Physics-informed neural network for gridded SSH from SWOT observations considering the next-order balanced model

This study presents an evaluation of the Surface Water and Ocean Topography (SWOT) mission for monitoring riverine hydrodynamics, using the Po River (Northern Italy) as a test case. Given the recent launch of SWOT, its application to river hydraulics remains relatively unexplored and requires thorough validation against in-situ observations and specially, physically based models. We assess SWOT Water Surface Elevation (WSE), water surface slope, and recently released discharge products during the science phase, by comparing them with gauge measurements and hydrodynamic simulations over a ~300 km reach of the Po River, including the delta section (a coupled 1D/2D HEC-RAS model is employed to dynamically simulate river hydraulics).The analysis integrates multiple SWOT products, including the Level-2 High-Rate Pixel Cloud (SWOT_L2_HR_PIXC) and Level-2 River Single-Pass Vector Product (SWOT_L2_HR_RiverSP - RiverSP), explicitly accounting for quality flags and performance under different flow regimes.Results highlight the critical importance of quality-aware filtering for reliable use of SWOT observations. Good- and degraded-flagged WSE data generally show strong agreement with both in-situ measurements and model simulations, whereas suspect and bad flagged observations exhibit significantly larger discrepancies, with deviations reaching several meters. The analysis also reveals spatial patterns in SWOT performance linked to geophysical and orbital factors.Comparison of RiverSP WSE node data against 10 in-situ stations shows biases up to ~10 cm for good and degraded data, with mean Kling–Gupta Efficiency (KGE) values of 0.92 and 0.82 for high-flow and low-flow regimes, respectively. Across all 114 analysed SWOT passes (each representing a longitudinal river WSE profile), on average, 68% of node observations per pass, are flagged as good or degraded, while 12 passes contain no usable data. Nevertheless, approximately 82% of the profiles show high agreement with the hydrodynamic model (KGE ≥ 0.8), highlighting the strong performance of SWOT in reproducing river WSE profiles. Profile-based comparisons also reveal orbit-dependent performance variability among different SWOT passes.To address data limitations and improve spatial coverage, complementary Pixel Cloud products are leveraged for their higher spatial resolution, although these require extensive preprocessing, including spatial filtering and noise/outlier removal.The study further explores the spatial and temporal performance of SWOT observations in relation to (i) distance from nadir track, (ii) satellite pass orientation, (iii) river planform geometry (e.g. straight vs. meandering reaches), and (iv) flow regime (e.g. rising limb, peak, recession, low flow). Although based on a single case study, the results illustrate both the potential and current limitations of SWOT products for riverine applications. The findings emphasize the importance of integrating quality-controlled satellite observations with physically based hydrodynamic models to support operational hydrology, long-term monitoring, and decision-making for flood and drought risk mitigation in inland-to-coastal environments. The proposed methodology is readily transferable to other river systems for inter-basin comparative analyses under diverse hydraulic conditions.

The 29 July 2025, M w 8.8 Kamchatka earthquake caused a major tsunami in the west Pacific Ocean. We use the sea surface height measurements from the recently launched wide-swath satellite altimeter, Surface Water and Ocean Topography (SWOT) mission, to extract the tsunami signal. The ascending pass (P0267) of SWOT mission captured the perturbation on the ocean surface in two-dimensions after about 70 min. The tsunami signal sampled by SWOT has a peak amplitude of 0.7 m spread across a horizontal distance of ∼250 km. We compare the tsunami signal extracted from SWOT with the wave fields simulated using the seafloor deformation computed from co-seismic fault slip model. SWOT observations could capture major features of the simulated wave field with a correlation coefficient (r) of 0.77. Our results suggest that rapid, two-dimensional imaging of tsunami waves by SWOT could improve both earthquake source estimation and tsunami wave predictions, which are important for the mitigation of tsunami-related hazards.

In the near future, the Surface Water Ocean Topography (SWOT) mission will provide images of altimetric data at kilometric resolution. This unprecedented 2-dimensional data structure will allow the estimation of geostrophy-related quantities that are essential for studying the ocean surface dynamics and for data assimilation uses. To estimate these quantities, i.e., to compute spatial derivatives of the Sea Surface Height (SSH) measurements, the uncorrelated, small-scale noise and errors expected to affect the SWOT data must be smoothed out while minimizing the loss of relevant, physical SSH information. This paper introduces a new technique for de-noising the future SWOT SSH images. The de-noising model is formulated as a regularized least-square problem with a Tikhonov regularization based on the first-, second-, and third-order derivatives of SSH. The method is implemented and compared to other, convolution-based filtering methods with boxcar and Gaussian kernels. This is performed using a large set of pseudo-SWOT data generated in the western Mediterranean Sea from a 1/60 ∘ simulation and the SWOT simulator. Based on root mean square error and spectral diagnostics, our de-noising method shows a better performance than the convolution-based methods. We find the optimal parametrization to be when only the second-order SSH derivative is penalized. This de-noising reduces the spatial scale resolved by SWOT by a factor of 2, and at 10 km wavelengths, the noise level is reduced by factors of 10 4 and 10 3 for summer and winter, respectively. This is encouraging for the processing of the future SWOT data.

Lakes are among the most prevalent and predominant water repositories on the Earth's land surface. A primary objective of the Surface Water and Ocean Topography (SWOT) satellite mission is to monitor surface water elevation, area, and storage change in lakes globally. To meet this objective, prior information on lakes, such as locations and benchmark extents, is required to organize SWOT's KaRIn observations for computing lake storage variation over time. Here, we present the SWOT mission Prior Lake Database (PLD) to fulfill this requirement. This paper emphasizes the development of the “operational PLD,” which consists of (a) a high‐resolution mask encompassing approximately 6 million lakes and reservoirs that meet the minimum size criterion of 1 ha, as defined in SWOT’s lake observation science goals, and (b) multiple operational auxiliaries that support the lake mask in generating SWOT's standard lake vector data products. We built the prior lake mask by harmonizing the UCLA Circa‐2015 Global Lake Dataset and several state‐of‐the‐art reservoir databases. Operational auxiliaries were produced from multi‐theme geospatial data to provide essential information for PLD functionality, including lake catchments and influence areas, ice phenology, relationship with SWOT prior rivers, and spatiotemporal coverage by SWOT overpasses. Globally, over three quarters of the prior lakes are smaller than 10 ha. About 97% of the lakes, constituting half of the global lake area, are fully observed at least once per orbit cycle. The PLD will be recursively improved throughout the mission lifetime and serves as a critical framework for organizing, processing, and interpreting SWOT observations over lacustrine environments with fundamental significance to lake system science.

The future Surface Water and Ocean Topography (SWOT) mission aims to map sea surface height (SSH) in wide swaths with an unprecedented spatial resolution and subcentimeter accuracy. The instrument performance needs to be verified using independent measurements in a process known as calibration and validation (Cal/Val). The SWOT Cal/Val needs in situ measurements that can make synoptic observations of SSH field over an O(100) km distance with an accuracy matching the SWOT requirements specified in terms of the along-track wavenumber spectrum of SSH error. No existing in situ observing system has been demonstrated to meet this challenge. A field campaign was conducted during September 2019–January 2020 to assess the potential of various instruments and platforms to meet the SWOT Cal/Val requirement. These instruments include two GPS buoys, two bottom pressure recorders (BPR), three moorings with fixed conductivity–temperature–depth (CTD) and CTD profilers, and a glider. The observations demonstrated that 1) the SSH (hydrostatic) equation can be closed with 1–3 cm RMS residual using BPR, CTD mooring and GPS SSH, and 2) using the upper-ocean steric height derived from CTD moorings enable subcentimeter accuracy in the California Current region during the 2019/20 winter. Given that the three moorings are separated at 10–20–30 km distance, the observations provide valuable information about the small-scale SSH variability associated with the ocean circulation at frequencies ranging from hourly to monthly in the region. The combined analysis sheds light on the design of the SWOT mission postlaunch Cal/Val field campaign.

Bogotá, the capital of Colombia, relies on one of the largest and most complex urban water supply systems in the country. Drinking water is primarily sourced from high-altitude reservoirs located within the Chingaza National Park, situated in the Andean páramo ecosystems surrounding the metropolitan area. Beginning in late 2023 and continuing into 2024, severe drought conditions linked to the El Niño phenomenon led to historically low storage levels in the Chingaza system. As a consequence, in April 2024, Bogotá implemented water rationing for the first time in recent decades.In this context, this study evaluates the potential of satellite-based observations to support reservoir monitoring and water resources management in Bogotá. We analyze water surface elevation (WSE) and water surface area (WSA) for the Chuza and San Rafael reservoirs—both part of the Chingaza system—by integrating in situ observations with products from the Surface Water and Ocean Topography (SWOT) mission and Sentinel-2 imagery.First, WSE estimates from SWOT Level-2 products (LakeSP and Raster) were validated against observed WSE between September 2023 and February 2026. Over the same period, WSA derived from SWOT and Sentinel-2 was validated against in situ WSA estimated from reservoir hypsometric curves.Results show an excellent agreement between SWOT LakeSP WSE and observations for the Chuza reservoir, with a Pearson correlation coefficient of 0.9934. In contrast, performance for the San Rafael was substantially lower, with a correlation of 0.5971 and a systematic negative bias of −8.83 m, indicating reduced accuracy of SWOT-derived WSE in this smaller reservoir. Similar patterns were observed for the SWOT Raster product with moderate correlation for Chuza (0.7138), and large discrepancies for San Rafael. In contrast, WSA time series derived from the Normalized Difference Water Index (NDWI) from Sentinel-2 exhibited acceptable performance for San Rafael, with a correlation of 0.8535 and a bias of −0.37 km², and 0.6207 correlation and -0.61 km² bias for the Chuza reservoir.Overall, the results demonstrate the strong potential of SWOT and Sentinel-2 products for monitoring strategic water supply reservoirs in the Colombian Andes, while also highlighting pronounced performance differences linked to reservoir size, shape and surrounding topography. The findings emphasize the usefulness of these satellite products for hydrological applications in the Colombian Andes but also underscore challenges such as persistent cloud cover and the need for more robust algorithms that integrate the high precision of SWOT with complementary datasets to improve area estimation.

SWOT is a pathfinder mission using new technology to address transformative questions on energy and water of the Earth System in a warming climate.  The excess heat energy entering the Earth system as a result of the greenhouse effect is largely stored in water, and changes in the water cycle and water resources have profound effects on life on Earth.             SWOT is a next generation radar altimeter that uses synthetic aperture radar interferometry to measure the elevation of water surface over both continents and oceans in two dimensions with a radar footprint 1000 times smaller than that of a conventional altimeter. SWOT will cover the world between 78N and 78S every 21 days, leaving only small gaps comprising <5% of Earth’s surface.  More than 90% of the heat from global warming since the industrial revolution has been absorbed and stored in the ocean.  A major part of this process takes place in the ocean on scales too small to be observed from space in the past.  SWOT will improve the two-dimensional spatial resolution of sea surface height from present 200 km to 20 km to address the processes of heat uptake from the atmosphere. In a warming climate earth’s water cycle is accelerating, making it difficult to track and manage water resources as well as predicting floods and droughts.  The areal extent of surface water on land can be observed by conventional spaceborne sensors, but the volume of surface water in lakes and rivers will be surveyed by SWOT from space for the first time.  The numbers of rivers and lakes to be surveyed by SWOT are orders of magnitude more than the present observations. The high-resolution data of SWOT near the coasts will allow us to study sea level variations in unprecedented detail. Storm surge and other impacts like salt water intrusion and river diversion will be exacerbated by the continuing sea level rise.  SWOT data will help improve models to monitor and forecast these impacts. After nearly 20 years’ development, SWOT was launched on December 16, 2022 as a joint mission of NASA and the French Space Agency, CNES, with contributions from the Canadian Space Agency and the UK Space Agency. The satellite system was fully deployed within a week of launch and is in a 3-month phase of engineering checkout.  A 3-month calibration and validation phase will start afterwards in the one-day repeat initial orbit, which will transition into a 21-day repeat orbit during the science phase of the mission in mid 2023.  The release of SWOT data to the public for evaluation is expected to take place 10 months after launch.  The status of the mission at the end of April will be reported by this presentation.

The Surface Water and Ocean Topography (SWOT) mission provides a good opportunity to study fine‐scale processes in the global ocean but whether it can detect balanced submesoscale eddies is uncertain due to the “contamination” by unbalanced inertial gravity waves. Here, based on concurrent observations from SWOT and a mooring array in the northwestern Pacific, we successfully captured two submesoscale cyclonic eddies with negative sea level anomalies (SLAs) in spring 2023. We find that the SLA amplitude and equivalent radius of the first (second) eddy are 2.5 cm and 16.0 km (2.0 cm and 18.8 km), respectively. For both eddies, their vertical scales are around 150 m and their horizontal velocities and Rossby numbers exceed 15.0 cm/s and 0.4, respectively. Further analysis suggests that similar submesoscale eddies can commonly occur in the northwestern Pacific and that SWOT is capable to detect larger submesoscale eddies with scales greater than ∼10 km.

Mitigating errors in marine gravity recovery induced by sea level variability in SWOT observations

The new Surface Water and Ocean Topography (SWOT) satellite mission aims to provide sea surface height (SSH) measurements in two dimensions along a wide-swath altimeter track with an expected effective resolution down to 15–30 km. In this context our goal is to optimize the design of in situ experiments aimed to reconstruct fine-scale ocean currents (~20 km), such as those that will be conducted to validate the first available tranche of SWOT data. A set of Observing System Simulation Experiments are developed to evaluate different sampling strategies and their impact on the reconstruction of fine-scale sea level and surface ocean velocities. The analysis focuses (i) within a swath of SWOT on the western Mediterranean Sea and (ii) within a SWOT crossover on the subpolar northwest Atlantic. From this evaluation we provide recommendations for the design of in situ experiments that share the same objective. In both regions of study distinct strategies provide reconstructions similar to the ocean truth, especially those consisting of rosette Conductivity Temperature Depth (CTD) casts down to 1000 m and separated by a range of distances between 5 and 15 km. A good compromise considering the advantages of each configuration is the reference design, consisting of CTD casts down to 1000 m and 10 km apart. Faster alternative strategies in the Mediterranean comprise: (i) CTD casts down to 500 m and separated by 10 km and (ii) an underway CTD with a horizontal spacing between profiles of 6 km and a vertical extension of 500 m. In the Atlantic, the geostrophic velocities reconstructed from strategies that only sample the upper 500 m depth have a maximum magnitude ~50% smaller than the ocean truth. A configuration not appropriate for our objective in both regions is the strategy consisting of an underway CTD sampling one profile every 2.5 km and down to 200 m. This suggests that the thermocline and halocline need to be sampled to reconstruct the geostrophic flow at the upper layer. Concerning seasonality, the reference configuration is a design that provides reconstructions similar to the ocean truth in both regions for the period evaluated in summer and also in winter in the Mediterranean.

This study evaluates the feasibility of applying the Estimating the Circulation and Climate of the Ocean (ECCO) data assimilation (DA) framework to a submesoscale-resolving model [Massachusetts Institute of Technology General Circulation Model (MITgcm), at 1-km grid resolution]. This is in preparation for future studies to understand and assimilate the novel swath measurements of sea surface height from the Surface Water and Ocean Topography (SWOT) satellite mission. The model domain is centered at the SWOT calibration/validation (CalVal) site, located 300 km offshore of Monterey Bay, California. We assimilate vertical profiles of temperature and salinity from a linear array of three SWOT prelaunch CalVal moorings, between September and December 2019. Two model solutions are analyzed: 1) a nonassimilating forward simulation termed “first-guess” and 2) an optimized solution that assimilates the in situ observations. Both runs are nested within the global 1/12° Hybrid Coordinate Ocean Model that uses Navy Coupled Ocean Data Assimilation (HYCOM/NCODA) analysis. We evaluate the performance by comparing the two model solutions against assimilated and withheld in situ observations. We show that by assimilating hydrographic data, the model performance over the first-guess solution is improved with an error-to-observation reduction of 30%–45% for temperature, 14%–41% for salinity, and 44%–56% for steric height. Over the study period, the average steric height error at the three assimilated moorings was 1.27 cm for the optimized solution versus 2.6 cm for the first-guess solution. A comparison to withheld glider observations shows that the optimized solution outperforms the first-guess solution with an error-to-observation reduction of approximately 38% in steric height (1.5 versus 2.4 cm). This study indicates, for the first time, that the MITgcm–ECCO framework can be successfully applied to the reconstruction of submesoscale ocean variability, via the nesting of a high-resolution regional domain into a global outer domain.

Evaluating SWOT water level information using a large scale hydrology simulator: A case study over India

The volume variability and the hydrological functioning of the thousands of lakes in the Sahelian region are poorly known. The recently launched Surface Water and Ocean Topography (SWOT) mission carrying a wide-swath Ka-band radar interferometer offers new opportunities for large-scale monitoring of lake dynamics, and overcomes the spatial coverage limitations of the nadir altimeters. Here, we evaluate the performance of two SWOT data products, namely the PIXel Cloud (PIXC) and the Lake Single Pass (LakeSP), over sixteen small and medium-sized lakes in the Central Sahel. For both products, Water Surface Elevations (WSEs) are in excellent agreement with in-situ data on two lakes, with 1-σ errors (68th percentile of absolute errors) between 0.06 and 0.11 m, consistently with the mission science requirements. When compared to Sentinel-3 WSE, the PIXC product shows better results than LakeSP, with 1- σ differences of 0.16 m and 0.32 m, respectively. SWOT LakeSP Water Surface Area (WSA) estimates show a general overestimation with a median bias of 17.2% compared to Sentinel2 measurements. SWOT pixel classification errors are found to affect both products, especially for LakeSP. Elevation-area relationships derived from combined SWOT PIXC and Sentinel-2 compare well with in-situ (RMSEs below 0.28 m), highlighting the capabilities of SWOT for monitoring lake volume changes once complemented by external water masks. Finally, annual water level amplitude estimates of more than 600 lakes of different sizes are derived using SWOT PIXC, emphasizing the spatial coverage potential of SWOT.

Even though altimetry has redefined our understanding of global rivers and lakes, the sparse temporal sampling of altimeters is often a cause of concern for many applications. This study explores the efficiency of temporal sampling offered by the recently launched Surface Water and Ocean Topography (SWOT) mission for hydrological applications over India. In particular, two research hypotheses are being investigated, namely a). Potential of SWOT data for enhancing flood mapping capabilities across India and b) Impact of SWOT-based discharges for calibrating a hydrological model calibration. Toward answering the first hypothesis, we considered a hypothetical launch date for SWOT, generating overpass data based on the mission's spatiotemporal orbital configuration. These overpass data were then compared with flood-affected areas identified in the Indian Flood Inventory (IFI) data to assess SWOT's potential for flood mapping. Results show that the spatio-temporal resolution of SWOT facilitates the monitoring of diverse proportions of Indian districts based on the cycle. More specifically, 0.67%, 15.79%, 29.24%, 45.54%, and 8.06% of Indian districts have one, two, three, four, and more than four observations per SWOT cycle (~21 days), respectively. To evaluate the second hypothesis, namely, the feasibility of SWOT discharge in hydrological model calibration, we created proxy-SWOT data by sampling in-situ data in accordance with the SWOT orbit configuration. Subsequently, errors were introduced into the in-situ gauge data based on recommendations from the SWOT science team. Results are presented over selected case study region of the Mahanadi river basin in India.

Eddy identification and tracking are essential for understanding ocean dynamics. This study employed the elliptical Gaussian function (EGF) simulations and the py-eddy-tracker (PET) algorithm, validated by Surface Velocity Program (SVP) drifter data, to track eddies in the western North Pacific Ocean. The PET method effectively identified large- and mesoscale eddies but struggled with submesoscale features, indicating areas for improvement. Simulated satellite altimetry by EGF, mirroring Surface Water and Ocean Topography (SWOT)’s high-resolution observations, confirmed PET’s capability in processing fine-scale data, though accuracy declined for submesoscale eddies. Over 22 years, 1,188,649 eddies were identified, mainly concentrated east of Taiwan. Temporal analysis showed interannual variability, more cyclonic than anticyclonic eddies, and a seasonal peak in spring, likely influenced by marine conditions. Short-lived eddies were uniformly distributed, while long-lived ones followed major currents, validating PET’s robustness with SVP drifters. The launch of the SWOT satellite in 2022 has enhanced fine-scale ocean studies, enabling the detection of submesoscale eddies previously unresolved by conventional altimetry. SWOT observations reveal intricate eddy structures, including small cyclonic features in the northwestern Pacific, demonstrating its potential for improving eddy tracking. Future work should refine the PET algorithm for SWOT’s swath altimetry, addressing data gaps and unclosed contours. Integrating SWOT with in situ drifters, numerical models, and machine learning will further enhance eddy classification, benefiting ocean circulation studies and climate modeling.