## 3 Method
### Validation
#### 3.5.2 Quality Evaluation of Time Series NDVI Data  
The quality of time series NDVI data has an important influence on the extraction of phenology and crop mapping. According to the method proposed by [PERSON] [45] and [PERSON] [50], the data quality was evaluated using both the proportion of good observations (PGQ) and the model performance index in the time series NDVI data. These two parameters were analyzed for various land cover types and sensors. The land cover types were mapped using the method described in the Section 3.4.  
The number of good quality observations in time series NDVI data reflects to a great extent the reliability of detecting the vegetable phenology and mapping crops. As the dormant phase provided no information about vegetation seasonal dynamics, only NDVI data during the vegetation growing season were used in the calculation of PGQ. Since the temporal NDVI trajectory could be well reconstructed with a good NDVI observation within an eight-day period [41], a good NDVI observation was counted if there was one good observation within the eight-day windows centered on the date of a scene image. PGQ during a vegetable growing season was calculated as follows:  
\[P_{gq}=\frac{N_{gq}}{T}\times 100\% \tag{5}\]  
where \(P_{gq}\) is the proportion of good observations, \(T\) is the total number of images during a vegetable growing season, and \(N_{gq}\) is the total number of good quality observations.  
Model performance was evaluated using the satellite recorded values with good quality during a vegetation growing season. Several indexes, such as coefficient of determination (\(R^{2}\)), coefficient of efficiency (\(E\)), modified \(E\) (\(E_{1}\)), Root Mean Square Error (\(RMSE\)), and Coefficient of Residual Mass(_CRM_), were calculated to quantitatively evaluate the performance of HLPS. Those indexes were defined as follows:  
\[R^{2}=\left[\frac{\sum\limits_{i=1}^{n}\left(o_{i}-\overline{o}\right)\left(p_{i }-\overline{p}\right)}{\sqrt{\sum\limits_{i=1}^{n}\left(o_{i}-\overline{o} \right)^{2}}\sqrt{\sum\limits_{i=1}^{n}\left(p_{i}-\overline{p}\right)^{2}}} \right]^{2} \tag{6}\]  
\[E=1-\frac{\sum\limits_{i=1}^{n}\left(o_{i}-p_{i}\right)^{2}}{\sum\limits_{i=1} ^{n}\left(o_{i}-\overline{o}\right)^{2}} \tag{7}\]  
\[E_{1}=1-\frac{\sum\limits_{i=1}^{n}\left|o_{i}-p_{i}\right|}{\sum\limits_{i=1 }^{n}\left|o_{i}-\overline{o}\right|} \tag{8}\]  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(p_{i}-o_{i}\right)^{2}}{n}} \tag{9}\]  
\[CRM=\frac{\sum\limits_{i=1}^{n}o_{i}-\sum\limits_{i=1}^{n}p_{i}}{\sum\limits_ {i=1}^{n}o_{i}} \tag{10}\]  
where \(n\) is the number of NDVI with good quality, \(p_{i}\) is the HPLM simulated NDVI values, \(o_{i}\) is the NDVI value with good quality, and \(\overline{o}\) is the mean value of \(o_{i}\). This method was widely used to evaluate the performance of different models [50,51]. According to the work of [PERSON] and [PERSON] [52], \(E\) values greater than or equal to 0.75 indicates the observed value can be modeled very well, \(E\) values between 0.75 and 0.36 indicates the observed value can be satisfactorily modeled, and \(E\) values lower than 0.36 means the modeled value is not reliable.