METHODOLOGICAL APPROACHES TO THE FRECTAL ANALYSIS OF WATERCOURSE NETWORK Melnik Mariya Institute for Monitoring of Climatic and Ecological Systems SB RAS
The morphologically homogeneous parts of The morphologically homogeneous parts of Tomsk oblast rivers by fractal analyzed oblast rivers by fractal analyzed Tomsk
• Mandelbrot formula L= λ m 1-D н L – length of curve , m – scale , λ – scaling multiplier of the fractal curve , D Н – fractal dimension of the fractal curve • Self-similarity formula kL= λ (km) 1-D н
The graphics graphics of fractal of fractal researching researching The morphologically homogeneous parts of Ket Ket river river morphologically homogeneous parts of Кеть _2 длина , км Lg(L(m)) 2,0 1,9 79,4 1,8 63,1 1,7 50,1 y = -0,3323x + 1,8515 39,8 1,6 31,6 1,5 1,4 25,1 -1,0 -0,5 0,0 0,5 1,0 1,5 Lg(m) 10 тыс 25 тыс 50 тыс 100 тыс 200 тыс 500 тыс 1 млн 1,5 млн 3 млн масштаб k=1-D Н , k=-0.3323, D Н =1.3323
The fractal characteristic characteristics of morphologically homogeneous s of morphologically homogeneous The fractal one- -branch parts of branch parts of Tomsk Tomsk oblfst oblfst rivers rivers one Characteristic of part L D m M P k Chulym_1 31 1,1257 0,5 10 1,31 1,4 316 - 347 km Chulym _2 42 1,2395 1,0 8,5 1,6 1,6 147 - 216 km Chulym _3 42 1,3141 0,65 8,5 1,948 2,3 720 - 762 km Chulym _4 55 1,2853 0,65 12 2,039 2,3 392 - 447 km Tym_1 40 1,2532 0,45 6,0 1,896 1,9 455 - 495 km Tym _2 40 1,5097 0,5 5,0 2,77 3,2 225 - 265 km Tym _3 40 1,4187 0,4 5,0 2,42 2,6 100 - 140 km Vasugan_1 30 1,1969 0,5 9,5 1,621 1,7 40 - 70 km Vasugan _2 20 1,3815 0,35 5,0 2,7 3,1 400 - 420 km Vasugan _3 30 1,4363 0,4 6,0 2,67 2,9 545 - 575 km Vasugan _4 30 1,1961 0,4 5,0 1,796 1,7 500 - 530 km Ket_1 73 1,2396 0,25 4,5 1,856 1,9 663 - 736 km Ket _2 89 1,3323 0,45 8,5 2,31 2,3 272 - 361 km Ket _3 152 1,2294 0,8 10 1,654 1,6 0 - 152 km от устья р . Лайги до устья Ket _4 76,5 1,3002 0,35 4,5 1,961 2,1 р . Озерной
The fractal characteristic characteristics of morphologically homogeneous s of morphologically homogeneous The fractal poly- -branch parts of branch parts of Tomsk Tomsk oblfst oblfst rivers rivers poly D m M Characteristic of part Ob_1 1,207 0,45 15,0 754 - 828 km, l =74 km О b_2 1,303 0,45 10,0 919 – 986 km, l = 67 km О b_3 1,287 0,5 15,0 1125 -1229 km, l= 104 km О b_4 1,301 0,5 10,0 1767 – 1882 km, l =115 km То m_1 1,382 0,35 10,0 108 km - Tomsk, l= 38 km То m_2 46 km – creek of Tom , l = 46 km 1,301 0,35 10,0
The calculation of the fractal dimension 1 . of a watercourse network provides for saving the information on its morphometry when changing the observation scale.
The forms of channel of Chuya Chuya The forms of channel of river in different scale maps different scale maps river in 1:200 000 1:50 000
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