# Assimilation of Earth Observation Data Over Cropland and Grassland Sites into a Simple GPP Model
## 5 Discussion  
Crop and grassland GPP was estimated inverting the Sim model against MODIS 250 m NDVI and validated with EC data. The Sim model showed better performances in GPP estimation as compared to MOD17 that was found to be affected by GPP underestimation, in agreement with [PERSON] et al. (2018). Table 4 shows that the improvement of the agreement statistics is large when comparing the Sim model with MOD17, e.g., the variance of measured GPP explained by the estimates (i.e., R\({}^{2}\)) is increased of a 26.4% and RMSE is reduced by a 22.2% when considering all EC sites. In addition to the obvious differences between the Sim model and MOD17 modelling approaches, we note that the different spatial resolution of the two GPP estimates may contribute to explain the poorer performances of MOD17. In fact, while the Sim model uses NDVI at 250 m, MOD17 is driven by FAPAR at 500 m. Therefore, MOD17 may be more affected by site heterogeneity and less representative of the flux tower footprint ([PERSON] et al., 2018; [PERSON] et al., 2018). It is noted that the removal of the intra-annual variability of GPP operated by the computation of the annual GPP reduces the R\({}^{2}\) of both modelling approaches (compare Figures 8 and 9). The Sim model captures better the seasonal dynamics of GPP than the variability among sites (Figure 10) and years (Figure 11) in agreement with the findings of [PERSON] et al. (2018) that, comparing a suite of remote  
Figure 11: Histograms of the site-level Pearson correlation coefficient (r) between EC and modelled annual GPP for the Sim model (**top** row) and MOD17 (**bottom** row). Distribution of r for all sites (**left** column), crop sites (**central** column), and grassland sites (**right** column). Incomplete years (with partial EC measurements temporal cover) were excluded from this analysis. The site-level correlation was computed only when at least four years were available (average, minimum, and maximum years per site is 6, 4 and 11). sensing based GPP model, found reduced skills in tracking inter-annual as compared to intra-annual GPP variability  
Regarding the potential underestimation of C4 crops, we showed that although some maize sites are underestimated by the Sim model, a systematic negative bias of the Sim model is not verified, as maize samples are well distributed above and below the 1:1 line of Figure 9. Moreover, the discrepancies between the Sim model and observed annual GPP seems not influenced by latitude (used to color-code the data points in Figures 9 and 10), and thus climatic differences--essentially temperature--among sites are not introducing an additional bias. This is relevant, as temperature was not considered directly as a reduction factor of \(\varepsilon_{m}\). Performances of the Sim model GPP estimation are in line with those of other remote sensing based models calibrated with EC flux data. For instance, similar RMSEs are achieved by [PERSON] et al. (2016) over croplands and grasslands using leave-one-out cross-calibration (i.e., n \(-\) 1 sites are used to calibrate the model used to predict GPP at the left-out nth site). Larger R\({}^{2}\) for GPP estimation (0.78) were achieved by [PERSON] et al. (2015) using MODIS and meteorological data to train machine learning methods on EC observations. In this study, accuracy was evaluated using 10-fold cross-validation. Despite comparable accuracy, it is noted that the validation protocol is much more conservative in this study: we used four sites for the determining and fixing the value of \(\varepsilon_{max}\) and the remaining 53 sites for validation. This study demonstrated that the assimilation of NDVI observations into simple growth model is effective for estimating crop and grassland GPP. In contrast to MOD17 and other approaches using of EO data as input, the proposed model is driven solely by weather variables and remote sensing is used to re-calibrate the model parameters.