# Improving Spatial-Temporal Data Fusion by Choosing Optimal Input Image Pairs
## 4 Results and Analysis
### Effect of Pair Date  
Figure 5 shows that the annually averaged MAD between predicted and observed reflectance at Landsat scale varies with the input pair date and shows a seasonal variation. The errors may be partially due to the inconsistency between Landsat and MODIS data products. Figure 8 shows the MAD between the observed Landsat NDVI and the fused results at each Landsat overpass date using the simulated MODIS data, segregated by land cover type. In the MAD panels in this figure, the different color lines signify different pair dates used as fusion input to predict NDVI on different prediction dates (x axis). It can be seen that the predictability from a certain pair date varies with the prediction date. Generally, the closer the predicted date is to the pair date, the more accurate (smaller MAD) the prediction. Within a short time period (<50 days in our cases), the predictability decreases as the time interval between input and prediction date increases. For a long time period, phenology also plays a role in predictability. In Figure 8a, all pairs show poor predictions around the crop green-up and senescence times. This is likely due to the fact that crops are changing rapidly  
Figure 7: Comparison of fused images (site 2) on DOY 2015-219 to the direct Landsat observation on that date (**a**). Three data combinations used in the fusion include (**b**) Terra + L8, (**c**) Aqua + L8, and (**d**) the Terra and Aqua combined NBAR + L8 from DOY 2015-027. The correlation coefficients (R) between the fused images and observed Landsat image are listed. during these periods, and vegetation patterns are very different from patterns at other times during the year. Human management activities such as irrigation and harvest are also an impact factor. In the forest study area (site 2, Figure 8b), pair dates in the growing or non-growing season can be used to reasonably predict reflectance within the same season, but will less accurately predict reflectance in different seasons. Figure 8: Comparison of MAD between observed and predicted Landsat-scale NDVI for different prediction dates (x-axis) using different input pair dates (signified by different color lines) for crops at site 1 (**a**) and forest types at site 2 (**b**). Mean NDVI from vegetation land cover types (corn and soybean in site 1, and deciduous, evergreen and mixed forests in site 2) were extracted and averaged based on observed Landsat and CDL data. Each symbol represents the MAD between the observed Landsat (not used in data fusion) and the fused result. Four pair dates, including days 80 (non-growing season), 167 (around green-up dates), 224 (around peak growing dates), and 279 (around senescence) are highlighted (enlarged dots) for site 1. Two pair dates, including day 43 from the non-growing season and day 195 from the growing season are highlighted (enlarged dots) for site 2. The temporally-averaged MAD (<MAD>) for each selected pair image is calculated by comparing data fusion results to Landsat observations from the entire year and is shown in Figure 9. For all vegetated land covers, <MAD> based on the pair dates from the growing season are relative larger than those from the non-growing season, partially due to the fact that the growing season is short and there are more validation images from the non-growing season, especially for agricultural site 1. For crop fields (corn and soybeans), the MAD function with prediction date has a characteristic \"M\" shape for most pair dates (Figure 8a); i.e., we obtain larger MAD during the green-up and senescence periods, but relatively smaller MAD in the non-growing seasons and at the time of peak growth. For forests, MAD patterns for different prediction dates are straightforward; i.e., pairs from the growing season have better prediction skill during the growing season than the non-growing season and vice versa (Figure 8b).