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EVALUATION OF VECTOR COASTLINE FEATURES EXTRACTED FROM ‘STRUCTURE FROM MOTION’-DERIVED

ELEVATION DATA

NICOLE KINSMAN1, ANN GIBBS2, MATT NOLAN3

1. Alaska Division of Geological & Geophysical Surveys, 3354 College Road, Fairbanks, AK 99709, USA. nicole.kinsman@alaska.gov

2. U.S. Geological Survey, Pacific Coastal & Marine Science Center, 400 Natural Bridges Drive, Santa Cruz, CA 95060, USA. agibbs@usgs.gov

3. Institute of Northern Engineering, University of Alaska Fairbanks, Fairbanks, AK 99775, USA

Abstract: For extensive and remote coastlines, the absence of high-quality elevation models—for example, those produced with lidar—leaves some coastal populations lacking one of the essential elements for mapping shoreline positions or flood extents. Here, we compare seven different elevation products in a low-lying area in western Alaska to establish their appropriateness for coastal mapping applications that require the delineation of elevation-based vectors. We further investigate the effective use of a Structure from Motion (SfM)-derived surface model (vertical RMSE<20 cm) by generating a tidal datum-based shoreline and an inundation extent map for a 2011 flood event. Our results suggest that SfM-derived elevation products can yield elevation-based vector features that have horizontal positional uncertainties comparable to those derived from other techniques. We also provide a rule-of-thumb equation to aid in the selection of minimum elevation model specifications based on terrain slope, vertical uncertainties, and desired horizontal accuracy.

Introduction

It has become common practice to utilize digital elevation models (DEMs) in coastal mapping applications to delineate elevation contours of significance; for example, a vector shoreline position based on local tidal datum or an inundation extent based on a known or modeled flood level. These elevation-derived features are useful in coastal mapping because they can be produced rapidly and consistently in a GIS workspace. For shoreline geo-location, elevation-based vectors also minimize interpretation errors associated with visual identification of proxy shoreline indicators such as the vegetation line, dune toe, or High Water Line (HWL; White, 2007). DEM-based cartographic procedures have also introduced standardization to management tools such as flood maps (NRC, 2007).

The Ground Sample Distance (GSD) and absolute positional accuracy of a DEM surface are paramount in the determination of which types of coastal mapping applications these datasets can be incorporated into. For example, a DEM with a

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coarse GSD may be suitable for mapping regional-scale vulnerabilities to relative sea level rise, but the same topographic dataset would be inappropriate for use in a community-scale flood map designed for regulatory purposes. Similarly, a DEM with a poor absolute accuracy may mirror the vertical uncertainties associated with a modeled tsunami inundation level, but much smaller vertical accuracies are required to correctly delineate a features such as navigational shoreline positions.

While the usefulness of a DEM increases with resolution and accuracy, many high-quality DEM data sources remain prohibitively expensive for investigations that require frequent re-measurement, cover large areas, or are in geographically remote areas. Alternative DEM products in areas lacking lidar coverage may include those derived with standard softcopy photogrammetry from aerial- or satellite-based sensors, Interferometric Synthetic Aperture Radar (IfSAR), or newly-adopted Structure from Motion (SfM) photogrammetry.

Fundamentally, SfM photogrammetry uses parallax triangulation algorithms similar to those used in traditional photogrammetry to calculate a surface point cloud from overlapping image pairs; the advantage of the SfM approach is that it harnesses modern computational power so that this triangulation also calculates variables that previously needed to be measured independently, such as the internal camera calibration values and photo tilt. This capability allows more minimal constraints on the data collection, which results in a relaxation of equipment requirements and a significant decrease in hardware expense. Here, we present a case study in western Alaska to assess the adequacy of SfM-derived products for use in applied coastal mapping.

Study Location

The village of Unalakleet (pop. 688), on the central west coast of Alaska, USA (Fig. 1), is situated on a sand and gravel barrier spit that is bounded to the west by Norton Sound. The area experiences a mean tidal range of approximately 1 m and is exposed to coastal storms that develop in the Bering Sea and build up storm surge levels of >3 m in the shallow western waters of Alaska’s Chukchi Sea. The ground elevation on the Unalakleet spit is less than 6 m above MSL.

On average, three large low-pressure systems (winds >15 m/sec) move through the Norton Sound region each year and these storms frequently cause flooding in the developed portions of Unalakleet. Past coastal flooding events have moved structures off their foundations, shut down the power plant, damaged the coastal revetment, and in 1965 a 5.5 m (relative to local MSL) storm surge triggered a partial evacuation of the village (Kinsman and DeRaps, 2012). Unalakleet does not presently participate in the U.S. National Flood Insurance Program and there are no regulatory flood maps for the area.

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Unalakleet was selected as a case study because it is characteristic of many Alaska coastal communities at risk of storm-surge flooding, both in the nature of the area’s coastal setting and in the limited quality and availability of datasets for the production of coastal map products. Additionally, a number of datasets that do not typically exist for other villages in Alaska are available for Unalakleet, such as recently calibrated tidal datums and lidar elevation data from 2005. Opportunistic field activities in the region allowed for the collection of an SfM-type dataset as well as independent ground control points (GCPs).

Fig. 1. (a) Aerial orthoimage (September 2014) of Unalakleet, Alaska, with dots marking the positions of 12 independent GCPs collected in October 2014. (b) Oblique aerial image of the Unalakleet spit, looking northwest from across the inlet. The map inset illustrates the location of Unalakleet in Alaska (63.8789° N, 160.7897° W). (c) Oblique perspective view, looking northwest, of the SfM-derived orthoimage draped on the DEM.

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Methods

2014 SfM Airborne Image Collection and DEM Production

For the purpose of this comparative evaluation, DGGS contracted a new DEM for the Unalakleet area in September 2014. This DEM was produced with a photogrammetric technique utilizing the SfM algorithm (Koenderink and Van Doorn, 1991; Westoby et al., 2012; Nolan et al., 2015) to achieve high-precision elevation data and co-registered orthoimages. The imagery for this elevation surface was collected with a low-cost mapping system consisting of a digital single lens reflex camera (DSLR) with a time-linked, dual-frequency, post-processed GPS mounted on a small fixed-wing aircraft (FodarTM; for additional details see Nolan et al., 2015; www.fairbanksfodar.com). The GPS provides initial image georeferencing, and the photogrammetric calculations were completed with the aid of AgiSoft Photoscan software. The resultant orthoimagery (Fig. 1; a, c) was a product with 9-cm horizontal resolution, and the initial point clouds were processed into a 20 cm DEM product that was fitted to archived, photo-identifiable, z-control points (2011; n=6; NAD83(2011), NAVD88(Geoid12A)) using an affine transformation in Quick Terrain Modeler. Although a GSD of <20 cm for the elevation model was selected for computational efficiency and file size, a finer GSD of 10 cm could have been achieved with this image collection. Independent Ground Control

Twelve independent GCPs were collected within a 5-km area surrounding the developed portion of Unalakleet in October 2014. To accommodate possible temporal variations in elevation due to DEM collection year, GCPs were selected in stable areas (based on field investigation), with minimal vegetative cover and away from the influence of active shoreline processes. Sampled elevations ranged from 2 m to 140 m relative to NAVD88(Geoid12A), with a mode of approximately 6 m. These GCPs were collected using a hand-held rapid-static technique with a survey-grade DGPS system consisting of two dual-frequency GNSS receivers. With post-processing, this configuration yields measurements with a total vertical uncertainty of <5 cm (Kinsman and DeRaps, 2012). DEM Comparison

In addition to the 2014 SfM-derived product, six archived DEMs were identified from a 10-year period for the Unalakleet area. The existing DEMs consist of both Digital Terrain Models (DTMs), which are “bare earth” representations of the ground elevation; and Digital Surface Models (DSMs), which include above-ground features such as vegetation and buildings. These data are summarized in

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Table 1 and they span the full range of “best-available” DEMs typical of Alaska. A 5 m GSD product (IfSAR-based) is the updated standard for the National Elevation Dataset (NED) in this part of the U.S., and the NED in Alaska is in the process of being updated from a 30 m GSD product. The digital elevation models were prepared in a GIS environment. For this analysis, the non-raster datasets were converted to raster using a natural neighbor interpolation from either the point cloud or the Triangular Integrated Network (TIN; for DCRA dataset with breaklines). All of the raster elevations were transformed to a common horizontal datum and the elevation value of each raster was sampled at every independent GCP that coincided with the DEM extent. For each DEM product, differences between the GCP elevations and the raster elevation values were used to calculate accuracy statistics.

Table 1. Available DEMs (2004 through 2014) for the Unalakleet area and relevant attributes.

DEM and source Method and native data format DEM Type

Ground Sample

Distance (GSD, m)

Year

ALOS PRISM1 Digital Photogrammetry (satellite) Raster product

DSM 2.5 2010

Alaska DCRA2 Community Map

Digital Photogrammetry (airborne) Ground points and breaklines

DTM Variable 2004

ASTER GDEM3 (v.2)

Digital Photogrammetry (satellite) Raster product

DSM 30 2011

NED4 IfSAR5 (satellite) Raster product

DTM 5 2012

Airbus Pléiades stereo-3D

Digital Photogrammetry (satellite) Raster product

DSM 4 2013

DGGS Lidar Lidar (airborne)

Minimally classified point cloud DTM 0.75 2005

DGGS FodarTM SfM

SfM Photogrammetry (airborne) Unclassified point cloud

DSM 0.2 2014

1 Advanced Land Observing Satellite, Panchromatic Remote-sensing Instrument for Stereo Mapping 2 Department of Community and Regional Affairs 3 Advanced Spaceborne Thermal Emission and Reflection Radiometer, Global Digital Elevation Model 4 National Elevation Dataset 5Interferometric synthetic aperture radar

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DEM-derived Inundation Extents and Shoreline Positions With lidar data, a TIN based on the point cloud is typically preferred over a raster for elevation-based vector mapping to preserve the most accurate vector boundary position. The small GSD (20 cm) of the SfM-derived DEM in this study, however, allowed for comparable mapping results requiring less computational time because the DEM is an excellent representation of the surface features found in this setting.

To experiment with an SfM-derived elevation product for elevation-based vector mapping we first used the mean residual results to adjust the DSM from the pre-existing control to the new GCP values; thus improving the absolute accuracy from 19 to 16 cm RMSE. Next, we used water-level elevations from field measurements following a November 2011 flood to interpolate a flood-water surface based on the maximum storm tide, open-ocean setup, and runup elevations. This interpolated peak water-level surface was combined with the DEM to produce a flood inundation map that approximates the horizontal inland extent of overland flooding during that event.

Unalakleet, unlike many areas in Alaska, has published local tidal datum values [Mean High Water (MHW) is 1.92 m relative to NAVD88(Geoid12A); (DGGS, 2014)]. We used the SfM-derived DEM to obtain a MHW shoreline position (datum-based) using elevation intercept methods typically applied to lidar point clouds (e.g., Stockdon et al., 2002; Ruggiero et al., 2013). This shoreline position is compared to a visually-interpreted HWL shoreline (proxy-based; indicated by the wet/dry line) that was digitized using the contemporaneous orthoimagery (after Moore, 2000), and to the best-available digital vector shoreline for this area from the National Hydrography Dataset (NHD). Results

DEM Comparison

The results of the DEM absolute accuracy tests with the independent GCPs are presented in Table 2. Mean residual values varied from 4 to 70 cm, likely due to the quality of the original or pre-existing vertical control used in the generation of each DEM. For the 2004 DCRA DEM, which was developed in tandem with rigorous ground surveys and had a very low standard deviation of residuals (7 cm), no RMSE could be calculated because the elevation values are reported relative to NGVD29. The 2005 lidar had the lowest overall vertical RMSE (8 cm) of all the datasets tested in this study. Of the satellite sensors, the Airbus Pléiades stereo-3D DEM demonstrated the lowest RMSE of 44 cm in this setting. It should be noted that these absolute accuracy assessments apply only

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to the DEM surfaces analyzed in this study area and results may vary in settings with different terrain. An approximately 250 m cross-section of the Unalakleet beachface sampled from all seven DEMs illustrates the differences between the DTM and DSM surfaces as well as the anomalies caused by the different GSD values (Fig. 2). Although every effort was made to collect GCPs for this test in stable areas, it is possible that landscape changes or other variables over the last decade did contribute to some of the residuals for independent GCPs (e.g., one GCP was removed from an area where cars routinely park). We have inferred that this effect is very minimal, given that some of the oldest datasets in the collection produced very good accuracy values. Another consideration is that the DEMs with a greater GSD might appear to perform well in the low-lying terrain because they are characterized by average elevations that are statistically likely to coincide with the GCP values on flat, stable surfaces; this effect could introduce a bias to the accuracy reports. The magnitude of this bias was not explored.

Table 2. Absolute accuracy statistics for seven common types of DEMs in rural Alaska evaluated with independent GCPs (2014 ground condition).

DEM source Ground Control

Residual Count

Mean residual (m)

Standard Deviation of residuals (m)

RMSE (m)

ALOS PRISM 12 0.06 1.19 1.19

Alaska DCRA Community Map

81 n/a2 0.07 n/a2

ASTER GDEM (v.2)

12 0.69 4.40 4.46

NED 12 0.18 0.57 0.61

Airbus Pléiades stereo-3D

12 0.19 0.40 0.44

DGGS Lidar 71 0.04 0.07 0.08

DGGS FodarTM SfM

111 0.10 0.16 0.19

1 Only a subset of the 12 independent GCPs coincided with the DEM footprint. 2 Vertical datum of DEM (NGVD29) differed from that of the GCPs.

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Fig. 2. Plot of elevations from all seven DEM surfaces, normalized to this study’s GCPs with use of the mean residual values from MHW (A) to inland (B; see location of A-B in Fig. 3).

Evaluation of Applied SfM-derived DEM Coastal Vectors The flood inundation extent map, derived from the SfM DEM, in combination with peak 2011 flood-water-level elevation measurements collected in the field, is shown in Fig. 3. This map agrees well with the observed flood extents described by Kinsman and DeRaps (2012) and documented by photos and accounts by local residents. Maps of this type that document past floods are used by the National Weather Service to iteratively enhance their “Impacts Catalog” to improve coastal flood warnings and advisories.

Fig. 3. Flood inundation extent map for the November 9, 2011, storm-surge event based on observed water-level indicators and the SfM-derived DSM that was classified by elevation and areas of hydro-connectivity. Profile A-B indicates the location of the cross-sectional elevations shown in Fig. 2.

The results of a MHW intercept (datum-based) shoreline position for a portion of the Unalakleet coastline are illustrated in Fig. 4; at no location along the 1 km section of low-slope beach that was tested did the DEM-derived shoreline vector

A B

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depart from the manually-digitized HWL shoreline proxy vector by more than 4 m in the cross-shore direction. Furthermore, the elevation-based MHW shoreline was rapidly generated and is a marked improvement over the best-available “contemporary” digital shoreline vector for this area, an NHD 1:63,360 shoreline of uncertain date. To further evaluate agreement between the manually-digitized HWL and elevation-based MHW shorelines, we extracted SfM-derived elevation values at points along the manually-digitized segment to obtain an average elevation of the digitized HWL shoreline position. This yielded an average elevation of 2.00 ±0.14 m NAVD88(Geoid12A) for the proxy MHW feature, which is only 8 cm higher than the published MHW tidal datum value of 1.92 m NAVD88(Geoid12A) and within the variability introduced by local wave setup and runup, which act to elevate, or shift HWL shorelines landward, relative to MHW-datum based shorelines (Moore et al., 2006).

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Fig. 4. Shoreline positions for a 1 km segment on the open-ocean side of the Unalakleet spit calculated from a MHW intercept (datum-based), the manually-digitized HWL (wet/dry line), and best-available NHD shoreline. Note in the inset that the HWL shoreline is typically located just inland from the MHW shoreline.

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Discussion

Advantages and Disadvantages of SfM-derived DEMs for Coastal Mapping In many regions, workflows for shoreline position and inundation mapping have evolved in tandem with the quantity and quality of underlying datasets. Based on our preliminary analysis, SfM-derived DEMs appear to be a viable alternative to lidar or detailed ground surveys for use in these applications. In Alaska, these DEMs are a significant improvement over other available datasets based on the GSD and absolute accuracy. The next most comparable datasets available in most of Alaska’s small population centers are the DCRA elevation surfaces, which are re-collected with traditional photogrammetric techniques at a frequency of >10 years and at much greater expense. Many of Alaska’s coastal areas lack established tidal datum values, which can be a prohibitive element in many flood map endeavors. We propose that, as a stopgap measure until more tidal datums become available, co-registered high-resolution imagery from SfM collections could be used to obtain a MHW datum approximation by extracting the average elevation along a segment of manually digitized shoreline and applying appropriate corrections for beach slope and local wave climate (after Ruggiero and List, 2009). Using the orthoimagery, the technique of backtracking elevations out of digitized features could also be used on repeat SfM imagery collected immediately after a flood event to capture strandline elevations still visible in the snow or on the ground. This approach could provide much-needed ground truth values of maximum flood elevations to improve inundation modeling in Alaska. One drawback of SfM-derived DEMs in typical lidar-based workflows for shoreline delineation is that the photogrammetric approach is limited to the subaerial portions of the beach; lidar can be used to map nearshore water depths using a green laser under low turbidity conditions. However, it may be possible to map navigational shorelines (MLLW datum) with photogrammetric techniques if the image collection is timed to occur during spring low tides or periods of high atmospheric pressure when water levels are well below MLLW to capture the maximum intertidal interface. Another disadvantage is that, as in any photogrammetric-derived DEM, the resultant surface is a DSM that includes structures and vegetation. While most buildings and some vegetation can be removed algorithmically, the presence of low, dense vegetation can high-bias the elevation surface. Fortunately, for most shoreline mapping this is not a concern, as upper shorefaces and back beaches are typically unvegetated. Furthermore, the sparse and low-lying vegetation patterns that are characteristic of arctic tundra make this region an ideal setting

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for extending the use of DSM-type topography for flood mapping. In fact, some of the SfM DEMs associated with this project have already been incorporated into a set of experimental color-indexed elevation map products designed to facilitate flood communication in emergency scenarios that are currently undergoing testing by the National Weather Service (Tschetter et al., 2014). Calculation of Minimal DEM Specifications for Elevation-Derived Vectors

Minimizing absolute accuracies are necessary for mapping vector features in low-slope environments because the horizontal position of an elevation-based feature is highly dependent on the vertical accuracy of the underlying dataset; on a beach with a slope of 1.9 degrees, a 50-cm vertical error translates to a 15-m error in the horizontal position. These horizontal displacement effects are compounded when combined with the uncertainties associated with not just the DEM, but also the intersect value of the vector feature. The relationships between these uncertainties and the beach slope are schematically illustrated in Fig. 5 along with an equation (Eq. 1) that can be used to provide guidance for the minimum GSD appropriate for the quality of the vector being produced or for calculating the minimum RMSE necessary to achieve a desired horizontal accuracy of the resultant intercept vector.

Fig. 5. Schematic of the variables necessary for calculating minimum elevation model specifications based on terrain slope, vertical uncertainties, and horizontal accuracy of intercept vector features.

< = (1)

where α = slope of the topography; Htσ = vertical RMSE of the elevation-based feature; Eσ = vertical RMSE of the DEM; Sσ = the horizontal RMSE of the vector shoreline position; and dx = the GSD of the DEM.

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We can also use Eq. 1 to calculate the uncertainty in the cross-shore position of the elevation-derived MHW shoreline that we produced for Unalakleet. In our study area, the typical beach slope (α) is approximately 5 degrees. The vertical RMSE of the MHW datum can be assumed to be typical of datum errors in the Bering Strait region that are based on three-month water level records (Htσ = 10.8 cm; Michalski et al., 2014). Using the RMSE of the vertically-adjusted SfM DEM (Eσ = 16 cm), we arrive at a cross-shore positional uncertainty of 3.1 m.

Some guidelines exist in both shoreline and flood mapping literature about recommended minimum specifications for DEMs. In the 2014 Standards for Flood Risk Analysis and Mapping, FEMA requires that elevation surfaces for floodplain mapping have a maximum RMSE of 36.3 cm in low-lying areas that have a high level of flood risk. The FEMA Map Modernization initiative concluded that additional accuracy is desired to 9.25 cm RMSE. FEMA also recommends that the minimum GSD for raster datasets be <1 m (NRC, 2007; FEMA, 2014). The SfM-derived DEM tested in this study easily surpasses these minimum accuracy and GSD requirements. When conducting a cost-benefit analysis for the collection of new DEM datasets, consideration of the maximum allowable horizontal uncertainty in the elevation-derived vectors (particularly those used for community planning or to define land ownership) is a critical first step in determining which type of DEM is most appropriate for use.

Conclusions

Alaska has an extremely long (>11,000 km) and remote coastline that lacks critical baseline elevation data necessary to conduct inundation modeling and vulnerability mapping for community planning and emergency decision support. Not only is there a shortage of coastal topographic data, but less than 10 percent of the state has a contemporary (1960 or newer) mapped shoreline position (NOAA, 2012). In addition to remoteness and inaccessibility, a limited arctic field season and shortage of in-state resources also contribute to the challenges associated with acquiring new DEMs in this region, especially lidar-based surfaces.

These preliminary findings suggest that SfM-derived elevation products can be comparable to lidar data products for coastal mapping, particularly in areas with minimal vegetative cover. SfM-derived DEMs have the added advantage of being relatively low-cost and include co-registered orthoimagery. For Alaska, the use of SfM technology may have a profound influence on our ability to generate necessary coastal products in remote parts of the state. In addition to exploring the uses for SfM-derived DEMs, this investigation has provided a method to compare the quality and appropriate uses for other types of elevation datasets that are commonly available to the public.

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Acknowledgments

This work is funded with qualified outer continental shelf oil and gas revenues by the Coastal Impact Assistance Program, U.S. Fish and Wildlife Service, U.S. Department of the Interior. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the opinions or policies of the U.S. Government. Mention of trade names or commercial products does not constitute their endorsement by the U.S. Government. Special thanks to Alexander Gould (DGGS) for assistance with the manual MHW digitizing, Pléiades photogrammetry, and the 2014 field GCP survey. Thanks also to Fairbanks FodarTM for the timely acquisition and SfM processing that allowed for this pilot project to be completed in advance of the 2015 summer field season. References

Division of Geological & Geophysical Surveys (DGGS) (2014) “Alaska Tidal Datum Portal” [website], doi:10.14509/ak-tidal-datum-portal

Federal Emergency Management Agency (FEMA) (2014) “Standards for Flood Risk Analysis and Mapping, Federal Insurance and Mitigation Administration Policy,” FP 2014-078-1, 92 p.

Kinsman, N.E.M., and DeRaps, M.R. (2012) “Coastal hazard field investigations in response to the November 2011 Bering Sea storm, Norton Sound, Alaska,” Alaska Division of Geological & Geophysical Surveys Report of Investigation 2012-2 v. 1.1, 51 p., 1 sheet, doi:10.14509/24484

Koenderink, J.J., and Van Doorn, A.J. (1991) “Affine Structure from Motion,” Journal of the Optical Society of America A, 8(2), 377-385, doi:10.1364/JOSAA.8.000377

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Moore, L.J., Ruggiero, P., and List, J.H. (2006) “Comparing mean high water and high water line shorelines: Should proxy-datum offsets be incorporated into shoreline change analysis?” Journal of Coastal Research, 22(4), 894-905.

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Ruggiero, P., Kratzmann, M.G., Himmelstoss, E.A., Reid, D., Allan, J., and Kaminsky, G. (2013) “National assessment of shoreline change—Historical shoreline change along the Pacific Northwest coast,” U.S. Geological Survey Open-File Report 2012–1007, 62 p.

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Tschetter, T.J., Kinsman, N.E.M., and Fish, A.M. (2014) “Color-indexed elevation maps for flood-vulnerable coastal communities in western Alaska,” Alaska Division of Geological & Geophysical Surveys Miscellaneous Publication 154, 20 p., 20 sheets, doi:10.14509/29129

Westoby, M.J., Brasington, J., Glasser, N.F., Hambrey, M.J., and Reynolds, J.M. (2012) "‘Structure-from-Motion’ Photogrammetry: A low-cost, effective tool for geoscience applications," Geomorphology 179, 300-314.

White, S. (2007) “Utilization of LiDAR and NOAA’s vertical datum transformation tool (VDatum) for shoreline delineation,” Proceedings of the Marine Technology Society/IEEE Oceans Conference, Vancouver, BC, 6 p.

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