Drought begets drought: self-exciting onsets, spell persistence, and network structure in hydroclimatic extremes

Understanding the spatio-temporal structure and persistence of meteorological droughts is critical for climate risk assessment, particularly in regions with pronounced climatic gradients. Here, we present the first application of Hawkes self-exciting point processes to model dry-spell onset events —defined as threshold-based transitions into contiguous sequences of dry days. We analyse daily precipitation data from 462 locations during austral winter (May–August, 1980–2021) in Chile. The Hawkes framework explicitly quantifies baseline onset rates, self-excitation strengths, and memory time scales, capturing temporal clustering in onset events. A multivariate extension yields an event-based statistical excitation network whose directed edges represent conditional cross-excitation between stations. Parameters are estimated in overlapping 10 year moving windows to resolve temporal evolution. Community detection on symmetrised Hawkes networks reveals spatially coherent mesoscale clusters that partially align with, but are not reducible to, climatic zones derived from dynamic time warping clustering. Complementarily, we model dry-spell durations using heavy-tailed parametric families and survival diagnostics, confirming strong deviations from memoryless persistence. Spatial mapping of log-normal parameters provides an interpretable baseline for gradients in typical duration and dispersion, while Pareto fits emphasise tail-risk heterogeneity across zones. Finally, linear mixed-effects and generalised additive models show that large-scale climate modes exert statistically significant yet spatially heterogeneous control over dry-spell persistence. The proposed framework provides a rigorous and reproducible methodology to diagnose onset clustering, persistence, and event-based hydroclimatic dependence patterns for drought-risk assessment.