Multivariate Analysis of Extreme Rainfall Events in Tuscany: Comparing Factor Analysis and Copula-Based Models

Design rainfall estimation is critical for hydrological infrastructure planning and risk management. Traditional methods often rely solely on rainfall intensity, overlooking essential event-scale characteristics like spatial extent, duration, and precipitation volume, which play an important role in rainfall-runoff modeling. To address these limitations, this study adopts a multivariate approach to incorporate additional physical characteristics of rainfall events and enhance design rainfall estimation.

A key preliminary step involved the construction of a comprehensive rainfall event dataset for Tuscany, Italy, using high-resolution time series data from 270 rain gauges (1999–2024). To shift from point-based intensity data to event-scale analysis, specific criteria were defined to identify individual rainfall events. This process involved grouping measurements based on their spatial and temporal proximity and applying interpolation techniques to derive a unified set of physical characteristics for each event. The resulting dataset includes attributes such as total volume, duration, and spatial extent, offering a holistic representation of each rainfall event.

Two distinct approaches were employed to model the relationships between event characteristics and estimate return periods for extreme events. The first approach employs Factor Analysis to reduce the dimensionality of the dataset by identifying independent latent variables that capture the linear relationships within the features. This method allows for the separate analysis of the marginal distribution using conventional univariate Peak Over Threshold (POT) techniques, though it sacrifices direct physical interpretability. The second approach utilizes copulas to model dependencies among the original event characteristics, providing a flexible and physically meaningful framework for joint distribution analysis.

This work contributes to the ongoing research by providing a robust framework for multivariate analysis of rainfall events, offering more informative design rainfall estimates to support flood modeling and risk management.

This study was conducted within the RETURN Extended Partnership and received funding from the European Union Next-Generation EU (National Recovery and Resilience Plan – NRRP, Mission 4, Component 2, Investment 1.3 – D.D. 1243 2/8/2022, PE0000005)