## 2 Materials and Methods
### NDVI Time Series Preparation and Seasonality Extraction  
Vegetation indices (VI) are correlated to photosynthetically active radiation absorbed by plants in the visible spectrum [45]. Normalized Difference Vegetation Index (NDVI) is the most widely used VI [46]. This NDVI signal allows us to estimate seasonal changes in light absorption of a surface [9] and may summarize the annual and interannual variability of plant phenology [47]. The fused images produced by STARFM were used to calculate NDVI values (for example, see Figure 5) at an eight-day time series interval for each of the three methods with the following formula [46]:  
\[NDVI=(NIR-RED)/(NIR+RED)\]Figure 4: The steps contained in the python script to match MODIS scenes without a corresponding Landsat scene with the appropriate MODIS/Landsat base pair and create the STARFM input texts reflecting this.  
This produced a range of values from \(-1\) to 1, where negative values were related to areas with open water and positive values were areas covered by green vegetation [47]. All locations with no data in either of the synthetic images were set to be well outside of this range. For the time series produced by the statistical methods, areas where the Landsat image used in the base pair had a value for fill, water, shadow, snow, or cloud in the CFMask were also set to be well outside of this range. Based on the three NDVI time series values, the SOS, EOS, and LOS were all extracted using TIMESAT 3.2 software.  
TIMESAT is an accurate method for extracting seasonality parameters [48]. The SOS and EOS were defined as points in time where the value has increased or decreased by a certain amount [49]. We used the following settings for this study: no spike method, logistic function for data smoothing, one envelope iteration, an amplitude season start method, an adaptation strength of two, and the amplitude value of 0.2 (or 20%) for both SOS and EOS. For specific details on these parameters, please consult the TIMESAT manual [50]. In addition to using the calculated NDVI values in TIMESAT, since according to the software manual TIMESAT requires the same number of images for each year, a dummy image with values well outside of the NDVI value range was created and used for the day when no MODIS data was collected and every eight days between Day 1 and Day 41 of 2000. In addition, to ensure TIMESAT extracted data for all of the years in our study, two dummy years were included in the TIMESAT input that were duplicates of the first and last years of data and placed at the beginning and end of the time series. During seasonality extraction, the date range of synthetic images that specified when each SOS was expected to occur included three images (time steps) before the start of the year through the end of the year (i.e., image range 44-92 was used for the year 2000 which spanned images 47-92), for EOS the date range included the start of the year to three images after the end of the year (i.e., image range 47-95 for the year 2000), and the date range for LOS included three images before the start of the year through three images after the end of the year (i.e., image range 44-95 for the year 2000).