Global Journal of Engineering Sciences (GJES)
Determination
Of The Relief Complexity Factora
Authored by Bafo Khaitov
Mini Review
Determination of relief
complexity degree is the most important factor for decision of implementation
of different engineering tasks and at the same time the least studied. It shall
be noted that the degree of complexity or roughness has a word description as a
flat or undulating terrain, rugged topography, smooth relief, etc. and has not
numerical characteristics, that, obviously, presents a basic difficulty of
their practical use.
In writings [1] there is a
description of determination of geometrical model TS complexity degree, where
accumulated absolute intrinsic and extrinsic curvatures of crests determine the
degree of model complexity. There is also a definition that the simplest
surface – plane – has complexity degree equal to “0” irrespective of number of
considered crests.
In the engineering practice
there is not a unified methodology of determination of relief complexity or
roughness degree. In writings [2] there is an approach to this task by methods
of probability theory and mathematical statistics based on data of topographic
location plan. The work is based on ratio of isolines concentration to dm2 and takes
into consideration indications of water parting lines, baffle-walls thalwegs,
bases, etc. This approach is not applicable to DMR (Digital Model of Relief) as
modern DMR is based on regular or irregular data grid. Consequently, the relief
complexity degree is directly related to these data and may be determined by
correlation of these data.
If surface may be considered
as aggregate of consecutive positions of line moving in space according to
definite law [3,4,5], let us determine some degree of complexity for plane
curve as interpolation of regular grid points by the least distance along X or
Y is a plane curve.
Let us consider the complexity
of line given by minimal quantity of points:
Two points of line simply
determine the right line for which degree of curvature will be “0”.
Three points on the plane may
lie either on the line, or outside the direct trajectory. Thus, the degree of
curvature –complexity of line may be defined through location of three points
on the plane.
Further, let us consider a surface
with minimum number of points. Three points in the space shall monotypically
determine the plane, for which is determined the degree of complexity equal to
«0». Four points in the space may determine either a plane, or skew plane, but
cannot determine closed convexity or concavity. Intersection of two or three
planes given on the rectangular regular mesokurtic form a truncated unclosed
vertex. Thus, for rectangular regular mesokurtic is fair the consideration of
four intercrossing planes, which shall determine in particular case, both the
plane, and the character of convexity or concavity of the considered surface
On the
rectangular regular mesokurtic, the considered four planes may be given by five
points. By connecting of intermediate four points it is possible to increase
the number of planes to eight. Hence, nine points of regular mesokurtic (3×3)
form a square of four cells (quadrants).
This equation
satisfies to the definition of degree of complexity of the surface ΞΎ=0 and
gives us different values, if the considered surface is not a plane.
The degree of
complexity of irregular (topographic) surface may be also defined by
considering the TS as a population of adjacent regular surfaces, and the sum of
degree of complexity of squares gives a rough idea of the degree of complexity
of TS in total. Thus, the degree of complexity of the whole section of the
surface will be:
The numerical value of complexity of project surface gives an option possibility of project realization, economical accounting of energy resources, bringing in some factors of complexity of realization of the project etc.
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