## 4 Results
### Comparison of Crop Yield Estimates Based on Data Assimilation at the Field Scale  
To explore the performances and uncertainty between different assimilation algorithms, two assimilation algorithms (PF and POD4 DVar) were applied to the crop model data assimilation at the field scale, respectively. To compare the performance of the PF-based and POD4 DVar-based data assimilation strategies, both methods were performed with the same simulation conditions, including model inputs, initial conditions and seven assimilating LAIs measured at each field plot. Additionally, the ensemble/particle size was set to 100 to accurately and stably estimate the crop yield [10; 16; 40; 66], and the standard deviation of the observation (10% of the observational LAI) was calculated from the measured observations. We firstly compared the three assimilated LAI trajectories with PF-based, POD4 DVar-based and without assimilation at the field scale (Figure 5). The results show that the simulated LAI trajectories with the two assimilation strategies are closer to the observations than the simulation curve without assimilation. Then, we compared the simulated LAIs with measured LAI (Figure 6). The accuracy is relatively low with an R\({}^{2}\) of 0.71, an RMSE of 0.91 and an RE of 25.94% between the simulated  
Figure 4: Comparison of the observed and inverted LAIs during critical growth periods of winter wheat. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Green-up** & **Jointing** & **Elongation** & **Booting** & **Heading** & **Anthesis** & **Maturity** \\ \hline R\({}^{2}\) & 0.66 & 0.54 & 0.83 & 0.74 & 0.64 & 0.66 & 0.78 \\ RE (\%) & 12.18 & 9.33 & 9.74 & 8.97 & 7.75 & 9.37 & 8.77 \\ RMSE & 0.09 & 0.19 & 0.46 & 0.51 & 0.45 & 0.44 & 0.32 \\ \hline \end{tabular}
\end{table} 
Table 5: Validation of winter wheat LAI at different phenological stages. RE, relative error. LAI without assimilation and observations at the field scale. Compared to the simulated LAI process without data assimilation, it was evident that the assimilation strategy dramatically improved the LAI estimates. The improved LAI estimates were observed with an R\({}^{2}\) of 0.85, an RMSE of 0.44 and an RE of 14.96% for the PF-based assimilation strategy and with an R\({}^{2}\) of 0.71, an RMSE of 0.31 and an RE of 11.38% for the POD4 DVar-based assimilation strategy. The results show that the POD4 DVar-based assimilation strategy provides a better promising approach for improving the wheat LAI estimation. Consequently, the yield estimates were dramatically improved because of the optimization of the LAI simulation process (Figure 7). Compared with the simulated yields with no assimilation  
Figure 5: Comparison of the LAI curves with PF-based assimilation, POD4 DVar-based assimilation and without assimilation at the field scale. Figure 6: Comparisons of winter wheat LAI with (**a**) no data assimilation; (**b**) the PF-based data assimilation and (**c**) the POD4 DVar-based data assimilation. (Figure 6a), the estimated yields with the PF-based assimilation better predicted the measured yields, with an R\({}^{2}\) of 0.57, an RMSE of 564 kg\(\cdot\)ha\({}^{-1}\) and an RE of 6.49% (Figure 7b). Comparing the three processes, the estimated yields with the POD4 DVar-based assimilation predicted the measured yields better, with an R\({}^{2}\) of 0.61, an RMSE of 523 kg\(\cdot\)ha\({}^{-1}\) and an RE of 5.65% (Figure 7c). Furthermore, less computing time was required for the POD4 DVar-based assimilation (4.41 s over an assimilation window) than the PF-based assimilation (35.69 s). A comparison of the yield estimate experiments without assimilation and assimilation with the two algorithms indicated that the employed crop model data assimilation provides a promising approach for improving the wheat yield estimation. The experimental results also support the practical feasibility of the POD4 DVar-based crop model data assimilation, especially in terms of yield estimation accuracy and computational efficiency.