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).