Outdoor acoustic data often include non-acoustic pressures caused by atmospheric turbulence, particularly below a few hundred Hz in frequency, even when using microphone windscreens. This paper describes a method for automatic wind-noise classification and reduction in spectral data without requiring measured wind speeds. The method finds individual frequency bands matching the characteristic decreasing spectral slope of wind noise. Uncontaminated data from several short-timescale spectra can be used to obtain a decontaminated long-timescale spectrum. This method is validated with field-test data and can be applied to large datasets to efficiently find and reduce the negative impact of wind noise contamination.

## 1. Introduction

When collecting acoustic data in uncontrolled environments, extraneous noise signals can contaminate or even invalidate measurements. Contaminating noise can be caused by both acoustic sources and by non-acoustic signals, and therefore correctly measuring a source signal alone can be difficult. Contamination can be more pronounced in outdoor measurements due to non-acoustic contamination caused by atmospheric and weather conditions. One particularly challenging source of outdoor contamination is wind, which not only creates additional acoustic sources—such as the rustling of leaves—but also introduces non-acoustic pressures, known as wind-induced microphone self-noise or hydrodynamic noise, that contaminate data.

Acoustic signals like the rustling of leaves caused by wind are a part of the acoustic environment and are not addressed in this paper. Conversely, wind-induced microphone self-noise—hereafter referred to simply as “wind noise”—is a non-acoustic signal which should not be considered as indicative of the acoustic environment.^{1} For outdoor acoustic measurements in the audible frequency range, the dominant source of wind noise is the stagnation pressure fluctuations caused by atmospheric turbulence interacting with the microphone diaphragm or windscreen.^{2,3} While microphone windscreens can reduce the overall amount of contamination measured by a microphone, they do not eliminate all wind contamination.

Various methods are used to mitigate the excess pressures resulting from wind noise,^{4–7} such as using multiple microphone coherence to eliminate uncorrelated noise.^{8} Another possible solution relies on measuring wind speeds along with acoustic data so that data taken during times of increased wind can be removed. For example, the National Park Service (NPS) Natural Sounds and Night Skies Division typically removes any data that were collected when the measured wind speed exceeds 5 m/s.^{9} However, when considering data sets that contain only a single-channel recording and that do not include measured wind speeds, or even for relatively low but still relevant wind speeds, it can be more difficult to determine which data are the result of acoustic sources and which are wind-contaminated data.

This paper describes the development of a wind contamination identification and reduction method for one-third-octave band data taken with unobstructed, outdoor, screened microphones and is based on known spectral characteristics of wind noise contamination. The method uses the characteristic spectral slope of wind noise to classify individual spectral frequencies as either contaminated or uncontaminated. When several short-timescale measurements (e.g., several two-second spectra) are available, a decontaminated long-timescale average spectrum can be calculated (e.g., a spectrum composed of one-hour median spectral levels at each frequency, also known as an $L50$). This method allows for automatic calculation of wind-noise-reduced or decontaminated spectra—and thus decontaminated overall sound pressure levels—for single-microphone data where wind speeds were not measured. By removing the wind-noise-contaminated data, the method can automatically estimate decontaminated acoustic levels for a wind-noise-contaminated sound field.

## 2. Characteristic slope of wind-contaminated spectral data

### 2.1 Theory

Wind noise is caused by non-acoustic turbulent pressure fluctuations on a microphone diaphragm. The sources of these pressure fluctuations may include turbulence that occurs naturally in the atmosphere or wake turbulence generated by the microphone and windscreen. In outdoor measurements, atmospheric turbulence is the dominant source of wind noise.^{3} The magnitude of the pressure fluctuations produced by atmospheric turbulence depends on the wind speed, height above the ground, stability of the atmosphere, and frequency.

The frequency spectrum of atmospheric turbulent pressure fluctuations can be grouped into three frequency ranges: the energy-containing range, the inertial subrange, and the dissipation range. The energy-containing range occurs at low infrasonic frequencies (often less than a few Hz), which are below the frequencies of interest for the outdoor acoustic measurements considered in this paper. In the dissipation range, turbulent fluctuations rapidly dissipate into heat, so wind noise is typically negligible compared with the acoustic sources or instrumentation noise. The frequency of the dissipation range increases with wind speed and typically occurs above 100–1000 Hz.

For most outdoor acoustic measurements, contaminating wind noise in the inertial subrange is of primary importance. The inertial subrange lies between the energy-containing range and the dissipation range and can occur between high infrasonic and mid-range audible frequencies. In the inertial subrange, the stagnation pressure fluctuations caused by atmospheric turbulence interacting with the microphone diaphragm or windscreen are proportional to $f\u22125/3$, where $f$ is the frequency. Turbulent-turbulent pressure fluctuations, which are proportional to $f\u22127/3$, are negligible compared with the stagnation pressure fluctuations.^{3} Thus, the magnitude frequency spectrum of wind noise varies linearly with logarithmic frequency, i.e., $SPL\u221dlogf$, where $SPL$ is the sound pressure level created by wind noise.

Windscreens are often used in an attempt to reduce wind noise in outdoor acoustic measurements. The pressure measured by a microphone at the center of a windscreen is a combination of the acoustic pressure and the turbulent pressure fluctuations as mitigated by the windscreen. Within the inertial subrange, the turbulent pressure fluctuations vary linearly with the fractional-octave band, which produces a characteristic spectral slope indicative of wind noise. However, the characteristic spectral slope changes at a crossover frequency of $fc=V/(3D)$, where $V$ is the mean wind speed and $D$ is the windscreen diameter.^{10} At frequencies below $fc$ in the inertial subrange, the turbulent pressure fluctuations are coherent over the entire surface of the windscreen, and the characteristic spectral slope is −6.7 dB per decade.^{3} At frequencies above $fc$ in the inertial subrange, the turbulent pressure fluctuations are incoherent over the surface of the windscreen, and the characteristic spectral slope is −26.7 dB per decade.^{3,11} This result implies that a windscreen reduces wind noise by “averaging out” incoherent turbulent pressure fluctuations over its surface.^{2,3}

For many outdoor acoustic measurements with reasonably low wind speeds compared to the size of the windscreen, the crossover frequency occurs at infrasonic frequencies, and the characteristic spectral slope is −26.7 dB per decade at audible frequencies. For example, for a windscreen with a diameter of 9 cm at a wind speed of 5.4 m/s, the crossover frequency is $fc=$ 20 Hz. Although an increase in wind speed results in higher measured sound pressure levels, the characteristic spectral slope is independent of wind speed above the crossover frequency. Thus, if the crossover frequency is not greater than the lowest frequencies of interest, the characteristic spectral slope can be used to detect the presence of wind noise in acoustic measurements without requiring knowledge of the wind speed.

### 2.2 Current work

Data for this paper were collected in a remote, barren location in a Utah desert with few ambient acoustic sources, while a powered SOUNDBOKS speaker was used to generate a brown noise signal. The low-frequency roll-off of the speaker occurs around 50 Hz, below which there was no dominant acoustic source, and so measured levels are primarily the result of wind noise. Brown noise was chosen as the source signal because its characteristic slope—approximately −32 dB per decade for the type of brown noise used here—is similar to that of wind noise, and so the limitations of correctly classifying wind noise-contaminated data could be investigated. A GRAS 40-AE 12.7 mm diameter microphone with a GRAS AM0069 9-cm diameter porous foam ball windscreen was placed on a tripod at a height of approximately 1.5 m. Recorded data totaled approximately 75 min after removing time intervals where data were contaminated by airplanes flying overhead. Wind speeds were measured using a Kestrel 5500 weather meter at the sound measurement height with a two-second temporal resolution. Short-timescale spectra were likewise calculated for each two-second interval so that each spectrum has an associated measured wind speed.

Figure 1(a) shows the short-timescale one-third octave band spectra collected, each colored by its respective measured wind speed. Levels increase at low frequencies for higher wind speeds. Greater wind speeds also cause contamination to reach higher in frequency—at 0.7 m/s the contamination reaches only to about 25 Hz, while for a wind speed of 4.3 m/s the contamination reaches up to around 40 Hz. Figure 1(b) shows a few representative spectra, and how each spectral slope at low frequencies, regardless of measured wind speed, follows the characteristic slope of wind noise in the inertial subrange; the increase in wind speed correlates with an increase in overall levels, while the slope of −26.7 dB per decade remains unchanged.

## 3. Classifying contamination

Identifying contamination in screened microphone data processed using one-third-octave bands is accomplished by finding data which approximates the characteristic wind noise slope of −26.7 dB per decade. However, measured spectra typically include contributions from both acoustic signals and wind noise, so the measured data will rarely fit the characteristic wind noise slope precisely. Therefore, it is necessary to find data which *approximately* match the characteristic slope.

### 3.1 Data transformation

The complexity of finding points that fall along the same line can be greatly reduced by transforming the data. Spectral data consist of several two-dimensional data points, each giving the sound pressure level in decibels for a particular logarithmic fractional-octave band frequency. By using the characteristic wind-noise slope, these data are transformed into single-dimensional, linear data to find points that approximately match the characteristic slope.

The transformation can be considered as a projection of each data point along a line with the characteristic slope onto a vertical axis, similar to finding a y-intercept value for data points in a two-dimensional, linear space. As any two points can be connected by a straight line, we can use the analytic slope to find the point on the vertical axis that connects with each data point. For an illustration of the transformation method see Fig. 2(a). Note that the intercept need not be calculated at a vertical line going through the origin (i.e., $100=1$ Hz in logarithmic frequency space); the absolute *difference* between any two intercept values will be equal when projecting onto *any* vertical—or even horizontal (in this case logarithmic)—axis. Points that yield the same intercept value necessarily lie along the same line, and points with similar intercept values lie approximately on the same line. The differences between intercept values are then used to find points that approximate the characteristic wind noise slope.

### 3.2 Classifying contamination

Ideally, all contaminated data for a particular spectrum would yield the same intercept value; in practice, however, there will be some standard deviation between intercept values, depending on the particular data used. Some maximum standard deviation needs to be chosen—a default of 2 dB will generally suffice—so that intercept values near one another can be considered as fitting the characteristic slope.

In the inertial subrange, data points with wind contamination will give the lowest intercept values. Any acoustic signal will increase overall levels, and therefore intercept values. While this is not generally true for frequencies in the dissipation range, in practice the acoustic noise floor and/or acoustic signal will generally be louder than the dissipation range wind-contaminated levels, and so inertial subrange wind-contaminated frequencies will still give the lowest intercept values. However, it is still important to account for potential low outliers in intercept values.

The classification algorithm finds a tight grouping of points among the lowest intercept values, allowing for possible low outliers. By iteratively adding points with similar intercept values, the average intercept value is calculated, along with the standard deviation of the differences. The absolute differences of intercept values are used as they are invariant to the vertical axis location, unlike intercept values themselves. Additional points are added until the standard deviation of intercept differences exceeds the determined maximum standard deviation; the default standard deviation of 2 dB requires the grouping of intercept values have a standard deviation of no more than 2 dB. This process yields a group of points with similar intercept values. This is shown in Fig. 2(b), where all frequencies below 40 Hz were found to be contaminated.

The data giving the grouped intercept values all lie along a line with the characteristic slope of −26.7 dB per decade. These points can therefore all be classified as contaminated data. If determined necessary, data points that are low outliers among the intercept values can also be classified as contaminated. In addition to finding contaminated points, this process also finds a best-fit intercept value, which determines the line that the data approximate. This is shown in Fig. 2(b).

This method for classifying wind noise contamination assumes a constant characteristic spectral slope of −26.7 dB per decade for wind noise contamination, so the lower frequency limit is determined by the crossover frequency $fc$, but makes no further assumptions about the frequency range of contamination. Contaminated frequencies need not be adjacent to one another, and no cutoff frequency must be specified. Additionally, no assumptions are made about the frequency output of the source signal. Thus, the method can classify wind noise contamination in measured signals that contain acoustic spectra and wind noise spectra in overlapping frequency ranges, even when the source signal—which could be broadband, band limited, tonal, or even more complex—is unknown.

### 3.3 Experimental validation

The data considered previously are used to validate the classification method. Each frequency band from every two-second spectrum is individually classified as either contaminated or uncontaminated. Figure 3(a) shows the results for all of the spectra together, while Fig. 3(b) shows the results for a few particular spectra. While there are some data points labeled as uncontaminated at lower frequencies with high levels, the classification is accurate for most spectra. Between 12% and 30% of the data below 25 Hz were classified as uncontaminated, corresponding to the amount of time the measured wind speed was below 1.1 m/s, showing that the algorithm is successfully able to find wind contamination. More than 99% of the data above 50 Hz were classified as uncontaminated, and so very little of the acoustic signal was incorrectly classified as contaminated.

One limitation of the method is that some acoustic data can be misclassified as wind noise. A single two-second brown noise spectrum, with a wind speed of 4.1 m/s, was classified as contaminated up to 1 kHz, showing that the classifier can mistake brown noise for wind-noise contamination. However, this only occurred for a single two-second spectrum (where the lower frequencies were indeed contaminated), meaning that less than 0.05% of the brown-noise spectra, despite having a similar characteristic slope as wind noise, were classified as contaminated.

Further validation of the classification algorithm's success can be obtained by calculating the correlation coefficient between the measured wind speed and the best-fit intercept value for each spectrum. Higher wind speeds should result in larger best-fit intercept values, and perfect correlation would yield a value of 1. The correlation value calculated is 0.9, which indicates that this is indeed the case—an increase in wind speed results in a higher intercept value. The contamination found is a result of wind noise.

## 4. Removing contamination

In addition to classifying data, a decontaminated average spectrum for a longer timescale can be calculated by using the results of the contamination classification method on short-timescale spectra. As frequency bands are classified as contaminated or uncontaminated individually, the average spectrum is calculated for each frequency independently. Figure 4 shows three different versions of an $L50$ (median level): (1) using only the data with a measured wind speed of 0 m/s, (2) using all of the data, and (3) using only the data classified as uncontaminated. The 0 m/s $L50$ represents the sought-after result where the signal is a result of the acoustic sources in the absence of wind noise. All three types of $L50$ correctly measure the speaker signal above 50 Hz, but below the speaker roll-off the 0 m/s $L50$ represents the acoustic noise floor. The spectral slope at low frequencies of the all-data $L50$ is about −26.7 dB per decade, as there were no relevant acoustic sources in this low frequency range, and so the data is a result of wind noise alone. The decontaminated $L50$ is similar to the 0 m/s $L50$ in both spectral slope and overall levels.

It should be noted that removing several contaminated data can overemphasize short-timescale acoustic signals: if a low-frequency source of similar level as the wind noise were emitting sound for only 20 min during an hour, but 50 min of data were contaminated at a particular frequency, the level at this frequency would not represent the true average non-wind-contaminated sound level for the entire hour; the source signal may be entirely removed, present in every non-contaminated spectra, or anything in between the two. This is a risk of removing data, though if the data discarded were contaminated, keeping them will also result in inaccurate sound levels.

These results show that by removing wind-contaminated data, the average spectrum calculated is much more representative of what would be measured in the absence of wind noise. While the 0 m/s $L50$ was obtained by using the measured wind speed, the decontaminated $L50$ was found using *only* spectral data and does *not* require having a measured wind speed. This method has myriad applications—while some measurements contain short-timescale measured wind speeds, many others do not, and the recorded spectra may contain high levels of wind contamination. This method can be applied to experimental data, past and future, that do not have measured wind speed, and can automatically detect and remove the effects of wind noise.

## 5. Conclusion and broader applications

The wind noise contamination classification and reduction algorithm described herein has broad application for validating and removing non-acoustic noise from experimental data. Computationally efficient and simple to apply, the method requires only spectral levels, and thus can be applied to data whether or not wind speeds were recorded. Whether using the highest quality recording equipment or a simple hand-held device, this method can improve measured spectra by removing non-acoustic pressures.

Finding wind noise contamination in acoustic data is not a simple endeavor. While not without the possibility of error, this method has proven useful in simply and elegantly identifying and removing wind noise from spectral data. For data taken with a windscreen (and for frequencies within the inertial subrange), wind noise creates a characteristic slope of −26.7 dB per decade. By using this characteristic spectral slope, this method can determine which frequencies in a spectrum are likely contaminated by wind noise.

Detection of wind noise is performed automatically, and so the method can quickly indicate which frequencies in a spectrum are probably contaminated. Beyond classification, when multiple short-timescale spectra are available, a decontaminated average spectrum can be calculated by removing contaminated data so that the non-acoustic wind noise pressures do not erroneously increase average levels. Possible applications are extensive because the method does not require measured wind speeds, and so can be performed on spectra for which other information is not readily available. This wind noise contamination detection and reduction method allows for a simple yet efficient way to identify and remove contaminated data.

## Acknowledgments

This work was supported by a U.S. Army Small Business Innovation Research contract to Blue Ridge Research and Consulting, LLC, with Dr. James Stephenson as the technical monitor.