The InSAR-derived SEC data in this study cover the central U.S. Gulf Coast during overlapping time periods. Because InSAR measures relative SEC with respect to a reference pixel, external constraints are required to tie InSAR estimates to an absolute reference frame. Different referencing strategies are applied for the two datasets. The first dataset (Ohenhen et al., 2024; henceforth O24) has a 50-m pixel spacing and covers the contiguous U.S. coastal zone from 2007 to 2020. O24 integrates InSAR line-of-sight (LOS) displacements from 2007 to 2011 and 2015 to 2020 with GNSS observations within a stochastic inversion framework. GNSS velocities are spatially interpolated and incorporated as distributed constraints, allowing the InSAR-derived SEC data to be directly referenced to a consistent, GNSS-defined reference frame across the domain. The second dataset (Wang et al., 2024; henceforth W24) provides SEC data with a 1-km pixel spacing for a 4-year observation window from 2017 to 2020 across the central Texas to western Mississippi coastal zone. W24 derives relative SEC maps solely from InSAR observations and adopts a reference-point-based calibration strategy. For each of the four Sentinel-1 paths, InSAR measurements are tied to a reference GNSS station located within the Sentinel-1 radar footprint. Four GNSS stations with minimal VLM (<3 mm yr⁻¹) were selected as reference calibration points, anchoring the relative InSAR estimates to the North American Plate-fixed reference frame. A Phase Reconstruction Algorithm, known as EigenSAR, was developed to mitigate severe decorrelation noise. Table 1 provides a more detailed comparison between these two datasets. In this study, we focus on the region where both datasets overlap geographically.

To evaluate the two datasets, we first converted O24 to match the pixel spacing of W24. For each pixel in W24, we applied a circular search area with a radius of 500 m (radii between 100–400 m plus 1000 m were tested, with only minor differences) to calculate the corresponding median SEC rate in the O24 dataset (mean rates were also tested, with minimal differences). The median was chosen as a representative value because it is robust to potential outliers and better captures the central tendency regardless of the data distribution within the search area. This conversion resulted in a total of 63 153 pixels.

The reference frame for O24 is the International GNSS Service 14 (IGS14), while W24 is referenced to the North American Plate-fixed frame (NA). However, the primary offset between IGS14 and NA occurs in the horizontal direction, and the vertical misalignment can be considered negligible.

For the GNSS data, we expanded the study area beyond the overlapping region of the O24 and W24 coverage to better characterize background VLM along the central U.S. Gulf Coast. This expansion allows for a more robust analysis by including a larger number of sites located in the Pleistocene landscape, immediately landward of the coastal zone. The boundary was set to 95 to 87° W and 28.5 to 31.5° N, representing the region stretching from southeastern Texas to the westernmost portion of Florida.

Daily GNSS data and the overall vertical velocities referenced to IGS14 were downloaded from the Nevada Geodetic Laboratory (Blewitt et al., 2018, https://geodesy.unr.edu/, last access: 21 January 2025). At the time of data acquisition, NGL products were aligned to IGS14, although more recent releases are aligned to IGS20. Vertical velocities over truncated timespans were independently estimated using the MIDAS algorithm (Blewitt et al., 2016). To ensure the reliability of these estimates, we applied the following criteria for GNSS site selection: (1) each site must have at least five years of continuous data; (2) data completeness must exceed 70 %; and (3) the data must overlap with the 2007–2020 period, with at least 20 % coverage within this interval.

We also compared the GNSS-derived vertical velocities referenced to NA and IGS14 frames and found them to be consistent for all GNSS sites used in this study. Similarly, GNSS velocities expressed in a regional Gulf of Mexico reference frame exhibit sub-mm yr⁻¹ vertical stability (Yu and Wang, 2016), suggesting that differences in reference-frame definition introduce only minor effects on long-term vertical velocity estimates. Therefore, reference-frame choice is unlikely to affect the vertical velocity comparison in this study.

Land cover data were obtained from the National Land Cover Database (NLCD) (https://www.sciencebase.gov/catalog/item/664e0d2bd34e702fe8744536, last access: 4 November 2024). We used the 2020 dataset to match the most recent time frame of the InSAR observations from the two datasets. Within the study area, 15 land cover types were identified in the NLCD. Pixels classified as open water were excluded, and the remaining 14 land cover types were grouped into five broader categories (Fig. S1 in the Supplement).

To identify potential anthropogenic processes that may influence GNSS vertical velocities, we examined groundwater withdrawal and the distribution of active oil and gas wells surrounding each GNSS site in the study area. For groundwater, we calculated the total volume of withdrawal within a 5 km radius centered on the GNSS site by summing yearly data (Houston et al., 2021) from 2000 to 2017. Oil and gas well information was obtained from a variety of sources, depending on the state (Figs. S2 and S3).

The SEC rates from O24 span from -5.0 mm yr⁻¹ (10th percentile) to -1.7 mm yr⁻¹ (90th percentile), with a median of -3.0 mm yr⁻¹ and a mean of -3.3 ± 1.8 mm yr⁻¹ within the study area. The O24 map shows that the most negative rates occur in three distinct bowls (Fig. 1a). In comparison, W24 SEC rates range from -6.2 mm yr⁻¹ (10th percentile) to 0.4 mm yr⁻¹ (90th percentile), with a median of -2.5 mm yr⁻¹ and a mean of -2.8±2.8 mm yr⁻¹. The W24 map includes more negative SEC bowls but they generally do not overlap with those in O24 (Fig. 1b). In Louisiana's coastal wetlands, mean subsidence rates of nearly -10 mm yr⁻¹, much higher than the mean InSAR-derived rates, have been found based on a combination of rod surface-elevation table – marker horizon measurements and GNSS data (Nienhuis et al., 2017). This supports the notion that in wetland-dominated coastal settings, InSAR primarily captures SEC rather than VLM (i.e., subsidence) because vertical accretion offsets a substantial portion of the subsidence.

Although the summary statistics of O24 and W24 may appear broadly similar, we note that the W24 dataset has a considerably wider distribution as reflected by the larger standard deviation. A Kolmogorov-Smirnov test reveals significant distributional differences (p<0.001, Fig. 1d), with a maximum divergence of 0.31 between their cumulative distributions (values closer to zero indicate greater similarity). In other words, the two datasets follow statistically distinct distributions, and striking spatial discrepancies persist across the region (Fig. 1c).

To further investigate these differences, we performed a pixel-by-pixel comparison between O24 and W24 over the entire study area. As shown in Fig. 2a, the correlation between the two datasets is weak (R2=0.05). Nearly one-third of the pixels (28 %) show an absolute SEC rate difference >3 mm yr⁻¹, and 7 % show a difference >5 mm yr⁻¹ (Fig. 1e). We subsequently stratified the comparison by land cover categories. The correlation remains weak (R2<0.05) for wetlands, agricultural land, and upland vegetation (Fig. 2b–d). A modestly stronger correlation is observed only in developed land (R2=0.3; Fig. 2e), which increases further in medium to high developed areas (R2>0.5; Fig. 2f). In contrast, the correlation is lower in low-intensity development and open-space areas within developed land (R2<0.3, Fig. S4). These results suggest that InSAR measurements are only reasonably robust in densely urbanized settings.

Applying the initial filtering criteria yielded 110 GNSS sites spanning southeastern Texas to the westernmost portion of Florida, with a mean record length of 12.6 ± 5.0 years and a median of 11.1 years. Approximately 77 % of the records began after 2007, and the latest observation time was July 2024.

In Holocene depositional settings, notably coastal Louisiana, GNSS instruments primarily measure VLM at greater depth, given a mean foundation depth ∼ 15 m below the land surface (Keogh and Törnqvist, 2019). This implies that VLM above the GNSS foundation may not be fully captured, a limitation consistent with GNSS-IR (interferometric reflectometry) observations from the same region (Karegar et al., 2020). In contrast, the more stable Pleistocene landscape located immediately landward of the coastal wetland zone is characterized by negligible sediment compaction or accretion. In this setting, foundation depth is not a concern and GNSS-derived VLM can be expected to be equivalent to SEC. Accordingly, we excluded GNSS sites located in Holocene deposits.

Next, we considered potential anthropogenic influence by focusing on the annual groundwater withdrawal (gallons per year) and oil and gas production (number of active wells) within a 5 km radius of each GNSS site. In the Houston-Galveston region of Texas, fluid withdrawal, particularly groundwater extraction, is a major driver of land subsidence (Braun and Ramage, 2020). The high density of active oil and gas wells (Figs. S2 and S3b) suggests elevated production rates that may further contribute to subsidence in this area (Wang et al., 2024). Unlike the other states, 24 out of 30 (80 %) of Texas sites have active wells (Fig. S3b), indicating pervasive human influence. Therefore, all GNSS sites in Texas were excluded. These filtering steps left 41 sites situated in the Pleistocene upland along the central U.S. Gulf Coast (Fig. 3a), with a mean record duration of 13.8±4.8 years, a mean VLM rate of -1.3±0.9 mm yr⁻¹, and a similar median rate of -1.3 mm yr⁻¹ (Fig. 3b).

Although we excluded sites to minimize fluid withdrawal and sediment compaction effects, some anthropogenic influence may still persist. For example, subsidence in Baton Rouge, Louisiana, is known to be significant due to groundwater pumping (Hurtado-Pulido et al., 2024). To further minimize the potential role of fluid extraction at the retained sites, we examined the annual groundwater withdrawal within a 5 km radius around each GNSS site. While no clear temporal trends were observed, several sites consistently show higher annual withdrawal and substantial cumulative extraction (Fig. S5). We note that a major gap separates these high groundwater withdrawal cases from the majority of the sites, and a similar gap is observed when considering the number of active, nearby oil and gas wells (Fig. S3). Accordingly, we applied an additional filter and removed five sites which may be influenced by unusually high extraction rates. The remaining 36 GNSS records, representing sites with minimal anthropogenic influence (Fig. 3a) yield mean and median VLM rates of -1.1±0.7 and -1.2 mm yr⁻¹, respectively (Fig. 3c). These results establish a background VLM rate that is relatively uniform across the Pleistocene landscape along the central U.S. Gulf Coast.

With the background VLM rate established, a test of the InSAR datasets becomes possible: the InSAR-derived SEC rates from O24 and W24 across the Pleistocene landscape may be expected to reflect VLM and should therefore be comparable. To assess this, we focused on the portion of the Pleistocene landscape covered by both InSAR datasets, along with GNSS sites within the same region (Fig. 3a). The statistics of these GNSS sites are consistent with the values reported above, with a mean rate of -1.4±1.1 mm yr⁻¹ and a median of -1.3 mm yr⁻¹ (Fig. 3d). However, SEC rates from O24 and W24 in this region show more negative mean values of -3.0±1.5 and -3.0±2.6 mm yr⁻¹, respectively (Fig. 4). Kolmogorov-Smirnov tests indicate maximum divergences of 0.67 for O24 (Fig. 4a) and 0.47 for W24 (Fig. 4b), suggesting that both InSAR-derived SEC datasets differ significantly from the GNSS-derived rates of VLM (p<0.001). However, unlike the O24 dataset which is slightly offset relative to the GNSS data, the wider distribution of the W24 dataset shows better overlap, as reflected by the lower maximum divergence. The wider distribution of W24 may also capture some additional spatial variability in SEC that is not fully represented by the GNSS data.

Recognizing that InSAR captures regional signals that sparse GNSS sites might miss, we also conducted a site-level comparison to reduce potential bias from differing spatial coverage. Specifically, GNSS-derived VLM rates were compared with InSAR-derived SEC rates within varying search radii around each GNSS site (Fig. S6). Across all radii, the mean O24 SEC rates (-2.0±0.9 mm yr-1) are consistently more negative than the mean GNSS-derived rate. At the site level, O24 and GNSS rates show a clear linear correlation (R2≈0.3) with low root mean square errors (RMSE < 1 mm yr-1) across all search radii. A comparison using the original (50-m pixel) O24 SEC within 200 m of each GNSS site yields a similar result with significantly different distributions (p=0.03). In contrast, W24 SEC rates more closely match the GNSS-derived VLM rates in terms of mean, median, and distribution, yet correlations are weaker, with RMSE values of ∼ 1.5 mm yr⁻¹ and lower R2 values. These results suggest that neither InSAR dataset fully captures the background VLM rates over the Pleistocene landscape along the central U.S. Gulf Coast.

InSAR investigations over the greater New Orleans area have identified changes in local VLM rates over different time periods (Dixon et al., 2006; Jones et al., 2016; Fiaschi et al., 2025), largely attributed to changes in groundwater extraction. Therefore, the different timespans used by O24 (2007 to 2020) and W24 (2017 to 2020) could potentially contribute to the poor correlation. To explore this possibility, we focused again on the Pleistocene region and calculated VLM rates for 2007 to 2020 and 2017 to 2020, respectively, for each GNSS site using the MIDAS algorithm (Blewitt et al., 2016).

We do not observe any significant VLM rate differences between the two time periods (root-mean-square difference of 0.7 mm yr⁻¹; Fig. S7). We also conducted a z-test, noting that the z-scores computed under the assumption of independence slightly underestimate the true z-scores due to the correlation between the two period estimates. Nevertheless, all 19 sites have |z|<1, indicating that the two period-specific rates are consistent within the combined 1σ uncertainty. Accounting for the dependency would increase the z-scores slightly, but the differences remain statistically insignificant, confirming the robustness of the comparison. In other words, temporal variation cannot explain the poor correlation between O24 and W24.

As reported above, the background VLM rate derived from GNSS sites with minimal human influence along the central U.S. Gulf Coast is in the neighborhood of -1.2 mm yr⁻¹. Since the contribution from sediment compaction and fluid withdrawal has been excluded, we focus here on other processes that may cause this subsidence rate. Faulting, which occurs mainly in discrete fault zones, is a potential mechanism contributing to observed background VLM in this region (Yuill et al., 2009; Frederick et al., 2019). However, Shen et al. (2017) estimated fault-related subsidence rates at Pleistocene sites along the central U.S. Gulf Coast to be less than -0.05 mm yr⁻¹. Furthermore, most GNSS sites used in this study are located landward of the major fault zones, ruling out faults as a major driver of the observed VLM.

The Mississippi Delta serves as the primary depocenter for sediment delivered by the Mississippi River, where Holocene sediment accumulation exceeds 100 m near the river mouth (Russell, 1936). This thick sediment load exerts pressure on the underlying lithosphere, producing downward VLM through sediment isostatic adjustment (SIA). Reconstructed SIA rates are approximately -0.15±0.07 mm yr⁻¹ in central portions of the Mississippi Delta (Yu et al., 2012). However, the modeled SIA footprint with rates up to -0.3 mm yr⁻¹ closer to the shoreline (Kuchar et al., 2018) indicates that most of the 36 GNSS sites analyzed here lie at the margin of the SIA-induced subsidence bowl, suggesting only a minimal contribution to the observed background VLM.

This leaves glacial isostatic adjustment (GIA) as the main factor. González and Törnqvist (2009) inferred a rate of GIA-driven subsidence of -0.6 mm yr⁻¹ (or slightly less) from a late Holocene Mississippi Delta RSL record. This value is also within the range – albeit toward the lower end – of predictions for this region from global GIA models (Mitrovica and Milne, 2002; Peltier et al., 2015). GIA modeling explicitly tuned to Holocene RSL observations from the U.S. Atlantic and Gulf coasts (Love et al., 2016) produced results for New Orleans, Louisiana (-0.03 to -1.44 mm yr⁻¹) and Panama City, Florida (-0.09 to -1.60 mm yr⁻¹) that overlap with the rates exhibited by the GNSS data.

A regional study that modeled GIA (alongside SIA) along the central U.S. Gulf Coast produced VLM rates up to -2 mm yr⁻¹, with a best estimate in the neighborhood of -1.3 mm yr⁻¹ (Wolstencroft et al., 2014), even though this value was considered to be anomalously high at the time. A subsequent study by Kuchar et al. (2018) suggested that the combined effect of GIA and SIA in this region resulted in a VLM rate of -0.8±0.1 mm yr⁻¹. To further evaluate modeled versus observed background VLM rates, we examined rate differences at each GNSS site (Fig. 5a, b). The agreement between site-level VLM estimates from Wolstencroft et al. (2014) and GNSS observations (Fig. 5c) suggests that GIA-driven subsidence rates in this area may be about a factor of two higher than previously believed. As a result, some regional projections of long-term RSL change (Love et al., 2016) may underestimate the GIA contribution. Using a recent GIA model that incorporates lateral variation in 3-D Earth structure, Thompson et al. (2023) successfully reconciled the complex regional pattern of RSL change in North America during the Last Interglacial. Notably, estimates along the central U.S. Gulf Coast were nearly double those obtained with a 1-D Earth model, further implying that our observed background VLM could be accurate, as simpler models may underestimate the regional signal. This would also be consistent with recently reported GNSS-derived rates from the Pleistocene basement in the Mississippi Delta by Zumberge et al. (2022) that would suggest a larger GIA contribution to regional subsidence than previously inferred.

The question, then, is how this can be reconciled with the precise late Holocene RSL constraints. We offer two possible explanations that are not mutually exclusive. First, one component of RSL change is equatorial ocean syphoning (Mitrovica and Peltier, 1991), often assumed to be -0.2 to -0.3 mm yr⁻¹ (Mitrovica and Milne, 2002). However, a more elaborate analysis of this process arrived at a wider range of -0.15 to -0.5 mm yr⁻¹ (Tamisiea, 2011). Second, recent work by Creel et al. (2024) has opened the door for possible slight global sea-level fall during the late Holocene (-0.2 to -0.3 mm yr⁻¹). Collectively, there may therefore be room to close the observed gap, but more research is needed to ascertain this.

With the large SEC discrepancies from InSAR reported above, we proceed to explore the potential causes. InSAR analysis over the U.S. Gulf Coast remains challenging, mainly for two reasons. First, interferograms are often corrupted by 10 cm or larger tropospheric turbulent noise (Emardson et al., 2003), while the expected rates of SEC are typically on the order of millimeters per year. Under such conditions, thousands of interferograms are required to achieve the desired millimeter-level accuracy. Second, much of the region is densely vegetated, and plant growth introduces random, unpredictable noise known as decorrelation (Zebker and Villasenor, 1992; Wang and Chen, 2022) which substantially limits the number of high-quality interferograms available for tropospheric noise mitigation. Furthermore, InSAR phase noise varies greatly among different interferograms over the same region, making inferred rates sensitive to the choice of interferogram subsets used in the analysis (Zebker and Chen, 2024).

Ohenhen et al. (2024) used 157 GNSS sites to validate the original pixel spacing (50 m) InSAR SEC map along the U.S. Gulf Coast, which yielded a standard deviation of 1.5 mm yr⁻¹. Wang et al. (2024) validated their InSAR SEC maps using VLM estimates independently collected at 183 permanent GNSS sites and six tide gauges. At 168 of the 183 GNSS sites, and at all six tide gauges, InSAR estimate errors were less than 3 mm yr⁻¹ (with RMSE of ∼ 2 mm yr⁻¹). Site-level comparisons between W24 and GNSS-derived VLM rates over the Pleistocene landscape along the central U.S. Gulf Coast (Fig. S6) and over Galveston County (Dehueck, 2024; GNSS surveys were independently conducted at 11 sites by the Galveston Subsidence District) both reported RMSE values within the 3 mm yr⁻¹ uncertainty range estimated in Wang et al. (2024).

Although O24 and W24 show comparable levels of uncertainty when validated against GNSS observations, significant discrepancies indicate internal inconsistencies. Differences in sensor characteristics (e.g., data fusion between L-band and C-band versus C-band only), interferometric network geometry, and coherence thresholds can each produce distinct spatial and temporal sensitivities to SEC. Processing choices, such as phase-unwrapping methods, atmospheric corrections, reference-strategy selection, and the approach to projecting LOS measurements into vertical motion, further amplify these inconsistencies. In low-coherence environments such as wetlands, small variations in filtering strategies, coherence masking, or multi-looking can lead to substantial differences in resulting SEC rates. These factors highlight the importance of communicating uncertainty to stakeholders. Based on the absolute SEC differences between O24 and W24 in the medium to high developed urban area (Fig. 1f, where InSAR performance is most reliable), an uncertainty of 5 mm yr⁻¹ (corresponding to the 95th percentile of absolute SEC differences) is recommended for regions lacking direct ground-truthing data (e.g., areas without nearby GNSS stations).

Mitigating these discrepancies requires harmonized processing frameworks, standardized reporting of metadata and assumptions, and the integration of independent constraints (e.g., GNSS, leveling, geotechnical benchmarks, rod surface-elevation table–marker horizons), as emphasized by Minderhoud et al. (2025). Similar community-driven efforts in other fields, such as the Coupled Model Intercomparison Project (CMIP) in climate science (Eyring et al., 2016) and radiocarbon dating intercomparison projects in geochronology (International Study Group, 1982), demonstrate how coordinated benchmarking and standardized protocols can substantially improve comparability and reduce structural uncertainty. Recent and upcoming InSAR missions have relatively short revisit cycles (6–12 d), which makes it possible to exploit the dramatic increase in SAR data volume to better characterize SEC as well as its uncertainties through comparing solutions derived from subsets of interferograms containing common signals of interest (Zebker et al., 2023). Future coastal InSAR products would benefit from cross-calibration exercises, shared testbeds, and open, reproducible pipelines that allow systematic comparison across datasets (e.g., OPERA, TRE, plus newer approaches). Collectively, these efforts would strengthen confidence in InSAR-derived SEC estimates and reduce interpretational uncertainty in coastal lowland environments. Moving forward, continued collaboration and systematic engagement within the InSAR community will be essential to further reduce uncertainties and improve the reliability of SEC measurements.