## 4 Discussion
### Time Series Functionalization and Compression  
The CCTM model also provides a solution to minimize time series storage, one-year time series can be precisely characterized with only 24 coefficients in the seasonal time series pattern. The 24 coefficients can replace the original huge dataset as the new input, conducive to analyzing and applying extensive time-series data. Because extracting statistical features with a function is easier than extracting from actual time series, the functionalization for the time series can also optimize the extraction efficiency of statistical characteristics. In addition, the coefficients have mathematical meanings, and the coefficients of different variation types represent the weights of different variations. More research is needed to explore the correlation of the coefficients with different variation types. The CCTM model can also be applied to time series image compression. The daily time series have 365 or 366 bands, the 4-day time series dataset has approximately 90 bands, and the 8-day time series dataset has about 46 bands. All these time series can be stored in only 24 bands in the seasonal time series pattern, with each seasonal time series being fitted by the CCTM model which has 6 coefficients. Therefore the 4-day time series can approximately reach the compression ratio of 3.75, the 8-day time series dataset can approximately achieve the compression ratio of 1.91, and the daily time series dataset can approximately achieve the compression ratio of 15. The DBF land cover type's daily reflectance dataset and 8-day NDVI dataset have been selected to evaluate the compression effects. The CCTM model separately compresses these two datasets with 24 coefficients in seasonal time series pattern and 6 coefficients in yearly time series pattern. The compression of the CCTM model has two patterns. The seasonal time series compression pattern which has 24 coefficients is to divide the yearly time series into four seasons. The yearly time series compression pattern which has 6 coefficients is to directly fit the yearly time series by using the CCTM model. By using the above compression patterns, the storage before or after compression is compared and the \(R^{2}\) between the original time series and compressed time series is calculated (Table 4). The original NDVI compression image has 383 rows, 307 columns, and 46 bands. Every pixel value is stored with a 32-bit integer, so the total image size is 20.63 MB. Similarly, the original consistent reflectance image has 365 bands, so the total image size is 163.7 MB. For the seasonal compression pattern, when applying the CCTM model to these datasets, the storage of the compressed time-series dataset for both NDVI and reflectance time series is only 10.7 MB, which is 52% of the original 8-day NDVI dataset and 6.5% of the original daily reflectance dataset. For the yearly time series compression pattern, the final compressed NDVI and reflectance time series can be stored with only 2.69 MB, which is 13% of the original 8-day NDVI dataset and 1.6% of the original daily reflectance dataset. The number of compression coefficients should be chosen using the actual data precision when selecting the compression method. The CCTM model is flexible on the number of the coefficients; a whole year time series can be compressed with 6 and 24 parameters. Remote sensing image compression \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **8-Day Time Series NDVI** & \multicolumn{2}{c}{**Daily Time Series**} \\  & & **Reflectance** & \\ \hline Compression pattern & seasonal & yearly & seasonal \\ \hline Coefficient number & 24 & 6 & 24 \\ Original storage (MB) & 20.63 & 21 & 163.7 \\ Compressed storage (MB) & 10.7 & 2.7 & 10.7 \\ \(R^{2}\) & 0.99 & 1 & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The time series compression evaluation in two compression patterns. has its standards, and the specified compression methods using the CCTM model need further research.