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).