## 3 Results
### Calibration of the MOD17A2H GPP Product  
Based on the upscaled results of GPPRF and GPPMOD at the station scale in the previous section, the relationship between GPPRF and GPPMOD is shown in Figure 11. Here, the daily GPPRF was aggregated to 8-day sums to match the 8-day GPPMOD product.  
Figure 8: Daily gross primary productivity (GPP) measured by EC (GPPBC) and predicted by the random forest (RF) model (GPPRF) at (**a**) Shouxian, (**b**) Dongtai, and (**c**) Dafeng during the rice and wheat growth seasons.  
Then, the linear relationship between GPP\({}_{\text{MOD}}\) (Figure 12a-c) and the calibrated GPP mod (GPP\({}_{\text{CMOD}}\)) (Figure 12d-f) at the grid scale was established as follows:  
\[GPP_{CMOD}=\begin{cases}1.5\times GPP_{\text{MOD}},&for\ wheat\\ 1.7\times GPP_{\text{MOD}},&for\ rice\\ 1.6\times GPP_{\text{MOD}},&for\ annual\end{cases} \tag{1}\]  
Both GPP\({}_{\text{MOD}}\) and GPP\({}_{\text{CMOD}}\) exhibited a higher value during the rice growth seasons than that during the wheat growth seasons. The annual mean GPP in most parts of the NYRD varied from 2 to 4 g C m\({}^{-2}\) d\({}^{-1}\) for GPP\({}_{\text{MOD}}\) and 4 to 6 g C m\({}^{-2}\) d\({}^{-1}\) for GPP\({}_{\text{CMOD}}\), with the higher values in the eastern coastal areas of the NYRD (Figure 12c,f). Here, sea  
Figure 10: Seasonal variations in gross primary productivity (GPP) predicted by the random forest (RF) model (GPP\({}_{\text{RF}}\)). The blue line represents the daily GPP\({}_{\text{RF}}\) averaged from 23 weather stations and 3 EC stations during the period of 2014–2018 over the rice–wheat-rotation cropland in the North Yangtze River Delta region.  
Figure 9: Spatial distributions of gross primary productivity (GPP) (**a–c**) predicted by the random forest (RF) model (GPP\({}_{\text{RF}}\)), (**d–f**) measured by the MODIS product (MOD17A2H) (GPP\({}_{\text{MOD}}\)), and (**g–i**) their difference ((GPP\({}_{\text{MOD}}\)–GPP\({}_{\text{RF}}\)) \(\times\) 100/GPP\({}_{\text{RF}}\)) at the station scale for wheat growth seasons, rice growth seasons, and the whole year during the period of 2014–2018. The dark yellow background represents cropland.  
land breezes prevail, carrying rainfall and water resources sufficient to favor crop growth. Figure 12g-i show the seasonal mean of the error ranges of daily GPP (\(\Delta\)GPP, as computed by subtracting GPP\({}_{\text{MOD}}\) (Figure 12a-c) from GPP\({}_{\text{CMOD}}\) (Figure 12d-f)) during the period of 2014-2018. \(\Delta\)GPP in most parts of the NYRD ranged between 2 and 4 g C m\({}^{-2}\) d\({}^{-1}\) during the rice growing seasons, while they were smaller (i.e., 0-1.5 g C m\({}^{-2}\) d\({}^{-1}\)) for wheat. The probability density function (PDF) of \(\Delta\)GPP in the NYRD is shown in Figure 13. The PDF of \(\Delta\)GPP varies seasonally, which play a pivotal role in regulating the carbon dynamics in the NYRD. Rice paddies had a broader distribution in the peak PDF of the mean \(\Delta\)GPP than that for wheat fields, i.e., between 0.75 and 1.25 g C m\({}^{-2}\) d\({}^{-1}\) during the wheat growth seasons, between 2.5 and 3.25 g C m\({}^{-2}\) d\({}^{-1}\) during the rice growth seasons, and around 1.75 g C m\({}^{-2}\) d\({}^{-1}\) for the annual mean.  
Figure 11: Relationship between the gross primary productivity (GPP) predicted by the random forest (RF) model (GPP\({}_{\text{RF}}\)) and that measured by MODIS (GPP\({}_{\text{MOD}}\)) for the (**a**) wheat growth seasons, (**b**) rice growth seasons, and (**c**) the annual mean during the period of 2014–2018.  
Figure 12: Spatial patterns of the gross primary productivity (GPP) (**a–c**) measured by MODIS (GPP\({}_{\text{MOD}}\)), (**d–f**) measured by MODIS and then calibrated (GPP\({}_{\text{CMOD}}\)), and (**g–i**) their difference (GPP\({}_{\text{CMOD}}\) minus GPP\({}_{\text{MOD}}\)) (\(\Delta\)GPP) at the grid scale for wheat growth seasons, rice growth seasons, and the annual mean during the period of 2014–2018.