## 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, Yp\({}_{0}\), Yg\({}_{0}\), and CYg\({}_{0}\) of summer maize over the NCP in the period 2010 to 2015. We have the following conclusions:  
1. The modified RS crop yield model reasonably estimated the Ya of summer maize over the NCP, but the model's accuracy was limited by input RS data.
2. Modeled Yp showed close relationships with site-level results given by CGMs in previous studies, which demonstrated that the proposed RS-based approach to estimate Yp was effective in modeling Yp over the NCP.  
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 (Yg\({}_{0}\)), was approximately 41% of Yg. However, not all Yg\({}_{0}\) could be filled by optimizing SDT because Yg\({}_{0}\) 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 Yg\({}_{0}\).  
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.  
The following are available online at [[https://www.mdpi.com/article/10.3390/rs13183582/s1](https://www.mdpi.com/article/10.3390/rs13183582/s1)]([https://www.mdpi.com/article/10.3390/rs13183582/s1](https://www.mdpi.com/article/10.3390/rs13183582/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 Yg\({}_{0}\) (a) and 5-km Yg\({}_{0}\) (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 Yp\({}_{0}\) 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.  
The authors declare no conflict of interest.  
The authors would like to show great appreciation to three anonymous reviewers for their valuable comments, the editor of \"Remote Sensing\" and the guest editor of \"Remote Sensing of Land Surface Phenology special issue\" for offering us this opportunity to submit our manuscript, and [PERSON] for the English language editing.  
The authors declare no conflict of interest.