3.3.4. Silage Yield (Maximum FBA) Forecasting in Area by MOD11A1-LST Values

The shapes of the FBA and RFBA curves depicted above suggest that the silage yield should be near the peak of the curve to maximize profits. Therefore, the areal silage yield could be simulated by the validated Equation (6) in 2019 with *T*LST from MOD11A1 as a substitute for *T*canopy in combination with the field FBA observations on three different days at different growth stages (Figure 16). The differences in spatial distribution were captured. Similarly, the predicted FBA increased and got closer to the maximum output when the field observation date was near harvest.

**Figure 16.** Predicting silage yield values using the NR-logistic model calibrated in 2019 based on the field observations in three different days: (**a**) 2017/7/16; (**b**) 2017/8/10; (**c**) 2017/8/31.

According to the summarized data in Table 6, the model simulation showed only a slight difference on the observation day (31 August) in the experimental station. This is not surprising given that the measured silage yield was recorded on the same date. The results on 10 August still produced a satisfying accuracy, which indicates that it might be an appropriate harvest date for silage yield in view of various factors. There were no measurements of silage yield in the three subareas, so the comparison could not be analyzed and displayed between observations and predictions in the region.

**Table 6.** Comparisons between the forecasted silage yields (maximum FBAs) based on the field observation <sup>1</sup> in different days and experimental station.


<sup>1</sup> Sample numbers in experimental station are 13 and 30. <sup>2</sup> The data were measured on 2017/8/31.

#### *3.4. Verification in Jiefangzha Sub-Irrigation District*

As mentioned in Section 2.3, an LST map (30 m) of Jiefangzha showed the results fused from Landsat 8 and MOD11A1 images by the ESTARFM algorithm. Scatters of the fused LSTs and Landsat-LSTs were evenly distributed on both sides of the 1:1 line, showing the fused LSTs were relatively reliable (Figure 17a). The fused LSTs were also compared with the Tc recorded at 11:30 a.m., in which the values of *R*<sup>2</sup> (0.547), *RMSE* (3.96◦C), and *d* (0.79) indicate good consistency between the observed values and the fused ones (Figure 17b). The grain yield forecasting map was constructed by employing the N-Logistic model described previously with the fused LSTs (Figure 18).

**Figure 17.** Regressions for accuracy evaluation of the fused LST: (**a**) the fused LST vs. the inversed values from Landsat 8; (**b**) the fused LST vs. the observed Tc in experimental station in 2016.

**Figure 18.** Forecasting results of grain yield in the Jiefangzha sub-irrigation district using the 2019 calibrated model based on the field observations in four different days: (**a**) 2016/7/4; (**b**)2016/7/21; (**c**) 2016/8/4; (**d**) 2016/8/26.

Figure 18 shows the spatial grain yield estimates retrieved using DBA measured on four acquisition dates that include (a) 4 July, (b) 21 July, (c) 4 August, and (d) 26 August in 2016 based on the model calibrated in 2019. The predicted yield showed a significant upward trend as the acquisition date of DBA approached harvest. Meanwhile, the comparisons between the predicted and measured yield in situ were conducted with statistical parameters as evaluation metrics of accuracy (Table 7). The predicted yields coincide with the measured ones with *RE* values, ranging from −16.14% to 9.84%, which confirms that assimilating once-measured data into the model can produce a great estimate of grain yield. Comparatively speaking, DBA assimilation closer to the harvest date allows for a more accurate prediction of yield except for the results based on the data on 21 July, which may be caused by the irrigation measures or the model parameters. Assimilating DBA measured on 4 July also provides a reliable result, albeit with a slightly lower *R*2. Such a result proves the feasibility of the approach for early yield forecasting in other large areas though the optimal date of sampling still needs to be explored and determined further.

**Table 7.** Comparisons between the forecasted grain yields in the Jiefangzha sub-irrigation district based on field observation in different days and the measurements 1.


1. The data were measured on 2016//9/15.

#### **4. Discussion**

According to results reported above, our data on maize biomass show that the Tc should be included as a valuable proxy of other independent variables in models because the Tc can be recognized as LST in large regions covered by maize that can be derived from remote sensing data [50,51].

This study demonstrated the benefits of integrating remote sensing LST into crop growth models in combination with once-observed values (DBA or FBA) to enhance yield prediction. The introduction of remote sensing LST to the logistic models offers effective information about regional crop status, overcoming the limitation of model in regional application. Moreover, the ground crop truth was profitably considered by using oncemeasured observations as the drive of the yield forecasting model. Another point worth emphasizing is that the subsequent consequences, after undertaking necessary agronomic measures based on the yield forecasting results, can be assessed with just one observation as input again because the effect on the crop can be reflected by LST and measured biomass. All in all, LST as a key factor for characterizing field drought [52] provides an intuitive basis to determine the water shortage of crops in large regions. This offers a solid theoretical basis for the synergistic prediction of future crop drought and yield evaluation in combination using remote sensing technology.

In addition, to obtain a more robust estimate of maize yield, data fusion technology may be recommended to improve the spatio-temporal resolution of LST [40]. Unfortunately, this method is unavailable due to the scarce Landsat images caused by the cloud cover on most days in maize growing season in Changchun. Our attempt in the Jiefangzha sub-irrigation district indicated that the data fusion technology improved the performance of spatial variation of grain yield forecasting under available conditions of suitable Landsat images. It follows that high-resolution satellite imagery such as Sentinel-2 might be a further exploration tool for improving yield forecasting precision.

The values of *t*<sup>m</sup> in models of RDBA and RFBA are key input data, which can be obtained for different hydrological years by analysis of the local yearly rainfall. When the hydrological year of the current growing season is estimated, the N-logistic model and the NR-logistic model can be utilized with the corresponding value of *t*m. To obtain the values of *y*Dm and *y*Fm, the data of DBA and FBA should be collected in field at least once during the maize growing period. Furthermore, the growth patterns of DBA and FBA can be simulated when the models are set up and calibrated. HI, an empirical value describing the relationship between DBA and grain yield, offers an opportunity to evaluate grain yield. By combining the growth curves for DBA and FBA with the future market demands, maize can be flexibly harvested as silage or grain during the growing season.

Apparently, the early yield forecasting accuracy varies depending on the growth stages, which may be caused by many factors. Firstly, the retrieval of *t*<sup>m</sup> is pivotal, as mentioned above. Secondly, the quality of remote sensing images obtained over time varies slightly, which can introduce some uncertainty into the yield forecasting results. Thirdly, the date of acquiring DBA or FBA is particularly critical for yield forecasting accuracy. As shown in Tables 3 and 7, the optimal predicting date is clearly different in different areas. In Changchun, the optimal date at which the DBA provides more accurate yield forecasting is approximately 38 days (10 August) ahead of harvest. As for the Jiefangzha sub-irrigation district, the results on 26 August produced a better prediction of yield, relatively speaking. Furthermore, the latter is better than the former in statistical parameters. This phenomenon may be caused by a variety of factors. For instance, a rare downpour amounting to more than 160 mm of rain occurred in Changchun on 21 July 2017, which may destroy plants and influence yield forecasting results. In addition, the area of Changchun is larger than the Jiefangzha sub-irrigation district, which may have an impact on the results. Taking the three results into account (Tables 3, 6 and 7), it is suggested to forecast yield by using the field data (DBA or FBA) measured at the middle growth period (early August). Furthermore, it is necessary to determine the optimal date by taking into consideration multiple factors.

Another noteworthy point about the results presented here is that the field soil water content was sufficient or at least was not in water deficit in the research area. The FBA, RFBA, and silage yield may be impacted by the crop and soil water conditions. Future efforts to prove model generality should include examination of changes in the model parameters for different levels of plant and field soil moisture.
