تحليل فضايي لندفرم‌هاي بادي با استفاده از نظريه فركتالي (مطالعه موردي: ريگ اردستان)

Spatial Analysis of Aeolian landforms by Fractal Theory (Case study: Ardestan Rig)

هندسه فركتالي يكي از روش‌هاي آماري است كه سعي دارد پيچيدگي?هاي طبيعت را در قالب رياضيات و آمار مطرح سازد. هدف اين مطالعه تحليل فركتالي لندفرم‌هاي بادي ريگ اردستان است. بدين منظور از تصاوير ماهواره كارتوست سال‌هاي 2008 و 2011 با قدرت تفكيك 3 متر استفاده شد. به‌منظور تحليل فركتالي، چهار لندفرم بادي شاخص شامل تپه‌هاي ماسه‌اي طولي، تپه‌هاي ماسه‌اي عرضي، برخان و برخان‌هاي تاغ‌كاري‌شده در منطقه‌اي با وسعت 1350 كيلومترمربع تفكيك شد. براي تعيين بعد فركتالي از روش شمارش خانه استفاده شد. نتايج نشان داد كه الگوي هندسي لندفرم‌ها خاصيت فركتالي دارد. تحليل بعد فراكتالي نشان داد كه بيشترين ميزان بعد فركتالي متعلق به لندفرم‌هاي بادي تثبيت شده است كه بيشترين وسعت را در منطقه دارد. پس مساحت لندفرم‌ها در بعد فركتالي آن‌ها متاثر است. همچنين، عدم تغييرات اين بعد طي مدت بررسي، نشان‌دهنده تثبيت اين لندفرم‌ها و عدم تغيير آن‌ها طي اين مدت بررسي است. بيشترين ميزان تغييرات مربوط به تپه‌هاي ماسه‌اي عرضي و طولي است كه گستره آن‌ها رو به كاهش است. اين امر با كاهش بعد فركتال نشان داده شد و تطبيق مي‌كند. به‌طور كلي، نتايج به‌دست‌آمده از تحليل فراكتالي به طور نسبي واقعيت‌هاي مورفولوژيكي لندفرم‌هاي بادي را تحليل مي‌كند.

Extended Abstract Introduction Today, mathematics is a strong way for explain process and the complexity of nature so this turmoil have 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, use of fractal geometry and its dimension for understanding the heterogeneity in natural environments is common Agency of this study is the morphological behavior of each wind geomorphic forms in the environment. It should be noted that the behavior of landforms are nonlinear in nature, so they can be analyzed with statistical methods and fractal geometry is one of the approaches that attempt to use their theories and formulas can 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 by using geometry and use mathematics for determine the rate of changes. So, focus on wind landform because of having more variability than other landforms due to faster to better results may be achieved in a shorter timeframe. Special analyses are the major challenges facing researchers. Also evaluated in terms of the fractal dimension is other goal of this study. Materials and methods The study area is between 33 30- 33 45 North longitude and 52 15- 53 east latitude and the divisions in the Zavareh- ARDESTAN-Isfahan. The height of the southwestern region to the north in 1410 to 910 and an average gradient is 0.5 percent. In this study aims to identify 5 index landforms and determine the limit of the development extracted carefully. The data used for this purpose are: - CARTOSAT1 image 2008 - CARTOSAT1 image 2011 - Geological map 1: 100,000 geological Box counting is one of the most widely used methods in fractal studies and in this research has been implemented. The different between the fractal dimensions that obtained in different periods show that they will be 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 fractal analysis of aeolian landforms of Ardestan Rig. 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, barkhans and planted sand dunes. To determine the fractal dimension, we used Box counting method. The results showed that Natural sciences, such as geomorphology are face to inherent variable that are not very repeatable or predictable and have highly sensitive to initial conditions. Since geomorphologic landforms have a special sizes and dimension, the spatial arrangement of these shapes to each other can determined many effective factors in their formation that we can identify these effective factors accurately. Behavior of landforms in nature is non-linear and can be analyzed by statistical methods. Wind landforms set of complex systems, which sometimes act in a rotational manner and at a time when the irregularities leading to the order. 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 of in nature. Because of the size and dimensions of the special landforms they could analysis by mathematics and statistics and the following factors in their changing were studied. In this study, the fractal theory in geomorphology and particularly in landforms analyzed exactly and were used and it could give us satisfactory results by mathematic and statics. The fractal dimension of landforms was studied. In addition, this study showed the ability of fractal theory to identify the changes that happened in landforms. Conclusion Natural sciences face to a great revolution, nowadays. Now, scientists think the world as a collection of complex systems which prediction of consequences of this complex systems is so difficult. In this situation the systems have rotational act so irregularly lead to regular and regularly lead to irregular. 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. So, in this study results show that the geometric patterns of landforms have fractal characteristics so it can be analyzed for different years. The dimension of fractal as a main index, show that planted sand dunes that have a most extent, have a great dimension because it don’t changed during the study period, and indicating 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 matches with realities of aeolian landforms.