بررسي نظريه ي فركتال در ژيومورفولوژي رودخانه اي: مطالعه ي موردي زرينه‌رود

Study of Fractal Theory in River Geomorphology: Zarrineroud case study

هندسه فركتال، كه عنوان زبان رياضي طبيعت بر آن نهاده شده است، مي‌تواند به عنوان ابزار كمي مناسب جهت بررسي ژيومورفولوژي رودخانه‌ها و مدل‌سازي بسياري از پديده‌هاي پيچيده طبيعي به كار گرفته شود. مهم‌ترين ويژگي فركتالي كه در مورد اين پديده ها تحليل مي‌شود، بعد فركتال است كه اهميت زيادي در شناخت رفتار و پيش‌بيني تغييرات مسير رودخانه دارد. اين مقاله باهدف تعيين بعد فركتال و تحليل آن با استفاده از تيوري هندسه فركتال و روش شاخه-بندي هورتون- استرالر و توكوناگا، به مطالعه ويژگي هاي رودخانه زرينه‌رود مي پردازد. بر اين اساس، رودخانه زرينه‌رود و تمامي شاخه هاي فرعي آن مرتبه بندي شده و به كمك طول شاخه-ها، بعد فركتالي محاسبه شد. نتايج نشان داد كه شاخه اصلي اين رودخانه داراي مرتبه چهارم بوده و همچنين بعد فركتالي آن مقداري برابر با 98/1 دارد. بعد فركتالي بالاي رودخانه معرف تراكم زهكشي بيشتر و زمان كمتر براي رسيدن به جريان دايمي است. به اين ترتيب تعداد انشعابات رودخانه از مرتبه‌هاي گوناگون، همچنين سطح و طول اين انشعابات از رابطه فركتالي پيروي مي‌كنند. بعد فركتالي مي‌تواند شاخص مناسبي براي بيان تغييرات رودخانه باشد و به عنوان پارامتر هندسي جديد وارد مدل‌هاي ريخت‌شناسي رودخانه‌ها گردد. از اين روابط مي‌توان جهت بررسي تغييرات انشعابات رودخانه‌ها و نيز حوضه‌ي آن‌ها در گذر زمان بهره جست. بنابراين با كمك بعد فركتال مي توان به پيش بيني مسايل مربوط هندسه رودخانه و همچنين فرآيندهاي فيزيكي درون رودخانه پرداخت.

Introduction 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. Usually, ‘‘meandering’’ analysis in rivers is started by considering pattern characteristics such as whether the meanders are regular or not, their degree of periodicity and their spatial configuration. 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. Principles of numerical analysis of the characteristics of any drainage basin, is connected with the concept of order. So the first step in the study of nonlinear properties of the system, combined analysis of channels and consider them as the lines are an equal level. Methodology Fractal trees have been employed in a wide variety of applications including drainage networks, actual plants and trees, root systems, bronchial systems, cardiovascular systems, and evolution. Prior to the introduction of fractals by Mandelbrot, empirical studies of drainage networks had given power-law relations between stream numbers, stream lengths, drainage areas, and stream slopes. The original branch ordering taxonomy for fractal trees was developed as a stream-ordering system in geomorphology by Horton and Strahler streams on a standard topographic map with no upstream tributaries are defined to be first order (i= 1). When two first-order streams combine they form a second-order (i = 2) stream. When two second-order streams combine, they form a third order (i = 3) stream, and so forth. Horton introduced the bifurcation ratio R_b=N_i/N_(i+1) And the length-order ratio R_r=r_(i+1)/r_i Where Ni is the number of streams of order i, and ri is the mean lengh of streams of order i. with the introduction of the fractal dimension D as the power-law scaling exponent between number and length, it was recognized that the fractal dimension of a stream network is given by D= ln??R_b ?/ln??R_r ? Zarrineroud is a constant stream of length 302 km, 2500 m latitude source, outfall height of 1275 m, the average slope of 0.4%. Average monthly discharge is 139500000 m3 and the mean annual discharge is 1813000000 m3. Results To investigation the fractal theory in Zarrineroud, first all its branches are classified using a system of Strahler order. The main branch is the branch that from XQ begins and ends in the lake, is of order 44. Fractal dimension is according to equation D= ln??R_b ?/ln??R_r ? = ln??(3.125)?/ln??(1.78)? =1.96 This value is obtained according to the following table. Number of streams of order i Bifurcation ratio (Rb) mean length of streams of order i (km) length-order ratio (Rr) N_1=27 N_1/N_2=3.375 r_1=25.35 r_2/r_1=1.22 N_2=8 N_2/N_3=4 r_2=30.97 r_3/r_2=1.43 N_3=2 N_3/N_4=2 r_3=44.73 r_4/r_3=2.69 N_4= 1 Average= 3.125 r_4=120.22 Average = 1.78 Conclusions When branches are ordered based on Strahler system is done, problems due to specific local conditions appear. These issues should be considered by those particular geomorphological features that will determine the area under consideration. As seen, the fractal dimension is a value between 1 and 2. This means that the the fractal neither line nor surface, but will expand the line on the page. Acknowledgements: "We would like to thank Khorramshahr University of Marine Science and Technology for supporting this work under research grant contract