Geographic Variability of Sea-Level Change
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Local sea-level changes differ significantly from global-mean sea-level change as a result of (1) non-climatic, geological background processes; (2) atmosphere/ocean dynamics; and (3) the gravitational, elastic, and rotational “fingerprint” effects of ice and ocean mass redistribution. Though the research communities working on these different effects each have a long history, the integration of all these different processes into interpretations of past changes and projections of future change is an active area of research. Fully characterizing the past contributions of these processes requires information from sources covering a range of timescales, including geological proxies, tide-gauge observations from the last ~3 centuries, and satellite-altimetry data from the last ~2 decades. Local sea-level rise projections must account for the different spatial patterns of different processes, as well as potential correlations between different drivers.
KeywordsSea level Ocean modeling Glacial-isostatic adjustment Sea-level fingerprints Tide gauges Satellite altimetry
Sea level is often conceived as being analogous to the depth of water in a bathtub, rising or falling everywhere as water is removed or added. The truth is far more complicated: sea level is more like the depth of water in a rotating, self-gravitating bathtub with wind and buoyancy fluxes at its surface; heterogeneous density; and a viscoelastic, deforming bottom. In other words, sea-level change is far from uniform.
Sea level in the sense used here, also known as relative sea level (RSL), is defined as the difference in elevation between sea-surface height (SSH) and the height of the solid-Earth surface. SSH, also called geocentric sea level, is defined with respect to a reference ellipsoid. RSL—the parameter that matters for those communities and ecosystems on land at risk from coastal flooding—can be measured with tide gauges; SSH is measured with satellite altimetry. While in the global mean, the difference between these two measures of sea level is small, local differences in RSL and SSH changes can be quite significant.
Changes in RSL arise from one of three types of effects: (1) vertical land motion (VLM), (2) changes in the height of the geoid, and (3) changes in the height of the sea surface relative to the geoid. VLM, which can be measured directly using global positioning system (GPS) receivers, arises from a range of sources, including tectonics (both fast and slow), soft-sediment compaction (either under the weight of over-burden or accelerated by the withdrawal of interstitial fluids such as groundwater or hydrocarbons), and deformation associated with ice-ocean mass transfer. The last is generally separated into two components: glacial-isostatic adjustment (GIA), which is the ongoing viscoelastic response of the Earth to past, deglacial changes in the cryosphere, and the elastic response to recent mass flux in glaciers and grounded ice sheets. Both of these load components also drive perturbations in SSH and the geoid [1••], and both are computed using a static sea-level theory. Dynamic departures of the sea surface from “static equilibrium” are driven by wind and buoyancy fluxes and by oceanic currents, which act to change sea level by redistributing mass and volume [2, 3].
RSL rise poses a risk to communities, ecosystems, and economies, through inundation and by influencing the frequency and magnitude of coastal flooding. This risk is geographically variable, as both RSL changes and socioeconomic exposure vary with location [4, 5, 6]. Failure to account for the differences between RSL change and global-mean sea-level (GMSL) change can lead to either under- or over-estimation of the magnitude of the allowance necessary to accommodate RSL rise . Accordingly, stakeholders and agencies responsible for quantifying the flooding hazard require local RSL projections for risk assessment and decision-making [e.g., 8].
Here, we first review the major non-climatic and climatic contributors to RSL change over decadal and longer timescales and then assess their implications for both interpretations of records of past changes and projections of future changes.
The Geological Background of RSL Change
Tectonics and Mantle Dynamic Topography
At active continental margins and on volcanic islands, tectonic uplift or subsidence is often a significant contributor to observed sea-level changes on both historical and Pleistocene (last 2.6 My) timescales. On historical timescales, tectonic events can give rise to both gradual changes and abrupt coseismic changes in RSL [e.g., 12]. On longer timescales, tectonic effects are usually approximated as following an average long-term rate [e.g., 13].
Throughout the world (not just on active margins), mantle flow linked to plate tectonics also drives variations in crustal elevation. This “mantle dynamic topography” [14, 15, 16] leads to uplift and subsidence rates that may reach the order of 1–10 cm/kyr, even at sites on passive continental margins [16, 17•]. Models of mantle flow are complicated by uncertainties in mantle buoyancy and viscosity structure, and recent global calculations can disagree significantly in both amplitude and sign [16, 17•, 18, 19, 20, 21]. Nevertheless, mantle dynamic topography becomes increasingly important as one considers progressively older sea-level markers.
Many of the world’s coastal areas are located not on lithified bedrock but on coastal plains composed of unconsolidated or loosely consolidated sediments. These sediments compact under their own weight, as the pressure of overlying sediments leads to a reduction in pore space [22, 23]. In the Mississippi Delta, for example, compaction-related Late-Holocene subsidence has been estimated to be as high as 5 mm/year .
Anthropogenic withdrawal of water or hydrocarbons accelerates sediment compaction. For example, in the Mississippi Delta at the Grand Isle, Louisiana, tide gauge, subsidence over 1958–2006 CE, was 7.6 ± 0.2 mm/year, with a peak rate of 9.8 ± 0.3 mm/year over 1958–1991 coinciding with the period of peak oil extraction . Tide gauges in other delta regions, including the Ganges, Chao Phraya, and Pasig deltas, also indicate high rates of subsidence. These high rates of subsidence, linked to a combination of natural and anthropogenic sediment compaction, drive some of the highest rates of RSL rise today [9••] (Fig. 1a).
GIA is the multi-millennial, viscoelastic response of the Earth to the redistribution of ice and ocean loads (Fig. 1b–d). During an ice age glaciation phase, the crust subsides beneath the ice cover and uplifts at the periphery of the ice. This pattern reverses during the deglaciation; the crust beneath the melting ice sheet experiences post-glacial rebound and the peripheral bulges subside.
GIA is sensitive to the time history of loading, and GIA-driven changes in RSL continue through periods where ice volumes may have been nearly static, such as the pre-industrial Late Holocene [25, 26]. At present, Hudson Bay, near the location of maximum thickness of the former Laurentide Ice Sheet, and the northern Gulf of Bothnia, at the center of the former Fennoscandian Ice Sheet, are subject to RSL falls of ~1 cm/year, while sites at their periphery (e.g., the east and west coasts of the USA and northern Europe) are experiencing GIA-driven RSL rises of 1–3 mm/year.
In so-called near-field regions like Hudson Bay, GIA-induced RSL changes are dominated by VLM. By contrast, in the “far field” of the Late Pleistocene ice sheets, changes in SSH tend to dominate the GIA sea-level signal. In particular, over a broad swath of low-latitude ocean regions, a process called “ocean syphoning” leads to a RSL fall during the deglacial and interglacial stages of the ice age cycle. Syphoning refers to the migration of water into subsiding peripheral bulges . The peak present-day GIA-related RSL fall, ~0.5 mm/year, occurs in interior regions of the northwest Pacific, southeast Pacific, and south Atlantic ocean basins, well away from continental margins. Since the start of the current interglacial, syphoning has led to RSL falls of up to ~3 m, recorded by exposed coral reefs that now lie several meters above sea level or by notches in the coastline marking ~5000-year-old shorelines . Near continental margins, a process called “continental levering” is superposed on top of the broader-scale signals [25, 28]. Levering is crustal tilting—downward towards offshore and upward towards the continents—in response to the loading by meltwater entering the ocean during the deglacial phase. The amplitude of the effect depends on the location of the site relative to the hinge of the tilting, but it can produce signals of up to ~0.5 mm/year.
Calculations of GIA effects on sea level are generally performed using theory and numerical algorithms that assume 1-D, depth-varying viscoelastic structure. However, relatively recent developments in numerical modeling now permit the inclusion of more realistic, 3-D variations in lithospheric thickness and mantle viscosity [29, 30, 31, 32]. The use of such codes has been relatively limited, but calculations have shown that lateral variations in structure can significantly impact estimates of Last Glacial Maximum ice volume based on the analysis of far-field sea-level trends  and predictions of present-day GIA-related RSL changes .
Climatically Driven RSL Change
Climate change influences RSL via (1) density changes and mass redistribution within the ocean and (2) mass exchanges between the cryosphere and the ocean. This section addresses each of these in turn, focusing on the factors that cause RSL changes to differ from GMSL changes.
Dynamic sea-level (DSL) changes induced by wind and buoyancy fluxes at the sea surface occur over a vast range of spatial scales and can be driven by local or remote atmospheric forcing. Atmospheric forcing is moderated by and coupled to the response of the ocean circulation over various timescales [35, 36, 37•, 38, 39]. Remotely forced DSL changes, particularly over longer timescales, are often associated with natural modes of variability of the climate system (e.g., the North Atlantic Oscillation [40, 41] and Pacific Decadal Oscillation (PDO) [42, 43]). Secular climate trends and variability over these longer timescales may interact with shorter-period sea-level variability, such as the seasonal cycle  or El Niño Southern Oscillation [45, 46]. DSL changes are coupled to static sea-level effects that can amplify or reduce DSL changes by up to ~±16 % [47•].
DSL variability is often decomposed into density-driven and mass-driven components [2, 35, 36, 48••]. Ocean density (steric) changes reflect surface fluxes or redistribution of heat and salt, while mass changes can be driven either by addition of freshwater or mass redistribution (e.g., by wind stress). On decadal timescales, gravimetric data, in conjunction with altimetry, allow the separation of steric and mass components [49, 50, 51]; in situ ocean observations facilitate further partitioning into halosteric and thermosteric components that can be traced back to their origin in surface fluxes and/or redistribution [38, 52, 53]. Recent studies have shown that satellite-era changes are dominated by the baroclinic response to wind stress and buoyancy fluxes, with mass redistribution and barotropic adjustment influencing sea level at larger spatial scales [50, 51]. Thermosteric redistribution—driven by wind stress curl and isopycnal displacement—underlies sea-level variability over most of the world’s oceans. Halosteric changes—driven by redistribution and external sources (melting of sea and land ice)—contribute substantially in polar regions [52, 53, 54].
The WTP, for example, has experienced the fastest local rate of DSL rise over the altimetry record . Recent efforts are converging on a mechanistic pathway that involves increasing trade winds, deepening of the WTP thermocline, and subsequent surface heat flux . A substantial fraction of the wind stress change is related to the PDO and is thus linked to changes in western USA, where DSL rise has been suppressed for several decades . While WTP DSL has been linked to anthropogenically attributed warming in the tropical Indian Ocean, the partition between anthropogenic and natural signals remains unclear [61, 62].
Along the EUS coastline, DSL has also risen faster than GMSL since ~1900, particularly north of Cape Hatteras. Much recent literature has focused on detecting an acceleration outside of the range expected for natural variability [63, 64]. However, while these studies remain contentious, they have been complemented by increasing understanding of the modes and spatial scale of coherent sea-level variability along the EUS—including underlying mechanisms, their characteristic timescales, and their sensitivity to climate changes. Such physical insight may facilitate the isolation of secular trends and guide statistical analyses in the EUS and elsewhere [40, 65, 66].
Yin and Goddard [67•] have merged earlier hypotheses that EUS sea-level dynamics are subject to a dividing line near Cape Hatteras, with the argument that NAO and Atlantic Meridional Overturning Circulation (AMOC) baroclinic variability is driving changes to the north and barotropic variability in the position and strength of the Gulf Stream is driving changes to the south [46, 68, 69]. A recent study  concludes that the observed interannual to decadal coherence of sea level north of Cape Hatteras  is largely driven by alongshore wind stress, rather than AMOC. However, longer-term variability may still be driven by changes in the large-scale hydrography, AMOC, or Sverdrup transport divergence in the North Atlantic [72, 73].
In addition to their direct influence on DSL, atmosphere-ocean dynamics also govern the mass balance of glaciers and ice sheets via the delivery of heat to the ice mass. As most satellite-era DSL changes are driven by density and mass redistribution , we do not discuss in detail the mechanisms involved in ice-ocean or glacier mass balance. (Interested readers should begin with recent reviews [75, 76]). Freshwater fluxes from glaciers and ice sheets can affect DSL [e.g., 77•]. In addition, they give rise to sea-level fingerprint effects that are discussed in the following section.
The sea-level fingerprint results from the superposition of flexural VLM, geoid changes driven by ice/ocean mass redistribution, and redistribution-driven changes in the rate and orientation of Earth’s rotation that give rise to both VLM and geoid changes [e.g., 81]. RSL falls in the vicinity of a shrinking ice sheet because of the tandem effects of crustal uplift due to unloading and SSH fall due to the migration of water away from the ice sheet in response to its reduced gravitational attraction. At the edge of a melting ice complex, the two effects contribute roughly equally to the predicted RSL fall, and the total amplitude of the signal is approximately an order of magnitude higher than the GMSL rise associated with the melt event. In the far field of the melting ice, RSL will rise by up to ~30 % more than the global average, an amplification due largely to the migration of water from the near field. Far-field VLM is relatively small.
Predictions of these fingerprints are based on the same static sea-level theory used to predict GIA [82, 83••], although most such predictions assume that the melting event is sufficiently rapid that viscous effects in the Earth’s response to the changing surface load may be neglected (but see ). Fingerprints may be thought of as a sub-class of GIA, but their importance in analyzing modern sea-level records has led to a distinction between the two processes.
Mitrovica et al. [83••] have presented a variety of sensitivity tests in predicting sea-level fingerprints of ice sheet melting. While the fingerprints in the vicinity of the ice sheets can be very sensitive to the detailed geometry of the ice melting, this sensitivity progressively decreases at greater distance from the ice sheet. For example, in the mid-Atlantic USA, differences in melt geometries affect the Greenland ice sheet fingerprint by <~10 %. They also find that 3-D variations in the Earth’s elastic structure have small, percent-level effects on the fingerprints.
In addition to redistribution of mass between the cryosphere and the ocean, static sea-level changes can be induced by the dynamic redistribution of mass within the ocean (<~16 % of the dynamic signal, as described in the previous section, so <~±0.4 mm/year throughout the ocean over the twenty-first century) [47•], and by changes in water storage on land (<~± 0.3 mm/year over most of the ocean between 2002–2009, relative to a global-mean hydrological signal of −0.20 ± 0.04 mm/year) .
Interpreting and Projecting Geographic Patterns of Sea-Level Change
The different processes described above must be taken into account when interpreting and merging satellite, tide-gauge, and proxy observations of sea level. Models of these processes must also be carefully integrated to develop a comprehensive and consistent representation of processes and uncertainties in RSL projections.
Interpreting Observational Records
Tide-gauge and satellite-altimetry data provide two different perspectives on modern sea-level change. As noted previously, tide gauges measure RSL, while satellite altimetry measures SSH. In addition, their spatial and temporal coverage differs. Tide-gauge data extend to the eighteenth century in some locations but are sparsely distributed, while satellite-altimetry data are limited in time to the last ~2 decades but provide much better spatial coverage of the low- and mid-latitude sea surface at regular intervals (e.g., every ~10 days). Although efforts are being made to re-process altimetry data near to the coast [86, 87], integrating these two data sets is complicated by small-scale processes at coastal locations and by the degradation of altimetric SSH measurements close to the coast, where most tide gauges are located [55, 70, 88, 89, 90].
Estimating GMSL change requires correcting observational data for GIA (Fig. 1b–d). As discussed above, the GIA correction to present-day RSL trends peaks at ~1 cm/year in regions of maximum ice cover at Last Glacial Maximum, 1 to 3 mm/year at the periphery of the now-vanished ice cover, and <1 mm/year in the far field. The global-mean SSH signal associated with GIA (appropriate for correcting satellite-altimetry data) is 0.15–0.50 mm/year, where the range largely reflects uncertainty associated with Earth structure model adopted in the GIA calculation [1••]. The local SSH signal due to GIA can reach ~1 mm/year near the center of now-vanished ice sheets, as in Hudson Bay.
Complementary satellite gravity observations constrain the combined redistribution of solid-Earth, ice, and water mass. However, there are important differences between these observations and satellite-altimetric estimates of SSH changes. For example, gravity observations constrain perturbations to the geoid and have a global average value of zero. In addition, satellite gravity measurements are only sensitive to mass redistribution, and they will not feel the perturbation in centrifugal potential that an Earth-bound observer will experience during true polar wander (i.e., during a reorientation of the rotation axis relative to the solid Earth). By contrast, SSH will be impacted by this perturbed potential. As noted by Tamisiea [1••], failure to recognize the differences between gravity and SSH observations can introduce significant errors in estimates of global-mean changes in ocean (or ice) mass.
Estimating GMSL also requires a statistical methodology that recognizes the non-uniformity of RSL change. For example, Jevrejeva et al.  estimate GMSL as an average of regional averages, without explicitly incorporating information about the processes that drive differences in regional averages. Church and White , Ray and Douglas , and Wenzel and Schröter  employ empirical orthogonal functions or neural networks, trained on satellite-altimetry data, to identify spatial patterns of sea-level change. They then apply these spatial patterns to tide-gauge data to reconstruct past regional-mean and global-mean changes. These methods empirically account for the patterns of interannual DSL changes, but do not account for the difference between SSH and RSL or for the possibility that long-term DSL changes may exhibit different spatial patterns than short-term changes. They also do not account for the fingerprints of glacier and ice-sheet mass balance, which are dwarfed by DSL variability on an interannual scale but may prove important over longer time periods [e.g., 79]. Most recently, Hay et al. [11•, 94] attempt to address these limitations in Kalman smoother and Gaussian process regression frameworks that explicitly incorporate sea-level fingerprints, as well as information about the spatial patterns of long-term DSL change derived from atmosphere/ocean general circulation models. Efforts to develop new statistical techniques to interpret and analyze the sparse tide-gauge records, as well as to combine the tide-gauge data with satellite-altimetry observations, will likely continue for many years.
Resolving DSL variability in the pre-satellite altimetry era and partitioning forced changes from long-period modes of natural variability not captured by the 20-year altimetry record (Fig. 2b) require complementing tide-gauge records with reanalyses and/or geological sea-level proxies. Reanalysis products augment the reconstruction of offshore sea level [e.g., 95]. Though these products have limitations, reconstructions with ocean models dating back to 1950 show strong evidence of long-term climate oscillations, with moderation or reversal of the trends observed over the satellite period [e.g., 96]. However, without longer and more consistently fused records, it will remain difficult to determine the mechanisms underlying the longest observed modes, or to distinguish natural variability from a forced trend at a local level [63, 97].
Interpreting Geological Proxy Records
Proxy records (such as salt-marsh records, archaeological ruins, fossil reefs, speleothems, and other sedimentological indicators) provide insight into RSL and GMSL variability in the pre-observational period, over timescales ranging from centuries to millions of years. Simplistic interpretations of RSL proxy reconstructions have traditionally assumed that, once the geological background signal is removed, the remaining signal reflects “eustatic” GMSL change [e.g., 98, 99]. More sophisticated interpretations recognize that regional DSL [e.g., 100] and fingerprint effects [e.g., 84, 101] may significantly influence these records. Accordingly, extracting a GMSL signal from local RSL reconstructions may require a physically informed statistical methodology that accounts for these processes [e.g., 102].
Over the Late Holocene, long-term tectonics, sediment compaction, and GIA are often approximated as the long-term trend in sea-level records, under the assumption that the climatic contribution to late Holocene RSL change has been small [e.g., 103]. For multi-century observational records, these components can similarly be approximated as the long-term difference in rate from the global mean [e.g., 9••]. Over longer periods, however, GIA cannot be approximated as a constant-rate trend and must be fully modeled [e.g., 26].
A common approach for estimating the average Pleistocene tectonic uplift or subsidence rate at a specific site is to compute the difference between the observed elevation of a highstand marker of Last Interglacial (LIG) age and a standard estimate of the peak GMSL value for this period, generally chosen as 6 m, and dividing the difference by the age of the LIG (~125 kyr). This approach is, however, subject to potentially significant errors arising both from common underestimates of the LIG GMSL highstand [99, 102] and from failure to account for GIA and fingerprint effects .
Projections of future GMSL change are generally based on either a bottom-up assessment of the different contributory processes or on top-down semi-empirical methods [e.g., 104], which are based on the past relationship between temperature and rates of GMSL change; top-down reasoning by analogy to geological precedents is also sometimes used [e.g., 105]. As top-down methods aggregate the contributing processes together, they cannot be directly used for projecting RSL changes. Instead, projecting RSL changes requires methodologies that distinguish the different contributing processes discussed in previous sections [e.g., 9••, 74, 106, 107, 108]. Historically, these different processes have been modeled separately and then merged.
Much effort has been invested in capturing the response of DSL to a changing climate, principally using coupled atmosphere-ocean general circulation models (AOGCMs) [e.g., 36, 109•]. Griffies et al. [48••] demonstrate that the current generation of ocean climate models, using a common atmospheric state, can reproduce steric trends subject to errors that are likely related to the deep ocean’s long memory. Model spread is largest in polar regions, which they attribute to complex dynamics in water mass formation processes and boundary currents. In coupled simulations, Landerer et al. [109•] note improvement in the current generation of coupled models, but find large biases and spread in the equatorial and Southern Oceans.
Further research is required to gauge the ability of models to project future changes in DSL occurring over multidecadal to centennial timescales (Fig. 2c). Both locations highlighted here (the EUS and WTP) illustrate the lags inherent in the sea-level response and the interplay of natural and forced variability in DSL that is expected to persist through the twenty-first century [110, 111]. In particular, the processes underlying high, but uncertain, DSL rise projections on the Northeast US coastline demand closer attention [36, 110, 111].
However, these AOGCM improvements and uncertainty reductions must take place in the context of the complete RSL budget. Although climate modeling centers are pursuing the integration of the continental ice sheets, the process will take time. Furthermore, the remaining terms (non-climatic background processes, water storage, and glaciers) also possess significant uncertainties, and some are coupled to the climate. For future assessments and reconstructions, it is important that the broader sea-level research community consider which effects should be coupled and, if they are combined offline, how to consistently aggregate uncertainties.
As recently as a decade ago, researchers working on the various processes contributing to regional differences in sea-level change were often ignorant of each others’ existence . For example, in its discussion of future regional sea-level change, the IPCC’s Third Assessment Report acknowledged isostatic and tectonic effects in two sentences but otherwise focused exclusively on DSL—not recognizing the potentially larger contribution from fingerprint effects . The Fourth Assessment Report inaccurately dismissed future sea-level fingerprint effects as “small over most of the ocean” (, p. 814). By contrast, the Fifth Assessment Report  acknowledged the complex interplay of the processes described above.
Further work is needed to refine understanding of some key processes and especially their interactions. Models of GIA have incorporated progressively more realistic physics; however, applications to modern sea-level studies have rarely considered 3-D Earth structure in the GIA calculations, although numerical methods exist to do so [e.g., 32]. Furthermore, while sea-level fingerprints are well understood, projections of DSL change in the North Atlantic Ocean and Southern Ocean remain subject to considerable uncertainty. Separating the roles of long-period DSL variability and forced DSL changes remains a challenge [65, 66]. Moreover, DSL changes are related to changes in atmospheric circulation and heat content that also influence the mass balance of ice sheets. The interactions and dependencies between fingerprint effects and DSL also remain only rarely modeled . Feedbacks from sea-level processes, including GIA [e.g., 114], fingerprint effects [e.g., 115, 116, 117], and DSL [e.g., 118], may play important roles in ice-sheet evolution, but exploration of these feedbacks has been limited.
The last few years have also seen this knowledge applied to practical applications, with an increasing number of local sea-level rise projections that confront the complex set of contributory processes [e.g., 9••, 107, 119, 120, 121]. Their effective use for sea-level rise adaptation and planning will require the impacts community to develop and employ localized tools and forward-looking risk assessments [e.g., 4, 6]. New, rigorous methods of probabilistically interpreting geological and observational records of past changes are similarly incorporating model-based physical understanding of multiple processes [e.g., 11•, 102], but await wider application.
We thank M. Buchanan, E. Morrow, and two anonymous reviewers for the helpful comments. Funding was provided by National Science Foundation awards ARC-1203414 and ARC-1203415, National Oceanic & Atmospheric Administration grant NA11OAR4310101, and New Jersey Sea Grant project 6410–0012. This paper is a contribution to the PALSEA2 (Palaeo-Constraints on Sea-Level Rise) project of Past Global Changes/IMAGES (International Marine Past Global Change Study).
Conflict of Interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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