For decades, hydrologic studies in homogeneous regions and river basins have shown that quantiles of the annual peak streamflow distribution (e.g. the mean annual peak flow, the 100-year peak flow) have a power-law dependence on upstream basin area with an exponent that usually varies between 0.5 and 1.0. A new geophysical theory has been developing to understand this non-linear dependence (scaling) in peak flows (floods) in terms of space-time rainfall, runoff generation processes and water transport dynamics in channel networks. The central hypothesis of the theory is that scaling in peak flows for rainfall-runoff events arises from solutions of mass and momentum conservation equations in self-similar network topologies and geometries in the limit of large drainage areas.
The research being pursued is built on diagnosis, in contrast to the widely used practice of fitting a model to data to minimize errors. The purpose of diagnosis is to understand the relationships between data, theory, and computer simulations without fitting. Based on diagnostic results, new hypotheses can be introduced, assumptions can be modified and diagnosis repeated. The researchers have prior experience in diagnosing the role of rainfall, infiltration, and runoff generation on the slopes and intercepts of spatial scaling relations for floods at the event time scale in the Goodwin Creek Experimental Watershed (GCEW), Mississippi. This project is building on their published results and extending them to an annual time scale. They are diagnosing peak streamflow scaling relations in GCEW using a probabilistic (ensemble) framework. An ensemble is defined as a collection of different hydrographs that are produced from the same rainfall field but from a different set of initial hillslope infiltration and runoff generation conditions. This definition is made because published research indicates that hillslope runoff conditions substantially impact the timing and scaling features of streamflows in small basins like GCEW. Two key questions being addressed are, "How sensitive is the spatial scaling of peak flows to spatial variability in hillslope infiltration and runoff generation?" and "How is the scaling of annual maximum peak flows connected to the scaling of peak flows in rainfall-runoff events."
A recent article in Science (319, 2008) stated that, "In view of the magnitude and ubiquity of the hydro-climatic change apparently now under way, however, we assert that stationarity is dead and should no longer serve as a central default assumption in water-resource risk assessment and planning. Finding a suitable successor is crucial for human adaptation to changing climate". Self-similarity in river networks changes little over the decadal and centennial time scales of climate change. Consequently, the emerging scaling theory of peak streamflows, which is based on network self-similarity, applies whether or not climatic stationarity holds. If we can better understand how basins operate physically and how physical processes and conditions can be used to predict observed spatial scaling in peak streamflows, then the theory can be used to predict floods under a non stationary climate change. Results from this research are also making fundamental contributions to Prediction in Ungauged Basins (PUB), the decade-long research initiative (2003-2013) of the International Association of Hydrologic Sciences.
Accurate estimates of the magnitude and frequency of stream flows during floods are needed for the design of water-use and water-control projects, for floodplain definition and management, and for the design of transportation infrastructure such as bridges and roads. These estmates are given in terms of flood quantiles, for example, 100-year flood or 50-year flood. The method that the US Geological Survey uses in the United States is called regional flood frequency analysis. It provides qaantile estimates in a geographic region using historic stream flow data that correspond to the annual maximum flows. Unfortunately, the accuracy of quantile estimates is constrained by the data available at a site: record lengths are often limited to 100 years, and are typically less than 30 years. Furthermore, quantile estimates are often needed for sites with no stream flow records, called ungauged sites. To overcome these limitations, numerous statistical methods have been developed through the years to estimate needed quantiles. The potential impact of climate change on floods makes historical data less reliable for future projections. Our proosal was focused on research towards understanding the underlying physical processes as a basis for regional flood frequency analysis. The significance of this line of research lies in predicting floods from rainfall-runoff events at multiple spatial locations in a river basin in real time, and the regional flood frequencies in ungaged basins. The theroy can incorporate the impact of climate change on flood response. It is a very challenging scientific problem. The PI and his collaborators have spent over a qauter century in making progress on this problem that has significant societal and engineering implications for the US and the rest of the world.
