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date: 29 May 2017

Scaling Theory of Floods for Developing a Physical Basis of Statistical Flood Frequency Relations

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Natural Hazard Science. Please check back later for the full article.

The United States Geological Survey developed the Regional Flood Frequency (RFF) analysis to make flood frequency predictions at locations, called ungauged basins, where no stream flow data exist. Prediction in ungauged basins is a global issue because most, if not all countries do not have adequate stream flow records. RFF analysis uses historical stream flow records to carry out regressions. It is purely statistical in nature. In the face of a changing climate, historic stream flow data cannot automatically be assumed to represent the future scenarios. The hydrologic challenge has been and continues to be to develop a physical basis for RFF that explicitly uses space-time rainfall intensity fields and the hydrologic processes producing floods.

The scaling theory of floods in river basins is another name for a nonlinear geophysical theory of floods that has developed in the last 20 years. It has the explicit goal to link flood producing physical processes with statistical power law relations between peak flows and drainage areas. Research on this challenging objective has shown that self-similarity in channel networks provides the scientific foundation for developing the scaling theory of floods. The primary objective of this article is to review the highlights of published research to date on self-similarity in channel networks, its role in developing the scaling theory of floods, and finally, its applications to hydraulic geometry in channel networks and to biological diversity in riparian vegetation along a network.

To link RFF at the annual time scale with the physics of flood generating processes, it is necessary to go to the event scale to understand power laws in peak flows in individual rainfall-runoff (RF-RO) events. The RF-RO models in practice use a variety of techniques to calibrate their parameters, using observed stream flow hydrographs. In ungagged basins, no stream flow data are available, and in a changing climate, the reliability of historic data becomes questionable, so calibration of parameters is not a viable option. Recent progress on developing a suitable theoretical framework to test RF-RO model parameterizations without calibration will be briefly reviewed. RF-RO models partition a river basin using different conceptual schemes. A unique physically based partition scheme will be reviewed. The scaling theory of floods provides a unified theoretical umbrella to address all the above challenges.

The next major step is to use the scaling theory to develop innovative applications to practical hydrologic engineering problems that need solutions. Examples include, real-time flood forecasting, flood plain mapping, and design of spatially distributed small dams in a river network to compare and contrast with building a single dam at one location for flood control. All these problems require simulation models that can be based in the scientific foundations that the scaling theory has developed. To conduct focused research along these lines, a new generation of graduate students will need to be educated. This urgent need is being fulfilled through the Iowa Flood Center (IFC), University of Iowa, which is the only facility of its kind in the United States and the world.