Introduction

The Chesapeake Bay region, which we define as the region of longitudes − 78° to −74° and latitudes 36.5° to 40°, contains the highest rates of relative sea-level rise (RSLR) on the East Coast of the United States1,2. In addition to global sea-level rise with local variations due to thermal expansion and ocean dynamics, regional and local vertical land motions (VLM) substantially contribute to changes in relative sea-level. The densely populated and ecologically valuable Chesapeake Bay region, containing largely low-lying topography, is particularly vulnerable to flooding and other coastal hazards as sea-level rise continues throughout this century3. A study conducted in 2016 predicted that with two meters of sea-level rise (estimated for some cities by the year 2100), 46,287 properties worth $14.4 billion in Virginia, 64,299 properties worth $19.6 billion in Maryland, and 11,670 properties worth $3.6 billion in Delaware are at risk of inundation4. Further, 120,000 acres of ecologically valuable wetland and marsh ecosystems may be inundated by 2100 in the southern Chesapeake Bay region alone5. Accurately quantified rates of VLM in the Chesapeake Bay region can be used to assess future relative sea-level changes and support coastal hazards planning and mitigation.

The first documented reports of VLM in the Chesapeake Bay region were from geodetic leveling surveys between 1940 and 1971, which identified subsidence with rates ranging from − 1.2 to −4.8 mm/yr6. In recent years, Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS) methods that cover various timescales have been utilized to quantify VLM in the Chesapeake Bay region as well. However, studies using InSAR7,8, GNSS9,10,11,12, or both13,14 contain significant differences both in spatial resolution and rates of VLM, including areas of localized uplift. Discrepancies are typically attributed to differing observation periods as well as high uncertainties. Thus, an accurate baseline measurement of VLM could inform monitoring of spatiotemporal variations and assessing the potential extent and magnitude of VLM in the Chesapeake Bay region. In this work, we provide a baseline VLM solution for the specific 5-year period of 2019–2023 constrained by both campaign and continuous data.

The East Coast of the United States is considered a passive margin (i.e. tectonically inactive transition zone between continental and oceanic crust), however several dynamic processes are contributing to VLM in the Chesapeake Bay region. The dominant long-term source of VLM in the Chesapeake Bay region is glacial isostatic adjustment (GIA) due to the collapse of an ancient forebulge15. Bedrock in the mid-Atlantic region is subsiding as part of the solid Earth’s response to the melting of the Laurentide Ice Sheet, which covered Canada and the northern United States at the Last Glacial Maximum (~ 19–26 ka16,17). Present-day rates of GIA-driven subsidence are estimated between approximately − 1 to −2.5 mm/yr throughout the Chesapeake Bay region9,10,15. Mantle-induced dynamic topography has been proposed as another source of long-term VLM in the Chesapeake Bay region18,19,20,21, however estimates for present-day rates of dynamic topography throughout the East Coast of the United States are negligible (within ± 0.1 mm/yr) when considering present-day rates of VLM22. Moreover, some dynamic topography studies predict uplift instead of subsidence23,24. Additional tectonic processes that may affect VLM in the Chesapeake Bay region include intraplate lateral stress-induced deformation25 and effects associated with ridge-push produced by gravitational effects of the cooling oceanic North American plate26. The Chesapeake Bay region is underlain by the Northern Atlantic Coastal Plain (NACP) aquifer system, which is characterized by sedimentary strata composed of highly permeable aquifer layers interspersed with less permeable confining layers that restrict groundwater flow27. Heavily relied upon for regional water supply, certain aquifers in this system have experienced water-level declines of more than ~ 38.5 m (~ 100 feet) from their predevelopment levels resulting in sediment compaction and rapid localized subsidence, particularly during the last century7,16,28,29. Further, there may be shifts in the VLM signal associated with present-day geologic effects, such as compaction in brecciated strata, that resulted from the ~ 35 Ma Chesapeake Bay meteor impact crater16.

Global Navigation Satellite System (GNSS) measurements, specifically U.S. Global Positioning System (GPS) measurements, in both continuous and campaign-mode have been used to measure Earth’s surface movements since the 1980’s. Campaign-mode surveys involve deploying GNSS instruments for short periods of time, such as 72 h, repeatedly, usually over multiple years. Although campaign-mode GNSS surveys generally improve spatial resolution, they tend to produce higher uncertainties in velocity estimates compared to continuous GNSS observations30,31,32. However, extending both the number of campaign epochs33 and observation durations34 can improve the precision of positions and velocities derived from campaign GNSS. Another challenge of obtaining accurate and precise vertical velocities from campaign-mode GNSS surveys is handling the effects of seasonal variations stemming from atmospheric and hydrological sources. Previous work found that the velocity bias, in the presence of an annual signal, is unacceptably large using less than 2.5 years for continuous GNSS data and becomes less significant beyond 4.5 years33. We attempt to mitigate velocity bias in our campaign data by observing the sites annually within the same season (October-November), ensuring our dataset spans more than 4.5 years, and whenever possible, using the same equipment at each site.

The main objective of this paper is to present and discuss a new, present-day VLM solution of the Chesapeake Bay region that leverages an advanced interpolation scheme (see Sect. “GNSS Processing”) derived from a new GNSS velocity solution of both campaign and continuous data35. The VLM solution is provided in an online repository35 such that it can be used by stakeholders in the region affected by land subsidence. Our findings indicate a pattern of regional subsidence with a range of −2.97 to −0.40 mm/yr and an average rate of −1.4 mm/yr. Overall, 1-sigma uncertainties are determined to be at less than 1 mm/yr with only a few exceptions. This subsidence signal continues to be a key component of the relative sea-level rise rates and associated coastal hazards affecting the Chesapeake Bay region.

Methods

Data collection

From 2019 to 2023, annual GNSS campaigns were held each year for a total of 5 years of observations in October through early November to minimize variations in seasonal signals. We occupied up to 61 geodetic benchmarks each year using tripods that are measured annually to a precision of 0.1 mm. GNSS antennas are mounted on the tripods and centered over benchmarks by 10 collaborating agencies including state, federal, and university-led efforts. Benchmarks include various monumentation types (Figure S1), however the majority are deep rod types that extend to refusal at depths between 3 and 6 m. Therefore, observations represent tectonic and confined aquifer processes but likely exclude the effects of the surficial aquifer. High precision, dual-frequency GNSS receivers were used at all sites to specifically collect Global Positioning System (GPS) data. Our methods for data collection and technical validation are described in Troia et al.36. We aimed to collect at least 72 h of continuous data for each campaign site, and we did not process any days of data with less than 12 h of observations. Of the 61 GNSS campaign sites that were occupied, 50 sites contained enough high quality data that met our qualifications to be processed for the final solution. RINEX2 files (i.e. a standardized format for level 2 unprocessed GNSS satellite observation data) for 20 global reference stations were accessed from the EarthScope37, SOPAC38, and CDDIS39 repositories (NLIB, GOLD, MDO1, PDEL, YEBE, GODZ, HLFX, UNBJ, STJO, SCH2, CHUR, FLIN, PIE1, DRAO, SCUB, CRO1, ABMF, LPAL, FUNC, MAS1), of which 5 were located in the Chesapeake Bay region (GODN, GODS, HNPT, MRC1, USN8). Locations of these global reference stations are plotted in Figure S2. The continuous GNSS stations used in this study collect positioning data information every 15–30 s throughout the year. Beyond the 20 global reference stations, we obtained RINEX2 files for 120 continuous GNSS stations in the Chesapeake Bay region to include in our processing. Continuous stations that contained less than 2.5 years of data were excluded from our GNSS velocity solution33 that combines both campaign and continuous data.

GNSS processing

We use the software GAMIT-GLOBK v10.7140 to process, specifically, the GPS data. We use the doubly-differenced GPS phase observations, combined with the 20 continuous International GNSS Service (IGS) stations, to estimate orbital parameters and loosely constrained daily positions with associated variance-covariance matrices (quasi-observables as h-files), satellite state vectors with orbits fixed, phase ambiguities, seven tropospheric delay parameters per station per day, and two horizontal tropospheric gradients per day. Solid Earth tides, ocean loading, and polar tides are corrected for by applying International Earth Rotation Service standards41 and absolute antenna phase center corrections (IGS14) are based on the work by Schmid et al.42. We employ the IGS final orbits and Earth Orientation Parameters for quasi-observables (International Earth Rotation Service, 2003). These quasi-observations are then combined with global solutions (h-files) processed at the Massachusetts Institute of Technology (MIT) to solve for precise positions and velocities taking into account all 20 reference stations in a global reference frame (IGB14) by minimizing position estimates at common, stable IGS reference stations. When realizing the reference frame, we did not estimate scale.

We produce coordinate time-series data also using the software GAMIT-GLOBK v10.7140 using the daily solutions to identify outliers and discontinuities. The time-series analysis uses all 20 reference stations stated above for robustness against outlier stations on some days. Example campaign and continuous time-series are shown in Fig. 1. We use a site and day dependent, elevation angle dependent white noise model for the phase data and apply a correlated noise model to the phase observations and quasi-observations to obtain realistic uncertainties for position coordinates and velocities for both campaign and continuous sites. To apply a correlated noise model to the campaign data, we first estimate the median random walk values for the north, east, and up components of all continuous sites in the Chesapeake Bay region (N = 0.98e-7 E = 1.10e-7 U = 7.44e-7 m2/yr) and then apply these values as a simplified random walk noise model for the campaign sites40. With this approach, we add +- 2 mm of correlated noise over the 5 years to the Up component. In addition, noise models for flicker noise, annual and semi-annual seasonal signals, and temporally correlated noise (i.e., First-Order Gauss Markov, aka. FOGMEX) are applied to the continuous data43,44. Figure 2 presents the vertical velocities and 1-sigma uncertainties from the GNSS observations. Horizontal velocities are depicted in Figure S3 and provided in Table S2.

Fig. 1
Fig. 1
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Example of site position time-series that show N-S, E-W, and Up components for the campaign site TASK (left) and continuous station LOYZ (right) in the IGb14 reference frame. Site TASK and station LOYZ are approximately 40 km (~ 25 miles) apart.

Robust network imaging for vertical land motions

In a final step to produce the main contribution of this work, we interpolate the GNSS-derived vertical velocities and propagate the 1-sigma uncertainties to the interpolated values using the Robust Network Imaging (RNI) technique45, which is based on the GPS Imaging algorithm of Hammond et al.46. RNI is pertinent for interpolating vertical velocities because it is data-adaptive and robust to outliers. With RNI, vertical velocities are replaced by ‘despeckled’ rates (the weighted median) derived from the rates of nearby local campaign sites or continuous stations, which include the site or station itself, sites or stations connected to it by an iterative Delaunay triangulation scheme (Figure S4), and sites or stations that are within the median distance between the site or station itself and those connected to it. Weights are computed by 1/, where is the standard deviation of the vertical velocities. The standard deviation of the despeckled rate uses the absolute standard deviation around the median. The despeckled rates and their associated standard deviations are then used to estimate the weighted median vertical velocities at a set of gridded points. A revised Delaunay triangulation is computed on a set of points that include the evaluation point with all site and station locations. The weighted mean vertical velocity at grid points is then estimated from the despeckled vertical rates and the standard deviations of the despeckled value for all used campaign sites and continuous stations. The standard deviation in the gridded vertical velocities is based on the median absolute deviations between the gridded velocities and the original velocities at the sites and stations used. See Kreemer et al.45 for more details.

Results and discussion

In total, 175 sites and stations (50 campaign sites, 120 continuous stations, and 5 continuous reference stations within the Chesapeake Bay region) are included in our VLM solution derived from RNI of the Chesapeake Bay region. Figure 2 presents the vertical velocities and 1-sigma uncertainties for the GNSS sites and stations throughout the Chesapeake Bay region that are used in the RNI VLM solution shown in Fig. 3. Table S1 contains the GNSS vertical velocities and uncertainties of sites and stations plotted in Fig. 2. VLM at GNSS sites and stations contain some variability including 14 sites and stations that observe uplift including 6 campaign sites and 8 continuous stations. However, of these 14 sites and stations indicating uplift, only 6 are statistically significant within 1-sigma uncertainties (3 campaign sites and 3 continuous stations). Several campaign sites near continuous stations appear to have larger rates of subsidence. However, considering that the campaign sites have larger uncertainties than the continuous stations, the VLM rates are consistent within uncertainties. We note that the reference stations in our region have an average Root Mean Square value of 4.99 in the vertical component, which indicates a reasonable fit to a linear model. The average velocity rate computed from all campaign sites and continuous stations is approximately − 1.77 mm/yr with a range of −7.19 to 3.96 mm/yr and a mean uncertainty of 0.76 mm/yr. Only 5 of these sites and stations contain subsidence rates greater than 6 mm/yr. The average vertical velocity rate computed only from campaign sites is approximately − 2.30 mm/yr with a range of −7.19 to 3.96 mm/yr and a mean uncertainty of 1.47 mm/yr. The average velocity rate computed only from continuous stations is approximately − 1.58 mm/yr with a range of −6.98 to 1.18 mm/yr and a mean uncertainty of 0.49 mm/yr. Although the signal-to-noise ratio is small, only ~ 17% of our total VLM GPS observations in the Chesapeake Bay region are statistically insignificant at the 1-sigma level.

Fig. 2
Fig. 2
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Vertical velocities and 1-sigma uncertainties at campaign (circles) and continuous (triangles) stations. Stars represent reference stations. Basemap coastlines are from the full resolution version Global Self-consistent Hierarchical High-resolution Geography dataset64 plotted with Generic Mapping Tools65.

Our interpolated solution for vertical velocities using the RNI technique, which is the main contribution of this work, is presented in Fig. 3 and shows ubiquitous subsidence throughout the region. To account for the low signal-to-noise ratio, areas that are masked gray in the VLM map are statistically insignificant within 1-sigma. Future VLM interpolations could be improved in these regions by including more GNSS observations and the establishment of additional observation locations. With the RNI technique, high uncertainties are more likely to occur at locations with fewer sites and stations nearby, sites and stations containing high uncertainties attributed to factors such as shorter spans of data or more correlated noise, or locations with discrepancies in rates among neighboring GNSS sites and stations. We choose to plot areas that are near zero (ranging from − 0.5 to 0 mm/yr) to prevent misinterpreting these locations as statistically insignificant. The average rate of VLM throughout the Chesapeake Bay region is −1.38 mm/yr with a range of −2.97 and − 0.40 mm/yr and an average uncertainty of 0.98 mm/yr (see Figure S5 for uncertainties). Maximum subsidence occurs in the Hampton Roads region and the central eastern Delmarva Peninsula with the magnitude of subsidence decreasing northwards and inland.

Fig. 3
Fig. 3
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Vertical velocity solution of the Chesapeake Bay region based on GNSS observations and the RNI technique of Kreemer et al. (2020),. Areas that are masked gray in the VLM map are statistically insignificant within 1-sigma with one exception: areas that are between − 0.5 and 0 are plotted in color regardless of their uncertainties to avoid misinterpreting near-zero regions as statistically insignificant. All of these regions are located away from the coastline. VA = Virginia, MD = Maryland, DE = Delaware, PA = Pennsylvania, NJ = New Jersey.

We analyze the impacts of adding the campaign data by comparing an RNI solution using continuous data only (Figure S6) with our VLM solution shown in Fig. 3. The residual plot is presented in Fig. 4 and demonstrates where the VLM solution is different as a result of including the campaign data. Negative values indicate where VLM rates decrease after including the campaign data.

Fig. 4
Fig. 4
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The residuals between the continuous-only and combined interpolated RNI solutions. Positive values indicate where VLM velocity rates increase, and negative values indicate where velocity rates decrease after including the campaign data. VA = Virginia, MD = Maryland, DE = Delaware.

We also evaluate how VLM rates have changed over the past 50 years by comparing our computed present-day VLM rates (spanning 2019–2023) with the published rates from Holdahl and Morrison6 (HM74), which were produced using geodetic leveling surveys between 1940 and 1971 in all cases except Lewes, DE where surveys began in 1921. The reference frame of Holdahl and Morrison6 is effectively an Earth-centered, Earth-fixed (ECEF) reference frame derived by removing a global eustatic rise of + 1 mm/yr from tide-gauge trends. Although this study predates modern geodetically constrained reference frames, our VLM observations are also in an ECEF frame, thus it is reasonable to compare the two estimates of VLM. Table 1 contains the HM74 and present-day VLM rates with 1-sigma uncertainties derived from our RNI VLM solution at 51 cities throughout the Chesapeake Bay region. Figure 5 illustrates the residuals between HM74 and present-day rates of VLM using rates from our final interpolated solution. Negative residuals indicate where the subsidence has decreased since 1974, and positive residuals indicate where the subsidence has increased since 1974. From a regional perspective, we find that subsidence rates have decreased in the northern Chesapeake Bay region, particularly in Delaware, but subsidence rates have increased in the mid-Chesapeake Bay region, especially throughout the southern Delmarva Peninsula. Eggleston and Pope47 determined that the locations of maximum subsidence in Maryland and Virginia reported in HM74 coincided with areas of maximum groundwater level declines, illustrating a relationship between subsidence driven by aquifer-system compaction and rates of groundwater withdrawals. During the HM74 study period, groundwater withdrawal rates in the NACP aquifer system increased substantially, rising from approximately 3,785 m3 (~ 400 million gallons a day) in the mid-1940s to approximately 5000 m3 (~ 1,300 million gallons) a day in the early 1980’s29. In recent decades, groundwater withdrawal rates from the NACP aquifer system have remained relatively stable (Masterson et al., 2016), potentially leading to a reduction in the overall rates of present-day subsidence. Monitoring VLM in conjunction with water levels throughout the Chesapeake Bay region can support effective land and water resource management.

Table 1 VLM rates and 1-sigma uncertainties (Std.) in mm/yr for published values from HM74 vs. present-day as derived from our RNI VLM solution. Differences in the VLM rates are also shown in the last column in mm/yr. Negative values indicate the rate of subsidence has decreased since 1974, and positive values indicate the rate of subsidence has increased since 1974. Velocities at additional notable cities: Virginia Beach, VA (−2.14 ± 1.42 mm/yr), Virginia Beach, VA (−1.41 ± 0.52 mm/yr), ocean City, MD (−2.4 ± 0.5 mm/yr).
Full size table
Fig. 5
Fig. 5
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Difference VLM between the published vertical velocity rates from HM746 and present-day rates from our interpolated VLM solution. Positive values indicate that the rate of land subsidence has increased since 1974. Negative values indicate that the rate of land subsidence has decreased since 1974. VA = Virginia, MD = Maryland, DE = Delaware. Numbers below the triangles correspond to the ID# in Table 1.

Accurate estimates of VLM can refine present-day and future projections of relative sea-level rise throughout the Chesapeake Bay region. Land subsidence increases the risks associated with flooding, which can be exacerbated by the loss of flood protection provided by drowning wetlands48. To better understand potential anthropogenic factors acting in the region, Fig. 6 depicts the interpolated RNI vertical velocity solution with a GIA signal removed. The GIA signal was calculated using the preferred coastal viscosity model of Williams et al.15. Removing the GIA-driven VLM signal results in estimates of subsidence throughout large regions of the Chesapeake Bay, mostly near the coasts, with maximum subsidence of 1.58 mm/yr. However, uplift is also predicted after removing the GIA-driven VLM signal primarily inland of the Chesapeake Bay coastlines. A study that encompasses a larger region could further understanding the GIA-removed VLM signal and is beyond the scope of this work. However, one potential cause of this uplift may be the result of using a viscosity model calibrated to best fit the coastal regions of eastern North America, rather than the inland region15.

The variability in our RNI interpolated VLM solution shown in Fig. 3, as well the variable VLM shown in Fig. 6 after a GIA signal is removed, suggests there are both long-term geodynamic as well as short-term anthropogenic processes influencing VLM in the Chesapeake Bay. Of note, the increase in subsidence along the middle portion of the western shore of the Delmarva Peninsula coincides with a large low–lying, low-slope region with extensive salt marshes. These marshes stationed along the Atlantic flyway provide critical habitats for a number of at-risk bird species50. Marshes in the region have already faced considerable loss in extent51, research has demonstrated extensive marsh migration over the past 150 years52, recent acceleration in marsh migration rates53, and substantial marsh migration potential in the future54. Predictions of both the conversion of marshes to open water and the conversion of uplands to marsh within the region rely on interactions between RSLR and plant productivity55. VLM estimates from nearby sites and stations may not be adequate56,57. Improved estimates of RSLR based on new VLM estimates and well constrained rates of sea level rise, which range from 4.5 to 6.1 mm/yr across the Chesapeake Bay based on tide gauge data from 1975 to 202158, can aid in preparing for future changes and managing key resources. Further, our improved estimates of VLM can be used as a geodetic constraint to better understand large-scale tectonic processes compared to localized processes contributing to land movements throughout the Chesapeake Bay region.

Summary and conclusions

From 2019 to 2023, 5 years of campaign GNSS data were collected at over 60 sites throughout the Chesapeake Bay region in a multi-agency, collaborative effort led by the U.S. Geological Survey. We also gathered continuous GNSS data for the same time span at 120 stations in the region. We use the software GAMIT-GLOBK to process both the campaign and continuous data to produce a GNSS-derived vertical velocity solution for the Chesapeake Bay region (50 campaign sites, 120 continuous stations, and 5 continuous reference stations). We interpolate our GNSS-derived vertical land motions (VLM) and 1-sigma uncertainties using the Robust Network Imaging (RNI) technique to identify regional trends of VLM throughout the Chesapeake Bay region as the main contribution of this work. The average rate of VLM using the RNI solution is −1.38 ± 0.98 mm/yr, with a range between − 2.97 and − 0.4 mm/yr, however we find more variability at individual GNSS sites and stations. We evaluate how rates of VLM have changed over time by comparing our present-day VLM solution with the published rates of subsidence from Holdahl and Morrison (1974). We find changes in the locations of maximum subsidence since 1974, indicating meaningful shifts in VLM patterns, that may be in response to changes in adjustments in groundwater withdrawal rates. This new VLM solution can be used to better project relative sea-level changes and support the assessment of coastal hazards risk, particularly flooding, throughout the Chesapeake Bay region.

Fig. 6
Fig. 6
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Our RNI interpolated VLM solution with a GIA signal removed based on Williams et al.15. VA = Virginia, MD = Maryland, DE = Delaware. Regions that are masked as gray are associated with the RNI VLM solution that is statistically insignificant at the 1-sigma level, hence these are areas of low signal-to-noise ratios, with one exception: if the RNI VLM solution is between − 0.5 and 0, those regions are not masked to avoid misinterpreting areas that are near-zero as statistically insignificant.