scaling theory of floods for predictions in a changing climate: a model to generate ensembles of runoff from a large number of hillslopes (Invited)

Peak flows in individual rainfall-runoff events exhibit spatial scaling in the 21 km2 Goodwin Creek Experimental Watershed (GCEW) in Mississippi, USA. A nonlinear geophysical theory has been developing to understand how scaling in peak flows for Rainfall-Runoff events arises from solutions of mass and momentum conservation equations in channel networks with self-similar topologies and geometries. The conservation equations are specified at the natural hillslope-link scale. The central hypothesis of the theory is that scaling is an emergent property in the limit of large drainage area. To develop a physical understanding of scaling, runoff generation from each hillslope in the basin is needed. GCEW contains 544 hillslopes, and direct observations of infiltration only exist, at best, at few locations. This situation is typical of all river basins in the world. As a result, representing the spatial and temporal variability of runoff generation throughout any river basin presents a great scientific challenge. Most models use point-scale equations for infiltration and point-scale observations to represent runoff generation at a larger scale, e.g. hillslope scale. We develop a physical-statistical hypothesis, combining both top-down and bottom-up observations, that hillslope water loss is inversely related to a function of a lognormal random variable. We take a top-down approach to develop a new runoff generation model to test our hypothesis. The model is based on the assumption that the probability distributions of a runoff-loss ratio have a space-time rescaling property. For over 100 rainfall-runoff events in GCEW, we found that the spatial probability distributions of a runoff-loss ratio can be rescaled to a new distribution that is common to all events. We interpret that random within-event differences in runoff-loss ratios in the model arise due to soil moisture spatial variability of water loss during events that is supported by observations. As an application of the model, we develop a method for representing ensembles of runoff in a large number of hillslopes within an unnested subbasin in GCEW. Our model preserves water balance in a mean statistical sense and supports our hypothesis. Self-similarity in river networks is not expected to change over decadal to centennial time scales at which climate change is viewed. Therefore, applicability of the theory does not depend on assumptions regarding climatic stationarity or non-stationarity.