## 4 Data Processing
### Pre-Processing
#### 4.2.3 Identifying Individual Vegetative Seasons  
The successive vegetative seasons must be identified before attempting to fit a double S-shaped model through the data, accounting for the fact that their growth and senescence phases can start and last differently in different years, mostly as a result of climatic fluctuations. This process is implemented as follows. A power spectrum for the entire time series is computed first, using the Lomb-Scargle algorithm [77; 78] since the remote sensing data are provided on irregular dates. The resulting periodogram indicates whether the record exhibits primarily an annual variation (as is the case in Skukuza), or a biannual cycle, as would occur in agricultural regions where two crops can be grown per year. Figure 7 shows the Lomb periodogram for the FAPAR time series at the pixel location of the Skukuza Flux tower. This area exhibits a strong annual cycle (peak power: 71.72, frequency: 0.0027 day\({}^{-1}\), and period: 364.75 days) and a minor semi-annual fluctuation (peak power: 16.63, frequency: 0.00548 day\({}^{-1}\), and period: 182.37 days).  
Figure 6: The pixel reference grids used to co-register the MISR-HR FAPAR variable for Paths 168 and 169 of Block 110 to geographic coordinates for the Skukuza flux tower.  
Since satellite records may start and end at arbitrary times relative to climatic or ecological cycles, the second step consists in identifying the start of the first complete vegetative season that can be documented on the basis of the data record. This is achieved as follows:  
* compute the median of the entire FAPAR record,
* search, from the start of the record, the date of the first observation whose value is lower than this threshold,
* define a time interval equal to 1/3 of the expected length of the vegetative period (as determined from the Lomb-Scargle algorithm), starting on this date, and
* set the start date of the first vegetative season to the date of acquisition of the minimum FAPAR value within this limited time period.  
From that point onwards, the end date of each vegetative season is automatically considered the start of the next one. The end of each season date is determined as follows:  
* add the expected average length of the vegetative season to the starting date just identified to estimate a nominal end date,
* define a new limited time window located around that nominal end date, extending 1/6 of the expected length of the vegetative season on either side of that nominal date, and
* set the end date of the vegetative season to the date of acquisition of the minimum FAPAR value within this limited time period.  
This process is repeated until the nominal date of the end of the nth vegetative season exceeds the length of the remote sensing record. As a result, some data may be discarded at the start and end of the entire record, since they only document parts of vegetative seasons.  
Figure 8 plots a subset of the FAPAR time series at the pixel location of the Skukuza flux tower, showing the first few years of the MISR-HR FAPAR time series: the vegetative season ending in August 2000 is ignored because it is incomplete, and the next three are properly identified. The successive search periods are indicated by the blue dotted lines, and the red lines mark the start and end dates of the vegetative seasons.  
Figure 7: Lomb periodogram of the FAPAR time series at the reference pixel of the Skukuza flux tower.