Estimating Flood Peaks from Event Runoff Depth and Hydrograph Time Scales

Flood estimation in ungauged basins is important for flood design, and for improving our understanding of the sensitivity of flood magnitude to changes in climate and land cover. Flood estimates by current methods (e.g. statistical regression, unit hydrograph) have high uncertainty, even in places with dense observing networks (e.g. +/- 50-100% in the UK). Reductions in this uncertainty are being sought by using alternative methods, such as continuous simulation using hydrological models (spatially-distributed or lumped), and event-scale derived distribution approaches. The very significant challenges for reliable application of continuous simulation models in ungauged catchments are well described in the literature.

The research reported here is part of a larger project to estimate the probability distribution of flood peak magnitude in ungauged catchments, using an event-based derived distribution method. The derived distribution approach at the event scale typically combines the following elements: a stochastic rainfall model, an event-scale rainfall-runoff model (usually with “losses” and a “baseflow” component), and a runoff routing model. In principle, every element of this approach may be considered as a (seasonally varying) random variable, though previous research has typically considered only the rainfall as stochastic. The flood peak distribution is obtained by integrating over joint distributions of the model elements.

One of the novel aspects of the proposed approach is that, in place of an explicit routing method, we estimate the flood peak magnitude as the ratio of the event runoff depth (mm) to a characteristic timescale of the hydrograph (hours). The event runoff depth is the product of rainfall depth and event runoff coefficient, which in turn depends on both antecedent conditions and event rainfall. The characteristic timescale of the hydrograph is a second temporal moment (temporal “width” of the hydrograph). Although a comprehensive theory exists for space-time influences on this hydrograph time scale, research to date suggests that it depends, to first order, on time scales associated with rainfall and catchment response.

Here we report on extensive (many events, many catchments) testing in the UK of (i) whether the temporal standard deviation of the flow hydrograph is a good choice for the characteristic time scale of the hydrograph in the context of predicting the flood peak (Viglione et al 2010, Journal of Hydrology) (ii) whether the temporal standard deviation of the hydrograph can be predicted from time scales associated with rainfall and catchment response, as proposed by Woods and Sivapalan (1999, Water Resources Research) and Gaál et al (2012, Water Resources Research).