# Improving Spatial-Temporal Data Fusion by Choosing Optimal Input Image Pairs
## 1 Introduction
Accuracy depends not only on the data fusion model used but also on characteristics of the input image pairs including: (1) the consistency between the coarse and fine resolution images in both radiometric and geometric aspects (such as solar-viewing geometry); (2) the number of available pair images and the time lag between the pair and prediction dates; and (3) the input pair dates as they relate to surface vegetation phenology and other changes. First, spatial-temporal data fusion models require consistency between fine and coarse resolution satellite data acquired at the same or close dates. Many studies have found that inconsistency in image pairs is a major issue in data fusion. MODIS and Landsat are two important data sources in remote sensing and are also the most common satellite data sources used by spatial-temporalfusion models. The consistency of MODIS and Landsat images may be affected by many factors, including differences in spectral response functions, solar-viewing geometry ([PERSON] et al., 2016; [PERSON] et al., 2017), geolocation accuracy, etc. ([PERSON] et al., 2016; [PERSON] et al., 2017). Although Terra, Aqua, and Landsat are all sun-synchronous polar-orbiting satellites, the solar-viewing geometries are different in Landsat and MODIS images. Landsat images are acquired close to nadir view (\(\pm\)7.5 degrees), while MODIS data could be acquired at a very large view angles (\(\pm\)55 degrees) and be impacted by angular effects. The angular effects can be corrected to the nadir view by using the bidirectional reflectance distribution function (BRDF) ([PERSON] et al., 2016). Daily Nadir BRDF-Adjusted Reflectance (NBAR) products at 500 m spatial resolution (MCD43A4) are now available in MODIS Collection 6 ([PERSON] et al., 2017) and can be downloaded from the MODIS data product website directly. Even after BRDF correction, however, the footprint of a MODIS pixel varies on the view angle, and this can also cause differences between MODIS images from the Terra and Aqua platforms. The effective spatial resolution of MODIS daily NBAR products is variable (typically between 500 m and 1 km) and dependent on the view angles from valid observations during a 16-day period ([PERSON] et al., 2016). Given these effects, it is important to assess the consistency between NBAR data and Landsat surface reflectance. [PERSON] et al. (2017) compared the prediction accuracy of a STARFM dataset based on MODIS daily directional reflectance data, the eight-day composite reflectance product and the 16-day NBAR and found that NBAR data produced better results even though the compositing window is 16 days. In an operational data fusion system ([PERSON] et al., 2016; [PERSON] et al., 2017), the daily NBAR at 250 m (for red and NIR bands) and 500 m resolution have been generated using the MODIS daily surface reflectance products and the 16-day MODIS BRDF parameter product. Second, if the surface is changing substantially, data fusion accuracy will depend on the time lag between pair and prediction dates. Comparisons of data fusion accuracy using STARFM and other spatial-temporal fusion models have been conducted ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2017). [PERSON] et al. (2016); [PERSON] et al. (2017) found that STARFM based on a single input pair can produce accurate predictions, but the accuracy of these predictions depends on the similarity of the single input pair to the prediction date. They suggested it was better to use the images acquired near the prediction time as input to the data fusion. [PERSON] and [PERSON] (2016) hypothesized that one image pair was not enough for STARFM to predict highly accurate time-series data and its predictive accuracy was dependent on the number of input base images. According to their test results, when using only one base pair to create temporal vegetation index (VI) profiles, STARFM failed to capture phenological variations. However, two clear image pairs in reasonable temporal proximity are difficult to obtain in many cloudy regions.