## 4 Data Processing
### Modeling Phenology  
Once each individual vegetative season has been identified, the evolution of the plant canopy properties during that period can be modeled. This is beneficial (i) to estimate the timing of events, such as the start, end, and length of the season (SOS, EOS, and LOS, respectively), (ii) to document the probable value of biogeophysical variables, such as FAPAR, when direct observations are missing, and (iii) to characterize the long-term evolution of the environment, in this case, for the environment around the Skukuza flux tower, in the Lowveld savanna of north-eastern South Africa, during the period 2000-2018, despite the presence of noise in the data. Global and local methods have been used in the literature for similar purposes. Local approaches take existing data at face value and generate estimates of missing observations on the basis of the values of neighboring measurements [79]. They include rank based filters, e.g., minimum, median, and maximum filters [80], linear/polynomial filters, such as moving average and adaptive Savitzky-Golay filters [81; 82; 83], locally weighted scatterplot smoothing (in [79; 84]), and Whittaker smoother (in [85]) to name a few. Advantages include the applicability to any time series, irrespective of their semantic or thematic context, and an ability to match arbitrary fluctuations, but at the risk of simulating fluctuations that may be suggested by noisy or erroneous data. Global models, by contrast, impose a functional shape that is intended to represent the likely evolution of the variable of interest, in this case, the phenology of vegetation, which is expected to exhibit a growth phase, followed by a senescence phase. They include function-fitting approaches, e.g., polynomial, double logistic, asymmetric Gaussian [86; 87; 88; 89], and signal smoothing or decomposition techniques, e.g., wavelet transform, Fourier analysis, Lomb-Scargle [90; 91; 92; 93; 94; 95]; see [79]. Signal decomposition techniques provide forecasts over a season by decomposing the time series into noise, seasonal variability and trend [96]. The Lomb-Scargle algorithm, initially developed by [PERSON] [97] and subsequently elaborated by [98], implements an approach similar to Fourier analysis [99], adapted to estimate the power spectral density of unevenly sampled data [77; 78]. Local and global phenology models both have advantages and drawbacks: The selection of a global versus a local model must depend on the intended usage of the resulting information. Global models are deemed particularly suited to represent the temporal evolution of vegetation when the empirical evidence exhibits unusual or unexpected fluctuations (as is the case here): they are used as low-pass filters to screen out the influence of extraneous or uncontrolled processes, such as biomass burning, random browsing, the possible contamination due to thin clouds or aerosols, or simply noise in the data. A local modeling  
Figure 8: A subset of the FAPAR time series at the reference pixel for the Skukuza flux tower showing the start of the first vegetative season between 2000 and 2001 and the vegetative seasons for 2001–2002, 2002–2003, and 2003–2004. The dotted blue lines delimit the search periods for the start and end of the vegetative seasons, and the solid red lines indicate those boundaries. The dashed green line represents the median value for the record, in this case, 0.25.  
approach would definitely be more appropriate if the objective were to specifically monitor biomass burning events, for instance. This study explores the suitability of four different global models, each constructed as a pair of S-shaped functions (one to simulate the growth phase and the other to represent the senescence phase): Gaussian, hyperbolic tangent, logistic (these two functions are mathematically equivalent, but they exhibit differences in terms of numerical efficiency, as will be shown below), and sine.