the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 May 2025
Predicting oceanic Lagrangian trajectories with hybrid space-time CNN architecture
Abstract. Lagrangian dynamics simulation is a challenging task, as it typically depends on integrating velocity fields, whose estimation is inherently difficult due to both theoretical and technical constraints. Neural Network approaches provide practical methods to overcome most of related complications by learning directly from data. In this paper a deep Convolutional Neural Network (CNN) for Lagrangian trajectories simulation is presented. The proposed architecture is inspired by existing Computer Vision methods, combining Long-Short Term Memory and U-Net architectures to enforce causality. Several training setups are considered, including conditional Generative Adversarial Network (cGAN) training. The results are evaluated using Lagrangian metrics.
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RC1: 'Comment on egusphere-2025-1136', Anonymous Referee #1, 03 Jun 2025
The paper introduces a modification of a CNN architecture to predict lagragian trajectories in the ocean. The work uses synthetic data simulated with a numerical model. Most of the effort of the work is focused on the presentation of the CNN architecture. The work concludes that the developed architecture correctly reproduces the underlying dynamics of the model.
The main contribution from the work lies on the development of the CNN architecture. Not much attention is paid to the underlying dynamics or to justify why the proposed method may be desirable over classical approaches. The paper's focus is more about deep learning methods than about geosciences modeling, which suggests that GMD may not be the most appropriate venue for this work.
On top of this misalignment, I have two main concerns, the first one with the rationale of the paper. In the paper's introduction, it is discussed that models are not able to capture all the relevant dynamics and that their predictions are then off with observations. However, then, the paper proceeds to derive lagragian trajectories from model's data. What would then be the gain? Why developing a deep learning method if the main information required to derive the trajectories is already computed by the model? This way to proceed (using DL methods to reproduce model results) is what is normally called an emulator or metamodel and tends to make sense when computational cost is a concern. I do not see the value of such approach in any other case, unless a compelling justification is provided.
The second concern refers to the methodology. Although I will provide more details below, I do miss many details about the input data used -which are the heart of any machine learning method- and I do miss a more robust methodology to compare the new method with classical approaches, to understand the value of the proposed approach. Therefore, my recommendation is to reject the paper. Below, I develop some of these points with more detail.
1. In my opinion, the paper is much more focused on the deep learning method developed than on the ocean dynamics that drive the trajectories mentioned in the title. This is not a problem in itself, but I wonder if a journal about geosciences modeling is the right outlet for the work. Almost all the methodological detail provided is related to the CNN used, and therefore, I believe that an artificial intelligence journal would be a much better outlet, where AI scientists will judge the method with much more rigor and knowledge that geoscientists may do.
2. The title and the introduction of the paper convey the idea that the model is going to be fed with real data, making the DL method a way to circumvent the need for modeling. Although I tend to dislike this kind of approach, I have seen methods in the geosciences (specially in atmospheric sciences) that outperform classical methods clearly. So, if the paper showed a DL method that was more able to forecast trajectories than classical methods, I would have seen value in it. However, the work focuses on emulating the results of a model, which is less interesting, since the model results will always be required to feed the model. This emulation tends to make sense when computational cost is a concern, but it does not seem to be the case in this specific work.  It is also important to note here that model emulation is one of the tasks where machine learning shines, so I would not be surprised at all that it does also in this case. However, if this is the application that the authors have in mind, I would say that the most important analysis is about the proposed DL method, and thus, an AI journal would be the better place to get a robust review of the contribution.
3. The paper requires methodological improvements. Any new method should be compared with an old one for the reader to understand the advantages of the newly proposed method. In this case, the new method is presented and many metrics computed, but without a comparison, it is difficult to evaluate the real contribution of the newly proposed model. When working with model emulators, the comparison may be done using the DL method to compute trajectories generated with the model, but that the DL method has never seen before. In the specific case of this paper, I am not really sure how the comparison could be made, and that is why I mentioned above that I see a problem with the rationale of the work.
4. Much more detail is needed about the input data used to calibrate the method. Since ML model performance heavily relies on the data used, the paper should present those data in much more detail that it does. If possible, it would also be appreciated if a figure presenting the input data was created, so that the reader can have a better picture of the data used in training. The current description is not clear enough.
5. Several figures seem to be missing in the manuscript, making it impossible to properly judge the results and conclusions of the paper. My recommendation is mostly based on the rationale, the main aim and the methodology, but I wanted to highlight this point anyway.Citation: https://doi.org/10.5194/egusphere-2025-1136-RC1 -
CC1: 'Reply on RC1', Lorenzo Della Cioppa, 01 Jul 2025
Dear reviewer,Â
thank you for your review. We found your comments very contructive and we detail our answers to each point in the attached document. We considered carefully your review and we think that it significantly contributes to the improvement of this paper.
Best regards
On the behalf of the authors
Lorenzo Della Cioppa
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AC2: 'Reply on RC1', Lorenzo Della Cioppa, 07 Jul 2025
Please note that the authors' response has been posted as a community comment.
Citation: https://doi.org/10.5194/egusphere-2025-1136-AC2
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CC1: 'Reply on RC1', Lorenzo Della Cioppa, 01 Jul 2025
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RC2: 'Comment on egusphere-2025-1136', Anonymous Referee #2, 30 Jun 2025
The authors have developed a neural network approach to predict Lagrangian trajectories. As the authors state, this is equivalent to solving an ordinary differential equation for a given integration time. The prediction of Lagrangian trajectories from known velocity fields is well-established with known inaccuracies from both the numerical integration, wind effects, and poorly resolved sub-mesoscale features when using geostrophic approximations. Â Their neural network approach requires specifying beforehand the length time of interest for both the training and the prediction. Presumably a new model would need to be trained for longer integration times, or their model would be iterated. The model requires the same velocity fields that conventional Lagrangian integration requires, in addition to temperature fields.
Given the reduced universality of their approach when compared to a simple numerical integration, the requirement of additional data sources, and the black-box nature of such machine learning, I see no reason why this method should be published. They have proposed a method with reduced utility, limited transparency, and no clear explanation why this is necessary or beneficial when compared with standard approaches.
General Comments:
The introduction is inadequate when reviewing earlier Lagrangian machine learning approaches.
Specific Comments:
L16: Qualify this statement as there is a nonzero slip velocity between a drifter and the surrounding fluid.
L25-27: This under sampling needs quantification or citation
L38: Examples of such models?
L38-40: what metrics? You need a citation here too.
L40-41: Due to the chaotic nature of ocean surface currents, no model is capable of simulating Lagrangian trajectories without error. Please clarify what you mean by this.
L41-42: Remove this sentence
L47-57: This is far from a sufficient review of recent attempts to improve models of lagrangian trajectories with deep learning or neural networks. Please perform a meaningful literature review so as to put your results in context
L115-116: You require more data to perform a task which is already mathematically well-defined (equation 1) and has well-defined numerical accuracy.
Technical Comments:
Fix your citation style
L23-25 Rephrase this sentence for clarity
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Citation: https://doi.org/10.5194/egusphere-2025-1136-RC2 -
AC1: 'Reply on RC2', Lorenzo Della Cioppa, 04 Jul 2025
Dear Reviewer,
Thank you very much for your review. We greatly appreciate your comments, which we believe contribute substantially to the improvement of the manuscript. Please find attached our detailed responses, addressing each of your points.
Best regards,
On behalf of all authorsLorenzo Della Cioppa
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AC1: 'Reply on RC2', Lorenzo Della Cioppa, 04 Jul 2025
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