Drought Begets Drought: Self-Exciting Onsets, Spell Persistence, and Network Influence 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 univariate and multivariate Hawkes self-exciting point processes to model dry spell onsets in Chile. We analyze high-resolution daily precipitation data from 462 stations during austral winter (May--August), 1980--2022. The Hawkes process framework allows for explicit quantification of baseline initiation rates (\mu _i ), excitation strengths (\alpha _ij ) and memory timescales (1/\beta _ij ), revealing both localized event clustering and dynamically inferred influence networks. Parameters are estimated in overlapping 10-year moving windows to capture temporal evolution. Community detection on symmetrized Hawkes networks uncovers spatially coherent mesoscale clusters that partially align with, but are not reducible to, climatic zones derived from Dynamic Time Warping (DTW) clustering. Complementing this, we fit log-normal and heavy-tailed distributions to dry spell durations, with information-theoretic criteria confirming strong deviations from memoryless models. Spatial mapping of log-normal parameters (\mu, \sigma) reveals marked latitudinal and orographic gradients in both the median duration and the tail risk. Critically, we demonstrate that large-scale climate modes (ENSO, PDO, AAO, SOI) exert a statistically significant, but spatially heterogeneous, control over dry spell persistence, as revealed through linear mixed effects and generalized additive models. This study provides a mathematically rigorous framework for diagnosing the onset, propagation, and persistence of drought, establishing a novel paradigm for the assessment of hydroclimatic risk.