*3.1. Derivation of Vegetation Indices*

Five VIs were selected and derived from MODIS daily NBAR data for phenology detection, including NDVI, EVI2, NDPI, NDGI, and NIRv. Their definitions and corresponding references are given in Table 1.


**Table 1.** Derivation of vegetation indices used in the study.

Note: RGreen, RRed, RNIR, and RSWIR are the surface reflectance values in the green, red, NIR, and SWIR bands, respectively.

Among the five VIs, NDVI is the most commonly used VI for monitoring land surface phenology. EVI2 was developed from the enhanced vegetation index (EVI) [46] to adapt to satellite sensors without a blue band [17], while both EVI and EVI2 were designed to overcome the saturation problem and sensitivity to the soil background with NDVI. The NDPI and NDGI and NIRv were recently developed and are rather new. Both NDPI and NDGI were proposed to maximize the contrast between vegetation and soil/snow [21]. The NDPI assumes that the reflectance of soil and snow increases or decreases monotonically from red to SWIR wavelengths. In contrast, the reflectance of vegetation is high in the NIR band and low in both the red and SWIR bands [40]. The NDPI is thus designed by replacing the red band in NDVI with a weighted sum of the red and SWIR bands. As a result, the NDPI is close to zero for soil and snow but high for vegetation [31,40]. NDGI is a semi-analytical snow-free VI based on a linear mixture model. It connects a straight line between the reflectance of the green and NIR bands, and the difference between this line and the reflectance of the red band is defined as the NDGI [21]. NDGI is positive for vegetation but is close to zero for snow, soil, and dry grass. NIRv has been proposed as a proxy for SIF, a very effective indicator of vegetation photosynthesis [47], and has been successfully used in phenology detection [33]. The comparison of these five typical VIs would provide a useful reference for the performance of both structural-based and physiological-based VIs, as well as the traditional VIs and snow-free VIs.
