Capturing the extremes: a quasi-comonotonicity-based algorithm for disaggregating daily to hourly rainfall

Abstract. Disaggregating daily precipitation data into hourly time scale is crucial for hydrological modelling, urban drainage design, and extreme rainfall risk assessment. This study presents Q-CODA, a novel Quasi-Comonotonicity-based Disaggregation Algorithm that leverages the quasi-comonotonic relationship between daily precipitation totals and their sub-daily maxima to generate hourly rainfall sequences consistent with observed extremes. The method first assumes the Fréchet–Hoeffding upper bound copula to simulate sub-daily maximum precipitation values conditioned on daily totals, which serve as target constraints. An initial hourly pattern is obtained via a K-Nearest Neighbours (KNN) approach and subsequently refined through an iterative adjustment algorithm to ensure coherence with both the daily precipitation total and previously calculated multiple sub-daily target constraints. We evaluated Q-CODA through a rigorous 5-fold cross-validation over 91 meteorological stations across Spain, spanning 1996–2024. Performance was benchmarked against state-of-the-art approaches including nearest-neighbour resampling methods, Poisson cluster-based rainfall generators, multiplicative random cascades models and deep learning techniques. Evaluation metrics were tailored to different aspects of the rainfall data: distributional distance (1-D Wasserstein), accuracy measures (mean absolute error, Nash–Sutcliffe efficiency), and extreme quantiles (90th to 99.9th percentiles) were computed on the hourly maximum precipitation over 1-hour windows, focusing on the representation of rainfall extremes. In contrast, autocorrelation and rainfall event duration statistics were calculated on the entire hourly rainfall time series to assess temporal coherence and event structure. Additionally, intensity-duration-frequency (IDF) curves were analysed. Results demonstrate that Q-CODA substantially improves the representation of rainfall extremes while maintaining temporal coherence and event structure. This approach offers a robust, data-driven framework for accurate sub-daily rainfall disaggregation, with significant implications for hydrometeorological applications and infrastructure design.