3.1 Bayesian calibration of GECROS
The varying range of residual error parameter \(\sigma_{1}\) affected the simulation performance in calibration using the data from the 2019 field experiment (Fig. 2). When the upper bound of \(\sigma_{1}\) was set at 1.0, the simulated W grain,N leaf and LAI had the highest NRMSE . After decreasing the upper bound of \(\sigma_{1}\), their NRMSE tended to decrease, although the NRMSE of simulatedN grain tended to increase (Fig. 2a). Meanwhile,R 2 of simulations in calibration also varied with the upper bound of \(\sigma_{1}\). Especially, theR 2 of simulations while setting the upper bound of \(\sigma_{1}\) at 0.2 tended to be higher than those while setting upper bounds of \(\sigma_{1}\) at other levels. Due to the overestimation (results not shown), even though simulatedN grain achieved the lowest NRMSE while setting the upper bound of \(\sigma_{1}\) at 1.0, itsR 2 values were rather low (Fig. 2b). The estimated means of posterior distribution of \(\sigma_{1}\) for most of the observations were close to the fixed upper bound (Table 5, Fig. S2a-c). Although fixing the value of upper bound of \(\sigma_{1}\) at 1.0 reduced this phenomenon, due to the unexpected residual error from the upper bound expansion of \(\sigma_{1}\), the estimated\(\sigma_{1}\) and \(\xi\) did not converge well during the Bayesian calibration process (see Fig. S2 for the simulatedW above as an example). Consequently, based on the sensitivity analysis of the upper bound of \(\sigma_{1}\), the upper bound of \(\sigma_{1}\) was set at 0.2 to conduct the following analysis.
While fixing the upper bound of \(\sigma_{1}\) at 0.2, the simultaneously calibrated uncertain parameters in GECROS and residual error parameters are shown in Table 5. Compared withW above and N above, the estimated error parameters \(\xi\) for W leaf,N leaf, LAI, W grain andN grain were farther away from one, indicating that the residual errors in those types of observations were supposed to be non-Gaussian (Table 5). Besides the residual error parameters, the uncertain parameters in GECROS were calibrated reasonably well (Table 5). Meanwhile, the uncertainty problem caused by the preset photosynthetic parameters was solved by introducing the parameter rASSA (Table 4), and the overestimation in the simulations was reduced accordingly (Fig. S3).
With the estimated posterior distributions of the uncertain parameters in the crop model GECROS (Fig. S4), the parameter uncertainty was analyzed for the field measurements in 2019, while the total uncertainty was calculated by further integrating the estimated residual error (Fig. 3). Taking no N input (0 kg N ha-1) and locally common N input (240 kg N ha-1) as examples, the simulations of different types of observations agreed well with the measured data and most of the points of the average measurements were within the range of simulated total uncertainty (Fig. 3).