METHODOLOGICAL APPROACHES TO THE FRECTAL ANALYSIS OF WATERCOURSE - - PowerPoint PPT Presentation

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 Tomsk oblast rivers by fractal analyzed

• blast rivers by fractal analyzed

• Mandelbrot formula

L=λm1-Dн

L – length of curve, m – scale, λ – scaling multiplier of the fractal curve, DН – fractal dimension of the fractal curve

• Self-similarity formula

kL=λ(km)1-Dн

The The graphics graphics of fractal

• f fractal researching

researching morphologically homogeneous parts of morphologically homogeneous parts of Ket Ket river river

Кеть_2 y = -0,3323x + 1,8515 1,4 1,5 1,6 1,7 1,8 1,9 2,0

• 1,0
• 0,5

0,0 0,5 1,0 1,5 Lg(m) Lg(L(m))

10тыс 25тыс 50тыс 100 тыс 200тыс 500тыс 1млн 1,5млн 3млн масштаб

63,1 50,1 39,8 31,6 25,1 79,4

длина, км

k=1-DН, k=-0.3323, DН =1.3323

The fractal The fractal characteristic characteristics of morphologically homogeneous s of morphologically homogeneous

• ne
• ne-
• branch parts of

branch parts of Tomsk Tomsk oblfst

• blfst rivers

rivers

от устья р. Лайги до устья р.Озерной 2,1 1,961 4,5 0,35 1,3002 76,5 Ket _4 0 - 152 km 1,6 1,654 10 0,8 1,2294 152 Ket _3 272 - 361 km 2,3 2,31 8,5 0,45 1,3323 89 Ket _2 663 - 736 km 1,9 1,856 4,5 0,25 1,2396 73 Ket_1 500 - 530 km 1,7 1,796 5,0 0,4 1,1961 30 Vasugan _4 545 - 575 km 2,9 2,67 6,0 0,4 1,4363 30 Vasugan _3 400 - 420 km 3,1 2,7 5,0 0,35 1,3815 20 Vasugan _2 40 - 70 km 1,7 1,621 9,5 0,5 1,1969 30 Vasugan_1 100 - 140 km 2,6 2,42 5,0 0,4 1,4187 40 Tym _3 225 - 265 km 3,2 2,77 5,0 0,5 1,5097 40 Tym _2 455 - 495 km 1,9 1,896 6,0 0,45 1,2532 40 Tym_1 392 - 447 km 2,3 2,039 12 0,65 1,2853 55 Chulym _4 720 - 762 km 2,3 1,948 8,5 0,65 1,3141 42 Chulym _3 147 - 216 km 1,6 1,6 8,5 1,0 1,2395 42 Chulym _2 316 - 347 km 1,4 1,31 10 0,5 1,1257 31 Chulym_1 Characteristic of part k P M m D L

The fractal The fractal characteristic characteristics of morphologically homogeneous s of morphologically homogeneous poly poly-

• branch parts of

branch parts of Tomsk Tomsk oblfst

• blfst rivers

rivers

46 km – creek of Tom, l = 46 km 10,0 0,35 1,301 Тоm_2 108 km - Tomsk, l=38 km 10,0 0,35 1,382 Тоm_1 1767 – 1882 km, l =115 km 10,0 0,5 1,301 Оb_4 1125 -1229 km, l=104 km 15,0 0,5 1,287 Оb_3 919 – 986 km, l =67 km 10,0 0,45 1,303 Оb_2 754 - 828 km, l =74 km 15,0 0,45 1,207 Ob_1

Characteristic of part

M m D

The calculation of the fractal dimension

• f a watercourse network provides for

saving the information on its morphometry when changing the

• bservation scale.

1:200 000 1:50 000

The forms of channel of The forms of channel of Chuya Chuya river in river in different scale maps different scale maps