# Improving Spatial-Temporal Data Fusion by Choosing Optimal Input Image Pairs
## 1 Introduction  
Although a large number of remote sensing sensors with different spatial, temporal, and spectral characteristics have been launched, resulting in a dramatic improvement in the ability to acquire imagesof the Earth's surface, these sensors typically represent a trade-off between spatial and temporal resolution due to technological and financial constraints [1; 2; 3]. For example, Landsat can acquire images with relatively high spatial resolution (30 m), but low temporal resolution (every 16 days), while the Moderate Resolution Imaging Spectroradiometer (MODIS) can acquire images every day, but with low spatial resolution (250 m in red and NIR bands and 500 m in other land reflectance bands). Enhancing spatial resolution and temporal coverage simultaneously is required for global change studies and for resource management, especially for studying inter- and intra-annual vegetation dynamics [3; 4; 5]. A feasible solution is to use a data fusion method which blends images from different sensors to generate high temporal and spatial resolution data, thereby enhancing the capability of remote sensing for monitoring land surface dynamics. Several different spatiotemporal data fusion models have been developed, typically based on weighted functions [6], unmixing approaches [7], Bayesian theory, learning theory, and hybrid methods [8]. [PERSON] et al. [9; 10] summarized the main spatiotemporal fusion models developed in recent years. Among weighted function-based methods, the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) [6] is the initial attempt to blend fine- and coarse-resolution satellite data to generate synthetic high-spatial and high-temporal surface reflectance products. Its accuracy is often taken as a standard for comparison with the other data fusion models. The STARFM model has subsequently been extended to include several new model formulations [11; 12; 13; 14; 15]. These formulations were developed for different purposes, but are based on the same concept: using Landsat and MODIS image pairs collected on the same date to predict Landsat-scale reflectance on other MODIS imaging dates. The STARFM algorithm has demonstrated flexibility in prediction and has been widely used in many areas, such as forest monitoring [16], forest phenology [17], mapping land cover [18], gross primary productivity (GPP) [19], and evapotranspiration [20], and crop productivity estimation [21]. The STARFM model shows a high level of accuracy in capturing temporal changes (phenology) in vegetation in the target study areas [22; 23]. Based on its wide usage and application potential, in this study we use the STARFM method to test strategies for optimal input image pair selection. The optimal image pair is defined in this paper as the one to produce a smaller mean absolute difference (MAD) between the data fusion results and Landsat observations that were not used in the data fusion process. These findings also have potential applicability to other weighting function-based data fusion approaches. Among the existing spatiotemporal data fusion models, one advantage of STARFM is that it can predict a time series of land surface reflectance maps based on one input image pair. Most of the spatial-temporal fusion models require at least two or more prior pairs of images with fine and coarse spatial resolutions acquired from the same day as the input to predict a bracketed temporal series of fine spatial resolution images. In many cloudy regions, it is difficult to acquire two or more clear and high-quality images pair within a reasonable time period. For real-time applications, such as crop condition monitoring and disaster assessment, we have to rely on the most recent available clear pair image to predict current conditions. This issue has also been addressed in other recent spatial-temporal fusion models [8; 9]. Even though one pair of Landsat and MODIS images can be used to predict Landsat-like images for a long period using STARFM, the accuracies of the fused results vary.