The effects of sea-level rise (SLR) and other sources of increased water levels along the world’s coastlines are pervasive and varied (Williams, 2013). Because of the low-lying nature of many coastal lands, the topography, or elevation in relation to sea level, largely controls their exposure to adverse effects of increased water levels, both chronic conditions (SLR) and episodic events (storm surge inundation or king tide flooding). Elevation data, often in the form of digital elevation models (DEMs), are therefore critical for assessments of exposure, and corresponding vulnerability and risk, to permanent or temporary flooding and other effects of increased water levels along the coast.

For nearly four decades, elevation data, most often in the form of DEMs, have been used to identify low-lying coastal lands over broad areas to conduct assessments of the effects of rising sea levels (Schneider and Chen, 1980; Titus et al., 1991; Titus and Richman, 2001; Small and Nicholls, 2003; Ericson et al., 2006; Rowley et al., 2007; Dasgupta et al., 2008, 2010; Weiss et al., 2011; Haer et al., 2013; Blankespoor et al., 2014; Neumann et al., 2015; Hardy and Nuse, 2016; Kulp and Strauss, 2017; Small et al., 2018; Wolff et al., 2018). Over this period, the quality of DEMs available for use in assessments has improved, especially in terms of spatial resolution and vertical accuracy. For large-area assessments (regional, continental, global), several choices are available for DEMs for the required topographic information to project potential impacts of increased coastal water levels, whether a simple inundation model is used or a more complex process-based or probabilistic model is employed. Previous research has demonstrated that the quality of data, and associated transformations, used for elevation-based assessments must be well understood and applied to properly model potential impacts (Gesch, 2009; Coveney and Fotheringham, 2011; Cooper and Chen, 2013; Cooper et al., 2013, 2015; Gesch, 2013; Schmid et al., 2014; Dahl et al., 2017; Jones et al., 2017; West et al., 2018).

Uncertainty in climate change and coastal hazard assessments has been addressed in numerous studies. Le Cozannet et al. (2015, 2017) and Stephens et al. (2017) discuss the importance of considering uncertainties from all sources in assessments of sea-level change, but they do not specifically mention vertical uncertainty of topographic data used to map potential impact zones on the land surface. A number of studies address the effects of input elevation data uncertainty (Gesch, 2009; Kettle, 2012; Bell et al., 2014; Hinkel et al., 2014; Valentine, 2014) and conclude that higher resolution data with better vertical accuracy significantly improve assessment results. The choice of elevation model for an assessment study can also have a substantial effect on results owing to combined uncertainties of input datasets, especially elevation and population distribution (Lichter et al., 2011; Mondal and Tatem, 2012; Wolff et al., 2016). The result of many SLR assessments is a set of maps that spatially show the areas exposed to inundation or other adverse effects of specific scenarios of sea-level change, and such maps are enhanced by including a description of mapping uncertainty (Kostelnick et al., 2013; Retchless, 2018), often expressed as a confidence level.

Recently, within the coastal hazard modeling community there has been continued recognition that vertical uncertainty should be accounted for quantitatively to improve impact mapping and assessment. National Oceanic and Atmospheric Administration [NOAA] (2010) and Doyle et al. (2015) recognize that DEM vertical accuracy is a critical element in SLR impact assessments and that the uncertainties contributed by elevation data and its associated transformations should be explicitly addressed. Fortunately, there is a rich heritage of technical work on assessing vertical uncertainty (DEM error), its consequences and implications, and its use in improving applications (Hunter and Goodchild, 1995; Fisher and Tate, 2006; Wechsler and Kroll, 2006; Maune et al., 2007; Wechsler, 2007; Höhle and Höhle, 2009), and this body of work can be relied upon as a basis for approaches to rigorous handling of uncertainty in coastal inundation assessments.

The importance of the quality (spatial resolution and vertical accuracy) of the input elevation information in inundation assessments has been well recognized in some studies (Bales and Wagner, 2009; Coveney and Fotheringham, 2011; Zhang, 2011; Fraile-Jurado and Ojeda-Zújar, 2012; Sampson et al., 2016; Wolff et al., 2016; Mogensen and Rogers, 2018; Paprotny et al., 2018; Vousdoukas et al., 2018); however, numerous other studies make no mention of the uncertainty of the critical input elevation layer and the implications for the reliability of the results. There is a variety of DEMs with global or near global coverage mostly derived from remote sensing (Gesch, 2012b; Sampson et al., 2016) available for use in inundation modeling and assessment, yet better data are needed (Simpson et al., 2015). Therefore, it is critical that producers of such assessments understand, characterize, and describe the cumulative uncertainties from the underlying elevation data and associated transformations that propagate to the assessment results (maps and estimates of impacted area and resources). The purpose of this paper is to document the best practices in properly accounting for the vertical uncertainty inherent in all elevation-based SLR and coastal flooding assessments. Additionally, other best practices for such assessments extracted from the scientific record of successful studies are listed and described. Establishment of best practices, or standardized methodology, is recognized as an important advance in improving the usefulness of climate change vulnerability mapping at various scales and for multiple classes of stakeholders and end users (Preston et al., 2011).

When an elevation-based SLR or coastal flooding assessment is conducted, especially over broad areas, a simple inundation method known as the “bathtub” model is often used, an approach that has also been referred to as the “single-value surface” (National Oceanic and Atmospheric Administration [NOAA], 2010), “equilibrium” (Gallien et al., 2011), “planar” (Bates and De Roo, 2000), “hydrostatic” (Habel et al., 2017), and “static inundation” (Paprotny et al., 2018) method. To delineate the inundation zone with the bathtub method, the water level is simply raised on a coastal DEM by selecting all areas that are below the specified new water level height. The approach is improved by enforcing hydrologic connectivity (Poulter and Halpin, 2007; Poulter et al., 2008), ensuring that flooded areas have a direct hydrologic connection to the ocean, which is recommended as a best practice for coastal assessments. Limitations of the bathtub modeling approach have been identified (Passeri et al., 2015; Boyd et al., 2016), including failure of the DEM to represent the detailed hydraulic connections and barriers needed for accurate spatially explicit flood mapping (Gallien et al., 2011, 2013). Bathtub modeling can overpredict flood extent compared to hydraulic and hydrodynamic modeling approaches (Gallien et al., 2011, 2014; Seenath et al., 2016), especially at local scales, yet the simple approach realizes savings in input data and computation requirements (Kovanen et al., 2018) and under certain conditions can perform nearly as well as more complex models (Bates and De Roo, 2000). Another important consideration in using simple inundation models to assess potential impacts of raised coastal water levels is to recognize that not all areas will respond to increased water levels by simply becoming inundated (Gesch et al., 2009; Passeri et al., 2015; Lentz et al., 2016). Instead, some areas will adapt by responding dynamically. In these cases, maps of potential impact zones derived from simple bathtub models will indicate areas that may be affected by sea-level change, but not necessarily transition to permanent open water.

Notwithstanding the known limitations of bathtub modeling, the approach remains widely employed for coastal impact assessments, likely due to its ease of application, especially for initial screening and inventory across large areas. Thus, the analysis and discussion below on properly accounting for vertical uncertainty is directly relevant to simple inundation modeling. However, it is also applicable to more complex physical process-based and probabilistic models because they too invariably need to measure increased water levels, and elevation data are required to do so; therefore, vertical uncertainty must be considered.

The initial accuracy assessment was conducted on the DEMs for which coverage was available for all of CONUS: SRTM, ASTER GDEM (version 3), NED, and NED derived from lidar DEM source data (Gesch et al., 2014). Table 1 shows the accuracy assessment results for the full range of elevations across CONUS included in the reference data, as well as the results for only areas in the LECZ. The LECZ is defined as elevations less than or equal to 10 m above sea level, which is a commonly used elevation threshold to delimit coastal zones (McGranahan et al., 2007; Lichter et al., 2011; Neumann et al., 2015). For SRTM and ASTER GDEM, the elevation accuracy in the LECZ is degraded compared to the accuracy for all of CONUS, while for NED and NED with lidar source data, the accuracy is slightly improved in the LECZ. Because the primary interest for coastal assessments is in the low-lying areas subject to inundation and other adverse effects of increased water levels, the remainder of the results presented are for the LECZ. This approach follows the recommendation in other studies that emphasize accuracy testing with reference data representative of the area of interest to guard against overly optimistic results (Bolkas et al., 2016). Thus, limiting accuracy assessment to coastal areas (Du et al., 2015) is appropriate for this study.

When the inherent vertical uncertainty is considered, it is clear that global DEMs are not adequate for modeling fine increments of SLR (<1 m) over short planning horizons (<100 years) at high confidence levels (Table 4). SLRI_min and TL_min are easily calculated metrics based on the stated DEM accuracy (usually expressed as an RMSE) and are useful to quantify elevation-based coastal assessment parameters and their associated confidence levels. Numerous studies have used global DEMs for SLR and coastal flooding assessments without any regard for vertical uncertainty (elevation error), leading to large uncertainties in the assessment results with low confidence levels. There is ample evidence that SRTM and ASTER GDEM are severely limited for use in coastal assessments (Gesch, 2009; Gesch et al., 2009; van de Sande et al., 2012; Doyle et al., 2015; Griffin et al., 2015; Yan et al., 2015; Kulp and Strauss, 2016; Walczak et al., 2016; Yunus et al., 2016; Santillan and Makinano-Santillan, 2017; Smith et al., 2018). Both SRTM and ASTER GDEM are DSMs that generally overestimate elevations (especially in vegetated and built-up areas), so their use in coastal assessments leads to underestimating areas exposed to a given inundation level (van de Sande et al., 2012; Griffin et al., 2015; Kulp and Strauss, 2016; Smith et al., 2018). The results from the DEM accuracy assessment in this study (Table 3) do indicate the overestimation of elevation (positive bias) by SRTM and ASTER GDEM as reflected in the positive mean error for each. A bias (that is, a larger negative or positive mean error) is often an indicator that the error distribution is non-normal; therefore, applying linear scaling factors to the RMSE to derive LE90 or LE95 is not valid, so percentile error methods should be used (Maune et al., 2007; ASPRS, 2015). In the analysis presented here, the RMSE was used to derive SLRI_min even when the DEMs had a positive bias, as often only the RMSE is known and the individual error values are not available for percentile error calculations. As shown in Table 3, however, SLRI_min68 and SLRI_min95 calculated based on the 68th percentile and 95th percentile errors, respectively, are not much different than those calculated based on the RMSE, so the finding that none of the global DEMs support an increment of 1 m is not changed.

There have been some recent improvements to SRTM (O’Loughlin et al., 2016; Kulp and Strauss, 2018; Moudrý et al., 2018) and ASTER GDEM (Arefi and Reinartz, 2011; Yang et al., 2018) by removing vegetation and other elevated features that caused the positive bias in the original datasets, often with the correction implemented by integrating Ice, Cloud and land Elevation Satellite (ICESat) spaceborne lidar data,. Merges of SRTM and ASTER GDEM (Satgé et al., 2015; Crippen et al., 2016; Yamazaki et al., 2017) have resulted in improved data as well. However, none of these improvements bring the DEMs to the level where they will support high confidence, quantitative coastal assessments with sub-meter water level change increments and planning horizons within the current century. The improvements to SRTM, namely CoastalDEM, NASADEM, and MERIT, all still have an RMSE of about 3 m, which equates to a minimum increment of more than 6 m at 68% confidence (Table 4 and Supplementary Table S1). AW3D30 is in this same class, with an RMSE of slightly more than 3 m (Table 4 and Supplementary Table S3). TanDEM-X does offer an improvement over SRTM, ASTER GDEM, and AW3D30 (Grohmann, 2018) and exhibits very little positive bias (Wessel et al., 2018), although its vertical error does result in a SLRI_min of several meters (Table 4 and Supplementary Table S4).

Despite ample evidence of the significant limitations of global DEMs, especially SRTM, for coastal assessments, they have been used extensively for mapping and describing potential impacts of SLR and coastal flooding, often with assessment parameters (small water level increments and short planning horizons) that fall well within the error bounds of the underlying elevation data (Dasgupta et al., 2008, 2010; Hanson et al., 2010; Curtis and Schneider, 2011; Blankespoor et al., 2014; Hardy and Nuse, 2016; Kopp et al., 2017; Runting et al., 2017; Brown et al., 2018a,b; Gebremichael et al., 2018; Haer et al., 2018; Jevrejeva et al., 2018; Lincke and Hinkel, 2018; Nicholls et al., 2018; Prahl et al., 2018; Rasmussen et al., 2018; Schuerch et al., 2018; Wolff et al., 2018). Some of these studies used a model or database in which the global DEM is embedded, such as the Dynamic Interactive Vulnerability Assessment (DIVA) modeling framework (Hinkel, 2005; Vafeidis et al., 2008), so the inherent vertical uncertainty is contained within model or database components. This serves as a caution that even if a DEM is not a direct input or is not processed or analyzed directly in an inundation modeling exercise, vertical error may be implicit in sub-model or database components, thus modelers should be aware of an obscured source of uncertainty in their assessment. Some assessments have used even coarser global elevation models (1-km spatial resolution) with water level increments in the range of 0.3–2 m (Xingong et al., 2009; Nicholls et al., 2011; Brown et al., 2013; Neumann et al., 2015). All these assessments present statistics about the potential impact zones, including the areas and oftentimes the corresponding population and economic assets that are at risk of adverse effects. However, there is no quantitative statement about the quality of the reported results, for instance confidence level, and no expression of the uncertainty contributed by vertical error. In all cases, the water level change increments used in the assessments are not supported at high confidence levels, as the increments are very small compared to the DEM vertical error (and the derived minimum increment), which calls into question the veracity of the reported results. Reporting of inundated areas (and population and resources contained therein) at intervals of 1 m or less implies a degree of accuracy that is not present in global DEMs, and providing such numbers can be misleading to readers, especially because most will not be familiar with the concepts of vertical uncertainty of elevation models. As much as there is a desire and need for global SLR and coastal flooding analyses with water level increases on the order of a meter or less, current global DEMs do not have the requisite vertical accuracy to derive results with high confidence levels using fine increments, and thus they should not be used for such mapping.

Even though global DEMs are not appropriate for spatially explicit mapping of small increments of inundation with high confidence, they can be used effectively for delineation of general LECZs, and inventorying the population and resources contained within. As the RMSE improves for global DEMs, the confidence level for delineation of 10- and 20-m coastal zones increases (Table 5). The LECZ can be the framework for entire studies (McGranahan et al., 2007; Geisler and Currens, 2017), so a quality delineation of such a zone at a known confidence level is critical. For finer vertical slices, and subsequent spatially explicit exposure maps, much higher accuracy elevation data, such as that derived from lidar, high-resolution stereo photogrammetry, and ground survey, are required (Gallien et al., 2013). Airborne lidar, in particular, is an important elevation data source for coastal assessments (Gesch, 2009; Cooper et al., 2013; Runting et al., 2013; Zhu et al., 2015; Enwright et al., 2017), as it can meet the requirements for modeling fine increments of water level changes at high confidence and generally covers larger areas, even regional to national coverage.

Vertical uncertainty is a critical factor to consider and account for in elevation-based assessments of SLR and coastal flooding exposure. Some studies have properly handled the vertical uncertainty, as expressed in the combined elevation data and transformation errors, and in doing so provide valuable additional information to the user about confidence in the mapping and likelihood of projected impacts. However, many other studies ignore the vertical uncertainty stemming from the underlying elevation data and use assessment parameters (water level change increments and planning horizons) that are well within the error bounds and are not appropriate for generating high confidence results, thus leading to questionable delineations of impact zones and inventories of the population and resources contained therein.

The simple methods described herein for selecting coastal assessment parameters (minimum increment of water level change, SLRI_min, and planning horizon, TL_min) that are supported at high confidence levels by the vertical qualities of the elevation data are useful for characterizing the capabilities of global DEMs. Application of these methods to current global DEMs (SRTM and its derivatives NASADEM, CoastalDEM, and MERIT; ASTER GDEM; AW3D30; and TanDEM-X) demonstrates that none of these DEMs support coastal inundation or flood assessment at high confidence levels for small water level increments (<1 m) or short planning horizons (<100 years). High confidence assessments of scenarios with cumulative SLR of less than 1 m or planning horizons within the current century require elevation data with much better vertical accuracy than that afforded by global DEMs, which points to high-accuracy sources such as terrestrial and airborne lidar, high-resolution photogrammetry, and ground surveys. These technologies produce high-quality elevation data that facilitate development of detailed spatially explicit inundation maps.

The key finding demonstrated in this study leads the list of best practices to follow in elevation-based coastal inundation assessments.

As the use of these best practices increases, assessments will improve and become more valuable, especially by having quantified and published uncertainty information (confidence levels and likelihood statements), and results will be directly comparable across different assessments.

In the future, as elevation datasets with large-area coverage improve, analyses utilizing the improved elevation information and the community best practices will result in robust assessments. Ongoing enhancements to widely used methods will also help to improve progress, such as better incorporation of information on physical processes, including tidal regimes (Hanslow et al., 2018) and water level attenuation due to surface roughness (Vafeidis et al., 2017), into bathtub modeling used for broad area screening. However, for elevation-based coastal assessments, the primary factor affecting quality and usefulness of results remains the choice of the elevation model used (National Oceanic and Atmospheric Administration [NOAA], 2010; Doyle et al., 2015; Wolff et al., 2016; Yunus et al., 2016), and how the DEM vertical uncertainty is characterized and accounted for (West et al., 2018). Open-access global DEMs have been a major advance for many Earth science and environmental modeling applications, but the findings from the present evaluation of currently available datasets for detailed assessments of SLR and coastal flooding exposure add to the recent recognition (Schumann et al., 2014; Simpson et al., 2015; Sampson et al., 2016) that the requirement remains for a freely available, high-accuracy, high-resolution global elevation model that supports quantitative coastal inundation hazard assessments at high confidence levels.

All data generated or analyzed during this study are included in the main text of this publication.

DG designed the study, performed the data collection, processing, and analysis, and wrote the manuscript.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.