Air pollution remains a critical environmental and public health challenge, demanding high-resolution spatial data to better understand its spatial distribution and impacts. This study addresses the challenges of conducting multivariate spatial analysis of air pollutants observed at aggregated levels, particularly when the goal is to model the underlying continuous processes and perform spatial predictions at varying resolutions. To address these issues, we propose a continuous multivariate spatial model based on Gaussian processes (GPs), naturally accommodating the support of aggregated sampling units. Computationally efficient inference is achieved using R-INLA, leveraging the connection between GPs and Gaussian Markov random fields (GMRFs). A custom projection matrix maps the GMRFs defined on the triangulation of the study region and the aggregated GPs at sampling units, ensuring accurate handling of changes in spatial support. This approach integrates shared information among pollutants and incorporates covariates, enhancing interpretability and explanatory power. This approach is used to downscale PM2.5, PM10 and ozone levels in Portugal and Italy, improving spatial resolution from 0.1{\deg} (~10 km) to 0.02{\deg} (~2 km), and revealing dependencies among pollutants. Our framework provides a robust foundation for analyzing complex pollutant interactions, offering valuable insights for decision-makers seeking to address air pollution and its impacts.

翻译：空气污染仍是严峻的环境与公共卫生挑战，亟需高分辨率空间数据以深入理解其空间分布与影响。本研究针对在聚合层面观测的空气污染物进行多元空间分析所面临的挑战，尤其当建模目标为刻画潜在的连续过程并在不同分辨率下进行空间预测时。为解决这些问题，我们提出一种基于高斯过程（GPs）的连续多元空间模型，其天然适应聚合采样单元的空间支持域。通过利用GPs与高斯马尔可夫随机场（GMRFs）之间的关联，采用R-INLA实现计算高效的统计推断。自定义投影矩阵将定义在研究区域三角剖分上的GMRFs与采样单元的聚合GPs相映射，确保空间支持域变化的精确处理。该方法整合了污染物间的共享信息并纳入协变量，从而增强模型的可解释性与解释力。本研究应用该框架对葡萄牙与意大利的PM2.5、PM10及臭氧浓度进行降尺度分析，将空间分辨率从0.1°（约10公里）提升至0.02°（约2公里），并揭示了污染物间的依存关系。该框架为解析复杂的污染物相互作用提供了稳健基础，为决策者应对空气污染及其影响提供了重要科学依据。