## 2 Data and Methodology
### Methodology
#### 2.3.1 Sentinel-2 Time Series Curve Composition  
The Sentinel-2 NDVI curves time series were obtained from October 2021 to June 2022 using the GEE Sentinel-2 dataset and combined with field survey data to accurately understand the climatic characteristics of garlic, winter wheat, and other crops. The Sentinel-2 NDVI was calculated using the following formula:  
\[\text{NDVI}=\frac{\rho_{\text{NIR}}-\rho_{\text{RED}}}{\rho_{\text{NIR}}+\rho_{ \text{RED}}} \tag{1}\]  
where \(\rho_{\text{NIR}}\) is the reflectance in the near-infrared band and \(\rho_{\text{RED}}\) is the reflectance in the red band. Figure 4 shows that October corresponds to the sowing stage, while June marks the harvest period for both garlic and winter wheat, which are planted and harvested nearly simultaneously. Notably, the NDVI patterns of garlic and winter wheat exhibit similarity, with considerable overlap between the upper and lower boundaries of the two crops, posing challenges in their differentiation solely based on NDVI values from a single day. It is noteworthy that the overall changes in winter wheat were smoother relative to garlic, consistently displaying higher NDVI values than garlic throughout most of the growing season. Additionally, although both crops reach their peaks at nearly the same time, garlic demonstrates more rapid fluctuations in its rise and fall. These distinctive variations aid in facilitating a more accurate differentiation between the two crops. Due to various factors such as weather conditions, obtaining high-quality time series data for all image elements can be challenging. To maximize data quality, this study  
Figure 4: The time series of Sentinel-2 NDVI for garlic and winter wheat. The curves in the figure represent the average NDVI values derived from the samples, while the upper and lower boundaries indicate the standard deviation. Figure 3: Workflow of garlic extraction based on active–passive remote sensing time series data. employs a two-step optimization process for time series data. Firstly, monthly median values of each image element are used to generate time series data. Subsequently, a method utilizing historical data is employed to correct data anomalies within the vegetation growth period, thereby enhancing the data quality. This method identifies anomalies in each image value through harmonic regression analysis and replaces them with normal historical data, thereby improving the reliability of the time series data. The method for splicing the time series data involves using MSAVI or SAVI to calculate the time series data for the study area during periods with low NDVI values. For periods with higher NDVI values, NDVI, GNDVI, or EVI are used instead. For instance, MSAVI time series data from October 2021 to January 2022 are combined with EVI time series data from February 2022 to June 2022 to create complete time series data, referred to as double index time series data (DITS). A time node between January and March was selected for splicing the DITS data based on NDVI time series data and field surveys. Several potential time nodes were tested to determine the optimal one, and through comparison of classification results using different time nodes, January was identified as the most suitable time node for DITS.