## 4 Results
### Regional Estimation of GPP and ET Using the PML-V2 Model  
We applied the PML-V2 model to estimate the regional (28-29\({}^{\circ}\)N, 115.7-116.7\({}^{\circ}\)E) distribution of GPP and ET in 2000, 2005, 2010, and 2015 at the spatial resolution of the NDVI data (0.0025\({}^{\circ}\)). The calibrated parameters, including those at different growing stages for the early rice and late rice at the Xiangtang Station, were used. Despite the relatively small extent of our study area (\(\sim\)10\({}^{4}\) km\({}^{2}\)), some of the meteorological conditions exhibit large spatial variations even on an annual time scale, especially for the specific humidity, the wind speed, and the precipitation (Figures 7 and S1-S3). For example, annual precipitation ranges from 1400 mm to over 2200 mm across the region in 2005 (Figure S2). In addition, meteorological conditions exhibit inter-annual variations (Figures 7 and S1-S3). For example, T\({}_{\rm a}\) increases in the 2000-2015 period. NDVI also increases, although the solar radiation peaked in 2005 and the precipitation was the largest in 2010. The estimated annual GPP of paddy rice (including early rice and late rice) was 1314 \(\pm\) 286 gC m\({}^{-2}\), 1358 \(\pm\) 311 gC m\({}^{-2}\), 1319 \(\pm\) 314 gC m\({}^{-2}\), and 1453 \(\pm\) 359 gC m\({}^{-2}\) in 2000, 2005, 2010, and 2015, respectively. No significant trend exists during the 2000-2015 period. The annual GPP showed large spatial variations, with the largest GPP in the southeast of the region and relatively small GPP in the west region (Figure 8). We further demonstrated the spatial variability of GPP (ET and WUE) using the violin plot (Figure 9), which combines the boxplot of GPP (ET and WUE) with its probability density distribution. As shown in Figure 9, the total amount of GPP for the early rice and late rice also exhibits small inter-annual variations but large spatial variations within a single year. The probability density distribution of GPP was generally symmetric (Figure 9), indicating that the mean value of GPP is close to the median value of GPP. The total amount of GPP of the early rice was 709 \(\pm\) 167 gC m\({}^{-2}\), 723 \(\pm\) 174 gC m\({}^{-2}\), 681 \(\pm\) 164 gC m\({}^{-2}\), and 707 \(\pm\) 183 gC m\({}^{-2}\), and the total amount of GPP of the late rice was 605 \(\pm\) 149 gC m\({}^{-2}\), 635 \(\pm\) 167 gC m\({}^{-2}\)  
Figure 7: Regional distribution of annual averages of meteorological variables and NDVI in 2010. The estimated annual ET of paddy rice (including early rice and late rice) was 988 \(\pm\) 49 mm, 1075 \(\pm\) 56 mm, 968 \(\pm\) 46 mm, and 984 \(\pm\) 48 mm in 2000, 2005, 2010, and 2015, respectively. No significant trend exists during the 2000-2015 period. Compared to the GPP, the estimated annual ET was also relatively large, but not always the largest, in the southeast of the region. For example, ET was the largest in the northern part of the region in 2005 due to the heavy rain in this area (Figure S2). ET exhibits smaller spatial variations compared to that of GPP (Figure 9). The probability density distribution of ET was also generally symmetric (Figure 9). The total amount of ET of the early rice was 517 \(\pm\) 19 mm, 551 \(\pm\) 25 mm, 449 \(\pm\) 15 mm, and 488 \(\pm\) 22 mm, and the total amount of ET of the late rice was 471 \(\pm\) 33 mm, 524 \(\pm\) 34 mm, 518 \(\pm\) 33 mm, and 496 \(\pm\) 29 mm in 2000, 2005, 2010, and 2015, respectively. ET for the early rice was not strongly correlated with NDVI (r = 0.37). In contrast, ET was highly correlated with the solar radiation (r = 0.80) and air temperature (r = 0.77) for the early rice (Figure 10). ET for the late rice was highly correlated with NDVI (r = 0.73), followed by wind speed (r = 0.54) and solar radiation (r = 0.48). The median value of WUE is \(\sim\)1.40 gC/kgH\({}_{2}\)O for both the early rice and late rice. Despite the relatively small spatial variations in ET, the WUE exhibits larger variations than those of GPP and ET (Figure 9).