Spatiotemporal dependence in floods with the Heffernan and Tawn conditional exceedance model: from synthesis to a new application

Flood behavior is characterized by complex spatial and temporal interdependencies that have been often overlooked in hazard and risk assessment, where traditional approaches have been either assuming independence across large regions or imposing uniform return periods within catchments. By contrast, the need for a crucial change in flood risk assessment has been recognized in recent decades. The conditional extremes model by Heffernan and Tawn, originally proposed in 2004, has emerged as an effective tool to represent extremal spatial dependence across scales, enabling the simulation of synthetic events that preserve observed multivariate dependence structures. The first part of the present manuscript presents a thematic synthesis of studies applying the Heffernan and Tawn model to floods, covering methodological developments, characterization of spatiotemporal dependence, derivation of boundary conditions for hydraulic modelling, integration with risk and impact modelling, and continental-scale applications. The synthesis organizes a fragmented body of literature, identifies common underlying patterns, and aims at facilitating the application of the model in operational flood risk assessment. The second part of the manuscript illustrates a practical implementation of the model to discharges measured at five stations along the Lambro River (Northern Italy). In the presented application, specific attention has been devoted to the scaling properties of joint return periods for synthetic events generated through Monte Carlo simulations, comparing them with the limiting cases of complete dependence and independence. The generation of 10,000 years of events demonstrated that, even within a small river system, simultaneous exceedances at all stations were substantially rarer than implied by complete dependence, supporting the explicit modelling of spatial dependence when estimating joint return periods.