Evaluation of smoothing methods for GREENNESS time series reconstruction and phenological estimation from Landsat 8 satellite data

Extended abstract
Introduction
Vegetation indices (VI) time-series have been used for land surface phenology retrieval but these time series are affected by clouds and aerosols, which add noise to the signal sensor. In this sense, several smoothing functions are used to remove noise introduced by undetected clouds and poor atmospheric conditions, but a comparison between methods is still necessary due to disagreements about its performance in the literature. The application of a smoothing function is a necessary previous step to describe land surface phenology in different ecosystems. Satellite-derived phenological parameters do not specifically provide information on the phenology of a single plant, their species or pheno-phases (e.g., bud opening, leaf emergence, leaf opening and flowering). Remote sensing Vegetation Indices are usually able to estimate a few phenological parameters such as start of season (SOS), end of season (EOS). The aims of this research were to evaluate the consistency of different smoothing functions from TIMESAT software and agricultural regions using the Greenness-Landsat time-series. To overcome the problems associated with remaining noise, various methods have been developed to estimate phenology and production metrics based on the VI time series. Some of them are wavelet decomposition, double logistic (DL) function, the asymmetric Gaussian (AG) function fitting, Savitzky–Golay (SG) filters, the Weighted Least Square (WLS). Some studies have compared these smoothing approaches, but most of them focus on coarse spatial resolution satellite image time series, such as the Moderate Resolution Imaging Spectroradiometer (MODIS). Due to the variety of results and the lack of consensus on smoothing methods, quality evaluation of smoothing operations should be done for each plant index and crop. Thus, the objectives of this paper are to evaluate and analyze the performance of various smoothing functions in TIMESAT software and their effects on estimating the phenological parameters of start of season (SOS) and end of season (EOS) of rapeseed.
 
Methodology
In this study, we used two kinds of data: 1- phenological data of rapeseed that was obtained from Field observation, and 2- GREENNESS index data extracted from Landsat 8 satellite images in the Agricultural Years (2016-2017, 2017-2018, 2018-2019). Geometric and radiometric corrections were applied to satellite images. The DN value was also converted to TOA to calculate Vegetation Indices. An adaptive Savitzky–Golay (SG) filter, Asymmetric Gaussian (AG), and Double Logistic (DL) functions to fitting Greenness data were used and their performances were assessed using the measures root mean square error (RMSE), Pearson correlation coefficient(r). Besides, differences in the estimation of the SOS and EOS were obtained. In all methods, the adaptation to upper envelope with the raw GREENNESS time series was used to reduce bias. In the Savitsky-Goli method, in addition to adapting upper envelope, the window size parameter (r) was also used.
 
Results and discussion
Statistical evaluation of smoothed time series
Statistical analysis of the output of smoothing functions showed that the time series produced by the AG model compared to the raw time series of the GREENNESS index had the lowest root mean square error (RMSE = 0.415) and the highest correlation (r = 0.935) belong to S-G model. The advantage of DL and AG models is that the difference between the mean correlation coefficient for all performances and the correlation coefficient for the best execution is small and it can be inferred that the software parameter settings have little effect on the outputs of these models. After plotting the smoothed time series curves, the results showed that the use of smoothing models effectively eliminated noise and disturbed the raw time series of the GREENNESS index, and reconstructed smoother and softer time series. The results also showed that time series that have a higher correlation coefficient show more details and changes within the inter-season, such as the recession stage(dormancy). Overall, it can be concluded that for reconstructing GREENNESS time series data, Pearson correlation coefficient (r) is more accurate than root mean square error (RMSE) and S-G model is more accurate than the other two models.
 
Conclusions
In this study, we showed to what extent the time series of the three smoothing methods SG, AG and DL in the reconstruction of the raw time series of the GREENNESS from the Landsat 8 and estimating the phenological parameters of the start and end of the season are accurate. The results of this study showed that the adaptive S-G model is more robust for reconstructing raw time series than AG and DL functions, and this is due to the sensitivity of this model to small changes in the GREENNESS time series. The AG and DL functions tend to eliminate noise at the peaks and bottoms of the time series. The results also showed that the time series with the highest correlation coefficient (r) are more suitable for reconstructing the raw time series of the GREENNESS index compared to the time series that produced the smallest RMSE. In SOS estimation, the S-G model performs worse than the AG and DL functions. Compared to the observational data, all smoothing methods used in this study estimate EOS late and SOS early. The results also showed that both AG and DL functions have time lag in SOS estimation compared to S-G model and time precedence in EOS estimation compared to S-G model. The efficiency of any smoothing method depends on the choice of parameters. For example, the use of adaptation upper envelope generally improves the results. AG and DL fitting function methods are the preferred option for smoothing low-quality data (eg high noise and high data loss) due to less sensitivity to regulatory parameters. The AG and DL fitting functions are limited when giving inter-seasonal details of the time series curve. Numerous factors such as vegetation index selection, satellite sensor data and vegetation type are affected in evaluating time series and estimating phenological parameters. However, the results of this study are valid for the data and the location under study, and the results may vary with other data or under other circumstances.
This study showed that the statistical criterion of Pearson correlation coefficient (r) is superior to the root mean square error (RMSE) and the S-G model is superior to the AG and DL models for reconstruction of time series. The DL function and AG function show the best performance for estimating SOS and EOS phenological parameters, respectively.