A new nonlinear geophysical theory of floods, henceforth called the scaling theory, has been developing for nearly a decade. It has the explicit goal to predict spatial statistical power laws in floods from conservations equations and related physical processes at the scale of hillslope-channel links that partition a natural terrain. In many empirical studies of regional flood frequencies, power law relationships have been observed between annual peak discharge statistics and drainage areas, and recently in individual rainfall-runoff events. Preliminary analyses show that event-based scaling exponents and the annual flood quantile scaling exponents are closely related. A close relationship between these two sets of exponents suggests a very important hypothesis, namely that it is possible to predict flood-scaling parameters from physical processes not only for individual RF-RO events, but also for annual floods by considering multiple events in a year.
Intellectual Merit: Research in idealized deterministic self-similar networks has shown that statistical power laws emerge asymptotically as drainage area goes to infinity. They are not built into the physical equations governing floods. It has led to a key scientific hypothesis that power laws in floods have their physical origins in the self-similarity (self-affinity) of channel networks, which is also the basis for the widely observed fractal structure of networks and their Horton relations. The current challenge is to generalize the theory to real networks. To achieve this important goal, we propose to test a diagnostic framework using existing data from two Agricultural Research Service basins, Walnut Gulch, Arizona and Goodwin Creek, Mississippi. The key idea is to predict power laws from physical processes under a set of distributed parametric assumptions. Then compare the predictions with observed power laws for diagnosing the validity of our physical assumptions, and proposing a new set of assumptions. For predicting scaling laws in floods, a mass conservation equation, which parameterizes physical processes at the scale of hillslope-channel links in a natural terrain, is solved and flow hydrographs are computed for every link in a network. For solving the mass conservation equation, we will use a GIS-based digital watershed-modeling framework that our research group has developed in last five years. The objectives are exploratory in nature and are designed to establish a "proof of concept".
Broader Impacts: Scientific consensus has grown that global warming is real and in substantial part is caused by human activities. This anthropogenic perturbation to the planetary hydro-climate is causing a non-stationary change, which precludes making statistical flood predictions from long-term historic rainfall and stream flow data. Historical hydrologic data are routinely used in statistical hydrologic models for the purposes of water resources management in the United States and other countries of the World. Therefore, hydrologic predictions in a non-stationary climate present an enormous problem for future management of water resources. The scaling theory of floods is developing new scientific foundations that would be particularly suited to make flood predictions in the context of the emerging problem of non-stationary hydro-climate change due to global warming. The scientific foundations of the scaling theory of floods can be generalized to include ecological and bio-geo-chemical processes that are coupled to water, for example, riparian evapotranspiration, and to make predictions in a changing hydro-climate.
