IEEE Geoscience and Remote Sensing Magazine - December 2020 - 138

EDUCATION
B.S. DAYA SAGAR

Digital Elevation Models: An Important
Source of Data for Geoscientists

S

atellite technology has revolutionized the way we
-acquire terrestrial surface data. Such remotely sensed
terrestrial data have made it possible to generate digital
elevation models (DEMs) at multiple spatial and temporal scales by exploiting stereographic, interferometric,
radargrammetric, and lidar principles [1]-[10]. Schemes
adapted to generate DEMs are hugely successful, and,
as such, DEM generation is considered an engineering
marvel. In turn, the availability of DEMs to the geoscientific community is a blessing.
Both terrestrial and Earth-like planetary DEMs [e.g.,
Advanced Spaceborne Thermal Emission and Reflection
Radiometer Global DEM, NASA DEM, Shuttle Radar Topography Mission (SRTM) DEM, Cartosat DEM, SPOT
Stereo DEM, Chandrayaan DEM, Orbiter High Resolution Camera DEM, Mars DEM, Venus DEM, and lidar
DEM] provide rich geometric, topologic, and morphologic information. As a result, DEMs offer an excellent
resource for geoscientists, mathematicians, statisticians,
geophysicists, computer scientists, cartographers, geographic information science professionals, engineers,
and spatial planners in various phases of research to
understand the spatiotemporal behavior of Earth and
Earth-like planetary processes and visualize them in
real time.
DEMs offer much more than is apparent at a visual
inspection for those who are able to extract information of relevance to geometry, topology, and morphology from these models, which are available at multiple
spatial and temporal scales. Until now, DEMs have been
underutilized due to the lack of awareness of how they
could be mathematically exploited, and they have not
yet been studied for their geoscientific relevance. DEMs
contain incredibly rich information that is best extracted with novel mathematical methods [11]-[26], such
Digital Object Identifier 10.1109/MGRS.2020.3031910
Date of current version: 16 December 2020

138



as discrete mathematics, geostatistics, exploratory data
analysis, fractal geometry and scaling theory, fuzzy set
theory, stochastic geometry, mathematical morphology, geomathematics, graph theory, compositional data
analysis, nonlinear dynamical systems, and wavelets. It
would serve the educational needs of the Society to encourage the training of experts in the relevance of DEMs
in these areas. This would enrich the application of
DEMs not only in geosciences but also in a host of other
studies, such as resource estimation and identification,
spatial planning, decision making, predictive analytics,
and many more.
Processing and analysis of DEMs by these mathematical techniques would lead to sequentially intertwined outcomes, such as the application of these
methods to unique valley-ridge connectivity networks,
partitioned basins, surface roughness, geodesic spectra, categories of basins, ridge-valley spacing, geodesic
distances, the rate of surficial evolution, synthetic terrestrial surfaces, revealing spatiotemporal behavior,
and many more. Readers may refer to several technical
papers for demonstrations on how these approaches
are employed in the processing and analysis of DEMs
as well as how challenges ranging from feature retrieval [27]-[37] to quantitative analysis and reasoning
[38]-[52] and modeling and visualization [52]-[55] of
the phenomenon- or process-specific spatiotemporal
behavior are addressed.
Two illustrative examples, selected from numerous e xamples of our g roup, show t he application
of one of the previously mentioned mathematical
theories on a synthetic random discrete topographic
function [Figure 1(a)] and on a realistic DEM [Figure  2(b)] in mapping the unique connectivity network s [Fig ure 1(b)] and hierarc hical watershed
partitioning [Figure 1(c)] and the watershed-wise
classification [Figure 2(b) and (c)] via directional
roughness values computed through multivariate
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

DECEMBER 2020
IEEE Geoscience and Remote Sensing Magazine - December 2020

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