Recent Developments in the Application of the Derived Distribution Approach to Flood Frequency
Authors: Woods Ross , Zheng Yanchen , Quaglia Roberto , Yin Yiming , Giani Giulia , Coxon Gemma , Han Dawei , Rico-Ramirez Miguel , Rosolem Rafael 
Published: February 2023

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. There are very significant challenges for reliable application of continuous simulation models to extreme events in ungauged catchments.The event-scale derived distribution approach also has challenges, which we explore below. The derived distribution approach at the event scale typically combines the following elements: a stochastic rainfall model, an event-scale rainfall-runoff model (including &#8220;losses&#8221; and a &#8220;baseflow&#8221; component), and a runoff routing model. In principle, every element of this approach may be considered as a (seasonally varying) random variable. The flood peak distribution is obtained by integrating over joint distributions of the model elements.First challenge: what is the physical basis for estimating the event runoff coefficient? In the 1970s, this was addressed using infiltration theory, but other runoff generation mechanisms are often more important. We suggest: (i) begin with locations which are dominated by a small number of runoff generation mechanisms (ii) make use of existing theory on links between climate, catchment characteristics and seasonal water balance (iii) exploit large samples of data where available. I will briefly summarise our progress on this topic in the UK, using a largely empirical approach, though with an eye to later exploring a process-based explanation.Second challenge: how do we parsimoniously quantify the impacts of within-storm temporal and spatial rainfall patterns on the flood hydrograph? Existing approaches use stochastic rainfall models to explicitly generate (hourly) time series (or fields) of rainfall; since catchments damp out high frequency forcing, these rainfall series often contain excessive detail and obscure the most informative interactions between rainfall and catchment response. We propose stochastic models that can generate hydrologically relevant attributes of rainfall events (e.g. intensity/depth/duration, spatial and temporal moments), and then apply rainfall-runoff transformations which operate on rainfall moments, and do not require excess detail in temporal (or spatial) patterns of rainfall. I will present recent results showing that it is feasible to summarise rainfall characteristics in this way, and that spatial patterns in rainfall do play a role in determining flood magnitude, but only in some events.Third challenge: How well does existing theory (Woods & Sivapalan et al 1999, Viglione et al 2010, Ga&#225;l et al, 2012) combine the spatial and temporal moments of a rainfall event with catchment characteristics, in order to predict the hydrograph temporal characteristics, especially the temporal variance, a measure of temporal dispersion? Successful applications of this theory (which depends ultimately on geomorphological dispersion) will require (i) neglect of some covariance terms (ii) a strategy for estimating hillslope travel times relevant to floods (iii) reasonable estimates of the characteristic river network celerity for ungauged catchments.