## 2 Materials and Methods
### Time Series Reconstruction Flow  
The data processing consists of three parts (Figure 1). (1) Preprocessing includes setting a mask for the dataset according to the quality control information, outlier recognition, gap-filling, and enhanced SG filtering, which is only necessary for time series datasets that contain noise. If \(>\)50% of the points in the yearly time series are invalid, the invalid points are filled with zeros, and gap-filling and enhanced SG filtering are not needed. (2) The reconstruction results are compared in seasonal time series patterns and yearly time-series patterns. In the yearly time series pattern, four models are applied to reconstruct the yearly segment time series, but in the seasonal segment time series, four models are separately used to reconstruct every seasonal segment time series.  
The NDVI time series dataset is based on the MOD09Q1 product. MCD15A3H, MOD11A2, MOD17A2H, and MOD09Q1 time-series datasets are provided with detailed quality control instructions. The NDVI, LAI, and GPP products were chosen as they are important in reflecting vegetation changes. The MSR product (including near-infrared and red band data) was chosen as it is a representative primary remote sensing product.  
These four-time series reconstruction models include: (i) the CCTM model developed in this paper, (ii) the Harmonic model (an eight-parameter harmonic model), (iii) EXP (an exponential model), and (iv) LN model (a logarithmic model). (3) Accuracy assessment  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Date** & **URL** & **Description** \\ \hline MCD15A3H (MODIS Leaf & & [[https://developers.google.com/](https://developers.google.com/)]([https://developers.google.com/](https://developers.google.com/)) & The MCD15A3H V6 level 4, Combined \\ Area Index/FPAR 4-Day & 2001–2005 & earth-engine/datasets/catalog/ & Fraction of Photosynthetically Active \\ Global 500 m) & & MODIS006\_MCD15A3H & Radiation (FPAR), and Leaf Area Index (LAI) \\  & & (accessed on 21 April 2022) & product is a 4-day composite data set with \\  & & & 500 m pixel size. \\ \hline MOD17A2H (Terra Gross & & [[https://developers.google.com/](https://developers.google.com/)]([https://developers.google.com/](https://developers.google.com/)) & The MOD17A2H V6 Gross Primary \\ Primary Productivity & 2001–2005 & earth-engine/datasets/catalog/ & Productivity (GPP) product is a cumulative \\
8-Day Global 500 M) & & MODIS006\_MOD17A2H & 8-day composite with a 500 m resolution. \\ \hline MOD9Q1 (Terra Surface & & [[https://developers.google.com/](https://developers.google.com/)]([https://developers.google.com/](https://developers.google.com/)) & The MOD09Q1 product provides an estimate \\ Reflectance 8-Day Global & 2001–2005 & earth-engine/datasets/catalog/ & of the surface spectral reflectance of bands 1 \\
250 m) & & MODIS006\_MOD09Q1 (accessed on 21 April 2022) & and 2 at 250 m resolution and corrected for \\  & & MODIS006\_MOD09Q1 (accessed on 21 April 2022) & atmospheric conditions such as gasses, \\  & & & aerosols, and Rayleigh scattering. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed information about the dataset used in the study.  
Figure 1: Flowchart of time series reconstruction.  
evaluates the reconstruction accuracy between the original time series processed by SG filter and gap-filling methods and the continuous-time series reconstructed by the four models.