## 3 Methods
### Geometric Unification Schemes by Upscaling and Downscaling  
In data processing, there is no need to do further geometric correction for L1C products, and only atmospheric correction and spatial resolution unification are required. The atmospheric effects can be well eliminated by the Sen2 Cor algorithm [51]. After Sen2 Cor processing, the L1C TOA reflectance values were converted into Level-2A (L2A) Bottom-of-Atmosphere (BOA) reflectance values. The spatial resolution was unified by one upscaling and six downscaling methods. As the most common way in re-scaling the pixel resolutions, nearest neighbor resampling was used both in upscaling and downscaling in our study, and the downscaled image by resampling is regarded as the benchmark. For downscaling, it just divides one pixel into four adjacent pixels with the same value and has the advantages of completely preserving original information, simple and fast [17]. Besides resampling, five popular pansharpening algorithms, namely, GS, NNDiffusion, PANSHARP, WTF, and HPF were used in downscaling. GS is a representative pansharpening method based on CS. The CS-based methods substitute an HR image for the selected band after spectral transformation. GS replace the HR band (usually refers to PAN band) for the first band of Gram-Schmidt transformation performed by a simulated low  
Figure 2: Technical flow chart. resolution (LR) image averaged by the LRMS bands as the first band and followed by these LRMS bands [20]. NNDifusion and PANSHARP are all based on statistics. They use statistics to decide the contribution of each MS bands to the PAN band [52]. Different from PANSHARP, NNDifusion decides the weights according to a diffusion model inferred from the Pan band that relates the similarity of the pixel of interest to the neighboring superpixels [53]. The statistics-based algorithms have advantages over traditional CS-based algorithms (e.g., IHS and PCA) in spectral fidelity for those sensors whose PAN band's wavelength extended into near infrared. WTF and HPF are traditional image fusion algorithms based on MRA. Both of them extract the high frequency information from HR image and inject to LRMS image; however, their high frequency components extraction methods are distinct. WTF extracts the high frequency information by a wavelet transformation and integrated with every LRMS bands by replacing the low frequency approximation generated from wavelet transformation with the LRMS image and followed by an individual inverse wavelet transformation [54]. HPF extracts the high frequency information by a high pass filter and integrates that with LR bands by a specified weight [55]. The MRA-based pansharpening algorithms can highly preserve the spectral characteristics since its spatial information obtained from the HR band and spectral information obtained from the LRMS image. After preprocessing, one BOA reflectance image at a 20-m GSD and six images at 10 m were generated, and as shown in Table 1.  
For the task of downscaling Sentinel-2 images by fusion, each of its four 10-m bands can be treated as a PAN-like band as mentioned before. The criterion for optimal PAN-like band selection can be decided by the center wavelength proximity or the spectral similarity between the bands at 10 m and 20 m [56; 57]. The central wavelength is sensor property, which was fixed in hardware manufacturing. By this criterion, each sensor can achieve a consistent result. Band correlation is affected not only by sensor parameters but also by surface factors, such as surface composition and topography. Therefore, it may cause distinct results between different scenes obtained by the same sensor. Table 2 shows the results of the most suitable PAN-like band to each 20-m bands of our two image tiles by these two criteria. The two tiles achieved the same result that band 4 to be the PAN-like band for bands 5 and 6, and band 8 for bands 7, 8a, 11, and 12 by central wavelength proximity.