Return period of high-dimensional compound events. Part I: Conceptual framework

Abstract. Natural hazards like floods and droughts result from the complex interplay of multiple physical processes across various spatial and temporal scales. Traditional univariate analyses fall short in capturing the devastating impacts of compound events—where multiple drivers interact, often leading to more severe outcomes. This study expands on existing methodologies to quantify compound events by introducing a robust framework that integrates hydrological, statistical, and machine learning techniques. We propose a novel approach for defining the critical layer associated with multivariate return periods in higher-dimensional spaces, addressing the challenges in modeling interactions beyond two or three variables. This research not only enhances the understanding of compound events but also provides practical tools for their analysis, offering significant implications for climate risk assessment and environmental management. A forthcoming second paper will demonstrate the practical application of this methodology, focusing on calculating the multivariate return period in five dimensions for rainfall dependencies across different locations.