We estimate the SST gradient magnitude G from the gridded SST field T(i,j) using centered finite differences: 1Dx(ij)=Ti,j+1-T(i,j-1)2Δx2Dy(ij)=Ti+1,j-T(i-1,j)2Δy3G(ij)=Dx(i,j)2+Dy(i,j)2 Here Δx and Δy are the grid spacings (in km), and (i,j) denotes the grid indices.

Ocean fronts were manually delineated using Labelme (Wada, 2021), a Python-based open-source image annotation tool (10.5281/zenodo.5711226, Wada, 2021). For each SST gradient map, polygon boundaries were drawn around visually continuous front features. Multiple polygons may be drawn within a single map, as multiple ocean fronts can appear in one image. Each annotated map was saved as a Labelme JSON file containing the polygon coordinates and corresponding metadata.

The annotated SST gradient maps were derived from the 30-year dataset created using the gradient method (Sect. 3.1), based on the GLORYS12V1 L4 reanalysis and L3 satellite SST data described in Sect. 2. The labeled dataset comprises 5000 samples, where each sample consists of one SST gradient map and its associated JSON annotation file.

Mask R-CNN extends Faster R-CNN by adding a branch parallel to the existing target detection frame to predict the target mask. Mask R-CNN has three outputs: a class label, a bounding-box offset and the target mask. The difference between the target mask and the class-box output is that more refined extraction of the target's spatial layout is needed. The network architecture diagram of Mask R-CNN is shown in Fig. 2. Mask R-CNN is an instance segmentation network that takes an input image of arbitrary size, predicts class labels, bounding boxes, and pixel-level masks for each detected object. The success of this architecture is based on several factors, such as the availability of large datasets, increased computing power, and the availability of GPUs. It also depends on the implementation of additional techniques, such as dropout, data augmentation to prevent overfitting, and rectified linear units to accelerate the training phase.

The residual neural network (Res-Net) and feature pyramid network (FPN) are the key networks used to extract features in Mask R-CNN. Res-Net is a residual learning framework used to reduce the burden of network training, and the FPN extracts region of interest (ROI) features from different feature levels according to the size of the features. A region generation network (RPN) is used to generate candidate regions. Then, ROI Align collects the image features and candidate region features as the input to the subsequent full connection layer and then determines the target category.

Applying deep learning methods to ocean front detection is challenging because fronts have significant visual similarity and are indistinguishable in colour and shape. Ocean fronts are regions in which sharp transitions in oceanic properties such as temperature, salinity and density occur. These fronts are critical for understanding the dynamics of the ocean and global climate system. However, detecting and characterizing these fronts is challenging due to their complex and dynamic nature. In particular, the visual similarities among different fronts can make them difficult to distinguish based on gradient magnitude patterns and shape alone. Deep learning methods offer a promising approach to overcome these challenges (Fig. 3). By leveraging large datasets of oceanographic data, including satellite imagery and in situ measurements, deep learning models can learn to identify the patterns and features that are characteristic of different types of ocean fronts. These models can then be used to classify and characterize fronts with high accuracy and efficiency. To develop effective deep learning models for ocean front detection, it is essential to carefully curate and preprocess the training data to ensure that it is representative of the range of oceanographic conditions and front types that may be encountered in the real world. Additionally, the choice of neural network architecture and training parameters significantly affect the performance of the model, and careful tuning and evaluation are required to ensure optimal results.

In our framework, ocean fronts are represented as a pixel band with finite width (i.e., a narrow binary mask region), rather than a single-pixel wide line or a bounding box enclosing a high-gradient region. This approach better reflects the physical nature of the front as a transition zone between two water masses. As a connected region, it is directly compatible with the instance segmentation mask output by Mask R-CNN and the IoU area calculation. While the front is geographically quasi-linear, modelling it as a “finite-width band” transforms the problem into a region segmentation task. The task of Mask R-CNN is to predict a corresponding binary mask for each front instance. Then, the IoU is calculated based on the area overlap between the predicted mask and the ground-truth mask, which is used to evaluate the detection performance. This process follows the standard evaluation procedure for instance segmentation. Additionally, we designed a non-maximum suppression (NMS) algorithm based on spatial location and mask similarity specifically for merging duplicate detections of the same front segment in overlapping areas with adjacent tiles and for connecting broken parts across boundaries, thereby forming a complete and continuous front vector.

The Mask R-CNN loss involves the addition of the loss on the Mask branch on top of Faster R-CNN, which is described as follows: 4Loss=Lrpn+Lfast_rcnn+Lmask Lrpn generates objects by proposing potential bounding box regions in the image. The Lfast_rcnn network extracts the proposed region from the RPN and performs region classification and bounding box regression, and the Lmask loss measures the accuracy of the predicted mask by comparing it with the actual mask. By combining these three losses, Mask R-CNN's overall loss function guides the network to simultaneously perform accurate region proposals, object classification, bounding box regression and instance segmentation. The network learns to balance these different objectives during training to improve its performance in tasks such as object detection and instance segmentation.

The loss function is usually associated with optimization problems, for which it is employed as a learning criterion; that is, the model is solved and evaluated by minimizing the loss function. According to the above task description, the loss function of RPN training consists of two parts: classification loss and position regression loss. 5Lpi,ti=1Ncls∑iLclspi,pi∗+λ1Nreg∑ipi∗Lregti,ti∗ Lpi,ti refers to the entire loss function, which represents the total loss of the model. 1Ncls is a scalar that represents the normalization factor of the classification loss term, where Ncls denotes the number of categories in the classification task. ∑iLclspi,pi∗ represents the sum of the classification loss terms, which is usually used to measure the performance of the model in classification tasks. The classification loss involves each sample i, where pi is the predicted probability distribution of the model and pi∗ is the probability distribution of the actual label. Lcls is usually a cross-entropy loss or other classification loss function. λ is a nonnegative constant used to balance the classification loss term and the regression loss term, and 1Nreg is the normalization factor for the regression loss term, where Nreg represents the number of samples. ∑ipi∗Lregti,ti∗ represents the sum of the regression loss terms. The regression loss for each sample i is involved, where ti is the predicted regression value of the model and ti∗ is the actual regression target value.

During the training process, the gradient image of the SST data on the target date was selected to detect and extract ocean fronts. An overview of the experimental workflow is provided in Fig. 4, which illustrates the sequential steps involved in detecting and evaluating ocean fronts by using the Mask R-CNN model. This flow chart helps to visualize the process and highlights the key stages in the experiment. The process can be summarized as follows:

Acquisition of SST Data: The experiment commenced with the acquisition of SST data for the study area, specifically incorporating both the L3 remote sensing satellite SST data and the GLORYS12V1 L4 reanalysis SST product.

The mean average precision (mAP) was chosen as the evaluation metric. First, the accuracy of the front was represented by the IoU (Intersection over Union), and the general threshold was set to 0.5, which means that if the IoU ≥ 0.5, the detection is considered correct. Then, by using the recall as the horizontal axis and the accuracy as the vertical axis, the P-R curve was obtained. Ideally, both P and R can achieve results that are infinitely close to 1 at the same time. Therefore, ideally, the area covered under the P-R curve is infinitely close to 1. The area below P-R is called the average accuracy of ocean front detection, known as the AP (Average Precision). The average of multiple APs is the mAP. The definitions of the IoU, P, R, and AP are as follows: 6IoU=AreaofOverlapAreaofUnion7P=TPTP+FP8R=TPTP+FN9AP=∫01P(R)dR

In the equation, the area of overlap refers to the intersection of two prediction boxes, and the area of union is the union of two prediction boxes. TP denotes predicted ocean-front instances that correctly match a ground-truth front, FP denotes predicted instances that do not correspond to any ground-truth frons, and FN denotes ground-truth fronts that were not detected by the model.

To generate the frontal indicator field, we first calculated the temperature gradient by using Eqs. (1)–(3). Figure 5 shows the resulting field for January 2023, which highlights regions in which the sea surface temperature changes rapidly, revealing the spatial structure of ocean fronts. Warmer colours correspond to stronger transitions. This representation clearly outlines areas of active frontal variability and facilitates a straightforward visual assessment of their distribution and evolution during the month.

Sufficient training samples are essential for deep learning-based ocean front detection. However, ocean fronts appear as small-scale and weak-edge features in SST imagery, making it difficult to construct a large and effective training dataset, particularly in regions in which the frontal edges are diffuse or ambiguous. To address this limitation, we collected SST images from regions known to exhibit frequent global frontal activity and applied data augmentation and feature enhancement techniques. In addition, a frontal indicator field was derived from the SST data to highlight the frontal structures.

To create the labeled dataset (Fig. 6), each ocean front was manually annotated by using the Labelme software. Annotators outlined the frontal boundaries in the SST and gradient-enhanced images to generate polygonal masks representing individual fronts. These masks were then converted into COCO-style instance labels (i.e., JSON-formatted annotations containing polygon coordinates and instance-level segmentation information) to train the Mask R-CNN model (Lin et al., 2014).

In the field of deep learning, datasets are divided into three parts: a training set, a validation set, and a testing set. The data in the training set are used to construct the model, and the validation set is used to evaluate the predictive performance of each model and choose the model with the best performance. After selecting the model with the best accuracy via the validation set, the performance of the optimal model is evaluated on the test set. Notably, to ensure the accuracy of the evaluation, the test set data do not participate in the training process. The quality of the training dataset is the key to affecting the accuracy of the target detection model. To achieve the automatic extraction and learning of the high-level essential features of ocean fronts in temperature images, a multilevel network model was constructed, thereby achieving the automatic detection of ocean fronts. The entire process does not require manual intervention; thus, during the dataset construction process, multisource temperature data were used to ensure the diversity of training data and enhance the generalization ability of the model.

Mask R-CNN exhibits excellent feature learning, but it requires multiple adjustments of various network parameters to optimize the network and detection results and thus obtain the best ocean front detection model. The network parameters commonly adjusted in deep learning include the momentum, learning rate, batch size, weight attenuation ratio, number of iterations. The learning rate is usually set to 0.0002, the weight attenuation is typically set to 0.0005, and the batch size is set to 2 due to memory limitations. The network parameter settings with the best detection accuracy are obtained primarily by adjusting the proportion of training and validation set, the learning rate, and the number of iterations.

To evaluate the data efficiency of the proposed model, we conducted comparative experiments by gradually decreasing the proportion of training set while increasing the proportion of validation set. For each data split, the model was trained with fixed hyperparameters (learning rate = 0.0002, batch size = 2, number of iterations = 1000), and the performance was evaluated on the corresponding validation set. As shown in Table 3, when the training set proportion decreased from 0.8 to 0.75, the average precision (AP) and average recall (AR) improved, suggesting that a moderate increase in validation set may help better assess model generalization. However, as the training proportion further decreased to 0.6, both AP and AR gradually declined, indicating that insufficient training data hinder the model's ability to learn representative features. Based on these observations, we selected a training/validation split of 75 %/25 % as a balance between training sufficiency and validation reliability. Hyperparameters were tuned using this validation set, and the final model performance was evaluated on a separate test set consisting of SST data from 2023, which was not used during model development. The test set results are reported in the subsequent section.

To verify the accuracy of the model's detection results, the model was tested by using the test dataset, and the mAP was calculated. The results were compared with the manually annotated results, and the IoU value was also computed. Additionally, to further improve the ocean front detection performance, the model parameters were continuously adjusted to enhance both the mAP and IoU. Finally, after 30 000 iterations, the trained network successfully demonstrated the ability to detect ocean fronts. The training loss and detection mAP according to different numbers of iterations are shown in Table 4.

As the number of training iterations increases from 5000 to 30 000, the training loss decreases from 0.327 to 0.118, the IoU increases from 0.671 to 0.916, and the mAP improves from 0.680 to 0.920. These findings indicate that the network gradually learns better feature representation and classification capabilities during the training process, thereby improving its performance in detection tasks. Notably, although both the loss and detection accuracy significantly improved during training, the rate of loss reduction slows down after 30 000 iterations, whereas the detection accuracy continues to improve. This finding may indicate that the network has approached or reached its optimal performance on this dataset, and further training may result in only minor improvements. In summary, the loss and detection accuracy of the training network improve with an increasing number of training iterations, demonstrating that the network's performance in learning tasks gradually improves.

Figure 7 shows the detection results for ocean fronts based on the Mask R-CNN model in January 2023. Through the application of deep learning algorithms, the positions and shapes of ocean fronts were identified and displayed by using markers and contours. From the graph, it can be observed that the ocean front detection results based on deep learning algorithms can display obvious features. Furthermore, the position and shape of ocean fronts are clearly visible in the figure, indicating that the algorithm can effectively capture the spatial distribution of ocean fronts and accurately distinguish it from the surrounding sea area. Second, the ocean front detection results shown in the figure demonstrate the manifestation of small-scale information. Ocean fronts typically have complex shapes and variations, including slender strip structures and local eddies. Deep learning algorithms can capture these small-scale features, making the detection results more refined and continuous.

In addition, the ocean front detection results based on the Mask R-CNN model show good continuity over a time range. Ocean fronts shown in the figure exhibits a relatively stable distribution and evolution trend over time, indicating that the detection algorithm has high stability and reliability and can effectively track and analyse changes in ocean fronts.

To further test the accuracy of deep learning methods in terms of identifying ocean fronts, sea surface temperature data for April 2023 were used. The traditional gradient method was employed to obtain reference ocean front maps, against which the deep learning results were compared (Fig. 8). As shown, ocean fronts extracted by the deep learning model are highly consistent with those derived from the traditional gradient method, demonstrating the model's effectiveness in capturing frontal structures.

Furthermore, based on the ocean front detection results, the intensity and width at the corresponding latitude and longitude were extracted, thereby enabling intelligent extraction of the position, intensity, and width of ocean fronts. Here, intensity refers to the temperature gradient magnitude, and the width was calculated as twice the distance from the centerline to the boundary. Specifically, the centerline is extracted by computing the morphological skeleton of the predicted binary front mask. The width at each point along the skeleton is then calculated as twice the value of the Euclidean distance transform at that point, which represents the shortest distance from the centerline point to the mask boundary. The reported frontal width is the average of these per-point width values over the entire skeleton. As shown in Fig. 8, the intensity and width of ocean fronts identified by traditional and deep learning methods were also examined. The numerical results are shown in Table 5. In terms of the intensity of a single ocean front, the table presents both the gradient-based and deep learning–based measurements, which are expressed in °C km⁻¹ with an error of 0.013 °C km⁻¹. The width of a single ocean front detected by the gradient and deep learning methods is measured in kilometres with an error of 0.155 km. These results indicate that the deep learning method is consistent with the gradient detection method in terms of capturing ocean fronts characteristics. Overall, these findings highlight the effectiveness of the deep learning approach in ocean front detection.

Research on the seasonal patterns of ocean fronts is extremely important for better understanding the Earth's climate system, as it helps to gain a deeper understanding of ocean circulation and its impact on seawater temperature, salinity, and nutrient distribution, which is crucial for ecosystems, fisheries, and marine resource management.

Ocean front detection results for the entire year of 2023 are divided by season: spring (March, April, and May), summer (June, July, and August), autumn (September, October, and November), and winter (December, January, and February). In addition, the seasonal averages were calculated to obtain the spatial and temporal distributions of ocean fronts during each season. In terms of the seasonal distribution, ocean fronts activity is most frequent and most common in the winter, followed by the autumn. Spring and summer exhibit relatively weaker gradient magnitudes and less extensive frontal structures, with the weakest signals observed in summer. In terms of frontal activity inferred from gradient intensity, the order, from weakest to strongest, is summer < spring < autumn < winter. Regarding spatial distribution, ocean fronts are more active in nearshore waters. In the South China Sea, ocean fronts are concentrated primarily between Hainan and the Taiwan Strait, with a higher frequency of ocean fronts near the Taiwan Strait. In spring and summer, ocean fronts activity in the South China Sea is relatively inactive, with fewer ocean fronts. In terms of seasonal and spatial distribution characteristics, the results align with prior observations (Hickox et al., 2000).