Data-Driven Analysis of Ocean Fronts’ Impact on Acoustic Propagation: Process Understanding and Machine Learning Applications, Focusing on the Kuroshio Extension Front

Abstract

Ocean fronts, widespread across the global ocean, cause abrupt shifts in physical properties such as temperature, salinity, and sound speed, significantly affecting underwater acoustic communication and detection. While past research has concentrated on qualitative analysis and small-scale research on ocean front sections, a comprehensive analysis of ocean fronts’ characteristics and their impact on underwater acoustics is lacking. This study employs high-resolution reanalysis data and in situ observations to accurately identify ocean fronts, sound speed structures, and acoustic propagation features from over six hundred thousand Kuroshio Extension Front (KEF) sections. Utilizing marine big data statistics and machine learning evaluation metrics such as out-of-bag (OOB) error and Shapley values, this study quantitatively assesses the variations in sound speed structures across the KEF and their effects on acoustic propagation shifts. This study’s key findings reveal that differences in sound speed structure are significantly correlated with KEF strength, with the channel axis depth and conjugate depth increasing with front strength, while the thermocline intensity and depth excess decrease. Acoustic propagation features in the KEF environment exhibit notable seasonal variations.

1. Introduction

Ocean fronts, characterized by significant changes in the temperature, salinity, density, or other physicochemical properties of water masses, typically occur in the upper hundreds of meters of the ocean [1]. These frontal boundaries profoundly impact the distribution of marine life [2] and substantially influence the propagation paths and speeds of sound waves in the ocean [3]. The physical environment of ocean front regions is marked by horizontal non-uniformity in the sound speed profile within the water column, affecting sound waves’ refraction, scattering, and reflection, which are crucial for military oceanography [4], marine environmental monitoring [5], and underwater acoustic communication [6].

To systematically understand and predict the specific impacts of ocean fronts on acoustic propagation, researchers have employed various methods, including field observations [7], sound speed reconstruction [8], and simulation modeling [9]. The influence of oceanic fronts on underwater acoustics can be divided into two main aspects: Firstly, oceanic fronts affect the sound speed structure of seawater. As proposed by Etter [10], this impact is reflected in the surface sound speed structure and the sound channel axis. Comprehensive reviews of previous studies [11,12] have shown that the morphology and location of oceanic fronts significantly influence acoustic propagation, leading to transmission loss increases of 6~20 dB. Chen, Yang [13] analyzed the typical features of the Kuroshio Extension Front (KEF) and constructed a typical oceanic front profile spanning 100 km, with a sound channel axis depth ranging from 1000 m on the south side to 300 m on the north side. Their findings indicate that the KEF mainly affects acoustic propagation by altering the depth of the sound channel axis. DeCourcy, Lin [14] examined the effects of oceanic front width and sound speed on acoustic propagation. Liu, Piao [7] conducted multi-feature observations of marine acoustics and physical oceanography targeting the subarctic oceanic front in 2019, discovering that the oceanic front significantly changed the depth of the sound channel axis on both sides of the front, thereby altering the direction of acoustic wave propagation. Shafiee Sarvestani [15] investigated the effects of the Red Sea water mass on sound speed structure and seasonal changes using a ray model, finding that the Red Sea intrusion current significantly altered the propagation paths of sound rays, causing the convergence zone to widen and move closer to the sound source.

Secondly, the impact of oceanic fronts on acoustic propagation characteristics is noteworthy. Colosi and Rudnick [16] analyzed high-resolution towed conductivity–temperature–depth (CTD) profiler sections in the eastern North Pacific from March to April 2005, quantifying the spatial scale of the upper ocean sound speed structure. Their study, combined with acoustic propagation experiments and simulations, revealed that the upper ocean sound speed structure in the mixed and transition layers can cause transmission loss (TL) variations of ±5~20 dB at medium and low frequencies. Wang, Zhu [17] employed the finite feature method to examine the effects of various oceanic fronts on acoustic propagation, finding that low-frequency sound energy significantly leaks towards the seabed when transitioning from warm to cold water areas, whereas more energy is confined to the surface layer when transitioning from cold to warm water areas. Ozanich, Gawarkiewicz [18] conducted acoustic experiments on low-frequency sound waves passing through the New England shelf front, demonstrating that significant changes in the received pulse occur when the geometric shape of the oceanic front changes. These findings, confirmed by two-dimensional and three-dimensional parabolic equation models, highlight the sensitivity of acoustic propagation to the geometric shape of oceanic fronts observed via satellite sea surface temperature images. Liu, Chen [19] used a two-dimensional parameterized model to show that sound waves propagating from warm to cold water masses cause the convergence zone to move closer to the sound source, while propagation from cold to warm water masses causes the convergence zone to move backward. This shift varies with the strength of the oceanic front. Li, Liu [20] quantitatively analyzed the impact of the subarctic front on underwater acoustic detection using observational data from the Northwest Pacific, noting that sound sources in front of the cold water mass had superior detection performance, especially for cold water detection (horizontal detection range > 60 km), whereas those in the warm water mass exhibited poorer detection performance (shallow-water horizontal detection range < 10 km).

With technological advancements, acoustic propagation and prediction in complex marine environments have garnered significant attention. The development of unmanned, informational, and intelligent maritime operations has progressed substantially [21]. Key technological breakthroughs include real-time inversion of sound speed structure [22,23], underwater early warning detection [24], intelligent communication [25], and prediction of acoustic transmission loss [26]. For instance, Mallik, Jaiman [26] proposed a convolutional recurrent autoencoder network architecture capable of learning the transmission loss of sound signals affected by geometric spreading, refraction, and reflection from the two-dimensional ocean surface and seabed. McCarthy, Sarkar [27] used a decision tree model based on Bellhop to predict transmission loss, validating their model with field data collected by AUVs and achieving promising results. However, research indicates that different oceanographic analysis schemes and data inputs significantly impact the accuracy of underwater acoustic prediction [28]. The importance of understanding the typical distribution features of ocean sound speed structure in the study area and selecting appropriate marine environmental factors for the real-time inversion of underwater acoustics is crucial.

In oceanic frontal zones, drastic changes in temperature and salinity can cause the sound speed profile to vary significantly over very short horizontal and vertical distances. This necessitates a higher accuracy in understanding the sound speed field features and the properties of acoustic propagation in these regions. Previous studies on oceanic fronts, a significant marine phenomenon affecting acoustic propagation, have primarily focused on the overall impact on propagation loss [14,17] or on specific features of the acoustic propagation [13,16]. However, there remains a gap in the quantitative analysis of the impact of oceanic fronts on acoustic propagation features and the comprehensive analysis of various sound speed structural features. Although our previous research [29] explored the characteristics of oceanic fronts, it was found that linear feature evaluation methods and small-sample datasets could not fully capture the impact of the KEF on underwater acoustic structure and propagation.

This study addresses this gap by focusing on the KEF, one of the world’s strongest oceanic fronts, utilizing the advantages of big ocean data. Thousands of oceanic front sections were extracted, and the sound speed structure and acoustic propagation features in these environments were analyzed. The importance of different features was assessed using machine learning (ML) methods. This paper is structured as follows: Section 1 reviews the research progress and gaps identified by previous scholars; Section 2 introduces the data and feature evaluation methods; Section 3 investigates the impacts of oceanic fronts on underwater acoustic structure and propagation in detail; Section 4 evaluates the application scenarios and prospects of the quantitative impact of oceanic fronts; and Section 5 summarizes the study and provides future outlooks.

2. Data and Methods

Near latitude 35° N and longitude 141° E, the Kuroshio Current, after departing from the coast of Japan, meanders eastward and gradually dissipates around longitude 165° E. This section, commonly referred to as the Kuroshio Extension (KE) [29], is a zonal jet stream characterized by large-amplitude bending; it intersects with the Oyashio, a cold and low-salinity current from the north, in the eastern region of Japan. The confluence of these two western boundary currents forms a narrow transition zone, known as the KEF [30], where physical and chemical features change drastically.

To investigate the impact of the KEF on acoustic propagation and conduct quantitative assessments, this study evaluated the effects of the oceanic front on sound speed structure and acoustic propagation using high-resolution reanalysis data and in situ observation profiles. The position of the KEF was determined through a front line extraction method within the study area, and research sections were defined at specific longitudinal intervals. Nine types of sound speed structure features were analyzed based on typical oceanic sound speed structures. Additionally, the acoustic propagation features of the research sections were determined using ray acoustics. The impact of the sound speed structure in oceanic front environments on acoustic propagation was systematically evaluated by integrating the out-of-bag (OOB) error and Shapley value assessment methods. The research process is illustrated in Figure 1.

2.1. Data

2.1.1. Marine Environmental Data

The high-resolution Japan Coastal Ocean Predictability Experiment 2 Modified (JCOPE2M) reanalysis dataset encompasses the Northwest Pacific, offering a temporal resolution of one day, a horizontal resolution of 1/12°, and 46 σ vertical layers [31,32]. This dataset integrates high-resolution satellite sea surface temperature data and various observational sources, providing high resolution and accuracy, and is extensively utilized in mesoscale phenomenon research [33,34,35]. The data span from January 1993 to December 2022. In situ observation data are derived from the KE System Study (KESS), a large-scale observational project funded by the National Science Foundation of the United States. The KESS aims to identify and quantify the dynamic and thermodynamic processes controlling the variability and interactions between the KE and the recirculation gyres [36]. This study employs CTD data from an in situ observation conducted by the Research Vessel Melville from June to July 2006, which extracted four sets of parallel continuous sections exhibiting distinct KEF features. The measured profile data were interpolated to the seabed using JCOPE2M data.

2.1.2. Etopo2022 Bathymetric Data

Bathymetric data were sourced from ETOPO 2022 [37], featuring an enhanced 15-arcsecond resolution. This global dataset integrates terrain, bathymetric, and coastline data from both regional and global sources, providing a comprehensive and high-resolution depiction of the Earth’s surface geophysical features; it incorporates the latest advancements in data sources and processing techniques since the release of ETOPO1 in 2010. The ETOPO 2022 model combines data from numerous airborne lidar, satellite topography, and shipborne bathymetric datasets from the United States, significantly improving the relative and absolute horizontal geolocation and vertical accuracy of the global topographic model. This dataset is used for providing seafloor topography inputs for acoustic propagation simulations and for calculating depth excess.

2.2. Methodology

2.2.1. Ocean Front Identification and Section Extraction Method

Previous research has often relied on contour lines of specific oceanic features to represent the position of ocean fronts [38]. This study enhances front extraction by integrating the OFFD parameter with isovelocity lines in the KE region. Initially, the JCOPE2M temperature and salinity data were converted into sound speed data using the Mackenzie sound speed empirical formula. Subsequently, the absolute gradient method was used to calculate the horizontal sound speed gradient (C_Grad) in the study area, as shown in Equation (1):

$$C_{Grad}=\sqrt{{\left(\partial {\varphi }_U/\partial lx\right)}^2+{\left(\partial {\varphi }_V/\partial ly\right)}^2}$$

(1)

where $\partial {\varphi }_U$ and $\partial {\varphi }_V$ represent the differences in the zonal and meridional directions of the study feature (sound speed), respectively; ∂lx is the zonal distance; and ∂ly is the meridional distance.

Utilizing the maximum horizontal sound speed gradient near the Kuroshio Current axis at 144° E as the search center, and defining a 10 m/s variation in sound speed from this center as the search interval, sound speed contour lines were drawn. These isovelocity lines were interpolated to the reanalysis data grid points (with a resolution of 1/12°), duplicate points were removed, and the front line coincidence degree (C_OFFD) for each contour line was calculated. The isovelocity line with the highest C_OFFD was selected as the front line. Equation (2) details the calculation method, where m represents the number of grid points with the highest sound speed gradient in the meridian direction within the front zone crossed by the isovelocity line, and N denotes the total number of meridians traversed:

$$C_{OFFD}={\displaystyle \frac{{\displaystyle {\sum }_1^{\mathrm{m}}{C}_{Grad}}}{N}}$$

(2)

Previous studies found that the KEF is particularly strong at a depth of 300 m [39]. Utilizing the sound speed at this depth, the KEF was pinpointed, and cross-sections centered on the front line position with a 100 km span were analyzed. Only cross-sections where the horizontal sound speed gradient at the front line exceeded 0.1 m/s/km were included, resulting in 651,316 KEF cross-sections being retained for this study. Each cross-section was linearly interpolated to a horizontal resolution of 1 km and vertically interpolated to a vertical resolution of 1 m using Akima interpolation. The strength of the ocean front was defined as the horizontal sound speed gradient at the front line at 300 m depth, while the width was determined by the distance between the start and end positions of the continuous interval where the horizontal sound speed gradient exceeded 0.1 m/s/km, centered on the front line at 300 m depth. Schematic diagram of front line identification and oceanic front section extraction as shown in Figure 2.

2.2.2. Underwater Acoustic Features and Calculation Methods

Ocean fronts significantly affect the distribution of sound speed in the upper layers of seawater, thereby impacting acoustic propagation. According to ray acoustics theory, the sound speed distribution can be divided into multiple layers, each with a constant sound speed gradient. The upper interface of the first layer is the sea surface, with a sound speed of $c_0$, and the lower interface of the nth layer is the seabed, with a sound speed of $c_n$. Assuming that both the source and the receiver are placed at 150 m depth, where the sound speed is $c_{s_0}$, the model also accounts for the minimum sound speed in the convergence zone. It is essential to ensure that sound rays emitted at an angle α can reflect off the seabed, as illustrated in Equations (3) and (4), where k represents different water layers, and s denotes the water layer in which the sound source is located.

$$c_n>c_k\hspace{1em} k=s_0,s_0+1,\cdot \cdot \cdot n-1$$

(3)

$$c_k=c_{s_0}/\cos {\alpha }_0=c_{s_0+1}/\cos {\alpha }_1=\cdot \cdot \cdot c_{n-1}/\cos {\alpha }_{n-1}$$

(4)

where $c_k$ refers to the feature parameter of a given sound ray (a sound ray with an emission angle of ${\alpha }_0$), which equals the sound speed at the horizontal flipping depth (conjugate depth) of that sound ray. Among the numerous sound rays emitted from an omnidirectional sound source, the minimum emission angles forming the convergence zone are determined by Equation (5). Sound rays with $c_n<c_k$ will be reflected by the seabed, forming seabed reflection propagation. In the sound source layer, when $c_{s_0}<c_0$, the surface layer functions as a mixed-layer duct.

$${\alpha }_{\min }\ge \arccos c_0/c_{s_0}$$

(5)

Combining the typical stratified structure of seawater sound speed (Figure 3) with ray acoustics theory, we extracted sound speed structural features on both sides of the oceanic front section based on the characteristics of the mixed layer, thermocline, and deep-sea isothermal layer. These features included the following: (1) surface acoustic speed (SSS, m/s), (2) sonic layer depth (SLD, m), (3) bottom sonic layer speed (BSLS, m/s), (4) transition layer sound speed gradient (TLSS, m/s/m), (5) sound channel axis depth (SCAD, m), (6) sound channel axis speed (SCAS, m/s), (7) conjugate depth (CD, m), (8) conjugate depth speed (CDS, m/s), and (9) depth excess (m). The depth excess is the difference between the conjugate depth of the sampling point and the ETOPO2022 depth. It is noteworthy that the profile data used for feature extraction on both sides of the ocean front were obtained from two endpoints of an extracted 100 km ocean front section, representing the cold-water side and the warm-water side, respectively.

Bellhop is a widely used simulation method in acoustic propagation research [40,41,42] and has shown strong performance in convergence zone studies [43]. This study employed Bellhop for acoustic propagation simulations in KEF environments. In the Bellhop model, the evolution of the sound beam is determined by the beam width p(s) and beam curvature q(s), governed by the following differential equations, where s represents the arc length along the ray path.

$${\displaystyle \frac{dq}{ds}}=c(s)p(s)$$

(6)

$${\displaystyle \frac{dp}{ds}}=-{\displaystyle \frac{c_m}{c^2(s)}}q(s)$$

(7)

where $c_m$ is the second derivative of the sound speed, as shown in Equation (8), and $(N_{(r)},N_{(z)})$ are the unit normals in two directions.

$$\begin{array}{l}{c}_m=c_{rr}{\left({\displaystyle \frac{dr}{dn}}\right)}^2+2c_{rz}\left({\displaystyle \frac{dr}{dn}}\right)\left({\displaystyle \frac{dz}{dn}}\right)+c_{zz}{\left({\displaystyle \frac{dz}{dn}}\right)}^2\\ \hspace{1em}=c_{rr}{(N_{(r)})}^2+2c_{rz}(N_{(r)})(N_{(z)})+c_{zz}{(N_{(z)})}^2\end{array}$$

(8)

Bellhop’s primary distinction from traditional ray models lies in its use of Gaussian beam tracking instead of traditional geometric beam tracking, enabling the calculation of sound fields in horizontally inhomogeneous environments. The model’s simulation of sound ray propagation closely aligns with the results of the full wave model [44]. It effectively addresses the limitations of traditional ray models, such as zero sound intensity in the shadow zone and infinite sound intensity at the caustic line cross-section. The parameters for this study were established as follows: the sound source frequency was 1 kHz, the sound source depth was 150 m, and the seabed parameters, based on the work of Hamilton [45], included a density of 1.421 g/cm³, a compressional wave speed of 1520 m/s, and an attenuation coefficient of 0.12 dB/λ.

This study primarily investigated the features of acoustic propagation, specifically the direct detection distance and convergence zone distance. In typical deep-sea environments, when the source and receiver are positioned shallower than the sound channel axis, sound rays reflect above and below the axis, forming periodic high-intensity focal regions known as convergence zones (CZs) [46]. These zones facilitate underwater target detection and long-range underwater acoustic communication. Bellhop is used to simulate the propagation of sound rays with a minimum launch angle α_min. Direct detection distance is defined as the distance from the sound source to the location where the sound ray first reaches the receiving depth (300 m), while convergence zone distance is the distance between the first reversal point near the sea surface and the sound source. Figure 4 illustrates the source deployment position and acoustic propagation.

2.2.3. Feature Importance Evaluation Method

Feature importance refers to the degree of impact that features have on the target feature, offering a valuable perspective for feature analysis. By identifying which features significantly influence decision-making processes, ML demonstrates substantial potential in evaluating feature importance [47,48]. This study used the OOB error [49] and the Shapley value method [50] to assess the impact of various changes in sound speed structures on acoustic propagation features.

The Random Forest (RF) algorithm is a parallel ensemble learning method comprising numerous decision trees. Beyond its capabilities in classification and regression, it excels in feature importance analysis [51], data imputation [52], and survival analysis [53]. The RF algorithm utilizes a bootstrap method to randomly draw N datasets from the original data, each containing approximately two-thirds of the total data. Through the RF algorithm’s unique generalization error estimation method, known as the OOB error, the optimal parameters for decision trees (number of feature nodes and number of decision trees) are determined. This error is derived from the unbiased estimation of conventional error using the one-third of the dataset not involved in model construction.

The Shapley value method, a non-additive measure of weighting, calculates weights by evaluating the contribution of each combination of indicators to higher-level indicators and objectives, ensuring more objective and realistic indicator weights. The steps for calculating indicator weights based on Shapley values are as follows:

(1) Normalize the initial data on the importance of a single performance indicator $(b_1,b_2,\dots ,b_n)$ to determine the contribution of a single indicator $v(i)$:

$$v(i)={\displaystyle \frac{b_i}{{\displaystyle {\sum }_{i=1}^n{b}_i}}}$$

(9)

(2) Calculate the combined contribution of acoustic propagation $v(1,\dots ,n)$. Let $N=\left\{1,2,\dots ,n\right\}$ be the set of indicators for the same section, while the real-valued function corresponding to any subset S is $V(S)$. For $V(\varphi )=0$, if the correlation between indicators is very weak, satisfying $V(S_1\cup S_2)>V(S_1)+V(S_2)$ while $S_1\cap S_2=\varphi$, the combined contribution rate should account for a larger proportion by multiplying it with the coefficient 1.2 to increase the contribution of the indicator combination; conversely, if the correlation between indicators is strong, satisfying $V(S_1\cup S_2)<V(S_1)+V(S_2)$ while $S_1\cap S_2=\varphi$, the combined contribution should account for a smaller proportion by multiplying it with the coefficient 0.8 to reduce the contribution of the indicator combination. The combined contribution of multiple indicator combinations is calculated based on whether they reflect the majority of correlations [54].

$$v(1,2,\dots ,n)=\left\{\begin{array}{l}0.8{\displaystyle \sum _{i=1}^{n}v(i), v(n)\in [0,1]}\\ 1.2{\displaystyle \sum _{i=1}^{n}v(i), v(n)\in [0,1]}\end{array}\right.$$

(10)

(3) Calculate the Shapley values for each change in sound speed structure, that is, the corresponding weights $w_i$ for each indicator, where $\left|S\right|$ is the number of indicator combinations in subset S, and $\left|S\right|/i$ is the combination of subset S after removing indicator i.

$$w_i={\displaystyle \sum _{S\subset N,i\subset S}^n\frac{(n-\left|S\right|)!\times (\left|S\right|-1)!}{n!}}[v(\left|S\right|)-v(\left|S\right|/i)]$$

(11)

3. Detailed Investigation of the Impact of Oceanic Fronts on Acoustic Structure and Propagation

3.1. Quantitative Assessment of the Impact of the KEF on Acoustic Structure Features

A statistical analysis of the 651,316 obtained oceanic frontal sections revealed a significant positive correlation between the intensity and width of oceanic fronts, as shown in Figure 5a. A Spearman correlation analysis of the strength and width sequences showed a correlation coefficient of 0.461, with a p-value significantly less than 0.001. Consequently, this study primarily used strength as the key feature of oceanic fronts when investigating the impact of the KEF on sound speed structure and acoustic propagation. Subsequently, the frequency of oceanic front strengths was tallied at intervals of 0.1 m/s/m, revealing that the KEF strength exhibits an overall distribution pattern of ‘significant increase followed by a slow decrease’, typical of a skewed distribution with a peak at 0.7 m/s/m, as shown in Figure 5b. A lognormal distribution was used to fit the data (Equation (12)), where μ = −0.36 and σ = 0.38. Using a threshold of 2.20 m/s/km for the horizontal sound speed gradient, the KEF was divided into two groups: Group I (0~2.20 m/s/km) and Group II (2.20+ m/s/km). Group I accounts for over 99% of the KEF cross-sections and is the main focus of this research.

$$f(\ln x)={\displaystyle \frac{1}{\sqrt{2\pi }\sigma }}{e}^{-{\displaystyle \frac{{(\ln x-\mu )}^2}{2{\sigma }^2}}}$$

(12)

By subtracting the sound speed structure features of the warm-water side from those of the cold-water side, the difference in sound speed structure across the oceanic front was determined. To further refine this study, the KEF intensity was divided into intervals of 0.01 m/s/km, and the mean values within 1σ for nine oceanic structural features were calculated for each interval. This study examined the impact of the KEF on the acoustic structure changes in Group I (black solid line) and Group II (gray scatterplot), with significant change intervals statistically represented in Figure 6.

Research has demonstrated that oceanic fronts significantly impact the features of underwater acoustic structures. Across a 100 km oceanic front section, the sound speed structure changes considerably with the strength of the oceanic front. The overall trend of the KEF’s impact on the changes in nine types of sound speed structure, as shown in Figure 6, can be categorized into three main patterns:

(1) Features where the difference between the two sides of the front increases with the strength of the KEF: The change in SCAD (Figure 6e) increased significantly with the intensity of the KEF, ranging from 389.14 m to 781.00 m, with a first-order trend of 450.8 m/(m/s/km). As the KEF strength increased, SCAS showed a significant rising trend, from 6.01 m/s to 29.63 m/s. For CD (Figure 6g), the difference in conjugate depth on both sides of the front increased markedly with the KEF’s intensity, from 1849.78 m to 3352.00 m, indicating a substantial effect of the KEF on conjugate depth. Similarly, the CDS (Figure 6h) showed a significant upward change trend with increasing KEF strength, exhibiting a first-order trend of approximately 35.52 (m/s)/(m/s/km).

(2) Features where the difference between the two sides of the front decreases with the increase in KEF strength: The change in TLSS (Figure 6d) continued to decrease, with a first-order change rate of −0.08 (m/s/m)/(m/s/km) as the KEF strength increased. The change in DE (Figure 6i) also decreased with increasing KEF strength, correlating with the increase (decrease) in the amount of CD change caused by the rise (fall) in KEF strength.

(3) Features where the difference between the two sides of the front initially increases and then decreases with the increase in KEF strength: As the KEF strength increased, the change in SSS first rose to 8.42 m/s at 0.5 m/s/km and then fell to 3.96 m/s at 3 m/s/km. Similarly, SLD increased from nearly 0 m to 29.04 m at 1 m/s/km and then decreased to 12 m at 3 m/s/km. BSLS followed a similar trend, initially increasing and then decreasing, as reflected in the fitting curve.

The changes in horizontal temperature and salinity gradients in the KEF significantly drive changes in acoustic features. These features exhibit complex responses to varying KEF intensities, displaying nonlinear behavior. First-order fitting curves do not sufficiently capture these complex changes. To address this, third-order polynomial fitting, determined by the least squares method, provides more accurate coefficients, as shown in

Table 1. Statistics and fitting of changes in sound speed structure across the front with varying KEF strength.

Features	Ocean Front Strength (m/s/km)						Coefficients of Curve Fitting (y = ax3 + bx2 + cx + d)
	0.5	1	1.5	2	2.5	3	a	b	c	d	MAE
SSS (m/s)	8.42	9.60	8.80	7.50	7.33	3.96	2.02	−11.96	20.00	−0.22	1.10
SLD (m)	27.41	29.04	19.47	16.27	11.87	12.00	9.25	−48.65	68.98	−1.15	2.66
BSLS (m/s)	9.12	10.29	9.22	7.69	7.68	4.03	2.21	−13.00	21.49	−0.20	1.22
TLSS (m/s/m)	−0.02	−0.06	−0.10	−0.15	−0.16	−0.17	0.00	−0.01	−0.06	0.01	0.01
SCAD (m)	389.14	587.26	668.18	720.29	791.62	781.00	45.18	−348.85	890.64	−6.70	25.85
SCAS (m/s)	6.01	12.44	17.32	24.75	26.91	29.63	−0.67	1.17	12.29	−0.40	0.54
CD (m)	1849.78	2719.48	2915.50	2860.05	2958.94	3352.00	321.39	−2181.10	4637.43	−122.16	173.69
CDS (m/s)	29.99	50.44	63.68	72.80	72.14	67.72	3.10	−26.74	79.46	−4.47	2.51
DE (m)	−1789.85	−2656.08	−2856.79	−2779.06	−2967.97	−3224.82	−313.92	2146.28	−4570.81	145.01	185.31

Note: The numerical values in the table represent the difference between the structure on the warm-water side and that on the cold-water side, and the meanings of the abbreviations are shown in Section 2.2.2.

, aiding related research in the KEF region. In the fitting curve, the independent feature x is the oceanic front intensity, and the dependent feature y is the amount of structural change.

3.2. Impact of Changed Sound Speed Structure on Acoustic Propagation

The influence of the marine environment on the sound speed structure is a key factor affecting changes in acoustic propagation [10]. The previous section highlighted the close relationship between ocean fronts and the depth and speed differences in sound speed structure features, such as SLD, BSLS, CD, and CDS. This section examines the impact of changes in sound speed structure depth across ocean fronts on acoustic propagation by placing the sound source on both the relatively warm and cold sides of the front, as shown in Figure 7 and Figure 8, respectively, with significant change intervals highlighted in yellow.

Unlike the impact of ocean fronts on the sound speed structure, the influence of the changed sound speed structure on acoustic propagation tends to be more linear. When the sound source is located on the warm-water side, the studied sound speed structure features show a significant positive correlation with both types of acoustic propagation features. As the KEF causes an increase in the differences among five sound speed structures on both sides of the front, the direct detection distance and the first convergence zone distance tend to increase. For the convenience of analyzing the impact of different sound speed structure features on underwater acoustic propagation, we have summarized the significant change intervals and slopes of different features, as shown in

Table 2. Significant intervals and slopes of the KEF-induced changes in sound speed structure on the acoustic propagation features.

Features	Direct Detection Distance (Warm)		Convergence Zone Distance (Warm)		Direct Detection Distance (Cold)		Convergence Zone Distance (Cold)
	Slope	Interval	Slope	Interval	Slope	Interval	Slope	Interval
SSS (m/s)	8.64	1.8~3.4	0.68	40.0~55.0	4.36	2.3~3.6	−0.49	45~60
SLD (m)	164.27	2.8~3.4	5.72	50.0~65.0	−20.63	2.6~3.6	−4.77	52~59
TLSS (m/s/m)	3.57 × 10−2	1.8~3.4	3.4 × 10−3	55.0~65.0	9.61 × 10−2	1.6~2.6	3.50 × 10−2	40~60
SCAD (m)	589.73	1.8~2.5	30.51	47.0~57.5	−175.19	1.6~2.6	−20.66	40~60
CD (m)	3.06 × 103	1.8~2.5	204.75	48.5~59.0	−623.64	1.6~5.4	−111.80	40~60

Notes: The units in the table are the ratio of the unit of the sound speed structure feature to the unit of the acoustic propagation feature (km). When studying the changes in acoustic propagation features caused by changes in the sound speed structure, the values in the table should be inverted. Warm (cold) indicates that the sound source is located on the warm (cold)-water side.

. For example, the slope of the SSS change is 8.64 m/s/km, with a significant impact range of 1.8–3.4 km. In the warm-water area, even small changes in sound speed can significantly affect direct detection results. In the farther convergence zone, the slope decreases to 0.68 m/s/km, with an impact range of 40.0–55.0 km. The SLD affects near-field acoustic propagation over a concentrated range (2.8–3.4 km), with a change rate of 164.27 m/km, and has a continuous and widespread impact on convergence zone propagation (50.0–65.0 km). Additionally, TLSS is particularly sensitive to changes in direct detection, with a high slope of 3.57 × 10⁻² m/s/m/km, though this change has less impact on the convergence zone compared to other factors. SCAD and CD exhibit high consistency in their impact trends on acoustic propagation on the warm-water side, with rates of change for direct detection (1.8–2.5 km) of 589.73 m/km and 3.06 × 10³ m/km, respectively, and showing continuous and significant effects on the convergence zone, approximately within the range of 45–60 km, with change rates of 30.51 m/km and 204.75 m/km, respectively.

On the cold-water side, except for the positive correlation between the differences in TLSS across the front and the two acoustic propagation features, the remaining differences in sound speed structure exhibit significant negative correlations. The impact on direct detection distance falls within the 2–4 km range. However, the effect of changes in sound speed structure on direct detection distance is weakened, and the rate of change is significantly lower than when the sound source is on the warm-water side. For sound speed structure features affecting the distance of the convergence zone, SCAD and CD show significant negative correlations, with change rates of −20.66 m/km and −111.80 m/km, respectively. Their impact range is broader (40–60 km), due to the convergence zone formed by the sound source on the cold-water side in the ocean front environment being closer to the sound source than on the warm-water side [19].

3.3. Understanding the Process of the KEF’s Impact on Underwater Acoustic Propagation Based on Artificial Intelligence

The previous subsection quantitatively analyzed the impact of KEF-induced differences in sound speed structure across the front on acoustic propagation features. However, due to the holistic nature of oceanic sound speed structure, there is a strong coupling relationship between different features of sound speed structure. Feature importance calculates the significance of sample features, quantitatively describing their contribution to classification or regression, and is widely used in underwater acoustic research [55,56]. This study investigated the main factors affecting acoustic propagation in the changing sound speed structure caused by oceanic fronts, using OOB error and Shapley values.

Given the large volume of data in this study’s oceanic front sample set, some information redundancy exists. This study considered both representativeness and computational resources, using Latin hypercube sampling [57] to stratify according to the oceanic front intensity interval (0.1–3.5 m/s/km). This efficient sampling technique ensures that the entire distribution range of each feature is sampled evenly and effectively. Ultimately, surrogate datasets with 3000, 6000, and 9000 groups were obtained, using the median during extraction to ensure data consistency and reproducibility.

Next, based on the OOB error and Shapley values, the feature importance of different sound speed structures affecting acoustic propagation under the KEF environment (three surrogate datasets) was calculated, as shown in Figure 9 and Figure 10. To facilitate the statistical analysis and calculation of average feature importance across different surrogate datasets, the OOB errors and Shapley values in Figure 9 were normalized.

Figure 9 illustrates that, in the KEF environment, when the sound source is on the warm-water side, the feature importance derived from the three surrogate datasets shows high consistency. The primary factor determining the direct detection distance is SLD, with feature importances of 31.88% and 39.22% based on the OOB error and Shapley values, respectively. This correlation is related to the propagation characteristics of underwater sound in the sonic layer [58]. Despite setting the sound source depth to 150 m and the emission angle to α_min to avoid trapping sound rays in the sonic layer, as the depth of the sound channel increases, the sound rays still bend towards the seabed, but their curvature decreases. Consequently, when the sound rays reach the same descent depth, their propagation distance significantly increases. A high correlation between research features may cause the OOB error to underestimate key features [59], resulting in the highest feature importance of each change in sound speed structure affecting the convergence zone distance not exceeding 16%. The Shapley values, however, suggest a more reliable conclusion: CD is identified as the key factor influencing the waveguide of the convergence zone on the warm-water side, with an average feature importance of 21.98% across the three surrogate datasets. Previous research has examined the offset characteristics of the convergence zone using the law of refraction [60], and Snell’s law elucidates why the inversion depth plays a crucial role in determining the convergence zone distance. When the sound source is at depth $x=0$, $z=z_s$ and emits at an initial angle ${\alpha }_0$, the horizontal distance traveled by the sound ray ${\mathrm{CZ}}_D\left(\mathrm{S}\right)$ is expressed in the following integral form, where $n(z)=c_0/c(z)$ is the refractive index and z is the conjugate depth, indicating the depth where the sound speed reaches the conjugate sound speed.

$$\mathrm{CZ}\mathrm{Distance}\left(\mathrm{Snell}\right)=2\cos {\alpha }_0{\displaystyle {\int }_{z_s}^z\frac{dz}{\sqrt{n^2(z)-{\cos }^2{\alpha }_0}}}$$

(13)

When the sound source is positioned on the cold-water side, the intrusion of cold water from the north weakens the sound layer features. Key factors affecting the direct detection distance include CDS, SCAD, and TLSS, with feature importances ranging from 15% to 30%. The Shapley values reveal that CDS significantly influences the convergence zone distance, with a feature importance of 30.65%. Figure 10, which uses the 9000-set surrogate dataset as an example, shows that, on the warm-water side, larger changes in SLD increase the direct detection distance, while larger changes in CD extend the convergence zone distance. These findings are consistent with the results in Section 3.2.

In summary, artificial intelligence methods effectively reveal the complex effects of changes in sound speed structure on acoustic propagation in the KEF environment:

(1)

Warm-Water Side

Direct detection distance: SLD is the key factor, with a feature importance of 39.22% among the nine evaluated features. The main impact range is 2.8 to 3.4 km. Each 1 m increase in SLD difference across the front extends the direct detection distance by approximately 6.09 m.

Convergence zone distance: CD is the key factor, with an impact range of 48.5 to 59.0 km. Each 1 m increase in CD difference across the front extends the convergence zone distance by approximately 4.88 m.

(2)

Cold-Water Side

Direct detection distance: The key factors are CDS, SCAD, and TLSS, with feature importances from 15% to 30%.

Convergence zone distance: CDS is the key factor. Supplementary statistics show a trend similar to CD in Figure 8b. The main impact range is 40 to 60 km. Each 1 m/s increase in CDS difference across the front shortens the convergence zone distance by approximately 437.48 m.

4. Exploring the Application Scenarios of Quantitative Analysis of Oceanic Front Effects on Underwater Acoustics

4.1. Typical Acoustic Propagation Features in the KEF Environment

Oceanic fronts influence acoustic propagation by altering the sound speed structure, with the KEF exhibiting significant seasonal variations [31]. Utilizing the marine big data from this study, statistical values of acoustic propagation features and offsets across different months under the KEF environment were derived. These values offer guidance for underwater acoustic communication and detection in the KEF region. The statistical values are based on 651,316 oceanic front sections controlled by the 1σ principle. Offsets represent the differences between acoustic propagation features from two-dimensional oceanic front sections and one-dimensional sound profiles at the source location, as shown in Figure 11.

The KEF environment demonstrates pronounced seasonal features in acoustic propagation. On the warm-water side, direct detection distances are greater in spring and winter, peaking in February at 4.10 km, and shorter in summer and autumn, reaching a minimum in November at 2.43 km. The direct detection distance offset shows the opposite trend, with the largest offset in February, reducing by 0.11 km compared to a non-frontal environment, and an offset close to 0 km from June to November. The convergence zone distance extends from the sound source during spring and winter, peaking in November at 58.68 km, and shortens during summer and autumn, reaching a minimum in May at 56.49 km. The convergence zone offset follows the same seasonal trend, indicating that the convergence zone in a frontal environment is generally closer to the sound source than in a non-frontal environment. This trend is most significant in February, at 4.10 km, and weakest in October, at 1.22 km.

When the sound source is positioned on the cold-water side, the seasonal trend of direct detection distance weakens. The distance is generally farther in spring and summer, peaking in February at 2.54 km, and closer in November, at 2.20 km. The offset varies monthly but remains relatively low, with the direct detection distance in a frontal environment increasing by ~0.01 km compared to a non-frontal environment. The overall features of the convergence zone are similar to those of the sound source on the warm-water side. The distance is farther from the sound source during spring and winter, peaking in December at 48.46 km, and closer during summer and autumn, with the closest distance in June, at 44.97 km. The offset is largest in November, with the KEF causing the convergence zone distance to increase by 0.12 km, and the smallest in March, where the convergence zone moves 0.52 km closer to the sound source in a frontal environment compared to a non-frontal environment.

4.2. Analysis of Potential Application Scenarios Based on Multivariate Nonlinear Regression

A detailed quantitative assessment enhances the understanding of oceanic fronts’ impact on acoustic propagation, supporting underwater acoustic operations and predictions in the oceanic front environment. This study explores potential applications in researching the relationship between multivariate sound field structural features and acoustic propagation, using examples such as acoustic propagation features and oceanic front reconstruction, as illustrated in Figure 12. The input of the regression model is the nine types of sound speed structure changes mentioned in Section 3.1, and the output is the acoustic propagation features and ocean front features. This subsection mainly briefly explores the predictability of acoustic propagation features and ocean front structure based on feature extraction, where related feature selection and the optimization of ocean front reconstruction models can be considered as future research directions.

4.2.1. Research on the Predictability of Acoustic Propagation Features in the KEF Environment

Subsequent to our prior research investigations, we selected the RF algorithm augmented by Sparrow Search Algorithm (SSA) [61] optimization, which has exhibited superior performance in the realm of underwater acoustic prediction accuracy [62]. As a case study, we developed a multivariate regression model based on the RF framework, leveraging a surrogate dataset consisting of 9000 samples, and further refined it through the application of the SSA optimization methodology, specifically targeting the convergence zone waveguide situated on the warm-water side of the KEF with an embedded sound source. The dataset was divided into training, validation, and testing sets at a ratio of 8:1:1. The optimization hyperparameters included the number of trees (2–500) and minimum samples per leaf (1–10).

Figure 13 presents line graphs (based on the first three hundred examples of the test set) and scatter density plots for predicting the convergence zone distance under the KEF environment, with the sound source positioned on both the warm- and cold-water sides, for nine different changes in sound speed structure. The SSA-RF model effectively utilizes oceanic front features to predict convergence zone characteristics with limited data. The line graphs demonstrate the model’s ability to capture the trend of changes in the convergence zone, while the scatterplots show points distributed near the 1:1 line.

For the warm-water side sound source, the mean absolute error (MAE) for predicting the convergence zone distance is 1.10 km, with an accuracy rate of 97.90% for predictions with errors of less than 3 km. The correlation between sound speed structure features and acoustic propagation features is lower on the cold-water side, reducing the prediction accuracy for the convergence zone distance, with an MAE of 1.84 km and an accuracy rate of 89.13% for predictions with errors less than 3 km. Overall, multivariate nonlinear regression based on changes in sound speed structure effectively predicts acoustic propagation features. This ‘feature-to-feature’ acoustic propagation prediction framework supports efficient decision-making in underwater acoustic communication and detection.

4.2.2. Serving Ocean Front Reconstruction

Accurately reconstructing the ocean sound speed field is crucial for various marine acoustic applications. This task is challenging due to the sparsity and uncertainty of sound speed samples over vast ocean areas [63]. Ocean fronts cause significant deviations in sound speed below the sea surface, further complicating this work [64]. With a comprehensive understanding of sound speed structure features under ocean front conditions, this study proposes an ocean front reconstruction strategy based on multivariate linear regression and a parameterized two-dimensional feature model of ocean fronts. This strategy provides a correction scheme for sound field reconstruction in environments with ocean fronts. Firstly, combining the formation mechanism of oceanic fronts with historical statistical data, an ideal large-scale oceanic front sound speed model is established [8], fitting the sound speed profile feature equation:

$$C(r,z)=[C_2(z)-C_1(z)]\Phi (r)+C_1(z)$$

(14)

$$\Phi (r,z)={\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\tanh [2\pi {({\displaystyle \frac{r}{R}})}^{{10}^a}-\pi ]$$

(15)

where r and z represent the horizontal and vertical directions of the oceanic front section, respectively; R denotes the horizontal span of the oceanic front section (100 km); $C_1(z)$ and $C_2(z)$ represent the sound speed profiles on both sides of the oceanic front; $\Phi (r,z)$ is the vertically normalized sound speed profile; and the parameter ranges from −1.5 to 1.5 with a step of 0.01, indicating different frontal positions in the section.

Firstly, by combining the single sound speed profile $C_1(z)$ on one side of the oceanic front with the statistical characteristics from Table 1, the profile $C_2(z)$ is calculated. Subsequently, the regression relationship between the sound speed structure of the single profile and the intensity of the oceanic front is fitted using the SSA-RF model, and the oceanic front sound speed reconstruction is performed based on Equation (14). During the sound speed reconstruction process, by calculating the maximum horizontal sound speed gradient in the KEF section reconstructed from different parameters a, the absolute error from the predicted intensity of the SSA-RF model is computed. The value of a that minimizes this error is selected as the optimal parameter for the two-dimensional parameterized oceanic front model. Taking four measured sections from the KESS project as examples, the sound speed reconstruction effects are illustrated in Figure 14. The calculated mean absolute errors for the sound speed reconstruction of the four sections are 1.35 m/s, 1.06 m/s, 1.13 m/s, and 0.67 m/s, respectively. This oceanic front reconstruction strategy effectively inverts the cross-sectional features of the oceanic front, and its vertical sound speed structure closely matches in situ observations. In future work, the input oceanic front intensity can be set at the sea surface, constructing a model that allows for sound speed reconstruction in the oceanic front region based solely on the input sea surface sound speed gradient and single profile, thereby enhancing the practical application value of the model.

5. Conclusions

This study investigated the impact of the KEF on sound speed structure and acoustic propagation. Utilizing high-resolution reanalysis data and in situ observation sections, methods such as front line extraction, classical sound speed stratification, and ray acoustics models were employed to analyze the sound speed structure and acoustic propagation features within the KEF environment. Capitalizing on the advantages of extensive oceanographic datasets and ML assessment metrics, a quantitative analysis was conducted to discern the disparities in sound speed structure induced by the KEF on either side of the front, as well as the resulting deviations in acoustic propagation. Finally, the foundational role of this study in informing KEF-related research and support missions was deliberated upon.

By analyzing over six hundred thousand typical sections of the KEF, the frequency distribution of the front’s intensity and width was determined. The KEF’s intensity and width showed a high degree of consistency, with a correlation coefficient of 0.46. The intensity distribution followed a lognormal distribution, with μ = −0.36 and σ = 0.38. According to the 3σ principle, the KEF’s intensity distribution was mainly concentrated between 0 and 2.2 m/s/km. The differences in sound speed structure across the frontal boundary, caused by varying KEF strengths, were statistically analyzed. This study found significant changes in sound speed structure on both sides of a cross-section spanning 100 km with varying KEF intensity. Generally, three types of changes were observed: (1) differences in the depth of the sound channel axis and conjugate depth increasing with the increase in front strength, (2) differences in the strength and depth margin of the thermocline decreasing as KEF intensity increased, and (3) differences in sea surface sound speed and sound layer depth showing a trend of initially increasing and then decreasing with the increase in front strength.

Secondly, the offset in acoustic propagation caused by the difference in sound speed on both sides of the front was quantitatively analyzed using big data statistics, the OOB error, and Shapley values. The key factor affecting direct detection on the warm-water side among the nine sound speed structure features evaluated was the sound layer depth, with a contribution rate of 39.22%, mainly affecting the range of 2.8–3.4 km. Within this interval, each 1 m increase in the difference in sound layer depth across the KEF resulted in an approximate increase of 6.09 m in the direct detection distance. The key factor affecting the convergence zone distance was the conjugate depth, with a contribution rate of 21.98%, primarily affecting the range of 48.5–59.0 km. Each 1 m increase in the CD difference across the ocean front can increase the convergence zone distance by approximately 4.88 m.

Finally, the applications in underwater acoustic support, underwater acoustic propagation prediction, and sound field reconstruction were discussed through the distribution of seasonal characteristics and feature studies. Consistent with the KEF, underwater acoustic propagation characteristics in the KEF environment exhibit significant seasonal trends, generally showing that direct detection is farther in spring and closer in autumn. When the sound source is located on the warm-water side, the KEF causes a maximum reduction in direct detection distance of ~0.1 km. The distance to the first convergence zone is closer to the sound source in summer and further in winter, with the KEF bringing the convergence zone closer to the sound source, most significantly in spring, exceeding 1 km at its maximum. Additionally, this study explored the mapping relationship between changes in sound speed structure and underwater acoustic propagation, as well as the intensity of the KEF, based on multiple nonlinear regression. The regression model based on SSA-RF achieved excellent performance in underwater acoustic propagation prediction and sound speed reconstruction in the marine front environment.

This study aims to fill the gap in quantitative analysis of the impact of oceanic fronts on acoustic propagation. The findings of this research significantly enhance the understanding of acoustic propagation in complex marine environments, with applications in fields such as underwater acoustic communication and detection. Furthermore, this research, which focuses on the KEF, holds promise for extension to oceanic fronts globally. However, several issues have been identified: The current analysis primarily relied on statistical methods and fixed source parameter models. The considered source depths and the relative relationship between the source and the oceanic front are relatively simple. Furthermore, while ML-based evaluation indicators can be used to effectively analyze key factors affecting acoustic propagation, their generalization ability and sensitivity to outliers require further verification. Lastly, this study mainly used reanalysis data to ensure a large sample set, which may have overlooked factors such as sub-mesoscale phenomena and noise in the oceanic front environment. Future research should enhance in situ observations, multi-scale analysis, and three-dimensional acoustic propagation studies to better understand the impact mechanisms of the KEF and improve the accuracy and reliability of acoustic propagation models.