Tidally adjusted estimates of topographic vulnerability to sea level rise and flooding for the contiguous United States

Because sea level could rise 1 m or more during the next century, it is important to understand what land, communities and assets may be most at risk from increased flooding and eventual submersion. Employing a recent high-resolution edition of the National Elevation Dataset and using VDatum, a newly available tidal model covering the contiguous US, together with data from the 2010 Census, we quantify low-lying coastal land, housing and population relative to local mean high tide levels, which range from ∼0 to 3 m in elevation (North American Vertical Datum of 1988). Previous work at regional to national scales has sometimes equated elevation with the amount of sea level rise, leading to underestimated risk anywhere where the mean high tide elevation exceeds 0 m, and compromising comparisons across regions with different tidal levels. Using our tidally adjusted approach, we estimate the contiguous US population living on land within 1 m of high tide to be 3.7 million. In 544 municipalities and 38 counties, we find that over 10% of the population lives below this line; all told, some 2150 towns and cities have some degree of exposure. At the state level, Florida, Louisiana, California, New York and New Jersey have the largest sub-meter populations. We assess topographic susceptibility of land, housing and population to sea level rise for all coastal states, counties and municipalities, from 0 to 6 m above mean high tide, and find important threat levels for widely distributed communities of every size. We estimate that over 22.9 million Americans live on land within 6 m of local mean high tide.


Introduction
Anthropogenic greenhouse gas emissions by 2100 may be sufficient to irreversibly commit the planet to 4-6 m of global sea level rise within the next several hundred years [1][2][3]. This century, global rise may approach 1 or even 2 m [4,5]. In the coming few decades, rising seas threaten to interact with localized storm surges to generate more frequent floods reaching just as high [6,7]. And factors such as land subsidence [8,9] and shifting ocean currents [10][11][12] are expected to boost sea level increases in some regions. Together, these findings underscore the critical importance of quantifying land, population and infrastructure in low-lying coastal zones-or what might be called topographic vulnerability-as a basic input for risk assessments and policy decisions.
However, geographic variation in baseline water levels has posed an important complication for completing this work at US regional to national scales. Topographic vulnerability to sea level rise at any location must properly be assessed with respect to local water levels, not an arbitrary external reference (e.g. a nationwide definition of elevation zero). The most involved approaches integrate projected sea rise with modeled standard local flood levels, such as annual or century flood levels. Requiring significant detail, data and computation, this family of methods has been applied narrowly in some US cities and states [13][14][15][16]. More simply, sea level rise can be referenced against high tide levels as measured by local tide gauges [17]. Some wide-area studies have gone to great lengths to interpolate and infer high water elevations extensively [18,19]. However, other state through national-scale studies have skipped this labor-intensive step and not incorporated local water level references at all [20][21][22][23].
A valuable development now signals the time for a new national assessment at the scale of the contiguous United States (CONUS): the National Oceanic and Atmospheric Administration (NOAA) has just completed and validated tidal elevation models covering the entire coast at fine resolution. Outputs are available through a product called VDatum (vdatum.noaa.gov; [24]). It is now relatively straightforward to conduct a national-scale analysis of potential sea level rise impacts that accounts for local differences in mean sea level and tidal amplitude, which together determine high tide levels. Based on VDatum estimates, the 99% range of the elevation of mean high tide at shoreline is −0.2 to 2.8 m (North American Vertical Datum of 1988, or NAVD 88) for CONUS (see figure 1), a scale of variation that clearly cannot be ignored in analyses of coastal vulnerability contemplating the critical first meter-plus above the water line.
Steady and widespread improvement in elevation data since the last national analysis of topographic vulnerability to sea level rise in 1991 [18] also suggests the timeliness of a new effort.
In this letter, we estimate the land, housing and population within 0-6 m in elevation of local high tide lines across the contiguous US, and present aspects of this topographic vulnerability at CONUS, state, county and municipal levels. We capitalize on VDatum and use best-available CONUS-wide elevation data to develop a new dataset characterizing elevation above local mean high tide, and employ this as the basis for our analysis. We also compare this approach against one without tidal adjustment, to assess the importance of taking local tide levels into account; and against two further methodological variants, to demonstrate the robustness of our approach.

Data
The National Elevation Dataset (NED) and VDatum constitute the core data inputs for our analysis. The NED is a digital elevation model (DEM) produced by the United States Geological Survey (USGS) and available at a variety of horizontal resolutions. Elevations are provided in NAVD 88. Previous regional and national sea level rise analyses have used the 1 arcsec NED (∼30 m resolution) [23,22], but the USGS has now completed coverage of coastal CONUS at 1/3 arcsec resolution (∼10 m). We use the 1/3 arcsec dataset, the finest resolution data publicly available with full coastal coverage. The USGS has most recently estimated vertical root mean square error for the 1 arcsec NED at 1.89 m [40], down from 3.74 m in 1999 [25], as the dataset has been revised to incorporate more source lidar data and improved algorithms for interpolation. Local error levels generally depend on the quality of local NED source data [26,27], and may commonly be lower than average in coastal plains [21]. A recent study suggests 1/3 arcsec data perform slightly better than 1 arcsec data for sea rise vulnerability analyses [17].
VDatum makes available NAVD 88 elevations for different modeled tidal datums on lattices of varying resolution, but near-shore point spacing is generally on the order of 100 m. 36 regional models, adding up to total coverage of the CONUS coast, are each calibrated across extensive networks of water level stations. Standard deviation of vertical error is on the order of 0.1 m in each region [28,29]. We use VDatum version 01, except for parts of the Gulf of Mexico where we use version 02, released in a 10 August 2011 update.

Analysis
Our analysis consists of four main steps: delineating land area, incorporating tidal elevations, identifying potential risk zones and tabulating assets within various administrative boundaries.
Ocean or saltwater marsh misclassified as land leads to overestimates of susceptible total land area [19]. We therefore begin by admitting 1/3 arcsec NED cells as land according to a consensus of three independent data sets. First, the cells must be designated as land (have non-zero elevation) within the NED itself. Second, we include only cells with centers landward of NOAA's Medium Resolution Digital Vector Shoreline (shoreline.noaa.gov). Finally, we eliminate NED cells with centers inside areas classified in the National Wetlands Inventory (NWI, [30]) as estuarine or marine wetland or deepwater. In computing total land area susceptible, we include NWI freshwater wetlands. We also compute dry land area susceptible, excluding NED cells with centers inside areas classified as freshwater wetlands. True water chemistry may vary from NWI classification.
For each delineated land cell, we estimate what we call 'tidally adjusted elevation', or TIDEL-the elevation above local Mean High Water. Mean High Water is formally defined by NOAA as the elevation of high tides averaged within a reference 'epoch', or period (currently 1983-2001 for most locations). To calculate TIDEL, we first assign a Mean High Water value to each NED cell by matching it with the nearest point covered by VDatum. We then subtract the cell's assigned Mean High Water elevation from its unadjusted elevation (UNEL) given by the NED. We use Mean High Water and UNEL as expressed in NAVD 88. In areas where spring high water-not available in VDatum-extends well above Mean High Water, this study understates vulnerability.
After calculating values for TIDEL, we identify potential risk zones at different elevations using four methods for comparison. (1) For our main analysis, we simply identify cells under each threshold from 0 to 6 m according to each cell's TIDEL. (2) We use the same method applied to UNEL values, in order to evaluate the error that would be introduced by ignoring the difference between NAVD and Mean High Water. (3) From the sets of cells under each TIDEL threshold, we eliminate areas not contiguous to the ocean via eight-way connectivity [31]. And finally, (4) we employ the first method but substitute the 1 arcsec NED for 1/3 arcsec (both editions from February 2011). Neither 1/3 arcsec data nor VDatum were available for previous wide-area studies, but these studies are split between using pure thresholds [20,32,22,17] or also enforcing connectivity [21,16,23]. We emphasize the pure threshold approach here for simplicity and in a spirit of conservative protectiveness. Apparently isolated depressions may be connected to water via porous bedrock geology, a feature of densely populated southeast Florida, one of the most topographically vulnerable areas nationwide [33,34]. Depressions may also be connected via channels the NED fails to pick up, due to error or limited resolution. In addition, sea level rise may cause problems in isolated low zones during rainstorms by reducing drainage and creating backups into wastewater treatment facilities [35].
To tabulate population and housing potentially affected, we use block-level data from the 2010 US Census (www. census.gov), and assume development on dry land only, following Gill et al [36]. For each Census block, we divide the population and number of housing units by the number of dry land cells with centers inside the block. We assign the resulting per-cell density values back to each cell, creating two new 1/3 arcsec raster data sets for population and housing unit density. To estimate the population or housing at risk for a particular water level and method, we simply add up population and housing densities of land cells affected under the specification. Our analysis considers the elevation of land upon which housing stands, and makes no special provision for elevated or multi-story buildings.
To tabulate risks within states, counties or municipalities (alternatively, 'cities', by which we here refer to incorporated towns or cities, or Census Designated Places, of any size), we total affected area, population and housing within administrative boundaries as specified by 2010 Census TIGER Line data.

Error and the resolution of vertical increments
We conduct our analyses at 1 m vertical increments, following previous work with equal or finer vertical resolution [32,16,17,23]. At the same time, a recent review cautions that NED elevation error is too great to support inundation vulnerability map-making with 1 m intervals [27]. This concern sensibly applies with respect to confidence in the classification of each individual point on a map as higher or lower than closely spaced elevation thresholds. However, sub-meter vertical resolutions should be acceptable for aggregate vulnerability analyses at municipal and larger scales, where numerous individual errors should largely offset each other across ∼10 3 -10 20 elevation values. Recent work comparing vulnerable area tabulations using 1 arcsec NED data versus high accuracy lidar-based data implicitly supports this argument, finding agreement within 4-9% at scales from 10 to 4000 km 2 for the affected area, despite an order-of-magnitude difference in root mean square error values between the elevation datasets used [21,17]. We do not conduct our own error analysis here, instead limiting ourselves to generation of best estimates. Data sources of varying quality underlie the NED in a complex spatial patchwork, with varying consequences for vertical error from place to place [26,27]. Terrain slope and roughness and other factors likely play further roles [37,21]. A national-scale assessment of NED vertical error in coastal areas, as it applies to various metrics of topographic vulnerability, merits separate and detailed study, and is a continuing project of these authors. Although we do not consider the impact of future shore protection activities on the magnitude of inundation from sea level rise, this study complements a recent assessment that did so [38].

General impacts
We begin with a focus on pure threshold-based results below 1 m TIDEL, because this level represents the first front of vulnerability, where some impacts should be felt by mid-century as storm surges combine with sea level rise [6]. Furthermore, a recent survey showed almost 60% of Atlantic coastal land under 1 m UNEL is expected for development [38], adding urgency to provision of sea rise risk information at lowest elevations.
We find that ∼32 000 km 2 of total land area, a footprint larger than Maryland, lies less than one vertical meter above the high tide line in the coastal contiguous US, including ∼9000 km 2 of dry land. 1.9 million housing units occupy this land, and shelter 3.7 million people, or 1.2% of the national population. These totals include a fraction of land already below high tide line-for example, in the New Orleans area.
Among states (see table 1), land below 1 m TIDEL is most concentrated in the Gulf and lower mid-Atlantic (Louisiana, Florida, the Carolinas), well-known loci of concern around sea level (see e.g. [23]). With respect to potential population vulnerability, Florida stands out most, followed by Louisiana, California, New York and New Jersey, illustrating significant exposure on every coast. Variable population densities drive the differences among numbers and rankings between population and land. Ranked housing exposure tracks population vulnerability well. For economy of presentation, we focus on land and population over housing results hereafter, but more extensive results are available in tables A.1-A.6 and online (see below).
Results for counties (figure 2) and cities (figure 3) help further pinpoint hotspots of potential vulnerability, even within wider areas of lower topographic risk. Particularly large populations are exposed in: New York City and Long Island; the New Jersey shore; the Norfolk, Virginia area; near Charleston, South Carolina; coastal cities across Florida, especially its southeast and the Tampa area; New Orleans; the San Francisco Bay Area and San Joaquin Delta; and greater Los Angeles. This last center of concern merits special note because recent research suggests that coastal floods may reach locally rare heights more swiftly in southern California than almost any other CONUS area, when considering effects of sea level rise integrated with storm surge patterns [6].  Expanding our analysis to include higher water levels, we find a total area of ∼127 000 km 2 under 6 m TIDEL (∼70 000 km 2 of dry land), occupied by 11.1 million housing units and 22.9 million people, or 7.4% of the national population. 6 m represents a possible multi-century sea level rise commitment based on greenhouse gas emissions this century. Table 2 shows land, housing, and population statistics below 0 m TIDEL (some land is below water level but protected by levees, such as in New Orleans) and then in 1 m elevation bands up to 6 m TIDEL. The most striking feature is how dry land population density varies inversely with TIDEL, underscoring vulnerability. Louisiana (with high densities under 0 m TIDEL) and Florida (with high densities under 2 m TIDEL) drive this trend (see tables A.5 and A.6). However, CONUS dry land population density under 0 m TIDEL still appears slightly greater than at any level from 1 to 6 m, even when Louisiana and Florida are excluded (figure A.1).   Figure 4 shows populations under 1-6 m TIDEL in selected states. Florida commands a far lead in vulnerability at every level. Among other states, California and New York overtake Louisiana as hotspots at the higher elevations, with Virginia and New Jersey not far behind. In 1269 cities, over half the residents live below 6 m TIDEL. Of these cities, 448 are in Florida.
Previous work has generally assumed uniform fine-scale population densities over total land area [16,17], including at scales considerably larger than the great majority of Census blocks [22]. We refine this approach slightly, by limiting the area over which we calculate density to dry land only. We therefore compute greater densities, over smaller footprints, for Census blocks intersecting freshwater wetland. These footprints tend to occupy slightly higher terrain than mean block elevations, since dry land is generally higher than adjacent wetland. Screening out freshwater wetlands in this way reduces our vulnerable population estimates by 6.4% and 1.7% at 1 m and 6 m TIDEL, respectively, across the contiguous US, but with effects up to 31% in individual states at 1 m.
Other authors have argued that estimates based on uniform density assumptions should be viewed as upper bounds, expressing concern that housing is commonly concentrated within the upper elevation portions of low-lying Census blocks [36]. To our knowledge, no such bias has been quantified. Such a pattern would mean the results presented here overestimate population and housing vulnerability, and may misconstrue the vertical distribution of coastal population densities at state and national scale. However, over 90% of the susceptible population identified in our analysis (at 1 and 6 m TIDEL alike) reside in Census blocks which exceed the population density threshold set by the US Census to define an urban area 'core' (at 386 km −2 , double the density required for 'surrounding' urban blocks). Core urban density would appear to leave modest room for housing to sort by elevation within Census blocks, depending upon local geography. Roughly 40% of susceptible population identified lives at densities equal to or greater than that of Washington, DC (3806 km −2 ). Development may also concentrate close to the water in places, biased toward lower elevations (as suggested but not demonstrated by the large-scale elevational gradient of dry land density just described). Future research to refine population and housing vulnerability estimates by quantifying any vertical bias in coastal area development would be a welcome contribution to this field.

Effects of methodology
We also examine the effects of various methodological choices on our results, summarized in tables 3 and 4. We Table 3. Differences in CONUS vulnerability estimates across methodology contrasts, at different water level thresholds. Each contrast compares results based on the core methodology-which uses TIDEL, pure thresholds, and 1/3 arcsec data-against an alternative approach differing by one methodological variable, as indicated. compare our core approach, which employs TIDEL, pure thresholds, and 1/3 arcsec data, against three alternatives, which each differ with respect to one of these dimensions.
Making tidal adjustments to elevation-using TIDEL as compared to UNEL-unsurprisingly drives the largest differences among methodologies we explore. CONUS total land area under 1 m increases by 32%, and population almost doubles (87% jump). The difference between land and population effects is consistent with the increasing fraction of dry and thus habitable land with elevation (see table 2).
The contrast between TIDEL-and UNEL-based results must and does decrease asymptotically toward zero with increasing elevation, as the area of non-overlap shrinks relative to the area of overlap. However, at 6 m, TIDEL-based CONUS estimates still exceed UNEL-based ones by 4.9% and 8.3%, respectively, for land area and population vulnerable (table 3). The availability of VDatum combined with the unsurprising but large effects of using tidally adjusted elevation data together suggest that future studies in this area should not neglect to employ tidal adjustments.
The methodological choice second in consequence is whether to use only thresholds, or also to enforce connectivity to the sea. This choice may also be viewed simply as a decision about what to measure. Using tidally adjusted elevations, we find that the pure threshold approach generates CONUS estimates 3.9% and 8.2% higher for topographically vulnerable total land area and population, respectively, at 1 m TIDEL. Miami-Dade and Broward counties in southeast Florida account for much of this contrast; without them, differences in these estimates would drop to 3.0% and 2.7%. A similar dynamic drives results at 3 m TIDEL, where Palm Beach County, also in southeast Florida, includes about two-thirds of the total CONUS land under the threshold but not connected to the ocean. In each of these cases, very narrow and often long, nearly linear margins separate connected and unconnected areas below elevation thresholds, underscoring the sensitivity of results (under connectivity) to fine topographical variation or small NED errors. Southeast Florida has a flat and engineered landscape, full of canals and levees, features likely responsible for the patterns identified here. But the region's porous geology means seawater may pose lateral threats even where surface topography would appear to block it, and southeast Florida is already struggling with saltwater intrusion into aquifers, exacerbated by recent historic sea level rise [35].
The excesses of threshold-over connectivity-based estimates decline to 0.8% for CONUS land and 0.4% for population by 6 m TIDEL, driven at least in part by the same logic of overlapping areas applicable to the UNEL/TIDEL contrast. The one strong contrast occurs, as expected, at less than 0 m TIDEL, where, in principal, all nontidal land should be protected by levees or other features, leaving zero exposure when connectivity is considered. Our analysis captures some of this protection, but finds 5410 km 2 of vulnerable land even when applying connectivity. This result suggests limitations in assessing connectivity employing the elevation dataset used, likely due to its horizontal resolution.
Finally, we compare results across 1/3 and 1 arcsec editions of the NED, using TIDEL and the pure threshold approach. At the scale of CONUS, the differences are negligible. Table 3 summarizes each of these three methodological comparisons at CONUS scale. However, contrasts may be much greater when considering smaller areas, due to the smaller and more geographically concentrated samples of NED cells involved. Table 4 compares distributions of 1 m results for cities, the smallest geographic unit in this study. Results here reconfirm the strong effect of tidal adjustment, the only factor with a notable median influence. At higher percentiles, astronomical TIDEL:UNEL potential impact ratios are not surprising, considering the many municipalities with high tides at or above 1 m UNEL. Pure threshold-based results exceed results enforcing connectivity by no more 4-7% in three quarters of affected cities, although threshold results more than double their counterparts in about 5% of municipalities. Finally, the switch from 1 to 1/3 arcsec NED resolution shows a narrower range of effects. The few changes in total land area greater than doublings or less than halvings are confined to towns under 0.2 km 2 in size, where stochastic effects from small sample size loom large.

Concluding remarks
In this letter, we have presented an analysis of the topographic vulnerability of the coastal contiguous US to sea level rise and flooding, adjusted to account for local high tide levels. This adjustment carries large consequences. We estimate 3.7 million people live within one vertical meter of their local high tide line-87% more than an estimate of population living below 1 m in unadjusted elevation (NAVD 88).
Our simple threshold elevation approach may overestimate vulnerability because it includes areas the NED identifies as isolated depressions, potentially protected from flooding by natural topography or engineered features, such as levees in southeast Florida. However, our threshold-based results are generally quite close to those incorporating connectivity, and are fundamentally more robust: error in one cell or cluster cannot amplify by changing landscape connectivity and thus forcing the inclusion or exclusion of potentially large areas. Both approaches still include areas protected by features not fully represented in the DEM used-for example, low-lying parts of New Orleans protected by levees. The threshold method conservatively includes areas that appear isolated on the surface but might experience impacts via reduced drainage, via channels too fine to appear in the DEM, or via porous bedrock. As already noted, the last appears a key concern in Florida, where connectivity makes the largest difference in our topographic vulnerability estimates. Greater understanding of this threat should be a priority for future research.
More broadly, our main goal is to indicate levels of potential concern, and inspire more detailed local work; not to generate precise flood or risk maps. Topographic vulnerability is an important factor contributing to inundation risk, but it is also one among many acting at various time scales.
For example, patterns of development will probably play one of the strongest roles in both the short and long terms. At the highest level, the amount of population and infrastructure potentially under threat will depend on whether low-lying coastal development continues unabated (see e.g. [38]) or, at the other end of the spectrum, communities begin to retreat. At a secondary level, adaptive measures such as enhancing ecological buffers or building levees or seawalls will influence vulnerability, and already do so today.
Over the long term, coastal erosion may speed impacts, while sediment deposition, wetland accretion and beach migration may buffer vulnerability. However, coastal development inhibits many of these buffers, while often enhancing erosion, and generally more so in more populated areas [39].
As a final factor, the speed of sea level rise itself, and its relationship to the distribution of local flood sizes, will set the pace at which progressively higher elevation zones become exposed to significant risk. It is our hope and belief that analyses of topographic vulnerability, such as this one, combined with assessments of temporal vulnerability (e.g. [6]), can provide useful guidance concerning which locations may see the greatest sea rise induced risks soonest.
Topographic vulnerability estimates for every coastal city, county and state in the contiguous US are available at sealevel.climatecentral.org/data01.