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.
Peak streamflow discharge tends to be a Power Law function of drainage area in river basins. The overall goal of the project was to better understand peak discharge Power Laws or scaling relationships in Goodwin Creek Experimental Watershed, Mississippi. We studied the role of rainfall and runoff generation on the slopes and intercepts of scaling relationships, from event to annual time scales. Two results from the project stand out: 1. A fundamental question in hydrology is: How can space–time variable runoff generation in a river basin be modeled at a large number of hillslopes when the finest scale of observed runoff is substantially larger, and the scale of existing infiltration equations and related measurements is much smaller? In addressing this question, nearly all hydrologic models take a bottom-up approach to representing processes in river basins. Essentially, they extrapolate small-scale observations and equations to larger spatial scales. By contrast, we developed a top-down approach where large-scale observations are, based on water balance, disaggregated stochastically down to small-scale (hillslope) elements. Creation of a top-down model was needed for the project. For a given rainfall event, the model allows for the creation of ensemble simulations of hillslope runoff and corresponding basin runoff. There is no calibration in running the model, and, for a given rainfall event, differences in scaling relationships of peak streamflow discharge can be studied. 2. The USGS uses regional flood frequency (RFF) equations to predict floods in basins with no streamflow data (ungauged). These equations take a Power Law or scaling form. They are statistical characterizations of floods at an annual time scale and, as a result, are disconnected from the physical processes and conditions that generate floods. These equations are based on historical data, and a key assumption is that the hydroclimate system has been stationary and will remain so in the future, despite evidence for the contrary. These issues motivate the need to understand the physical underpinnings of RFF equations, with the long-term goal of improving flood predictions in ungauged basins. We developed a Nested Mixed-Effects Linear Model that characterizes event-to-event variability in scaling relationships between stream discharge peaks and drainage area (Furey et al. 2014, paper in progress). It shows how scaling in discharge peaks for events connects to scaling in discharge peak quantiles and to scaling in maximum annual peak (MAP) quantiles. The model connects events, for which physical processes are known and can be studied, to RFF equations that are based on MAP data.
