Figure 2 compares GPS-derived rates of land motion to the nuisance flooding level. The latter is defined as a fixed height threshold elevation above the 1983–2001 MHHW (Mean Higher High Water) tidal datum at a given location, above which a rise in water level begins to impact lives, property, or commerce27. Thus, lower nuisance flood levels indicate a higher likelihood of flooding - the low elevation threshold is easily exceeded by even moderate flood events. The GPS and nuisance flood level data sets show moderate positive correlation (see also Fig. S3) with a Pearson correlation coefficient of 0.54 (P-value 0.02). We used a non-parametric bootstrap calculation to assess the influence of data uncertainty on the estimate of correlation coefficient, and to rigorously estimate the standard error and confidence interval of this estimate. We generate data subsets by random sampling from normal distributions with means equal to GPS rates and standard deviations equal to the rate uncertainty. We repeatedly estimate the Pearson correlation coefficient based on 107 bootstrap resamples of the data points. The resulting distribution of correlation coefficient defines the 95% bootstrap confidence interval (Fig. 3b). The bootstrap estimated Pearson correlation coefficient (the mean of bootstrapped sampling distributions) is 0.52 with estimated bias of −0.05 and standard error of 0.21. These parameters are used to form the bias-corrected and accelerated (BCa) confidence interval28 to adjust for both bias (the skewness in the bootstrap sampling distribution) and non-normality of the sampling distribution. The BCa 95% confidence interval is 0.10 to 0.84. Even the lowest value of correlation coefficient at the 95% significance level is positive. Hence there is a likely connection between subsidence and nuisance flooding. The nuisance flooding database shows a local minimum in nuisance flooding level (i.e., lowest threshold elevation, highest likelihood of flooding) near the maximum subsidence rate associated with the collapse of the peripheral bulge. Recent increases in flood frequency are focused here (Figs 2, 4 and S3). This should not be surprising - much of the eastern seaboard is a low-slope coastal plain. Coastal settlements here were established close to sea level, hence even small increases in relative sea level will have a significant impact on flood frequency.

Figure 3 (a) Scatter plot of GPS-derived vertical rate compared to nuisance flooding level. The simple Pearson correlation coefficient and the bootstrap-estimated Pearson correlation coefficient (accounting for uncertainty in GPS rates) are 0.54 and 0.52, respectively. The red shaded area is 95% confidence interval for the regression line. Error bar are 1.96σ. The bootstrap estimated slop and 95% confidence interval is significantly different from zero. (b) Histogram showing bootstrap result for correlation coefficients. The red line represents the mean of the population (0.52) and the green lines bracket 95% of the estimates (0.10–0.84). Full size image

Although the peak subsidence rate from GIA (1.5 mm yr−1) is only half the current rate of global sea-level rise estimated from satellite altimetry29, it is the dominant factor in east coast nuisance flooding because it has been operating much longer, and thus has had the largest impact on changes in relative sea level. Many coastal towns in the region were established in the late 1600’s and early 1700’s. Those established near the GIA subsidence maximum have experienced approximately 0.45 meters of land subsidence from GIA (1.5 mm yr−1 × 300 years). Combined with 1.2 mm yr−1 of global sea-level rise for 90 years (1901–1990)30 (assumed insignificant prior to 1900) and the effects of recently accelerated global sea-level rise (ranging from 2.5 mm yr−1 to 3.4 mm yr−1) over the past two and a half decades, these urban centers have experienced a total of approximately 0.6 meters of RSLR since their establishment, with 75% of it due to GIA. This area may also be experiencing recent accelerated sea-level rise due to ocean dynamics and ice-mass loss from Greenland31. Increased frequency of nuisance flooding here (Fig. 4) is thus easy to understand. The combination of factors contributing to RSLR here also puts the region at greater risk from catastrophic flooding during storm surge events.

Figure 4 Nuisance flooding frequency versus time for various latitudes, rate of relative sea-level rise for 1990-present from tide gauges, and vertical rate from GPS. The flood frequency is defined as the number of days per year above a threshold flood level (nuisance flood level), for 34 tide gauges from St John’s in eastern Canada to Mayport, Florida. “max. GIA” refers to maximum subsidence due to the collapse of a peripheral bulge as observed by geologic data and GPS measurements. The southern anomaly refers to groundwater-induced subsidence as shown in Figs 2, S3 and S4. Full size image

Nuisance flooding frequency shows a second maxima centered near 34° North, close to the southern anomaly defined by our GPS data (Figs 1 and 4). A recent study31 suggests ice-mass loss from Greenland, ocean dynamics and the inverted barometer effect explains accelerated sea-level rise along much of the East Coast of North America. However, this model produces a poor fit (see Fig. 4 of ref. 31) along our southern anomaly. Figures 1, 2 and 4 show that the GPS-measured subsidence rates, while variable, can be as high or higher here as they are in the “max GIA” anomaly. We suggest that the recent increased rate of RSLR here includes a contribution from subsidence of the land surface associated with recent groundwater loss, where pumping rates have exceeded the rate of natural recharge for a number of years14. The resulting loss of pore fluid pressure in the aquifer leads to compaction, loss of porosity, and surface subsidence. A database showing changes in groundwater level (Fig. S4) shows a large degree of spatial variability (aquifers tend to be locally managed) but also exhibits a broad minima (extreme drop in groundwater level) near 34° North, similar to the GPS-geological rate. This is encouraging for short-term (next few decades) mitigation, since groundwater management practices can be modified, reducing induced subsidence, and perhaps even promoting moderate uplift via groundwater recharge32.

In the area between 36° North and 38° North (south of Chesapeake Bay, Virginia) despite the higher rate of RSLR (tide gauge) and vertical land motion (GPS), the nuisance flooding frequency data show only a small increase (Fig. 4). Perhaps GPS-measured subsidence is sufficiently recent to have only a marginal effect on elevation. Our previous study14 shows that groundwater levels in most of the southern Chesapeake Bay region (south of Virginia) declined from the early 1970s until the late 2000s in response to excessive withdrawal but reversed from the late 2000s until 2015, indicating groundwater recharge (Fig. 4 of ref. 14). This indicates that groundwater-related subsidence can be a short-term phenomenon, and suggests that recent groundwater management efforts have been effective at reducing aquifer compaction and subsequent land subsidence in this area.

The northern anomaly is positive (GPS indicates slow uplift, differing by about 1 mm yr−1 from the geologic rate, which indicate slow subsidence) and does not appear to be related to recent changes in groundwater usage. The northern anomaly might reflect a modern peripheral bulge associated with recent loading by dams in northern Quebec, Canada14. The James Bay Project is a massive hydro-electric project involving construction of many dams on rivers draining into James Bay, Hudson Bay, and the Gulf of St Lawrence, constructed between the mid-1970’s and the late 1990s. Here we explore a quantitative test of this hypothesis.

Figure 5a shows the recent (2002–2015) change in Total Water Storage (TWS) in Quebec using data from the GRACE satellite gravity mission33. These data define the magnitude and approximate location of recent changes to water load, in this case concentrated southeast (upstream) from dams draining into James and Hudson Bay, and northwest of dams draining into the Gulf of St Lawrence. TWS is an estimate of total surface and near surface water stored on the continent, including groundwater, soil moisture, surface water, snow, ice, and biomass. Details of the GRACE processing and the TWS estimation are described in the Methods section. Although dam construction was completed prior to the start of the GRACE mission, reservoir filling continued for some time. To verify this, we also used satellite altimetry estimates for nine large lakes and reservoirs in the area (Figs 5a and S5). Time series of water-level changes here during part of the GRACE mission show significant positive trends, consistent with the GRACE observations (Figs S5, S6 and Table S2). While the main effect of this excess mass in the immediate area of the James Bay project is subsidence, distal areas experience uplift due to the peripheral bulge effect.

Figure 5 GRACE TWS and finite element model prediction. (a) Trend in total water storage (in equivalent water height) for eastern North America estimated from GRACE DDK2-filtered Stokes coefficients (corrected for GIA model51). The data represent an average for the period 2002–2015. The location of active major dams (red dots) and formal boundaries for the James Bay hydroelectric project (yellow line) are also shown. The white dashed circle with radius 400 km approximates the excess mass observed with GRACE. The mass anomaly is centered southeast of dams on rivers running northwest into James and Hudson Bay, and northwest of dams on rivers running southeast into the Gulf of St Lawrence. (b) Axisymmetric finite element model results for the peripheral bulge uplift rate in the vicinity of the northern anomaly induced by a load comparable to the total water storage estimated by GRACE for the James Bay Hydro-Electric Project in Quebec. The gray band shows distance of coast of Maine from the load centre. Triangles with error bar represent GIA-corrected vertical rate (GPS rate – geologic rate) for two regions where GPS and geologic rates are available14. Black line and dashed gray lines represent the average vertical rate (mean of two rates) and its uncertainty (1-σ error) along the northern anomaly. Dashed green line corresponds to a model where the elastic thickness (h) transitions from 100 km (elastic thickness for the Canadian Shield) for distances closer than 500 km, to 50 km (elastic thickness for the Appalachians) for distances farther than 780 km. Map is generated using GMT software version 5.1.0 (http://gmt.soest.hawaii.edu/)66. Full size image

Figure 5b shows the modeled response of the lithosphere to this recent load, including the far field response along the coast of Maine. The model simulates the elastic (short-term) response of the lithosphere (an elastic plate with thicknesses between 50 and 100 km)34, 35 overlying a dense inviscid substratum. Details of the modeling procedure are described in the Methods section. The coast of Maine is ~ 780–880 km from the load maximum, close to the region of maximum uplift associated with the peripheral bulge predicted by the model, assuming elastic thickness transitioning from 100 km (elastic thickness for the Canadian Shield)34 to 50 km (elastic thickness for the Appalachians)35.

While the model correctly predicts the location of anomalous uplift, it underpredicts the amplitude by ~0.5 mm yr−1. This may be related to the uncertainty of GIA models used to correct GRACE TWS data36 (a range of 20% is often assumed for GIA models) and the greater uncertainty associated with geologic rates along the southern coast of Maine (±0.5 mm yr−1), but we cannot preclude the possibility of additional or alternate processes. Better understanding of these processes will be important for interpreting tide-gauge data in terms of future oceanographic changes. For example, rates of RSLR are lower in the northern anomaly than surrounding areas (Fig. 4).

Both nuisance flooding associated with periods of high tide, and catastrophic flooding associated with tropical storms and hurricanes, are increasing due to sea-level rise. While the latter cannot yet be predicted with any certainty, both the timing and location of nuisance flooding can in principle be predicted. In the short term, such predictions are useful in several ways. First, they can assist municipalities in mitigating the worst effects of flooding through improved infrastructure. Second, better management practices for extraction of groundwater from coastal aquifers can reduce nuisance flooding, by reducing or eliminating the coastal subsidence associated with over-extraction, temporarily reducing the rate of RSLR. On longer time scales however, many areas currently affected by nuisance flooding can expect to experience loss of coastal land unless significant infrastructure investments are made. Recognition of this fact can assist municipalities in making the necessary long-term plans and investments.