## 5 Discussion  
Crop growth models often oversimplify actual crop growth conditions. Some uncertainty is introduced by the model's structure, the model assumed, observation errors and meteorological parameters, resulting in a biased simulation of the true growth process. Without altering the crop models' structure, the uncertainties of the crop model can be reduced using the assimilation of observational LAI during the crop growing season. To obtain better estimates of regional crop information, a series of remotely-sensed LAIs during the crop growing season must also be accurately estimated [6]. Unfortunately, current remote sensing LAIs have several shortcomings in their temporal and spatial resolutions due to the limits of the revisit circle, the cloud coverage and/or mixed pixels, which may result in poor performance of the assimilation process. To reduce these uncertainties in observation errors, we retrieved LAIs using the PROSAIL model with multiple sensors' optical data (i.e., Landsat OLI, HJ-1 and GF-1) to improve accuracy and increase the effective temporal resolution of remotely-sensed LAI. On the other hand, we constructed two strategies (PF and POD4 DVar) to assimilate the observed LAI directly into the CERES-Wheat model and compared the performances of these two strategies at the field scale. It was found that the employed POD4 DVar-based assimilation strategy is the better approach for improving the wheat modeled LAI and yield estimation. Then, based on the POD4 DVar-based assimilation framework, we analyzed the performance of crop model assimilation of LAI at different temporal scales (phenological stages and temporal frequencies) and spatial scales. Compared with traditional EnKF-based strategy and re-recalibration strategies (e.g., SCE-UA [5]), the PF-based strategy can sample particles and update particle weights according to any distribution function and is able to express the model estimation as a recursive process that avoids the higher dimensions of control variables and a high computational burden [22]. In this study, the resampling and reperturbation of the resampled particles were used to avoid the particle degeneracy and lack of particle diversity under the constraints of the model by using fewer particles. However, the particles would increase exponentially in order for the posterior mean from the particle filter to have an expected error smaller than either the prior or the observations [83]. This study provides new progress and challenges that will be addressed in our future work. Compared with the EnKF-based strategy, the POD4 DVar-based strategy can perfectly solve the issues in non-Gaussian dynamic distributions and nonlinear models, which avoids the greater dimensions of control variables and computational costs, so as to obtain higher accuracy and lower computational costs than EnKF [9]. By merging the Monte Carlo and POD into the 4 DVar method, the POD4 DVar-based strategy retains the main advantages  
Figure 12: Accuracy and computation time of estimated wheat yield using LAI from a different spatial scales compared with the official statistical yields. of the traditional 4 DVar (i.e., dynamic constraint and assimilation of multiple time observations) [40] and need not maintain and update the adjoint or tangent linear models of the forecast models [9]. Compared with the PF-based strategies, our results indicated that the POD4 DVar-based assimilation strategy results in better performance and higher computational efficiency of the assimilation process and is the better approach for improving the wheat modeled LAI and yield estimation. However, the uncertainty of the ensemble size and the initial perturbation fields on the assimilated results were not shown in this study and will be addressed in our future work. Unfortunately, few studies have focused on the application of PF-based and POD4 DVar-based assimilation strategies to yield estimations.