چكيده لاتين :
Introduction
At first glance, river morphology seems complex, because two phenomena (in this
case rivers) are not similar. According to Chaos theory, the river network geometry
can be regulated using mathematical techniques. This pattern is applied for every
structure that shows chaotic behavior. The study of nonlinear dynamics on earth
surface processes and landscapes has been dominated by the application of analytical
techniques derived largely from mathematics, statistics, physics, computational
science, and other fields characterized by experimental laboratory techniques and
numerical models. While much of this has been quite fruitful, geomorphology is
dominantly (and appropriately) a field-based discipline where the ground truth is
paramount. One powerful method is calculating the fractal dimension relative to
landscape. Fractals are defined as geometric objects that are self-similar under a
change of scale, i.e. their shape remains the same under any magnification or
reduction. The fractal dimension characterizes the extent to which the fractal 'fills up'
the embedding space and, in this example, will attain a value between 1 and 2.
Generally, meanders are described in terms of radius of curvature, wavelength, and
other parameters applied on simple geometric configurations. Numerical analysis
principles of any drainage basin characteristics, is connected with the order concept.
So the first step in the study of system nonlinear properties, is the combined analysis
of channels, and consider them as the lines, are an equal level. In fractals, dimension
is very important and measurement scales don't play a role as the effective factor.
two kinds of fractals could be found: (a) self-affine fractals: the object changes when
the scale varies whereas its fractal dimension does not change, and (b) self-similar
fractal: the object is statistically identical to any scale. This property causes the
application of fractal in different sciences. Determination of fractal dimension has a
great importance in behavior recognition and the prediction of change in river
trajectory. Furthermore, fractal dimension can provide information about branch1S
length and sources of river that are not accessible.
Matherials and Methods
Zarrineroud River is located in the northwest of Iran, and it is one of the longest rivers
in this region. It is 302 km long, arising from the mountains of Kurdistan Province,
south of Saqqez, where it is also known as the Jaqtoo (Jaqalu) River. The river
continues north and slightly west to the cities of ShahinDezh, Kashavar and Miandoab
and pours into Lake Urmia.
The structure observed in the demonstrations of chaotic systems does not seem to
be a space filling nor a simple curve (a line). This complex geometry can be
characterized by a non-integral dimension, and the structure is then called a fractal.
The capacity or box counting dimension is a simple way of defining a dimension. It is
related to the Hausdorff dimension, and is usually equal to this (and often assumed
to be so in the context of dynamical systems), although there are counter examples.
The construction is as follows. Suppose we have a set in an m-dimensional space.
Imagine covering the space with equal size m-cubes of side; and count how many mcubes
contain points in the set, say N. The capacity is defined as Fractal dimension is
a useful concept in describing natural objects, which gives their degree of complexity.
There are various closely related notions of fractional dimension. From the
theoretical point of view, the most important are the Hausdorff dimension, the
packing dimension. However, the box counting dimension is widely used in practice,
which may be due to the ease of implementation. Satellite imagery and topographic
maps, at 1:50000-scale, are used for calculations. The number of covering cells of
Zarrineroud River are calculated at seven different scales (25, 50, 100, 200, 400, 800
and 1600 meters) and river systems are extracted by using Arc GIS program. Then the
input of calculating two-dimensional fractal number was inserted to the software
through correlation function. Regarding the fact that in analyzing fractal dimension
through reducing scale more accurate detail can be achieved, for coastal lines, rivers
or any two-dimensional phenomenon L=NS equation is used to generally estimate
length (L). N, the number of cells, and S, the side-length, are required to measure that
phenomenon. Therefore, the apparent length of a line, like a river, increases in nonlinear
manner; however, the scale decreases in proportion to the measured pattern;
that is as N increases, based on the rule of proportion, S decreases.
Discussion
First, according to Rodriguez-lturbe and Rinaldo's method in seven various scales, we
count the covering cells by river, then from equation 1 acquire the box-counting
dimension. In each step taken, the value of the dimension decreases. Thus, in order
for the dimension value to reach values of an open interval (1, 2) more steps are
required than for the other mentioned fractal dimensions. Since the fractal
dime'nsion has a limitation of this logarithm value when the grid size is too small, we
