the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Jul 2025
A Black Hole Eddy Dataset of North Pacific Ocean Based on Satellite Altimetry
Abstract. The methodologies employed for the identification of ocean coherent eddies can be categorized as either Eulerian and Lagrangian. Among Lagrangian structures, Black Hole Eddies (BHEs) exhibit the highest degree of material coherence and conservation, making them particularly suitable for studying the transport and retention of oceanic materials. This study presents an efficient Graphics Processing Unit (GPU) -based BHE identification algorithm, enhancing computational efficiency by approximately 13 times compared to the existing methods. Using this algorithm, the North Pacific Black Hole Eddy dataset (BHE v1.0) is constructed for the first time, based on satellite-derived surface geostrophic velocity data from January 1, 1993 to May 5, 2023 (Tian et al., https://doi.org/10.5281/zenodo.15597447, 2025a). BHE v1.0 contains 18387 eddies with radius larger than 20 km and lifetimes longer than 4 weeks and captures both the spatial-temporal characteristics and the trajectories of coherent eddies throughout lifetimes. Through the advection of Lagrangian particles in Eulerian eddy, rotationally coherent Lagrangian vortices (RCLVs) and BHEs, it is confirmed that BHEs maintain strong material coherence and are able to maintain concentration during their life cycle, preserving their structure without significant filamentation or mixing with surrounding waters. Additionally, approximately 6 % of BHEs, which do not overlap with any RCLVs or Eulerian eddies, are identified and referred to as the Naked Black Hole Eddy and further analyze its coherence through advection. And Transport analysis shows that BHEs induce westward transport about 1.5 Sv, three times weaker than RCLVs, suggesting that they may offer a more accurate estimate of oceanic transport than RCLVs. These finding addresses the existing gap in Black Hole Eddy datasets within the field of oceanography and provides a novel perspective for studying the interactions between coherent eddies and oceanic physical phenomena.
- Preprint
(3464 KB) - Metadata XML
-
Supplement
(25253 KB) - BibTeX
- EndNote
Status: open (extended)
-
RC1: 'Comment on essd-2025-384', Chao Liu, 17 Jul 2025
reply
Dear editor, thank you for the opportunity to review the manuscript “A Black Hole Eddy Dataset of North Pacific Ocean Based on Satellite Altimetry” by Tian et al. My comments are attached.
-
AC1: 'Reply on RC1', Fenglin Tian, 06 Aug 2025
reply
We deeply appreciate your time and effort in reviewing our manuscript. Your comments have been really helpful in refining our work. Please see the attached PDF for our responses to the comments.
-
AC1: 'Reply on RC1', Fenglin Tian, 06 Aug 2025
reply
-
CC1: 'Comment on essd-2025-384', Alexandra Jones-Kellett, 11 Sep 2025
reply
It is nice to see components of the methodology developed in our paper (Jones-Kellett & Follows 2024; https://doi.org/10.5194/essd-16-1475-2024) implemented in this work. I was excited to read this preprint due to the related topic and the need for increased computational efficiency for Lagrangian eddy tracking. In reading it, however, I noticed that several pieces of text appear to be copied from our manuscript, and similar figures were reproduced without appropriate attribution. Out of curiosity, I ran a comparison with another foundational paper to this work that was published in ESSD (Liu & Abernathey 2023; https://doi.org/10.5194/essd-15-1765-2023) and found that some parts of the text are also eerily similar to that manuscript. For the sake of time, I did not compare the preprint directly with any other texts. I documented the incidents I found here. Since I read the paper quite closely, I also provided other comments and scientific inquiries that I hope will serve to improve the manuscript.
Instances of replicated text and missing attribution
- Lines 126-7: “previous studies found that fewer and smaller structures maintain coherency for longer timescales”; Text copied directly from Jones-Kellett & Follows 2024 (page 1477), please rephrase in your own words.
- Lines 131-2: “eddy atlases can answer these questions, revealing how the coherent properties of mesoscale features manifest in space and time.” ; Text copied directly from Jones-Kellett & Follows 2024 (page 1477), please rephrase in your own words or quote the text with a citation to the source.
- Figure 3: The premise of this figure was replicated from Jones-Kellett & Follows 2024 (Figure 3), with embellishments, namely the symbolic particles. I suggest citing the original study at the end of the sentence in lines 358-9.
- Lines 405-8: Nearly identical text as in Liu & Abernathey 2023 pg. 1771
- Lines 459-62: Nearly identical text as in Liu & Abernathey 2023 pg. 1771
- Figure 10: This presentation of results was replicated from Jones-Kellett & Follows 2024 (Figure 4, pg 1483). Please provide appropriate attribution, including a citation to the original study. Note that the caption to this figure is also nearly identical to that of the analogous figure from Jones-Kellett & Follows 2024.
- Figure 11: The second sentence of this caption is copied directly from the Figure 5 caption of Liu & Abernathey 2023, corresponding to a similar figure presentation without attribution.
- Lines 482-3: Nearly identical text as in Jones-Kellett & Follows 2024 pg. 1484
- Lines 492-4: This text was copied directly from Jones-Kellett & Follows 2024 (page 1484), except for the citation (Chaigneau et al., 2008). Here, the incorrect paper is cited for defining the polarity probability, given that Chaigneau et al., 2008 make no mention of this metric. The appropriate citation is Chaigneau et al., 2009: https://doi.org/10.1016/j.pocean.2009.07.012
- Lines 500-1: “reveals two stark Lee Eddy pathways depending on the polarity, whereas RCLVs Lee Eddies have a more diffuse polarity probability”; text copied directly from Jones-Kellett & Follows 2024 (page 1484); please rephrase in your own words or quote the text with a citation to the source.
- Figure 14: Caption structure copied directly from Figure 10 of Jones-Kellett & Follows 2024.
- Lines 513-4: “consistent with previously noted summer peaks of eddy kinetic energy in subtropical gyres (Zhai et al., 2008)”; text copied directly from Jones-Kellett & Follows 2024 (page 1482), please rephrase in your own words.
- Figure 15: This presentation of results was replicated from Jones-Kellett & Follows 2024 (Figure 6, pg 1485). Please provide appropriate attribution, including a citation to the original study. Note that the caption is nearly identical to that of the analogous figure from Jones-Kellett & Follows 2024.
- Figure 16: Figure caption mostly replicated from Figure 8 caption of Liu & Abernathey 2023, pg. 1774.
- Line 597: “It is convenient to load the data using Python or other language.” Phrasing replicated from Liu and Abernathey 2023 on pg. 1775 (Section 4)
Major Comments
- Section 2.1.1: The authors claim to have used Level 3 data, yet the link provided is to a Level 4 product (Line 158). Additionally, they used a near-real time product, which is made for short-term monitoring and is inappropriate for a long-term study, for which the delayed time products are preferred (e.g., see the Quality Information Manuals provided by CMEMS). The product that is linked in Line 158 only has spatial coverage from 2022-2025, yet the study covers 1993-2023. The authors build a new eddy dataset in this work that they compare to a previous product developed by some of the same authors (Tian et al. 2022; https://doi.org/10.1175/JTECH-D-21-0103.1), which used Level 4 delayed-time data. If the authors are actually using the same data as in Tian et al. 2022, this entire paragraph needs to be rewritten.
- Section 3.2, Figure 8 & 9: The authors highlight two BHEs to draw general conclusions about the coherence of all BHEs. However, the regions analyzed in Figs 8 and 9 are problematic due to the decreasing accuracy of satellite-derived geostrophic currents near the equator (Fig 8), and near coastlines (Fig 9). Especially with only two qualitative examples of the difference in coherence, the authors should provide examples from regions with lower known errors in the satellite products. I am especially confused about Figure 8 being used as a demonstration of the difference in the coherence of BHEs and RCLVs (e.g. Line 438), given that the RCLV appears also to have minimal filamentation, potentially suggesting that BHEs are underestimating the full scope of the coherent vortex.
- How the authors were able to compare BHEs tracked weekly with the RCLV dataset from Tian et al. 2022 (https://doi.org/10.1175/JTECH-D-21-0103.1) is never described in this preprint. Tian et al. 2022 derive RCLVs over fine times every 90 days. Do the authors subset the weekly BHE dataset to match the RCLV dataset for figures 10, and 13-19? If so, that means the comparison is made every 3 months, which will affect the results. However, Fig. 15 states “frequency refers to the number of eddies per 7 day time step”, suggesting that the authors somehow obtained weekly RCLV boundaries. In general, the comparison between these datasets is questionable, given the apparent difference in satellite products used and the difference in detection frequency of the Lagrangian eddies. The size threshold may also have been different (see Major Comment #5).
- The authors claim to have tracked the BHEs weekly, but then provide results from 30 day intervals in Figs 13 and 14. Since 30 is not divisible by 7, how did the authors obtain 30-day eddies, as opposed to 28-day? In Line 553, the authors switch to 28-day results for the transport analysis. Furthermore, if the authors have weekly BHEs tracked, why are the results only being shown for one time interval? That seems to defeat the purpose of tracking the features over their full lifetimes. The authors only provide a dataset for BHEs with T=30 and 90 day lifespans (Line 610), rather than the weekly dataset described in the methods.
- Figure 16 & Lines 521-524: It is difficult to visually see the difference between these statistics in panels (a) and (b) because the y-axis changes. Plotting the data together in one plot may help. The conclusion that RCLV is weakly influenced by latitude is confusing (Lines 523-4 and 639-40), considering that RCLVs on average decrease in size with increasing latitude, whereas BHEs appear not to have a latitudinal dependence above latitudes of 20N in Figure (a). A constant radius contradicts expectations based on the Rossby radius of deformation, which is not commented on in the text. Figure 16 also gives the impression that the minimum radius for the BHEs was 20km, whereas the RCLVs was around 25km. If that is the case, it is an issue for comparing BHEs and RCLVs if the size minimum for detection differed between the datasets.
Minor Comments
- Line 24: “And” at the beginning of the sentence is likely a typo
- Lines 25: How does weaker transport by the RCLVs suggest that BHE offer a “more accurate estimate of transport”? Aren’t they both contributing to transport considering the significant overlap?
- Lines 29 & 31: Contains repeated information, e.g. “Mesoscale eddies, one of the most prominent processes in the ocean,” and “Mesoscale eddies are ubiquitous in the ocean”
- Lines 74-75: “This approach demonstrates greater efficiency compared to previous Lagrangian eddy identification methods and enhances the objectivity of eddy boundary identification.” This seems to be the major assumption driving this analysis, however, citations for this conclusion are not provided, and the other Lagrangian methods have not yet been introduced in the introduction at this point (lines 102-125)
- Lines 107: “Lagrangian-averaged vorticity deviation (LAVD) method”; I suggest adding a citation to the original study, Haller et al. 2016 (https://doi.org/10.1017/jfm.2016.151)
- Figure 3: Why are yellow particles drawn outside of the contours in the second and third timesteps, which gives the impression of eddy leakiness rather than coherence?
- Figure 6: Are these the boundaries of eddies at age 30-day or with total 30-day lifetimes?
- Figs 11 & 12: I am confused about how the features relate to each other in these panels. Are the authors arguing this is an evolution of a single eddy or two different eddies in each row? I can’t tell which color corresponds to which feature due to how small the figure caption labels are.
- Line 525: Double citation typo
- Lines 551-552: The assumptions made here of constant size with depth do not align with the structures previously reported for Lagrangian eddies (see Deogharia et al. 2024; https://doi.org/10.1038/s41598-024-61744-6), which should at least be discussed.
- Figure 18: The caption has a typo, “distribution distributions”
- Line 617: “Unlike Eulerian eddies and RCLVs, which experience significant boundary deformation and mixing with the surrounding water during motion”: it is misleading to couple Eulerian eddies with RCLVs in this way, considering that the BHEs are only marginally different than RCLVs, but both RCLVs and BHEs are substantially more coherent than Eulerian eddies.
Citation: https://doi.org/10.5194/essd-2025-384-CC1
Data sets
A Black Hole Eddy Dataset of North Pacific Ocean Based on Satellite Altimetry Fenglin Tian et al. https://doi.org/10.5281/zenodo.15597447
Video supplement
A Black Hole Eddy Dataset of North Pacific Ocean Based on Satellite Altimetry Fenglin Tian, Yingying Zhao, Lan Qin, Shuang Long, and Ge Chen https://doi.org/10.5446/s_1945
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 599 | 44 | 27 | 670 | 33 | 15 | 21 |
- HTML: 599
- PDF: 44
- XML: 27
- Total: 670
- Supplement: 33
- BibTeX: 15
- EndNote: 21
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1