Under-ice ambient noise in the Arctic Ocean: observations at the long-term ice station

1. Introduction

Ocean ambient noise is one of the most important research topics in underwater acoustic as it can greatly affect the performance of underwater sonars (i.e., communication and detection). Therefore, a large amount of literature has been reported on ocean ambient noise in order to understand its temporal, spatial and frequency characteristics (Audoly et al., 2017; Brooker and Humphrey, 2016; Bittencourt et al., 2017; Da et al., 2014; Lin et al., 2005; Yang et al., 2018). In most oceans on the earth, ambient noise is mainly caused by thermal movement of seawater, hydrodynamic force (i.e., waves, tides, and currents), ocean biology (i.e., dolphins and whales), and man-made activity (i.e., shipping and exploration). However, the ocean ambient noise in the Arctic Ocean can also be produced by the combination of thermal, wind, and current stresses on the ice canopy in addition to the above sources. Ice events due to ice cracking, ice fracturing, ice breaking, ice shearing, ice ridging, ice collision, ice melting, and ice drifting can all produce ice-induced noise (Milne and Ganton, 1964; Ganton and Milne, 1965; Urick, 1984; Carey and Evans, 2011; Roth et al., 2012).

Under-ice ambient noise in the Arctic Ocean has been extensively studied since the end of last century and most of these researches focus on under-ice noise characteristics and the relationship between under-ice noise and meteorological variables. A new method is presented to explain how noise is generated under pack ice by ridging of the pack ice and simulated noise was compared with observations for an experiment conducted during the winter in the Beaufort Sea (Pritchard, 1984). Makris and Dyer (1986) showed that low-frequency ambient noise under pack ice was highly correlated with comprehensive stress caused by wind, current and drift. They then studied low-frequency ambient noise under drifting floes of the marginal ice zone and found that the long-term variations of the noise are strongly related to surface gravity wave forcing (Makris and Dyer, 1991). Under-ice ambient noise in the Beaufort Sea has been studied including its seasonal characteristics, seasonal space and time scales, and seasonal relationship to sea ice (Lewis and Denner, 1987, 1988a). Lewis also analyzed higher frequency (1 000 Hz) ambient noise in the Arctic Ocean (Lewis and Denner, 1988b) and the relationship between Arctic ambient noise and thermally induced fracturing of the ice pack (Lewis, 1994). Greening (1994) found that spatial distribution of ice cracking was consistent with a uniform distribution and source levels were usually from 110 dB re μPa²/Hz to 180 ${\rm{dB}}\;{\rm{re}}\;{\rm{μ}} {\rm{P}}{{\rm{a}}^{\rm{2}}}/{\rm{Hz}}$.

The research of ambient noise in the Arctic Ocean is not so active from the end of last century to almost 2010 and only few literature reported on this topic during this period of time. Johannessen et al. (2003) demonstrated that acoustic hotspots along the ice-edge region are due to mesoscale eddy currents interacting with the broken-up ice floes in the Greenland and Barents Seas’ marginal ice zone. Recently, ambient noise in the Arctic Ocean has re-attracted attention of researchers. Roth et al. (2012) analyzed the mean monthly spectrum levels of ambient noise on the Chukchi Sea continental slope from 2006–2009 and found that months with open-water had the highest noise levels and months with both ice cover and low wind speeds had the lowest noise levels. Kinda et al. (2013) studied under-ice ambient noise in Eastern Beaufort Sea, Canadian Arctic, and its relation to environmental forcing and showed that under-ice ambient noise had consistent correlations with large-scale regional ice drift, wind speed, and measured currents in upper water column. The noise transients in the under-ice ambient noise were further analyzed and sorted into three categories (Kinda et al., 2015). The directionality of the ambient noise field in an Arctic, glacial bay was measured and the results showed that different classes of source radiate noise in distinct spectral bands and were spatially diverse (Deane et al., 2014). Ambient noise in the eastern Arctic was studied using a drifting vertical hydrophone array and showed that the main sources of under-ice noise are broadband and tonal ice noises, bowhead whale calling, seismic airgun surveys, and earthquake T phases (Ozanich et al., 2017).

Although under-ice ambient noise in the Arctic Ocean has been extensively studied, most of the existing work analyzes the characteristics of large time scale noise and its relationship with the environment variables and there is little work reporting the characteristics of sea ice-induced impulsive ambient noise in detail. In this paper, we will show the time, frequency and amplitude distribution characteristics of two sea ice-induced impulsive ambient noises (ice collision noise and ice breaking noise) which were recorded by autonomous hydrophones at the long-term ice station during the 9th Chinese National Arctic Research Expedition and reveal the relationship between under-ice ambient noise and meteorological variables. The rest of this paper is organized as follows: Section 2 gives the details of the under-ice ambient noise observation experiment; Section 3 shows the analysis results of impulsive ambient noise and its relationship with meteorological variables; and Section 4 summarizes the whole paper.

2. Under-ice ambient noise observation experiment

Under-ice ambient noise observation experiment was conducted at the long-term ice station at 84°09′47.10′′N, 167°15′44.38′′W (as shown in Fig. 1a) on August 18, 2018 from 01:46 to 18:56 (GMT) during the 9th Chinese National Arctic Research Expedition. Figure 1b shows the ice condition at the edge of the long-term ice station from which one can see many stacked ices which were caused by ice canopy events. A vertical array with eight autonomous hydrophones which were uniformly spaced by 10 m was used to record under-ice ambient noise. Figure 1c shows two hydrophones used in this experiment. Note that the vertical array was deployed very close to the edge of the long-term ice station in order to record more sea ice-induced noise. The data from the hydrophone deployed to 30 m depth is used in this paper. The receiving sensitivity of hydrophones is relatively flat at $(-170 \pm 2)\;{\rm{d}}{{\rm{B}}_{}}\;{\rm{r}}{{\rm{e}}_{}}\;1\; {\rm{V}} \;{\rm{μP}}{{\rm{a}}^{ - 1}}$ over the working bandwidth 20 Hz to 20 kHz and the sampling frequency is 50 kHz. From 16:00 to 17:00 (GMT) on August 18 during this experiment, the ice activity near the vertical array was relatively intense and a large crack appeared on the ice canopy at the long-term ice station. Therefore, a few ice collision and ice breaking noises happened to be recorded by the hydrophones.

Figure  1.  The under-ice ambient noise observation experiment location of the long-term ice station (a), the ice condition at the edge of the long-term ice station (b), and two hydrophones used in the experiment (c).

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3. Analysis of under-ice ambient noise

3.1 The Arctic ice collision noise

The raw acoustic recordings were converted to instantaneous sound pressure using the analog-to-digital conversion parameters, the gain, and the hydrophone receiving sensitivity calibration. Figure 2 shows a sample of the ice collision noise in time domain from which one can clearly see many outliers. The amplitudes of these outliers are much greater than those of normal under-ice ambient noise. It can also be seen from Fig. 2a that the ice collision noise lasts for a few seconds (>3 s). It is reasonable because the collision event between ice canopies was not instantaneous and a lot of ice cracking and squeezing phenomenon happened during this process. One can also calculate the spectrogram of under-ice ambient noise using the “spectrogram” function in MATLAB software. In this paper, the fast Fourier transform point was 2 048, the overlap rate was 50%, and the window function was the default Hamming window of the spectrogram function. Figure 2b is the corresponding time-frequency analysis (spectrogram) of the Arctic ice collision noise shown in Fig. 2a. The Arctic ice collision noise has very abundant frequency components which are from very low frequency to very high frequency. However, most of its energy is concentrated in the lower frequency band (<1 kHz).

Figure  2.  The time domain waveform of the Arctic ice collision noise recorded by autonomous hydrophone at the long-term ice station during the 9th Chinese National Arctic Research Expedition (a); and the corresponding time-frequency analysis (spectrogram) of the Arctic ice collision noise shown in Fig. 2a (b).

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We use two distributions (symmetric alpha stable (${\rm{s}}\alpha {\rm{s}}$) distribution and Gaussian distribution) to fit the under-ice ambient noise. ${\rm{s}}\alpha {\rm{s}}$ distribution is a kind of heavy-tailed distribution and usually used in economics and physics as models of rare, but extreme events (i.e., earthquakes or stock market crashes) (Huang et al., 2013; Shen et al., 2016; Stoyanov et al., 2006). Suppose $\left\{ {{x_1},{x_2}, \cdots,{x_n}} \right\}$ are independent and identically distributed random variables with ${\rm{s}}\alpha {\rm{s}}$ distribution, then the characteristic function can be given by $\varphi (t) = {{\rm{e}}^{ - r|t|{}^{\alpha}}}$, where $\alpha $ is characteristic exponent and describes the tail of the distribution. The smaller $\alpha $ is, the more severe the tail of the distribution is. $\gamma $ is scale parameter and is similar to the variance in Gaussian distribution. This paper uses the method presented by McCulloch (1986) to estimate the two parameters when fitting the amplitude of under-ice ambient noise. Figure 3 shows the probability density function (PDF) curves of amplitude of the Arctic ice collision noise. Note that we use the raw data (the data after analog-to-digital conversion) rather than the converted sound pressure to do the statistical analysis. The red line in Fig. 3 is the fitting result by ${\rm{s}}\alpha {\rm{s}}$ distribution with the characteristic exponent $\alpha $=1.22 and the scale parameter $\gamma $=529 while the black line is the fitting result by Gaussian distribution with the mean $\mu $=18.7 and the variance δ=1 744. One can easily find from Fig. 3 that ${\rm{s}}\alpha {\rm{s}}$ distribution can fit better with the experimental data than Gaussian distribution. As well known, ${\rm{s}}\alpha {\rm{s}}$ distribution degenerates into a Gaussian distribution when $\alpha $=2. A much smaller characteristic exponent in the fitting result means that this ice collision noise sample is very impulsive. Therefore, algorithms which assume that ambient noise follows Gaussian distribution will suffer severe performance degradation under the ice collision noise environment. Note that we use log-scale for both axes in Fig. 3. By using the log-scale for x-axis, one can easily see how well different distributions fit the real data especially for the outliers. In order to plot the log-scale figures, this paper uses the absolute value of the real data in the statistic. It can also be seen from Fig. 3 that the PDF of the real data has a very heavy tail. ${\rm{s}}\alpha {\rm{s}}$ distribution also has a heavy tail while Gaussian distribution has a sharp PDF decrease for the large values (i.e., >3 000) which again demonstrates that ${\rm{s}}\alpha {\rm{s}}$ distribution can fit better for the real data compared with Gaussian distribution.

Figure  3.  The statistical characteristics of the Arctic ice collision noise shown in Fig. 2a and the fitting results by two distributions (${\rm{s}}\alpha {\rm{s}}$ distribution and Gaussian distribution) (a); and a zoom in Fig. 3a when limiting the amplitude greater than 1 000 (b).

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3.2 The Arctic ice breaking noise

Figure 4a shows a sample of the Arctic ice breaking noise in time domain from which one can also see some outliers. Though their amplitudes are much greater than other under-ice ambient noise, they last very short time (i.e., several milliseconds or dozens of milliseconds). It is also reasonable because the ice breaking event happened instantaneously. Figure 4b is the corresponding time-frequency analysis (spectrogram) of the Arctic ice breaking noise shown in Fig. 4a. The Arctic ice breaking noise also has very abundant frequency components which are from very low frequency to very high frequency. However, most of its energy is also concentrated in the lower frequency band (<3 kHz) which is much higher than the ice collision noise. Note that the 12 kHz interference (marked by red circles in Fig. 4) was from the ocean depth measuring sonar on the R/V Xuelong.

Figure  4.  The time domain waveform of the Arctic ice breaking noise recorded by autonomous hydrophone at the long-term ice station during the 9th Chinese National Arctic Research Expedition (a); and the corresponding time-frequency analysis (spectrogram) of the Arctic ice breaking noise shown in Fig. 4a (b).

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Figure 5 shows the amplitude statistical characteristics of the Arctic ice breaking noise. Note that we also use the raw data (the data after analog-to-digital conversion) to do the statistical analysis. The red line in Fig. 5 is the fitting result by ${\rm{s}}\alpha {\rm{s}}$ distribution with the characteristic exponent $\alpha $=1.91 and the scale parameter γ=262 while the black line is the fitting result by Gaussian distribution with the mean $\mu $=24.6 and the variance δ=779. One can easily find from Fig. 5 that the ${\rm{s}}\alpha {\rm{s}}$ distribution can fit better with the data than Gaussian distribution. A much larger characteristic exponent in the fitting results means that the ice breaking noise sample is not so impulsive as the ice collision noise sample. It is understandable because though the instantaneous ice breaking activity can produce strong impulsive noises, this phenomenon did not always happen. Actually, it happened rarely with very short duration. Therefore, these occasional ice breaking noises cannot greatly affect the characteristic exponent in terms of long-time statistics. Note that we also use log-scale for both axes in Fig. 5. It can be seen from Fig. 5 that the PDF of Arctic breaking noise also has a heavy tail. ${\rm{s}}\alpha {\rm{s}}$ distribution can fit well for the outliers while Gaussian distribution has a sharp PDF decrease for the large values (i.e., >2 000).

Figure  5.  The statistical characteristics of the Arctic ice breaking noise and the fitting results by two distributions (${\rm{s}}\alpha {\rm{s}}$ distribution and Gaussian distribution) (a); and a zoom in Fig. 5a when limiting the amplitude greater than 1 000 (b).

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3.3 The relationship between under-ice noise and meteorological variables

Figure 6 shows the meteorological variables including atmosphere temperature and wind speed recorded on August 18 by meteorological stations on the R/V Xuelong. As mentioned above, the ice collision and ice breaking noises were recorded during the period from 16:00 to 17:00 which are marked by two red lines in Fig. 6. This phenomenon demonstrates that the ice canopy was relatively active during this period. Therefore, a natural question will arise why the ice canopy was so active during this period. One may find some clues from the recorded meteorological variables. It can be seen from Fig. 6 that the wind speed increased obviously from 9:00 and got to the maximum value around 16:00. During this period the atmosphere temperature also increased gradually. The increasing wind speed would definitely make the ice canopy move and the increasing atmosphere temperature would accelerate the melting of the ice canopy and make its structure more unstable. Therefore, it is reasonable to make the conclusion that the impulsive ambient noise was caused by the combined force of high wind speed and increasing atmosphere temperature on the ice canopy.

Figure  6.  Atmosphere temperature (a) and wind speed (b), recorded on August 18 by meteorological station on the R/V Xuelong. The red lines mark the period when the ice canopy was relatively active. The black lines show the increasing trend of the two meteorological parameters.

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The Pearson correlation coefficients between long-term power spectral density (PSD) variations of under-ice ambient noise and meteorological variables will be analyzed in the following context. Pearson correlation coefficient is a measure of the linear correlation between two variables. Given paired data $\left\{ {\left({{x_1},{y_1}} \right),\left({{x_2},{y_2}} \right), \cdots,\left({{x_n},{y_n}} \right)} \right\}$ consisting of n pairs, Pearson correlation coefficient ${r_{xy}}$ is defined as

where n is the sample size, ${x_i}$ and ${y_i}$ are the individual sample points indexed with i, $\bar x = \dfrac{1}{n}\displaystyle\sum\limits_{i = 1}^n {{x_i}} $ (the sample mean) and analogously for $\bar y$.

Note that the first hour and the last hour noise data are excluded in data processing as many scientific researchers were working on the long-term ice station to deploy or recycle their facilities during these periods, producing a lot of noise which may influence the analysis results. The hydrophones autonomously stored ambient noise data every 8 min. A total of 114 segments of 8-min-long noise data were obtained for this under-ice ambient noise observation experiment. Figure 7 shows the meteorological variables that are averaged every 8 min corresponding to the length of each data file. It can be seen from Fig. 7a that the temperature was relatively stable at the beginning of the experiment, but there is a sharp fall around 05:42. The atmosphere temperature fluctuated from 06:42 to 12:42. Then the temperature gradually increased from 12:42. The wind speed also decreased around 05:42 and it gradually increased from 06:42 to 15:42 and then became relatively stable.

Figure  7.  Atmosphere temperature (a) and wind speed (b) recorded on August 18 by meteorological station on the R/V Xuelong from 02:50 to 17:54. Note that the meteorological data are averaged every 8 min corresponding to the length of each signal file.

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Figure 8a shows the PSD variations along with time at 150 Hz, 450 Hz, 750 Hz, and 1 050 Hz. The PSDs of under-ice ambient noise are calculated using the “pwelch” function in MATLAB software with default Hamming window and 50 000 (equals to the sampling frequency) point FFT length, yielding 1 Hz frequency bins with 50% overlap. It can be seen that the PSDs fluctuate a lot before 06:42, are much stable from 06:42 to 11:42, increase slowly from 11:42 to 15:42, and increase rapidly during the period when the ice canopy was active. Figure 8b shows the Pearson correlation coefficients between the PSDs of under-ice ambient noise at different frequencies and meteorological variables. In this paper, we limit the maximum frequency to 3 kHz as previous works (Milne and Ganton, 1964; Ganton and Milne, 1965; Urick, 1984) have demonstrated that the frequency of thermally induced and wind induced under-ice ambient noise mainly focus in the low-frequency. It can be seen that the PSDs of under-ice ambient noise show higher correlation with the atmosphere temperature especially when the frequency is lower than 2 kHz (Pearson correlation coefficients>0.5). However, the Pearson correlation coefficients fluctuate a lot when the frequency is greater than 2 kHz. One can also find that the PSDs show weak correlation with the wind speed (Pearson correlation coefficients at most frequency are smaller than 0.3). This result is reasonable because the wind cannot induce ocean waves in the experimental area due to the almost fully covered ice canopy. Therefore, wind cannot directly cause changes in the under-ice ambient noise. However, atmosphere temperature variations can cause direct influence to the ice canopy such as melting and breaking, making the under-ice ambient noise change.

Figure  8.  The PSD variations along with time at different frequencies of under-ice ambient noise (a); and the Pearson correlation coefficients between the PSDs of under-ice ambient noise at different frequencies and meteorological variables (b).

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4. Conclusions

In this paper, under-ice ambient noise recorded at the long-term ice station during the 9th Chinese National Arctic Research Expedition is studied. Sea ice-induced impulsive noises (ice collision and ice breaking noise) are firstly analyzed using two 7-s-long noise samples. Both noises show obvious impulsive characteristic and their amplitude can be better fitted by ${\rm{s}}\alpha {\rm{s}}$ distribution. However, the durations of two noises are very different that the ice collision noise lasts for several seconds while the duration of ice breaking noise is much shorter (i.e., less than tens of milliseconds). Using the limited meteorological variables, we deduce that the impulsive ambient noise was caused by the combination of high wind speed and increasing atmosphere temperature on the ice canopy. The Pearson correlation coefficients between long-term PSD variations of under-ice ambient noise and meteorological variables indicate that the under-ice ambient noise was more correlated with the atmosphere temperature (especially the low frequency) compared with wind speed. Other meteorological variables such as currents in the upper water column are definitely important contributors to under-ice ambient noise. Therefore, the relationship between under-ice ambient noise in the Arctic Ocean and more meteorological variables will be considered in future work.

Acknowledgement

We thank all participants of the under-ice noise observation experiment of the 9th Chinese National Arctic Research Expedition for their assistance.