3.4 Performance of assimilating observations into crop growth simulations
While assimilating observations into crop simulations, the filter divergence did not show up and the updated simulations agreed better with the measurements. In line with the illustrated trajectories of time series states from open-loop without assimilating observations and updated states by DAfm and DArs (Fig. S7), the differences in DAfm or DArsbetween updated states and measured states tended to diminish with progress of the growing season (Fig. S8). Moreover, the performance of updated states hardly changed with the varied ensemble size from 50 to 500 in EnKF (Fig. S9). The f rc for directly updated leaf traits by DAfm and DArscentered around 0.1 and 0.2 (Fig. 6a-b), respectively, indicating improved filter performance after assimilating observations and no filter divergence occurrence. Although the f rcfor traits indirectly updated by DAfm and DArs centered around 0.8, there was no pattern that thef rc tended to be close to one with the progress of the growing season (Fig. 6c-d), which was another indication of the absence of filter divergence. Due to the method for simulating grain formation in the crop model GECROS, unlike withW above and N above,W grain and N grain could not be updated immediately once the leaf traits were updated, but only could be updated gradually in the following growth days (Fig. S7). Thef rc values of W grain andN grain were not included here.
The NRMSE of the updated states by DAfm and by DArs decreased, compared with those of open-loop (Fig. 7). Analyzed states like W leaf,N leaf and LAI by DAfm and DArs were directly updated and unsurprisingly performed better than those by open-loop across the whole growing season, in which their NRMSE on average decreased from 0.468, 0.551 and 0.434 to 0.161, 0.228 and 0.136, respectively (Fig. 7a). More importantly, theNRMSE of the indirectly updated states,W above and N above, by DAfm across the whole growing season decreased to 0.222 and 0.227, respectively, while those by DArs further decreased to 0.203 and 0.196 (Fig. 7b). Especially at the harvesting stage, those indirectly updated states of DAfm and DArs also agreed better with the field measurements than those of open-loop (Fig. 7c). Taking advantage of the in-situprediction of crop growth status by the GPR modelling of remote sensing images, updated states of DArs tended to perform better than those of DAfm (Fig. 7b-c). Particularly, compared with arbitrarily assumed uncertainties of crop model simulations and remote sensing predictions, analyzed states of DArsbased on the estimated uncertainties from the proposed Bayesian methodology showed better performance (Fig. 8a-b). Fixing the CVs of crop model simulations and remote sensing predictions at 0.1 and 0.01, respectively, resulted in a better performance than using other combinations of CVs. Thus, these CV values were selected for further evaluating the performance of varied inflation factor (Fig. 8), in which the inflation factor was expected to enlarge \(\mathbf{K}\) in the DA process (Eqn 15) for better filter performance. The updated states ofN leaf and N above benefited from the further incorporated inflation factor, on which ranged from 1.05 to 1.25. However, the NRMSE of updated states based on the assumed uncertainties combined with the inflation factor was in general higher than that based on the assumed uncertainties only, which was also higher than that based on the proposed Bayesian methodology (Fig. 8c).