Exploring rainfall thresholds for shallow landslides using effective half-life precipitation indices and cluster analysis: a case study in Santos and Guarujá, Brazil

Santos and Guarujá have a long history of shallow landslides, with rupture surfaces generally reaching depths of up to 3 m. The slopes are underlain by gneissic and migmatitic bedrocks, where failures occur in immature residual soils, often at the soil–saprolite interface and exacerbated by anthropogenic interventions. An extreme rainfall event in March 2020 triggered a major disaster, resulting in 41 fatalities. This study investigates the relationship between landslides and rainfall using simple and effective half-life rainfall indices over a 5-year period (2018–2022). Rainfall accumulated over 1, 12 and 96 h was computed using the Automatic Rainfall Half-Life Cluster System (ARHCS), while K-means clustering and threshold identification were performed. The dataset comprised 136 landslide rainfall indices in Santos, 178 in Guarujá, and 665 non-occurrence rainfall events. The results show that effective half-life rainfall indices reduce data dispersion compared with simple rainfall indices, particularly when analyzed using K-means clustering. They also identify distinct rainfall reference levels from moderate to extreme, associated with induced, occasional, multiple, and generalized landslide scenarios. The established threshold levels are consistent with the empirical curves adopted by the São Paulo Preventive Civil Defense Plan, while soil moisture data from CEMADEN stations provide additional support for interpreting the landslide-rainfall relationship. The study demonstrates that the application of the Effective Half-Life method to landslide forecasting improves the definition of rainfall conditions associated with occurrence and non-occurrence rainfall events. Validation of the results indicated better predictive performance for the Half-Life method (98%) than for the Simple method (88%).