Geomorphometry

[1] It gathers various mathematical, statistical and image processing techniques that can be used to quantify morphological, hydrological, ecological and other aspects of a land surface.

Geomorphometrics is the discipline based on the computational measures of the geometry, topography and shape of the Earth's horizons, and their temporal change.

[3] Extracted surface parameters and objects can then be used, for example, to improve mapping and modeling of soils, vegetation, land use, geomorphological and geological features and similar.

With the rapid increase of sources of DEMs today (and mainly due to the Shuttle Radar Topography Mission and LIDAR-based projects), extraction of land surface parameters is becoming more and more attractive to numerous fields ranging from precision agriculture, soil-landscape modeling, climatic and hydrological applications to urban planning, education, and space research.

Today, land surface parameters are successfully used for both stochastic and process-based modeling, the only remaining issue being the level of detail and vertical accuracy of the DEM.

[4] Geomorphology (which focuses on the processes that modify the land surface) has a long history as a concept and area of study, with geomorphometry being one of the oldest related disciplines.

This has only recently been developed since the availability of more flexible and capable geographic information system (GIS) software, as well as higher resolution Digital Elevation Model (DEM).

[6] It is a response to the development of this GIS technology to gather and process DEM data (e.g. remote sensing, the Landsat program and photogrammetry).

Recent applications proceed with the integration of geomorphometry with digital image analysis variables obtained by aerial and satellite remote sensing.

[7] As the triangulated irregular network (TIN) arose as an alternative model for representing the terrain surface, corresponding algorithms were developed for deriving measurements from it.

That said, the algorithms typically used in GIS and other software use approximate calculations that produce similar results in much less time with discrete datasets than the pure continuous function methods.

In principle, it is the angle between the gradient vector and the horizontal plane, given either as an angular measure α (common in scientific applications) or as the ratio

This can make it a significant factor in modeling and mapping microclimates, vegetation distribution, wildlife habitat, and precision agriculture.

As a relatively new and unknown branch of GIS the topic of geomorphometrics has few 'famous' pioneer figures as is the case with other fields such as hydrology (Robert Horton) or geomorphology (G. K. Gilbert[21]).

A surface with a sample of normal vectors
The geometry of calculating slope
Shaded relief map of New Jersey
Slope effect of vegetation that is different on north-facing and south-facing slopes.
Map depicting cut and fill areas for a construction site.