The polarization combination enhancement method includes (1) data preprocessing; (2) HH-polarized IAC; (3) HV-polarized TNR; (4) polarized data enhancement, and (5) RGB false-color composite. Figure 4 illustrates the flowchart of the polarization combination enhancement process. Data preprocessing mainly involves orbit correction, radiometric calibration, filtering, conversion to dB values, and geocoding processing.

In the process of ice eddy detection, the variation in the backward scattering coefficient caused by changes in the incidence angle may introduce significant errors, necessitating the correction of the incidence angle for HH-polarized data. In this study, the IAC algorithm (Qiu and Li, 2022; Li et al., 2020) is utilized, and the calculation formula is presented in Equation 1.

where σ is the corrected backward scattering coefficient (in dB), σ 0 is the backward scattering coefficient before correction, θ is the incidence angle of the pixel, and θ 0 is the corrected standard incidence angle, which is taken as 34.5°. Figure 5D illustrates the effects following the correction of the HH polarization incidence angle.

In Sentinel-1 EW-mode SAR images that are strongly affected by scallop stripe noise in the azimuth direction and by noise gradients in the distance direction, especially in HV-polarized images, thermal noise is particularly prominent as displayed in Figures 5A, B . Although ESA provides a standard method of noise vector correction, the effect of residual noise cannot be ignored due to the narrow distribution of HV polarization backscatter.

The denoising algorithm (Park et al., 2017; Sun and Li, 2020) was improved for the removal of thermal noise. The average noise power was added to the denoised results. This adjustment enabled the conversion of noise power from a linear scale to a logarithmic scale (dB) sigma zero conversion, ensuring that these pixels did not become invalid values. By appropriately scaling and balancing the noise vectors given by ESA, the algorithm can approximate the actual noise values as much as possible by using the azimuthal antenna element pattern in the azimuthal direction, so that the effects of the scallop stripe and the noise gradient in the distance direction can be effectively eliminated. The specific processing steps are as follows.

To eliminate the noise step phenomenon between sub-bands, it can be assumed that the denoising process model satisfies a linear relationship. It is calculated using Equation 2.

where s ( k ) is the denoised σ 0 value. σ S N 0 is the uncorrected original σ 0 value. σ N 0 is the σ 0 calculated by bilinear interpolation using the thermal noise vector provided by ESA. K n s , n is the optimal noise scaling factor. K p b , n 0 is the interstrip noise power balance factor. n is the number of sub-bands, n = 1, 2, 3, 4, 5. K n s , n can be obtained by least squares solution using a large amount of HV polarized data. K p b , n 0 can be calculated using Equation 3.

where α n and β n are the slopes and intercepts, respectively, of the linear models for the different sub-strips. i is the number of image elements in the range direction at the boundary between the strips n = 2, 3, 4, 5. Since there are only four interstrip boundaries. K p b , 1 0 is set to 0.

When the original image is subtracted from the thermal noise acquired using the described method, some image element points become negative. To eliminate the effect of negative noise power, noise compensation is required. By appropriately scaling and balancing the noise vectors provided by ESA, the algorithm can closely approximate the actual noise values using the azimuthal antenna element pattern, effectively eliminating the effects of scallop stripes and noise gradients in the range direction.

First, the Signal-Noise Ratio (SNR) is defined as the ratio of the σ 0 value ( s 0 g ) after Gaussian filtering to the noise equivalent sigma zero (NESZ). The SNR is calculated using Equation 4.

Subsequently, further calculations were conducted to obtain the power compensated using Equation 5.

where s 0 o is the residual noise power compensated σ 0 . s 0 offset is the noise field compensation value, which can be taken as the average value of the reconstructed noise field.

Finally, the HV polarization grayscale image with thermal noise removed can be obtained. Figure 5C illustrates the effects after the removal of thermal noise from the HV polarization.

In this paper, a high-quality dual-polarization SAR RGB false-color ice eddy image production method is proposed, compositing HH and HV polarizations into a single false-color image. Since the ice eddy information in the Sentinel-1 EW model is primarily contained in the HH-polarized data, the HH-polarized image is used for the blue channel and the HV-polarized image for the red channel. To optimize the visual quality, the square root is applied to the HH and HV channels, with a slight offset added to mitigate the effect of grain noise on the data. The calculation formula is presented in Equation 6 and Equation 7.

The green channel image is produced by combining the offset-processed HH and HV polarization data, as shown Equation 8.

Finally, the SAR image was enhanced using SAR image stretching and contrast-limited adaptive histogram equalization (CLAHE). Figure 6 illustrates a comparison the RGB false color images before and after denoising.

The data expansion of 702 dual-polarized false-color ice eddy images was achieved through noise perturbation transformations, rotations (90°, 180°, 270°), and up-down flip transformations, resulting in dual-polarized ice eddy samples. Eddies that rotate clockwise in the northern hemisphere are referred to as anticyclonic eddies, while those that rotate counterclockwise are referred to as cyclonic eddies. Figure 7 illustrates examples of anticyclonic and cyclonic ice eddies.

In this paper, we propose the neural network component of OIEDNet, a multiscale rotating frame model designed for the automatic detection of ice eddies. The model structure is illustrated in Figure 8 . Traditional target detection algorithms typically utilize HBB, assuming that object positions in the image are calculated relative to the image center. However, this assumption is not always accurate, particularly for objects with distinct directional features, as the HBB often fails to accurately locate the true position of such objects. OIEDNet addresses this limitation by introducing OBB, which allow bounding boxes to be positioned at any arbitrary angle, making it more adaptable for detecting target objects with various orientations.

Based on the obtained location information, the center and diameter of the ice eddy in the predicted box can be determined, laying the foundation for subsequent ice eddy studies. The center of the tangent ellipse inside the rotating frame was used as the eddy center, and the average distance from the center of the ice eddy to all points on the fitted ellipse is used as the radius of the ice eddy. According to the ice eddy automatic detection model, the rotating frame parameters ( c x , c y , w , h , θ ) of the ice eddy are obtained. Using the eddy center ( c x , c y ) as the starting point, the coordinate positions of the four vertices A,B,C,D can be calculated.

During the data preprocessing stage, SAR images are geocoded using the WGS1984 standard, transforming pixel coordinates (rows and columns) into geographic coordinates (longitude and latitude). Consequently, it becomes possible to calculate the location of the ice eddy center and the eddy diameter. The Feature Statistical Analysis Module primarily facilitates the extraction of ice eddy center and diameter information, and performs statistical analyses to produce thematic maps of ice eddies for any time period and any region. These maps depict the spatial distribution of ice eddies and related scale histograms (see Chapter 4.4). These analyses support researchers in examining the generative mechanisms and evolutionary processes of ice eddies.

The experimental setup configuration is provided in Table 2 . Computation was performed on GPUs with 16 multithreads, and the training data share was configured to 0.75. The RGB ice eddy training set and S1 annotations were employed for training, and the model’s parameters were fine-tuned based on experience and experimental results to attain optimal performance.

YOLOX is an open-source high-performance detector that builds upon YOLOv3 by introducing decoupled heads, data augmentation, anchor-free detection, and the SimOTA sample matching method, thus constructing an end-to-end anchor-free object detection framework (Zheng et al., 2021). YOLOv8 is a real-time object detection model that utilizes advanced techniques such as anchor-free detection and multi-scale feature fusion within a HBB framework (Varghese and Sambath, 2024). We conduct comparative experiments on OIEDNet, YOLOX and YOLOv8. In addition, we conduct multi-model comparison experiments to evaluate performance before and after denoising, and between single polarization and dual polarization.

The precision evaluation of the model is based on the validation set, and the evaluation metrics include the precision rate (P), the recall rate (R) and the F1-Score (F1), as shown in Equations 9–11.

TP denotes the number of correctly detected ice eddies, FP denotes the number of false positive detections of ice eddies, and FN denotes the number of missed ice eddies.

The results of OIEDNet,YOLOX and YOLOv8 were compared using the same test set, as presented in Table 3 . Both YOLOv8 and YOLOX are traditional HBB detection models. The experimental results indicate that the OIEDNet model exhibits a precision of 94.40% and a recall of 93.65%, while YOLOv8 and YOLOX exhibit precisions of 93.50% and 87.90%, as well as recalls of 92.00% and 86.51%. In comparison to YOLOv8 and YOLOX, the OIEDNet model demonstrates superior performance in detecting dense eddy regions. The rotational detection of OIEDNet more accurately detects eddies with irregular shapes and changing directions, and the inspection frame fits the eddies more closely, significantly reducing the redundancy of the horizontal inspection frame, as shown in Figure 11 . For eddies with large differences in scales and similar locations, there is obvious overlapping of inspection frames in horizontal detection, while rotational detection effectively avoids overlapping of inspection frames ( Figure 11B ). The interaction between ocean circulation and ocean currents is accompanied by the splitting and fusion of ocean eddies, leading to the multinucleated structure of ice eddies, which the rotational detection method can detect more accurately ( Figure 11D ). The IEDNet model reduces the leakage and false alarms of ice eddies to a certain extent. The OIEDNet model has obvious advantages in the precision and recall of ice eddy detection, and it can effectively detect submesoscale and mesoscale ice eddies.

This study evaluates the enhancement effects of IAC, TNR, and dual-polarization RGB false color synthesis in the OIEDNet model. Comparison of four sets of ice eddy detection results for the same OIEDNet model ( Figure 12 ). Before and after the denoising of dual-polarized false-color images, the detection accuracy increases from 88.71% to 94.40%, reflecting an improvement of 5.69%. In contrast, the detection accuracy of ice eddies in HV-polarized images without TNR is 85.04%, while the detection accuracy in HH-polarized images without IAC is 89.06%. This indicates that thermal noise significantly reduces the detection accuracy of ice eddies, whereas the incidence angle has a relatively minor effect on detection accuracy. The detection performance of the proposed model shows significant improvement with the adoption of the Polarization Combination Enhancement, resulting in an approximate 8.65% increase in the F1 score. This enhancement effectively boosts detection accuracy in noise-heavy environments.

Altimeters and SWOT satellites rely on radar echo signals for measuring sea surface height. However, sea ice leads to attenuation and scattering of radar signals, rendering the echo signals unstable, which makes it difficult to obtain accurate sea surface height data and, therefore, makes it unable to accurately detect ice eddies, as shown in Figures 13 , 14 . SAR, on the other hand, can clearly detect ice eddies in this environment due to its high-resolution imaging and penetration capabilities. Mesoscale eddies can be identified from sea level height data using altimetry, but the daily mesoscale eddy dataset is identified by measuring different time trajectories, which results in low spatial and temporal resolution. Figures 13B , 14B shows a comparison of eddies identified by OIEDNet and altimeters. It is clear that SAR is able to detect more submesoscale ice eddies and that SAR is even more advantageous in detecting high-latitude ice eddies.

The ice eddies detected by OIEDNet were compared and validated against in situ data collected from OpenMetBuoys-v2021 (OMBs) deployed in the marginal ice zone. Figure 15 illustrates the movement trajectories of two ice buoys in the marginal ice zone around Svalbard from August 18, 2022, to August 26, 2022. Red triangles are used to denote the starting positions of the buoys, while pentagrams indicate the ending positions of their trajectories. The ice buoy trajectories exhibit a counterclockwise rotation consistent with the direction of the ice eddy, indicating a cyclonic ice eddy.

Using the OIEDNet ice eddy detection framework, ice eddy identification and scale information extraction were performed on 702 SAR images containing ice eddies in the Nordic Seas from January 2022 to December 2023. To ensure the accuracy of the statistical feature information of the ice eddies, the detected ice eddy types were annotated using a manual visual inspection method. A total of 2283 ice eddies were identified, including 1724 cyclonic eddies (CEs) and 559 anticyclonic eddies (AEs). The number of cyclonic ice eddies is 3.08 times that of anticyclonic eddies, which may be related to the mechanism of anticyclonic eddy generation and the interaction between the two (McWilliams, 2016).

The spatial density distribution of ice eddies was calculated using a 0.1° × 0.1° grid, as shown in Figure 16A , revealing that the densest distribution of ice eddies is located in the north-central Greenland Sea, which exhibits a high number of both cyclonic and anticyclonic ice eddies. The monthly variation is shown in Figure 16B , indicating that Nordic Seas ice eddies are present throughout the year, with two peaks in the total number of ice eddies in May and October, and a low in March. Overall, May to November is the period when ice eddies are most frequent. The formation of ice eddies in the Nordic Seas results from a combination of dynamical and thermal forces (Perovich and Jones, 2014). Spatially, areas of high ice eddy occurrence are often closely linked to the Arctic Current, with the East Greenland Cold Current flowing along the east coast of Greenland. Temporally, with the onset of the Arctic summer polar day, sea surface temperatures (SSTs) rise, and glacier melting causes the expansion of marginal ice areas, leading to high ice eddy occurrence. In contrast, the Nordic Seas ice cover decreases rapidly to reach a minimum at the beginning of October, after which the ice area starts to expand rapidly. Thus, the thermodynamic factors in the Nordic Seas are more complex in October, which is conducive to the formation of ice eddies.

Figure 17A shows that the sizes of ice eddies in the Nordic Seas are primarily concentrated in the mesoscale and submesoscale intervals. The diameters of these eddies are mostly in the range of 10-100 km. The diameter of cyclonic ice eddies is mainly between 10-60 km, while the diameter of anticyclonic ice eddies is mostly between 30-70 km, indicating that anticyclonic ice eddies tend to be larger than cyclonic ice eddies. Large ice eddies are primarily located in the north-central Greenland Sea.

From Figure 17B , we observe that the proposed model maintains detection performance despite increasing wind velocity. Although the number of ice eddy detections decreases with higher wind speeds, this does not indicate a decline in model performance; instead, it reflects the inherent difficulty of eddy formation in areas with strong winds, resulting in a reduced number of eddies. The lack of a sharp downward trend in detections further illustrates the robustness of the proposed model across varying wind speeds. Regarding wind velocity, 79.7% of the detected ice eddies formed under low wind conditions of 1-4 m/s, while about 20.3% occurred under medium wind conditions. Similarly, from Figure 18 , as ice concentration increases, the number of ice eddies decreases. The rate of detected ice eddies shows a gradual decline, which further demonstrates the robustness of the proposed model under varying ice concentrations.