Daily Global Sea Surface Ageostrophic Current Dataset from 1993&ndash;2023 via Physics-Informed Deep Learning

Cui, Guangxi; Yuen, Ka-Veng; Chen, Ying; Liu, Zhiqiang; Yang, Dingqi; Liu, Guangliang; Cai, Zhongya

doi:10.5194/essd-2026-341

Preprints

https://doi.org/10.5194/essd-2026-341

Preprints

13 May 2026

| 13 May 2026

Status: this preprint is currently under review for the journal ESSD.

Daily Global Sea Surface Ageostrophic Current Dataset from 1993–2023 via Physics-Informed Deep Learning

Guangxi Cui, Ka-Veng Yuen, Ying Chen, Zhiqiang Liu, Dingqi Yang, Guangliang Liu, and Zhongya Cai

Abstract. Surface ocean circulation shapes climate, air-sea exchange, and the transport of heat, carbon, and other tracers, yet most long-term satellite-based global datasets rely primarily on geostrophic balance and therefore miss important ageostrophic motions. Here, we reconstruct global daily sea surface circulation at 0.25° resolution from 1993 to 2023 using a physics-informed deep learning framework that integrates satellite altimetry with momentum constraints from geostrophic balance, wind stress, and nonlinear advection. The resulting dataset is dynamically consistent, with a mean momentum-balance error below 1.5 %, and reduces the median velocity error against independent mooring observations to 0.07 m s⁻¹, compared with 0.20 m s⁻¹ for geostrophic currents and 0.10 m s⁻¹ for Ekman-corrected currents. We show that geostrophic flow sets the large-scale circulation, whereas Ekman and nonlinear contributions are smaller but comparable in magnitude to each other. Although nonlinear advection contributes little to relative vorticity, it strongly shapes surface divergence and the fine-scale structure of eddy kinetic energy. Our results show that nonlinear ageostrophic flow is an essential component of global surface circulation and that neglecting it limits our ability to resolve surface transport and variability on climatically relevant scales.

Received: 02 May 2026 – Discussion started: 13 May 2026

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Preprint (PDF, 2426 KB)

Supplement (949 KB)

Download & links

Guangxi Cui, Ka-Veng Yuen, Ying Chen, Zhiqiang Liu, Dingqi Yang, Guangliang Liu, and Zhongya Cai

Status: open (until 04 Jul 2026)

Post a comment Subscribe to comment alert

RC1:
'Comment on essd-2026-341', Anonymous Referee #1, 10 Jun 2026 reply
This manuscript uses a physics-informed deep learning approach to reconstruct a global daily sea surface ageostrophic current dataset for 1993-2023. The topic is meaningful, since many existing surface current products are mainly based on geostrophic currents, or geostrophic currents with Ekman corrections, while ageostrophic processes, especially nonlinear ageostrophic motions, are less well represented. The attempt to introduce momentum-balance constraints into a neural-network framework and generate a long-term global dataset is valuable.
Major Comments
In Section 4.1, the observational validation is based on only one TAO mooring site. This example is helpful, but its representativeness is limited. Additional observational sites from different regions (such as polar regions, equatorial regions, and coastal areas), or other independent observational data, would better demonstrate the applicability of the dataset under different dynamical regimes. Whether the errors exhibit systematic differences across different ocean regions should be clarified.

Comparisons with existing mature surface current products, such as OSCAR, or other commonly used products, would strengthen the manuscript. At present, the manuscript mainly compares AC-PIDNN with geostrophic currents, Ekman-corrected currents, an iterative method, and ROMS simulations. However, readers will likely want to know how this new dataset differs from, or improves upon, existing surface current products. Such comparisons would help clarify the actual added value of the proposed dataset.

A simple ablation experiment would help show what the physics loss actually contributes. Since the first training stage already uses only Loss_data, the authors could simply save the Stage 1 output and use it as a data-loss-only baseline. Comparing this baseline with the final AC-PIDNN output using station-based observational errors and the Bal balance would make it clearer whether the later physics-informed stages provide a real improvement beyond the initial data fitting.

The data upload method on the Zenodo website may not meet the requirements of ESSD. Data must be submitted in a more appropriate manner and additional information must be provided regarding the format of the data set, file naming conventions, variable units, missing values, metadata, and whether the NetCDF files comply with the CF standard.

Specific Comments
The method description is not yet sufficiently clear, especially regarding the training labels. Based on the code provided by the authors, the input variables described in the manuscript do not seem to fully match the inputs used in the code. Also, the training labels in the code appear to be a pseudo-target obtained by adding the geostrophic current and the Ekman current, rather than an independently observed total current. This approach may be reasonable, but it should be stated clearly in the method section. Otherwise, it is hard to understand how the model moves from a geostrophic + Ekman baseline toward a nonlinear ageostrophic correction.

The manuscript mentions an activation function, but it does not specify which activation function was actually used. The final model settings should be included in the manuscript.

In Figure 4(a-c), the nonlinear advective component is relatively weak, and under the current color scale its main spatial patterns are difficult to see by eye.

Line 157 contains “Error! Reference source not found.” This should be fixed.

The Figure 3 caption contains the phrase “the second column and column,” which appears to be incorrect.

Around line 430, “Guanglinag Liu” appears to be a spelling error.

Reply
Citation: https://doi.org/10.5194/essd-2026-341-RC1
RC2:
'Comment on essd-2026-341', Anonymous Referee #2, 26 Jun 2026 reply
General assessment
This manuscript presents a global daily sea-surface ageostrophic current dataset for 1993–2023 at 0.25° resolution using a physics-informed dense neural network, AC-PIDNN. The topic is timely and relevant for ESSD. A long-term global dataset that goes beyond purely geostrophic currents could be highly useful for studies of surface transport, eddy energetics, air-sea exchange, and model evaluation.
However, I recommend major revision before publication. The dataset is potentially significant, but the manuscript does not yet provide sufficient evidence that the reconstructed currents represent physically realistic ageostrophic circulation rather than a velocity field constrained to minimize the prescribed momentum residual. The most important issues are the limited independent validation, insufficient discussion of physical assumptions, and incomplete documentation of the dataset and machine-learning workflow.
Dataset validation is not sufficient for a global ESSD data product

The main validation is based on one TAO mooring location and one ROMS regional simulation. This is not sufficient for a 30-year global dataset. The authors should provide broader independent validation using multiple observational references, such as surface drifters, additional TAO/PIRATA/RAMA moorings, OSCAR or other current products, and regional comparisons in western boundary currents, the Southern Ocean, the tropics, and eastern boundary current systems.
The current validation demonstrates some skill in selected cases, but it does not establish global reliability.
Momentum residual is not an independent validation metric

The manuscript emphasizes that the reconstructed currents satisfy the imposed momentum balance. However, the momentum residual is part of the training objective. Therefore, a low residual is expected and should not be interpreted as independent evidence that the currents are accurate.
The authors should clearly distinguish between internal consistency with the imposed equations and external validation against independent observations or simulations.
The physical problem is underdetermined

The reconstruction attempts to infer total surface currents and ageostrophic components from SSH-derived geostrophic currents, Ekman currents, coordinates, and physical constraints. However, the steady momentum equations do not uniquely determine the ageostrophic current field. Multiple velocity fields may satisfy similar residual constraints.
The authors should discuss uniqueness, regularization, and sensitivity to initialization and loss weighting. This is essential because the dataset is being presented as a physical product, not only as a machine-learning output.
Loss function design and training strategy

The novelty of this work lies primarily in the loss function design and the three-stage training strategy rather than in the neural network architecture itself. While the approach is interesting, its implications deserve further discussion.
Stage 1 trains the network using only the data loss, effectively reproducing the geostrophic current field. Stage 2 combines the data and physics losses, allowing the solution to deviate from geostrophy while satisfying the momentum balance. However, Stage 3 removes the data loss entirely and optimizes only the physics loss. Consequently, the final solution is no longer explicitly constrained by the observational prior, but instead by the momentum equations.
This raises two important questions. First, does the final training stage improve agreement with independent observations, or does it primarily reduce the momentum residual? Second, does minimizing the physics loss alone lead to a unique and physically meaningful reconstruction?
A simple ablation experiment (as suggested by Reviewer #1) comparing the outputs after Stages 1, 2, and 3 against independent observations would help quantify the contribution of each training stage and clarify the balance between observational fidelity and dynamical consistency.

Reply
Citation: https://doi.org/10.5194/essd-2026-341-RC2

Guangxi Cui, Ka-Veng Yuen, Ying Chen, Zhiqiang Liu, Dingqi Yang, Guangliang Liu, and Zhongya Cai

Supplement

https://doi.org/10.5194/essd-2026-341-supplement

Data sets

Daily Global Sea Surface Ageostrophic Current Dataset from 1993–2023 via Physics-Informed Deep Learning Guangxi Cui and Zhongya Cai https://zenodo.org/records/19966716

Model code and software

AC-PIDNN Guangxi Cui https://github.com/cgxcgxcgxcgx/AC-PIDNN

Guangxi Cui, Ka-Veng Yuen, Ying Chen, Zhiqiang Liu, Dingqi Yang, Guangliang Liu, and Zhongya Cai

Viewed

Total article views: 407 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	Supplement	BibTeX	EndNote
305	91	11	407	32	13	13

HTML: 305
PDF: 91
XML: 11
Total: 407
Supplement: 32
BibTeX: 13
EndNote: 13

Views and downloads (calculated since 13 May 2026)

Month	HTML	PDF	XML	Total
May 2026	246	77	7	330
Jun 2026	59	14	4	77

Cumulative views and downloads (calculated since 13 May 2026)

Month	HTML	PDF	XML	Total
May 2026	246	77	7	330
Jun 2026	59	14	4	77

Viewed (geographical distribution)

Total article views: 403 (including HTML, PDF, and XML) Thereof 403 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 26 Jun 2026

Download

Preprint (2426 KB)
Metadata XML

Short summary

Most long-term satellite-based global current datasets capture only large-scale flows driven by pressure differences, missing important nonlinear motions. We used satellite data and a physics-informed deep learning method to create a new global dataset, including these previously missing components. Our currents are more accurate than traditional products, and we show that motions driven by nonlinear effects strongly influence the transport of heat, carbon, and nutrients in ocean.


Total:	0
HTML:	0
PDF:	0
XML:	0