SIMPLE COMPUTER-MODEL OF A FRACTAL RIVER NETWORK WITH FRACTAL INDIVIDUAL WATERCOURSES

A random walk computer model of river network is proposed. It is shown that the length and the width of both network and of individual strea ms that constitute it exhibit scaling sigma(parallel-to)BAR is similar to L(nu)parallel-to and sigma(perpendicular-to)BAR is similar to L(nu )perpendicular-to (sigma(parallel-to)BAR and sigma(perpendicular-to)BA R are the longitudinal and lateral sizes of the object, L is the overa ll length of the object). The simulated individual streams display sel f-similar behaviour at small L (nu(parallel-to) = nu(perpendicular-to) = 0.80 +/- 0.03) and self-affine behaviour at large L (nu(parallel-to ) = 0.99+/-0.03, nu(perpendicular-to) = 0.50+/-0.03). Similar behaviou r is observed for simulated river networks too: nu(parallel-to) = nu(p erpendicular-to) = 0.66+/-0.03 correspond to these in the self-similar ity region, while in the self-affinity region nu(parallel-to) = 0.74+/ -0.03 and nu(perpendicular-to) = 0.43 +/- 0.03. Proceeding from the se lf-affinity of individual rivers and river networks Hack's empirical l aw L is similar to F(beta) has been substantiated (L is the length of the main river, F the catchment area), where beta = 1/(1 + H), H = nu( perpendicular-to)/nu(parallel-to), Hurst's exponent for river networks . The scaling for the water mass distribution over the river network i n the self-affine region is also revealed: sigma(m parallel-to)BAR is similar to L(nu)m parallel-to, sigma(m perpendicular-to)BAR is similar to L(nu)m perpendicular-to, nu(m parallel-to) = 0.72 +/- 0.03, nu(m p erpendicular-to) = 0.38 +/- 0.03. It is shown that in this region the water mass M depends upon the network total length and upon the catchm ent area as a power law: M is similar to L1.67 is similar to F1.43.