# Improving Spatial-Temporal Data Fusion by Choosing Optimal Input Image Pairs
## 5 Discussion
### The Impact of Temporal and Spatial Variations on Prediction Accuracy  
Complex heterogeneous areas with high temporal and spatial variations in surface reflectance may have lower prediction accuracies than more homogeneous areas [46]. This may be caused by several factors. First, vegetation in different climate regions has different temporal growing patterns. In our cases, the forest in site 2 has a longer growing season and shows less temporal variation in reflectance and NDVI than crops in site 1. The mean NDVI ranges from 0.5 to 0.8 for deciduous forest, and from 0.7-0.8 for evergreen forest. In comparison, the range of the mean NDVI for crops, both corn and soybean, is from \(\sim\)0.2 to \(\sim\)0.9 (Figure 8). Additionally, the growing period from green-up to senescence for crops in site 1 is about 140 days, while for forest in site 2 it is about 200 days. It is more difficult to capture the rapid changes in reflectance associated with the crop land classes, especially during the green-up and senescence stages (Figure 9).  
Second, the accuracy of data fusion is also affected by the spatial heterogeneity within the study area. For example, land cover in site 2 is more homogenous than in site 1 during the growing season. There are large continuous patches of forest at site 2. Forests (deciduous, evergreen and mixed forests) in the area have similar NDVI during the growing season. Although over 90% of land covers at site 1 are crops, the spatial heterogeneity caused by the different crops and planting schedules is observed. Data fusion accuracy for forests is slightly higher than for croplands in these tests.  
To assess the relative spatial variability for each study site, the mean squared displacement (MSD; Equation (5)) was computed for each Landsat image and plotted in Figure 13. Again, MSD represents the spatial heterogeneity of land cover in reflectance or NDVI. It can be seen that MSD is smallest for red reflectance, followed by NIR and NDVI. As the crops grow, the spatial variability in NIR first increases, and then decreases (opposite for the red band). The MSD for NDVI varies greatly over the course of the year, and attains high values indicating large spatial variability. Near peak growth, however, the NDVI of corn and soybean is more similar and the landscape at site 1 appears more homogeneous; therefore, NDVI MSD decreases during this period. When the NDVI MSD reaches a maximum during the green-up and senescent stages, the different seeding/harvest schedules and different growth rates of various crop types lead to rapid changes in the image texture causing stronger spatial heterogeneity. The prediction accuracies during these two periods are lower than for other stages.  
For site 2, reflectances in the red and NIR bands are relative stable during the entire growing season. Unlike crops, the MSD for forest in the non-growing season is slightly higher than in the growing season, which means that forests are more homogeneous during the growing season. Therefore, the data fusion accuracies from forests are normally higher than for crops, as illustrated in Figure 9.