Morales et al. (2026) Improvement of the Rnnmm-type climate index approach with a spatio-temporal model based on the Hawkes process

Identification

• Journal: Geoscientific model development
• Year: 2026
• Date: 2026-06-30
• Authors: Fidel Ernesto Castro Morales, Marina Silva Paez, Daniele Tôrres Rodrigues, Carla de Moraes Apolinario
• DOI: 10.5194/gmd-19-5689-2026

Research Groups

• Department of Statistics, Federal University of Rio Grande do Norte
• Department of Statistical Methods, Institute of Mathematics, Federal University of Rio de Janeiro
• Department of Statistics, Federal University of Piauí

Short Summary

This paper proposes an innovative geostatistical model based on self-exciting Hawkes processes for modeling the Rnnmm-type extreme climate index. 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.

Objective

• To develop a novel geostatistical model based on self-exciting Hawkes processes for modeling extreme climate indices.
• To evaluate the performance of the proposed model compared to existing methodologies.

Study Configuration

• Spatial Scale: Regional scale, focusing on the northern region of Maranhão State, Brazil.
• Temporal Scale: Daily time step, analyzing precipitation data from 2013 to 2022.

Methodology and Data

• Models used: Weibull-Hawkes model, a self-exciting Hawkes process with a Weibull-distributed baseline hazard function.
• Data sources: Daily accumulated precipitation data (mm) obtained from 20 rain gauges located at national meteorological stations in Maranhão State.

Main Results

• The proposed model outperforms non-homogeneous Poisson models with and without seasonality in terms of predictive accuracy.
• The excitation parameters provide additional insights into the persistence and intensity of extreme events, revealing patterns not captured by conventional models.
• The study demonstrates the potential of the Weibull-Hawkes model to enhance the analysis of climate extremes in regions with high spatio-temporal variability in precipitation.

Contributions

• Original value of the article with respect to existing literature lies in the development and application of a novel geostatistical model based on self-exciting Hawkes processes for modeling extreme climate indices.
• The study provides insights into the underlying drivers of extreme rainfall events in the northern region of Maranhão State, Brazil.

Funding

• This research was funded by the National Council for Scientific and Technological Development (CNPq) under grant number 305177/2020-1.

Citation

@article{Morales2026Improvement,
  author = {Morales, Fidel Ernesto Castro and Nascimento, Antonio Marcos Batista do and Paez, Marina Silva and Rodrigues, Daniele Tôrres and Apolinario, Carla de Moraes},
  title = {Improvement of the Rnnmm-type climate index approach with a spatio-temporal model based on the Hawkes process},
  journal = {Geoscientific model development},
  year = {2026},
  doi = {10.5194/gmd-19-5689-2026},
  url = {https://doi.org/10.5194/gmd-19-5689-2026}
}