This work is motivated by the ECMWF CAMS reanalysis data, a valuable resource for researchers in environmental-related areas, as they contain the most updated atmospheric composition information on a global scale. Unlike observational data obtained from monitoring equipment, such reanalysis data are produced by computers via a 4D-Var data assimilation mechanism, thus their stochastic property remains largely unclear. Such lack of knowledge in turn limits their utility scope and hinders them from wider and more flexible statistical usages, especially spatio-temporal modelling except for uncertainty quantification and data fusion. Therefore, this paper studies the stochastic property of these reanalysis outputs data. We used measure theory and proved the tangible existence of spatial and temporal stochasticity associated with these reanalysis data and revealed that they are essentially realisations from digitised versions of real-world hidden spatial and/or temporal stochastic processes. This means we can treat the reanalysis outputs data the same as observational data in practice and thus ensures more flexible spatio-temporal stochastic methodologies apply to them. We also objectively analysed different types of errors in the reanalysis data and deciphered their mutual dependence/independence, which together give clear and definite guidance on the modelling of error terms. The results of this study also serve as a solid stepping stone for spatio-temporal modellers and environmental AI researchers to embark on their research directly with these reanalysis outputs data using stochastic models.

翻译：本研究以ECMWF的CAMS再分析数据为出发点，该数据作为环境相关领域研究人员的宝贵资源，包含了全球尺度上最新的大气成分信息。与监测设备获取的观测数据不同，此类再分析数据通过计算机利用四维变分数据同化机制生成，因此其随机特性在很大程度上尚不明确。这种认知局限进而限制了其应用范围，阻碍了其在更广泛、更灵活的统计应用中的使用，特别是在除不确定性量化和数据融合之外的时空建模领域。基于此，本文研究了这些再分析输出数据的随机特性。我们采用测度论，证明了这些再分析数据在空间和时间上确实存在随机性，并揭示其本质上是真实世界中隐藏的空间和/或时间随机过程离散化版本的实现。这意味着在实践中可将再分析输出数据与观测数据同等对待，从而确保更灵活的时空随机方法可适用于此类数据。我们还客观分析了再分析数据中的不同类型误差，并厘清了它们的相互依赖/独立关系，为误差项建模提供了明确指导。本研究结果也为时空建模者和环境人工智能研究者直接采用随机模型处理这些再分析输出数据奠定了基础。