Deep-water ambient sound over the Atlantis II seamounts in the Northwest Atlantic^a) Free

Ambient underwater sound is an essential environmental characteristic for a number of species of marine fauna and is often a limiting factor for underwater communication and performance of biological and man-made sonars.^1–4 A large and expanding body of experimental and theoretical research has been devoted to characterization and understanding of dominant noise sources, noise statistics, spectra of ambient underwater sound in various geographical regions, seasonal variations and multi-year trends in noise spectra, and dependence of underwater noise on wind and precipitation. Reviews of such work can be found in Refs. 1 and 3–9.

Less is known about variability of ambient sound and its intensity on subseasonal time scales and submesoscale spatial scales and a connection between the ambient sound variability and ocean dynamics. An assessment of such variability is necessary to characterize predictability of the statistical properties and spectra of ambient sound, reliably model sonar performance, and develop optimal signal processing algorithms. Understanding ambient sound variability on such scales is also important in the context of noise interferometry, where diffuse ambient noise is used as a probing signal for passive ocean acoustic thermometry,^10–12 tomography,^13,14 and seabed characterization.¹⁵ Variability of ambient sound intensity and directionality often controls the optimal noise averaging time and the very possibility of application of noise interferometry to passive remote sensing of the ocean.^10,16

In this paper, we experimentally investigate temporal and spatial variability and statistical properties of deep-water ambient sound intensity in an area with very strong ocean dynamics, which is dominated by the Gulf Stream (GS) and its interactions with complex bathymetry.¹⁷ Preliminary results of this research were presented in Ref. 18. The data analyzed here were acquired in April–June 2023 by a small noise interferometry network deployed in the vicinity of the Atlantis II Seamounts (Fig. 1) as a part of the 2023 New England Seamounts Acoustic (NESMA) Pilot experiment. The multi-institutional NESMA Pilot experiment was organized by the Office of Naval Research (ONR).

This paper is organized as follows. The site of the experiment and acoustic data acquisition are described in Sec. II. Various ambient sound spectra observed in the experiment are presented in Sec. III. Sections IV and V discuss statistical distribution of ambient sound intensity and variability of intensity level in various bands. Systematic changes of ambient sound spectra with time of the day and the receiver position are discussed in Sec. VI. Dependence of the ambient sound intensity on atmospheric conditions and position of the GS is established in Sec. VII. Section VIII summarizes our findings.

The four acoustic recorders used for this experiment were Moored Autonomous acoustic Noise Recorders (MANRs) developed at the Naval Postgraduate School in Monterey, CA. The Moored Autonomous acoustic Noise Recorder (MANR) depths ranged from 2573 to 4443 m with horizontal spacing from just over 5–18 km. The location of the New England Seamounts in relation to the East Coast of the United States is illustrated in Fig. 1(a). The locations of the MANRs in the vicinity of the New England Seamounts are illustrated in Fig. 1(b). MANRs 1 and 2 were located on the slopes of the seamounts at water depths 2573 and 2994 m, respectively. MANRs 3 and 4 were located on slight knolls on the bottom of the ocean at water depths 4067 and 4443 m, respectively. The position of each noise recorder was N 38° 29.342′ W 63° 02.113′ (MANR 1), N 38° 25.627′ W 62° 51.139′ (MANR 2), N 38° 29.224′ W 62° 55.364′ (MANR 3), and N 38° 29.367′ W 62° 51.613′ (MANR 4). Selection of receiver location was conducted using the General Bathymetric Chart of the Ocean (GEBCO)¹⁹ gridded bathymetry data with 25 m spatial resolution, seasonally predicted sound speed profiles (SSPs) derived from the U.S. Navy's Generalized Digital Environmental model (GDEM),²⁰ and the Bellhop²¹ sound propagation model. Due to deployment and recovery schedules, MANRs 1 and 2 spent 55 days total collecting data and MANR 4 spent 60 days collecting data. However, all MANRs were simultaneously in the water for 52 days.

Each MANR had a single hydrophone and a Microsemi (San Jose, CA) SA.45s chip-scale atomic clock for precise timing. The electronics and power supply were housed in a full ocean depth–rated titanium pressure vessel. To minimize hydrophone movement for the noise interferometry portion of the experiment, it was necessary for each MANR to have a short tether as illustrated in Fig. 1(c). No signs of strumming were detected in the noise data, and the tether did not appear to affect acoustic measurements. Short tethers resulted in hydrophones which were approximately 4 m above the bottom of the ocean at their respective locations, which added a level of complexity to the experiment design. Each MANR was lowered by winch to the desired location to ensure precise placement in a region with significant bottom slope variability on the seamount flanks, as each MANR was required to be placed within 200 m of the planned location to ensure propagation along reliable acoustic paths in an environment with an upward refracting sound speed profile, also for the concurrent noise interferometry experiment. The final MANR locations were surveyed and found to be within 30 m of their planned locations. A mooring diagram of a typical MANR is presented in Fig. 1(c). Of the four MANRs deployed for this experiment, one failed to collect acoustic data. This paper is based on the data acquired by MANRs 1, 2, and 4.

Data from each MANR were recorded continuously as standard .wav files at an 8 kHz sampling rate. Data were broken up into files as small as 56.25 s for processing and for brevity will be referred to as “one-minute” measurement periods. Most of the data analysis was conducted in the frequency domain using the hybrid millidecade,²³ decidecade, and third-octave frequency bands. During the MANR deployment, there were many additional experiments ongoing simultaneously as part of the NESMA Pilot. Several of these experiments employed controlled research sound sources, which included signal underwater sound (SUS) charges deployed by the University of Rhode Island and an airgun operated by the Woods Hole Oceanographic Institute. Since the addition of SUS and airgun sources are not typically considered part of an ambient underwater soundscape, data logs were used to verify the times these systems were active, and those time blocks were excluded from the data analyzed in this study.

Power spectral density (PSD) was analyzed for all three MANRs for the entire 52 days they were all in the water. For each receiver, the PSD presented was calculated in 1 m non-overlapping observation periods. Additionally, the PSD was calculated using the hybrid millidecade method, which produces 1 Hz resolution up to 455 Hz and then millidecade frequency bands above 455 Hz.²³ The PSD figures in this paper are illustrated using a linear interpolation between each of the band center frequencies.

The PSD in this section illustrates the mean spectra along with the temporal and spatial variability. As a representation of temporal variability, Fig. 2(a) illustrates power spectral densities (PSDs) from MANR 1 segmented into 6 h non-overlapping blocks of time for the duration of the deployment, omitting only the times that SUS and airgun sources were active. This approach retained 97% of the original data. The variability between any two blocks of time was up to 20 dB, depending on the frequency selected. The three bold lines on Fig. 2(a) illustrate the mean PSD (black), the predicted PSD at the minimum observed wind speed of 2.8 m/s (red) and the predicted PSD at the mean observed wind speed of 8.8 m/s (blue). The observed wind data were from the National Oceanic and Atmospheric Association (NOAA) satellite observations while the wind speed plots are based on the Applied Physics Lab–University of Washington (APL-UW) model of wind-generated noise²⁴ and both will be discussed further in Sec. VII. In Fig. 2(b), the mean PSD and the 25th, 50th, 75th, and 97th percentiles are shown in different colors. The solid, dashed-dotted, and dashed lines in the figure refer to the PSDs obtained at MANR 1, MANR 2, and MANR 4, respectively.

With finer temporal resolution than what is illustrated in Fig. 2(b), MANR PSDs were also used to identify a variety of specific acoustic events during the experiment. These events included reception of broadband signals from local shipping near the MANRs and signals transmitted from SIO tomographic moorings. The PSDs were also used for discerning flow noise around the MANRs and hydrophones, which was beneficial for corroborating and extending direct measurements of exceptionally strong near-bottom flows around the Atlantis II Seamounts.^18,26

The PSDs in Figs. 2(a) and 2(b) also indicate a dip in the spectra at approximately 2.2 kHz. Though the reason for this is unknown, several occurrences of a similar dip in spectra have been reported in the literature. In each of these cases, there was no additional analysis on the cause of the spectra dip. One example of this 2.2 kHz dip in spectra was reported in data collected at the Challenger Deep in the Marianas Trench where the 90th percentile contour in the spectra showed this effect.²⁷ Another example was in an ambient noise analysis that investigated locations and the dip was observed in both the East China Sea ambient sound and the tropical biological background.⁵ The dip is observed consistently in our measurements on all MANRs and under various conditions. Stability of the dip suggests that it may be related to the receiver itself rather than noise sources or sound propagation conditions. In particular, the spectrum distortion could be caused by sound scattering from the large syntactic foam float [Fig. 1(c)].²⁸ Though the analysis of this spectral feature is outside the scope of this paper, the presence of the dip is a noteworthy characteristic.

Continuous observations of ambient sound on three stationary receivers for nearly 2 months provide a large set of 1 min measurements to investigate ambient sound statistics. A common assumption in an underwater environment is that the ambient sound is random and has a normal (Gaussian) statistical distribution,^1,4,29–31 which implies Rayleigh distribution of acoustic pressure amplitude and exponential distribution of noise intensity.²⁵ Most sonar performance predictions and signal processing techniques assume a Gaussian noise background.^32,33 Based on the central limit theorem, a Gaussian statistical distribution is expected to arise in a given frequency band when a large number of independent sound sources make comparable contributions to the ambient acoustic field. Deviations from the normal distribution are expected to occur when there are dominant localized sound sources or the number of contributing independent sources is small, e.g., due to local shipping in shallow water,^34,35 or when statistics of random sources change during the data acquisition process, e.g., for long observation periods encompassing different seasons.^1,9 Deviations from the normal distribution of ambient noise are also encountered when intensity is calculated from data in short time windows on the order of seconds.³⁶ However, with time windows of tens of seconds or longer, ambient sound is expected to have a normal distribution at deep-water locations with light local shipping,^32,36 such as around the Atlantis II Seamounts.

Several methods are employed in this section to examine the statistical properties of intensity of ambient sound recorded during the NESMA experiment and compare them to those of the expected exponential distribution. These methods include analysis calculation of the scintillation index (SI), estimation of the cumulative distribution function (CDF) of intensity in various frequency bands, comparison of sample cumulative distribution functions (CDFs) of data to the theoretically expected CDFs, and application of the Kolmogorov–Smirnov (KS) test to evaluate the consistency between the intensity data and its expected statistical distribution.

SI was calculated for MANR 1, 2, and 4 using decidecade frequency bands using 1 min time intervals for the entire 52 day deployment apart from the times that SUS or airgun sources were active. As a result, over 97% of the original data were preserved for statistical analysis. The SI was evaluated for all MANRs in all decidecade bands and is illustrated in Fig. 3(a). There is a large spike in the SI for MANR 1 and 4 centered around the 794 Hz frequency bin, which is attributed to the M71 low-frequency towed source (with peak frequency around 803 Hz) used during the NESMA Pilot experiment. Sound radiated by this source was also observed as an obvious large spike in the mean PSD in Fig. 2(b). The transmission schedule of the M71 and ITC-2015 towed sources was frequent enough that it was not conducive to removing that data for this analysis, as it would have led to a significant reduction in the usable data by over 20%. Outside of that 794 Hz bin peak, most of the frequency range shows low single-digit SI for all three MANRs. This is indicative of amplitude distributions that differ from the Rayleigh distribution and tend to have heavier tails, i.e., higher probabilities of amplitudes deviating far from the mean. The moderately elevated SI values in Fig. 3(a) can potentially result from the intermittent sound sources employed in the NESMA experiment, intermittent local shipping, or from naturally occurring environmental factors, such as changing weather.

The tails of the statistical distribution of sound intensity are revealed by comparing the complementary CDFs of measured intensity to that of the expected exponential distribution. Complementary CDF is defined as 1- CDF(X) and equals the probability of intensity I exceeding the value X. For the exponential distribution of intensity, 1– CDF(I) = exp(– I/⟨I⟩), where stands for the mean intensity. Complementary CDFs of the sound intensity measured at different locations are illustrated in Fig. 3(b) for 2 decidecade bands. The bands centered at 794 and 2512 Hz were chosen because they had some of the highest and lowest SI values, respectively, and were considered indicative of the range of statistical distributions.

In all the cases shown in Fig. 3(b), sound intensities above about seven average intensities are encountered orders of magnitude more frequently than expected for the exponential distribution. It should be noted, however, that just a few 1 mine samples make up the large-intensity events in the tails. Although Fig. 3(b) is truncated at I/⟨I⟩ = 30 for all MANRs, the maximum observed I/⟨I⟩ values for the 794 Hz data exceeded 1000 for MANR 4 and 2000 for MANR 1. The rare high-intensity events contribute to the previously noted elevated difference between the average and median PSDs and large SI values. These are attributed to the M71 towed source. In the 2512 Hz frequency bin, the maximum observed values of I/⟨I⟩ are about 150 for all MANRs. This is indicative of heavy probability distribution tails, even in the frequency bins with the lowest SI. In addition to the heavy tails, a significant deviation from the exponential distribution can be seen in Fig. 3(b) at moderate values of I/⟨I⟩.

With a finite dataset, apparent deviations of the observed frequency of occurrence from the event probability cannot by itself prove or disprove applicability of a particular probability distribution. We used the KS test³⁹ to rigorously determine whether MANR data are consistent with the exponential distribution of sound intensity. The KS test for the exponential distribution with unknown mean was developed by Lilliefors.³⁹ The test is based on comparing the maximum of the absolute value of the difference between the sample CDF and the exponential distribution CDF (or, equivalently, of the difference in complementary CDFs) to a pre-computed threshold. The threshold value depends on the number N of samples and the statistical significance of the conclusion. For the exponential distribution hypothesis to be rejected at the 99% confidence level, the CDF discrepancy should exceed 1.25 N^−½ when the dataset contains N > 30 samples.³⁹ The thresholds are progressively lower for lower confidence levels.

Figure 3(c) illustrates application of the KS test to the complementary CDFs shown in Fig. 3(b). Note that the CDF discrepancy exceeds the 99% threshold in both frequency bands and for all MANRs. However, the CDF discrepancy exceeds the threshold, not in the distribution tails, but rather at moderate values of relative intensity I/⟨I⟩ ∼ 1–3. Although the tails, which are prominent in the complementary CDF plot in Fig. 3(b), did not fit the expected tails of an exponential distribution, they were not the main culprit in the context of the KS test. This is due to the need for an extremely large number of samples to meaningfully constrain the probability of rare events in the large-intensity tail of the distribution.

The KS testing was extended to all 38 decidecade bands from 1 Hz to 4 kHz, across three MANRs. The exponential distribution hypothesis was rejected at the 99% confidence level in each of the 114 intensity datasets. This is illustrated by the solid lines in Fig. 3(d) in which the excess CDF discrepancy was calculated for each MANR.

Deviations from the exponential distribution of acoustic intensity are often attributed to environmental variability that changes the mean intensity.⁴⁰ The primary environmental factor controlling mean intensity of ambient sound at frequences above a few hundred Hz is wind speed, which will be discussed further in Sec. VII. To check whether the non-exponential distribution resulted from the wind speed variations, the KS test was applied to the smaller datasets corresponding to the same wind speed (within 1 m/s). The wind speed data and grouping of acoustic measurements are described in detail in Sec. VII A. Results of the KS test showed that grouping the data by wind speed in 1 m/s intervals did not vastly change the maximum CDF discrepancy and again resulted in rejecting the exponential distribution hypothesis with the maximum CDF discrepancies still occurring at relative intensities of approximately 1–3. This is illustrated in Fig. 3(d) which presents the excess CDF discrepancy for the most populated wind speed bin of 8–9 m/s as dashed lines across all decidecade frequency bins. The excess CDF discrepancy is defined here as the difference between the maximum CDF discrepancy and the KS test threshold for the appropriate number of samples.

With the intensity level being a logarithmic measure of intensity, changes in the spectral level characterize relative intensity variations. These are better suited for comparison of ambient sound intensity variability in different frequency bands than the absolute changes, when spectral density changes by orders of magnitude between infrasonic and mid-frequencies [Fig. 2(b)] as well as between various observation periods [Fig. 2(a)]. Statistics of spectral levels differ from intensity statistics and may provide insights into the underwater ambient acoustic environment and the nature of noise sources.^1,41,42 Because of its significance in signal processing and communication theory, variability of acoustic spectral levels has been extensively studied. A review of relevant theoretical and experimental work in underwater acoustics can be found in Refs. 1, 4, and 43.

This section focuses on the root mean square (RMS) variation of the observed spectral levels of ambient sound. Note that variations of the spectral level are independent of the reference pressure chosen to calculate the spectral level but generally retain dependence on the frequency band in which the spectral level was calculated. As in Sec. III, ambient sound spectra were calculated for each MANR in non-overlapping time windows of 1 min duration. Spectral levels were calculated in the hybrid millidecade²³ bands and, for a more direct comparison with previously published experimental results, third-octave frequency bands. Standard deviation σ of band intensity levels was calculated for the entire 52-day time series for each receiver. The results are illustrated in Fig. 4.

When hybrid millidecade²³ bands are used, σ varies from just below 2 dB to almost 8 dB [Fig. 4(a)]. Very little difference is found between different receivers except below 10 Hz. Between 10 and 455 Hz, where bandwidth of hybrid millidecade²³ bands switches from 1 Hz to millidecade, σ is slightly above 5.6 dB, which is the standard deviation of intensity level when noise has Rayleigh-distributed pressure amplitude.¹ Exceedance of the 5.6 dB by σ is interpreted as a manifestation of non-Rayleigh amplitude distribution in measurements that was established in Sec. IV. After a sharp drop around 455 Hz, σ decreases with frequency and experiences stronger fluctuations. At least some of these fluctuations, e.g., around 1, 2, and 3 kHz are due to research sound sources, which were discussed in Sec. III. The decreasing trend in σ above 455 Hz is associated with increasing bandwidth of millidecade bands. It is consistent, at least qualitatively, with the predicted decrease in spectral level variability when the product of the bandwidth and noise correlation increases.⁴³ 

The strongest variations of the intensity level and the largest differences between receivers occur below 10 Hz in both Figs. 4(a) and 4(b). In this band, ambient sound is likely due to fewer dominant sources than at higher frequencies. The reasons why variability at MANR 2 is higher than at the other receivers are not clear but may be related to partial bathymetric shielding of MANR 1 and MANR 4 from the closest shipping lane to the northwest of the experiment site [Fig. 1(b)] or to the highly variable flow noise observed at MANR 2.²⁶ 

Comparison of Figs. 4(a) and 4(b) demonstrates the strong effect of the bandwidth, in which broadband sound is analyzed, on the fluctuations of the spectral levels. Figure 4(b) shows the results of data processing in 38 third-octave bands with central frequencies f_n = 2^(n−1)/3 f₁, n = 1, 2, …, and f₁ = 1 Hz. The third-octave bands are wider than the hybrid millidecade²¹ bands at f > 3 Hz. With the wider bands, σ in Fig. 4(b) is smaller than in Fig. 4(a) and tends to decrease gradually with frequency above 4 Hz and is between 1 and 2 dB above 40 Hz.

Bannister et al.⁴¹ investigated variability of noise spectral levels in the South Fiji Basin in the South Pacific. The water depth at their experiment site was approximately 4000 m. Spectral levels were found in third-octave frequency bands using 1 min time windows, similar to our results shown in Fig. 4(b). The data were acquired in the 10–500 Hz frequency band within a relatively short 7 day period and further split into periods with stronger and lighter winds and two levels of shipping activity.⁴¹ Their low-frequency results for more active shipping periods and the results at frequencies above 200 Hz in all regimes are illustrated in Fig. 4. Overall, the trends of the frequency dependence and the numerical values of σ in the short-term data (see Fig. 5 in Ref. 41) are consistent with our results in Fig. 4(b). The most significant difference is that the low-frequency limit of σ ∼ 6 dB in the shipping-dominated regime in the short-term data⁴¹ is reached at 10 Hz rather than at 4 Hz in our longer-term analysis, as illustrated in Fig. 4(b).

The variability of the spectrum level of ambient sound at deep-water locations with light local shipping, such as our NESMA site, differs substantially from the variability in shallow water, straits, and channels with significant or heavy shipping. We illustrate this using the data acquired in 2017–2020 by the Atlantic Deepwater Ecosystem Observatory Network (ADEON).^35,44 Of the various ADEON sites, we chose the Virginia Inter-Canyon (VAC) site which was equipped with a GeoSpectrum Technologies M36-V35-100 (Nova Scotia, Canada) omnidirectional hydrophone, located at N 37° 14.77′ W 74° 30.79′ and at a depth of 212 m.^35,44 This site was located close to the edge of the continental shelf in the vicinity of the GS and was the site closest to the New England Seamounts.

Magenta lines in Figs. 4(a) and 4(b) show the RMS values σ of the spectral levels in a 2 month period in May–July 2020 at the ADEON VAC site. When ambient sound is analyzed in hybrid millidecade frequency bands [Fig. 4(a)], σ at the VAC site has a sharp drop around 415 Hz followed by a gradual decrease with frequency, as at the MANRs. These features are due to the bandwidth effects discussed above, which are not site-specific. Note that the drop in σ between 400 Hz and 4 kHz is several times smaller at the VAC site than at the MANRs [Fig. 4(a)]. Hypothetically, the distinct rates of the σ decrease with frequency reflect the qualitative difference in the sound propagation in deep and shallow water. At frequencies of 4–500 Hz, spectral level variability is much larger in shallow water than it is over the Atlantis II Seamounts or is expected when sound has Rayleigh-distributed pressure amplitude.¹ This is likely due to effects of local shipping. When spectral level variability is analyzed in the wider third-octave frequency bands [Fig. 4(b)], σ remains higher at the VAC site than on any of the MANRs from 4 Hz to 4 kHz. Instead of the steady decrease in the third-octave σ with frequency to below 2 dB at f > 40 Hz in deep water, at the VAC site σ approaches the 5.6 dB level of Rayleigh-distributed pressure amplitude around f = 10 Hz and oscillates around that value through 4 kHz. When comparing MANR and ADEON data, observed spectral level variability at these shallow-water (∼200 m) and deep-water (∼3000–4500 m) sites is distinct with f > 10 Hz.

Concurrent measurements of ambient sound at three horizontally and vertically separated, near-identical MANRs offer some insights into spatial variability of ambient sound spectra. For various MANR combinations, Fig. 5(a) shows the difference between the average ambient sound spectra measured by two MANRs. The spectra were calculated in decidecade bands. When the spectra are calculated in the narrower hybrid millidecade²³ bands, as in Fig. 2, the trends remain the same but stronger and less regular variability is observed with up to twice as many decibels compared to Fig. 5(a). In contrast to the results of the Spice Experiment (SPICEX) in the North Pacific, where a steady decrease in the mean PSD of ambient sound with depth from 500 m to below 4200 m was reported at frequencies of 50, 150, and 350 Hz,⁴⁵ the mean PSD on the deepest MANR, MANR #4, can be appreciably higher or lower, depending on frequency, than on the shallower MANRs #1 and #2 [see Fig. 5(a)].

To provide context for interpretation of the spatial variability data, consider a basic model of ambient sound in range-independent ocean due to random sources uniformly distributed on the ocean surface. Then, sound spectra are independent of horizontal coordinates. Sound absorption leads to frequency-dependent variation of ambient sound spectra with depth. Neglecting bottom reflections, in the model of the ocean as a homogeneous water column with sound sources as vertical dipoles uniformly distributed on the ocean surface,²⁴ it can be shown that the effect of sound absorption in water on ambient sound spectral density is the same as for a compact source at the distance of two ocean depths from the receiver. This simple relation is valid as long as attenuation is weak (within several decibels). The latter condition is met throughout the frequency band considered in this paper. The purple line in Fig. 5(a) illustrates the expected attenuation-induced difference in the ambient sound spectral levels at the shallowest (MANR 1) and the deepest (MANR 4) receivers, which were separated in depth by approximately 2000 m. The underlying calculation employed the frequency-dependent attenuation coefficient from Ref. 34. The observed frequency dependence of the spatial variation of the measured spectra in Fig. 5(a) does not follow the predicted depth-dependence and is significantly stronger.

The basic ambient sound model does not account for the water column stratification. Sound speed profiles (SSPs) measured within 40 km from the MANR deployment site are shown in Fig. 5(b). Near-surface sound speed was less than the sound speed at MANR 4 but was likely to exceed the sound speeds at MANRs 1 and 2. For the near-bottom receivers, contributions of distant sound sources into the observed ambient sound are expected to be suppressed, except for very low frequencies, due to surface and especially bottom losses. Sound refraction due to depth-dependence of the sound speed contributes to changes in the ambient sound intensity with depth. These changes in the ambient sound spectral level are frequency-independent,⁴⁶ at least in the ray approximation, and cannot help to explain the difference between the ambient sound spectra observed on different MANRs [Fig. 5(a)]. Therefore, the observed spatial variability of the average spectra is likely due to a non-uniform distribution of ambient sound sources, bathymetric shadowing due to the seamounts, and sound reflection by the seafloor.

The observed trends in Fig. 5(a) can be subdivided into two frequency regimes. The first frequency range is below 2 kHz, where the spatial variability of the spectra is stronger and has a more complex frequency dependence. In part, this variability is due to research sound sources employed in the NESMA experiment. The three MANRs were at different ranges from these sources and experienced different bathymetric shadowing of the sources by the Atlantis II Seamounts [Fig. 1(b)]. Specifically, the two largest spikes are attributed to the M71 low-frequency towed source, which strongly contributed to the 1 and 1.26 kHz decidecade bins. Noise from local shipping and a shipping lane to the northwest of the site and its partial and unequal bathymetric shadowing contributed to the spectral differences below ∼800 Hz in Fig. 5(a). Different bottom reflectivity on the steep flanks of the seamounts, where MANRs 1 and 2 were located, and at the deepest MANR 4 may have also contributed to the spectral differences.

The second frequency regime is from 2 to 4 kHz. This is a frequency range that is dominated by ambient sound generated at the ocean surface. The PSL difference between the MANR pairs is minimal and is less than 0.5 dB at these frequencies. This suggests that natural sources of ocean surface noise approach uniformity after 52 day averaging and may also reflect decreased role of bottom reflection at higher frequencies. The difference between MANR 1 and MANR 2 is shown to be as large or larger than their differences from the MANR 4 spectrum [Fig. 5(a)] and thus it appears that bathymetric shadowing has a stronger effect than the expected decrease in ambient sound intensity below the critical depth,¹ where the sound speed equals its value at the ocean surface.

To examine the extent of ambient sound diurnal variability in the vicinity of the New England Seamounts, mean and median PSD values were evaluated based on the hour of the day. This was done for all MANRs and the results for MANR 1 are illustrated in Fig. 6(a). Additionally, RMS variations of the intensity level were also analyzed based on the hour of the day with the results for MANR 1 illustrated in Fig. 6(b).

The data illustrated in Fig. 6(a) are based on the mean PSD for MANR 1 and the temporal scale is in daily UTC time. During the time of deployment, sunrise was at approximately at 0900 UTC and sunset at 2300 UTC. Peaks in spectra occurred from approximately 0800 UTC and 2000–2100 UTC, which are approximately 1 h before sunrise and 2–3 h before sunset. The mean PSD varied from 2.9 to 4.6 dB above the surrounding times of day. Remarkably, PSD increase occurred simultaneously in a wide frequency band encompassing the 1–4 kHz range. Similarly, RMS variation of the intensity level illustrated in Fig. 6(b) showed a slight rise at the same hours of the day of approximately 0.2 dB above the surrounding times of day.

A periodic increase in PSD, such as what was observed on the MANRs, could take many forms. These include occurrence at a stationary time, as observed by Wenz,^1,47 seasonal occurrence,⁴⁸ it can follow the tidal cycle, or occur at or around sunrise and sunset.⁴⁹ The increased PSD that was observed on the MANRs is considered a relatively common time of day for an increase in spectra due to fish chorusing.^49,50 However, long-term spectral analysis of the MANR ambient sound data for biological sound sources using the Triton⁵¹ software failed to identify any fish chorusing while revealing abundant whale and fish sounds. The cause for the increased PSD before sunrise and sunset has yet to be determined.

The counterpart of Fig. 6(a) for median PSD (not shown) exhibits the same trends as the mean values in Fig. 6(a) only at slightly lower levels. At those same times of the day as in Fig. 6(a), the median spectra are increased by 1.1–1.4 dB above the surrounding times. Because the rise in spectra is present in the median values, it is not caused by infrequent, high amplitude broadband events. Rather, it is due to an overall increase in the spectra due to more persistent and continuous sources at these times of day. In contrast, the spikes in PSD below 1 kHz in Fig. 6(a) are only present on the mean PSD plot. Those are not present on the median PSD plot and are attributed to the previously discussed M71 and ITC-2015 towed sound sources.

The results presented in Fig. 6 are common for all MANRs, with PSD increases occurring at the same times of the day on different MANRs. However, the PSD variations were slightly more prominent on MANR 1 by approximately 0.5 dB higher in the mean PSD. In addition to the diurnal variations of the spectra, which are likely to be of biological origin, temporal variations were also found on longer time scales. These changes are driven by environmental factors and are discussed in Sec. VII.

At frequencies above 400 Hz, wind noise is a dominant source of ambient sound^6,24 and varying surface wind speeds affect the ambient noise spectra.^24,52 This section analyzes measured ambient sound spectra that are grouped according to the surface wind speeds at the receiver locations. NOAA blended surface wind data at 10 m elevation with 6 h temporal resolution and 0.25° spatial resolution was used and downloaded from the NOAA ERDDAP website.^53–55 Occurrence of different wind speed at all MANRs is illustrated by a histogram in Fig. 7(a). The most common wind speed during the MANR deployment was from 8 to 9 m/s with a minimum observed wind speed of 2.8 m/s and a maximum observed wind speed of 20.9 m/s. The PSD in this section takes the mean of each of the MANRs and matches the 6 h resolution bin for surface wind speed for the same period of time.

Five evenly spaced wind bands from 3 to 16 m/s were plotted with error bars in Fig. 7(c). The error bars were calculated using the sample variance for every tenth hybrid millidecade²³ frequency bin. Overall, the data show very distinct ambient sound spectra associated with each wind speed apart from the 15–16 m/s wind bin. However, it should be noted that even though the error bars are small on the 15–16 m/s band, it was populated by only six data blocks (6 h duration).during the deployment while the other wind bands had from 33 to 156 data blocks (6 h duration).

The most populated wind speed bin was 8–9 m/s with 196 data blocks (6 h duration). Figure 7(d) illustrates the difference in spectra between each of the previous PSD wind speed bins from 3 to 16 m/s and the most populated bin. Figure 7(d) shows that, as expected,^6,24,52 from approximately 400 Hz to 1 kHz, PSD steadily increases with wind speed. The irregular behavior of the PSD differences around 800 Hz is due to the occasional presence of towed sound sources discussed above and should be ignored. In qualitative agreement with the APL-UW model equation, the change in the ambient sound spectral level with wind is nearly frequency-independent above 1 kHz [Fig. 7(d)]. However, the rate of increase with the wind speed differs from the APL-UW model as does the PSD frequency dependence. A longer time series of observations with more acoustic observations in each wind band and/or higher temporal resolution in the wind speed data would be needed to reliably quantify the wind dependence at various frequencies.

Overall, wind speed was found to be the single most important parameter determining the spectral level of ambient sound at MANRs, with the wind-induced variations exceeding 10 dB in the 1–4 kHz frequency range.

MANRs were deployed in an area with a very strong mesoscale variability that is dominated by the GS and its interaction with the New England Seamounts. Proximity of the observation point to the GS may affect ambient sound through the changes in sound propagation conditions and in the intensity and distribution of the ambient sound sources at the ocean surface.

The GS is a composite system of currents in the Atlantic Ocean that begins in the Gulf of Mexico and moves towards the North Atlantic Ocean. It is usually warmer than its surrounding water and forms the boundary between the Sargasso Sea and the slope water. It is well known for its meandering activity where the sudden change in the pattern of meandering is a permanent fixture of the GS, where the shape is also influenced by various bathymetric features, such as the New England Seamounts.^56,57

As a consequence of the continuously changing and meandering GS, there are many different methods for defining the boundaries of the GS. A few common methods include following the 25 cm sea surface height (SSH) contour,⁵⁸ defining the path of maximum current,⁵⁹ or determining the northern edge of the current, which is a location marked by a sharp temperature front that separates the GS waters from the slope sea to the north and is typically referred to as the Gulf Stream North Wall (GSNW). There are several approaches used to define the GSNW, which include the 15 °C isotherm at 200 m, the 12 °C isotherm at 400 m, the 17 °C isotherm at 200 m, frontal analysis of sea surface temperature,^59–61 or sea surface temperature (SST) isotherms from 15 °C to 18 °C.^62,63 The difficulty of defining the GS and GSNW increases near the New England Seamounts due to the presence of mesoscale eddies in that region.⁶⁴ For the purposes of this study, the path of maximum current as defined by the highest SST^59-61 was chosen as a simple means to define the GS sea surface temperature front (GSF). The same NOAA blended surface wind data at 10 m elevation was used as in Sec. VII A. NOAA advanced very high-resolution radiometer (AVHRR) optimum interpolation sea surface temperature (OISST) was also used for this analysis. AVHRR contains 0.25° spatial resolution and daily temporal resolution.^54,65

Figure 8(a) illustrates the SST on May 17, 2023, where each black line represents a 1° temperature gradient. The magenta circles show the deployment location of the four MANRs. As this figure illustrates, the GS tends to meander and evolve in time. This makes the GS difficult to track and establish the distance of the MANRs from a part of the GS at any given occasion. For this investigation, the distance of the main flow of the GS from the MANRs was calculated by using the minimum distance from the MANRs to the line of maximum SST as illustrated by the red line in Fig. 8(a). These distances were separated into three categories, which were distances of less than 25, 25–50, and more than 50 km, respectively.

To isolate the effects of ocean variability on ambient sound spectra from the effects of atmospheric conditions, observations were compared within groups corresponding to the same wind speed. The same 1 m/s wind speed bands were used as in Sec. VII A. The effect of ocean variability was analyzed only for winds between 6 and 11 m/s, for which each wind speed band was sufficiently populated for distinctly different GS positions. Figure 8(b) compares the mean PSD for all times when the wind was reported between 7 and 8 m/s when the GSF was less than 25 km (dark blue) and greater than 50 km (light blue). This plot is indicative of results for all wind speeds in that all showed the same trend when comparing PSD recorded by MANRs when the GS was near and far. The data show that given the same surface wind conditions, the PSD was greater when the MANRs were closer to the GSF as compared to when the GSF was much farther north. This dependence was present over all frequencies but was particularly noticeable from 1 to 4 kHz, which is typically dominated by wind and environmental noise.

Figure 8(c) expands further on the comparison of varying PSDs with varying distance to the GSF. This figure presents the difference (in decibels) in PSD by subtracting the PSD when the GS is farther than 50 km from the PSD when the GS is closer than 25 km. This is done at the five wind speeds in 1 m/s bands from 6 to 11 m/s. At all frequencies, but especially in the surface noise-dominated band of 1–4 kHz, the mean PSD is greater when the GSF is closer to the MANRs, even with similar wind conditions. It is illustrated in Fig. 8(c) that the PSD relationship in the surface noise-dominated regime of 1–4 kHz has a steadily increasing relationship based on wind speed.

In all cases, the mean PSD of the middle regime of 25–50 km was in between the near (<25 km) and far (>50 km) distance bins. It was rarely exactly in the middle of the two mean PSDs. Rather, the mean PSD could be found anywhere between the near and far regimes. This is likely due to the difficulty of precisely determining an exact distance with a GS that meanders and constantly evolves with time. However, by both quantitative and qualitative analysis of the SST, the two main distance bins of less than 25 km and greater than 50 km were recognizably and distinctly different at distance regimes from the GSF that were easy to differentiate in an experimental setting. Though the GSF did cross over the MANRs at the beginning of the deployment, at no time did the GSNW 16 °C temperature gradient cross to the south of the MANRs. Therefore, there are no data to compare PSD and wind speed in the colder water north of the GSNW.

We attribute the robust, broadband ambient sound intensity increase caused by the GSF proximity to the effect of the GS currents on the sources of the surface-generated ambient sound. The speed of surface currents in the GS is comparable to that of wind-generated surface gravity waves. The surface currents and their horizontal gradients refract wind waves, modulate their spectra, and arguably contribute to wave breaking, thus enhancing ambient sound generation. The 25 km distance from the GS axis, around which the currents are near-maximum, equals 5–10 MANR depths and is comparable to the expected dimensions of the ocean surface area that effectively contributes to the surface-generated noise at the receivers. This is consistent with the hypothesis of the enhancement of locally generated surface noise by the GS currents.

The alternative mechanisms of ambient sound enhancement, due to change in the sound propagation conditions, appear less likely because MANRs stayed in the warmer GS and Sargasso Sea waters and outside the Sound Fixing and Ranging channel and experienced only moderate changes in the SSP during the deployment.

Spatial and temporal variability of ambient sound at deep, near-bottom receivers has been investigated in a 13-octave frequency band from 0.5 to 4000 Hz in a bathymetrically complex area of the northwest Atlantic near the GS.

The spatial variability of ambient sound spectra appears to be controlled by bathymetric shadowing, nonuniform distribution of the sound sources on the sea surface, and possibly by the seafloor properties near the receivers rather than water or receiver depth.

At each receiver, the RMS variation of spectral levels decreases with frequency from about 6 dB at infrasonic frequencies below 10 Hz to about 2 or 1 dB around 4 kHz in, respectively, hybrid millidecade²³ or wider third-octave frequency bands.

Observed statistical distributions of ambient sound intensity exhibit heavy high-intensity tails. The data do not support the common assumption of normally distributed ambient sound in deep water. In fact, rigorous statistical analysis of ambient sound intensity in decidecade frequency bands rejects the hypothesis of an exponential distribution of the ambient sound intensity (and, hence, of normal distribution of the acoustic pressure) with 99% statistical significance.

At frequencies above 800–1000 Hz, elevated levels of ambient sound intensity and intensity variations were found 1 h before sunrise and 2–3 h before sunset suggesting contributions of marine fauna to ambient sound, while longer-term variability correlates with the wind speed and changes in the GS position relative to the moorings. A robust, broadband increase in ambient sound intensity of up to 10 dB, depending on wind speed, was found when the GS approached the receivers. The increase in ambient sound intensity is likely caused by the GS currents' effect on breaking of surface gravity waves.

Further experimental and modeling studies, including longer-term observations, are needed to quantify the role of various environmental factors and assess the predictability of spectra, statistics, directionality, and correlation properties of underwater ambient sound in the northwest Atlantic.

O.A.G. is grateful to N. J. Williams for his generous advice at the initial stages of MANR design and to P. Leary for his expertise in the initial integration of Chip Scale Atomic Clocks into the MANR data acquisition electronics. The data used in this study were collected by Naval Postgraduate School in conjunction with the 2023 NESMA Pilot Experiment. The authors greatly appreciate assistance from John Kemp and the Woods Hole Oceanographic Institution Mooring Operations and Engineering team for MANR anchor design and deployment. MANR deployment would not have occurred without the professional expertise of the crews of the R/V Armstrong and R/V Endeavor, the program manager, Bob Headrick, and the chief scientists, Y. T. Lin and J. Colosi. This work was supported in part by the Office of Naval Research, Awards Nos. N00014-23WX01775 and N00014- 23WX01289, and in part by Taiwan Grant No. 113‐2611-M-012-002.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.