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This chapter discusses the basic physical and mathematical concepts of digital terrain analysis. First, we introduce the notion of the topographic surface and its limitations. Second, we discuss contour lines, special and nonspecial points, slope lines, and flow lines. Third, we present definitions, formulae, and physical meanings for five main groups of morphometric variables, such as local, nonlocal, solar, and combined attributes, as well as structural lines. In particular, we present the derivation of formulae for slope gradient, aspect, plan curvature, horizontal curvature, vertical curvature, unsphericity curvature, rotor, difference curvature, ring curvature, accumulation curvature, the generating function, and insolation. Finally, we discuss three key types of landform classifications: the Gaussian classification, the Efremov-Krcho classification, and the Shary classification.

Within geomorphology, geomorphometry applies morphometric analysis to the land surface as a continuous surface (general geomorphometry), and to objects such as landforms, elementary forms, channels, and drainage basins extracted from that surface (specific geomorphometry). Special attention is paid here to a comprehensive taxonomy of fundamental geomorphometric variables, both those related to fields and those characterizing objects. The former include field-specific and field-invariant as well as local and regional variables. Derivatives of the land surface related to the gravity field are traditionally important in geomorphology, but an extended system of field-invariant curvatures has potential. Solar radiation and wind fields in relation to topography are of both climatic and geomorphological (process) importance. The morphometry of linear objects has been not only dominated by channels and drainage networks but also includes structural and tectonic morpholineaments. The problem of elementary form extraction from digital elevation models (DEMs) is basic to the analysis of areal objects. Scaling and scale-specificity questions are documented with quantile and allometric plots. Major prospects for the future development of geomorphometry are perceived as resulting not only from great technological development (new remote-sensing methods providing high-precision DEMs) but also from the effective integration of the empirical and theoretical streams of geomorphometry.

Earth's surface is continuously evolving and is the result of the complex interactions between Earth's internal (endogenetic) and external (exogenetic) processes. Endogenetic and exogenetic interactions result in landforms and landscapes that are the product of numerous different processes, and thus are ‘polygenetic’ in origin. Recent tectonic–geomorphic studies have led to the realization that complex links, interactions, and feedback exist among tectonics, climate, and landscape development. Key issues in the evolution of polygenetic landscapes included examining the role of tectonics and isostatic uplift, the nature of exhumation rates, climate control and erosion distribution, glaciers and relief production, focused erosion and spatial coincidence, geomorphometry and erosion modeling, and equilibrium concepts such as topographic steady state. Notably, the new models based on these complex relationships include: the glacial buzzsaw model whereby topography is limited by glaciation; the tectonic aneurysm model in which localized uplift at syntaxes is caused by enhanced fluvial and glacial erosion that, in turn, weaken the lithosphere and enhance bedrock uplift; and glacial damming leading to differential erosion and uplift. In addition to natural factors, human influences are now contributing to polygenetic landscapes and pose greater challenges for predicting the nature of future geomorphic change.

Classical geomorphological maps are representations of the spatial distribution of landforms, materials and of the processes responsible for their formation, in a single paper map. They contain a wealth of information that is generally documented with the aid of symbol and color legends. Uniformity among geomorphological legends does not exist, mainly because the traditional mapping ‘schools’ independently developed systems for use at different scales in a variety of landscapes. Technological advances have changed the preparation, data collection, analysis, storage, and visualization of the modern geomorphological map. Modern geomorphological maps are digital collections of information layers consisting of georeferenced vector, raster and tabular data that are stored in a geodatabase. The data depicted in classical geomorphological maps can be scanned and converted into digital geomorphological information layers using conversion legends. Both the content and the precision of digital geomorphological information can be updated by using information from digital elevation models (DEMs). A further development is the (semi-)automated extraction and classification of geomorphological features from DEMs. Extraction and classification of geomorphological features are based on land-surface parameters derived from DEMs. The visualization and publication of digital geomorphological information layers have drastically changed. Birds-eye views, three-dimensional display and animations, virtual globe visualizations, geospatial portable document format maps or access to geomorphological maps via web-based services are possible through remote servers. The end-user interactively controls the information that is on-screen displayed, analyzed, and distributed. A case study from the Austrian Alps is presented to illustrate how: (1) geomorphological information from classical maps can be converted to digital information layers; (2) detailed DEMs are used in semi-automated object-based classification of landforms; and (3) a modern geomorphological map is used for application to geoconservation.

The study of surface processes and landforms requires quantitative characterization of the topography. New theoretical/conceptual and practical advances in understanding and mapping various aspects of geomorphological systems have emerged from new geospatial data and analysis of the topography. This chapter describes geomorphometry, or the science of quantitative land-surface characterization, and how it can be used to represent and sample the land surface, generate digital elevation models (DEMs), correct errors and artifacts from surface models, compute land-surface parameters and objects, and use various forms of quantitative information in different application domains to address or solve problems.

The rapid proliferation of remote sensing and geographic information systems (GIS) into geomorphologic mapping has increased the objectivity and efficiency of landform segmentation, measurement, and classification. The near ubiquitous presence of Earth-observing satellites provides an array of perspectives to visualize the biophysical characteristics of landscapes, access inhospitable terrain on a predictable schedule, and study landscape processes when conditions are hazardous. GIS technology has altered the analysis, visualization, and dissemination of landform data due to the shared theoretical concepts that are fundamental to geomorphology and GIScience. The authors review geospatial technology applications in landform mapping (including emerging issues) within glacial, volcanic, landslide, and fluvial research.

This chapter presents a brief historical overview of the progress of digital terrain modeling in the context of soil and geological studies. It is demonstrated that at present there are four main research trends in soil- and geology-oriented digital terrain modeling: (1) analysis and modeling of relationships between soil properties and topographic characteristics; (2) use of the resulting data and knowledge in predictive mapping of soil properties; (3) analysis of forms of geological features, such as folds and domes; and (4) revelation and analysis of lineaments and faults, as well as their relationships with other components of geosystems.

Publisher Summary This chapter defines the key criteria in the algorithm's sensitivity to DEM high-frequency noise and the possibility of its suppression. This is because any DEM contains errors, but filtering techniques are unable to remove all the errors from DEMs. All calculation methods of geomorphometry more or less increase the manifestation of high-frequency noise in models of topographic variables that may limit the possibility to use and interpret such models. One other important factor influences the selection of a particular calculation algorithm. This is the type of DEM grid. It is important to realize that widespread calculation methods to process DEMs on a plane square grid cannot be applied to handle DEMs on a spheroidal equal angular grid. This is associated with principal differences in the geometry of these grid types.

Publisher Summary This chapter describes the topographic surface and landform classifications. The Earth's surface is too complex for rigorous mathematical treatment because it is not smooth and regular. However, for many practically important problems, it is sufficient to approximate the Earth's surface by the topographic surface. Here, the topographic surface as a closed, oriented, continuously differentiable, two-dimensional manifold S in the three-dimensional Euclidean space E3 are described. Three key restrictions are true for the topographic surface. The planar size of the topographic surface is essentially less than the Earth's radius. It is generally assumed that the curvature of the planet may be ignored if the size of the surface portion is less than 0.1 of the average radius of the planet. Landform classifications based on local morphometric attributes are of fundamental importance to the theory of geomorphometry and digital terrain modeling. There are three main quantitative approaches to classifying landforms using information on the local geometry of the surface: the Gaussian classification based on the signs of the Gaussian and mean curvatures, the EfremovKrcho classification using the signs of the horizontal and vertical curvatures, and the Shary classification based on the signs of the Gaussian, mean, difference, horizontal, and vertical curvatures.

Geomorphological maps that are automatically extracted from digital elevation data are gradually replacing classical geomorphological maps. Commonly, digital mapping projects are based upon statistical techniques, object-based protocols or both. In addition to digital elevation data, expert knowledge can still be used to calibrate feature extraction algorithms. Such hybrid expert/statistical-based methods translate land surface parameters into areal extents of geomorphological features in an automated, reproducible manner, which increases spatial detail of final products and speeds up map production. The development of efficient statistical methods for the extraction of geomorphological features is today promoted by high-resolution digital elevation data from light detection and ranging (LiDAR) technology. In this chapter, case studies from the Netherlands (very low relief) and Austrian Alps (high relief) are presented to illustrate how statistical-based and object-based supervised classification can be used for the semi-automated identification and extraction of geomorphological features using high-resolution LiDAR digital elevation models (DEMs). In the first case study, multinomial logistic regression is used to increase the detail of a classic geomorphological map. Medial axes of the manually delineated polygons are used to locate the training pixels and to build the statistical model, which is then implemented over the whole area of interest. In the second case study, object-based segmentation of slope and topographic openness extracted from LiDAR data are used for rule-based mapping of geomorphological features. Both studies confirm that LiDAR DEMs can be used to increase detail of existing geomorphological maps. In addition, semi-automated techniques provide a more objective framework for geomorphological mapping.

This chapter deals with types, purposes, contents and perspectives of geomorphological mapping, from the widely applied, ‘traditional’ symbol-based maps to the modern geographical information system (GIS)-based, object-oriented geomorphological mapping models, capable of providing reliable multiscale cartographic support to environmental analysis and land planning projects. In the last decades, the availability of new tools such as satellite imagery, global positioning systems, digital elevation models and GIS has induced a new, more effective approach in the acquisition, storage and display of geomorphological features. By this approach, geomorphologists can produce geomorphological models, consisting of land surface ‘objects’, organised into hierarchically arranged classes with spatially and temporally variable properties and geometric relationships. Unlike ‘traditional’ maps, object-oriented models can provide a full geometric description of landforms and near-surface deposits. Moreover, generalisation/decomposition procedures allow the translation of geomorphological objects from larger to smaller scales and vice versa. A case study of a GIS-based, object-oriented geomorphological model, in which ‘traditional’ symbol-oriented mapping is associated with grid-based/object-based analysis, is provided by the Salerno University (Italy) GeoMorphological Information System (GmIS). Some significant examples of traditional geomorphological maps and multiscale object-oriented mapping models produced at the Salerno University are presented in the annexes.

Publisher Summary Advances in geographic information system (GIS) technology and the mathematical/statistical tools for modeling and simulation, as well as the increasing availability of digital elevation models (DEMs), have led to many applications and a growing literature. The methods and techniques employed range from empirical and heuristic to statistical and physically-based, and each brings its own unique advantages and disadvantages that determine its suitability for a given type of mass movement and application. This chapter samples two of the many approaches that employ geomorphometry. Geomorphometry provides analytical tools and generates DEM-derived data that have revolutionized the spatial modeling of slope failure and mass movements. The resulting large body of findings has advanced the understanding of landslide processes in the natural environment, and is being applied to the protection of human life and property. This chapter concludes with a brief appraisal of the GIS models that illustrate the two general topics, downslope spread of material released in alpine mass movements and the mapping of landslide susceptibility in hilly topography. GIS can model the propagation of mass movements in mountainous areas in many ways; existing approaches include the specific, as well as the general, and are based on different principles. Various regional models of the landslide hazard have been proposed for GIS implementation, and each has its strong and weak points.

Publisher Summary The role of vegetation maps nowadays is increasing. Statistical models are used in almost all vegetation mapping. Exceptions are local large-scale projects and in corine land cover (CLC) projects for which a methodological prerequisite is that the boundaries of the RS images are delineated manually. In all other cases, the statistical approaches applied are almost as diverse as the vegetation itself. Among the most frequently used methods in vegetation mapping are generalized linear models (GLM), classification and regression trees (CART) and, general additive models (GAM). These could be combined with ordination and/or classification analyses. Depending on thematic and spatial mapping resolutions and the diversity of the terrain at the time of mapping, mappers use land-surface parameters combined with field observations to create polygons that covered the entire area of interest. When these estimators are not sufficient for estimating the occurrence of a particular type of vegetation, land-surface parameters are used in combination with estimators. Land-surface parameters and objects are used for constructing very complex statistical models to predict the spatial distribution of vegetation. The chapter tabulates several examples of how geomorphometry is applied in mapping vegetation. It demonstrates, using the land-surface parameters of the Baranja Hill case study, how to map the distribution of the presence of a particular plant species and the corine land-cover categories.

Publisher Summary RiverTools is a software toolkit with a user-friendly, point-and-click interface that was specifically designed for working with digital elevation models (DEMs) and extracting hydrologic information from them. This chapter aims to provide an overview of what RiverTools can do and how it can be used to rapidly perform a variety of tasks with elevation data. It explains the layout of the RiverTools menus and dialogs. It also briefly discusses geographic information system (GIS) issues, such as ellipsoids and map projections. Some tools in the prepare menu that simplify the task of preparing a DEM that spans a given area of interest have been introduced and how dialogs in the extract menu can be used to extract various grid layers and masks from a DEM are discussed. The chapter highlights some of the visualization tools in the display menu and introduces some of the interactive window tools that can be used to query and interact with an image. RiverTools and MicroDEM may be the only GIS applications that always take the latitudedependence of pixel geometry into account when working with geographic DEMs.

Publisher Summary Geographic Resources Analysis Support System (GRASS) is a general-purpose geographic information system (GIS) for the management, processing, analysis, modeling, and visualization of many types of georeferenced data. This chapter is based on GRASS 6.2 version available for all commonly used operating systems. It includes 2D raster and 3D voxel data support, a new topological 2D/3D vector engine and capabilities for vector network analysis. Attributes are managed in a SQL-based DBMS. Advances in mapping technologies, especially the rapid evolution of airborne and ground-based laser scanning, as well as satellite and airborne radar interferometry are bringing significant changes to geomorphic analysis. The point densities exceed the level of detail required for most applications and digital elevation models (DEMs) with resolutions of 3 m and better are becoming common even for large areas. The high mapping efficiency makes repeated mapping at relatively short time intervals feasible, resulting in multi-temporal DEMs. These developments require new concepts and approaches in geomorphometry. In response, GRASS modules are being further enhanced to accommodate very large data sets produced by the new mapping technologies; new tools are added for efficient handling of very dense elevation or bathymetry data, hierarchical watershed analysis and quantification of land-surface change.

Publisher Summary This chapter aims to demonstrate how uncertainty in digital elevation model (DEM) attributes can be quantified using geostatistical methods and to show how the propagation of errors to DEM derived products may be computed. To attribute errors DEMs may have positional errors like a shift along one or both coordinate axes, rotational errors, scaling errors, projection errors, or a combination of these. In this chapter, only attribute errors are considered. It describe how propagation of attribute errors in spatial modeling can be computed using the Monte-Carlo method. This method is the most often used error propagation method because it is generic, flexible, and intuitively appealing. In order of increasing complexity, the chapter considers the propagation of error from DEMs to three derivatives, namely slope (a local land-surface parameter), topographic wetness index (a regional land-surface parameter), and soil redistribution resulting from water erosion (a complex model). It also describes the uncertainty propagation analysis in detail.

Publisher Summary Geomorphology may be defined as the science, which studies the nature and history of landforms, and the processes that created them. This chapter focuses on the uses of digital elevation models (DEMs) for geomorphological mapping that is, extraction of geological and geomorphological features out of DEMs. Basic concepts in geomorphology include the magnitude and frequency of processes, spatial scales of landforms and processes, temporal scales of adjustment, equilibrium and historical inheritance, relations between internal and external processes, and the sediment cascade. Most of these involve the use of geomorphometric measures, increasingly from DEMs. A major application of geomorphometry in geomorphological studies is the automated extraction of geological/hydrological features and landforms. Using a small case study, the chapter demonstrates various approaches to extraction of predefined, generic, and empirically defined landform objects. It has also shown that geomorphometry has gone beyond the experimental stage and produced many substantive results in geomorphology.

Publisher Summary System for Automated Geoscientific Analyses (SAGA) is a full-fledged geographic information system (GIS) and many of its features have some relation with geomorphometry that makes it an ideal tool for operational work. This chapter emphasizes the particular characteristics of SAGA and the relation between some of its features and concepts. SAGA is GIS software with support for raster and vector data. It includes a large set of geo-scientific algorithms and is especially powerful for the analysis of digital elevation models (DEMs). The chapter introduces SAGA with a strong focus on the analysis and application of DEM data. SAGA has been designed to be a flexible and useful tool for the geoscientific community and a large part of its actual structure is due to that particular aim. Conceptually, the architecture of SAGA consists of three different components: (1) The application programming interface (API) provides all the basic functions for performing geographical analysis and is the true “heart” of SAGA itself. (2) A set of modules that are organized in module libraries, represents the geo-scientific methods. (3) The graphical user interface (GUI) is the system's front end, through which the user manages data and executes modules.

Publisher Summary This chapter addresses advance in concepts, land-surface measurement, and analytical tools and methods of geomorphometry. The overarching drivers of progress in geomorphometry, especially in the environmental context, promise to be global warming and the world's growing population, and how these challenges will be accommodated. Geomorphometry is essential to the understanding of worldwide concerns, such as water and food supply, natural hazards, climate change, and sea-level rise. Despite conceptual advances, the emphasis of this largely empirical science is likely to remain on method and technique rather than theory. The field continues to evolve as computing power increases, and new instrumentation is developed for sensing the Earth and its interacting processes. Few analytical tools will be more effective in furthering knowledge of the Earth and the activities of its inhabitants than a digital surface model and the methods to manipulate it at varied spatio-temporal scales. Among the many prospects for geomorphometry are tighter coupling of remote sensors with in-situ arrays to capture the dynamics of Earth's moisture and energy balances.

Publisher Summary Geomorphometry is the science of quantitative land-surface analysis. It evolved directly from geomorphology and quantitative terrain analysis, two disciplines that originated in 19th century geometry, physical geography, and the measurement of mountains. Modern geomorphometry addresses the refinement and processing of elevation data, description and visualization of topography, and a wide variety of numerical analyses. It focuses on the continuous land-surface, although it also includes the analysis of landforms, discrete features, such as watersheds. The operational goal of geomorphometry is extraction of measures and spatial features from digital topography. Geomorphometry supports countless applications in the Earth sciences, civil engineering, military operations, and entertainment. Geomorphometric analysis commonly entails five steps: Sampling a surface, generating and correcting a surface model, calculating land-surface parameters or objects, and applying the results. The three classes of parameters and objects include both landforms and pointmeasures, such as slope and curvature. Landform elements are fundamental spatial units having uniform properties. Complex analyses may combine several parameter maps and incorporate non-topographic data. The procedure that extracts most land-surface parameters and objects from a digital elevation model (DEM) is the neighborhood operation. Because parameters can be generated by different algorithms or sampling strategies, and vary with spatial scale, no DEM-derived map is definitive.

Publisher Summary Precision farming or precision agriculture is an emerging field in agriculture that tries to optimize the in-field variability of biomass production from an economic and ecological perspective. This chapter focuses on biomass parameters. In the application of geomorphometry in the field of precision agriculture, two main approaches are distinguished. The first one delineates practical, agronomically-meaningful management zones that contained distinct plant growth controlling parameters. The second main approach is based on the use of continuous land-surface parameters. The chapter focuses on two case studies, where it presents examples of how land-surface parameters of different complexity have been used in practice. The first example uses a model applied under farm conditions to estimate the biomass development and to predict the amount of nitrogen fertilizer applications in a precision agriculture approach. The second example provides results for post harvest analysis to increase our understanding about crop yield development processes using landform classification.

Publisher Summary Integrated land and water information system (ILWIS) is an integrated geographic information system (GIS) package. The most recent version of ILWIS offers a range of image processing, vector, raster, geostatistical, statistical, database, and similar operations. The biggest advantage of ILWIS is that it is a compact package with a diverse vector and raster-based GIS functionality and the biggest disadvantage are bugs and instabilities, and necessity to import data to ILWIS format from other more popular GIS packages. In the most recent version of ILWIS, one can import GIS layers from a wide range of packages and formats. This is possible due to two built-in translation tools: GeoGateway and GDAL. The chapter explains how to import an existing digital elevation model (DEM) or derive it from the sampled elevations. It works with sampled elevations digitized from the 1:50,000 topo maps and the 30 m resolution SRTM image. The chapter also presents two ways to derive LSPs/LSOs in ILWIS: (a) By using built in commands and (b) by building and running scripts. ILWIS has a limited number of built-in land-surface parameterization algorithms. These are mainly focused on derivation of land-surface parameters related to hydrology.

Publisher Summary Environmental Systems Research Institute (ESRI) has for decades been a key provider of software solutions for analysis, management, and visualization of spatial data. ESRI products are especially powerful in providing support for large digital elevation model (DEM) databases and include a wide variety of land-surface parameter functions. Other software that is closely linked with the ESRI products and can provide similar commands is for example the Terraflow4 approach. This chapter covers graphical user interface (GUI) and command line options for geomorphometric analysis in ESRI products. The user has a choice of high- and low-level programming languages to interact with these products in order to create new datasets and models. The learning curve can be quite steep, unless the user has prior programming experience. A strong user community is available to provide support for people working on these commercial systems. Several external applications can be used in conjunction with ESRI products, therefore providing a seamless workflow for geomorphometric analysis in different model systems.

Publisher Summary TAS is freely available geographic information system (GIS) for Windows ® operating systems that have been developed to analyze digital elevation data. The software is predominantly used for academic research and education in universities worldwide. Interest in TAS as a research tool reflects its substantial capabilities for modeling catchment processes. The software contains an extensive list of land-surface parameters, beyond that is generally available in commercial GIS packages. Several stream network and basin morphometrics can also be calculated from digital elevation model (DEM)-extracted streams and watersheds. The chapter presents the lists of the primary and secondary land-surface parameters that can be extracted from DEMs using TAS. Many of these parameters are not commonly available in GIS packages and several are only available in TAS. TAS is easy to install and simple to use, which makes it ideal for educational purposes and for use by non-experts. Development of TAS has been directed largely by feedback provided by the user community and is ongoing. Most of the bugs that occurred in early versions of TAS have been fixed in later versions.

Publisher Summary MicroDEM is a full-featured geographic information system (GIS), geared for geological applications with digital elevation models (DEMs). It features unique capabilities for computing terrain organization and computing regional geomorphic parameters. MicroDEM began with a heavy emphasis on practical application of DEMs, including slope maps, 3D oblique views, line of sight profiles, and viewsheds. MicroDEM reads DEMs in both geographic and rectangular (UTM-like) grids, and can read many other DEMs. A partial list of supported data formats includes: DTED, SRTM in both DTED and .hgt formats, USGS ASCII and SDTS, and netCDF. MicroDEM can create a number of statistical graphs for the DEM, either for the entire DEM or a subset currently on the screen. These choices occur on the Analyze menu, available with an active DEM map. The chapter discusses derivative terrain grids for local morphometric land-surface parameters in MicroDEM that can be created in several ways. MicroDEM can also create parameter maps for regional statistics, which require a much larger neighborhood around the point than the typical 8 neighbors used for slope, aspect, and curvature.

Publisher Summary While geomorphometric grids are used to prepare input data for virtually all hydrologic models, fully spatial models make direct use of these grids. This chapter focuses on fully spatial models. A few representative examples of some highly developed spatial models are Mike SHE, gridded surface subsurface hydrologic analysis (GSSHA), CASC2D, PRMS, DHVSM, and TopoFlow. The main goal of this chapter is to discuss basic concepts that are common to virtually all spatial hydrologic models. Several key hydrologic processes and how they are typically incorporated into spatial models are discussed. Spatial hydrologic models integrate many branches of hydrology and there are many different approaches for modeling any given process, from simple to very complex. It aims to highlight the most fundamental concepts that are common between spatial models and to show how they incorporate geomorphometric grids. The chapter also discusses scale issues in spatial hydrologic modeling and provides a brief discussion of preprocessing tools that are typically needed in order to prepare required input data. It presents a simple case study in which a model called TopoFlow is used to simulate the hydrologic response of a small ungauged watershed in the Baranja Hill case study.

Publisher Summary This chapter examines how digital elevation models (DEMs) can act as affordable sources of information to support mapping and modeling of natural landscapes. It provide an overview of many of the ways in which DEM parameters can be used to map various environmental conditions efficiently, and consider the capabilities and limitations of different approaches. Topography is one of the key factors in controlling many of the most significant natural processes of interest to humans. The chapter focuses on the most common groups of applications of geomorphometry in environmental and Earth sciences, they are: Geomorphology and geology, hydrology, soil science, vegetation science, and climatology and meteorology. Relevant and detailed geoinformation is a prerequisite for successful management of natural resources in many applied environmental and geosciences. With the rapid development of remote sensing and geoinformation science, survey teams have increasingly created their products (geoinformation) using ancillary data sources and computer programs. The chapter distinguishes two major approaches to modeling of reality that vary with respect to the exactness of the understanding and to the amount of the random component in the model: Direct estimation models and indirect estimation models.

Publisher Summary This chapter examines three approaches in which LandSerf can be used to consider scale dependencies in land-surface parameters. Firstly, standard land-surface parameters, such as slope and curvature are measured at any arbitrary scale; a scale determined by setting the local window size over which the parameter is estimated. Secondly, the variation in land-surface parameters with scale is considered explicitly either by plotting the scalesignature at points over a surface or by finding the scales at which land-surface parameters are most extreme. Thirdly, variation of land-surface parameters with scale is explored visually through the use of mipmapping in a dynamic 3D environment. The strong visual control that underlies the design of LandSerf remains one of its strengths. One of the consequences and weaknesses of this design is that all handling of spatial data is carried out in memory in order to increase the speed of visual interaction. The non-commercial status of Landserf and the fact that it is written in Java makes it a package easily accessible to most geomorphometry researchers. The weakness of this model of development is that it does not have the distributor-led support that commercial packages provide.

Publisher Summary Landform types are conceptualize as mainly consisting of waveform features that exhibit entire repeating cycles of variation in morphological properties, such as slope gradient, slope lengths, relief, curvatures, and moisture regime. These cyclic patterns can be identified and characterized by analyzing the distribution of variation in morphological attributes within neighborhoods defined by windows of appropriate dimensions and shape, as morphological variables computed for any given cell describe only a small portion of the total cyclic variation that characterizes a repeating landform type. Landform types provide information on the size and scale of landform features and how this size and scale might affect the amounts of energy available for geomorphic, pedogenic, and hydrological processes. Landform types provide context that can be used to inform and improve the further sub-division of the landscape into landform elements. Landform elements have been classified based solely on consideration of their local surface shape, on consideration of a combination of surface shape and slope gradient, and on consideration of a combination of surface shape, slope gradient, and contextual measures of relative landform position. Procedures for automatically extracting and classifying landform types and landform elements differ in terms of the kinds of classification methods applied to extract the entities. Repeating landform types have mainly been classified using Boolean rules based on expert knowledge and Heuristic beliefs. Classification of landform elements has been achieved using a wide variety of classification methods including knowledge-based heuristic approaches, supervised classification, and unsupervised classification.