# Spatial analysis of aeolian landforms by fractal theory (Case study: Ardestan Rig)

Document Type : Full length article

Authors

1 Assistant Professor of Physical Geography, Tarbiyat Modarres University, Tehran, Iran

2 Associate Professor of Physical Geography, University of Tehran, Iran

3 Assistant Professor of Statistics, Faculty of Statistics and Mathematic, Tarbiyat Modarres University, Tehran, Iran

4 Associate Professor of Remote Sensing and GIS, Tarbiyat Modarres University, Tehran, Iran

5 PhD Candidate of Geomorphology, Tarbiyat Modarres University, Tehran, Iran

Abstract

Introduction
Today, mathematics is a strong way to explain process and the complexity of nature so this turmoil has to be made in the form of mathematical and quantitative relationships and to some extent predict their effects. For this purpose, to illustrate the complexity, we used fractal geometry and its dimension to understand the heterogeneity in natural environments. The purpose of this study is to examine the morphological behavior of each wind geomorphic forms in the environment. It should be noted that the behavior of landforms are nonlinear in nature. They can be analyzed with statistical methods and fractal geometry as one of the approaches that attempt to use their theories and formulas to represent the complexity and quantity in the form of mathematics. The term nonlinear is unequal relations between influential forces or stress and geomorphic response to states.
This paper aims to explain the behavior of fractal geometry and morphological landforms using geometry and use of mathematics to determine the rate of changes. Therefore, we focus on wind landform because of having more variability compared with other landforms because faster and better results may be achieved in a shorter timeframe. Special analyses are the major challenges by researchers. We have also evaluated the fractal dimension as other goal of this study.
Materials and Methods
The study area is located between 33 30- 33 45 North longitude and 52 15- 53 east longitude  in the Zavareh- Ardestan-Isfahan. The elevation from southwestern region to the north is ranged from 1410 to 910 m and the area has an average slope of 0.5 percent.
In this study we attempt to identify 5 index landforms and determine the limit of the development. The data used for this purpose are:
- CARTOSAT1 image 2008
-  CARTOSAT1 image 2011
- Geological map 1: 100,000
Box counting as one of the most widely used methods in fractal studies has been employed in this research. The difference between the fractal dimensions obtained in different periods show that they will have more changes occurred in the phenomenon. In addition, this study shows the ability of fractal geometry to identify the changes that happened in landforms.

Result and Discussion
The purpose of this study is to apply fractal analysis of aeolian landforms of Ardestan Rigion. For this purpose, we used Cartosat images of 2008 and 2011, and for fractal analysis, we divided typical aeolian landforms of study area into four categories; longitudinal sand dunes, cross sand dunes, barchans, and planted sand dunes. To determine the fractal dimension, we used Box counting method.
The results indicated that natural sciences, such as geomorphology are faced with inherent variable that are not very repeatable or predictable. They are highly sensitive to initial conditions. Since geomorphologic landforms have a special sizes and dimension, the spatial arrangement of these shapes to each other can determine many effective factors in their formation and we can identify these effective factors accurately.
Behavior of landforms in nature is non-linear and can be analyzed by statistical methods. Wind landforms of complex systems sometimes act in a rotational manner. This complex behavior is contrasts with the simple laws of physics and is nonlinear and dynamic. In this study, it was observed that mathematics is a powerful tool to describe landforms and processes, in nature.
Because of the size and dimensions of the special landforms, they could analyze mathematics and statistics. In this study, the fractal theory in geomorphology and particularly in landforms can be analyzed exactly. It could give us satisfactory results by mathematic and statics. The fractal dimension of landforms was studied. In addition, this study indicated the ability of fractal theory to identify the changes that happened in landforms.

Conclusion
Natural sciences are faced with a great revolution, nowadays. Now, scientists think the world as a collection of complex systems can predict consequences of this complex system. In this situation, the systems have rotational behavior. In the meantime, geomorphic landforms have special shapes, sizes and special aspects, and the spatial arrangement of these shapes to each other can be determined by many influence factors in their formation. Since the landforms behaviors are nonlinear in nature, it can be analyzed using statistical methods which Fractal geometric is one of them. The theory attempts to use its equations to represent the complexity by mathematical way. Thus, results of this study show that the geometric patterns of landforms have fractal characteristics and it can be analyzed for different years. The dimension of fractal as a main index shows that planted sand dunes have a great dimension because it cannot change during the study period and indicate the stabilization of sand dunes. The maximum rate of change belongs to longitudinal and cross sand dunes that their extent is decreasing and this has been shown to reduce the fractal dimension and its implementation. In general, the result of fractal analysis is consistent with realities of aeolian landforms.

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### History

• Receive Date: 05 July 2015
• Revise Date: 20 September 2015
• Accept Date: 01 November 2015