*5.2. Limitations*

The relatively low number of test sites (100) and the restricted geographic location (Europe) limit the importance of the evaluation results. Rather than showing the superiority of the proposed RTSR method, the objective of the evaluation was to show the potential of dynamic smoothing where the time series approaches the trustworthy observations. The smoothing method can hereby be adopted from other methods, such as that proposed in DTS. A diverse set evaluation metric was hereby selected. Results of the TSI showed minor differences in smoothness for the three methods under comparison. All three methods were also able to fill gaps in the time series, which is driven by interpolating clear observations near the missing values. The strength of the proposed RTSR is that in addition to producing a smooth reconstructed time series, it is capable of retaining trustworthy observations in the original time series.

A number of limitations of the proposed RTSR method do apply. The time series to be reconstructed must include the spectral bands to calculate the index used as a proxy for the reliability of observations (e.g., the B4 and B8 bands of the Sentinel-2 sensor in the case of NDVI). Another limitation is the assumption that clouds or poor atmospheric conditions depress NDVI values [18]. This holds mostly for vegetated land but not for all land cover types. Clear observations of water bodies, for example, can result in lower NDVI values than cloudy observations. This is not a limitation of the method, but of the proxy used for trustworthy observations. The proxy can be adapted, for example, by distinguishing pixels using a water mask. Instead of NDVI, water surface-reflectance values in the near infrared band can be compared in the iterative algorithm. Clear water pixels usually have lower reflectance values in this part of the electromagnetic spectrum than clouds. When applying the RTSR reconstruction algorithm to create analysis-ready data for other applications beyond vegetation monitoring, the proxy could be adapted in this way. Further evaluation will be needed and is to be part of future research.

The Savitzky–Golay smoothing filter used in the reconstruction algorithm imposes another limitation. The RTSR reconstruction method requires a time series of at least 15 observations, i.e., the full width of the Savitzky–Golay filter, to obtain the long-term change trend curve. A longer time series is needed in practice to improve the results, typically 20 observations or more. In the case of Sentinel-2 acquisitions, this corresponds to a seasonal to annual coverage. The maximum length of the time series is only constrained by the memory resources available, as our implementation reads the entire time series in memory. Because the RTSR algorithm is a pixel-wise operation and requires no spatial contextual information, there is no upper limit in the spatial dimension. The image can be split into smaller tiles that can be run independently in parallel. Tiles can be made as small as needed to fit in the available memory. For instance, the test sites of 256 by 256 pixels and covering 62 acquisitions can be processed with less than 2 GB of memory.

Due to the extent of the smoothing window size, there is an edge effect inherent to the filtering process that impacts the first and last observations of the reconstructed time series. In this study, the acquisition period was extended by one month before and after the period of interest. The respective observations (December 2018 and January 2020) were afterwards removed from the reconstructed time series. This approach is not suited for near real-time applications. The Whittaker smoother has a number of advantages over the SG filter [21,40,50,51]. It employs only past observations and would be a good candidate for the smoothing filter, in particular for near real-time applications. This will be part of future research. Another interesting topic is the effect of the cloud mask on the reconstructed time series and to investigate whether more sophisticated cloud masks can improve results.
