ارتباط بین ضریب فشردگی حوضه آبریز با ویژگی های فراکتال آن

نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار/ گروه مهندسی عمران- آب ، واحد مرودشت، دانشگاه آزاد اسلامی، مرودشت، ایران

2 دانشجوی دکتری مهندسی عمران/مهندسی و مدیریت منابع آب، واحد مرودشت، دانشگاه آزاد اسلامی، مرودشت، ایران

چکیده

تأثیر شکل حوضه بر رواناب سطحی و هیدروگراف امریست محرز،از این رو عده ی زیادی از محققین این موضوع را مورد بررسی قرار داده اند.هندسه فراکتال نیز به عنوان یکی از روش‌های جدید می‌تواند در علم ژئومورفولوژی رودخانه‌ای به کار گرفته شود و به یافتن روابطی بین شکل حوضه و هیدروگراف کمک کند.اساسی ترین ویژگی فرکتالی که در مورد این پدیده ها تحلیل مـی شـود، بعد فرکتال است که اهمیت زیادی در شناخت رفتار و پیش بینی تغییرات رودخانـه دارد . در این تحقیق به دنبال بررسی میزان انطباق هیدروگراف واحد مصنوعی فراکتال و هیدروگراف واحد مثلثی NRCS و ارتباط آن با میزان ضریب فشردگی حوضه می باشیم. به این منظور حوضه ی وال نات گولچ آمریکا را انتخاب و برای 12 زیر حوضه ی آن ضریب فشردگی محاسبه و هیدروگراف واحد مثلثی (NRCS) ، همچنین هیدروگراف واحد مثلثی فراکتالی رسم و با هم مقایسه کردیم، نتایج حاکی از آن بود که هر چه ضریب فشردگی به 5/1 نزدیکتر باشد یعنی حوضه دایره ای تر باشد هیدروگراف ها تطابق بیشتری دارند در واقع روش ابداعی هیدروگراف فراکتالی بهتر جواب می دهد، مانند زیر حوضه های 5، 7 ، 8 ، 9 و 11 وهر چه عدد ضریب فشردگی از 5/1 فاصله بگیرد تطابق کمتر می شود مانند زیر حوضه های 1 و 10 .

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

The relationship between watershed compactness coefficient and the fractal characteristics

نویسندگان [English]

  • M . H Fattahi 1
  • Z. Talebzadeh 2
1 Assistant Professor, Civil Eng. Department, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
2 Ph.D. Candidate, Civil Eng. Department, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
چکیده [English]

The effect of watershed form on the surface runoff and hydrograph is an obvious issue. Hence a large number of researchers have considered the issue. Fractal geometry, as one of new methods, can be applied in geomorphology of rivers and also help to find some relationship between watershed form and hydrograph. The most fundamental fractal characteristic which is analyzed about the phenomenon is the fractal dimension that have a great importance for understand and prediction of river changes. In this study, we consider the consistency (match) level of artificial unit hydrograph of fractal and NRCS triangular unit hydrograph and its relationship with the compactness coefficient of watershed. To this end, Walnut Gulch watershed of America was chosen and the compactness coefficient was also calculated for its 11 sub-watershed (sub- basin), and then, NRCS triangular unit hydrograph, fractal triangular unit hydrograph were depicted and compared with each other. Results showed that whether compactness coefficient is closer to 1.5, namely watershed is more circular, hydrographs are more compatible. In fact, the innovative method of fractal hydrograph is more appropriate, like watersheds 5,7,9 and 11, and whether compactness coefficient is far from 1.5, the consistency is reduced, like sub-basins 1 and 11.

کلیدواژه‌ها [English]

  • fractal
  • geomorphology
  • unit hydrograph
  • walnut gulch
  • Compactness coefficient
Alizadeh A (2015) principles of applied hydrology. Ferdowsi University of Mashhad Press 40p (In Persian)

Baas ACW (2002) Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments. Journal of Geomorphology 48(1):309-328

Beauvais A, Montgomery DR (1996) Influence of valley type on the scaling properties of river plan forms. Journal of Water Resource 5(32):1441-1448

Bi L, He H, Wei Z, Shi F (2012) Fractal properties of landform in the Ordos block and surrounding areas. Journal of China Geomorphology 175:151-162

Buczkowski S, Hildgen P, Cartilier L (1998) Measurement of fractal dimension by Box-Counting: a critical analysis of data scatter. Journal of Physical A 252(1):23-34

Chow VT, Maidment DR and Mays LW (1988) Applied Hydrology. McGraw-Hill, 572p

De Bartolo SG, Veltri M and Primavera L (2006) Estimated generalized dimensions of river network. Journal of Hydrology 322:181-191

Elmizadeh H, Mahpeykar O, Saadatmand M (2014) The study of fractal theory in the geomorphology of rivers. Journal of Quantitative Geomorphology Research 2(3):130-141 (In Persian)

Fttahi MH, Jahangiri H (2014) Studying the relation between fractal properties of river networks and river flow time series. Journal of Water Resources Engineering 7(20):1-10 (In Persian)

Fttahi MH, Talebzadeh Z (2016) Synthetic unit hydrograph based on fractal watersheds characteristics. Journal of Water Resources Engineering, Accepted (In Persian)

Klinkenberg B (1994) A Review of methods used to determine the fractal dimensions of Linear Features. Journal of Mathematical Geology 26(1):23-46.

La Barbera P, and Ross R (1989) On the fractal dimension of stream networks. Journal of Water Resources Research 25(4):735-741

Li J, Du Q and Sun C (2009) An improved box-counting method for image fractal dimension estimation. Journal of Pattern Recognition 42(11):2460-2469

Liebovitch LS, Tibor T (1989) A fast algorithm to determine fractal dimensions by box-counting. Journal of Physics Letters A 141(8/9):386-390

Mandelbrot B (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Journal of Science 156: 636-638

Molteno TCA (1993) Fast O (N) box-counting algorithm for estimating dimensions. Journal of Physical Review E 48(5):3263-3266

Nikooyi E, Heydari M, Talebbeydokhti N, Hekmatzadeh AA (2008) Fractal geometry in river engineering: ideas, concepts and achievements. National Congress on Civil Engineering, 14-15 May, University of Tehran (In Persian)

Nikora VI (1991) Fractal structures of river plan forms. Journal of Water Resource 27(6):1327-1333

Nikora VI, Sapozhinov VB, Noever DA (1993) Fractal geometry of individual river channels and its computer Simulation. Journal of Water Resource 29:3561-3568

Peckham SD (1989) New results for self-similar trees with applications to river networks. Journal of Water Resource 31(4):1023-1029

Rodriguez I and Rinaldo A (1997) Fractal river basins. Chance and self-organization, Cambridge:Cambridge University Press

Shang P and Kamae S (2005) Fractal nature of time series in the sediment transport phenomenon. Journal of Chaos Solutions & Fractals 26:997-1007

Shen XH, Zou LJ, Li HS (2002) Successive shift box counting method for calculating fractal dimension and its application in identification of fault. Journal of Acta Geol, Sin.-Engl 76:257-263.

Turcotte DL (1992) Fractal and chaos in geology and geophysics. Geophysics Cambridge University Press, 121p