Improving Relief Classification with Contextual ... - Semantic Scholar
Improving Relief Classification with Contextual Merging Bård Romstad Department of Physical Geography, University of Oslo P.O. Box 1042 Blindern, N-0316 OSLO, Norway [email protected]
Abstract. Automatic classification of relief attributes into meaningful morphological units has a great potential within the field of geomorphology. When applying common classification algorithms such an iterative cluster analysis to relief data, the result is often a set of classes with a marked lack of coherence in geographical space. The scattering of classes occurs because there is an authentic overlap between different classes in both attribute and geographical space. Therefore other procedures should be used for relief structuring that take the class overlap into account. Such a procedure could be the application of a contextual merging, or generalisation, prior to classification. As a case study, an area close to Ny-Ålesund, Spitsbergen, is classified using this procedure, and it is shown that in this specific relief the coherence and interpretability of the result is increased compared to a simple cluster analysis alone.
1 Introduction Generalisation of data into a smaller number of classes, relevant to a certain application, is a task we perform every day without giving it much consideration. In geomorphology such generalisations include the classification of a continuous surface into units, or landforms, such as a valley, hill or cliff. These are terms that make sense to most people as spatial units with a certain shape, extent and topography, but can usually also be defined as a domain within which a specific physical surface-process is dominant. Hence the quantification of such units is useful not only as an objective description of a landscape, but also as a component in spatial modelling of geomorphological processes. Topographic parameters, derived from digital elevation models, can give us valuable information on the characteristics of a certain surface element. However, the spatial aspect, which is essential in a geomorphological context, is often neglected in the statistical algorithms most commonly used to classify large sets of multivariate data. The aim of this paper is to illustrate how contextual merging, an algorithm for generalisation of continuous data into spatial units, can be used to improve classification based on topographic parameters. Since the procedure is at an experimental stage, an attempt is also made to point out some problematic issues
associated with the procedure, and some modifications are suggested that might improve the classification results.
2. Theory Geomorphological processes are primarily controlled by topography. With the increasing availability of digital elevation models, and technology enabled to process these, it has become necessary to define quantitative relationships between topography and processes [1, 2, 9, 10, 12]. Pike [13] introduces the concept of describing a landform by a geometric signature. He shows that disparate landscapes can be distinguished with a set of measures that describe the topographic form. This concept has been taken further within the field of geomorphometry [4, 6, 14, 15]. The basic assumption in geomorphometry is that there is a close relationship between surface processes and surface characteristics that can be expressed as topographic parameters. Combinations of topographic parameters define topographic regions (relief units) after a classification process (relief classification). The units are assumed to represent areas with a predominance of certain surface processes and therefore also landforms. If an empirical or physical relationship between a set of topographic parameters and a surface processes can be established, geomorphometry can be used as a tool for spatial modelling. If we further assume that these relationships are scale independent, at least within a certain range, it becomes possible to up-scale and downscale spatially distributed information [5]. The classification of a landscape into functional morphological units, describing physical or conceptual domains, is a task commonly performed within the geosciences. This task is conventionally carried out during field surveys or by interpreting aerial photographs. This method is both time-consuming and dependent on the surveyor’s interpretation of a more or less qualitative set of rules. However, the numerical description of a surface’s geometrical or topographical characteristics, coupled with the relationship between topography, process and landform, gives us the possibility to set up a more consistent set of rules for landform delineation. Thus the problem can be approached more objectively. Still, as the number of variables needed to delineate a certain terrain type increases, the classification process becomes more complex and soon it becomes too complicated to be performed without the help of statistical analysis and computer technology. Generalisation of multivariate data by means of statistical analysis, such as iterative cluster analysis, has become a common practice within the fields of GIS and remote sensing. Iterative cluster analysis defines classes based on the natural clustering of the data in attribute space and is used in many off-the-shelf software packages such as ESRI’s ArcInfo and ERDAS’ Imagine. The use of such algorithms for spatial structuring has proved successful when applied to data that represent innate crisp classes with little overlap in attribute or geographical space. This is often the case for spectral data from air- or space-borne sensors; the classes that emerge from such data reflect different types of land-cover that are more or less distinct, any overlap between classes is mainly an issue of scale rather than ambiguity in class
definitions. Relief data, however, most commonly represents a multivariate continuum that has little or no distinct class-boundaries because there is an authentic overlap between different classes, in both space and characteristics. This fact suggests that other procedures should be used for relief structuring that take the class overlap into account. Irvin [8] and Burrough [3] describe the use of continuous classification (fuzzy set) methods. In these methods individual cells or data points are assigned an affinity to each cluster rather than an absolute membership. They can easily be integrated in a cluster analysis, but the result of a fuzzy classification is hard to visualise, and assessment requires a comprehensive understanding of how the algorithms work and the nature of the data. Furthermore, these methods take overlap only in attribute space into account, and the issue of spatial overlap is not addressed. Friedrich [7] suggests a different approach; he couples the cluster analysis with a preliminary spatial-neighbourhood analysis. The approach is somewhat similar to smoothing the data by a window operation, except instead of using the rigidly defined window an iterative procedure is applied. The generalisation algorithm is based on the proximity distance vector in multivariate space between neighbouring cells in the terrain. Initially each cell is considered a unique class. For each step of the procedure the two neighbouring classes with the shortest distance vector between them are merged, and new attribute values calculated. When a satisfactory degree of generalisation is reached, the algorithm is halted. The idea is that the resulting classes represent individual, unique landform units present in the terrain. The total amount of classes and their suitability for further analysis will therefore depend on the size and relief of the study area and the variables used for similarity assessment.
3. Method A case study was carried out on an area close to Ny-Ålesund, Spitsbergen (Fig. 1). The study area was 1300 × 1200 metres and covered the eastern slope of the Schetelig Mountain. Total relief in the area was 640 metres, and at the base of the slope several large talus cones indicated extensive slope activity. From the area a relatively good digital elevation model (DEM) with a cell size of 10 × 10 metres was available. A digital map of the talus cones was produced from field data and aerial photos. Building on the generalisation algorithm suggested by Friedrich[7], the approach taken here was to use the algorithm to break up the study area into homogenous landscape units. Because each cell’s relation to its neighbourhood, or context, determines whether or not it should be generalised, this process will be referred to as “contextual merging.” For each of the relief units, new attribute values were calculated and used as input to a cluster analysis that classified the units into more general landform types (see Fig. 2). The resulting map was then compared to the landform map and to a classification based on iterative cluster analysis alone.
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Fig. 1. Location of the study area at the Brøgger peninsula close to the community of NyÅlesund.
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Fig. 2. The classification process: To the left the original continuous datasets, after the contextual merging the study area is divided into unique areas with internal homogeneity. These areas are then classified into more general landform types by iterative cluster analysis.
3.1 Contextual Merging In order to pinpoint some of issues that need to be addressed before contextual merging is applied, it is useful to look at the algorithm in more detail. The basic unit in the procedure is the distance vector between two classes. This vector is calculated for each neighbouring class in the dataset and can be described as in (1).
ÿ n v = ÿ (ai − bi ) 2 . i
(1)
ÿ
Where v is the vector between classes a and b, n is the total number of attributes, and ai and bi are the values of attribute i in classes a and b respectively. When all the vectors have been calculated they are put in an array and sorted. Then the two neighbouring classes with the shortest vector between them can be merged. New attribute values are calculated for the class by averaging the values in the two original classes, and the distance vectors between the new class and its neighbours are updated before the procedure is iterated. The merging was performed using IVHG, a program described by Friedrich [7] and modified by the author. The modifications were made mainly to allow the distance vectors to be monitored during the cell merging process. This provided, as explained below, valuable information that was used to decide on a halting criterion. Selecting and Processing Geomorphometric Attributes. The first problem that arises is determining suitable morphometric attributes for the contextual merging. To be suitable, the attributes should have relatively smaller variation within landforms than between them. If this is the case the algorithm will merge neighbouring cells into meaningful units, even though we may not be able to say anything qualitative about them. The attributes should be normalised prior to generalisation, but attributes that are expected to have greater salience in the given context may be weighted accordingly. If certain ranges of attribute values are more relevant than others, one could apply a non-linear stretch function to the data. Defining weights and especially stretch functions does, however, require a deeper understanding of the relationship between the selected attributes and the landforms in the study area. The following four variables were used as input to the algorithm (for a detailed explanation of these variables see [6, 10, 11]): • Slope; magnitude of the maximum slope angle between each cell and its eight neighbours • Profile curvature; the curvature of the land surface in the direction of the maximum slope • Planform curvature; the curvature of the land surface perpendicular to the maximum slope • Wetness index; defined as ln(As/tanB) where As is the upslope contributing area and B is the slope To best focus on active slope processes, the attribute of slope gradient was weighted by two prior to generalisation. While curvature measures provide important information about the characteristics of a landscape unit, they are very sensitive to even small changes in their local neighbourhood and therefore often appear in a rather chaotic pattern. This was especially evident in the strong relief in the study area, and the curvatures were therefore only weighted by one. The topography of talus cones will always lead to a relatively high wetness index in the concave areas along their edges, thus the wetness index is also suitable for their delineation. It is also a measure that gives information, not only on a cell’s immediate neighbourhood, but also on its total drainage area. Given its relevance for this application, the wetness index was weighted by four.
Choosing Degree of Generalisation. The degree of generalisation chosen will act as a halting criterion for the contextual merging. A suitable degree of generalisation will primarily be dependant on the scale of the data relative to the scale of the features being classified: the higher the resolution of the data, the greater the degree of generalisation. The texture, or roughness, also affects when the algorithm should be halted, i.e., the smoother the terrain, the greater degree of generalisation is possible. This is because morphological units in smooth areas by definition are more homogeneous than they are in rugged terrain. Thus problems arise when you have landscapes with different textures within the study area. The algorithm will then have a tendency to start merging dissimilar landforms in the smooth areas before merging cells within single landforms in rougher areas. To make the selection of generalisation degree less arbitrary, the distance vectors were monitored during the cell merging process. By defining the halting criterion as the maximum displacement allowed rather than the degree of generalisation, the same criterion can be used in areas with different relief given that the same attributes are used as input. When a satisfactory degree of generalisation was reached, the distance vector between merged classes represented a displacement of about 15% of the total variation in all attribute values. The original 15,600 cells in the study area had then been reduced to about 1,500 relief units, which is a generalisation of about 91% (see Fig. 3b). 3.2 Cluster Analysis To classify the relief units into more general landscape types, an iterative cluster analysis was used. Before applying this analysis, however, input attributes needed to be determined. In this study, the attributes used were the same four as used in the generalisation, supplemented with the following: • Overall curvature; the overall curvature of the land surface • Wetness index × Planform curvature All of the variables were calculated from the original DEM, and then averaged over the relief units generated by the contextual merging. The six averaged datasets were then classified into 10 classes using the ArcInfo procedures ISOCLUSTER and MLCLASSIFY (cluster analysis with maximum likelihood). For comparison the same cluster analysis was performed with the same data, but without averaging them over the relief units.
Fig. 3. A photo of the study area (a) and the terrain model with the mapped talus cones and the contextually merged relief units (b).
4 Results The results can be seen in Fig. 4. From the figure it is evident that even though the main patterns are the same between the two, the classes resulting from classification without contextual merging are more scattered and spatially inconsistent. The classification based on generalised data also proved to classify the mapped landforms more accurately. Of the 976 cells mapped as taluses, 884 (91%) matched one single class. The total number of cells in this class was 1,029, which means that only 14% of the cells had occurred elsewhere. For the other classification the most significant class only covered 59% of the mapped talus cells, and about 55% occurred elsewhere. Most of the remaining talus cells were included in a cluster with a very
distinct convex planform curvature, and within this cluster the cells matching the mapped taluses only represented 54% of the class.
Fig. 4. The resulting classifications from the cluster analysis with (a) and without (b) contextual merging.
The contextual merging also exposed a pattern overlooked by the other procedure, that is, the horizontal strata seen in the photo in Fig. 3a. This is probably because, for the merging algorithm, these steep and curved features acted as distinctive barriers between the smoother areas above and below, and were consequently merged into separate units. In the generalised dataset they were distinctive enough to be identified as a separate class by the cluster analysis, but when looked at cell by cell, these features were not distinguished from steep and curved areas elsewhere. Classes representing ravines leading down to each of the talus cones can be seen in both classifications, even though the generalisation produced a less ambiguous pattern. There seem to be a clear relationship between the size of these ravine classes and the size of the talus cones below them. This supports the suggestion that the classes represent actual physical domains: in this case, one of weathering and erosion
(the ravines) and another of accumulation (the talus cones). By looking at the concurrence of ravine classes and classes of talus cones, it seems clear that it is possible to determine areas correctly classified as talus cones without the use of auxiliary field data. Not unexpectedly the attributes’ variation within clusters was generally lower when only cluster analysis had been applied. Standard deviations here were between 8% and 12% of the total variation in the dataset for all attributes, whereas the classification with contextual merging had standard deviations between 8% and 18%.
5 Discussion and Conclusion This paper showed how the algorithm suggested by Friedrich [7] could be used for classification of a specific landform type in an alpine relief. In this specific setting it delivered a more spatially correlated and apparently also more accurate classification than was achieved with an iterative cluster analysis alone. However, little effort was made to find the optimal number of classes for the cluster analysis. Both classifications might have performed better if number of classes had been increased and the most similar ones merged. Furthermore the employment of a continuous (fuzzy) classification, rather than a crisp iterative cluster analysis, might have allowed a better assessment of the spatial variations within classes and the transition zones between them. It was found that using degree of displacement, rather than degree of generalisation, as a halting criterion added transferability to the procedure. With little effort, changes could be made to the algorithm so that maximum displacements could be defined for each attribute rather than, or in addition to, maximum total displacement. This would make it easier to determine halting criteria for different types of terrain, scale and applications by the use of field data or general knowledge of the landforms and geomorphometric attributes under consideration. Because the attribute values for the relief units were calculated simply by averaging the value of the individual cells, the full potential of contextual merging was not realised in this study. A more comprehensive approach would be to calculate attribute values for each relief unit on the basis of its general shape, internal topography and context in the terrain, for example, by using parameters such as the relief unit’s length/width ratio, length in slope direction, area/elevation skew, and so on. Using these kinds of higher order parameters could result in a more nuanced classification result, one that not only reflects the physical processes at the cell level, but also at the level of the entire relief unit. This study shows that contextual modelling can augment current methods used in spatial modelling of geomorphological processes. It was not only able to reaffirm geomorphological assumptions about the relationships between topographical parameters and landforms, but it also indicates a clear, and perhaps quantifiable, relationship between some of the classes created. This not only simplifies the interpretation of the classification results, but may also improve the accuracy.
Acknowledgments This study was carried out as part of my MSc dissertation at the Department of Physical Geography, University of Oslo, under the supervision of Dr. Bernd Etzelmüller. The field data was collected during the course "Arctic geomorphology", arranged by Dept. of Phys. Geography and funded by the Faculty of Mathematics and Natural Sciences. I would like to thank PhD student Eva Heggem for help with the collection of field data, the analysis of these and productive comments and ideas during the initial stages of the study. I would also like to thank Bernd Etzelmüller and Lynn Nygård for valuable comments on this paper.
References 1. Beven, K.J. and M.J. Kirkby. A physically based, variable contributing area model of basin hydrology. Hydrological Sciences, 1979. 24: p. 43-69. 2. Beven, K.J., M.J. Kirkby, N. Schofield, and A.F. Tagg. Testing a physically-based flood forecasting model (TOPMODEL) for three U.K. catchments. Journal of Hydrology, 1984. 69(1-4): p. 119-143. 3. Burrough, P.A., P.F.M. vanGaans, and R.A. MacMillan. High-resolution landform classification using fuzzy k-means. Fuzzy sets and systems, 2000. 113(1): p. 37-52. 4. Dikau, R., The application of a digital relief model to landform analysis in geomorphology, in Three dimensional applications in geographical information systems., J. Raper, Editor. 1989, Taylor and Francis: London, United Kingdom. p. 51-77. 5. Etzelmüller, B., R. Ødegård, I. Berthling, and J.L. Sollid. Terrain parameters and remote sensing data in periglacial reseach. Permafrost and Periglacial Processes, 2001. 12(1): p. 7992. 6. Evans, I.S., General geomorphometry, derivatives of altitude, and descriptive statistics., in Spatial analysis in geomorphology, R.J. Chorley, Editor. 1972, Mathuen & Co Ltd. p. 17-92. 7. Friedrich, K. Multivariate distance methods for geomorphographic relief classification. in Proceedings EU Workshop on Land Information Systems: Developments for planning the sustainable use of land resources. 1996. Hannover: European Soil Bureau. 8. Irvin, B.J., S.J. Ventura, and B.K. Slater. Fuzzy and isodata classification of landform elements from digital terrain data in Pleasant Valley, Wisconsin. Geoderma, 1997. 77(2-4): p. 137-154. 9. Moore, I.D., P.E. Gessler, G.A. Nielsen, and G.A. Peterson. Soil attribute prediction using terrain analysis. Soil Science Society of America Journal, 1993. 57(2): p. 443-452. 10.Moore, I.D., R.B. Grayson, and A.R. Ladson. Digital terrain modelling: a review of hydrological, geomorphological, and biological applications. Hydrological Processes, 1991. 5(1): p. 3-30. 11.Moore, I.D., A. Lewis, and J.C. Gallant, Terrain attributes; estimation methods and scale effects, in Modelling change in environmental systems., A.J. Jakeman, M.B. Beck, and M.J. McAleer, Editors. 1993, John Wiley and Sons: Chichester, United Kingdom. p. 189-214. 12.Moore, I.D., A.K. Turner, J.P. Wilson, S.K. Jenson, and L.E. Band, GIS and land-surfacesubsurface process modeling, in Environmental modeling with GIS, M.F. Goodchild, B.O. Parks, and L.T. Steyaert, Editors. 1993, Oxford University Press: New York, NY. p. 196230.
13.Pike, R.J. The geometric signature; quantifying landslide-terrain types from digital elevation models. Mathematical Geology, 1988. 20(5): p. 491-511. 14.Pike, R.J. Geomorphometry - progress, practice, and prospect. Zeitschrift fur Geomorphologie, Supplementband, 1995. 101: p. 221-238. 15.Pike, R.J. Geomorphometry - diversity in quantitative surface analysis. Progress in Physical Geography, 2000. 24(1): p. 1-20.
Abstract. Automatic classification of relief attributes into meaningful morphological units has a great potential within the field of geomorphology. When applying common classification algorithms such an iterative cluster analysis to relief data, the result is often a set of classes with a marked lack of coherence in geographical space. The scattering of classes occurs because there is an authentic overlap between different classes in both attribute and geographical space. Therefore other procedures should be used for relief structuring that take the class overlap into account. Such a procedure could be the application of a contextual merging, or generalisation, prior to classification. As a case study, an area close to Ny-Ålesund, Spitsbergen, is classified using this procedure, and it is shown that in this specific relief the coherence and interpretability of the result is increased compared to a simple cluster analysis alone.
1 Introduction Generalisation of data into a smaller number of classes, relevant to a certain application, is a task we perform every day without giving it much consideration. In geomorphology such generalisations include the classification of a continuous surface into units, or landforms, such as a valley, hill or cliff. These are terms that make sense to most people as spatial units with a certain shape, extent and topography, but can usually also be defined as a domain within which a specific physical surface-process is dominant. Hence the quantification of such units is useful not only as an objective description of a landscape, but also as a component in spatial modelling of geomorphological processes. Topographic parameters, derived from digital elevation models, can give us valuable information on the characteristics of a certain surface element. However, the spatial aspect, which is essential in a geomorphological context, is often neglected in the statistical algorithms most commonly used to classify large sets of multivariate data. The aim of this paper is to illustrate how contextual merging, an algorithm for generalisation of continuous data into spatial units, can be used to improve classification based on topographic parameters. Since the procedure is at an experimental stage, an attempt is also made to point out some problematic issues
associated with the procedure, and some modifications are suggested that might improve the classification results.
2. Theory Geomorphological processes are primarily controlled by topography. With the increasing availability of digital elevation models, and technology enabled to process these, it has become necessary to define quantitative relationships between topography and processes [1, 2, 9, 10, 12]. Pike [13] introduces the concept of describing a landform by a geometric signature. He shows that disparate landscapes can be distinguished with a set of measures that describe the topographic form. This concept has been taken further within the field of geomorphometry [4, 6, 14, 15]. The basic assumption in geomorphometry is that there is a close relationship between surface processes and surface characteristics that can be expressed as topographic parameters. Combinations of topographic parameters define topographic regions (relief units) after a classification process (relief classification). The units are assumed to represent areas with a predominance of certain surface processes and therefore also landforms. If an empirical or physical relationship between a set of topographic parameters and a surface processes can be established, geomorphometry can be used as a tool for spatial modelling. If we further assume that these relationships are scale independent, at least within a certain range, it becomes possible to up-scale and downscale spatially distributed information [5]. The classification of a landscape into functional morphological units, describing physical or conceptual domains, is a task commonly performed within the geosciences. This task is conventionally carried out during field surveys or by interpreting aerial photographs. This method is both time-consuming and dependent on the surveyor’s interpretation of a more or less qualitative set of rules. However, the numerical description of a surface’s geometrical or topographical characteristics, coupled with the relationship between topography, process and landform, gives us the possibility to set up a more consistent set of rules for landform delineation. Thus the problem can be approached more objectively. Still, as the number of variables needed to delineate a certain terrain type increases, the classification process becomes more complex and soon it becomes too complicated to be performed without the help of statistical analysis and computer technology. Generalisation of multivariate data by means of statistical analysis, such as iterative cluster analysis, has become a common practice within the fields of GIS and remote sensing. Iterative cluster analysis defines classes based on the natural clustering of the data in attribute space and is used in many off-the-shelf software packages such as ESRI’s ArcInfo and ERDAS’ Imagine. The use of such algorithms for spatial structuring has proved successful when applied to data that represent innate crisp classes with little overlap in attribute or geographical space. This is often the case for spectral data from air- or space-borne sensors; the classes that emerge from such data reflect different types of land-cover that are more or less distinct, any overlap between classes is mainly an issue of scale rather than ambiguity in class
definitions. Relief data, however, most commonly represents a multivariate continuum that has little or no distinct class-boundaries because there is an authentic overlap between different classes, in both space and characteristics. This fact suggests that other procedures should be used for relief structuring that take the class overlap into account. Irvin [8] and Burrough [3] describe the use of continuous classification (fuzzy set) methods. In these methods individual cells or data points are assigned an affinity to each cluster rather than an absolute membership. They can easily be integrated in a cluster analysis, but the result of a fuzzy classification is hard to visualise, and assessment requires a comprehensive understanding of how the algorithms work and the nature of the data. Furthermore, these methods take overlap only in attribute space into account, and the issue of spatial overlap is not addressed. Friedrich [7] suggests a different approach; he couples the cluster analysis with a preliminary spatial-neighbourhood analysis. The approach is somewhat similar to smoothing the data by a window operation, except instead of using the rigidly defined window an iterative procedure is applied. The generalisation algorithm is based on the proximity distance vector in multivariate space between neighbouring cells in the terrain. Initially each cell is considered a unique class. For each step of the procedure the two neighbouring classes with the shortest distance vector between them are merged, and new attribute values calculated. When a satisfactory degree of generalisation is reached, the algorithm is halted. The idea is that the resulting classes represent individual, unique landform units present in the terrain. The total amount of classes and their suitability for further analysis will therefore depend on the size and relief of the study area and the variables used for similarity assessment.
3. Method A case study was carried out on an area close to Ny-Ålesund, Spitsbergen (Fig. 1). The study area was 1300 × 1200 metres and covered the eastern slope of the Schetelig Mountain. Total relief in the area was 640 metres, and at the base of the slope several large talus cones indicated extensive slope activity. From the area a relatively good digital elevation model (DEM) with a cell size of 10 × 10 metres was available. A digital map of the talus cones was produced from field data and aerial photos. Building on the generalisation algorithm suggested by Friedrich[7], the approach taken here was to use the algorithm to break up the study area into homogenous landscape units. Because each cell’s relation to its neighbourhood, or context, determines whether or not it should be generalised, this process will be referred to as “contextual merging.” For each of the relief units, new attribute values were calculated and used as input to a cluster analysis that classified the units into more general landform types (see Fig. 2). The resulting map was then compared to the landform map and to a classification based on iterative cluster analysis alone.
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Fig. 1. Location of the study area at the Brøgger peninsula close to the community of NyÅlesund.
Contextual merging
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Fig. 2. The classification process: To the left the original continuous datasets, after the contextual merging the study area is divided into unique areas with internal homogeneity. These areas are then classified into more general landform types by iterative cluster analysis.
3.1 Contextual Merging In order to pinpoint some of issues that need to be addressed before contextual merging is applied, it is useful to look at the algorithm in more detail. The basic unit in the procedure is the distance vector between two classes. This vector is calculated for each neighbouring class in the dataset and can be described as in (1).
ÿ n v = ÿ (ai − bi ) 2 . i
(1)
ÿ
Where v is the vector between classes a and b, n is the total number of attributes, and ai and bi are the values of attribute i in classes a and b respectively. When all the vectors have been calculated they are put in an array and sorted. Then the two neighbouring classes with the shortest vector between them can be merged. New attribute values are calculated for the class by averaging the values in the two original classes, and the distance vectors between the new class and its neighbours are updated before the procedure is iterated. The merging was performed using IVHG, a program described by Friedrich [7] and modified by the author. The modifications were made mainly to allow the distance vectors to be monitored during the cell merging process. This provided, as explained below, valuable information that was used to decide on a halting criterion. Selecting and Processing Geomorphometric Attributes. The first problem that arises is determining suitable morphometric attributes for the contextual merging. To be suitable, the attributes should have relatively smaller variation within landforms than between them. If this is the case the algorithm will merge neighbouring cells into meaningful units, even though we may not be able to say anything qualitative about them. The attributes should be normalised prior to generalisation, but attributes that are expected to have greater salience in the given context may be weighted accordingly. If certain ranges of attribute values are more relevant than others, one could apply a non-linear stretch function to the data. Defining weights and especially stretch functions does, however, require a deeper understanding of the relationship between the selected attributes and the landforms in the study area. The following four variables were used as input to the algorithm (for a detailed explanation of these variables see [6, 10, 11]): • Slope; magnitude of the maximum slope angle between each cell and its eight neighbours • Profile curvature; the curvature of the land surface in the direction of the maximum slope • Planform curvature; the curvature of the land surface perpendicular to the maximum slope • Wetness index; defined as ln(As/tanB) where As is the upslope contributing area and B is the slope To best focus on active slope processes, the attribute of slope gradient was weighted by two prior to generalisation. While curvature measures provide important information about the characteristics of a landscape unit, they are very sensitive to even small changes in their local neighbourhood and therefore often appear in a rather chaotic pattern. This was especially evident in the strong relief in the study area, and the curvatures were therefore only weighted by one. The topography of talus cones will always lead to a relatively high wetness index in the concave areas along their edges, thus the wetness index is also suitable for their delineation. It is also a measure that gives information, not only on a cell’s immediate neighbourhood, but also on its total drainage area. Given its relevance for this application, the wetness index was weighted by four.
Choosing Degree of Generalisation. The degree of generalisation chosen will act as a halting criterion for the contextual merging. A suitable degree of generalisation will primarily be dependant on the scale of the data relative to the scale of the features being classified: the higher the resolution of the data, the greater the degree of generalisation. The texture, or roughness, also affects when the algorithm should be halted, i.e., the smoother the terrain, the greater degree of generalisation is possible. This is because morphological units in smooth areas by definition are more homogeneous than they are in rugged terrain. Thus problems arise when you have landscapes with different textures within the study area. The algorithm will then have a tendency to start merging dissimilar landforms in the smooth areas before merging cells within single landforms in rougher areas. To make the selection of generalisation degree less arbitrary, the distance vectors were monitored during the cell merging process. By defining the halting criterion as the maximum displacement allowed rather than the degree of generalisation, the same criterion can be used in areas with different relief given that the same attributes are used as input. When a satisfactory degree of generalisation was reached, the distance vector between merged classes represented a displacement of about 15% of the total variation in all attribute values. The original 15,600 cells in the study area had then been reduced to about 1,500 relief units, which is a generalisation of about 91% (see Fig. 3b). 3.2 Cluster Analysis To classify the relief units into more general landscape types, an iterative cluster analysis was used. Before applying this analysis, however, input attributes needed to be determined. In this study, the attributes used were the same four as used in the generalisation, supplemented with the following: • Overall curvature; the overall curvature of the land surface • Wetness index × Planform curvature All of the variables were calculated from the original DEM, and then averaged over the relief units generated by the contextual merging. The six averaged datasets were then classified into 10 classes using the ArcInfo procedures ISOCLUSTER and MLCLASSIFY (cluster analysis with maximum likelihood). For comparison the same cluster analysis was performed with the same data, but without averaging them over the relief units.
Fig. 3. A photo of the study area (a) and the terrain model with the mapped talus cones and the contextually merged relief units (b).
4 Results The results can be seen in Fig. 4. From the figure it is evident that even though the main patterns are the same between the two, the classes resulting from classification without contextual merging are more scattered and spatially inconsistent. The classification based on generalised data also proved to classify the mapped landforms more accurately. Of the 976 cells mapped as taluses, 884 (91%) matched one single class. The total number of cells in this class was 1,029, which means that only 14% of the cells had occurred elsewhere. For the other classification the most significant class only covered 59% of the mapped talus cells, and about 55% occurred elsewhere. Most of the remaining talus cells were included in a cluster with a very
distinct convex planform curvature, and within this cluster the cells matching the mapped taluses only represented 54% of the class.
Fig. 4. The resulting classifications from the cluster analysis with (a) and without (b) contextual merging.
The contextual merging also exposed a pattern overlooked by the other procedure, that is, the horizontal strata seen in the photo in Fig. 3a. This is probably because, for the merging algorithm, these steep and curved features acted as distinctive barriers between the smoother areas above and below, and were consequently merged into separate units. In the generalised dataset they were distinctive enough to be identified as a separate class by the cluster analysis, but when looked at cell by cell, these features were not distinguished from steep and curved areas elsewhere. Classes representing ravines leading down to each of the talus cones can be seen in both classifications, even though the generalisation produced a less ambiguous pattern. There seem to be a clear relationship between the size of these ravine classes and the size of the talus cones below them. This supports the suggestion that the classes represent actual physical domains: in this case, one of weathering and erosion
(the ravines) and another of accumulation (the talus cones). By looking at the concurrence of ravine classes and classes of talus cones, it seems clear that it is possible to determine areas correctly classified as talus cones without the use of auxiliary field data. Not unexpectedly the attributes’ variation within clusters was generally lower when only cluster analysis had been applied. Standard deviations here were between 8% and 12% of the total variation in the dataset for all attributes, whereas the classification with contextual merging had standard deviations between 8% and 18%.
5 Discussion and Conclusion This paper showed how the algorithm suggested by Friedrich [7] could be used for classification of a specific landform type in an alpine relief. In this specific setting it delivered a more spatially correlated and apparently also more accurate classification than was achieved with an iterative cluster analysis alone. However, little effort was made to find the optimal number of classes for the cluster analysis. Both classifications might have performed better if number of classes had been increased and the most similar ones merged. Furthermore the employment of a continuous (fuzzy) classification, rather than a crisp iterative cluster analysis, might have allowed a better assessment of the spatial variations within classes and the transition zones between them. It was found that using degree of displacement, rather than degree of generalisation, as a halting criterion added transferability to the procedure. With little effort, changes could be made to the algorithm so that maximum displacements could be defined for each attribute rather than, or in addition to, maximum total displacement. This would make it easier to determine halting criteria for different types of terrain, scale and applications by the use of field data or general knowledge of the landforms and geomorphometric attributes under consideration. Because the attribute values for the relief units were calculated simply by averaging the value of the individual cells, the full potential of contextual merging was not realised in this study. A more comprehensive approach would be to calculate attribute values for each relief unit on the basis of its general shape, internal topography and context in the terrain, for example, by using parameters such as the relief unit’s length/width ratio, length in slope direction, area/elevation skew, and so on. Using these kinds of higher order parameters could result in a more nuanced classification result, one that not only reflects the physical processes at the cell level, but also at the level of the entire relief unit. This study shows that contextual modelling can augment current methods used in spatial modelling of geomorphological processes. It was not only able to reaffirm geomorphological assumptions about the relationships between topographical parameters and landforms, but it also indicates a clear, and perhaps quantifiable, relationship between some of the classes created. This not only simplifies the interpretation of the classification results, but may also improve the accuracy.
Acknowledgments This study was carried out as part of my MSc dissertation at the Department of Physical Geography, University of Oslo, under the supervision of Dr. Bernd Etzelmüller. The field data was collected during the course "Arctic geomorphology", arranged by Dept. of Phys. Geography and funded by the Faculty of Mathematics and Natural Sciences. I would like to thank PhD student Eva Heggem for help with the collection of field data, the analysis of these and productive comments and ideas during the initial stages of the study. I would also like to thank Bernd Etzelmüller and Lynn Nygård for valuable comments on this paper.
References 1. Beven, K.J. and M.J. Kirkby. A physically based, variable contributing area model of basin hydrology. Hydrological Sciences, 1979. 24: p. 43-69. 2. Beven, K.J., M.J. Kirkby, N. Schofield, and A.F. Tagg. Testing a physically-based flood forecasting model (TOPMODEL) for three U.K. catchments. Journal of Hydrology, 1984. 69(1-4): p. 119-143. 3. Burrough, P.A., P.F.M. vanGaans, and R.A. MacMillan. High-resolution landform classification using fuzzy k-means. Fuzzy sets and systems, 2000. 113(1): p. 37-52. 4. Dikau, R., The application of a digital relief model to landform analysis in geomorphology, in Three dimensional applications in geographical information systems., J. Raper, Editor. 1989, Taylor and Francis: London, United Kingdom. p. 51-77. 5. Etzelmüller, B., R. Ødegård, I. Berthling, and J.L. Sollid. Terrain parameters and remote sensing data in periglacial reseach. Permafrost and Periglacial Processes, 2001. 12(1): p. 7992. 6. Evans, I.S., General geomorphometry, derivatives of altitude, and descriptive statistics., in Spatial analysis in geomorphology, R.J. Chorley, Editor. 1972, Mathuen & Co Ltd. p. 17-92. 7. Friedrich, K. Multivariate distance methods for geomorphographic relief classification. in Proceedings EU Workshop on Land Information Systems: Developments for planning the sustainable use of land resources. 1996. Hannover: European Soil Bureau. 8. Irvin, B.J., S.J. Ventura, and B.K. Slater. Fuzzy and isodata classification of landform elements from digital terrain data in Pleasant Valley, Wisconsin. Geoderma, 1997. 77(2-4): p. 137-154. 9. Moore, I.D., P.E. Gessler, G.A. Nielsen, and G.A. Peterson. Soil attribute prediction using terrain analysis. Soil Science Society of America Journal, 1993. 57(2): p. 443-452. 10.Moore, I.D., R.B. Grayson, and A.R. Ladson. Digital terrain modelling: a review of hydrological, geomorphological, and biological applications. Hydrological Processes, 1991. 5(1): p. 3-30. 11.Moore, I.D., A. Lewis, and J.C. Gallant, Terrain attributes; estimation methods and scale effects, in Modelling change in environmental systems., A.J. Jakeman, M.B. Beck, and M.J. McAleer, Editors. 1993, John Wiley and Sons: Chichester, United Kingdom. p. 189-214. 12.Moore, I.D., A.K. Turner, J.P. Wilson, S.K. Jenson, and L.E. Band, GIS and land-surfacesubsurface process modeling, in Environmental modeling with GIS, M.F. Goodchild, B.O. Parks, and L.T. Steyaert, Editors. 1993, Oxford University Press: New York, NY. p. 196230.
13.Pike, R.J. The geometric signature; quantifying landslide-terrain types from digital elevation models. Mathematical Geology, 1988. 20(5): p. 491-511. 14.Pike, R.J. Geomorphometry - progress, practice, and prospect. Zeitschrift fur Geomorphologie, Supplementband, 1995. 101: p. 221-238. 15.Pike, R.J. Geomorphometry - diversity in quantitative surface analysis. Progress in Physical Geography, 2000. 24(1): p. 1-20.
