HR: 16:00h
AN: T22E-01 INVITED     [PDF]
TI: Length Scale and Scaling in Both Topography Shape and Topography Dynamics
AU: * Davy, P
EM: Philippe.Davy@univ-rennes1.fr
AF: Geosciences Rennes, Campus de Beaulieu, Rennes, 35042 France
AB: Erosion processes both shapes topography and control topography dynamics so that it should be feasible to constrain the latter from the analysis of the former. During the last ten years, a bunch of studies have been done on analyzing topography in terms of erosion and transport laws. A kind of consensus has emerged around the power-law stream model which assumes that the erosion flux can be adequately described by its dependency on water flow and local topographic slope, and which gives that power laws with threshold are adequate functions to describe these dependencies, and that several processes (i.e. power-law functions) are necessary to cover the complete range of basin areas. But the consequences of these results in terms of dynamics have not been fully appraised yet. Thanks to a numerical surface-process model, we explore the relationship between form and dynamics, and especially the existence of characteristic time scales and their relationship to both structural and erosional parameters. Basically landscape erosion has a two-step evolution: an early phase which corresponds to the onset of drainage network, and a gentle back-to-equilibrium history. The former is very sensitive to initial topographic conditions and its dynamics is intimately related to drainage captures. We are mainly concerned with the latter which gives the long-term response of a continental system to any tectonic or climatic perturbation. Its characteristic time scale $\tau$ depends on the system size $L$ in a power-law relationship which defines the nature of the continental-scale diffusion equation. For processes which depends linearly on slope (with or without threshold), this scaling can be written as: $\tau = \tau_H * (L/\sqrt{a_H})^{\alpha}$, where $\tau_H$ and $a_H$ are the characteristic time scale and drainage area of hillslope, $L$ the system size, and $\alpha$ the diffusion exponent which only depends on the river process. In all relevant cases, $\alpha$ is smaller than 1 leading to abnormally fast diffusion. In some cases (if erosion flux is highly dependent on river flux and/or if the sediment are efficiently transported in rivers), $\alpha$ is 0 and the system evolution is entirely controlled by hillslope dynamics. An analytical solution of $\alpha$ has been derived with the assumptions described above. We also show that the complete analytical solution of the topography history takes the general form: $h(t)=h_o \exp(-(t/\tau)^{\beta})+h_{\infty}$ All parameters will be physically explained and related to system characteristics and erosion transport parameters.
DE: 1815 Erosion and sedimentation
DE: 1824 Geomorphology (1625)
DE: 3220 Nonlinear dynamics
DE: 8110 Continental tectonics--general (0905)
SC: Tectonophysics [T]
MN: 2003 Fall Meeting