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.

翻译：植被物候学研究同步的静止事件，例如植被返青和叶片衰老，这些事件可被视为对气候约束的适应性响应。本文提出一种从卫星影像植被指数时间序列的多年度观测中估计年度物候曲线的方法。我们将经典谐波回归模型拟合到年度时间序列上，从而将原始数据集解释为功能过程的实现。应用层次聚类定义一组近似同质的年度（平滑）时间序列，进而在像元尺度上估计出具有代表性的理想化物候曲线。该曲线通过将基于功能主成分的混合模型拟合到同质时间序列组而得到。利用理想化物候曲线，我们采用标准微积分准则估计以下物候参数（静止事件）：返青期、生长季开始、成熟期、衰老期、生长季结束和休眠期。通过将所提方法应用于墨西哥北部某动植物保护区的草地、森林和旱作农业区的四个不同数据立方体（2000年至2023年一种常用卫星植被指数的时间序列），我们验证了该方法能够准确表征草原和农业区等具有近似周期性动态的植被物候周期。本文所有计算均使用R包sephora完成。