## 3 Phenology-Based Crop Identification  
### Derivation of Phenological Metrics  
The NDVI was used to derive the phenological metrics of crops. The NDVI is the ratio of the differences in reflectivity for the near-infrared band and the red band to their sum [48]. In case of HJ-1A/1B satellite, the corresponding bands are bands 4 and 3, and NDVI can be calculated from  
\[\mathrm{NDVI}=\frac{(\rho_{1,4}-\rho_{t,3})}{(\rho_{t,4}+\rho_{t,3})} \tag{6}\]  
where \(\rho_{t,3}\) and \(\rho_{t,4}\) are the reflectivity of the near-infrared and the red band, respectively. Generally, NDVI \(>\) 0 indicates soil or vegetation, while NDVI \(\leq\) 0 indicates water or snow. The NDVI has been used to monitor vegetation dynamics for over twenty years [42; 49]. Recent studies have paid more attention to the relationship between NDVI series and vegetation phenology [26; 29], which confirmed the effectiveness of NDVI series in identifying crop phenology parameters. Thus, we calculated NDVI from the preprocessed images according to Equation (6). In order to decrease the effects of noise of existing data, the resulting HJ-1A/1B NDVI time series was further fitted with an asymmetric logistic curve [50] (Figure 4), which was also used by [PERSON] et al. [11] in crop identification. The fitting curve equation is  
\[\mathrm{NDVI}=a\ +(b/k)\cdot(1+n)^{-(k+1)/k}\cdot n\cdot(k+1)^{(k+1)/k} \tag{7}\]  
\[n=\exp[(t+d\cdot\ln(k)-c)/d] \tag{8}\]  
where \(t\) is DOY; \(a\), \(b\), \(c\), \(d\) and \(k\) are curve parameters (Figure 4) to be estimated from NDVI series by the least-squares method. The characteristic points of the asymmetric logistic curve (i.e., phenological metrics) can be computed from the zeroes of the first and second derivatives of Equation (7). The derivatives are \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Image Type**} & **Band 1** & **Band 2** & **Band 3** & **Band 4** \\ \hline \multirow{2}{*}{HJ-1A} & CCD1 & 1914.32 & 1825.42 & 1542.66 & 1073.83 \\  & CCD2 & 1929.81 & 1831.14 & 1549.82 & 1078.32 \\ \hline \multirow{2}{*}{HJ-1B} & CCD1 & 1902.19 & 1833.63 & 1566.71 & 1077.09 \\  & CCD2 & 1922.90 & 1823.99 & 1553.20 & 1074.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ESUNA of HJ-1A/1B (W\(\cdot\)m\({}^{-2}\) \(\upmu\)m\({}^{-1}\)). \[\frac{\mathrm{d}(\mathrm{NDVI})}{\mathrm{d}t}=(b/k)\cdot[(k+1)/(1+n)]^{(k+1)/k} \cdot[(k-n)/(1+n)]\cdot(n/d) \tag{9}\]  
\[\frac{\mathrm{d}(\mathrm{NDVI})^{2}}{\mathrm{d}t^{2}}=(b/k^{2})\cdot(k+1)^{(k+1) /k}\cdot(n/d^{2})\cdot(1+n)^{-[(k+1)/k]-2}\cdot[(n^{2}/k)-n(k+3)+k] \tag{10}\]  
Letting \(\mathrm{d}(\mathrm{NDVI})/\mathrm{d}t=0\), we can obtain \(t\_\mathrm{max}=c\). If \(\mathrm{d}(\mathrm{NDVI})^{2}/\mathrm{d}t^{2}>0\) at this point, then we can obtain the peak value of NDVI, \(\mathrm{NDVI}\_\mathrm{max}=a+b\), at \(t\_\mathrm{max}=c\). Letting \(\mathrm{d}(\mathrm{NDVI})^{2}/\mathrm{d}t^{2}=0\), we can obtain two inflection points of the NDVI curve, \(t\_\mathrm{inf}=c+d\) ln [\((k+3\pm(k^{2}+6k+5)^{0.5}/2)\) (\"\(-\)\" for the left and \"\(+\)\" for the right inflection points). The NDVI values corresponding to \(t\_\mathrm{inf}\), \(\mathrm{NDVI}\_\mathrm{inf}\), can be calculated by replacing \(t\) with \(t\_\mathrm{inf}\) in Equation (7). The area of the sampling point is at least 100 m \(\times\) 100 m, which includes at least 9 pixels. Generally, one to three pixels were selected corresponding to each sampling point, and we finally got 160 and 140 pixels representing maize and sunflower, respectively. The NDVI series of each sampling pixel in 2012 were calculated based on HJ-1A/1B CCD images, and the average NDVI values of those 160 and 140 pixels were obtained as the representative NDVI series of maize and sunflower, respectively. Then the maize and sunflower NDVI time series were fitted with the asymmetric logistic curve (Figure 5). The curve fitting was also performed for NDVI time series of each pixel in the study area to obtain phenological metrics of each pixel to monitor the growth regime of crops.