Satellite remote sensing data are important to the study of environment problems at a global scale. The GloboLakes project aimed to use satellite remote sensing data to investigate the response of the major lakes on Earth to environmental conditions and change. The main challenge to statistical modelling is the identification of the spatial structure in global lake ecological processes from a large number of time series subject to incomplete data and varying uncertainty. This paper introduces a comprehensive modelling procedure, combining adaptive smoothing and functional data analysis, to estimate the smooth curves representing the trend and seasonal patterns in the time series and to cluster the curves over space. Two approaches, based on an irregular basis and an adaptive penalty matrix, are developed to account for the varying uncertainty induced by missing observations and specific constraints (e.g. substantive periods of measurement values of zero in winter). In particular, the adaptive penalty matrix applies a heavier penalty to smooth curve estimates where there is higher uncertainty to prevent over-fitting the noisy/biased data. The modelling procedure was applied to the lake surface water temperature (LSWT) time series from 732 largest lakes globally and the lake chlorophyll-a time series from 535 largest lakes globally. The procedure enabled the identification of nine global lake thermal regions based on the temporal dynamics of LSWT, and the extraction of eight global lake clusters based on the interannual variation in chlorophyll-a and ten clusters to differentiate the seasonal signals.

卫星遥感数据对于在全球范围内研究环境问题具有重要意义。GloboLakes 项目旨在利用卫星遥感数据来调查地球上主要湖泊对环境条件和变化的反应。统计建模的主要挑战是从大量数据不完整和不确定性变化的时间序列中识别全球湖泊生态过程的空间结构。本文介绍了一种综合建模程序，结合自适应平滑和功能数据分析，估计表示时间序列中趋势和季节模式的平滑曲线，并在空间上对曲线进行聚类。两种方法，基于不规则基础和自适应惩罚矩阵，被开发以解释由于缺少观测和特定限制（例如，冬季测量值为零的实质性时期）引起的各种不确定性。特别是，自适应惩罚矩阵将更重的惩罚应用于平滑曲线估计，其中存在更高的不确定性，以防止过度拟合嘈杂/有偏差的数据。该建模程序应用于全球 732 个最大湖泊的湖面水温 (LSWT) 时间序列和湖叶绿素-来自全球 535 个最大湖泊的时间序列。该程序能够基于 LSWT 的时间动态识别 9 个全球湖泊热区，并根据叶绿素a的年际变化提取 8 个全球湖泊群和 10 个群以区分季节性信号。