RIVER NETWORK FRACTAL GEOMETRY AND ITS COMPUTER-SIMULATION

The hierarchical ordinal and statistical models of river networks are proposed. Their investigation has been carried out on the basis of riv er networks computer simulation as well as on empirical data analysis. The simulated river networks display self-similar behavior on small s cales (the fractal dimension D almost-equal-to 1.52 and Hurst's expone nt H = 1.0) and self-affine behavior on large scales (the lacunary dim ension D(G) almost-equal-to 1.71, H almost-equal-to 0. 58). Similar be havior is also qualitatively characteristic for natural river networks (for catchment areas from 142 to 63,700 km2 we obtained D(G) almost-e qual-to 1.87 and H almost-equal-to 0.73). Thus in both cases one finds a region of scales with self-affine behavior (H < 1) and with D(G) < 2. Proceeding from fractal properties of the river networks, the theor etical basis of scaling relationships L approximately A(beta) and L ap proximately A(epsilon), widely used in hydrology, are given (L, L, and A denote the main river length, the total length of the river network , and catchment area, respectively); beta = 1/(1 + H) and epsilon = D( G)/2.