# Improving Spatial-Temporal Data Fusion by Choosing Optimal Input Image Pairs
## 4 Results and Analysis
### Pair Selection Strategies  
To test the two automatic pair selection strategies (ND and HC), image pairs on DOY 80 and DOY 263 were used to predict the entire year for site 1. Results show that the split day is 170 for the ND approach and 193 for the HC approach. Figure 11 shows the variation in MAD with the prediction date using these two pair selection strategies. Only results for prediction dates between the split days (170-193) differ based on strategy. During that period, the HC strategy yields lower <MAD> values, indicating superior performance in comparison with ND in this case.  
Figure 10: Comparison of NDVI time series for corn (**a**) and soybean (**b**) from original Landsat observations (black) and the fused images using pair images on day 80 (red), 224 (green), and 283 (blue) for site 1.  
While the tests portrayed in Figure 11 limit available pairs to two, Figure 12 explores the impact on <MAD> of increasing the number of pairs available to choose from. Except for the first point on the left (only one pair available and, thus, <MAD> for ND and HC are identical), <MAD> using HC is always smaller than one using ND. If two pairs with a very long lapse (e.g., 80-224 and 80-263) are used, the difference between the HC and ND strategies becomes larger. With increasing number of available image pairs, the MADs from both HC and ND decrease and the differences between the two strategies become smaller since the split dates decided by the ND and HC strategy are close. Generally, the HC strategy is superior to ND in this study. The HC strategy requires more time to compute the correlation coefficient between the predicted and pair date images. When there are only a small number of available image pairs during a long time interval, the HC strategy is a better choice. If there are a large number of image pairs and the pair dates are close, both HC and ND yield similar accuracy, while ND is a simple and fast method to decide the split dates operationally.  
Figure 11: MAD for different prediction dates based on one image pair option from either day 80 or 263 when using the nearest date (ND) and higher correlation (HC) strategies. The HC strategy shows the smaller MAD (red) and better data fusion results than the ND strategy (black).  
Figure 12: <MAD> of NDVI decreases as the available number of pair images increases for both the ND and HC pair selection strategy. Each point in the plot shows a combination of pair dates, as indicated by the adjacent label.  
Figure 12 also reveals that the year-long predictability of each image pair is different. The overall prediction accuracy for a long period may drop if an image pair with low predictability is included. In our study, the <MAD> based on the pair on DOY 80 decreases (improves) when a pair image on DOY 263 is added (Figure 12). However, the overall <MAD> increases (worsens) when another pair from DOY 224 is added. Although DOY 224 is around the peak growing stage (close to maximum NDVI), the year-long predictability of this pair is the lowest among all (see maximum <MAD> for corn in Figure 9). The year-long predictability of pairs in certain growth stages (e.g., green-up and senescence) is usually poor (Figure 8). In order to achieve high prediction accuracy for a long period, the pair dates during green-up and senescence stages should be used, but only limited to predictions for nearby dates. In our study, the MAD can be kept under 0.01 for no more than 50 days around these pair dates.