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).