Many advancements have been introduced to tackle spatial and temporal structures in data. When the spatial and/or temporal domains are relatively large, assumptions must be made to account for the sheer size of the data. The large data size, coupled with realities that come with observational data, make it difficult for all of these assumptions to be met. In particular, air quality data are very sparse across geographic space and time, due to a limited air pollution monitoring network. These “missing” values make it difficult to incorporate most dimension reduction techniques developed for high-dimensional spatiotemporal data. This article examines aerosol optical depth (AOD), an indirect measure of radiative forcing, and air quality. The spatiotemporal distribution of AOD can be influenced by both natural (e.g., meteorological conditions) and anthropogenic factors (e.g., emission from industries and transport). After accounting for natural factors influencing AOD, we examine the spatiotemporal relationship in the remaining human influenced portion of AOD. The presented data cover a portion of India surrounding New Delhi from 2000–2006. The proposed method is demonstrated showing how it can handle the large spatiotemporal structure containing so much missing data for both meteorologic conditions and AOD over time and space.

中文翻译：

---

不规则间隔的气溶胶光学深度数据的时空建模。


为了解决数据的空间和时间结构，已经引入了许多进步。当空间和/或时间域相对较大时，必须做出假设来考虑数据的绝对大小。庞大的数据量，加上观测数据带来的现实，使得所有这些假设都很难得到满足。特别是，由于空气污染监测网络有限，空气质量数据在地理空间和时间上都非常稀疏。这些“缺失”值使得很难合并大多数为高维时空数据开发的降维技术。本文研究了气溶胶光学深度 (AOD)、辐射强迫的间接测量方法和空气质量。 AOD 的时空分布可能受到自然因素（如气象条件）和人为因素（如工业和交通排放）的影响。在考虑了影响 AOD 的自然因素后，我们检查了 AOD 其余受人类影响的部分的时空关系。所提供的数据涵盖 2000 年至 2006 年期间印度新德里周边的部分地区。所提出的方法经过论证，展示了它如何处理包含大量气象条件和时间和空间 AOD 缺失数据的大型时空结构。