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21 pages, 8944 KiB  
Article
BiST-SA-LSTM: A Deep Learning Framework for End-to-End Prediction of Mesoscale Eddy Distribution in Ocean
by Yaoran Chen, Zijian Zhao, Yaojun Yang, Xiaowei Li, Yan Peng, Hao Wu, Xi Zhou, Dan Zhang and Hongyu Wei
J. Mar. Sci. Eng. 2025, 13(1), 52; https://doi.org/10.3390/jmse13010052 - 31 Dec 2024
Viewed by 343
Abstract
Mesoscale eddies play a critical role in sea navigation and route planning, yet traditional prediction methods have often overlooked their spatial relationships, relying on indirect approaches to capture their distribution across extensive maps. To address this limitation, we present BiST-SA-LSTM, an end-to-end prediction [...] Read more.
Mesoscale eddies play a critical role in sea navigation and route planning, yet traditional prediction methods have often overlooked their spatial relationships, relying on indirect approaches to capture their distribution across extensive maps. To address this limitation, we present BiST-SA-LSTM, an end-to-end prediction framework that combines Bidirectional Spatial Temporal LSTM and Self-Attention mechanisms. Utilizing data sourced from the South China Sea and its surrounding regions, which are renowned for their intricate maritime dynamics, our methodology outperforms similar models across a range of evaluation metrics and visual assessments. This is particularly evident in our ability to provide accurate long-term forecasts that extend for up to 10 days. Furthermore, integrating sea surface variables enhances forecasting accuracy, contributing to advancements in oceanic physics. Full article
(This article belongs to the Section Ocean Engineering)
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Figure 1

Figure 1
<p>Instance of mesoscale vortex splitting, where the upper warm vortex becomes two as time evolves.</p>
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<p>Data collection environment: South China Sea and adjacent areas.</p>
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<p>Visualization of mesoscale eddy distributions derived from the SLA of the CMEMS dataset. The upper panels display the initial identification of eddy contours using the py-eddy-tracker tool [<a href="#B66-jmse-13-00052" class="html-bibr">66</a>,<a href="#B67-jmse-13-00052" class="html-bibr">67</a>]. The lower panels depict the same eddies after enhancement through color-filling to improve the robustness of model training. Anticyclonic (cold) and cyclonic (warm) eddies are represented in rose red and green, respectively. The values in brackets correspond to the number of eddies within the depicted regions. The images are organized into left and right columns, corresponding to adjacent time steps (1 h). A zoomed-in view of the central grid is elaborated in <a href="#jmse-13-00052-f001" class="html-fig">Figure 1</a>.</p>
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<p>Overall routine of the framework.</p>
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<p>Illustration of the BiST-SA-LSTM model structure.</p>
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<p>Detailed data flow of the BiST-SA-LSTM model in the top and bottom temporal blocks between adjacent time steps.</p>
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<p>Example of the inner structure of the LSTM module (forward).</p>
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<p>Comparison of different models from the predicted mesoscale eddy distribution maps during the prediction window. (<b>a</b>) Ground Truth; (<b>b</b>) BiST-SA-LSTM; (<b>c</b>) LSTM; (<b>d</b>) Attention-LSTM; (<b>e</b>) Conv-GRU.</p>
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<p>Performance criteria comparison between the different models from the predicted mesoscale eddy distribution maps during the prediction window.</p>
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<p>RMSE error over time of the test set for the BiST-SA-LSTM, LSTM, Attention-LSTM, and Conv-GRU models.</p>
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<p>Box plots of evaluation metrics for BiST-SA-LSTM across different seasons: (<b>a</b>) represents the RMSE and (<b>b</b>) represents the SSIM.</p>
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<p>Error distribution maps indicating the discrepancy between the predicted and ground truth values. (<b>a</b>) LSTM; (<b>b</b>) Attention-LSTM; (<b>c</b>) Conv-GRU; (<b>d</b>) BiST-SA-LSTM.</p>
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21 pages, 18678 KiB  
Article
Response of Subsurface Chlorophyll Maximum Depth to Evolution of Mesoscale Eddies in Kuroshio–Oyashio Confluence Region
by Ziwei Chuang, Chunling Zhang, Jiahui Fan and Huangxin Yang
J. Mar. Sci. Eng. 2025, 13(1), 24; https://doi.org/10.3390/jmse13010024 (registering DOI) - 28 Dec 2024
Viewed by 288
Abstract
The subsurface chlorophyll maximum depth (SCMD) is an indicator of the spatial activity of marine organisms and changes in the ecological environment. Ubiquitous mesoscale eddies are among the important factors regulating the Kuroshio–Oyashio confluence region. In this study, we use satellite altimeter observations [...] Read more.
The subsurface chlorophyll maximum depth (SCMD) is an indicator of the spatial activity of marine organisms and changes in the ecological environment. Ubiquitous mesoscale eddies are among the important factors regulating the Kuroshio–Oyashio confluence region. In this study, we use satellite altimeter observations and high-resolution reanalysis data to explore seasonal variations in the SCMD and its responses to different types of eddies based on methods of composite averaging and normalization. The results show that variations in the SCMD induced by the evolution of the eddies were prominent in the summer and autumn. The monopoles of the SCMD exhibited internally shallow and externally deep features in the cyclonic eddies (CEs), while the contrary trend was observed in the anticyclonic eddies (ACEs). The SCMD was positively correlated with the intensity of the eddies and sea surface temperature, and was negatively correlated with the depth of the mixed layer. These correlations were more pronounced in the CEs (summer) and ACEs (autumn). Both the CEs and ACEs prompted the westward transport of chlorophyll-a (Chl-A), where ACEs transported it over a longer distance than the CEs. Full article
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Figure 1
<p>Research area (<b>a</b>) and sea surface current corresponding to Chl-A on 3 June 2020 (<b>b</b>). The black frame in panel (<b>a</b>) denotes the research area. Blue and red arrows and circles represent CEs and ACEs, respectively.</p>
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<p>The number of eddies generated in different seasons.</p>
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<p>Anomalies in Chl-A over an area three times the radius of the eddy during different stages of its evolution. (<b>a1</b>–<b>a3</b>) represent anomalies in Chl-A corresponding to the stages of development, stability, and decay of CEs, while (<b>b1</b>–<b>b3</b>) represent the corresponding anomalies for ACEs. The solid black line represents the mean radius of the eddy, and the dashed black line represents twice its radius. The eastward and northward directions were set as the positive axes of the longitude and latitude, respectively. The anomalies in Chl-A concentration were obtained by subtracting the spatial average value within the region of the eddy, to obtain the composite average of each part for all eddies.</p>
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<p>The south–north sections of Chl-A concentration along the meridians of centers of the CEs (<b>a1</b>–<b>a4</b>) and ACEs (<b>b1</b>–<b>b4</b>) in different seasons. The positive radius is directed northward and the negative radius southward. The solid and dashed lines represent the mean radius and twice the mean radius, respectively.</p>
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<p>Spatial distributions of the SCMD in CEs and ACEs in different seasons. (<b>a1</b>–<b>a4</b>) show the horizontal distribution of the SCMD of the CEs, and (<b>b1</b>–<b>b4</b>) show the horizontal distribution of the SCMD of the ACEs. The solid black lines represent the mean eddy radius and the dashed black lines represent twice the eddy radius. (<b>c1</b>–<b>c4</b>) show the vertical profile of the average Chl-A concentration within the mean eddy radius. The dashed blue and red lines denote the SCMDs in the CEs and ACEs, respectively. (<b>d1</b>–<b>d4</b>) show the observed chlorophyll profiles in the eddies. “N” indicates the number of profiles.</p>
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<p>Spatiotemporal distributions of the SCMD of the CEs in summer (<b>a1</b>–<b>a3</b>,<b>b1</b>–<b>b3</b>) and autumn (<b>c1</b>–<b>c3</b>,<b>d1</b>–<b>d3</b>) in different stages of eddy evolution. (<b>a1</b>–<b>a3</b>,<b>c1</b>–<b>c3</b>) show the distributions of the SCMD in the stages of development, stability, and decay of the eddy, while (<b>b1</b>–<b>b3</b>,<b>d1</b>–<b>d3</b>) show the radially averaged monopoles of the SCMD.</p>
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<p>Spatiotemporal distributions of the SCMD of the ACEs in summer (<b>a1</b>–<b>a3</b>,<b>b1</b>–<b>b3</b>) and autumn (<b>c1</b>–<b>c3,d1</b>–<b>d3</b>) in different stages of eddy evolution. (<b>a1</b>–<b>a3</b>,<b>c1</b>–<b>c3</b>) show the distributions of the SCMD in the stages of development, stability, and decay of the eddy, while (<b>b1</b>–<b>b3</b>,<b>d1</b>–<b>d3</b>) show the radially averaged monopoles of the SCMD.</p>
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<p>Time series of the SCMD, <span class="html-italic">APD</span>, SST, and MLD within the mean radius of the eddies on each day. (<b>a1</b>,<b>a2</b>) show the sequences of parameters of the CEs, while (<b>b1</b>,<b>b2</b>) show those of the ACEs.</p>
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<p>Changes in the SCMD, <span class="html-italic">APD</span>, SST, and MLD within the mean radius of the eddies during their evolution in summer (<b>a1</b>,<b>b1</b>) and autumn (<b>a2</b>,<b>b2</b>). (<b>a</b>) shows the CEs and (<b>b</b>) shows the ACEs.</p>
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<p>Spatial distributions of the SCM in the stages of development, stability, and decay of eddy evolution. (<b>a1</b>–<b>a3</b>) CEs. (<b>b1</b>–<b>b3</b>) ACEs.</p>
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<p>Spatiotemporal transport of the SCM by the CEs (<b>a</b>) and ACEs (<b>b</b>) during their evolution. (<b>a1</b>–<b>a3</b>) represent SCM transport during the stages of development, stability, and decay of the CEs, while (<b>b1</b>–<b>b3</b>) show the corresponding results for the ACEs. The direction of the polar coordinates was divided into 16 azimuthal angles, and the radius was assumed to be the relative distance from the eddy center.</p>
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26 pages, 19766 KiB  
Article
Reconstructing the Three-Dimensional Thermohaline Structure of Mesoscale Eddies in the South China Sea Using In Situ Measurements and Multi-Sensor Satellites
by Zhiyuan Zhuang, Yanwei Zhang, Liuzhenyi Zhang, Weihan Ruan, Danni Lyu and Jiancheng Yu
Remote Sens. 2025, 17(1), 22; https://doi.org/10.3390/rs17010022 - 25 Dec 2024
Viewed by 288
Abstract
The evolution of the three-dimensional thermohaline structure of mesoscale eddies is crucial for assessing energy and mass transfer during their long-distance propagation in the ocean. However, the understanding and quantitative evaluation of the role that mesoscale eddies play in driving variations of thermohaline [...] Read more.
The evolution of the three-dimensional thermohaline structure of mesoscale eddies is crucial for assessing energy and mass transfer during their long-distance propagation in the ocean. However, the understanding and quantitative evaluation of the role that mesoscale eddies play in driving variations of thermohaline in the deep sea remains constrained due to the scarcity of in situ observations, particularly in marginal seas such as the South China Sea (SCS). In this study, we propose an artificial intelligence (AI)–physics-based deep learning model that integrates satellite measurements and Argo data from 2003 to 2021 to reconstruct the three-dimensional thermohaline structure of mesoscale eddies in the SCS. Besides utilizing basic sea surface hydrodynamic parameters obtained from satellite data for model training, an additional branch incorporating eddy physical parameters was introduced to optimize the model. The results demonstrate that the model effectively reconstructs thermohaline properties within mesoscale eddies in the SCS. Compared to Argo observations, the average root mean square error (RMSE) for temperature (salinity) within anticyclonic eddies was 0.34 °C (0.036 PSU), while it was 0.36 °C (0.032 PSU) within cyclonic eddies in the upper 1500 m. Further validation using high-resolution glider observations tracking an anticyclonic eddy originating in the SCS confirms the model’s efficiency, achieving an RMSE of 0.2962 °C (0.0138 PSU) for temperature (salinity). The accuracy of our proposed model significantly outperforms that of HYCOM and GLORYS simulations, with the RMSE reduced by 40% to 60%. The distinctive capabilities provide valuable insights into understanding the fine-scale structures of mesoscale eddies, especially in regions with limited in situ data. Full article
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<p>The spatial distribution of research datasets. (<b>a</b>) Argo profiles from 2003 to 2021 are used in the study region. Red dots indicate the Argo profiles within anticyclone eddies, while blue dots are the Argo profiles within cyclone eddies. The black dashed box shows the area of all the Argo profiles for validation. (<b>b</b>) Surface track of the glider. The map has combined SLA and surface geostrophic current velocity data distributed by AVISO (<a href="https://www.aviso.oceanobs.com" target="_blank">https://www.aviso.oceanobs.com</a>) (accessed on 23 May 2021). The sampling trajectory of Glider j003 is represented by the black line, and the green triangle marks the initial position of Glider j003. The background map shows the sea level anomaly (SLA) on 8 July 2016.</p>
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<p>The schematic of the reconstruction model. (<b>a</b>) The convolutional neural network (CNN) branch: this branch integrates five types of satellite data as inputs, which are then processed through convolutional layers (Conv), feature Maxpooling layers (Maxpooling), and the Convolutional Block Attention Module (CBAM) during model training. The Particle Swarm Optimization (PSO) algorithm is employed to fine-tune the optimal channels of the CNN at various layers. (<b>b</b>) The physics parameters branch: this branch incorporates seven distinct physical parameters associated with the eddies into the reconstruction model using a regression algorithm. (<b>c</b>) The Backpropagation Neural Network (BPNN) branch: this branch merges the outputs from the CNN and physics parameters branches as inputs. It then processes these inputs through three hidden layers, utilizing a backpropagation mechanism to generate predictions for subsurface temperature and salinity anomalies.</p>
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<p>Surface track of the anticyclonic eddy and time-series of various variables. (<b>a</b>) The thick line represents the trajectory of the eddy center, with the green thick line indicating the trajectory during the observation period. The asterisk stands for the birth site of the eddy. The survey conducted by the glider took place from 3 to 16 July 2016. The black thin line represents the eddy edge on 8 July 2016, with the eddy center located at 17.07°N and 113.465°E (the red dot). The black dots are the observation sites of the glider. The background map is SLA for July 8. Several dynamic parameters are given: (<b>b</b>) topographic depth (blue line) and rotational speed (U, red line); (<b>c</b>) radius (Rad, blue line) and amplitude (Amp, red line); (<b>d</b>) eddy kinetic energy (EKE, blue line); and eddy intensity (EI, red line). The yellow shading indicates the period during which the glider captured the eddy (from 3 to 16 July 2016).</p>
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<p>Comparison of subsurface temperature and salinity anomalies between glider observations and reconstruction model. Panels (<b>a</b>,<b>e</b>) depict the SLA and the distance between the eddy center and the glider observation station. Panels (<b>b</b>,<b>c</b>) show the temperature anomalies from the glider observations and the reconstruction model, respectively. Panel (<b>d</b>) illustrates the residual error, calculated as the difference between the glider observations and the data inverted by the reconstruction model. Panels (<b>f</b>–<b>h</b>) are the same as panels (<b>a</b>–<b>d</b>), respectively, but for the comparison of salinity anomalies. The three dashed lines represent three specific dates that the glider sampled at the eddy center and eddy edge, respectively.</p>
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<p>Linear fitting between glider data and reconstructed data (red line) with 95% confidence interval (pink shading). The green, orange, and blue dots represent the HYCOM, the GLOYRS, and the reconstructed results, respectively. (<b>a</b>) Temperature; (<b>b</b>) salinity.</p>
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<p>Detailed examination of glider observations, model outputs, and the reconstructed results. (<b>a</b>) The location of the glider (green stars) was colored by SLA on 4 July 2016. The arrows represent the ocean current field. Panels (<b>b</b>,<b>c</b>) present the same as panel (<b>a</b>), but for 7 July 2016, and 11 July 2016, respectively. Panels (<b>a1</b>,<b>b1</b>,<b>c1</b>) display the glider temperature (black line), reconstructed temperature (blue line), HYCOM temperature (green line), and GLOYRS temperature (orange line); panels (<b>a2</b>,<b>b2</b>,<b>c2</b>) illustrate the differences between the temperature profiles along with their 95% confidence interval where the blue intervals, green intervals, and orange intervals represent the differences between the glider data and reconstructed temperature, HYCOM temperature, and GLOYRS temperature, respectively. Panels (<b>a3</b>,<b>b3</b>,<b>c3</b>) show temperature gradients. Panels (<b>a4</b>,<b>b4</b>,<b>c4</b>), (<b>a5</b>,<b>b5</b>,<b>c5</b>), and (<b>a6</b>,<b>b6</b>,<b>c6</b>) are the same as panels (<b>a1</b>,<b>b1</b>,<b>c1</b>), (<b>a2</b>,<b>b2</b>,<b>c2</b>), and (<b>a3</b>,<b>b3</b>,<b>c3</b>), respectively, but for salinity.</p>
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<p>The comparison of the RMSE between reconstructed results, HYCOM simulation, GLORYS reanalysis data, and glider observations. (<b>a</b>) The root mean square error (RMSE) of temperature. (<b>b</b>) The RMSE of salinity. The blue lines represent the RMSE between the data from the reconstruction model and the glider observations, the green lines represent the RMSE between the HYCOM simulation and the glider observations, and the orange lines represent the RMSE between the GLORYS reanalysis and the glider observations.</p>
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<p>Comparison of the subsurface temperature and salinity anomalies reconstructed by three settings of the model. Panels (<b>a</b>,<b>e</b>): the temperature and salinity anomalies observed by the glider. Panels (<b>b</b>–<b>d</b>): the residual error calculated from Glider_TA minus the data reconstructed by the three models. Panels (<b>f</b>–<b>h</b>) are same as panels (<b>b</b>–<b>d</b>) but focus on the comparison of salinity anomalies.</p>
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<p>Comparison of the three-dimensional structure of the anticyclonic eddy according to the reconstruction model, HYCOM, and GLORYS outputs on 8 July 2016. Panels (<b>a</b>,<b>d</b>): 3D temperature and salinity structures reconstructed by the deep learning model. Panels (<b>b</b>,<b>e</b>): structures from HYCOM. Panels (<b>c</b>,<b>f</b>): structures from GLORYS.</p>
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<p>Comparison of temperature anomalies (TAs) between the Argo observations and the reconstruction model. Panels (<b>a</b>–<b>d</b>): the comparison of the temperature anomalies within AEs. (<b>a</b>) Times series of temperature anomalies (350 m, red solid line) is overplotted against SLA (blue solid line). (<b>b</b>,<b>c</b>) The temperature anomalies derived from Argo observations and the reconstruction model, respectively; (<b>d</b>) the residual error of subsurface temperature within AEs. The residual error is calculated as the difference between Argo observations and the data reconstructed by the model; panels (<b>e</b>–<b>h</b>) are the same as panels (<b>a</b>–<b>d</b>), but for the comparison of temperature anomalies within CEs.</p>
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<p>Comparison of salinity anomalies (SAs) between the Argo observations and the reconstruction model. Panels (<b>a</b>–<b>d</b>): the comparison of the salinity anomalies within AEs. (<b>a</b>) Times series of salinity anomalies (350 m, red solid line) is overplotted against SLA (blue solid line); (<b>b</b>,<b>c</b>) the salinity anomalies derived from Argo observations and the reconstruction model, respectively; (<b>d</b>) the residual error of subsurface salinity within AEs. The residual error is calculated as the difference between Argo observations and the data inverted by the model; panels (<b>e</b>–<b>h</b>) are the same as panels (<b>a</b>–<b>d</b>), respectively, but focus on the comparison of salinity anomalies within CEs.</p>
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<p>Comparison of RMSE and R<sup>2</sup> of the reconstruction model applied in AEs (blue lines) and CEs (red lines). Panels (<b>a</b>,<b>c</b>): the comparison of the RMSE of temperature and salinity. Panels (<b>b</b>,<b>d</b>): the comparison of the R<sup>2</sup> of temperature and salinity.</p>
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<p>The residual error of subsurface temperature and salinity at the centers and edges of the eddies. Panels (<b>a</b>–<b>d</b>) represent the AEs (eddy centers in panels a-b and eddy edges in panels (<b>c</b>,<b>d</b>). Panels (<b>e</b>–<b>h</b>) are the same as panels (<b>a</b>–<b>d</b>), respectively, but focus on the CEs.</p>
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20 pages, 10713 KiB  
Article
Detecting Ocean Eddies with a Lightweight and Efficient Convolutional Network
by Haochen Sun, Hongping Li, Ming Xu, Tianyu Xia and Hao Yu
Remote Sens. 2024, 16(24), 4808; https://doi.org/10.3390/rs16244808 - 23 Dec 2024
Viewed by 339
Abstract
As a ubiquitous mesoscale phenomenon, ocean eddies significantly impact ocean energy and mass exchange. Detecting these eddies accurately and efficiently has become a research focus in ocean remote sensing. Many traditional detection methods, rooted in physical principles, often encounter challenges in practical applications [...] Read more.
As a ubiquitous mesoscale phenomenon, ocean eddies significantly impact ocean energy and mass exchange. Detecting these eddies accurately and efficiently has become a research focus in ocean remote sensing. Many traditional detection methods, rooted in physical principles, often encounter challenges in practical applications due to their complex parameter settings, while effective, deep learning models can be limited by the high computational demands of their extensive parameters. Therefore, this paper proposes a new approach to eddy detection based on the altimeter data, the Ghost Attention Deeplab Network (GAD-Net), which is a lightweight and efficient semantic segmentation model designed to address these issues. The encoder of GAD-Net consists of a lightweight ECA+GhostNet and an Atrous Spatial Pyramid Pooling (ASPP) module. And the decoder integrates an Efficient Attention Network (EAN) module and an Efficient Ghost Feature Integration (EGFI) module. Experimental results show that GAD-Net outperforms other models in evaluation indices, with a lighter model size and lower computational complexity. It also outperforms other segmentation models in actual detection results in different sea areas. Furthermore, GAD-Net achieves detection results comparable to the Py-Eddy-Tracker (PET) method with a smaller eddy radius and a faster detection speed. The model and the constructed eddy dataset are publicly available. Full article
(This article belongs to the Special Issue Artificial Intelligence for Ocean Remote Sensing)
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<p>GAD-Net’s overall structure.</p>
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<p>Ghost module’s structure.</p>
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<p>Ghost bottleneck with different step sizes.</p>
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<p>ECA+Net’s structure.</p>
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<p>EAN module’s structure.</p>
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<p>EGFI module’s structure.</p>
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<p>The dataset area is shown in a black box (10°N−30°N, 120°E−150°E).</p>
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<p>Confusion matrix calculations for the models. (<b>a</b>) Base model. (<b>b</b>) Base model integrating ECA+GhostNet. (<b>c</b>) Base model integrating ECA+GhostNet and EAN module. (<b>d</b>) GAD-Net.</p>
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<p>Results of ablation experiments with the spatial information loss. Red regions are anticyclonic eddies and blue regions are cyclonic eddies. White boxes are undetected eddies and yellow boxes are more detected eddies. (<b>a</b>) Input. (<b>b</b>) Ground truth. (<b>c</b>) GAD-Net with the input size of <math display="inline"><semantics> <mrow> <mn>640</mn> <mo>×</mo> <mn>640</mn> </mrow> </semantics></math>. (<b>d</b>) GAD-Net with the input size of <math display="inline"><semantics> <mrow> <mn>480</mn> <mo>×</mo> <mn>480</mn> </mrow> </semantics></math>. (<b>e</b>) GAD-Net without the ASPP module. (<b>f</b>) GAD-Net without the EGFI module.</p>
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<p>Eddy detection results of the comparison experiment. Red regions are anticyclonic eddies and blue regions are cyclonic eddies. White boxes are undetected eddies and yellow boxes are more detected eddies. (<b>a</b>) Input. (<b>b</b>) Ground truth. (<b>c</b>) UNet with ResNet. (<b>d</b>) UNet with GhostNet. (<b>e</b>) PSPNet with ResNet. (<b>f</b>) PSPNet with GhostNet. (<b>g</b>) Deeplabv3+ with ResNet. (<b>h</b>) Deeplabv3+ with GhostNet. (<b>i</b>) LR-ASPP. (<b>j</b>) HRNetv2. (<b>k</b>) Segformer. (<b>l</b>) GAD-Net.</p>
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<p>Eddy detection results within the dataset. Red regions are anticyclonic eddies and blue regions are cyclonic eddies. White boxes are undetected eddies and yellow boxes are more detected eddies. (<b>a</b>) Input. (<b>b</b>) Ground truth. (<b>c</b>) UNet with ResNet. (<b>d</b>) Deeplabv3+ with ResNet. (<b>e</b>) Segfomer. (<b>f</b>) GAD-Net.</p>
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<p>Eddy detection results outside the dataset. Red regions are anticyclonic eddies and blue regions are cyclonic eddies. Yellow boxes are more detected eddies. (<b>a</b>) Input. (<b>b</b>) UNet with ResNet. (<b>c</b>) Deeplabv3+ with ResNet. (<b>d</b>) Segfomer. (<b>e</b>) GAD-Net.</p>
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<p>Validation experiment results. Red regions are anticyclonic eddies and blue regions are cyclonic eddies. Yellow boxes are more detected eddies, green boxes are incorrectly detected eddies, and the arrows indicate the regional geostrophic flow. (<b>a</b>) Input. (<b>b</b>) PET. (<b>c</b>) GAD-Net. (<b>d</b>) Regional geostrophic flow.</p>
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<p>Distribution of eddy radius detected by GAD-Net and PET.</p>
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18 pages, 8559 KiB  
Article
A Deep Learning Method for Inversing 3D Temperature Fields Using Sea Surface Data in Offshore China and the Northwest Pacific Ocean
by Xiangyu Wu, Mengqi Zhang, Qingchang Wang, Xidong Wang, Jian Chen and Yinghao Qin
J. Mar. Sci. Eng. 2024, 12(12), 2337; https://doi.org/10.3390/jmse12122337 - 20 Dec 2024
Viewed by 377
Abstract
Three-dimensional ocean temperature field data with high temporal-spatial resolution bears a significant impact on ocean dynamic processes such as mesoscale eddies. In recent years, with the rapid development of remote sensing data, deep learning methods have provided new ideas for the reconstruction of [...] Read more.
Three-dimensional ocean temperature field data with high temporal-spatial resolution bears a significant impact on ocean dynamic processes such as mesoscale eddies. In recent years, with the rapid development of remote sensing data, deep learning methods have provided new ideas for the reconstruction of ocean information. In the present study, based on sea surface data, a deep learning model is constructed using the U-net method to reconstruct the three-dimensional temperature structure of the Northwest Pacific and offshore China. Next, the correlation between surface data and underwater temperature structure is established, achieving the construction of a three-dimensional ocean temperature field based on sea surface height and sea surface temperature. A three-dimensional temperature field for the water layers within the depth of 1700 m in the Northwest Pacific and offshore China is reconstructed, featuring a spatial resolution of 0.25°. Control experiments are conducted to explore the impact of different input variables, labels, and loss functions on the reconstruction results. This study’s results show that the reconstruction accuracy of the model is higher when the input variables are anomalies of sea surface temperature and sea surface height. The reconstruction results using the mean square error (MSE) and mean absolute error (MAE) loss functions are highly similar, indicating that these two loss functions have no significant impact on the results, and only in the upper ocean does the MSE value slightly outperform MAE. Overall, the results show a rather good spatial distribution, with relatively large errors only occurring in areas where the temperature gradient is strong. The reconstruction error remains quite stable over time. Furthermore, an analysis is conducted on the temporal-spatial characteristics of some mesoscale eddies in the inversed temperature field. It is shown that the U-net network can effectively reconstruct the temporal-spatial distribution characteristics of eddies at different times and in different regions, providing a good fit for the eddy conditions in offshore China and the Northwest Pacific. The inversed eddy features are in high agreement with the eddies in the original data. Full article
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<p>Schematic diagram of structure of U-net deep learning architecture [<a href="#B31-jmse-12-02337" class="html-bibr">31</a>].</p>
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<p>Diagram of MAE loss function.</p>
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<p>MSE loss function.</p>
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<p>Changes of RMSE of the temperature reconstruction results in different months of the Northwest Pacific in 2018 with depth: (<b>a</b>) Changes of RMSE of the temperature reconstruction results in January 2018 with depth; (<b>b</b>) those in April 2018; (<b>c</b>) those in July 2018; (<b>d</b>) those in October 2018.</p>
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<p>RMSE variation with depth.</p>
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<p>Spatial distribution of temperature field reconstructed by MAE and MSE loss functions at different depths, as of 1 July 2018. (<b>a</b>,<b>d</b>,<b>g</b>) are the reanalysis data results, (<b>b</b>,<b>e,h</b>) are the MSE results, (<b>c,f,i</b>) are the MAE results.</p>
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<p>MSE and MAE loss functions reconstruct the RMSE spatial distribution of the temperature field.</p>
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<p>Time distribution of reconstruction errors of the MSE and MAE loss functions. (<b>a</b>) 55 m, (<b>b</b>) 109 m, (<b>c</b>) 541 m, (<b>d</b>) 1062 m.</p>
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<p>Reconstructed value distribution scatterplot of the temperature field and the original one in different months in 2018.</p>
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<p>Meridional-depth distribution of RMSE over the zonal mean in the Northwest Pacific and offshore China. (<b>a</b>) January 2018, (<b>b</b>) April 2018, (<b>c</b>) July 2018, (<b>d</b>) October 2018.</p>
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<p>RMSE distribution of the reconstructed temperature field at 55 m (<b>left</b>) and 109 m (<b>right</b>) underwater in the Northwest Pacific Ocean and offshore China in 2018.</p>
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<p>The two selected observation points and their respective regions ((<b>a</b>–<b>d</b>) are SLA on 1 January, 1 April, 1 July, and 1 October).</p>
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<p>Eddy A: (<b>a</b>–<b>d</b>) Reconstructed vertical distribution of the eddy; (<b>e</b>–<b>h</b>) vertical distribution of the original data.</p>
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<p>Eddy B: (<b>a</b>–<b>d</b>) Reconstructed vertical distribution of the eddy; (<b>e</b>–<b>h</b>) vertical distribution of the original data.</p>
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19 pages, 6806 KiB  
Article
Mesoscale Eddy Properties in Four Major Western Boundary Current Regions
by Wei Cui, Jungang Yang and Chaojie Zhou
Remote Sens. 2024, 16(23), 4470; https://doi.org/10.3390/rs16234470 - 28 Nov 2024
Viewed by 528
Abstract
Oceanic mesoscale eddies are a kind of typical geostrophic dynamic process which can cause vertical movement in water bodies, thereby changing the temperature, salinity, density, and chlorophyll concentration of the surface water in the eddy. Based on multisource remote sensing data and Argo [...] Read more.
Oceanic mesoscale eddies are a kind of typical geostrophic dynamic process which can cause vertical movement in water bodies, thereby changing the temperature, salinity, density, and chlorophyll concentration of the surface water in the eddy. Based on multisource remote sensing data and Argo profiles, this study analyzes and compares the mesoscale eddy properties in four major western boundary current regions (WBCs), i.e., the Kuroshio Extension (KE), the Gulf Stream (GS), the Agulhas Current (AC), and the Brazil Current (BC). The 30-year sea surface height anomaly (SSHA) data are used to identify mesoscale eddies in the four WBCs. Among the four WBCs, the GS eddies have the largest amplitude and the BC eddies have the smallest amplitude. Combining the altimeter-detected eddy results with the simultaneous observations of sea surface temperature, sea surface salinity, sea surface density, and chlorophyll concentration, the local impacts of eddy activities in each WBCs are analyzed. The eddy surface temperature and salinity signals are positively correlated with the eddy SSHA signals, while the eddy surface density and chlorophyll concentrations are negatively correlated with eddy SSHA signals. The correlation analysis of eddy surface signals in the WBCs reveals that eddies have regional differences in the surface signal changes of eddy activities. Based on the subsurface temperature and salinity information provided by Argo profiles, the analysis of the vertical thermohaline characteristics of mesoscale eddies in the four WBCs is carried out. Eddies in the four WBCs have deep influence on the vertical thermohaline characteristics of water masses, which is not only related to the strong eddy activities but also to the thick thermocline and halocline of water masses in the WBCs. Full article
(This article belongs to the Special Issue Recent Advances on Oceanic Mesoscale Eddies II)
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Graphical abstract

Graphical abstract
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<p>The maps of bathymetry (<b>a</b>–<b>d</b>), geostrophic current and mean dynamic topography (MDT, <b>e</b>–<b>h</b>), and eddy kinetic energy (EKE, <b>i</b>–<b>l</b>) in the four WBCs (KE: Kuroshio Extension, GS: Gulf Stream, AC: Agulhas Current, BC: Brazil Current). The specific ranges of the four WBCs (KE: 30–40°N, 140–170°E; GS: 33–43°N, 45–75°W; AC: 34–44°S, 10–60°E; BC: 35–50°S, 30–60°W) are marked by dashed rectangles in (<b>i</b>–<b>l</b>).</p>
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<p>The map of eddy trajectories (<b>a</b>–<b>d</b>) and relative propagation trajectories (<b>e</b>–<b>h</b>) with a lifetime ≥ 6 months; the numbers (<b>i</b>–<b>l</b>), the west- and eastward proportions Q (<b>m</b>–<b>p</b>), and the south- and northward proportions Q (<b>q</b>–<b>t</b>) of eddy trajectories exceeding a certain lifetime (e.g., 2, 4, 6 months, etc.) in the four WBCs. The blue lines or bars represent cyclonic eddies, the red lines or bars represent anticyclonic eddies, and the dashed lines in a-d are the specific ranges of the four WBC; the gray lines in a-d represent eddy trajectories that do not enter the WBCs.</p>
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<p>The mean lifetime (<b>a</b>) and propagation distance (<b>b</b>) of all SSHA-identified eddies (CEs are cyclonic eddies; AEs are anticyclonic eddies; All includes all eddies) with a lifetime ≥ 1 month in the four WBCs.</p>
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<p>The maps of eddy number (<b>a</b>–<b>d</b>), polarity (<b>e</b>–<b>h</b>), amplitude (<b>i</b>–<b>l</b>), and radius (<b>m</b>–<b>p</b>) from SSHA-identified eddies with a lifetime ≥ 1 month in the four WBCs. The specific ranges of the four WBCs are marked by dashed lines in (<b>i</b>–<b>l</b>).</p>
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<p>The regionally averaged amplitude (<b>a</b>) and radius (<b>b</b>) of all SSHA-identified eddies (CEs are cyclonic eddies; AEs are anticyclonic eddies; All includes all eddies) with a lifetime ≥ 1 month in the four WBCs.</p>
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<p>The SSTA (<b>a</b>), SSSA (<b>c</b>), SSDA (<b>e</b>), and CHLA (<b>g</b>) signals of the normalized eddy (CE is the cyclonic eddy; AE is anticyclonic eddy; the solid lines represent the normalized eddy area; the dotted lines represent the range of two times the eddy radius), and the averaged SSTA (<b>b</b>), SSSA (<b>d</b>), SSDA (<b>f</b>), and CHLA (<b>h</b>) values within the normalized eddy area (solid line) in the WBCs based on a 30-year period of SSHA-identified eddies and multi-source remote sensing data.</p>
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<p>The average of SSTA (<b>a</b>), SSSA (<b>b</b>), SSDA (<b>c</b>), and CHLA (<b>d</b>) signals of eddies for the different SSHA signals in the four WBCs; the regression coefficients <span class="html-italic">k</span>(SSTA/SSHA), <span class="html-italic">k</span>(SSSA/SSHA), <span class="html-italic">k</span>(SSDA/SSHA), and <span class="html-italic">k</span>(CHLA/SSHA) are labeled in the figure.</p>
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<p>Mean vertical profiles of temperature anomaly <span class="html-italic">θ′</span> (<b>a</b>–<b>d</b>) and salinity anomaly <span class="html-italic">S′</span> (<b>e</b>–<b>h</b>) inside eddies (CEs are cyclonic eddies; AEs are anticyclonic eddies) in the four WBCs; the shading indicates one standard deviation value range. The climatological temperature and salinity profiles of water masses based on WOA 2023 in a 5°lon × 2°lat subregion for the four WBCs are also given in the lower-right corner of the figure (colors represent different latitudes, blue represents the low latitude, and red represents the high latitude; absolute values are taken for the latitudes of AC and BC in the Southern Hemisphere).</p>
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<p>(<b>a</b>–<b>d</b>) The scatterplots of SSHA signals and maximum vertical temperature anomaly <span class="html-italic">θ′</span> of eddies, (<b>e</b>–<b>h</b>) the scatterplots of SSHA signals and maximum vertical salinity anomaly <span class="html-italic">S′</span> of eddies in the four WBCs. The maximum vertical <span class="html-italic">θ′</span> or <span class="html-italic">S′</span> of an eddy is the value of the eddy <span class="html-italic">θ′</span> or <span class="html-italic">S′</span> profile at the depth of maximum mean <span class="html-italic">θ′</span> or <span class="html-italic">S′</span> profile of all eddies in <a href="#remotesensing-16-04470-f008" class="html-fig">Figure 8</a>. Colors indicate the point density, the black lines are the linear regression of the scatterplots, and the regression coefficients <span class="html-italic">k</span>(<span class="html-italic">θ′</span>/SSHA) and <span class="html-italic">k</span>(<span class="html-italic">S′</span>/SSHA) are labeled in the figure.</p>
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24 pages, 33437 KiB  
Article
Global Assessment of Mesoscale Eddies with TOEddies: Comparison Between Multiple Datasets and Colocation with In Situ Measurements
by Artemis Ioannou, Lionel Guez, Rémi Laxenaire and Sabrina Speich
Remote Sens. 2024, 16(22), 4336; https://doi.org/10.3390/rs16224336 - 20 Nov 2024
Viewed by 680
Abstract
The present study introduces a comprehensive, open-access atlas of mesoscale eddies in the global ocean, as identified and tracked by the TOEddies algorithm implemented on a global scale. Unlike existing atlases, TOEddies detects eddies directly from absolute dynamic topography (ADT) without spatial filtering, [...] Read more.
The present study introduces a comprehensive, open-access atlas of mesoscale eddies in the global ocean, as identified and tracked by the TOEddies algorithm implemented on a global scale. Unlike existing atlases, TOEddies detects eddies directly from absolute dynamic topography (ADT) without spatial filtering, preserving the natural spatial variability and enabling precise, high-resolution tracking of eddy dynamics. This dataset provides daily information on eddy characteristics, such as size, intensity, and polarity, over a 30-year period (1993–2023), capturing complex eddy interactions, including splitting and merging events that often produce networks of interconnected eddies. This unique approach challenges the traditional single-trajectory perspective, offering a nuanced view of eddy life cycles as dynamically linked trajectories. In addition to traditional metrics, TOEddies identifies both the eddy core (characterized by maximum azimuthal velocity) and the outer boundary, offering a detailed representation of eddy structure and enabling precise comparisons with in situ data. To demonstrate its value, we present a statistical overview of eddy characteristics and spatial distributions, including generation, disappearance, and merging/splitting events, alongside a comparative analysis with existing global eddy datasets. Among the multi-year observations, TOEddies captures coherent, long-lived eddies with lifetimes exceeding 1.5 years, while highlighting significant differences in the dynamic properties and spatial patterns across datasets. Furthermore, this study integrates TOEddies with 23 years of colocalized Argo profile data (2000–2023), allowing for a novel examination of eddy-induced subsurface variability and the role of mesoscale eddies in the transport of global ocean heat and biogeochemical properties. This atlas aims to be a valuable resource for the oceanographic community, providing an open dataset that can support diverse applications in ocean dynamics, climate research, and marine resource management. Full article
(This article belongs to the Special Issue Recent Advances on Oceanic Mesoscale Eddies II)
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<p>Frequency maps of first (<b>a</b>–<b>d</b>) and last (<b>e</b>–<b>h</b>) detection points of mesoscale eddies per year derived from TOEddies, META3.2, TIAN, and GOMEAD datasets, respectively. The data are aggregated into <math display="inline"><semantics> <mrow> <msup> <mn>1</mn> <mo>∘</mo> </msup> <mo>×</mo> <msup> <mn>1</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> bins and normalized by the number of observation years for each dataset. The mean dynamic topography (MDT; in cm) is shown by black contours.</p>
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<p>Scatter plot representing the distribution of eddy occurrences for (<b>a</b>) merging and (<b>b</b>) splitting events based on TOEddies atlas for eddies with lifetimes longer than 4 weeks in each <math display="inline"><semantics> <mrow> <msup> <mn>1</mn> <mo>∘</mo> </msup> <mo>×</mo> <msup> <mn>1</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> region. Bathymetric contours at −500 m, −1000 m, −2000 m, and −4000 m are indicated by gray lines.</p>
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<p>Histograms of eddy lifetimes (weeks) (<b>a</b>,<b>b</b>) and histograms of eddy characteristic radius <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> (km) (<b>c</b>,<b>d</b>) and velocity <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> (m/s) (<b>e</b>,<b>f</b>) of anticyclonic (first column) and cyclonic eddies (second column) for the TOEddies, META3.2, TIAN, and GOMEAD datasets. We consider only mesoscale eddies having lifetimes ≥ 16 weeks, as indicated by the dashed lines in panels (<b>a</b>–<b>d</b>), and characteristic radii larger than <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>≥</mo> </mrow> </semantics></math> 30 km.</p>
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<p>Maps of the speed-based radius scale <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> (km) for eddies with lifetimes ≥ 16 weeks for each <math display="inline"><semantics> <mrow> <msup> <mn>1</mn> <mo>∘</mo> </msup> <mo>×</mo> <msup> <mn>1</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> region from the (<b>a</b>) TOEddies, (<b>b</b>) META3.2, (<b>c</b>) TIAN, and (<b>d</b>) GOMEAD datasets. Zonal averages of the eddy characteristic radius are illustrated in panel (<b>e</b>). The dashed line indicates the estimated first baroclinic Rossby radius of deformation <math display="inline"><semantics> <msub> <mi>R</mi> <mi>d</mi> </msub> </semantics></math> (km) [<a href="#B10-remotesensing-16-04336" class="html-bibr">10</a>].</p>
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<p>Cyclonic (blue) and anticyclonic (red) eddy trajectories as detected from the TOEddies algorithm having lifetimes of at least (<b>a</b>) ≥52 weeks, (<b>b</b>) ≥78 weeks, and (<b>c</b>) ≥104 weeks. The numbers of detected eddies are labeled at the top of each panel for each polarity.</p>
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<p>Trajectories of long-lived (≥78 weeks) cyclonic (blue) and anticyclonic (red) eddies from the (<b>a</b>) TOEddies, (<b>b</b>) META3.2, (<b>c</b>) TIAN, and (<b>d</b>) GOMEAD datasets. The numbers of eddies are labeled at the top of each panel for each polarity.</p>
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<p>Trajectories of long-propagating (≥1100 km) eddies of both types from the (<b>a</b>) TOEddies, (<b>b</b>) META3.2, (<b>c</b>) TIAN, and (<b>d</b>) GOMEAD datasets tracked for ≥26 weeks.</p>
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<p>Eddy-network example of anticyclonic (first column) and cyclonic (second column) trajectories for the (<b>a</b>,<b>b</b>) California Upwelling System, (<b>c</b>,<b>d</b>) western Australian boundary, and (<b>e</b>,<b>f</b>) extended South Benguela System. Each eddy trajectory is colored according to its assigned order.</p>
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<p>Temporal evolution of dynamical characteristics of anticyclone A0 and cyclone C0, as tracked by all considered datasets. The evolution of the eddy characteristic radius <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> (km) and outermost radius <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </semantics></math> (km) as tracked by TOEddies is shown in panel (<b>a</b>,<b>b</b>) for A0 and C0, respectively in black. The TOEddies network reconstruction composed of all detected trajectories, anticyclonic (red) and cyclonic (blue, that have merged and splitted with the main trajectories is shown in panels (<b>c</b>,<b>d</b>). The evolutions of the eddy radii and characteristic velocity <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math> (m/s) from the different datasets are shown in panels (<b>e</b>–<b>h</b>). Panels (<b>i</b>,<b>j</b>) depict the equivalent A0 and C0 trajectories as tracked from the META3.2, TIAN, and GOMEAD datasets. Bathymetric contours at −500 m, −1000 m, −2000 m, and −4000 m are indicated by gray lines.</p>
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<p>Snapshots along the temporal evolution of anticyclone A0 (panels <b>a</b>–<b>f</b>) propagating westward in the Southern Ocean. The background colors correspond to the ADT (m) fields while the gray arrows correspond to surface geostrophic velocities. The characteristic and outer contours as detected by TOEddies are shown in the black solid and dashed lines. The Argo floats trapped in the eddies are shown with the magenta diamond points.</p>
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<p>Snapshots along the temporal evolution of cyclone C0 (panels <b>a</b>–<b>f</b>) propagating westward in the Indian Ocean. The background colors correspond to the ADT (m) fields while the gray arrows correspond to surface geostrophic velocities. The characteristic and outer contours as detected by TOEddies are shown in the black solid and dashed lines. The Argo floats trapped in the eddies are shown with magenta diamond points.</p>
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<p>Temporal evolution of anticyclone A0 and cyclone C0 vertical structures as obtained by Argo floats trapped inside the eddy core (<math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mrow> <mi>A</mi> <mi>R</mi> <mi>G</mi> <mi>O</mi> </mrow> </msub> <mo>≤</mo> <mi>R</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math>) (shown as magenta points in panels (<b>a</b>,<b>b</b>). Vertical profiles of temperature <math display="inline"><semantics> <mrow> <mi>T</mi> <msup> <mo>(</mo> <mo>∘</mo> </msup> <mi mathvariant="normal">C</mi> <mo>)</mo> </mrow> </semantics></math> and temperature anomalies <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mi>A</mi> </msub> <mi> </mi> <mrow> <msup> <mo>(</mo> <mo>∘</mo> </msup> <mi mathvariant="normal">C</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> are shown in panels (<b>c</b>,<b>e</b>) for anticyclone A0, and in panels (<b>d</b>,<b>f</b>) for cyclone C0.</p>
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18 pages, 13617 KiB  
Article
Observation and Numerical Simulation of Cross-Mountain Airflow at the Hong Kong International Airport from Range Height Indicator Scans of Radar and LIDAR
by Ying Wa Chan, Kai Wai Lo, Ping Cheung, Pak Wai Chan and Kai Kwong Lai
Atmosphere 2024, 15(11), 1391; https://doi.org/10.3390/atmos15111391 - 19 Nov 2024
Viewed by 481
Abstract
Apart from headwind changes, crosswind changes may be hazardous to aircraft operation. This paper presents two cases of recently observed crosswind changes from the range height indicator scans of ground-based remote sensing meteorological equipment, namely an X-band microwave radar and a short-range LIDAR. [...] Read more.
Apart from headwind changes, crosswind changes may be hazardous to aircraft operation. This paper presents two cases of recently observed crosswind changes from the range height indicator scans of ground-based remote sensing meteorological equipment, namely an X-band microwave radar and a short-range LIDAR. Both instruments have a range resolution down to around 30 m, allowing the study of fine-scale details of the vertical profiles of cross-mountain airflow at the Hong Kong International Airport. Rapidly evolving winds have been observed by the equipment in tropical cyclone situations, revealing high levels of turbulence and vertically propagating waves. The eddy dissipation rate derived from radar spectrum width indicated severe turbulence, with values exceeding 0.5 m2/3 s−1. In order to study the feasibility of predicting such disturbed airflow, a mesoscale meteorological model and a computational fluid dynamics model with high spatial resolution are used in this paper. It is found that the mesoscale meteorological model alone is sufficient to capture some rapidly evolving airflow features, including the turbulence level, the waves, and the rapidly changing wind speeds. However, the presence of reverse flow could only be reproduced with the use of a building-resolving computational fluid dynamics model. This paper aims at providing a reference for airports to consider the feasibility of performing high-resolution numerical simulations of rapidly evolving airflow to alert the pilots in advance for airports in complex terrains and the setup of buildings. Full article
(This article belongs to the Special Issue Tropical Cyclones: Observations and Prediction (2nd Edition))
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Figure 1
<p>(<b>a</b>) The surface synoptic chart at 0200 Hong Kong time on 2 September 2023 and (<b>b</b>) the surface synoptic chart at 0200 Hong Kong time on 7 September 2024.</p>
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<p>The locations of the X-band dual polarisation phased array weather radar (PAWR) and the wind profiler at Sha Lo Wan (SLW), as well as the short-range LIDAR at the Government Flying Service (GFS) headquarters at the Hong Kong International Airport (HKIA).</p>
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<p>(<b>a</b>) The RHI spectral width scan and (<b>b</b>) the associated cross-section of the eddy dissipation rate (EDR) as well as (<b>c</b>) the three-dimensional wind fields (left: horizontal wind field at height of around 34 m above sea level. Right: wind field projected on the cross-sectional plane A–B on the left panel) obtained/retrieved using the SLW radar data at around 0255 Hong Kong time on 2 September 2023.</p>
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<p>(<b>a</b>) The RHI spectral width scan and (<b>b</b>) the associated cross-section of the eddy dissipation rate (EDR) as well as (<b>c</b>) the three-dimensional wind fields (left: horizontal wind field at height of around 34 m above sea level. Right: wind field projected on the cross-sectional plane A–B on the left panel) obtained/retrieved using the SLW radar data at around 0255 Hong Kong time on 2 September 2023.</p>
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<p>(<b>a</b>) The RHI spectral width scan and (<b>b</b>) the associated cross-section of the eddy dissipation rate (EDR) as well as (<b>c</b>) the three-dimensional wind fields (left: horizontal wind field at height of around 34 m above sea level. Right: wind field projected on the cross-sectional plane A–B on the left panel) obtained/retrieved using the SLW radar data at around 0305 Hong Kong time on 2 September 2023.</p>
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<p>(<b>a</b>) The RHI spectral width scan and (<b>b</b>) the associated cross-section of the eddy dissipation rate (EDR) as well as (<b>c</b>) the three-dimensional wind fields (left: horizontal wind field at height of around 34 m above sea level. Right: wind field projected on the cross-sectional plane A–B on the left panel) obtained/retrieved using the SLW radar data at around 0305 Hong Kong time on 2 September 2023.</p>
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<p>(<b>a</b>) The 1st, 2nd, and 3rd nested domains of the RAMS simulation. (<b>b</b>) The 3rd, 4th, and 5th nested domains of the RAMS simulation.</p>
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<p>(<b>a</b>) Observations of horizontal wind profiles from the SLW wind profiler from 18:00 Hong Kong time on 1 September 2023 to 06:00 Hong Kong Time on 2 September 2023 (+8 UTC). (<b>b</b>) Simulated horizontal wind profiles (wind barbs) and vertical velocities (background colour) from the RAMS on 1 September 2023 from 15UTC to 22UTC.</p>
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<p>Simulation of RHI scans of (<b>a</b>) the EDR and (<b>b</b>) wind field from the RAMS on 18:54:10 UTC, 1 September 2023.</p>
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<p>(<b>a</b>) The domain of the PALM simulation denoted by a red rectangle where the boundary is the 5th nested domain of the RAMS simulation. The blue line indicates the location of the RHI scan of the GFS LIDAR. (<b>b</b>) The PALM simulation domain with building heights indicated by the colour bar. The blue cross symbol indicates the location of the GFS LIDAR, and the blue line shows the location of its RHI scan.</p>
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<p>(<b>a</b>) RHI scans of radial wind velocity from the GFS LIDAR at 00:40:18 Hong Kong time (+8 UTC) on 7 September 2024. (<b>b</b>) RHI scans of radial wind velocity from the GFS LIDAR at 00:42:36 Hong Kong time (+8 UTC) on 7 September 2024.</p>
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<p>(<b>a</b>) The RAMS simulation for RHI scans of radial wind velocity from the GFS LIDAR at 16:40:10 UTC on 6 September 2024. (<b>b</b>) The RAMS simulation for RHI scans of radial wind velocity from the GFS LIDAR at 16:43:40 UTC on 6 September 2024.</p>
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<p>The RAMS simulation of radial wind velocity from the GFS LIDAR with an extended range at 16:40:10 UTC on 6 September 2024.</p>
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<p>The PALM simulation for RHI scans of radial wind velocity from the GFS LIDAR at four different instances, namely (<b>a</b>) 16:40UTC, (<b>b</b>) 16:42 UTC, (<b>c</b>) 16:43 UTC, and (<b>d</b>) 16:45 UTC on 6 September 2024.</p>
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17 pages, 2807 KiB  
Article
Anomalous Diffusion by Ocean Waves and Eddies
by Joey J. Voermans, Alexander V. Babanin, Alexei T. Skvortsov, Cagil Kirezci, Muhannad W. Gamaleldin, Henrique Rapizo, Luciano P. Pezzi, Marcelo F. Santini and Petra Heil
J. Mar. Sci. Eng. 2024, 12(11), 2036; https://doi.org/10.3390/jmse12112036 - 11 Nov 2024
Viewed by 760
Abstract
Understanding the dispersion of floating objects and ocean properties at the ocean surface is crucial for various applications, including oil spill management, debris tracking and search and rescue operations. While mesoscale turbulence has been recognized as a primary driver of dispersion, the role [...] Read more.
Understanding the dispersion of floating objects and ocean properties at the ocean surface is crucial for various applications, including oil spill management, debris tracking and search and rescue operations. While mesoscale turbulence has been recognized as a primary driver of dispersion, the role of submesoscale processes is poorly understood. This study investigates the largely unexplored mechanism of dispersion by refracted wave fields. In situ observations demonstrate significantly faster and distinct dispersion patterns for objects influenced by wind, waves and currents compared to those solely driven by ocean currents. Numerical simulations of wave fields refracted by ocean eddies corroborate these findings, revealing diffusivities that exceed those of turbulent diffusion at scales up to 10 km during energetic sea states. Our results highlight the importance of ocean waves in dispersing surface material, suggesting that refracted wave fields may play a significant role in submesoscale spreading. As atmospheric forcing at the ocean surface will only strengthen due to anthropogenic contributions, additional research into wave refraction is necessary. This requires concurrent high-resolution measurements of wind, waves and currents to inform the revisions of large-scale coupled models to better include the submesoscale physics. Full article
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Figure 1
<p>Mean square separation distance <math display="inline"><semantics> <msup> <mi>s</mi> <mn>2</mn> </msup> </semantics></math> of drogued (blue) and undrogued (red) drifter pairs derived from the Global Drifter Program dataset. Shaded area gives the 95% confidence interval of the mean, determined using bootstrap algorithm (1000 samples with replacements). Only pairs with minimum separation distance of up to 1 km were considered. Geographical bias was limited by restricting the number of observations per area per unit time. Fits to the undrogued drifter data are given by <math display="inline"><semantics> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>≈</mo> <mn>50</mn> <msup> <mi>t</mi> <mrow> <mn>9</mn> <mo>/</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>≈</mo> <mn>300</mn> <msup> <mi>t</mi> <mrow> <mn>8</mn> <mo>/</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>≈</mo> <mn>5</mn> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> </semantics></math> for the drogued drifter data, with <span class="html-italic">t</span> in days.</p>
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<p>Root mean square separation distance of three wave buoy clusters deployed in the Southern Ocean (red). Simplified model was fitted to the observations (green, Equation (<a href="#FD10-jmse-12-02036" class="html-disp-formula">10</a>) with <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.03</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> as given in <a href="#app1-jmse-12-02036" class="html-app">Figure S2</a>). Black and gray lines represent the simulated tracer dispersion by an eddy refracted wave field, with eddy radius of 5 and 2.5 km, respectively. Four different values of the eddy velocity scale <span class="html-italic">U</span> are used, namely 0.05, 0.1, 0.2 and 0.4 m/s.</p>
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<p>(<b>a</b>) Pattern of refracted wave rays by an idealized ocean eddy. (<b>b</b>) Tracer particle trajectories following the Stokes drift velocity field of the refracted wave field.</p>
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<p>Horizontal diffusivity of drogued (blue) and undrogued (red) drifter pairs against root mean square separation distance as derived from the GDP dataset. Simulated wave-induced diffusivity of a refracted wave field is given in gray for different properties of the wave field and turbulent eddy, where the solid line represents a fit to the simulations and dashed lines are an extrapolation thereof. Best fits to GDP data when <math display="inline"><semantics> <mrow> <mn>2</mn> <mo>≤</mo> <mi>s</mi> <mo>≤</mo> <mn>20</mn> </mrow> </semantics></math> km are <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>≈</mo> <mn>1.3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> <msup> <mi>s</mi> <mrow> <mn>1.4</mn> </mrow> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>≈</mo> <mn>7.5</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mi>s</mi> <mrow> <mn>1.0</mn> </mrow> </msup> </mrow> </semantics></math> for the drogued and undrogued drifters, respectively.</p>
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<p>Mean square separation distance <math display="inline"><semantics> <msup> <mi>s</mi> <mn>2</mn> </msup> </semantics></math> of drogued (blue) and undrogued (red) drifter pairs derived from the Global Drifter Program dataset. Shaded area encloses the 10th and 90th percentiles of the undrogued (red) and drogued (blue) datasets, where the top of the shaded area represents the 10th percentile and the bottom represents the 90th percentile. Only pairs with minimum separation distance of up to 1 km were considered. Geographical bias was limited by restricting the number of observations per area per unit time. Fits to the undrogued drifter data are given by <math display="inline"><semantics> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>≈</mo> <mn>50</mn> <msup> <mi>t</mi> <mrow> <mn>9</mn> <mo>/</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>≈</mo> <mn>300</mn> <msup> <mi>t</mi> <mrow> <mn>8</mn> <mo>/</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>s</mi> <mn>2</mn> </msup> <mo>≈</mo> <mn>5</mn> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> </semantics></math> for the drogued drifter data, with <span class="html-italic">t</span> in days.</p>
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22 pages, 6213 KiB  
Article
Simulation of the Neutral Atmospheric Flow Using Multiscale Modeling: Comparative Studies for SimpleFoam and Fluent Solver
by Zihan Zhao, Lingxiao Tang and Yiqing Xiao
Atmosphere 2024, 15(10), 1259; https://doi.org/10.3390/atmos15101259 - 21 Oct 2024
Viewed by 601
Abstract
The reproduced planetary boundary layer (PBL) wind is commonly applied in downscaled simulations using commercial CFD codes with Reynolds-averaged Navier–Stokes (RANS) turbulence modeling. When using the turbulent inlets calculated by numerical weather prediction models (NWP), adjustments of the turbulence eddy viscosity closures and [...] Read more.
The reproduced planetary boundary layer (PBL) wind is commonly applied in downscaled simulations using commercial CFD codes with Reynolds-averaged Navier–Stokes (RANS) turbulence modeling. When using the turbulent inlets calculated by numerical weather prediction models (NWP), adjustments of the turbulence eddy viscosity closures and wall function formulations are concerned with maintaining the fully developed wind profiles specified at the inlet of CFD domains. The impact of these related configurations is worth discussing in engineering applications, especially when commercial codes restrict the internal modifications. This study evaluates the numerical performances of open-source OpenFOAM 2.3.0 and commercial Fluent 17.2 codes as supplementary scientific comparisons. This contribution focuses on the modified turbulence closures to incorporate turbulent profiles produced from mesoscale PBL parameterizations and the modified wall treatments relating to the roughness length. The near-ground flow features are evaluated by selecting the flat terrains and the classical Askervein benchmark case. The improvement in near-ground wind flow under the downscaled framework shows satisfactory performance in the open-source CFD platform. This contributes to engineers realizing the micro-siting of wind turbines and quantifying terrain-induced speed-up phenomena under the scope of wind-resistant design. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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Figure 1
<p>(<b>a</b>) Schematic of the full-scale CFD domain with flat terrain. Five positions of wind profiles (D0~D2500) are extracted along the streamwise direction, where the number represents the straight-line distance from the inlet. The purple gridlines represent the mesh grid. (<b>b</b>) Details of the surface-grid resolution in the streamwise direction.</p>
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<p>(<b>a</b>,<b>b</b>) are the structured grids on Askervein Hill case with central refinements close to measurements (Line A-A, AA-AA, RS and HT). Note that the positive X and Y axes represent the east and north directions, respectively. The green color gridlines represent the surface mesh grid. (<b>c</b>) Details of the XZ plane grid along with the hilltop HT. The red gridlines represent the spatial mesh grid, and blue background color is the working space during grid generation.</p>
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<p>The concerned parameters in the <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>−</mo> <mi>ε</mi> </mrow> </semantics></math> turbulence solver using the multiscale modeling.</p>
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<p>Summary of the inlet conditions used in the flat terrain case. (<b>a</b>) Wind magnitude profile, (<b>b</b>) turbulent kinetic energy profile, (<b>c</b>) dissipation profile.</p>
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<p>Summary of the three-hour averaged wind profiles extracted from WRF solutions on the Askervein TU-03B field campaign. Twenty-eight positions are specified on the west (W-WRF) and south (S-WRF) of CFD lateral boundaries. (<b>a</b>–<b>c</b>) Wind components and directions. (<b>d</b>,<b>e</b>) Turbulent kinetic energy and dissipation profiles from WRF PBL parameterizations.</p>
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<p>Illustration of offline data transfer between mesoscale coarse profiles data (<b>left</b>) and CFD fine-grained boundaries (<b>right</b>). The different colors represent the interpolated variables.</p>
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<p>Comparison of inlet and outlet wind velocity profiles (<b>a</b>,<b>d</b>), turbulent kinetic profiles (<b>b</b>,<b>e</b>), and turbulent kinetic energy dissipation (<b>c</b>,<b>f</b>). The model constants and wall functions are configured with the standard treatments listed in <a href="#atmosphere-15-01259-t003" class="html-table">Table 3</a>. The different color lines represent the position extracted in <a href="#atmosphere-15-01259-f001" class="html-fig">Figure 1</a>. (FL-Fluent code, OF-OpenFOAM code).</p>
Full article ">Figure 7 Cont.
<p>Comparison of inlet and outlet wind velocity profiles (<b>a</b>,<b>d</b>), turbulent kinetic profiles (<b>b</b>,<b>e</b>), and turbulent kinetic energy dissipation (<b>c</b>,<b>f</b>). The model constants and wall functions are configured with the standard treatments listed in <a href="#atmosphere-15-01259-t003" class="html-table">Table 3</a>. The different color lines represent the position extracted in <a href="#atmosphere-15-01259-f001" class="html-fig">Figure 1</a>. (FL-Fluent code, OF-OpenFOAM code).</p>
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<p>Comparison of inlet and outlet wind velocity profiles (<b>a</b>,<b>d</b>), turbulent kinetic profiles (<b>b</b>,<b>e</b>), and turbulent kinetic energy dissipation (<b>c</b>,<b>f</b>). The numerical cases are configured with the standard model constants and modified wall functions as listed in <a href="#atmosphere-15-01259-t003" class="html-table">Table 3</a>. The different color lines represent the position extracted in <a href="#atmosphere-15-01259-f001" class="html-fig">Figure 1</a>.</p>
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<p>Comparison of inlet and outlet wind velocity profiles (<b>a</b>,<b>b</b>), turbulent kinetic profiles (<b>c</b>,<b>d</b>), and turbulent kinetic energy dissipation (<b>e</b>,<b>f</b>). The numerical cases are configured with the modified model constants and the standard wall functions, as listed in <a href="#atmosphere-15-01259-t003" class="html-table">Table 3</a>. The different color lines represent the position extracted in <a href="#atmosphere-15-01259-f001" class="html-fig">Figure 1</a>.</p>
Full article ">Figure 9 Cont.
<p>Comparison of inlet and outlet wind velocity profiles (<b>a</b>,<b>b</b>), turbulent kinetic profiles (<b>c</b>,<b>d</b>), and turbulent kinetic energy dissipation (<b>e</b>,<b>f</b>). The numerical cases are configured with the modified model constants and the standard wall functions, as listed in <a href="#atmosphere-15-01259-t003" class="html-table">Table 3</a>. The different color lines represent the position extracted in <a href="#atmosphere-15-01259-f001" class="html-fig">Figure 1</a>.</p>
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<p>Profiles of terrain-induced wind speed-up <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>S</mi> </mrow> </semantics></math> and turbulent kinetic energy <math display="inline"><semantics> <mi>k</mi> </semantics></math>. Numerical cases are configured with the standard model constants (SC) and the wall function (SW). (<b>a</b>,<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>S</mi> </mrow> </semantics></math> along line A-A and line AA-AA. (<b>c</b>) <math display="inline"><semantics> <mi>k</mi> </semantics></math> along lines A-A. The horizontally distributed profiles are 10 m AGL in height. (<b>d</b>) The vertical <math display="inline"><semantics> <mi>k</mi> </semantics></math> profile in the hilltop HT site. D-HT and D-CP represent the distance from HT and CP positions.</p>
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<p>Contours of the horizontal wind velocities (<b>a</b>,<b>b</b>) and turbulent kinetic energy (<b>c</b>,<b>d</b>) distributed with 10 m AGL height. The black and white circles in (<b>a</b>,<b>b</b>) denote the maximum and minimum wind speeds in the hilltop and leeward regions, respectively. The numerical cases are configured with the standard model constants (SC) and near-wall treatments (SW).</p>
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<p>The modified wall functions (MW) are configured in the numerical cases. (<b>a</b>,<b>b</b>) are <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>S</mi> </mrow> </semantics></math> along line A-A and line AA-AA. (<b>c</b>) <math display="inline"><semantics> <mi>k</mi> </semantics></math> along lines A-A. The horizontally distributed profiles are 10 m AGL in height. (<b>d</b>) The vertical <math display="inline"><semantics> <mi>k</mi> </semantics></math> profile in the hilltop HT site.</p>
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<p>The horizontally distributed contours of wind velocities (<b>a</b>,<b>b</b>) and turbulent kinetic energy (<b>c</b>,<b>d</b>) are configured using the modified near-wall functions.</p>
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<p>The modified turbulence model constants (MC) are configured in the numerical case. (<b>a</b>,<b>b</b>) are <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>S</mi> </mrow> </semantics></math> along line A-A and line AA-AA. (<b>c</b>) <math display="inline"><semantics> <mi>k</mi> </semantics></math> along lines A-A. The horizontally distributed profiles are 10 m AGL in height. (<b>d</b>) The vertical <math display="inline"><semantics> <mi>k</mi> </semantics></math> profile in the hilltop HT site.</p>
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<p>As for <a href="#atmosphere-15-01259-f011" class="html-fig">Figure 11</a>, the horizontally distributed contours of wind velocities (<b>a</b>,<b>b</b>) and turbulent kinetic energy (<b>c</b>,<b>d</b>) are configured using the modified turbulence closures.</p>
Full article ">Figure 15 Cont.
<p>As for <a href="#atmosphere-15-01259-f011" class="html-fig">Figure 11</a>, the horizontally distributed contours of wind velocities (<b>a</b>,<b>b</b>) and turbulent kinetic energy (<b>c</b>,<b>d</b>) are configured using the modified turbulence closures.</p>
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17 pages, 7040 KiB  
Article
Observation of Statistical Characteristics and Vertical Structures of Surface Warm Cyclonic Eddies and Cold Anticyclonic Eddies in the North Pacific Subtropical Countercurrent Region
by Yaowei Ma, Qinghong Li, Xiangjun Yu, Song Li and Xingyu Zhou
J. Mar. Sci. Eng. 2024, 12(10), 1783; https://doi.org/10.3390/jmse12101783 - 8 Oct 2024
Viewed by 829
Abstract
Conventional wisdom about mesoscale eddies is that cyclonic (anticyclonic) eddies are commonly associated with cold(warm) surface cores. Nevertheless, plenties of surface warm cyclonic eddies (WCEs) and cold anticyclonic eddies (CAEs) in the North Pacific Subtropical Countercurrent (STCC) region are observed by a synergistic [...] Read more.
Conventional wisdom about mesoscale eddies is that cyclonic (anticyclonic) eddies are commonly associated with cold(warm) surface cores. Nevertheless, plenties of surface warm cyclonic eddies (WCEs) and cold anticyclonic eddies (CAEs) in the North Pacific Subtropical Countercurrent (STCC) region are observed by a synergistic investigation based on data from satellite altimetry, microwave radiometer, and Argo float profiles in this study. The results indicate that these two types of abnormal eddies (WCEs and CAEs) are prevalent in the STCC region, comprising approximately 30% of all eddies detected via satellite observations. We then analyze their spatial-temporal distribution characteristics and composite vertical structures. A statistical comparison with surface cold cyclonic eddies (CCEs) and warm anticyclonic eddies (WAEs) reveals notable differences between the anomalous and typical eddies. Additionally, we present the composite vertical structures of temperature and salinity anomalies for the anomalous eddies across five delineated subregions within an eddy-coordinate system. Furthermore, the close relationship between these abnormal eddies and subsurface-intensified mesoscale eddies are discussed. Full article
(This article belongs to the Section Physical Oceanography)
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Figure 1
<p>(<b>a</b>) Topographic maps of the North Pacific Subtropical Countercurrent region, based on the ETOPO1 dataset (doi:10.7289/V5C8276M), where black lines give the dividing lines between five areas (Areas A to E). (<b>b</b>) Spatial distribution of the base-10 logarithm of eddy kinetic energy (EKE, cm<sup>2</sup>/s<sup>2</sup>) in the STCC region (20°–28° N, 120°–160° E), based on daily sea level anomaly data provided by the Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) from January 2007 to December 2014.</p>
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<p>Example cases of (<b>a</b>) cold anticyclonic eddy and (<b>b</b>) warm cyclonic eddy detected from the combination of SSHA and SSTA maps provided by satellite observation. The red (blue) contour line depicts the boundary of the CAE (WCE) case. Arrows and shading represent the surface geostrophic currents and temperature anomalies after band-pass filtering, respectively.</p>
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<p>Spatial distributions of the occurrence frequency of the (<b>a</b>) WCEs, (<b>b</b>) CCEs, (<b>c</b>) CAEs, and (<b>d</b>) WAEs in 0.5° × 0.5° bins. Vertical dash lines are the boundaries between different Areas A and E.</p>
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<p>Monthly distributions of four types of eddies. The yellow, blue, purple, and red bars represent warm cyclonic eddies, cold cyclonic eddies, cold anticyclonic eddies, and warm anticyclonic eddies, respectively.</p>
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<p>Yearly distributions of four types of eddies. The yellow, blue, purple, and red bars represent warm cyclonic eddies, cold cyclonic eddies, cold anticyclonic eddies, and warm anticyclonic eddies, respectively.</p>
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<p>UF and UB line in the Mann–Kendall test result for a monthly number of four types of eddies (<b>a</b>) wce, (<b>b</b>) cce, (<b>c</b>) cae, and (<b>d</b>) wae.</p>
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<p>UF and UB line in Mann–Kendall test result for an annual number of four types of eddies (<b>a</b>) wce, (<b>b</b>) cce, (<b>c</b>) cae, and (<b>d</b>) wae.</p>
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<p>Statistical histogram of the eddy amplitude (units: cm) and eddy radius (units: km) of the four types of eddies in the STCC region. Comparisons between (<b>a</b>) the eddy amplitude of CCEs and WCEs, (<b>b</b>) the eddy amplitude of WAEs and CAEs, (<b>c</b>) the eddy radius of CCEs and WCEs, and (<b>d</b>) the eddy radius of WAEs and CAEs are shown. The yellow, blue, purple, and red bars represent warm cyclonic eddies, cold cyclonic eddies, cold anticyclonic eddies, and warm anticyclonic eddies, respectively.</p>
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<p>Spatial distributions of the Argo profiles captured by (<b>a</b>) CCEs, (<b>b</b>) WAEs, (<b>c</b>) WCEs, and (<b>d</b>) CAEs. The profile numbers are shown at the northeastern corner of each subfigure.</p>
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<p>Vertical zonal sections of the temperature anomalies <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>′</mo> </msup> </mrow> </semantics></math> (°C) of composite CAE (cold anticyclonic eddy) in Areas A–E (<b>a</b>–<b>e</b>).</p>
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<p>Same as <a href="#jmse-12-01783-f010" class="html-fig">Figure 10</a>, but for temperature anomalies <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>′</mo> </msup> </mrow> </semantics></math> (°C) of composite WCE.</p>
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<p>Same as <a href="#jmse-12-01783-f010" class="html-fig">Figure 10</a>, but for the salinity anomalies <math display="inline"><semantics> <msup> <mi>S</mi> <mo>′</mo> </msup> </semantics></math> (PSU) of composite CAE.</p>
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<p>Same as <a href="#jmse-12-01783-f010" class="html-fig">Figure 10</a>, but for the salinity anomalies <math display="inline"><semantics> <msup> <mi>S</mi> <mo>′</mo> </msup> </semantics></math> (PSU) of composite WCE.</p>
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19 pages, 7635 KiB  
Article
Enhanced Transformer Framework for Multivariate Mesoscale Eddy Trajectory Prediction
by Yanling Du, Jiahao Huang, Jiasheng Chen, Ke Chen, Jian Wang and Qi He
J. Mar. Sci. Eng. 2024, 12(10), 1759; https://doi.org/10.3390/jmse12101759 - 4 Oct 2024
Viewed by 745
Abstract
Accurately predicting the trajectories of mesoscale eddies is essential for comprehending the distribution of marine resources and the multiscale energy cascade in the ocean. Nevertheless, current approaches for predicting mesoscale eddy trajectories frequently exhibit inadequate examination of the intrinsic multiscale temporal data, resulting [...] Read more.
Accurately predicting the trajectories of mesoscale eddies is essential for comprehending the distribution of marine resources and the multiscale energy cascade in the ocean. Nevertheless, current approaches for predicting mesoscale eddy trajectories frequently exhibit inadequate examination of the intrinsic multiscale temporal data, resulting in diminished predictive precision. To address this challenge, our research introduces an enhanced transformer-based framework for predicting mesoscale eddy trajectories. Initially, a multivariate dataset of mesoscale eddy trajectories is constructed and expanded, encompassing eddy properties and pertinent ocean environmental information. Additionally, novel feature factors are delineated based on the physical attributes of eddies. Subsequently, a multi-head attention mechanism is introduced to bolster the modeling of the multiscale time-varying connections within eddy trajectories. Furthermore, the original positional encoding is substituted with Time-Absolute Position Encoding, which considers the dimensions and durations of the sequence mapping, thereby improving the distinguishability of embedded vectors. Ultimately, the Soft-DTW loss function is integrated to more accurately assess the overall discrepancies among mesoscale eddy trajectories, thereby improving the model’s resilience to erratic and diverse trajectory sequences. The effectiveness of the proposed framework is assessed using the eddy-abundant South China Sea. Our framework exhibits exceptional predictive accuracy, achieving a minimum central error of 8.507 km over a seven-day period, surpassing existing state-of-the-art models. Full article
(This article belongs to the Section Physical Oceanography)
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Figure 1
<p>Preprocessing flowchart for multivariate mesoscale eddy time series data.</p>
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<p>Azimuth illustration. <span class="html-italic">P</span> and <span class="html-italic">Q</span> represent the centers of two eddies. The dihedral angle <span class="html-italic">θ</span> formed by the planes <span class="html-italic">OPQ</span> and <span class="html-italic">OPN</span> represents the azimuth of <span class="html-italic">P</span> relative to <span class="html-italic">Q</span>.</p>
Full article ">Figure 3
<p>Illustration of mesoscale eddy trajectory prediction. The center of the eddy is defined as the center of the speed best-fit circle (solid deep blue lines), which represents a geometric representation that approximates the eddy’s speed contour, connecting all points in the flow field with the same velocity magnitude, as indicated by the black and orange dots. The radius of eddy is the radius of the effective best fit circle (solid deep blue dashed lines), which fits the contour of maximum circum-average geostrophic speed for the detected eddy using the least squares method. And the vector formed by ugos and vgos represents the geostrophic flow velocity vector (black arrows).</p>
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<p>Flowchart of enhanced transformer-based mesoscale eddy trajectory prediction framework.</p>
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<p>Comparison of the similarity corresponding to distances between different positions in the sequence with TAPE and OPE. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mi>T</mi> <mi>r</mi> <mi>a</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>256</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mi>T</mi> <mi>r</mi> <mi>a</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>21</mn> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mi>T</mi> <mi>r</mi> <mi>a</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>256</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mi>T</mi> <mi>r</mi> <mi>a</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>300</mn> </mrow> </semantics></math>.</p>
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<p>Partial prediction results of different models trained with Soft-DTW loss. (<b>a</b>–<b>c</b>) respectively represent the prediction results with different input lengths.</p>
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<p>Partial prediction results of different models trained with Soft-DTW loss. (<b>a</b>–<b>c</b>) respectively represent the prediction results with different input lengths.</p>
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<p>The correlation between model train and test times and RMSE performance with different input lengths.</p>
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<p>Visualization of the 7 × 7 attention matrices for the four randomly sampled heads in the decoder.</p>
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17 pages, 11892 KiB  
Article
The Mesoscale SST–Wind Coupling Characteristics in the Yellow Sea and East China Sea Based on Satellite Data and Their Feedback Effects on the Ocean
by Chaoran Cui and Lingjing Xu
J. Mar. Sci. Eng. 2024, 12(10), 1743; https://doi.org/10.3390/jmse12101743 - 3 Oct 2024
Viewed by 711
Abstract
The mesoscale interaction between sea surface temperature (SST) and wind is a crucial factor influencing oceanic and atmospheric conditions. To investigate the mesoscale coupling characteristics of the Yellow Sea and East China Sea, we applied a locally weighted regression filtering method to extract [...] Read more.
The mesoscale interaction between sea surface temperature (SST) and wind is a crucial factor influencing oceanic and atmospheric conditions. To investigate the mesoscale coupling characteristics of the Yellow Sea and East China Sea, we applied a locally weighted regression filtering method to extract mesoscale signals from Quik-SCAT wind field data and AMSR-E SST data and found that the mesoscale coupling intensity is stronger in the Yellow Sea during the spring and winter seasons. We calculated the mesoscale coupling coefficient to be approximately 0.009 N·m−2/°C. Subsequently, the Tikhonov regularization method was used to establish a mesoscale empirical coupling model, and the feedback effect of mesoscale coupling on the ocean was studied. The results show that the mesoscale SST–wind field coupling can lead to the enhancement of upwelling in the offshore area of the East China Sea, a decrease in the upper ocean temperature, and an increase in the eddy kinetic energy in the Yellow Sea. Diagnostic analyses suggested that mesoscale coupling-induced variations in horizontal advection and surface heat flux contribute most to the variation in SST. Moreover, the increase in the wind energy input to the eddy is the main factor explaining the increase in the eddy kinetic energy. Full article
(This article belongs to the Special Issue Air-Sea Interaction and Marine Dynamics)
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<p>The probability distributions of the mesoscale magnitude of SST perturbations as a function of the different half-span parameters.</p>
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<p>The flow chart of mesoscale wind field calculation in MESO-E.</p>
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<p>Spatially high-pass filtered WS<sub>meso</sub> (contours) and SST<sub>meso</sub> (colors) in the different months in 2006. The contour interval is 0.003 N·m<sup>−2</sup>. The zero contours are not included.</p>
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<p>Spatially high-pass filtered (upper panel) Div(WS<sub>meso</sub>) (contours) and ∇<sub>down</sub> SST<sub>meso</sub> (colors), and (lower panel) Curl(WS<sub>meso</sub>) (contours) and ∇<sub>cross</sub> SST<sub>meso</sub> (colors) in (<b>a</b>,<b>e</b>) February, (<b>b</b>,<b>f</b>) June, (<b>c</b>,<b>g</b>) August, and (<b>d</b>,<b>h</b>) December 2006. The contour interval is 0.3 N·m<sup>−2</sup> per 10,000 km. The zero contours are not included.</p>
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<p>Scatterplots of the spatially high-pass filtered Quik-SCAT Div(WS<sub>meso</sub>) and Curl(WS<sub>meso</sub>) binned by ranges of AMSR-E ∇<sub>down</sub> SST<sub>meso</sub> and ∇<sub>cross</sub> SST<sub>meso</sub> perturbations. The coupling coefficient is denoted as S. Points and error bars represent the mean and standard deviation in each bin, respectively.</p>
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<p>The monthly variations in the coupling coefficient (N·m<sup>−2</sup>/(°C·100 km)) between (<b>a</b>) Div(WS<sub>meso</sub>) and ∇<sub>down</sub> SST<sub>meso</sub> and (<b>b</b>) Curl(WS<sub>meso</sub>) and ∇<sub>cross</sub> SST<sub>meso</sub>.</p>
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<p>The SST<sub>meso</sub> (colors) and WS<sub>meso</sub> (contours) obtained from (<b>a</b>) observation, (<b>b</b>) MESO-E, and (<b>c</b>) CONTROL-E in summer; the SST<sub>meso</sub> (colors) and WS<sub>meso</sub> (contours) obtained from (<b>d</b>) observation, (<b>e</b>) MESO-E, and (<b>f</b>) CONTROL-E in winter. The observations are from AMSR-E and Quik-SCAT data in 2006; the simulated results are from 10-year averaged outputs of MESO-E and CONTROL-E. The contour interval is 0.006 N·m<sup>−2</sup>. The zero contours are omitted.</p>
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<p>The (<b>a</b>) 6-year averaged coupling coefficient between Quik-SCAT WS<sub>meso</sub> and AMSR-E SST<sub>meso</sub>, (<b>b</b>) 10-year averaged coupling coefficient between WS<sub>meso</sub> and SST<sub>meso</sub> from the MESO-E output, and (<b>c</b>) 10-year averaged coupling coefficient between WS<sub>meso</sub> and SST<sub>meso</sub> from the CONTROL-E output. Points and error bars represent the mean and standard deviation in each bin, respectively.</p>
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<p>The 10-year averaged differences (MESO-E minus CONTROL-E) in (<b>a</b>) sea temperature, (<b>b</b>) surface heat flux, (<b>c</b>) horizontal advection, and (<b>d</b>) vertical diffusion in the upper 50 m. The units are °C in (<b>a</b>) and °C/month in (<b>b</b>–<b>d</b>).</p>
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<p>The 10-year average (<b>a</b>–<b>c</b>) zonal and (<b>d</b>–<b>f</b>) meridional current differences (m/s) in winter between the SODA3.4.2 2011–2020 data and CONTROL-E (SODA minus CONTROL-E, <b>left panel</b>); between MESO-E and CONTROL-E (MESO-E minus CONTROL-E, <b>middle panel</b>), and between MESO-E and SODA (MESO-E minus SODA, <b>right panel</b>). The zonal and meridional current was calculated by averaging vertically up to a depth of 50 m.</p>
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<p>Differences in the 10-year average (left panel) Curl(WS<sub>meso</sub>) (1 × 10<sup>−6</sup> N/m<sup>3</sup>) and (right panel) vertical current (1 × 10<sup>−7</sup> m/s) in (<b>a</b>,<b>b</b>) winter and (<b>c</b>,<b>d</b>) summer between MESO-E and CONTROL-E (MESO-E minus CONTROL-E). The vertical current was calculated by averaging vertically up to a depth of 50 m.</p>
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<p>The 10-year averaged difference in (<b>a</b>) EKE, (<b>b</b>) eddy wind work, and (<b>c</b>) baroclinic conversion from eddy available potential energy to EKE. (<b>d</b>) Conversion between mean kinetic energy and EKE between MESO-E and CONTROL-E (MESO-E minus CONTROL-E). The units are cm<sup>3</sup>/s<sup>3</sup> in (<b>a,b,c</b>) and 1 × 10<sup>−2</sup> cm<sup>3</sup>/s<sup>3</sup> in (<b>d</b>).</p>
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17 pages, 8493 KiB  
Article
Fine-Scale Eddies Detected by SWOT in the Kuroshio Extension
by Tianshi Du and Zhao Jing
Remote Sens. 2024, 16(18), 3488; https://doi.org/10.3390/rs16183488 - 20 Sep 2024
Viewed by 992
Abstract
Conventional altimetry has greatly advanced our understanding of mesoscale eddies but falls short in studying fine-scale eddies (<150 km). The newly launched Surface Water and Ocean Topography (SWOT) altimeter, however, with its unprecedented high-resolution capabilities, offers new opportunities to observe these fine-scale eddies. [...] Read more.
Conventional altimetry has greatly advanced our understanding of mesoscale eddies but falls short in studying fine-scale eddies (<150 km). The newly launched Surface Water and Ocean Topography (SWOT) altimeter, however, with its unprecedented high-resolution capabilities, offers new opportunities to observe these fine-scale eddies. In this study, we use SWOT data to explore these previously elusive fine-scale eddies in the Kuroshio Extension. During SWOT’s fast sampling phase from 29 May 2023 to 10 July 2023, we identified an average of 4.5 fine-scale eddies within each 120 km wide swath. Cyclonic eddies, which are slightly more frequent than the anticyclonic ones (ratio of 1.16), have a similar mean radius of 23.4 km. However, cyclonic eddies exhibit higher amplitudes, averaging 3.5 cm compared to 2.8 cm for anticyclonic eddies. In contrast to the mesoscale eddies detected by conventional altimeters, the fine-scale eddies revealed by SWOT are characterized by smaller sizes and weaker amplitudes. This study offers a preliminary view of fine-scale eddy characteristics from space, highlighting SWOT’s potential to advance our understanding of these dynamic processes. Nonetheless, it also emphasizes the necessity for comprehensive analysis to fully exploit the satellite’s capabilities in monitoring and interpreting complex eddy behaviors. Full article
(This article belongs to the Special Issue Applications of Satellite Altimetry in Ocean Observation)
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<p>Eddy kinetic energy averaged over the SWOT Cal/Val period. The gray swaths denote the SWOT Cal/Val orbit in the northwest Pacific. The number of orbit passes are labeled at the bottom of the figure. The black box represents the KE region. The red box denotes the study region of the fine-scale eddies.</p>
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<p>(<b>a</b>) A snapshot of SWOT-observed SSH anomalies, including both the nadir altimeter (scattered points in the middle) and KaRIn measurements (filled color on the sides). (<b>b</b>) Linear interpolation across the swath with both the nadir and KaRIn measurements. (<b>c</b>) Linear interpolation across the swath with only the KaRIn measurements. The black ellipse highlights the significant differences between (<b>b</b>) and (<b>c</b>).</p>
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<p>(<b>a</b>) Snapshot of the SLA (color), surface geostrophic velocity (black quiver), and eddy identification results (white circle) on 30 May 2023. The solid circles represent anticyclonic eddies while dashed circles denote cyclonic eddies. The gray swaths denote the SWOT Cal/Val orbit in this region. (<b>b</b>) The timeseries of the eddy numbers identified per day, with cyclonic eddies colored in blue while anticyclonic eddies colored in red. The vertical gray line denotes the date of the snapshot shown in (<b>a</b>).</p>
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<p>(<b>a</b>) Heatmap of the relationship between mesoscale eddy radius and amplitude. The blue and red line denote the linear regression of cyclonic eddies and anticyclonic eddies, respectively. (<b>b</b>,<b>c</b>) demonstrate the histogram of eddy radius and amplitude. Blue bars and red lines stand for cyclonic and anticyclonic eddies, respectively.</p>
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<p>SLA spectrum from SWOT (red) and DUACS (blue) data averaged over the Cal/Val period. The solid and dashed colored lines represent the results from SWOT passes 004 and 019, respectively. The black line denotes the baseline of the SWOT error requirement. The power law of k<sup>−11/3</sup> is displayed in the figure. The two vertical dashed lines denote the reference wavenumbers of 150 km and 20 km.</p>
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<p>Maps of SLAs from (<b>a</b>) the DUACS product and (<b>b</b>) SWOT data on 15 May 2023 from pass 004. (<b>c</b>) The differences between (<b>a</b>,<b>b</b>). Gray lines indicate the extent of SWOT’s swath, with gaps between two swaths filled through linear interpolation. Circles denote the eddy identification results, with the white circles being particular fine-scale eddies that are reinforced in the main text. (<b>d</b>–<b>f</b>) Same as (<b>a</b>–<b>c</b>) but for results on 28 April 2023 from pass 019.</p>
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<p>The case-selected fine-scale eddies and SLA differences evolve with time. (<b>a</b>–<b>c</b>) Results from pass 004 from 13 May 2023 to 17 May 2023. The black circles represent the case-selected eddy. (<b>d</b>–<b>f</b>) Same as (<b>a</b>–<b>c</b>) but for results from pass 019 from 24 April 2023 to 28 April 2023.</p>
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<p>The timeseries of identified (<b>a</b>) cyclonic and (<b>b</b>) anticyclonic fine-scale eddy numbers during the Cal/Val period. White circles denote missing values but are filled using the nearest interpolation. (<b>c</b>) The total number of fine-scale eddies during the Cal/Val period, with blue and red representing the cyclonic and anticyclonic eddies, respectively. The original result denotes the eddy numbers with SWOT’s missing values, with the interpolate representing the result after filling the missing values.</p>
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<p>Same as <a href="#remotesensing-16-03488-f004" class="html-fig">Figure 4</a>, but for fine-scale eddy properties detected by SWOT.</p>
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<p>(<b>a</b>) Along-swath SLA derived from SWOT within a 21-day repeat cycle from 25 May 2024 to 14 June 2024. (<b>b</b>) The averaged SLA results during the same period derived from DUACS. (<b>c</b>) The mapped SLA field from (<b>a</b>) using linear interpolation. (<b>d</b>) The SLA differences between SWOT and DUACS. The black dashed box denotes the central region range. (<b>e</b>–<b>h</b>) Same as (<b>a</b>–<b>d</b>), but for one subcycle from 25 May 2024 to 4 June 2024.</p>
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17 pages, 2165 KiB  
Review
The Generation and Propagation of Wind- and Tide-Induced Near-Inertial Waves in the Ocean
by Yang Li, Zhao Xu and Xianqing Lv
J. Mar. Sci. Eng. 2024, 12(9), 1565; https://doi.org/10.3390/jmse12091565 - 6 Sep 2024
Viewed by 1301
Abstract
Near-inertial waves (NIWs), a special form of internal waves with a frequency close to the local Coriolis frequency, are ubiquitous in the ocean. NIWs play a crucial role in ocean mixing, influencing energy transport, climate change, and biogeochemistry. This manuscript briefly reviews the [...] Read more.
Near-inertial waves (NIWs), a special form of internal waves with a frequency close to the local Coriolis frequency, are ubiquitous in the ocean. NIWs play a crucial role in ocean mixing, influencing energy transport, climate change, and biogeochemistry. This manuscript briefly reviews the generation and propagation of NIWS in the oceans. NIWs are primarily generated at the surface by wind forcing or through the water column by nonlinear wave-wave interaction. Especially at critical latitudes where the tidal frequency is equal to twice the local inertial frequency, NIWs can be generated by a specific subclass of triadic resonance, parametric subharmonic instability (PSI). There are also other mechanisms, including lee wave and spontaneous generation. NIWs can propagate horizontally for hundreds of kilometers from their generating region and radiate energy far away from their origin. NIWs also penetrate deep into the ocean, affecting nutrient and oxygen redistribution through altering mixing. NIW propagation is influenced by factors such as mesoscale eddies, background flow, and topography. This review also discussed some recent observational evidence of interactions between NIWs from different origins, suggesting a complicated nonlinear interaction and energy cascading. Despite the long research history, there are still many areas of NIWs that are not well defined. Full article
(This article belongs to the Special Issue Ocean Internal Waves and Circulation Dynamics in Climate Change)
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<p>Propagation diagram for NIWs, including current vector helices. The negative wavenumber is corresponding to the component rotating CW, upward energy propagation, and downward phase propagation.</p>
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<p>Schematic diagram showing the generation of wind-generated NIWs.</p>
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<p>Schematic diagram showing the PSI-generated NIWs.</p>
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<p>Schematic showing processes associated with near-inertial generation, dissipation, and propagation. As storms move along the storm track (thick white arrow), a local response occurs with frequencies near the local Coriolis frequency. Both high- and low-mode internal gravity waves are excited. High modes propagate along curving characteristics downward and equatorward. The higher modes have strong shear that results in mixing, ϵ(z). Low-mode wave radiation (indicated in gray) takes the form of oscillations that propagate equatorward. Upward characteristics and topographic scattering have been observed, but the processes involved are not completely understood.</p>
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<p>(<b>a</b>) The model domain and the location of mooring (red triangle) on the continental shelf. The shading denotes the bathymetry, which is from General Bathymetric Chart of the Oceans. The colored line denotes the tracks of Typhoon Danas (3–8 October 2013), and the colors indicate the typhoon intensity. The black line indicates the horizontal projection of the section. (<b>b</b>–<b>d</b>) Three snapshots along the section. The shaded colors show the magnitude of near-inertial velocities at corresponding moments in units of m s<sup>−1</sup>. The black contours show the magnitude of cross-axis horizontal velocities averaged from 6–9 October at increments of 0.2 m s<sup>−1</sup>, and the minimum is 0.4 m s<sup>−1</sup>. The dashed line indicates the latitude of the mooring location. The black solid lines indicate the NIW ray tracing results. The packets of NIW were released on 6 October. Modified from Li et al. [<a href="#B133-jmse-12-01565" class="html-bibr">133</a>].</p>
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<p>Results of the ray tracing method considering baroclinity or not. Ray tracing results of the near inertial internal wave with a frequency of 0.99 <span class="html-italic">f</span> propagating downward in the condition of considering baroclinity (red dashed lines) and not considering baroclinity (blue solid lines) in the zonal section of the observation position. The green line indicates the movement range of wave packets only considering vorticity. The magenta line indicates the range considering both vorticity and baroclinity. The black, thin contour lines in the figure represent the background density in units of kg m<sup>−3</sup>. Modified from Li et al. [<a href="#B133-jmse-12-01565" class="html-bibr">133</a>].</p>
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