TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-10-1245-2016Which are the highest peaks in the US Arctic? Fodar settles the debateNolanMattmatt2013@drmattnolan.orgDesLauriersKitInstitute of Northern Engineering, University of Alaska, Fairbanks, Fairbanks, AK, USAThe North Face, Teton Village, Wyoming, USAMatt Nolan (matt2013@drmattnolan.org)23June20161031245125719November201516December201515April201619May2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/10/1245/2016/tc-10-1245-2016.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/10/1245/2016/tc-10-1245-2016.pdf
Though an outstanding achievement for their time, the United States
Geological Survey (USGS) topographic maps of the eastern Alaskan Arctic
nonetheless contain significant errors, and in this paper we address one of
them. Specifically, USGS maps of different scale made in the late 1950s
alternate between Mt. Chamberlin and Mt. Isto as the tallest peak in the
US Arctic. Given that many of the peaks here are close in height and covered
with glaciers, recent climate change may also have changed their height and
their order. We resolved these questions using fodar, a new airborne
photogrammetric technique that utilizes structure-from-motion (SfM) software
and requires no ground control, and validated it using GPS measurements on
the peaks as well as airborne lidar. Here we show that Mt. Chamberlin is
currently the third tallest peak and that the order and elevations of the
five tallest mountains in the US Arctic are Mt. Isto (2735.6 m), Mt. Hubley
(2717.6 m), Mt. Chamberlin (2712.3 m), Mt. Michelson (2698.1 m), and an
unnamed peak (2694.9 m); these heights are relative to the NAVD88 GEOID12A
vertical datum. We find that it is indeed plausible that this ranking has
changed over time and may continue to change as summit glaciers continue to
shrink, though Mt. Isto will remain the highest under current climate trends.
Mt. Isto is also over 100 m taller than the highest peak in Arctic Canada, making it
the highest peak in the North American Arctic. Fodar elevations compared to
within a few centimeters of our ground-based GPS measurements of the peaks
made a few days later and our complete validation assessment indicates a
measurement uncertainty of better than ±20 cm (95 % RMSE). By
analyzing time series of fodar maps, we were able to detect topographic
change on the centimeter level on these steep slopes, indicating that fodar
can be used to measure mountain snow packs for water resource availability
or avalanche danger, glacier volume change, and slope subsidence,
as well as many other applications of benefit to society. Compared to lidar, the
current state-of-the-art airborne topographic mapping, we found this SfM
technique as accurate, more useful scientifically, and significantly less
expensive, suggesting that fodar is a disruptive innovation that will enjoy
widespread usage in the future.
Elevations of the five tallest peaks in the US Arctic. USGS
peak elevations in feet are taken directly from labels on the printed map
sheets except for Mt. Okpilak at 1 : 63 360, which was interpolated from the
contours surrounding the peak; Mt. Okpilak is our unofficial name for that
unnamed peak. Fodar data were processed in WGS84 for comparison with ground
control; as described in the text, we selected one of these measurements
(bold) for the final value, which was converted to NAD83 using GEOID12A and
presented in column 6, with its geographic coordinate shown in column 7.
USGSUSGS2011 LidarFodarFodarLatitude,1 : 63 3601 : 250 000(WGS84)(WGS84)(NAVD88longitude(NGVD29)(NGVD29)Geoid 12A)Mt. Isto2735.6 m2758.4 m2739.63 m2739.59 m (24 March 2014)2735.6 m69.202506∘ N,(8975′)(9050′)2739.40 m (22 April 2014)(8975.1′)143.800941∘ W2738.75 m (6 July 2015)Mt. Hubley2717.3 m2717.3 m2720.64 m2720.97 m (13 June 2014)2717.6 m69.276101∘ N,(8915′)(8915′)2720.55 (6 July 2014)(8916.0′)143.799277∘ WMt. Chamberlin2749.3 m2749.3 m2717.29 m2716.51 m (24 March 2014)2712.3 m69.277673∘ N,(9020′)(9020′)2716.59 m (22 April 2014)(8898.6′)144.911625∘2717.56 (23 April 2015)Mt. Michelson2699.0 m2699.0 m2702.29 m2701.30 m (30 June 2014)2698.1 m69.307756∘ N,(8855′)(8855′)2701.69 m (6 July 2015)(8852.0′)144.268992∘ WMt. Okpilak2697.5 m2670.0 m2699.84 m2699.95 m (23 April 2015)2694.9 m69.14572∘ N,(8850′)(8760′)2699.80 m (6 July 2015)(8841.5′)144.041046∘ WIntroduction
Here we seek to answer the overarching question: “how well does modern
airborne photogrammetry measure the topography of steep terrain?” We chose
to settle the question of the height and order of the tallest mountains in
the US Arctic both for its intrinsic value and because these rugged peaks
are located in a highly glacierized region in northeastern Alaska (Fig. 1)
where we have ongoing glacier research with suitable validation data
(Nolan et al., 2011; Weller et al., 2007). The topographic discrepancies
in question are shown in Table 1. Here United Sates Geological Survey (USGS)
maps indicate Mt. Isto as either being 8975 or 9050 ft, depending on map
scale, while Mt. Chamberlin is listed as 9020 ft on both (USGS map elevations
are reported in feet; see Table 1 for metric conversions). Further, the elevations of Mt. Michelson and an
unnamed peak in the Okpilak River valley (which we herein refer to
unofficially as Mt. Okpilak) are within a few meters difference, well within
the half-contour accuracy specification (50 ft or 15 m) of the maps. Accurate peak
elevations are intrinsically interesting to many segments of the public and
academia, as well as serving a practical function in aviation planning. Our
interest in measuring these peaks stems primarily from our studies of the
glaciers that descend from them. Located in the pristine Arctic National
Wildlife Refuge along with all of these peaks, McCall Glacier has served as
the sole benchmark glacier for the entire US Arctic since 1957, such that we
extrapolate our local measurements from there to inform us on the impacts of
climate change on the broader landscape and its ecology
(Nolan et al., 2011). Ideally we wish to avoid such
extrapolation by directly measuring volume change for all of the
800 + Arctic glaciers annually, which is not feasible to do from the ground in
this remote, roadless terrain. We have in the past used airborne InSAR and
airborne lidar and found them useful but prohibitively expensive for
sustainable academic research budgets (Geck et al., 2013). This
financial obstacle led us to the development of a new photogrammetric
technique. Our study of the tallest peaks in the US Arctic thus serves a
dual purpose – both to resolve the discrepancies in existing maps and to
use those same data to validate this technique as a means to affordably
measure changes to snow and ice on the centimeter scale within steep
mountain environments.
The five tallest peaks in the US Arctic are located within about 40 km
of each other in northeastern Alaska, within the Arctic National Wildlife Refuge.
We have given this photogrammetric technique its own name, fodar, because we
believe it is substantially different from existing techniques and
represents a new standard in performance and cost. Note that fodar is a
portmanteau of “foto” and “lidar” (https://en.wikipedia.org/wiki/Lidar); it is
not an acronym nor is it capitalized. Our design goal was to affordably map
the topography of large, remote areas at high accuracy using manned aircraft
and requiring no ground control. In previous work, we demonstrated our
success by creating maps with 10–20 cm ground sample distances (GSDs) over
tens of square kilometers and validating that they had a directly georeferenced accuracy and map precision (repeatability) better than ±30 and
±8 cm, respectively, at 95 % root-mean-square error (RMSE) (Nolan et al., 2015). The
method is distinguished from traditional methods of photogrammetry by its
use of the structure-from-motion (SfM) algorithm (Koenderink and Van Doom,
1991; Westoby et al., 2012; Nolan et al., 2015), and it is distinguished from
other forms of SfM photogrammetry by the fact that no ground control is
required to achieve such accuracy and precision. Ground control is not
required because the precise timing between the shutter of the camera and
survey-grade GPS yields absolute photo locations with less than 10 cm error,
and this constrains the SfM bundle adjustment sufficiently to meet these
specs. Thus if any ground control is utilized, it is only after the map is created, to shift the
entire map uniformly by less than 30 cm some direction. Though SfM
photogrammetry is currently exploding in scientific popularity with cameras
mounted on inexpensive drones (d'Oleire-Oltmanns et al., 2012; Hugenholtz
et al., 2013; Lucieer et al., 2013; Rinaudo et al., 2012; Ryan et al., 2015),
directly georeferenced results from these systems generally have accuracies
and precisions 10–100x worse than fodar because they lack survey-grade GPS
on-board to constrain photo locations as well as fodar. Without precise
positioning in the air, substantial
photo-identifiable survey-grade ground control needs to be incorporated into
the bundle adjustment before the map is created, a time-consuming process similar to traditional
photogrammetric methods, in order to improve accuracy and precision. Practically speaking it is unclear as yet whether
sufficient ground control can ever be acquired to match fodar specs over the
spatial scales we are operating at. Thus fodar could be regarded as
survey-grade SfM photogrammetry and considered in much the same way that
consumer GPS is distinguished from survey-grade GPS – both are useful, but
which tool to use depends on the questions trying to be answered.
In prior work, we have shown that fodar is as accurate as alternative
methods but substantially less expensive. By subtracting snow-free digital
elevation models (DEMs) from snow-covered ones, we found fodar was suitable
for measuring thin (< 30 cm) Arctic snow depths on the watershed
scale with accuracies as good as hand probing (Nolan et al., 2015).
Studies of coastlines in Alaska independently validated fodar specifications,
demonstrating that coastal erosion could be measured by such DEM
differencing as accurately as ground measurements but over much larger areas
(Gibbs et al., 2015) and that coastal mean high water vectors could
be extracted from fodar DEMs with about the same accuracy as manual
digitization but much more efficiently (Kinsman et al., 2015).
Independent validation using about 100 ground control
points (GCPs) by the state of Alaska of
DEMs we made of 26 coastal villages revealed that directly georeferenced
horizontal accuracy was < 10 cm in all cases, that the mean
directly georeferenced vertical offset was 21 cm, and that vertical
precision was 10 cm at 2 standard deviations (Overbeck et al., 2016); since
then we have mapped over 3000 km2 of coast in Alaska for similar
purposes (Nolan, unpublished data). In remote locations like these, the
field effort to collect ground control can greatly exceed the cost of the
airborne survey itself; thus fodar can result in tremendous savings of
both cost and time. Fodar specifications also meet or exceed the
capabilities of most airborne lidars, the current state-of-the-art topographic mapping (Deems et al., 2013; Höfle and Rutzinger, 2011), yet
fodar hardware costs less than USD 30 000 compared to USD 500 000 to USD 1 million
for airborne lidar hardware suitable for mapping mountain ranges. As
described in detail in Nolan et al. (2015), the primary underlying
reason for the difference in price is due to the software utilization of
the SfM algorithm that allows for prosumer-grade cameras to be
used without the need for an IMU, an on-board computer, or a separate
equipment operator.
Mt. Isto, currently the tallest peak in the US Arctic, shown as a
3-D visualization of our fodar data. Yellow dots indicate the position of some of
the ground control points collected (yellow) used for validation, spanning
∼ 1000 m. Closely spaced points are on the climb up; widely
spaced points are on the ski down.
To address the overarching question of this paper, we mapped each of the
five highest peaks photogrammetrically between two and four times in 2014–2015.
These repeat measurements let us not only determine the
repeatability (precision) of our methods in steep terrain but also detect
change of snow and ice surfaces over time. We compared these measurements to
survey-grade GPS measurements we made by climbing to the top of Mt. Isto
(Fig. 2) and Mt. Chamberlin, as well as to lidar measurements we made of
all five peaks between 2008 and 2011. Comparing all measurements also
allowed us to examine rates of change of peak elevation, caused by ice and
rock loss from their summits.
MethodsFodar
We mapped each of the five mountains at least two times in 2014–2015 (Table 1)
using our photogrammetric system, flown in a Cessna 170B or Piper Lance
by the first author. In total we flew 10 airborne missions from Fairbanks,
Alaska, to the study area 500 km away (Fig. 1), though not every flight
resulted in data published here due to weather or acquisition issues. Our
flight lines were typically flown at between 10 000 and 11,000 ft (3050 m–3350 m),
resulting in image GSDs ranging from 5 cm near the
summits to about 50 cm within the valleys. We processed the images into
DEMs with postings ranging from 37 to 51 cm. The
photogrammetric system and its processing is fully described in Nolan
et al. (2015). In short, it utilizes a Nikon D800E, a Nikkor 24 mm lens, a
Trimble 5700 with roof-mounted L1/L2 antenna, and a custom intervalometer
that triggers the camera and sends an event pulse to the GPS. GPS processing
was done in Novatel's Grafnav software using the PPP method (Gao and Shen,
2002) to create an exterior orientation file that is imported in Agisoft's
Photoscan for bundle adjustment and DEM creation. We processed our GPS data
from the start time forwards in time and separately from the end time
backwards in time, a common technique for assessing error. Comparison of
forward/reverse solutions and other internal software metrics indicates that
the positional accuracy of the camera was 10 cm or better typically, except
when excursions occurred due to loss of satellite numbers or lock, usually
caused by banking too steeply. The subsequent bundle adjustment within
Photoscan confirmed this accuracy with mean shifts in photo locations of
less than 10 cm. GPS solutions and the subsequent DEMs were processed
relative to the WGS84 ellipsoid to facilitate comparison with lidar data,
with peak elevations converted to NAD83(2011) NAVD88 GEOID12A using NOAA's online tools
(http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/geoid12A_prompt1.prl). Fodar creates not only a DEM
but also a perfectly co-registered orthoimage; herein we use “map” generically
to refer to both products.
GPS ground control
We conducted field campaigns to climb Mt. Isto (27 April 2014) and Mt. Chamberlin
(3 May 2014) to directly measure peak elevations, shortly after our
primary airborne mapping mission there (22 April 2014), with a climbing team
led by the second author. A Trimble 5700 GPS receiver with compact
L1/L2 antenna was mounted on a backpack and continuously recorded during the
ascents and descents (e.g., Fig. 2). Static occupations near the summits of
both peaks ranged from 10 to 20 min, with the antenna either placed on a
spike mount or left on the backpack which was dug into the snow for
stability; because the peaks themselves were on or near cornices, the summit
occupations were made ∼ 5 m horizontally away from the actual
peaks for safety concerns. Novatel's Grafnav software using the PPP method
was used for all processing, given that the nearest high-quality CORS site
(Snay and Soler, 2008) was over 160 km away and no local base station was
installed due to weight and logistical requirements. The nominal antenna
height on the backpack was 2.14 m; practically it varied from 0 while
climbing steep ice to 1 m while wading through deep snow, and thus it varied
between 0 and 2.14 m. Given the extreme antenna motion during climbing,
broad sections of this kinematic session failed to process and much of it
had errors on the 1 m level. We therefore filtered these GCPs to those locations where we were mostly walking upright on
hard ice, as here we knew the antenna height and the improved antenna
stability led to forward/reverse solution separation less than 20 cm; this
occurred mostly near the summit ridges. Comparison of forward/reverse
solutions indicated that static sessions had an accuracy of about ±10 cm.
Note that our fodar validation comparisons were made to these offset
measurements and that the peak measurements published here are from the
highest point on the maps, not the height of these GCP locations. The same
GPS system was used on McCall Glacier, directly beneath Mt. Hubley, prior to
our June 2014 airborne measurements of it. The antenna was mounted on a
snow machine with a nominal antenna height of 1.08 m and variations likely
less than ±0.15 m. These data were processed the same way and further
filtered by distance to provide 5 m spacing between points and to ensure
their solutions were accurate to < 10 cm.
Lidar
The lidar DEMs were acquired by a commercial vendor using an Optech ALTM
Gemini system and delivered to us both as individual-swath point clouds and
merged DEMs between 2008 and 2011. Using the swath data, we compared
overlapping regions of adjacent swaths to assess system precision using
repeatability as a metric. Two DEMs were acquired in 2008: one small DEM of
just McCall Glacier had a precision of 16 cm (95 % RMSE) and a second
larger DEM one that covered all of the glaciers in this region (as well as
the five peaks) at a precision of over 3 m due to a variety of quality
control and planning issues. Acquisitions of the larger area was thus
repeated in 2009 and 2010, but these also suffered from a variety of issues.
In 2011, a new map of the entire area had a measured precision of ±50 cm
(95 %) between adjacent swaths, and related swath-edge artifacts could
be found within the DEM at this level. We extracted several large blocks of
data (all with n> 106) from both the small (better) 2008 DEM
and the large 2011 DEM over ice-free rocks to further assess repeatability
and found similar scatter of about ±0.50 m (95 %) about the mean.
This value was apparently driven by the 2011 data quality, as the point
density of the 2008 data was more than 4 times higher than the 2011 data,
leading to 1 and 2 m postings, respectively, and thus spatial biasing of the
coarser pixels in rough terrain may be the limiting factor in repeatability
here. According to the metadata, the 2011 data were shifted down 0.75 m,
based on co-registration with the worse of the two 2008 DEMs that covered a
much larger area, which had apparently already been shifted down 0.20 cm
based on some limited ground control on tundra acquired by the vendor. We
therefore used GCPs collected by us within a few weeks of the 2011 lidar
acquisition using a snow machine transect on McCall Glacier (n= 1703,
1500–2340 m HAE) as described above and found a mean offset of 0.61 cm (upward
DEM shift) with standard deviation of 0.10 m. Unfortunately the 2011 data
were delivered in two non-contiguous blocks and our GCPs come only from the
eastern one; however, as described later, comparison of rock areas between
the lidar and our SfM maps on both blocks showed that this 0.61 m shift reduced
the mean residual difference to within ±0.10 m, and thus we applied this
shift to both lidar blocks.
Accuracy and precision assessments
We assessed horizontal geolocation accuracy of the fodar DEMs by assessing
co-registration offsets between our repeat maps, because none of our GCPs
were photo-identifiable. While in principle comparing maps to themselves
only assesses precision and not accuracy, our prior work with
photo-identifiable GCPs demonstrated that such comparisons yield the same
results as GCP comparisons (Gibbs et al., 2015; Kinsman et al., 2015; Nolan
et al., 2015; Overbeck et al., 2016). Using two orthoimages each on Mt. Isto,
Mt. Chamberlin, and Mt. Michelson made in 2014, we used standard
image-correlation techniques in Matlab to determine there was a sub-pixel
(5–10 cm) horizontal coregistration between them. In other work, we have
also mapped the McCall Glacier valley five times from 2013 to 2015 and again
found that horizontal coregistration was subpixel (Nolan, unpublished data).
Given that our pixels are roughly 25 cm GSD and our camera positioning
accuracy is 10 cm or better, this subpixel horizontal accuracy makes sense,
but given the ambiguities caused by the amount of real change on the surface
due to snow, it was not possible to determine a precise value. Thus our
assessment of the horizontal geolocation accuracy of our maps is that they
are accurate to the subpixel level as we found in previous studies and we
therefore applied no horizontal geolocation offsets to these data. We
validated this horizontal accuracy visually by creating difference maps of
all peaks and found no systematic horizontal alignment issues, though this
was difficult to assess visually at the decimeter level because real changes
on ground revealed correlations with aspect, largely due to wind direction
and solar aspect. Figure 3a shows an example of this on Mt. Chamberlin. On a
broad scale, the southeast face (right) shows strong avalanche dynamics, the
southwest face (left) shows melt dynamics, and the northwest face (top)
shows glacier motion and wind redistribution. Note that the color scale here
is only ±50 cm, so even if these differences were caused by
misalignment, that misalignment must be quite small in this steep
(> 45∘) terrain. On the scale of a few hundred meters
(e.g., small rock outcrops), dozens of informal transects revealed no
systematic offsets, providing further validation.
Precision assessments. (a) Difference in elevation between March
and April 2014 acquisitions at Mt. Chamberlin, shown as a top view with
slight sun shading to highlight underlying topography. Color represents
change (-50 to +50 cm). The consistency of color shift between
mountain faces is not due to a spatial misalignment of the data but rather
to substantial, real changes that are dependent on aspect, as described in
the text. Such real changes confound our repeatability estimates which
assume no change on the ground. (b) 3-D oblique view of domain in (a), draped
with orthoimage from April, indicating the locations of snow-filled gullies
on the southeast face. Profile line is shown as both a straight line and
terrain hugging line and is about 1000 m long, crossing five gullies. (c) Profile
of elevation difference (that is, data in a), revealing patterns of snow
redistribution. Much of the snow that had recently fallen in March
avalanched out of the gullies, leaving them up to 6 m deeper in April. Note
that the ridges in between show little to no change, qualitatively
indicating the high quality of the data and the technique's suitability for
measurement of snow depth in steep terrain. (d) Difference in elevation
between March and April 2014 acquisitions at Mt. Isto, with same coloration
as (a). Again, there is substantial real change between acquisitions, but less
than in (a). Histogram of differences of elevations calculated from boxes in
(a) and (e) shown in (d) and (f) respectively over smoother glacier surfaces. Both are roughly gaussian
with 95 % of points within ±38 and ±20 cm. Inspection of
orthoimages here reveals that real changes are still occurring on the
glaciers in these smaller domains, but there are no large locations that
have less change, so these estimates of precision are conservative as they
are confounded by real change.
We assessed vertical geolocational accuracy by comparison with our GCPs. On
Mt. Chamberlin, the 24 March and 22 April fodar elevations were -0.18 and
-0.04 m different, respectively, from the near-summit GPS measurement on 3 May
of 2716.38 m HAE (note that this measurement was taken about 10 m from the
true summit and relative to the WGS84 ellipsoid). Kinematic points near the
summit (n= 288, 2411–2513 m HAE) were -0.17 and +0.08 m from the
March and April map elevations, respectively, with a ±0.10 m standard
deviation. Though the March map has a larger offset, it is not unreasonable
to expect 10–20 cm of change on these snow- and ice-covered locations over
the intervening month. Given that these residuals for the 22 April map are
within the accuracy of the GPS, we did not apply any shifts to these maps to
geolocate them further. On Mt. Isto, we found the 24 March and 22 April maps
within -0.06 and -0.03 m, respectively, of the 27 April near-summit GCP
measurement of 2738.88 m HAE. Kinematic points near the summit (n= 1247,
2735–2736 m HAE) showed residuals of +0.26 and -0.05 m for the March and
April maps, respectively, with a 0.27 m standard deviation. Again given that
the April residuals (made 5 days apart) are within their error bounds and
March measurements so close, we did not apply any geolocation offsets to
these maps either. For the Mt. Hubley map, we compared snow machine GCPs from
McCall Glacier (n= 1432, 1500–1900 m HAE) acquired on 28 April 2014 to
the SfM map made on 16 June and found a mean offset of -0.10 m with a
standard deviation of 0.15 m. Given that this is within the noise level of
both measurements and an unknown amount of melt occurred (probably less than
10 cm), we applied no shift to these data either. That is, we consider the
fodar maps to be as accurate as our GCP validation data in all cases, with
those measurements having the least temporal influence all within ±10 cm.
We have no GCPs for comparison to Mt. Chamberlin or Mt. Okpilak, though
informal comparison of some rock areas here to the 2011 lidar showed near
perfect vertical agreement.
We assessed precision of the fodar DEMs primarily by comparing repeat maps
to each other in areas where real changes to the surface were minimized. In
the context of this paper, we consider precision to be analogous with
repeatability, and we use this repeatability to determine the measurement
uncertainty in our peak measurements. Unfortunately 2014 was an unusually
snowy spring and it was impossible to find large blocks of data that were
free of change due to snow or ice (e.g., Fig. 3a). Figure 3b and c give a
clear example of the real changes on the ground that confound attempts to
use large-scale repeatability as a measure of precision with measurements
only 1 month apart. Here a fresh snowfall in March has largely avalanched
off in the gullies by April, causing the April DEM to be up to 6 m lower
within them, as seen in Fig. 3c. The ridges in between the gullies show
little to no change, as validated by the orthoimages, and this profile is
typical of many that we extracted here. Figure 3d shows Mt. Isto similar to
Mt. Chamberlin in Fig. 3a; note that there is somewhat less
aspect-dependent difference. In the full domains of Fig. 3a and d, we found 95 %
of points were within ±140 and ±52 cm, respectively
(n> 107). Within the subdomains indicated by the black
rectangles, however, these values dropped to ±38 and ±20 cm,
respectively (n> 106), as shown in Fig. 3e and f;
carefully choosing yet smaller domains results in yet smaller differences.
We believe these values are more representative of our actual precision,
though are still erroneously high due to real changes still being captured
here (more so on Mt. Chamberlin). We found values of ±20 cm on the other
mountains as well for areas of about this size. This precision is about
twice as high as we found previously (∼ 8 cm) on smooth,
low-relief surfaces like runways and frozen lakes (Nolan et al., 2015),
and we suspect that the bulk of the difference is due to real change and to
spatial biasing caused by averaging of steep terrain into relatively large
pixels. The scatter in our GCP comparisons is another measure of precision,
and perhaps a better one since there was less intervening real change on the
ground. As described previously, in our April comparisons (5-day interval),
we found 95 % of points within ±7 cm combining data for both peaks,
similar to the values we found in our prior study. Thus we believe a
conservative reasonable estimate of our precision on mountain peaks to be ±20 cm.
Based on these comparisons, our assessment is that the horizontal and
vertical geolocation accuracy of ±10 cm in steep terrain is better than we
found previously in flat to moderate terrain at ±30 cm (Nolan et
al., 2015), and we thus made no corrections to our maps based on ground
control. That is, the DEMs we created using only airborne data cannot be
improved further using all of the ground control available to us. Given that
we found our precision was ±20 cm and that we found no consistent
systematic bias in our accuracy, we conservatively consider this our
accuracy level too, noting that our precision values are likely
artificially high due to undocumented real changes to the surface and due to
spatial biasing. In any case, based on this analysis, we conservatively
consider the measurement uncertainty in our peak elevations to be ±20 cm
at 95 % confidence.
Oblique 3-D visualizations using our fodar data of (a) the south
face of Mt. Hubley with Schwanda Glacier in foreground, (b) the south face of
Mt. Michelson descending to Esetuk Glacier, and (c) the south and east faces
of Mt. Okpilak. Red markers indicate peak location. Note the slight noise
seen at the shadow on the right of (b); this was common at the edge of dark,
fast-moving shadows. Despite the range of exposure value and contrast, this
technique is able to map nearly all terrain, and the orthoimage eliminates
guesswork when it comes to distinguishing rock and ice and even ice and snow.
Peak elevations
We determined peak elevations simply by locating the highest pixel for each
mountain within its DEM, which all had postings of 51 cm or smaller. For our
final results (Table 1, in bold), we selected the values from those maps
that were made closest in time to our GCPs for the tallest three, and
because we had no GCPs for the other two we used the 6 July 2015
measurements for both to provide the best comparison by eliminating
uncertainties due to any temporal changes. As seen in Table 1, the measured
differences in peak elevations (3–18 m) are all greater than the
uncertainty of those measurements (20 cm), lending strong confidence that
they are currently ranked correctly by elevation. Our fodar and GPS
measurements confirm that none of the peaks are over 9000 ft (2743 m) and that
Mt. Chamberlin is not the tallest peak in the US Arctic, as indicated by the
1 : 63 360 scale maps, but rather is currently the third tallest peak, as
originally indicated by our lidar. Figure 4 presents 3-D synthetic
visualizations of several of these peaks using fodar DEMs and orthoimages.
Discussion
Based on our results, there is no longer doubt regarding the
tallest peak in the US Arctic today: Mt. Isto at 2736 m. Given the
consistency between our results and the 1 : 63 360 (8975 ft) maps, it seems clear that
the 9050 ft measurement indicated on the 1 : 250 000 scale map was in error.
Note that none of the peaks today are over 9000 ft, as indicated on the USGS
maps (made over 60 years ago) and still re-published today in the FAA's
aviation sectional charts. Given that the highest peak in the Canadian
Arctic is Barbeau Peak on Ellesmere Island at 2616 m and that it is unlikely
that any potential mapping errors there exceed the 120 m difference, Mt. Isto
is also the highest peak in the North American Arctic and, to our knowledge,
the highest Arctic peak outside of Greenland.
Given the survey control available in Arctic Alaska in the late 1950s, it is
remarkable how well the USGS elevations compared to our own. As there is no
official transformation between the USGS map datum of NGVD29 and the current
NAVD88 datum in Alaska, we cannot directly compare these elevations, but
likely these transformations would be less than 2 m, based on several
benchmark surveys. Note too that the latest official geoid model available
from NOAA, GEOID12A, will soon be replaced by GEOID15B, and our use of
the 15B model indicates the elevations will uniformly decrease by about
1.4 m. Ignoring these uncertainties, four out of five peaks on the 1 : 63 360 maps
are within 1–2 m of our measurements, well within the published
uncertainty of those maps of 15 m, and truly a testament to the quality of
the survey teams and photogrammetrists that produced those maps in such
challenging circumstances. Unfortunately, given the published uncertainty of
15 m, we cannot rule out that this amazing correspondence in actual peak
values was not spurious. However, given that the 33 m difference at
Mt. Chamberlin is more than double the published uncertainty and that the other
peaks showed a much closer correspondence with our measurements, it is
conceivable that some portion of this difference at Mt. Chamberlin could be due to a real
change here over the past 50 years.
Our own results show that elevation change occurs here essentially
continually; that is, the scatter in our own measurements is not due solely
to measurement error either. For example, on Mt. Okpilak we found that the
location of the peak moved more than 15 m laterally between April and July 2015
even though the elevation changed by only 15 cm, as the peak is located
on a broad, flat corniced ridge. Similarly, the 1 m difference on Mt. Chamberlin
between April 2014 and April 2015 was largely real, since nearby
rock did not show any such difference with analyses similar to Fig. 3.
Thus the short-term temporal variations in actual peak height are likely as
high or higher than the uncertainty in our measurements, and any future
measurements should anticipate at least a ±1 m uncertainty due to recent
storms. While such dynamics are noise for this study, our results indicate
that our methods are a valuable new tool in the study of snow thickness
(e.g., Fig. 3c), wind redistribution (e.g., Fig. 5), and avalanche
redistribution (e.g., Fig. 3a) in steep mountain environments. However, such
dynamics are not large enough to explain the 33 m difference in Mt. Chamberlin.
Temporal dynamics of cornices near the peak of Mt. Isto (red
push pin). Shown here are 3-D oblique visualizations of fodar from
(a) 6 July 2015 and (b) a difference image between 6 July 2015 and 22 April 2014. The
consistency of the greens and yellows on either side of the ridge in (b)
indicates that there are no spatial misalignments of the two data sets and
clearly reveals the differences in cornice size between acquisition dates.
The profile comparison (c) confirms visual inspection of the ridge line – a
cornice about 5 m wide and 10 m high formed, perhaps during a single
storm. With these tools we can clearly measure subtle topographic changes in
steep mountain environments that would otherwise be impossible to detect or
measure, and comparisons like these show change down to the centimeter
scale. Dynamics can also be addressed, as the crevassing behind these new
cornices (a) indicates the existing ones are ready to spall and the blue
colors (b) indicate that many already have.
Evidence for recent ice and rock loss from Mt. Chamberlin. (a) The
northwest face shows massive, catastrophic loss of ice. (b) The southeast
face is now completely free of ice, and rock debris piles have accumulated
at its base. (c) Looking down from the peak to towards the southeast face
reveals a curious notch in its shape, suggesting rock and ice avalanches may
have occurred here in the past. The large map discrepancy along with these
clues suggests that Mt. Chamberlin may have been the first or second tallest
mountain in the US Arctic at one time.
Perhaps not coincidentally, of all of five peaks Mt. Chamberlin is covered by
the largest glacier and also shows signs of the largest changes to its peak.
In recent years, many glaciated peaks in Alaska have experienced massive
rock/ice avalanching (Molnia and Angeli, 2014), and the destabilizing effect
of climate warming on mountain peaks has been noted worldwide (Gruber and
Haeberli, 2007; Huggel, 2009; Huggel et al., 2012; Enkelmann et al., 2015). For
example, Mt. Cook in New Zealand lost more than 10 m of its peak due to a
rock avalanche, and the subsequent destabilization has caused another 20 m
rock and ice loss (Vivero et al., 2012; http://blogs.agu.org/landslideblog/2014/01/16/aoraki-mount-cook/). Thus if Mt. Chamberlin was indeed over 30 m higher when the USGS maps were made, likely
the change occurred abruptly rather than through gradual melting. The
northwest face of Mt. Chamberlin was once covered by a glacier tens of meters
thick that likely avalanched catastrophically, as can be deduced by the ice
that still remains there through various visualizations (Fig. 6a). The
steep southeast face is now completely free of ice, and at its base there
are also large accumulations of rock debris that appears to originate from
Mt. Chamberlin rather than the valley glacier at its base (Fig. 6b). The
rock near and under these corniced peaks is also prime for frost shattering
and rock avalanches, with liquid water from the surface now able to
percolate into the bed where temperatures are still below freezing and
likely near the optimum -5 to -15 ∘C to cause failures (Walder and Hallet,
1985), and our images show that minor rockfalls are common here. Overall,
the evidence of massive avalanching on the northwest face combined with the
notched shape of the peak with ∼ 75∘ slopes heading into
debris fields at the base of the southeast face (Fig. 6c) lend strong
credibility that either rock or ice or both have been lost here. Whether a
33 m loss could have occurred here is beyond the scope of this paper to
determine, but a 5 m loss seems probable at some point in the recent past,
which is enough for Mt. Chamberlin to have once claimed second place in
elevation, above
Mt. Hubley. We were unable to locate the original photos used to create the
USGS maps, and unfortunately other photos we found from that time period are
inconclusive due to resolution or snow cover, so for the time being this
debate is not fully settled.
Will the ranking of these peaks change in the future? As long as current
climate trends continue and no massive rock avalanches occur, the order of
the top three is not likely to change due to loss of ice or snow on the
summits. Mt. Isto would have to lose over 18 m of ice to lose its crown, but
there is no evidence that such a thickness exists there: the ice is only a
few meters thick as gaged from the lee side and exposed rock is encroaching
from nearly all sides. Mt. Hubley is the only peak that is not covered by a
glacier or permanent cornice as it is on an arête (Fig. 7a), though it
does accumulate snow in winter. Mt. Chamberlin will continue to lose
elevation, perhaps in catastrophic events, and single storm events are
unlikely to even temporarily increase it by the 5 m needed. Our measurements
showed that Mt. Michelson and Mt. Okpilak were only ∼ 1.5 m
apart relative to the WGS84 ellipsoid; a relative geoid anomaly between them
of 1.5 m increased that spread to about 3 m. Both mountains are covered by
glaciers that are at least 3 m thick at their peaks, though where the
eventual rock peaks will be is uncertain (Fig. 7b and c). Adding to the
uncertainty are future improvements to the geoid model here. We tested the
experimental 15B model and found it gave all peaks ∼ 1.4 m
downward shift compared to the 12B model we used but, given that the 12B
model indicates a spatial gradient of 1.5 m between these peaks, future
higher-resolution data could yield gradients of that size but with opposite
sign, suggesting that this debate is not fully settled. Given that the
ranking of these peaks is determined by height differences of 3 to 19 m, a
rock avalanche smaller than the size of Mt. Cook's in 1991 could change the
order of any of these at any time, though determining whether the local
geology is likely to support such large changes will take further research.
The peak of Mt. Hubley (a) is on a rock arête along a ridge
that is too steep and narrow to support large glaciers. Mt. Michelson (b) and
Mt. Okpilak (c) are only a few meters apart in height and both are covered by
cornices several meters thick. As climate continues to warm, the ranking of
these two may yet change. The location of Mt. Okpilak's “peak” moved more
than 15 m between 2014 and 2015, as it lies on a nearly flat ridge, but its
elevation changed by less than 20 cm.
Spatially coherent grooves seen in a 22 April 2014–6 July 2015
difference image on Mt. Isto (a, arrows) are clearly revealed in the July
orthoimage (b) to be caused from a small avalanche. As seen in (c), the left arrow
points to a ∼ 20 cm chute and the right arrow points to a
∼ 20 cm ridge between chutes on this ∼ 40∘
slope. Resolving 20 cm features like this requires centimeter-scale signal
detection, despite the noise being on the 5–20 cm level. This snow fell
recently and is over a meter thicker than in 2014, located just downhill
from the 5–10 m cornices found in Fig. 5. (d) In the deepest shadows of
this fresh snow, the noise level increased ∼±1 m (up to
10 m, not shown), but these regions were quite small compared to the whole.
Note that the 2014 data (red line) show no such noise.
We found other sources of error in our data which did not affect our peak
measurements, so we did not include them in our uncertainty estimates. Deep
shadows on fresh snow on steep headwalls occasionally caused a reduced point
density in the fodar point clouds. Here there was essentially no contrast
available to find match points. These areas were small and isolated,
amounting to less than 5 % of the total areas mapped, as even the track
left by a rock rolling downhill can provide enough contrast to constrain
elevations there (Fig. 8). Where this point density was simply reduced, a
coarser mesh could be applied and the results interpolated into the DEM;
further research is required to determine how well our accuracy and
precision specs apply to such areas, but spatial biasing errors will
certainly be larger. Where there were no points, gaps could only be filled
by pure interpolation or by re-acquiring with a different sun angle. Because
our areas could take an hour or more to acquire, moving shadows also caused
some noise artifacts at the edges of the shadows moving over low-contrast
snow. Occasionally these artifacts were quite large, on the order of 10 m,
but in all cases it was clearly apparent that they were actually artifacts
and were easily distinguishable from valid data (e.g., Fig. 8d).
The results of our analyses indicate that our photogrammetric measurements
are essentially as accurate as either our GPS or lidar measurements in
determining peak elevations, as well as many measuring other features of
interest. Table 1 shows that the fodar measurements on all peaks were within
40 cm of the 2011 lidar. Our repeated fodar measurements at Mt. Isto and
Mt. Chamberlin in spring 2014 had differences of only 8 and 19 cm,
respectively (Table 1), noting that the cornices on these peaks could have
changed on this level or higher due to wind redistribution and melt between
measurements. Comparisons of our 22 April maps of Mt. Isto and Mt. Chamberlin
to our GPS measurements made 5–11 days later were within only 4 cm,
which is better than the accuracy level of the GPS measurements
themselves. Note that these fodar measurements involved no corrections for
ground control – these are directly georeferenced results utilizing only
airborne data. Comparison of two Mt. Isto fodar maps to each other over small
areas indicate a repeatability on the order of ±20 cm (95 % RMSE),
including real changes due to snow and ice. This repeatability is superior
to the precision we measured using our two best lidar maps over large
ice-free areas by more than double. Given that all techniques experience
worse precision in steep mountain environments due to spatial biasing caused
by GSDs being large compared to terrain variations, fodar outperforms lidar
in the sense that fodar GSDs are much smaller than lidar GSDs for the same
amount of flight time. That is, fodar's data acquisition rate is over
100 × higher than lidar (e.g., 20–30 megapixels per second compared to 200–300 kHz)
and this results in lower GSDs for the same flying heights and swath widths.
In addition to having better precision than lidar, we find photogrammetry
much more useful scientifically due to the creation of a perfectly
co-registered orthoimage. Using this image, we can, for example, easily
distinguish snow from rock (important for snow-free assessments of vertical
accuracy or distinguishing landslides from avalanches), determine snow
lines on the glacier (important for estimating the density component of
volume change), or distinguish vegetation types (important for estimating
the compressibility of vegetation due to snow compaction).
The potential value of fodar to earth sciences is difficult to overestimate.
The impacts of modern climate change on the Arctic landscape are profound,
yet nearly impossible to grasp without a means for affordable time series of
landscape-scale measurements of topography with centimeter resolution.
Though our main usage relates to climate change, there are many other
changes occurring globally that can now be measured with improved accuracy
and interpretative ability for the benefit of society, such as measurement
of snow packs in mountain environment for water resource planning,
measurement of avalanche danger, or measurement of coastal erosion. Given
that we can now not only measure topographic change as accurately from the
air than we can from the ground but do so economically over much larger
spatial scales, the design, accuracy, and sustainability of our field
research programs and operational monitoring efforts can be improved
tremendously. In one way or another, landscape change is a driver or
response in nearly every physical and ecological study of our planet, and
thus we believe that this technology will have a major impact on our
understanding of these dynamics.
Conclusions
Here we have demonstrated a new airborne photogrammetric method that is
capable of measuring mountain peaks with an accuracy and precision of better
than ±20 cm at 95 % RMSE. We used this method to measure the heights
of the five tallest mountains in the US Arctic, which, in order, are Mt. Isto,
Mt. Hubley, Mt. Chamberlin, Mt. Michelson, and an unnamed peak we refer to as
Mt. Okpilak. From these results and our substantial prior work in flat and
moderate terrain (Gibbs et al., 2015; Kinsman et al., 2015; Nolan et al.,
2015; Overbeck et al., 2016), we conclude that this photogrammetric method,
fodar, works without reservation to measure ground surface elevation in all
terrain types at roughly the same accuracies and precision. The implications
of this are manifold – we now have the capability to measure topographic
change on the centimeter to decimeter level in flat or mountainous regions
using an airborne tool that requires no ground control and is more than 10
times
less expensive than the current state of the art.
Matt Nolan led all aspects of technique development, fodar acquisitions, data
processing, and data analysis. Kit DesLauriers led all aspects of the climbing
expeditions and their GPS measurements.
Acknowledgements
The 2014 climbing expedition and the 22 April 2014 mapping was supported by
the National Geographic Society (Expedition Council Grant EC0667-14 to
Kit DesLauriers). Development of the methods and other flights were supported by
the US Fish and Wildlife Agency and the USGS AK Climate Science Center
(CESU 701817K403 and G11AC20549 to Matt Nolan), by The National Science Foundation
(PLR-1418274), and by Fairbanks Fodar (http://www.fairbanksfodar.com). The National
Science Foundation supported acquisition of the 2008–2011 lidar (ARC-0714045
to Matt Nolan) and McCall Glacier field research (ARC-1023509 to Matt Nolan). We would
like thank expedition team members Andy Bardon, Don Carpenter, Hester Jiskoot,
Martha Reynolds, and Kasha Rigby for the assistance in the field, as
well as Coyote Air and Kristin Nolan for their logistical support.
Edited by: Andreas Kääb
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