**5. Conclusions**

The knowledge of how field managements contribute to Yg can help improve crop yield. In this study, we modified a process-based RS crop yield model for simulating Ya and proposed a new approach based on the modified model to quantifying Yp and the contribution of suboptimum SDT to Yg over a broad region. The above methods were used to estimate Ya, Yp, Yg, Yp0, Yg0, and CYg0 of summer maize over the NCP in the period 2010 to 2015. We have the following conclusions:


3. Large gaps, Ygs, remained between Ya and Yp of summer maize over the NCP and suboptimum SDT, which considerably contributed to Yg; regional Yg over the NCP in the period 2010 to 2015 was 5.0 t hm−2, and the Yg, which accounted for suboptimum SDT (Yg0), was approximately 41% of Yg. However, not all Yg0 could be filled by optimizing SDT because Yg0 was also affected by non-persistent factors. Thus, studies on small regions with higher-resolution RS data are required to decompose the persistent portion from Yg0.

PRYM–Maize's robust performance under extreme weather conditions, such as drought and heatwaves, will need to be improved in the future. In addition, it is necessary to improve the performance of the RS-based method in estimating Yp within a specific region in conjunction with finer-resolution data or a pixel downscaling method.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/2072-429 2/13/18/3582/s1, Figure S1: The diagram for calculating Small yield gap (SYg) and Large yield gap (LYg) in ranking and non-ranking rasters, Figure S2: 1-km pixels that were continuously cropped with summer maize in 2010–2015 over the NCP, Figure S3: Persistent factor percentage (PFP) based on 1-km Yg0 (a) and 5-km Yg0 (b), and a comparison between 1-km PFP and 5-km PFP over space (c). The value intervals in the legends of panel (a) and (b) are right-closed and left-open. PFPSYg denotes the PFP value calculated in terms of Yg of croplands grouped in small Yg as defined in Farmaha, Lobell, Boone [25] (Reference [25] is cited in the supplementary materials) or illustrated in Supplementary Text S2. In this study, PFP was calculated for each pixel using surrounding pixels within a buffer of 50 km. But not all pixels within the buffer were used, only pixels meet the criteria (see Section 2.3.4—Step 4) for computing Yp from Yp0 were kept. Figure S4: Modeled yield potential (Yp) vs. modeled farmers' yield penitential (Ypf), Table S1: Values of coefficients for calculating maize respiration and dry matter allocation.

**Author Contributions:** S.Z.: Methodology, writing—original draft preparation, writing—review and editing, investigation, formal analysis; Y.B.: Conceptualization, methodology, data curation, writing—review and editing; J.Z.: Writing—review and editing, supervision, project administration. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Shandong Provincial Natural Science Foundation (grant number ZR2020QD016), National Natural Science Foundation of China (grant number 41901342, 31571565, 31671585), "Taishan Scholar" Project of Shandong Province (grant number TSXZ201712), Key Basic Research Project of Shandong Natural Science Foundation of China (grant number ZR2017ZB0422), National Key Research and Development Program of China (grant number 2016YFD0300101), and CAS Strategic Priority Research Program (grant number XDA19030402).

**Acknowledgments:** The authors would like to show grea<sup>t</sup> appreciation to three anonymous reviewers for their valuable comments, the editor of "Remote Sensing" and the gues<sup>t</sup> editor of "Remote Sensing of Land Surface Phenology special issue" for offering us this opportunity to submit our manuscript, and Rufino O for the English language editing.

**Conflicts of Interest:** The authors declare no conflict of interest.
