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.
The team of hydrologists and mathematicians investigated two problems involved in predicting how rainfall over a river basin is transformed into discharge. The first problem is computational: devising methods suitable for high performance computers to quickly and accurately calculate discharge at the basin’s outlet. This is a challenging problem considering that there are millions of elements of the landscape, such as streams, fields, soils, relief, and urban areas that affect how much water fallen on the ground reaches the streams and rivers. Also, since rainfall intensities vary as storms move across basins, it is important to track those changes and account for them in the computations. The team developed a highly effective and fast algorithm to perform the computations. The algorithm takes advantage of the intricacies of how water flows in the stream and river network draining the landscape. For small streams changes occur fast but are independent between places in the basin. As discharge from small streams aggregates into larger and larger rivers, the changes are slower and the computations easier. The algorithm has been implemented by the Iowa Flood Center into a real-time flood forecasting system serving the people of the state. The system provides forecasts for over 1000 communities, large and small, across the state. The algorithm allows the system to update its forecasts up to several days ahead every 15 minutes. In contrast, the National Weather Service forecasts are updated every six hours. The second problem the team studied concerned the details of how rainfall is transformed into runoff at a small scale (that of single field). The key question is whether this transformation can be accurately described mathematically based on information that is readily available everywhere. The relevant information includes relief, soil type, land use and land cover, i.e. whether it is a cultivated field, pasture, grassland, or urban area. The percentage of rainfall that is transformed into runoff and thus may contribute to flooding somewhere downstream depends on the intensity of rainfall, on how much water is already stored in the soil and on how water flows through the soil and on the land surface. All these factors interact in complicated ways and need to be accurately tracked over time: before, during and after a storm to enable correct prediction of river discharge and flooding. The results of the study suggest that the importance of different factors which need to be taken into account varies with the basin size. For small basins more information is typically needed to accurately describe water flow within the soil and on the land surface. As the basin size increases, some errors made at small basins cancel out and prediction becomes easier. These findings have important implications for the design and implementation of streamflow and flood forecasting systems. For example, consider rainfall. It is clear that accurate measurement of rainfall amounts is crucial for flood prediction. And yet, accurate rainfall measurement is difficult even with a sophistical network of weather radars. The study provides a foundation to better understand how the uncertainties in rainfall observations affect flood forecasting.
