digital terrain modeling and glacier topographic...

CHAPTER5

Digital terrain modeling and glaciertopographic characterization

Duncan J. Quincey, Michael P. Bishop, Andreas Kaab, 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

The Earth’s topography results from dynamic inter-actions involving climate, tectonics, and surfaceprocesses. In this chapter our main interest is indescribing and illustrating how satellite-derivedDEMs (and other DEMs) can be used to deriveinformation about glacier dynamical changes.Along with other data that document changes inglacier area, these approaches can provide usefulmeasurements of, or constraints on glacier volumebalance and—with a little more uncertainty relatedto the density of lost or gained volume—mass bal-ance. Topics covered include: basics on DEM gen-eration using stereo image data (whether airborneor spaceborne), the use of ground control pointsand available software packages, postprocessing,and DEM dataset fusion; DEM uncertainties anderrors, including random errors and biases; variousglacier applications including derivation of relevantgeomorphometric parameters and modeling oftopographic controls on radiation fields; and theimportant matters of glacier mapping, elevationchange, and mass balance assessment. Altimetricdata are increasingly important in glacier studies,yet challenges remain with availability of high-qual-ity data, the current lack of standardization formethods for acquiring, processing, and representingdigital elevation data, and the identification andquantification of DEM error and uncertainty.

5.1 INTRODUCTION

The Earth’s topography is the result of dynamicinteractions involving climate, tectonics, and sur-face processes (Molnar and England 1990, Bishopet al. 2003). Numerous feedback mechanisms oper-ate over unique spatiotemporal scales that governhypsometry and terrain parameters. Similarly, thetopography governs a variety of physical param-eters and processes including stress fields, erosionand mass wasting, precipitation, sediment deposi-tion, surface and groundwater flow direction andponding, surface energy budget, and glaciation in acomplex topographic feedback loop (Roe et al.2002, Reiners et al. 2003, Arnold et al. 2006a).Scientists have long recognized the significance oftopographic parameters for studying and modelingprocess mechanics, mapping the landscape, anddetecting spatiotemporal change. Consequently,digital terrain modeling and the generation andanalysis of terrain surface representations,commonly referred to as digital elevation models(DEMs) and geomorphometry, have become animportant research topic for studying and solvingproblems in hydrology, geomorphology, andglaciology (Wilson and Gallant 2000).Glaciological research indicates that glaciers in

most areas around the world are receding (Barry2006, Gardner et al. 2013). Internationally, scien-tists are attempting to inventory, monitor, and

understand current ice mass distributions and vol-ume, glacier–climate interactions, glacier sensitivityto climate change, as well as assess the impact ofglacier change related to water resources, naturalhazards, 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, Kargelet al. 2005). With many high-altitude glacial lakesnow forming in alpine areas (Huggel et al. 2002,Gardelle et al. 2011), with the threat of devastatinglandslides ever present and perhaps shifting (Kargelet al. 2010), with human habitation of risky placesnear glaciers rising (Kargel et al. 2011), and con-struction of valuable infrastructure increasing inalpine environments that never before had muchhuman presence (Kargel et al. 2012), accurateDEM data are crucial for hazard assessments. Thisis especially true for glacier hazard-prone regionswhere field access is difficult due to severe terrain,political sensitivity, or financial constraints.

Glaciological research is increasingly utilizingremote-sensing studies and topographic informa-tion generated from airborne and satellite imaging,radar and LiDAR (light detection and ranging)systems, and GNSS (global navigation satellite sys-tem) surveying. Furthermore, DEMs are requiredfor image orthorectification and radiometric cali-bration (Bishop et al. 2004), surface energy balancestudies (Arnold et al. 2006a), debris-covered glaciermapping (Paul et al. 2004b), glacier ice volumeloss and mass balance estimates (Berthier et al.2007), and equilibrium line altitude estimation(Furbish and Andrews 1984, Leonard and Fountain2003).

The mere availability of satellite imagery andDEMs, however, does not necessarily equate toaccurate thematic information production andglacier parameter estimation (Raup et al. 2007).Consequently, researchers must account for avariety of issues in digital terrain modeling andgeomorphometric analysis. Digital terrain modelingis a complex process that focuses on terrain surfacerepresentation schemes, acquisition of source data,terrain descriptors and sampling strategies, inter-polation techniques and surface modeling, qualitycontrol and accuracy assessment, data manage-ment, and interpretation and applications (Wilsonand Gallant 2000, Li et al. 2005, Fisher and Tate2006). Accurate glacier assessment using topo-graphic information is frequently an issue ofDEM quality and methodological approach (Raupet al. 2007).

The purpose of this chapter is to address the topicof digital terrain modeling and geomorphometryfor glacier assessment and mapping. Specifically,we consider numerous issues that must be effec-tively dealt with in order to estimate selected glacierparameters and delineate glacier boundaries. Wefirst provide background information on digitalterrain modeling to set the stage for DEM produc-tion using satellite imagery and methodologicalapproaches. We then provide examples of analyticaltechniques that can be used to study glaciers.

5.2 BACKGROUND

Digital elevation models are digital representationsof the Earth’s relief and are fundamental to manyapplications. The majority of currently availabledigital elevation datasets are the product of photo-grammetric software, which exploits the techniqueof stereoscopy using overlapping image data,although increasing volumes of elevation data arealso derived from radar interferometry and fromlaser altimetry. Additional elevation datasets areavailable from digitized map sheet topographyand, although usually spatially limited, ground sur-veys. As with many remote-sensing exercises, thegeneration of digital elevation data represents acomplex process involving image acquisition, com-putation and modeling, data management, andanalysis. The terrain itself is spatially complex,and the need to represent it digitally and describeit quantitatively has led to various mathematicalapproaches for different scale and data constraints.Examples include the analysis of systematic highor low-frequency periodicity in altitude usingFourier analysis, and the identification of self-similar, spatially autocorrelated, and scale-dependent topography using fractal geometry andsemivariograms.Digital elevation data are normally represented in

one of four ways, including use of: (1) a regulargrid; (2) a triangulated irregular network (TIN);(3) contour lines; or (4) point profiles. Regularlygridded DEMs comprise square pixels of constantspatial resolution (the effective ground dimension)or constant latitude/longitude resolution, with eachpixel assigned an elevation value, usually in metersand with respect to some datum (sea level or ahigher order representation of the geoid). Theyare favored by geoscientists because they aredirectly comparable with remote-sensing imageryof equal spatial resolution, simple to analyze statis-

114 Digital terrain modeling and glacier topographic characterization

tically, computationally easy to represent, and canbe saved in a range of formats (e.g., GeoTIFF,HDF). Conversely, they are poor at representingabrupt changes in elevation and heterogeneoustopography, particularly at coarse resolutions, cangenerate large file sizes at fine resolution, and mayhave a large amount of data redundancy across flatareas. TINs represent topography using a mesh ofadjacent, nonoverlapping triangles with each vertexassigned an elevation value. The TIN model storestopological information allowing proximity andadjacency analyses across a range of spatial scales.TINs usually require fewer data points than a DEMgrid and are particularly useful for accurately repre-senting extreme topographic features (e.g., channelsand ridges) as well as for surface modeling (e.g., thecalculation of slope, aspect, surface area and length,etc.). Contour maps, some digitized from papertopographic maps, provide more generalized repre-sentations of the terrain, but they are not so com-monly used in glacial applications given theavailability of contemporary DEMs for the entireglobe; however, for the derivation of ice thicknesschanges over multiple decades, such digitized mapscan be crucial. Lastly, point profile data normallyrepresent elevations collected by laser altimetry(e.g., GLAS on board the ICESat), which illumi-nate a circular sampling area (footprint), the sizeand spacing of which is generally dependent on thealtitude of the sensor. These data therefore tend toprovide sparse coverage when acquired by satellite,and repeat pass data are not necessarily spatiallycoincident.

The terms DEM, DSM (digital surface model),and DTM (digital terrain model), are often usedinterchangeably to describe any digital representa-tion of the Earth’s topography, but differ funda-mentally in their inclusion or exclusion of surfacecover in the data. DSMs can be thought of asincluding all elevation data recorded regardless ofsurficial cover; thus they represent tree canopyheight across a forested area and building heightsin the urban environment, for example. DTMs‘‘strip out’’ such surface features and attempt torepresent only the solid Earth, which can be a chal-lenging task (sometimes requiring large amounts ofinterpolation) where dense ground cover(s) exist.The term DEM is used more generally to describean elevation dataset without specifying the eleva-tion reference (e.g., solid Earth, surface cover,subsurface topography). Many satellite-derived ele-vation datasets are of insufficient vertical resolutionto require an explicit declaration of whether they

include surface cover or not, and are therefore gen-erally referred to simply as DEMs.The use of elevation data derived from remotely

sensed imagery has a number of advantages overalternative sources. First, the range of sensors avail-able for producing DEMs offers flexibility in scale.Many medium-resolution (10–30 m) satellite sen-sors (e.g., ASTER, ERS-1/2) are able to providestereoscopic imagery for DEMs of wide areal cover-age, while local to catchment-scale DEMs can bederived from an increasing number of fine resolu-tion (1–10 m) sensors (e.g., SPOT 5 HRS, Quick-bird, GeoEye) or aerial imagery. Normally, thescale of the topographic variability to be modeledinforms the selection of the source imagery (seeSection 5.3.1). Second, many glacierized areas ofthe world are inaccessible for logistical or politicalreasons, so for the inclusion of three-dimensionaldata in global databases such as GLIMS, remotelysensed elevation information provides the onlyoption. Third, as historical archives of these dataare accumulating, the opportunity to conductmultitemporal (and thus dynamical) studiesbecomes possible. Fourth, and finally, the increas-ing availability of no-cost data derived fromremotely sensed sources opens up the discipline ofcryospheric remote sensing to all interested parties,which can only ultimately advance scientific under-standing at a greater pace.In relation to this last point, however, it is impor-

tant that standards and procedures for DEMgeneration and analysis are available for scientistsworldwide, an issue that is discussed later in thischapter (p. 137). In brief, the utility of a DEM isdependent upon a certain level of expertise from theoperator to ensure the correct scale of representa-tion, accurate characterization of terrain param-eters, and overall planimetric and verticalaccuracy. For example, a major difficulty in usingdigital photogrammetry to generate elevation dataover glacier surfaces is that accurate DEMs canonly be derived if the glacier surface shows sufficienttopographic and/or radiometric heterogeneity tocorrelate image pairs (Favey et al. 1999), whichotherwise can result in grossly inaccurate elevationestimates over some large expanses of bare ice and/or snow. Image saturation or low dynamic numbersin deeply shadowed areas also result in either nullvalues or erroneous elevations. Consequently, greatcare is required to ensure that the data selected foran application are appropriate, processing is carriedout with a high level of expertise, and errors in anyderived data are accurately reported, so that real

Background 115

geophysical patterns and features can be differen-tiated from image and processing artifacts.

5.3 DIGITAL ELEVATION

MODEL GENERATION

5.3.1 Source data

Topographic maps exist for every country, andthese can be utilized to generate a DEM, providedthe map is of sufficient quality for the intendedapplication. In developing countries, issues ofcartographic scale, map coverage, quality, andavailability may be problematic. In some countriesthe maps are military secrets, or have been degradedin quality given the scale, contour interval, or intro-duction of error (e.g., Soviet topographic 1:50,000map series of Afghanistan). If suitable maps existDEMs can be generated by cartographic digitiza-tion using techniques such as line-following digiti-zation or raster scanning.

High-resolution aerial and satellite images arealso effective ways to generate and update topo-graphic information. Digital elevation models canbe derived using stereo (overlapping) pairs andphotogrammetric techniques, which depend onknowledge of the exact image and terrain geom-

etries at the time of acquisition. Numerous investi-gators have reported on the generation of DEMsfrom aerial photography and a multitude ofsatellite-imaging systems including ASTER, IRS,and SPOT for glaciological applications (Kaab2002, Berthier and Toutin 2008). Although satelliteimagery is generally available, aerial photography ismore difficult to acquire for many glacierizedregions of the world (e.g., Karakoram) because ofpolitical sensitivities and poor archiving, and someair photos are expensive (e.g., Alaska), which canlimit historical analyses. However, the demilitariza-tion of Corona satellite imagery provides historicaldata for many regions of the world at relatively fine(<10 m) spatial resolution; Corona also providesstereo coverage facilitating photogrammetricanalyses (Surazakov et al. 2007, Bolch et al. 2008).For cryospheric applications, and especially

useful for three-dimensional information, ASTERis one of the most appropriate and accessible sen-sors available for several reasons. First, and mostimportantly, the coupled nadir and backward-looking sensor systems in the near-infrared enablesfine-resolution and routine along-track stereoscopicvision (Fig. 5.1). Second, the spatial resolution ofthese stereoscopic data (15 m) provides the perfectbalance 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 oneminute to cover the same area of groundwith both sensors, thus yielding

a stereo pair of 60 km swath from which DEMs can be extracted (adapted from Hirano et al., 2003).

studies. Third, the adjustable sensor gain settingsprovide increased contrast over bare ice and snow,which is critical for the derivation of accurateelevation data using photogrammetric techniques.Fourth, the relatively short revisit period of thesensor (16 days for nadir viewing or 2 days foroff-nadir pointing) provides high-intensity coveragein cases of natural disaster emergencies or otherspecial needs; in more routine cases, the short revisittime provides many chances to acquire a cloud-freeimage of an area of interest, even in notoriouslycloudy areas. ASTER data are routinely used toprovide DEMs for the derivation of three-dimensional glacier parameters for all glacierizedregions, and are available at no cost to regionalcenters involved in the GLIMS project. However,the actual performance of ASTER has resulted infar less frequent data acquisitions and often sub-optimal sensor gain settings than the observationplan calls for, thus reducing the system’s value fromwhat it could be.

Images acquired by synthetic aperture radar(SAR) contain information relating to both themagnitude and phase of the backscatter signal, bothof which are useful for deriving DEMs. Radargram-metry exploits the magnitude element of the returnsignal. Similar to photogrammetry, radargram-metry makes use of two spatially separated back-scatter images to form a stereo model of the terrain(Toutin et al. 2013), with the exact image geometrybeing supplied by increasingly accurate orbital datarecords (Scharroo and Visser 1998). InterferometricSAR (InSAR) makes use of the phase element ofradar return. The phase difference between twoindependent return signals is very sensitive to topo-graphic variations (as well as any surface displace-ments between image acquisitions) and can be‘‘unwrapped’’ to derive a digital terrain surface,often with very high accuracy. DEMs over glacier-ized terrain have been successfully derived using arange 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 byKaab et al. has a detailed treatment of variousmethodologies and glacier applications using radardata.

Airborne laser scanning systems are an importantoperational tool for generating high-resolutiontopographic information. Numerous researchershave utilized and evaluated DEMs generated fromLiDAR data for glaciological applications (Reesand Arnold 2007). Pulses of electromagnetic energy

interact with surface materials to regulate the inten-sity of the returning signal. A LiDAR system pro-duces data that may be characterized as a 3D pointcloud, which must be processed to remove erron-eous measurements relating to reflectance fromclouds, smoke, or birds, for example (Arnold etal. 2006b). Consequently, filtering, classification,and modeling are required to generate a DEMfrom laser-based measurements. The high qualityof LiDAR-based DEMs permits improved geo-morphometric characterization of the terrain andglacier surfaces, which translates into improvedassessment and modeling of a variety ofprocesses.Finally, Global Navigation Satellite Systems

(GNSS) can be used for direct measurement ofthe Earth’s surface topography, and are increas-ingly replacing the use of traditional theodolitesand total stations. Earth scientists are routinelyutilizing GPS receivers on a variety of platformsto collect point and profile measurements for ter-rain and glacier surface representation (Miller andPelto 2003). Differential GPS (dGPS) refers to cal-culation of an accurate roving receiver position withrespect to a reference station and can yield accura-cies as fine as 10 mm when the differential phase ofmultiple satellite signals is exploited. This method isparticularly relevant for the collection of groundcontrol data as input to DEM generation.

5.3.2 Aerial and satellite

image stereoscopy

The process of deriving elevation data by photo-grammetric techniques is well established andwidely documented (Kaab et al. 1997, Kaab andFunk 1999). Deriving elevation data from stereophotographs relies on recreating the geometrybetween sensor and terrain at the exact time ofimage acquisition. The user supplies approximatedata relating to the aircraft location and the averageterrain height above sea level in addition to accuratestatistics on the camera geometry and image dimen-sions. The software applies least-squares regressionto reduce errors in the approximations and arrivesat a stereo model that realistically represents thereal-life situation at the time of image acquisition.The least-squares adjustment algorithm is used toestimate the unknown parameters associated with asolution while also minimizing error within thesolution. This is regarded as one of the most accu-rate techniques to:

Digital elevation model generation 117

. estimate or adjust the values associated withexterior orientation (sensor positioning andview direction at time of image acquisition);

. estimate the X , Y , and Z coordinates associatedwith tie points;

. estimate or adjust the values associated with inter-ior orientation (sensor geometry, including focallength); and

. minimize and distribute data error—introducedby ground control point (GCP) coordinates, tiepoint locations, and camera information—through the network of observations

(list modified from Leica Helava 2004).

The least-squares algorithm processes the dataiteratively until the errors associated with the inputdata are minimized. These errors are measured interms of residuals (the degree to which the observa-tions deviate from the functional model). Residualvalues (the distance between calculated statisticsand user input values) are summarized by the rootmean square error (RMSE), which should ideally beless than twice the pixel size of the imagery for the

resultant orthoimages and elevation information tobe considered accurate when compared with theactual terrain properties.Once the error is within thresholds considered

satisfactory by the user, the DEM is extracted bythe generation of spatial rays from the first imagethat intersect in three dimensions with the corre-sponding points on the second image (identifiedby image-matching algorithms), thus giving aheight value for each modeled pixel (Fig. 5.2). Ele-vation is determined by measuring shifts in the x-direction (x parallax) of the rectified images. Theexact process followed in DEM generation maydiffer slightly depending on the software employed(see Section 5.3.4) but typically follows a series ofkey stages (Fig. 5.3).

5.3.3 Ground control points

Ground control data may be derived by traditionalsurveying techniques (such as triangulation, tri-lateration, traversing, and leveling), contemporarysurvey techniques (such as dGPS measurement and


Figure 5.2. A typical stereo photogrammetric model (or block), illustrating themonotemporal generation of height

information from overlapping images (imagery of time 1 only).Wheremultitemporal imagery is available (imagery of

time 1 and imagery of time 2), calculations of surface elevation change become possible. By processing multi-

temporal images in a single block, potential errors, particularly those relating to external ground control, can be

minimized.

laser ranging), and/or the identification of clearlydefined features (e.g., mountain peaks and roadintersections) on large-scale map sheets. Theymay give information on horizontal positioning,height, or both. Collectively, ground control datainform the stereo model of the spatial position andorientation of a photograph or satellite image rela-tive to the ground at the time of exposure (or scan-ning), and their quality is important to the accuracyof derived elevation data. As a minimum, the accu-racy and precision of any ground control datashould be twice that of the expected DEM to avoidadversely affecting the derived data. Research hasshown that the accuracy, number, and distributionof ground control points used in the iterative least-squares adjustment to refine the geometric modelcan also impact DEM accuracy significantly(Toutin 2008). While three GCPs are theoreticallysufficient to compute a stereo model from frameimagery (Goncalves and Oliveira 2004), the mini-mum number for other sensors depends on thesensor model employed and the number ofunknowns in it. A larger number than the mini-mally required is usually employed to ensure redun-dancy in least-squares adjustment, to reduce theimpact of map and plotting errors, and to facilitate

post-derivation accuracy tests (Toutin 2002). Onthe other hand, where GCPs are known to havelow accuracy it is beneficial to limit the number usedin the adjustment to avoid errors propagatingthrough to the output DEM.In addition to the quality of any ground control

data used in a stereo model, the theoretical accuracyof a DEM is also dependent on the base-to-heightratio of the system and the quality of the imagematching used to refine the stereo model. If noground control data are available, only relativeDEMs may be derived (where horizontal and ver-tical values are only known relative to an arbitrarydatum). Their accuracy is thus dependent only onsensor characteristics and the success of imagematching. Further parameters that can influencethe accuracy of any derived elevation data includethe quality of geometric and radiometric image cali-brations (which also impact matching success andground control point identification) and the qualityof sensor ephemeris and attitude data that is enteredinto the stereo model. Check points, which are mostoften surplus ground control data, can be used toquantify DEM errors but, similarly, the quality ofaccuracy assessment is only as good as that of thecheckpoints used.


Figure 5.3. Themajor 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.

5.3.4 Software packages

In addition to the software used by NASA and theJapanese Aerospace Exploration Agency (JAXA)for the operational generation of ASTER DEMs,there are four university or private softwarepackages, as well as five commercial off-the-shelf(COTS) software modules for processing stereoASTER data to generate DEMs (Toutin 2008).We now give a brief description of some of the mainsoftware packages available.

The Geomatica2 OrthoEngine SE of PCI Geo-matics (www.pcigeomatics.com), adapted to ASTERstereo data, was developed in 1999 under USGScontract with the collaboration of the Canada Cen-tre for Remote Sensing, Natural Resources Canada,for mathematical, 3D modeling, and algorithmicaspects. It may be the most-used software forperforming 3D sensor orientation and DEM andorthoimage generation. Both relative DEMs with-out GCPs and absolute DEMs with GCPs can begenerated while an existing DEM can be added inthe processing. The accuracies obtained in differentresearch studies were similar to those obtained atUSGS: horizontal and vertical accuracy of �15 mand �20 m (1�) respectively, depending on GCPs,study site, and relief.

The LPS photogrammetric software suite fromERDAS (http://www.erdas.com) includes ASTER-specific data import, radiometric correction, andsensor model functions. It uses a feature-based,automatic terrain-adaptive, hierarchical image-matching scheme for automatic DEM extractionand can output grid, TIN, and point cloud data.Of the software described here, LPS provides themost comprehensive control over the DEM extrac-tion and editing process. A number of automaticspike and blunder detection algorithms aid thedetection of local extraction errors, and automaticblending and smoothing around the perimeter ofarea edits leads to seamless data continuationthrough interpolated or replaced values. The mostpromising of these algorithms fuses independentdatasets to achieve a complete DEM; in oneapproach, Crippen (2010 and unpublished results)used parallax–elevation cross-correlation as ameans of detecting artifacts in the ASTER DEMso as to determine where replacement with otherdata (e.g., from SRTM) should be done.

The AsterDTM module, developed by SulSoft,the exclusive ENVI distributor in Brazil, was addedto 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 withthe aid of orbit/sensor modeling, quasi-epipolarimage generation, cross-correlation matching, andautomatic detection of water bodies. An existingDEM can be added to fill in low-correlation areas.The claimed accuracy by ENVI for a relative DEMwithout GCPs is better than �20 m and for anabsolute DEM with GCPs �30 m in planimetryand �15 m in elevation (all with 90% confidenceinterval). These results were confirmed by end usersgenerating DEMs from Level 1A stereo pairs bothwith and without GCPs, and from Level 1B stereopairs without GCPs.The Desktop Mapping System Softcopy2,

Version 5.0 is designed to run under the Microsoft1

Windows1 XP Professional operating system andprovides a complete two-dimensional and three-dimensional photogrammetric mapping capabilityusing scanned aerial photographs or digitalimages recorded by airborne or satellite sensor sys-tems. Experiments with stereo ASTER data overdifferent mountainous study sites achieved RMSerrors of about �15–25 m (1�), showing equivalentresults to those derived by USGS (see PCI).DMS Softcopy 5.0 retains the speed, functionality,and ease of use of earlier versions of the DMSsoftware, but has been streamlined to allow foreven faster, more efficient implementation ofoperations.SilcAst, produced by Sensor Information

Laboratory Corp. Japan (www.silc.co.jp) and exclu-sively developed for ASTER, is written in IDLR6.1and can be executed with IDL VM without an IDLlicense. The main functions are digital elevationextraction either from Level 1A and Level 1Bimagery, water body identification, orthorectifica-tion, and Level 1B data generation, but the softwaredoes not accept GCPs. ASTER 3D data productsare provided as Standard (fully automatic) withpotential miscalculated elevations, and High(semi-automatic) with interactively corrected mis-calculated elevations. In 2009, SILC with SilcAstproduced a high-quality global DEM (G-DEM1;see Section 5.3.6) from ASTER data acquiredwithin an 83� latitudinal limit. Covering all the landon Earth, it is freely available to all users in 1� 1�

grid tiles in latitude and longitude. While theASTER G-DEM1 contains 30 m grid spacing with�7 m accuracy (1�), recent scientific studies demon-strated some high-frequency errors (appearingwithin tile grids as pits, bumps, ‘‘mole runs’’, andother residuals and artifacts), requiring down-sampling to 90 m spacing.


5.3.5 Postprocessing (interpolation and

smoothing)

DEM generation often requires the interpolation ofelevation values between available sample points,particularly when contour maps or satellite imageryare the source data. Consequently, various ap-proaches for how to interpolate this calculated(not measured) elevation in the DEM productionprocess have been developed. The choice ofapproach depends mainly on relief within theimagery, the type of information that will bederived from the DEM, and the proposed applica-tion (Rasemann et al. 2004). Interpolation accuracydepends on interpolation algorithm type, surfacecharacteristics, and the distance between samplepoints (Kubik and Botman 1976). There is a paucityof quantitative evaluation of interpolation accuracyover glacierized terrain and, of the few studies thatdo exist, only a handful have employed grounddata to make the assessment (Cogley and Jung-Rothenhausler 2004). At present, uncertainties inDEM accuracy do exist depending on the choiceof the interpolation algorithm employed; therefore,all qualitative and, in particular, quantitative resultsfrom glaciological analyses that include DEMsmust be interpreted with caution.

Some of the interpolation methods that havebeen used in glacier research include (but are notlimited to) Triangular Irregular Network (TIN;Gratton et al. 1990); Inverse Distance Weighted(IDW; Etzelmuller and Bjornsson 2000); spline(Mennis and Fountain 2001, Bolch et al. 2005);and kriging (Burrough and McDonnell 1998).

Triangulation: since this method produces indi-vidual triangles with constant exposition and aspectrather than a continuous relief, the final DEM is notdifferentiable. To ensure that information on cur-vature can be extracted, the DEM has to be con-verted to a grid. Problems occur at sharp edges,deep valleys, and cliffs. Often, valleys and ridgesshow a typical ‘‘terracing’’ effect. Such artifactscan be eliminated by manually adding elevationinformation, by using structural information withelevation values (Heitzinger and Kager 1999,Rickenbacher 1998), or by subdividing the triangles(Schneider 1998).

Inverse Distance Weighted: a relatively simple algo-rithm that weights the sample point value accordingto its distance from the pixel of interest. The weight-ing and number of sample points have a strong

influence on DEM quality. For example, a strongweighting based on only few sample locations pro-duces a rough surface in which the sample pointsthemselves are heavily emphasized.

Spline: this interpolation method applies a specialfunction that is defined step by step by piecewisepolynomials that are continuously differentiable.Most common in DEM generation are low-ordercubic (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 ofovershoots (i.e., unnatural ‘‘holes’’ and ‘‘spikes’’).To prevent such overshoots, a regularized spline-with-tension algorithm is used (Mitasova and Mitas1993). This method uses a function that specifieshow fast the collection of sample points decreaseswith increasing distance thereby attenuating themagnitude of overshoots.

Kriging: a geostatistical method, based on astochastic model, which predicts the elevation at aspecific location and is particularly used when atrend (here: the spatial correlation of elevationvalues) exists. One disadvantage of this method isthat adjustment of the semivariogram model to theexisting data structure requires experience.

Various studies have considered the relativeaccuracy and appropriateness of each of the aboveapproaches. For example, Kamp et al. (2005) testedthree interpolation methods—IDW, spline, andTIN—when generating a DEM from 1:50,000 topo-graphical maps of Cerro Sillajhuay in the Andes ofBolivia and Chile using Esri ArcGIS 3.2 software.In this study, both IDW and spline methods pro-duced very good results in high relief areas, but alarge number of artifacts in generally flat terrain.The authors concluded that both algorithms hadproblems handling larger distances between con-tour lines. Instead, the most accurate DEM wasgenerated using the TIN method, although a firstraw DEM contained many artifacts—mainly overflat terrain, caused by the triangles that are used bythe TIN method for interpolation.Tests similar to those made by Kamp et al. (2005)

were described by Racoviteanu et al. (2007) for theCordillera Ampato (southern Peru). In this study,the examination of RMSEz (vertical error) valuesfor DEMs derived from topographic data (1:50,000maps constructed from 1955 aerial photography)revealed that no interpolation method performed


perfectly. While the IDW DEM and TIN DEMshowed accuracies of only 21 m and 24 m, respec-tively, the spline (here: TOPOGRID) DEM pro-duced a vertical accuracy of �15 m,outperforming the other available algorithms.However, the authors noted that all three DEMsproduced ‘‘terracing’’ effects, an artifact of prefer-ential sampling along the contour lines, with pointscloser to the contour lines being interpolated usingthe same elevation values. The terracing effect wasmost severe using the IDW interpolator. Similarterracing artifacts were described by Etzelmullerand Bjornsson (2000) using the same interpolator,and by Mennis and Fountain (2001) using thespline-with-tension interpolator. Wilson and Gallant(2000) showed that such terracing artifacts affectcalculations of topographic characteristics such asslope, aspect, and profile curvature.

DEMs constructed over largely featureless ter-rain often fail to characterize subtle (or evenabrupt) changes in surface topography, which canbe rectified by the use of breaklines. Breaklines arelinear features that describe interruptions in surfacesmoothness and are typically used to define chan-nels or ridges, for example, where there is a clearchange in surface topography. However, the devel-opment of real 3D breaklines is still a problem, andBolch and Schroder (2001) actually concluded thatthe integration of simple breaklines does not sig-nificantly improve the overall quality of the DEM.As a solution, in their DEM generation processKamp et al. (2005) manually added some contourlines using elevation information from stereoscopicanalysis of aerial photographs. Eventually, the TINDEM was converted into a grid-based DEM usingEsri ArcInfo 7.2 software, and two nearest neighborfilters helped smooth the final model, albeit at theexpense of some topographic detail (e.g., the loss ofsome edges, frost cliffs, and gorges). The authorsconcluded that the final DEM was of sufficientquality for macro and mesoscale geomorphologicalanalysis (e.g., of rock glaciers); however, processingthe DEM from contour lines was relatively timeconsuming.

5.3.6 Data fusion

While small gaps in DEM data can be filled byinterpolation, large voids stemming from shadow-ing, correlation failures, and other effects require adifferent approach. It is sometimes desirable to

combine, or fuse, DEMs from different sources inorder to obtain the most complete coverage of anarea. As well as filling in any gaps in the respectiveDEMs, such fusion can also help to identify anysevere vertical and horizontal errors in commonareas (Kaab et al. 2005). DEM-merging techniquesrange from replacement of data (Kaab 2005a) andweighted fusion, resulting in smooth transitionsbetween DEMs (Weidmann 2004), to merging insupport of DEM processing itself (e.g., DEMapproximation in order to geometrically constrainstereo parallax matching or interferometric phaseunwrapping) (Honikel 2002). One successfulapproach involves identification of artifacts in asingle-scene ASTER DEM and then infilling witha global dataset such as SRTM or the ASTER G-DEM. Artifact delineation is almost perfect (almostno errors of omission or commission), so the infilledproduct is usually of very high quality (Crippen2010).The ASTER G-DEM1 is the result of the fusion

of suitable individual ASTER-derived DEMs byaveraging all elevations in the vertical stack. WhileDEM fusion using this approach is helpful forderiving a spatially more complete and accurateset of geomorphometric parameters, it should beavoided or handled with care for DEM-based stu-dies of glacier thickness changes. The number ofstereo images used to produce a given G-DEM1grid point elevation varies from one to several tens.Whereas the number of scenes used for each gridpoint is known globally, G-DEM1 ancillary data donot support knowledge of when the images wereacquired. The mean date is about 2004/2005, butfor a given locale it could be earlier or later by a fewyears. Variance of the mean from 2004/2005 is lessthan a year in most areas, but it can be much greaterfor some places where few ASTER images havebeen acquired. G-DEM1 carries some of the arti-facts present in individual DEMs, and is generallyvery noisy, often rendering it unsuitable for detailedstudies requiring high resolution, although forstudies of basin-scale hypsometry, G-DEM1 canbe convenient. A new G-DEM2, of similar con-struction but lacking the severity of noise and arti-facts of the earlier version, was released in October2011. G-DEM2 benefits from 260,000 additionalASTER scenes, and preliminary tests indicateimproved accuracy in both horizontal and verticaldimensions, and a substantial reduction in the num-ber of voids (Tachikawa et al. 2011). Still remainingfor the future is development of a new GDEM thatwould allow better tracking of input images.


5.4 DEM ERROR AND UNCERTAINTY

5.4.1 Representation of DEM error

and uncertainty

Given the number of stages involved in generating aDEM, errors are inevitable in both the vertical andplanimetric coordinates. In general, error can beclassified as: (1) gross errors that are associated withequipment failure; (2) systematic error that repre-sents the results of a deterministic system that canbe accounted for by using functional relationships;and (3) random errors that occur within (or becauseof) the multitude of operational tasks that areinvolved in computation. In this context, error istypically defined as systematic and/or random var-iations about a ‘‘true’’ reference value (Fisher andTate 2006). The magnitude of vertical error can bean important consideration, as changes in glaciersurface altitude over shorter time frames maybecome undetectable, depending upon the natureof the source data. Consequently, the usefulnessof a DEM for estimating mass balance must becarefully evaluated (Bamber and Payne 2004).

A common descriptor of error is root meansquare error (RMSE):

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P

i

P

jðzi; j � zi; j;rÞ2

n

s

ð5:1Þ

where zi; j is the elevation at location (i; j ) in theDEM, and zi; j;r is a reference elevation at the samelocation. The metric has been used when comparingelevations off-glacier in a variety of glaciologicalstudies, although it does not describe very wellthe statistical distribution of vertical error (Fisherand Tate 2006). It has, however, become a standardmeasure of map accuracy. Other researchers haveused additional error metrics such as mean error(ME) and standard deviation (S) (Cuartero et al.2004):

ME ¼PP

ðzi; j � zi; j;rÞn

ð5:2Þ

S ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

PP

½ðzi; j � zi; j;rÞ �ME�2n� 1

s

ð5:3Þ

Systematic under or overestimation (biases) aredepicted as positive or negative ME values.

Such global summary (single-value) metrics arequick to calculate and easy to report, but they fail tocharacterize the spatial pattern of error, which iscritical to environmental applications. DEM errorscan vary spatially, and research indicates that the

spatial structure of error in DEMs remains poorlyunderstood (Carlisle 2005). Numerous researchershave attempted to study and describe the nature ofspatial error and have found that patterns of errorcan be anisotropic, scale dependent, spatially vari-able, and spatially correlated, but most importantlyDEM error is closely related to the complexity andcharacteristics of the terrain (Kyriakidis et al. 1999).Work in alpine environments often reveals patternsof error over mountain terrain and glacier surfacesthat are highly variable in spatial extent and loca-tion, 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 determiningthe parallax between pixels matched by cross-correlation there is always a need for postprocessingdue to mistakes in pixel matching, correlation fail-ures, and, if present, the impact of clouds in thescenes. Further, shadowing in regions of high relief,low image contrast over clean snow and ice, andself-similar surface features on glaciers will lead tovoids and artifacts in the resulting DEM. Somesoftware packages, such as SilcAst, will try toremove such features automatically, with no usercontrol over the process. Alternatively, ENVI, LPS,and PCI Orthoengine all provide a suite of post-processing tools for manual editing. However,Eckert et al. (2005) found that in some cases thepostprocessing tools provided by software packageswere not sufficient and further morphologicallybased interpolation algorithms were required toproduce a suitable DEM. Such matching mistakesand voids are relatively easy to identify and correctfor, but where inaccurate GCPs and poorly chosentie points are used, distortions, biases, and plani-metric shifts may also be introduced into thederived DEM, which can be difficult to modelwithout the use of a reference elevation dataset.This is particularly problematic where multi-temporal DEMs are required for the measurementof 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 refersto horizontal shift of often correct elevation valuesto erroneous easting/northing locations. This canbe either a systematic or a variable shift, and canbe exhibited in one or more directions. Such shiftsare easily quantified by correlating correspondingorthoimages and quantifying the orthophoto paral-

DEM error and uncertainty 123

lax (Li et al. 1996, Georgopoulos and Skarlatos2003), since there should be no relief displacementin either image if the DEMs are accurate. Altimetricerror refers to systematic biases that may artificiallyincrease or decrease elevation in a given directionacross part of, or the whole, DEM, as well as morelocally variable slope or aspect-related biases (Fig.5.4). The correction of both types of error usuallyrequires some form of mathematical modeling. Themost promising approach has focused on the useof ordinary least-squares regression modeling tocreate spatially nonstationary, spatially correlatedand heteroskedastic error surfaces from only asmall number of sample locations (Kyriakidis etal. 1999, Carlisle 2005). These error surfaces canthen be used either to create higher accuracyDEMs, or to inform analyses of error propagationin the computation of surface derivatives (Oksanenand Sarjakoski 2005). It is crucial that both plani-metric and altimetric errors are identified, particu-larly in the case of glacier monitoring as they canlead to erroneous volume changes (Schiefer et al.2007) or even change the sign of the resulting massbalance calculation (Berthier et al. 2006).

Systematic errors are common in some of themost widely available topographic datasets, makingit essential for users to make appropriate errorassessments, even if they believe biases are removed

prior to analysis. Particularly relevant in thisrespect is the widely used continuous DEM pro-duced by the Shuttle Radar Topography Mission,which was flown in February 2000 and provides atopography covering continental areas from 60�Nto 56�S (Rabus et al. 2003) with a 1 and 3 arcsecspatial resolution (about 30 and 90 m, respectively).It has yielded significant advances in the monitoringof glacier wastage in Alaska and neighboringCanada (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 centralAsia (Surazakov and Aizen 2006). However, sinceits release, significant biases in SRTM data havebeen identified by a number of authors, and a clearexamination of the bias still needs to be performed.For example, Kaab (2005a) found a systematicmean error of about 7 m for the Gruben area inSwitzerland. Still in the Alps, Berthier et al. (2006)found a small mean error (<3 m) but detected a biasthat increased linearly with elevation. Such a biasrelated to elevation is still not fully understood buthas since been confirmed for Patagonia (Moller etal. 2007), the Himalayas (Berthier et al. 2007), andthe Canadian province of British Columbia (Schie-fer et al. 2007). The latter authors used a piecewisemodel to correct elevation bias (constant bias at lowelevation and linear bias above a threshold alti-tude). The regional pattern of the biases in SRTMdata is also complex. Surazakov and Aizen (2006)found a localized ice-free region with systematicerror in the SRTM data ranging from �20 to 12m on a 30 km spatial scale. Berthier and Toutin(2008) found a 20� 20 km region where SRTMdata are systematically 5–10 m higher than SPOT5or ICESat elevation data. Note here that, althoughsensor platform orbits are too widely spaced formountain glacier elevation change mapping, ICE-Sat elevation profiles have been shown to be a goodsource of data to detect and understand errors inSRTM data for ice-free regions where no elevationchanges are expected (Carabajal and Harding 2005,Berthier and Toutin 2008).

5.5 GEOMORPHOMETRY

Glacier geomorphometry refers to the three-dimensional topographic characteristics of aglacier surface including its size, shape, hypsometry,orientation, and position. Geomorphometricanalyses have historically pursued fine-resolutiondigital elevation models to improve and refine land


Figure 5.4. Scatterplot of mean difference altitude

generated from a SRTM DEM (2000) and an

ASTER-derived DEM (2004). Mean values were com-

puted off-glacier over the Nanga Parbat Massif in

Pakistan. Variations in viewing geometry and/or space-

craft orbital parameters result in a nonlinear bias that

significantly deviates from zero. Consequently, linear

and nonlinear systematic biases must be removedwhen

comparing DEMs generated from different sensor prod-

ucts.

surface parameters and objects (Dragut� et al. 2009).However, with the increasing availability of detailedDEMs it is becoming clear that the relationshipbetween DEM scale and the ability to extract geo-morphometric information is not straightforward.Indeed, for many applications, increased DEMresolution only serves to introduce noise into theanalysis. Accordingly, a number of methods havebeen applied to account for scale-related problemsthrough DEM generalization, although furtherwork along these lines is needed if accurate topo-graphic characterization of glacierized areas is to beachieved (Dragut� et al. 2009). Despite this currentimperfection, many quantitative analyses of land-scape and landscape evolution remain heavilydependent on the derivation of geomorphometricdata in their methods.

5.5.1 Geomorphometric land

surface parameters

When deriving geomorphometric information fromDEM data it should be noted that, for every orderof differentiation, the effective resolution of theproduct declines and noise increases. The firstderivative (based on calculations between twopoints) normally defines slope, whereas the secondderivative (based on calculations between threepoints) normally defines curvature. For every orderof differentiation, small errors in the primary data-set become exaggerated. Thus, a DEM having a30 m posting can report the first and second deriva-tive values still with 30 m postings, but each grid cellof the derivatives includes information from neigh-boring cells and so the effective resolution isreduced for the derivatives, even though a value iscomputed for each grid cell. Effectively this meansthat derivative information for very small glaciers isuseless, especially if the derivatives, such as curva-ture, are used to define lateral moraines, computeddrainages, or other landforms or hydrological units.Thus, differential geomorphometric parameterscarry both great power to discriminate distinctterrains and landforms, and great risk that noiseor systematic bias is transmitted into geomorpho-metric mapping products.

Depending on the tolerance for noise or lowspatial resolution, geomorphometric analysis canemphasize nondifferential parameters (based onhypsometry), first-order differential analysis (slope,slope aspect), or second-order differentials (curva-ture, tangential curvature) (Fig. 5.5). Most off-the-shelf image-processing software is capable of pro-

ducing such metrics using standard algorithms, withthe quality of the derived geomorphometric databeing largely dependent on the accuracy of theinput elevation data. In an applied context, landsurface parameters are a useful means of comparingthe topographic characteristics of glacierized areasand, in addition, are increasingly being used incombination with satellite imagery to derive morerobust 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 ongravity-driven processes. For example, land surfaceparameters such as slope gradient can indicate thegravitational potential available for geomorphicwork (i.e., erosion), and slope aspect the directionof the work carried out (Smith and Pain 2009).It is important to note that geomorphometric

data may vary dramatically between adjacent sub-catchments and, less obviously, for the same glacieror glacierized area through time. Changes in glaciertopography, for example, may be caused by a sus-tained change in mass balance, or by a change in icedynamics (or both). Basic elevation data reflectingthese changes may be derived by taking a topo-graphic profile along the flow line of the glacierfrom multitemporal DEMs or by computing thealtitude–distance function, which effectively com-pares every pixel representing the surface of theglacier to a terminus position by plotting the aver-age altitude in a distance bin. More complex eleva-tion change data can be derived by hypsometricanalysis, essentially a frequency analysis, character-izing the altitude–area distribution of a glaciersurface. However, the generation of more complexdata such as these is not always desirable; forexample, small changes in surface elevation maybe easily detected in simple multitemporal topo-graphic profiles, but not so in a multitemporalhypsometric analysis where large volumes of(potentially noisy) data can mask subtle surfacechanges. Whichever geomorphometric approach isadopted, it is essential that systematic biases in theDEM are removed prior to analysis and interpreta-tion of the results (see Section 5.4).

5.5.2 Scale-dependent analysis

A range of interacting geomorphic processes shapethe glacial environment, leading to landforms thatare rarely strictly spatially delimited (Schneevoigtand Schrott 2006). Such landforms are diverse insize and shape, even within a single land cover

Geomorphometry 125

classification, and microscale landforms may com-pose local-scale landforms, which may themselvescompose catchment-scale landforms. In modelingsuch dynamic and diverse environments, linearprocess-form relations and those that are spatiallyrestrictive are therefore unrepresentative. There isthus increasing focus on the hierarchical organiza-tion of topography in studies on mountain geo-morphology, and the subsequent adoption ofscale-dependent analyses. These can be simplydefined as methods that examine the variability ofthe three-dimensional spatial structure of morpho-logical features on multiple levels.

With the increasing availability of DEMs fromairborne and spaceborne platforms, automatedapproaches have been developed to identify specific

geomorphometric features (e.g., glacier extent, loca-tion and density of crevasses) based on their shapeand textural properties. One such method is tomeasure surface roughness on multiple scales andin multiple directions, by variogram analysis. Thevariogram is effectively an index of dissimilaritybetween pairs of points that are separated by apredefined vector and within a specified search win-dow. Multiple variograms can be used to character-ize terrain morphological features, such as debrisflow deposits, channels, and rockfall deposits, andto calibrate secondary morphological indices suchas anisotropy, periodicity, and the spatial vari-ability calculated at specific lags. These indices,while providing useful quantitative landscapecharacterization data in their own right, can then


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.

be used as input into further, perhaps more complex(e.g., pattern recognition) landscape classificationtechniques (van Asselen and Seijmonsbergen 2006).

A further derivative of the variogram is the frac-tal dimension (D), which provides a measure ofwhether topographic surfaces and spectral reflec-tances of land cover units are self-similar over arange of spatial scales. Many landscape featuresand other environmental data have been shownto exhibit self-similarity, at least statistically (Good-child and Mark 1987). The limited number ofstudies that have evaluated the utility of fractalsfor these purposes indicate that the majority ofgeomorphic surfaces exhibit scale-dependent fractaldimensions (i.e., limited to certain spatial ranges;Bishop et al. 1998), with the range in scales oftendetermined by the controlling geophysical processesthat have shaped, or continue to shape, the land-scape (Lathrop and Peterson 1992). Fractal dimen-sions have also been employed to improveclassification accuracy (de Jong and Burrough,1995) and to provide insight into operational-scaleand process–structure relationships. This approachappears to have great potential in this respect,although to investigate self-similarity in surfaceroughness characteristics over the full range ofspatial scales requires the use of high-qualityDEMs, which may not always be available inglacierized areas.

5.5.3 Topographic radiation modeling

Digital elevation models are fundamental to thethree-dimensional modeling of solar radiation var-iation across a landscape. Insolation modeling caneither be point specific or area based. Point-specificmodeling considers the geometry of surfaceorientation, the visible sky, and the effect of localtopography. Local topographical effects can bedetermined using empirical relations, visual estima-tions, or, where field data are logistically possible,by upward-looking hemispherical photography.Such calculations can give locally very accurateresults, but are clearly limited in spatial coverage.Area-based insolation modeling relies solely on theuse of a DEM to calculate surface orientation andshadowing across a subcatchment, for example, andas a result has much greater application for under-standing large-scale landscape processes. Alongthese lines, a number of studies have made surfaceirradiance and ablation gradient calculations toidentify locations most suitable for past and presentglaciation (Carr and Coleman 2007, Allen 1998) by

identifying site shelter and exposure, and to beapplied as input to energy balance melt models,which are clearly fundamental to understandingthe relationship between glacier behavior andclimate.Net radiation (also known as net flux) is defined

as the balance between incoming and outgoingenergy and can be computed as:

Qn ¼ Eð1� �Þ þ L#s þ L#t þ L"

where E is total surface irradiance, � is surfacealbedo, L#s is longwave sky radiation, L#t is long-wave radiation from the surrounding terrain, andL" is emitted longwave radiation. It is regulated bynumerous processes and can be highly variabledepending on atmospheric, topographic, and sur-face biophysical conditions. Indeed, in mountain-ous areas radiative fluxes are particularly complex,fluctuating considerably in space and time becauseof the effects of slope, aspect and the effective hor-izon, and the input of reflected and emitted radia-tion from surrounding slopes (Hock 2005). As such,there is a movement towards the use of increasinglyfine temporal (hourly) and spatial (�25 m) resolu-tion modeling, with the latter again dependent onthe availability of suitably fine-resolution andaccurate digital elevation data. Where such datado exist, studies have shown that the melt rate ofsnow and ice and spatial and temporal patterns inenergy balance can be calculated accurately across aglacier, albeit with dependence on accurate field andmeteorological data (Brock et al. 2000).

5.5.4 Altitude functions

Most glacier parameters vary as a function ofaltitude, and these relationships can give insightinto glacier dynamics and processes that simpletwo-dimensional analyses would not reveal. Aglacier’s most fundamental altitude parameter isthe equilibrium line altitude (ELA) because itdivides the glacier into accumulation and ablationareas (Braithwaite and Raper 2010). This can besimply estimated using multispectral satelliteimagery in combination with a DEM, by assumingthat the ELA is equal to the snow line position atthe end of the melting season (Bamber and Rivera2007). Such information is fundamental to massbalance calculations, which are useful indicatorsof climatic variations where no actual ELA dataor better alternative proxies exist (Yadav et al.2004). In the absence of calculated mass balancedata or transient end-of-season snow line data,

Geomorphometry 127

the topographic profile of a glacier can be used as arelative proxy for the dynamic state of glaciers, withthose glaciers in rapid recession tending to exhibitconcave-up or flattened (planar) surface profiles inthe ablation zone, and those accumulating or main-taining mass characterized by convex-up surfaceprofiles (transverse profiles especially) in the abla-tion zone (Quincey et al. 2009).

The altitude–area profile (or the hypsometriccurve) for each glacier represents a distinct 3Dspatial signature that is the end result of thousandsor millions of years of erosion and reflects interac-tion of the regional climate with subglacial bedrock(Tangborn 1999). It has been used in many cases toinfer the state of geomorphic development within aglacial system (Katsube and Oguchi 1999). Glaciererosion processes are determined most significantlyby glacier velocity, ice thickness, subsurface geol-ogy, and basal thermal conditions. Differentialerosion therefore occurs with altitude as each ofthese parameters changes accordingly. Topographicanalyses of the Nanga Parbat Massif in Pakistanrevealed a spatially variable relief structure thatcorrelated to geomorphic events and dominantsurface processes (Bishop et al. 2001). Glaciationwas found to generate the greatest mesoscale reliefat high altitudes and warm-based glaciation wasfound to reduce relief at intermediate altitudes.More recently, numerical modeling has shown thatmountain heights can be explained by a combina-tion of glacier erosion above the snow line andisostatic uplift caused by erosional unloading, withmaximum elevations being constrained to an alti-tude window just above the snow line (Egholm et al.2009).

More generally, glacier hypsometry determineshow responsive glacier-wide mass balance is toclimatic perturbations (Furbish and Andrews1984). For example, a rise in the snow line of200 m in a given region (in response to local atmo-spheric warming, for example) would have a muchgreater impact on a low-gradient valley glacier thana steeply sloping one, as in the former case agreater proportion of the overall ice mass wouldbecome subject to net annual mass loss. Thus, asan example, if there were a rise in local atmospherictemperature in the Hunza Valley of the Karakoram,the mass balance of the Batura Glacier would beaffected to a greater extent than that of theGhulkin Glacier, and the mass balances of the Pasuand Ghulmit Glaciers would change somewherebetween those two end members (Fig. 5.6). Simi-larly, glacier clinometry (characterization of the

slope/altitude function) expresses glacier relief,and is thus also useful for determining erosion ratesand mass balance fluctuations.The relationship between altitude and glacier

velocity is not straightforward. Glaciers with lowrelief tend to exhibit flow that is relatively uniformacross the altitudinal range, whereas those withhigh relief (and are thus fed predominantly by snowand avalanche material) tend to have very high flowrates at altitude and much reduced flow towardstheir termini. Altitude–velocity profiles can be use-ful for proxy assessments of mass balance (Luck-man et al. 2007), for identifying areas susceptible toglacial lake development (Quincey et al. 2007), andfor determining predominant glacier flow regimes(Copland et al. 2009). In the case of the latter,generally flat transverse velocity profiles with arapid reduction in flow at the margins indicate‘‘block flow’’, suggesting down-glacier movementof ice en masse by basal sliding, whereas convexvelocity profiles that display greatest displacementstowards the centerline of the glacier indicate aflow regime dominated by ice deformation. Largeseasonal variability in flow can further highlight theimportance of meltwater availability for a givenglacier, and may even help to identify different flowmechanisms that exist at different altitudes within asingle 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 cal-culate glacier surface elevation changes for many


Figure 5.6. Hypsometric curves for the Batura,

Ghulkin, Ghulmit, and Pasu Glaciers located in the

Hunza Valley, Pakistan.

years, using images acquired by both airborne andsatellite sensors. The most reliable source of DEMsfor volume change estimates is still aerial photos.Given their very fine resolution, if precise GCPs areavailable, DEMs with RMS accuracies the size ofapproximately one pixel (few tens of centimeters)can be obtained (Kaab 2002). Consequently, aerialDEMs are still frequently employed to study vol-ume changes at the scale of a single glacier anddetect systematic errors in cumulative mass balanceestimates obtained from the traditional (pit andstake) glaciological method (Østrem and Haaken-sen 1999). However, aerial photographs cover alimited surface on the ground (generally one glacier)and it is difficult to fly a plane in remote and high-relief areas. Consequently, they cannot be regardedas a means of obtaining regular coverage of glaciertopography at the regional scale. Given the largefootprint of satellite images (typically 60� 60 km),it is tempting to apply the geodetic method to space-borne DEMs. The principle is the same as for aerialphotography: two sequential glacier surface modelsare derived from pairs of stereoscopic images andsubtracted to yield a map of elevation changes.

Satellite-derived DEMs are less accurate than thosecomputed from aerial photographs so caution mustbe taken when interpreting the signal and compre-hensive error analysis is mandatory.Changes in surface elevation can be measured

most accurately by processing all imagery withina single block or, put more simply, using a singlemathematical model (Kaab 2000; Fig. 5.2). Thequality of derived surface elevation data using thistechnique is mainly dependent on the interiororientation of the stereo model (Baltsavias 1999)rather than the accuracy of any ground controlused, which makes the technique particularlyappropriate for assessing remote terrain. Factorssuch as scanned resolution of the images, accuracyof fiducial mark locations, and accuracy of cameracalibration parameters are particularly importantin such analyses. Model GCPs introduce a second-order error that is small (of the order of a fewpercent) in relation to final vertical displacements,which is consistent between the two DEMs, provid-ing they are bundle-adjusted as a single imageblock. Therefore, the technique can, in theory, beused without any ground control at all, while still

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.

producing accurate vertical displacement resultsfrom the relative image orientation alone (Kaab2002).

A major source of error in vertical differencesbetween multitemporal DEMs is their three-dimensional co-registration. In cases where no com-mon GCPs and tie points have been applied, severebiases might exist in particular between space-derived DEMs. Errors in elevation differences fromsuch a lack of precise co-registration might easilyexceed real elevation changes, and should thereforebe investigated as part of every DEM-differencingwork (cf. Fig. 5.4). The most efficient method toinvestigate and possibly correct DEM biases isthe cosine method that relates elevation differencesfound for stable terrain to the combination of ter-rain slope and aspect (Kaab 2005a, Nuth and Kaab2011).

While a 10–20 m elevation error may be accept-able for the orthorectification of images, it is notfor glacier elevation change mapping. Typically, aglaciologist aims at measuring the rate of change insurface elevation within �0.5 m/yr (this is the upperbound for the error). Larger errors are acceptableonly when massive (tens of meters), but unusualelevation changes are monitored (Stearns andHamilton 2007). A glaciologically relevant accuracycan be obtained by (1) increasing the time periodbetween the two datasets and/or (2) improving thequality and limiting the biases of the DEMs. Thefirst strategy is generally explored by comparingrecent spaceborne DEMs (ASTER, SRTM, SPOT)with maps from the 1950s, 1960s, or 1970s. Apply-ing such historic topographic datasets with morerecently derived DEMs may permit determinationof glacier elevation changes across several time-steps. For example, Kargel et al. in this book’sFigure 15.4F show a technique that captures threesequential DEM elevation-differencing analyses(over a 40-year total period) into one RGB compo-site image. Each color channel (RGB) representsthe earliest, middle, and the latest elevation-differ-encing analysis, respectively; the composited imageprovides immediate visual perception of the accel-eration or deceleration of elevation changes coin-cident with the color-scaled time period. In thisway, spatial, dynamic, and multitemporal informa-tion on elevation changes are uniquely viewedwithin one image. The second strategy relies onhigher resolution satellite images with stereo cap-abilities such as SPOT5 HRS or ALOS PRISM.Even in the latter case a minimal image time spanof about 3 to 5 years is required.

The accumulation zone is the most critical part ofthe glacier when mapping elevation changes. IfDEMs are derived from optical images or aerialphotographs, the high reflectance of the year-roundsnow-covered accumulation zone may lead to lim-ited features in the photographs/images or, in theworst case, saturation of the sensor (Kaab 2002). Inthe case of old maps derived from aerial photo-graphs, errors may have been introduced by inter-polation of contours (Schiefer et al. 2007). Forsatellite images, featureless terrain can lead to datagaps or erroneous pits and spikes in DEMs of theaccumulation zone. Enhanced elevation changeerrors may also affect the accumulation zonebecause the ice-free regions, which are used fordetecting and modelling any elevation biases, arelocated at lower altitude. Only a few nunataksmay be visible to check the presence of relativeelevation biases at higher altitude, but, in practice,even this is difficult because they are generally steepand small features. Consequently, any elevationbiases need to be extrapolated from the lowest tothe highest elevations. Other reasons for increaseduncertainties in the accumulation zone relate todifficulty in choosing density values to convertvolume-to-mass changes and, when DEMs derivedfrom SAR images are used, the necessity to takeinto account penetration of the radar signal(depending on its frequency) into the snow/firn(Rignot et al. 2001). Consequently, good practiceis to compute separate estimates of glacier volumechanges for the ablation and accumulation zones,even if only a rough estimate of the position of theequilibrium line altitude (ELA) is available. Differ-ent uncertainties can thus be attributed to each ofthe two regions.A number of strategies exist to actually compute

glacier volume changes from a set of glacier eleva-tion changes (Kaab 2008). (1) If the two (or more)DEMs to be differenced are complete, the summa-tion of vertical differences gives the volume differ-ence. Since this is often not the case (see above),either (2) the hypsographic method can be usedwhere mean thickness change for each elevationbin is multiplied by its area and all bins summed,or (3) polynomial variation of elevation changeswith height can be fitted to measured elevationdifferences and the elevation differences for eachglacier point then computed according to its heightusing the polynomial parameters. In cases whereone of the multitemporal elevation datasets is nota grid, or elevation information is distributedunevenly, such as in contour lines or altimetry


footprints, calculations must be made carefully. Forexample, it might be advantageous in terms of mini-mizing error propagation not to interpolate pointelevation data to a DEM and then difference twodatasets, but rather to first calculate differencesbetween the elevation points and the DEM, andthen to interpolate elevation differences across thewider glacier surface. In a number of cases, eleva-tion differences will show less spatial variabilitythan elevation itself, and interpolation routines willthus produce less serious artifacts.

Data from nonoptical sensors can also provideaccurate measurement of glacier surface eleva-tions and, with multitemporal datasets, elevationchanges. Spaceborne radar altimeters (on boardERS-1, ERS-2, or Envisat, for example) are wellsuited to flat and large ice sheets or ice caps butare not suitable to survey mountain glacierstargeted by GLIMS because of their kilometricfootprints. The smaller (60 m) footprint of theGeoscience Laser Altimeter System (GLAS) onboard ICESat makes it a potential source of datafor large mountain glaciers and ice caps (Zwally etal. 2002). However, the large spacing of the orbits,the fact that they are not repetitive, and the diffi-culty of removing the influence of clouds limit theusefulness of ICESat data. Still, ICESat data canbe used to evaluate the quality of other DEMs(Berthier and Toutin 2008) or to estimate glacierelevation changes when compared with othermultitemporal elevation data (Sauber et al. 2005,Surazakov and Aizen 2006, Kaab 2008). Repetitivesurveys by airborne laser altimetry have been shownto be extremely accurate. However, central line sur-face profiling may lead to errors due to the difficultyof extrapolating to the whole glacier surface(Arendt et al. 2006).

It is clear then that DEMs derived from remotesensing can provide glacier elevation change dataon a range of temporal and spatial scales. Whileuseful in their own right, elevation change dataare also a fundamental component of glacier massbalance calculations. If two DEMs cover the wholeglacier, their difference (i.e., volume change) can beconverted to mass balance assuming a constantdensity of 900 kg m�3 in the ablation area, althoughthe true density value to use in the accumulationzone is still the topic of ongoing research. Mostauthors use the same density as in the ablation zone,as using a density different from 900 kg m�3 impliesa change in the rate of densification. Ideally thecalculation should include quantification describingany shift in the underlying ground (e.g., due to

isostatic rebound or tectonic movement) althoughin reality this is normally small compared withglacier surface elevation change. The ultimate resultis mass balance quantification expressed in meterswater equivalent (MWE) over the imaged timeperiod.A number of studies have used this approach to

assess the mass balance of alpine glaciers, usingcombinations of historical topographic maps (Riv-era et al. 2007) and DEMs derived from SPOTimagery (Berthier et al. 2007), SRTM (Racoviteanuet al. 2007), ASTER (Khalsa et al. 2004), Corona(Bolch et al. 2008), and laser altimetry (Sauber et al.2005). Very few have compared remotely sensedmass balance calculations with those derived byfield investigation, but those that have (e.g., Hagget al. 2004, Rabatel et al. 2005, Zemp et al. 2010)have found good agreement between datasetresults. As noted above, because of the limited accu-racy of elevation data derived by remote-sensingmethods, many studies have strived to obtain massbalance estimates derived over longer, preferentiallydecadal time-scales, to ensure the change inobserved data exceeds the uncertainty in theapproach.

5.6 GLACIER MAPPING

Snow and ice exhibit distinct spectral propertiesthat make accurate delineation of debris-freeglaciers possible using a variety of remote-sensingtechniques (e.g., thresholded ratio images), but theautomatic classification of debris-covered ice ismore complex, because of the inherent difficultyof spectrally distinguishing supraglacial sedimentand landslide material from that present in thesurrounding terrain (Paul et al. 2004b). For thisreason, DEMs are widely used for terrain visualiza-tions and to provide additional information onlandscape morphometry, land surface context,and spatial topology, all of which facilitate a moreaccurate and reliable classification result for debris-covered glaciers.At the most basic level, DEM data can be used to

generate terrain visualizations to aid the manualdelineation of glacier boundaries (Fig. 5.8). Glaciertermini are often difficult to identify using plani-metric imagery alone because, particularly whenheavily debris-covered, they appear contiguouswith the proglacial zone, but small elevation varia-tions visible in three-dimensional visualizations can

Glacier mapping 131

sometimes remove this ambiguity. Similarly, theexact location of a catchment divide may beunclear, especially where fresh snowfall masks theheadwall ridge; three-dimensional information isparticularly useful in this respect. For the glacieritself, DEM data are useful for identifying areasof low slope angle (see Fig. 5.5b), which are char-acteristic of debris-covered glacier tongues in mostparts of the world. When combined with comple-mentary data such as land cover classifications, andwith results from neighborhood and change detec-tion analyses, it has been shown that slope angledata can be used as the primary morphologicalcharacteristic to delineate glacierized terrain (Paul

et al. 2004b, Bolch et al. 2007). However, specificslope thresholds used to delineate glacier facies varyfrom region to region, with ice masses in the Euro-pean Alps generally characterized by short, steeptongues relative to the long (>10 km) flat tonguesof parts of the Himalaya, for example. Further, thisapproach depends on slope angle being calculatedacross a sufficiently broad spatial kernel to avoidhighlighting local slope variability (e.g., naturalpeaks and troughs across the glacier surface), whileretaining sufficient detail so that small-scale featuressuch as inner moraine flanks are not excluded fromthe analysis.Additional first-order information that can be

calculated from DEM data include landscape planand profile curvatures, which can be used to defineboth glacial and nonglacial landform elements(Bolch and Kamp 2006; see Fig. 5.5c–f ). By cluster-ing surfaces with similar curvature characteristics itis possible to differentiate between glacier surfacesand valley bottoms (low convexity), ridges andlateral moraines (high convexity), medial moraines(moderate convexity), and transitions betweenglacier margins and lateral moraines (high concav-ity). A similar but more complex approach is to usehierarchical object-oriented modeling, whichemploys various DEM-derived terrain object prop-erties such as slope angle, slope azimuth, curvature,and relief to identify locally contiguous portions ofthe landscape, which are iteratively aggregated toform higher order landform objects at smaller andsmaller scales (Bishop et al. 2001). Glacier bound-aries can thus be delineated at a landform level, andobjects and the relationships between objects canbe used for further landscape analyses, such asstudying the role of surface processes (e.g., ero-sion/uplift) in topographic evolution. Morpho-metric approaches such as these show greatpotential for glacier mapping across the world,but are heavily dependent on the input of high-quality DEM data for accurate results.A range of satellite sensors already have stereo-

scopic imaging capability and some recent missions(e.g., Cartosat-1, ALOS PRISM, Terra-SAR-X,and the TanDEM-X-mission) have significantlyincreased the potential for extracting DEM dataat very high resolution for use in glacier mapping.For many remote high-mountain regions of theworld, however, gaining access to high-qualityDEMs can be problematic, with ASTER andSRTM data often providing the best (or only) avail-able sources. Errors common in ASTER-derivedDEMs of steep, high-mountain relief can sometimes


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 catch-

ment 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 Sup-

plement 5.2.

produce artifacts in classification results, but maystill provide a quality of output that exceeds classi-fication methods not employing a DEM of any sort(Paul et al. 2004b). DEM resolution can be anequally important consideration, with aerialphotography DEMs (such as those provided bythe Swiss Topo Survey) outperforming satellite sen-sor–derived data in almost all cases (Bolch andKamp, 2006), particularly in the delineation ofsmall ice masses. In areas where accurate andfine-resolution DEMs are not available, manualdigitization of small samples may still thereforebe necessary to achieve a satisfactory classificationresult. Therefore, attempts have been made to intro-duce additional information into the classificationprocess, such as metrics relating to geomorph-ometry, texture, and context (Bishop and Shroder2000, Bishop et al. 2001, Taschner and Ranzi 2002,Paul et al. 2004b, Ranzi et al. 2004, Buchroithnerand Bolch 2007, Bolch et al 2008). Sophisticatedclassification approaches use both first and sec-ond-order topographic derivatives to segment land-scape units accordingly, and make use of statistical,artificial intelligence and hierarchical–structuralmethods.

5.6.1 Pattern recognition

Pattern recognition techniques perform two keytasks: description and classification. Given anobject (or set of objects—pixels in a satellite image,for example), pattern recognition systems first seekto describe those object(s), often in three dimen-sions, and subsequently classify the objects basedon those descriptions. The rigor with which theprior task is performed largely governs the qualityof the latter. The description and classification ofinput data in this way can be handled by statisticalor structural methods or, more frequently, a com-bination of both (the hybrid approach). Statisticalmethods make use of decision theory concepts tosegment the landscape based on their quantitativefeatures, whereas structural methods make use ofsyntactic grammars to segment the landscape basedon the arrangement of their morphological features(see Section 5.6.3). Either way, DEM data are afundamental input to the classification procedure.

Statistical pattern recognition techniques arelargely dependent on the choice of model param-eters, the quality of the expert knowledge used inthe prior part of the model, and the resolution ofthe image and DEM data. For example, and withspecific reference to debris-covered glacier classifi-

cation, let R denote the pixel domain of a set ofco-registered data layers (e.g., satellite imagery,elevation and geomorphometric parameters). Com-bining all these layers into vector space results in afeature vector per pixel. Similar vectors can bederived to describe a shading field (to handleacross-image slope and exposition variability) anda segmentation field, such that:

~xx : R! R 000 vector field of features (observable)

~�� : R! R 000 shading field (unknown)

s : R! K segmentation field (unknown)

where K denotes the set of labels used for segmen-tation. In the simplest case there are only two poss-ible labels—one for a debris-covered glacier andanother for ‘‘background’’, but more are usuallyemployed to gain a full description of the environ-ment. The statistical model relates the three quan-tities (above) by a probability distribution:

pð~xx; ~��; sÞ ¼ pð~xx j~��; sÞpð~��ÞpðsÞ

where it is assumed that shading and segmentationare a priori independent.If the parameters of the normal distribution are

already known, then the recognition task simplyrequires the following: given the observation field~xx we have to estimate the best shading field ~�� andthen estimate the best segmentation field s. Routinealgorithms such as the Gibbs sampler (Geman et al.1990) and the Expectation Maximization algorithm(Schlesinger 1968, Dempster et al. 1977) are nor-mally employed to make the estimations.If the parameters of multivariate normal distri-

butions are unknown (first factor in the equationabove) they can be estimated by maximum likeli-hood learning given an expert’s segmentation of thescene. In this case the Expectation Maximizationalgorithm is again applied but with partial super-vision. The expert’s segmentation is relaxed bydefining only three regions: background, fore-ground, and a zone between, leaving the systemto learn the optimal boundary. The resulting itera-tive learning scheme comprises repetition of thefollowing subtasks:

1. Given the actual parameters of the normal dis-tributions and the actual estimation of the shad-ing field, sample the segmentations and estimatethe marginal probabilities prðsr ¼ k j~��;~xxÞ foreach pixel r.

Glacier mapping 133

2. Use these marginals to improve the parametersof the normal distributions (i.e., the covariancematrices and mean vectors for all segments).

3. Re-estimate the shading field ~�� based on thecurrent marginal probabilities and parametersof the normal distributions.

When the optimal boundary is reached, the itera-tion is stopped and the pixels are assigned theirsegment label (Fig. 5.9).

5.6.2 Artificial intelligence techniques

Artificial intelligence techniques (often referred toas knowledge-based systems) essentially comprise aset of logical rules that provide an analog for thereasoning 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., apixel) for certain characteristics (e.g., to be within a

range of spectral values) and then follow one of twopaths based on the result. Such ‘‘expert systems’’systematically arrive at a single classification foreach pixel by ruling out alternatives based on inputdata values. This mimics the decision-making pro-cesses employed by a field geomorphologist, forexample; indeed it is important to note that suchsystems can also exploit three-dimensional contex-tual and shape information in the sameway a humancan. DEMs are therefore a fundamental componentof a comprehensively designed (and truly three-dimensional) expert system.Artificial neural networks (ANNs) aim to process

information in a similar way to the human brain, byusing a large number of highly interconnected pro-cessing elements (neurons) working in parallel tosolve a specific problem. The key difference betweenANNs and other artificial intelligence techniquesis that ANNs learn by example and cannot bedesigned to perform a specific task in the firstinstance. ANNs are particularly useful for handling


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.

diverse and nonparametric datasets and for model-ling nonlinear relationships, making them a particu-larly attractive method for mapping glacierizedterrain. Nevertheless, the value of the output classi-fication is only as good as the quality of the inputdata; for ANN techniques to be truly robust theymust learn to recognize patterns associated withgeomorphometric land surface parameters, suchas texture, context, and spatial topology, whichcan be derived (at least partly) from first-orderand second-order DEM analyses (Bishop et al.2001, 2004).

Fuzzy classification algorithms are able to incor-porate inaccurate sensor measurements, vague classdescriptions, and imprecise modeling into the anal-ysis (Binaghi et al. 1997, Benz et al. 2003), and canresult in accurate portrayals of subpixel mixtures ofclasses. Fuzzy classification procedures assignvalues to each pixel representing the pixel’s degreeor probability of membership in each class, ratherthan clustering similar pixels together into athematic set. The fuzzy approach is analogous tohuman perception, in which there can be uncer-tainty even between experts analyzing the same en-vironment. Fuzzy sets are a classification tool inthemselves; they can be used alone or incorporatedinto higher level artificial intelligence techniquessuch as expert systems; either way it is assumed thatthere is a priori expert knowledge about the en-vironment under investigation to be able to designfuzzy membership functions. In a similar way toexpert systems and ANNs, the addition of a topo-graphic dataset into the classification is fundamen-tal to the accurate identification of glaciallandforms through shape and contextual analyses(Schneevoigt et al. 2008).

5.6.3 Object-oriented mapping

Object-oriented mapping describes the segmenta-tion and partitioning of the landscape into discretespatial entities based upon their geomorphometriccharacteristics (e.g., slope angle, slope azimuth, cur-vature and relief; Bishop et al., 2001). These entitiesrepresent the lowermost level of a hierarchical land-scape structure, which in total describes the sup-position of surface processes that comprise thetopography of a glacierized landscape (Bishopand Shroder 2000). Therefore, by combining spatialentities at the lowermost level, specific terrain feat-ures can be identified; by combining terrain featuresat the second level, landforms can be identified, andso on. High-quality DEMs are clearly fundamental

to this approach, if the spatial entities at the lowerend of the hierarchical structure are to be accuratelyquantified and error propagation through the sys-tem is to be avoided. This approach has beensuccessfully employed to accurately delineate theablation zone of the heavily debris-covered RaikotGlacier in the Nanga Parbat Himalaya, for example(Bishop et al. 2001). Terrain object properties werefound to be diagnostic of glacier processes repre-senting glacierization, thereby differentiating glaciertopography from other surfaces governed by differ-ent surface processes.Object-oriented mapping can be used as a classi-

fication technique in its own right, but it has beenshown to be particularly effective when used incombination with ANNs (see above) to classifyalpine glacial environments. In this specific context,the procedure may follow five key stages (Raup etal. 2007):

1. Classification of land cover using spectral dataand topography.

2. Spatial analysis of imagery to generate geo-metric, shape, and topological information.

3. Generation of geomorphometric parametersfrom DEMs.

4. Fusion of data into an object-oriented param-eterization scheme.

5. Classification of supraglacial features andglaciers by neural networks.

This hybrid approach appears to reduce error andincrease consistency in results when compared withother approaches. Indeed, it is true of all the pre-viously described techniques for glacier mappingthat they may yield useful terrain classification intheir own right, but they have even greater potentialwhen they are integrated together. Fundamental totheir success is the provision of a three-dimensionalanalysis, however. Topological, contextual, shape,and geomorphometric analyses are limited withoutthe use of a DEM, and numerous studies havedemonstrated the need for such three-dimensionalproperties if fully automated glacier mapping is tobe realized (Bishop et al. 2004, Paul et al. 2004b,Bolch and Kamp 2006).

5.7 DISCUSSION

It is clear that digital elevation data derived fromstereoscopic airborne and satellite imagery are fun-damental to many essential cryospheric applica-

Discussion 135

tions, and in particular to deriving glacier statisticsfor inclusion in global databases. Square-gridded(raster) DEMs are most widely employed byresearchers because they provide more realistic ter-rain representations than data interpolated fromtopographic maps and are easier to derive and tohandle than DEMs derived by radar interferometryor airborne laser scanning. However, they are farfrom perfect, particularly for detecting the abruptchanges in topography that characterize glacialenvironments, and the challenge of producingfine-resolution DEM data with low data storagerequirements remains an issue. Further, the genera-tion of reliable elevation data at any resolution finerthan that offered by the SRTM (90 m) remainsproblematic for many glacierized areas of theworld. This is partly because of persistent cloudcover, particularly in mountain regions, and a lackof ground control data, particularly in areas ofpolitical sensitivity. Additionally, SRTM data arestatic and do not allow for multitemporal analyses.While the recently released G-DEM2 may representa possible breakthrough in terms of spatial detail(30 m pixel size) and accuracy, elevation valuesrepresent the combined period of ASTER opera-tions (2000–2011), so offer no better temporal reso-lution than the SRTM DEM.

Indeed, it is this variability in data quality thatremains the major limiting factor in global glaciermapping and characterization. It has consequencesfor the type, number, and quality of glacier param-eters that can be derived for any given area.Furthermore, it influences the effectiveness of dif-ferent methods and approaches, and makes thestandardization of procedures a challenging task.Ideally, elevation data at resolutions and accuraciescomparable with those offered by airborne laseraltimetry are required for all glacierized regionsof the world. Unfortunately, without a wide-swathspaceborne altimeter, we are many years (if notdecades) from being able to achieve such a dataset.Even then, it will raise numerous issues regardinghigh-density point clouds and preprocessing.Nevertheless, there remains great potential in theuse of various approaches, such as the integrationof multiple multiscale elevation datasets for deriv-ing multiscale information about a single glacier-ized catchment, and the use of LiDAR data asaccurate ground control for photogrammetricDEM extraction, among others. While novelapproaches to deriving glacier parameters havebeen successful, some are yet to be effectively andcomprehensively employed on a regional basis. For

example, the geodetic method has been proven auseful tool to assess glacier surface lowering and,subsequently, to produce estimates of mass balance.This work, however, has yet to be systematicallyconducted in many regions of the world. Further,where independent studies have been carried outusing such approaches, they are not always directlycomparable because of methodological incon-sistencies, or inconsistency in the reporting of dataerror.Although remote-sensing sensor technology

has advanced significantly in recent years, thechallenges of representing topography in high-mountain high-relief regions, and accurately quan-tifying the error within those topographic data,remain significant. For example, a range of studieshave shown that for many glacierized regions of theworld (mostly those of moderate relief ) the topog-raphy can be characterized by ASTER DEMs withan accuracy of �15–30 m (68% confidence level)after some significant postprocessing, but only to�60 m (68% confidence) in areas with steep rockheadwalls and large low-contrast accumulationareas (Kaab 2002, Toutin 2008). The issue is com-plicated further in high-relief mountain areas byslope–aspect error dependence (Bolch 2004), whichtends to result in better quality elevation data beingderived on slopes facing south (in the northernhemisphere) because of advantageous illuminationand sensor–terrain viewing angle. Illuminationvariations can be compensated for (to a certaindegree) using topographic normalization methods,but this itself requires a DEM, which is not alwaysavailable at this processing step. In terms oferror quantification, some standardization ofmethods is required. Inconsistencies currently existbetween studies in the manner in which errorsare reported: some studies quote errors to twostandard deviations whereas some only quote theRMSE. A limited number do not even quantify theexpected error (or uncertainty) in the presented dataand, of those that do, the accuracy of data cansometimes be highly dependent on the numberand positioning of chosen check points (Toutin2008). It is often difficult, therefore, for an indepen-dent researcher to replicate results, or to establishthe exact error analysis that has taken place andhow reliable it is.Where reliable topographic data do exist they can

be used very effectively for mapping and changedetection studies. First-order geomorphometricparameters have been successfully employed toenhance glacier boundary delineation, calculate sur-


face lowering rates, and inform numerical models(e.g., surface uplift/erosion). This latter effort,specifically the integration of remote sensing andmodeling for the analysis of landform–processcoupling, remains in its early stages, along withseveral other interesting possibilities that are bene-fiting from better and more widely available digitalelevation data. For example, space-based methodsnow exist capable of generating a mass balanceindex to improve ELA estimation, and glacier flowand erosion modeling are being enhanced byimproved and accurate boundary conditions. Withsuch ventures come further challenges, of course,such as accounting for spatial and temporal fluctua-tions that were previously beyond modeling resolu-tion; many glacier simulations have until recentlyneglected to account for daily and seasonal abla-tion, ice velocity, and erosion fluctuations, forexample (MacGregor et al. 2000).

The accurate modeling of glacierized terrain isessential because it plays such a fundamental rolein the modulation of atmospheric, Earth surface,and glaciological processes (as well as being shapedby these same processes). The glacial environment,and in particular the glacier surface, is extremelylabile; this is especially so at present with majoradjustments occurring due to climatic forcing. Ona catchment scale, topography governs sedimenttransport and ice fluxes, collectively influencingglacier erosion. On a more local scale, glacier sur-face topography can influence debris cover distri-butions, debris depth, meltwater routing, andsupraglacial ponding. Conversely, processes andparameters provide feedback that affects glaciertopography—thick debris covers can insulateglacier ice, for example, and meltwater ponds ther-mally erode ice at their margins and their bases. Atthe most local level glacial features such as ogives,moraines, seracs, and crevasse fields define thetopography of glacier surfaces. It is therefore clearthat there is complex two-way interaction betweentopography and surface processes across a range ofspatial and temporal scales that needs to be betterunderstood to inform ideas relating to geomorpho-logical landscape evolution.

The interaction between topography and mostgeophysical processes occurs over a range of spatialscales, which cannot currently be truly representedwithin DEM data. Therefore, while the resolutionof the generated DEM is limited by the resolutionof input source data, scientific interpretationsshould also be mindful to restrict analyses to thenatural scale of the terrain-dependent application.

As a guide, the resolution of the derived DEM canprovide a practical indication of the scale of infor-mation content; analyses of processes or featuresthat occur on a finer scale than this should be madewith caution. For example, relatively small-scalefeatures (e.g., moraine ridges) can be entirely missedby medium-resolution datasets, yet may change aninterpretation of a process or set of features withtheir presence. Conversely, with a fine-resolutionDEM, analyses made on a coarser scale may behampered by noise, and indeed a coarser resolutionDEM may be more appropriate for use. With con-stant computational developments, methods forrepresenting fine-scale shape and structure are con-tinually improving and so is the incorporation ofterrain structure into considerations of spatial scale.A classic example of this is the development ofscale-dependent classification methods, which areincreasingly considering terrain hierarchies withthe realization that landforms are often notspatially delimited and that one landform may par-tially comprise another.Consequently, research on glacier mapping and

the extraction of glacier parameters indicates thatthe integration of topographic information on avariety of spatial scales is important in order toproduce reliable results. However, methodologiessignificantly vary, and some problems remain forhigh-mountain areas, particularly in change detec-tion studies. For example, surface features must bemaintained across the imaged period for accurateelevation datasets to be derived. This depends onthere being sufficient optical contrast between thefeature and its surroundings as well as the featurebeing large enough to be resolved given the sensorresolution; and it is also dependent on there beingno (or minimal) modification of the feature shape,size, and contrast during the change, or the maskingof the feature by snow cover, for example. Further,the magnitude of the change(s) to be detected maynot exceed the uncertainty in the method employed.Errors in satellite-derived DEMs of high-reliefterrain are particularly problematic; consequentlyit is unlikely that researchers will be able to reliablydetect surface lowering on a timescale of less than adecade. The solution is to either increase the imageresolution (and thus accuracy) or to extend theobservation period (thus increasing the magnitudeof change). The latter solution is becoming increas-ingly possible as data archives extend with time andnew sources of historical data (e.g., Corona; Bolchet al. 2008) emerge. The former issue is aided by thelaunch of new and improved sensors.

Discussion 137

Remote sensing is a constantly advancing disci-pline, so the launch of a new and/or improvedsensor is often imminent and the promise of moreaccurate or more detailed imagery is never far away.Some of the most promising developments for thegeneration of new elevation data come from non-optical sources. For example, the recently successfullaunch of TanDEM-X, the interferometric partnerof TerraSAR-X, promises to provide a global DEMto HRTI-3 specifications (Weber et al. 2006; i.e., 12m spatial resolution,<2 m relative vertical accuracyand <10 m absolute vertical accuracy). Thesespecifications can only currently be achieved byaerial photogrammetry and very fine–resolutionoptical satellite imagery such as WorldView, butwith associated costs. Spaceborne laser altimeters(e.g., GLAS, on board ICESat-1) provide compar-able accuracy, but with very limited swath widthand low point density, and there is no real prospectof routine collection of such data again until theproposed launch of ICESat-2 in 2015.

If topographic and spectral data are to be trulyintegrated into surface process modeling, andresults compared between independent studies,there is a requirement for a representational frame-work that scientists can work towards. Currently,scientists employ a range of analytical tools, algo-rithms, processing approaches, and software for thegeneration, manipulation, and interpretation oftopographic data. Methods are highly empirical,thus the type and quality of the derived data aredependent, to a large extent, on the analyst. Con-sequently, replication of existing results can bedifficult (even more so the application of one pub-lished technique to a new area). Standardizationand protocols for information extraction and inte-gration are therefore required if data quality, resultaccuracy, and the validity of comparing measure-ments across different studies (and study areas) areto be assured.

5.8 CONCLUSIONS

Digital elevation models are fundamental to theextraction of three-dimensional glacier parametersfor inclusion in global databases (e.g., WGI,GLIMS, GlobGlacier) as well as for calculatingmass balance data, automatically delineatingglacier boundaries, modeling surface energy bal-ance and radiation fluxes, characterizing geomor-phometry, and analyzing altitudinal-dependentprocesses. A range of sensors exists that offers data

appropriate for the extraction of elevation informa-tion, but ASTER remains the most widely used datasource because of its stereoscopic capability, widespectral range, medium-to-fine spatial resolutionand, importantly, low cost. The extraction of eleva-tion information from ASTER data performs wellin areas with low relief and gently sloping topog-raphy, but errors can be large in areas with steeprock headwalls and in areas with low contrast (e.g.,fresh snow cover). A range of postprocessing toolscan be used to identify and reduce such errorsbefore any secondary analyses are undertaken.Digital elevation models from nonoptical sources

(e.g., LiDAR, InSAR) are becoming increasinglycommon and can often improve on, or be fusedwith, existing elevation datasets to enhance cryo-spheric studies. Such sources have tremendouspotential for the extraction of three-dimensionaldata over glacierized terrain in the future, and inparticular for increasing the temporal resolution ofchange detection analyses, which is currently of theorder of a decade or more. However, they mayalso bring new challenges in terms of handling datavolume (particularly in the case of LiDAR pointclouds) and in upscaling acquired information,where such detail is not required. For this reason,the development and publication of standard meth-ods (or protocols) for acquiring, processing, andrepresenting digital elevation data will becomeincreasingly important. In the short term, chal-lenges remain in identifying and quantifying alti-metric errors, particularly when comparing DEMsfrom different sources, and in simply gaining accessto reliable data for some of the most politicallysensitive regions of the world.

5.9 ACKNOWLEDGMENTS

Quincey was funded by a Research Council U.K.Fellowship; Bishop was funded by the NationalAeronautics and Space Administration under theNASA OES-02 program (Award NNG04GL84G).ASTER data courtesy of NASA/GSFC/METI/Japan Space Systems, the U.S./Japan ASTERScience Team, and the GLIMS project.

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