# Effective Surface Roughness Impact in Polarimetric GNSS-R Soil Moisture Retrievals
## 6 Conclusions  
This manuscript has presented different methodologies to estimate the effect of the surface roughness in polarimetric GNSS-R. Data from SMAP-R has been collocated to SMAP L3 enhanced dataset. Soil moisture, VOD, and static SMAP ancillary files such as DEMSTD or DEMSLPSTD, products derived from the DEM, have been used. A methodology to estimate the surface rms height using the coherent component, and the surface slope rms using the incoherent component have been presented and evaluated. First, a single-polarization approach has been implemented for all four possible polarizations, H, V, R, and L, and for coherent and incoherent components. The roughness product assuming coherent reflection has shown a large correlation with the roughness product estimated using incoherent reflection. The correlation between these roughness products and SMAP static DEM products have been evaluated. Potential soil moisture errors are analyzed for a given \(\sigma_{h}\) uncertainty of its half standard deviation. This shows errors on the order of 0.12 cm\({}^{3}\)/cm\({}^{3}\) for the V-polarization case, which presents its maximum polarimetric sensitivity at 40\({}^{\circ}\) of incidence angle. Additionally, a dual-polarization model has been presented using the ratio (or difference in dB) between either L-R and H-V components, named polarization decoupling. Results for the linear polarizations show that even with an uncertainty of 2-sigma when estimating the polarization decoupling for \(HV\) polarization. A linear model based on the SMAP-R surface reflectivity and SMAP VOD product is shown to be linearly dependent to the \(Q_{HV}\) parameter. Following this approach, a soil moisture product can be estimated with 2-sigma errors of \(\sim\)0.08 cm\({}^{3}\)/cm\({}^{3}\) for incidence angles close to 40\({}^{\circ}\). For the circular polarization case, it is found that the \(Q_{LR}\) parameter linearly correlates with VOD, and this can be used with a linear regression to estimate the polarization difference. In this case, if the RHCP component is strong enough, a soil moisture product with a 2-sigma error of \(\sim\) 0.08 cm\({}^{3}\)/cm\({}^{3}\) can be produced at virtually any incidence angle. Dual-polarization retrievals, where the ratio between H and V or L and R are used, allow for soil moisture retrieval without the need for absolute signal calibration. Hence, providing a more robust and independent soil moisture retrieval algorithm. Finally, the importance of choosing the proper antenna polarization configuration soil moisture retrieval using polarimetric GNSS-R signals is discussed, showing that synthetic RHCP/LHCP component can be retrieved by means of slightly higher directive H/Vantennas and using the Stokes parameter (as performed in this manuscript), and on such cases that the RHCP is masked under the receiver's noise floor, differential H/V algorithms could be used to retrieve soil moisture. Conceptualization, J.F.M.-M., N.R.-A., X.B.-L. and K.O. ; methodology, J.F.M.-M., N.R.-A. and X.B.-L.; software, J.F.M.-M., N.R.-A. and X.B.-L.; validation, J.F.M.-M., N.R.-A., X.B. [PERSON] and K.O. ; formal analysis, [PERSON], [PERSON], [PERSON] and K.O. ; investigation, [PERSON], [PERSON], [PERSON] and K.O. ; resources, K.O. ; data curation, [PERSON]-[PERSON]; writing--original draft preparation, [PERSON], [PERSON] and [PERSON]; writing--review and editing, [PERSON], [PERSON], [PERSON] and K.O. ; visualization, [PERSON]-[PERSON]; supervision, [PERSON] and K.O. ; project administration, [PERSON] and K.O. ; funding acquisition, [PERSON]-[PERSON], [PERSON] and K.O. All authors have read and agreed to the published version of the manuscript. This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The research was supported by NASA ROSES fund on R&A Hydrology & Weather from the Soil Moisture Active Passive (SMAP) project. (c) 2023. California Institute of Technology. Government sponsorship acknowledged.