2.4.2 Integration of the estimated uncertainties into Ensemble Kalman filter
In this study, the simulated states were analyzed and updated by the observations of W leaf,N leaf and LAI, which were from the field measurements or from the remote sensing observations. Thus, \(N_{y}\)was set at three. Meanwhile, \(N_{\text{ens}}\) was set at 100 in this study, due to the reasonable trade-off between efficiency and pdf representation (de Wit and van Diepen, 2007). The residual error\(\mathbf{\varepsilon}_{t}\) of the crop model simulations was generated following the abovementioned procedure (in Section 2.3.4). For the field observations, \(\mathbf{Y}_{t}^{y}\) was the measured data at each sampling date, and \(\mathbf{R}_{t}\) was derived from their replications, assuming that the CV for each single measurement was the same as the CV of the replications of each treatment at each sampling date. As for remotely sensed observations, both \(\mathbf{Y}_{t}^{y}\)and \(\mathbf{R}_{t}\) were predicted from the regressed GPR model. Moreover, the performances of crop model simulations without assimilating observations (open-loop ) were also evaluated for comparison. To test the end-of-season forecast ability of the updated crop model, the assimilation of leaf traits ended at the grain-filling stage (20 days before maturity).