Improvement of the Rnnmm-type climate index approach with a spatio-temporal model based on the Hawkes process

Abstract. This paper proposes an innovative geostatistical model based on self-exciting Hawkes processes for modeling the Rnnmm-type extreme climate index, representing a novel contribution to the literature on climate extremes. The proposed approach generalizes non-homogeneous spatio-temporal Poisson models by incorporating temporal dependence between events through excitation functions, enabling the capture of clustering patterns commonly observed in precipitation time series. The model is formulated within a Bayesian framework, with parameter estimation performed via Markov Chain Monte Carlo (MCMC) methods. Spatial dependence is introduced through hierarchical Gaussian processes, allowing for interpolation in locations without observed data. The model is applied to the R20mm index (annual number of days with precipitation exceeding 20 mm) using data from northern Maranhão (Brazil) for the period 2013–2022. Cross-validation results demonstrate that the proposed model outperforms non-homogeneous Poisson models with and without seasonality in terms of predictive accuracy. Furthermore, the excitation parameters provide additional insights into the persistence and intensity of extreme events, revealing patterns not captured by conventional models. These findings highlight the model’s potential to enhance the analysis of climate extremes in regions with high spatio-temporal variability in precipitation.