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

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.

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.

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  ∼ 10³–10²⁰ 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 km² 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].

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 km² 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 km² 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].

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An alternative perspective considers the fraction, not total, of county and city populations at vulnerable elevations, disentangling the influence of population density. More than 10% of the population lives below 1 m TIDEL in 38 counties and 544 cities (mean city population, 13 200). Half of these municipalities are in Florida and Louisiana, but North Carolina and New Jersey include over 40 each, New York 37, Maryland 27 and California 26. In 196 cities, more than 50% of the population lives below 1 m TIDEL. All told, 2150 towns and cities in the contiguous US have at least some residents living within one vertical meter of the high tide line.

Expanding our analysis to include higher water levels, we find a total area of ∼127 000 km² under 6 m TIDEL (∼70 000 km² 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.

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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.

We also examine the effects of various methodological choices on our results, summarized in tables 3 and 4. We 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 km² 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 km² in size, where stochastic effects from small sample size loom large.