## 6 Conclusions  
The paper developed an empirical model to invert both moisture content \(mv\) and surface roughness \(Hrms\) based on the database simulated by CIEM. In this study, the effects of the surface roughness \(Hrms\), empirical correlation length \(lopt\), and soil moisture \(mv\) on the backscattering coefficient using CIEM simulations were discussed. The relationship of backscattering coefficient \(\sigma\), \(Hrms\) and soil moisture \(mv\) was used to invert the soil moisture and avoid the actual measurement error of correlation length \(l\).  
The main results of this work are summarized below:  
(1) When the incidence angle varied from 33.5\({}^{\circ}\) to 26.3\({}^{\circ}\), R\({}^{2}\) of the retrieved and measured soil moisture values decreased from 0.67 to 0.57, and RMSE increased from 2.53% to 5.4%. When the incidence angle varied from 33.5\({}^{\circ}\) to 26.3\({}^{\circ}\), R\({}^{2}\) of the retrieved and measured \(Hrms\) decreased from 0.64 to 0.51, and RMSE increased from 0.33 to 0.4 cm. The results show that there is good consistency between simulated and measured data, but the inversion accuracy of soil moisture is higher than that of the surface roughness. Thus, using \(Hrms\) and the empirical correlation length \(lopt\) as the roughness parameters in the simulations is sufficient to invert the soil moisture and \(Hrms\);  
(2) The empirical model had favorable validity when the incidence angle was 33.5\({}^{\circ}\) and 26.3\({}^{\circ}\) at the C-band, but the accuracy was higher when the incidence angle was 33.5\({}^{\circ}\);  
(3) It is valid to invert soil moisture and \(Hrms\) based on CIEM, which uses an empirical correlation length \(lopt\) as proposed by [PERSON], which avoids the actual measurement error of the correlation length and improves the inversion accuracy.  
In summary, using \(Hrms\) and the calibration parameter \(lopt\) as the roughness parameters in CIEM is sufficient to invert the soil moisture and soil \(Hrms\).  
However, the computation of incidence angles in CIEM depends on the derivation and verification of the model because of the limited measured data. Therefore, a new incidence angle handling method will be studied. There is a dependence on the research area about the empirical model. In the future, we will attempt to develop a new calibrated advanced integral equation model to optimize the empirical model coefficients, so that the accuracy of soil moisture retrieval can be improved as much as possible.  
[PERSON] was involved in all parts of the study, including conceptualization, methodology, software, investigation, visualization, original draft preparation, reviewing, editing, and discussion of the results. [PERSON] was mainly involved in supervision and validation. [PERSON] was mainly the guidance of the paper revision. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China under Grant Nos. 41971279 and 41901401, and by the Fundamental Research Funds for the Central Universities under Grant No. 0009-2014G2270012.  
The data set was provided by the National Tibetan Plateau Data Center ([[http://data.tpdc.ac.cn](http://data.tpdc.ac.cn)]([http://data.tpdc.ac.cn](http://data.tpdc.ac.cn))). We sincerely appreciate the Editor and Reviewers for reviewing our manuscript and providing valuable and constructive suggestions and comments, which have greatly helped us to improve the technical quality and presentation of our manuscript.  
The authors declare no conflict of interest. The funders had no role in the design of the study, the collection, analyses, or interpretation of data, the writing of the manuscript, or the decision to publish the results.