*2.5. Yield Forecasting*

When the model was validated to obtain suitable parameters, namely the RDBA and *y*Dm, the RFBA and *y*Fm could be simulated by Equations (4) and (6) with field monitoring data once at least, respectively, when combined with the map of the independent variable (LST) inversed from remote sensing images. Grain yield (*Y*) will be forecasted by the DBA in harvest period and HI as follows:

$$Y = \mathsf{HI} \times y\_{\mathsf{Dom}} \tag{7}$$

where *Y* is grain yield; HI is the weight of a harvested product as a percentage of the total plant weight of a crop; and *y*Dm is the DBA at harvest time as mentioned above. The values of maize HI in some subareas in Changchun [49] and the measured ones in the experimental station (Table S2) were used to obtain the HI map (Figure S2) in Changchun by the kriging interpolation method.

A flow chart of this approach using canopy temperature to forecast yield is shown in Figure 4. Firstly, the logistic model/R-logistic model was used to prove the possibility to simulate DBA/FBA based on Tc. Secondly, the logistic model/R-Logistic model was changed to N-logistic model/NR-logistic model by the data normalization method for regional biomass (RDBA/RFBA) estimation. Finally, the grain/silage yield can be forecasted using remote-sensing-derived LST and once-measured biomass (DBA/FBA) as inputs to the N-logistic model/NR-logistic model after obtaining the HI value. In Section 3, the grain/silage yield in Changchun would be forecasted using measured DBA on three dates (7/16, 8/10, and 8/31 in 2017), and the grain yield in Jiefangzha would be forecasted by once-measured DBA on four dates (7/6, 7/21, 8/4, and 8/26 in 2016). The independent variable for the N-logistic model and NR-logistic model, i.e., *T*canopy, was a scale factor for yield forecasting from point to area through the LST map from remote sensing images (*T*LST) in a large irrigation district.

**Figure 4.** Schematic of the approach for yield forecasting using crop canopy temperature. Notes: DBA is dry biomass accumulation, kg ha<sup>−</sup>1; FBA is fresh biomass accumulation, kg ha−1; RDBA is relative DBA; RFBA is relative FBA; *T*canopy represents relative effective accumulated temperature in canopy; LST is land surface temperature,◦C; *T*LST represents relative effective accumulative temperature calculated by LST; *y*Di is DBA in the maize growing season, kg ha<sup>−</sup>1; *y*Dm is DBA at harvest, kg ha<sup>−</sup>1; *y*Fi is the above-ground FBA in the maize growing season, kg ha−1; *y*Fm represents the maximum FBA, kg ha<sup>−</sup>1; HI is harvest index.

#### *2.6. Statistical Evaluation*

The index of model agreement (*d*), root mean square error (*RMSE*), relative error (*RE*), the coefficient of determination (*R*2), and the coefficient of variation (*CV*) were used to evaluate the models. Model accuracy increased as the values of *d* and *R*<sup>2</sup> approached 1.0, and the values of *RMSE* and *RE* decreased. Origin Pro 9.1 software was used to calculate and fit the data to the model. Statistical analyses were performed in Microsoft Excel 2013. The calculation formulas are listed in Equations (S1)–(S5).
