Adaptive smoothing to identify spatial structure in global lake ecological processes using satellite remote sensing data

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.