Observations of the refraction of microbaroms generated by large maritime storms by the wind field of the generating storm

Authors


Abstract

Microbaroms are a continuous infrasonic signal in the 0.15 to 0.3 Hz band caused by the collision of oceanic surface waves of equal period. Such signals are often generated by large maritime storms. Current formulation of the generation mechanism predicts that the microbarom source location due to a large maritime storm in the open ocean is generally located several hundreds of kilometers from the eye of the storm. Assuming such a source location to be correct, propagation of the microbaroms along paths which pass near the storm center as well as those which propagate away from the storm structure have been examined using geometric acoustics. Microbarom propagation paths which pass near the storm center are refracted by the storm winds and are found to have back azimuths directed toward a virtual source around the storm center. Microbarom propagation paths which do not pass near the storm center are found to have back azimuths directed toward the actual source region. To validate these predictions, data from microbarom signals generated by hurricanes in the Atlantic Ocean have been collected along the east coast of the United States during the 2010 and 2011 Atlantic hurricane seasons. Data from several storm events are presented here for comparison with model predictions. In general, the observations are in agreement with the predictions of the propagation model.

1 Introduction

The term infrasound is generally applied to acoustic signals with frequencies below 20 Hz, the approximate limit of human hearing. Such energy is known to be produced by natural and anthropogenic mechanisms. Microbaroms are a specific, continuous form of infrasonic radiation in the 0.15–0.3 Hz band generated by the collision of ocean surface waves with equal wavelength [Longuet-Higgins, 1950; Waxler and Gilbert, 2006]. The first published observations of microbaroms and microseisms, a seismic signal generated by the same mechanism, are those by Benioff and Gutenberg [1939] and Baird and Banwell [1940]. The understanding of how active sea states generate microbaroms has been incrementally extended over several decades, with a thorough treatment of atmospheric microbarom generation given by Waxler and Gilbert [2006] and a broader discussion of microseism and microbarom generation by Ardhuin and Herbers [2013].

Observations have repeatedly indicated that large maritime storms produce microbaroms; however, the specifics of such generation is still a topic of some debate [Banerji, 1930; Bremaecher, 1965; Hetzer et al., 2008; Stopa et al., 2011, 2012]. It has been proposed by Hetzer et al. [2008] that the interaction of the storm-induced swell with the background swell can produce the counterpropagating waves required to generate microbaroms. Using such a model, microbaroms are predicted to radiate from a region several hundred kilometers away from the storm center in a direction perpendicular to that of the pelagic swell, as illustrated in Figure 1. Stopa et al. [2011, 2012] have developed models for ocean surface wave generation and propagation by ocean-born cyclones and have used output from these models to estimate microbarom source levels using the Waxler and Gilbert source strength. Stopa et al. [2011] considered the swell generated by an isolated storm in the absence of background swell from other sources and suggested that microbaroms can be generated by a large, stationary maritime storm without requiring interaction with the pelagic swell; however, in more recent work by Stopa et al. [2012], the interaction of storm-generated waves with background swell was investigated and results were more consistent with the model of Hetzer et al. [2008] in that the expected source region is some distance from the storm center.

Figure 1.

Qualitative model of the microbarom radiation mechanism of Hetzer et al. Shown are the dominant wave directions of cyclone produced waves superimposed on a pelagic swell field. The source region is due to the collision of the two wave fields.

In order to understand and analyze the microbarom signal received far from a large maritime storm, one must not only account for the generating mechanism but also the interaction of the propagating microbarom signal with the atmospheric variations associated with the storm. It has been suggested by Bedard that the strong horizontal wind gradients in a large maritime storm will refract the microbarom signal as it propagates through the storm winds [A. Bedard, personal communication, 2008]. Assuming that the source of microbarom radiation from large maritime storms in the open ocean is located far from the eye of the storm, there is a possibility that the characteristics of the microbarom signal at various locations away from the storm can be used to probe the interior of the storm by relating the degree of refraction of the signal by the storm winds to the intensity of those winds. It is the aim of the investigations reported here to demonstrate that, under the assumption that the source region is located far from the storm center, propagation modeling predicts asymmetry in the back azimuth of the observed signal far from the storm depending on the relative location of the observer and microbarom source. Such asymmetries have been observed in microbarom signals observed during the 2010 and 2011 Atlantic hurricane seasons.

The paper is organized as follows. In section 2, propagation model predictions are presented and the observable results discussed. These are followed in section 3 with descriptions of the 2010 and 2011 deployment of networks of infrasound sensor arrays along the East Coast of the United States to capture microbarom signals from hurricanes passing through the Atlantic Ocean. The methods used to process and analyze the data collected are presented in section 4. In section 5 the resulting observations are presented and then discussed in section 6. We end in section 7 with conclusions and an outlook for future research.

2 Propagation Modeling and Predictions

In this section, propagation modeling results are presented using the assumption that the primary microbarom source due to an ocean-born large maritime storm is several hundred kilometers from the eye of the storm. In the case of a large maritime storm, the radius of maximum wind is typically 30–60 km [Stull, 2000]. Microbarom energy peaks around 0.2 Hz which corresponds to a wavelength of 1.7 km for typical sound speeds near the ocean surface. Comparing the scale of the storm with the wavelength of the microbaroms, one finds that microbaroms propagating horizontally through a large maritime storm are well described by the approximation of geometric acoustics [Pierce, 1981; Brekhovskikh and Godin, 1999]. The geometric approximation predicts the orientation of the wavefront as sound propagates through the atmosphere. This allows the back azimuth of the predicted arrival, that is, the direction from which the sound appears to emanate, to be calculated quickly using geometric acoustics.

In addition to the strong cyclonic winds associated with a large maritime storm, the low-pressure region in the eye column produces small, but measurable, temperature gradients in the region. The resulting gradients in the adiabatic sound speed are, however, negligible compared to those associated with the storm winds. Thus, the interaction of the microbarom signal with the cyclonic wind field will dominate the propagation effects.

The raypath equations in Brekhovskikh and Godin [1999, section 5.1.3] have been solved numerically using a constant adiabatic sound speed and a wind field defined by the storm wind model developed by [Holland, 1980, 2010]

display math(1)

The storm model used for propagation modeling included a 50 km radius of maximum wind and 55 m/s maximum wind speed, consistent with a Category 3 storm [Stull, 2000]. The parameter x has been set to 0.5, coinciding with Holland's original model. In the 1980 publication, the parameter b is assumed to range between 1 and 2.5, with larger values describing a storm with lower pressure in the eye column. Here b = 2.0produces a model storm with a well-developed eye column and strong radial wind gradients in the eye wall [Holland, 1980, 2010]. The resulting storm wind model is shown in Figure 2 (top). Note that the cyclonic winds on opposite sides of the storm center are oriented in opposite directions.

Figure 2.

The (top) cyclonic wind amplitude and (bottom) geometric acoustic prediction for propagation through the storm winds. The red ring denotes the radius of maximum winds.

It should be noted that the model used here neglects any vertical structure of the storm and models the propagation in a horizontal plane at or below the altitude of maximum winds of a simple model storm. The storm winds increase from zero at the ocean surface to their maximum speeds roughly 1 to 2 km above the surface which produces a downward refracting acoustic duct for sound propagating in the direction of the wind. Therefore, one can expect the horizontal refraction predicted here to be accurate for raypaths propagating in the direction of the storm winds. A full three-dimensional propagation model requires additional analysis to incorporate interactions with the ocean surface and propagation above the storm structure. The storm system often extends just above the tropopause; however, the microbarom signal can propagate into the stratosphere and lower thermosphere before being refracted back to the Earth. The mathematical details of modeling propagation through an inhomogeneous moving medium are involved, and we intend to present the method and results in a separate publication.

A microbarom source location has been assumed several hundred kilometers away from the storm center along a path directly to the south. Such a source location is qualitatively consistent with hurricanes in the open Atlantic where the dominant pelagic swell is associated with the easterly trade winds [Stull, 2000]. The exact source location could be determined by identifying the location at which the storm-induced swell and background pelagic swell would be counterpropagating and equal in magnitude, as proposed by Hetzer et al. [2008]. It will be shown in the following results that the true source location can be estimated using observations of microbaroms which propagate along paths which do not interact with the strong winds near the storm center. It should be noted that the microbaroms source radiates in all directions, and therefore, some fraction of the energy will always propagate toward the storm center regardless of the source location. Because of this, the propagation that results in the following discussion are applicable to a source located at any azimuth around the storm due to the axial symmetry of the storm system. That is, the storm source system can be rotated to coincide with an arbitrary pelagic swell direction, and the results presented here remain valid. It is straightforward to model the propagation field due to multiple sources in the case that the pelagic swell is not uniform or multiple storms interact; however, the results of such models are not consistent with the observations presented here and will not be discussed.

The propagation paths from the source along azimuths toward the storm are shown in Figure 2 (bottom). The red ring in the figure denotes the radius of maximum winds for the model. Along azimuths away from the storm center, propagation is nearly planar and the influence of the storm winds is negligible. The back azimuths of microbaroms propagating along such paths would be oriented toward the true source region. Raypaths which propagate into the storm center are strongly refracted resulting in geometric attenuation to the north and multipathing to the northwest of the storm center as seen in the figure. A more detailed view of the refraction around the storm center is shown in Figure 3. The red circle in Figure 3 (left) again denotes the radius of maximum winds. Examining the radial wind profile in Figure 3 (right), one finds that the large positive radial gradient in the winds just inside the radius of maximum winds produces significant refraction as the sound propagates northward through the storm center. That is, as sound propagates past the storm eye, the portion of the wavefront slightly farther from the storm center propagates faster than that nearer to the storm center which results in refraction of the sound in the counterclockwise direction around the storm center. For comparison, the gradient of the winds beyond the radius of maximum winds is shown in Figure 3 and is found to be several orders of magnitude smaller. Therefore, the storm winds are not expected to produce noticeable refraction for microbaroms propagating through the region beyond the radius of maximum winds.

Figure 3.

(left) A closer view of the refraction around the storm center near the radius of maximum winds. The red ring again denotes the radius of maximum winds. (right) The radial profile of the cyclonic wind speed.

The propagation model results have been used to predict the back azimuth of microbaroms observed at various locations along an arc 1000 km from the storm center. In the region to the northwest of the storm, multiple contributions to the signal are expected. One contribution's back azimuth is oriented toward the actual microbarom source. The other contributions are due to refraction of the microbaroms as they pass near the storm center. The back azimuths of the refracted contributions are oriented toward an extended virtual source around the storm center. For observations south of the storm, interaction with the storm winds is much weaker and the observed back azimuth is oriented toward the actual source region. In the case that observations are made at multiple azimuths, the resulting back azimuths can be combined to estimate the apparent source location.

Ideally, one would hope to resolve the multiple microbaroms incident on the arrays in the northwest region around the storm center. However, for a given array design, a coherent signal produces a response characterized by an azimuth angle from which the signal emanates and a spatial spectral width related to the uncertainty in the azimuth angle. For an array containing a finite number of microphones, the spatial response for a coherent signal emanating from a given direction will have a finite width. Because of this, two coherent signals incident from azimuths separated by less than this width are likely to be indistinguishable. Assuming that the observing arrays have a limiting spatial spectral width of ∼15°, the individual contributions to the signal observed north of the storm become indistinguishable and result in a single detection with larger uncertainty in the azimuth angle.

The combined results for multiple arrays simultaneously observing the strongly refracted signal from northwest of the storm is shown in Figure 4 (left). The color scaling in the figure is proportional to the combined probability density of the three beams detecting the refracted signal using von Mises distributions to describe each beam [Mardia and Jupp, 2009]. The limiting resolving power of the arrays results in a large region around and south of the storm from which the microbaroms appear to be emanating. Alternately, if the storm is observed from the south as in Figure 4 (right), the negligible interaction with the storm results in a combined probability density which is much more tightly bounded and located near the actual source region south of the storm. Note that the source location observed from the south is still biased slightly toward the west due to the residual effects of the winds on observations at very near the storm latitude.

Figure 4.

Predictions of the apparent source region for microbaroms propagating from a source located 500 km to the south of a Category 3 large maritime storm using arrays with 15° limiting beam width. The red dot denotes the location of the storm center. The black and gray lines denote the back apparent azimuths of the microbarom signals detected at each location. The color scaling represents the source location distribution using the detections with black back azimuth lines.

To summarize, for a microbarom source several hundred kilometers from the center of a large maritime storm, the apparent source location inferred by the observed microbarom back azimuths far from the storm varies depending on the relative location of the source and observer. For observations along propagation paths which do not pass near the storm center, the apparent source and true source regions are nearly identical. However, propagation paths which pass near the storm center are strongly refracted by the radial gradient of the cyclonic winds and produce a virtual source extended around the storm center. This virtual source is only detected by observers located along the refracted propagation paths.

3 Deployment of the Infrasound Sensor Network

A network of infrasound arrays were deployed along the East Coast of the United States during the 2010 and 2011 Atlantic hurricane seasons in order to test the qualitative predictions presented in Figure 4. Each array consisted of multiple infrasound-recording elements. The elements each contained an infrasound microphone, a data acquisition system sampling data at 31.25 samples per second, a GPS antenna, a 12 V battery, and a solar panel. The sensor and data storage system is a single unit designed by the infrasound group at the National Center for Physical Acoustics specifically for rapid, temporary deployments [Alberts et al., 2013]. Data were stored locally on each unit and were manually retrieved periodically throughout the experiment during array maintenance visits. The power draw per sensor element is about 4 W, and an element can operate for roughly 10 days without sunlight. In an attempt to provide wind noise reduction, the arrays were deployed in pine forests. The forests were neither very tall nor dense, and, as will be shown below, afforded little to no wind noise reduction. As a consequence, detections were made predominantly at night, when conditions are generally quiet. Several elements occasionally lost power during the experiment due to insufficient solar exposure caused by dense foliage and overcast skies in some locations.

In 2010, four-element arrays were deployed in Ocala National Forest in Florida, Francis Marion National Forest in South Carolina, Croatan National Forest in North Carolina, and on private land owned by the McCoy family outside of Maxton, North Carolina. In 2011 these four sites were repopulated and additional four- and six-element arrays were deployed in Bass River State Forest in New Jersey and at Brookhaven National Laboratory (BNL) in New York, respectively. This initial deployment at BNL was restricted to forested lands on the outskirts of the grounds, which limited the array geometry. The four-element arrays were deployed using centered triangular geometries and apertures of approximately 1.5 km, with deviations due to local geography. The BNL array consists of six elements with 2 and 3 km latitudinal and longitudinal aperture, respectively. The locations of the arrays deployed in 2010 and 2011 are shown in Figure 5. The geometry of each individual array is included in the presentation of observations in section 5.

Figure 5.

Array deployment locations for the 2010 and 2011 Atlantic hurricane seasons (blue boxes and diamonds). Storm trajectories and maximum wind speeds for Hurricanes Igor (circles), Katia (triangles), and Ophelia (pentagons).

The Atlantic hurricane season begins in early June and lasts until late November. In 2010 the network installation began late in August and was completed by early September. The 2011 installation was completed during July, with the exception of the site at BNL which was installed during the last week in September. The four-element arrays were left in place both years through late November. The BNL array has been left in place and has been continuously recording infrasound since late September 2011.

4 Data Processing Methods

The data collected during the 2010 and 2011 Atlantic hurricane seasons have been analyzed using the minimum variance distortionless response (MVDR) beamformer in the frequency domain [Capon, 1969]. Our choice of the MVDR beamformer was based on its well-established ability to outperform the standard/Bartlett beamformer in the presence of multiple coherent sources which are likely due to additional microbaroms generated by sources other than the storm. Each array's data record has been divided into 6 min segments, and within each segment, an estimate of the spectral density matrix, math formula, has been computed using 30 s subwindows, overlapped by 50%. Analysis was performed in the 0.15–0.3 Hz frequency band.

Consider the Fourier transform of the time record contained in the mth subwindow, math formula. An estimate of the spectral density matrix can be obtained by averaging over the outer product of math formula with itself from multiple subwindows,

display math(2)

where the superscript denotes a conjugate transpose, the tilde denotes that this is an estimate of S(f), and in this analysis M = 23. For the four- and six-element arrays used in the deployments, the number of independent subwindows is greater than the dimensionality of the spectral density matrix, which guarantees that the spectral density matrix estimate in equation (2) is full rank, and the matrix inversion used in the MVDR will not fail [Capon, 1969; Krim and Viberg, 1996].

The MVDR spatial spectrum, P(θ,f), can be calculated for a steering vector, math formula, associated with a specific direction of arrival (DOA), θ. The elements of the steering vector are given by

display math(3)

where p is the number of elements in the array and τj(θ)is the time delay for a plane wave incident with DOA θ moving across the array and arriving at element j. The MVDR can then be written in terms of S(f)and math formula[Capon, 1969; Krim and Viberg, 1996]

display math(4)

It is useful to perform analysis using the maximum of the spatial spectrum and some measure of the width of the maximum. In order to estimate the beam width from the spatial spectrum, consider writing equation (4) in terms of the eigenvalue decomposition of S(f). Denoting the jth eigenvalue of the spectral density matrix as λj(f) and the associated eigenvector as math formula, the MVDR can be written as follows:

display math(5)

where the coefficient, math formula, is the projection of the steering vector on the jth eigenvector. Consider the case that a single coherent signal is present in a data record. In such a case, the largest eigenvalue λsis markedly larger than the others and the eigenvector associated with λs is nearly identical to the steering vector associated with the signal's DOA [Krim and Viberg, 1996]. The spatial spectrum can then be approximated

display math(6)

As a function of θ, P(θ,f) is sharply peaked near the true DOA, θ0, and can be approximated by

display math(7)

where Λ(f)is given by

display math(8)

This formulation allows one to define the beam half width as,

display math(9)

in the sense that

display math(10)

Spatial spectrum estimates can be improved by combining the results across the frequency band of interest to produce a frequency-independent spatial spectrum. Instead of a simple average, a weighted spectra has been computed using the pure state filter derived by Samson and Olson to calculate the coherence at each frequency [Samson, 1973; Olson, 1982]. The pure state filter provides what is, in the sense of coherence, an ideal band-pass filter for the data set being studied. We have chosen to use the pure state filter rather than the more commonly used filters such as, for example, a Butterworth filter, because it gives some improvement in signal to noise. The weighting coefficients have been calculated from the pure state filter applied to the correlation matrix, γ(f), where

display math(11)

Applying the pure state filter to γ, one obtains the weighting function

display math(12)

where Tr[…] is the trace of the matrix inside the brackets, p is the dimension of the matrix, and W is some overall normalization. The weighting function, w2(f), produces a real scalar value between zero and unity which measures the coherence in S(f) at frequency f. From this weighting, one obtains

display math(13)

where the sum is over the frequency bins in the band of interest. Local maxima of the resulting spatial spectrum as well as the beam width of the maximum calculated from equation (8) are used to produce the results in the following discussion.

5 Observations of Microbaroms Generated by the Storms

Nineteen storms reached at least Category 1 hurricane intensity during the 2010 and 2011 Atlantic hurricane seasons, with maximum wind speeds in excess of 55 m/s [Stull, 2000; National Hurricane Center, 2010, 2011]. In this investigation we focus on storms in the mid-Atlantic which stay sufficiently far from the coast so that microbarom generation is not complicated by possible coastal reflections. Therefore, a large number of the storms have not been investigated due to their making landfall or moving into the Gulf of Mexico instead of the open Atlantic. Some storms were missed due to the late deployment in 2010 and to power issues due to limited solar exposure. Other storms did not generate sufficiently strong winds to produce observable microbarom signals.

Three storms have been selected for detailed discussion here to demonstrate the asymmetric nature of the microbarom back azimuth observed around the storm center. Hurricanes Igor (8–23 September 2010) and Katia (29 August to 13 September 2011) exhibited similarities in trajectory and energy levels. Hurricane Ophelia (20 September to 3 October 2011) intensified at a more northern latitude than Igor and Katia, and its trajectory was farther east; however, it produced measurable microbaroms along the Atlantic Coast. Microbaroms observed during these three storms provide a useful data set to test the predictions presented in section 2.

Hurricanes Igor and Katia reached Category 4 intensity, with maximum wind speeds of 70 and 63 m/s, respectively [Pasch and Kimberlain, 2011; Stewar, 2012]. Storm trajectories and maximum wind speeds for Igor and Katia are plotted in the circle and triangle icons in Figure 5. Note that Hurricanes Igor and Katia reached their maximum intensities while south of all array locations in the region 20–30°N latitude and 70–55°W longitude. Hurricane Ophelia, designated by pentagons in the figure, reached its maximum intensity as a Category 4 storm with maximum winds of 61 m/s as it passed to the east of Bermuda [Cangialosi, 2012].

Large maritime storms produce microbaroms regardless of time of day; however, the signal can be overwhelmed by local noise sources. The dominant noise source at infrasonic frequencies is due to atmospheric pressure fluctuations, or turbulence, carried by local winds over a sensor. Figure 6a shows the power spectral density on the Croatan, McCoy, and Ocala arrays during Hurricane Igor in 2010. In each panel, the power spectral density has been averaged over an hour of data. The black line is an average over 1 h during the nighttime, and the gray line is 1 h during the daytime. Note that in the daytime data, the power law relation for wind noise amplitude is clearly present, indicating that the noise is most likely the result of turbulence and shear from the wind flowing over the sensor [Raspet et al., 2008]. The microbarom energy around 0.2 Hz is evident in all three arrays during the night; however, the signal is overwhelmed by the wind noise during the day. Figure 6b contains 24 h of data on a single element. The noise level increases at approximately 08:00 local time (EDT) and doesn't decrease back to nighttime levels until 18:00. In the following discussions, all times are local, EDT. Five minutes of unfiltered data taken during the nighttime and daytime are shown in Figures 6c and 6d, respectively (note the 2 order of magnitude difference in scale). The microbarom signal, with 5 s period, is easily seen in the nighttime data record. Because of this difference in noise level during the day and night, analysis of this data set is limited to using data recorded during the nighttime in order to reduce the wind noise and increase the signal-to-noise ratio of the microbarom signal.

Figure 6.

Unfiltered infrasonic data from 20 September 2010 during Hurricane Igor. (a) Spectral densities at Croatan, McCoy, and Ocala during daytime and nighttime. (b) Twenty-four hours of data on a single element of the McCoy array. (c) Five minutes of data during the nighttime. (d) Five minutes of data during the daytime.

It has been found that the back azimuth of the storm-induced microbarom signals observed on each array exhibit consistent behavior as the generating storm progresses through the Atlantic. The beam width, coherence measure, and back azimuth relative to the storm center for microbaroms recorded on the McCoy array during Hurricane Igor and on the Ocala array during Hurricane Katia are shown in Figure 7. Although there are noticeable differences in signal quality between the two array records, a similar trend is evident. As the storm moves northward through the Atlantic the observed back azimuths indicate an apparent source located around the north of the storm center. Once the storm passes the array latitude (denoted by the gray point in each plot), the back azimuth consistently tracks a location south of the storm center. Combining these observations from multiple arrays, one can infer that the actual microbarom source is trailing to the south of the storm center for these storms. The beam width and Pure State Filter output at 0.2 Hz indicate that the coherence of the signal increases once the storm passes to the north of the array location as one would expect since the signal no longer propagates through the storm winds.

Figure 7.

Back azimuth half width, pure state filter coherence measure at 0.2 Hz, and back azimuth relative to the storm center for the microbarom signal observed on the McCoy array during Hurricane Igor in 2010 and Ocala array during Hurricane Katia in 2011.

Following the results of section 2, detailed analysis of the back azimuth observations made during these storm events have been separated into those when the storm center was located south of the array latitude and those once the storm had passed to the north of the array latitude. By separating observations in such a manner, the asymmetric behavior of the back azimuths predicted in section 2 and shown in Figure 4 can be observed. Spatial spectra, beams, and the combined probability densities at specific times when each storm was south of the array latitude are shown in Figure 8. Each panel corresponds to 6 min of data centered at the date and time indicated in the panel title. The red circle indicates the location of the storm center at the time of observation. In each panel, the spatial spectra of the various arrays have been calculated using equation (13) and are shown in the left column along with the array geometry and radial scale. The maximum of the spatial spectrum associated with coherent signal from the Atlantic has been used to generate the beams shown on the right of each panel of the figure. Each figure contains a density plot obtained by fitting the beam maximum and half width at each array to a von Mises distribution [Mardia and Jupp, 2009]. The beam at each array is only included in the density plot if the half width is less than 40° and the maximum indicates a common apparent source. The product of the von Mises distributions across all arrays is shown in the color scale and provides an estimate of the apparent source location from the combined observations. In these results, propagation effects are not considered. The color scale indicates the apparent source location determined from the back azimuths alone.

Figure 8.

Observations of Hurricanes (top) Igor in 2010, (middle) Katia 2011, and (bottom) Ophelia 2011, respectively, when the storm center is located south of the array latitudes. The color scaling represents the probability distribution of the apparent source from the combined beams, the red dot denotes the storm center at the time of observation, and the red dashed line denotes the storm path.

Figure 8 (top) shows observations of Hurricane Igor at 03:06 and 05:15 EDT on 18 September 2010. In each case, coherent energy is observed with back azimuths directed around the storm center. The spatial spectral maxima are not well defined in the result at 03:06, although the beams at McCoy, Francis Marion, and Ocala indicate coherent energy emanating from the region around and ahead of the storm. In the observation at 05:15, the spatial spectra maxima on all arrays have become more narrowly peaked and indicate coherent energy from the region around and behind the storm. Figure 8 (middle) shows observations of Hurricane Katia made on 5 and 6 September 2011. The arrays at Ocala and McCoy detect coherent microbarom energy emanating from around the storm center in both cases; however, the maxima are not well defined and the area containing the apparent source region is very large. Figure 8 (bottom) shows the observations during Hurricane Ophelia as it moved north of the Croatan array on 2 October 2011. In both results, the gray line originating at Croatan indicates coherent energy from south of the storm center where the true source region is likely located. The arrays at Bass River and BNL detect coherent energy from around the storm and southeast of it. The beams again narrow as the storm progresses farther northward and indicate signal around and south of the storm. However, the beams at Bass River and BNL do not indicate a common source with that detected by the Croatan array, unless the source is much farther away (around 50°W longitude).

Once the storms progressed farther northward, the characteristics of the microbarom signal were found to change considerably. Figure 9 contains several examples of observations made once the storm center had moved north of the array latitude. In Figure 9 (top), Hurricane Igor has progressed to the north side of Bermuda, and the spatial spectra on the arrays at Croatan, McCoy, and Ocala narrow significantly and indicate a common source region south of the storm. Because one element of the array in Ocala lost power, the beam width on the array is large, leading to the larger east-west uncertainty in the apparent source region. Multiple elements in the Francis Marion array lost power between 18 and 20 September due to decreased solar exposure which prevented data from that array from being used in the analysis. In Figure 9 (middle), the spatial spectra observed during Hurricane Katia are not as strongly peaked as during Igor; however, the arrays again identify a common source region to the south of the storm center. The apparent source region is much more localized in Figure 9 (middle, right) due to the well-defined beam at Ocala and the addition of the Bass River beam. Finally, the results during Hurricane Ophelia are shown in Figure 9 (bottom). At northern latitudes, the ocean surface temperature decreases and the storm decreased in intensity. However, microbaroms continued to radiate from an extended region south of the storm. In Figure 9 (bottom, right) the storm has progressed to the northeast while the apparent source has shifted to the southwest of the storm.

Figure 9.

Observations of Hurricanes (top) Igor in 2010, (middle) Katia 2011, and (bottom) Ophelia 2011 once the storm center progressed north of the array latitudes. The color scaling represents the probability distribution of the apparent source from the combined beams, the red dot denotes the storm center at the time of observation, and the red dashed line denotes the storm path.

6 Discussion

The qualitative predictions shown in Figure 4 suggest that if the source is located some distance away from the storm center, back azimuths obtained from observations made from the same side of the storm as the source are close to back azimuths to the true source location. The observations made during the passage of Hurricanes Igor, Katia, and Ophelia, and shown in Figure 9, consistently indicate a tightly bound apparent source region some distance from the storm center which is consistent with the predictions in Figure 4 (right). In all of these cases, the beam-forming results indicated a single coherent signal emanating from a region some distance away from the storm. Note that in the results in Figure 9 for all three storms, there are no secondary maxima in the spatial spectra which would indicate coherent energy emanating from the storm center. Thus, one can infer that during these storm events, a single microbarom source region was located several hundred kilometers south of these storms as they progressed through the open Atlantic. Assuming that the microbarom source was located to the south of the storm while it progressed through the central Atlantic and that there were no additional sources associated with the storm, the signal observed previously while the storm was south of the array latitudes must have propagated through the storm structure and interacted with the winds there. The propagation modeling discussed here predicts that observations of the microbarom signal which has propagated through the storm winds will result in a virtual source near the storm center, as shown in Figure 4 (left). Such observations are made consistently, as seen in Figure 8, for all three storms.

In only one case, that of Hurricane Ophelia, was it possible to observe the storm from the south and the north simultaneously. For a period of time, simultaneous microbarom source localization from north and south of Hurricane Ophelia was possible. In Figure 8 (bottom), the back azimuth of the Croatan array indicates a microbarom source trailing south of the storm consistent with the observations of Igor and Katia, and in Figure 8 (bottom, right), one sees that there was also a weak beam from the Francis Marion array, locating the source region to the south of the storm. Once Ophelia progressed to the north of the Bass River and BNL arrays, the back azimuths indicate a microbarom source which moves from southeast of the storm to southwest of it. The reason for this is unclear from these observations; however, this is not inconsistent with the Hetzer et al. model, since the background wave field can become quite complicated [Stopa et al., 2012].

In future deployments it is recommended that the array network increases in extent so that storms can be observed from multiple azimuths simultaneously. This would require deployment of arrays on several islands in the Caribbean Sea if possible and at additional locations along the Atlantic Coast of the United States. Additional improvements to the results of analysis of microbaroms from large maritime storms could be made by improving the performance of the individual arrays in the network. The beam width at a set frequency for an array is related to the number of elements, the total aperture, and the geometric configuration of the elements [Krim and Viberg, 1996]. Larger aperture arrays with more elements are needed to improve detection and localization capability. Tests with synthetic microbarom data using various array designs have shown that in order to sufficiently reduce the beam width to distinguish the multiple arrivals in the northwest of the storm, it is necessary to use at least 10–12 elements in each array [Blom, 2013]. The exact geometry of the array is less important, other than requiring that the nearest neighbor element pairs be separated by approximately a half wavelength—850 m in the case of microbaroms [Steinberg, 1976; Kim and Jaggard, 1986].

7 Conclusions

Although the physical mechanism which generates microbaroms has been studied and advanced over the past decades, the manner in which large maritime storms produce microbaroms has remained somewhat unclear. The qualitative model proposed by Hetzer et al. predicts that the oceanic swell generated by the cyclonic winds of the storm produces waves which are equal in period and opposite in propagation direction to those of the pelagic swell at a location several hundred kilometers away from the storm center along a perpendicular to the direction of the pelagic swell. If this source location is correct, the propagation of the microbarom signal through the storm can provide information about the interior of the storm that is otherwise difficult to obtain.

Geometric acoustic propagation methods have been used to show that when observed along propagation paths which do not pass near the storm center, the back azimuth of the observed signal provides a quality estimate of the true microbarom source region. Alternately, when observed along propagation paths that pass through the intense winds near the storm center, horizontal refraction of the signal by the large radial wind gradient results in observation of microbarom back azimuths indicating a virtual source around the storm center. Observations made repeatedly during the passage of several storms through the open Atlantic show precisely this asymmetry in the back azimuth observations and estimation of the apparent source region when observed from north and south of the storm latitude. We find it unlikely that the striking similarities between the model results in Figure 4 and observational results in Figures 8 and 9 are incidental. Given these predictions and observations, it is likely that a single dominant microbarom source is produced by a large maritime storm at some location several hundred kilometers away from the storm center, and the propagation of the microbaroms through the storm winds produces variation in the apparent source location when observed far from the storm along different propagation paths.

Acknowledgments

This publication was prepared by the University of Mississippi under award NA08NWS4680044 from National Oceanic and Atmospheric Administration, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations are those of the author(s) and do not necessarily reflect the views of the National Oceanic and Atmospheric Administration or the U.S. Department of Commerce. We thank the McCoy family of Laurinburg, North Carolina, for allowing us to deploy equipment on their land. In addition, we thank Ocala National Forest, FL, Francis Marion National Forest, SC, Croatan National Forest, NC, Bass River State Forest, NJ, and Pachaug State Forest, CT. The infrasonic data collected during these experiments have been archived by the Infrasound Research Group at the National Center for Physical Acoustics, University of Mississippi (ncpadata@olemiss.edu).

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