An Event-Based Framework for Multivariate Return Periods of Extreme Rainfall

Rainfall events are inherently spatially extended phenomena that can be described through multiple physical attributes. Nevertheless, return period estimates are still commonly derived from point-scale rainfall intensity series, whose extension to regional-scale hazard assessment and rainfall–runoff modeling relies on strong and often implicit assumptions.

This study presents an event-based framework for the multivariate analysis of extreme rainfall events and the estimation of their return periods at regional scale. Rainfall events are reconstructed over Tuscany (Italy) from high-resolution precipitation records collected from a dense rain gauge network over the period 1999–2024, using a spatio-temporal aggregation approach. Aggregated events are represented through a set of physically meaningful attributes describing their intensity, spatial extent, duration, and precipitation volume, allowing a coherent characterization at event scale.

Extreme-value behavior is modeled through a Peak Over Threshold approach applied to the selected event attributes. Multivariate dependence among extreme events is described using flexible dependence models, enabling the joint behavior of intensity- and extent-related characteristics to be captured without imposing restrictive assumptions. A large synthetic population of extreme events is then generated to support a probabilistic interpretation beyond the limits of the observed sample.

To define multivariate return periods in a consistent manner, events are analyzed within a reduced space of independent latent variables derived from the original attributes. This representation allows extreme events with different physical signatures to be compared within a unified probabilistic framework, while accounting for the multivariate nature of rainfall extremes.

The proposed approach provides a robust basis for the regional-scale assessment of extreme rainfall hazards and highlights key challenges related to the definition and interpretation of return periods for spatially extended events. The framework is designed to support more physically consistent comparisons of extreme rainfall events and to improve their integration into hydrological risk analyses.