## 4 Results and Discussions
### Discussions  
There were two critical issues when reconstructing cloud-free Sentinel-2 images time-series using our proposed image fusion approach: the quality of the blended images and the accuracy of clouds/cloud shadow pixels identification. In this study, we used the PSRFM model for predicting cloud-free synthetic Sentinel-2 images when clear-sky Sentinel-2 images were not available. Some pixels of these synthetic images were used to replace those cloudy and cloud shadow pixels of the corresponding observations. Apparently, high quality of the synthetic Sentinel-2 images was the first key component in the chain of the reconstruction process to warrant high quality output. PSRFM is a well-developed spatiotemporal reflectance fusion model and has been validated and compared to some well-known image fusion models [24; 26]. It works well for both gradual and abrupt land cover change situations, as well as for heterogeneous landscapes. Therefore, it was chosen for the synthetic image production. In addition to PSRFM model, other well-developed image fusion models can also be used for the reconstruction purpose as long as it can predict high quality of synthetic images such as STARFM, ESTARFM, FSDAF, and KFRFM [25]. To reconstruct cloud-free time-series Sentinel-2 images, MODIS MCD43A4 images were used as the coarse resolution image input. MODIS MCD43A4 images were generated from the cloud-free pixels of both Terra and Aqua satellites over a 16 days period for NBAR computation. The product provided a consistent cloud-free and nadir view image that was one of the best MODIS datasets for image fusion even though some pixels were of higher quality (full inversion), and some pixels were of lower quality (magnitude inversion) [29]. The latter could be a source of the synthetic Sentinel-2 image bias. When using MODIS MCD43A4 images to reconstruct cloud-free time-series Sentinel-2 images, a question was raised: Why not apply the same composite method of generating cloud-free MODIS MCD43A4 images to reconstruct the cloud-free Sentinel-2 image time-series? Technically, it is possible as long as there are enough cloud-free pixels available from the Sentinel-2 observations over a 16 day period. Practically, depending on the season and the location of interest, the useful cloud-free pixels from Sentinel-2 observations over the 16 days period may be limited. For instance, according to the analysis about the cloud-free pixels of the Sentinel-2 images used for the test case in Section 3.2.1, fewer than half of the total image pixels of the time-period from 26 April 2018 to 10 October 2018 were useable. With MODIS's daily revisit, the number of images available for the composite was triple the number of Sentinel-2 images (at about a 3-day revisit frequency) available for the same period of 16 days. Therefore, in comparison to the composite method, the proposed method in this study can augment the stronger temporal intensity of MODIS and circumvent the sparsity of clear-sky observations in Sentinel-2 time series. The second critical issue of this proposed approach was the identification of clouds and cloud shadows. The case study proposed a new method for cloudy and cloud shadow as well as haze pixel identification by analyzing the differences between observations and their synthetic images. Our proposed method has obvious advantages. It is simple and effective. A conventional cloud identification was based on the spectral difference between cloudy pixels and other cloud-free ones within an image. As some land surface objects such as buildings, bare dry soil, and roads have similar high reflectance as clouds do, it is usually problematic to distinguish clouds from those objects. However, by our method, those objects can be easily excluded from clouds.