Number range CHAPTER

**Low-Frequency Atmospheric Acoustic Energy**

**Associated with Vortices Produced by Thunderstorms**

A. J. BEDARD, JR.

*National Oceanic and Atmospheric Administration/Environmental Research
Laboratories/*

*Environmental Technology Laboratory, Boulder, Colorado*

Received: 27 February 2002

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

*Corresponding author address*: A. J. Bedard, Jr.,
NOAA/ERL/Environmental Technology Laboratory, R/ET1, 325 Broadway,
Boulder, CO 80305-3328.

**Low-Frequency Atmospheric Acoustic Energy**

**Associated with Vortices Produced by Thunderstorms**

A. J. BEDARD, JR.

*National Oceanic and Atmospheric Administration/Environmental Research
Laboratories/*

*Environmental Technology Laboratory, Boulder, Colorado*

ABSTRACT

An infrasonic observatory collocated with the Colorado State University
CHILL radar during the summer of 1995 permitted unique comparisons
between severe storm kinematics and detected acoustic energy at
subaudible frequencies near 1 Hz. Radar observations of a velocity
couplet aloft (evolving into a tornado) showed a circulation maximum
descending for about 30 min while moving to the east. The detected
infrasound followed the trend of these observations. A model of sound
radiated from vortex systems predicts frequencies in the range observed.
These data are interpreted in the context of past infrasonic
observations, and implications for detection and warning are discussed.
An ongoing study comparing regional tornado and funnel sightings with
archived infrasonic data has identified over a 100 cases to date where
the infrasonic signals occurred at the time of, and from the direction
of, the vortices. For some of these cases, the distances were greater
than 100 km. We continue to collect data sets to permit evaluation of
infrasonic detection as a method of improving short-term storm warnings
and plan this as the first of a series of papers detailing the
potential.

**1. Introduction**

This paper reviews the background of past measurements of acoustic
energy at audible and infrasonic frequencies from severe weather and
tornadoes. Infrasonic frequencies (i.e. sound below 20 Hz) can travel
for great distances without significant absorption. Whereas a 1
kilohertz signal will have 90% of it's energy absorbed after traveling 7
kilometers at sea level, for a 1 Hz signal this distance is 3000
kilometers. Most past observations used acoustic passbands much lower in
frequency than the 0.5- to 5-Hz frequency range focused on in this
paper. Differences between the infrasonic measurement systems applied in
the 1970's and 1980's as a part of a global observing network and the
higher frequency near infrasound system detecting the 7June 1995 event
are significant. Several features of the global observing system
(including the array dimensions, the spatial filter, and the sensor
itself) combined to limit the high frequency response to below 0.5 Hz.
The severe weather-related infrasound reported in the literature from
the global infrasonic network involves sound two orders in magnitude
longer in wavelength than the newer system and at continental scales of
1000's of kilometers. In contrast, the near infrasound system used to
take the measurements reported here focuses on frequencies in the range
.5 to 10 Hz and regional range scales of 100's of kilometers or less.
Table 1 summarizes the differences between these systems.

A recent observation using an infrasonic observatory collocated with a
Doppler radar provided a unique dataset for comparing infrasonic
measurements with well-defined storm kinematics. The sound direction and
elevation angle followed the trend of the movement of the vortex
circulation maximum as a function of time. Sufficient information was
available to compare the acoustic spectra with that predicted by sound
generation models, suggesting that the sound originated from vortex
radial modes of vibration.

Often we have noted that often when a number of strong cells are present
in the region of an infrasonic observatory, acoustic energy is radiated
by only one of the systems. Also, past lower frequency geoacoustic
measurements noted a relationship with large hail. This inspired the
study of two significant hail-producing storms, well documented by
Doppler radar. No acoustic energy was detected from either of these
storms, and no evidence of vortices occurred. This indicates that near
infrasound is not a common feature of all severe weather.

Finally, the implications for detection and warning are discussed and a
scenario presented to indicate how infrasonic observatories might
contribute to improved identification of storms containing concentrated,
strong vortices. Although the preliminary results are very encouraging,
we need to continue additional case study analysis, to make additional
collocated Doppler radar measurements, and to create a rapid deployment
infrasonic system with a broadband recording capability. Such a mobile
system operated from a van would chase storms and make near-field
acoustic measurements over an extended frequency range. We have operated
a series of infrasonic measurement field studies, some involving
multiple observing systems. We plan to summarize results in a series of
papers covering case studies, detection statistics, scale model
measurements, and potential strategies for operational use.

**2. Historical perspective**

*a. Audible sounds*

Numerous reports have described audible sounds from tornadoes (e.g.,
Brooks 1957; Hazen 1890), but few have included actual measurements of
these sounds. An exception is the analysis of acoustic spectra from
three tornadoes reported by Arnold et al. (1976). They used audio tape
recordings taken by citizens at ranges of 1/2 mile, 200--300 yards, and,
in one case, directly beneath a tornado as it traveled over the
recording site. The dominant acoustic power for all three storms
occurred at frequencies below 200 Hz. The sounds observed were between
100Hz and 2 kHz. They also attempted to identify the sources of sounds
that occurred at higher frequencies. They concluded that a study of
variations in both low-frequency and high-frequency sounds as a tornado
approaches and recedes seems a most promising method of gaining insight
about internal circulations. They also noted the desirability of making
measurements with arrays of microphones. However, because of the strong
atmospheric attenuation at higher audible frequencies and the influence
of wind noise, such measurements will be most useful relatively close to
the vortex.

*b. Atmospheric infrasound*

Bedard and Georges (2000) provide background on measurements of
atmospheric infrasound. In the past, using arrays of sensors designed to
detect sounds at frequencies less than about 0.5 Hz, investigators
measured infrasound originating from regions of severe weather. In some
instances (e.g., Bowman and Bedard 1971), these detections were made at
distances of over 1000 km from the source. Severe weather infrasound was
investigated in a series of papers (e.g., Georges 1973, 1976, Beasley et
al., 1976). They compared the measured characteristics of the infrasound
with a variety of potential sound generation mechanisms, considering a
range of possible sources including release of latent heat, dipole
radiators, turbulence, lightning, electrostatic sources, and vortex
sound. In a comprehensive comparative study, Georges (1976) eliminated
many sources as likely candidates and concluded that vortex sound was
the most likely model. He also noted (Georges and Greene 1975) that
infrasound often precedes an observed tornado by up to an hour. In
retrospect, it seems unlikely that the much lower frequencies detected
by these geoacoustic observatories had any direct connection with
tornado formation. Georges (1976) recommended that direct comparisons be
made between infrasonic and Doppler radar measurements. However, at that
time the sound generation process (or processes) had not been verified
and low-frequency sound investigations were not continued, in part
because of funding issues.

Other types of pressure wave disturbances radiate or are predicted to
radiate from severe weather. These include atmospheric gravity waves
(Bowman and Bedard 1971) and thermal acoustic waves (Nicholls et al.
1991). These much lower frequency pressure disturbances (having periods
of tens of minutes) will not be considered further in this paper.
Thermal acoustic waves are predicted from the energy release of growing
thunderstorms and propagate at acoustic velocities in the form of Lamb
waves with horizontal particle motions (Gossard and Hooke, 1975). These
as well as atmospheric gravity waves could be valuable indicators of
storm processes.

*c. Near infrasound*

As an analog to the optical spectrum, the frequency range from about 1
to 20 Hz (just below the audible) is referred to as \"near infrasound,\"
as light just below the visible is called \"near infrared.\" During the
1980s, as a component of a Department of Energy program to evaluate
long-range acoustic detection capabilities, NOAA's Environmental
Technology Laboratory (ETL) developed new hardware and software to
monitor infrasound in a frequency range centered just above 1 Hz. This
near infrasonic system had quite different capabilities from the
geoacoustic observatories operated prior to the mid-1980's as described
in the introduction. As part of an ongoing effort to evaluate the
near-infrasonic system, it was operated episodically to collect data on
the types of signals occurring and to determine their origins. Since
that time, it has detected signals related to a variety of sources
including earthquakes, meteors, airflow over mountains, explosions, and
avalanches, as well as severe weather. Bedard (1988) presented examples
of some of these sources. Balachandran (1979) and Bohannon et al. (1977)
also reported infrasound from severe weather in this frequency range.

A focus in this 0.5- to 2.5-Hz passband was on documenting
severe-weather-related infrasound. Specifically, data were summarized
during the summer months and the acoustic signals were compared with
radar summary data. Bedard et al. (1986) provided some statistics
comparing the acoustic bearings with storm location bearings, finding
excellent agreement (typically within several degrees). They also
provided data on signal amplitude as a function of range. One important
case study demonstrated that the sounds being detected did not originate
from cloud-to-ground lightning strike locations, as documented by a
spherics network. This is consistent with the fact that the dominant
frequencies of thunder measured by Few (1979) occurred at higher
frequencies. Following on the work of Few several researchers confirmed
that the acoustic spectral peaks are in the audible range. For example,
Bass (1980) in a theoretical and experimental study found that a typical
spectral peak at longer ranges is near 100 Hz. Depasse (1994) made
measurements of the dominant frequencies for lightning discharges at
various distances, finding spectral peaks between 205 to 1715 Hz.

Beasley et al. (1976) searched for a relationship between infrasound
detected from severe weather and lightning, concluding that infrasound
is not caused by lightning. However, at near infrasonic frequencies we
continue to search for acoustic source mechanisms involving electrical
activity. There still remains a possible alternative electrostatic
generation mechanism, as suggested by Dessler (1973).

NOAA's National Hourly Radar Summaries were quite valuable for making
comparisons with acoustic signals. The observation of 27 July 1985
(Figure 1) is an example of long-range detection of infrasound
associated with severe weather. In this case, , the infrasonic
observatory detected energy from a cell in Minnesota, 1000 km distant.
Typically the infrasound recorded is from specific cells, but at such
long ranges it is not possible to identify the particular storm features
at the origin of the sound. At times the signal amplitudes were small
causing low signal-to-noise ratios and reduced azimuth resolution in
processing. This degradation could cause a sector of azimuths to be
displayed (typically +/- 5 degrees). The center of the sector usually
corresponded to the storm locations to within 1-2 degrees. At shorter
ranges of 100-200 kilometers or less, usually sharp, discrete azimuths
were obtained with sector widths often 1-2 degrees.

Figure 2 is an example of a nearby detection on 23 July 1985, which
showed a shift of azimuth with time. The upper panel shows higher
correlation azimuth values from which infrasound was detected. The
clearest persistent signal initially comes from the SE at 150 degrees
and than shifts to a second persistent direction from about 130 degrees.
The trend is for a shift from 170 to 120 degrees over about a half hour.
The lower panel is the dominant frequency for each processing interval
indicating an increase in frequency corresponding to the start of the
higher correlation and azimuth shifts. Often for nearby signals
associated with severe weather such discrete changes in direction are
observed.

Data for the summer of 1985 were summarized by dominant storm features
in Fig. 3. These signal characterizations were based upon radar summary
data, so no detailed knowledge of the storm's internal dynamics was
available. Practically all of the storms generating infrasound could be
classified as significant in that they produced hail, had tops of \>45
000 ft, or created a hook echo. During the spring and summer months in
Colorado and nearby regions there are no other sources of infrasound
having the characteristics of those associated with severe weather.
Rather the evidence to date is that sources of potential false alarms
could be signals originating from non-tornadic storm processes.

Figure 4 summarizes data on amplitude as a function of distance to the
storm, together with inverse distance and the square root of inverse
distance lines. The expected decay of sound pressure level with distance
from geometrical spreading is inversely with range. However, the
atmospheric temperature and wind structure trap much of the acoustic
energy, producing a wave-guide. Thus, if we assume that the sound
generation pressures are approximately the same for the various sources,
an inverse square root of the distance is a better fit to these data.
This rough pressure amplitude range relationship permits us to make
estimates of detection threshold at various distances. Most distant
storms have pressure amplitudes from 0.01 to 0.1 Pa (peak to peak),
which are easily detected under normal conditions.

Bedard et al. (1988) also presented evidence that avalanches radiated
infrasound that could be detected at distances of hundreds of
kilometers. In 1993, an evaluation program was started, and during the
winter of 1993/1994, a system was installed at a location near numerous
avalanche paths. Bedard (1994) summarized results showing the clear
detection of avalanches, and work began on creating a practical,
multi-observatory monitoring system. A system located in Colorado near
Red Mountain Pass during the winter of 1994/1995 provided more
detections, but it was clear that two systems working together would be
necessary to pinpoint locations. Thus, we set about to develop the data
transfer and multi-station analysis capability for an avalanche system,
working during the summer months of 1995. This set the stage for the
measurements described in this paper.

Another factor was the prediction by Nicholls et al. (1991) of the
severe weather generation of thermal acoustic waves and a system was
planned for their detection (Pielke et al. 1993). The plan for the
detection of thermal acoustic waves included three mobile, single
pressure sensor, observing systems to be located under the direction of
a Doppler radar. Therefore, it seemed logical to place one of the two
near infrasound observatories at the site of the Doppler radar to
monitor severe weather and exercise the avalanche detection system.

**3. Instrumentation overview**

Each infrasonic detection system consists of an array of four sensors in
a roughly square configuration about 100 m on a side. Because of the
need to reduce the pressure noise from atmospheric turbulence and other
sources, each sensor is connected to a device that filters out sub-scale
spatial noise. The long wavelength infrasonic signals are not affected
by this filter. The theory of operation of these noise-reducing devices
is described by Bedard (1977). Over the years, changes have made the
filters more effective, but the basic principle of operation has
remained essentially the same. Cook and Bedard (1971) described a
typical infrasonic system design. Processing was performed by
cross-correlating data from the various sensors and beamsteering the
array, searching for coherent energy propagating at acoustic or higher
phase speeds. Processing details are provided by Einaudi et al. (1989).

In the early 1970s and before, processing was performed using an analog
correlator. This was replaced by a large dedicated computer, and
processing was done after the fact. Data are now processed and archived
using two personal computers: one is dedicated to acquisition and
archiving; the other, to beamsteer processing of data blocks and
archiving of the processed data. A Global Positioning System is used to
synchronize and maintain accurate time. Modems are used to maintain
telephone contact with a central computer at a remote site. Calls are
made automatically from the central site at preset times, and the
observatory computer is programmed to listen for these incoming calls.
Every few days, the data are downloaded from the observatory computer to
tape. Under development is the capability to ingest data from two
observatories and display the acoustic bearings and azimuth
intersections in essentially real time. During the summer of 1995, one
observatory operated to the east of Boulder at the Boulder Atmospheric
Observatory (BAO), and the other operated at the Colorado State
University CHILL[^1] radar site in Greeley, Colorado.

The CHILL radar is an 11-cm-wavelength Doppler radar used with an
8.5-m-diameter parabolic antenna, providing a 1.1 half-power beamwidth.
Range gates from 15 to 150 m are available. Several real-time display
options make the system ideal for guiding field operations. Datasets
from the CHILL radar and infrasonic observatory will be compared in the
next section.

**4. Observations of the evolution of vortices**

*a. Doppler radar observations*

On 7 June 1995, the CSU CHILL Doppler radar tracked a storm system
moving from southwest to northeast. Cary and Rutledge (1998) made hail,
lightning and radar comparisons for this storm following the evolution
from 1731 to 2028 MDT. Between 1748 and 1812 MDT the storm produced a
tornado on the southern flank. They describe the tornado sighted at 1924
MDT as appearing to occur on a descending hail curtain adjacent to the
storm updraft. Hubbert et al. (1998) described the synoptic scale
environment of this system. Hubbert et al. (1998) focused on the storm
microphysics from 1720 until about 1835 MDT. They characterized the
storm as a high plains supercell storm. They tracked the storm motion
from 1720 until 1850 about the time when the storm was south of the
CHILL radar and infrasound

was first clearly detected. The storm had a diameter of about 15
kilometers and except for having heights \>10 kilometers could have been
designated a "mini supercell" (Stalker et al., 1993, Davies, 1993,
Burgess et al., 1995). Early in the sequence of scans (starting about
1900 MDT), several cyclonic radial-velocity couplets occurred along a
flanking line. Shortly, these small couplets seemed to be amalgamated
into an evolving, larger-scale circulation. The volume scans were
analyzed between 1850 and 1929 MDT and the radar elevation angle
containing the strongest circulations in each volume scan identified.
Some of the scans showed clear radial velocity couplets, while for
others it was more difficult to identify the vortices, suggesting the
circulation was weakly organized. In spite of this, two vortices could
be tracked. Vortex 1 at a range of about 14 Km could be identified from
1850 to 1924 MDT. The largest values of circulation were seen first at
higher elevations and later at lower elevations. At 1924 MDT, the region
of maximum circulation was near the surface and a tornado was sighted.
The cyclonic rotation couplet moved to the east throughout this
interval. At 1929 MDT, the couplet was no longer evident. Figues 5
through 9 show reflectivity and radial velocity images at 1901 and 1924
MDT.

Near 1924 MDT tornado sightings were reported to the NWS for the region
of Kersey (which is at an azimuth of 138 and a range of 7.6 km from the
radar). The locations of the two most persistent vortices are plotted on
a map of the area as a function of time (Figure 9). The sequence of
radar observations provided a unique picture of the evolution and
interplay between various scales of vortices, and will be a fruitful
dataset for future study. The focus here, however, is to compare the
radar documentation of intensity and radial velocity with infrasound
detected during the same time interval. Thus, we address defining the
characteristics of the circulations as a function of time to help
identify any acoustic source generation mechanisms present. Estimates
were made of the vortex azimuth, range, and elevation angle to the
circulation maximum. In addition, estimates made of the circulation
outside the vortex core (which is a measure of the total angular
momentum of the system), the core diameter, and the average maximum
tangential speed are plotted together in Fig.10. Note that the
circulation remains approximately constant throughout most of the time
interval.

*b. Infrasonic observations*

. This section reviews the acoustic signals that occurred on 7 June 1995
between about 1850 MDT and 1924 MDT at the Greeley Observatory. A second
infrasonic observatory at the Boulder Atmospheric Observatory had not
yet been installed. Figure 11 shows plots of correlation coefficient and
azimuth as a function of time, covering the interval of the radar
observations.

The correlation coefficient is a critical index for identifying signals
in a quantitative way. We measure the cross correlation between sensor
outputs as relative time delays consistent with the passage of plane
wave fronts across the array elements are imposed. With a measuring
network of N sensors the average correlation coefficient R~ave~ is

$R_{\text{ave}} = \frac{2}{N(N - 1)}\sum_{}^{}{\sum_{}^{}R_{\text{ij}}}$~.\ (1)~

The signal-to-noise ratio, S/N, is related to R~ave~ by the expression

S/N = R~ave~/(1- R~ave~). (2)

For R~ave~ =0.5 the S/N is 1 and such signals can usually be easily
identified. At R~ave~ =1 the S/N is infinite and often we have high
quality signals approaching this value. For a persistent low-level
signal we can often identify signals with values of R~ave~ near 0.3 or a
S/N value of about 0.4. As an example, with a infrasonic signal level of
0.1 Pa at S/N of 0.4 would correspond to boundary layer eddy noise of
0.25 Pa. Measurements of wind-induced pressure fluctuations in the .5 to
5 Hz passband indicate that without the use of spatial filters pressure
fluctuations of this magnitude would correspond to a wind speed of about
7 meters per second under most conditions (Bedard et al.1992). The use
of spatial filters can reduce this form of noise by an order of
magnitude or more (Bedard, 1977), enabling signal detection in the
presence of winds in excess of 20 meters per second. An improved
understanding of boundary layer turbulent pressure fluctuations will
certainly lead to improvements in wind noise reduction and measurement
site selection.

Note that during the period of interest, a region of higher correlation
coefficients corresponds to azimuths changing from southeast to
east-southeast. These data for the critical period were then
reprocessed, with only time blocks with correlation coefficients greater
than 0.4 displayed in Fig. 12. The signal does appear at correlation
coefficients less than 0.4 for a longer period of time until 1924, but
Fig. 12 shows the trend more clearly by removing noise. A clear trend of
azimuth shift with time is evident, with the direction from which
signals are arriving shifting from about 160 near 1900 MDT to 100 near
1924 MDT, following the trends of the variation of the velocity couplet
radar azimuth with time. A puzzling aspect of this observation is that
the radar bearings to the dominant vortex superimposed on the plot are
consistently more westerly by 10 to 40 degrees. A possible explanation
involving refraction effects by horizontal wind gradients will be
discussed in a following section. Another interesting feature of the
infrasonic observations is illustrated in Fig. 13, a plot of horizontal
phase speed and dominant frequency as a function of time. An acoustic
phase speed of about 330 m s^-1^ indicates that the sound wave is moving
across the array horizontal to the surface of the earth, at a 0
elevation angle. If phase speeds higher than the local speed of sound
are recorded, one likely explanation is that the sound is arriving from
above, at some angle to the surface of the earth. An alternative
explanation is that the measured pressure waves are locally coupled from
seismic waves, which propagate at about ten times the speed of sound in
air (Bedard 1971). Measurements of infrasound having high phase speeds
shifting with time are often related to meteors (Bedard and Greene,
1981). However, meteor infrasonic signals are usually less than a minute
in duration showing quite rapid shifts in phase speed and azimuth. In
this case, the waves arrived near 1900 MDT at speeds of about 700 m
s^-1^, decreasing to the local speed of sound near 1924 MDT, indicating
an initial source region aloft that moved slowly down to the surface of
the earth.

The dominant frequency was the spectral peak in a passband from 0.5 to
2.5 Hz. The processing was done over the entire frequency range of .5 to
2.5 Hz, but the processing algorithm only picks out the dominant
frequency for display. The dataset was processed over a range of
passbands, but the 0.5- to 2.5-Hz passband best represented the signals
detected (having the highest correlation coefficient). Most of the peak
frequencies occurred between 0.5 and 1 Hz, with a trend for some
sporadic data at higher frequencies (near 1.5 Hz) to occur midway
through the time interval. Figure 14 presents infrasonic time series for
two of the array microphone channels. The wave forms are similar for the
two channels, indicating a coherent wave moving across the array at
least the speed of sound. The other two channel time series are
essentially identical in waveform, only shifted slightly with time. The
amplitude is about 10 b (peak to peak). Such signals could be detected
at ranges of hundreds of kilometers from a source for typical acoustic
propagation conditions.

*c. Comparisons of radar and acoustic measurements*

It was observed (Fig. 12) that both the radar azimuths for the location
of the circulation and the acoustic azimuths showed similar trends,
indicating a source moving from the southeast to the east-southeast over
the same half-hour interval. There is a small delay time for sound
propagation, but at ranges of 10 km this is only about 30 s.

Similarly, it was observed that the elevation angle for the maximum
vortex circulation descended to near the surface from initial values of
about 20. The angle corresponding to the acoustic measurements is
computed and plotted together with the radar angle in Fig. 15. The
acoustic energy was apparently originating higher in the system for the
first 15 min than the velocity couplet maximum indicated by the radar.
If the sound source was, in fact, related to the circulation,
higher-angle radar scans may not have detected significant radial
velocity components initially because of the orientation of the vortex
relative to the radar beam. During the last 15 min, there was good
agreement between the angle-of-descent measurements with time for the
two systems.

d.  *Estimates of wind shear induced bearing errors for the 7June 1995
    case study*

The consistent difference between the infrasonic bearings and the radar
bearings requires more examination. These differences are emphasized by
the composite view in figure 16, showing the infrasonic bearing sectors
relative to the vortex location at 1903 and 1924 UTC. In spite of the
fact that elevation angle and bearing trends track, the infrasonic
bearings to the vortex are more easterly by 10 to 40 degrees. The array
geometries used in the infrasound involve sensor separations of about
100 meters, which routinely provide bearing accuracies to one degree.
The most likely causes of the disagreement are either that another
source was being detected or that refraction effects were responsible
for bearing deviations. The vortex descending from aloft was embedded in
a larger scale mesocyclone circulation creating horizontal wind speed
gradients. There was no other storm feature that followed the bearing
and elevation angle trends. There was also a second vortex at closer
ranges detected for some of the interval along similar radar bearings.
Early in the period, this second vortex created horizontal wind speed
gradients almost directly along the expected acoustic bearing from the
first vortex to the infrasonic observatory at the radar site. Thus,
there are two possible explanations for acoustic bearing errors One
mechanism is that the intermediate vortex disrupted the direct sound ray
path with complex focusing and defocusing (e.g. Georges, 1972). However,
this vortex was not detected during the later portion of the period.
Another possibility is that the segement of mesocyclone circulation just
to the north of the vortex refracted the acoustic ray paths. Because the
vortex moved with the mesocyclone there was a strong horizontal wind
speed gradient (e.g. 20 meters per second over several kilometers)
present throughout the time of these observations. Performing ray trace
calculations for a horizontal wind speed gradient of 20 meters per
second over 2 kilometers indicated that bearing deviations in the range
of 10 to 40 degrees could easily occur under these conditions. Because
of the complex three-dimensional structure of the wind field surrounding
the vortex it is possible that some focusing of sound also was taking
place making the easterly infrasonic bearings more dominant than direct
ray paths. This case indicates the importance of horizontal gradients
and the need to model a variety of situations using three-dimensional
ray trace simulations. Figure 17 is a radar image for an intermediate
scan at 1913 MDT when the circulations are not as evident. The locations
of circulations are indicated by circles. The radial velocity towards
the radar is to the north and possible refracted ray paths are
indicated.

e.  *Bearing errors and travel time delays*

Past measurements made from infrasound from weather and other
geophysical events used instrumentation that responded to frequencies
below .5 Hz. In addition, the array spacings were typically 5 to 10
kilometers because frequencies less than 0.1 Hz were of primary
interest. Most of our early knowledge about propagation and signal
characteristics involved these lower frequencies and typical ranges were
at continental scales. Usually global arrays of geoacoustic
observatories detected signals after long propagation paths and
atmospheric temperature and wind structure had important effects on the
measured waveforms, travel times, and bearings. Georges and Beasley
(1977) computed the effects of wind refraction on such long distance
paths (1000 kilometers). Past measured bearing errors over long paths
frequently were 6 degrees or greater. The summer mean wind model results
of Georges and Beasley (1977) for mid latitudes show quite small bearing
deviations (usually less than 1 degree). In addition the effects of
horizontal gradients of wind and temperature are also important.

However, in contrast with continental propagation paths acoustic systems
intended to provide tornado warnings need to be close enough to the
source of sound so that the delays caused by acoustic propagation time
do not remove any warning potential. Figure 18 is a plot of acoustic
travel time in seconds as a function of distance in kilometers. At a
range of 100 kilometers there is a delay of about 5 minutes in detecting
the sound (about the same as the time between NEXRAD scan repetitions).
In fact, our detection of a tornado occurring at Spenser, South Dakota
was delayed at a range of 750 kilometers by about one hour. The impacts
of acoustic travel time delays are an important consideration in the
design of infrasonic systems to provide warnings.

Our experiences with the detections of known regional sources of sound
(e.g. sporadic ignited releases of combustible gas over an 8 month
period at a range of 12 kilometers) show accurate bearings to about 1
degree.

If sound radiation comes from sources on smaller scales than the storm
system in which it is embedded there is the possibility that nearby
larger scale wind speed and temperature gradients (e.g. from outflows or
inflows) will refract sound rays causing bearing errors, focusing, and
de-focusing. Georges (1971) computed the ray paths for sound waves
traversing a vortex showing the important effects that can occur. If
such refraction becomes important we would expect to detect large,
chaotic and rapid bearing and elevation angle deviations. A typical
detection associated with a tornado shows a well-defined azimuth that
progressively tracks the storm with time. Our experiences of usually
detecting accurate bearings could be because vortices extended
vertically and radiating sound along the length of their cores create
numerous ray paths. Only a sub-set of these rays may encounter strong
refraction effects. However, bearing errors and their sources should
continue to be documented and the case study presented here probably
represents an example of important refraction effects.

**5. A comparison with sound generation models**

*a. A review of possible sound generation mechanisms*

Many, but not all, of the past theories of processes capable of
generating infrasound were directed toward frequencies either lower than
0.5 Hz or higher than 5 Hz; thus, they did not include our measurement
passband. However, it is still useful to summarize the range of
potential infrasound generation processes, since many of these theories
could still describe other important aspects of severe weather physics.
Table 2 summarizes a number of these investigations.

Many of the proposed sound-source mechanisms involve vortex sound
production, either by radial vibration processes (e.g., Abdullah 1966)
or flow instabilities (Georges 1976), and corotating multiple vortices
(e.g., Mitchell et al. 1992). An additional process involves
boundary-layer pressure fluctuations (Tatom et al. 1995). Because a past
study showed no correlations with cloud-to-ground lightning discharges
in the 0.5- to 2.5-Hz frequency range, and because electrostatic
processes (e.g., Dessler 1973) seemed unlikely to descend slowly to the
surface, these electrical mechanisms are not considered further here.
Any combination of the generation mechanisms mentioned above could be
important at different frequencies.

Figure 19 is an example of the signal power spectra as a function of
time. The individual time block processed is 12.8 s in duration with a
Hanning window applied and overlapped in time. This plot covers about 6
min in time and shows a trend for higher frequencies early in the
interval, with a dominant frequency near 0.5 Hz near the end

*b. Infrasonic data compared with selected sound generation models*

Three sound generation models were chosen for comparison with the
infrasonic data and are shown conceptually in Fig. 20 These models are
the radial modes of vibration model of Abdullah (1966), the
tornado/boundary interaction model of Tatom et al. (1995), and the
corotating vortex model (Powell (1964), Georges (1976); Mitchell et al.
(1992)). The infrasonic data seemed most consistent with the model of
Abdullah.

Abdullah (1966) found expressions for the fundamental (F0) and first
harmonic (F1) of the vibrational modes in Hertz to be

$F0 = \left( \frac{4U^{2}}{C^{2}} + \frac{\text{25}\pi^{2}}{\text{16}} \right)^{2}\frac{C}{2}\pi R$,
(3)

and

$F1 = \left( \frac{4U^{2}}{C^{2}} + \frac{\text{81}\pi^{2}}{\text{16}} \right)^{2}\frac{C}{2}\pi R$,
(4)

where *C* is the speed of sound in meters per second, *U* is the
tangential wind speed of the core, and *R* is the core radius. The first
term in brackets involving the Mach number squared represents only a
small second-order correction for core speeds below the speed of sound.
Thus, for practical purposes, the expressions for the fundamental and
first harmonic reduce to

F0 = 207/*R* , (5)

and

F0 = 371/*R* (6)

where *R* is in meters.

The relations for the fundamental and first harmonic frequencies, F0 and
F1, are plotted in Fig. 21. Two data points, together with an estimate
of the range of frequencies observed, also appear on the plot at times
corresponding to clearly detected tornadic rotations by the radar. The
radius of the tornado was estimated from the Doppler radar measurements.

Although this case shows evidence of a sound source that was initially
active aloft, which would preclude the boundary-layer mechanism from
explaining these measurements, it is nevertheless of interest to
estimate the frequency range expected from such an acoustic generation
process, which may be active under other situations. Similarly, the
multiple-vortex corotation process is also of interest here, especially
since multiple vortices were evident along a flanking line early in the
interval. If these velocity couplets approached each other corotation
could have occurred as the system evolved.

Tatom et al. (1995) made estimates of the dominant frequencies of
pressure fluctuations produced by tornadoes at the surface of the earth
in order to determine the frequencies of seismic waves excited. They
estimated the frequency produced as

F~e~ = U~∞~ k~e~/2π, (7)

Where U~∞~ is the wind speed, and k~e~ is the wave number of the energy
containing eddies. If x is the distance from the leading edge of the
flow (using a value of one half the radius of the vortex), and the
displacement of the boundary layer between the tornado and the surface
is δ, then L~e~ the scale of the energy containing eddies is
approximately equal to δ. Using results for the boundary layer on a
rough flat surface (Blake 1970, Harrison 1967)

δ/x = .009 = 2δ/r and F~e~ = U~∞~ /(.009 π r), (8)

The boundary layer noise model cannot explain the measurements of
infrasound at lower frequencies nor observations of sound from funnels
aloft. Nevertheless, it is an important model once vortex touchdown has
occurred and could explain the audible components from the smaller scale
populations of boundary layer eddies. This model also suggests that
measurements should be made at higher infrasonic frequencies between 10
and 20 Hz. Evidence to date indicates that the entire length of vortex
columns emit sound whether they are in contact with the ground or not.

Two vortices having the same circulation will rotate about a common
center by mutual induction (Powell (1964), Georges (1976); Mitchell et
al. (1992)). The frequency of the sound emitted is twice the rotational
frequency. Thus,

f = ω/π = Γ/4πr^2^ = U/πr, (9)

where Γis the circulation, U is the tangential speed of the co rotation,
and r is the separation radius. Assuming rotational speeds in the range
of 50 to 100 meters per second, the system will radiate sound at
frequencies between about .1 to .2 Hertz.

Table 3 estimates the expected dominant frequency of these three
mechanisms for a variety of conditions. The multiple-core characteristic
frequency estimates were made using the assumption of two corotating
vortices.

This table shows that the mechanism of Abdullah (1966) produces sound in
the frequency range of our observations and suggests that a limited
range of frequencies will occur for a considerable range of vortex
properties. Corotating vortices will tend to produce sound at
significantly lower frequencies (typically, less than 0.1 Hz) than those
focused on here. However, if more than two cores corotate, the
frequencies produced will be higher. Note that a system of up to six
vortices has been shown to be stable (Thompson (1868),

Morikawa and Swenson (1971)). The tornado/boundary-layer interaction
mechanism tends to produce sounds at higher frequencies and shows strong
variability with the strength of the vortex and the core size. The
nature of sounds predicted from these latter two mechanisms suggests
that measurements should also be made over a broader frequency range.
For the case analyzed here we cannot eliminate the possibility that
these other mechanisms also produced sound outside the limits of our
measurement passband.

Table 4 summarizes the frequencies predicted for various atmospheric
vortices as a function of typical radii (Glossary of meteorology,
Glickman, 2000) using the radial vibration model. For the range of
funnel radii, the lower limit of 50 meters is based largely upon our
acoustic measurements to date. In addition, aircraft wake vortices can
have tangential speeds in excess of 100 m s^-1^ and quite concentrated
cores. The predicted (and measured) frequencies for wake vortices are
greater than 100 Hz, well above those of natural atmospheric vortices.
Most dust devils should radiate sound above the range of tornadic
sounds, while mesocyclones should produce sound below the frequencies of
all but the very largest tornadoes. Thus, based upon this sound
production model it is logical to define three passbands for monitoring
the acoustics of intense atmospheric vortices. A passband from 1 to 5 Hz
will cover most tornadoes, while a passband between 0.2 and 1 Hz will
cover larger tornadoes and some mesocyclones. At higher frequencies
between 5 and 10 Hz smaller tornadoes and funnels may be observed. We
have detected a unique type of constant tone during some severe weather
events between 5 and 10 Hz for which we have no explanation, so that
there may be other interesting processes producing infrasound.
Currently, our real-time processing displays data in three passbands;
from 0.5 to 1 Hz, 1 to 5 Hz, and 5 to 10 Hz. Simultaneously we have
detected infrasound from different weather systems in these various
frequency ranges. With post-processing we can cover frequencies below or
above these passbands and continue to evaluate optimum processing and
display techniques.

**6. Two significant hail storms that did not produce infrasound**

Carey and Rutledge (1998) indicate that the storm of 7 June 1995 was
electrically quite active and produced large hail (up to 5 cm in
diameter). Although the storm was tracked from 1731 until 2028 MDT, the
largest amounts of hail occurred between 1850 and 1924 MDT (the interval
when we detected infrasound). But is the radiation of near infrasound a
common feature of most if not all storms, resulting from a combination
of processes including wind shear, electrical activity, and releases of
energy by changes of state? To address this question the two hail storms
chosen for comparison were unique in that they were monitored by Doppler
radar while also being studied intensively by a variety of other
techniques (e.g., aircraft, mobile surface observers). One storm was
documented as a CHILL radar case study and details for the other
documented by Brandes et al. (1995). The storms were significant in that
they had tops extending to about 30 000 ft and produced hail with
diameters greater than 2 cm. No tornadoes, funnels, or mesocyclones were
reported for either of these storms, which were intensely observed.

Acoustic observatories operating for both storms (which were at ranges
of less than 60 km) had low local noise levels and could have detected
quite low amplitude sounds had they been present. The fact that no sound
was detected in the passband between 0.5 and 2.5 Hz indicates that a
required acoustic generation mechanism was not present for these cases.
The implication is that the presence of vortex motions may be a primary
cause of severe weather infrasound near 1 Hz. These hailstorm
observations are summarized in Table 5.

**8. Summary and conclusions**

The case study of 8 June 1995 compared near infrasonic measurements with
Doppler radar tracking of the maximum circulation of a vortex as it
descended from higher altitudes to the surface. The collocated
infrasonic observing system followed the trend of the position of
strongest rotation for about 30 min, but easterly of the Doppler radar
bearings. It is probable that wind shear refraction caused the bearing
offsets. An important note is that even with retrospective analysis of
radar data, for some of the intermediate scans it was difficult to
identify vortex circulations. This unique dataset permitted comparisons
between the measured acoustic signatures and sound generation models.
The dominant frequencies closely matched those predicted by Abdullah
(1966) for the radial modes of vibration of vortices. It will also be
valuable to apply fully compressible models to explore the sound
generated by a variety of fluid dynamic processes. Comparative studies
would be a valuable area for future collaborative research.

In addition, two intensively measured, significant hail storms with no
observed vortices did not produce infrasound. This implies that
vorticity in the form of mesocyclones or tornadoes may be a primary
mechanism for infrasound production near 1 Hz and that other severe
weather sound production mechanisms will not complicate interpretation
in the 0.5- to 5-Hz passband focused on here. This point needs further
examination. A review of other possible acoustic generation mechanisms
suggests possibilities for monitoring a range of other aspects of storm
processes and dynamics in other frequency ranges. Table 6 reviews some
key results and implications.

A key need is to insure that the infrasonic system design is optimized
and covers the region or regions of the acoustic spectrum that contain
important information about severe weather dynamics. A mobile infrasonic
observatory, using a van capable of rapid deployment and equipped with
sensors having an extended passband (0.1--200 Hz), would permit the
gathering of complete \"voice prints\" of storm vorticity at relatively
close ranges. It would be especially valuable operated in coordination
with other systems to better document storm details. Simultaneous
operation with mobile Doppler radar systems (Bluestein, H.B., and
W.P.Unruh, (1989)) would be the ideal way to expand the dataset and
define the optimum passband.

Infrasonic observatories can be used in a number of ways to monitor
severe weather. One valuable use when they are collocated with NEXRAD
sites is to complement the radar in identifying and tracking severe
storm vorticity. Conversely, the radar data would help insure more
definitive interpretations of infrasonic signals as originating from
storm cells. Other sources of acoustic signals range from quite distant
severe weather not affecting some local region, to sounds generated by
other phenomena entirely (such as turbulence aloft or large explosions).
Thus, using the radar data and requiring that the acoustic azimuth
coincide with a storm cell will greatly increase confidence in the
interpretation of data from a single observatory.

The use of two regional observatories would provide the advantage of
being able to triangulate and locate the origin of the sound source.
Data could be fed to a central point and combined with radar data for
display. In the event that the signal-to-noise ratio at one observatory
was reduced by high winds (e.g., from an outflow boundary), the second
system would continue to provide acoustic azimuth data. Developments in
noise-reducing techniques have continued to raise the wind speed
threshold below which infrasound can be reliably detected. Signals have
been successfully detected from the direction of mesocyclones while the
station was in an outflow from a nearby thunderstorm. Further
improvements in wind-noise reduction are expected.

In several situations acoustic detection of severe weather vorticity
could be a valuable adjunct to Doppler radar measurements, especially in
conditions where the phenomenon of interest is aloft. For example, when
a vortex is quite close to the radar site (e.g., less than 10 km) and
the strongest circulation is aloft, rapid three-dimensional scans are
necessary (WSR-88D does not scan above 20). At high radar scan angles,
only small radial components of the vortex might be detected, if its
axis is vertically oriented. In such a situation, the acoustic data
could help locate the vortex and guide the radar to the best scan
elevation angle and azimuth.

At intermediate ranges (e.g., 10--30 km), where the Doppler radar is
exceptionally effective, the acoustic data could be helpful under two
conditions. Where a number of cells are located at various azimuths and
ranges, it may not be clear which is potentially more hazardous.
Acoustic data showing that one cell is radiating infrasound could help
guide decisions concerning the choice of sector scans. This would
require changing the current NEXRAD surveillance scan philosophy, which
is restricted to 360 azimuth scans. Also, if small-radius vortices are
present, the associated radial velocity couplets may be difficult to
identify with confidence by radar. An acoustic signal corresponding to
such a radial velocity could also help to increase confidence in issuing
warnings.

At longer ranges, where the size of the radar range sample volume
increases, regions of significant rotation may not be resolved. In such
situations the existence of acoustic energy from a distant cell could
provide a valuable indication of hazard potential. In addition, where
radar coverage is limited by problems with ground clutter, infrasound
instrumentation has the potential for filling in coverage for such
regions. A need exists for testing and demonstrating these potential
uses.

A series of papers are in progress with goals of providing background
for understanding the strengths and weaknesses of infrasonic tornado
detection. These papers with tentative titles are listed in Appendix A
together with the topics and questions being addressed. These papers,
drawing on data from a series of on-going field and laboratory
measurements, especially those measurements dating from 1995, are in
various stages of completion. Hopefully, these will provide the bases
for a definitive assessment of near infrasound as a warning tool.

*Acknowledgments*. The author is most grateful to a number of colleagues
for making the datasets described herein possible. The impetus for the
key installation at the CHILL radar site came from our collaboration
with Colorado State University's Geosciences Program. Particular thanks
are due R. Pielke, M. Nicholls, T. Vonder Haar, and K. Eis. For support
with logistics and data at the CHILL radar site, we are grateful to S.
Rutledge, P. Kennedy, and D. Brunkow. The support of W. Bach of the U.S.
Army Research Office is also acknowledged.

In assisting with instrumentation, both R. T. Nishiyama and S. Pezoa
worked to insure that two observing systems worked reliably.

Finally, a team of students assisted with installations, data archiving,
preliminary analyses, collection of meteorological data, and many other
tasks. These included R. Bloemker, R. Craig, L. Ferber, S. Nash, and K.
Taga.

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**Appendix A**

A list of papers planned in the evaluation of near infrasound tornado
warning potential: Goals and questions to be answered

*Low-frequency atmospheric acoustic energy associated with vortices
produced by thunderstorms*-(This publication) This paper documents
general background, a Doppler radar comparison case study, and discusses
possible sound generation mechanisms.

*Infrasound from Funnels Aloft*- This paper reviews 3 cases where
extended fields of short-lived, sporadic funnels produced infrasound.
The questions addressed are: Do these represent a false

alarm potential? Can detection algorithms identify these cases? Can we
obtain more insight into

the sound generation processes?

*Infrasonic Detection of Tornadoes and Mesocyclones at Various Ranges*-
This paper contrasts case studies of detections of vortices of a variety
of strengths, sizes, and ranges. The questions addressed are: What
portions of vortices radiate sound? How does the vortex strength affect
the infrasonic signal radiated? Can more than one acoustic signal be
detected simultaneously? What segments of the vortex life cycles produce
sound?

*Sounds from Laboratory Vortices and Aircraft Wake Vortices*- This paper
documents the results from laboratory experiments measuring sounds
generated by vortices created in a water tank and also from the wake
vortices of a variety of aircraft. The questions addressed are: What are
the sound generation processes and how do these compare with the sounds
generated by larger-scale atmospheric vortices?

*A Search for Low-Frequency Acoustic Waves Associated with Sprites, Blue
Jets, Elves, and Storm Electrical Activity*- This paper documents the
evidence for correlations between infrasound and transient luminescent
phenomena. The questions addressed are: Do sounds associated with these
processes represent a potential source of false alarms? What are the
acoustic source mechanisms and can they be a useful indicator of storm
processes? Can detection algorithms identify these cases?

*Networks of Infrasound Observatories for Tornado Detection and Warning:
Design Considerations*- This paper evaluates the potential of infrasonic
observing systems for tornado detection and warning and suggests
possible deployment strategies. The questions addressed are: What are
the detection rates, miss rates, and false alarm rates? What are the
impacts of acoustic travel time delays on warnings? What bearing errors
can occur and what is their impact on location? What are the mechanisms
causing bearing errors? What are the warning time statistics? What are
the sources of noise that could mask detection? Under the assumption
that infrasonic systems could provide valuable improvements in detection
and warning time- What network deployment configurations are indicated?
What are the ratios of warning time improvements to system costs
estimated?

**Figures**

FIG. 1. Detection of infrasound on 27 July 1985 from severe weather
located about 1000 km away from the observatory. The dashed line
indicates the azimuth of the infrasonic signal detected.

FIG. 2. Detection of infrasound from nearby severe weather showing
shifts in azimuth as a function of time and an increase in the dominant
frequency measured.

FIG. 3. Histogram showing the distribution of dominant storm features
associated with infrasound as derived from hourly radar summaries.

FIG. 4. Peak-to-peak amplitude of measured infrasound as a function of
distance from severe weather sources.

FIG. 5. 7 June 1995 1901 MDT: reflectivity (dBZ); elevation angle, 9.6;
range rings are 5 km. The circles indicate locations of reflectivity
eyes.

FIG. 6. 7 June 1995 1901 MDT: radial velocity (m s^-1^); elevation
angle, 9.6; range rings are 5 km. The circles indicate the locations of
velocity couplets.

FIG. 7. 7 June 1995 1924 MDT: radial velocity (m s^-1^); elevation
angle, 0.4; range rings are 5 km. The circle indicates the location of
the velocity couplet.

FIG. 8. 7 June 1995 1924 MDT: reflectivity (dBz); elevation angle, 0.4;
range rings are 5 km. The circle indicates the location of the velocity
couplet

Fig. 9 Summary map showing the locations of the two most persistent
vortices as a function of time.

FIG. 10. Radar estimates of elevation angle, core diameter and
tangential speed of the vortex maximum throughout its lifetime.

FIG. 11. Infrasonic correlation coefficient (a) and azimuth (b) as a
function of time for all values of correlation coefficient.

FIG. 12. Infrasonic correlation coefficient (a) and azimuth (b) as a
function of time for data with correlation coefficients greater than
0.4. The triangular points on the azimuth plot (b) are the radar
bearings to the vortex.

FIG. 13. Infrasonic horizontal phase speed (a) and dominant frequency
(b) as a function of time.

FIG. 14. Infrasonic time series for two of the array microphones.

FIG. 15. Elevation angle of detected infrasound and radar elevation
angle of the circulation maximum as a function of time.

Fig. 16 Composite view showing the infrasonic bearing sectors relative
to the vortex location at 1903 and 1924 MDT.

Fig. 17 Radial velocity radar image with possible refracted ray paths
indicated. 7 June 1995 1913 MDT: elevation angle 21.7°, range rings are
10 kilometers. The circles indicate the locations of velocity couplets.

Fig. 18 Acoustic travel time as a function of range in kilometers.

FIG. 19. Acoustic signal power as a function of frequency between 1909
and 1914 MDT.

Fig. 20. Conceptual view of three vortex sound production models.

FIG. 21. Frequency of the fundamental and first harmonic of the radial
modes of vibration of a vortex. Data points shown on the plot are based
upon infrasonic and radar data for two times during the event.

.

.

Table 1. Contrasting properties of the infrasound global network and
current near infrasound observing systems

+-------------+-------------+-------------+---------------+-----------+
| System      | Typical     | Spatial     | Typical       | Maximum   |
|             | Sensor      | Filter      | Acoustic      | HF        |
|             |             |             |               | Response  |
|             | Spacings    | Type        | Wavelengths   |           |
+-------------+-------------+-------------+---------------+-----------+
| Global      | 10          | 1000 Feet   | 3 to 30       | .5 Hz     |
| Infrasound  | Kilometers  | Linear      | kilometers    |           |
| Observing   |             |             |               |           |
| System      |             |             |               |           |
+-------------+-------------+-------------+---------------+-----------+
| Near        | 100 meters  | 50 feet in  | 30 to 300     | \>20 Hz   |
| -Infrasound |             | diameter    | meters        |           |
| Observing   |             |             |               |           |
| System      |             |             |               |           |
+-------------+-------------+-------------+---------------+-----------+

TABLE 2. Theoretical investigations of potential severe weather sound
generation processes.

+---------------------+------------------------+----------------------+
| Investigators       | Physical process       | Comments             |
+---------------------+------------------------+----------------------+
| Hicks (1884)        | Vortex vibrations      | Hollow core vortex   |
+---------------------+------------------------+----------------------+
| Thompson (1910)     | Vortex vibrations      | Realistic model      |
+---------------------+------------------------+----------------------+
| Lamb (1945)         | Review of past work on |                      |
|                     | vortex                 |                      |
|                     |                        |                      |
|                     | vibrations and waves   |                      |
+---------------------+------------------------+----------------------+
| Powell (1964)       | Theory of vortex sound |                      |
+---------------------+------------------------+----------------------+
| Anderson and Freier | Tornado wave motion    |                      |
| (1965)              |                        |                      |
+---------------------+------------------------+----------------------+
| Abdulla (1966)      | Tornado radial mode    | Focused on audible   |
|                     | vibrations             | detection            |
|                     |                        |                      |
|                     | as a sound source      |                      |
+---------------------+------------------------+----------------------+
| Colgate and McKee   | Electrostatic sound    |                      |
| (1969)              |                        |                      |
+---------------------+------------------------+----------------------+
| Dessler (1973)      | Electrostatic sound    |                      |
+---------------------+------------------------+----------------------+
| Meecham (1971)      | Turbulence             |                      |
+---------------------+------------------------+----------------------+
| Georges (1976)      | Comparative review of  | Concluded vortex     |
|                     |                        | sound                |
|                     | generation processes   |                      |
|                     |                        | processes were most  |
|                     |                        | likely               |
+---------------------+------------------------+----------------------+
| Few (1979)          | Lightning              |                      |
+---------------------+------------------------+----------------------+
| Lyamshev and        | Review of vortex sound |                      |
| Skvortsov           |                        |                      |
|                     | mechanisms             |                      |
| \(1988\)            |                        |                      |
+---------------------+------------------------+----------------------+
| Kozel et al. (1992) | Vortex wave effects    |                      |
+---------------------+------------------------+----------------------+
| Mitchell et al.     | Sounds from corotating | Numerical model      |
| (1992)              |                        | showing              |
|                     | vortices               |                      |
|                     |                        | evolution of the     |
|                     |                        | system               |
+---------------------+------------------------+----------------------+
| Tatom et al. (1995) | Seismic waves from     | Suggested the basis  |
|                     | tornado/               | for a                |
|                     |                        |                      |
|                     | surface interactions   | detection system     |
+---------------------+------------------------+----------------------+

TABLE 3. The dominant predicted frequency for three acoustic source
types.

+-------------+-------------+-------------+-------------+-------------+
| Wind speed  | Radius      | Radial      | Torn        | Corotation  |
|             |             | modes       | ado/surface |             |
| (m s^-1^)   | \(m\)       |             |             | frequency   |
|             |             | frequency   | frequency   |             |
|             |             |             |             | (Hz)        |
|             |             | (Hz)        | (Hz)        |             |
+-------------+-------------+-------------+-------------+-------------+
| 50          | 100         | 2.07        | 18          | 0.2         |
|             |             |             |             |             |
|             | 250         | 0.83        | 8           | \<0.1       |
|             |             |             |             |             |
|             | 500         | 0.41        | 5           | \<0.1       |
|             |             |             |             |             |
|             | 1000        | 0.2         | 1           | \<0.1       |
+-------------+-------------+-------------+-------------+-------------+
| 75          | 100         | 2.07        | 30          | 0.3         |
|             |             |             |             |             |
|             | 250         | 0.83        | 10          | \<0.1       |
|             |             |             |             |             |
|             | 500         | 0.41        | 7           | \<0.1       |
|             |             |             |             |             |
|             | 1000        | 0.2         | 2           | \<0.1       |
+-------------+-------------+-------------+-------------+-------------+
| 100         | 100         | 2.07        | 42          | 0.4         |
|             |             |             |             |             |
|             | 250         | 0.83        | 15          | 0.15        |
|             |             |             |             |             |
|             | 500         | 0.41        | 10          | \<0.1       |
|             |             |             |             |             |
|             | 1000        | 0.2         | 4           | \<0.1       |
+-------------+-------------+-------------+-------------+-------------+

Table 4 Characteristic Frequencies of Various Vortices Using the Radial
Vibration Model

  ----------------- ------------------- ---------------- -----------------
  Vortex Type       Typical Radius      Fundamental      First Harmonic
                    Range               Frequency (Hz)   (Hz)

  Mesocyclones      1 to 5 Km           .21 to .04       .37 to .07

  Tornadoes         100's of meters to  2.1 to .21       3.7 to .37
                    1 Km                                 

  Funnels           50 meters to 100's  4.1 to 2.1       7.4 to 3.7
                    of meters                            

  Dust Devils       3 to \>30 m         69 to 6.9        124 to 12.4

  Aircraft Wake     1 to 2 m            207 to 104       371 to 196
  Vortices                                               
  ----------------- ------------------- ---------------- -----------------

TABLE 5. Summary of observations of two hail storms.

+-----------------------------------------------------------------------+
| • Observatories operating near significant hail storms with no        |
| reported funnels                                                      |
|                                                                       |
| or tornadoes did not detect infrasound at frequencies from 0.5 to 5   |
| Hz.                                                                   |
+-----------------------------------------------------------------------+
| • 22 June 1995 1809 MDT, CHILL radar:                                 |
|                                                                       |
| 43-km range at 37                                                    |
|                                                                       |
| 3--4 cm hail                                                          |
|                                                                       |
| Tops to 12 km                                                         |
+-----------------------------------------------------------------------+
| • 24 June 1992 1537 MDT, CP-2 radar:                                  |
|                                                                       |
| 60-km range at 330                                                   |
|                                                                       |
| 4.5-cm hail                                                           |
|                                                                       |
| Tops to 14 km                                                         |
+-----------------------------------------------------------------------+

TABLE 6. Key results of the study and implications for future work.

+-----------------------------------------------------------------------+
| • Frequency detected matched analytical model for radial modes of     |
|                                                                       |
| vibration of a vortex.                                                |
+-----------------------------------------------------------------------+
| • Provided unique comparison between collocated infrasonic            |
| observatory                                                           |
|                                                                       |
| and Doppler radar.                                                    |
+-----------------------------------------------------------------------+
| • Acoustic energy was detected earlier than the radar velocity        |
| couplet,                                                              |
|                                                                       |
| both originating at higher altitudes and moving to the northeast      |
| before                                                                |
|                                                                       |
| reaching the surface.                                                 |
+-----------------------------------------------------------------------+
| • Other possible acoustic radiation mechanisms exist that could       |
| radiate sounds                                                        |
|                                                                       |
| higher or lower than 1 Hz.                                            |
+-----------------------------------------------------------------------+
| • Infrasonic observatories could complement Doppler radars, detecting |
|                                                                       |
| small-scale vorticity at higher altitudes and shorter ranges where    |
| radial                                                                |
|                                                                       |
| velocity components may be small or difficult to resolve.             |
+-----------------------------------------------------------------------+
| • Since infrasound is detectable from long ranges (hundreds of        |
| kilometers                                                            |
|                                                                       |
| or more), long-distance identification of storms containing           |
| concentrated                                                          |
|                                                                       |
| vorticity may be possible.                                            |
+-----------------------------------------------------------------------+

[^1]: .

    ^?^Historically, the radar was operated by both the University of
    Chicago and the University of Illinois; hence, the origin of the
    name CHILL