Approximately 11 400 h of acoustic recordings from two sites off the Oregon coast have been evaluated to characterize and model the frequency and wind dependence of wind noise in the northeast Pacific continental margin. Acoustic data are provided by two bottom-mounted broadband hydrophones (64 kHz sampling frequency) deployed at depths of 81 and 581 m at the continental shelf and slope, respectively. To describe the spectral level versus frequency relation, separate linear models for the 0.2–3 kHz and 3–25 kHz frequency range are fitted to the data. While spectral slopes for the 0.2–3 kHz range generally decrease with increasing wind speed, slopes remain constant (shallow location) or increase with increasing wind speed (deep location) above 3 kHz. The latter is in strong contrast to results from previous studies. The relation between spectral level and wind speed is described by a piecewise linear model where spectral levels are approximately constant below a critical wind speed vc and increase linearly with logarithmic wind speed above vc. It is shown that the critical wind speed and the slopes of the piecewise linear model strongly depend on the acoustic frequency.

Characterizing wind noise is crucial for gaining a better understanding of the acoustic environment in the ocean. As wind is present most of the time, the spectral characteristic of wind noise can serve as a baseline for the ocean ambient soundscape. Furthermore, wind noise measurements also lay the foundation for acoustic remote sensing of wind speeds over the open ocean. Those acoustic based measurement techniques can outperform satellite systems, buoys, or ship-born systems in terms of spatial and temporal resolution. Successful estimations of wind parameters using ambient noise measurements can be found, for example, in Cauchy et al. (2018), Riser et al. (2008), Shaw et al. (1978), Taylor et al. (2021), Vagle et al. (1990), and Vakkayil et al. (1996), and are crucial for an accurate modeling of air-sea fluxes and the ocean gas exchange, thus, providing important knowledge in understanding the global climate system (Wanninkhof, 2014).

Wind generated ocean ambient noise has been first characterized statistically by Knudsen et al. (1948). Since then, many studies have analyzed the spectral characteristic of wind noise for different frequency ranges, wind speeds, and locations. Between 0.1 and 30 kHz, wind noise is the result of a multitude of mechanisms (Kerman, 1984). The main contributors are noise from breaking waves and whitecaps, flow noise, cavitation noise, and noise from wave generating actions of wind on the sea surface (Urick, 1983). However, different sound mechanisms dominate different frequency bands (Urick, 1984) and, as a result, the spectral behavior of wind noise varies over frequencies.

In this study we add to the characterization of wind generated ocean noise by evaluating acoustic and meteorological data at the northeast Pacific continental margin between 2015 and 2019 provided by the Ocean Observatories Initiative (OOI). Our data allow for a detailed analysis of wind noise as we have access to approximately 11 400 h of “clean” wind noise recordings at two locations off the coast of Oregon (“clean” here means that the wind noise is largely free of other noise sources). Given the amount of data and the hydrophone's sampling frequency of 64 kHz, we accurately describe the characteristics of wind noise at this location for low and high frequencies, as well as for various wind speeds.

The remainder of the paper is outlined as follows: Section II will describe the measurement setup, data acquisition system, and signal processing pipeline. Sections III and IV discuss the frequency and wind speed dependence of wind noise and compare our results with measurements conducted in the past. Section V summarizes this research effort, and states the conclusions drawn from it.

Data from the hydrophones used in this work have recently been used to describe noise during rain in the northeast Pacific (Schwock and Abadi, 2021a). As measurement setup, data collection, and processing techniques are identical to this study, we will summarize only the most important aspects here and refer the reader to the aforementioned study for further details.

Acoustic and meteorological data were recorded between September 2015 and June 2019 by two hydrophones and two-surface buoys deployed off the coast of Oregon at the continental slope and shelf, respectively [see Fig. 1(a)]. The hydrophones are mounted at the sea floor in depths of 581 m (deep hydrophone) and 81 m (shallow hydrophone), respectively. At each site, a surface buoy measuring wind speed and direction is deployed in the vicinity of the hydrophones. The surface buoys are horizontally displaced from the hydrophones as illustrated in Fig. 1(b). All instruments are managed by the Ocean Observatories Initiative (OOI) and the data can be accessed through the OOI data portal.1

FIG. 1.

(Color online) (a) Locations of the deep and shallow site in the northeast Pacific Ocean [figure made with GeoMapApp (GeoMapApp, 2021; Ryan et al., 2009)] and (b) displacement of hydrophone (H) and surface buoy (B) at each location. [Figure from Schwock and Abadi (2021a).]

FIG. 1.

(Color online) (a) Locations of the deep and shallow site in the northeast Pacific Ocean [figure made with GeoMapApp (GeoMapApp, 2021; Ryan et al., 2009)] and (b) displacement of hydrophone (H) and surface buoy (B) at each location. [Figure from Schwock and Abadi (2021a).]

Close modal

The wind data are provided by Gill Windobserver II wind speed sensors which measure the mean northward and eastward wind velocity over 30–65 s (on average 60 s) intervals at a mean elevation of 4.7 m above the water surface (sensor elevation ranges between 4.45 and 4.8 m). Errors in wind speed measurements due to different sensor elevations and the logarithmic wind profile in the atmospheric boundary layer (Tennekes, 1973) are assumed to be negligible. The Windobserver sensors have a nominal precision of 2% and 1°. Northward and eastward wind component are used to compute the overall wind magnitude and direction. We found that the 1-min wind speed signal from the surface buoy exhibits a large variance due to local fluctuations in wind speed at the measurement location. As a result, the wind speed often rapidly changes from one sample to the next as the gray line in Fig. 2 indicates. It is known, however, that surface noise recorded by omnidirectional hydrophones does not originate from a single point at the surface, but is rather the average over a certain surface area. Therefore, a spatially averaged wind speed, rather than a point measurement, should be correlated to the measured noise levels. The surface area generating the acoustic energy received by the hydrophone is generally a function of frequency, hydrophone depths, sound absorption, and scattering (Anagnostou et al., 2008). In Schwock and Abadi (2021a) we found that areas generating 90% of the acoustic energy received by the hydrophones have radii of 200 m for the shallow and 1 km for the deep location and are approximately independent of frequency for frequencies between 0.5 and 15 kHz. This 90% area is referred to as effective surface listening area in the context of this work. Given the lack of spatially averaged wind measurements, we applied a sliding 21-point symmetric Hann-window to the 1-min wind signal measured at the surface buoy to reduce the variance in the wind measurements. This smoothed wind signal can be regarded as a proxy for wind averaged over a larger surface area and is shown by the black line in Fig. 2.

FIG. 2.

Example of original and smoothed 1-min wind speed signal (data from January 1, 2017 at the deep location). The smoothing is performed using a 21-point sliding Hann-window.

FIG. 2.

Example of original and smoothed 1-min wind speed signal (data from January 1, 2017 at the deep location). The smoothing is performed using a 21-point sliding Hann-window.

Close modal

Acoustic data are recorded continuously with a sampling rate of 64 kHz by broadband icListen HF hydrophones from Ocean Sonics with an average sensitivity of −169 dB V re 1 μPa. For each 1-min wind sample, the acoustic data are used to calculate a power spectral density (PSD) estimate using the Welch 50th-percentile estimator (Schwock and Abadi, 2021b) and the python package ooipy (Schwock et al., 2020). The procedure of the spectral estimation is as follows: (1) A Hann window was applied to 64 ms (4096 samples) data blocks, whereby adjacent blocks overlap by 32 ms (50%). (2) For each windowed data block, the magnitude square of its 4096-point fast Fourier transform is computed resulting in 937 to 2031 periodograms (the number of periodograms varies as the wind samples cover intervals between 30 and 65 s) (3) A frequency-wise median averaging is applied to the periodograms to obtain a single PSD estimate. (4) A frequency dependent sensitivity correction using calibration data provided by Ocean Sonics for the icListen hydrophones is applied to the PSD estimates. This procedure produces calibrated sequential 1-min PSD estimates for all wind speed samples in the data set. The median averaging ensures that interfering pings from Acoustic Doppler Current Profilers (ADCPs) co-located with the hydrophones have no significant effect on the spectral estimate.

To solely focus on wind noise, acoustic data contaminated by other noises was manually flagged and removed from the analysis. The procedure is described in Schwock and Abadi (2021a) and removes noise compromised by ships, broadband stationary interfering signals with a spectral level significantly above the background noise, and strong bioacoustic signatures in the low frequency region. Furthermore, spectrograms that contain rain events as defined in Schwock and Abadi (2021a) have also been excluded from the analysis. The distributions of wind noise data over the entire measurement period for the shallow and deep hydrophone—after removing all spurious data—is shown in Fig. 3. Large gaps are usually due to times when hydrophones or surface buoys were not operating or when strong interfering signals were observed in the acoustic recordings over a long time period.

FIG. 3.

(Color online) Distribution of wind noise data over the measurement period after removing data corrupted by interfering signals.

FIG. 3.

(Color online) Distribution of wind noise data over the measurement period after removing data corrupted by interfering signals.

Close modal

Finally, multiple narrow band tones, presumably caused by other measurement instruments, can be detected in the acoustic signal. The center frequencies of the tones are approximately 6.27, 8.34, 12.53, 14.03, 16.09, and 16.7 kHz at the deep location and 7.45, 11.17, 13.28, 15.31, and 19.38 kHz at the shallow location. Those tones have been removed from Figs. 4, 7, and 11 by linearly interpolating the spectral level over a range of approximately 190 Hz (12 samples) around each tone.

FIG. 4.

(Color online) Average power spectral density (PSD) estimates for (a) deep and (b) shallow location for various wind speed categories and frequencies between 30 Hz and 25 kHz. The number of 1-min PSD samples within each category is listed in the legend. The dashed lines are obtained by linear regression of the average PSDs mapped into one-third octave bands (0.2–3 kHz frequency range) and one-sixth octave bands (3–25 kHz frequency range). Slopes and R2 scores of the linear regression lines are shown in Fig. 6 and  Appendix, Table III. The shaded areas around the average PSDs illustrate one quarter of the standard deviation.

FIG. 4.

(Color online) Average power spectral density (PSD) estimates for (a) deep and (b) shallow location for various wind speed categories and frequencies between 30 Hz and 25 kHz. The number of 1-min PSD samples within each category is listed in the legend. The dashed lines are obtained by linear regression of the average PSDs mapped into one-third octave bands (0.2–3 kHz frequency range) and one-sixth octave bands (3–25 kHz frequency range). Slopes and R2 scores of the linear regression lines are shown in Fig. 6 and  Appendix, Table III. The shaded areas around the average PSDs illustrate one quarter of the standard deviation.

Close modal

Wind noise spectral levels for wind speeds between 0 and 14 m/s have been grouped into seven wind speed categories, where each category covers an interval of 2 m/s. An eighth category for wind speeds above 14 m/s is also included. Average PSD estimates for each wind speed category are shown in Fig. 4 for both locations. The frequency dependent standard deviation is illustrated by the shaded area around each average PSD. (For a better representation, only one quarter of the standard deviation is plotted.)

The OOI dataset allows for the analysis of wind noise over a broad frequency range from 30 Hz up to 25 kHz. Figure 4 indicates that the wind noise spectra can be divided into three frequency ranges: (1) low frequencies from 30 to 200 Hz, (2) mid-range frequencies from 0.2 to 3 kHz and (3) high frequencies from 3 to 25 kHz. Frequencies below 30 Hz and above 25 kHz are filtered out and, thus, excluded from the analysis. Choosing a corner frequency of 3 kHz is based on the observation that the spectral levels in Fig. 4 seemingly drop off around 3 kHz especially for higher wind speeds. A similar phenomenon can also be observed in the spectra by Duennebier et al. (2012) showing spectral levels for different wind speeds recorded 100 km north of Oahu, Hawaii at a depth of 4720 m. The sudden drop off suggests that wave breaking events have a different effect on the noise level in different frequency bands. Indeed for wind speeds below 4 m/s, where wave breaking events are assumed to be not significant (Monahan, 1971; Monahan and Lu, 1990), the figure indicates that a single linear model would seem sufficient to describe the spectral behavior. Nevertheless, separate linear models for the 0.2–3 kHz and 3–25 kHz range are used in the following for all wind speed categories.

To better compare spectral levels at the deep and shallow location, Fig. 5 shows the ratio between spectral level at the deep (SPLdeep) and spectral level at the shallow location (SPLshallow). For frequencies between 30 and 200 Hz, the spectral levels at the deep location are up to 23% higher than at the shallow location, whereby the difference between deep and shallow location increases with decreasing frequency and decreasing wind speed. A similar phenomenon was also reported in Schwock and Abadi (2021a), as well as other studies such as Berger et al. (2018) and Farrokhrooz et al. (2017), and is likely caused by noise from distant ships (Anderson, 1979; Wagstaff, 1981; Wenz, 1962) and high latitude winds (Bannister, 1986) that propagate in the deep sound channel over long distances. As the acoustic environment at the shallow location is dominated by steep bottom and surface reflections, the influence of distant sources is negligible and, except for the 0–2 m/s wind speed category, no increased spectral levels at very low frequencies can be observed. Thus, it is concluded that the frequency range between 30 and 200 Hz is not strongly correlated to the surface wind speed, a fact that is also established in Sec. IV and Fig. 8, which shows a low correlation between wind speed and spectral level for low frequencies. Therefore, we do not focus on this frequency range in the remainder of this study. It is interesting to note that, for the entire frequency range, the ratio SPLdeep/SPLshallow in Fig. 5 deviates stronger from unity for lower than for higher wind speeds. That is, while hydrophone location and depths have a significant effect on the wind noise spectral levels at lower wind speeds, their influence diminishes as the wind speed increases.

FIG. 5.

(Color online) Ratio of average spectral levels at the deep location (SPLdeep) to average spectral levels at the shallow location (SPLshallow) for different wind speed categories. The largest deviation from unity and therefore the strongest influence of hydrophone location and depth on the wind noise spectral levels occurs at low wind speeds.

FIG. 5.

(Color online) Ratio of average spectral levels at the deep location (SPLdeep) to average spectral levels at the shallow location (SPLshallow) for different wind speed categories. The largest deviation from unity and therefore the strongest influence of hydrophone location and depth on the wind noise spectral levels occurs at low wind speeds.

Close modal

For both, the mid-frequency (0.2–3 kHz) and the high frequency range (3–25 kHz), linear models of the form

SPL(f)=slog10(f)+a,
(1)

where SPL is the spectral level, f the frequency, and s and a are the linear regression coefficients, were fitted to the data. The regression curves are shown as dashed lines in Fig. 4. To equally weight each frequency, the PSDs were first mapped into one-third octave bands for the mid-frequency range and one-sixth octave bands for the high frequency range, respectively (median averaging was used to mitigate the effect of outliers). The linear regression slopes for both locations are shown in Fig. 6(a) and the  Appendix, Table III. Furthermore, the coefficient of determination, denoted by R2, has been computed as a metric for evaluating the performance of the regression model [Fig. 6(b), Table III].

FIG. 6.

(Color online) (a) Slope s in dB/dec according to Eq. (1) and (b) R2 scores of linear regression performed on the average spectra in Fig. 4 for the 0.2–3 kHz and 3–25 kHz range.

FIG. 6.

(Color online) (a) Slope s in dB/dec according to Eq. (1) and (b) R2 scores of linear regression performed on the average spectra in Fig. 4 for the 0.2–3 kHz and 3–25 kHz range.

Close modal

In numerous past experiments and field measurements, a variety of spectral trajectories for the mid-frequency range were found (the mid-frequency range was usually defined as frequencies below 1 kHz). For example, Knudsen et al. (1948) reported that the spectral level of wind noise decreases with a rate of approximately –17 dB/decade (dB/dec) over frequency. On the other hand, Piggott (1964), Reeder et al. (2011), and Wenz (1962) have found a broad spectral peak between 0.1 and 1 kHz. Using hydrophone vertical line arrays (VLAs) to discriminate between local and distant sources, Chapman and Cornish (1993) found a similar decrease in spectral level of the local noise to the Kundsen curves of about −20 dB/dec for wind speeds above 5 m/s. On the other hand, Burgess and Kewley (1983) have found that while the omnidirectional noise shows an overall decrease in spectral level with increasing frequency, local wind noise spectral levels are essentially flat for frequencies between 100 and 800 Hz. Those results are consistent with VLA measurements by Kewley et al. (1990), where wind noise measurements from the southern and northern hemisphere for wind speeds above 10 m/s were combined.

Similar to the studies by Knudsen et al. (1948) and Chapman and Cornish (1993), the 0.2–3 kHz wind noise spectral level in this study decreases with increasing frequency. However, as Fig. 6(a) indicates the slopes are not constant, but rather their absolute values decrease with increasing wind speed. Furthermore, the change in slope is not uniform. That is, for wind speeds below 6 m/s the absolute value of the slope decreases rapidly with increasing wind speed, whereas above 6 m/s the decrease in absolute value is more gradual. In Fig. 6(a) we can also observe that the slopes at the deep location are steeper for all wind speed categories than at the shallow location. Furthermore, Fig. 5 indicates that absolute spectral levels at the shallow location are up to 10% higher than at the deep location. Those are likely results of the greater measurement depth at the deep location and therefore an increased attenuation of sounds at high frequencies.

R2 scores for the low frequency linear regression at the deep location are very close to one for wind speeds above 4 m/s and therefore support the linear model. The slightly lower R2 scores for wind speeds below 4 m/s can be attributed to the larger variability in the spectral level, probably caused by other noise sources that become dominant in the absence of wind. On the other hand, the R2 scores for the shallow site tend to decrease as the wind speed increases. Figure 4(b) indicates that this can be attributed to an increasingly non-linear trajectory of the wind noise spectral levels for higher wind speeds.

While studies have reported different spectral trajectories for the mid-frequency range, spectral levels in the high frequency range are known to decrease with a constant rate in a logarithmic frequency scale and, thus, can be modeled by Eq. (1). The spectral slope s325kHz according to Eq. (1) (the subscript indicates the frequency range) obtained from various past measurements is shown in Table I. While most studies reported an average slope between –17 dB/dec and –20 dB/dec, a few studies have found values that are significantly below (Hildebrand et al., 2021; Ma et al., 2005; Reeder et al., 2011) or above [Bourassa (1984), Atlantic data] this range. Almost all studies in Table I found that the spectral slope is independent of the wind speed for low and moderate winds (typically below 8–10 m/s). However, we were able to show that this does, in general, not hold for the northeast Pacific data in this study. While for the shallow location and for wind speeds below 10 m/s the slopes for all wind speed categories are nearly identical with an average value of –13.6 dB/dec, spectral slopes at the deep location are not independent of the wind speed, but instead increase (in absolute value) from 11.6 dB/dec at 0–2 m/s to 18.7 dB/dec at 8–10 m/s [see Fig. 6(a) and Table III]. This suggests that the spectral slopes are highly dependent on the measurement site and depth even if the acoustic recordings are obtained from similar oceanic environments. A similar wind-dependent slope was also recently reported by Hildebrand et al. (2021), who analyzed over 100 years of recording-time from deep and shallow hydrophones deployed across the globe in near-shore and open ocean environments. It is also interesting to note that the average value of –13.6 dB/dec for the shallow location and wind speeds below 10 m/s has a magnitude lower than any slope listed in Table I. This emphasizes the claim that wind noise levels cannot be easily generalized across different oceanic environments, but rather distributed, large-scale measurements are necessary for an accurate characterization of wind noise at various locations.

TABLE I.

Slope s according to Eq. (1) from various studies for frequencies above 1 kHz. The page or figure number from which the values are obtained is given in parenthesis after the reference. Most studies report an average slope between –17 dB/dec and −20 dB/dec.

s (dB/dec)Frequency range (kHz)Location
Vagle et al. (1990) (p. 582) −19 3–20 Tropical Atlantic 
Bourassa (1984) – Pacific (p. 24) −18.9 4.3–14.5 Equatorial Pacific 
Bourassa (1984) – Atlantic (p. 31) −21.9 4.3–14.5 North Atlantic 
Lemon et al. (1984) (p. 3465) −17±4.3–14.5 Queen Charlotte Sound 
Ma et al. (2005) (Fig. 6) −15.7 1–50 Tropical Pacific 
Wenz (1962) (p. 1942) −18.3±1.7 1–20 Various 
Knudsen et al. (1948) (p. 418) −16.7±3.3 0.1–25 Various 
Vakkayil et al. (1996) (Fig. 3) −18.8±1.2 3–25 Off DelMarVa Peninsula 
Evans et al. (1984) (p. 3460) −17±4.3–14.5 Equatorial Pacific 
Reeder et al. (2011) (p. 71) −15 0.5–20 Tongue of the Ocean, Bahamas 
Hildebrand et al. (2021) (p. 4525) −15 0.4–20 Various 
s (dB/dec)Frequency range (kHz)Location
Vagle et al. (1990) (p. 582) −19 3–20 Tropical Atlantic 
Bourassa (1984) – Pacific (p. 24) −18.9 4.3–14.5 Equatorial Pacific 
Bourassa (1984) – Atlantic (p. 31) −21.9 4.3–14.5 North Atlantic 
Lemon et al. (1984) (p. 3465) −17±4.3–14.5 Queen Charlotte Sound 
Ma et al. (2005) (Fig. 6) −15.7 1–50 Tropical Pacific 
Wenz (1962) (p. 1942) −18.3±1.7 1–20 Various 
Knudsen et al. (1948) (p. 418) −16.7±3.3 0.1–25 Various 
Vakkayil et al. (1996) (Fig. 3) −18.8±1.2 3–25 Off DelMarVa Peninsula 
Evans et al. (1984) (p. 3460) −17±4.3–14.5 Equatorial Pacific 
Reeder et al. (2011) (p. 71) −15 0.5–20 Tongue of the Ocean, Bahamas 
Hildebrand et al. (2021) (p. 4525) −15 0.4–20 Various 

For wind speeds above 10 m/s, the absolute value of the slope significantly increases with increasing wind speed at both locations. This phenomenon follows the pattern reported by Black et al. (1997), Farmer and Lemon (1984), and Hildebrand et al. (2021) during strong winds and can be explained by a growing layer of bubbles forming underneath the water surface and penetrating deeper into the ocean as the wind speed increases. This bubble layer changes the sound speed profile and causes increased sound attenuation and scattering, which predominantly affects sound at higher frequencies and therefore results in a steeper drop off of the spectral level. One can also observe that the 3–25 kHz linear regression slopes are, except for the 0–2 m/s wind speed category, always steeper at the deep location than at the shallow location, which can likely be attributed to the greater measurement depth and, thus, increased volume attenuation at the deep location.

A comparison of the wind noise spectra for the 4–6 m/s wind speed category with spectra from previous studies is given in Fig. 7. The literature results are taken from Ma et al. (2005) who analyzed ambient noise in the tropical Pacific, Wenz (1962) who combined results from various open ocean and coastal environments, Lemon et al. (1984) who focused on continental shelf data from the Queen Charlotte Sound off the coast of Canada, and Knudsen et al. (1948) who evaluated data from multiple near-shore locations around the world collected during World War II. Note that all studies reported a uniform slope for frequencies above 1 kHz (Knudsen even reported a uniform slope above 100 Hz). The data in this study show the greatest similarity with the results reported by Lemon and Knudsen. The similarity with the Lemon data is less surprising as their measurements were conducted in a similar environment. They reported a slope around –17 dB/dec, which is very close to s325kHz= –16.47 dB/dec at the deep location. Lemon used hydrophones deployed at the bottom in a depth of approximately 250 m, which can explain why their noise levels are in between the ones of the shallow location (81 m) and deep location (581 m). The comparison with the Lemon data supports the claim that wind noise spectral levels behave similar in absolute value and trajectory at comparable environments. The strong similarity of the deep hydrophone spectral levels with the Knudsen data is more surprising as their measurements where not obtained from an environment similar to the northeast Pacific continental margin.

FIG. 7.

(Color online) Wind noise spectral levels for the 4–6 m/s wind speed category compared with results from Ma et al. (2005), Wenz (1962), Lemon et al. (1984), and Knudsen et al. (1948). Our results are shown in blue and red for the deep and shallow location, respectively. Our spectral levels show good agreement in terms of absolute value and slope with the study by Lemon, which was conducted in a similar oceanic environment.

FIG. 7.

(Color online) Wind noise spectral levels for the 4–6 m/s wind speed category compared with results from Ma et al. (2005), Wenz (1962), Lemon et al. (1984), and Knudsen et al. (1948). Our results are shown in blue and red for the deep and shallow location, respectively. Our spectral levels show good agreement in terms of absolute value and slope with the study by Lemon, which was conducted in a similar oceanic environment.

Close modal

The studies by Wenz and Ma show lower spectral levels compared to the results in this work. This is likely caused by the difference in measurement location and depth (most of Ma's hydrophones were deployed in a depth of 38 m, whereas the exact measurement depth in Wenz's study is unknown). On the other hand, the spectral slopes obtained from those studies are similar to s325kHz from the deep location.

In this section we analyze and model the dependence of the spectral level on the wind speed. Thereby, we put a special emphasis on how this relation depends on the acoustic frequency.

The dependence of the spectral level on the wind speed has been studied extensively in the past and it is known that this relation highly depends on the frequency. As most algorithms for estimating wind speeds from underwater acoustic recordings are based on a simple linear conversion between spectral level and wind speed at a single frequency (Cauchy et al., 2018; Riser et al., 2008; Shaw et al., 1978; Vagle et al., 1990; Vakkayil et al., 1996), one key question is: For which acoustic frequency does the spectral level show the strongest correlation with the wind speed? In order to address this question for the northeast Pacific continental margin, we have computed the Pearson correlation coefficient between spectral level and wind speed v for all frequency bins between 0.03 and 25 kHz. The resulting frequency dependent correlation coefficient is median-averaged into one-third octave bands and shown in Fig. 8 (dashed lines). In past studies, the spectral level is usually related to the logarithm of the wind speed. Thus, the solid lines in Fig. 8 show the Pearson coefficient between spectral level and log(v). One can observe that the correlation coefficient has a similar trajectory for both locations, with low values below 100 Hz and a correlation of at least 0.8 at the shallow and 0.9 at the deep location for frequencies between 1 and 10 kHz. For frequencies below 7 kHz, the correlation is always higher when using v instead of log(v). However, this difference is not very large, especially for frequencies between 1 and 10 kHz, which is where most algorithms that convert between spectral level and the logarithm of the wind speed operate. Nevertheless, the Pearson coefficient does not favor the logarithmic over the linear wind speed variable. The curves in Fig. 8 are qualitatively similar to correlation curves obtained by Duennebier et al. (2012) (data recorded about 100 km north of Oahu, Hawaii at a depth of 4720 m), who reported a maximum of around 0.8 between 0.2 and 5 kHz and a drop off in correlation at lower and higher frequencies. This suggests that the general relation between wind speed and sound spectral level depicted in Fig. 8 also applies to other oceanic locations.

FIG. 8.

(Color online) Pearson correlation coefficient between spectral level and wind speed v. For the solid curve, v is replaced by log(v). The correlation is computed for all frequency bins between 0.03 and 25 kHz before being median-averaged into one-third octave bands.

FIG. 8.

(Color online) Pearson correlation coefficient between spectral level and wind speed v. For the solid curve, v is replaced by log(v). The correlation is computed for all frequency bins between 0.03 and 25 kHz before being median-averaged into one-third octave bands.

Close modal

It is interesting to note that the correlation at the deep location is almost always higher than at the shallow location. The lower correlation for the shallow location is likely a result of the smaller effective surface listening area and therefore lesser spatial averaging of wind noise [see Sec. II A or Schwock and Abadi (2021a) for a discussion about the effective surface listening area at both locations]. That is, single wave breaking events have a stronger effect on the sound levels received by the shallow hydrophone resulting in a larger variability of the sound spectral levels for a given wind speed. This also reflects in the variance of the PSD estimates shown by the shaded areas in Fig. 4. Therein, spectral levels at the shallow location consistently show a larger variance than at the deep location, especially for frequencies below 1 kHz.

Past studies have shown that the relation between sound spectral level and wind speed is best modeled using a two regime model (Chapman and Cornish, 1993; Curtis et al., 1999; Farrokhrooz et al., 2017; Kewley et al., 1990; Reeder et al., 2011). For wind speeds lower than a critical wind speed vc the spectral level is either constant or only slowly increasing with increasing wind speed. For wind speeds above vc a linear relation between spectral level and the logarithm of the wind speed can be observed. This relation is typically expressed as

SPL(v)=20nlog10(v)+b,
(2)

where SPL is the spectral level, v is the wind speed in m/s, and n and b are the slope factor and intercept, respectively. A value of n = 1 indicates that the spectral level increases with a rate of 20 dB/dec. The widely accepted explanation for the occurrence of two wind speed regimes is that breaking waves and whitecaps are not emerging for low wind speeds and, thus, the influence of wind generated noise on the underwater soundscape is only marginal in this case (Monahan, 1971; Monahan and Lu, 1990). Different values for the critical wind speed vc have been reported in the past, but typically they range between 2.5 and 5 m/s. This phenomenon is also reflected in Fig. 4, where a big jump in noise level can be observed between the 2–4 m/s and 4–6 m/s wind speed categories.

Several values for the slope factor n from previous studies are shown in Table II. For frequencies between 0.1 and 1 kHz, n ranges between 0.5 and 1.7, whereby the variations are often large within a study. In general, n highly depends on frequency, location, and measurement depth, however, no clear relation between those factors and the value of n was found. For frequencies above 1 kHz, the variability is significantly smaller with n ranging between 0.9 and 1.54 and usually staying in a range of 1.0–1.2. However, it is noted that many studies only considered a single wind speed regime, which could possibly result in an underestimation of n.

TABLE II.

Slope factor n according to Eq. (2) from various studies. The page, table, or figure number from which the values are obtained is given in parenthesis after the reference. For frequencies between 0.1 and 1 kHz, n ranges between 0.5 and 1.7, whereas for frequencies above 1 kHz, n only ranges from 0.9 to 1.54 and usually stays between 1.0 and 1.2. For frequencies above 1 kHz, the model has been fitted for a small set or range of frequencies indicated by the footnotes.

nWind speed range (m/s)Location
Frequency between 0.1–1 kHz 
Crouch and Burt (1972) (Table I) 0.81–1.39 5–25 Near Bermuda 
Burgess and Kewley (1983) (Table I) 0.46–0.72 1–15 East off Australia 
Farrokhrooz et al. (2017) (Fig. 8) 0.5–1.5 5–12 Northeast Pacific 
Piggott (1964) (Fig. 6) 1.29–1.7 1.5–18 Scotian shelf 
Chapman and Cornish (1993) (Table III) 1.09–1.49 6–15 Northeast Pacific 
Shooter and Gentry (1981) (Table I) 1.01–1.57 9–14 Parece-Vela basin 
Hildebrand et al. (2021) (Table II) 0.5–1.2 5–31 Various 
Frequency1 kHz 
Vagle et al. (1990) a (Table III) 1.36 4–15 Tropical Atlantic 
Bourassa (1984) a—Pacific (Table III) 1.1–1.54 0–10 Equatorial Pacific 
Bourassa (1984) a—Atlantic (Table III) 0.9–0.95 0–20 North Atlantic 
Lemon et al. (1984) a (Table II) 1.08–1.52 0–12 Queen Charlotte Sound 
Crouch and Burt (1972) b (Table I) 0.93–1.03 5–25 Near Bermuda 
Shaw et al. (1978) c (p. 1229) 0.99 4–20 Tropical Atlantic 
Piggott (1964) d (Fig. 6) 1.2–1.24 1.5–18 Scotian shelf 
Evans et al. (1984) a (Table I) 1.15–1.2 5.5–10 Equatorial Pacific 
Reeder et al. (2011) e (Fig. 4) 1.31 2.5–9.6 Tongue of the Ocean, Bahamas 
Hildebrand et al. (2021) f (Table II) 0.9–1.22 5–31 Various 
nWind speed range (m/s)Location
Frequency between 0.1–1 kHz 
Crouch and Burt (1972) (Table I) 0.81–1.39 5–25 Near Bermuda 
Burgess and Kewley (1983) (Table I) 0.46–0.72 1–15 East off Australia 
Farrokhrooz et al. (2017) (Fig. 8) 0.5–1.5 5–12 Northeast Pacific 
Piggott (1964) (Fig. 6) 1.29–1.7 1.5–18 Scotian shelf 
Chapman and Cornish (1993) (Table III) 1.09–1.49 6–15 Northeast Pacific 
Shooter and Gentry (1981) (Table I) 1.01–1.57 9–14 Parece-Vela basin 
Hildebrand et al. (2021) (Table II) 0.5–1.2 5–31 Various 
Frequency1 kHz 
Vagle et al. (1990) a (Table III) 1.36 4–15 Tropical Atlantic 
Bourassa (1984) a—Pacific (Table III) 1.1–1.54 0–10 Equatorial Pacific 
Bourassa (1984) a—Atlantic (Table III) 0.9–0.95 0–20 North Atlantic 
Lemon et al. (1984) a (Table II) 1.08–1.52 0–12 Queen Charlotte Sound 
Crouch and Burt (1972) b (Table I) 0.93–1.03 5–25 Near Bermuda 
Shaw et al. (1978) c (p. 1229) 0.99 4–20 Tropical Atlantic 
Piggott (1964) d (Fig. 6) 1.2–1.24 1.5–18 Scotian shelf 
Evans et al. (1984) a (Table I) 1.15–1.2 5.5–10 Equatorial Pacific 
Reeder et al. (2011) e (Fig. 4) 1.31 2.5–9.6 Tongue of the Ocean, Bahamas 
Hildebrand et al. (2021) f (Table II) 0.9–1.22 5–31 Various 
a

4.3, 8, 14.5 kHz.

b

1–3 kHz.

c

5 kHz.

d

1.1, 2.2 kHz.

e

1–20 kHz.

f

1–10 kHz.

A different behavior can usually be observed for very high wind speeds, approximately above 14–15 m/s, where the spectral level can actually decrease with increasing wind speed at high frequencies (Black et al., 1997; Farmer and Lemon, 1984; Hildebrand et al., 2021). While this behavior can be observed for frequencies around 8 kHz, it is more distinct for frequencies well above 10 kHz. As mentioned in Sec. III B, this is caused by a layer of bubbles that forms below the water surface and predominantly attenuates surface generated sound in the high frequency range. It is noted that many studies considered in Table II only used frequencies up to a few kilohertz so that this phenomenon does not have a significant effect on their estimated slope.

To model the spectral level versus wind speed relation at our location, we have fitted the following two-regime linear model to our data:

(3)
SPL(v)={20n1log10(v)+c1,v<vc20n2log10(v)+c2,vvc,
(3a)
c1=SPL(vc)20n1log10(vc),
(3b)
c2=SPL(vc)20n2log10(vc),
(3c)
where vc is the critical wind speed and n1 and n2 are the slope coefficients. The SciPy function scipy.optimize.curve_fit (Virtanen et al., 2020) was used for fitting the model. Note that the model is chosen such that the linear regression lines below and above vc intersect at vc.

An example of the two regime model fitted to the spectral level at 5 kHz is shown in Fig. 9. For the deep location, the critical wind speed is 2.33 m/s, and n1 and n2 are 0.089 and 1.55, respectively. For the shallow location, vc= 2.55 m/s, and n1 and n2 are 0.099 and 1.47, respectively. The average spectral level within each 2 m/s wind speed category is shown by the square markers. One can observe that the two regime model coincides very well with the average spectral levels. Only for very high wind speeds (above approximately 15 m/s) the model seems to underestimate the prevailing wind speed, but more data for very high wind speeds is necessary to confirm this trend and extend the model to higher wind speeds.

FIG. 9.

Spectral level at 5 kHz versus the logarithmic wind speed for (a) deep and (b) shallow location. The gray dots are the spectral levels from the 1-min PSD estimates. The dashed lines are the two regime linear models according to Eq. (3) fitted to the spectral levels from the 1-min PSD estimates. The squares show the average spectral level within each wind speed category, and triangles and diamonds are the spectral levels found by Lemon et al. (1984) and Vagle et al. (1990) for a frequency of 4.3 and 5 kHz, respectively.

FIG. 9.

Spectral level at 5 kHz versus the logarithmic wind speed for (a) deep and (b) shallow location. The gray dots are the spectral levels from the 1-min PSD estimates. The dashed lines are the two regime linear models according to Eq. (3) fitted to the spectral levels from the 1-min PSD estimates. The squares show the average spectral level within each wind speed category, and triangles and diamonds are the spectral levels found by Lemon et al. (1984) and Vagle et al. (1990) for a frequency of 4.3 and 5 kHz, respectively.

Close modal

The results are also compared to data taken from Lemon et al. (1984) and Vagle et al. (1990), who both used a single wind speed regime model. The Lemon and Vagle data are shown for frequencies of 4.3 and 5 kHz, respectively. Vagle evaluated wind noise measurement from the tropical Atlantic Ocean with hydrophones deployed in a depth of approximately 150 m. Additionally, he normalized the spectral levels to a depth of 1 m and used a quadratic model to describe the spectral level versus log wind speed relation. The results from both studies agree very well in absolute spectral level with the data at the shallow location. At the deep location on the other hand, our data show consistently lower spectral levels than the Lemon and Vagle data, which is likely a result of the greater measurement depth and, therefore, an increased volume attenuation of the acoustic signals. However, despite the good agreement in absolute spectral level, the presented data clearly show that a single linear model is not sufficient to accurately model the relation between spectral level and wind speed over a wide wind speed range.

The model coefficients from Eq. (3) are computed for all frequency bins between 0.03 and 25 kHz followed by a median-averaging into one-third octave bands. The resulting vc, n1, n2, and R2 score for the high wind speed regime (i.e., for the linear model when vvc) are shown in Fig. 10 for both locations. As the spectral level below vc is approximately constant, R2 scores of the regression in the low wind speed regime assume values around zero. Therefore, a combined R2 score for both regimes becomes difficult to interpret, which is why only R2 scores for the high wind speed regime are shown.

FIG. 10.

(a) R2 score above vc, (b) critical wind speed vc, and (c) and (d) slope coefficients n1 and n2 of the two wind speed regime linear model according to Eq. (3). Each parameter is computed for all frequency bins between 0.03 and 25 kHz before being median-averaged into one-third octave bands. Very low frequencies at the deep location are not related to the local wind speed but are driven by distant shipping and high latitude winds, which explains the strong fluctuations in vc, n1, and n2 below 150 Hz.

FIG. 10.

(a) R2 score above vc, (b) critical wind speed vc, and (c) and (d) slope coefficients n1 and n2 of the two wind speed regime linear model according to Eq. (3). Each parameter is computed for all frequency bins between 0.03 and 25 kHz before being median-averaged into one-third octave bands. Very low frequencies at the deep location are not related to the local wind speed but are driven by distant shipping and high latitude winds, which explains the strong fluctuations in vc, n1, and n2 below 150 Hz.

Close modal

The R2 score in Fig. 10(a) shows the same pattern as the Pearson correlation coefficient in Fig. 8. The critical wind speed vc in Fig. 10(b) steadily decreases between 50 Hz and 1 kHz. Above 1 kHz, vc remains almost constant with values between 2 and 3 m/s for both locations. This behavior is consistent with observations made in the past [for example, see Fig. 6 in Piggott (1964)], but to the best of our knowledge, has not been quantitatively analyzed over a wide frequency range. Note that for the deep location and frequencies below approximately 150 Hz, the spectral level is mainly determined by distant sources rather than local winds. Therefore, the two-regime model cannot be fitted to the data in a meaningful way, which explains the strong fluctuations in vc that can be observed below 150 Hz. The slope coefficients n1 and n2 in Figs. 10(c) and 10(d) also behave similar among both locations. n1 assumes values around 0.1 over the entire frequency range, indicating that the spectral level is almost independent of the wind speed below vc. On the other hand, n2 assumes values between 1.0 and 1.6 with a broad maximum between 1 and 10 kHz. For frequencies below 1 kHz those values are well in the range of the values reported in the past (see Table II). However, for frequencies above 1 kHz our values for n2 are at the upper end of the range found in previous studies. This could be due to the fact that many studies in the past used a single wind speed regime model, thus, potentially underestimating the slope above vc. The drop in n1 and n2 for frequencies around 100 Hz at the deep location can again be attributed to the effect of distant sources on the sound spectral levels in the low frequency range.

In the previous sections, we have shown that wind noise spectral levels are strongly correlated to the surface wind speed. However, a more realistic assumption is that the spectral levels depend on the amount of surface agitation, which is not only affected by the wind speed, but also by other parameters such as wind duration, fetch, direction, swell, and currents (Wenz, 1962). For high wind speeds, the fetch (i.e., the distance over which wind blows in a constant direction) is of particular interest since a fetch on the order of a few hundred kilometers might be necessary to allow for a fully developed sea [see Table I in Wenz (1962)]. Since our hydrophones have a distance to shore of approximately 18.5 km (shallow hydrophone) and 68 km (deep hydrophone), it can be concluded that wind noise spectral levels might differ for eastward (unlimited fetch) and westward (limited fetch) wind.

In order to analyze the dependence of the noise level on the wind direction, we have computed average PSD estimates over all wind speeds for the eastward, northward, westward, and southward wind direction shown in Fig. 11. It is noted that most 1-min PSD estimates correspond to southward winds which is consistent with findings by Dorman and Winant (1995) who analyzed the statistics of wind along the west coast of the United States between 1981 and 1990. While we found that especially at the deep location the northward and southward wind noise spectral level are higher than the eastward and westward noise levels, we also found that this can be explained by different average wind speeds v¯ for the different directions (northward and southward winds are on average stronger than eastward and westward winds as seen in Fig. 11). Furthermore, if the wind speed is restricted to a single wind speed category to ensure an almost equal v¯ for each direction, spectral levels for the four wind directions approximately match. Therefore, we conclude that no clear dependence of the wind noise spectral levels on the wind direction can be established for our location.

FIG. 11.

(Color online) Average power spectral density (PSD) estimates for (a) deep and (b) shallow location for the eastward, northward, westward, and southward wind direction. The wind angles included in each category are illustrated in (a) and cover a range of 45° around each direction. The number of 1-min PSD estimates and the average wind speed v¯ for each direction are given in the legend in parenthesis. Higher spectral levels consistently correspond to higher values of v¯ suggesting that no clear dependence of the spectral levels on the wind direction can be observed.

FIG. 11.

(Color online) Average power spectral density (PSD) estimates for (a) deep and (b) shallow location for the eastward, northward, westward, and southward wind direction. The wind angles included in each category are illustrated in (a) and cover a range of 45° around each direction. The number of 1-min PSD estimates and the average wind speed v¯ for each direction are given in the legend in parenthesis. Higher spectral levels consistently correspond to higher values of v¯ suggesting that no clear dependence of the spectral levels on the wind direction can be observed.

Close modal

In this work, we have evaluated approximately 11 400 h of wind noise data between 2015 and 2019 from two locations in the northeast Pacific continental margin. It was found that the spectral level above 200 Hz decreases with increasing frequency, however, in contrast to studies conducted in the past [notably Knudsen et al. (1948)], a single linear model seems not sufficient to model the spectral level versus frequency relation. Instead, two separate linear models, one for frequencies between 0.2 and 3 kHz and one for frequencies between 3 and 25 kHz, were necessary to model this relation. Using the two linear models, the following key observations about the spectral trajectory were made: (1) Spectral levels between 0.2 and 3 kHz decrease on average more gradual then spectral levels above 3 kHz. (2) Absolute values of the slopes of the linear model in the 0.2–3 kHz range decrease with increasing wind speed. (3) Above 3 kHz, absolute values of the slopes increase with increasing wind speed at the deep location. This is in contrast to results from previous studies (Bourassa, 1984; Evans et al., 1984; Knudsen et al., 1948; Lemon et al., 1984; Ma et al., 2005; Vagle et al., 1990; Vakkayil et al., 1996; Wenz, 1962), which all report wind-independent slopes. For the shallow location on the other hand, slopes are approximately constant around –13.6 dB/dec for wind speeds up to 10 m/s before decreasing as the wind speed further increases. (4) Comparisons with data from the literature show that spectral levels cannot be easily generalized across locations, but rather in situ long-term measurements are required to accurately characterize wind noise in different oceanic environments.

Furthermore, the dependence of the spectral level on the wind speed was analyzed for various acoustic frequencies. It was found that the highest correlation between spectral level and wind speed is obtained for frequencies between 1 and 10 kHz. The relationship was further modeled by a two wind speed regime linear model in a logarithmic wind speed scale as proposed in the past. The dependence of the model parameters on the acoustic frequency was analyzed in detail and the key observations are as follows: (1) A single wind speed regime as used in many previous studies is not sufficient to accurately model the spectral level versus wind speed relation for the presented data set. (2) The critical wind speed vc that separates the low wind speed regime from the high wind speed regime decreases with increasing frequency. For frequencies above 1 kHz, vc assumes values between 2 and 3 m/s, which is consistent with the results by Ma et al. (2005), Reeder et al. (2011), and Shaw et al. (1978). (3) The spectral level in the low wind speed regime is almost independent of the wind speed, whereas the spectral level in the high wind speed regime increases with a rate of 20–32 dB/dec at both locations, with a broad maximum between 1 and 10 kHz.

Finally, we have analyzed the dependence of the spectral levels on the direction of the wind. In contrast to the assumption that fetch-limited directions should result in lower spectral levels than fetch-unlimited directions, we found that differences in spectral level for different wind directions can be explained by different mean wind speeds rather than the direction of the wind.

The analysis in this study serves as an accurate description of the spectral properties of wind generated noise in the northeast Pacific continental margin. The presented spectra can be used as a baseline for the acoustic environment of this location. The assumption that wind noise solely depends on the wind speed is clearly a simplified one and in the future other wind and wave related parameters should be considered. Nevertheless, the results in this work can be used for estimating wind speeds along the northeast Pacific continental margin from underwater acoustic recordings.

This research was supported by the Office of Naval Research Grant No. N00014-19-1–2644.

Table III shows slopes and R2 scores of linear regression performed on the average spectra in Fig. 4. The results are also illustrated in Fig. 5.

TABLE III.

Slope s in dB/dec according to Eq. (1) and R2 scores of linear regression performed on the average spectra in Fig. 4 for the 0.2–3 kHz and 3–25 kHz ranges.

Wind speed (m/s)Deep hydrophoneShallow hydrophone
s0.23kHzs325kHzR0.23kHz2R325kHz2s0.23kHzs325kHzR0.23kHz2R325kHz2
0-2 −17.53 −11.55 0.968 0.891 −12.28 −13.70 0.996 0.958 
2-4 −14.51 −14.07 0.970 0.953 −9.89 −13.42 0.993 0.974 
4-6 −8.77 −16.47 0.993 0.964 −6.84 −12.86 0.967 0.981 
6-8 −7.39 −17.46 0.990 0.966 −6.05 −13.39 0.960 0.982 
8-10 −6.72 −18.73 0.984 0.967 −5.67 −14.63 0.968 0.984 
10-12 −6.04 −21.38 0.980 0.968 −5.36 −17.51 0.971 0.988 
12-14 −5.47 −26.95 0.982 0.972 −4.09 −23.76 0.931 0.991 
>14 −4.73 −37.50 0.983 0.975 −3.74 −31.65 0.936 0.985 
Wind speed (m/s)Deep hydrophoneShallow hydrophone
s0.23kHzs325kHzR0.23kHz2R325kHz2s0.23kHzs325kHzR0.23kHz2R325kHz2
0-2 −17.53 −11.55 0.968 0.891 −12.28 −13.70 0.996 0.958 
2-4 −14.51 −14.07 0.970 0.953 −9.89 −13.42 0.993 0.974 
4-6 −8.77 −16.47 0.993 0.964 −6.84 −12.86 0.967 0.981 
6-8 −7.39 −17.46 0.990 0.966 −6.05 −13.39 0.960 0.982 
8-10 −6.72 −18.73 0.984 0.967 −5.67 −14.63 0.968 0.984 
10-12 −6.04 −21.38 0.980 0.968 −5.36 −17.51 0.971 0.988 
12-14 −5.47 −26.95 0.982 0.972 −4.09 −23.76 0.931 0.991 
>14 −4.73 −37.50 0.983 0.975 −3.74 −31.65 0.936 0.985 
1

NSF Ocean Observatories Initiative Data Portal (National Science Foundation, 2021): deep hydrophone: Broadband Acoustic Receiver (CE04OSBP-LJ01C-11-HYDBBA105), shallow hydrophone: Broadband Acoustic Receiver (CE02SHBP-LJ01D-11-HYDBBA106), deep site surface buoy: Bulk Meteorology Instrument Package (CE04OSSM-SBD11-06-METBKA000), shallow site surface buoy: Bulk Meteorology Instrument Package (CE02SHSM-SBD11-06-METBKA000); data from 01 September 2015 to 30 June 2019.

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