Towards a Nonlinear Geophysical Theory of Floods in River Networks: An Overview of 20 Years of Progress
 Vijay K. Gupta,
 Brent M. Troutman,
 David R. Dawdy
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Abstract
Key results in the last 20 years have established the theoretical and observational foundations for developing a new nonlinear geophysical theory of floods in river basins. This theory, henceforth called the scaling theory, has the explicit goal to link the physics of runoff generating processes with spatial powerlaw statistical relations between floods and drainage areas across multiple scales of space and time. Published results have shown that the spatial power law statistical relations emerge asymptotically from conservation equations and physical processes as drainage area goes to infinity. These results have led to a key hypothesis that the physical basis of power laws in floods has its origin in the selfsimilarity (selfaffinity) of channel networks. Research within the last 20 years has also shown that selfsimilarity is the basis for the widely observed fractal structure and Horton relations in river networks. Observed power laws in floods span a broad range of spatial scales and multiple time scales that range from hours of individual flood events to annual time scale of flood frequencies. They serve as the foundation for developing a new diagnostic framework to test different assumptions governing spatial variability in physical processes that arise in predicting power law statistical relations between floods and drainage areas. The structure of the diagnostic framework is illustrated using two examples. Contemporary relevance and future applications of the scaling theory come from predicting floods in the context of a significant warming of the Earth’s climate, which is altering local, regional, continental and global balances of water and energy. This anthropogenic perturbation to the planetary hydroclimate precludes making flood predictions at gauged and ungauged sites based on regional statistics from historical stream flow data, which is a wellestablished practice in hydrologic engineering.
 Title
 Towards a Nonlinear Geophysical Theory of Floods in River Networks: An Overview of 20 Years of Progress
 Book Title
 Nonlinear Dynamics in Geosciences
 Pages
 pp 121151
 Copyright
 2007
 DOI
 10.1007/9780387349183_8
 Print ISBN
 9780387349176
 Online ISBN
 9780387349183
 Publisher
 Springer New York
 Copyright Holder
 Springer Science+Business Media, LLC
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 Authors

 Vijay K. Gupta ^{(3)}
 Brent M. Troutman ^{(4)}
 David R. Dawdy ^{(5)}
 Author Affiliations

 3. University of Colorado, Dept. of Civil, Environmental and Architectural Engineering, Cooperative Institute for Research in Environmental Sciences, Boulder, CO, USA
 4. U. S. Geological Survey, Lakewood, CO
 5. Hudrologic Consultant, Lakewood, CO
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