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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. [email protected]
2. U.S. Geological Survey, Pacific Coastal & Marine Science Center, 400 Natural Bridges
Drive, Santa Cruz, CA 95060, USA. [email protected]
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 lowlying 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 SfMderived 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 SfMderived 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, postprocessed 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 dualfrequency 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 aboveground 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 preexisting 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.
datum of DEM (NGVD29) differed from that of the GCPs.
2
Vertical
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A
B
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 hydroconnectivity. 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
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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 highresolution 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.
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