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  • View in gallery

    Pressure data from barometer B1 at different time scales. Boxes indicate segments shown in detail in the respective subsequent panel. (a) The entire 2-week period from 26 Feb through 10 Mar 2008, showing four high pressure and four low pressure episodes, with pressure ranging from 972 to 1018 hPa. (b) A 24-h section, from 0000 to 2400 EST 3 Mar. (c) A 2-h segment, from 0100 to 0300 EST 3 Mar, showing gravity waves with amplitudes of about 10 Pa and periods between 5 and 10 min. (d) A 5-min segment, from 0115 to 0120 EST, showing microbaroms with amplitudes of up to 0.1 Pa (1 μbar) and periods of 5 s.

  • View in gallery

    The 10-Hz raw data (small dots) and 0.5-s block averages (large dots) during the 60-s-long segment between 0116:10 and 0117:10 EST (see box in Fig. 1d) on 3 Mar. Microbaroms are clearly visible.

  • View in gallery

    (a) Bandpass-filtered pressure signals from the collocated barometers B1–B3 between 0115 and 0120 EST 3 Mar 2008 (the raw data for the same interval were shown in Fig. 1d). A FIR filter based on a Blackman window was used. The passband ranged from 0.1 to 0.5 Hz. (b) The difference between the bandpass-filtered B1 and B3. The rms value of the difference signal is 9.98 mPa.

  • View in gallery

    Power spectral densities from all 3e barometers for the 2-h interval from 0100 to 0300 EST 3 Mar 2008.

  • View in gallery

    (a) Microbarom spectrogram (barometer B1) for the 2-week period from 26 Feb through 10 Mar 2008. The reference spectral density (0 dB) has been set to 0.1 Pa2 Hz−1. The time resolution is 30 min. (b) The 15-min block averages of the horizontal wind speed near the trailer. (c) The 15-min block averages of the temperature near the trailer.

  • View in gallery

    As in Fig. 5a, but for the 4 days from 5 to 8 Mar.

  • View in gallery

    Microbarom spectrogram for the 24-h interval from 1200 EST 6 Mar to 1200 EST 7 Mar. The time resolution is 10 min.

  • View in gallery

    Time series of microbarom amplitudes during the 2 weeks from 26 Feb through 10 Mar 2008, estimated for 30-min intervals from spectra measured with barometers B1 (black) and B3 (red). The data gaps coincide with episodes contaminated by wind noise (see Fig. 5).

  • View in gallery

    As in Fig. 8, but for centroid frequencies.

  • View in gallery

    The microbarom amplitudes, observed with barometer B1 on six different days, plotted as a function of the the time of day.

  • View in gallery

    The microbarom period 1/fc (where fc is the centroid frequency), observed with barometer B1 on six different days, plotted as a function of the time of day.

  • View in gallery

    Power spectral density of the barometer B3 between 0100 and 0300 EST 3 Mar 2008 after subtraction of the constant noise spectral density, presented in a log–log plot. The spectrum follows an f−5 law, consistent with Phillips’s f−5 law for the ocean wave height spectrum in the saturated wind sea.

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First Observations of Microbaroms with Single Absolute Barometers

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  • 1 Department of Electrical and Computer Engineering, University of Massachusetts Amherst, Amherst, Massachusetts
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Abstract

The first observations of microbaroms with single absolute barometers are presented and discussed. Microbaroms are pulses of atmospheric infrasound emitted by ocean surface waves. They can propagate over thousands of kilometers through the atmosphere, and they can reach altitudes well into the upper atmosphere before they are refracted down to the earth’s surface. Typical microbarom periods are 5 s, typical wavelengths are 1.5 km, and typical surface amplitudes are 100 mPa (1 μbar). The data presented here were collected during the 2-week period from 26 February through 10 March 2008 in Amherst, Massachusetts, which is located about 150 km away from the Atlantic Ocean. The authors report for the first time, to the best of their knowledge, an f−5 microbarom frequency spectrum, which is consistent with Phillips’s f−5 ocean surface wave equilibrium spectrum.

Corresponding author address: Andreas Muschinski, 151 Holdsworth Way, Department of Electrical and Computer Engineering, University of Massachussetts Amherst, Amherst, MA 01003-9284. E-mail: muschinski@ecs.umass.edu

Abstract

The first observations of microbaroms with single absolute barometers are presented and discussed. Microbaroms are pulses of atmospheric infrasound emitted by ocean surface waves. They can propagate over thousands of kilometers through the atmosphere, and they can reach altitudes well into the upper atmosphere before they are refracted down to the earth’s surface. Typical microbarom periods are 5 s, typical wavelengths are 1.5 km, and typical surface amplitudes are 100 mPa (1 μbar). The data presented here were collected during the 2-week period from 26 February through 10 March 2008 in Amherst, Massachusetts, which is located about 150 km away from the Atlantic Ocean. The authors report for the first time, to the best of their knowledge, an f−5 microbarom frequency spectrum, which is consistent with Phillips’s f−5 ocean surface wave equilibrium spectrum.

Corresponding author address: Andreas Muschinski, 151 Holdsworth Way, Department of Electrical and Computer Engineering, University of Massachussetts Amherst, Amherst, MA 01003-9284. E-mail: muschinski@ecs.umass.edu
Keywords: Pressure; Waves; oceanic

1. Introduction

Air pressure is one of the most important observables in meteorology, geophysics, and the related sciences, and a wide range of phenomena leave characteristic signatures in pressure time series and in the pressure field. Time scales, length scales, and amplitudes of air pressure fluctuations vary by many orders of magnitude. Typically, amplitudes decrease with decreasing time and length scales, that is, with increasing frequency and wavenumber. Pressure amplitudes associated with synoptic-scale processes are on the order of several kilopascals, on the order of tens of pascals for gravity waves, and on the order of tens or hundreds of millipascals for natural infrasound.

Atmospheric pressure waves can be divided into Rossby waves, gravity waves (Gossard and Munk 1954), Lamb waves (Lamb 1910), sound waves (Lord Rayleigh 1894a,b), and atmospheric tides (Chapman and Lindzen 1970). Waves in geophysical fluid systems are comprehensively covered in several classical textbooks and monographs, such as the works by Lamb (1932), Gossard and Hooke (1975), Turner (1979), and Gill (1982). More recent monographs on gravity waves are those by Nappo (2002) and Pedlosky (2003).

Excellent monographs on atmospheric acoustics are provided by Ostashev (1997) and Salomons (2001). Infrasound is addressed by Tabulevich (1992) and Gossard and Hooke (1975, chapter 9). Bedard and Georges (2000) point out that atmospheric infrasound is generated by a wide variety of natural and manmade sources and phenomena, including avalanches, meteors, ocean waves, severe weather systems, tornadoes, turbulence on the ground and at higher levels, earthquakes, volcanoes, ground and air traffic, mine blasts, and nuclear explosions.

An important subcategory of atmospheric infrasound are “microbaroms.” Microbaroms were discovered by Benioff and Gutenberg (1939) by means of “electromagnetic microbarographs” at the Seismological Laboratory in Pasadena, California. In their short note, Benioff and Gutenberg (1939) report a dominating period of 4 s for natural infrasound, as opposed to anthropogenic infrasound from ships, aircraft, gunfire, mine blasts, etc. Similar to their seismic cousins known as “microseisms” (e.g., Tabulevich 1992), microbaroms are acoustic pressure waves that are generated by standing or quasi-standing ocean surface waves (Daniels 1953; Posmentier 1967; Arendt and Fritts 2000; Waxler and Gilbert 2006). Gossard and Hooke (1975, 295ff.) review the early history of research on microbaroms, including the work by Saxer (1954), who observed a strong correlation between ocean wave heights in the Northern Sea and microbarom amplitudes in Fribourg, Switzerland. In a series of papers, Donn, Rind, and their collaborators explored the possibility of using microbaroms as a means for passive remote sensing of the upper atmosphere (Donn and Rind 1972; Rind et al. 1973; Rind and Donn 1975; Rind and Donn 1978).

Infrasound detection is a key element of international efforts to monitor nuclear explosions in the context of the Comprehensive Nuclear-Test-Ban Treaty. From that perspective, microbaroms are viewed as noise, and substantial research has been devoted to determining microbarom characteristics that are a function of geographical location, time of day, and time of year (e.g., Hedlin et al. 2002; Bowman et al. 2005).

Thus far, atmospheric infrasound has been observed almost exclusively with differential sensors, that is, with microbarographs or infrasound microphones. However, recent developments in pressure measurement technology, particularly more accurate quartz-crystal resonance frequency measurements, have led to absolute barometers with submicrobar precision for subsecond integration times.

In this paper, we present and discuss the first observations of microbaroms by means of single, absolute barometers. The paper is organized as follows: Section 2 describes the barometers, the datalogger, and the experimental setup near Amherst, Massachusetts, during the winter and spring 2007/08. Section 3 summarizes observations from an uninterrupted 2-week period from 26 February through 10 March 2008, and it describes the signal processing methods that we employed. A discussion follows in section 4. Summary and conclusions are provided in section 5.

2. Instrumentation and experimental setup

a. The barometer

The quartz-crystal barometer (Intelligent Transmitters Series 6000) that we used for this study is manufactured by Paroscientific, Inc. It consists of a high-precision, low-power, quartz-crystal pressure transducer and a digital interface board in a single package. Temperature-sensitive crystals are included for the thermal compensation of calculated pressure to provide high pressure accuracy over a wide range of temperatures (see Subramanian 2009, section 5.3 for details). The frequency of the quartz-crystal oscillator is a nearly linear function of the ambient air pressure to which the barometer is exposed. That calibration function, including the coefficients for the temperature compensation, is measured accurately for each individual barometer, and the coefficients are provided by the manufacturer. Mechanical acceleration compensation using small balance weights within the unit mitigates shock and vibration effects.

The resonator frequency is estimated in real time with a built-in digital signal processing unit. At the time of our field study (winter–spring 2007/08), two algorithms were available: the old “start–stop algorithm” and the then new “regression line algorithm.” The start–stop algorithm simply counts the number of cycles Nc of the built-in clock between the first and last upward zero crossing of the resonator output signal during the preset integration time Ti. Therefore, the relative estimation error Δfr/fr of the resonator frequency fr is of the order of 1/Nc, such that Δfr/fr and the relative air pressure estimation error Δp/p are proportional to the ratio of clock period and integration time.

The barometers provide the option of quadrupling the clock frequency from the default value of 14.7 to 58.8 MHz, in order to further improve the pressure resolution. Independently of the choice of the clock frequency, the regression line algorithm results in improved resolution over the start–stop algorithm; see Subramanian (2009, section 3.1.1).

There are significant advantages of applying absolute pressure sensors of this kind for the measurement of infrasound. For example, this eliminates the need for a reference volume and flow resistors to define a high-pass filter (e.g., Cook and Bedard 1971). Also, there are practically no dynamic range limitations, and temperature sensitivity problems are considerably reduced.

b. The datalogger

The datalogger that we used to collect the barometer data had been developed at the University of Massachusetts (Behn et al. 2008) and had been deployed in various meteorological field experiments (e.g., Cheon et al. 2007; Whiteman et al. 2008). The logger has eight serial ports and it can accommodate up to eight sensors operating simultaneously. The measured data are recorded on an onboard hard drive of 160-GB capacity. Such a large data storage space enables the continuous operation of multiple micrometeorological sensors (with sampling rates of order 10 Hz each) for several months. The data from each of the serial ports are written to a separate file on the hard drive. Accurate time stamping is provided by a global positioning system (GPS) receiver (manufactured by Motorola, Model M12+) that is connected to the datalogger via a separate serial interface. The testing of the time stamping provided by this system showed that the offset between the local PC clock and the reference GPS clock stayed within ±10 μs (Behn et al. 2008).

The datalogger also provides for online access, which helps to monitor the data in real time and control the system operation. This feature is provided by a 802.11 b/g 54 Mbit s−1 network card and a wired 10/100 Mbit s−1 network connection. The option of wireless access is very useful, particularly during severe weather conditions or in difficult terrain. The datalogger is powered either by alternating current (ac) grid power (110 V) or by 12-V marine batteries. Because the datalogger is usually installed outside, it needs to be protected from precipitation, dust, winds, and extreme solar radiation. To ensure this, the datalogger system is mounted inside a weather-resistant enclosure (manufactured by Campbell Scientific). Additional details and information on the dataloggers’ construction and operation can be found in Behn et al. (2008).

c. Experimental setup

Three collocated barometers of the type mentioned above were used to measure air pressure close to the northeastern town limit of Amherst, Massachusetts from 7 December 2007 through 4 June 2008. The three barometers were placed a few centimeters apart from each other on a table inside a travel trailer. The trailer was located at 42°24.354′N, 72°29.148′W at an elevation of 128 m MSL in a sparsely populated, wooded residential area. The relatively thick forest acted as an effective filter against wind noise, as described by Hedlin et al. (2002, 1142–1145).

During the months before 26 February 2008, the barometers were operated in various configurations (Subramanian 2009). In this paper, we present the data collected from 26 February through 10 March 2008. During these 2 weeks, the three barometers were operated in the regression line mode; they had their internal clock counter frequency quadrupled (58.8 MHz), and the integration time was set to 0.1 s, resulting in a pressure sampling frequency of 10 Hz. In this paper, we refer to the three barometers as B1, B2, and B3. Barometers B1 and B2 were “naked,” that is, they were operated inside the trailer without any wind noise protection. B3 was also inside the trailer, but its inlet was connected through an airtight hose to a mechanical wind noise protector of the “quad-disk” type (Nishiyama and Bedard 1991) outside the trailer.

A three-dimensional ultrasonic anemometer–thermometer (Model 81000, manufactured by R. M. Young Company) was deployed close to the trailer at a height of 2 m AGL. The “sonic” sampled the three velocity components and the temperature at 32 Hz. The sonic data and the barometer data were collected with the same datalogger.

3. Observations and signal processing

a. Pressure time series

1) 10-Hz raw data

Figure 1 gives an overview of the 10-Hz raw data collected with B1 during the 2-week period from 26 February through 10 March 2008. During these 2 weeks (Fig. 1a), there were four high pressure and four low pressure episodes, with the pressure ranging between 972 and 1018 hPa. Within the 24-h period from 0000 through 2400 eastern standard time (EST) 3 March (Fig. 1b, and the box in Fig. 1a), the pressure dropped from 1010 to 997 hPa. Gravity waves dominated the pressure variations during the quiet 2-h nighttime episode from 0100 to 0300 EST (Fig. 1c, and the box in Fig. 1b), with amplitudes of the order of 10 Pa. At further magnification, microbaroms become visible. Figure 1d (and the box in Fig. 1c) shows a 5-min-long section, from 0115 to 0120 EST. During this episode, the microbaroms had a period of about 5 s, and the amplitude reached a maximum of about 0.1 Pa. The microbaroms occurred in packets, or pulses, of 3–10 oscillations, with lower-amplitude episodes of a few tens of seconds in between. For example, the segment from 0115 to 0116 EST showed amplitudes close to 0.1 Pa, while between 0118:00 and 0118:30 EST the microbaroms were barely visible.

Fig. 1.
Fig. 1.

Pressure data from barometer B1 at different time scales. Boxes indicate segments shown in detail in the respective subsequent panel. (a) The entire 2-week period from 26 Feb through 10 Mar 2008, showing four high pressure and four low pressure episodes, with pressure ranging from 972 to 1018 hPa. (b) A 24-h section, from 0000 to 2400 EST 3 Mar. (c) A 2-h segment, from 0100 to 0300 EST 3 Mar, showing gravity waves with amplitudes of about 10 Pa and periods between 5 and 10 min. (d) A 5-min segment, from 0115 to 0120 EST, showing microbaroms with amplitudes of up to 0.1 Pa (1 μbar) and periods of 5 s.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

2) 0.5-s averages

The 10-Hz data provided by the barometers were not exactly equidistant in time, and the barometers were not synchronized with respect to each other. However, we “time stamped” each arriving data point with an accuracy of better than 10 μs, which enabled us to synchronize the pressure time series a posteriori. To this end, we calculated temporally equidistant and synchronous sequences of 0.5-s block averages of the 10-Hz raw data collected with B1–B3. This simplified the spectral analysis and the direct comparison between observations made with the different barometers.

Figure 2 shows a 60-s segment (same data as in the box in Fig. 1d) of the 10-Hz raw data and the 2-Hz averages from B1.

Fig. 2.
Fig. 2.

The 10-Hz raw data (small dots) and 0.5-s block averages (large dots) during the 60-s-long segment between 0116:10 and 0117:10 EST (see box in Fig. 1d) on 3 Mar. Microbaroms are clearly visible.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

3) Bandpass-filtered data

To isolate the relatively narrowband microbarom signals from pressure fluctuations at lower frequencies and from high-frequency wind noise and system noise, we designed a finite-impulse response (FIR) bandpass filter by means of the windowing method (Proakis and Manolakis 2007; Oppenheim et al. 1999). We used a Blackman window.

Figure 3a shows a 5-min segment (same episode as in Fig. 1d) of bandpass-filtered signals calculated from the 2-Hz time series from all three barometers. We set the passband from 0.1 to 0.5 Hz. The three bandpass-filtered signals track each other closely, even during the low-amplitude section between 0118:00 and 0118:30 EST, when the amplitude dropped to about 20 mPa (200 nbar).

Fig. 3.
Fig. 3.

(a) Bandpass-filtered pressure signals from the collocated barometers B1–B3 between 0115 and 0120 EST 3 Mar 2008 (the raw data for the same interval were shown in Fig. 1d). A FIR filter based on a Blackman window was used. The passband ranged from 0.1 to 0.5 Hz. (b) The difference between the bandpass-filtered B1 and B3. The rms value of the difference signal is 9.98 mPa.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

The difference Δ between the bandpass-filtered signals from B1 and B3 is shown Fig. 3b. The rms value is 9.98 mPa. If Δ were solely due to instrument noise, if the noise from B1 and B3 were uncorrelated, and if the noise rms values of B1 and B3 were equal, the noise spectral density were
e1
where B is the width of the passband. With B = 0.4 Hz, we find Sn = 1.25 × 10−4 Pa2 Hz−1.

b. Power spectra

We computed power spectra from estimates of time-averaged modified periodograms (Welch 1967; see also Oppenheim et al. 1999, p. 732). A modified periodogram is a periodogram computed from a time series windowed with a nontrivial (i.e., nonrectangular) window. We used a Blackman window of 60-s duration, and we chose an overlap of 30 s (50%) for subsequent time windows. Figure 4 shows the one-sided power spectral densities Spp(f) estimated from the three barometer signals measured during the 2-h interval between 0100 and 0300 EST (raw data shown in Fig. 1c). (A one-sided power spectrum is normalized such that the integral over positive frequencies is equal to the variance.) There is very little scatter in the spectral estimates because each spectrum is an average of 239 (=2 × 120 − 1) individually modified periodograms.

Fig. 4.
Fig. 4.

Power spectral densities from all 3e barometers for the 2-h interval from 0100 to 0300 EST 3 Mar 2008.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

The three spectra show a pronounced minimum at 0.12 Hz and a pronounced peak at 0.20 Hz. The peak frequency corresponds to a microbarom period of 5.0 s. The maximum spectral density is 1 × 10−4 Pa2 Hz−1, and the spectral density at the minimum is 6 × 10−4 Pa2 Hz−1, which is 17 times lower than the peak spectral density. That is, there is a sharp spectral cutoff of the microbarom spectrum toward lower frequencies.

According to Fig. 4, most of the microbarom energy is contained in the frequency interval between 0.1 and 0.3 Hz, which we refer to as the “microbarom band.” The pressure rms values within the microbarom band were 30.1, 29.8, and 30.1 mPa for B1–B3, respectively. That is, they differed by less than 1 mPa (10 nbar). In the flat part of the spectrum, the spectral density is about 1 × 10−4 Pa2 Hz−1, close to the noise spectral density estimated above. For the microbarom band with the bandwidth B = 0.2 Hz, this leads to a noise rms value of .

Because the microbaroms are contained within a relatively narrow frequency band, the square of the microbarom amplitude A is twice the pressure variance within the microbarom band, such that
e2
With σp = 30 mPa we obtain A = 42 mPa. That is, the average microbarom amplitude during the 2-h interval between 0100 and 0300 EST was 42 mPa (0.42 μbar).

c. Spectrograms

Figure 5a shows, in the form of a spectrogram, the temporal evolution of Spp(f) estimated from B1 data during the 2-week period. The spectral density is color-coded such that spectral densities between 0 (deep red) and −25 (deep blue) dB can be distinguished. The reference spectral density (0 dB) was set to 0.1 Pa2 Hz−1, such that −25 dB corresponds to 3 × 10−4 Pa2 Hz−1, which is 3 times the noise spectral density. Spectral densities were estimated for 30-min blocks, again using Welch’s method, with Blackman windows of 60-s duration and 50% overlap. That is, each 30-min estimate of Spp(f) is the average of 59 individual modified periodograms. The frequency resolution Δf is determined by the duration of the segments from which individual modified periodograms are estimated: Δf = 1/(60s) = 0.017 Hz.

Fig. 5.
Fig. 5.

(a) Microbarom spectrogram (barometer B1) for the 2-week period from 26 Feb through 10 Mar 2008. The reference spectral density (0 dB) has been set to 0.1 Pa2 Hz−1. The time resolution is 30 min. (b) The 15-min block averages of the horizontal wind speed near the trailer. (c) The 15-min block averages of the temperature near the trailer.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

Figures 5b,c show time series of 15-min averages of wind speed and temperature, respectively, measured with the sonic near the trailer, less than 2 m away from the barometers.

In Fig. 5a, microbaroms are visible as Spp(f) maxima between 0.1 and 0.3 Hz at times when the wind speed was lower than about 0.3 m s−1. At higher wind speeds, fluctuations of the dynamic pressure associated with turbulent wind speed fluctuations (“wind noise”) dominated the observed pressure signals and obscured the microbaroms. There is a strong correlation between high wind speed and the occurrence of broadband wind noise.

The microbaroms were strongest during the early morning hours of 26 February 2008, while the weakest microbaroms occurred on 8 March 2008 EST.

Figure 6 shows a microbarom spectrogram for the 4 days from 0000 EST 5 March through 2400 EST 8 March. There is a textbook-like microbarom event around midnight on 6 March and a “microbarom chirp” event during the night of 5–6 March, when the frequency of the spectral maximum increased from 0.18 to 0.23 Hz within a few hours. In the early morning hours of 6 March, there appeared an unusual secondary peak at about 0.35 Hz (with a period of 2.9 s).

Fig. 6.
Fig. 6.

As in Fig. 5a, but for the 4 days from 5 to 8 Mar.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

Figure 7 shows the microbarom event of 6–7 March in detail, with increased time resolution (10 instead of 30 min). The microbaroms “built up” nearly uniformly during the 5 h from 2000 EST 6 March to 0100 EST 7 March, while the lower cutoff frequency remained constant at about 0.16 Hz, consistent with the 3 March event shown in Fig. 4.

Fig. 7.
Fig. 7.

Microbarom spectrogram for the 24-h interval from 1200 EST 6 Mar to 1200 EST 7 Mar. The time resolution is 10 min.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

d. Amplitudes

Figure 8 shows the time series of the microbarom amplitude A observed with the barometers B1 and B3 during the entire 2-week period. We developed an algorithm that computed the amplitudes from Spp(f) for each 30-min interval as follows. First, it looked for a minimum at a frequency around 0.1 Hz. If no such minimum could be identified, then it was concluded that the spectrum was contaminated by wind noise, and no amplitude was calculated. If there was a minimum, the frequency f0 of the minimum was determined, and the microbarom pressure variance was estimated as the integral of Spp(f) from f0 to f1 = 0.3 Hz. Then, the amplitude A was calculated by means of Eq. (2).

Fig. 8.
Fig. 8.

Time series of microbarom amplitudes during the 2 weeks from 26 Feb through 10 Mar 2008, estimated for 30-min intervals from spectra measured with barometers B1 (black) and B3 (red). The data gaps coincide with episodes contaminated by wind noise (see Fig. 5).

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

As expected, the gaps in Fig. 8 coincide with the events of strong wind noise (Fig. 5). During the calmer episodes, the two amplitude time series track each other well. The microbarom amplitude ranged from 90 to slightly below 20 mPa during the 2 weeks. There are pronounced maxima around 0000 EST 29 February and 1, 3, 6, and 7 March. At the beginning of the 2-week period, the amplitude drops from 90 to less than 20 mPa within 30 h.

e. Frequencies

Figure 9 shows the microbarom centroid frequencies fc during the 2 weeks. For each 30-min interval for which a spectral minimum was detected, fc was estimated by means of
Fig. 9.
Fig. 9.

As in Fig. 8, but for centroid frequencies.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

e3
Again, the estimates from the two barometers agree well with each other. The lowest fc of about 0.18 Hz was observed early at 2008 EST 26 February, and increased to about 0.21 Hz by 0400 EST 27 February. As mentioned above, the amplitude decreased during the same 30-h period. A similar reciprocal behavior of amplitude and centroid frequency can be observed during the nights of 2–3, 5–6, and 6–7 March. The centroid frequency reached a maximum of 0.24 Hz in the early morning of 6 March.

4. Discussion

When we set up the three barometers in and next to a travel trailer in North Amherst, our original intention was to collect data in order to quantify the system performance of the barometers after the manufacturer has provided us with a test version of a new algorithm (the regression line algorithm, instead of the former start–stop algorithm) and with the option of quadrupling the internal clock frequency, from 14.7 to 58.8 MHz. When we first saw the 5-s oscillations in a sample dataset from 18 March 2008, we misinterpreted them as artifacts caused by wind-induced oscillations of the trailer. When we discovered, however, that the oscillations were even more pronounced under calm conditions, we studied the literature more closely and found that our observations were entirely consistent with microbaroms. Until March 2008, we had been unaware of the fact that microbaroms can be detected far from the ocean. In other words, our observations of microbaroms were entirely serendipitous.

a. Wind noise

It is well known that turbulence-induced pressure fluctuations are ubiquitous and may severely contaminate infrasound measurements even under light wind conditions (e.g., Nishiyama and Bedard 1991; Hedlin et al. 2002). In the pressure spectrogram presented in Fig. 5a, microbaroms are visible only if the wind speed next to the trailer is below about 0.3 m s−1. The dynamic pressure resulting from a wind speed U is about ρU2/2, which for an air density of ρ = 1kg m−3 amounts to 31 mPa (0.31 μbar) for U = 0.25 m s−1, 125 mPa (1.25 μbar) for U = 0.5 m s−1, and 500 mPa (5.0 μbar) for U = 1 m s−1. This explains why the spectrum of wind-induced pressure fluctuations dominates the microbarom spectrum observed with single barometers if the wind speed is comparable to or larger than 0.5 m s−1.

b. Diurnal cycle of microbarom amplitudes

The 14-day spectrogram in Fig. 5a suggests that the spectral density in the microbarom frequency band (say, between 0.15 and 0.30 Hz) often reaches a maximum around local midnight. This is corroborated by the time series of the microbarom amplitudes shown in Fig. 8. With the exception of the night of 25–26 February, when the microbarom amplitude reached about 90 mPa (0.9 μbar), typical midnight amplitudes were between 40 and 50 mPa. On most days, microbaroms could not be observed during daytime because of the higher level of wind noise. On a few days, however, the wind during daytime was weak enough to not obscure the microbarom spectrum.

Figure 10 shows microbarom amplitudes observed during six different days plotted against the time of day, from noon to noon. While there are considerable differences from day to day, it can be clearly seen that there is a semidiurnal cycle, with maxima around 50 mPa around midnight and around noon, and with minima of typically 20 mPa at about 0600 and about 1800 EST. This semidiurnal cycle in Fig. 10 agrees quite well with Fig. 9 in Donn and Rind (1972), which shows a relatively sharp maximum at 1100 LT and a broader maximum around 2200 LT. Donn and Rind (1972) collected their data at Palisades, New York, which is located 190 km southwest of Amherst.

Fig. 10.
Fig. 10.

The microbarom amplitudes, observed with barometer B1 on six different days, plotted as a function of the the time of day.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

As explained in detail by Donn and Rind (1972), the semidiurnal cycle of the microbarom amplitudes are caused by the semidiurnal tides in the upper-atmospheric wind field: The vertical gradient of the effective acoustic refractive index depends sensitively on the vertical shear of the horizontal wind, such that the trajectories of the sound rays depend sensitively on the vertical shear profile. Therefore, the maximum height of an acoustic ray that is launched at a certain elevation angle (assuming the initial elevation angle is shallow enough so that the ray is ultimately refracted back to the surface) varies with the tides in the wind field. At heights above 100 km, the kinematic viscosity is so large that even infrasound waves with a frequency of 0.2 Hz (wavelength about 1.5 km) are significantly damped: “Travelling horiontally, a ray at 105 km will suffer an amplitude decrease of 1/e every 170 km, while a ray at 115 km has an amplitude decrease of 1/e every 39 km” (Donn and Rind 1972, p. 165).

The good agreement between our observations of the diurnal cycle of the microbarom amplitudes and the observations by Donn and Rind (1972) is to be expected because the characteristic horizontal length scales of the upper-atmospheric tide patterns are large compared to the distance between Amherst and Palisades (190 km).

c. Diurnal cycle of microbarom periods

We have seen in Fig. 9 that the centroid frequencies of the microbaroms varied between 0.18 (with a period of 5.6 s) and 0.24 Hz (with a period of 4.2 s). Figure 11 shows the microbarom periods for the same 6 days selected for Fig. 10, defined as the reciprocals of the centroid frequencies, as a function of the time of day. There appears to be a semidiurnal cycle also for the period of the microbaroms, with a broad maximum centered around 2100 EST and a second maximum around noon. While the ratio between maximum amplitude and minimum amplitude is about 3, the ratio between the longest and shortest period is only about 1.3.

Fig. 11.
Fig. 11.

The microbarom period 1/fc (where fc is the centroid frequency), observed with barometer B1 on six different days, plotted as a function of the time of day.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

d. A universal f−5 equilibrium microbarom spectrum?

The shape of the pressure spectrum in the microbarom band is determined, among other things, by the frequency spectrum of the source and the frequency dependence of the viscous dissipation along the propagation path. Higher frequencies suffer more viscous damping than lower frequencies (e.g., Lord Rayleigh 1894b, article 346). If viscous damping is negligible, then, under ideal conditions one would expect that the microbarom spectrum is simply proportional to the ocean surface elevation spectrum. The classical theory (Phillips 1958) predicts an f−5 law for the ocean surface elevation spectrum in the saturated wind sea.

Figure 12 shows, in log–log representation, the pressure spectrum estimated from B3 data collected between 0100 and 0300 EST 3 March. The data are the same as those shown in Fig. 4, but now the noise floor has been subtracted. For frequencies between 0.2 and 0.5 Hz (with periods between 5 and 2 s), the spectrum in Fig. 12 follows an f−5 power law very closely. We calculated spectra from each 1-h segment of our 2-week-long dataset, and in the majority of the cases where there was a pronounced microbarom peak, the spectral tail was consistent with the f−5 power law.

Fig. 12.
Fig. 12.

Power spectral density of the barometer B3 between 0100 and 0300 EST 3 Mar 2008 after subtraction of the constant noise spectral density, presented in a log–log plot. The spectrum follows an f−5 law, consistent with Phillips’s f−5 law for the ocean wave height spectrum in the saturated wind sea.

Citation: Journal of Atmospheric and Oceanic Technology 28, 7; 10.1175/2011JTECHA1526.1

To the best of our knowledge, an f−5 microbarom spectrum has never been reported. An f−5 microbarom equilibrium spectrum would be the atmospheric equivalent of the microseism equilibrium spectrum at the seafloor suggested by Webb (1992). Further research is needed to clarify under what conditions the f−5 microbarom equilibrium spectrum can be observed.

5. Summary and conclusions

The main results, based on 2 weeks of 10-Hz pressure data collected with three collocated quartz-crystal barometers, are as follows:

  • State-of-the-art, absolute barometers based on quartz-crystal technology are sufficiently sensitive for the observation of microbaroms. For a barometer integration time of 0.1 s, the uncorrelated noise spectral density is 1 × 10−4 Pa2 Hz−1, which leads to an rms pressure of 4.5 mPa (45 nbar) within the “microbarom band” from 0.1 to 0.3 Hz.
  • Microbarom amplitudes estimated during a calm 2-h period observed with three collocated barometers differed from with each other by less than 1 mPa (10 nbar).
  • Microbarom amplitudes observed during the 2-week period from 26 February through 10 March 2008 near Amherst showed a semidiurnal cycle, with maxima of typically 50 mPa (500 nbar) at midnight and at noon, and minima of typically 20 mPa (200 nbar) at 0600 and 1800 EST. The phases of the semidiurnal cycle agree with observations by Donn and Rind (1972).
  • We report for the first time, to the best of our knowledge, an f−5 tail in the microbarom frequency spectrum. It is natural to interpret this result as empirical evidence for the existence of a universal microbarom equilibrium spectrum directly connected with Phillips’s f−5 ocean surface equilibrium spectrum (Phillips 1958).

Acknowledgments

This material is based on work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under Grant 49393-EV and by the National Science Foundation under Grant ATM-0444688. The senior author is the first holder of the Jerome M. Paros Professorship in Measurement Sciences at the University of Massachusetts Amherst, and he thanks Jerry and Linda Paros for their generous support. The authors are grateful for helpful discussions with Al Bedard, Dave Fritts, Jerry Paros, Luke Root, Theo Schaad, and Keith Wilson.

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