CHAPTER
5
Digital terrain modeling and glacier
topographic characterization
Duncan J. Quincey, Michael P. Bishop, Andreas Kääb, Etienne Berthier, Boris Flach,
Tobias Bolch, Manfred Buchroithner, Ulrich Kamp, Siri Jodha S. Khalsa, Thierry Toutin,
Umesh K. Haritashya, Adina Racoviteanu, John F. Shroder, and
Bruce H. Raup
ABSTRACT
5.1
INTRODUCTION
The Earth’s topography results from dynamic interactions involving climate, tectonics, and surface
processes. In this chapter our main interest is in
describing and illustrating how satellite-derived
DEMs (and other DEMs) can be used to derive
information about glacier dynamical changes.
Along with other data that document changes in
glacier area, these approaches can provide useful
measurements of, or constraints on glacier volume
balance and—with a little more uncertainty related
to the density of lost or gained volume—mass balance. Topics covered include: basics on DEM generation using stereo image data (whether airborne
or spaceborne), the use of ground control points
and available software packages, postprocessing,
and DEM dataset fusion; DEM uncertainties and
errors, including random errors and biases; various
glacier applications including derivation of relevant
geomorphometric parameters and modeling of
topographic controls on radiation fields; and the
important matters of glacier mapping, elevation
change, and mass balance assessment. Altimetric
data are increasingly important in glacier studies,
yet challenges remain with availability of high-quality data, the current lack of standardization for
methods for acquiring, processing, and representing
digital elevation data, and the identification and
quantification of DEM error and uncertainty.
The Earth’s topography is the result of dynamic
interactions involving climate, tectonics, and surface processes (Molnar and England 1990, Bishop
et al. 2003). Numerous feedback mechanisms operate over unique spatiotemporal scales that govern
hypsometry and terrain parameters. Similarly, the
topography governs a variety of physical parameters and processes including stress fields, erosion
and mass wasting, precipitation, sediment deposition, surface and groundwater flow direction and
ponding, surface energy budget, and glaciation in a
complex topographic feedback loop (Roe et al.
2002, Reiners et al. 2003, Arnold et al. 2006a).
Scientists have long recognized the significance of
topographic parameters for studying and modeling
process mechanics, mapping the landscape, and
detecting spatiotemporal change. Consequently,
digital terrain modeling and the generation and
analysis of terrain surface representations,
commonly referred to as digital elevation models
(DEMs) and geomorphometry, have become an
important research topic for studying and solving
problems in hydrology, geomorphology, and
glaciology (Wilson and Gallant 2000).
Glaciological research indicates that glaciers in
most areas around the world are receding (Barry
2006, Gardner et al. 2013). Internationally, scientists are attempting to inventory, monitor, and
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Digital terrain modeling and glacier topographic characterization
understand current ice mass distributions and volume, glacier–climate interactions, glacier sensitivity
to climate change, as well as assess the impact of
glacier change related to water resources, natural
hazards, and sea level fluctuations (Meier 1984,
Dyurgerov and Meier 2000, Haeberli et al. 2000,
Kaser 2001, Arendt et al. 2002, Huggel et al.
2002, Meier et al. 2003, Bishop et al. 2004, Kargel
et al. 2005). With many high-altitude glacial lakes
now forming in alpine areas (Huggel et al. 2002,
Gardelle et al. 2011), with the threat of devastating
landslides ever present and perhaps shifting (Kargel
et al. 2010), with human habitation of risky places
near glaciers rising (Kargel et al. 2011), and construction of valuable infrastructure increasing in
alpine environments that never before had much
human presence (Kargel et al. 2012), accurate
DEM data are crucial for hazard assessments. This
is especially true for glacier hazard-prone regions
where field access is difficult due to severe terrain,
political sensitivity, or financial constraints.
Glaciological research is increasingly utilizing
remote-sensing studies and topographic information generated from airborne and satellite imaging,
radar and LiDAR (light detection and ranging)
systems, and GNSS (global navigation satellite system) surveying. Furthermore, DEMs are required
for image orthorectification and radiometric calibration (Bishop et al. 2004), surface energy balance
studies (Arnold et al. 2006a), debris-covered glacier
mapping (Paul et al. 2004b), glacier ice volume
loss and mass balance estimates (Berthier et al.
2007), and equilibrium line altitude estimation
(Furbish and Andrews 1984, Leonard and Fountain
2003).
The mere availability of satellite imagery and
DEMs, however, does not necessarily equate to
accurate thematic information production and
glacier parameter estimation (Raup et al. 2007).
Consequently, researchers must account for a
variety of issues in digital terrain modeling and
geomorphometric analysis. Digital terrain modeling
is a complex process that focuses on terrain surface
representation schemes, acquisition of source data,
terrain descriptors and sampling strategies, interpolation techniques and surface modeling, quality
control and accuracy assessment, data management, and interpretation and applications (Wilson
and Gallant 2000, Li et al. 2005, Fisher and Tate
2006). Accurate glacier assessment using topographic information is frequently an issue of
DEM quality and methodological approach (Raup
et al. 2007).
The purpose of this chapter is to address the topic
of digital terrain modeling and geomorphometry
for glacier assessment and mapping. Specifically,
we consider numerous issues that must be effectively dealt with in order to estimate selected glacier
parameters and delineate glacier boundaries. We
first provide background information on digital
terrain modeling to set the stage for DEM production using satellite imagery and methodological
approaches. We then provide examples of analytical
techniques that can be used to study glaciers.
5.2
BACKGROUND
Digital elevation models are digital representations
of the Earth’s relief and are fundamental to many
applications. The majority of currently available
digital elevation datasets are the product of photogrammetric software, which exploits the technique
of stereoscopy using overlapping image data,
although increasing volumes of elevation data are
also derived from radar interferometry and from
laser altimetry. Additional elevation datasets are
available from digitized map sheet topography
and, although usually spatially limited, ground surveys. As with many remote-sensing exercises, the
generation of digital elevation data represents a
complex process involving image acquisition, computation and modeling, data management, and
analysis. The terrain itself is spatially complex,
and the need to represent it digitally and describe
it quantitatively has led to various mathematical
approaches for different scale and data constraints.
Examples include the analysis of systematic high
or low-frequency periodicity in altitude using
Fourier analysis, and the identification of selfsimilar, spatially autocorrelated, and scaledependent topography using fractal geometry and
semivariograms.
Digital elevation data are normally represented in
one of four ways, including use of: (1) a regular
grid; (2) a triangulated irregular network (TIN);
(3) contour lines; or (4) point profiles. Regularly
gridded DEMs comprise square pixels of constant
spatial resolution (the effective ground dimension)
or constant latitude/longitude resolution, with each
pixel assigned an elevation value, usually in meters
and with respect to some datum (sea level or a
higher order representation of the geoid). They
are favored by geoscientists because they are
directly comparable with remote-sensing imagery
of equal spatial resolution, simple to analyze statis-
Background 115
tically, computationally easy to represent, and can
be saved in a range of formats (e.g., GeoTIFF,
HDF). Conversely, they are poor at representing
abrupt changes in elevation and heterogeneous
topography, particularly at coarse resolutions, can
generate large file sizes at fine resolution, and may
have a large amount of data redundancy across flat
areas. TINs represent topography using a mesh of
adjacent, nonoverlapping triangles with each vertex
assigned an elevation value. The TIN model stores
topological information allowing proximity and
adjacency analyses across a range of spatial scales.
TINs usually require fewer data points than a DEM
grid and are particularly useful for accurately representing extreme topographic features (e.g., channels
and ridges) as well as for surface modeling (e.g., the
calculation of slope, aspect, surface area and length,
etc.). Contour maps, some digitized from paper
topographic maps, provide more generalized representations of the terrain, but they are not so commonly used in glacial applications given the
availability of contemporary DEMs for the entire
globe; however, for the derivation of ice thickness
changes over multiple decades, such digitized maps
can be crucial. Lastly, point profile data normally
represent elevations collected by laser altimetry
(e.g., GLAS on board the ICESat), which illuminate a circular sampling area (footprint), the size
and spacing of which is generally dependent on the
altitude of the sensor. These data therefore tend to
provide sparse coverage when acquired by satellite,
and repeat pass data are not necessarily spatially
coincident.
The terms DEM, DSM (digital surface model),
and DTM (digital terrain model), are often used
interchangeably to describe any digital representation of the Earth’s topography, but differ fundamentally in their inclusion or exclusion of surface
cover in the data. DSMs can be thought of as
including all elevation data recorded regardless of
surficial cover; thus they represent tree canopy
height across a forested area and building heights
in the urban environment, for example. DTMs
‘‘strip out’’ such surface features and attempt to
represent only the solid Earth, which can be a challenging task (sometimes requiring large amounts of
interpolation) where dense ground cover(s) exist.
The term DEM is used more generally to describe
an elevation dataset without specifying the elevation reference (e.g., solid Earth, surface cover,
subsurface topography). Many satellite-derived elevation datasets are of insufficient vertical resolution
to require an explicit declaration of whether they
include surface cover or not, and are therefore generally referred to simply as DEMs.
The use of elevation data derived from remotely
sensed imagery has a number of advantages over
alternative sources. First, the range of sensors available for producing DEMs offers flexibility in scale.
Many medium-resolution (10–30 m) satellite sensors (e.g., ASTER, ERS-1/2) are able to provide
stereoscopic imagery for DEMs of wide areal coverage, while local to catchment-scale DEMs can be
derived from an increasing number of fine resolution (1–10 m) sensors (e.g., SPOT 5 HRS, Quickbird, GeoEye) or aerial imagery. Normally, the
scale of the topographic variability to be modeled
informs the selection of the source imagery (see
Section 5.3.1). Second, many glacierized areas of
the world are inaccessible for logistical or political
reasons, so for the inclusion of three-dimensional
data in global databases such as GLIMS, remotely
sensed elevation information provides the only
option. Third, as historical archives of these data
are accumulating, the opportunity to conduct
multitemporal (and thus dynamical) studies
becomes possible. Fourth, and finally, the increasing availability of no-cost data derived from
remotely sensed sources opens up the discipline of
cryospheric remote sensing to all interested parties,
which can only ultimately advance scientific understanding at a greater pace.
In relation to this last point, however, it is important that standards and procedures for DEM
generation and analysis are available for scientists
worldwide, an issue that is discussed later in this
chapter (p. 137). In brief, the utility of a DEM is
dependent upon a certain level of expertise from the
operator to ensure the correct scale of representation, accurate characterization of terrain parameters, and overall planimetric and vertical
accuracy. For example, a major difficulty in using
digital photogrammetry to generate elevation data
over glacier surfaces is that accurate DEMs can
only be derived if the glacier surface shows sufficient
topographic and/or radiometric heterogeneity to
correlate image pairs (Favey et al. 1999), which
otherwise can result in grossly inaccurate elevation
estimates over some large expanses of bare ice and/
or snow. Image saturation or low dynamic numbers
in deeply shadowed areas also result in either null
values or erroneous elevations. Consequently, great
care is required to ensure that the data selected for
an application are appropriate, processing is carried
out with a high level of expertise, and errors in any
derived data are accurately reported, so that real
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Digital terrain modeling and glacier topographic characterization
geophysical patterns and features can be differentiated from image and processing artifacts.
5.3
DIGITAL ELEVATION
MODEL GENERATION
5.3.1 Source data
Topographic maps exist for every country, and
these can be utilized to generate a DEM, provided
the map is of sufficient quality for the intended
application. In developing countries, issues of
cartographic scale, map coverage, quality, and
availability may be problematic. In some countries
the maps are military secrets, or have been degraded
in quality given the scale, contour interval, or introduction of error (e.g., Soviet topographic 1:50,000
map series of Afghanistan). If suitable maps exist
DEMs can be generated by cartographic digitization using techniques such as line-following digitization or raster scanning.
High-resolution aerial and satellite images are
also effective ways to generate and update topographic information. Digital elevation models can
be derived using stereo (overlapping) pairs and
photogrammetric techniques, which depend on
knowledge of the exact image and terrain geom-
etries at the time of acquisition. Numerous investigators have reported on the generation of DEMs
from aerial photography and a multitude of
satellite-imaging systems including ASTER, IRS,
and SPOT for glaciological applications (Kääb
2002, Berthier and Toutin 2008). Although satellite
imagery is generally available, aerial photography is
more difficult to acquire for many glacierized
regions of the world (e.g., Karakoram) because of
political sensitivities and poor archiving, and some
air photos are expensive (e.g., Alaska), which can
limit historical analyses. However, the demilitarization of Corona satellite imagery provides historical
data for many regions of the world at relatively fine
(<10 m) spatial resolution; Corona also provides
stereo coverage facilitating photogrammetric
analyses (Surazakov et al. 2007, Bolch et al. 2008).
For cryospheric applications, and especially
useful for three-dimensional information, ASTER
is one of the most appropriate and accessible sensors available for several reasons. First, and most
importantly, the coupled nadir and backwardlooking sensor systems in the near-infrared enables
fine-resolution and routine along-track stereoscopic
vision (Fig. 5.1). Second, the spatial resolution of
these stereoscopic data (15 m) provides the perfect
balance between image detail and wide swath width
(60 km) that is required for regional-scale glacier
Figure 5.1. Imaging geometry of the ASTER sensor, on board the Terra satellite, launched in December 1999. The
satellite is in a 705 km, Sun-synchronous orbit that results in a 16-day revisit period for any given location on Earth.
The ASTER sensor is equipped with two bands in the near-infrared: one at nadir (3N) and one backward looking
(3B). It takes the sensor approximately one minute to cover the same area of ground with both sensors, thus yielding
a stereo pair of 60 km swath from which DEMs can be extracted (adapted from Hirano et al., 2003).
Digital elevation model generation
studies. Third, the adjustable sensor gain settings
provide increased contrast over bare ice and snow,
which is critical for the derivation of accurate
elevation data using photogrammetric techniques.
Fourth, the relatively short revisit period of the
sensor (16 days for nadir viewing or 2 days for
off-nadir pointing) provides high-intensity coverage
in cases of natural disaster emergencies or other
special needs; in more routine cases, the short revisit
time provides many chances to acquire a cloud-free
image of an area of interest, even in notoriously
cloudy areas. ASTER data are routinely used to
provide DEMs for the derivation of threedimensional glacier parameters for all glacierized
regions, and are available at no cost to regional
centers involved in the GLIMS project. However,
the actual performance of ASTER has resulted in
far less frequent data acquisitions and often suboptimal sensor gain settings than the observation
plan calls for, thus reducing the system’s value from
what it could be.
Images acquired by synthetic aperture radar
(SAR) contain information relating to both the
magnitude and phase of the backscatter signal, both
of which are useful for deriving DEMs. Radargrammetry exploits the magnitude element of the return
signal. Similar to photogrammetry, radargrammetry makes use of two spatially separated backscatter images to form a stereo model of the terrain
(Toutin et al. 2013), with the exact image geometry
being supplied by increasingly accurate orbital data
records (Scharroo and Visser 1998). Interferometric
SAR (InSAR) makes use of the phase element of
radar return. The phase difference between two
independent return signals is very sensitive to topographic variations (as well as any surface displacements between image acquisitions) and can be
‘‘unwrapped’’ to derive a digital terrain surface,
often with very high accuracy. DEMs over glacierized terrain have been successfully derived using a
range of SAR image sources including ERS-1/2
(Eldhuset et al. 2003), Radarsat (Peng et al.
2005), and sensors on board fixed wing aircraft
(Muskett et al. 2003). The preceding chapter by
Kääb et al. has a detailed treatment of various
methodologies and glacier applications using radar
data.
Airborne laser scanning systems are an important
operational tool for generating high-resolution
topographic information. Numerous researchers
have utilized and evaluated DEMs generated from
LiDAR data for glaciological applications (Rees
and Arnold 2007). Pulses of electromagnetic energy
117
interact with surface materials to regulate the intensity of the returning signal. A LiDAR system produces data that may be characterized as a 3D point
cloud, which must be processed to remove erroneous measurements relating to reflectance from
clouds, smoke, or birds, for example (Arnold et
al. 2006b). Consequently, filtering, classification,
and modeling are required to generate a DEM
from laser-based measurements. The high quality
of LiDAR-based DEMs permits improved geomorphometric characterization of the terrain and
glacier surfaces, which translates into improved
assessment and modeling of a variety of
processes.
Finally, Global Navigation Satellite Systems
(GNSS) can be used for direct measurement of
the Earth’s surface topography, and are increasingly replacing the use of traditional theodolites
and total stations. Earth scientists are routinely
utilizing GPS receivers on a variety of platforms
to collect point and profile measurements for terrain and glacier surface representation (Miller and
Pelto 2003). Differential GPS (dGPS) refers to calculation of an accurate roving receiver position with
respect to a reference station and can yield accuracies as fine as 10 mm when the differential phase of
multiple satellite signals is exploited. This method is
particularly relevant for the collection of ground
control data as input to DEM generation.
5.3.2 Aerial and satellite
image stereoscopy
The process of deriving elevation data by photogrammetric techniques is well established and
widely documented (Kääb et al. 1997, Kääb and
Funk 1999). Deriving elevation data from stereo
photographs relies on recreating the geometry
between sensor and terrain at the exact time of
image acquisition. The user supplies approximate
data relating to the aircraft location and the average
terrain height above sea level in addition to accurate
statistics on the camera geometry and image dimensions. The software applies least-squares regression
to reduce errors in the approximations and arrives
at a stereo model that realistically represents the
real-life situation at the time of image acquisition.
The least-squares adjustment algorithm is used to
estimate the unknown parameters associated with a
solution while also minimizing error within the
solution. This is regarded as one of the most accurate techniques to:
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Digital terrain modeling and glacier topographic characterization
Figure 5.2. A typical stereo photogrammetric model (or block), illustrating the monotemporal generation of height
information from overlapping images (imagery of time 1 only). Where multitemporal imagery is available (imagery of
time 1 and imagery of time 2), calculations of surface elevation change become possible. By processing multitemporal images in a single block, potential errors, particularly those relating to external ground control, can be
minimized.
. estimate or adjust the values associated with
exterior orientation (sensor positioning and
view direction at time of image acquisition);
. estimate the X, Y, and Z coordinates associated
with tie points;
. estimate or adjust the values associated with interior orientation (sensor geometry, including focal
length); and
. minimize and distribute data error—introduced
by ground control point (GCP) coordinates, tie
point locations, and camera information—
through the network of observations
(list modified from Leica Helava 2004).
The least-squares algorithm processes the data
iteratively until the errors associated with the input
data are minimized. These errors are measured in
terms of residuals (the degree to which the observations deviate from the functional model). Residual
values (the distance between calculated statistics
and user input values) are summarized by the root
mean square error (RMSE), which should ideally be
less than twice the pixel size of the imagery for the
resultant orthoimages and elevation information to
be considered accurate when compared with the
actual terrain properties.
Once the error is within thresholds considered
satisfactory by the user, the DEM is extracted by
the generation of spatial rays from the first image
that intersect in three dimensions with the corresponding points on the second image (identified
by image-matching algorithms), thus giving a
height value for each modeled pixel (Fig. 5.2). Elevation is determined by measuring shifts in the xdirection (x parallax) of the rectified images. The
exact process followed in DEM generation may
differ slightly depending on the software employed
(see Section 5.3.4) but typically follows a series of
key stages (Fig. 5.3).
5.3.3 Ground control points
Ground control data may be derived by traditional
surveying techniques (such as triangulation, trilateration, traversing, and leveling), contemporary
survey techniques (such as dGPS measurement and
Digital elevation model generation
119
Figure 5.3. The major steps required for the extraction of DEMs from satellite imagery. Exact processing sequences
vary according to the software used, with some offering total user control over all sensor/model parameters and
processing algorithms (white box), and others offering no control over internal implementation (black box). In both
cases, users should be careful to understand associated uncertainties in derived elevation data.
laser ranging), and/or the identification of clearly
defined features (e.g., mountain peaks and road
intersections) on large-scale map sheets. They
may give information on horizontal positioning,
height, or both. Collectively, ground control data
inform the stereo model of the spatial position and
orientation of a photograph or satellite image relative to the ground at the time of exposure (or scanning), and their quality is important to the accuracy
of derived elevation data. As a minimum, the accuracy and precision of any ground control data
should be twice that of the expected DEM to avoid
adversely affecting the derived data. Research has
shown that the accuracy, number, and distribution
of ground control points used in the iterative leastsquares adjustment to refine the geometric model
can also impact DEM accuracy significantly
(Toutin 2008). While three GCPs are theoretically
sufficient to compute a stereo model from frame
imagery (Gonçalves and Oliveira 2004), the minimum number for other sensors depends on the
sensor model employed and the number of
unknowns in it. A larger number than the minimally required is usually employed to ensure redundancy in least-squares adjustment, to reduce the
impact of map and plotting errors, and to facilitate
post-derivation accuracy tests (Toutin 2002). On
the other hand, where GCPs are known to have
low accuracy it is beneficial to limit the number used
in the adjustment to avoid errors propagating
through to the output DEM.
In addition to the quality of any ground control
data used in a stereo model, the theoretical accuracy
of a DEM is also dependent on the base-to-height
ratio of the system and the quality of the image
matching used to refine the stereo model. If no
ground control data are available, only relative
DEMs may be derived (where horizontal and vertical values are only known relative to an arbitrary
datum). Their accuracy is thus dependent only on
sensor characteristics and the success of image
matching. Further parameters that can influence
the accuracy of any derived elevation data include
the quality of geometric and radiometric image calibrations (which also impact matching success and
ground control point identification) and the quality
of sensor ephemeris and attitude data that is entered
into the stereo model. Check points, which are most
often surplus ground control data, can be used to
quantify DEM errors but, similarly, the quality of
accuracy assessment is only as good as that of the
checkpoints used.
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5.3.4
Digital terrain modeling and glacier topographic characterization
Software packages
In addition to the software used by NASA and the
Japanese Aerospace Exploration Agency (JAXA)
for the operational generation of ASTER DEMs,
there are four university or private software
packages, as well as five commercial off-the-shelf
(COTS) software modules for processing stereo
ASTER data to generate DEMs (Toutin 2008).
We now give a brief description of some of the main
software packages available.
The Geomatica 2 OrthoEngine SE of PCI Geomatics (www.pcigeomatics.com), adapted to ASTER
stereo data, was developed in 1999 under USGS
contract with the collaboration of the Canada Centre for Remote Sensing, Natural Resources Canada,
for mathematical, 3D modeling, and algorithmic
aspects. It may be the most-used software for
performing 3D sensor orientation and DEM and
orthoimage generation. Both relative DEMs without GCPs and absolute DEMs with GCPs can be
generated while an existing DEM can be added in
the processing. The accuracies obtained in different
research studies were similar to those obtained at
USGS: horizontal and vertical accuracy of 15 m
and 20 m (1) respectively, depending on GCPs,
study site, and relief.
The LPS photogrammetric software suite from
ERDAS (http://www.erdas.com) includes ASTERspecific data import, radiometric correction, and
sensor model functions. It uses a feature-based,
automatic terrain-adaptive, hierarchical imagematching scheme for automatic DEM extraction
and can output grid, TIN, and point cloud data.
Of the software described here, LPS provides the
most comprehensive control over the DEM extraction and editing process. A number of automatic
spike and blunder detection algorithms aid the
detection of local extraction errors, and automatic
blending and smoothing around the perimeter of
area edits leads to seamless data continuation
through interpolated or replaced values. The most
promising of these algorithms fuses independent
datasets to achieve a complete DEM; in one
approach, Crippen (2010 and unpublished results)
used parallax–elevation cross-correlation as a
means of detecting artifacts in the ASTER DEM
so as to determine where replacement with other
data (e.g., from SRTM) should be done.
The AsterDTM module, developed by SulSoft,
the exclusive ENVI distributor in Brazil, was added
to ENVI as an add-on module in 2004 (http://
www.ittvis.com). The software can create DEMs
from ASTER Level 1A and 1B stereo pairs with
the aid of orbit/sensor modeling, quasi-epipolar
image generation, cross-correlation matching, and
automatic detection of water bodies. An existing
DEM can be added to fill in low-correlation areas.
The claimed accuracy by ENVI for a relative DEM
without GCPs is better than 20 m and for an
absolute DEM with GCPs 30 m in planimetry
and 15 m in elevation (all with 90% confidence
interval). These results were confirmed by end users
generating DEMs from Level 1A stereo pairs both
with and without GCPs, and from Level 1B stereo
pairs without GCPs.
The Desktop Mapping System Softcopy 2 ,
Version 5.0 is designed to run under the Microsoft 1
Windows 1 XP Professional operating system and
provides a complete two-dimensional and threedimensional photogrammetric mapping capability
using scanned aerial photographs or digital
images recorded by airborne or satellite sensor systems. Experiments with stereo ASTER data over
different mountainous study sites achieved RMS
errors of about 15–25 m (1), showing equivalent
results to those derived by USGS (see PCI).
DMS Softcopy 5.0 retains the speed, functionality,
and ease of use of earlier versions of the DMS
software, but has been streamlined to allow for
even faster, more efficient implementation of
operations.
SilcAst, produced by Sensor Information
Laboratory Corp. Japan (www.silc.co.jp) and exclusively developed for ASTER, is written in IDLR6.1
and can be executed with IDL VM without an IDL
license. The main functions are digital elevation
extraction either from Level 1A and Level 1B
imagery, water body identification, orthorectification, and Level 1B data generation, but the software
does not accept GCPs. ASTER 3D data products
are provided as Standard (fully automatic) with
potential miscalculated elevations, and High
(semi-automatic) with interactively corrected miscalculated elevations. In 2009, SILC with SilcAst
produced a high-quality global DEM (G-DEM1;
see Section 5.3.6) from ASTER data acquired
within an 83 latitudinal limit. Covering all the land
on Earth, it is freely available to all users in 1 1
grid tiles in latitude and longitude. While the
ASTER G-DEM1 contains 30 m grid spacing with
7 m accuracy (1), recent scientific studies demonstrated some high-frequency errors (appearing
within tile grids as pits, bumps, ‘‘mole runs’’, and
other residuals and artifacts), requiring downsampling to 90 m spacing.
Digital elevation model generation
5.3.5 Postprocessing (interpolation and
smoothing)
DEM generation often requires the interpolation of
elevation values between available sample points,
particularly when contour maps or satellite imagery
are the source data. Consequently, various approaches for how to interpolate this calculated
(not measured) elevation in the DEM production
process have been developed. The choice of
approach depends mainly on relief within the
imagery, the type of information that will be
derived from the DEM, and the proposed application (Rasemann et al. 2004). Interpolation accuracy
depends on interpolation algorithm type, surface
characteristics, and the distance between sample
points (Kubik and Botman 1976). There is a paucity
of quantitative evaluation of interpolation accuracy
over glacierized terrain and, of the few studies that
do exist, only a handful have employed ground
data to make the assessment (Cogley and JungRothenhausler 2004). At present, uncertainties in
DEM accuracy do exist depending on the choice
of the interpolation algorithm employed; therefore,
all qualitative and, in particular, quantitative results
from glaciological analyses that include DEMs
must be interpreted with caution.
Some of the interpolation methods that have
been used in glacier research include (but are not
limited to) Triangular Irregular Network (TIN;
Gratton et al. 1990); Inverse Distance Weighted
(IDW; Etzelmüller and Björnsson 2000); spline
(Mennis and Fountain 2001, Bolch et al. 2005);
and kriging (Burrough and McDonnell 1998).
Triangulation: since this method produces individual triangles with constant exposition and aspect
rather than a continuous relief, the final DEM is not
differentiable. To ensure that information on curvature can be extracted, the DEM has to be converted to a grid. Problems occur at sharp edges,
deep valleys, and cliffs. Often, valleys and ridges
show a typical ‘‘terracing’’ effect. Such artifacts
can be eliminated by manually adding elevation
information, by using structural information with
elevation values (Heitzinger and Kager 1999,
Rickenbacher 1998), or by subdividing the triangles
(Schneider 1998).
Inverse Distance Weighted: a relatively simple algorithm that weights the sample point value according
to its distance from the pixel of interest. The weighting and number of sample points have a strong
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influence on DEM quality. For example, a strong
weighting based on only few sample locations produces a rough surface in which the sample points
themselves are heavily emphasized.
Spline: this interpolation method applies a special
function that is defined step by step by piecewise
polynomials that are continuously differentiable.
Most common in DEM generation are low-order
cubic (r ¼ 3) and bicubic (r ¼ 2) splines. In general,
the surface of the final DEM is smooth and even.
However, the main problem is the occurrence of
overshoots (i.e., unnatural ‘‘holes’’ and ‘‘spikes’’).
To prevent such overshoots, a regularized splinewith-tension algorithm is used (Mitasova and Mitas
1993). This method uses a function that specifies
how fast the collection of sample points decreases
with increasing distance thereby attenuating the
magnitude of overshoots.
Kriging: a geostatistical method, based on a
stochastic model, which predicts the elevation at a
specific location and is particularly used when a
trend (here: the spatial correlation of elevation
values) exists. One disadvantage of this method is
that adjustment of the semivariogram model to the
existing data structure requires experience.
Various studies have considered the relative
accuracy and appropriateness of each of the above
approaches. For example, Kamp et al. (2005) tested
three interpolation methods—IDW, spline, and
TIN—when generating a DEM from 1:50,000 topographical maps of Cerro Sillajhuay in the Andes of
Bolivia and Chile using Esri ArcGIS 3.2 software.
In this study, both IDW and spline methods produced very good results in high relief areas, but a
large number of artifacts in generally flat terrain.
The authors concluded that both algorithms had
problems handling larger distances between contour lines. Instead, the most accurate DEM was
generated using the TIN method, although a first
raw DEM contained many artifacts—mainly over
flat terrain, caused by the triangles that are used by
the TIN method for interpolation.
Tests similar to those made by Kamp et al. (2005)
were described by Racoviteanu et al. (2007) for the
Cordillera Ampato (southern Peru). In this study,
the examination of RMSEz (vertical error) values
for DEMs derived from topographic data (1:50,000
maps constructed from 1955 aerial photography)
revealed that no interpolation method performed
122
Digital terrain modeling and glacier topographic characterization
perfectly. While the IDW DEM and TIN DEM
showed accuracies of only 21 m and 24 m, respectively, the spline (here: TOPOGRID) DEM produced a vertical accuracy of 15 m,
outperforming the other available algorithms.
However, the authors noted that all three DEMs
produced ‘‘terracing’’ effects, an artifact of preferential sampling along the contour lines, with points
closer to the contour lines being interpolated using
the same elevation values. The terracing effect was
most severe using the IDW interpolator. Similar
terracing artifacts were described by Etzelmüller
and Björnsson (2000) using the same interpolator,
and by Mennis and Fountain (2001) using the
spline-with-tension interpolator. Wilson and Gallant
(2000) showed that such terracing artifacts affect
calculations of topographic characteristics such as
slope, aspect, and profile curvature.
DEMs constructed over largely featureless terrain often fail to characterize subtle (or even
abrupt) changes in surface topography, which can
be rectified by the use of breaklines. Breaklines are
linear features that describe interruptions in surface
smoothness and are typically used to define channels or ridges, for example, where there is a clear
change in surface topography. However, the development of real 3D breaklines is still a problem, and
Bolch and Schröder (2001) actually concluded that
the integration of simple breaklines does not significantly improve the overall quality of the DEM.
As a solution, in their DEM generation process
Kamp et al. (2005) manually added some contour
lines using elevation information from stereoscopic
analysis of aerial photographs. Eventually, the TIN
DEM was converted into a grid-based DEM using
Esri ArcInfo 7.2 software, and two nearest neighbor
filters helped smooth the final model, albeit at the
expense of some topographic detail (e.g., the loss of
some edges, frost cliffs, and gorges). The authors
concluded that the final DEM was of sufficient
quality for macro and mesoscale geomorphological
analysis (e.g., of rock glaciers); however, processing
the DEM from contour lines was relatively time
consuming.
5.3.6 Data fusion
While small gaps in DEM data can be filled by
interpolation, large voids stemming from shadowing, correlation failures, and other effects require a
different approach. It is sometimes desirable to
combine, or fuse, DEMs from different sources in
order to obtain the most complete coverage of an
area. As well as filling in any gaps in the respective
DEMs, such fusion can also help to identify any
severe vertical and horizontal errors in common
areas (Kääb et al. 2005). DEM-merging techniques
range from replacement of data (Kääb 2005a) and
weighted fusion, resulting in smooth transitions
between DEMs (Weidmann 2004), to merging in
support of DEM processing itself (e.g., DEM
approximation in order to geometrically constrain
stereo parallax matching or interferometric phase
unwrapping) (Honikel 2002). One successful
approach involves identification of artifacts in a
single-scene ASTER DEM and then infilling with
a global dataset such as SRTM or the ASTER GDEM. Artifact delineation is almost perfect (almost
no errors of omission or commission), so the infilled
product is usually of very high quality (Crippen
2010).
The ASTER G-DEM1 is the result of the fusion
of suitable individual ASTER-derived DEMs by
averaging all elevations in the vertical stack. While
DEM fusion using this approach is helpful for
deriving a spatially more complete and accurate
set of geomorphometric parameters, it should be
avoided or handled with care for DEM-based studies of glacier thickness changes. The number of
stereo images used to produce a given G-DEM1
grid point elevation varies from one to several tens.
Whereas the number of scenes used for each grid
point is known globally, G-DEM1 ancillary data do
not support knowledge of when the images were
acquired. The mean date is about 2004/2005, but
for a given locale it could be earlier or later by a few
years. Variance of the mean from 2004/2005 is less
than a year in most areas, but it can be much greater
for some places where few ASTER images have
been acquired. G-DEM1 carries some of the artifacts present in individual DEMs, and is generally
very noisy, often rendering it unsuitable for detailed
studies requiring high resolution, although for
studies of basin-scale hypsometry, G-DEM1 can
be convenient. A new G-DEM2, of similar construction but lacking the severity of noise and artifacts of the earlier version, was released in October
2011. G-DEM2 benefits from 260,000 additional
ASTER scenes, and preliminary tests indicate
improved accuracy in both horizontal and vertical
dimensions, and a substantial reduction in the number of voids (Tachikawa et al. 2011). Still remaining
for the future is development of a new GDEM that
would allow better tracking of input images.
DEM error and uncertainty
5.4
DEM ERROR AND UNCERTAINTY
5.4.1 Representation of DEM error
and uncertainty
Given the number of stages involved in generating a
DEM, errors are inevitable in both the vertical and
planimetric coordinates. In general, error can be
classified as: (1) gross errors that are associated with
equipment failure; (2) systematic error that represents the results of a deterministic system that can
be accounted for by using functional relationships;
and (3) random errors that occur within (or because
of ) the multitude of operational tasks that are
involved in computation. In this context, error is
typically defined as systematic and/or random variations about a ‘‘true’’ reference value (Fisher and
Tate 2006). The magnitude of vertical error can be
an important consideration, as changes in glacier
surface altitude over shorter time frames may
become undetectable, depending upon the nature
of the source data. Consequently, the usefulness
of a DEM for estimating mass balance must be
carefully evaluated (Bamber and Payne 2004).
A common descriptor of error is root mean
square error (RMSE):
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
sP
P
2
i
j ðzi; j zi; j;r Þ
RMSE ¼
ð5:1Þ
n
where zi; j is the elevation at location (i; j ) in the
DEM, and zi; j;r is a reference elevation at the same
location. The metric has been used when comparing
elevations off-glacier in a variety of glaciological
studies, although it does not describe very well
the statistical distribution of vertical error (Fisher
and Tate 2006). It has, however, become a standard
measure of map accuracy. Other researchers have
used additional error metrics such as mean error
(ME) and standard deviation (S) (Cuartero et al.
2004):
PP
ðzi; j zi; j;r Þ
ME ¼
ð5:2Þ
n
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PP
½ðzi; j zi; j;r Þ ME 2
S¼
ð5:3Þ
n1
Systematic under or overestimation (biases) are
depicted as positive or negative ME values.
Such global summary (single-value) metrics are
quick to calculate and easy to report, but they fail to
characterize the spatial pattern of error, which is
critical to environmental applications. DEM errors
can vary spatially, and research indicates that the
123
spatial structure of error in DEMs remains poorly
understood (Carlisle 2005). Numerous researchers
have attempted to study and describe the nature of
spatial error and have found that patterns of error
can be anisotropic, scale dependent, spatially variable, and spatially correlated, but most importantly
DEM error is closely related to the complexity and
characteristics of the terrain (Kyriakidis et al. 1999).
Work in alpine environments often reveals patterns
of error over mountain terrain and glacier surfaces
that are highly variable in spatial extent and location, and are related to acquisition of source data,
spatial interpolation, and terrain geometry.
5.4.2 Type and origin of errors
Once a DEM has been generated by determining
the parallax between pixels matched by crosscorrelation there is always a need for postprocessing
due to mistakes in pixel matching, correlation failures, and, if present, the impact of clouds in the
scenes. Further, shadowing in regions of high relief,
low image contrast over clean snow and ice, and
self-similar surface features on glaciers will lead to
voids and artifacts in the resulting DEM. Some
software packages, such as SilcAst, will try to
remove such features automatically, with no user
control over the process. Alternatively, ENVI, LPS,
and PCI Orthoengine all provide a suite of postprocessing tools for manual editing. However,
Eckert et al. (2005) found that in some cases the
postprocessing tools provided by software packages
were not sufficient and further morphologically
based interpolation algorithms were required to
produce a suitable DEM. Such matching mistakes
and voids are relatively easy to identify and correct
for, but where inaccurate GCPs and poorly chosen
tie points are used, distortions, biases, and planimetric shifts may also be introduced into the
derived DEM, which can be difficult to model
without the use of a reference elevation dataset.
This is particularly problematic where multitemporal DEMs are required for the measurement
of elevation changes (see Section 5.5.5).
Two types of error affect the measurement of
glacier elevation changes: horizontal (planimetric)
and elevation (altimetric). Planimetric error refers
to horizontal shift of often correct elevation values
to erroneous easting/northing locations. This can
be either a systematic or a variable shift, and can
be exhibited in one or more directions. Such shifts
are easily quantified by correlating corresponding
orthoimages and quantifying the orthophoto paral-
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Digital terrain modeling and glacier topographic characterization
Figure 5.4. Scatterplot of mean difference altitude
generated from a SRTM DEM (2000) and an
ASTER-derived DEM (2004). Mean values were computed off-glacier over the Nanga Parbat Massif in
Pakistan. Variations in viewing geometry and/or spacecraft orbital parameters result in a nonlinear bias that
significantly deviates from zero. Consequently, linear
and nonlinear systematic biases must be removed when
comparing DEMs generated from different sensor products.
lax (Li et al. 1996, Georgopoulos and Skarlatos
2003), since there should be no relief displacement
in either image if the DEMs are accurate. Altimetric
error refers to systematic biases that may artificially
increase or decrease elevation in a given direction
across part of, or the whole, DEM, as well as more
locally variable slope or aspect-related biases (Fig.
5.4). The correction of both types of error usually
requires some form of mathematical modeling. The
most promising approach has focused on the use
of ordinary least-squares regression modeling to
create spatially nonstationary, spatially correlated
and heteroskedastic error surfaces from only a
small number of sample locations (Kyriakidis et
al. 1999, Carlisle 2005). These error surfaces can
then be used either to create higher accuracy
DEMs, or to inform analyses of error propagation
in the computation of surface derivatives (Oksanen
and Sarjakoski 2005). It is crucial that both planimetric and altimetric errors are identified, particularly in the case of glacier monitoring as they can
lead to erroneous volume changes (Schiefer et al.
2007) or even change the sign of the resulting mass
balance calculation (Berthier et al. 2006).
Systematic errors are common in some of the
most widely available topographic datasets, making
it essential for users to make appropriate error
assessments, even if they believe biases are removed
prior to analysis. Particularly relevant in this
respect is the widely used continuous DEM produced by the Shuttle Radar Topography Mission,
which was flown in February 2000 and provides a
topography covering continental areas from 60 N
to 56 S (Rabus et al. 2003) with a 1 and 3 arcsec
spatial resolution (about 30 and 90 m, respectively).
It has yielded significant advances in the monitoring
of glacier wastage in Alaska and neighboring
Canada (Muskett et al. 2003, Larsen et al. 2007,
Schiefer et al. 2007, Berthier et al. 2010), Patagonia
(Rignot et al. 2003, Rivera et al. 2005), and central
Asia (Surazakov and Aizen 2006). However, since
its release, significant biases in SRTM data have
been identified by a number of authors, and a clear
examination of the bias still needs to be performed.
For example, Kääb (2005a) found a systematic
mean error of about 7 m for the Gruben area in
Switzerland. Still in the Alps, Berthier et al. (2006)
found a small mean error (<3 m) but detected a bias
that increased linearly with elevation. Such a bias
related to elevation is still not fully understood but
has since been confirmed for Patagonia (Möller et
al. 2007), the Himalayas (Berthier et al. 2007), and
the Canadian province of British Columbia (Schiefer et al. 2007). The latter authors used a piecewise
model to correct elevation bias (constant bias at low
elevation and linear bias above a threshold altitude). The regional pattern of the biases in SRTM
data is also complex. Surazakov and Aizen (2006)
found a localized ice-free region with systematic
error in the SRTM data ranging from 20 to 12
m on a 30 km spatial scale. Berthier and Toutin
(2008) found a 20 20 km region where SRTM
data are systematically 5–10 m higher than SPOT5
or ICESat elevation data. Note here that, although
sensor platform orbits are too widely spaced for
mountain glacier elevation change mapping, ICESat elevation profiles have been shown to be a good
source of data to detect and understand errors in
SRTM data for ice-free regions where no elevation
changes are expected (Carabajal and Harding 2005,
Berthier and Toutin 2008).
5.5
GEOMORPHOMETRY
Glacier geomorphometry refers to the threedimensional topographic characteristics of a
glacier surface including its size, shape, hypsometry,
orientation, and position. Geomorphometric
analyses have historically pursued fine-resolution
digital elevation models to improve and refine land
Geomorphometry
surface parameters and objects (Drăgut et al. 2009).
However, with the increasing availability of detailed
DEMs it is becoming clear that the relationship
between DEM scale and the ability to extract geomorphometric information is not straightforward.
Indeed, for many applications, increased DEM
resolution only serves to introduce noise into the
analysis. Accordingly, a number of methods have
been applied to account for scale-related problems
through DEM generalization, although further
work along these lines is needed if accurate topographic characterization of glacierized areas is to be
achieved (Drăgut et al. 2009). Despite this current
imperfection, many quantitative analyses of landscape and landscape evolution remain heavily
dependent on the derivation of geomorphometric
data in their methods.
5.5.1 Geomorphometric land
surface parameters
When deriving geomorphometric information from
DEM data it should be noted that, for every order
of differentiation, the effective resolution of the
product declines and noise increases. The first
derivative (based on calculations between two
points) normally defines slope, whereas the second
derivative (based on calculations between three
points) normally defines curvature. For every order
of differentiation, small errors in the primary dataset become exaggerated. Thus, a DEM having a
30 m posting can report the first and second derivative values still with 30 m postings, but each grid cell
of the derivatives includes information from neighboring cells and so the effective resolution is
reduced for the derivatives, even though a value is
computed for each grid cell. Effectively this means
that derivative information for very small glaciers is
useless, especially if the derivatives, such as curvature, are used to define lateral moraines, computed
drainages, or other landforms or hydrological units.
Thus, differential geomorphometric parameters
carry both great power to discriminate distinct
terrains and landforms, and great risk that noise
or systematic bias is transmitted into geomorphometric mapping products.
Depending on the tolerance for noise or low
spatial resolution, geomorphometric analysis can
emphasize nondifferential parameters (based on
hypsometry), first-order differential analysis (slope,
slope aspect), or second-order differentials (curvature, tangential curvature) (Fig. 5.5). Most off-theshelf image-processing software is capable of pro-
125
ducing such metrics using standard algorithms, with
the quality of the derived geomorphometric data
being largely dependent on the accuracy of the
input elevation data. In an applied context, land
surface parameters are a useful means of comparing
the topographic characteristics of glacierized areas
and, in addition, are increasingly being used in
combination with satellite imagery to derive more
robust approaches to accurate glacier delineation
(see Chapter 4, and Section 5.6 for further details).
They are also often employed in process modeling,
with elevation providing useful information on
gravity-driven processes. For example, land surface
parameters such as slope gradient can indicate the
gravitational potential available for geomorphic
work (i.e., erosion), and slope aspect the direction
of the work carried out (Smith and Pain 2009).
It is important to note that geomorphometric
data may vary dramatically between adjacent subcatchments and, less obviously, for the same glacier
or glacierized area through time. Changes in glacier
topography, for example, may be caused by a sustained change in mass balance, or by a change in ice
dynamics (or both). Basic elevation data reflecting
these changes may be derived by taking a topographic profile along the flow line of the glacier
from multitemporal DEMs or by computing the
altitude–distance function, which effectively compares every pixel representing the surface of the
glacier to a terminus position by plotting the average altitude in a distance bin. More complex elevation change data can be derived by hypsometric
analysis, essentially a frequency analysis, characterizing the altitude–area distribution of a glacier
surface. However, the generation of more complex
data such as these is not always desirable; for
example, small changes in surface elevation may
be easily detected in simple multitemporal topographic profiles, but not so in a multitemporal
hypsometric analysis where large volumes of
(potentially noisy) data can mask subtle surface
changes. Whichever geomorphometric approach is
adopted, it is essential that systematic biases in the
DEM are removed prior to analysis and interpretation of the results (see Section 5.4).
5.5.2 Scale-dependent analysis
A range of interacting geomorphic processes shape
the glacial environment, leading to landforms that
are rarely strictly spatially delimited (Schneevoigt
and Schrott 2006). Such landforms are diverse in
size and shape, even within a single land cover
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Digital terrain modeling and glacier topographic characterization
Figure 5.5. Geomorphometric analysis of the Batura Glacier, Hunza Valley, Pakistan: (a) SPOT HRVIR
panchromatic satellite imagery (acquired October 17, 2008), copyright CNES 2008/Distribution Spot Image.
(b) SPOT HRS-derived composite DEM (image dates 2002–2004), from which (c) slope, (d) aspect, (e) shaded
relief, and (f ) plan convexity, can all be calculated. Figure can also be viewed as Online Supplement 5.1.
classification, and microscale landforms may compose local-scale landforms, which may themselves
compose catchment-scale landforms. In modeling
such dynamic and diverse environments, linear
process-form relations and those that are spatially
restrictive are therefore unrepresentative. There is
thus increasing focus on the hierarchical organization of topography in studies on mountain geomorphology, and the subsequent adoption of
scale-dependent analyses. These can be simply
defined as methods that examine the variability of
the three-dimensional spatial structure of morphological features on multiple levels.
With the increasing availability of DEMs from
airborne and spaceborne platforms, automated
approaches have been developed to identify specific
geomorphometric features (e.g., glacier extent, location and density of crevasses) based on their shape
and textural properties. One such method is to
measure surface roughness on multiple scales and
in multiple directions, by variogram analysis. The
variogram is effectively an index of dissimilarity
between pairs of points that are separated by a
predefined vector and within a specified search window. Multiple variograms can be used to characterize terrain morphological features, such as debris
flow deposits, channels, and rockfall deposits, and
to calibrate secondary morphological indices such
as anisotropy, periodicity, and the spatial variability calculated at specific lags. These indices,
while providing useful quantitative landscape
characterization data in their own right, can then
Geomorphometry
be used as input into further, perhaps more complex
(e.g., pattern recognition) landscape classification
techniques (van Asselen and Seijmonsbergen 2006).
A further derivative of the variogram is the fractal dimension (D), which provides a measure of
whether topographic surfaces and spectral reflectances of land cover units are self-similar over a
range of spatial scales. Many landscape features
and other environmental data have been shown
to exhibit self-similarity, at least statistically (Goodchild and Mark 1987). The limited number of
studies that have evaluated the utility of fractals
for these purposes indicate that the majority of
geomorphic surfaces exhibit scale-dependent fractal
dimensions (i.e., limited to certain spatial ranges;
Bishop et al. 1998), with the range in scales often
determined by the controlling geophysical processes
that have shaped, or continue to shape, the landscape (Lathrop and Peterson 1992). Fractal dimensions have also been employed to improve
classification accuracy (de Jong and Burrough,
1995) and to provide insight into operational-scale
and process–structure relationships. This approach
appears to have great potential in this respect,
although to investigate self-similarity in surface
roughness characteristics over the full range of
spatial scales requires the use of high-quality
DEMs, which may not always be available in
glacierized areas.
5.5.3 Topographic radiation modeling
Digital elevation models are fundamental to the
three-dimensional modeling of solar radiation variation across a landscape. Insolation modeling can
either be point specific or area based. Point-specific
modeling considers the geometry of surface
orientation, the visible sky, and the effect of local
topography. Local topographical effects can be
determined using empirical relations, visual estimations, or, where field data are logistically possible,
by upward-looking hemispherical photography.
Such calculations can give locally very accurate
results, but are clearly limited in spatial coverage.
Area-based insolation modeling relies solely on the
use of a DEM to calculate surface orientation and
shadowing across a subcatchment, for example, and
as a result has much greater application for understanding large-scale landscape processes. Along
these lines, a number of studies have made surface
irradiance and ablation gradient calculations to
identify locations most suitable for past and present
glaciation (Carr and Coleman 2007, Allen 1998) by
127
identifying site shelter and exposure, and to be
applied as input to energy balance melt models,
which are clearly fundamental to understanding
the relationship between glacier behavior and
climate.
Net radiation (also known as net flux) is defined
as the balance between incoming and outgoing
energy and can be computed as:
Qn ¼ Eð1 Þ þ L #s þ L #t þ L "
where E is total surface irradiance, is surface
albedo, L #s is longwave sky radiation, L #t is longwave radiation from the surrounding terrain, and
L " is emitted longwave radiation. It is regulated by
numerous processes and can be highly variable
depending on atmospheric, topographic, and surface biophysical conditions. Indeed, in mountainous areas radiative fluxes are particularly complex,
fluctuating considerably in space and time because
of the effects of slope, aspect and the effective horizon, and the input of reflected and emitted radiation from surrounding slopes (Hock 2005). As such,
there is a movement towards the use of increasingly
fine temporal (hourly) and spatial (25 m) resolution modeling, with the latter again dependent on
the availability of suitably fine-resolution and
accurate digital elevation data. Where such data
do exist, studies have shown that the melt rate of
snow and ice and spatial and temporal patterns in
energy balance can be calculated accurately across a
glacier, albeit with dependence on accurate field and
meteorological data (Brock et al. 2000).
5.5.4 Altitude functions
Most glacier parameters vary as a function of
altitude, and these relationships can give insight
into glacier dynamics and processes that simple
two-dimensional analyses would not reveal. A
glacier’s most fundamental altitude parameter is
the equilibrium line altitude (ELA) because it
divides the glacier into accumulation and ablation
areas (Braithwaite and Raper 2010). This can be
simply estimated using multispectral satellite
imagery in combination with a DEM, by assuming
that the ELA is equal to the snow line position at
the end of the melting season (Bamber and Rivera
2007). Such information is fundamental to mass
balance calculations, which are useful indicators
of climatic variations where no actual ELA data
or better alternative proxies exist (Yadav et al.
2004). In the absence of calculated mass balance
data or transient end-of-season snow line data,
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Digital terrain modeling and glacier topographic characterization
the topographic profile of a glacier can be used as a
relative proxy for the dynamic state of glaciers, with
those glaciers in rapid recession tending to exhibit
concave-up or flattened (planar) surface profiles in
the ablation zone, and those accumulating or maintaining mass characterized by convex-up surface
profiles (transverse profiles especially) in the ablation zone (Quincey et al. 2009).
The altitude–area profile (or the hypsometric
curve) for each glacier represents a distinct 3D
spatial signature that is the end result of thousands
or millions of years of erosion and reflects interaction of the regional climate with subglacial bedrock
(Tangborn 1999). It has been used in many cases to
infer the state of geomorphic development within a
glacial system (Katsube and Oguchi 1999). Glacier
erosion processes are determined most significantly
by glacier velocity, ice thickness, subsurface geology, and basal thermal conditions. Differential
erosion therefore occurs with altitude as each of
these parameters changes accordingly. Topographic
analyses of the Nanga Parbat Massif in Pakistan
revealed a spatially variable relief structure that
correlated to geomorphic events and dominant
surface processes (Bishop et al. 2001). Glaciation
was found to generate the greatest mesoscale relief
at high altitudes and warm-based glaciation was
found to reduce relief at intermediate altitudes.
More recently, numerical modeling has shown that
mountain heights can be explained by a combination of glacier erosion above the snow line and
isostatic uplift caused by erosional unloading, with
maximum elevations being constrained to an altitude window just above the snow line (Egholm et al.
2009).
More generally, glacier hypsometry determines
how responsive glacier-wide mass balance is to
climatic perturbations (Furbish and Andrews
1984). For example, a rise in the snow line of
200 m in a given region (in response to local atmospheric warming, for example) would have a much
greater impact on a low-gradient valley glacier than
a steeply sloping one, as in the former case a
greater proportion of the overall ice mass would
become subject to net annual mass loss. Thus, as
an example, if there were a rise in local atmospheric
temperature in the Hunza Valley of the Karakoram,
the mass balance of the Batura Glacier would be
affected to a greater extent than that of the
Ghulkin Glacier, and the mass balances of the Pasu
and Ghulmit Glaciers would change somewhere
between those two end members (Fig. 5.6). Similarly, glacier clinometry (characterization of the
Figure 5.6. Hypsometric curves for the Batura,
Ghulkin, Ghulmit, and Pasu Glaciers located in the
Hunza Valley, Pakistan.
slope/altitude function) expresses glacier relief,
and is thus also useful for determining erosion rates
and mass balance fluctuations.
The relationship between altitude and glacier
velocity is not straightforward. Glaciers with low
relief tend to exhibit flow that is relatively uniform
across the altitudinal range, whereas those with
high relief (and are thus fed predominantly by snow
and avalanche material) tend to have very high flow
rates at altitude and much reduced flow towards
their termini. Altitude–velocity profiles can be useful for proxy assessments of mass balance (Luckman et al. 2007), for identifying areas susceptible to
glacial lake development (Quincey et al. 2007), and
for determining predominant glacier flow regimes
(Copland et al. 2009). In the case of the latter,
generally flat transverse velocity profiles with a
rapid reduction in flow at the margins indicate
‘‘block flow’’, suggesting down-glacier movement
of ice en masse by basal sliding, whereas convex
velocity profiles that display greatest displacements
towards the centerline of the glacier indicate a
flow regime dominated by ice deformation. Large
seasonal variability in flow can further highlight the
importance of meltwater availability for a given
glacier, and may even help to identify different flow
mechanisms that exist at different altitudes within a
single glacial system (Fig. 5.7; Quincey et al. 2009).
5.5.5 Glacier elevation changes and
mass balance calculations
Stereo photogrammetry has been employed to calculate glacier surface elevation changes for many
Geomorphometry
129
Figure 5.7. Selected seasonal and annual centerline velocity profiles for the Baltoro Glacier, Pakistan Karakoram.
Date format is year, month, day. Note varying flow rates across summer and winter seasons, and varying patterns
with altitude. In particular, note the similarity of flow profiles in the lowermost 400 m of the glacier, and contrasting
profiles with greater altitude, which may be related to the availability of meltwater at the glacier bed.
years, using images acquired by both airborne and
satellite sensors. The most reliable source of DEMs
for volume change estimates is still aerial photos.
Given their very fine resolution, if precise GCPs are
available, DEMs with RMS accuracies the size of
approximately one pixel (few tens of centimeters)
can be obtained (Kääb 2002). Consequently, aerial
DEMs are still frequently employed to study volume changes at the scale of a single glacier and
detect systematic errors in cumulative mass balance
estimates obtained from the traditional (pit and
stake) glaciological method (Østrem and Haakensen 1999). However, aerial photographs cover a
limited surface on the ground (generally one glacier)
and it is difficult to fly a plane in remote and highrelief areas. Consequently, they cannot be regarded
as a means of obtaining regular coverage of glacier
topography at the regional scale. Given the large
footprint of satellite images (typically 60 60 km),
it is tempting to apply the geodetic method to spaceborne DEMs. The principle is the same as for aerial
photography: two sequential glacier surface models
are derived from pairs of stereoscopic images and
subtracted to yield a map of elevation changes.
Satellite-derived DEMs are less accurate than those
computed from aerial photographs so caution must
be taken when interpreting the signal and comprehensive error analysis is mandatory.
Changes in surface elevation can be measured
most accurately by processing all imagery within
a single block or, put more simply, using a single
mathematical model (Kääb 2000; Fig. 5.2). The
quality of derived surface elevation data using this
technique is mainly dependent on the interior
orientation of the stereo model (Baltsavias 1999)
rather than the accuracy of any ground control
used, which makes the technique particularly
appropriate for assessing remote terrain. Factors
such as scanned resolution of the images, accuracy
of fiducial mark locations, and accuracy of camera
calibration parameters are particularly important
in such analyses. Model GCPs introduce a secondorder error that is small (of the order of a few
percent) in relation to final vertical displacements,
which is consistent between the two DEMs, providing they are bundle-adjusted as a single image
block. Therefore, the technique can, in theory, be
used without any ground control at all, while still
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Digital terrain modeling and glacier topographic characterization
producing accurate vertical displacement results
from the relative image orientation alone (Kääb
2002).
A major source of error in vertical differences
between multitemporal DEMs is their threedimensional co-registration. In cases where no common GCPs and tie points have been applied, severe
biases might exist in particular between spacederived DEMs. Errors in elevation differences from
such a lack of precise co-registration might easily
exceed real elevation changes, and should therefore
be investigated as part of every DEM-differencing
work (cf. Fig. 5.4). The most efficient method to
investigate and possibly correct DEM biases is
the cosine method that relates elevation differences
found for stable terrain to the combination of terrain slope and aspect (Kääb 2005a, Nuth and Kääb
2011).
While a 10–20 m elevation error may be acceptable for the orthorectification of images, it is not
for glacier elevation change mapping. Typically, a
glaciologist aims at measuring the rate of change in
surface elevation within 0.5 m/yr (this is the upper
bound for the error). Larger errors are acceptable
only when massive (tens of meters), but unusual
elevation changes are monitored (Stearns and
Hamilton 2007). A glaciologically relevant accuracy
can be obtained by (1) increasing the time period
between the two datasets and/or (2) improving the
quality and limiting the biases of the DEMs. The
first strategy is generally explored by comparing
recent spaceborne DEMs (ASTER, SRTM, SPOT)
with maps from the 1950s, 1960s, or 1970s. Applying such historic topographic datasets with more
recently derived DEMs may permit determination
of glacier elevation changes across several timesteps. For example, Kargel et al. in this book’s
Figure 15.4F show a technique that captures three
sequential DEM elevation-differencing analyses
(over a 40-year total period) into one RGB composite image. Each color channel (RGB) represents
the earliest, middle, and the latest elevation-differencing analysis, respectively; the composited image
provides immediate visual perception of the acceleration or deceleration of elevation changes coincident with the color-scaled time period. In this
way, spatial, dynamic, and multitemporal information on elevation changes are uniquely viewed
within one image. The second strategy relies on
higher resolution satellite images with stereo capabilities such as SPOT5 HRS or ALOS PRISM.
Even in the latter case a minimal image time span
of about 3 to 5 years is required.
The accumulation zone is the most critical part of
the glacier when mapping elevation changes. If
DEMs are derived from optical images or aerial
photographs, the high reflectance of the year-round
snow-covered accumulation zone may lead to limited features in the photographs/images or, in the
worst case, saturation of the sensor (Kääb 2002). In
the case of old maps derived from aerial photographs, errors may have been introduced by interpolation of contours (Schiefer et al. 2007). For
satellite images, featureless terrain can lead to data
gaps or erroneous pits and spikes in DEMs of the
accumulation zone. Enhanced elevation change
errors may also affect the accumulation zone
because the ice-free regions, which are used for
detecting and modelling any elevation biases, are
located at lower altitude. Only a few nunataks
may be visible to check the presence of relative
elevation biases at higher altitude, but, in practice,
even this is difficult because they are generally steep
and small features. Consequently, any elevation
biases need to be extrapolated from the lowest to
the highest elevations. Other reasons for increased
uncertainties in the accumulation zone relate to
difficulty in choosing density values to convert
volume-to-mass changes and, when DEMs derived
from SAR images are used, the necessity to take
into account penetration of the radar signal
(depending on its frequency) into the snow/firn
(Rignot et al. 2001). Consequently, good practice
is to compute separate estimates of glacier volume
changes for the ablation and accumulation zones,
even if only a rough estimate of the position of the
equilibrium line altitude (ELA) is available. Different uncertainties can thus be attributed to each of
the two regions.
A number of strategies exist to actually compute
glacier volume changes from a set of glacier elevation changes (Kääb 2008). (1) If the two (or more)
DEMs to be differenced are complete, the summation of vertical differences gives the volume difference. Since this is often not the case (see above),
either (2) the hypsographic method can be used
where mean thickness change for each elevation
bin is multiplied by its area and all bins summed,
or (3) polynomial variation of elevation changes
with height can be fitted to measured elevation
differences and the elevation differences for each
glacier point then computed according to its height
using the polynomial parameters. In cases where
one of the multitemporal elevation datasets is not
a grid, or elevation information is distributed
unevenly, such as in contour lines or altimetry
Glacier mapping 131
footprints, calculations must be made carefully. For
example, it might be advantageous in terms of minimizing error propagation not to interpolate point
elevation data to a DEM and then difference two
datasets, but rather to first calculate differences
between the elevation points and the DEM, and
then to interpolate elevation differences across the
wider glacier surface. In a number of cases, elevation differences will show less spatial variability
than elevation itself, and interpolation routines will
thus produce less serious artifacts.
Data from nonoptical sensors can also provide
accurate measurement of glacier surface elevations and, with multitemporal datasets, elevation
changes. Spaceborne radar altimeters (on board
ERS-1, ERS-2, or Envisat, for example) are well
suited to flat and large ice sheets or ice caps but
are not suitable to survey mountain glaciers
targeted by GLIMS because of their kilometric
footprints. The smaller (60 m) footprint of the
Geoscience Laser Altimeter System (GLAS) on
board ICESat makes it a potential source of data
for large mountain glaciers and ice caps (Zwally et
al. 2002). However, the large spacing of the orbits,
the fact that they are not repetitive, and the difficulty of removing the influence of clouds limit the
usefulness of ICESat data. Still, ICESat data can
be used to evaluate the quality of other DEMs
(Berthier and Toutin 2008) or to estimate glacier
elevation changes when compared with other
multitemporal elevation data (Sauber et al. 2005,
Surazakov and Aizen 2006, Kääb 2008). Repetitive
surveys by airborne laser altimetry have been shown
to be extremely accurate. However, central line surface profiling may lead to errors due to the difficulty
of extrapolating to the whole glacier surface
(Arendt et al. 2006).
It is clear then that DEMs derived from remote
sensing can provide glacier elevation change data
on a range of temporal and spatial scales. While
useful in their own right, elevation change data
are also a fundamental component of glacier mass
balance calculations. If two DEMs cover the whole
glacier, their difference (i.e., volume change) can be
converted to mass balance assuming a constant
density of 900 kg m 3 in the ablation area, although
the true density value to use in the accumulation
zone is still the topic of ongoing research. Most
authors use the same density as in the ablation zone,
as using a density different from 900 kg m 3 implies
a change in the rate of densification. Ideally the
calculation should include quantification describing
any shift in the underlying ground (e.g., due to
isostatic rebound or tectonic movement) although
in reality this is normally small compared with
glacier surface elevation change. The ultimate result
is mass balance quantification expressed in meters
water equivalent (MWE) over the imaged time
period.
A number of studies have used this approach to
assess the mass balance of alpine glaciers, using
combinations of historical topographic maps (Rivera et al. 2007) and DEMs derived from SPOT
imagery (Berthier et al. 2007), SRTM (Racoviteanu
et al. 2007), ASTER (Khalsa et al. 2004), Corona
(Bolch et al. 2008), and laser altimetry (Sauber et al.
2005). Very few have compared remotely sensed
mass balance calculations with those derived by
field investigation, but those that have (e.g., Hagg
et al. 2004, Rabatel et al. 2005, Zemp et al. 2010)
have found good agreement between dataset
results. As noted above, because of the limited accuracy of elevation data derived by remote-sensing
methods, many studies have strived to obtain mass
balance estimates derived over longer, preferentially
decadal time-scales, to ensure the change in
observed data exceeds the uncertainty in the
approach.
5.6
GLACIER MAPPING
Snow and ice exhibit distinct spectral properties
that make accurate delineation of debris-free
glaciers possible using a variety of remote-sensing
techniques (e.g., thresholded ratio images), but the
automatic classification of debris-covered ice is
more complex, because of the inherent difficulty
of spectrally distinguishing supraglacial sediment
and landslide material from that present in the
surrounding terrain (Paul et al. 2004b). For this
reason, DEMs are widely used for terrain visualizations and to provide additional information on
landscape morphometry, land surface context,
and spatial topology, all of which facilitate a more
accurate and reliable classification result for debriscovered glaciers.
At the most basic level, DEM data can be used to
generate terrain visualizations to aid the manual
delineation of glacier boundaries (Fig. 5.8). Glacier
termini are often difficult to identify using planimetric imagery alone because, particularly when
heavily debris-covered, they appear contiguous
with the proglacial zone, but small elevation variations visible in three-dimensional visualizations can
132
Digital terrain modeling and glacier topographic characterization
Figure 5.8. Simple 3D visualization (SPOT) HRVIR
panchromatic imagery acquired October 17, 2008,
overlain on SPOT HRS-derived DEM from imagery
spanning 2002–2004) of the Batura Glacier, Pakistan,
which could be used to aid glacier boundary or catchment headwall delineation, where they are unclear
using planimetric data in isolation, for example. For
scale, the glacier is approximately 2 km in width across
the main trunk. Copyright CNES 2008/Distribution
Spot Image. Figure can also be viewed as Online Supplement 5.2.
sometimes remove this ambiguity. Similarly, the
exact location of a catchment divide may be
unclear, especially where fresh snowfall masks the
headwall ridge; three-dimensional information is
particularly useful in this respect. For the glacier
itself, DEM data are useful for identifying areas
of low slope angle (see Fig. 5.5b), which are characteristic of debris-covered glacier tongues in most
parts of the world. When combined with complementary data such as land cover classifications, and
with results from neighborhood and change detection analyses, it has been shown that slope angle
data can be used as the primary morphological
characteristic to delineate glacierized terrain (Paul
et al. 2004b, Bolch et al. 2007). However, specific
slope thresholds used to delineate glacier facies vary
from region to region, with ice masses in the European Alps generally characterized by short, steep
tongues relative to the long (>10 km) flat tongues
of parts of the Himalaya, for example. Further, this
approach depends on slope angle being calculated
across a sufficiently broad spatial kernel to avoid
highlighting local slope variability (e.g., natural
peaks and troughs across the glacier surface), while
retaining sufficient detail so that small-scale features
such as inner moraine flanks are not excluded from
the analysis.
Additional first-order information that can be
calculated from DEM data include landscape plan
and profile curvatures, which can be used to define
both glacial and nonglacial landform elements
(Bolch and Kamp 2006; see Fig. 5.5c–f ). By clustering surfaces with similar curvature characteristics it
is possible to differentiate between glacier surfaces
and valley bottoms (low convexity), ridges and
lateral moraines (high convexity), medial moraines
(moderate convexity), and transitions between
glacier margins and lateral moraines (high concavity). A similar but more complex approach is to use
hierarchical object-oriented modeling, which
employs various DEM-derived terrain object properties such as slope angle, slope azimuth, curvature,
and relief to identify locally contiguous portions of
the landscape, which are iteratively aggregated to
form higher order landform objects at smaller and
smaller scales (Bishop et al. 2001). Glacier boundaries can thus be delineated at a landform level, and
objects and the relationships between objects can
be used for further landscape analyses, such as
studying the role of surface processes (e.g., erosion/uplift) in topographic evolution. Morphometric approaches such as these show great
potential for glacier mapping across the world,
but are heavily dependent on the input of highquality DEM data for accurate results.
A range of satellite sensors already have stereoscopic imaging capability and some recent missions
(e.g., Cartosat-1, ALOS PRISM, Terra-SAR-X,
and the TanDEM-X-mission) have significantly
increased the potential for extracting DEM data
at very high resolution for use in glacier mapping.
For many remote high-mountain regions of the
world, however, gaining access to high-quality
DEMs can be problematic, with ASTER and
SRTM data often providing the best (or only) available sources. Errors common in ASTER-derived
DEMs of steep, high-mountain relief can sometimes
Glacier mapping 133
produce artifacts in classification results, but may
still provide a quality of output that exceeds classification methods not employing a DEM of any sort
(Paul et al. 2004b). DEM resolution can be an
equally important consideration, with aerial
photography DEMs (such as those provided by
the Swiss Topo Survey) outperforming satellite sensor–derived data in almost all cases (Bolch and
Kamp, 2006), particularly in the delineation of
small ice masses. In areas where accurate and
fine-resolution DEMs are not available, manual
digitization of small samples may still therefore
be necessary to achieve a satisfactory classification
result. Therefore, attempts have been made to introduce additional information into the classification
process, such as metrics relating to geomorphometry, texture, and context (Bishop and Shroder
2000, Bishop et al. 2001, Taschner and Ranzi 2002,
Paul et al. 2004b, Ranzi et al. 2004, Buchroithner
and Bolch 2007, Bolch et al 2008). Sophisticated
classification approaches use both first and second-order topographic derivatives to segment landscape units accordingly, and make use of statistical,
artificial intelligence and hierarchical–structural
methods.
5.6.1 Pattern recognition
Pattern recognition techniques perform two key
tasks: description and classification. Given an
object (or set of objects—pixels in a satellite image,
for example), pattern recognition systems first seek
to describe those object(s), often in three dimensions, and subsequently classify the objects based
on those descriptions. The rigor with which the
prior task is performed largely governs the quality
of the latter. The description and classification of
input data in this way can be handled by statistical
or structural methods or, more frequently, a combination of both (the hybrid approach). Statistical
methods make use of decision theory concepts to
segment the landscape based on their quantitative
features, whereas structural methods make use of
syntactic grammars to segment the landscape based
on the arrangement of their morphological features
(see Section 5.6.3). Either way, DEM data are a
fundamental input to the classification procedure.
Statistical pattern recognition techniques are
largely dependent on the choice of model parameters, the quality of the expert knowledge used in
the prior part of the model, and the resolution of
the image and DEM data. For example, and with
specific reference to debris-covered glacier classifi-
cation, let R denote the pixel domain of a set of
co-registered data layers (e.g., satellite imagery,
elevation and geomorphometric parameters). Combining all these layers into vector space results in a
feature vector per pixel. Similar vectors can be
derived to describe a shading field (to handle
across-image slope and exposition variability) and
a segmentation field, such that:
~
x : R ! R 000
~: R ! R
s:R!K
000
vector field of features (observable)
shading field (unknown)
segmentation field (unknown)
where K denotes the set of labels used for segmentation. In the simplest case there are only two possible labels—one for a debris-covered glacier and
another for ‘‘background’’, but more are usually
employed to gain a full description of the environment. The statistical model relates the three quantities (above) by a probability distribution:
~; sÞ ¼ pð~
~; sÞpð~
pð~
x; xj
ÞpðsÞ
where it is assumed that shading and segmentation
are a priori independent.
If the parameters of the normal distribution are
already known, then the recognition task simply
requires the following: given the observation field
~
~ and
x we have to estimate the best shading field then estimate the best segmentation field s. Routine
algorithms such as the Gibbs sampler (Geman et al.
1990) and the Expectation Maximization algorithm
(Schlesinger 1968, Dempster et al. 1977) are normally employed to make the estimations.
If the parameters of multivariate normal distributions are unknown (first factor in the equation
above) they can be estimated by maximum likelihood learning given an expert’s segmentation of the
scene. In this case the Expectation Maximization
algorithm is again applied but with partial supervision. The expert’s segmentation is relaxed by
defining only three regions: background, foreground, and a zone between, leaving the system
to learn the optimal boundary. The resulting iterative learning scheme comprises repetition of the
following subtasks:
1. Given the actual parameters of the normal distributions and the actual estimation of the shading field, sample the segmentations and estimate
~; ~
the marginal probabilities pr ðsr ¼ k j xÞ for
each pixel r.
134
Digital terrain modeling and glacier topographic characterization
Figure 5.9. (a) Optical satellite image of the classification area (ASTER image acquired October 23, 2003);
(b) relaxed expert segmentation (see text); (c) first component of estimated shading; and (d) final segmentation
obtained after learning. Black, green and red encode background labels, blue and violet encode foreground labels,
yellow encodes the boundary label, and cyan encodes lakes. Figure can also be viewed as Online Supplement 5.3.
2. Use these marginals to improve the parameters
of the normal distributions (i.e., the covariance
matrices and mean vectors for all segments).
~ based on the
3. Re-estimate the shading field current marginal probabilities and parameters
of the normal distributions.
When the optimal boundary is reached, the iteration is stopped and the pixels are assigned their
segment label (Fig. 5.9).
5.6.2 Artificial intelligence techniques
Artificial intelligence techniques (often referred to
as knowledge-based systems) essentially comprise a
set of logical rules that provide an analog for the
reasoning used in anthropogenic decision making.
These can be as simple as a series of IF–THEN–
ELSE-type statements that test input data (e.g., a
pixel) for certain characteristics (e.g., to be within a
range of spectral values) and then follow one of two
paths based on the result. Such ‘‘expert systems’’
systematically arrive at a single classification for
each pixel by ruling out alternatives based on input
data values. This mimics the decision-making processes employed by a field geomorphologist, for
example; indeed it is important to note that such
systems can also exploit three-dimensional contextual and shape information in the same way a human
can. DEMs are therefore a fundamental component
of a comprehensively designed (and truly threedimensional) expert system.
Artificial neural networks (ANNs) aim to process
information in a similar way to the human brain, by
using a large number of highly interconnected processing elements (neurons) working in parallel to
solve a specific problem. The key difference between
ANNs and other artificial intelligence techniques
is that ANNs learn by example and cannot be
designed to perform a specific task in the first
instance. ANNs are particularly useful for handling
Discussion
diverse and nonparametric datasets and for modelling nonlinear relationships, making them a particularly attractive method for mapping glacierized
terrain. Nevertheless, the value of the output classification is only as good as the quality of the input
data; for ANN techniques to be truly robust they
must learn to recognize patterns associated with
geomorphometric land surface parameters, such
as texture, context, and spatial topology, which
can be derived (at least partly) from first-order
and second-order DEM analyses (Bishop et al.
2001, 2004).
Fuzzy classification algorithms are able to incorporate inaccurate sensor measurements, vague class
descriptions, and imprecise modeling into the analysis (Binaghi et al. 1997, Benz et al. 2003), and can
result in accurate portrayals of subpixel mixtures of
classes. Fuzzy classification procedures assign
values to each pixel representing the pixel’s degree
or probability of membership in each class, rather
than clustering similar pixels together into a
thematic set. The fuzzy approach is analogous to
human perception, in which there can be uncertainty even between experts analyzing the same environment. Fuzzy sets are a classification tool in
themselves; they can be used alone or incorporated
into higher level artificial intelligence techniques
such as expert systems; either way it is assumed that
there is a priori expert knowledge about the environment under investigation to be able to design
fuzzy membership functions. In a similar way to
expert systems and ANNs, the addition of a topographic dataset into the classification is fundamental to the accurate identification of glacial
landforms through shape and contextual analyses
(Schneevoigt et al. 2008).
5.6.3 Object-oriented mapping
Object-oriented mapping describes the segmentation and partitioning of the landscape into discrete
spatial entities based upon their geomorphometric
characteristics (e.g., slope angle, slope azimuth, curvature and relief; Bishop et al., 2001). These entities
represent the lowermost level of a hierarchical landscape structure, which in total describes the supposition of surface processes that comprise the
topography of a glacierized landscape (Bishop
and Shroder 2000). Therefore, by combining spatial
entities at the lowermost level, specific terrain features can be identified; by combining terrain features
at the second level, landforms can be identified, and
so on. High-quality DEMs are clearly fundamental
135
to this approach, if the spatial entities at the lower
end of the hierarchical structure are to be accurately
quantified and error propagation through the system is to be avoided. This approach has been
successfully employed to accurately delineate the
ablation zone of the heavily debris-covered Raikot
Glacier in the Nanga Parbat Himalaya, for example
(Bishop et al. 2001). Terrain object properties were
found to be diagnostic of glacier processes representing glacierization, thereby differentiating glacier
topography from other surfaces governed by different surface processes.
Object-oriented mapping can be used as a classification technique in its own right, but it has been
shown to be particularly effective when used in
combination with ANNs (see above) to classify
alpine glacial environments. In this specific context,
the procedure may follow five key stages (Raup et
al. 2007):
1. Classification of land cover using spectral data
and topography.
2. Spatial analysis of imagery to generate geometric, shape, and topological information.
3. Generation of geomorphometric parameters
from DEMs.
4. Fusion of data into an object-oriented parameterization scheme.
5. Classification of supraglacial features and
glaciers by neural networks.
This hybrid approach appears to reduce error and
increase consistency in results when compared with
other approaches. Indeed, it is true of all the previously described techniques for glacier mapping
that they may yield useful terrain classification in
their own right, but they have even greater potential
when they are integrated together. Fundamental to
their success is the provision of a three-dimensional
analysis, however. Topological, contextual, shape,
and geomorphometric analyses are limited without
the use of a DEM, and numerous studies have
demonstrated the need for such three-dimensional
properties if fully automated glacier mapping is to
be realized (Bishop et al. 2004, Paul et al. 2004b,
Bolch and Kamp 2006).
5.7
DISCUSSION
It is clear that digital elevation data derived from
stereoscopic airborne and satellite imagery are fundamental to many essential cryospheric applica-
136
Digital terrain modeling and glacier topographic characterization
tions, and in particular to deriving glacier statistics
for inclusion in global databases. Square-gridded
(raster) DEMs are most widely employed by
researchers because they provide more realistic terrain representations than data interpolated from
topographic maps and are easier to derive and to
handle than DEMs derived by radar interferometry
or airborne laser scanning. However, they are far
from perfect, particularly for detecting the abrupt
changes in topography that characterize glacial
environments, and the challenge of producing
fine-resolution DEM data with low data storage
requirements remains an issue. Further, the generation of reliable elevation data at any resolution finer
than that offered by the SRTM (90 m) remains
problematic for many glacierized areas of the
world. This is partly because of persistent cloud
cover, particularly in mountain regions, and a lack
of ground control data, particularly in areas of
political sensitivity. Additionally, SRTM data are
static and do not allow for multitemporal analyses.
While the recently released G-DEM2 may represent
a possible breakthrough in terms of spatial detail
(30 m pixel size) and accuracy, elevation values
represent the combined period of ASTER operations (2000–2011), so offer no better temporal resolution than the SRTM DEM.
Indeed, it is this variability in data quality that
remains the major limiting factor in global glacier
mapping and characterization. It has consequences
for the type, number, and quality of glacier parameters that can be derived for any given area.
Furthermore, it influences the effectiveness of different methods and approaches, and makes the
standardization of procedures a challenging task.
Ideally, elevation data at resolutions and accuracies
comparable with those offered by airborne laser
altimetry are required for all glacierized regions
of the world. Unfortunately, without a wide-swath
spaceborne altimeter, we are many years (if not
decades) from being able to achieve such a dataset.
Even then, it will raise numerous issues regarding
high-density point clouds and preprocessing.
Nevertheless, there remains great potential in the
use of various approaches, such as the integration
of multiple multiscale elevation datasets for deriving multiscale information about a single glacierized catchment, and the use of LiDAR data as
accurate ground control for photogrammetric
DEM extraction, among others. While novel
approaches to deriving glacier parameters have
been successful, some are yet to be effectively and
comprehensively employed on a regional basis. For
example, the geodetic method has been proven a
useful tool to assess glacier surface lowering and,
subsequently, to produce estimates of mass balance.
This work, however, has yet to be systematically
conducted in many regions of the world. Further,
where independent studies have been carried out
using such approaches, they are not always directly
comparable because of methodological inconsistencies, or inconsistency in the reporting of data
error.
Although remote-sensing sensor technology
has advanced significantly in recent years, the
challenges of representing topography in highmountain high-relief regions, and accurately quantifying the error within those topographic data,
remain significant. For example, a range of studies
have shown that for many glacierized regions of the
world (mostly those of moderate relief ) the topography can be characterized by ASTER DEMs with
an accuracy of 15–30 m (68% confidence level)
after some significant postprocessing, but only to
60 m (68% confidence) in areas with steep rock
headwalls and large low-contrast accumulation
areas (Kääb 2002, Toutin 2008). The issue is complicated further in high-relief mountain areas by
slope–aspect error dependence (Bolch 2004), which
tends to result in better quality elevation data being
derived on slopes facing south (in the northern
hemisphere) because of advantageous illumination
and sensor–terrain viewing angle. Illumination
variations can be compensated for (to a certain
degree) using topographic normalization methods,
but this itself requires a DEM, which is not always
available at this processing step. In terms of
error quantification, some standardization of
methods is required. Inconsistencies currently exist
between studies in the manner in which errors
are reported: some studies quote errors to two
standard deviations whereas some only quote the
RMSE. A limited number do not even quantify the
expected error (or uncertainty) in the presented data
and, of those that do, the accuracy of data can
sometimes be highly dependent on the number
and positioning of chosen check points (Toutin
2008). It is often difficult, therefore, for an independent researcher to replicate results, or to establish
the exact error analysis that has taken place and
how reliable it is.
Where reliable topographic data do exist they can
be used very effectively for mapping and change
detection studies. First-order geomorphometric
parameters have been successfully employed to
enhance glacier boundary delineation, calculate sur-
Discussion
face lowering rates, and inform numerical models
(e.g., surface uplift/erosion). This latter effort,
specifically the integration of remote sensing and
modeling for the analysis of landform–process
coupling, remains in its early stages, along with
several other interesting possibilities that are benefiting from better and more widely available digital
elevation data. For example, space-based methods
now exist capable of generating a mass balance
index to improve ELA estimation, and glacier flow
and erosion modeling are being enhanced by
improved and accurate boundary conditions. With
such ventures come further challenges, of course,
such as accounting for spatial and temporal fluctuations that were previously beyond modeling resolution; many glacier simulations have until recently
neglected to account for daily and seasonal ablation, ice velocity, and erosion fluctuations, for
example (MacGregor et al. 2000).
The accurate modeling of glacierized terrain is
essential because it plays such a fundamental role
in the modulation of atmospheric, Earth surface,
and glaciological processes (as well as being shaped
by these same processes). The glacial environment,
and in particular the glacier surface, is extremely
labile; this is especially so at present with major
adjustments occurring due to climatic forcing. On
a catchment scale, topography governs sediment
transport and ice fluxes, collectively influencing
glacier erosion. On a more local scale, glacier surface topography can influence debris cover distributions, debris depth, meltwater routing, and
supraglacial ponding. Conversely, processes and
parameters provide feedback that affects glacier
topography—thick debris covers can insulate
glacier ice, for example, and meltwater ponds thermally erode ice at their margins and their bases. At
the most local level glacial features such as ogives,
moraines, seracs, and crevasse fields define the
topography of glacier surfaces. It is therefore clear
that there is complex two-way interaction between
topography and surface processes across a range of
spatial and temporal scales that needs to be better
understood to inform ideas relating to geomorphological landscape evolution.
The interaction between topography and most
geophysical processes occurs over a range of spatial
scales, which cannot currently be truly represented
within DEM data. Therefore, while the resolution
of the generated DEM is limited by the resolution
of input source data, scientific interpretations
should also be mindful to restrict analyses to the
natural scale of the terrain-dependent application.
137
As a guide, the resolution of the derived DEM can
provide a practical indication of the scale of information content; analyses of processes or features
that occur on a finer scale than this should be made
with caution. For example, relatively small-scale
features (e.g., moraine ridges) can be entirely missed
by medium-resolution datasets, yet may change an
interpretation of a process or set of features with
their presence. Conversely, with a fine-resolution
DEM, analyses made on a coarser scale may be
hampered by noise, and indeed a coarser resolution
DEM may be more appropriate for use. With constant computational developments, methods for
representing fine-scale shape and structure are continually improving and so is the incorporation of
terrain structure into considerations of spatial scale.
A classic example of this is the development of
scale-dependent classification methods, which are
increasingly considering terrain hierarchies with
the realization that landforms are often not
spatially delimited and that one landform may partially comprise another.
Consequently, research on glacier mapping and
the extraction of glacier parameters indicates that
the integration of topographic information on a
variety of spatial scales is important in order to
produce reliable results. However, methodologies
significantly vary, and some problems remain for
high-mountain areas, particularly in change detection studies. For example, surface features must be
maintained across the imaged period for accurate
elevation datasets to be derived. This depends on
there being sufficient optical contrast between the
feature and its surroundings as well as the feature
being large enough to be resolved given the sensor
resolution; and it is also dependent on there being
no (or minimal) modification of the feature shape,
size, and contrast during the change, or the masking
of the feature by snow cover, for example. Further,
the magnitude of the change(s) to be detected may
not exceed the uncertainty in the method employed.
Errors in satellite-derived DEMs of high-relief
terrain are particularly problematic; consequently
it is unlikely that researchers will be able to reliably
detect surface lowering on a timescale of less than a
decade. The solution is to either increase the image
resolution (and thus accuracy) or to extend the
observation period (thus increasing the magnitude
of change). The latter solution is becoming increasingly possible as data archives extend with time and
new sources of historical data (e.g., Corona; Bolch
et al. 2008) emerge. The former issue is aided by the
launch of new and improved sensors.
138
Digital terrain modeling and glacier topographic characterization
Remote sensing is a constantly advancing discipline, so the launch of a new and/or improved
sensor is often imminent and the promise of more
accurate or more detailed imagery is never far away.
Some of the most promising developments for the
generation of new elevation data come from nonoptical sources. For example, the recently successful
launch of TanDEM-X, the interferometric partner
of TerraSAR-X, promises to provide a global DEM
to HRTI-3 specifications (Weber et al. 2006; i.e., 12
m spatial resolution, <2 m relative vertical accuracy
and <10 m absolute vertical accuracy). These
specifications can only currently be achieved by
aerial photogrammetry and very fine–resolution
optical satellite imagery such as WorldView, but
with associated costs. Spaceborne laser altimeters
(e.g., GLAS, on board ICESat-1) provide comparable accuracy, but with very limited swath width
and low point density, and there is no real prospect
of routine collection of such data again until the
proposed launch of ICESat-2 in 2015.
If topographic and spectral data are to be truly
integrated into surface process modeling, and
results compared between independent studies,
there is a requirement for a representational framework that scientists can work towards. Currently,
scientists employ a range of analytical tools, algorithms, processing approaches, and software for the
generation, manipulation, and interpretation of
topographic data. Methods are highly empirical,
thus the type and quality of the derived data are
dependent, to a large extent, on the analyst. Consequently, replication of existing results can be
difficult (even more so the application of one published technique to a new area). Standardization
and protocols for information extraction and integration are therefore required if data quality, result
accuracy, and the validity of comparing measurements across different studies (and study areas) are
to be assured.
5.8
CONCLUSIONS
Digital elevation models are fundamental to the
extraction of three-dimensional glacier parameters
for inclusion in global databases (e.g., WGI,
GLIMS, GlobGlacier) as well as for calculating
mass balance data, automatically delineating
glacier boundaries, modeling surface energy balance and radiation fluxes, characterizing geomorphometry, and analyzing altitudinal-dependent
processes. A range of sensors exists that offers data
appropriate for the extraction of elevation information, but ASTER remains the most widely used data
source because of its stereoscopic capability, wide
spectral range, medium-to-fine spatial resolution
and, importantly, low cost. The extraction of elevation information from ASTER data performs well
in areas with low relief and gently sloping topography, but errors can be large in areas with steep
rock headwalls and in areas with low contrast (e.g.,
fresh snow cover). A range of postprocessing tools
can be used to identify and reduce such errors
before any secondary analyses are undertaken.
Digital elevation models from nonoptical sources
(e.g., LiDAR, InSAR) are becoming increasingly
common and can often improve on, or be fused
with, existing elevation datasets to enhance cryospheric studies. Such sources have tremendous
potential for the extraction of three-dimensional
data over glacierized terrain in the future, and in
particular for increasing the temporal resolution of
change detection analyses, which is currently of the
order of a decade or more. However, they may
also bring new challenges in terms of handling data
volume (particularly in the case of LiDAR point
clouds) and in upscaling acquired information,
where such detail is not required. For this reason,
the development and publication of standard methods (or protocols) for acquiring, processing, and
representing digital elevation data will become
increasingly important. In the short term, challenges remain in identifying and quantifying altimetric errors, particularly when comparing DEMs
from different sources, and in simply gaining access
to reliable data for some of the most politically
sensitive regions of the world.
5.9
ACKNOWLEDGMENTS
Quincey was funded by a Research Council U.K.
Fellowship; Bishop was funded by the National
Aeronautics and Space Administration under the
NASA OES-02 program (Award NNG04GL84G).
ASTER data courtesy of NASA/GSFC/METI/
Japan Space Systems, the U.S./Japan ASTER
Science Team, and the GLIMS project.
5.10
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