Connecting Event-Based Scaling of Flood Peaks to Regional Flood Frequency Relationships

Regional flood frequency (RFF) equations are statistical characterizations that, in their simplest form, show how peak discharge quantiles scale with drainage area. They remain separated from the physical processes that occur during flood-generating rainfall-runoff events. A physical understanding of RFF equations is a long-standing unsolved problem in hydrology. This study addresses this problem using a scaling framework. Two hypotheses are introduced that collectively state that scaling slopes of event peak discharges are on average equivalent to the mean scaling slope of annual peak quantiles; the later quantity refers to an average taken over a set of exceedance probabilities under consideration. To test these hypotheses, a nested mixed-effects linear (NMEL) model was developed that characterizes event-to-event variability in scaling relationships between stream discharge peaks and drainage area. The model leads to scaling relationships for event peak discharge quantiles and annual peak quantiles that are the basis for RFF equations. Because event-based scaling relationships can be connected to physical processes, the model provides a way of investigating whether quantile-based scaling relationships can be connected as well. The model was tested against data for 148 rainfall-runoff events from the $21{\mathrm{km}}^2$ Goodwin Creek Experimental Watershed (GCEW) located in the state of Mississippi. Test results support the NMEL model and the two hypotheses, but raise new questions that need to be addressed in future research.