## Data and Methodology
### Characterizing Land Surface Phenology in VODs and NDVI  
We used the AMSR-E and MODIS data from all eight years (2003-2010) for all pixels. The AMSR-E data record has winter data gaps as it was pre-filtered for snow covered or frozen land surfaces [35]. To avoid the frozen season and to maintain a consistent analysis period across all pixels, we restricted our focus to data from DOY 89-305, i.e., 30 March to 1 November for non-leap years and 29 March to 31 October for leap years. An 8-day forward moving average filter was applied to the AMSR-E data to minimize data gaps due to orbit and swath width, and to align the AMSR-E data with the corresponding compositing periods of the MODIS NBAR data (MCD43C4) (Figure 3). Growing degree-day (GDD) is the daily thermal time increment above a certain threshold (base temperature) for plant growth [36; 37; 38], and accumulated growing degree-days (AGDD) are the summation of daily thermal time increments throughout the whole growing period [24; 39; 40]. In other words, the passage of days is weighted by the quantity of growing degrees occurring that day, with zero (but not negative) degrees being a permissible weight [41]. [PERSON] [42] concluded that the base temperature of 0 \({}^{\circ}\)C is a robust and sufficient threshold for wheat phenology, which is the main crop in our study region. GDD was calculated from the AMSR-E air temperature (ta) data with a base temperature of 273.15 K (=0 \({}^{\circ}\)C) as follows:  
\[\mathrm{GDD}=\mathrm{max}[\frac{t_{\mathrm{ASC}}+t_{\mathrm{DES}}}{2}-273.15, \ 0] \tag{1}\]  
where \(t_{\mathrm{ASC}}\) and \(t_{\mathrm{DES}}\) are ascending and descending pass temperatures, which roughly corresponds to the daytime (~13:30) and nighttime (~22:30) temperatures, respectively. We applied an 8-day forward moving summation to the GDDs and picked up those values corresponded with the MODIS reflectance data (MCD43C4) acquisition dates to mimic the whole growing season GDD (DOY 89-305 in this case) and to align it with the MODIS data. Thus, each annual growing period has 28 GDD values. These GDD values were accumulated to yield AGDD. \[\mathrm{AGDD}_{t}=\mathrm{AGDD}_{t-1}+\mathrm{GDD}_{t} \tag{2}\]  
where \(\mathrm{GDD}_{t}\) is daily temperature increment of growing degree days at time \(t\). Daily GDD from AMSR-E tracked seasonal, weekly and monthly dynamics of corresponding weather station GDD [22]. The root mean square deviation (RMSD) between these daily datasets from the two sources was very low, 1.86-3.16 \({}^{\circ}\)C [22]. Linear regression of AMSR-E GDD with weather station GDD on these cropland sites yielded R\({}^{2}\) > 0.82 [22]. This result is in line with [PERSON] et al. [43] who found a bias of 1.0-3.5 K between WMO weather station and AMSR-E daily air temperature data on vegetated lands across the Northern Hemisphere. NDVI was calculated from the MODIS NBAR reflectance data using the standard formula by [PERSON] [44]. NDVI was calculated for each 0.05-degree (~5.6 km) pixel and zonal-averaged to the 0.25-degree (25 km) AMSR-E study pixels. We fitted the MODIS NDVI as a function of AMSR-E AGDD using the downward CxQ model. \[\mathrm{NDVI}_{t}=\alpha+\beta\ \times\ \mathrm{AGDD}_{t}\ \mathrm{-\ }\gamma\ \times\ \mathrm{AGDD}_{t}{}^{2} \tag{3}\]The intercept \(\alpha\) is the background NDVI at the start of observation period, the linear parameter \(\beta\) affects the slope, and the quadratic parameter \(\gamma\) controls the curvature. Since the model is downward convex quadratic, the sign of \(\beta\) coefficient is positive and \(\gamma\) coefficient is negative. Two phenometrics were derived from the fitted parameter coefficients of the CxQ model. These are Peak Height NDVI (PH; Equation (4)) and Thermal Time to Peak NDVI (\(\mathrm{TTP_{NDVI}}\); Equation (5)):  
\[\mathrm{PH}=\alpha-(\beta^{2}/4\times\gamma) \tag{4}\]  
\[\mathrm{TTP_{NDVI}}=-\beta\ /2\times\gamma \tag{5}\]  
where \(\alpha\), \(\beta\), and \(\gamma\) are the fitted parameter coefficients.