosphere and did not include air attenuation, which is very small in this low frequency band. Fig. 9 shows the calculated excess attenuation as a function of frequency for the four snow cover conditions encountered during the winter measurement period. The excess attenuation for a grass-covered ground (with an assumed effective flow resistivity of 300 kPa s m− 2) also is shown for comparison, and is nearly flat at a level of + 6 dB relative to a free field without a ground boundary. When snow is present, the excess attenuation has a maximum of + 8 dB near 30 Hz, then rapidly decreases as the frequency increases, reaching a level greater than −20 dB at 200 Hz. The differences between the snow covers are significant, with a range in excess attenuation of 9 dB at 100 Hz and 6 dB at 150 Hz. The figure shows that the acoustic attenuation was the greatest in January before the formation of a wind crust (Period A in Table 2). After the wind crust formed (B), the attenuation was 9 dB less at 100 Hz. The attenuation increased after an additional snowfall (C), then decreased again once the wind had reworked the snow pack (D). As the frequency increases, the excess attenuation generally decays to lower values indicating higher attenuation at higher frequencies. However, in some cases (usually for shallow snow) at low frequencies, the levels will actually increase above 6 dB to a maximum of around 8 dB. This increase is caused by an acoustic surface wave that can exist only under certain conditions

To illustrate these effects, the excess attenuation (EA) during the Alaska measurements was calculated using the snow parameters determined by the waveform inversion procedure. The excess attenuation, defined as the ratio of the received pressure at a given distance compared to the received pressure in free space without the ground surface can be used to determine the effect of the snow cover on acoustic propagation. It is given by  EAðrÞ ¼ 20 log 10

P ðr Þ Pdirect ðrÞ

 ð10Þ

where r is the propagation distance, Pdirect(r) is the direct pressure wave given by the first term on the right side of Eq. (1), and P(r) is the total received pressure given by all of the terms on the right side of Eq. (1). For the excess attenuation calculations presented here, the source was assumed to have a flat emission spectrum. The calculations used the snow parameters determined from the waveform analysis for a configuration with a source 1 m and a receiver 25 cm above the

Fig. 9. Excess attenuation produced by the snow cover for a propagation distance of 100 m and frequencies up to 250 Hz during the winter test period. These calculations used the snow cover parameters A–D determined by the waveform analysis and listed in Table 4. Snow covers B and C are plotted with solid lines, A and D using dashed lines. An effective flow resistivity value of σe = 300 kPa s m− 2 was used to calculate the excess attenuation for grass.

142

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

(Raspet and Baird, 1989; Daigle 1991; Albert, 2003). In fact, this acoustic surface wave is the main low frequency pulse that appears in all of the waveform displays presented here. Although the higher frequencies are strongly attenuated by the snow cover, in some cases the low frequencies are enhanced by the acoustic surface wave. This phenomenon can be exploited to act as a passive amplifier of specific frequencies (Daigle and Stinson, 2004). Any signal that an acoustic sensor measures when a snow cover is present will be low pass filtered as shown by Fig. 9, and this filtering may degrade the performance of detection or classification algorithms, because the received signal will have different characteristics compared to signals measured under temperate conditions that were used in the design of the algorithms. One possible method of improving sensor performance in the presence of a snow cover would be to apply a frequency dependent amplification to restore the signals to the levels expected if a snow cover were not present. If the acoustic sensor records a broadband source when snow is present, an algorithm to determine whether this low pass filtering effect is present can be used to automatically compensate for the low pass filtering effect. To determine the effect of snow cover thickness on acoustic propagation, the excess attenuation was calculated for a typical seasonal snow cover with constant acoustic properties but variable snow depths from 0.02 to 0.50 m. Fig. 10 shows that the low pass filtering effect is present even for a thin snow cover of 2 cm depth, but in this case the cutoff frequency is located near 250 Hz. The cutoff frequency decreases as the snow depth increases, reaching 100 Hz for a depth of 8 cm and 50 Hz by about 20 cm in depth. As the snow cover depth increases beyond 20–30 cm, there is little further change in the excess attenuation. These calculations show that there is a strong acoustic effect on signal propagation even for very thin snow covers. Thus one simple way to determine whether a sensor algorithm needs to be adjusted for a snow cover would be to use an inexpensive camera (like a Webcam) to look for a white ground surface, since the depth is less important than the presence or absence of any snow at the surface. 5.2. Range estimation from peak pressure level Some passive acoustic sensor systems use the received sound pressure to estimate the distance or range to a moving source. In this procedure, the sensor system first identifies the emitter (for example the type of vehicle) based on other signal characteristics, and then determines the range or distance to the source using the

Fig. 10. Excess attenuation calculations as a function of frequency and snow depth for a typical seasonal snow cover at an acoustic propagation distance of 200 m. The assumed snow density was 150 kg m− 3 and permeability was 6 × 10− 10 m2 (corresponding to an effective flow resistivity of σe = 13 kPa s m− 2). Solid lines are for snow depth from 2 cm to 50 cm in increments of 2 cm. The 2 cm depth shows the least excess attenuation at low frequencies, and the excess attenuation increases with snow cover depth until a limit is reached at around 30 cm for this snow cover. The dashed line is the attenuation for a relatively hard frozen soil surface, with a density of 1600 kg m− 3 and a permeability of 0.09 × 10− 10 m2 (corresponding to an effective flow resistivity of σe = 1900 kPa s m− 2).

ratio of the emission sound level to the received sound level, assuming spherical spreading or a non-absorbing ground surface. However, when a snow cover is present and not accounted for in the sensor algorithm, this method can produce serious errors. For short propagation distances of a few hundred meters or less, previous work has shown that the change in peak sound pressure level with propagation distance can be represented by PðrÞ ¼ P0 ra

ð11Þ

where P(r) is the peak pressure [Pa] at propagation distance r [m], and α is the attenuation coefficient. This equation neglects atmospheric effects and molecular attenuation, and so applies to frequencies of a few hundred Hz or less. Geometrical spreading of the wavefront is represented by a value of α = 1, while measurements for grass and soils are usually around 1.2 (e.g., ANSI, 1983; Albert and Orcutt, 1989). Albert (2001) found values of 1.5–1.9 for various seasonal snow covers. Fig. 11 shows the passive acoustic procedure

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

143

operating in the frequency band below 500 Hz. Daily measurements of this snow cover effect were conducted during an Alaskan winter by measuring the waveform changes produced as a pulse from a blank pistol traveled over the snow cover. These waveform changes were analyzed to determine the permeability and depth of the snow cover as well as the excess acoustic attenuation as a function of frequency and distance. Because the temperatures are very low and there are few storms in Alaska in the winter, the snow cover remained stable over long periods of time. Four different snow conditions were revealed by the acoustic measurements during this period:

Fig. 11. Estimation of distance to a source from the acoustic loudness at a microphone. If the source can be identified (as a particular vehicle, for example), then the known emission level can be used to determine the distance from the acoustic pressure decay. The plot shows that if a temperate attenuation rate is used when a snow cover is present, the estimated distance can be in error by more than a factor of two: the same amplitudes are expected at 219 m for grass or 100 m for snow.

sometimes used to estimate the distance to a sound source (for example, a particular vehicle). The emission level is assumed to be known based on the identification of the type of source either from the acoustic signature or from other means. This emission level is set to 0 dB at a reference distance, and the predicted decrease in sound level as a function of propagation distance is shown in the figure. Under temperate conditions with grasscovered ground, a decrease in the sound level of 25 dB would indicate that the source was about 220 m from the acoustic sensor. However, if a snow cover is present, the same sound level would be received when the distance was only 100 m. If the snow cover effect is not recognized or included in the sensor algorithm, the acoustic distance estimate would be more than a factor of two in error. Such an error would seriously degrade the sensor performance, but if the correct “snow attenuation” coefficient of − 1.8 is used by the algorithm, an accurate distance estimate can be obtained.

• A — 18–27 Jan 98: strong acoustic attenuation from the snow cover. • B — 28 Jan–12 Feb 98: after the formation of a wind crust on 27–28 Jan, the acoustic attenuation was reduced. • C — 13–18 Feb 98: new snow on top of the snow cover increased the attenuation once more, to almost as much as it had been in January. • D — 26 Feb–11 Mar 98: a wind event removed the upper snow layer, returning to a low acoustic attenuation condition. For all of these cases, the acoustic attenuation was greater than would occur for any type of ground without snow. Typically, the attenuation reached − 30 dB at a propagation distance of 100 m and a frequency of 250 Hz. The snow effect we measured in Alaska was smaller than most seasonal snow covers encountered elsewhere, so larger snow cover effects on sensor system performance are possible under more typical snow conditions. Theoretical calculations also showed that a snow cover as thin as 2 cm is sufficient to cause significant acoustic effects. The acoustic techniques presented in this paper can provide a rapid, accurate method for determining and monitoring snow cover characteristics. The methods used to analyze the acoustic conditions are nearly automatic, and have the potential to be incorporated directly into future sensor systems so that adjustments to the performance algorithms could be done autonomously. Acknowledgements

6. Summary Previous work has shown that a snow cover on the ground can have a large effect on horizontally traveling acoustic waves and attenuate frequencies in the band of interest to autonomous acoustic sensor systems

We thank the many Cold Regions Test Center personnel for their assistance during the tests and for providing the meteorological data. Mr. Art Gelvin, ERDCCRREL Alaska, provided helpful assistance with the logistics. The authors also thank Dr. Richard Raspet

144

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145

for pointing out the reference Sabatier et al. (1993) and for useful discussions about the uniqueness of the waveform inversion. We also thank an anonymous reviewer for useful comments. Mr. Frank Ardino, U.S. Army PM-MCD (now PM-CCS), provided funding for the Alaska field measurements. We also thank the U.S. Army Corps of Engineers ERDC research program for additional funding. References Albert, D.G., 1987. The effect of snow on vehicle-generated seismic signatures. Journal of the Acoustical Society of America 81, 881–887. Albert, D.G., 1998. Environmental effects on acoustic wave propagation at Ft. Greely, Alaska. 1998 Meeting of the IRIS Specialty Group on Acoustic and Seismic Sensing. Johns Hopkins University, Laurel, MD, pp. 273–280. Albert, D.G., 2001. Acoustic waveform inversion with application to seasonal snow covers. Journal of the Acoustical Society of America 109, 91–101. Albert, D.G., 2003. Acoustic surface waves propagating over a snow cover. Journal of the Acoustical Society of America 113, 2495–2500. Albert, D.G., Orcutt, J.A., 1989. Observations of low frequency acoustic-to-seismic coupling in the summer and winter. Journal of the Acoustical Society of America 86, 352–359. Albert, D.G., Orcutt, J.A., 1990. Acoustic pulse propagation above grassland and snow: comparison of theoretical and experimental waveforms. Journal of the Acoustical Society of America, 87, 93–100. Albert, D.G., Hole, L.R., 2001. Blast noise propagation above a snow cover. Journal of the Acoustical Society of America 109, 2675–2681. Albert, M.R., Arons, E.M., Davis, R.E., 1996. Firn properties affecting gas exchange at Summit, Greenland: ventilation possibilities. In: Wolff, E.F., Bales, R.C. (Eds.), Chemical Exchange Between the Atmosphere and Polar Snow. Springer-Verlag, Berlin, pp. 561–565. Albert, M.R., Shultz, E.F., Perron Jr., F.E., 2000. Snow and firn permeability at Siple Dome, Antarctica. Annals of Glaciology 31, 353–356. Allard, J.F., 1993. Propagation of Sound in Porous Media. Elsevier, London. American National Standards Institute, 1983. Estimating Airblast Characteristics for Single Point Explosions in Air, with a Guide to Evaluation of Atmospheric Propagation and Effects, ANSI S2.20–1983. Acoustical Society of America, New York. Attenborough, K., 1983. Acoustical characteristics of rigid fibrous absorbents and granular materials. Journal of the Acoustical Society of America 73, 785–799 (Equations 45 and 46). Attenborough, K., 1985. Acoustical impedance models for outdoor ground surfaces. Journal of Sound and Vibration 99, 521–544. Attenborough, K., 1988. Review of ground effects on outdoor sound propagation from continuous broadband sources. Applied Acoustics 24, 289–319. Attenborough, K., 1992. Ground parameter information for propagation modeling. Journal of the Acoustical Society of America 92, 418–427. Attenborough, K., Buser, O., 1988. On the application of rigid-porous models to impedance data for snow. Journal of Sound and Vibration 124, 315–327.

Attenborough, K., Hayek, S.I., Lawther, J.M., 1980. Propagation of sound above a porous half-space. Journal of the Acoustical Society of America 68, 1493–1501. Chacho Jr., E.F., Johnson, J.B., 1987. Air permeability of snow. Eos, Transactions of the American Geophysical Union 68, 1271 (abstract). Chandler-Wilde, S.N., Hothersall, D.C., 1995. Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane. Journal of Sound and Vibration, 180, 705–724. Chien, C.F., Soroka, W.W., 1975. Sound propagation along an impedance plane. Journal of Sound and Vibration, 43, 9–20. Colbeck, S., Akitaya, E., Armstrong, R., Gubler, H., Lafeuille, J., Lied, K., McClung, D., Morris, E., 1990. International classification for seasonal snow on the ground, Int. Comm. Snow and Ice (IAHS). World Data Center A for Glaciology. University of Colorado, Boulder, CO. Dai, R., Young, C.T., 1996. Design and test of a sonic permeameter for dry unconsolidated porous materials. Water Resources Research 32, 43–54. Daigle, G.A., 1991. Role of surface waves in outdoor noise propagation. In: A. Lawrence (Editor), International Conference on Noise Control Engineering (Inter-noise 91). Noise Control Foundation, Poughkeepsie, NY. Daigle, G.A., Stinson, M.R., 2004. Passive amplification and directivity from air-coupled surface waves generated above a structured ground. Journal of the Acoustical Society of America 115, 1988–1992. Delany, M.E., Bazley, E.N., 1970. Acoustical properties of fibrous absorbent materials. Applied Acoustics 3, 105–116. Don, C.G., Cramond, A.J., 1985. Soil impedance measurements by an acoustic pulse technique. Journal of the Acoustical Society of America 77, 1601–1609. Don, C.G., Cramond, A.J., 1987. Impulse propagation in a neutral atmosphere. Journal of the Acoustical Society of America 81, 1341–1349. Embleton, T.F.W., Piercy, J.E., Olson, N., 1976. Outdoor sound propagation over ground of finite impedance. Journal of the Acoustical Society of America 59, 267–277. Embleton, T.F.W., Piercy, J.E., Daigle, G.A., 1983. Effective flow resistivity of ground surfaces determined by acoustical measurements. Journal of the Acoustical Society of America 74, 1239–1244. Gubler, H., 1977. Artificial release of avalanches by explosives. Journal of Glaciology 19, 419–429. Habault, D., Filippi, P.J.T., 1981. Ground effect analysis: surface wave and layer potential representations. Journal of Sound and Vibration 79, 529–550. Hess, H.M., Attenborough, K., Heap, N., 1990. Ground characterization by short-range propagation measurements. Journal of the Acoustical Society of America 87, 1975–1986. Ingard, K.U., 1951. On the reflection of a spherical wave from an infinite plane. Journal of the Acoustical Society of America 23, 329–335. Ishida, T., 1965. Acoustic properties of snow. Low Temperature Science, Series A: Physical Sciences 20, 23–63. Jordan, R.E., Hardy, J.P., Perron Jr., F.E., Fisk, D.J., 1999. Air permeability and capillary rise as measures of the pore structure of snow: an experimental and theoretical study. Hydrological Processes 13, 1733–1753. Moore, H.M., Attenborough, K., Rogers, J., Lee, S., 1991. In-situ acoustical investigations of deep snow. Applied Acoustics 33, 281–301. Moore, H.M., Attenborough, K., 1992. Acoustic determination of airfilled porosity and relative permeability of soils. Journal of Soil Science 43, 211–228.

D.G. Albert et al. / Cold Regions Science and Technology 52 (2008) 132–145 Nicolas, J., Berry, J.-L., Daigle, G.A., 1985. Propagation of sound above a finite layer of snow. Journal of the Acoustical Society of America 77, 67–73. Raspet, R., Baird, G.E., 1989. The acoustic surface wave above a complex impedance ground surface. Journal of the Acoustical Society of America 85, 638–640. Raspet, R., Bass, H.E., Ezell, J., 1983. Effect of finite ground impedance on the propagation of acoustic pulses. Journal of the Acoustical Society of America 74, 267–274. Raspet, R., Ezell, J., and Bass, H.E., 1985. Additional comments on and erratum for ‘Effect of finite ground impedance on the propagation of acoustic pulses’ [Journal of the Acoustical Society of America 74:267–274 (1983)], Journal of the Acoustical Society of America, 77:1955–1958. Rudnick, I., 1947. Propagation of an acoustic wave along a boundary. Journal of the Acoustical Society of America 19, 348–356.

145

Sabatier, J.M., Raspet, R., Frederickson, C.K., 1993. An improved procedure for the determination of ground parameters using level difference measurements. Journal of the Acoustical Society of America 94, 396–399. Shimizu, H., 1970. Air permeability of deposited snow. Low Temperature Science, Series A: Physical Sciences 22, 1–32. Sumner, A.L., Shepson, P.B., 1999. Snowpack production of formaldehyde and its effect on the Arctic troposphere. Nature 398 (6724), 230–233. Waddington, E.D., Cunningham, J., Harder, S.L., 1996. The effects of snow ventilation on chemical concentrations. In: Wolff, E.F., Bales, R.C. (Eds.), Chemical Exchange Between the Atmosphere and Polar Snow. Springer-Verlag, Berlin, pp. 403–451.