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).

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 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 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 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.

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 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.