چکیده:
تحقیقات انجامشده در جهان بیانگر رابطه نزدیکی بین رفتار پدیدههای جهان طبیعی با الگوهای هندسی یا بعد فراکتال آنها است. هدف از این پژوهش بررسی ارتباط ابعاد فراکتال با شاخصهایی نظیر دبی سیل و دبی رسوب و حساسیت واحدهای سنگشناسی در محدودههای حوزههای آبخیز استان ایلام می-باشد. جهت دستیابی به نتایج بهتر بهمنظور یکسانسازی شرایط محیطی و مقایسه آماری از مقادیر ویژه دبی آب و رسوب استفادهشده است. نتایج بهدستآمده نشان داد که بین بعد فراکتال سازندها و مقاومت آنها به فرسایش ارتباط معنادار و معکوس برقرار میباشد و با افزایش مقاومت سازند تراکم آبراهه در واحد سطح و بعد فراکتال آن کاهش مییابد، بین بعد فراکتال حوزههای آبخیز موردمطالعه با دبی ویژه آب ارتباط معنیداری وجود ندارد؛ ولی بین عدد فراکتال و دبی رسوب ویژه ارتباط معنادار و مستقیم در سطح ۵ درصد وجود دارد، بهنحویکه با افزایش تراکم آبراهه در واحد سطح دبی رسوب ویژه افزایش مییابد. بیشترین مقادیر بعد فراکتال مربوط به حوزههایی است که ازنظر سنگشناسی بسیار حساس تا حساس هستند، (نظرآباد معادل 48/1، دویرج معادل 49/1) و کمترین مقدار آن مربوط به حوزههایی است که ازنظر سازندهای زمینشناسی مقاوم تا نیمه مقاوم هستند، (کلم معادل 14/1 و چم گز 11/1). با توجه به نتایج بهدستآمده و همبستگی آماری بیش از 95% بین بعد فراکتال و دبی رسوب میتوان در سایر حوزه-های فاقد آمار با محاسبه بعد فراکتال، دبی ویژه رسوب را برآورد نمود ولی این پیشبینی برای دبی ویژه آب مقدور نمیباشد.
The Relation of Fractal Dimension with Discharge and Sediment Indices in Ilam WatershedExtended AbstractIntroductionSince there are not enough tools to measure flood, erosion and sediment in many watersheds of the country, it is necessary to use indirect methods such as fractal geometry to estimate them. There is very little accurate information about erosion in our country (Mohammadi et al. 2008). Understanding the sedimentation status and sedimentation of basins provides an accurate understanding of erosion and its consequences (Piri et al. 2005). Some parameters of watersheds have a special geometric shape that can be examined with fractal geometry. Mathematically, the basins that have the same fractal dimensions are equivalent to each other and are very similar in terms of geomorphological and hydrological characteristics (Adl and Mehrvand, 2004). The aim of this study is to obtain a significant relationship between fractal drainage network and erosion and sedimentation rates, and to generalize the results to unmeasured areas.2. Introducing the studied areaThe studied area consists of 12 basins of Ilam province, which are in the western foothills of Zagros Mountain.Figure 1- The position of studied basins in the country and in the Ilam provinceTable 1- Specifications of basins and their stream gauging stations3-MethodologyThese networks were provided based on 50DEM coordinates that in many cases, there isn’t enough accuracy and some channels are not displayed. Therefore, after transferring data to Google Earth, it was fully matched with the natural drainages and with a 5-meter accuracy, hydrographic network map was drawn and completed to reflect the full details of the network.Thence one cannot scale maps via “Fractalys”, fields with the same space of 25 kilometers on similar formations in different areas were accidentally chosen via “Fish Net” –in Arc GIS, to fix this problem. For each study formation, three 25sq.km. Fields were chosen and by the accuracy of 5 meters. These maps that had the same drawing accuracy and space, were drawn in the same scales via GIS on an A4 page in .bmp” and then were brought to Fractalys and finally, their fractal dimensions were calculated and extracted by the geometric method of counting boxes.4-Results and discussionFigure 2- Hydrographic network and fractal dimension of the nazarabad watersheds before hydrographic network modificationTable 2- Fractal dimension of watersheds before and after hydrographic networks modificationIn the following figures, the calculated fractal dimensions are observed for several samples of 25 km units before and after the hydrographic network modification.After the modification before the modification Amiran Aghajari1.134 1.481 1.149 1.435Figure 3- Fractal dimension of a hydrographic network of Aghajari and Amiran formations before and after hydrographic network modification.Quaternery GachsaranFigure 4- Hydrographic network modification in the 25km unit on Google EarthFigures (3) to (4) show that after hydrographic network modification, the density of the hydrographic network and consequently the fractal dimension are increased in units of 25 km. Also, hydrographic network density changes in more sensitive formations are more than resistant formations, so their fractal dimension changes are also higher.Figure 5- Investigating the correlation of fractal dimension with hydrological indexes of Ilam watershedsthe R2 value that is representing the correlation value is 0.0905. Therefore there is no significant relationship between the specific flood discharge of watershed and its fractal number.Table (3) Correlation test of specific flood discharge data (Qw) in terms of (m3/s/ Km2) and fractal number (Fr) of the basins after modification of 25km unitsIn Table 3, the specified number (-.240) indicates the correlation value of the data. Due to the obtained value, there is no correlation between the specific flood discharge and the fractal number of the basin.Figure 6- Correlation line chart of specific flood discharge data and fractal number of basins after modification of 25km un itsFigure 7- Investigating the correlation of fractal dimension with the sedimentation index of Ilam watershedsIn Figure 8, Due to the R2 value (0.939), it can be also concluded that there is a significant and direct correlation between the specific sediment discharge value and fractal dimension of the watershed. The following tables show the results of the calculations performed in SPSS software.Table 4- Correlation test of specific sediment discharge data (Qs) and fractal number (Fr) of basins after modification of 25km unitsThe results of SPSS in Table (4) show that there is a high correlation between the specific sediment discharge data and fractal number. Because the number of 0.996 equals the correlation value between the two variables of the specific sediment discharge and the fractal dimension of the basins.The dispersion of data in the figure represents a high correlation in the data. Because the data are not scattered.5. ConclusionThe fractal dimension gives more accurate results by the box-counting method than the magnification and radial methods..The results of the research show that there is a significant and inverse relationship between the fractal dimension of the formations and their resistance to erosion.As the strength of the formation increases, its fractal dimension decreases and therefore the density of the hydrographic network is lower.There is no regular trend between the hydrographic network density and the fractal dimension of the basin with the specific flood discharge of basins.Also, there is no significant relationship between this index and the fractal dimension of the basin.There is a significant and direct relationship between the fractal number and the specific sediment discharge (at a level of 5%), which indicates the erosion and roughness rate in the basin The highest value of fractal dimension can be observed in areas that are very sensitive, including Doiraj basin to 1.49.The least value of fractal dimension can be observed in areas that are resistant to semi-resistant in terms of geological formations, such as Kolm and Chamagaz equal to 1.14 and 1.11, respectively.Keywords: Quantitative parameters, Fractal dimensions, Hydrology and sediment indices, Ilam Province.
خلاصه ماشینی:
ارتباط بعد فراکتال با شاخص هاي دبي و رسوب در حوزه هاي آبخيز استان ايلام مهتاب عليمرادي - دانشجوي دکتري علوم و مهندسي آبخيزداري ، گروه مرتع و آبخيزداري ، دانشگاه يزد ،ايران محمدرضا اختصاصي - استاد گروه مرتع و آبخيزداري ، دانشکده منابع طبيعي و کويرشناسي ، دانشگاه يزد، ايران مهدي تازه - استاديار، گروه مرتع و آبخيزداري ، دانشکده کشاورزي و منابع طبيعي ، دانشگاه اردکان ، ايران حاجي کريمي - دانشيار، گروه مرتع و آبخيزداري ، دانشکده کشاورزي ، دانشگاه ايلام ، ايران پذيرش مقاله : ۱۴۰۰/۰۲/۲۱ تائيد نهايي : ۱۴۰۰/۰۸/۱۲ چکيده تحقيقات انجام شده در جهان بيانگر رابطه نزديکي بين رفتار پديده هاي جهان طبيعي با الگوهاي هندسي يا بعد فراکتال آن ها است .
ir مقدمه در بسياري از حوزه هاي آبخيز کشور به دليل عدم وجود د ستگاه ها و ابزارهاي منا سب جهت اندازه گيري سيل ، اطلاعات دقيق و صحيح از فر سايش بسيار کم ا ست (محمدي و همکاران ، ۱۳۸۶) و بين اندازه گيري هاي مستقيم و برآوردهاي انجام شده نيز اختلاف هاي زيادي مشاهده مي شود؛ بنابراين ضروري است تا از روش هاي غيرمستقيم مانند کاربرد هندسه فراکتال در برآورد آن ها ا ستفاده شود.
مقدار R٢ که برابر ۰/۹۳۹ است نيز تأييدي بر اين نتيجه مي باشد که بين داده هاي دبي رسوب ويژه و بعد فراکتال حوزه آبخيز ارتباط معنادار و مستقيم وجود دارد.