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Drift Field Net: Learning Ocean Lagrangian advection fields from in-situ and satellite observations

Théo Archambault, Pierre Garcia, Mattia Romero, Anastase Charantonis, Dominique Béréziat

arXiv:2609.16288v1cs.LG

TL;DR

Accurate forecasts of Lagrangian particle drift are important for assessing plastic transport in the North Pacific Subtropical Gyre. DFN predicts surface velocity fields from satellite observations and trains them with an advection-based trajectory loss; on real drifter data, fine-tuning lowered LPD by 14% and yielded an LPD 19 km below Mercator v3.6.

  • Problem

    Directly predicting particle trajectories from gridded ocean observations is difficult, and individual-particle inference is computationally costly, despite the need for accurate drift forecasts in pollutant-accumulation regions.

    Source: §1 · p. 3, c. Particle trajectory prediction · p. 6

  • Method

    DFN predicts Eulerian surface velocity fields from satellite observations and uses differentiable advection with an observed-versus-simulated trajectory loss for Lagrangian fine-tuning.

    Source: d. Contributions · p. 6, a. Summary · p. 29

  • Results

    Lagrangian fine-tuning decreased LPD by 14% on real data, compared with 9% in OSSE, and achieved an LPD 19 km lower than Mercator v3.6.

    Source: 1) Quantitative evaluation · p. 22

  • Takeaways & Limitations

    The predicted flow fields can advect many particles efficiently, and the results support using physical constraints in deep learning for operational ocean forecasting and marine pollution monitoring.

    Source: a. Summary · p. 29

    The full ground truth is unavailable during training, making field and trajectory predictions more prone to errors.

    Source: 1) Quantitative evaluation · p. 21

Abstract

from arXiv · show

The North Pacific Subtropical Gyre (NPSG) is a major accumulation zone for floating plastic debris, resulting from basin-scale convergent ocean circulation. Effective cleanup strategies in this region rely on accurate forecasts of Lagrangian particle drift. Here, we introduce Drift Field Net (DFN), a deep neural network that predicts ocean surface flow fields from operational satellite observations. DFN is trained using a novel two-stage strategy that combines pretraining on simulated data with Lagrangian fine-tuning based on an advection-consistent loss function. This physics-informed optimization directly improves the accuracy of particle trajectory predictions. We evaluate DFN against an operational physics-based forecasting system and demonstrate the potential of deep learning for ocean surface flow prediction. On in situ drifter trajectories, DFN reduces the mean positioning error by 20 km after a 7-day forecast compared with the operational model. Furthermore, Lagrangian fine-tuning with the proposed advection loss further reduces the positioning error by 10 km, highlighting the benefits of incorporating Lagrangian constraints into the training process.

1. Introduction

Accurate surface-flow forecasts matter for tracking pollutants and supporting cleanup in the North Pacific Subtropical Gyre, but direct neural prediction of individual trajectories is computationally costly and difficult. Drift Field Net predicts Eulerian velocity fields and trains them against Lagrangian trajectories, with evaluations reporting improvements from its physics-informed loss.

1. Introduction

  • Accurate surface-flow prediction in the North Pacific Subtropical Gyre matters because basin-scale convergence accumulates floating waste there, making drift forecasts relevant to pollutant assessment and cleanup.The introduction also situates mesoscale and sub-mesoscale currents as important to climate, surface-material transport, and human activity.Source: §1 · p. 3
  • Direct neural trajectory methods require separate inference for each particle and still show errors even when the underlying velocity fields are known perfectly.The challenge is compounded by the mismatch between gridded Eulerian fields and sequential Lagrangian positions.Source: c. Particle trajectory prediction · p. 6
  • DFN predicts Eulerian velocity fields while using an advection loss to compare simulated and observed drifter trajectories.The predicted fields can then advect an arbitrary number of particles at negligible additional computational cost.Source: d. Contributions · p. 6
  • DFN uses past satellite observations of SST, SSH, and surface winds to forecast surface currents over seven days.The introduction frames it as an operational forecasting system, rather than a method only for trajectory reconstruction or delayed-time estimation.Source: d. Contributions · p. 6
  • Evaluations in simulations and real-world observations report that the physics-informed loss consistently improves trajectory reconstruction across multiple metrics.The predicted flow fields are also used to estimate plastic accumulation regions from in-situ plastic observations.Source: d. Contributions · p. 7

2. Data

The study focuses on the North Pacific region containing the Great Pacific Garbage Patch and uses satellite, drifter, and simulated observations to develop and assess current reconstruction. Its Observing System Simulation Experiment creates pseudo-observations from a reanalysis treated as the reference ocean state.

2. Data

  • The study domain spans 15°N–45°N and 165°W–115°W, encompassing the Great Pacific Garbage Patch, where buoyant plastic converges under large-scale currents.Accurate particle-drift prediction in this region is relevant to understanding plastic transport and planning cleanup and mitigation operations.Source: §2 · pp. 7–8
  • Satellite inputs include SSH, SST, and surface winds, which provide information about geostrophic circulation, advected thermal structures, and wind-driven currents.SSH gradients inform circulation through geostrophic balance; SST supplies indirect circulation information, while daily mean winds are derived from six-hourly CCMP fields.Source: a. Satellite data · p. 8
  • The study uses Global Drifter Program measurements as direct near-surface current observations, applying a one-day moving average and excluding undrogued drifters.The processing reduces high-frequency variability and limits direct wind and wave contributions to displacement.Source: b. Drifter data · p. 9
  • An Observing System Simulation Experiment generates paired pseudo-observations and known reference states by emulating realistic observational errors and sampling.The paper first assesses its methodology in this simulated-observation framework.Source: c. Observing System Simulation… · p. 9
  • For the OSSE, GLORYS fields serve as the reference ocean state, with CCMP winds used because GLORYS includes atmospheric forcing.The pseudo-observations include realistically sampled, noisy satellite altimetry and cloud-masked, noisy SST fields.Source: c. Observing System Simulation… · pp. 9–10
  • OSSE drifter trajectories are integrated from randomly initialized positions, replacing particles that leave the domain or encounter land to maintain 160 active drifters.The count corresponds to the daily mean number of drifters in the study region in 2024.Source: c. Observing System Simulation… · p. 10

3. Proposed method

The proposed method trains a network to predict Eulerian velocity fields while optimizing the resulting Lagrangian trajectories against drifter observations. Its workflow combines numerical advection, field reconstruction training options, and patch-based forecasting of seven-day currents.

3. Proposed method

  • The advection calculation evaluates gridded velocities by trilinear interpolation and advances particle positions with Euler integration.The Euler method is first-order but provides a simple, computationally efficient approximation; higher-order schemes are also possible.Source: a. Problem statement · p. 11
  • With complete velocity fields, the network can be trained by minimizing reconstruction error such as MSE; with sparse drifter measurements, the loss can instead be computed at observed positions.The paper calls the pointwise current-distance losses Eulerian loss and notes that sparse-measurement training can work without fully gridded ground truth.Source: b. Training method · p. 12
  • The proposed training method predicts Eulerian fields but uses an advection-informed loss on trajectories generated from those fields, mitigating DriftNet’s limitations while outperforming Eulerian training on Lagrangian metrics.The simulated trajectory is formed by recursively integrating the estimated velocity field from an initial position, then compared with the true trajectory.Source: b. Training method · pp. 12–13
  • The ORCast-based network takes SSH, SST, and wind observations as inputs and predicts two current components for seven forecast days from 12 input days.Spatial encoders process each variable, a temporal encoder aggregates timesteps with positional information, and separate decoders produce the current components.Source: c. ORCAst model · pp. 13–14
  • The forecast uses 400×400-grid patches at 1/30° resolution, each covering roughly 13.33° or 1,400 km.The model processes consecutive observations from day -11 to day 0.Source: c. ORCAst model · p. 14
  • Overlapping 13.3° patches are combined with Gaussian Kernel Weighted Average to smooth patch-border artifacts when producing regional currents.The reported patch stride is 10°.Source: d. Training details · p. 14

4. Experiments and results

The experiments compare Eulerian and Lagrangian training strategies in a GLORYS-based OSSE and on real drifters against Mercator v3.6. Lagrangian fine-tuning improves trajectory prediction, while additional evaluations examine current-field realism and basin-scale accumulation.

Experimental setup

  • Across the OSSE, GLORYS supplies the reference state, and evaluation compares simulated seven-day drifter positions with model-based estimates using LPD and NLPD.LPD is absolute haversine error in kilometers; NLPD divides LPD by true trajectory length.Source: §4 · p. 14, 1) Lagrangian Particle Distance · p. 16

OSSE: Lagrangian Particle Distance

  • In the OSSE, the Eulerian model fine-tuned with Lagrangian loss achieves the best LPD and NLPD, outperforming the purely Lagrangian model.The comparison evaluates seven-day drift metrics against a no-motion baseline.Source: 1) Lagrangian Particle Distance · p. 16, Table 2 · p. 17
  • The OSSE mean NLPD reaches approximately 60% of trajectory length after seven drift days, while errors for trajectories exceeding 200 km stabilize near 25% of trajectory length.Shorter trajectories have larger relative errors; the loss does not explicitly normalize errors by trajectory length.Source: 1) Lagrangian Particle Distance · p. 17

OSSE: Spatial scales dynamics

  • OSSE spectral results show decreased activity for Lagrangian-trained models versus the Eulerian model, and Lagrangian fine-tuning gives a small, consistent low-frequency improvement in PSRR.Eulerian pretraining substantially reduces errors across scales; first-day effective resolution is 171.4 km for the Lagrangian model versus 102.9 km for the other two, and seventh-day values are 285.8 km versus 190.5 km.Source: 2) Spectral analysis · pp. 19–20, Figure 5 · p. 20, Figure 6 · p. 21

Real-world experiments

  • On real drifters, Lagrangian fine-tuning decreases LPD by 14% and achieves an LPD 19 km lower than Mercator v3.6.It outperforms Mercator and the Eulerian model for approximately all trajectory lengths, except above 200 km.Source: 1) Quantitative evaluation · p. 22, Table 3 · p. 22

Real-world quantitative evaluation

  • For OSSE current metrics, both deep learning models outperform Mercator v3.6, while Lagrangian fine-tuning modestly improves direction and mean error norm but slightly degrades skill at higher velocities.The table reports current direction and error norm for real drifters.Source: 1) Quantitative evaluation · p. 23, Table 4 · p. 23

Real-world visual comparison of trajectories

  • In the real-world trajectory comparison, the Eulerian model with Lagrangian fine-tuning produces shorter trajectories and smoother, weaker FTLE fields than the Eulerian model and Mercator v3.6.The comparison uses seven days of operational forecasts with one-hour Euler integration steps.Source: Figure 8 · p. 24, 2) Visual comparison of trajectories · p. 25

Basin-scale circulation

  • A three-year simulation with 50,000 particles qualitatively reproduces the NPGP accumulation region, which overlaps areas of highest ADIS-observed plastic density.The experiment is limited by uniform particle initialization, an Eastern NPSG domain, a three-year integration, and a temporal mismatch with ADIS observations; one Eulerian forecast can advect tens of thousands of particles.Source: 3) Basin-scale circulation · pp. 25–27, Figure 10 · p. 27

5. Conclusion

Drift Field Net (DFN) uses satellite observations to forecast surface velocity fields for the following week, with three-stage training that includes Lagrangian fine-tuning. In situ drifter results show lower seven-day positioning error than the operational system, while the conclusion identifies limits and future directions for longer-term accumulation modeling.

5. Conclusion

  • Approximately 60 km mean 7-day position error on in-situ drifters, about 20 km lower than the operational Mercator system; Lagrangian fine-tuning improves DFN by a further 10 km.DFN uses daily SSH, SST, and surface winds to predict a complete surface velocity field; training proceeds through OSSE, observational-data, and Lagrangian fine-tuning stages.Source: a. Summary · p. 29
  • The seven-day prediction horizon is considerably shorter than the timescales of large-scale plastic accumulation-zone formation and evolution.The conclusion proposes longer-sequence hindcast training, which would increase computational costs and may require weekly-averaged currents.Source: b. Perspectives · pp. 29–30
  • Future inference could incorporate wind and wave forecasts, which may improve predictions of wind-driven currents but require higher temporal resolution.The paper used only past surface winds; it proposes jointly predicting geostrophic and Ekman currents or correcting geostrophic currents with wind-driven effects.Source: b. Perspectives · p. 30
  • The satellite and reanalysis datasets used are publicly available, while data developed in the study are not.Source: b. Perspectives · p. 30

APPENDIX A

Appendix A examines directional predictions after Lagrangian fine-tuning. It reports improvements at all scales on the final forecast day, with a negligible short-wavelength error increase on the first day.

APPENDIX A

  • Figure A1 summarizes the year-2024 average of one minus the ratio of directional reconstruction-error PSD to the ground-truth GLORYS directional PSD.Source: Figure A1 · p. 31
  • Directional predictions improve at all scales on the final forecast day after fine-tuning, with a negligible short-wavelength error increase on the first day.Source: Appendix A · p. 31
  • Appendix A reports improved first-day effective resolution and a general improvement in directional predictions after Lagrangian fine-tuning.Source: Appendix A · p. 31
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