A robust method for reconstructing global MODIS EVI time series on the Google Earth Engine
Introduction
Remote sensing vegetation indices are required to be not significantly affected by abiotic factors for monitoring vegetation activity (Kong et al., 2017, Yang et al., 2015), detecting vegetation phenology (Chen et al., 2004, Jönsson and Eklundh, 2002, Zhang et al., 2018a, Zhang et al., 2018b, Zhang, 2015), classifying land cover types (Shao et al., 2016, Xiong et al., 2017, Zhang et al., 2015), monitoring drought (Klisch and Atzberger, 2016, Kogan, 1995), and investigating the interaction of climate changes with vegetation activity (Kong et al., 2017). However, remote sensing vegetation indices are often contaminated by cloud, shadow, snow, aerosol and many other different source noises. Even though MODIS vegetation index (Huete et al., 2002) has been well calibrated, it is still seriously affected by contaminated points. Therefore, it is critical to seek a reliable reconstruction method for archived remote sensing vegetation indices.
Google Earth Engine (GEE) is a planetary-scale platform for Earth science data and analysis (Gorelick et al., 2017). It has a multi-petabyte catalog of satellite imagery and geospatial dataset with planetary-scale analysis capabilities which are available for users to detect changes, map trends, and quantify difference on the Earth’s Surface (Gorelick et al., 2017). However, there is still no applicable denoising algorithms available on the GEE. Many vegetation reconstruction methods have been proposed over the last several decades, including Fourier-based approach (hereafter referred to Fourier) (Geerken, 2009, Verhoef, 1996, Yang et al., 2015, Zhou et al., 2015), Savitzky-Golay (SG) filter (Chen et al., 2004, Orfanidis, 2010, Savitzky and Golay, 1964), asymmetric Gaussian (AG) (Jönsson and Eklundh, 2002), and double logistic (DL) (Beck et al., 2006, Eklundha and Jönssonb, 2017). Those methods can reduce noises efficiently. However, it is hard to apply them on the GEE because of the following two reasons:
- i.
Difficult to select the appropriate parameter. Fourier and SG are sensitive to parameter. It is hard for these methods to get a universal suitable parameter, when applied at global scale. In Fourier, a small harmonic will lead to failing to capture quick changes in vegetation time series. In contrast, a large harmonic will lead to emphasising too much on regional signal and over fluctuating. SG faces a similar issue for its key parameter of half-width of smoothing window (Cai et al., 2017, Chen et al., 2004). Besides, AG and DL are only applicable for the vegetation with a clear seasonal pattern.
- ii.
Low computing efficiency or low performance. Parameters in AG and DL rely on nonlinear optimization that is time-consuming and complex to implement on the GEE. Being a moving window polynomial regression requiring many times iterations, SG is dozen times slower than Fourier and Whittaker (Eilers, 2003). While, Fourier has an apparent shape of sine and cosine, which may fail to simulate static background value in non-growing season and plateau peak value (Yang et al., 2015).
Whittaker smoother is one of the well-known reconstruction methods (Eilers, 2003), which has been successfully applied for vegetation index time series reconstruction (Atzberger and Eilers, 2011a, Atzberger and Eilers, 2011b, Klisch and Atzberger, 2016, Qiu et al., 2017, Zhang et al., 2019), vegetation phenology extraction (Atkinson et al., 2012, Atzberger et al., 2014a), land cover classification (Shao et al., 2016, Song et al., 2018), hyperspectral remote sensing (Atzberger et al., 2014b, Doneus et al., 2014). Whittaker has single parameter, the smoothing parameter λ. Unlike AG and DL, Whittaker can avoid the problem of growing season dividing and smooth time series in multiple years. In addition, Whittaker is extremely computationally efficient since it takes only a few seconds in an ordinary PC to smooth a series of 100,000 observations (Eilers, 2003). These advantages (single parameter and computationally high efficiency) make Whittaker promising for large scale and high-resolution remote sensing data application on the GEE platform.
However, Whittaker still has some issues to be solved before large-scale application. First, how to assign an appropriate λ for different pixels in spatial. The success of Whittaker relies on an appropriate smoothing parameter λ (Frasso and Eilers, 2015), since λ is used to penalize the roughness. A larger (or smaller) λ leads to the more (or less) smoothing result (Atzberger and Eilers, 2011a). A large λ is needed for regions where vegetation index fluctuates acutely or is contaminated seriously; a small λ is required for regions where vegetation index changes sharply. Atzberger and Eilers (2011a) used cross-validation to automatically generate the optimal λ. However, Frasso and Eilers (2015) pointed out that cross-validation will be failed when the noise is correlated and suggested that V-curve is a better solution. Eilers et al. (2017) further incorporated V-curve and expectile smoothing to upper envelope of time series. Nevertheless, no matter for cross-validation or V-curve, λ optimization needs many times iterations and runs slower than using constant λ Whittaker. This severely handicaps its large-scale application. Second, how to well deal with contaminated points. Contaminated remote sensing vegetation index is often negatively biased (Beck et al., 2006, Chen et al., 2004). But when vegetated surface with a dark (wet) soil background, vegetation index also can be positively biased (Atzberger and Eilers, 2011a, Huete et al., 2002). Previous studies (Atzberger and Eilers, 2011a, Chen et al., 2004) usually approach the upper envelope by replacing low points with smoothed value during iterations. However, if a positive bias outlier occurs in non-growing season, the upper envelope is very likely to submerge the non-growing season, which will lead to a fake earlier starting of growing season and later ending of growing season (Shen et al., 2013). Last, due to the coarse scale of the sensors and the required representativeness of the reference measurements in spatial and temporal (Atzberger and Eilers, 2011b), there are quite limited (ground-based) reference measurements which could serve for validation. In this study, we synthesized reference vegetation time series from multi-annual good-quality points. This method has been successfully used for evaluating many global reconstruction methods (Liu et al., 2017, Yang et al., 2015, Zhou et al., 2016).
The major objectives of this study include to: (1) solve the above-mentioned Whittaker issues, and provide a reliable and highly computational efficient vegetation reconstruction method, namely wWHd (weighted Whittaker with dynamic parameter λ in spatial); and (2) evaluate the relative merits of wWHd, compared to the other four widely used (Fourier, SG, AG, and DL).
Section snippets
Remote sensing vegetation index
This study used MODIS MOD13A1 version 6 enhance vegetation index (EVI) data (with the resolution of 500 m and 16-day from 2000 to 2017) for time series reconstruction study. MOD13AI EVI is composed by using the best available pixel value, which has low clouds, low view angle and the highest EVI value, from all the acquisitions from the 16-day period (Didan, 2015, Huete et al., 2002).
To test the reliability of wWHd at different land cover types, 1000 sites were randomly sampled for each land
The Whittaker smoother
Whittaker smoother (Whittaker, 1922) is a penalized least squares algorithm, which minimizes fitting error and penalises the roughness of the smooth curve (Atkinson et al., 2012, Atzberger and Eilers, 2011a). Whittaker can well balance fidelity of original time series and roughness of the fitted time series (Eilers, 2003). Fidelity S can be calculated from Eq. (1); the roughness R is expressed as differences when difference order is 2 (Eq. (2)). The idea of penalized least squares is to find
The optimal smoothing parameter λ
We first test the robustness of the multiple linear regression (Eq. (7)), i.e. the uncertainty in its parameters for obtaining the V-curve optimized lambda (abbreviated as λopt) (Eq. (7)) at the 16,000 randomly sampled sites. Backward stepwise was performed 100 times to select significant variables. To improve model’s prediction ability, each time only 60% sites were randomly selected from the 16,000 sites in Fig. 1a. Table. 2 shows that CV is the only variable not significant at majority time,
Discussion
The major strength of wWHd is balancing fidelity to original observations and roughness of final smoothed time series, which strengthens wWHd the ability of detecting vegetation gradual change without too much sacrifice of fidelity to original observations. wWHd can work in multiple growing seasons, which avoids the problem of growing season dividing in DL and AG. Besides, the single parameter λ in wWHd can be determined automatically by Eq. (15), which makes wWHd easily applied at global
Conclusions
This study developed a practical vegetation index reconstruction method, i.e. weighted Whittaker with dynamic λ (abbreviated as wWHd), which incorporates traditional Whittaker smoother with an automatic parameter generation module and weights updating module. wWHd has advantages over traditional smoothing methods in the following aspects: (1) The single parameter λ can be determined automatically; (2) wWHd is more stable and can capture vegetation gradual change even for seriously contaminated
Acknowledgements
This study was supported the CAS Pioneer Hundred Talents Program, IGSNRR Supporting Fund (YJRCPT2019-101), the National Key Research and Development Program of China (Grant No. 2018YFA0605603), the National Natural Science Foundation of China (41501037) and International Program for Ph.D. Candidates, Sun Yat-Sen University. The authors appreciate the constructive reviews by two anonymous referees and the associate editor, which noticeably improved our paper quality. We thank FLUXNET community
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