\bibitem{ager} Ager, D.V., {\it The New Catastrophism}, Cambridge Univ. Press, New York, 1993. \bibitem{ahnert} Ahnert, F., Local relief and the height limits of mountain ranges, {\it Am. J. Sci, 284}, 1035-1055, 1984. \bibitem{amar} Amar, J.G., and F. Family, Numerical solution of a continuum equation for interface growth in 2+1 dimensions, {\it Phys. Rev. A, 41}, 3399-3402, 1989. \bibitem{balmino} Balmino, G., The spectra of the topography of the earth, Venus, and Mars, {\it Geophys. Res. Lett., 20}, 1063-1066, 1993. \bibitem{barabasi} Barabasi, A.-L., and H.E. Stanley, {\it Fractal Concepts in Surface Growth}, Cambridge Univ. Press, New York. \bibitem{beer} Beer, T., and M. Borgas, Horton's laws and the fractal nature of streams, {\it Water Resour. Res., 29}, 1475-1487, 1993. \bibitem{begin} Begin, Z.B., Application of "diffusion" degradation to some aspects of drainage net development, in {\it Badland Geomorphology and Piping}, edited by R. Bryan and A. Yain, pp. 169-179, Geobooks, Norwich, 1982. \bibitem{begin} Begin, Z.B., and S.A. Schumm, Instability of alluvial valley floors: A method for its assessment, {\it Trans. ASAE, 22}, 347-350, 1979. \bibitem{begin} Begin, Z.B., D.F. Meyer, and S.A. Schumm, Development of longitudinal profiles of alluvial channels in response to base level lowering, {\it Earth Surf. Processes, 6}, 49-68, 1981. \bibitem{bell} Bell, T.H., Statistical features of sea-floor topography, {\it Deep-Sea Res., 22}, 883-892, 1975. \bibitem{bretz} Bretz, J.H., The Lake Missoula floods and the channeled scablands, {\it J. Geol., 77}, 505-543, 1969. \bibitem{brown} Brown, S.R., and C.H. Scholz, Broad bandwidth study of the topography of natural rock surfaces, {\it J. Geophys. Res., 90}, 12575-12582, 1985. \bibitem{calver} Calver, A., Modelling drainage headwater development, {\it Earth Surf. Proc., 3}, 233-241, 1978. \bibitem{carlston} Carlston, C.W., Slope-discharge relations for eight rivers in the United States, {\it U.S. Geol. Surv. Prof. Pap., 600}, 45-47, 1968. \bibitem{chase} Chase, C.G., Fluvial landsculpting and the fractal dimension of topography, {\it Geomorphology, 5}, 39-57, 1992. \bibitem{cogley} Cogley, J.G., Hypsometry of the continents, {\it Z. Geomorph. N. F. Supp., 53}, 1-48, 1985. \bibitem{costa} Costa-Cabral, M.C., and S.J. Burges, Sensitivity of channel network planform laws and the question of topological randomness, {\it Water Resour. Res., 33}, 2179-2197, 1997. \bibitem{crave} Crave, A., and P. Davy, Scaling relationships of channel networks at large scales: examples from two large-magnitude watersheds in Brittany, France, {\it Tectonophysics, 269}, 91-111, 1997. \bibitem{culling} Culling, W.E.H., Analytical theory of erosion, {\it J. Geol., 68}, 336-344, 1960. \bibitem{culling} Culling, W.E.H., Soil creep and the development of hillside slopes, {\it J. Geol., 71}, 127-161, 1963. \bibitem{culling} Culling, W.E.H., and M. Datko, The fractal geometry of the soil-covered landscape, {\it Earth Plan. Sci. Lett., 12}, 369, 1987. \bibitem{dunne} Dunne, T., Formation and controls of channel networks, {\it Prog. Phys. Geogr., 4}, 211-239, 1980. \bibitem{edwards} Edwards, S.F., and D.R. Wilkinson, The surface statistics of a granular aggregate, {\it Proc. R. Soc. London A, 381}, 17-31, 1982. \bibitem{evans} Evans, I.S., and C.J. McClean, The land surface is not unifractal: variograms, cirque scale, and allometry, {\it Z. Geomorph. N. F. Supp., 101}, 127-147, 1995. \bibitem{fielding} Fielding, E., B. Isacks, M. Barazangi, and C.C. Duncan, How Flat is Tibet?, {\it Geology, 22}, 163-167, 1994. \bibitem{giacometti} Giacometti, A., A. Maritan, and J.R. Banavar, Continuum model for river networks, {\it Phys. Rev. Lett., 75}, 577-580, 1995. \bibitem{gilbert} Gilbert, L.E., Are topographic datasets fractal?, {\it Pure and Appl. Geophys., 131}, 241-254, 1989. \bibitem{gill} Gill, M.A., Diffusion model for aggrading channels, {\it J. Hyd. Res., 21}, 355-367, 1983. \bibitem{gill} Gill, M.A., Diffusion model for degrading channels, {\it J. Hyd. Res., 21}, 369-378, 1983. \bibitem{griffiths} Griffiths, G.A., Estimation of landform life expectancy, {\it Geology, 21}, 403-406, 1993. \bibitem{gray} Gray, D.M., Interrelationships of watershed characteristics, {\it J. Geophys. Res., 66}, 1215-1223, 1961. \bibitem{hack} Hack, J.T., Studies of longitudinal profiles in Virginia and Maryland, {\it U.S. Geol. Surv. Prof. Pap., 294B}, 1957. \bibitem{hanks1} Hanks, T.C., R.C. Buckman, K.R. Lajoie, and R.E. Wallace, Modification of wave cut and faulting-controlled landforms, {\it J. Geophys. Res, 89}, 5771-5790, 1984. \bibitem{hanks} Hanks, T.C., and R.E. Wallace, Morphological analysis of the Lake Lahontan shoreline and beachfront fault scarps, Pushing County, Nevada, {\it Bull. Seismol. Soc. Am., 75}, 835-846, 1985. \bibitem{harrison} Harrison, C.G.A., K.J. Miskell, G.W. Brass, E.S. Saltzmann, and J.L. Sloan II, Continental hypsometry, {\it Tectonics, 2}, 357-378, 1983. \bibitem{horton} Horton, R.E., Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology, {\it Bull. Geol. Soc. Am., 56}, 275-370, 1945. \bibitem{howard} Howard, A.D., A detachment-limited model of drainage basin evolution, {\it Water Resour. Res., 30}, 2261-2285, 1994. \bibitem{hunag} Huang, J., and D.L. Turcotte, Fractal mapping of digitized images: Applications to the topography of Arizona and comparisons with synthetic images, {\it J. Geophys. Res., 94}, 7491-7495, 1989. \bibitem{ijjasz-vasquez} Ijjasz-Vasquez, E.J., R.L. Bras, and I. Rodriguez-Iturbe, Hack's relation and optimal channel networks: the elongation of river basins as a consequence of energy minimization, {\it Geophys. Res. Lett., 20}, 1583-1586, 1993. \bibitem{ijjasz-vasquez} Ijjasz-Vasquez, E.J. , and R.L. Bras, Scaling regimes of local slope versus contributing area in digital elevation models, {\it Geomorphology, 12}, 299-311, 1995. \bibitem{inaoka} Inaoka, H., and H. Takayasu, Water erosion as a fractal growth process, {\it Phys. Rev. E, 47}, 899-910, 1993. \bibitem{kardar} Kardar, M., G. Parisi, and Y.-C. Zhang, Dynamic scaling of growing interfaces, {\it Phys. Rev. Lett., 56}, 889-892, 1986. \bibitem{kenyon} Kenyon, P.M., and D.L. Turcotte, Morphology of a delta prograding by bulk sediment transport, {\it Geol. Soc. Am. Bull., 96}, 1457-1465, 1985. \bibitem{kim} Kim, J.M., and J.M. Kosterlitz, Growth in a restricted solid-on-solid model, {\it Phys. Rev. Lett., 62}, 2289-2292, 1989. \bibitem{kirchner} Kirchner, J.W., Statistical inevitability of Horton's laws and the apparent randomness of stream channel networks, {\it Geology, 21}, 591-594, 1993. \bibitem{kondoh} Kondoh, H., and M. Matsushita, Diffusion-limited aggregations with anisotropic sticking probability: a tentative model for river networks, {\it J. Phys. Soc. Japan, 55}, 3289-3292, 1986. \bibitem{kooi} Kooi, H., and C. Beaumont, Large-scale geomorphology: Classical concepts reconciled and integrated with contemporary ideas via a surface processes model, {\it J. Geophys. Res., 101}, 3361-3386, 1996. \bibitem{koons} Koons, P.O., The topographic evolution of collisional mountain belts: A numerical look and the Southern Alps, New Zealand, {\it Am. J. Sci., 289}, 1041-1069, 1989. \bibitem{kramer} Kramer, S., and M. Marder, Evolution of river networks, {\it Phys. Rev. Lett., 68}, 205-208, 1992. \bibitem{krug} Krug, J., Origins of scale-invariance in growth processes, {\it Adv. Phys., 46}, 139-282, 1997. \bibitem{kucinskas} Kucinskas, A.B., D.L. Turcotte, J. Huang, and P.G. Ford, Fractal analysis of Venus topography in Tinatin Planatia and Ovda Regio, {\it J. Geophys. Res., 97}, 13635-13641, 1992. \bibitem{labarbera} La Barbera, P., and R. Rosso, On the fractal dimension of stream networks, {\it Water Resour. Res., 25}, 735-741, 1989. \bibitem{leheny} Leheny, R.L., S.R. Nagel, Model for the evolution of river networks, {\it Phys. Rev. Lett., 71}, 1470-1473, 1993. \bibitem{leopold} Leopold, L.B., M.G. Wolman, and J.P. Miller, {\it Fluvial Processes in Geomorphology}, Freeman, San Francisco, Calif., 1964. \bibitem{leopold} Leopold, L.B., and T. Maddock Jr., The hydraulic geometry of stream channels and some physiographic implications, {\it U.S. Geol. Surv. Prof. Paper 252}, 1953. \bibitem{loughridge} Loughridge, M.S., Relief map of the earth's surface, {\it EOS, Trans. Am. Geophys. Union, 67}, 121, 1986. \bibitem{luk} Luk, S.-H., Variability of rainwash erosion within small sample areas, in {\it Space and Time in Geomorphology}, edited by C. E. Thorn, pp. 243-268, Allen and Unwin, London, 1982. \bibitem{mandelbrot1} Mandelbrot, B., {\it The Fractal Geometry of Nature}, W. H. Freeman, New York, 1983. \bibitem{mandelbrot2} Mandelbrot, B., Stochastic models for the earth's relief, the shape and the fractal dimension of coastlines, and the number-area rule for islands, {\it Proc. Nat. Acad. Sci. U.S.A., 72}, 3825-3828, 1975. \bibitem{masek} Masek, J.G., and D.L. Turcotte, A diffusion-limited aggregation model for the evolution of drainage networks, {\it Earth Plan. Sci. Lett., 119}, 379-386, 1993. \bibitem{matsushita} Matsushita, M., and S. Ouchi, On the self-affinity of various curves, {\it Physica D, 38}, 246-251, 1989. \bibitem{maritan} Maritan, A., A. Rinaldo, R. Rigon, A. Giacometti, and I. Rodriguez-Iturbe, Scaling laws for river networks, {\it Phys. Rev. E, 53}, 1510-1515, 1996. \bibitem{meakin} Meakin, P., J. Feder, and T. Jossang, Simple statistical models for river networks, {\it Physica A, 176}, 409-429, 1991. \bibitem{meyer} Meyer, L., and D. Nash, eds., {\it Catastrophic Flooding}, Blackwell Sci., Cambridge, Mass., 1983. \bibitem{milliman} Milliman, J.D., and J.P.M. Syvitski, Geomorphic/Tectonic control of sediment discharge to the ocean: the importance of small mountainous rivers, {\it J. Geol., 100}, 525-544, 1992. \bibitem{milton} Milton, L.E., The geomorphic irrelevance of some drainage net laws, {\it Austr. Geograph. Stud., 4}, 89-95, 1966. \bibitem{moglen} Moglen, G.E., and R.L. Bras, The importance of spatially heterogeneous erosivity and the cumulative area distribution within a basin evolution model, {\it Geomorphology, 12}, 173-185, 1995. \bibitem{molnar} Molnar, P., and J.A. Ramirez, Energy dissipation theories and optimal channel characteristics of river networks, {\it Water Resour. Res., 34}, 1809-1818, 1998. \bibitem{montgomery} Montgomery, D.R., and W.E. Dietrich, Where do channels begin?, {\it Nature, 336}, 232-234, 1988. \bibitem{montgomery} Montgomery, D.R., and W.E. Dietrich, Channel initiation and the problem of landscape scale, {\it Science, 255}, 826-830, 1992. \bibitem{moussa} Moussa, R.T., Is the drainage network a fractal Sierpinski space?, {\it Water Resour. Res., 33}, 2399-2408, 1997. \bibitem{mueller} Mueller, J.E., Re-evaluation of the relationship of master streams and drainage basins: reply, {\it Geol. Soc. Am. Bull., 84}, 3127-3130, 1973. \bibitem{mulder} Mulder, T., and J.P.M. Syvitski, Climatic and morphologic relationships of rivers: implications of sea-level fluctuations on river loads, {\it J. Geol., 104}, 509-523, 1996. \bibitem{nash} Nash, D.B., Forms of bluffs degraded for different lengths of time in Emmet County, Michigan, USA, {\it Earth Surf. Processes, 5}, 331-345, 1980. \bibitem{newman} Newman, T.J., and A.J. Bray, Strong-coupling behavior in discrete Kardar-Parisi-Zhang equations, {\it J. Phys. A, 29}, 7917-7928, 1996. \bibitem{newman} Newman, W.I., and D.L. Turcotte, Cascade model for fluvial geomorphology, {\it Geophys. J. Int., 100}, 433-439, 1990. \bibitem{nikora} Nikora, V.I., On self-similarity and self-affinity of drainage basins, {\it Water Resour. Res., 30}, 133-137, 1994. \bibitem{ormi} Ormi, A.R., Temporal variability of a summer shorezone, in {\it Space and Time in Geomorphology}, edited by C. E. Thorn, pp. 285-313, Allen and Unwin, London, 1982. \bibitem{ossadnik} Ossadnik, P., Branch order and ramification analysis of large diffusion-limited-aggregation clusters, {\it Phys. Rev. A, 45}, 1058-1066, 1992. \bibitem{park} Park, K., and B. Kahng, Exact derivation of the Kardar-Parisi-Zhang equation for the restricted solid-on-solid model, {\it Phys. Rev. E, 51}, 796-798, 1995. \bibitem{patton} Patton, P.C., and S.A. Schumm, Gully erosion, Northwestern Colorado: A threshold phenomenon, {\it Geology, 3}, 88-90, 1975. \bibitem{peckham} Peckham, S.D., New results for self-similar trees with applications to river networks, {\it Water Resour. Res., 31}, 1023-1029, 1995. \bibitem{peckham2} Peckham, S.D., RiverTools 1.01, electronic software, available at http://cires.colorado.edu/people/peckham.scott/RT.html, 1997. \bibitem{phillips} Phillips, B.C., and A.J. Sutherland, Diffusion models applied to channel degradation, {\it J. Hyd. Res., 25}, 179-191, 1986. \bibitem{pierce} Pierce, K.L., and S.M. Colman, Effect of height and orientation (microclimate) on geomorphic degradation rates and processes, late-glacial terrace scarps in central Idaho, {\it Bull. Geol. Soc. Am., 97}, 869-885, 1986. \bibitem{plotnick} Plotnick, R.E., and K. Prestegaard, Fractal analysis of geologic time series, in {\it Fractals in Geography}, edited by L. De Cola and S. Lam, pp. 193-210, Prentice-Hall, Englewood Cliffs, Cal., 1993. \bibitem{rodriguez-iturbe2} Rodriguez-Iturbe, I., E. Ijjasz-Vasquez, R.L. Bras, and D.G. Tarboton, Power-law distributions of discharge mass and energy in river basins, {\it Water Resour. Res., 28}, 1089-1093, 1992. \bibitem{sadler} Sadler, P.M., Sediment accumulation rates and the completeness of stratigraphic sections, {\it J. Geol., 89}, 569-584, 1981. \bibitem{sayles} Sayles, R.S., and T.R. Thomas, Surface topography as a non-stationary random process, {\it Nature, 271}, 431-434, 1978. \bibitem{schmidt} Schmidt, K.-H., Regional variation of mechanical and chemical denudation, upper Colorado River basin, U.S.A., {\it Earth Surf. Processes, 10}, 497-508, 1985. \bibitem{schumm} Schumm, S.A., Evolution of drainage systems and slopes on badlands at Perth Amboy, New Jersey, {\it Geol. Soc. Am. Bull., 67}, 597-696, 1956. \bibitem{seginer} Seginer, I., Gully development and sediment yield, {\it J. Hydrol., 4}, 236-253, 1966. \bibitem{seidl} Seidl, M.A., W.E. Dietrich, and J.W. Kirchner, Longitudinal profile development into bedrock: an analysis of Hawaiian channels, {\it J. Geol., 102}, 457-474, 1994. \bibitem{shreve1} Shreve, R.L., Statistical law of stream numbers, {\it J. Geol., 74}, 17-37, 1966. \bibitem{slack} Slack, J.R., J.M. Landwehr, Hydro-climatic data network: A U.S. Geological Survey streamflow data set for the United States for the study of climatic variations: 1874-1988, {\it U.S. Geol. Surv. Open-File Rep. 92-129}, 1992. \bibitem{smith} Smith, T.R., and F.P. Bretherton, Stability and the conservation of mass in drainage basin evolution, {\it Water Resour. Res., 8}, 1506-1529, 1972. \bibitem{somfai} Somfai, E., and L.M. Sander, Scaling and river networks - a Landau theory for erosion, {\it Phys. Rev. E, 56}, R5-R8, 1997. \bibitem{sornette} Sornette, D., and Y.-C. Zhang, Non-linear Langevin model of geomorphic erosion processes, {\it Geophys. J. Int., 113}, 382-386, 1993. \bibitem{stark} Stark, C.P., An invasion percolation model of drainage network evolution, {\it Nature, 352}, 432-425, 1991. \bibitem{stark} Stark, C.P., Cluster growth modeling of plateau erosion, {\it J. Geophys. Res., 99}, 13957-13969, 1994. \bibitem{tarboton} Tarboton, D.G., R.L. Bras, and I. Rodriguez-Iturbe, The fractal nature of river networks, {\it Water Resour. Res., 24}, 1317-1322, 1988. \bibitem{tarboton} Tarboton, D.G., R.L. Bras, and I. Rodriguez-Iturbe, Scaling and elevation in river networks, {\it Water Resour. Res., 25}, 2037-2051, 1989. \bibitem{tokunaga} Tokunaga, E., Ordering of divide segments and law of divide segment numbers, {\it Trans. Jpn. Geomorphol. Union, 5}, 71-77, 1984. \bibitem{turcotte} Turcotte, D.L., A fractal interpretation of topography and geoid spectra on the earth, Moon, Venus, and Mars, {\it J. Geophys. Res., 92}, 597-601, 1987. \bibitem{turcotte} Turcotte, D.L., {\it Fractals and Chaos in Geology and Geophysics}, Cambridge Univ. Press, New York, 1992. \bibitem{usgs} United States Geological Survey, Digital Elevation Models, National Mapping Program Technical Instructions, Data Users Guide 5, U.S. Geological Survey, Second Printing (Revised), Reston, Virginia, 1990. \bibitem{veningmeinesz} Vening Meinesz, F.A., A remarkable feature of the earth's topography, {\it Proc. K. Ned. Akad. Wet. Ser. B, 54}, 212-228, 1951. \bibitem{voss} Voss, R., Fractals in nature: From characterization to simulation, in {\it The Science of Fractal Images}, edited by H. Peitgen and D. Saupe, pp. 22-70, Springer-Verlag, New York, 1988. \bibitem{wallace} Wallace, R.E., Profiles and ages of young fault scarps, north-central Nevada, {\it Geol. Soc. Am. Bull, 88}, 1267-1281, 1977. \bibitem{weissel} Weissel, J.K., L.F. Pratson, and A. Malinverno, The length-scaling properties of topography, {\it J. Geophys. Res., 99}, 13997-14012, 1994. \bibitem{willgoose2} Willgoose, G., A statistic for testing the elevation characteristics of landscape evolution models, {\it J. Geophys. Res., 99}, 13987-13996, 1994. \bibitem{willgoose} Willgoose, G., R.L. Bras, and I. Rodriguez-Iturbe, A coupled channel network growth and hillslope evolution model 1. theory, {\it Water Resour. Res., 27}, 1671-1684, 1991. \bibitem{willgoose} Willgoose, G., R.L. Bras, and I. Rodriguez-Iturbe, A physical explanation of the observed link area-slope relationship, {\it Water Resour. Res., 27}, 1697-1702, 1991. \bibitem{wolman} Wolman, M.G., and R. Gerson, Relative scales of time and effectiveness of climate in watershed geomorphology, {\it Earth Surf. Processes, 3}, 189-208, 1978.