Change Point Analysis for Land Surface Temperature using Spatiotemporal Functional Data Method

Weather stations collect various meteorological variables such as temperature, precipitation, and humidity. These variables have been measured at the regular and repetitive time points at the specific location in the year. However, ideally, the characteristic of the climate data is that these variables exist in the form of a continuous function regardless of the time points observed. This characteristic is considered to be close to the functional data perspective, which assumes that data are observed in the form of function values at discrete points from a random function that exists as a continuous function in an infinite-dimensional space, and they require statistical techniques that are different from existing approaches. In this study, we aim to analyze land surface temperature data to determine that there is a change point in the spatial average for almost domestic observatories, assuming that they measured over a total of 42 years from 1981 to 2022 at 48 sites is functional data. Specifically, after estimating the spatial and temporal covariances, the weight for integrating spatial information was extracted from the spatial covariance structure, and the eigenfunctions and eigenvalues for integrating temporal information were extracted from the temporal covariance structure. Based on this, we introduce a method of expressing statistics as a partial sum of the mean difference before and after a specific point in time, as well as an approximate distribution.