**3. Results**

#### *3.1. Evaluating the Values of LST from MOD11A in Changchun*

The regional map of LST can be obtained by remote sensing images products— MOD11A1. Afterwards, the grain yield in an area might be estimated through the validated model and retrieval values. Due to cloud cover, there were some incomplete data in MOD11A1 images from 25 May to 21 September 2017. The kriging interpolation method was used to fill the gaps in data.

It is necessary to obtain high-quality input data for precise estimates of crop yield. Therefore, the accuracy of the MOD11A1-LST retrievals was evaluated by comparison against the Tc observed in situ by the CTMS system in experimental fields. Figure 5 (Figure S3) shows the linear regressions between the LST (time of passing territory: 11:30 a.m.) and Tc (measured at 11:30 a.m.) in same pixel (sample number is 58). The *R*<sup>2</sup> values here ranged from 0.714 to 0.828, which were a little lower than the results of [40] in Hetao irrigation district of Inner Mongolia Autonomous Region. Those values of LST fused from the Landsat 8 images (30 m) and MOD11A1 data (1 km) might have more precision in large irrigation districts. Regardless, the *R*<sup>2</sup> values near 0.8 indicate that the retrieved LST directly is reliable.

**Figure 5.** Regressions between the LST from MOD11A1 product and the observed Tc in field in 2017 (sample number = 58, only at local satellite transit time). (**a**) H1; (**b**) H2; (**c**) H3.

As earlier stated, independent variables (*t*canopy and *T*canopy) in corresponding logistic models are calculated by the daily average value of Tc. However, the retrieved LSTs from MOD11A1 represent instantaneous values in time of passing territory. There is a need to verify the feasibility of instantaneous LST values replacing daily average ones to determine *T*canopy, when Equation (4) or Equation (6) is used in area.

Here, the relative effective accumulated temperature, calculated by instantaneous LST values of MOD11A1 (*T*LST) at 11:30 a.m. and daily average values observed from the CTMS system, were compared during maize growth period (Figures Figure 6 and S4). The linear regression results of points indicated the strong agreement between instantaneous and daily average values to obtain *T*canopy (*R*<sup>2</sup> > 0.987). The high consistency (*RMSE* < 0.05) means that the normalized LSTs from MOD11A1 can be used directly as independent variable in models as a robust approximation for the normalized Tc (daily average values). The result highlights that the normalization method in Equations (4) and (6) can eliminate

the temporal-scale difference between measured daily average value and the instantaneous value inversed from remote sensing images of crop canopy temperature.

**Figure 6.** Regressions between the *T*LST calculated by the remote sensing instantaneous values at 11:30 a.m. (interpolation results) and daily average values (*T*canopy) observed from the CTMS system in 2017 (sample number = 116, with Supplemented Data). (**a**) H1; (**b**) H2; (**c**) H3.

To verify its accuracy in spatial scale, the LSTs from MOD11A1 over two days (coupled with the time of passing territory of Landsat 8) were resampled to 30 m spatial resolution. These values were used to compare with the inversed LSTs from Landsat 8 using the inversion method in the reference of [40]. The values map of *RE* between two kinds of LST are mostly between −10% and 10% (Figure 7). Such high accuracy indicated that the MOD11A1-LST was reliable to be used to simulate maize growth and estimate the forthcoming yield.

**Figure 7.** Maps of *RE* values of LST (30 m) between Landsat 8 and MOD11A1 resample products.

#### *3.2. Grain Yield Forecasting in Changchun*

3.2.1. Calibration Results Based on the Logistic Model of DBA

Achieving high-quality estimates of DBA is necessary to predict crop yield. Using the logistic model, all of the DBA changes were simulated based on the field observations from 2017–2019. The simulations with four kinds of effective accumulated temperatures ran well, with *R*<sup>2</sup> average values exceeding 0.95 for five plots (Figure 8a). Figure 8b shows the results of DBA simulating in 2017 of five plots by using *t*canopy as model input. Each curve is extremely consistent with the measured values, revealing that it is feasible to realize crop growth monitoring by utilizing the Tc.

**Figure 8.** The performance of the DBA simulation results based on the logistic models. (**a**) Average values of *R*<sup>2</sup> of DBA simulating at five plots based on the logistic model with four kinds of effective accumulated temperature in 2017, 2018, and 2019; (**b**) DBA simulating in five plots based on the logistic model with effective accumulated canopy temperature (*t*canopy) in 2017.

However, model parameters (*a*, *b*, and *k*) calibrated in different plots represent an obvious discrepancy, as shown in Figure 9, which provides the *CV* values for each parameter among five plots in different years. The *CV* values of *a* and *b* fluctuate significantly more than the *k* value. In addition, the *t*canopy-based coefficients present as more stable due to lower *CV* values. Apparently, it is still hard to select universal model coefficients that best-simulate regional DBA owing to the existing variation in different plots and years.

**Figure 9.** The *CV* values for each logistic model parameter (*a*, *b*, *k*) with four inputs (*t*20, *t*40, *t*air, *t*canopy) among five plots in 2017–2019.

## 3.2.2. Calibration Results Based on the N-Logistic Model of RDBA

To address this issue, the N-logistic model was employed with different relative effective accumulated temperatures for the raw data from all the plots in 2017, 2018, and 2019 separately. The simulations for 2018 show the RDBA changes with *T*20, *T*40, *T*air, and *T*canopy (Figure 10), in which high values of *R*<sup>2</sup> (>0.98) suggest that it is feasible to simulate crop growth with good accuracy in regions when the data are normalized.

**Figure 10.** Simulations of RDBA based on the N-logistic model with four inputs from all plots in 2018: (**a**) *T*20; (**b**) *T*40; (**c**) *T*air; (**d**) *T*canopy.

The calibrated results of the N-logistic model parameters with *T*20, *T*40, *T*air, and *T*canopy in 2017–2019 presented the inter-annual differences of the model parameters, in which the *CV* values of *A* and *K* were relatively lower (Table 1). The results for *T*canopy performed better than other variables with lower *CV* values, suggesting that it is a good indicator to include.

**Table 1.** Calibration results and inter-annual differences of the N-logistic model parameters with *T*20, *T*40, *T*air, and *T*canopy in 2017–2019.


3.2.3. Validation Results Based on the N-Logistic Model of RDBA

To account for the inter-annual gap in the parameters of the N-logistic models, the calibrated models above were validated by the field observations of the other two years to identify the ideal set of regional parameters. A summary of the statistical characters of the N-logistic models with *T*20, *T*40, *T*air, and *T*canopy is presented in Table 2.

For the calibrated models in 2017, the measured and predicted values were in better agreement in 2018 than in 2019 because of high values for *d* and *R*<sup>2</sup> and low values of *RMSE* in 2018. The validation results for 2018 models were better in 2017 than in 2019. Likewise, the validation results in 2017 were better than in 2018 for the calibrated models in 2019. A comparison of all of the validation results showed that the statistical characters performed best in the calibrated models in 2019, with lower *RMSE* and *RE* and higher *d* and *R*2.

For the simulations based on *T*canopy, there were no large differences compared with *T*20, *T*40, and *T*air (Table 2), suggesting that it is feasible to simulate RDBA during the growing season.


**Table 2.** Validation results of the N-logistic model of RDBA with *T*20, *T*40, *T*air, and *T*canopy between the simulated and observed data from five plots in 2017–2019.

3.2.4. Grain Yield Forecasting in Area by MOD11A1-LST Values

Based on the results above, the validated N-logistic model for 2019 in Table 1 was used to simulate the pattern of RDBA in Changchun with *T*canopy, which was supposed to equal the *T*LST derived by the daily LST from MOD11A1. The *y*Dm (DBA at harvest) was ascertained by incorporating at least once-measured DBA (*y*D) in field through the growing season, and final grain yield could be forecasted then by the HI map. Here, the data in 2017 were used as an example to calculate and simulate to compare due to the limitation of research conditions and field observations.

Figure 11 demonstrates the spatial grain yield forecasted based on the field monitoring DBA of three different days in the growth period. Assimilating the DBA observation on 16 July into the model, the forecasted final grain yield was approximately 9750–10,500 kg ha−<sup>1</sup> in most regions (Figure 11a). However, these values were 10,500–11,250 kg ha−<sup>1</sup> and 12,000 kg ha−<sup>1</sup> while assimilating the DBA observed on 10 August and 31 August (Figure 11b,c), respectively. As expected, assimilating closer to the harvest date enables the yield prediction to reach greater values, coinciding with the trend in crop growing.

**Figure 11.** Forecasting results of grain yield using the N-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.

These predicted results were compared with the measured maize grain yield from the reference of An [49], which provided an average value of grain yield of 11,364.3 kg ha−<sup>1</sup> in three subareas of Dehui, Jiutai, and Nongan (Table 3). Simulated average values in the same regions in Figure 11 were 10,126.2 kg ha−1, 10,885.35 kg ha−1, and 13,492.8 kg ha<sup>−</sup>1, with corresponding *RE* values of −10.89%, −4.21%, and 18.73%, respectively. In addition, the simulated results were 10,778.57 kg ha−1, 10,976.90 kg ha−1, and 13,501.05 kg ha−<sup>1</sup> based on the DBA values in three days at the experimental site, respectively. When such values were compared with the field yield observations (12,442.74 kg ha−<sup>1</sup> on average here), then the values of *RE* were −13.38%, −11.78%, and 8.51% (Table 3), correspondingly. The yield prediction results confirm that the forecasting would be more precise along with the acquisition date of once-measured DBA closer to the harvest date.

**Table 3.** Comparisons between the forecasted grain yields based on the field observations in different days and the measurements <sup>1</sup> in three subareas and experimental station.


<sup>1</sup> Sample numbers in experimental station and three subareas are 13 and 30, respectively. <sup>2</sup> The data were measured on 2017/9/17. <sup>3</sup> The data were measured on 2017/10/1.

It is significant for the accuracy of estimated results to choose the sampling time of DBA when the N-logistic model is used to estimate the grain yield in regions. In theory, the closer sampling time is to harvest time, the more accurate the yield estimate is. However, from the viewpoint of practical application, it is preferable to estimate grain yield early in the growth stage so as to promptly adjust the irrigation and agronomic management according to the estimated results.
