River networks on the slope-correlated landscape

We study the morphologies of river networks on various landscapes. In general, the probability density distribution of drainage area a of the river network scales as P(a) approximately a(-tau). We consider a slope-slope correlation function G(r) and define the persistent length R where G(r=R) becomes zero. In our restricted solid on solid network model, R is independent of the system size L and tau is close to 4/3, which is the value of the Scheidegger's river network model with random walk process. We also consider an avalanche model, where R is proportional to L. There is a large slope-slope correlation length and the river network does not follow the directed random walk process with tau approximately 1.42.