Satellite remote sensing can provide indicative measures of environmental variables that are crucial to understanding the environment. The spatial and temporal coverage of satellite images allows scientists to investigate the changes in environmental variables in an unprecedented scale. However, identifying spatiotemporal patterns from such images is challenging due to the complexity of the data, which can be large in volume yet sparse within individual images. This paper proposes a new approach, state space functional principal components analysis (SS-FPCA), to identify the spatiotemporal patterns in processed satellite retrievals and simultaneously reduce the dimensionality of the data, through the use of functional principal components. Furthermore our approach can be used to produce interpolations over the sparse areas. An algorithm based on the alternating expectation–conditional maximisation framework is proposed to estimate the model. The uncertainty of the estimated parameters is investigated through a parametric bootstrap procedure. Lake chlorophyll-a data hold key information on water quality status. Such information is usually only available from limited in situ sampling locations or not at all for remote inaccessible lakes. In this paper, the SS-FPCA is used to investigate the spatiotemporal patterns in chlorophyll-a data of Taruo Lake on the Tibetan Plateau, observed by the European Space Agency MEdium Resolution Imaging Spectrometer.

卫星遥感可以提供指示性的环境变量度量，这些变量对于理解环境至关重要。卫星图像的时空覆盖范围使科学家能够以前所未有的规模研究环境变量的变化。然而，由于数据的复杂性，从这样的图像中识别时空模式是具有挑战性的，数据的体积可能很大，但在单个图像中却很稀疏。本文提出了一种新的方法，状态空间功能主成分分析（SS-FPCA），以通过使用功能主成分来识别处理后的卫星检索中的时空模式，并同时降低数据的维数。此外，我们的方法可用于在稀疏区域上生成插值。提出了一种基于交替期望-条件最大化框架的算法来估计模型。通过参数自举程序研究估计参数的不确定性。湖绿素一个数据保持水质状况的重要信息。通常只能从有限的原地采样位置获得此类信息，而对于偏远的人迹罕至的湖泊则根本无法获得此类信息。在本文中，SS-FPCA用于研究叶绿素的时空模式-欧洲航天局中分辨率成像光谱仪观测到的青藏高原塔罗湖的数据。