## 2 Study Area and Data
### Data  
#### 2.2.1 Satellite Images and L-M Blended Data  
Time series of Landsat-5 Thematic Mapper (TM), Landsat-7 Enhanced Thematic Mapper (ETM)+, and Landsat-8 Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) standardized surface reflectance data are sourced from Geoscience Australia ([[http://geoscienceaustralia.github.io/digitalearthau/index.html](http://geoscienceaustralia.github.io/digitalearthau/index.html)]([http://geoscienceaustralia.github.io/digitalearthau/index.html](http://geoscienceaustralia.github.io/digitalearthau/index.html))), which contains 239 scenes covering the Australian wheatbelt across seven  
Figure 1: Study sites and the crop growing season (April–October) average accumulated precipitation (mm for the years 2009–2015) across the Australian wheatbelt (–53 million ha) [13]. The precipitation data are sourced from [PERSON] et al. [37].  
years (2009-2015). These images are nadir-corrected, adjusted for bidirectional reflectance distribution function, and topographically corrected followed by [PERSON] et al.'s methods [38], resulting in a 25-m pixel resolution. This is as, in Geoscience Australia's processing stream, they oversample the Landsat imagery to 25 m to allow easier integration with other remote sensing data sources. Time series of normalized difference vegetation index (NDVI) are then computed using the red and near-infrared bands [39]. The 16-day composite of MODIS NDVI (MOD13Q1 v006) data are used due to the low clouds, low view angle, and the highest NDVI value at 250-m spatial resolution. The MODIS data are sourced from United States Geological Survey for the corresponding periods and area (16 tiles) and are then downscaled to 25 m by 25 m spatial resolution using nearest neighbor interpolation [40] for input to the blending algorithm and for consistency to enable further analysis.  
The inter-annual variability of precipitation (Figure 2b) illustrates that the probability of rain days is higher during June-August (i.e., tillering to flowering phase), which is a critical period for crop yield prediction [41, 42]. Figure 2b also shows the value of 0.58 in July at the 75 th quartile, which indicates that the probability of cloud-free Landsat images could be lower than 42% in most areas. Here, 75% of field-scale Landsat missing data occur during the growing season (i.e., 113-289 days of the year (DOY)), and only 25% of the Landsat data are complete sequences (Figure 3).  
Figure 2: Box–whisker plots of 1901 to 2018 averaged (**a**) monthly accumulated precipitation (mm/month) across the Australian wheatbelt (see Figure 1) and (**b**) monthly probability of rain days (bottom). For both parts, the horizontal line represents the median of the data, the box spans from 25 th to 75 th quartiles of the data, and the circles past the end of the whiskers are outliers, while the rain day threshold is 0 mm/day.  
To blend MODIS and Landsat NDVI data and create the 16-day time series of gap-filled Landsat-like images, we applied ESTARFM [11], which is superior when the spatial variance is dominant [10]. We follow [PERSON] et al.'s [22] recommendation to \"index then blend\", as it yields more accurate results and provides higher computational efficiency than the \"blend then index\" approach. Figure S2 (Supplementary Materials) illustrates the blending process and the resulting Landsat-like image. As a result of data blending, each pixel is described by 22 observations across the calendar year. For more details about ESTARFM see [11, 43].