t52 V. Roth and B. Cyffka

System Lake" was not a complete success in the monitoring of water quality. The rea-son for this is that in order to visualize and understand the whole complexity of thelake's ecosystem. more sampling and measurement work would have had to be done.

References

CHnrsvaN, N. R. (1991): The Error Component in Spatial Data. - In: Mrcurne, D. et al. (Eds.):Geographical Information Systems: 165-114.

HrrrNi, g. (t9Sl), Geogene Grundwasserbeschaffenheit und ihre regionale Verbrcitung inder Bundesrcpublik Deutschland. - In: Roserxnrnz, D. (Hrsg.) ( 1991 ): Ergnzbares Hand-buch der MafSnahmen und Empfehlung fr Schutz, Pflege und Sanierung von Boden, Land-schaft und Grundwasse r. 6. Lieferung. - Berlin.

F.srr ( 1990): PC SEM Users Guide. - Kranzberg.WEreel-. R. & M. Hr.rren (1991): DigitalTerrain Modell ing. - ln: Mecurne, D. et al. (Eds.): Geo-

graphical Information Systems: 269 297.

Authors' address

Volker Roth and Dr. Bernd Cyllka. Institute of Geography of Gttingen University, Gold-schmidstrae 5,D-31077 Gttingen. E-mail: bcyffka@gwdg.dc

J. Schmidt and R. Dikau

Extracting geomorphometric attributesand objects from digital elevation models -semantics, methods, future needs

ZusammenfassungAbstractl . Int roduct ion2. From geomorphometric phenomena to geomorphometric objects and attributes3. Towards a theoretical framework for geomorphometric modelling . . . .4. A system fbr extraction of geomorphometric attributes and objects using GIS

4.I Pr imary geomorphometr ic parameters4.2 Ceomorphometr ic objects4.3 Representative geomorphometric parameters4.4 Geomorphometr ic objects of a h igher scale4.5 The base data: Quality of DEMs

5. Current oroblems and future needsAcknowledsement

154t541 5 5156157158t62164r6'l169170170t 7 lt7l

R. Dikau & H. Saurer (eds.), GIS for Earth Surface SystemsO 1999 Gebrder Borntraeger. D-14129 Berlin . D-70176 Stuttgart

References

t54 J. Schmidt and R. Dikau

Zusammenfassuno

Dic For lschr i t te der letztcn Jahrzehnte in den Bereichen der Daten- und Satel l i tenbi ldverar-hei tung bedeutcn eine Neuor ient ierung fr Rel iefanalyse und Geomorphometr ie. Geo-Infornrat ionssystcme (GIS) und Digi ta le Hhenmodel le (DHM) in immer hhercn Auf l-sungen bietcn neuc Mgl ichkei ten fr d ie geomorphometr ische Analyse in untcrschiedl ichenSkalcn. I ) ie Anwendung dieser Werkzeuge fr d ie numerische Klassi f iz icrung, Parametr is ic-rung und Analyse topographischer Form bedcutet aber auch neu erwachsende Probleme.Diese werden in der vor l iegendn Arbei t d iskut ier t . Die numerische Analyse von Rel ief for-men sol l te auf c iner theoret ischen Grundlage basieren, d ie d ie Geomorphometr ie b isher nurte i lweisc bietet . E, ine ' l t teor ie geomorphometr ischer Phnomene bi ldet d ie Basis fr Def in i -t ionen geomorphometr ischer Formen, Objekte und Parameter und fr quant i tat ive Methodenzur Ablei tung und Beschreibung derselben. Weiterhin kann eine solche Theor ie bei der Ein-te i lung der verschiedenen vorhandenen Techniken im Bereich der computergesttzten Geo-morphometr ie in e in grundlegendes System von Nutzen sein. Hierzu wird in der vor l iegendenArbei t e in h ierarchischer Ansatz vorgestc l l t , der geomorphometr ische Methodcn. At t r ibuteund Objekte k lassi f iz icr t . Dieses Systenr g l iedert geomorphometr ische Tcchnikcn in Metho-den zur Ablei tung ( l ) pr imrer geomorphometr ischer Parameter, (2) geomorphometr ischerObjekte, (3) reprsentat iver geomorphometr ischer Parameter und (4) hherskal iger gcomor-phometr ischer Objekte. Das Model l wurde zur Analyse der CIS ARC/INFO'- 'und GRASS imHinbl ick auf ihre Fhigkci ten im Bere ich der geomorphometr ischen Anwendungc.n einge-setzt . Die Ergebnisse zeigen. da grundlegende Probleme bei der GlS-gesttzten Ablei tungvon geomorphometr ischen Parametern und Objekten exist ieren. Die Bearbei tung komplexerRel ic f fornten unter Bercksicht igung strukturel ler ( topologischer) und hierarchischer Kom-poncn(en is t beim Einsatz hcute exist ierender GIS nur e ingeschrnkt nrgl ich. Es bestehtinsofern der Bedarf nach ( l ) e iner detai l l ier ten theoret ischen Grundlagc fr d ie Geomorpho-nrc l r ie. wie auch nach (2) der Entwicklung von of fenen, objekt-or ient icr ten und anwender-f reundl ichen Programmicrwerkzeugen fr G IS-Umeebungen.

Abstract

Recent advances in computer and remote sensing technologies have revolut ionized terra inanalvsis and geomorphometry. Geographical lnformat ion Systems (CIS) and Digi ta l Eleva-t ion Models IDEMs). wi th increasingly h igh resolut ion. of fer powerfu l means for geomorpho-metr ic analysis on di f ferent scales. In th is paper problems in numerical c lassi f icat ion. parame(-r iz .at ion and analysis of topognphic fornr arc d iscussed in re lat ionship to the developing GIS-techniques. Numerical analysis of landforms using computer melhods should be based on theo-rct icaf foundat ions. which, unt i l now have only been part ia l ly real ized in geomorphometry. ' Iheunder ly ing theory of geomorphometr ic phenomena is the basis for def in ing geomorphometr icforms, objects. parameters as wel l as der iv ing and descr ib ing them in a quant i tat ive way.Thiscan also help to organize numerous exist ing techni

r56 J. Schmidt and R. Dikau

From geomorphometric phenomena to geomorphometricobjects and attributes

There is a large variety of geomorphometric phenomena on a range of differentscales from erosion rills (micro-topography) to megaforms of whole continents (Dr-xeu 1994). The reproduction and classification of this broad range of forms is ancssential contribution to geomorphology.To support this important scientific aim, thelnternational Association of Geomorphologists (IAG) founded the working group'Global Geometric Relief Classif icat ion' (GGRC) in 1994. Hence. the described sci-entific question offers some basic systematic and methodological challenges forfuture research: Numerical parametrization and classification of landforms usingcompuler methods require a basic theoretical foundation, which has not, unti l nowbeen realized in geomorphometry. The derivation and characterization of geomor-phometric forms is based on geometrical and topological topics (see Olltrn 1977).An adequate numerical formulation of these topics has only been solved partially(Drxau 1994,1996). Furthermore, computer techniques available for landform clas-sification are limited in some aspects (see section 5).

In computer-aided geomorphometry numerous methods have been developed toquantify landform surfaces ranging from simple slope angles to the spatial arrange-ment of landform components (Prxe & Dtxe.u 1995). Numerical analysis of landformsand their components is not only a research topic in its own right but also a basis forthe better understanding of process-response systems in geomorphology (CHonlevet al. 1984). Nearly all research topics concerning environmental processes and envi-ronmental management need morphometry as a fundamental boundary condition.Ollmn (1977) noted that terrain information and classification delivers a useful toolfor land management. Moonp et al. (1988, 1,991,1993) described some geomorpho-metric parameters used in modell ing hydrological processes. saturation zones, precip-itation, soil erosion and spatial soil distribution (see Table 4 and Scutrror et al. 1998).Scsmror (1996) reviewed attributes of drainage basin morphometry used in hydro-logic modelling.

The large variety of geomorphometric methods and attributes presents the needfor a system including different techniques, parameters, and landform classificationmethods under one scheme which has to be reliable in generating geomorphometricforms, objects and parameters from a continuous landform surface. This systemshould be based on a theory of geomorphometric phenomena. From a geomorphicpoint of view, such theory must include the processes which formed the phenomena,which means geomorphogenesis (Dlxeu 1996).The large range of geomorphic agentsand processes acting on different scales in time and space leads to a'palimpsest' oflandforms, based on a'nested hierarchy of differing sensitivity and recovery' (CHon-r-Ey et al. 1984).Therefore, the proposed system has to include a hierarchical classifi-cation of geomorphometric parameters and objects (Dtxnu 1990, 1994, 1996).

GIS and DEMs - sentant ics. methods. future needs

Towards a theoretical framework for geomorphometricmodelling

Fundamental geomorphometric components are the'geomorphometric pornt ' andthe'geomorphometric object ' .

Three dimensional spatial land surfaces can be defined by measuring the surfaceheight at each coordinate. Conscqucntly, the whole land surface consists of an infi-nite number of infinitesimal geomorphometric points (which means for example xyz-tr ipels). SoursncH (1978) described the seomorphometric point as the'basic elementof geomorphometry' .

Arcal and l inear elements of the land surface can be defined as geomorphometricobjects. They contain certain amounts of geomorphometric points. Geomorphomet-ric objccts can be derived by (1) clustering surface points or (2) by combining prede-fined areas or lines.The clustering processes require geomorphological knowledge insuch a way that the objects produced have maximum internal homogeneity (e. g.meso-scale landforms) and/or show a certain geomorphometric structure (e. g. slopesegments or catchments).

The components'geomorphometric point and object' show certain spatial arrange-ments (topology), which are called geomorphometric structures (ScHrr.rror et al.1998). For example, a hi l ls lope is bui l t up out of slope segments ptaced in a certaintopology. Geomorphometric structures depend on the spatial scale and on geomor-phologic boundary condit ions (cl imate, geology, etc.).

Geomorphometric points and objects can be described by geomorphometric para-meters (in a quantitative way) or geomorphometric attributes (in a more qualitativeway).This characterization means, that the same names or similar quantities are as-signed to similar forms (see HonueNN 1971). Usually, a geomorphometric point isdescribed by indices such as height, slope, aspect, curvature, and others. Objects areoften characterized by qualitative terms, fbr example. foot slope, hillslope, ridge, sec-ond order channel or dendrit ic network.These'terms'ref lect geomorphologic know-ledge of the object considered. Some effort has been made to translate this knowledgeinto quanti tat ive rules or indices (Ancrer-ns 1995). This'geomorphologic knowledge'can include the internal geomorphometry or the internal or external topology of ageomorphometric object.Thus, possible indices for an object could involve:( I ) the internal frequency distr ibution of point attr ibutes (e. g. height, slope, curva-

ture, see above) or their spatial arrangement (geomorphometric structure),(2) the top

158 J. Schmidt and R. Dikau

Therefore, the above-mentioned definit ions and relat ions include a soatial andnested hierarchy (cuonr-ev et al. 1984), where lower scale geomorphometric objectscan be used to derive higher scale objects using their geomorphometric attr ibutes.

A system for extraction of geomorphometric attributesand objects using GIS

Based on the above theoretical framework of geomorphometric attr ibutes, objectsand their quantification, an approach classifying the existing GIS-methods was de-veloped (He Nr.rnrcH et al. to appear, ScHuror et al. to appear). I t consists of a classif i-cation of geomorphometric objects and parameters (Tble l ) and a sysrem of geo-morphometric methods (Fig. 1).This approach was used to establ ish an inventory ofGIS-tools in order to derive geomorphometric objects and parameters (Tables 2. 3,5,6) from raster-based DEMs using GIS.This col lect ion does not include al l exist ingGIS-tools, but i t can be looked at as a more or less representative cross-section of thavailable possibi l i t ies. The GIS GRASS and ARC/lNFo@ and the geomorphometricsoftware DGRM (Drrau 1989,1992) were used for this study.

The approach consists of the following (hierarchical) methods and components(see Fig. I and Table 1).

Table l. Classification of geomorphometric parameters and objects.The scheme uses the three following categories: primary geomorphome tric paramerers. geo-morphometric objects, and representative geomorphometric parameters. primary geomor-phometric paramelers can be subdivided into three types (Fig.2). Areal and linear obfects canbe distinguished (Thle -5). Ttr derivc representative parameters for geomorphometric objectsthe internal variability, the object form and the object topology can be used(Tble 6).

GIS and DEMs - semant ics. mcthods. future needs 1 5 9

4.

Fig. 1. System of methods for the extraction of geomorphometric parameters and objects.The system is based on the extraction of primary geomorphometric parameters. In a secondstep these parameters are analyzed to derive geomorphometric objects.These objects are thebasis of a hierarchical system consist ing of object analysis and object aggregation leading toreprescntative geomorphometric parametcrs and geomorphometric objccts of a higher scale.

r Methods for the extraction of primary geomorphometric parameters are offeredby standard GIS. Primary geomorphometric parameters are landform parameters,which can be different at each point of a land surface. Therefore. they are attrib-utes of a geomorphometric point. These parameters can be simple (e. g. slope an-gle), complex (e. g. f low length) or compound (e. g. ln(a/tanB)).

sst ss*ss as oS q ). lE

primary geomorphometricparameters (Figure 1)

geomorphometricobjects (Table 5)

representattve geomorphometricparameters (Table 6)

. simple primary geomor-phometric parameters(Table 2)

. complex primary geo-morphometric parameters(Table 3)

. combined primary geo-morphometric parameters(Table 4)

. areal objects

. linear objects

attributes of internal distribu-t ion of pr imary parameters orobjects

dimension parameters ofobjects

geomorphometricparameters and objects

Digital elevation model(DEM)

Analysis of primaryparameters

Geomorphometricobjects

Geomorphometricobjects of a higher scale

Representativeparameters for objects

e topology/neighbourhood

l 6 l160 J. Schmidt and R. Dikau

Table 2. Primary geomorphometric parameters: examples and GIS-tools.Standard geomorphome tric parameters are shown. which are usually included in GIS systems.Note, that a l l of these parameters are usual ly dcr ived through a f i l ter operat ion wi th in a 3 x 3-moving window.

Parameter Funct ion/module G IS/software

GIS and DEMs semant ics, methods, futurc nceds

Table 3. Complex geomorphometric parameters: examples and CIS-tools.Complex pr imary geomorphometr ic parameters have rarely been included in standard Ci lS-tools.Thc tablc shows some addi t ional parameters which can bc calculated using the geomor-phometr ic system DGRM.

Parameter Funct ion/module GIS/sof tware

Height

Slope

Aspect

Profile curvature

Contour curvature

Drainage direct ion

Real area of p ixel

r.slope.aspectNEIGRSLOPE,CURVATTJREr.slope.aspectEXPCI.]RVATUREr.resample.tpsWRVERCURVATUREr.resample.tpsWRHORCURVATUREr.watershedFLOWDIRECTIONAREA

GRASSDGRMARC/INFO@

GRASSD G R MARC/INFO@GRASSDGRMARC/INFOOGRASSDGRMARC/INFO@CRASSARC/INFO'9DGRM

r.watershedGREFLOWACCU-MULATIONNEEGRFLOWACCU-MULATIONFLOWLENGTHFLOWLENGTH

ETLFLOWLENGTHFLOWLENGTH

REWETLHOWETLHO'TLWATERSHEDHDTLWATERSHEDKWS

FLOWLENGTHFLOWLENGTH

FLOWLENGTHPTKWS

rTGWSFLOWLENGTH

GRASSDGRMARC/INFO6'

DGRMARC/INFO.'

ARC/INFO(I 'ARC/INFO@

DGRMARC/INFO@ARC/INFO*

DGRMDGRMDGRMARC/INFOOTDGRMARC/INFO@DGRMDGRMDGRMDCRMDGRMDGRMARC/INFOU'ARC/INFO@

DGRMDGRMDGRMDGRMDGRMDGRMARC/INFOO,DGRM

DGRMARC/INFO6)

Analysis of primary parameters is used to derive geomorphometric objects (e. g.subcatchments, hillslopes, mesodimensional relief-units). Analysis methods in-clude filter techniques, classification techniques and pattern recognition. Thesemethods are applied to cluster surface points to objects.Analysis of geomorphometric objects is used to derive representative geomorpho-metric object parameters. These are parameters describing the characteristics of amorphometric object, for example the object form, internal morphometric proper-t ies or the external topology.Analysis of object heterogeneity aggregates higher dimensional geomorphomctricobjects. Methods include the analysis of representative object parameters and pat-tern recognit ion of morphontetr ic objects.Methods for the derivation of primary morphometric parameters offered by most

G IS. In the above mentioned latter cases (object derivation, object analysis and objectaggregation). methods are l imited to the descript ion of the heterogeneity of morpho-metric parameters and f i l ter techniques. Analysis of geomorphometric structure (e. g.through pattern analysis) is rarely available as Gls-tools. One reason for this is a ba-sic geomorphometric problem: Exact definitions and quantifications of geomorpho-metric structures are possible only in exceptional cases (e. g. drainage net structures).

Contr ibut ing area

Average s lope of contr ibut ing areaMean and variance of primary parameters

in contr ibut ing areaLength of f lowpath to out letMean and var iance of pr imary parameters

in f lowpath to out letLength of flowpath to stream

Mean and variance of primary parametersin flowpath to stream

x-coordinate of corresponding stream pointy-coordinate of corresponding streem pointHcight of corresponding stream point

Height d istance to corresponding stream poinl

Length oi minimum f lowpath to watershcd

Relat ive s lope posi t ion af ter minimumSlope length (ETKWS)Relative slope position after maxrmunrSlope lenglh (ETGWS)

x-coordinate of watershed point after KWS-calculation REWEKWSy-coordinatc of watcrshed point af ter KWS-calculat ion HOWTKWSHeight of watershed point af ter KWS-calculat ion HOKWSHeight d istance to watershed point af ter KWS-calculat ion HDKWSLength of maximum flowpath to watershed GWS

Mean and var iance of pr imary parametersin maximum flowoath to watershed

x-coordinate of watershed point af ter GWS-calculat ion REWEGWSy-coordinate of watershed point af ter GWS-calculat ion HOWEGWSHeight of watershed point af ter GWS-calculat ion HOGWSHeight d istance to watershed point af ter GWS-calculat ion HDCWSMinimum slope length (sum of KWS and ETL) ETKWSMaximum slope length (sum of GWS and ETL) ETGWS

163l o l J. Schmidt and R. Dikau

4.1 Primarygeomorphometric parameters

In this paper primary geomorphometric parameters are defined as indices of the geo-morphometric point. As a consequence, these parameters can be dif ferent at eachpoint of a gcomorphometric surfacc. In 1972 Evr,Ns dcscribed the primary geomorpho-metric paramcters height, slope, aspect, prof i le and plane curvature, which are nowcommonly avai lable as G IS-tools. He also presented some stat ist ical measures derivedin square-matrices out of gridded DEMs, such as rel ie f , standard deviat ion, and skew-ness of heights. Current GIS also use a second class of primary geomorphometricparameters such as f low accumulation (above drainage area) or f low length, whichdescribe the local i ty of the geomorphometric point in relat ion to a geonrorphometricobject (watershed or drainage l ine). Addit ional ly, the use of physical ly based paramc-ters in process models (sce Moone et at. 1991) brings a third class of parameters intoplay, which are combinations of the two parameters mentioned abovc (Table 4).

This leads to classifying primary geomorphometric parameters into three sub-types (Fig.2 and Table I ) according to thc method of obtaining them.

Table 4. Combined geomorphometrical parameters: examples and their significance in differ-ent processes. These parameters can be easily derived by GIS using standard ovcrlay algo-r i thms. which are included in most GIS.

Combincd gcomorphometr ic parametc r Significance for geomorphic process

GIS and DEMs - semantics, methods. future needs

Simple geomorphometric parameters can be generated from a gridded DEMthrough a moving-window operation. That means the calculat ion of the parameterinvolves the nearest neighbours of a central reference point within a clear definedneighbourhood (see EvrNs 1990,Nocar' ,rr 1995).Table 2 shows some simple geomor-phometric parameters which can be easi ly derived by most GIS. Noceur (1995)described some other parameters, which can be calculated in a moving window in-cluding, for example, stat ist ical measures or the entropy of the values in the window.Complex geomorphometric parameters are derived through the analysis of thewhole matrix of a DEM. They contain structural information about the surround-ing morphometry, such as slope posit ion, slope length or drainage area (Fig.2).Table 3 illustrates some complex geomorphometric parameters calculated byGRASS. ARC/INFO@ and DGRM.Combined (or compound) geomorphometric parameters are calculated from sim-ple or complex geomorphometric parameters through an analyt ical function (e. g.In(a/tanB), see Fig.2). Table 4 shows some combined parameters used to expressthe effect of landforms in modell ing dif ferent processes (see Scuvlor et al. 1998).

*y*

ln (a/ tan p)(a/ tan p) r ' rsf t"n,,l. V.ir"4i luu,in'"""

t lps lope area/hi l ls lope length

Slope/hi l ls lope length

a . ( t a n p ) :a . t a n p

a . t a n B r r r s

Length-slope factor:const. . (a)'""" . (sin f3)'u"'r

soi l water content (e.g. Moore et a l . 1991)soi l water content (MooRr- et a l . l99l )surface runof f volume and veloci ty(Honror 1945)soi l water content (O'Lou

165164 J. Schmidt and R. Dikau

Although these parameters are widely used in geomorphometry and diversemodell ing applications (Moonr 1991), there are st i l l fundamental problems in gett ingunambiguous definit ions and standard tools for calculat ion. Ouru (1995) presentedin his work the effect of different algorithms on slope and aspect calculations. Mostof the complex morphometric parameters suffer from a lack of objective foundation:parameters containing information about hi l ls lope length or hi l ls lope posit ion need,as a boundary condition, the definition of a drainage [ine, usually through a userdefined threshold.

Thc topographic parameter ln(a/tanB) proposed by BcvrN & KInxav (1979) ex-presses the effect of topography on soi l water content and saturation zones. I t is cal-culated from the slopc angle p and the f low accumulation area a (see Fig.2).The orig-inal FORTRAN programme GRIDATB by Bevrr.r calculates the flow accumulationthrough an algorithm which allows flow partitioning from each cell in eight neigh-bouring cel ls. The calculat ions of f low accumulation in the GIS GRASS andARC/INFO@ do not allow flow partitioning (flow direction considers the downhillneighbour with the value of greatest steepness only). The geomorphometric softwareDGRM calculates flow accumulation through flow partitioning of the three steepestneighbour cel ls. We integrated DGRM and GRIDATB within the GIS GRASS tostudy the effect of the different calculation schemes on the spatial distribution andfrequency distribution of the combined parameter In(a/tanB). Flow partitioning ledto lower values of ln(a/tanp) in the frequency distr ibution and high values ofln(a/tanl3) in areas surrounding the drainage l ines (comp. QUrNN et al. 1995).

4.2 Geomorphometricobjects

A geomorphometric object is a clearly defined landform unit, for example a flowpath, a catchment, an area of a defined range of slope or aspect (a slope facet).Geomorphometric objects can be subdivided into two main subclasses, linear ob-jects and areal objects (Table l ,Table 5). They are generated through analysis ofprimary geomorphometric parameters (Fig. 1).These methods include classif icat ion,f i l ters, and structural analysis appl ied to a matrix of primary geomorphometricparameters.

The classif icat ion of primary geomorphometric parameters leads to a definit ion ofobjects with a user defined internal morphometric variabi l i ty. The classif icat ionshould be carr ied out in such a way that the result has maximum internal homogene-ity and external heterogeneity (Drxnu 1989). Classif icat ion tools are avai lable in mostGIS (see Table 5). Drxeu ( 19tt9) proposed the classification of plane and profile cur-vature to define nine form elements, marking certain slope positions in the DEM(F ig .3a) .

Fi l ter techniques could be used to definc units with certain characterist ics of land-forms. Within a moving window an analysis of primary geom

Form elementsprofile/plan curvature

I I convevconvex

lltr ",r"igttuconvexconcave/convex

I conveVstraight

fff, straishUstraightconcave/straightconvex/concave

l-l straight/concaveconcave/concave

166

Relative hillslopeposrlronr 100%

Ffl1 . 8

IK

! o"r"Slope profile form

convex

straight

concave

concave

J. Schmidt and R. Dikau GIS and DEMs semant ics. mcthods. future needs

slope str ips or catchments. Algori thms calculat ing drainage basins or f low paths arecommonly included in GIS. Other objects involving geomorphometric structure (e. g.slope profi les) are mostly derived by specif ic geomorphometric software (Prxe & Dr-xeu 1995). Addit ional ly, they often include some uncertaint ies through the incorpo-rat ion of user-defined parameters (e. g. thresholds for the calculat ion of drainagencts ) .

4.3 Representative geomorphometric parameters

The dcscript ion o[ geomorphometric objects in a quanti tat ive way leads to parame-ters representing characterist ics of a geomorphometric object. The internal geomor,phometric variabi l i ty for example has to be replaced with one or more values (e.g.rel ief or average slope).The determination of these representative geomorphometricparametcrs is termed 'object analysis' . There are three types of information whichcould be used to characterize a geomorphometric object (Tables 1,6).( I ) The internal spatiaI variabi l i ty of geomorphometric parameters or gcomorpho-

metric objects. such as slope segments in a catchment. can be described in sev-erat ways.. Stat ist ical measurcs of the frequency distr ibution of primary geomorphomet-

r ic parameters are avai lable through several CIS-tools (Tble 6).. The spatial distr ibution of primary geomorphometric parameters can be de-

scribed by autocorrelat ion indices (avai lable in ARC/INFO@) and indicesusing the structural arrangement (geomorphometric structure) of these para-meters.

o The distribution or grouping of smaller gcomorphometric units inside oneobject can bc measured by simple area percentage ratios as well as by indicesof geomorphometric structure. The devclopment of parameters describinggeomorphometric structures is a basic problem in geomorphometry.

(2) Dimension parameters of an object such as area, perimeter, length, etc. can beeasi ly derived using standard GlS-tools (Tble 6). ScHrrlror (1996) calculatedsonre form parameters (e.g. circulari ty rat io) for catchments using GIS-tech-niques.

Fig.3. Der iv ing geomorphometr ic objects of a h igher scale.Form elements were aggregated to objects of a higher scale, in this case hillslope types:The oc-currence of form elements'profile-straight/plane-straight' in the midslope were used to classifyhillslope profiles in the types convex-straight-concave and convex-concave. The calculationswere carr ied out using the GIS GRASS and the geomorphometr ic sof tware DGRM. Theresul ts show the arrangement of d i f ferent h i l ls lope types wi th in the catchment.

167

169t6{J J. Schmidt and R. Dikau

Table 6. Representative geomorphometric parameters: examples and GIS-tools.Representativc parameters for geomorphometric objecls can describe the internal variabilityof pr imary geomorphometr ic paramelers, the object d imensions or the object topology.

Representat ive parameter Function/module GIS/software

Variability of primary geomorphomelric parameters

GIS and DE,Ms - semantics. methods. future needs

(3) Topological and neighbourhood relations of geomorphometric objecrs (Tables1,6) offer important information for the description oI geomorphometric struc-ture and for deriving geomorphometric objects of a higher scale (see below).Drxeu (1989) used a specific computer routine to gather neighbourhood infor-mation for geomorphometric objects and used a statistical package to analyzethem. However, topological methods have, unti l now rarely been included inGIS-packages.

It has become apparent that basic problems concerning the quantification of geo-morphometric structures exist.These include problcms concerning the definit ion ofgeomorphometric objects as wcll as the derivation of representative geomorphomet-ric oarameters.

4.4 Geomorphometric obtects of a higher scale

The model presented includes a hierarchical structure through the derivation of geo-morphometric objects of higher scales based on 'object aggregation', which is the pro-cess of combining lower scale objects to higher scale objects according to certain rules(Fig.1). The aggregation step is carried out through the analysis of parameters de-scribing characteristics of geomorphometric objects of lower scales (representativegeomorphometric parameters). Representative geomorphometric parameters candescribe topology, internal variability of geomorphometric parameters, and the out-line form of the lower scale object as specified in the previous section. Therefore,the process of object aggregation can include these three types of information. Com-bining stream segments to a stream network is a process of aggregating objects to thatof a higher scale.The derivation of meso-scale landform types by associat ing drain-age basins of certain relief classes is another example of object aggregation. In thefirst case, aggregation is based on topological information, the latter approach usesinternal characterist ics.

Aggregation of hi l ls lopes (Fig.3) requires both primary geomorphometric para-meters and topological information. For this study, form elements and hillslope pro-files calculated in a small catchment (Fig.3a) were used to aggregate two differenthi l ls lope types. The hi l ls lope posit ion (Fig.3b) of form elements which are straight inplane and profile and the relationship to the downslope and upslope form elementswere used to aggregate elements to hillslopes with a convex-concave and a convex-straight-concave profile (Fig.3c). The calculations were carried out using the GISGRASS and DGRM.

Aggregated objects can serve to determine representative parameters and anotheraggregation step can generate geomorphometric objects of the next higher scale. Ingeneral, object aggregation is carried out mainly through the determination of geo-morphometric structure and taxonometric methods and involves geomorphometricknowledge. Therefore, open, object-oriented programming tools are needed. Avail-able GlS-tools allow such approaches in crude ways only.

Stat is t ical measures: averagei var iance, skew-ness. kurtosis, moments, frequency dislribution

Areal portion o[ form elements or landformunits in objectsLength of linear slructures in objectsParameters of theoretical function fittedto frequency distribution

Measures of spat ia l concentrat ion.autocorrelations indizes

r.statistics*ZONALSTATSr.stats

r. lenglh.sh+r.fitmap.sh+

GEARY. MORAN

GRASSARC/INFO@GRASS

CRASSGRASS

ARC/INFO@

Dimension of a object: parameter for areal objects

Area

Perimeter

Maximum thickness

Centroid

r.statistics*, r.statsZONALAREAZONALPERIMETERZONALTHICKNESSZONALCENTROIDr.volume

GRASSARC/INFO@ARC/INFO.D

ARC/INFO@ARC/INFO@GRASS

Dimension of a object: parameter for linear objects

Length r. len.sh*, r . length.shxPATHDISTANCE

GRASSARC/INFO@

Dimension of a object: form parameters

Circularity index and other form factors(they can be mostly derived using otherparameters, l ikc d imension parameters)

r.mapcalc CRASSZONALAREA, ARC/INFO(9ZONALPERIMETER

Topology/neighboorhood attributes

Parameter of neighbor objects, lengthof object border, number of neighborsHydrologic input- and output objects

Hydrologic/morphometric order

r.aggreg*

r.tribs (Test-version)r.watershedS'IRAHLER, SHREVE

GRASS

GRASSGRASSARC/INFOC)

* developments o[ our team (not standard CIS-tools) .

171170 J. Schmidt and R. Dikau

4.5 The base data: Quality of DEMs

Even though the resolut ion of DEMs has been improved over thc last twcnty years,there are st i l l problems concerning the data qual i ty. Present resolut ion of raster-based DEMs range from 50 m to l0 m (in rare cases lower) in pixel width (Rrcranos1990, EvnNs 1990). In the past. digital elevation models were derived mainly fromtopographic maps, interpolation algorithms or from field survey. Nowadays, remotesensing techniques havc become very popular (RrcHenos 1990). However, eachmethod includes specific sources of errors. The production of DEMs by analyticalstereoplotters from aerial photographs results in specific linear structures in theDEM.The derivation of DEMs from digit ized contour l ines leads to systematic errorsin underestimating the r idges and overestimating thc val ley heights (tendency toreduce rel ief) through the interpolat ion algori thms. For some f ield areas in Germa-ny, we compared a 30 m DEM derived through interpolat ion from digit ized contourl ines with high quali ty 10m112.5 m DEMs.The results prove thar local deviat ionscould reach + 20 m of height. The average deviat i

173172 J. Schmidt and R. Dikau

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