(2006) 79–89www.elsevier.com/locate/geomorph

Geomorphology 77

Optimisation of relief classification for different levelsof generalisation

H.I. Reuter a,⁎, O. Wendroth b, K.C. Kersebaum c

a Institute for Soil Landscape Research, Centre for Agricultural Landscape Research, Muencheberg,Eberswalder Str. 84, D-15374 Muencheberg, Germany

b University of Kentucky, Department of Plant and Soil Sciences, N-122M Agri. Sci-North, Lexington, KY 40546-0098, USAc Institute for Landscape Systems Analysis, Centre for Agricultural Landscape Research, Muencheberg,

Eberswalder Str. 84, 15374 Muencheberg, Germany

Received 22 November 2004; received in revised form 2 December 2005; accepted 3 January 2006Available online 8 February 2006

Abstract

Relief plays an important role in the spatial and temporal distribution of soil water and matter transport processes. Eachlandscape can be segmented into different landform elements based on a digital elevation model. These landforms containcharacteristic properties in terms of energy and material balance. Several algorithms are available to classify landscapes at differentscales. However, lack of knowledge exists concerning the applicability of relief parameters for landscape stratification for differentgeneralisation levels of underlying data. The objective of this study was to develop a method for agricultural landscapes to classifylandform elements across a series of elevation datasets with different spatial resolutions. A non-linear parameter optimisationalgorithm was coupled with a relief classification scheme to optimize four classification parameters with regard to environmentallysensitive landforms: shoulder and footslope. Input datasets were based on a LIDAR scan and topographic maps. The magnitude ofthe optimized relief parameters decreased with decreasing map scale from 1:10,000 to 1 :100,000 or increasing contour lineinterval. The main conclusion is that if one set of classification rules for a specific landscape was determined for a high-resolutiondataset at a small subset, it could be applied for larger areas even if only coarser digital elevation model information were available.© 2006 Elsevier B.V. All rights reserved.

Keywords: Landform classification; Nonlinear optimisation; Scaling; Map generalisation; Contour lines

1. Introduction

The characteristics of environmentally and ecologi-cally sensitive landforms cannot be identified withsatisfactory accuracy if only generalized input data

⁎ Corresponding author. Current address: Institute for Environmentand Sustainability-Land management and Natural Hazards Unit,European Commission-DG Joint Research Centre, TP 280, ViaFermi 1, I-21020 Ispra (VA), Italy. Tel.: +39 0332 78 5535; fax: +390332 78 6394.

E-mail address: hannes.reuter@jrc.it (H.I. Reuter).

0169-555X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.geomorph.2006.01.001

sources—like contour lines—are used for digitalelevation model (DEM) generation, relief parameterextraction and subsequent landform classification.Nevertheless, information from high-resolution spatialdatasets is not always available. Relief propertiesdetermine ecologically important transport and storageprocesses at relatively small scales (Pennock et al.,1987). Even if the relevant properties and relations canbe identified successfully at small scales, the questionremains, how to conserve information about landformclassification obtained from high resolution data in

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cases when only coarse resolution datasets exist. Inother words, each of the landforms shown in Fig. 1 (e.g.shoulder, backslope, footslope, level) that exhibitcharacteristic physical, chemical, and biological pro-cesses and parameters (Dehn et al., 2001) should beidentifiable even from coarser resolution datasets.

Milne (1936) was one of the first to recognize thecatena principle of soil formation in a hilly terrain(Ruhe, 1960). Several authors followed his concept(Ruhe, 1956; Conacher and Dalrymple, 1977), which isprobably the basis for all present landform classificationsystems. Hugget (1975) presented a soil landscapesystem (not only a landform system), which overcamethe two-dimensional character of the catena principleand simulated the behaviour of a three dimensionalsystem. Based on that, Willgose et al. (1991) recentlydeveloped their SIBERIA model to understand theevolution of landforms over geomorphologic timescales.

Before the introduction of DEMs, landforms weredelineated manually using field surveys or by interpret-ing stereo aerial photographs. McBratney et al. (1992)showed that surveyors usually delineated a complexlandscape according to their personal bias. On anotherscale, Burrough et al. (2000) concluded that a global setof rules found at a national or international level did notprovide a satisfying stratification at the local level.Furthermore, Burrough et al. (2000) explained thatresearchers became frustrated by computational issuesassociated with the size of the datasets and the fact thatlandform classification algorithms often delineate dis-crete classes instead of overlapping property sets.

Fig. 1. Different landform elements and their preferred water movement and cvertical infiltration, empty arrows through flow of water, and dotted arrow s

MacMillan et al. (2000) described three main require-ments for an automated landform classification algo-rithm that would use a DEM in order to identify differenttypes of landscapes: (I) Selecting and computing anappropriate suite of terrain attributes derived from DEMdata; (II) identifying an appropriate number of mean-ingful different landform classes and describing theirsalient or defining characteristics; and (III) selecting andapplying a classification procedure capable of using theavailable terrain derivatives to produce the requiredclasses.

Pennock et al. (1987) used data published by Young(1972) to classify nine three-dimensional landformelements. A limitation in this study was the exclusionof planar landforms in the classification process,probably because these landforms did not appear inthe hummocky landscape being studied. A secondlimitation was caused by the given parameter set of thisclassification being valid for only a DEM cell size of 10m by 10 m. From another approach Park et al. (2001)concluded that the values of their four classificationcriteria were rather arbitrary and needed several trials toachieve a reasonable approximation for their fivelandforms.

DEMs provided by different data sources maycontain certain errors for different reasons—in mapsdue to cartographic errors or generalisation, or in a laserscan DEM due to positioning errors or false valuescaused by backscattering (Huising and Gomes Pereira,1998). During landform classification, errors due torelief parameters such as profile curvature, which isbased on the second derivative of the elevation, become

oncentrations adapted from Pennock et al. (1987). Solid arrows denoteurface runoff of water and sediments.

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accentuated as they are calculated based on the squareddifference of neighbouring points.

Differences between the magnitudes of topographicparameters caused by increasing spatial resolution ofdatasets were specified by different authors (Wilson etal., 1998; Wolock and McCabe, 2000; Thompson etal., 2001). However, any quantification of changes innumber or extent of landform elements with increasinggeneralisation within the datasets was missing.Moreover, although information about errors inDEMs and their influence on the computations ofsecondary and primary relief attributes was available(Holmes et al., 2000), it remained unspecified forlandform classifications.

The objective of this study was to develop anapproach to classify landform elements across a series ofelevation datasets obtained at different spatial resolu-tions. One aim of the approach was to quantify thesmoothing effect of contour datasets of different qualityon the spatial distribution of landform elements. Thesecond aim was to develop an unbiased methodology tooptimize topographic parameters for landform classifi-cation procedures for different data resolutions whileconserving information obtained from high-resolutiondatasets. In this study, we focussed on one defined cellsize to specify spatial and ordinal distribution in theoptimisation of landform classification by using diffe-rent generalized datasets only.

2. Methods

2.1. Input data

Two different sources of DEM were obtained for theinvestigated area in Luettewitz (Saxony), Germany(coordinates of the lower left corner 51.099N,13.166E; upper right corner 51.199N, 13.333E). Thefirst dataset consisted of an airborne laser-scan (LS, alsoknown as LIDAR) DEMwith a spatial resolution of 1 by1 m and a vertical accuracy better than 0.15 m for anarea of 2,000,000 m2. For computational purposes LS-DEM data were resampled to a coarser resolution of 10by 10 m, named LS10.

Topographic map sheets (TK) were used as thesecond data source. DEMs were digitized manuallyfrom contour lines and break lines from 1:10.000(TK10, contour interval 2.5 m), 1 : 25.000 (TK25,contour interval 5 m), and 1 :100.000 (TK100, contourinterval 20 m) map sources. The accuracy of TK-contour lines is known to be better than 80 cm comparedagainst static DGPS measurements (Grenzdörfer andGebbers, 2001). Raster DEMs with a resolution of 10 m

were created using the Topogrid submodule of ArcInfo(ESRI, 2000). Topogrid is an adaptation of theANUDEM procedure (Hutchinson, 1989), which cre-ates hydrologically correct DEM using a multi-resolu-tion iterative finite difference interpolation method.

In this study, the LIDAR-based DEMs were surfaceelevation models, including trees and buildings. Con-tour based DEMs represent only base surface elevationdata. Therefore, DEMs were only generated foragricultural areas because villages and forested areasshowed large differences in topographic parametersbetween TK data and LS data.

Additionally, DEMs were artificially generated basedon contour lines derived from the LIDAR dataset with a2.5 m interval. Contour lines were selected based ondifferent contour line intervals (2.5, 5, 10 and 20 m) andDEMs were generated with a resolution of 10 m usingthe Topogrid procedure. No line simplification of thecontour line was performed in terms of generalisation,which would usually be observed in the case of a mapsheet dataset. The DEMs were named ATK10, ATK25,ATK50 and ATK100, respectively. Uniformity of theDEMs was tested using a fractal estimation algorithmavailable in SAGA 1.2 (Conrad and Ringeler, 2005).

2.2. Topographic and landform analysis

Topographic attributes were computed using ArcInfo8.1 functionality (ESRI, 2000). Slope gradient wascomputed using the D8-algorithm (Burrough, 1986).Curvature parameters were based on the algorithms ofZeverbergen and Thorne (1987) and flow accumulationon algorithms by Tarboton et al. (1991). A method ofPennock et al. (1987, 1994) was implemented for theautomatic classification of landforms based on a DEM(Reuter, 2003a,b). The relief parameters slope, profilecurvature, planform curvature and the upstream flowarea were used to create a classification of elevendifferent landforms as shown in Table 1. Landformsboth with and without planar landform elements wereclassified for a selected field site of 200,000 m2. For theshoulder landform, 16 positions were classified asconvex and two as divergent, compared to a distributionof two for convergent shoulder (CSH) and 15 for planarshoulder (PSH) positions for the extended (includingplanar) classification (see Fig. 2 for an extendedclassification). Such patterns are more consistent withthe observed landscape structure at that field site.Therefore, in addition to the original classification byPennock et al. (1987), planar landform elements using acriterion of ±0.116 1/100 m of profile curvature (Young,1972) were classified. The criterion of ±0.1 1/100 m

Table 1Classification of landform elements (after Pennock et al., 1994, extended)

Landform elements Abbrev. Slope°

Profile curvature1/100 m

Plan curvature1/100 m

Upstream flowaccumulation m2

Divergent SHoulder DSH N0 N0.1 N0.1 NAPlanar SHoulder PSH N0 N0.1 ≤0.1 ≥−0.1 NAConvergent SHoulder CSH N0 N0.1 b−0.1 NADivergent BackSlope DBS N3.0 ≥−0.1 ≤0.1 N0.1 NAPlanar BackSlope PBS N3.0 ≥−0.1 ≤0.1 ≤0.1 ≥−0.1 NAConvergent BackSlope CBS N3.0 ≥−0.1 ≤0.1 b−0.1 NADivergent FootSlope DFS N0 b−0.1 N0.1 NAPlanar FootSlope PFS N0 b−0.1 ≤0.1 ≥−0.1 NAConvergent FootSlope CFS N0 b−0.1 b−0.1 NALow Catchment Level LCL ≤3.0 ≥−0.1 ≤0.1 NA b500High Catchement Level HCL ≤3.0 ≥−0.1 ≤0.1 NA N500

NA = not applicable.

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profile curvature was taken as granted for a DEMresolution of 10 by 10 m.

As explained, several types of errors can generally befound in DEMs. As a result, “misclassified” areas canappear in the mapped landform distribution. “Misclas-sified” pixels represent either (I) true micro-topographiclandform elements that differ strongly from theirsurrounding positions, or (II) “misclassified” landformsdue to errors in the DEM. Both errors increase thedifficulties in understanding landform relationships

Fig. 2. Landform classification for the field site showing detailed landform claDFS do not occur). View to the south.

connected to soil development and other processes.Therefore, such “misclassified” areas should be mini-mized by applying filtering procedures. The originalDEM can be filtered before relief analysis, or after therelief parameters are computed. In this work, we applieda threshold-area-based filtering after computing thelandform classification.

First, a preliminary landform classification wasperformed. Secondly, areas of similar relief positionswere aggregated in a clustering procedure. If a cluster

ssification with eleven possible landforms (notice that the CSH and the

Table 2Statistical parameters for the relief parameters slope, profile curvature,planform curvature and flow accumulation of generated 10 mresolution DEM

Slope°

Profilecurvature1/100 m

Planformcurvature1/100 m

Flowaccumulationm2

LS10Median 2.71 0.01 0.01 9.17Minimum 0.50 −0.19 −0.46 0.11Maximum 5.96 0.32 0.14 469.00

TK10Median 2.67 0.00 0.01 13.24Minimum 0.53 −0.29 −0.36 0.50Maximum 4.66 0.26 0.17 565.00

TK25Median 2.63 0.00 0.01 14.50Minimum 0.89 −0.17 −0.20 0.50Maximum 7.30 0.22 0.08 453.67

TK100Median 2.14 −0.01 0.01 9.00Minimum 0.09 −0.08 −0.05 0.50Maximum 4.54 0.02 0.05 92.50

Input data were derived from the datasets Laserscan (LS10), TK1:10,000 (TK10); TK 1:25,000 (TK25) and TK 1:100,000 (TK100).

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did not meet a user defined area threshold, twoadditional steps were initiated. If one of the cellsadjacent to another one met the minimum sizecriterion (here 5 cells), the value of that cell wasused for the respective cell. Multiple iterations of thatstep were performed until no further reclassificationwas necessary. However, if all four adjacent cells metthat criterion, the modal class of the eight cellssurrounding it was assigned to the respective cell. Inthe case of two different classes having the sameweight to be assigned to one cell, the window size forthe determination of the modal class was increasediteratively. Two differences existed between theoriginal work by Pennock et al. (1994) and thelandform classification used in our work. First, in thefiltering procedure, the detailed classified landforms(LFs), including planar landforms, were consideredinstead of the major landform positions (shoulder,backslope, footslope, level). Secondly, the areafiltering algorithm was based on a threshold area incombination with multiple iterations with increasingwindow sizes. For a more in-depth discussion, seeReuter (2004).

2.3. Nonlinear parameter optimisation

The parameter optimisation routine PEST (Doherty,2002) was applied to estimate the following topographicattributes: slope gradient, profile curvature, planformcurvature and area filtering threshold for landformclassification. PEST uses a Gauss–Marquardt–Leven-berg algorithm to find a global objective minimumfunction (Doherty, 2002). In our study, it was applied toadjust the landform classification model parameters byminimizing the weighted sum of squared differencesbetween the computed number of landform elements fora selected area and the corresponding defined ormeasured landform element numbers.

At the beginning of each optimisation run, therelationship between model-generated observations andmodel parameters was linearised by describing it as aTaylor equation using the current best parameters. Thederivatives of all observations with respect to alloptimisation parameters were computed and then solvedfor a better parameter set. At every step PEST predicts ifanother optimisation iteration needs to be performed bycomparing parameter changes and objective functionimprovement achieved through the current iteration withthose achieved in previous iterations.

The ranges for profile curvature and planformcurvatures were allowed to vary between 0.001 1/100 mand 0.4 1/100 m and for slope gradient between 0.001°

and 5°. The area filtering threshold value was allowedto vary between 1 and 8. The boundary optimisationvalues for the TK25 dataset had to be set to a lowerboundary of 0.5° for the slope gradient and an upperboundary for the area filter threshold of 5 due tootherwise unreasonable optimisation results. The lowerand upper boundaries of the optimizing parameterspace were chosen not to extend beyond the theory onwhich the landform classification is based. For eachoptimisation we checked carefully if the optimizedrelief parameters attained the limited parameter space.If such an event occurred, the upper and lowerboundaries were adjusted and the optimisation wasperformed again to ensure that the preset boundariesdid not influence the optimisation results (e.g. givenlimits were compared with optimized parameters givenin Table 4).

Optimisation was limited by searching for a globalobjective minimum function only for the divergentshoulder, planar shoulder, planar footslope and conver-gent footslope landforms from the different DEMs forthe agricultural area. These landforms were chosenbecause they represented locations of environmental andecological importance (Brubaker et al., 1993; Reuter etal., 2005).

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3. Results and discussion

3.1. Generalisation in topographic analysis andlandform analysis

Generalisation of elevation contour data generallyleads to a smoothing of the small-scale heterogeneity ofthe landscape. The resulting statistical properties for thedatasets TK10, TK25, TK100 and a DEM generatedfrom the contour lines of the LS (Table 2) reflected thedecrease in the variability in elevation due to general-isation of the underlying elevation dataset (Fig. 3). Thestatistical parameters for the relief parameters wereimportant for the landform classification later on.

With an increasing spatial generalisation of the datasets, the median slope gradient and maximum slopegradient decreased in a manner similar to the results ofWolock and McCabe (2000) (with the exception ofTK25). This is especially important as the slope gradient

Fig. 3. DEMs generated for the area of the LIDAR DEM (A) based on the con1 :100,000 (D).

is used to separate backslope landforms (LF). In general,curvature decreased and flow accumulation increased(Thieken et al., 1999). This agrees with Gallant andHutchinson (1997) who showed that with increasingspacing of elevation samples, fine scale features werelost and the surfaces became more generalized.

Landform was analysed based on different inputdatasets for a selected field site as an example for theLIDAR data area (Fig. 2). It can be concluded that amore generalized image was produced with increasingcontour line interval (see Table 3). A decreasingnumber of landforms were classified with decreasingresolution (TK10NTK25NTK100). The loss of detailbecame especially obvious for the small scaletopographic features in our landscape, such asdivergent shoulder and convergent footslope, as canbe seen in the high resolution data sets (LS10, TK10)in Table 3. Detailed information about specific land-forms was lost with increasing generalisation. For

tourlines of the mapsheets TK 1:10,000 (B), TK 1:25,000 (C), and TK

Table 3Number of classified landform (LF) units for a 10 m digital elevationmodel (DEM) for the datasets Laserscan (LS10), TK 1:10,000(TK10); TK 1:25,000 (TK25) and TK 1:100,000 (TK100) for the200,000 m2 field site “Bei Lotte”

DEM/LF DSH PSH DBS PBS CBS PFS CFS LCL HCL

LS10 1 15 4 42 3 8 9 47 63TK10 6 8 56 11 3 51 57TK25 2 54 5 10 1 42 78TK100 30 79 83

Classification parameters were 0.1 for planform and profile curvature,3.0 for slope, the area threshold was set to 5 and the LEVEL conditionwas set to 500 m2.

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example, a loss of 62.5% of all cells classified asshoulder position between the LS10 and the TK10 and87.5% from LS10 to TK25 was observed. A similarbehaviour was found for footslope positions, wherelosses occurred in both the TK10 (18%) and the TK25(35%) as compared to the LS10 dataset. Both of theseLF positions characterize specific positions in anygiven landscape with specific properties (e.g. soil andplant development, erosion processes). The “lost” LFareas were mainly classified as either backslope orlevel areas. The backslope positions increased by 31%in the TK10 and 42% in the TK25 analyses, whencompared to the LS10 dataset, whereas a reduction of39% was found for TK100. The total number of LevelLFs for LS10 and TK10 reached similar values. Thenumber of LCL cells remained lower for the LS10dataset. The TK25 and TK100 datasets showed anincrease of 10% and 52% for LEVEL areas comparedto the LS10 dataset.

Fig. 4. Uniformity test using fractal analysis for the defined

These “losses” in landforms highlight the importanceof using high resolution datasets for landform classifi-cation. Any other attempt, including the one describedbelow, can only partially overcome the problem.

3.2. Optimisation of parameters for relief classification

In the previous section the disappearance of certainLF elements was discussed for cases where classifica-tion parameters remained stable over different qualitydatasets with the same resolution. To overcome thedisappearance or shift of individual LF elementsbetween classes, parameters in the landform classifica-tion process such as profile curvature or DEM resolutionneed to be optimized. Before applying such landformparameter optimisation, the user should check if theuniformity of the elevation surfaces generated fromdifferent datasets is comparable. This means, that anyoptimisation will lead to questionable results if thedetailed features of a landscape are not recognized in acoarse resolution dataset. The results of fractal analysisshould indicate whether the surfaces of the generatedDEMs were similar. Results showed slight differencesbetween different resolutions for this case study (Fig. 4).

The parameters planform and profile curvature, slopegradient and threshold value were nonlinearly opti-mized. DEM resolution was not varied, even if theoptimal grid size for terrain representation was not met(Weibel and DeLotto, 1988). The optimisation results(Table 4) were based solely on the number of grid cellsof certain LF units observed for the agricultural area ofthe LS-DEM under defined LF classification conditions.

(LS10) and the optimised input DEM dataset (TK25).

Table 4Defined and optimised parameters for the landform (LF) classification algorithm for a 10 m digital elevation model (DEM) for the datasets Laserscan(LS), TK 1:10,000 (TK10); TK 1:25,000 (TK25) and TK 1:100,000 (TK100) for the agricultural area in the Luettewitz region (approximately2,000,000 m2)

Type LS (defined) TK10 (optimised) TK25 (optimised) TK100 (optimised)

Profile curvature (1/100 m) 0.1 0.09 0.07 0.03Planform curvature (1/100 m) 0.1 0.16 0.13 0.04Slope (°) 3 2.20 2.58 0.60Area filter threshold 5 2.53 5 1.55Number of cells per LFDSH 917 744 804 929PSH 1572 1359 1368 1345PFS 870 1126 1166 1240CFS 804 986 954 946SSQR 1.7396E+05 1.6015E+05 2.0874E+05CC 0.74 0.77 0.73

The sum of squared weighted residuals (SSQR) and the correlation coefficient (CC) as computed by PEST between the defined and the optimiseddataset.

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These results were compared against the number of gridcells of certain LF units by varying LF classificationconditions. The number of LF units within theagricultural area of the LS-DEM was determined fordivergent shoulder, planar shoulder, planar footslopeand convergent footslope.

Results given in Table 4 are examples of theclassification parameters in regard to the generalisationof input data sources. The optimized planform curvaturedecreased linearly with respect to contour line intervalfrom TK10NTK25NTK100 (Table 4). Optimizedprofile curvature always showed smaller values thandefined for the classification based on the LS10. Incontrast to the optimised profile curvature, the opti-mized planform curvature showed slightly larger valuesfor the TK10 and the TK25 dataset compared to thevalue used for the defined LS10 classification. Never-theless, a linear decrease can be observed with respect tothe contour line interval. The parameter slope and the

Table 5Defined and optimised parameters for the landform (LF) classification for 1

Type LS (defined) ATK10 (optimised)

Profile curvature (1/100 m) 0.1 0.07Planform curvature (1/100 m) 0.1 0.11Slope (°) 3 3.41Number of cells per LFDSH 917 922PSH 1572 1414PFS 870 1257CFS 804 1037SSQR 2.29E+05CC 0.74

Contour intervals were 2.5 m (ATK10), 5 m (ATK25), 10 m (ATK50) and 50correlation coefficient (CC) as computed by PEST between the defined and

threshold value show a decrease with the datasetsLS10NTK10NTK100, with the exception of the TK25dataset which exceeds values optimised for the TK10dataset.

To evaluate and quantify errors of DEM generationfrom contour lines of map sheets of different scales, anartificial multi-scale DEM dataset generated from theLIDAR data was tested on the optimisation procedurefor landform classification. Using such a dataset, wecould even make assumptions about optimizinglandform classification parameters for the non-existingdataset of a TK 1:50.000 (ATK50). The results (Table5) show similar decreases in profile curvature,planform curvature and slope as provided for theoriginal datasets in Table 4. However, profile andplanform curvature values start with lower values of theoptimized parameters for the more detailed datasets,whereas for the ATK100 dataset these values showhigher values. A linear decrease for profile curvature

0 m digital elevation model (DEM) derived from a Laserscan

ATK25 (optimised) ATK50 (optimised) ATK100 (optimised)

0.06 0.04 0.040.09 0.06 0.052.39 2.92 2.87

787 842 9651334 1369 12381149 1105 1218960 937 7971.76E+05 1.20E+05 2.35E+050.74 0.85 0.62

m (ATK100). The sum of squared weighted residuals (SSQR) and thethe optimised dataset.

Fig. 5. Example of optimised landform classification parameters applied to a DEM with a resolution of 10×10 m based on the contourlines of atopographic map sheet 1 :25,000. (A) Subsets for optimised (B) and non-optimised landform classification (C).

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and planform curvature could be observed up to acontour line interval of 10 m (ATK50). Such responsecould not be observed for the TK datasets due to themissing TK50 map sheet. The difference between theoptimized landform classification parameter of thedataset ATK50 and ATK100 was almost negligible(Table 5).

The optimized slope values of the ATK datasetstarted with higher values than the observed optimizedvalues for the TK dataset and decreased with decreasingdetail of the DEM (Table 5). Even more interesting,these values were actually higher than the initiallydefined values from the LS-DEM. Another aspect to benoted with slope, is the only slight decrease of the slopeproperty with the ATK datasets, from 3.41 for ATK10 to2.87 for ATK100 (Table 5). For the TK datasets, thedecrease in slope is from 2.2 for the TK10 dataset to 0.6for the TK100 dataset. These differences are related tothe generalisation of the contour line dataset generated

Table 6Differences in number of landform elements for a landform classification ba−column labeled “TK25(optimised)”) versus TK25 classification parameters

Param./LF DSH PSH CFS DBS PBS

Optimised 40,140 231,138 10,514 24,381 406,52Non-optimised 38,575 106,853 7025 56,185 423,13Percentage difference 96 46 67 230 10

from the topographic map sheets in contrast to theartificial dataset, which contained a generalisation onlyin height interval.

3.3. Application case study

The optimized landform classification parameterswere applied for a whole map sheet of the TK25.Optimized and non-optimized classification parameterswere used to classify a DEM with 10 m resolution of thearea of a map sheet of a TK25 (Fig. 5). The difference innumbers of landforms, which had been quantified at the200,000 m2 field site ‘Bei Lotte’ (Table 3), can beconfirmed at a much larger area (Table 6). A decrease innumbers of shoulder and footslope positions can be seenfrom Table 6, whereas the number of backslope andlevel landforms increased. Notice the enhanced differ-entiation of landform elements in the optimizedlandform classification in the subset of Fig. 5B,

sed on TK25 data using optimised classification parameters (Table 4defined for the LS (see Table 4-column labels “LS(defined)”)

CBS CFS PFS CFS LCL HCL

3 30,253 10,114 198,827 50,925 175,756 161,6435 55,897 9583 113,765 45,572 243,780 239,8444 185 95 57 90 139 148

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compared to the results based on the classification usingthe original values in Fig. 5C.

It should be noted that the optimisation techniquewas focused on the optimisation of the number of cellsonly. Further work needs to include the spatial locationof the classified LF, not only the pure statisticaldistribution. Additionally the optimisation procedurecould also use the occurrence of certain soil types andsoil properties at specific landforms.

4. Conclusion

The loss in precision or loss in detail for landformclassification were specified by using combined topo-graphic and landform analysis and several digitalelevation datasets. The landform elements of shoulderand footslope were shifted to the backslope and levellandforms with increasing generalisation scale byholding classification parameters constant. Differencesin number of relief elements between two map scaleswere as large as 62% between datasets based on aLIDAR Scan and the contour lines of map sheets of thescale 1 :10.000.

An objective non-linear optimisation routine wasapplied to overcome these limitations. The classificationparameters for landform elements were optimized for arange of contour line datasets for a given site in Saxony,Germany. It was shown that this optimisation techniquecould be executed at a small subset of the landscape andthen be applied to larger areas where only generalizedDEM information was available. In this study wefocused on a constant grid size of 10 m in all DEMgeneration procedures from different data sources.Further investigations will aim to investigate how theclassification parameters perform: (I) when differentDEM resolutions are used in comparison to results fromthe baseline LIDAR data; (II) when different DEMresolutions are used in comparison to results fromdifferent base line data; and (III) how optimisationresults differ between different landscapes.

The optimisation procedure is not limited to theimplemented relief classification as shown in this casestudy. It can also be applied to other landformclassification methods (see MacMillan and Pettapiece,1997; MacMillan et al., 2000; Park et al., 2001) as longthe classification parameters can be accessed.

Acknowledgements

Support of this study by German Research Founda-tion (DFG, Bonn, WE 1805/5-1, EH 170/2-1), Sued-zucker, Agrocom, andAmazonen-Werke is acknowledged.

The authors gratefully acknowledge helpful commentsof James Thompson given on an earlier version of thismanuscript.

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