## 2 Study Area and Materials  
The Midwestern US study area (Figure 1), one of the major agricultural regions in the world, includes 12 US states: North Dakota, South Dakota, Nebraska, Kansas, Minnesota, Iowa, Missouri, Michigan, Wisconsin, Illinois, Indiana, and Ohio. In this region, diversified crops are cultivated but corn (_Zea mays_) and soybeans (_Glycine max_) are the two dominant crops. In general, crop planting is completed by mid-May, when the daily soil temperatures are warm enough (above 13 \({}^{\circ}\)C) to initiate germination. Corn is often planted approximately one to two weeks earlier than soybeans [41]. The crops usually mature in late September and are harvested from early October until late October. The datasets used in this study (Table 1) were collected over a three-year span between 2009 and 2011. The satellite data include two standard Terra/MODIS products: the eight-day 1000 m Leaf Area Index (LAI) & Fraction of Photosynthetically Active Radiation (FPAR) product (MOD15A2) [42] and the eight-day 1,000 m vegetation productivity product (MOD17A2) [37]. The MODIS tiling scheme separates the earth into 10\({}^{\circ}\) by 10\({}^{\circ}\) sections referenced with horizontal (H) and vertical (V) notations. Six MODIS tiles (H09V05, H10V04, H10V05, H11V04, H11V05, and H12V04) that cover the Midwestern US were downloaded from the U.S. Geological Survey (USGS) EROS data center [43]. All products were composited every eight days, starting from Day-of-Year (DOY) 1 in each calendar year. The product details are available on the MODIS data website [44]. The Quick Stats database from the National Agricultural Statistics Service (NASS) of the US Department of Agriculture (USDA) provides reliable crop survey data at the county, state, and national levels [45]. We obtained statistical data describing the yields and harvested areas of corn and soybean in each county. Based on the Crop Production 2011 Summary released by the USDA, the Midwestern US produced 277.1 Tg of corn and 70.2 Tg of soybeans in 2011, which were approximately 88.3% and 84.4%, respectively, of the total US corn and soybean productions. Planted areas for corn and soybean in Midwestern US were \(5.6\times 10^{7}\) ha in 2011, which were approximately 70.9% of the total planted areas (\(7.9\times 10^{7}\) ha) for all principle crops such as corn, sorghum, oats, barley, rye, wheat, rice, soybeans, peanuts, sunflower, cotton, and potatoes. The NASS Cropland Data Layer (CDL) program produces crop-type specific classification maps based on multi-sensor satellite imagery using training data from extensive ground surveys [46]. The classification map is available for each state at a resolution of 30 m. In the present study, the CDL maps were reprojected to a sinusoidal projection, mosaicked, and scaled up to 500 m as percent maps (Figure 2) to match the spatial resolution of MODIS. To avoid errors in regions with sparse agriculture, our analysis was confined to counties that were planted with corn or soybean on at least 5% of their total areas. Although irrigation helps boost crop yields, most PEMs to date have not compensated for the impacts of irrigation. To investigate the yield estimation in irrigated areas, we sourced the irrigation map (Figure 3) from the USGS early warning program [47]. The irrigated areas in the Midwestern US were mapped for 2007 and were primarily located in Nebraska and Kansas. Because irrigation is unlikely to vary on a year-to-year basis, no change in irrigated area was assumed during the three years (from 2009 to 2011). The spatial pattern of irrigated areas was consistent with that of the agriculture areas (Figure 2), especially for corn (Figure 2A), which consumes large volumes of water before, during and for several weeks after pollination. To study the effects of irrigation, counties were considered as irrigated if more than 1% of the crop areas were under some form of irrigation.