In environmental and climate data, there is often an interest in determining if and when changes occur in a system. Such changes may result from localized sources in space and time like a volcanic eruption or climate geoengineering events. Detecting such events and their subsequent influence on climate has important policy implications. However, the climate system is complex, and such changes can be challenging to detect. One statistical perspective for changepoint detection is functional time series, where one observes an entire function at each time point. We will consider the context where each time point is a year, and we observe a function of temperature indexed by day of the year. Furthermore, such data is measured at many spatial locations on Earth, which motivates accommodating sets of functional time series that are spatially-indexed on a sphere. Simultaneously inferring changes that can occur at different times for different locations is challenging. We propose test statistics for detecting these changepoints, and we evaluate performance using varying levels of data complexity, including a simulation study, simplified climate model simulations, and climate reanalysis data. We evaluate changes in stratospheric temperature globally over 1984-1998. Such changes may be associated with the eruption of Mt. Pinatubo in 1991.

翻译：在环境和气候数据中，通常需要确定系统是否以及何时发生变化。此类变化可能源于空间和时间上的局部因素，例如火山爆发或气候地球工程事件。检测这些事件及其对气候的后续影响具有重要的政策意义。然而，气候系统十分复杂，此类变化可能难以检测。变点检测的一种统计视角是函数型时间序列，即在每个时间点观测到完整的函数。我们将考虑每个时间点为一年，并观测到以一年中天数为索引的温度函数的情况。此外，此类数据在地球的多个空间位置进行测量，这促使我们处理在球面上进行空间索引的函数型时间序列集合。同时推断不同位置在不同时间可能发生的变化具有挑战性。我们提出了检测这些变点的检验统计量，并通过不同数据复杂度水平（包括模拟研究、简化气候模型模拟和气候再分析数据）来评估性能。我们评估了1984-1998年间全球平流层温度的变化，这些变化可能与1991年皮纳图博火山喷发相关。