## 3 Results and Discussion  
### Correlation between BEPS-Simulated Crop GPP and Ground Measurements  
The uncertainty of Sentinel-2-derived LAI time-series after smoothing by LACC from our study has a Root Mean Square Error (RMSE) of 1.1 m\({}^{2}\) m\({}^{-2}\) (R\({}^{2}\) = 0.83) compared with the ground-measured plant area index (including crop stems and heads) collected during the SMAPVEX16-MB campaign [67]. A previous validation for the same LAI algorithm reported an RMSE of 0.81 m\({}^{2}\) m\({}^{-2}\)[68]. Knowledge of the starting and ending dates of the growing season, for each field, is important when simulating crop GPP; this information is clear from the LAI time series. Since the crops in different fields were sowed or planted on different dates, we simply run BEPS from the beginning of 2016. To avoid a numerical problem in the modeling, we have set the minimum LAI to 0.01; these two settings result in an intercept in the GPP-biomass relationships as shown in Figure 3 for all the crop types and in Figure 4, by crop type. Figure 3: The correlation between BEPS-simulated crop gross primary production (GPP) and ground-measured above-ground biomass for six crop types (oat, soybean, wheat, corn, canola and black bean) for SMAPVEX16-MB. The quality of the LAI time series is important for accurate estimation of AGB. As shown in Figure S2 and Table 1, two Sentinel-2 images are missing in August during key growth periods. This gap leads to inadequate inputs to the LACC method and subsequently, the failure of LAI time-series smoothing, i.e., extreme values in the peak growing season, as observed for the fields in the lower-right corner of our study area. The errors in LAI can  
Figure 4: The relationship between BEPS-simulated crop GPP and ground-measured above-ground biomass for each crop type for SMAPVEX16-MB. propagate into the biomass estimation as indicated by the red circle in Figure S3 and have led to some overestimations in biomass estimation. Although an overall strong correlation between simulated GPP and AGB is observed, these errors highlight the limitation of using Sentinel-2 data alone for biomass mapping. Fusion of Sentinel-2 data with other optical and/or SAR images is one strategy to improve the success of biomass mapping [69]. After excluding the sites with large biases in LAI, Figure 3 shows that the correlation between BEPS-simulated GPP and ground-measured AGB is stronger with R\({}^{2}\) of 0.82. As the comparison is conducted at a pixel size of 20 m while the AGB is sampled in a lesser area, the AGB samples may not capture all the variations in crop growth present within a 20 m pixel. Although the V\({}_{\text{cmax}}\) is likely to vary within the study area, it is set as a constant value. Figure 3 indicates that a unique GPP-biomass relationship is still practical for regional applications. The slope of 1.03 for the linear relationship between BEPS-simulated GPP and ground-measured AGB, as shown in Figure 3, is reasonable. The slope between GPP and total biomass in high latitudes should be larger than 1.0; however, GPP and only AGB are compared here. The fraction of AGB to total biomass is less than 1, e.g., 78% for maize [70]. Therefore, the CUE (larger than 1) compensates the AGB-to-total-biomass ratio (less than 1), leading to the slope between GPP and AGB close to 1. The coefficient of determination (R\({}^{2}\)) between the simulated GPP and AGB ranges from 0.65 to 0.96 for the six crop types (Figure 4). It is worth noting that the two legume crops, black bean and soybean, are characterized with smaller slopes of 0.71 and 0.4, respectively. Legume-cereals have a strong N rhizdeposition and are often cultivated in rotation cropping to enhance crop yield [71]. The N rhizdeposition is associated with large amounts of C rhizdeposition accompanying the senescence of roots and nodules which are made of C [72]. Therefore, a significant amount of biomass is allocated to the below-ground biomass for these crops, leading to a smaller ratio of AGB to total GPP. [PERSON] et al.