*3.3. Silage Yield Forecasting in Changchun*

#### 3.3.1. Calibration Results Based on the R-Logistic Model of FBA

Utilizing Equation (5), the FBA growth patterns were simulated and calibrated by the observed field values from 2017–2019. Similarly, the FBA simulations of each plot in three years based on the R-logistic model presented a high *R*<sup>2</sup> (*R*<sup>2</sup> > 0.95), indicating that the R-logistic model (previously applied to LAI growth) was capable of simulating the FBA patterns (Figure 12a). The FBA curves simulated in 2017 with the R-logistic model based on *t*canopy are shown in Figure 12b. It is apparent that the curves of FBA included an exponential increase at the beginning of growth, followed by a bell-shaped pattern around the peak period, and then a decline toward physiological maturity (similar to LAI). Among them, the disparity in H2 performance could be attributed to sampling error. The maximum silage yield occurs at the peak of this curve, indicating that this may be an ideal harvest period if only the silage yield is considered.

However, the parameters of the calibrated model varied across years and plots. Figure 13 depicts the *CV* values for each model parameter among five plots in different years using the computation method consistent with Figure 9. Apparently, the *CV* values of all coefficients in R-logistic models appear to be higher than those in Figure 9. The reason for this result may be that the occurring time of maximum FBA (silage yield) is harder to pin down since farmers usually harvest silage maize in advance of full maturity.

In brief, the calibrated model by ontogenetic growth data struggles to explain regional maize growth because of the variation in model parameters between years and plots. Therefore, it is necessary to determine a set of universal model parameters for depicting maize growth in large areas.

**Figure 12.** The performance of the FBA simulation results based on the R-logistic models. (**a**) Average *R*<sup>2</sup> values of FBA simulating at five plots based on the R-logistic model with four kinds of effective accumulated temperature in 2017–2019; (**b**) FBA simulating in five plots based on the R-logistic model with effective accumulated canopy temperature (*t*canopy) in 2017.

**Figure 13.** *CV* values for each R-logistic model parameter (*c*, *g*, *e*, *f*) with four inputs (*t*20, *t*40, *t*air, *t*canopy) among five plots in 2017–2019.

#### 3.3.2. Calibration Results Based on the NR-Logistic Model of RFBA

The NR-logistic model was used to simulate the RFBA and to address the issues of regional application. All of the RFBA simulations were based on *T*20, *T*40, *T*air, and *T*canopy for the raw data from 2017, 2018, and 2019 separately. During the results for 2017, the RFBA growth curve climbed to a peak and subsequently declined as the relative effective accumulated temperature increased (Figure 14). The values of *R*<sup>2</sup> (>0.94) imply that it is acceptable to simulate RFBA in the research area with the model calibrated by the relative effective accumulated temperature. Meanwhile, no significant differences in *R*<sup>2</sup> were found for models calibrated with *T*20, *T*40, *T*air, and *T*canopy.

The RFBA and different relative effective accumulated temperatures in the five plots were used to calibrate the NR-logistic model each year. The calibration results for the model parameters with *T*20, *T*40, *T*air, and *T*canopy are displayed in Table 4. The *CV* values in the model parameters *G, E*, and *F* were relatively lower than *C*, indicating different interannual variations in different parameters. The comparison of the parameters derived by different independent variables shows that the yearly gap of *T*canopy was lower, and the *CV* values of *C*, *G*, *E*, and *F* were 0.235, 0.047, −0.045, and 0.105, respectively.

**Figure 14.** Simulations of RFBA based on the NR-logistic model with four relative effective accumulated temperatures from all plots in 2017: (**a**) *T*20; (**b**) *T*40; (**c**) *T*air; (**d**) *T*canopy.

**Table 4.** Calibration results and inter-annual differences of NR-logistic model parameters with *T*20, *T*40, *Ta*ir, and *T*canopy in 2017–2019.


3.3.3. Validation Results Based on the NR-Logistic Model of RFBA

Each NR-logistic model was validated by field observations of the other two years in order to test its performance in providing estimates of RFBA. The agreement between the measured and predicted values of the RFBA was evaluated via the statistical characters of *RMSE*, *RE*, *R*2, and *d* (Table 5). The calibrated model for 2017 was better validated in 2019 than in 2018, with lower values of *RMSE* and *RE* and higher values of *d* and *R*2. For the calibrated model in 2018, there were no differences between the validations in 2017 and 2019. However, the validation results for 2017 were better than in 2018 when using the calibrated model in 2019.

There were no extreme variations in the validated results of the calibrated model with *T*20, *T*40, *T*air, and *T*canopy each year. The calibrated model in 2019 showed the optimal simulation precision for RFBA (compared to the other two years) even though it is somewhat poorer than the homologous model of RDBA in Table 2.

Using the NR-Logistic model calibrated in 2019 with *T*20, *T*40, *T*air, and *T*canopy, a scatter plot of the predicted and measured values of RFBA in 2017 and 2018 was added to evaluate the model (Figure 15). The excellent agreement between them can be verified by the high *R*<sup>2</sup> values (*R*<sup>2</sup> > 0.92). Additionally, the *R*<sup>2</sup> values were very close among the results for *T*20, *T*40, *T*air, and *T*canopy. With respect to the results from 2017 (Figure 15a–d), as observed, the fitting data were evenly distributed on both sides of the 1:1 line, indicating

a strong concordance between the measured and predicted RFBA. As for the results from 2018 (Figure 15e–h), the fitting data were somewhat over the 1:1 line, which showed that the RFBA was overestimated slightly. To summarize, the NR-logistic model calibrated in 2019 can predict the RFBA better in 2017 than in 2018.


**Table 5.** Validation results of NR-logistic model of RFBA with *T*20, *T*40, *T*air, and *T*canopy between the simulated and observed data from five plots in different years.

**Figure 15.** Regressions between the predicted and measured values of RFBA in 2017–2018 using the NR-logistic models calibrated in 2019 with four inputs: (**a**) *T*20, (**b**) *T*40, (**c**) *T*air, (**d**) *T*canopy, in 2017; (**e**) *T*20, (**f**) *T*40, (**g**) *T*air, (**h**) *T*canopy, in 2018.

The validated results with *T*20, *T*40, *T*air, and *T*canopy and the model parameters (Table 4) can be used to assess the RFBA. The selection of the model independent variable may depend only on the way to monitor temperature in situ. The model application will be more convenient if the temperature can be collected easily. However, it is important to highlight that the Tc is a good factor for scale expansion.
