An Environmental Cross-Domain Review of Hawkes Processes – Lessons and Roadmap for Hydroclimate

Rainfall, dry spells and storms tend to cluster in time and space, and this clustering drives flood, drought and water-supply risk.Hawkes (self-exciting) point processes model clustering explicitly by splitting event occurrence into a background rate and events triggered by earlier events.They are well established in seismology, where the epidemic-type aftershock sequence (ETAS) model is the standard, but their use in hydroclimate is only beginning.This review examines 55 environmental studies that use Hawkes processes, identified from a Scopus search of 1,737 records, to see what hydroclimate research can learn from the other environmental fields.We coded each study for 11 methodological features and compared four groups: seismicity (n = 25), hydroclimate (n = 8), other natural hazards (n = 10) and ecology (n = 12).All eight hydroclimate studies in the reviewed corpus appeared in 2025-2026.They cover rainfall generators, extreme-rainfall indices, flood-control operation, dry-spell onsets and storm clustering.Seismicity shows a four-phase path to maturity: description; testing of assumptions; flexible Bayesian inference; and scalable, physics-informed and neural modelling.Hydroclimate has phase I-II maturity but already uses phase III-IV tools.Within the reviewed corpus, it is ahead of the seismicity studies in modelling marks (event amounts) and in linking models to operational decisions.The other environmental fields contribute further tools: decomposing risk into climate-forced and self-excited parts, non-exponential and delayed kernels, inhibition between event types, explicit treatment of coarsened and imperfectly detected data, coupling with physical models, and decision tools.We bring these together in a roadmap of 12 research priorities and a reporting checklist for future hydroclimate Hawkes studies.