Cebrián et al. (2026) Spatio-temporal analysis of record-breaking temperature increments across Spain

Identification

• Journal: Stochastic Environmental Research and Risk Assessment
• Year: 2026
• Date: 2026-01-01
• Authors: Ana C. Cebrián, Jesús Asín, Jorge Castillo-Mateo, Alan E. Gelfand
• DOI: 10.1007/s00477-025-03159-x

Research Groups

• Departamento de Métodos Estadísticos, Universidad de Zaragoza, Zaragoza, Spain
• Department of Statistical Science, Duke University, Durham, NC, USA

Short Summary

This study develops a novel hierarchical Bayesian spatio-temporal model to analyze the magnitudes of daily record-breaking temperature increments across peninsular Spain from 1960 to 2021, revealing significant spatial and temporal heterogeneity, a strong dependence on previous day's records, and distinct seasonal patterns in extreme temperature increases.

Objective

• To fill the gap in spatio-temporal modeling of the values of record-breaking events by proposing an approach that models temperature increments relative to the previous record value, conditional on a record-breaking event having occurred.
• To address key climate-related questions: (i) Observe differences in seasonal behavior? (ii) Identify spatial patterns? (iii) Detect decadal temporal patterns to quantify climate change effects on record-breaking temperatures? (iv) Assess the effect of a previous day’s record-breaking event on increments? (v) Predict increment behavior at unobserved locations?

Study Configuration

• Spatial Scale: Peninsular Spain (approximately 492,175 km²), using 40 geo-referenced weather stations.
• Temporal Scale: Daily maximum temperature observations from January 1, 1960, to December 31, 2021, focusing on calendar-day records during the summer months (June, July, August).

Methodology and Data

• Models used: Bayesian hierarchical spatio-temporal model, conditional model for positive increments, Gamma distribution for increments, R-INLA for model fitting, SPDE approach for spatial dependence (Matérn Gaussian random field), Markovian AR(1) structure for temporal dependence.
• Data sources: Daily maximum temperature observations from 40 weather stations across peninsular Spain, extracted from the European Climate Assessment & Dataset (ECAD), provided by AEMET.

Main Results

• The selected model (MS3) uses a Gamma distribution for increments, includes eight covariates (logarithm of year and its square, logarithm of elevation, logarithm of distance to the coast, previous day's record indicator, and interactions), a global and a spatially varying intercept, and daily effects with an autoregressive structure.
• The posterior mean of the Gamma shape parameter ϕ is 1.8 (95% CI: 1.78, 1.86), confirming the suitability of a Gamma distribution over an Exponential one.
• The occurrence of a record on the previous day increases the posterior mean of the next day’s increment by between 0.3 °C and 0.6 °C, depending on the region.
• The posterior mean of the average increment on a record-breaking day during the decade 2012–2021 is approximately 1 °C inland, increasing to around 2 °C in some coastal areas (e.g., Basque Country, Galicia, southern Mediterranean coast).
• After the first 30 years (early 1980s), mean increments stabilize near 1 °C with a mild downward trend, though the upper tail of the distribution has remained stable over the last 30 years.
• The seasonal pattern of increments differs from the typical summer temperature cycle; June generally shows higher average increments than July and August, suggesting extreme temperatures in June are increasing more rapidly.
• The cumulative increment in record values from 1992 to 2021 reaches nearly 3 °C in the most affected coastal regions, while inland areas show cumulative values ranging from 1 °C to 2 °C.

Contributions

• Presents the first spatio-temporal modeling of the values of record-breaking events (specifically temperature increments), addressing a significant gap in environmental sciences literature.
• Proposes a novel approach of modeling increments relative to the previous record value, which simplifies implementation by treating increments as conditionally independent and offers a consistent basis for comparison across sites and time.
• Develops a robust hierarchical Bayesian spatio-temporal regression model that effectively captures complex dependencies and heterogeneity in record-breaking temperature increments, including spatial Gaussian processes and temporal autoregressive effects.
• Provides a comprehensive framework for inference using Monte Carlo simulations, enabling the characterization of conditional and marginal increment distributions, quantification of uncertainty, and generation of spatial and temporal maps of key metrics.
• Offers novel insights into the dynamics of record-breaking temperatures in peninsular Spain, highlighting regional differences, the impact of previous day's records, and distinct seasonal trends in extreme temperature increases.

Funding

• MCIN/AEI/10.13039/501100011033
• Unión Europea NextGenerationEU under Grants TED2021-130702B-I00 and PID2023-150234NB-I00
• Gobierno de Aragón under Research Group E4623R: Modelos Estocásticos and research project PROYT21_24-HIDROGIF
• Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

Citation

@article{Cebrián2026Spatiotemporal,
  author = {Cebrián, Ana C. and Asín, Jesús and Castillo-Mateo, Jorge and Gelfand, Alan E.},
  title = {Spatio-temporal analysis of record-breaking temperature increments across Spain},
  journal = {Stochastic Environmental Research and Risk Assessment},
  year = {2026},
  doi = {10.1007/s00477-025-03159-x},
  url = {https://doi.org/10.1007/s00477-025-03159-x}
}