*3.2. Modeled Yp*

The Yp of summer maize over the NCP was estimated using the RS-based method presented in Section 2.3.4. Yp estimated for each year in the period 2010 to 2015 was averaged over time (Figure 6a). Results show that Yp estimated in this study has a tight correlation (R = 0.81, RMSD = 0.87 t hm−2) with that estimated using a calibrated APSIM-Maize model at 10 agricultural meteorological (AM) sites from existing studies (Figure 6c). The result demonstrates that the performance of the developed approach in estimating Yp is comparable to that of a calibrated CGM. However, Yp values from the two methods were not the same (Figure 6c). Regardless of the differences in formulations between the two methods, Yp in this study represented the period 2010 to 2015, which is different from the data we used for comparisons in Figure 6.

Our results show that the mean annual Yp in the period 2010 to 2015 ranged between 9 and 16 t hm−<sup>2</sup> over the study region with a regional value of 11.99 t hm−2. Mean annual Yp over the study region generally increased from southwest to northeast. The northeast of Shandong Province had the highest Yp, whereas the lowest Yp appeared in the southeast of Henan province.

**Figure 4.** Maps of modeled Ya of summer maize in 2010 (**a**), 2011 (**b**), 2012 (**c**), 2013 (**g**), 2014 (**h**), and 2015 (**i**); and the pixel-level frequency distribution (FD) of pixel level values in 2010 (**d**), 2011 (**e**), 2012 (**f**), 2013 (**j**), 2014 (**k**), and 2015 (**l**). The scatter plot represents a comparison between modeled yield and reference yield on a prefecture-level, the modeled yield on a prefecture-level is the average of yield values of all pixels within a prefecture-level district, and each scatter plot has 44 samples; the solid line in each scatter plot represents the "1:1 line." The value ranges in the legend are right-closed and left-open.

**Figure 5.** Modeled maize yields vs. reference values on a prefecture-level for pooled data (**a**) and mean annual data (**b**) in the period 2010 to 2015; R, N, and RMSD denote correlation, sample size, and root mean standard deviation, respectively; the error bar represents the standard deviation of multi-year data.

**Figure 6.** The map (**a**) and frequency distribution (**b**) of mean annual modeled Yp of summer maize over the period 2010 to 2015, and the modeled Yp of 10 agricultural meteorological (AM) sites vs. the simulations of corresponding sites from Wang, Wang, Yin, Feng and Zhang [11] (**c**). The value ranges in the legend of panel (**a**) are right-closed and left-open. Yp data from Wang, Wang, Yin, Feng and Zhang [11] represent the average of annual Yp in the period 1982 to 2005 for Linyi, 1982 to 2008 for Zibo and Laiyang, and 1982 to 2009 for the remaining sites.

#### *3.3. Yg and the Contribution of Suboptimum SDT to Yg*

Modeled regional Ya and potential yield limited by suboptimal SDT (Yp0) and Yp in the period 2010 to 2015 are presented in Table 1 and Figure 7a. The ratio of Yg to Yp (Yg/Yp), the ratio of Ya to Yp (Ya/Yp), Yg caused by suboptimal SDT (Yg0), and the contribution of suboptimal SDT to Yg (CYg0) computed on the basis of Ya, Yp0, and Yp are also presented in Table 1 and Figure 7b. The spatial variations in annual mean Ya, Yg, Yg/Yp, Yp0, Yg0, and *C*Yg0 are shown in Figure 8. Results show that large gaps (Ygs) remained between Ya and Yp on a regional scale or at a specific location over the NCP. Most areas of the study region had Yg values greater than 3 t hm−2, and high Yp values were mainly distributed in the north and northeast (Figure 8b). Yg of approximately 99% of the study areas accounted for more than 30% of local Yp (Figure 8c). Annual regional Yg of summer maize in NCP ranged in 4.9–6.4 t hm−<sup>2</sup> with a mean value of 5.4 t hm−2, accounting for approximately 45% of the mean annual regional Yp (Table 1 and Figure 8). As shown in Table 1 and Figure 7, considerable proportions of Yg were induced by suboptimum SDT. An estimated 80% of the study areas, Yg0 ranged from 1 to 4 t hm−<sup>2</sup> (Figure 8e). Yg0 also contributed to more than 20% of Yg in ~85% of the study areas. Regional Yg0 in each year ranged from 1.4 to 2.2 t hm−2, accounting for 29–42% of the annual regional Yg. The annual average of regional Yg0 contributes to 35% of annual averaged regional Yg in 2010–2015 (Table 1). The analyses above demonstrate that large Yg remained in summer maize croplands over the NCP, and the values of Yg varied in space and could be considerably reduced by optimizing the SDT.

**Table 1.** Ya, potential yield limited by suboptimal SDT (Yp0), Yp, Yg, ratio of Yg to Yp (Yg/Yp), ratio of Ya to Yp (Ya/Yp), Yg caused by suboptimal SDT (Yg0), and contribution of suboptimal SDT to Yg (CYg0) in the period 2010 to 2015 for the entire NCP a.


a Values of Ya, Yp, and Yp0 were computed on the basis of the actual distribution of maize cultivation areas in each year, and Yg/Yp, Ya/Yp, and CYg0 were computed using the regional statistics.

**Figure 7.** Annual and the average of the annual regional Yg0, Yp0–Ya, and Ya (**a**), and proportions of regional Yg0, Yp0–Ya, and Ya in regional Yp (**b**) in the period 2010 to 2015.

**Figure 8.** Maps of simulated mean annual Ya (**a**), Yg (**b**), the ratio of Yg to Yp (Yg/Yp) (**c**), potential yield limited by suboptimum SDT (Yp0) (**g**), Yg induced by suboptimum SDT(Yg0) (**h**), and the contribution of suboptimum SDT to Yg (CYg0) (**i**), with a 5 km resolution in 2010–2015; and the frequency distribution (FD) of pixel-level values of Ya (**d**), Yg (**e**), Yg/Yp (**f**), Yp0 (**j**), Yg0 (**k**), and CYg0 (**l**). The value ranges in the legends are right-closed and left-open. Annual 1 km Ya, Yp0, and Yp were aggregated to 5 km and then averaged in time to derive the mean annual Ya, Yp0, and Yp. Yg and Yg/Yp were derived from the 5 km Ya and Yp, and Yg0 and CYg0 were derived from the 5 km Yp0, Yg, and Yp. Each 5 km grid represents all 1 km cropland pixels inside the grid.
