Sound Propagation in the Nocturnal Boundary Layer

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Sound Propagation in the Nocturnal Boundary Layer D. KEITH WILSON, JOHN M. NOBLE,

AND

MARK A. COLEMAN

U.S. Army Research Laboratory, Adelphi, Maryland (Manuscript received 10 July 2002, in final form 7 January 2003) ABSTRACT An experimental study of sound propagation near the ground in stable, nighttime conditions was performed in conjunction with the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99). Low-frequency sound transmissions were continuously recorded at microphones out to a distance of 1.3 km from a loudspeaker during CASES-99 intensive observation periods (IOPs) 6 and 7. Fading episodes in the received signal energy of 10 to 20 dB, lasting several minutes to an hour, were frequently observed. Strong discrete events, such as the density current and solitary wave of IOP 7, were found to have significant effects on acoustical signals, although substantial variability in received sound energy often occurred outside such events. Sound propagation model predictions demonstrate that wind and temperature data from a tall tower, such as the CASES-99 60-m tower, can be used to predict the momentary variations in a 50-Hz sound signal with good success. Tethersonde and rawinsonde data are generally too infrequent to model many of the strong variations present in the signal. The sensitivity of sound waves to changes in nocturnal boundary layer structure could allow development of new remote sensing methods.

1. Introduction Some basic features of sound propagation near the ground in very stable, nighttime conditions are well recognized. Most prominently, downward refraction resulting from temperature inversions traps sound energy in a ground-based duct, allowing the sound to propagate efficiently over long distances (see, e.g., Brown and Hall 1978; Pierce 1981). This phenomenon is of practical importance for prediction of community noise impacts (Bronsdon and Forschner 1999) and detectability of sound sources at long distances (Becker and Gu¨desen 1999). Beyond the occurrence of ducting, however, there remains much to be understood about sound propagation at night. For example, how strongly does the energy of received signals fluctuate and over what timescales? Which atmospheric phenomena play a primary role in driving this variability? What is the dependence of the signal properties on the acoustic frequency and the horizontal propagation distance? Answers to these questions may allow the development of new acoustic remote sensing methods for the nocturnal boundary layer based on transmission of sound over near-horizontal paths (Greenfield et al. 1974; Chunchuzov et al. 1997; Wilson et al. 2001). To improve forecasting of noise impacts and detectability, it would also be highly desirable to know whether widely available atmospheric observaCorresponding author address: Keith Wilson, U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Rd., Hanover, NH 03755-1290. E-mail: [email protected]

tions (such as those made from radiosondes) and numerical weather forecast models provide sufficient time–space resolution to accurately predict sound propagation. With issues such as these in mind, we participated in the Cooperative Atmosphere–Surface Exchange Study1999 (CASES-99; Poulos et al. 2002), by concurrently performing a set of sound propagation measurements. The comprehensive boundary layer data recorded during CASES-99 provide a unique opportunity to relate the acoustic signal behavior to the structure of the atmosphere. Our experimental scheme for the sound propagation measurements and data processing is described in section 2. Results over the course of intensive observation periods (IOPs) 6 and 7 are provided in section 3, including an in-depth examination of the signal behavior during three strong events occurring in IOP 7. Numerical modeling of the acoustic signals, on the basis of the main 60-m tower and sonde data recorded during CASES-99, is discussed in section 4. 2. Description of the experiment The single sound source in our experiment was positioned 1.25 km west and 1.15 km south of the CASES99 60-m tower. The sound transmission path, which was approximately horizontal over gently sloped terrain, ran due north from the source as indicated on Fig. 4 of Poulos et al. (2002). A series of five 6-m towers were placed at distances between 361 and 1180 m from the source. Each tower had four research-quality condenser

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FIG. 1. Layout of the sound transmission path, showing the locations of the loudspeaker and microphone arrays. Towers 1–5 each had four vertically spaced microphones. Arrays 1–3 were placed horizontally on the ground, transverse to the transmission path.

microphones, Bru¨el and Kjær–type 4166, which were placed at heights of 0.5, 1, 2, and 3 m. The exact distances of the microphone towers from the sound source are shown in Fig. 1. (Also shown in Fig. 1 are the locations of three horizontal linear microhpone arrays. Only the tower microphone data are considered in this paper, however.) Sound propagation trials were conducted during the CASES-99 IOPs 3 through 7. [The dates and an event log of the IOPs can be found in Poulos et al. (2002).] The source for IOP 3 consisted of a propane cannon, which generates a repeatable, impulsive signal with duration of about 10 ms. During the remaining IOPs, a continuous, 50-Hz square wave was broadcast from a loudspeaker consisting of a 16-in. subwoofer in a custom-built enclosure. The nominal speaker height was 1 m. The loudspeaker was powered by an audio amplifier. As the square wave includes higher odd harmonics of the 50-Hz fundamental (150, 250 Hz, . . .), usage of this signal was a simple way to generate a sequence of multiple, distinct frequencies. The tower microphone signals were recorded on Sony PC108Ax digital audio tape recorders. The sampling rate of the recorders was set to 12 kHz. Due to the huge amount of data being stored, the tapes had to be changed every 1-1/2 to 2 h. A pair of sessions, each lasting nearly 2 h, were conducted during IOPs 3, 4, and 5. The first session generally started shortly after sunset, whereas the second finished shortly before sunrise. For IOPs 6 and 7 (the nights of 13 and 17 October, respectively), the tapes were exchanged regularly throughout the night, providing a nearly continous recording from dusk until sunrise. In this paper, we focus on these latter two IOPs. The received power in the individual frequency components of the 50-Hz square wave signal were tracked using a fast Fourier transform (FFT) filtering technique. First, the raw signals from the tapes were partitioned into 60 000 sample (5 s) segments for processing. Each 5-s segment was further subdivided into 32 768 sample blocks at 80% overlap. [The purpose of the overlapping technique is to maintain a good spectral resolution (0.366 Hz in this case) while improving the accuracy of the spectral estimate (Welch 1967).] The 32 768 sam-

ple blocks were tapered with a Hanning window and then transformed to the frequency domain with a standard FFT. Next, the squared magnitudes of the resulting 32 768 point FFTs were averaged to form the overall spectral estimate associated with the 5-s segment. Finally, a squared sound pressure at each frequency of interest f (50, 150 Hz, etc.) was calculated by summing over all frequency bins within 62.5 Hz of f . This interval was large enough to capture spectral broadening of the sound energy due to Doppler shifts from random scattering (as is also observed in radar and sodar signals). The spectral broadening was found by examination of individual spectra to be less than 1 Hz at frequencies up to 350 Hz. As is traditional in acoustics, the squared sound pressures were converted to decibels by taking the base-10 logarithm and multiplying by 10. This quantity is referred to as the sound-pressure level (e.g., Pierce 1981), or sound level for short. In this paper, we do not concern ourselves with the absolute sound levels, since the power output of the speaker system is essentially arbitrary and not of interest. Rather, our emphasis is on the variability of the sound level at single microphones and on comparisons of the relative sound levels observed between various microphones. Therefore, the sound levels in this paper are reported in units ‘‘dB, arb. ref.,’’ which is shorthand for decibels referred to an arbitrary reference level. To compare sound levels between microphones, it is necessary to compensate for the individual microphone responses. The relative responses can vary by several decibels. At the beginning and end of each IOP, the microphones were calibrated with a pistonphone (Beranek 1988), which generates a 500-Hz tone at a known level. Data in this paper that have been compensated based on the pistonphone calibration are indicated as calibrated sound levels. The microphones used in this study essentially have a flat response from 10 Hz up to several thousand hertz, which allows the calibration at 500 Hz to be applied across the frequency range in our experiment. Although we are uninterested in the absolute sound pressures per se, the source must be loud enough to be detected using the narrowband FFT processing de-

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FIG. 2. Sound pressure levels for four different frequencies (in dB with an arbitrary reference level) at the 0.5-m microphone on tower 2 during IOP 6.

scribed earlier. Based on empirical comparisons of the signal lines with nearby spectral bins, the signal-to-noise ratio (SNR) was determined to be generally greater than 20 dB at 50 Hz for all of the towers. The SNR was better than 10 dB at all frequencies at tower 2. However, at times, the signal was lost in the background environmental noise at the more distant towers for frequencies 150 Hz and higher. We do not present any of this low SNR data, except for one example that is specifically flagged in section 3b. 3. Experimental results a. Composite records for IOPs 6 and 7 Complete processed sound levels for 50, 150, 250, and 350 Hz at the 0.5-m microphone on tower 2 (566 m from the loudspeaker) are shown in Fig. 2 and 3. These figures combine all the recordings for IOPs 6 and 7, respectively. The curves have been arbitrarily shifted in the vertical direction for better visibility (i.e., the relative sound levels between the frequencies have no particular significance in these figures). Breaks in the curves occur when the digital audio tape was changed. During IOP 6, there is a general tendency for the sound levels to increase from about 0000 to 0230 UTC, decrease from 0230 to 0500 UTC, and then increase once again until sunrise. Superimposed on this general behavior are many strong fading episodes where the sound levels decrease as much as 15 dB over periods ranging from a few minutes to an hour. These variations in sound level are most pronounced at higher frequencies. The signal behavior during IOP 7 is similar to IOP 6, although there is a trend for gradually increasing sound levels at all frequencies throughout the night. Standard deviations for the sound levels shown in Figs. 2 and 3 were calculated to better understand the dependence of signal variability on frequency. Prior to

FIG. 3. Same as in Fig. 2 except during IOP 7.

the calculation, each segment of the record between tape changes was linearly detrended. This detrending helps compensate for variations due to evolution in the nocturnal boundary layer structure occurring over timescales of about 2 h and greater. The resulting standard deviations for IOP 6 are 0.44 dB (50 Hz), 2.89 dB (150 Hz), 2.68 dB (250 Hz), and 2.95 dB (350 Hz). The results for IOP 7 are 0.75 dB (50 Hz), 1.93 dB (150 Hz), 3.16 dB (250 Hz), and 3.24 dB (350 Hz). A standard deviation of about 6 dB is characteristic of a fully saturated signal (Flatte´ et al. 1979), meaning that the signal reaching the receiver consists of a large number of random, statistically independent contributions. We conclude that the signal behavior at 50 Hz must be attributable to one dominant propagation path, whereas at 150 Hz and higher there are multiple contributions with some degree of statistical independence. For nearly horizontal propagation paths such as in the present experiment, the behavior of the acoustic signal is determined primarily by the ‘‘effective’’ sound-speed field ceff , which is the sum of the actual sound speed c and the component of the wind velocity in the nominal propagation direction. [The reader is referred to Ostashev (1997) and Blanc-Benon et al. (2001) for discussions of the effective sound speed and potential limitations of this concept.] Since our propagation path is due north, ceff 5 c 1 y , where y is the northward wind component. The sound speed is calculated from the equation (e.g., Ostashev 1997) c 5 Ïg d R d T(1 1 0.511r),

(1)

where g d is the specific heat ratio for dry air, R d is the gas constant for dry air, T is temperature, and r is the water vapor mixing ratio. Figures 4 and 5 show the effective sound speed during IOPs 6 and 7, respectively, calculated from temperature, humidity, and wind sensors at heights from 5 to 55 m, in 10-m increments, on the 60-m tower. [Standard slowresponse sensors were used in all cases, except for the

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FIG. 4. Effective sound speed at several heights on the 60-m tower during IOP 6.

winds at 5 and 55 m, where ultrasonic anemometer data were used. Poulos et al. (2002) describe the tower instrumentation in greater detail.] An increase in ceff with height causes downward refraction and ducting of sound near the ground, whereas a decrease causes upward refraction and acoustic ‘‘shadow’’ formation (e.g., Pierce 1981). Roughly similar patterns to the evolution of the ceff profile are evident during the two IOPs. Both evenings start with ceff decreasing weakly with height. Between roughly 0200 and 0500 UTC (0800 and 1100 LST), a transition occurs to very strongly increasing gradients in ceff , which persist until sunrise. For IOP 7, however, a very strong event occurs between 0130 and 0200 UTC. Sun et al. (2000) describe this as a density current. A second event of very short duration occurs around 0645 UTC. Immediately before the record ends at 1230 UTC, a third strong event occurs. Although there is much variation in the ceff profile during IOP 6, there appear to be no counterparts to the three events of IOP 7.


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FIG. 6. Bulk approximation to the effective sound-speed gradient during IOP 6. Contributions to the bulk gradient from air temperature, humidity, and horizontal wind velocity are shown.

Let us now examine the relative contributions of temperature, humidity, and the horizontal wind velocity to the gradient ]ceff /]z. This can be done by first rewriting the sound-speed Eq. (1) as

1

c . c0 1 1

2

T9 0.511r9 1 , 2T0 2

(2)

where T 5 T 0 1 T 9, r 5 r 0 1 r9, c 0 5 [g d R d T 0 (1 1 0.511r 0 )]1/2 , and only the first-order contributions in T9, r9, and r 0 have been retained. The subscript 0s indicate a reference value (e.g., the mean value at some fixed height) and the primed quantities are small perturbations. Differentiating with respect to height, we have ]c eff c ]T9 0.511c 0 ]r9 ]y . 0 1 1 . ]z 2T0 ]z 2 ]z ]z


(3)

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FIG. 8. Scatterplot of the sound level at 50 Hz vs the bulk approximation to the effective sound-speed gradient. Light points are IOP 6; dark are IOP 7.

Figures 6 and 7 show the relative contributions from temperature, humidity, and wind gradients to the effective sound-speed gradient, where each term in (3) has been estimated by taking the difference between data at the 55- and 5-m levels on the 60-m tower {i.e., ]ceff /]z . [ceff (z 2 ) 2 ceff (z1 )]/(z 2 2 z1 ), where z1 5 5 m and z1 5 55 m}. (Reference values of T 0 5 11.08C and r 0 5 5.0 g kg 21 were used. These values have very little effect on the calculation.) We observe that the contribution from humidity is negligibly small at this continental location. The wind and temperature contributions are comparable in magnitude during the evenings of both IOP 6 and IOP 7, although, because the propagation is initally upwind, there is a partial cancellation between the two contributions. On both nights there was a gradual shifting in the wind direction, resulting in a transition to downwind propagation at roughly midnight local time (0600 UTC). We see that the deepening, positive ceff gradient on both of these two nights resulted primarily from shifting wind direction, as opposed to strengthening of the temperature inversion. The inversion actually weakened after midnight local time on both nights. The behavior of the sound levels in Figs. 2 and 3 very roughly follows the ceff gradient. In IOP 6 (Fig. 2), the weakening of the negative gradient prior to 0230 UTC allows sound levels to increase. The sound levels increase again after roughly 0630 UTC, corresponding to the shifting wind direction. The reason for decreasing sound levels after 0230 UTC is not evident from the ceff profile (Fig. 4), however. In IOP 7 (Fig. 3), the gradual increase in sound levels throughout the night corresponds to a steadily increasing ceff gradient, with a notable disturbance between 0130 and 0200 UTC. Figure 8 shows a scatterplot of the sound level at 50 Hz (from Figs. 2 and 3) versus the bulk approximation to the effective sound-speed gradient (from Figs. 6 and 7). The acoustic data in the figure are again from the

FIG. 9. Same as in Fig. 8 except at 150 Hz.

0.5-m microphone on tower 2. A trend for elevated sound levels with increasing gradient is clearly evident, although there is substantial scatter to the data. The scatter can be attributed to factors such as the bulk approximation, the lack of measurements above 55 m, and the differing locations of the 60-m tower and propagation path. A similar plot, but for 150 Hz, is given in Fig. 9. This plot has a much less regular appearance than the one for 50 Hz. The more complex relationship between the sound level and gradient at this frequency is probably due to an interference between multiple, propagating modes. This will be discussed further in section 4. b. Discrete events during IOP 7 Three readily distinguishable events, producing sudden changes in the surface-layer structure and increased turbulent activity, occurred on the night of 17 October (IOP 7). The first of these (at 0135 UTC) is identified by Sun et al. (2002) as a density current. The nature of the second (0628 UTC) and third (1225 UTC) events is less clear, although they are likely associated with solitary or gravity waves. From the standpoint of sound propagation, these three events can elucidate the extent to which variability in signals at night is driven by strong, intermittent events in the NBL, or whether the variability is driven by gradual changes in the effective sound-speed gradient. The 2-h recordings encompassing the three events are shown in Figs. 10 through 15. The signals at 50 and 150 Hz, for the 2-m microphones on towers 2, 3, and 5 (570, 760, and 1170 m from the loudspeaker, respectively) are shown. The behavior of the sound levels at 50 Hz prior to and during event 1 (Fig. 10) is remarkably consistent among all microphones and displays a clear linkage to the passage of the density current. Prior to 0130 UTC, the sound levels gradually increase. Beginning at about 0140 UTC, they jump by 3 to 6 dB over a period of

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FIG. 10. Sound levels recorded at 50 Hz at three different distances from the loudspeaker during a 2-h period of IOP 7 including event 1.

just 1 to 2 min, with the increase becoming larger for the more distant microphones. Next, over an interval of about 15 min, the sound levels decrease by an amount ranging from 10 dB at the 570-m tower to 17 dB at the 1180-m tower. An oscillation in the sound levels, with a period of roughly 15 min, is evident. According to Sun’s analysis of the tower array data (J. Sun 2001, personal communication), event 1 propagated at 2.3 m s 21 from a compass bearing of 478 and reached the 60m tower at 0135 UTC. A simple trigonometric analysis predicts that event 1 would have arrived at the 1180-m distant microphone tower 6.5 min after its arrival at the 60-m tower, and then spread south over the propagation path, arriving at the loudspeaker position 5.8 min later. Close examination of Fig. 10 suggests that the 1180-m microphone signal was indeed the first affected by the event, and that this occurred several minutes after 0135 UTC. In comparison to the 50-Hz signals during event 1, the 150-Hz signals have a much less regular behavior (Fig. 11). With the arrival of the density current, there is a noticeable jump in signal level, amounting to about 10 dB at the 570-m tower and 18 dB at the 1180-m tower.1 Immediately afterward, the sound energy drops dramatically to levels below its pre-event values, roughly remains at this state (with some variability) for the next 15 to 20 min, and then increases again sharply. This increased level is maintained at the nearest tower, but not at the two more distant ones. We note that the overall duration of event 1 (Fig. 7 in Poulos et al. 2002) is about 25 min, after which the near-ground layer settles into a state with a deeper temperature inversion and strong winds aloft. This is also roughly the duration of 1 The sound level at the 1180-m tower for the 150-Hz signal occasionally falls below the level of the local environmental noise. This appears to occur for calibrated sound levels below about 263 dB.

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enhanced activity in the acoustic signals evident in the figures. Event 2 is very brief. The temperature at the 50-m thermocouple on the 60-m tower plunged by about 28C for just 1 min, accompanied by a momementary cycling of vertical velocity (positive during the initial part of the temperature drop and negative during the final part). After the event passage, irregular variations occur in the temperature and wind velocity components, which are gradually damped over the next 10 to 15 min. Some evidence of the passage of this event is evident in the acoustic signals (Figs. 12 and 13). Prior to 0625 UTC, the signal at 50 Hz is quite stable. At about 0630 UTC, particularly for the 50-Hz signal at the 760-m tower, there are small, but very sharp fluctuations in the sound level. Following these sharp fluctuations, some damped oscillations in the sound levels are evident. J. Sun (2001, personal communication) has determined that event 2


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propagated at 5.5 m s 21 from 1148. This places the event at the loudspeaker 2 min after its arrival at the 60-m tower (0628 UTC) and at the 1180-m tower 1.5 min later, a timing consistent with the observations in Fig. 12. While it is interesting that this short event does seem to affect sound levels, at least at some of the microphones, overall it plays a small role in the variability of the signals. In particular, there is an 18-dB increase in the 150-Hz signal at the 1180-m tower from 0525 to 0535 UTC; this cannot be caused by event 2. The period leading up to event 3 (Figs. 14 and 15) produces pronounced activity in the sound levels. At 50 Hz, a deep fading in the sound level centered on 1130 UTC is observed at the more distant microphones. At the same time, the sound level at the near microphone attains a local maximimum. More frequent fading episodes, occurring every 10–15 min, are observed at 150 Hz. Because the fading episodes at 50 and 150 Hz prior to event 3 are not well correlated, they are likely due to frequency-dependent, shifting interference patterns between propagating wave modes trapped in the nearground duct. Shortly after 1215 UTC, near the onset of event 3, very rapid fluctuations in the sound level are observed at all microphones. These fluctuations are particularly strong at the two more distant microphones. According to J. Sun (2001, personal communication), event 3 propagated at 1.72 m s 21 from 2678. This would imply that it passed the loudspeaker and all microphone towers at nearly the same time, about 12 min before the event was recorded at the 60-m tower (1213 UTC). Indeed, at about 1200 UTC, a significant drop in sound levels begins at 50 Hz for the 760- and 1180-m towers, followed by a damped oscillation. The sound level at the 570-m tower, however, does not exhibit this behavior. Activity associated with event 3 may be present at 150 Hz: there are some rapid oscillations in the sound levels at 1215 UTC. However, it is more difficult to

distinguish these from the prior signal behavior than it was at 50 Hz. Taken as a whole, these results show that the discrete events observed during IOP 7 produced complex effects on sound levels. However, there is still much activity in the acoustic signal outside of these events. 4. Sound propagation model results In this section, we use numerical sound propagation calculations and visualizations to better understand the atmospheric phenomena affecting acoustic signal behavior during the CASES-99 experiment. The calculations are performed primarily with a narrow-angle parabolic equation (PE) propagation code of the type described by West et al. (1992), which calculates sound pressure levels from effective sound-speed data. Parabolic equation methods, now widely used for low-frequency acoustics, are based on one-way approximations


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to the full wave equation. Such approximations are reasonable for the application considered here, since most of the sound energy reaching the microphones propagates within about 6158 of the horizontal axis, which is roughly the validity limit for the narrow-angle PE. The ground is assumed to be flat for the PE calculations in this paper. Interaction of sound with the ground is modeled with a frequency-dependent, impedance boundary condition. The impedance condition provides partial absorption of sound energy, as is realistic for a highly porous ground surface such as the grassy field at the CASES-99 site. The ground impedance was calculated from a viscous/thermal relaxation model for the acoustical properties of porous media as described by Wilson (1997). For the parameters of the porous ground medium, we have used values representative of those previously determined for uncultivated, dry, grassy sites (Martens et al. 1985; Attenborough 1985), since no direct determination was made as part of the CASES-99 experiment. These values are a static flow resistivity s 5 200 kPa s m 22 , porosity (volume void fraction) V 5 0.50, squared tortuosity q 2 5 1.4, and pore shape factor s B 5 1. Absorption of sound by the air (conversion of sound waves to heat in the air) is neglected in the present PE calculations, since such absorption is very small at frequencies below a few hundred hertz. [A calculation based on the American National Standard Method (ANSI 1999) for an ambient temperature 78C and 40% relative humidity, which are typical values for IOPs 6 and 7, yields a loss to air absorption of 0.056 dB per 1000 m at 50 Hz and 0.43 dB per 1000 m at 150 Hz. In comparison, the loss for a spherically spreading sound wave from 1 to 1000 m would be 60 dB.] In addition to the PE modeling, we consider in the following discussion some results of simple ray tracing. While the ray tracing is not as convenient or accurate as the PE for calculating sound levels, it can be helpful in visualizing the general nature of the propagation. Note that ray trajectories are independent of frequency, although the actual sound levels (as calculated by the PE, e.g.) do depend on frequency due to diffraction and wavelength-dependent interference between ray paths. The ray tracing equations, in the effective sound-speed approximation, are (Pierce 1990) dn dx 5 2=⊥ c eff , 5 c eff n, dt dt

(4)

where t is time, x 5 (x, y, z) is the position of the ray, n 5 (n x , n y , n z ) is the unit normal to the wavefronts, and =⊥ 5 = 2 n(n · =) . (2n z , 2n z , 1)(]/]z). This set of six, coupled differential equations can be advanced in time with standard numerical integration techniques. Specular reflections (equal angles of incidence and reflection) at the ground are assumed for the ray traces in this paper. The PE and ray calculations require atmospheric

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wind, temperature, and humidity fields as input. Strictly speaking, to predict all details of the sound propagation the atmospheric fields would need to be determined at a spatial resolution finer than an acoustic wavelength (where l, the acoustic wavelength, is about 6.6 m at 50 Hz and 2.2 m at 150 Hz) and a temporal resolution shorter than the acoustic wave period. But no currently available atmospheric observation system is able to provide such fine resolution over the entire sound-propagation path. Therefore, it is only practical to address the issue of whether the instrumentation available during CASES-99, which generally represented the state of the art, is sufficient for predicting certain important features of the propagation, such as the variations in received signal energy caused by changing atmospheric conditions. Since simultaneous data on the wind, temperature, and humidity fields are required, the three main CASES99 observation systems of potential interest are 1) the various surface-based towers, particularly the 60-m main tower; 2) the Argonne National Laboratory tethersonde system; and 3) the National Center for Atmospheric Research (NCAR) cross-chain loran atmospheric sounding system (CLASS) rawinsondes. [The various CASES-99 observation systems are described in Poulos et al. (2002).] The main advantages of the 60-m tower are the high sampling rate (1 s 21 for most of the instrumentation) and the consistent availability of data. The nearby, shorter towers can provide information on the propagation speed and direction of the discrete atmospheric events such as those discussed earlier for IOP 7. The tethersonde provides profiles up to roughly 300 m, with an ascent/descent cycle of about 1 h. The rawinsondes were typically launched at 1-h intervals. From the standpoint of sound-propagation predictions, one difficulty with the rawinsonde data is that the wind profiles below several hundred meters AGL are often unavailable due to the operational characteristics of the GPS system. To begin, let us consider PE and ray calculations derived from CLASS rawinsonde profiles for two illustrative propagation conditions. The first condition considered is from 2300 UTC on 17 October, an evening case with a very shallow temperature inversion and no significant development of low-level jet. The second is from 1100 UTC on 18 October, an early morning case with a deep temperature inversion and well-developed jet. Effective sound-speed profiles for these two cases, derived from rawindsonde data, are plotted in Fig. 16. (Neither of these balloon launches suffered from the inavailability of low-level data mentioned in the preceding paragraph.) Parabolic equation calculations for the evening case, at the frequencies of 50 and 150 Hz, are shown in Figs. 17 and 18, respectively. Plotted in these figures is the difference (in decibels) between the actual sound level and what would be observed in free space (i.e., for spherically spreading waves). A vertical plane running north from the source is shown. The ray trace for the

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FIG. 16. Example effective sound-speed profiles from CLASS rawinsondes.

evening case, shown in Fig. 19, demonstrates that refraction was predominantly upward at this time, except for trapping of sound in a very shallow surface duct below about 10 m. Despite the existence of the duct, the near-ground sound energy at 150 Hz diminishes rapidly with increasing distance from the source. The primary cause is absorption of sound energy by the ground, which becomes stronger with increasing frequency. Furthermore, the 150-Hz calculation exhibits a rather complicated interference pattern. This pattern results from sound being transmitted to receiver locations along a variety of paths of differing lengths (and therefore differing phases). Parabolic equation calculations for the morning case, again at the frequencies of 50 and 150 Hz, are shown in Figs. 20 and 21, respectively. The corresponding ray

FIG. 17. Sound levels calculated by the PE method from the rawinsonde data at 2300 UTC 17 Oct 1999. A vertical slice extending north from the source is shown. The source height is 1 m and the frequency is 50 Hz.

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FIG. 18. Same as in Fig. 17, except that the frequency is 150 Hz.

trace is shown in Fig. 22. At this time, there is a welldeveloped surface duct extending up to about 140 m. This duct creates a situation where the sound energy can travel over long distances with minimal interaction with the ground, resulting in comparatively high nearground sound levels at both 50 and 150 Hz. Interference patterns are observed at both frequencies, although the pattern is more complex at 150 Hz due to the shorter wavelength. At 50 Hz, there is one strong, near-ground zone of destructive interference (a ‘‘dip’’ in the sound level), centered approximately 1200 m from the source. It is unclear a priori whether the CASES-99 60-m tower and tethersonde data provide profiles high enough into the atmosphere to model the sound propagation well. A rough idea of the suitability of these can be had from the ray trace results in Figs. 19 and 22. In both of these figures, the rays reaching a ground-based receiver at 1500 m have not traveled far above 60 m. But,

FIG. 19. Ray trace calculated from the rawinsonde data at 2300 UTC 17 Oct 1999. A vertical slice extending north from the source is shown. The source height is 1 m.

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FIG. 20. Sound levels calculated by the PE method from the rawinsonde data at 1100 UTC 18 Oct 1999. A vertical slice extending north from the source is shown. The source height is 1 m and the frequency is 50 Hz.

in reality, the limiting height must also depend on the sound frequency and diffraction effects that are not captured in the ray trace. To address the limiting height issue more rigorously, we consider here a test based on truncating the CLASS rawinsonde data at various heights and using the truncated profiles as input to the PE. Above the truncation height, a terminating layer, extending from the truncation height to 500 m AGL, is added where the profiles have constant temperature, humidity, and wind velocity. Immediately above this terminating layer, an absorbing condition is added to minimize artificial reflections (Salomons 1998) occurring at the top of the numerical grid. The height of the truncation is moved from 0 m AGL (the case of a homogeneous, nonrefracting atmosphere) up to 500 m in 25m increments. Results of PE calculations at 150 Hz for the two cases shown in Fig. 16, with the source and

FIG. 21. Same as in Fig. 20, except that the frequency is 150 Hz.

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FIG. 22. Ray trace calculated from the rawinsonde data at 1800 UTC 11 Oct 1999. A vertical slice extending north from the source is shown. The source height is 1 m.

receiver both at 1-m height, are shown in Figs. 23 and 24. For horizontal receiver distances out to 1.5 km, the solution becomes nearly constant when the truncation height reaches 100 m for the first case and 75 m for the second. A separate test at 50 Hz (not shown) produced very similar results. We conclude that the tethersonde flights, which sampled up to 300 m AGL, sufficiently covered the altitudes of the atmosphere important in our experiment. The 60-m tower was marginally tall enough to be useful. Let us now consider predictions of the evolution of the sound levels during the discrete events 1 and 3 of IOP 7, for which the actual observations were described in section 3b. In order to predict the sound levels at a high temporal resolution, we must use data from the 60m tower and make some assumptions regarding the spatial structure of these events. In the following analysis,

FIG. 23. Sound-level predictions at 150 Hz for the rawinsonde launch at 2300 UTC 17 Oct. The effect of truncating the atmospheric profiles above the height indicated on the figure is shown.

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FIG. 24. Same as in Fig. 23 except at 1100 UTC 18 Oct.

FIG. 25. PE predictions for the sound level at 50 Hz for the 2-h period of IOP 7 including event 1. Lines represent predictions made from the 60-m tower data and circles from the tethersonde data.

we simply assume that these events have a fixed structure as they move across the CASES-99 site and have a width (spatial extent perpendicular to their direction of translation) that is much larger than the sound transmission path. These assumptions allow the atmospheric fields at any given time and observation point to be mapped back to the 60-m tower according to the equation Q P (t, z) 5 Q T [t 2 d cos(a 2 u)/y , z],

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where Q(t, z) is the time-varying vertical profile of interest (temperature, humidity, or wind), t is time, z is height AGL, the subscript T indicates the tower location, P indicates a position on the propagation path, d is the distance from the tower to the observation point, a is the polar angle of the point on the propagation path relative to the tower, u is the direction of translation of the event, and y is the speed of the event. To generate profiles for input to the PE, we spaced 100 points P evenly between the loudspeaker and the 1300-m microphone array. Parabolic equation predictions were run at 1-min intervals. The speeds and directions of the events were given in section 3b. Direct comparisons between the PE predictions and recorded sound levels also require a value for the strength of the sound source (loudspeaker). We infer a source level by calculating the mean observed soundpressure level at tower 2 for each frequency and IOP. After running PE predictions for a 0-dB source level (unit strength source) over the course of each IOP, the actual source level is then inferred a posteriori by subtracting the predicted, average sound-pressure level from the observed average (in decibels). Therefore, the comparisons between the PE predictions and recorded sound levels have been ‘‘calibrated’’ in the sense that they have the same average sound-pressure level at tower 2. This means that the quality of the PE predictions should be assessed primarily with regard to successful

prediction of the relative sound levels between the towers and of the variations in signal levels at each tower. Parabolic equation predictions of 50-Hz propagation for IOP 7 encompassing the 2-h periods of events 1 and 3 are shown in Figs. 25 and 26, respectively. The predictions generated from the 60-m tower data have many close similarities to the actual measurements. While the timing and magnitude of the various fluctuations in sound level are not exactly predicted, there are few substantial features in the observations that are not present in the predictions. The predictions could almost certainly be improved if the tower were somewhat higher and/or multiple towers were available closer to the sound propagation path. The predictions from tethersonde data in the figures are plotted at the time of the beginning of the ascent/descent. Profiles are available for only three predictions during the 2-h period shown

FIG. 26. Same as in Fig. 25, except for the 2-h period of IOP 7 including event 3.

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FIG. 27. PE predictions at 50 Hz before, during, and after the passage of event 1 during IOP 7. Dashed vertical lines are placed at the distances of towers 2, 3, and 5.

FIG. 29. PE predictions for the sound level at 150 Hz for the 2-h period of IOP 7 including event 1. Lines represent predictions made from the 60-m tower data and circles from the tethersonde data.

in Fig. 25 and once during the 2-h period of Fig. 26. This infrequency does not allow the evolution of the acoustic signal to be usefully modeled. Figure 27 shows PE predictions of the 50-Hz sound level as a function of range (horizontal source–receiver separation) at three different times. These times were selected as representative of the atmospheric state before, during, and after the passage of event 1. According to the PE model, the density current induced a temporary sound-level minimum at approximately 0200 UTC, centered at a distance of 1100 m from the source. The timing is actually about 10 min later than in the actual data (Fig. 10). More detailed modeling of this event (not shown) links the occurrence of the sound-level minimum to variations in the wind and temperature profiles along the propagation path; that is, the minimum does

not appear when horizontal gradients in the atmosphere are neglected. A similar plot, except for the interval centered around the time of the large signal fading episode at 1130 UTC during IOP 7, is shown in Fig. 28. By this time of the night, strong ducting has created multiple minima in the sound level. The locations of the sound-level minima gradually shift with changes in the effective soundspeed profile. At 1124 UTC, one of these minima strengthens and happens to be centered right at tower 5. A slight reduction in the sound level at tower 3 is also evident, whereas at tower 2, the sound level stays fairly constant relative to the prediction at 1100 UTC. On the whole, this behavior is borne out in the observations (Fig. 14), although the observations show a slight elevation in the sound level at tower 2. Predictions at 150 Hz (Figs. 29–30) are not nearly as

FIG. 28. Same as in Fig. 27, except that predictions are shown before, during, and after a strong signal fading episode centered on tower 5.

FIG. 30. Same as in Fig. 29, except that a 2-h period of IOP 7 including event 3 is shown.

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successful as the 50-Hz predictions. This outcome could have been anticipated from Fig. 9, which demonstrated a complex relationship between the meteorological measurements on the 60-m tower and the observed sound levels. The wind and temperature profiles along the propagation path would need to be known at a higher level of detail than provided by the 60-m tower to successfully predict variations in the sound levels at 150 Hz. 5. Conclusions The acoustical measurements during CASES-99 have provided unique insights into the characteristics of nearground propagation at night. Fading episodes in the received signal energy of 10 to 20 dB, lasting several minutes to an hour, were frequently observed. The variations in signal energy become more irregular and less clearly related to the effective sound-speed gradient as the sound frequency increases. Out to receiver distances of about 1 km from the source, sound levels are determined primarily by the wind and temperature profiles in the lowermost 100 m or so of the atmosphere. Strong discrete events, such as density currents and solitary waves, do have observable effects on acoustical signals, although substantial variability in sound levels occurs outside such events. Sound propagation model results demonstrated that data from a tall tower, such as the CASES-99 60-m tower, can be used to predict nighttime variations in sound levels at 50 Hz with good success. Predictions from the 60-m tower data were less successful at 150 Hz and higher, probably because of the greater sensitivity at these frequencies to small-scale structure along the propagation path. Regardless of the frequency, typical tethersonde and rawinsonde systems sample the atmosphere too infrequently to allow prediction of many of the strong variations that are present in real data. Therefore, it must be understood that predictions from sonde data, and by implication from numerical weather forecast models, at best provide approximate mean sound levels; they cannot account for the significant, intermittent episodes of depressed and elevated sound levels. These episodes can be important for assessing noise impacts and the detectability of sound sources at long distances. The sensitivity of sound waves to changes in nocturnal boundary layer structure suggests possibilities for acoustic remote sensing modalities that are distinct from sodar. Such schemes could potentially provide, with only ground-based sensors, continuous monitoring of the wind and temperature profiles up to heights of 50– 100 m. In addition to tomographic sensing based on travel time of sound pulses as proposed previously (Greenfield et al. 1974; Chunchuzov et al. 1997), the results of this experiment suggest that the range-dependent sound levels from harmonic wave transmissions may be invertible, particularly at frequencies of 50 Hz

and lower where there is a predictable dependence of sound-energy varations on atmospheric structure. The basic idea is to iteratively perturb the input temperature and wind profiles for the sound propagation model (the parabolic equation model in this paper) until good agreement with the observed sound level versus range curves (such as Figs. 10–15) is obtained. Similar schemes have been used, for example, in ocean acoustics to determine the geological structure of the ocean floor (Rajan et al. 1987). Acknowledgments. We thank S. Burns for his help in accessing the CASES-99 tower data and J. Sun for discussing preliminary results on the three events during IOP 7. We are also grateful to many other CASES-99 participants for the insights they have shared on various occassions, including at the workshops sponsored by W. Bach (U.S. Army Research Office). REFERENCES ANSI, 1999: American National Standard Method for Calculation of the Absorption of Sound by the Atmosphere. ANSI S1.26-1995 (R1999), Acoustical Society of America, 30 pp. Attenborough, K., 1985: Acoustical impedance models for outdoor ground surfaces. J. Sound Vib., 99, 521–544. Becker, G., and A. Gu¨desen, 1999: Passive sensing with acoustics on the battlefield. Appl. Acoust., 59, 149–178. Beranek, L. L., 1988: Acoustical Measurements. American Institute of Physics, 841 pp. Blanc-Benon, P., L. Dallois, and D. Juve´, 2001: Long range sound propagation in a turbulent atmosphere within the parabolic approximation. Acta Acust.–Acust., 87, 659–669. Bronsdon, R. L., and H. Forschner, 1999: A propagation model based on Gaussian beams that accounts for wind and temperation inversions. Noise Control Eng. J., 47, 173–178. Brown, E. H., and F. F. Hall, 1978: Advances in atmospheric acoustics. Rev. Geophys. Space Phys., 16, 47–110. Chunchuzov, I. P., A. I. Otrezov, I. V. Petenko, V. N. Tovchigrechko, A. I. Svertilov, A. L. Fogel, and V. E. Fridman, 1997: Travel time fluctuations of acoustic pulses propagating in the atmospheric boundary layer. Izv. Atmos. Ocean Phys., 3, 324–338. Flatte´, S. M., R. Dashen, W. H. Munk, K. M. Watson, and F. Zachariasen, 1979: Sound Transmission Through a Fluctuating Ocean. Cambridge University Press, 293 pp. Greenfield, R. J., M. Teufel, D. W. Thomson, and R. L. Coulter, 1974: A method for measurement of temperature profiles in inversions from refractive transmission of sound. J. Geophys. Res., 79, 5551–5554. Martens, M. J. M., L. A. M. Heijden, H. H. J. Walthaus, and W. J. J. M. Rens, 1985: Classification of soils based on acoustic impedance, air flow resistivity, and other physical soil parameters. J. Acoust. Soc. Amer., 78, 970–980. Ostashev, V. E., 1997: Acoustics in Moving Inhomogeneous Media. Spon Press, 259 pp. Pierce, A. D., 1981: Acoustics: An Introduction to Its Physical Principles and Applications. McGraw-Hill, 642 pp. ——, 1990: Wave equation for sound in fluids with unsteady inhomogeneous flow. J. Acoust. Soc. Amer., 87, 2292–2299. Poulos, G. S., and Coauthors, 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83, 555–581. Rajan, S. D., J. F. Lynch, and G. V. Frisk, 1987: Perturbative inversion methods for obtaining bottom geoacoustic parameters in shallow water. J. Acoust. Soc. Amer., 82, 998–1017. Salomons, E. M., 1998: Improved Green’s function parabolic equation

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method for atmospheric sound propagation. J. Acoust. Soc. Amer., 104, 100–111. Sun, J., S. Burns, D. Lenschow, and Q. Oosterhuis, 2000: Turbulence intermittency in the stable boundary layer. Preprints, 14th Symp. on Boundary Layer and Turbulence, Aspen, CO, Amer. Meteor. Soc., 329–331. ——, and Coauthors, 2002: Intermittent turbulence associated with a density current passage in the stable boundary layer. Bound.Layer Meteor., 105, 199–219. Welch, P. D., 1967: The use of fast Fourier transform for the esti-

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mation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust., AU-15, 70–73. West, M., K. Gilbert, and R. A. Sack, 1992: A tutorial on the parabolic equation (PE) model used for long range sound propagation in the atmosphere. Appl. Acoust., 37, 31–49. Wilson, D. K., 1997: Simple, relaxational models for the acoustical properties of porous media. Appl. Acoust., 50, 171–188. ——, A. Ziemann, V. E. Ostashev, and A. G. Voronovich, 2001: An overview of acoustic travel-time tomography in the atmosphere and its potential applications. Acustica, 87, 721–730.