## 2 Materials
### Data  
Multi-temporal Sentinel-2 images taken in 2019 that covered the study area were considered for the crop classification task. Using a twin-satellite constellation, the Sentinel-2A and -2B images can be acquired in the same area every two or three days. The Sentinel-2 level-2A Bottom-of-Atmosphere (BOA) products covering the study area were downloaded from the Copernicus Open Access Hub [59]. The reflectance values of nine spectral bands in Table 1 were considered inputs for the experiment by considering their effectiveness for crop classification. The spatial resolutions of the nine multi-spectral bands of the Sentinel-2 images vary from 10 m to 20 m. To match the spatial resolution of all the spectral bands, three red-edge bands and two SWIR bands with a spatial resolution of 20 m were resampled to 10 m using bilinear resampling. The Sentinel-2 images acquired from June to October were first collected by considering the growing stages of the corn and soybean in the study area. Before the selection of the Sentinel-2 images to be used for the experiment, the normalized difference vegetation index (NDVI) values for corn and soybean parcels were first calculated using multi-temporal Sentinel-2 images and the CDL data in the study area. In cases where the Sentinel-2 images covering the study area contained cloud-contaminated areas such as clouds and shadows, the NDVI values were only computed using cloud-free subareas. The temporal variations in the average NDVI values for corn and soybean were then analyzed to identify the optimal \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Spectral Band** & **Central Wavelength (nm)** & **Spatial Resolution (m)** \\ \hline B1 & Blue & 492.4 & \\ B2 & Green & 559.8 & 10 \\ B3 & Red & 664.6 & \\ B4 & RE1 & 704.1 & \\ B5 & RE2 & 740.5 & 20 \\ B6 & RE3 & 782.8 & \\ B7 & NIR & 832.8 & 10 \\ B8 & SWIR2 & 1613.7 & 20 \\ B9 & SWIR3 & 2202.4 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specification of Sentinel-2 multi-spectral bands (RE: red-edge; NIR: near-infrared; SWIR: shortwave infrared). Figure 1: Location of the study area. The black box denotes the subarea where virtual image generation and crop classification are conducted. The background in the left image is the Sentinel-2 image on 30 July 2019, and the cropland data layer in 2019 in the study area is enlarged. Figure 2 shows the temporal profiles of the average NDVI values for corn and soybean. The corn in the study area begins to grow from the end of June. After reaching the mature stage by the end of August, harvesting begins in mid-September. On the other hand, the growing stage of soybean begins later than corn (mid-July). Soybean grows continuously until the end of August and is harvested from mid-September, similar to corn. Based on the growth cycles of corn and soybean identified in Figure 2, the optimal date for early crop mapping is either the end of July or early August. As fewer images are preferred for early crop mapping, the Sentinel-2 images acquired from June to July should be used for crop classification. A total of 24 Sentinel-2 images were acquired from June to July, corresponding to the growing seasons of corn and soybean. However, as shown in Table 2, only seven cloud-free Sentinel-2 images were available in the study area, emphasizing the necessity of virtual cloud-free optical image generation for crop classification. Considering the temporal interval between the cloud-free Sentinel-2 images, four images, including two June images and two July images, were considered for crop classification (Figure 3). The 30 July Sentinel-2 image was selected as a target image for the virtual image generation because this image was acquired at the optimal date for early crop mapping. That is, the 30 July Sentinel-2 image was assumed to be unavailable or heavily contaminated by cloud. This image was considered the unavailable actual image to evaluate the predictive performance of virtual Sentinel-2 image generation using CGANs.