## 4 Results and Discussions
### Discussions
The reason is that if a land surface object, for example, a building or a road, has high spectral reflectance in nature, it should have high spectral reflectance in both observation and its synthetic images (if the synthetic image is correctly predicted which is the case from our PSRFM modelling). Therefore, their reflectance difference expressed in Equation (3) should be small, and the object can be easily identified as non-cloud object. In contrast, assuming an object has small spectral reflectance in nature, on the one hand, it will present big spectral reflectance if it is covered by clouds in a cloud contaminated image, and on the other hand, it still has a small spectral reflectance value in its corresponding cloud-free synthetic image. Hence,the large difference of the pixel values of the observation and the synthetic image would reveal it as a cloudy pixel. The advantage for the cloud identification can be extended to the cloud shadow identification. For example, cloud shadow pixels can often be mixed to water pixels as both cloud shadow and water have small spectral reflectance. For similar analysis, assuming a synthetic image is well predicted, a water pixel can have a small value in both observation and synthetic images. Therefore, a small difference between them indicates that it is not a cloud shadow pixel. That being said, a medium to high surface reflectance object has a small value if covered by cloud shadow. Hence, a large difference of a pixel between a cloud contaminated image and its corresponding synthetic image can uncover the cloud shadow pixel. It is possible that the difference between a haze or thin cloud contaminated pixel and its corresponding synthetic pixel is smaller than the top image fusion modelling bias or errors. This could result in false haze and thin cloud pixel masking. However, the chance is relatively small since from PSRFM model evaluation, majority of the pixels are well predicted for all the bands. A small number of outliers will not affect the overall accuracy of haze, cloudy, and cloud shadow pixel identification. To distinguish cloud-free and cloud contaminated pixels, our method determined the values of only three threshold parameters: \(T_{c}\) for clouds, \(T_{cs}\) for cloud shadows, and \(T_{h}\) for haze. They were easily determined by our proposed method, either visually or automatically. Like other methods, the cloud contaminated pixels (clouds, cloud shadow, and haze) can be over- or underestimated. Cloudier, cloud shadow, or haze pixels can be masked if decreasing the absolute value of the thresholds and vice versa. In our proposed reconstruction process, after we identified the cloud contaminated pixels of an observation image, those pixels were replaced by the pixels of the corresponding synthetic image. Since the synthetic images had high quality, we preferred to overestimate the cloud contaminated pixels instead of underestimating them as inclusion of more cloud contaminated pixels in the mask resulted in better results than omission of true cloud contaminated pixels in the mask. In the latter situation, unidentified cloud contaminated pixels remained in the reconstructed time-series. In contrast, in the former situation, some cloud-free pixels (which were wrongly identified as haze, cloudy/cloud shadow pixels) were replaced by the corresponding pixels of the synthetic image, which later were radiometrically calibrated to the observation values. Therefore, the impact of overestimating cloudy, cloud shadow, and haze pixels on the final reconstruction time-series was small. Like other cloudy pixel identification, this proposed method worked better for images with thick cloud contamination than with thin cloud coverage as thick clouds made the affected pixels dramatically distinguishable from cloud-free pixels, and a pixel with thin cloud or haze coverage showed surface reflectance underneath. For an image with thin cloud and/or haze coverage, we adjusted the value of threshold \(T_{h}\). A smaller \(T_{h}\) could identify more thin cloud or haze covered pixels.