## 3 Method
### Phenology Detection  
Land surface phenology (LPS) [43] is defined according to vegetation seasonal growing cycles recorded in time series satellite data. A seasonal cycle of vegetation growth includes a greenup phase, a maturity phase, a senescent phase, and a dormant phase [44]. Those four phases can be characterized using their start dates. The onset date of greenness increase (OGI) was called _greenup onset_. The onset date of greenness maximum was called _maturity onset_. The onset date of greenness decrease was called _senescence onset_ (OGD). The onset date of greenness minimum was called _domancy onset_.  
To identify the phenology, a Hybrid Piecewise Logistic Model (HPLM) algorithm was used to describe the temporal NDVI data using the following formula [45]:  
\[NDVI(t)=\left\{\begin{array}{ll}\dfrac{c_{1}}{1+e^{a_{1}+b_{1}t}}+NDVI_{b}& \text{Favorable growth condition}\\ \dfrac{c_{2}+dt}{1+e^{a_{2}+b_{2}t}}+NDVI_{b}&\text{Vegetation stress condition}\end{array}\right. \tag{3}\]  
where \(t\) is time in the day of the year (DOY), \(a\) is related to the vegetation growth time, \(b\) is associated with the rate of plant leaf development, \(c\) is the amplitude of NDVI variation, \(d\) is a vegetation stress factor, and \(NDVI_{b}\) is the background NDVI value. This model can be applied to detect seasonal vegetation growth successfully, using AVHRR data [46, 47] and MODIS data [44, 45, 48, 49].  
The vegetation greenup phase and senescence phase were separated using the first derivative value of time series NDVI curve. The first derivative curve shifted from positive to negative was considered the peak of a vegetation seasonal growing cycle. The day before the peak date was considered the greenup phase while the day after the peak date was considered the greenness decrease phase. Then, HPLM algorithm was applied for these two stages, respectively. Since the clouds were masked and snow-covered data were not used, the minimum value in these two stages was used as the background NDVI value. The data earlier than the date of \(NDVI_{b}\) were set to the \(NDVI_{b}\) value in the greenup phase. The data later than the date of \(NDVI_{b}\) were set to the \(NDVI_{b}\) value in the greenness decrease phase. The OGI and OGD of the land cover types in Bole and Luntai were calculated using the rate of change in the simulated curves. The date with the maximum first derivative curve in each greenup phase is set to OGI. The date with the minimum first derivative curve in each senescence phase is set to OGD.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**(a) Cop Calendars in Luntai** & & & & & & & & & & & & \\ \hline Crop & January & February & March & April & May & June & July & August & September & October & November & December \\ Winter wheat & Seeding & & Elongating & Earing & Mature & & & & & & & & \\ Cotton & & & & & & & & & & & & \\ Summer corn & & & & & & & & & & & & \\ \hline \hline
**(b) Cop Calendars in Bole** & & & & & & & & & & & & \\ \hline Crop & January & February & March & April & May & June & July & August & September & October & November & December \\ Cotton & & & & & & & & & & & & & \\ Spring wheat & & & & & & & & & & & & \\ Corn & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: The crop calendars of the main crops in Bole and Luntai.