HR: 1340h
AN: U43B-1129    [Abstracts]
TI: Channel Networks Driven by Subsurface Flow Break Scale Invariance
AU: * Petroff, A
EM: petroffa@mit.edu
AF: Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences 54-621 77 Massachusetts Avenue, Cambridge, MA 02139,
AU: Lobkovsky, A
EM: leapfrog@mit.edu
AF: Georgetown University Department of Physics, 527 Reiss Science 37th and O St NW, Washington, DC 20057,
AU: Abrams, D
EM: dmabrams@mit.edu
AF: Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences 54-621 77 Massachusetts Avenue, Cambridge, MA 02139,
AU: Rothman, D
EM: dhr@mit.ed
AF: Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences 54-621 77 Massachusetts Avenue, Cambridge, MA 02139,
AB: Broadly viewed, there are two qualitatively different mechanisms by which flowing water shapes topography. In the more common case, flow over land exerts a shear stress that erodes material. In the second case, erosion occurs when groundwater emerges at the base of channel heads. Both mechanisms---called, respectively, erosion by overland flow and erosion by subsurface, seepage flows---typically lead to the growth of ramified channel networks. In overland flow, variations in topography focus the flow of water; thus the long term evolution of the network depends sensitively on any initial variations in topography. In contrast, the focusing of subsurface flow is due to variations in the elevation of the water table, which is sensitive to the network geometry but relatively insensitive to small variations in topography. Consequently the growth of seepage-driven networks is in many respects a simpler process that derives more from the local competition of channels for water and less from small, non-local perturbations to topography. Here we report an empirical and theoretical study of networks driven by seepage. We hypothesize that seepage networks evolve via two mechanisms: the "nucleation" of new channels and their growth. Nucleation occurs at a rate proportional to drainage density while channels grow at a velocity proportional to flux through channel heads. We show that geometric features of the resulting network depend on the ratio of the characteristic time scale between the nucleation of new channel heads and the characteristic time scale over which a nucleated channel head advances to the groundwater divide. If new channels nucleate either much faster or much slower than the time required for existing tips to grow to the divide, the resulting dynamics produce networks that are scale invariant. The intermediate case, which necessarily occurs between the largest and smallest length scales, is however scale dependent. We test these ideas by analyzing a high-resolution digital elevation model of a kilometer-scale network of seepage-driven channels located on the Florida Panhandle. For each channel, we compute a dimensionless quantity η that is related to basin size and shape, and show that η varies with length scale as in our model. In contrast, the same measure confirms the scale-invariance of models of networks driven by overland flow. We also report studies of large-scale river networks. The breakdown of scale invariance in seepage networks exhibits a stark contrast to the well-known fractal properties of river networks driven by overland flow. This suggests that a quantitative distinction between seepage and overland flow may be possible in instances, such as Martian drainage networks, where the network's provenance is unclear.
DE: 1815 Erosion
DE: 1829 Groundwater hydrology
DE: 4440 Fractals and multifractals
DE: 4460 Pattern formation
DE: 4475 Scaling: spatial and temporal (1872, 3270, 4277)
SC: Union [U]
MN: 2007 Fall Meeting