Connecting the power-law scaling structure of peak-discharges to spatially variable rainfall and catchment physical properties

Abstract

We have conducted extensive hydrologic simulation experiments in order to investigate how the flood scaling parameters in the power-law relationship Q(A)=αAθ, between peak-discharges resulting from a single rainfall–runoff event Q(A) and upstream area A, change as a function of rainfall, runoff coefficient (Cr) that we use as a proxy for catchment antecedent moisture state, hillslope overland flow velocity (vh), and channel flow velocity (vc), all of which are variable in space. We use a physically-based distributed numerical framework that is based on an accurate representation of the drainage network and apply it to the Cedar River basin (A=16,861km2), which is located in Eastern Iowa, USA. Our work is motivated by seminal empirical studies that show that the flood scaling parameters α and θ change from event to event. Uncovering the underlying physical mechanism behind the event-to-event variability of α and θ in terms of catchment physical processes and rainfall properties would significantly improve our ability to predict peak-discharge in ungauged basins (PUB). The simulation results demonstrate how both α and θ are systematically controlled by the interplay among rainfall duration T, spatially averaged rainfall intensity E[I], as well as E[Cr], E[vh], and vc. Specifically, we found that the value of θ generally decreases with increasing values of E[I], E[Cr], and E[vh], whereas its value generally increases with increasing T. Moreover, while α is primarily controlled by E[I], it increases with increasing E[Cr] and E[vh]. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly.