Unsupervised Classification of Global Temperature Profiles Based on Gaussian Mixture Models

Abstract

Understanding ocean temperature distribution is vital for ocean stratification, currents, and marine ecosystems. This study analyzed the global 0.5-degree ocean temperature dataset from the Chinese Academy of Sciences Marine Data Center (July 2020) to identify regional temperature patterns. After standardizing the data, Principal Component Analysis (PCA) reduced the dimensionality from 32 to 7, preserving key temperature variations. A Gaussian Mixture Model (GMM) determined that 18 classifications were optimal by evaluating the variance and category weights. Applying GMM to the reduced data identified 18 distinct temperature distribution patterns across various marine environments, including polar currents, warm current mixing zones, ocean fronts, and enclosed basins, each with unique geographical and physical characteristics. Most classifications showed high posterior probabilities, indicating model accuracy, though lower probabilities were observed in complex regions like the Indian Ocean. The results highlight the significant roles of ocean currents, climatic phenomena, and ecological factors in temperature distribution, providing insights for ocean circulation studies, climate modeling, and marine biodiversity conservation. Future research should enhance the model accuracy by optimizing the parameters, expanding data coverage, integrating additional features, and combining marine observations with climate models to better understand ocean temperature patterns and their global climate impacts.

1. Introduction

The ocean, covering 71% of the Earth’s surface and holding 97% of its water, is the planet’s largest ecosystem. It plays a vital role in regulating the global climate and conserving biodiversity. Since 1970, the ocean has absorbed approximately 93% of excess heat from human activities, significantly affecting temperature patterns and, consequently, climate systems and marine ecosystems [1,2,3,4].

Ocean temperature profiles are essential in oceanography and climatology for understanding stratification, monitoring currents, identifying water masses, defining ocean fronts, and assessing climate change impacts [5,6]. They are crucial for evaluating marine ecosystem health, validating climate models, predicting extreme weather events, detecting ocean warming, sea level rise, and monitoring El Niño and La Niña events [7,8,9,10]. These profiles also provide insights into marine organism distribution, migration, growth, and vertical mixing processes essential for nutrient and heat transport [11,12]. However, the ocean temperature structure is extremely complex, influenced by factors such as sea–air heat exchange and ocean current movement, leading to significant vertical and horizontal variations in temperature across different regions.

Traditional methods for obtaining temperature profiles include fishing boat surveys and ocean station observations, which are limited by fixed locations and irregular data collection [13]. To address this, the Argo program was launched in 1999, deploying nearly 4000 floats worldwide to collect comprehensive temperature and salinity data [14,15,16]. Despite its accuracy, Argo’s coverage is uneven, with only 30% coverage at a 1° × 1° grid due to its initial 3° × 3° design [17]. Therefore, it is essential to integrate all field observation data to reconstruct a comprehensive global ocean temperature field.

Currently, vertical thermal profile reconstruction methods are widely employed and can be primarily categorized into dynamic methods and statistical methods. The dynamic method utilizes the physical constraints between the sea surface and specific depths to map temperature and salinity profiles. Notable dynamic approaches include the surface quasi-geostrophic (SQG) method, the effective SQG method, and the internal SQG method [18,19]. These algorithms are particularly effective in capturing strong geostrophic current physical processes, such as eddies. However, in other scenarios, the reconstruction error may increase significantly. In contrast, the statistical method employs mathematical techniques to establish statistical relationships between sea surface variables and the reconstructed profiles. Common statistical approaches include polynomial fitting and more complex regression analysis. For instance, Cheng Lijing et al. developed a new method for estimating the ocean heat content by analyzing the temperature signal with unbiased average sampling error and constructed a global, complete grid temperature field from the surface down to 2000 m [20].

In recent years, the Gaussian Mixture Model (GMM), based on unsupervised learning, has demonstrated significant potential in classifying ocean data. Maze et al. utilized the GMM to develop a Profile Classification Model (PCM), which categorizes the profile shape through unsupervised clustering of ocean vertical profiles [21]. They discovered that traditional simple methods, such as dividing areas into rectangles, were insufficient for identifying the structures and changes in heat storage patterns. Consequently, they applied unsupervised clustering to Argo data to uncover these patterns. By using PCM on Argo data from the North Atlantic, they discovered that each category’s distribution was concentrated in specific regions on the map, indicating that PCM can extract distinct ocean structure features in different areas. Additionally, PCM offers the capability to use labeling metrics to assess the robustness of clustering. Several studies have previously employed PCM in the Southern Ocean to detect the El Niño phenomenon. These studies have demonstrated that GMM can reveal the primary patterns of the ocean temperature structure by characterizing the collection of Gaussian distributions of temperature profiles. While numerous studies have focused on specific regional aspects of the global ocean structure, such as the classification of temperature profiles in the North Atlantic or the Southern Ocean [21,22], there has been limited research employing Gaussian Mixture Models (GMMs) for the unsupervised classification of global ocean temperature profiles at a high spatial resolution. Therefore, this paper aims to apply GMM to perform unsupervised classification of global ocean temperature grid data, identifying and analyzing temperature distribution patterns on a global scale. Through data preprocessing, Principal Component Analysis (PCA) for dimensionality reduction, and GMM fitting, we aim to uncover the main patterns of global ocean temperature profiles and explore the physical significance and potential applications in marine science research. In Section 1 and Section 2 of this paper, we introduce the basics of ocean temperature datasets and GMM. Section 3 presents the classification results, while Section 4 analyzes and discusses these results, summarizing our research findings.

2. Data

In this study, we selected the global ocean temperature grid data with a 0.5-degree resolution for July 2020 as our research subject, utilizing the data service provided by the Oceanographic Data Center, Chinese Academy of Sciences (CODC) (Accessed on 1 July 2020 http://www.ocean.iap.ac.cn/pages/dataService/dataService.html?languageType=en&navAnchor=dataService) [20]. This dataset is generated using an improved mapping method, ensuring high accuracy and reliability. The raw data include all in situ observations from the World Ocean Database (WOD), encompassing instruments such as XBT, CTD, Argo floats, Bottle, MBTs, Gliders, and moorings. Historical XBT data have been corrected for bias using the CH14 scheme, significantly reducing systematic errors. Furthermore, an enhanced Ensemble Optimal Interpolation method (EnOI-DE) was employed to fill the spatial data gaps by leveraging dynamical ensemble samples from CMIP5 multi-model historical simulations and high-resolution samples, thereby improving data coverage and accuracy [23,24].

The dataset used in this study encompasses depths from the surface down to 2000 m, which are stratified into 41 distinct layers. The depth intervals are structured as follows: 5 m between 1 and 10 m, 10 m between 10 and 100 m, 20 m between 100 and 200 m, 50 m between 200 and 500 m, and 100 m between 500 and 2000 m. For our analysis, we focused on temperature profiles extending to a depth of 1000 m, corresponding to 32 layers. After excluding extraneous values and handling NaNs, the dataset comprised 145,505 valid temperature profiles. These profiles exhibit a variety of vertical temperature structures, with surface temperature variance being relatively high but decreasing significantly with depth. Figure 1 illustrates 3000 randomly selected temperature profiles, along with the overall mean (represented by a solid line) and the mean plus or minus one standard deviation (depicted by dashed lines) for the entire dataset.

3. Method

3.1. Gaussian Mixture Mode

In this study, we utilize the Gaussian Mixture Model (GMM) as our unsupervised classification method. GMM is a probabilistic approach for describing and classifying data [25]. Unlike traditional clustering methods that rigidly assign each data point to a single cluster, GMM calculates the probabilities of each data point belonging to various clusters. It operates under the assumption that the data comprise a mixture of multiple Gaussian distributions, with each distribution representing a distinct cluster [26,27,28]. Let X be an array of N vertical temperature profiles, with each profile consisting of D depth values. Furthermore, let $p(X)$ denote the probability density function (PDF) of the entire dataset [29]. The Gaussian Mixture Model is mathematically expressed as a weighted sum of K Gaussian components, as illustrated by the following formula:

(1)$p(X)={\displaystyle \sum _{k=1}^K{\lambda }_k\mathrm{N}\left(\mathrm{X}\right|{\mu }_k,{\displaystyle {\sum }_k)}}$

where $\mathrm{N}(\mathrm{X} | {\mu }_k,{\sum }_k)$ represents the multivariate Gaussian probability density function, with ${\mu }_k$ being the mean vector and ${\sum }_k$ the covariance matrix for the k-th Gaussian component. The formula is as follows:

(2)$\mathrm{N}(\mathrm{X};{\mu }_k,{\displaystyle {\sum }_k)}={\displaystyle \frac{\exp [-\frac{1}{2}{(x-{\mu }_k)}^T{\sum }^{-1}(x-{\mu }_k)}{\sqrt{(2\pi )D\left|{\sum }_k\right|}}}$

The probability that a data point in the entire profile dataset belongs to the k-th class is $p(k)={\lambda }_k$ where ${\displaystyle \sum {\lambda }_k=1}$ and $0<{\lambda }_k<1$. The probability that a temperature profile x belongs to the k-th class is given by $p(k|x)={\lambda }_{k}N(x|{\mu }_k,{\sigma }_k$), where the vector x is a single profile extracted from the entire dataset X [30].

Typically, we do not have direct access to the parameters of the Gaussian Mixture Model (GMM). Instead, we observe a series of data points and, given a specified number of components K, aim to determine the optimal K Gaussian sub-models. This can be achieved by iteratively refining the means ${\mu }_k$ and covariance matrices ${\sum }_k$ using the Expectation–Maximization (EM) algorithm to find the best means ${\mu }_k$, covariance matrices, ${\sum }_k$ and weights ${\lambda }_k$.

The EM algorithm maximizes the objective function by iteratively optimizing one set of parameters while keeping the others fixed, thereby transforming the problem into a series of convex optimization tasks [31,32]. In each iteration, the algorithm computes the derivatives to determine the optimal parameter values and then updates the fixed parameters with these optimal values, proceeding to the next iteration. Specifically, when solving the GMM, the EM algorithm proceeds as follows [33]:

(1) Expectation Step (E-step): Based on the current parameter estimates, calculate the probability that each data point x belongs to each class k (i.e., the posterior probability), as given by the following formula:

(3)$\begin{array}{l}\gamma (x_k)={\displaystyle \frac{{\lambda }_{k}N(x|{\mu }_k,{\displaystyle {\sum }_k)}}{{\displaystyle {\sum }_{k=1}^K{\lambda }_{k}N(x|{\mu }_k,{\displaystyle {\sum }_k)}}}}, \\ x=1,2,3,\dots ,N; k=1,2,3,\dots ,K\end{array}$

(2) Maximization Step (M-step): Based on the probabilities of the data point assignments obtained in the E-step, re-estimate the parameters (mean and covariance) and weight coefficients for each component. The formulas are as follows:

(4)${\mu }_k={\displaystyle \frac{{\displaystyle {\sum }_x^N(\gamma (x_k)X_x)}}{{\displaystyle {\sum }_x^N\gamma (j_k)}}}, k=1,2,3,\dots ,K$

(5)${\sum }_k=\frac{{\displaystyle {\sum }_x^N\gamma (j_k)}(X_x-{\mu }_k){(X_x-{\mu }_k)}^T}{{\sum }_x^N\gamma (j_k)},k=1,2,\dots ,K$

(6)${\lambda }_k={\displaystyle \frac{{\displaystyle \sum _{x=1}^N\gamma (x_k)}}{N}}$

By alternately executing the E-step and M-step, the EM algorithm gradually increases the log-likelihood of the observed data until it converges to a local maximum.

3.2. Dimensionality Reduction

In GMM, each depth level is treated as a separate dimension, with corresponding Gaussian parameters assigned to each depth. However, not all depth levels are necessary to accurately describe the vertical temperature profile dataset. This is due to the presence of the thermocline and mixed layer in the ocean, where the temperature changes more rapidly compared to other depths. To reduce the computational complexity of the data, this study employs Principal Component Analysis (PCA) for dimensionality reduction on the global profile data [34,35]. PCA retains most of the data’s structure while minimizing the number of dimensions, thereby creating a new space. Consequently, the dataset can be decomposed as follows:

(7)$X(z)={\displaystyle \sum _{d=1}^{D}P(z,d)Y(d)}$

In the equation, z represents the depth of seawater, D is the total number of principal components, $P(z,j)$ is the transformation matrix between the depth space and the principal component space, and Y(d) is the component of the reduced-dimension data point on the j-th principal component. While PCA dimensionality reduction effectively decreases the computational complexity, it does result in some loss of detail from the dataset. To evaluate this loss of detail, we can invert Equation (7) using different values of d and compare the root mean square difference (RMSD) between the reconstructed dataset and the original dataset, as illustrated in Figure 2. Our analysis reveals that d = 7 captures 99.9% of the variance in the vertical structure, thereby significantly reducing the dimensionality required to describe the temperature profile data from 32 depth levels to 7.

The dataset used in this study to estimate the parameters of the Gaussian Mixture Model (GMM) includes mean values and standard deviations. To generate the GMM training set, temperature profiles are randomly selected from each category. Each training dataset consists of 37,696 profiles, which accounts for approximately 25% of the original dataset. Additionally, these profiles are uniformly distributed across the globe.

3.3. Determining the Number of Classes

A key parameter of the Gaussian Mixture Model (GMM) is the number of components that constitute the mixture. Typically, parameter estimation is performed by optimizing the likelihood function. As the volume of training data increases, the model accuracy is generally expected to improve. However, this can also lead to increased model complexity, thereby raising the risk of overfitting. To address this issue, researchers have developed various information criteria that apply penalties to model complexity, assisting in selecting the most appropriate model parameters to prevent overfitting. Maze et al. utilized the Bayesian Information Criterion (BIC) for model selection, which is calculated as follows [36,37]:

(8)$BIC=-2\ln (L)+k\ln (n)$

In the Bayesian Information Criterion (BIC) formula, L denotes the likelihood function, k represents the number of model parameters, n is the sample size, and kln(n) serves as the penalty term. When dealing with high-dimensional data and a relatively small number of training samples, introducing a penalty term can effectively mitigate the curse of dimensionality. However, this approach is not always effective for large-scale datasets, particularly in profile-type datasets. In such scenarios, the large dataset size causes the log-likelihood values to be significantly higher than the penalty term, thereby reducing the effectiveness of the model selection method. For the global 0.5-degree ocean temperature dataset, the issue of dimensional collapse is inevitable. To address this problem, Lin et al. proposed a novel method for determining the number of components in the GMM. This algorithm calculates the variance of each class’s profile subset across each dimension and the weights of each class. It then assigns a score to different values, where a lower score indicates a better model, thereby determining the optimal number of classes required for the GMM [38]. The score is calculated using the following formula:

(9)$Scor{e}_k={\displaystyle \frac{1}{k}}{\displaystyle \sum _{k=1}^{N_k}{\sigma }_k^2\times weigh{t}_k}$

As illustrated in Figure 3, the score value reaches its minimum when k equals 18. Consequently, 18 is identified as the optimal number of classes for the global temperature profile grid data.

4. Results and Analysis

4.1. Results of the Gaussian Mixture Model

We utilized K = 18 in the Gaussian Mixture Model to classify the processed and cleaned global ocean temperature grid dataset at a 0.5-degree resolution. Figure 4 displays the geographic distribution of the global ocean temperature profiles, along with their respective categories. To enhance comprehension, the data classifications were sorted in ascending order based on the mean sea surface temperature. As illustrated in the figure, the 18 categories are clustered within specific regions. We extracted profiles on a monthly and seasonal basis to examine their distribution and found that the geographic locations of these 18 categories remained consistent, with no significant differences observed. For clarity, Table 1 lists the mean temperature, number of profiles included, and the highest and lowest temperatures for each category.

4.2. Global Temperature Profile Clustering Analysis

As shown in Figure 4, the temperature profiles of Class 1 are located in the Arctic Ocean. Influenced by Arctic currents and polar ice caps, there is minimal temperature variation between the surface and deeper layers, with negligible seasonal changes [39]. The average temperature of Class 1 is −0.493 °C. Similarly, Class 2 temperature profiles are found in the Antarctic region, maintaining low temperatures year round, with an average temperature of −0.109 °C. However, due to the influence of the Antarctic Circumpolar Current, there is some fluctuation in the surface water temperatures, while deep water temperatures remain relatively stable [40]. The temperature curves in Figure 5 illustrate that the average temperature trends for Class 1 and Class 2 exhibit opposite patterns: surface temperatures are low, but as the depth increases, ocean temperatures gradually rise.

Class 3 temperature profiles are primarily distributed in the Westerlies Drift, one of the world’s largest ocean current systems driven by strong westerly winds. This system facilitates significant vertical mixing between warm surface waters and cold deep waters, transporting heat from the ocean surface to deeper layers and regulating the ocean’s temperature gradient. As indicated by the mean temperature curve, Class 3 exhibits minimal overall temperature variation, maintaining a nearly uniform temperature. Although Class 3 is located near Antarctica, its average temperature is significantly higher than that of Class 2 at 4.019 °C. This temperature difference results in oceanic fronts at the boundary between the two classes, such as the Antarctic Front. Class 4 temperature profiles are distributed in the high-latitude regions of the Northern Hemisphere, primarily influenced by cold currents. There are two main areas of distribution: one at the junction of the Atlantic and Arctic Oceans, where the East Greenland Current converges with the tail end of the North Atlantic Current, known as the Norwegian Current [41,42], and the other in the Northwest Pacific, where the Oyashio Current converges with the Kuroshio Current [43]. The convergence of these warm and cold currents forms subpolar fronts, leading to distinct temperature and salinity gradients. These frontal regions exhibit strong upwelling and eddies, resulting in substantial temperature variations at the ocean surface, as evidenced by the pronounced thermocline in the mean temperature curve shown in Figure 5.

Class 5 temperature profiles are concentrated in the North Pacific, primarily influenced by the North Pacific Current and the Kuroshio Current [44]. The North Pacific Current is a warm water flow moving east to west along the west coast of North America, bringing higher temperatures and significantly warming the coastal climate. Similarly, the Kuroshio Current, a warm current flowing north along the east coast of Japan, warms the coastal climate and provides abundant fish resources to Japan and the surrounding areas. In these regions, water masses with varying temperatures and salinities often converge, forming oceanic fronts such as the North Pacific Front and the Kuroshio Front. The North Pacific Front arises from the interaction between the warm current and colder water masses from higher latitudes, while the Kuroshio Front is formed by the Kuroshio Current meeting the surrounding cold water masses [45]. These fronts are distinct and exhibit significant temperature and salinity gradients, as shown in the average temperature curve of Class 5 in Figure 5.

Class 6 temperature profiles exhibit greater global dispersion but are primarily concentrated in regions influenced by cold currents, including the Peru Current, the Benguela Current, the California Current, and the Labrador Current [46,47,48]. These cold currents flow toward the equator, bringing cold water and forming oceanic fronts upon encountering warm currents. Notably, the Peru Current region is known for the occurrence of El Niño and La Niña phenomena [49]. The temperature curves for classes 7–12 are shown in Figure 6. Classes 7 and 8 share similarities; however, Class 7 displays some vertical temperature fluctuations due to the influence of the Agulhas Current, resulting in a slightly tilted mean temperature curve [50]. This class is mainly concentrated in the Southern Indian Ocean. In contrast, although Class 8 is distributed in the South Pacific and South Atlantic, its mean temperature curve remains relatively stable.

Class 9 temperature profiles are primarily distributed in the North Atlantic, extending from the Gulf of Mexico along the eastern coast northward to Newfoundland and parts of Northern Europe. The main ocean currents in this region include the Gulf Stream, the North Atlantic Drift, and the Canary Current [51,52]. The Gulf Stream transports a significant volume of warm water, resulting in relatively warm coastal regions, particularly in Western Europe. As it flows northward, the Gulf Stream branches into the North Atlantic Drift, which continues to carry warm water eastward, thereby moderating the climate of Western and Northern Europe. Conversely, the Canary Current flows southward along the west coast of Africa, bringing cold water to tropical and subtropical regions and influencing the coastal climate. The convergence of these currents creates distinct temperature and salinity fronts. A temperature front forms where the Gulf Stream meets the colder waters of the central and high-latitude North Atlantic, with its position shifting seasonally. Additionally, the higher salinity of the Gulf Stream’s warm water contrasts with the relatively lower salinity of the high-latitude North Atlantic water, resulting in a salinity front at their confluence. Similarly, the cold water brought about by the Canary Current forms local fronts when it meets the warm coastal waters. These fronts significantly impact the region’s climate and marine ecosystems, particularly during seasonal transitions and monsoon changes, when the position and intensity of the fronts can vary markedly.

Class 10 temperature profiles are primarily distributed in the Central Atlantic and Central Indian Oceans, extending from the Caribbean Sea and the Gulf of Mexico across the mid-Atlantic to the west coast of Africa and from east of Madagascar to the western coast of Australia. In the Atlantic, the Gulf Stream and the North Equatorial Current are the main influencing currents. The Gulf Stream transports a significant volume of warm water to the Central Atlantic, while the North Equatorial Current flows westward from the west coast of Africa, contributing to the region’s temperature. In the Indian Ocean, the South Equatorial Current plays a major role, creating distinct temperature and salinity fronts at the confluence of currents. The warm waters of the Gulf Stream meet the cooler waters of the mid-North Atlantic, forming a temperature front which position varies seasonally. Similarly, the convergence of warm waters from the currents with surrounding cooler waters generates local fronts, which experience significant changes in position and intensity during seasonal transitions. Class 11 is similar to Class 10 but is distributed in the Southern Atlantic and Central Pacific Oceans. It is influenced by the Equatorial Current systems (North Equatorial Current and South Equatorial Current), the Peru Current, the Equatorial Counter Current, and the California Current [53]. The Equatorial Current systems transport substantial amounts of warm water, resulting in higher surface temperatures. Conversely, the colder waters from the Peru Current and the California Current also have significant effects. The confluence of these currents forms distinct temperature and salinity fronts.

Class 12 temperature profiles are distributed in the Mediterranean Sea. The temperature profile indicates that surface seawater temperatures are relatively high, ranging from approximately 20 °C to 25 °C. As the depth increases, the temperature decreases sharply; however, at 1000 m, it remains close to 10 °C, the highest among all the classes and significantly higher than the others. This region is primarily influenced by the Mediterranean circulation system and the Mediterranean climate. The circulation system transports warm, saline water from the Atlantic into the Mediterranean, affecting both surface temperature and salinity [54]. The Mediterranean climate is characterized by hot, dry summers and mild, rainy winters. Furthermore, the Mediterranean is a relatively enclosed basin with limited direct influence from the open ocean, allowing its waters to accumulate more heat during the summer and retain some of that heat during the winter.

Figure 7 displays the temperature curves for classes 13 through 18. In contrast, the temperature profiles for class 13 are primarily distributed in the Northwest Pacific, extending eastward from the East China Sea and South China Sea to the Central North Pacific. In this region, a thermocline forms at approximately 200 m in depth. The area is mainly influenced by the Kuroshio Current, the North Pacific Current, and the monsoon climate. The Kuroshio and North Pacific Currents transport large volumes of warm water, elevating surface temperatures. However, to the north, the Kuroshio Current meets the colder Oyashio Current, resulting in a distinct temperature front along the eastern coast of Japan. Additionally, seasonal variations driven by the monsoon climate significantly impact the distribution of seawater temperature and salinity, leading to the formation of temperature and salinity fronts. Class 14 temperature profiles are predominantly found in the equatorial regions of the Atlantic and Pacific Oceans, extending westward from the west coast of Africa to the eastern coast of South America and the coasts of Central America, as well as westward to the Central Pacific. This region is influenced by the North Equatorial Current, the South Equatorial Current, the Equatorial Counter Current, and the Azores Current. The North and South Equatorial Currents bring substantial amounts of warm water, thereby increasing surface temperatures, while the colder waters transported by the Azores Current also have a significant impact.

Class 15 temperature profiles extend eastward from the Philippines and Indonesia to the Central Pacific. In the Northern Hemisphere, the coverage area is relatively narrow, whereas, in the Southern Hemisphere, it is broader. This class is primarily influenced by the North and South Equatorial Currents, without direct interaction with cold currents. As a result, thermoclines in Class 15 are less pronounced compared to Classes 14 and 11, and the temperature curves are relatively smooth. Class 16 temperature profiles are more dispersed, with the major areas extending from the eastern coast of North America to the Central Atlantic and the Arabian Sea region. This class is influenced by the Gulf Stream and the monsoon currents of the Arabian Sea, leading to the vertical mixing of water masses [55]. The strong flow of the Gulf Stream enhances vertical mixing, thereby accelerating heat exchange between the surface and deep waters.

Class 17 temperature profiles are distributed in the equatorial region of the Pacific, the northeastern corner of South America, and the Southern Indian Ocean. In the Pacific, the Equatorial Counter Current primarily influences this region by transporting warm water, resulting in higher surface temperatures and lower deep water temperatures, thereby creating a distinct temperature gradient. Class 18 temperature profiles are mainly found in the Central and Western Indian Ocean, extending eastward from the east coast of Africa to encompass the Arabian Sea, the Bay of Bengal, and a vast area of the Central Indian Ocean. This region is primarily influenced by the South Equatorial Current, the Somali Current, and the Equatorial Counter Current. The South Equatorial Current transports substantial warm water, elevating surface temperatures. Meanwhile, the Somali Current and the seasonal monsoon variations significantly impact the distribution of seawater temperature and salinity. The convergence of these currents results in distinct temperature and salinity fronts. Additionally, monsoon-driven vertical mixing and precipitation-induced salinity changes further enhance these fronts.

For the selected temperature profiles, the Gaussian Mixture Model (GMM) predicts the probability distribution of each profile belonging to the K classes. Specifically, it calculates the posterior probability for each class K, ensuring that the sum of these probabilities equals 1. The algorithm then assigns each profile to the class with the highest posterior probability. These posterior probabilities are derived from the entire dataset and serve as a measure of the GMM’s confidence in its classification, providing valuable insight into the reliability of each assignment. Table 2 illustrates the distribution of profiles across each category based on their posterior probabilities.

After applying the Gaussian Mixture Model (GMM) to the temperature profiles, the posterior probabilities for each class are illustrated in Figure 2. Over 91% of the class assignments have posterior probabilities exceeding 0.75 and more than 84% exceed 0.9. Specifically, Classes 1, 5, 12, 13, and 18 exhibit very high posterior probabilities, with over 90% of their assignments having posterior probabilities greater than 0.9. Notably, Class 12 achieves a posterior probability of 99.7%. In contrast, Classes 6, 10, 11, and 16 have fewer than 80% of their assignments with posterior probabilities above 0.9. However, for probabilities greater than 0.75, Classes 10, 11, and 16 exceed 85%.

Figure 8 reveals that Class 6 primarily represents cold water regions, significantly influenced by polar and cold currents. In the northwestern waters off South America, the convergence of the Peru Current and the Equatorial Counter Current frequently generates vortices and turbulence, which further enhances water mixing and results in unstable sea temperatures. Additionally, this convergence zone is a key area influenced by the El Niño phenomenon.

Figure 9 illustrates that Class 10 exhibits low posterior probabilities primarily along the region’s edges, where it competes with adjacent classifications. Meanwhile, Class 11 is situated in the Western Pacific Warm Pool near the Peru Current, an area characterized by temperature instability that results in reduced posterior probabilities. Class 16 comprises warm water masses adjacent to the cold water masses of Class 8. Additionally, lower posterior probabilities are observed in the northeastern corner, where the Gulf Stream’s influence weakens at higher latitudes and the surrounding cold currents further contribute to the sea temperature instability.

5. Discussion

In this study, we applied Gaussian Mixture Models (GMMs) to classify global ocean temperature profiles, identifying 18 distinct distribution patterns. This approach builds on previous works using unsupervised clustering methods for ocean data, such as the Profile Classification Model (PCM) by Maze et al. [21], which demonstrated that probabilistic classification techniques can reveal coherent patterns not easily captured by simple spatial subdivisions. Our results confirm that GMM-based classification provides insight into subtle vertical thermal structures and can delineate fronts and transition zones associated with major ocean currents and climatic phenomena.

Several key findings emerged from our analysis. First, the classification results captured well-known cold and warm water regimes at high latitudes and near major current systems, consistent with prior descriptions of water mass distributions. For instance, Classes 1 and 2 were dominated by near-freezing waters in the Arctic and Antarctic regions, respectively. These patterns align with known characteristics of Polar Water masses, such as Arctic Intermediate Water and Antarctic Surface Water. Similarly, the classes identified in regions influenced by the Kuroshio, Oyashio, and Gulf Stream Currents correspond to areas where distinct Subtropical and Subpolar Water masses meet and interact, forming well-documented fronts and transition zones [43,45,51].

Furthermore, the GMM classifications highlight regions influenced by particular circulation features known to shape water masses. For example, Class 3 in the Westerlies Drift and Class 12 in the Mediterranean Sea reflect local circulation patterns that confer unique vertical temperature structures. The Mediterranean Sea’s isolated basin dynamics, as noted by Bergamasco and Malanotte-Rizzoli [54], facilitate the development of exceptionally warm intermediate waters—a signature reflected in the GMM classification. Similarly, the presence of distinct classes in areas affected by the Equatorial Current systems and monsoon-driven circulation in the Indian and Pacific Oceans indicates that our classification captures patterns consistent with Equatorial, Monsoon, and Intermediate Water masses, which are crucial for biogeochemical cycling and heat transport [11,53].

These findings also demonstrate that the GMM-based classification is sensitive to water mass variability associated with inter-basin differences. For example, Classes 6 and 11, which showed somewhat lower posterior probabilities, occur in regions where water masses are strongly influenced by mixing, upwelling, and climate events like El Niño and La Niña. The presence of complex, transient features (e.g., the mixing of Equatorial Water masses with colder currents) and the known instability in such regions documented by Glantz [8] and Fu et al. [3] help explain why a purely statistical classification might yield more diffuse probabilistic assignments.

Overall, our classification confirms that large-scale water mass distributions, transitions, and frontal structures can be distinguished using unsupervised statistical approaches. The identified classes correspond well to known oceanographic features, including Polar Waters, Subpolar Waters, Subtropical Waters, Equatorial Waters, and unique marginal basin water masses. By mapping each class back to recognized hydrographic regimes and circulation patterns, we link our findings to a robust body of past research, providing a new, probabilistic perspective on the global water mass structure.

6. Conclusions

By applying GMM to a global ocean temperature dataset, we identified 18 distinct classes of ocean temperature profiles that probably correspond to known large-scale water masses and their frontal boundaries. These include polar-associated classes in the Arctic and Antarctic Oceans, classes reflecting Subpolar and Subtropical Water mass interactions in the North Atlantic and North Pacific, and groups capturing the influence of unique circulation regimes such as those in the Mediterranean Sea or the Western Pacific Warm Pool. Our results are consistent with previous observational and modeling studies that have characterized these water masses based on hydrographic data, circulation patterns, and climate indices [5,8,21,54].

Importantly, the approach provides a probabilistic measure of classification confidence, revealing areas where water mass boundaries, which are represented by the classes of ocean temperature profile, are more diffuse or variable—often locations of intensified mixing, complex current systems, or climate-driven anomalies. While some regions exhibit lower posterior probabilities due to their inherently dynamic water mass distributions, this uncertainty highlights areas for further study. In the future, we will consider processing other hydrological data such as salinity rather than just temperature data. By using multivariate high-dimensional data analysis methods, we can more comprehensively characterize ocean temperature profiles and water mass and improve the accuracy and detail of classification. At the same time, we will optimize algorithms, increase computing resources, and analyze time series to study the spatiotemporal evolution of ocean temperature profiles’ categories; explore the impact of seasonal changes, interannual variability, and long-term climate change on water mass structures; and better understand the vertical and horizontal transport of ocean heat and matter.

Author Contributions

Conceptualization, W.Z.; methodology, W.Z. and X.Y.; visualization: X.Y.; supervision, W.Z.; writing—original draft, X.Y. and W.Z.; writing—review and editing, W.Z.; visualization, X.Y.; project administration, W.Z.; funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original data presented in the study are openly available in the IAP global ocean temperature 0.5° gridded dataset. The dataset was accessed in July 2020 and can be found at [20] or through the following website: http://www.ocean.iap.ac.cn/pages/dataService/dataService.html?languageType=en&navAnchor=dataService.

Acknowledgments

We would like to thank the East China Sea Fisheries Research Institute, Chinese Academy of Fishery Sciences, for providing equipment support and the Oceanographic Data Center, Chinese Academy of Sciences (The dataset was accessed in July 2020 and through the following website: http://www.ocean.iap.ac.cn/pages/dataService/dataService.html?languageType=en&navAnchor=dataService), for providing data services.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. Three thousand randomly selected temperature profiles.

Figure 2. Root mean square deviation (RMSD) for different numbers of principal components.

Figure 3. The relationship between the number of mixture components and their corresponding score values.

Figure 4. GMM global data classification results.

Figure 5. Mean temperature curves for Classes 1–6.

Figure 6. Mean temperature curves for Classes 7–12.

Figure 7. Mean temperature curves for Classes 13–18.

Figure 8. Posterior probability distribution for Class 6.

Figure 9. Posterior probability distribution map.

Figure 9. Posterior probability distribution map.

Table 1

Temperature statistics for each classification.

Classification	Number of Profiles	Mean Temperature (°C)	Lowest Temperature (°C)	Highest Temperature (°C)
1	12,018	−0.493	−2.383	2.149
2	13,979	−0.109	−5.160	3.026
3	20,769	4.019	−2.722	15.294
4	4336	2.937	−2.958	25.405
5	4763	5.911	0.211	18.230
6	7975	8.575	−2.050	30.261
7	6341	11.911	3.414	22.660
8	14,808	12.783	1.912	28.660
9	4650	14.767	3.018	29.230
10	4641	16.495	3.412	29.770
11	8220	15.173	3.214	30.430
12	603	16.324	10.196	28.368
13	6792	14.526	1.551	30.565
14	9664	13.941	3.863	30.229
15	5908	17.242	3.970	30.655
16	3910	17.640	−1.052	31.359
17	9082	16.771	3.962	30.413
18	7028	16.563	3.883	30.551

Table 2

Percentage of the profiles assigned to each class based on posterior probability.

Classification	[0.0, 0.5)	[0.5, 0.75)	[0.75, 0.9)	[0.9, 1.0]
1	<1%	<1%	1.2%	97.8%
2	<1%	5.6%	6.6%	87.8%
3	<1%	5.9%	6.6%	87.1%
4	<1%	9.4%	6.6%	83.5%
5	<1%	2.9%	2.9%	93.8%
6	1.1%	17.5%	16.9%	64.5%
7	<1%	6.7%	7.7%	84.9%
8	<1%	10.0%	8.7%	80.5%
9	<1%	7.4%	7.5%	84.9%
10	<1%	13.4%	10.9%	74.7%
11	<1%	12.5%	14.9%	72.1%
12	0%	0%	<1%	99.7%
13	<1%	3.8%	4.2%	91.8%
14	<1%	4.4%	8.3%	87.1%
15	<1%	7.3%	7.9%	84.4%
16	<1%	11.5%	8.3%	79.8%
17	<1%	7.6%	8.9%	83.2%
18	<1%	3.4%	3.6%	92.6%

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