SYSTEMATIC DEM procedure for YOU

A procedure for the consistent application digital terrain analysis methods to identify geomorphology features in DEMs (Digital elevation Models) has been developed and demonstrated. Digital terrain modelling is carried out by means of the combined use of

  1. numerical differential geometry methods,
  2. digital drainage network analysis,
  3. digital geomorphometry,
  4. digital image processing,
  5. lineament extraction and analysis,
  6. spatial and statistical analysis, and
  7. DEM specific digital methods (shaded relief models, digital cross-section,3D surface modeling).


Novel numerical METHODS developed:

  • high density digital drainage line extraction
  • adaptive terrain smoothing
  • aspect analysis procedure
  • flat areas ID
  • wavelet for valley network.

Focus is on terrain pattern description, feature recognition and characterisation. Use of differential geometry and signal processing methods is emphasised. Applications include morphometry, tectonic geomorphology, terrain modelling for hydrological, soil erosion and sediment transport modeling for contour maps, photogrammetric data (TIN based on irregular control points), radar altimetry data (SRTM) and high-resolution airborn laser scan DEMs (LIDAR). Special emphasis is put on error assessment and uncertainty analysis. A sequential modelling scheme has been developed and implemented to analyse a variety of terrains.



Jordan DTA Methodology

Digital Terrain Analysis

research, development and publication



Jordan G., Meijninger B.M.L., van Hinsberen D.J.J., Meulenkamp J.E. and van Dijk P.M., 2005. A GIS framework for digital tectonic geomorphology: case studies. International Journal of Applied Earth Observation & Geoinformation, 7:163-182.

BOOK: Mathematical Development Paper:

Jordan G., 2007. Digital terrain modelling in a GIS environment. In: Peckham R.J. and Jordan (eds), 2007. Digital Terrain Modelling. Development and Applications in a Policy Support Environment, Series: Lecture Notes in Geoinformation and Cartography, pp. 1-44. Springer, Berlin. 313 p. ISBN: 978-3-540-36730.

Supporting Papers:

Univariate & GIS:
Jordan G., Csillag G., Szucs A., and Qvarfort U., 2003. Application of digital terrain modelling and GIS methods for the morphotectonic investigation of the Káli Basin, Hungary. Zeitschrift fur Geomorphologie, 47:145-169.

Bivariate & Advanced Spatial Analysis:

Jordan G., 2003. Morphometric analysis and tectonic interpretation of digital terrain data: a case study. Earth Surface Processes & Landforms, 28:807-822.


Methods Papers:

Jordan G., 2007. Adaptive smoothing of valleys in DEMs using TIN interpolation from ridgeline elevations: an application to morphotectonic aspect analysis. Computers & Geosciences, 33:573-585.

Jordan G. and B. Schott 2005. Application of wavelet analysis to the study of spatial pattern of morphotectonic lineaments in digital terrain models. A case study. Remote Sensing of Environment, 93:31-38.

Applications Papers:

Kereszturi G., Jordan G., Németh K. and Dóniz-Páez J.F., 2012. Syn-eruptive morphometric variability of monogenetic scoria cones on Tenerife (Canary Islands). Bulletin of Volcanology, 74:2171-2185.

Petrik A. and Jordan G., 2013. Morphotectonic analysis and field verification of thrust-faulted zone using DEMs. A case study for the Villány Hills, Hungary. Journal of Geomorphology (submitted)

Korody G. and Jordan G. 2013. 3D digital geological modelling of paleo-surfaces. A case study from the national nuclear waste depository site in Hungary. Mathematical Geosciences (submitted)




See Publications for papers.

For more information Contact Us.



Jordan & co-workers (see Publications) developed a mathematically founded elaborate system of terrain analysis and morphometry. The METHOD is specifically used for tectonic geomorphology, but it can be applied to any DEM morphological analysis.

Geometric characterisation of topographic surfaces

Based on point attributes, Evans (1972; 1980) developed geomorphometry using five basic parameters estimated from the elevation model: elevation, slope, aspect, profile and tangential curvatures that are calculated for regular points. We further expand his system with surface specific points: (1) inflexion points, (2) singular points, and (3) valley lines and ridge lines. Inflexion points (lines) are added as the sixth parameter calculated for regular points because they define convex and concave areas, essential in surface flow modelling. Singular points calculated are (1) local minima (pits), (2) local maxima (peaks), (3) saddle points (passes) and (4) horizontal planar points (flats). Finally, we add flow boundaries: (1) valley line (drainage line) and (2) ridge line (watershed divide). A complete geometric characterisation of topographic surface is obtained:

Singular points, inflexion points, valley lines and ridge lines are called ‘surface specific points’ because they are calculated only for certain isolated locations (points and lines). In contrast, elevation, gradient and curvature are calculated for points of areas.

In practice, first points of the topographic surface are classified as regular and singular points. Next, singular points are classified into peaks, pits, passes and flats, and are then excluded from further analysis. Third, the gradient vector (slope and aspect) and curvatures, together with inflexion points (convexity) are then calculated for areas of regular points. Finally, valley lines and ridge lines are calculated.

It is noted that length of surface curves (e.g. slope line or valley line length) or surface area (e.g. catchment drainage area) are given by line and surface integrals, respectively. Integrals are parts of exhaustive geometric characterisation of surfaces with flow, essential in surface hydrological and sediment transport modelling.

From the above analysis it can be concluded that the estimation of the necessary 12 geometric parameters can be reduced to the estimation of five partial derivatives only:

¦x = ¶z/¶x,      ¦y = ¶z/¶y,

¦xx = 22z/¶x2,      ¦yy =  22z/¶y2,      ¦xy =  22z/¶x2.

One of the main results of all the above discussions is this surprising simplification of the problem. The necessary numerical methods are presented below.

Feature recognition and parameter extraction from DEMs

The design of the modelling scheme is based on the following considerations:


–     the objective is the quantitative geometric characterization of landforms;

–     the objective is providing reproducible outputs;

–     analysis proceeds from simple to the more complex methods;

–     outputs from modelling steps are controlled by input data and parameters;

–     the procedure integrates a wide-range of available methods;

–     multi-source information is integrated in the database;

–     DTA is implemented in a GIS environment.



Analysis proceeds from simple univariate elevation studies, through differential geometric surface analysis and drainage network analysis, to the multivariate interpretation of results using GIS technology. Reproducibility of morphological analysis is achieved by the application of numerical data processing algorithms. Each modelling module has a set of defined input parameters. Subsequent steps are based on output of previous terrain models. Prior to the spatial analysis of each terrain attribute, its histogram is studied for systematic error and statistical properties such as multi-modality. Histograms are interpreted in terms of morphometry and used for classification of terrain data. Image stretching for enhancement of visual interpretation is also based on histograms.



For more details see Publications.


DTA – examples:

Some basics of DTA:

Digital terrain models (DTM) are ordered arrays of numbers that represent the spatial distribution of terrain attributes. A digital elevation model (DEM) is defined as an ordered array of numbers that represent the spatial distribution of elevations above some arbitrary datum in a landscape. DEMs are the most basic type of DTMs. Digital terrain analysis (DTA) is implemented on digital elevation models in order to derive digital terrain models of various terrain attributes. Topographic attributes, such as slope and aspect can be derived from contour, TIN and grid DEMs, however, the most efficient DEM structure for the estimation and analysis of topographic attributes is generally the grid-based method. Regular grid data structure is needed also for spatial data manipulation by GIS. In order to make maximum advantage of well-established methods of GIS technology, digital image processing and DTA, the present discussion on terrain analysis is confined to the most widely-used grid-based DEMs. Topographic attributes can be classified into primary and secondary (or compound) attributes according to their complexity. Primary attributes are directly calculated from a DEM and include (1) point attributes of elevation, slope, aspect and curvatures, and (2) area properties such as integrals (e.g. area or surface integrals such as catchment area, or line integrals such as flow path length), and statistical properties of elevation over an area (e.g. mean and standard deviation of elevation or slope).

Fractal dimension of terrain can also be regarded as a primary attribute. Compound attributes involve combination of primary attributes and can be used to characterise the spatial variability of specific processes occurring in the landscape, such as surface water saturation (wetness index) and sheet erosion. This classification originates from geomorphology. Topographic attributes can also be classified according to their spatial character. Point attributes result from spatial (also called local) operations that modify each pixel value based on neighbouring pixel values. Examples are gradients calculated for each pixel in a moving kernel. Spatial attributes result from point (also called global) operations that modify pixel values independently from neighbouring pixels. Line and area integrals, and overall or local statistical calculations yield spatial attributes. This classification originates from digital image processing.