## 3 Results and Discussion  
### The Influence of Meteorological Conditions on GPP  
Figure 2 compares year-to-year relationships across TCI, PCI, and GPP at the various spatial scales in the CONUS during summer. In the central and southeast US, TCI, and PCI are highly correlated (\(p<0.05\); see Appendix A Figure A1), indicating that a warm summer tends to be accompanied by a dryer condition, while their relationship is less  
Figure 1: The spatial distribution of mean LST and precipitation for July–August (**a**,**b**), the amount of state maize and soybean production, and the average irrigation rate for the state (**c**–**e**), and the percentage of US maize and soybean production indicated for each state (**f**). clear on the northeast and west coasts (Figure 2a). In these regions, an anomalously warm summer is occasionally accompanied by moist atmospheric advection resulting in the weaker relationship between TCI and PCI. In seeking GPP sensitivity to the meteorological conditions, GPP shows a higher correlation (\(p<0.05\)) with TCI and PCI in the central US (Figure 2b,c and Appendix A Figure A1b,c), where a strong relationship between TCI and PCI exists (Figure 2a). The regions of larger GPP sensitivity are stretched from south to north, particularly across the Great Plains. Contrarily, GPP in the southeastern US is less sensitive to TCI and PCI in spite of the higher correlation between them. It is presumably because a semi-arid climate in the Great Plains and a wet climate in the southeast have a different plant type, resulting in different sensitivity, which will be discussed below. In the southwest, the relationship between PCI and GPP is much weaker than in the other states, presumably due to widespread irrigation (Figures 1e and 2i). The GPP sensitivity to TCI in the Great Plains is remarkably stronger than that of PCI, implying that crop productivity can be linearly related more to the temperature than precipitation. The above-mentioned features shown in the 0.05\({}^{\circ}\) grid resolution are consistent with those at the county and state levels (Figure 2d-j). To aid an advantage of high-resolution data, we compare a few states in the Great Plains in the form of different spatial resolutions. The regional meteorological impact can be assessed effectively using high-resolution satellite images (Figure 3). In North Dakota (ND), for example, the correlation between TCI, PCI, and GPP varies significantly within the finer scales at the 0.05\({}^{\circ}\) and county levels but it is difficult to identify at the state level. Furthermore, in the western part of South Dakota (SD), a region with the Black Hills National Forest (BHNF) showed a low correlation between TCI, PCI, and GPP locally. The distinct characteristics of these forestry regions become more apparent as the scale is increased from state level to 0.05\({}^{\circ}\) resolution. To further examine the relationship between GPP and each meteorological condition (i.e., TCI and PCI), their correlation coefficients are compared at the various spatial scales in the 12 states representing major maize and soybean production (Figure 4). The majority of regional GPP values in 0.05\({}^{\circ}\) grid points exhibits a stronger relationship with TCI than PCI (i.e., the probability below the diagonal line in Figure 4a). This result indicates that GPP variation in summer is more sensitive to variation of temperature than that of precipitation, which is consistent with that shown in Figure 2. The correlation between  
Figure 2: Correlations of annual variation between TCI and PCI, TCI and GPP, and PCI and GPP for pixel level (**a–c**), county level (**d–f**), and state level (**g–i**) for the average of July and August. Their significance maps for the correlation are represented in Figure A1. GPP and TCI in most grid points exceeds 0.5. A stronger GPP-TCI relationship than the GPP-PCI relationship is also discerned in the county-level and state-level data (Figure 4b,c).