  Vegetation phenology consists of studying synchronous stationary events, such
as the vegetation green up and leaves senescence, that can be construed as
adaptive responses to climatic constraints. In this paper, we propose a method
to estimate the annual phenology curve from multi-annual observations of time
series of vegetation indices derived from satellite images. We fitted the
classical harmonic regression model to annual-based time series in order to
construe the original data set as realizations of a functional process.
Hierarchical clustering was applied to define a nearly homogeneous group of
annual (smoothed) time series from which a representative and idealized
phenology curve was estimated at the pixel level. This curve resulted from
fitting a mixed model, based on functional principal components, to the
homogeneous group of time series. Leveraging the idealized phenology curve, we
employed standard calculus criteria to estimate the following phenological
parameters (stationary events): green up, start of season, maturity,
senescence, end of season and dormancy. By applying the proposed methodology to
four different data cubes (time series from 2000 to 2023 of a popular
satellite-derived vegetation index) recorded across grasslands, forests, and
annual rainfed agricultural zones of a Flora and Fauna Protected Area in
northern Mexico, we verified that our approach characterizes properly the
phenological cycle in vegetation with nearly periodic dynamics, such as
grasslands and agricultural areas. The R package sephora was used for all
computations in this paper.
