Spatio-temporal joint modelling on moderate and extreme air pollution in Spain

Kai Wang, Chengxiu Ling*, Ying Chen, Zhengjun Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Very unhealthy air quality is consistently connected with numerous diseases. Appropriate extreme analysis and accurate predictions are in rising demand for exploring potential linked causes and for providing suggestions for the environmental agency in public policy strategy. This paper aims to model the spatial and temporal pattern of both moderate and extremely poor PM 10 concentrations (of daily mean) collected from 342 representative monitors distributed throughout mainland Spain from 2017 to 2021. We first propose and compare a series of Bayesian hierarchical generalized extreme models of annual maxima PM 10 concentrations, including both the fixed effect of altitude, temperature, precipitation, vapour pressure and population density, as well as the spatio-temporal random effect with the Stochastic Partial Differential Equation (SPDE) approach and a lag-one dynamic auto-regressive component (AR(1)). Under WAIC, DIC and other criteria, the best model is selected with good predictive ability based on the first four-year data (2017–2020) for training and the last-year data (2021) for testing. We bring the structure of the best model to establish the joint Bayesian model of annual mean and annual maxima PM 10 concentrations and provide evidence that certain predictors (precipitation, vapour pressure and population density) influence comparably while the other predictors (altitude and temperature) impact reversely in the different scaled PM 10 concentrations. The findings are applied to identify the hot-spot regions with poor air quality using excursion functions specified at the grid level. It suggests that the community of Madrid and some sites in northwestern and southern Spain are likely to be exposed to severe air pollution, simultaneously exceeding the warning risk threshold.

Original languageEnglish
Pages (from-to)601-624
Number of pages24
JournalEnvironmental and Ecological Statistics
Issue number4
Publication statusPublished - Dec 2023


  • Air pollution
  • Bayesian joint model with sharing effects
  • Extreme value analysis
  • Integrated nested Laplace approximation
  • Spatio-temporal model


Dive into the research topics of 'Spatio-temporal joint modelling on moderate and extreme air pollution in Spain'. Together they form a unique fingerprint.

Cite this