## 5 Conclusions  
In this study, we integrated multi-source remote sensing data, improved the ESV accounting framework of PFEs based on physical ecological processes, and conducted a study on the estimation of the ESV of PFEs in Tianjin in 2019. (1) The fusion of multi-source remote sensing data can replace statistical data, accurately obtain evaluation model  
Figure 6: Correlation between ESV and Influencing Factors. NESV is the net ESV of the PFE; Yield is the yield of rice; Tem\({}_{7}\) and Tem\({}_{8}\) are the average temperatures in July and August, respectively; Pre is the total rainfall during the rice growing season; ET is the total evapotranspiration in the rice growing season.  
parameters, enhance the credibility of evaluation results, and enable spatial mapping of ESV of PFEs at the provincial scale at medium-high spatial resolution. (2) The net ESV of PFEs in Tianjin in 2019 was RMB 29.68 \(\times\) 10\({}^{8}\), accounting for 0.21% of GDP, and the average ESV per unit area was RMB 5.47 \(\times\) 10\({}^{4}\)/ha. (3) The value of PFE regulating services is 11.4 times higher than the value of products, and the value of climate regulation accounts for 61.27% of the positive service value, validating the outstanding ecological role of PFE. (4) The total net ESV of Baodi District was RMB 16.85 \(\times\) 10\({}^{8}\), which was higher than that of other districts, and the net ESV per unit area shows significant spatial clustering, with 56.9% and 41.1% for hot spots (high-value ESV) and cold spots (low-value ESV), respectively. In this study, we realized a pixel-based ESV accounting of PFEs based on physical ecological processes, demonstrating the potential of multi-source remote sensing data in this ESV accounting framework, and provided a reference for using ESV accounting research based on physical ecological processes. Furthermore, our research finding not only provides data support for agricultural ecological compensation and agricultural sustainable development policy formulation, but also provides a methodology for evaluating the impact of land use change on ESV.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/su14159466/s1](https://www.mdpi.com/article/10.3390/su14159466/s1)]([https://www.mdpi.com/article/10.3390/su14159466/s1](https://www.mdpi.com/article/10.3390/su14159466/s1)), Supplementary Table S1: List of parameter values for the model in this study case.  
Conceptualization, T.H., K.W. and W.H.; methodology, T.H., K.W. and W.H.; formal analysis, T.H., K.W. and W.H.; investigation, Y.L. and Y.Y.; resources, Z.L. and Y.Y.; writing--original draft preparation, T.H.; writing--review and editing, T.H.; visualization, T.H.; supervision, K.W. and W.H.; project administration, K.W.; funding acquisition, K.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Plan Program (grant no. 2019 YFE0125300).  
Not applicable.  
Data Availability Statement: Data are available from the authors upon reasonable request as the data need further use.  
We appreciate the critical and constructive comments from three anonymous reviewers and thank all editors that participated in the revision process.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.