## 3 Materials and Methods
### Method for the Generation of High Temporal Resolution Time Series
#### 3.3.4 Automation and Improvement of Performance  
The original ESTARFM algorithm is designed for the generation of single synthetic scenes so that for the processing of a time series, it has to be run individually for each time step. To facilitate the generation of time series, a framework was designed in IDL (Figure 3), which requires as input all available MODIS and Landsat data for one Landsat tile and then generates the time series between a definable start and end date automatically. Input image pairs of Landsat and MODIS are automatically selected that are the temporally closest ones to the prediction date as well as the MODIS scene at the prediction date.  
Furthermore, for the application of ESTARFM to larger areas and long time series, the processing speed was optimized. So far, most ESTARFM functions only run on one CPU core, so that the prediction of an exemplary Landsat scene with four bands (B-G-R-NIR) takes more than 24 h (Table 1). Thus, the algorithm has been parallelized here, so that the number of used CPU cores can be defined individually. The images are then split into tiles and one tile is assigned to each core. This way, the user can adapt the algorithm to its system specifications and the processing time can be improved significantly (Table 1).  
3.5 Application of the Enhance Spatial and Temporal Adaptive Reflectance Fusion Model (ESTARFM) Framework in the Study Area  
Using the daily MCD43A4 MODIS product with the developed ESTARFM framework, the user can flexibly define the dates and time steps of the output time series. Though a daily ESTARFM time series could be produced, this also means a high amount of processing time and storage requirements while less time steps are sufficient for many applications. In this study, the ESTARFM framework was applied to the generation of an 8-day 30 m NDVI time series for the year 2014 (day of year, DOY 7 to 359) in the study area using all Landsat and MODIS input data described in Sections 3.1 and 3.2. Previous studies demonstrated that using NDVI directly as input to ESTARFM instead of using reflectances and calculating the NDVI from the fusion output results in higher accuracies due to reduced error propagation [10; 30].  
Of the 30 Landsat scenes from the year 2014, 17 were partly cloud-covered but could be included in the ESTARFM fusion due to the advancement of the algorithm (Section 3.3.2). For our study area, only one cloud-free (<1% cloud cover) Landsat scene for the vegetative season (DOY 159) was available for path 195 and none for path 194. However, especially the latter contained several scenes with a cloud cover of less than 40% that could be processed based on the developed cloud-filling approach (Figure 5). In particular, on the southeastern tile (194/53), some areas had persistent cloud coverage  
\begin{table}
\begin{tabular}{c c c} \hline
**Input** & **Original ESTARFM** & **ESTARFM Framework (9 Cores)** \\ \hline
4 bands & 24 h 49 min & 4 h 38 min \\ NDVI & 15 h 32 min & 1 h 45 min \\ \hline \end{tabular}
\end{table}
Table 1: Overview of processing times with the original ESTARFM and the ESTARFM framework using nine CPU cores. The processing was tested with four reflectance bands and one band of NDVI.  
over the year and had to be filled up to four times. In such regions, an application of the input scenes in ESTARFM without previous filling would result in gaps in the synthetic time series for most of the predictions.