Does the mid-Atlantic United States sea level acceleration hot spot reflect ocean dynamic variability?


  • Robert E. Kopp

    Corresponding author
    1. Department of Earth and Planetary Sciences and Rutgers Energy Institute, Rutgers University, Piscataway, New Jersey, USA
    • Corresponding author: R. E. Kopp, Department of Earth and Planetary Sciences and Rutgers Energy Institute, Rutgers University, Piscataway, NJ 08854, USA.(

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[1] To test a hypothesized faster-than-global sea level acceleration along the mid-Atlantic United States, I construct a Gaussian process model that decomposes tide gauge data into short-term variability and longer-term trends, and into globally coherent, regionally coherent, and local components. While tide gauge records indicate a faster-than-global increase in the rate of mid-Atlantic U.S. sea level rise beginning 1975, this acceleration could reflect either the start of a long-term trend or ocean dynamic variability. The acceleration will need to continue for 2 decades before the rate of increase of the sea level difference between the mid-Atlantic and southeastern U.S. can be judged as very likely unprecedented by 20th century standards. However, the difference is correlated with the Atlantic Multidecadal Oscillation, North Atlantic Oscillation, and Gulf Stream North Wall indices, all of which are currently within the range of past variability.

1 Introduction

[2] Three recent papers suggest that the increase in the rate of sea level rise (i.e., the sea level acceleration) along the mid-Atlantic coast of the United States is greater than the global average [Sallenger et al., 2012; Boon, 2012; Ezer and Corlett, 2012]. A plausible physical mechanism for producing such an acceleration exists: a slowing Gulf Stream (GS), associated with a weakening Atlantic Meridional Overturning Circulation (AMOC), should reduce the dynamic sea level gradient across the North Atlantic, causing a sea level decline in the central North Atlantic and a corresponding sea level rise (SLR) in the northwestern North Atlantic. A secular SLR associated with this mechanism is one of the few points of agreement in global climate model projections of regional sea level change [Yin et al., 2009]. Ezer et al. [2013] suggested that changes in the GS, reflected in the altimetry-observed altitudinal gradient across the GS, are indeed correlated with a pronounced SLR in mid-Atlantic U.S. tide gauges since 2007 but did not examine the relationship between the GS gradient and tide gauges before the start of the altimetry record in 1993.

[3] Regional and local sea level differ from mean global sea level (GSL) due to several factors. Glacial isostatic adjustment (GIA), driven by the viscous response of the mantle to the changes in ice mass loads since the Last Glacial Maximum, is causing the collapse of peripheral bulge of the former Laurentide ice sheet and thus a mid-Atlantic regional SLR [Farrell and Clark, 1976]. East of the Fall Line, which passes close to New York City and Washington, bedrock is overlain by the Mesozoic and Cenozoic sediments of the Coastal Plain, which can subside due to natural compaction and therefore experience a faster long-term rate of SLR. In the southern region of the Chesapeake Bay, high rates of subsidence may also be attributable to differential compaction of the breccia lens of the upper Eocene Chesapeake Bay impact structure [Poag, 1997].

[4] On shorter timescales, regional sea level anomalies can arise from land ice melt and ocean dynamics [e.g., Kopp et al., 2010]. Melting land ice leads to a slower or negative SLR near the meltwater source and to an enhanced SLR far from the source [Farrell and Clark, 1976]. Greenland melt will thus produce less-than-global SLR on the eastern seaboard of the United States, while West Antarctic melt will produce greater-than-global SLR [Mitrovica et al., 2001, 2009]. Regional anomalies also arise from changes in ocean dynamic factors such as GS strength, as previously noted and changes in the distribution of heat within the ocean [Ishii et al., 2006]; these factors can undergo both strong interannual variability and longer-period variations. Local sea level anomalies can also arise from direct anthropogenic effects such as groundwater withdrawal and dredging.

[5] The three recent studies examining the possible sea level acceleration in the eastern U.S. tide gauge records [Sallenger et al., 2012; Boon, 2012; Ezer and Corlett, 2012] each have distinctive limitations, discussed in the supporting information, that restrict their ability to assess the statistical significance of the acceleration. They also share a common limitation when evaluating the regional coherence of sea level trends. Specifically, they all model each tide gauge record in isolation; they do not model the covariance between records. As a consequence, they cannot estimate the uncertainty in the difference in sea level between different sites in a way that accounts for correlation among different sites. For example, while they can all generate estimates of differences in SLR acceleration along the coast, they will overestimate the uncertainty in these differences.

[6] Here I develop a new spatio-temporal statistical method for analyzing tide gauge data, with the goal of partially disaggregating the sources of SLR and assessing the statistical significance of the sea level acceleration “hot spot” in the mid-Atlantic region. The method is based upon Gaussian process (GP) regression [Rasmussen and Williams, 2006] (in this context, also known as spatio-temporal kriging). Similar approaches have previously been used for investigating temperature records [e.g., Higdon, 1998]. The approach is well suited for investigating possible regional accelerations for several reasons. First, it is fully probabilistic, so measurement and inferential uncertainties are propagated through the entire analysis. Second, it models sea level as a spatio-temporal field, naturally identifying regions with coherent sea level signals, appropriately sharing information among neighboring sites in the calculation of posterior sea level estimates and allowing calculation of the uncertainty in differences between sites. Third, being Bayesian in derivation (though in this analysis empirical Bayesian, rather than fully Bayesian, in implementation), it copes naturally with the missing data that characterize tide gauge records. Fourth, like empirical mode decomposition (EMD) [Ezer and Corlett, 2012], it is nonparametric, and so does not force a functional form on the interpretation of the tide gauge records. Unlike EMD, however, it employs a parametric estimate of the prior covariance of sea level; this parameterized prior covariance allows easy separation of global, regional, and local signals, and of linear trends, smooth but nonlinear variability, and red noise-type variability in a fashion consistent with prior expectations about the behavior of sea level.

[7] Below, I demonstrate this method through application to tide gauge records from the eastern coast of North America and employ it to assess claims about a regional “hot spot” of sea level acceleration.

2 Methodology

[8] Sea level is a spatio-temporal field f(x,t), which can be viewed as the sum of several component fields:

display math(1)

In this expression, the g terms denote GSL, and the r and l terms respectively denote regionally-coherent and local (site-specific) sea level anomalies (deviations from GSL). The subscripts denote different temporal patterns of variability. The terms denoted by a subscript l appear linear over the period of the tide gauge record, the terms denoted by a subscript s are smooth deviations from linearity, and the terms denoted by a subscript n are red-noise-like deviations from linearity. GIA appears as a linear, regional sea level anomaly (the dominant component of rl), while a regional acceleration in SLR that is faster than the global average would be reflected by an accelerating smooth, regional sea level anomaly (i.e., inline image). Oceanographic variability will appear primarily in the rs and rn terms.

[9] Note that these terms may not always be easy to separate; for example, an apparent regional acceleration in SLR (an increase in inline image) could represent either a coincidence of short-term variability (increasing inline image) or a more lasting deviation from the linear trend (increasing inline image). Only sustained observation allows their discrimination.

[10] Each term in equation (1) is modeled as a GP, as described in detail in the supporting information. The hyperparameters characterizing the temporal scales of variability of g are calibrated against the Church and White [2011] estimate of GSL, while the hyperparameters characterizing the amplitude and spatial scale of the variability of rl are calibrated against the ICE-5G VM2-90 GIA model of Peltier [2004]. Hyperparameters describing the amplitude, spatial scale, and temporal scale of other terms are maximum-likelihood estimates from the tide gauge records.

[11] The training data set includes mean annual sea level estimates from the 47 eastern North America tide gauges, stretching from Daytona Beach, Florida, to St. John's, Newfoundland, that are archived by the Permanent Service for Mean Sea Level ( and have a record length >30 years (Figure S2). Data from other sites are indirectly incorporated through the Church and White [2011] GSL estimate.

3 Decomposition of Tide Gauge Signals

3.1 Linear Components of Sea Level Anomaly

[12] The linear trends inline image estimated at each site differ significantly from those projected using the ICE-5G VM2-90 GIA model of Peltier [2004] (Figure 1, Table S1). The discrepancy is particularly severe in Virginia (e.g., Figures S4 and S5), where GIA projections lay outside the 95% confidence interval of the inline image estimate. The discrepancy suggests either considerable error in the VM2-90 solid Earth parameters or the ICE-5G ice sheet history, or the presence of an additional factor causing a close-to-linear SLR over the period of the tide gauge record. Davis and Mitrovica [1996] note that a lower-mantle viscosity 2.5 times higher than the mean lower-mantle viscosity of VM2 [Peltier, 2004] would extend the peripheral bulge region of elevated subsidence rates around the former Laurentide margin and increase GIA-related subsidence in Virginia. Their hypothesis is consistent with the current analysis.

Figure 1.

(a) Mean estimate of the long-term linear sea level anomaly rate (i.e., rate of change with respect to the global mean; inline image), due primarily to GIA and sediment compaction. Dotted grey denotes boundary of the Coastal Plain province. H—Halifax, P—Portland, N—New York, S—Sewell's Point, C—Charleston, B—St. George's. (b) Regional linear sea level anomaly rates inline image along U.S. coast (blue; dashed/dotted = 67%/95% confidence intervals), compared to ICE-5G projections of GIA rates (red) [Peltier, 2004] and geological estimates of late Holocene SLR [Engelhart et al., 2009] (green; lines = 1σ).

[13] One possible confounding factor is sediment compaction, which could be significant in sites, such as those in Virginia, that rest upon Coastal Plain sediments. In addition to the Virginia sites, high linear rates of SLR relative to the regional trend are observed on the New Jersey Coastal Plain at Sandy Hook and Atlantic City. The geographic spread of the high rate of SLR throughout the mid-Atlantic Coastal Plain, not just in the vicinity of the Chesapeake impact structure, suggests a dominant role for sediment compaction unrelated to the bolide impact. Nevertheless, the four sites in the southern Chesapeake vicinity of the impact structure exhibit considerable variability, with long term rates (inline image) ranging from 1.7±0.7(2σ) mm/y at Kiptopeke to 2.6±0.6 mm/y at Sewell's Point (Table S1).

3.2 Nonlinear Components of Regional Sea Level

[14] The smooth, nonlinear regional sea level anomaly rate inline image shows four multidecadal features (Figure 2a): significant rates of sea level anomaly rise along the entire seaboard in the 1930s and 1940s; significant rates of sea level anomaly fall in the mid-Atlantic region in the 1970s, followed by slightly delayed fall to the north; and current significant rates of sea level anomaly rise in the mid-Atlantic and significant rates of sea level anomaly fall in the southeastern U.S.

Figure 2.

(a) Smooth, nonlinear, regional sea level anomaly rates (inline image). Heavy regions indicate space-time points where the sign of the sea level anomaly rate component is likely (probability >67%) correctly identified. (b) Low-pass filtered nonlinear regional sea level anomaly at New York City (rs+rn) (black; dashed = 67% confidence), compared to low-pass filtered versions of the AMO (blue)/NAO (red)/GSNW (green) indices. Indices are scaled by their covariances (leading to a sign reversal for NAO and GSNW) and shifted by 7/2/0 years to maximize correlation.

[15] These patterns could be the result of either cryospheric or oceanographic variability. From a cryospheric perspective, the sea level anomaly rise in the 1930s and 1940s is contemporaneous with high rates of GSL rise, which could reflect the addition of meltwater to the ocean. The behavior of the Greenland ice sheet during this period is the subject of disagreement [Gregory et al., 2013], with some modelers suggesting that the warm Northern Hemisphere temperatures of the 1930s drove strong Greenland melt and others suggesting that it drove enhanced accumulation. The observed pattern of greater-than-global SLR off North America during this interval is consistent with that expected from West Antarctic melt and the opposite of what would be expected from the static sea level fingerprint of Greenland melt [Mitrovica et al., 2001, 2009]. However, the effects on AMOC of Greenland melt might be expected to operate in the opposite direction [Kopp et al., 2010]; it is therefore not possible from regional data alone to infer the role of Greenland. A global analysis as proposed by Hay et al. [2013] might succeed in this regard.

[16] As an exploratory analysis to identify possible oceanographic factors related to regional sea level variability, consider the cross correlations between the nonlinear regional sea level anomaly in six indicative sites—Halifax, Portland, New York City, Sewell's Point (Norfolk), Charleston, and St. George's, Bermuda—and three annually averaged climatic or oceanographic indices (Figures 2b and S9): the Atlantic Multidecadal Oscillation (AMO) [Van Oldenborgh et al., 2009], the Hurrell [1995] winter North Atlantic Oscillation (NAO) index, and the GS North Wall (GSNW) index [Taylor and Stephens, 1998].

[17] The AMO index averages detrended sea surface temperature anomalies in the Atlantic between 25°N and 60°N. Consistent with coherence between the AMO and regional sea level, previous work has identified a 60 year oscillation in North Atlantic sea level, a periodicity also seen in the AMO [Chambers et al., 2012]. Thermosterically, warmer temperatures (higher AMO index) might be expected to correlate with higher regional sea levels. On the other hand, the AMO index is a slightly lagging correlate of AMOC strength [Van Oldenborgh et al., 2009]. Weakening AMOC should give rise to higher mid-Atlantic sea levels, so the AMO index might be expected to be a lagging anticorrelate of mid-Atlantic sea level.

[18] A significant (p=0.03) lagging positive correlation with the AMO is present at New York (r=0.31, lag 6–9 years) and likely as far south as Sewell's Point (p=0.29,r=0.21, lag 6–8 years) and as far north as Portland (p=0.15,r=0.28, lag 9–10 years). The absence of an anticorrelation between the AMO index and mid-Atlantic regional sea level might be caused by the competing thermosteric and AMOC effects, with a lower-frequency, AMOC-related anticorrelation masked by a higher-frequency, thermosterically driven correlation. The lagging positive correlation might then reflect an underlying, quasi-periodic, AMOC-associated anticorrelation.

[19] The NAO index reflects the atmospheric pressure difference between Lisbon and Iceland. Most directly, the inverse barometer effect leads to the expectation of an anticorrelation between the NAO index and sea level in the northern North Atlantic. Consistent with this effect, there are highly significant (p<0.01) anticorrelations between the NAO index and regional sea level anomalies at Halifax (r=−0.34) and Portland (r=−0.33). The NAO index is also a leading correlate of northward Gulf Stream displacement [Frankignoul et al.2001]. As increased northward transport in the Gulf Stream is correlated with lower coastal sea levels (and higher off-shore sea surface heights) in the mid-Atlantic region [Ezer et al., 2013], the NAO index might be expected to be a leading anticorrelate of mid-Atlantic sea level. Consistent with these expectations are a likely (p=0.08,r=−0.18) anticorrelation at New York City and a significant positive correlation (p=0.02,r=0.25) at Charleston.

[20] Similarly, the GSNW index, which directly reflects the position of the northern edge of the GS, should be expected to anticorrelate with mid-Atlantic sea level. Significant anticorrelations are indeed observed at New York (p=0.04,r=−0.34) and Portland (p=0.03,r=−0.38), and likely anticorrelations are present at Sewell's Point (p=0.13,r=−0.26) and Halifax (p=0.10,r=−0.30). A likely positive correlation (p=0.33,r=0.17) is present at Charleston.

[21] Taken together, these results support a significant role for AMOC and GS variability in explaining regional sea level behavior in eastern North America, as suggested by Sallenger et al. [2012] and Ezer et al. [2013].

4 A Sea Level Acceleration “Hot Spot”?

[22] A weakening AMOC will reduce the north-to-south sea surface height gradient along the eastern North American coast [Yin et al., 2009]. In tide gauge records that use, as a reference datum, local sea level in a common year, this will appear as an increasing sea level difference between northern and southern sites. To evaluate the mid-Atlantic “hot spot,” we therefore consider the difference in the nonlinear regional sea level anomaly (rs+rn) between New York City and Charleston (Figure 3). The analysis removes signals associated with GSL change, with long-term linear changes due to effects such as GIA, and with purely local effects. (The supporting information includes a parallel analysis of the difference between Sewell's Point and Charleston, as well as an analysis of an alternative definition of the “hot spot” based upon regionally coherent sea level acceleration. The results are similar).

Figure 3.

The difference in the regional sea level anomaly between New York City and Charleston. Blue: rs+rn; green: rs. (a) Amplitude of the anomaly difference, (b) rate of change. Dashed (dotted) lines denote 67% (95%) confidence intervals.

[23] Between 1990 and 2012, the smooth, nonlinear regional sea level (rs) difference between New York City and Charleston increased by 16±25 mm (an average rate of 0.7±1.1 mm/y); it is therefore very likely (probability 90%) that the difference has increased over this time period. The mid-Atlantic hot spot as such therefore does appear to be robust. Its robustness does not, however, necessarily imply that the recent increases marks the start of a secular change in the GS; it could reflect variability within the system.

[24] The greatest increase in the difference over any 22 year period starting no earlier than 1900 and ending no later than 1990 was 17 mm (95% range of 1–38 mm) (0.8 mm/y, range of 0.1–1.7 mm/y). It is about as likely as not (probability 55%) that the rate of the 1990–2012 rise was exceeded at some point during the rest of the 20th century.

[25] The magnitude of the difference, referenced to the expected value in 1900 as a common datum, is currently 6±45 mm, about 11±35 mm below the maximum value attained between 1900 and 1990. The current magnitude will need to increase by 19 mm before it can be identified as likely (probability >67%) unprecedented within the 20th century and by 34 mm before it can be identified as very likely unprecedented. At the average rate of increase of the last 22 years, this would take about 30 and 50 years, respectively. However, it is likely (probability 65%) that the current rate of increase, 0.3±2.2 mm/y, is less than the average over 1990–2012.

[26] Yin et al. [2009] project that, under the A1B scenario, a weakening AMOC will establish a 150 mm dynamic sea level difference between New York and Miami during the century between 1980–2000 and 2080–2100. The difference between New York and Charleston will be similar. To attain such a difference, another 130 mm increase must occur over the next 70 years, on top of the 16 mm that has occurred since 1990. This will require an acceleration of >0.03 mm/y2. Comparing the mean rate of change over 1968–1990 to that over 1990–2012 yields an average acceleration of 0.05±0.08 mm/y2, which would likely be sufficient if sustained. If it is sustained for about two more decades, the resulting 1.0 mm/y increase in rate will very likely be unprecedented, and if it is sustained for about 25 years, it will yield a sea level difference that is very likely unprecedented in magnitude.

5 Conclusions

[27] While the current analysis is consistent with previous work identifying a recent shift to faster-than-global SLR in the mid-Atlantic region, neither the magnitude of the phenomenon, nor its rate of change, nor its acceleration appear to be beyond the bounds of the 20th century variability. It is therefore premature to validate the hypothesis of Sallenger et al. [2012] that the current regionally high rates of SLR along the U.S. east coast represent the start of a long-term reorganization of the GS, and it will take about two decades of additional observations before the sea level effects of such a reorganization can be identified in tide gauge records as very likely exceeding the range of past variability.

[28] Comparison of the sea level record with climatic and oceanographic indices suggest that the observed changes may be at least partially accounted for by known sources of variability. At long wavelengths (periods >10 years), the interval since 1995 has seen southward migration of the GSNW, while the period since about 1972 has seen an increase in the AMO index, and the period since 1990 has seen a decline in the NAO index. Based on the cross-correlation analysis, the AMO increase and GSNW migration would be expected to increase the regional sea level anomaly in the mid-Atlantic, while the NAO decline would be expected to decrease the regional sea level anomaly in the southeastern U.S. Together, these factors would serve to increase the gradient between the mid-Atlantic and the southeastern U.S. Consistent with the hypothesis that the regional sea level “hot spot” represents variability rather than the start of a trend, none of these indices currently exceeds its range of historical variability. As the changes in these indices have slowed over the last decade, if the indices reflect the driving factors underlying the “hot spot,” the phenomenon may not prove to be enduring.


[29] This work was supported by NSF grant ARC-1203415 and inspired by the SLR Expert Group of the Maryland Climate Change Commission. I thank A. Broccoli, R. Chant, T. Ezer, C. Hay, B. Horton, A. Kemp, K. Miller, J. Mitrovica, E. Morrow, F. Simons, V. Pavlovic, and an anonymous reviewer for helpful discussion.

[30] The editor thanks Tal Ezer and an anonymous reviewer for assistance in evaluating this manuscript.