A parsimonious tail compliant multiscale statistical model for aggregated rainfall

2026-01-13

Advances in Water Resources

AI Summary

This study addresses the challenge that existing rainfall intensity models struggle to simultaneously maintain mathematical consistency—such as non-crossing return periods across time scales—and parameter parsimony when applied across multiple temporal resolutions (from minutes to weeks). Moreover, most models are confined to seasonal extremes and lack the ability to characterize the full distribution of rainfall intensities. To overcome these limitations, this work proposes a parsimonious multiscale statistical framework based on the extended generalized Pareto distribution (EGPD), uniquely integrating EGPD with rainfall aggregation processes. By leveraging Poisson compounding and Panjer recursion, the method enables efficient likelihood-based inference. With only eight parameters, it consistently models rainfall intensity distributions from 6 minutes to 3 days, ensures naturally ordered return periods, and supports reliable sub-annual scale estimation. Validation at six climatically diverse sites in France demonstrates that the resulting IDF curves are cross-scale consistent, parameter-efficient, and computationally tractable.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Machine Learning: Multimodal Learning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Problem

• rainfall aggregation
• multiscale modeling
• statistical parsimony
• return level ordering
• IDF curves

Innovation

• Extended Generalized Pareto Distribution
• multiscale rainfall modeling
• composite likelihood
• Panjer algorithm
• IDF curves