CMG Research: On the Quest for Power Laws in Floods: Developing Numerical and Analytical Tools

University Of Iowa, Iowa City IA

Investigators

Abstract

The PIs shall develop a physics-based hydrologic model capable of simulating flood events. Their system dynamics are described by a large set of non-linear differential equations that are coupled by the selfsimilar network of stream and rivers draining the landscape. To enable the study of floods at scales compatible with significant societal impacts and climate scale effects (i.e. ~50,000 km2 basins such as the Iowa River basin that experienced severe flooding in 2008), the numerical solver requires an efficient and scalable algorithm. The exploration of complex scale interactions between atmospheric inputs and landscape properties including soil, vegetation, and topology of the river network requires tools of nonlinear dynamical systems. The confirmation of the model analysis findings requires analysis of a large dataset of empirical data. This project addresses all these issues in a way that will further the investigation and explanation of the complex behavior of floods. Comprehension of how power laws arise in flood events has implications for flood frequency prediction under changing environmental conditions. This would have profound effects on the water infrastructure design in much of the world. Based on statistical analysis of streamflow observations from numerous stream gauges across the nation, it has been documented in the literature that the upper tail quantiles of annual streamflow peaks (thus, often floods) display power laws with respect to drainage area. However, dependence of the power law exponents has not been linked to physical characteristics of the regions and their climates. Therefore, as these characteristics might change due to human intervention (e.g. urbanization) or climatic changes, our ability to predict future flood frequency is largely speculative or ad-hoc at best. There is increasing evidence that individual flood events also display power laws with respect to drainage area. Establishment of links between the physical processes essential to flood genesis and the exponents of the power laws of flood quantiles would enhance prediction of flood frequency. This proposal focuses on expanding the mathematical tools essential to establishing those links and improving our understanding of flood behavior across scales.