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The Method of Calculating the Permissible Sampling Step of the Digital Elevation Model Depending on the Degree of Terrain Roughness

A. I. Yakovlev, V. F. Alekseev, D. O. Medyannikov, K. K. Zhbanov

Transactions of IAA RAS, issue 57, 41–47 (2021)

Keywords: digital elevation models, sampling step, Markov models, zoning terrain, statistical characteristics of the terrain

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Abstract

The article discusses the method of calculating the sampling step of regular digital elevation models. The calculation of the discreteness of relief models is necessary for the optimal use of information resources of those computing tools in which digital relief models are used. The aim of the study was to establish such a step in the discretization of the relief model, which would allow to restore the relief function with the required accuracy for any physical and geographical area. To achieve the purpose of the study, 2 tasks were solved: terrain zoning was performed depending on its complexity, and possible values of the step of discretization of relief models for various initial conditions were calculated. The well-known approaches to solve the problem of function discretization based on V. A. Kotelnikov's theorem are considered. It is revealed that the initial data for calculating the discretization of a function are its statistical characteristics (dispersion and correlation radius). Statistical characteristics of various relief forms have been experimentally investigated. It is established that the dispersion of the relief obeys the law of equal-dimensional distribution, and the radius of correlation can vary widely. The ranges of variance values for all types of relief are calculated and a possible range of values of correlation radii is assigned. As a result, the values of the sampling step of digital relief models are calculated depending on the degree of terrain roughness and the required accuracy of restoring the height function using known approaches. Different approaches have produced similar results. Based on the calculated data, it is proposed to establish a fixed range of discreteness of relief models (45, 20, 13, 10 and 5 m) corresponding to five types of relief, which are classified by dispersion ranges.

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A. I. Yakovlev, V. F. Alekseev, D. O. Medyannikov, K. K. Zhbanov. The Method of Calculating the Permissible Sampling Step of the Digital Elevation Model Depending on the Degree of Terrain Roughness // Transactions of IAA RAS. — 2021. — Issue 57. — P. 41–47.

@article{yakovlev2021,
  abstract = {The article discusses the method of calculating the sampling step of regular digital elevation models. The calculation of the discreteness of relief models is necessary for the optimal use of information resources of those computing tools in which digital relief models are used. The aim of the study was to establish such a step in the discretization of the relief model, which would allow to restore the relief function with the required accuracy for any physical and geographical area. To achieve the purpose of the study, 2 tasks were solved: terrain zoning was performed depending on its complexity, and possible values of the step of discretization of relief models for various initial conditions were calculated.
The well-known approaches to solve the problem of function discretization based on V. A. Kotelnikov's theorem are considered. It is revealed that the initial data for calculating the discretization of a function are its statistical characteristics (dispersion and correlation radius). Statistical characteristics of various relief forms have been experimentally investigated. It is established that the dispersion of the relief obeys the law of equal-dimensional distribution, and the radius of correlation can vary widely. The ranges of variance values for all types of relief are calculated and a possible range of values of correlation radii is assigned.
As a result, the values of the sampling step of digital relief models are calculated depending on the degree of terrain roughness and the required accuracy of restoring the height function using known approaches. Different approaches have produced similar results. Based on the calculated data, it is proposed to establish a fixed range of discreteness of relief models (45, 20, 13, 10 and 5 m) corresponding to five types of relief, which are classified by dispersion ranges.},
  author = {A.~I. Yakovlev and V.~F. Alekseev and D.~O. Medyannikov and K.~K. Zhbanov},
  doi = {10.32876/ApplAstron.57.41-47},
  issue = {57},
  journal = {Transactions of IAA RAS},
  keyword = {digital elevation models, sampling step, Markov models, zoning terrain, statistical characteristics of the terrain},
  pages = {41--47},
  title = {The Method of Calculating the Permissible Sampling Step of the Digital Elevation Model Depending on the Degree of Terrain Roughness},
  url = {http://iaaras.ru/en/library/paper/2090/},
  year = {2021}
}

TY  - JOUR
TI  - The Method of Calculating the Permissible Sampling Step of the Digital Elevation Model Depending on the Degree of Terrain Roughness
AU  - Yakovlev, A. I.
AU  - Alekseev, V. F.
AU  - Medyannikov, D. O.
AU  - Zhbanov, K. K.
PY  - 2021
T2  - Transactions of IAA RAS
IS  - 57
SP  - 41
AB  - The article discusses the method of calculating the sampling step of
regular digital elevation models. The calculation of the discreteness
of relief models is necessary for the optimal use of information
resources of those computing tools in which digital relief models are
used. The aim of the study was to establish such a step in the
discretization of the relief model, which would allow to restore the
relief function with the required accuracy for any physical and
geographical area. To achieve the purpose of the study, 2 tasks were
solved: terrain zoning was performed depending on its complexity, and
possible values of the step of discretization of relief models for
various initial conditions were calculated.  The well-known
approaches to solve the problem of function discretization based on
V. A. Kotelnikov's theorem are considered. It is revealed that the
initial data for calculating the discretization of a function are its
statistical characteristics (dispersion and correlation radius).
Statistical characteristics of various relief forms have been
experimentally investigated. It is established that the dispersion of
the relief obeys the law of equal-dimensional distribution, and the
radius of correlation can vary widely. The ranges of variance values
for all types of relief are calculated and a possible range of values
of correlation radii is assigned.  As a result, the values of the
sampling step of digital relief models are calculated depending on
the degree of terrain roughness and the required accuracy of
restoring the height function using known approaches. Different
approaches have produced similar results. Based on the calculated
data, it is proposed to establish a fixed range of discreteness of
relief models (45, 20, 13, 10 and 5 m) corresponding to five types of
relief, which are classified by dispersion ranges.
DO  - 10.32876/ApplAstron.57.41-47
UR  - http://iaaras.ru/en/library/paper/2090/
ER  -