Understanding Power Laws of Flood Data to Unlock the Physics of Floods

Ricardo Mantilla, Ph.D. IIHR- Hydroscience & Engineering

College of Engineering

The University of Iowa

Recent studies have revealed the existence of power laws, or scaling, in the magnitude of peak flows for individual rainfall-runoff events with respect to drainage area. These findings offer a new theoretical framework to understand the physical basis of water transport mechanisms behind extreme flooding. Research in the last decade has led to the hypothesis that scale invariance, via self-similarity in the topology of river networks, is a fundamental ingredient to explain the existence of power-law behavior in flood data. Insights from these theoretical developments are used to explore the physical mechanisms that led to very-extreme flooding in Eastern Iowa in June 2008, and to solve the hydrological puzzle of “why were these floods not preceded by extreme rainfall?” In addition, several results that constitute the building blocks for a geophysical theory of floods will be presented. In particular, it is shown that the assumptions of the Random Self-similar Networks (RSNs) model are valid on 28 basins across the US, and observational evidence for a scale-invariant formulation of runoff-transport in river networks.