The joint CNES and NASA satellite SWOT was launched successfully on 16 December 2022 (used throughout this manuscript). It carries a Ka-band radar interferometer as the main scientific instrument. The SWOT mission aims to enhance our understanding of the global water cycle through measurements of ocean and inland surface water topography. It completed the initial calibration and test phase and has, since July 2023, been operating in its nominal 21 d science orbit .

Inland water SWOT data is available in various products with different processing granularity. The most detailed information is available in the KaRIn water mask point cloud L2 HR PIXC data set . In contrast, the L2 HR LakeSP product assigns and aggregates the PIXC data to lakes from the “prior lake database” (PLD) . River data is analogously available in the L2 HR RiverSP product . Here, we use the L2 HR PIXC data product version D as it provides the highest degree of freedom. From now on, we will refer to this dataset exclusively as PIXC.

SWOT sampling geometry is not uniform. The change of incidence angle across track is large, in relative terms, causing effective pixel spacings of ca. 60 to 10 m from close to far range . However, as noise levels increase toward the far-range, near-range observations provide higher data reliability. The along track resolution is fixed at 22 m .

We use all PIXC data within 54.7–57.2° N and 8.1–12.6° E. File duplicates are identified by the Composite Release Identifier (CRID) and product counter. Since the lakes included in the study have a sufficient number of “open water” observations, we only use class 4 PIXC data, and not “water near land” (class 3). SWOT PIXC vD data up to cycle 50, pass 180 (16 May 2026) was used. We present prior LakeSP data from Hydrocron for comparison with our approach.

The LakeSP is filtered on the summary quality indicator “quality_f” =0 (zero is best), the flag determining the cross-over calibration quality “xovr_cal_q” =0 or 1 (meaning good and suspect), and the fraction of the lake's total area covered by dark water “dark_frac” ≤0.1 . Where dark water is water with low backscatter typically representing lower quality measurements.

In-situ stations measuring lake WSE are available through Vandportalen , combining multiple operator institutions. Most gauges cover the timeframe from the first SWOT 21 d science orbit cycle over Denmark (26 July 2023) up to date. The used gauge data has a daily resolution, and the water level is referenced to the Danish height system DVR90. To assess SWOT's ability to measure relative WSE change, we remove the median offset between SWOT and the gauge on a per-lake-basis, before reporting any metric. The offset for each gauge is listed in Table . The gauge uncertainty depends on the sensor. The water level is mainly measured with pressure and ultrasound sensors, where the uncertainty is listed as 15 and 5–30 mm .

The investigated lakes are exclusively located in Denmark and are selected from the lake (danish: “sø”) vector layer product of GeoDanmark , documented in . The data set is updated cyclically every 5 years and contains permanent lakes above 100 m² in surface area. Additionally, the set of lakes used in this study is truncated below a surface area of 0.25 km², leaving the 228 lakes, presented in Fig. . The lake geometries are used to extract the relevant PIXC data. The available lake information from GeoDanmark is manually expanded by: annotating lake names, indicating whether a lake possesses a gauge, the gauge's IDs, location, and vertical reference. In total, 37 gauged lakes are used in the comparison. Their surface area distribution is shown in Fig. D in the Appendix.

Lakes within one cycle and pass can be covered by multiple tiles. We, therefore, concatenate all tiles within one unique cycle and pass before further analysis. If a given SWOT pass partially covers lakes, we do not discard the affected lake from our analysis, as long as it fulfills the selection criteria described in the following subsections. The PIXC data product contains many targets that can have vastly different WSEs at proximity. To minimize their influence, we extract the PIXC observations via the lake mask.

The SWOT WSE with respect to the EGM2008 geoid used in this work (Hswot) is based on points with the “open water” class through the following expression 1Hswot(P)=h(P)-Tsolid+Tload+Tpole(P)-Ngeoid(P), for one point (P) with the natively reported height (h) given with respect to the WGS84 reference ellipsoid , corrected for instrument and crossover calibrations, signal propagation delays due to iono- and troposphere (dry & wet) , all three earth tides (T) as provided in the PIXC product, and the geoid height above the reference ellipsoid (Ngeoid). Here we apply the EGM2008 geoid model provided in the SWOT product. Danish lakes are rarely ice covered in the winter. We therefore chose not to account for potential ice cover.

To account for outliers that persist after the spatial masking process, we utilise that SWOT surface elevations within one lake (on local spatial scales) are approximately normal-distributed. Therefore, an observation P (one point) is excluded if it is outside the 99.7 % confidence interval 2Hswot(P)∉μ-3σ,μ+3σHswot, with mean (μ) and standard deviation (σ) of the lake surface elevations Hswot for the respective acquisition. From this stage, we defined and tested six data selection criteria to understand which observation points should be used to summarize the WSE for the given timestamp. The criteria are presented in Table . We chose the median over the mean as the summary measure of the water level since it is more robust to outliers that might be missed by previous filtering. The median is applied to all points as filtered by the respective individual selection criterion (either all available points or points without a geo-flag). Where geo-flag refers to the point-wise 32 bit geolocation quality flag. In case of detected or suspected degradation the respective bits are turned to 1 according to Table 15 in the SWOT documentation . It indicates the quality of variables such as elevation h, latitude, and longitude. We use the geolocation quality flag over the other available quality flags, as it is the designated quality flag for e.g. height in the SWOT documentation .

The median WSE for a given timestamp and lake can be discarded based on WSE standard deviation, the number of points used for the median, or if too many points are geo-flagged. We found that acquisitions with fewer than 200 points produced outliers in the time series. We chose the threshold of 200 as an empirical threshold to balance retaining timestamps and removing outliers. Refer to Sect.  for further discussion. Generally, no lake is completely discarded based on the data selection criteria; it is strictly applied to the individual timestamps in the time series. Hence, if one lake's acquisition is discarded based on having fewer than 200 points, only that particular timestamp will be missing in the final time series. With this threshold, we deliberately accept less retained timestamps to trade off for “no” outliers in our timeseries. We do not perform weighting or spatial screening beyond the lake mask extraction. A flowchart of the method is shown in Fig. A in the Appendix.

The SWOT and gauge-based WSE time series have a constant offset, given the different vertical references. In addition, the SWOT KaRIn measurements are sensitive to errors in the roll angle and interferometric phase , which are addressed in the satellite crossover calibration. Hence, potential errors in the crossover correction might introduce additional, time – varying errors between the gauge and SWOT – based water level time series, similarly to what has been shown for the ocean . Hence, if present, a remaining roll error at a given time stamp would result in a larger error, between the gauge and SWOT WSE in one side of the swath and a smaller one in the other side. Danish lakes typically have seasonal WSE variations of less than 1 m, thus, even minor remaining crossover correction errors would influence the time series. We see the possibility for a time-varying residual roll error (ϵroll) that is a function of the lake's position relative to the ground track of a SWOT pass – similarly to a “slope”. It could vary from pass to pass. SWOT error sources, in particular the roll error, are discussed in detail by .

To report sensible metrics for relative WSE change, the constant offset per lake must be removed. The difference in WSE (ΔH) between the gauge (Hgauge) and SWOT is given by 3ΔH(id,c,p)=Hgauge(id,c,p)-Hswot(id,c,p), with data for all cycles (c) and passes (p) for the respective lake (id), if gauge data is available and valid surface elevations Hswot following the selection criteria of Sect.  exist. The constant offset per lake (b-) is then computed as 4b-(id)=medianΔH(id,c,p),⇒ΔH′=Hgauge-b--Hswot. The roll error depends on the lake's distance to SWOT's ground track (d∈[-60,60] km). We use the lake's centroid and define negative distances to the left of SWOT's ground track. If roll errors are present, we expect a correlation between the gauge–SWOT difference ΔH′ and the perpendicular ground track distance (d). We classify the acquisition to have a roll error if the correlation's p-value is ≤0.05 and if the ∣PCC∣≥0.7. The error budget is superimposed with random noise ϵrandom for each lake. The total error is hence conceptually described as 5ΔH(id,c,p)=b-(id)+d⋅ϵroll(c,p)+ϵrandom(id,c,p). We expect the residual roll error to occur only in some of SWOT's acquisitions and to be small. We investigate indications of the error over Danish lakes, while the main focus remains on evaluating SWOT’s capability to detect relative WSE changes in small Danish lakes.

The water level time series are evaluated per lake against gauge data. We are using the Root Mean Square Error (RMSE) and Pearson Correlation Coefficient (PCC) as performance metics. They are defined as: 6RMSE=1N∑xi-yi2,PCC=∑xi-x‾yi-y‾∑xi-x‾2∑yi-y‾2∈-1,1, with SWOT estimated water level (x), target offset removed gauge water level (y), and x‾/y‾ represent the mean. x is formed from Hswot, potentially with added corrections. Danish lakes typically have small seasonal signals (<1 m in 2023/24), deteriorating the expressiveness of the RMSE. Hence, it is important to consider both RMSE and correlation simultaneously.

To address our second research question, if SWOT inland water data contains residual roll errors, we present Fig. A, which shows the height difference (ΔH′) between the offset-removed gauge data and SWOT observations for lakes across all cycles of pass 152. SWOT observes up to 19 lakes in this pass, though data selection criteria reduce this number in individual cycles. This pass captures lakes in two hydrologically separate regions: blue markers designate lakes in Jutland, and red markers designate lakes outside Jutland. All lakes outside Jutland lie to the left of the SWOT ground track, whereas all but one Jutlandic lake lie to the right. While the ΔH′ distribution across cycles generally centers around zero, certain cycles exhibit a slight offset. Gray bars highlight cycles with a significant roll component, where the ΔH′ distributions for lakes in the right and left swaths differ considerably. Figure B–D plot ΔH′ against the distance to the SWOT ground track for three specific cycles containing a significant roll component. The slope varies across cycles and reverses direction. We use the 1σ spread of the ΔH′ distribution (shown in green) to quantify the roll error amplitude.

Figure A displays the SWOT-to-gauge error for all passes covering Denmark. Green and blue elements indicate the median ΔH′ and 1σ quantile spread (84.15 %–15.85 %) for acquisitions with and without a significant roll error component, respectively. To minimize random effects, the plot only includes the median and quantile spread for acquisitions capturing at least 10 lakes. Out of 160 such acquisitions, 29 (approximately 18 %) exhibit a significant roll error component. Figure G and H shows ΔH′ versus distance (d) for two acquisitions lacking a significant roll error; a slope is nevertheless visible. Figure B and D presents the median of the absolute ΔH′ distribution for acquisitions with and without a significant roll error component; both medians remain close to each other for the investigated lakes. Figure C and E shows the distribution of the 1σ quantile ΔH′ spread for these two categories, demonstrating a wider spread for acquisitions with a significant roll error. Aggregating these distributions yields a median ∣median(ΔH′)∣ of 1.79 cm. The spread across all acquisitions has a median of 5.43 cm and reaches 12.60 cm at the 0.95 quantile.

The cross-track variation in SWOT’s sampling geometry directly influences the operational performance of our 200 observation threshold. Because near-range pixel spacing is significantly larger (≈ 60 m) than far-range spacing (≈ 10 m), small lakes located in the near-range inherently yield fewer PIXC observations per pass, making the 200-point threshold harder to satisfy. Conversely, near-range observations benefit from lower noise levels and higher individual point reliability. While implementing an adaptive threshold based on a lake's cross-track position could potentially maximize temporal resolution, we chose to favor a uniform threshold to maintain pipeline simplicity and interpretability. Given that our uniform filtering approach already preserves a higher temporal resolution than the standard filtered LakeSP product, we think this choice is justified.

Similarly, our decision to restrict data extraction to the “open water” classification may limit analysis of small or narrow, elongated lakes, which naturally exhibit a higher proportion of “water near land” pixels. However, our results demonstrate that this constraint does not introduce a significant disadvantage at the spatial scales investigated in this study. For instance, Tivolisøen (the smallest gauged lake in this study, Fig. A) and Valsølille Sø (an irregularly shaped lake, Fig. ) display robust performance metrics that align well with the overall median of the 37 investigated lakes, confirming the “open water” restriction to be viable for local lake level monitoring within our study's size and hydrologic domain.

The aim of this study is to assess SWOT’s capability to capture relative changes in WSE in small Danish lakes, rather than absolute elevations. To derive the relevant metrics, we removed the median offset between SWOT and gauge measurements (b-). This adjustment is sufficient for evaluating SWOT’s performance in detecting relative WSE changes. Consequently, investigating the origin of the removed offset lies beyond the scope of this study.

Criterion 6 matched the performance of criterion 4 while eliminating flagged data. We chose to adopt it as the more conservative selection strategy for this paper. By doing so, we aim to reflect the importance of producing accurate WSE measurements that are not contaminated by outliers. Our experiment's results highlight the critical trade-off between standard data products and customized lower-level processing. While the operational LakeSP product provides accurate WSE estimates with slightly better metrics, our filtering approach for the HR PIXC data preserves substantially more valid timestamps, thereby maximizing the temporal resolution necessary for robust local lake monitoring and other hydrologic applications. Especially for lakes with highly variable WSE patterns: even in Tivolisøen (Fig. A) peaks in WSE (November 2023 to February 2024; March to Mai 2024; January to March 2026) are completely missed by filtered LakeSP, but retained by our approach. This demonstrates that, despite similar metrics, our approach displays a clear advantage over LakeSP, given its higher temporal resolution.

While both our approach and the baseline LakeSP product aggregate WSE values from the SWOT PIXC product, two methodological choices separate the pipelines. First, LakeSP includes “dark water” and “water near land” pixels, whereas we restrict extraction strictly to the “open water” class. Second, LakeSP dynamically adapts the initial Prior Lake Database mask instead of utilizing a static mask. Specifically, “dark water” observations often carry higher noise levels, and the dynamic mask can inadvertently expand over shoreline features – such as wet soil – misclassified as water (Fig. F). By relying on a static mask and open-water pixels, our method circumvents these noise and misclassification pathways, reducing non-water artifacts and thus preserving a greater number of valid timestamps.

For global use cases or applications, where the temporal resolution is not of the highest priority, but ease of use and computational resources, we see LakeSP as preferable. Querying LakeSP from Hydrocron takes seconds per lake. Querying commuted lake level values from our approach from a local database is comparable to that. However, computing the PIXC data takes about one to two minutes per SWOT pass over Denmark – this has to be done only once.

In the presented timeseries (Fig. ), the poor correlation observed at Søby Sø indicates that the lake's small WSE seasonal signal falls within the SWOT error budget. In contrast, the strong performance metrics at Tivolisøen demonstrate SWOT's capability to successfully monitor very small water bodies when they exhibit a high dynamic range. This shows, that a smaller lake surface area does not automatically result in worse mapping performance; the lake's annual hydrological amplitude must be considered concurrently.

The analysis on the temporal coverage of SWOT over Danish lakes highlights SWOT's capability to resolve the majority of WSE variations across the 37 studied lakes. While traditional missions like Sentinel-6 or Jason also achieve 10 d temporal resolution, their reliance on 1D ground tracks inherently limits the number of observable lakes. In contrast, SWOT's groundbreaking 2-D imaging capability allows it to monitor small lakes at high temporal frequencies that were previously unreachable. By successfully capturing these dynamics, SWOT advances our understanding of small lake hydrology and provides essential, high-resolution data to support water resource management for both policymakers and local communities.

A potential limitation of our proposed workflow concerns the reliance on a static water mask, as the resulting time series depend on the initial mask quality and the degree of seasonal variation in a lake's surface area. While Denmark features high-quality baseline masks and relatively stable lake extents, we evaluated this dependency by artificially expanding and shrinking the target lake polygons by 20 m. This buffer adjustment simulates both spatial uncertainties in the base mask and seasonal fluctuations in lake boundaries.

Modifying the polygons shifted the median RMSE from the baseline of 5.57 to 5.18 cm for the +20 m expansion and 5.02 cm for the -20 m contraction. The median PCC adjusted slightly from 0.91 to 0.92 in both scenarios, while the median number of retained timestamps remained nearly constant, moving from 125 to 126 and 125, respectively.

These minor variations suggest that the workflow is relatively insensitive to moderate boundary adjustments, indicating that a static mask may suffice despite spatial uncertainties or typical seasonal variations. This resilience likely demonstrates that SWOT's intrinsic water classification effectively excludes non-water pixels. Nevertheless, we suggest caution when applying a static mask to highly dynamic hydrological regimes, e.g. where lakes regularly dry out completely or double in surface area.

For such highly dynamic environments, users could incorporate a dynamic lake mask into the pipeline without encountering structural conflict. This modification would require a temporal matching routine to pair each SWOT acquisition with the closest available lake mask in time, while keeping a static mask as a fallback option. However, a notable downstream implication involves error propagation, as high spatial uncertainty within a dynamic mask can directly distort the aggregated WSE estimate. Excessively unstable masks, such as the example shown in Fig. F, could introduce significant error; therefore, we recommend that users only implement water masks they are confident in to prevent introducing artificial noise into the final time series.

The distinct geographical distribution of the Danish lakes relative to ground track 152 enables the clear detection of systematic spatial effects within the inland SWOT PIXC data. Lakes outside Jutland lie almost exclusively in the left swath and Jutlandic lakes largely occupy the right swath, a cross-track tilt manifests as a vertical discrepancy between the two regions. Based on the cases examined in Figs.  and , we observe temporal variations in both the magnitude and direction of this slope. As the sign of the slope varies between passes, we can rule out static reference surface issues, which would otherwise remain constant in time.

We are not trying to correct or quantify the residual roll error but only want to investigate its existence. Our set-up is not capable to robustly quantify it and perform an in-depth quantitative analysis of its amplitude. This is out of scope for our study and necessitates a dedicated research paper. However, our results clearly demonstrate its presence. Approximately 18 % of the acquisitions exhibit a tilting effect, suggesting that residual roll errors regularly affect inland SWOT data products. Crucially, while this roll component does not significantly alter the overall median error of a given pass, it degrades spatial precision by expanding the overall 1σ spread of the data distribution, with noticeable deviations appearing near the far-range edges of the swath.

Consequently, while researchers can likely ignore this effect for water bodies with large WSE variations, the tilt may influence the accuracy of WSE time series for lakes with small seasonal signals. More significantly, measurements of WSS could be superimposed with the residual roll error. Rivers perpendicular to a SWOT ground track would be particularly affected. We think, future SWOT users should maintain awareness of this potential error component. To mitigate this issue, researchers could estimate and correct for the tilt using linear approximations derived from gauge networks or virtual stations distributed across both swath sides. Ultimately, while future SWOT processing baselines will likely improve upon this issue, current applications require a deliberate choice on whether addressing this residual roll error for their respective use case.

We established successfully, that our lower-level data approach can improve local lake level monitoring and that residual roll errors are present. To move beyond the circumstances of Danish lakes, we want to discuss in the following, how we foresee various environmental and geomorphological circumstances affect our processing pipeline.

Geomorphology impacts our approach in two distinct ways: first, tall flanking topography creates radar layover, which the SWOT intrinsic DEM masks, thereby reducing the number of valid observations per timestamp and potentially forcing our filter to reject lake observations that fall below the 200-observation threshold. Second, significant WSE differences along a lake's extent complicate the use of a single aggregated WSE value, introducing a sampling bias depending on where the lake was sampled by the retained SWOT pixels. While this effect remains negligible for small lakes, researchers likely should exclude extremely elongated lakes in mountainous terrain from this lower-level data approach.

Furthermore, seasonal frozen conditions alter surface properties, as ice cover degrades radar coherence, reducing the density of reliable observations and lowering overall data quality compared to open water, though the precise Ka-band scattering mechanisms over ice and snow warrant further investigation .

Conversely, submerged vegetation and turbid water do not affect the WSE measurements because the Ka-band SAR signal does not penetrate the water surface, while surrounding canopy cover only blocks penetration along the immediate shoreline, functionally mirroring a slightly undersized lake polygon or the “water near land” class which we did not use in this paper.

Meteorological factors also modulate data quality, where wind conditions directly control radar backscatter intensity through an interplay of surface roughness, Ka-band wavelength, and satellite look angles; backscatter typically increases at wind speeds up to approximately 3 m s⁻¹ but decreases beyond this threshold , hence, in high wind regime environments, we expect worse data quality.

Changing hydrological regimes may impact SWOT measurements. The static lake mask could cause error by including land. However, we expect the impact to be small as we (i) use SWOT’s intrinsic water classification by using ‘open water’ only and (ii) using the median to aggregate a unified WSE measure per lake and time stamp – dampening the impact of outliers. We confirmed this in the mask expansion experiment. At the same time, if seasonal WSE signal is highly variable, higher temporal resolution increases in importance, which is where our approach retains more time stamps than filtered Lake SP.

Finally, regarding the transferability of our 200-observation threshold, heterogeneous shorelines affect our pipeline similarly to LakeSP but do not cause significant degradation when paired with an accurate lake mask. Using all 10 passes covering Denmark, our Danish lake dataset samples across the entire swath, hence cross-track positioning does not limit transferability; instead, we see steep terrain remaining as the primary operational bottleneck due to topographic observation loss. For applications targeting smaller lakes that intrinsically yield fewer pixels, users can easily adapt this pipeline by relaxing the 200-observation threshold or incorporating the “water near land” data classification.