Ž . Geomorphology 40 2001 37–55 www.elsevier.comrlocatergeomorph Impacts of surface elevation on the growth and scaling properties of simulated river networks Jeffrey D. Niemann a, ) , Rafael L. Bras b , Daniele Veneziano b , Andrea Rinaldo c a Department of CiÕil and EnÕironmental Engineering, The PennsylÕania State UniÕersity, UniÕersity Park, PA 16802, USA b Department of CiÕil and EnÕironmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA c Istituto di Idraulica A G. Poleni,B UniÕersita di PadoÕa, PadoÕa, Italy ` Received 1 July 1999; received in revised form 12 January 2001; accepted 13 January 2001 Abstract We investigate the connection between surface elevation and the growth and scaling of river networks. Three planar Ž . models Scheidegger, Eden, and invasion percolation are first considered. These models develop aggregating networks according to stochastic rules but do not simulate erosion because the network growth is independent of the surface elevation. We show that none of these planar growth models produces scaling results consistent with observations for natural river basins. We then modify the models to include elevation, simulating the effects of fluvial erosion by enforcing the slope–area Ž relationship. The resulting configurations have scaling properties that still depend on the model Scheidegger, Eden, or . invasion percolation but are closer to natural river networks when compared with those from the planar growth rules. We conclude that inclusion of the vertical dimension in these three models is critical for explaining the formation and regularities of fluvial networks. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Drainage networks; Models; Self-similarity; Fractal geometry 1. Introduction Ž . Primarily since the work of Mandelbrot 1983 , scale invariant structures have been observed in many fields of the natural sciences. River networks are well-known examples of such structures, and proper- Ž . ties such as Hack’s law Hack, 1957 and Horton’s ) Corresponding author. Tel.: q 1-814-865-9428; fax: q 1-814- 863-7304. Ž . E-mail address: jniemann@engr.psu.edu J.D. Niemann . Ž . bifurcation ratio Horton, 1945 are commonly cited as evidence for some form of scale invariance Ž . Rodriguez-Iturbe and Rinaldo, 1997 . One approach to understand river basin scaling is through the pro- cess by which river networks grow to fill an initially Ž undrained region we refer to this as the network’s . mode of growth . A classical example is Scheideg- Ž . ger’s model Scheidegger, 1967 , which develops directed networks with particular scaling properties. Several other models have been adapted from well- known cluster growth algorithms such as Eden Ž . growth Eden, 1961 and invasion percolation 0169-555Xr01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. Ž . PII: S0169-555X 01 00036-8