We assess the influence of different Eulerian geophysical input fields on Lagrangian drift simulations using DriftNet, a learning-based method designed to simulate Lagrangian drift on the sea surface. Two experiments are conducted: a fully numerical experiment (Benchmark B1) and a real-world drifters-based experiment (Benchmark B2). Both experiments are performed in two regions with different ocean dynamics: North East Pacific and Gulf Stream regions. The performance of DrifNet is evaluated with three different metrics: separation distance between simulated and ground-truth trajectories, the normalized cumulative Lagrangian separation and the autocorrelation of Lagrangian velocities. In both regions, results from B1 show that combining assimilated sea surface currents (SSC) with fully observed sea surface height (SSH) leads to greatest improvement in trajectory simulation. This configuration reduces separation distance by over 50% and significantly decreases normalized cumulative Lagrangian separation and metrics related to velocities autocorrelation functions compared to the baseline using SSC alone. On the other hand, the inclusion of sea surface temperature (SST) either alone or in combination with SSC generally degrades performance. In B2, using satellite-derived SSH, Ekman and winds velocities improves surface drifters trajectories simulation, particularly in the North East Pacific. While the satellite-derived SST in combination with reanalysis-based SSC configuration leads to better trajectories simulation in the Gulf Stream. Overall, we highlight the added value of combining multiple geophysical fields to improve Lagrangian drift simulation on both numerical and real-world experiments.
Figures & tables
Figure 1: Training and evaluation procedures of multivariate DriftNet’s extension: the input geophysical fields g over 9 days (here zonal U and meridional V components of the velocity field, SST and SSH) coupled to the intial spatio-temporal positional encoding y0 are fed to the DriftNet in order for it to generate the target trajectories to be compared to the ground-truth ones. Once DriftNet is trained, those geophysical fields are then used as input to it in order to simulate Lagrangian trajectories which are then evaluated on the set of test trajectories using evaluation metrics described in Section 3.4 .
Name
Source
Variable
Period
Spatial resolution
Temporal resolution
E1
Nature Run ( Le Traon et al.,, 2019 )
SSC, SSH, SST
2015
1/12 ∘
1 day
E2
OSSE-based assimilated free run ( Verrier et al.,, 2017 ; Verrier et al.,, 2018 )
SSC
2015
1/12 ∘
1 day
E3
GLORYS12 ( Lellouche et al.,, 2021 )
SSC
1992 - 2020
1/12 ∘
1 day
E3
DUACS ( Pujol et al.,, 2016 )
SSH
1992 - 2020
1/8 ∘
1 day
E3
OSTIA ( Good et al.,, 2020 )
SST
1992 - 2020
1/20 ∘
1 day
E3
GLOBCURRENT ( Rio et al.,, 2014 )
Ekman
1992 - 2020
1/4 ∘
1 day
Table 1: Summary description of Eulerian datasets used in the current study: Source makes reference to the used numerical or satellite product, Variable indicates the physical quantity of interest, Period the studied years. The spatial and temporal resolutions of each product are also indicated. SSC - Sea Surface Currents. SSH - Sea Surface Height. SST - Sea Surface Temperature.
Figure 2: North East Pacific: SSC velocity in m/s, SST in ∘C , SSH in m, wind velocity in m/s, Ekman in m/s. Snapshot on 01/06/2015 12:00:00 UTC.
Figure 3: Gulf Stream: SSC velocity in m/s, SST in ∘C , SSH in m, wind velocity in m/s, Ekman component in m/s. Snapshot on 01/06/2015 12:00:00 UTC.
Name
Source
Variable
Period
Temporal
resolution
L1
Ocean Parcels simulation using E1 SSC
Position
2015
6 hours
L2
Ocean Parcels simulation using E2 SSC
Position
2015
6 hours
L3
CMEMS drifters ( Etienne et al.,, 2023 )
Position
1992 - 2020
6 hours
Table 2: Summary description of Lagrangian datasets used in the current study: Source makes reference to the used numerical or satellite product, Variable indicates the physical quantity of interest, Period the studied years. The temporal resolution of each product is also indicated.
North East Pacific
Gulf Stream
D , km
LLiu
ΔRu
ΔRv
D , km
LLiu
ΔRu
ΔRv
L2
53.8
0.87
0.0086
0.016
168.3
0.75
0.01
0.02
SSC
45.4
0.70
0.12
0.12
154.6
0.63
0.16
0.14
SSH
31.2
0.32
0.06
0.07
160.3
0.70
0.07
0.06
SST
49.6
0.68
0.14
0.12
170.3
0.77
0.08
0.08
SSC, SSH
22.2
0.29
0.05
0.06
127.0
0.52
0.08
0.06
Table 3: Performance of DriftNet with different Eulerian geophysical input fields and Ocean Parcels (L2 dataset) in Benchmark B1 with respect to the reference trajectories (L1 dataset). We benchmark DriftNet scheme using as inputs data-assimilation-based SSC from dataset E2 and idealized ’fully observed’ SSH and SST fields from dataset E1. We illustrate performance in two study regions: North East Pacific and Gulf Stream. The evaluation metrics are the last time step mean separation distance ( D ), mean Liu index ( LLiu ) and error between autocorrelation functions of zonal and meridional components respectively ( ΔRu and ΔRv ). Bold indicates the best performance.
Figure 4: Examples of simulated trajectories for Benchmark B1 : Panel (a) : North East Pacific, Panel (b) : Gulf Stream. The reference trajectories simulated with Ocean Parcels using Nature Run SSC L1, the baseline ones L2 simulated using SSC from OSSE. Eight randomly-selected trajectories are superimposed to the mean relative vorticity of the Nature Run SSC.
North East Pacific
Gulf Stream
D , km
LLiu
ΔRu
ΔRv
D , km
LLiu
ΔRu
ΔRv
SSC
62.4
0.55
0.05
0.03
118.4
0.6
0.08
0.08
SSC, SSH
60.2
0.52
0.03
0.03
122.4
0.61
0.03
0.03
SSC, SST
63.6
0.55
0.03
0.02
103.2
0.51
0.04
0.03
SSC, Wind
63.2
0.55
0.06
0.06
136.4
0.7
0.08
0.08
SSC, SSH, Winds
60.1
0.52
0.05
0.04
136.2
0.65
0.1
0.1
Table 4: Performance of DriftNet with different Eulerian geophysical input fields from remote sensing and reanalysis models with respect to the reference trajectories (L3 dataset) in Benchmark B2. We indicate the considered input data: SSC, namely the velocity fields U and V from the GLORYS12 reanalysis ( Lellouche et al.,, 2018 ) , complemented by satellite-derived optimally-interpolated SSH fields ( Pujol et al.,, 2016 ) , SST fields ( Good et al.,, 2020 ) , winds fields ( Dee et al.,, 2011 ) and Ekman ( Rio et al.,, 2014 ) . We report the performance metrics in the two study regions: North East Pacific and Gulf Stream. The evaluation metrics are the last time step mean separation distance ( D ), mean Liu index ( LLiu ) and mean absolute error between autocorrelation functions ( ΔRu and ΔRv ). Bold indicates the best performance.
Figure 5: Examples of simulated trajectories for Benchmark B2 : Panel (a) : North East Pacific, Panel (b) : Gulf Stream. We depict real drifters trajectories in black (L3) and trajectories simulated with DriftNet using various input geophysical fields. Eight randomly-selected trajectories are superimposed to the mean relative vorticity of GLORYS12.
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.
Théo Archambault, Pierre Garcia, Mattia Romero +2
Amphitrite, Paris, France · Sorbonne Université, LIP6, Pequan, Paris, France · The Ocean Cleanup, Rotterdam, Netherlands +1
Floating-material transport is influenced by unresolved processes that are often absent from available circulation products. We develop a data-driven transport-learning framework for learning effective transport corrections from limited Lagrangian observations using physically motivated ocean--atmosphere diagnostics and finite-memory representations motivated in part by inertial-particle memory effects. The diagnostic representation is analyzed through predictive and sparse symbolic-discovery approaches under leave-one-trajectory-out validation. Applications to Sargassum-following drifters in the Puerto Rico region and the Gulf Stream show that the diagnostics contain transport-relevant information beyond the baseline circulation products. Multilayer perceptron (MLP) ensembles provide flexible predictive trajectory corrections, while Sparse Identification of Nonlinear Dynamics (SINDy) tests whether instantaneous or delayed sparse symbolic transport structure can be extracted from the diagnostics. The results differ across flow regimes: (i) in Puerto Rico, delayed sparse symbolic corrections provide modest but systematic improvement; (ii) in the Gulf Stream application, dynamically useful sparse symbolic corrections remain primarily instantaneous even though delayed predictive information persists. These results support finite-memory transport effects in coarse-grained floating-material transport while also illustrating the difficulty of obtaining stable delayed sparse symbolic closures.
F. J. Beron-VEra, M. J. Olascoaga, J. Morell +1
Department of Atmospheric Sciences Rosenstiel School of Marine, Atmospheric, and Earth Science University of Miami Miami, Florida, USA · Department of Ocean Sciences Rosenstiel School of Marine, Atmospheric, and Earth Science University of Miami Miami, Florida, USA · Department of Marine Sciences University of Puerto Rico Mayagüez, Puerto Rico
Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted on uniform regions because the dense particle neighborhoods required for stable gradients are applied indiscriminately, and rapid temporal drift, caused by purely local message passing that lacks a global anchor. Inspired by classical hybrid numerical solvers, we propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation. To address the spatial bottleneck, we introduce adaptive downsampling that eliminates kinematic redundancy, preserving micro-scale details on particles while aggregating compressed features onto Eulerian nodes to resolve large-scale dynamics. To counter temporal drift, we employ a cross-attention mechanism that queries these Eulerian features, using the fixed grid as a stable spatial anchor to correct trajectory deviations at every timestep. Comprehensive experiments show that this hierarchical, cross-attended design substantially suppresses error accumulation, establishing a new state-of-the-art for accuracy and rollout stability in Lagrangian fluid simulation.