We have estimated soil moisture (SM) by using circular horizontal polarization backscattering coefficient (σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document}), differences of circular vertical and horizontal σo(σRVo-σRHo)\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}} \, (\sigma ^{\mathrm{o}}_{\mathrm{RV}} {-} \sigma ^{\mathrm{o}}_{\mathrm{RH}})$$\end{document} from FRS-1 data of Radar Imaging Satellite (RISAT-1) and surface roughness in terms of RMS height (RMSheight\documentclass[12pt]{minimal}
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\begin{document}$${\hbox {RMS}}_{\mathrm{height}}$$\end{document}). We examined the performance of FRS-1 in retrieving SM under wheat crop at tillering stage. Results revealed that it is possible to develop a good semi-empirical model (SEM) to estimate SM of the upper soil layer using RISAT-1 SAR data rather than using existing empirical model based on only single parameter, i.e., σo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}$$\end{document}. Near surface SM measurements were related to σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document}, σRVo-σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RV}} {-} \sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document} derived using 5.35 GHz (C-band) image of RISAT-1 and RMSheight\documentclass[12pt]{minimal}
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\begin{document}$${\hbox {RMS}}_{\mathrm{height}}$$\end{document}. The roughness component derived in terms of RMSheight\documentclass[12pt]{minimal}
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\begin{document}$${\hbox {RMS}}_{\mathrm{height}}$$\end{document} showed a good positive correlation with σRVo-σRHo(R2=0.65)\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RV}} {-} \sigma ^{\mathrm{o}}_{\mathrm{RH}} \, (R^{2} = 0.65)$$\end{document}. By considering all the major influencing factors (σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document}, σRVo-σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RV}} {-} \sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document}, and RMSheight\documentclass[12pt]{minimal}
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\begin{document}$${\hbox {RMS}}_{\mathrm{height}}$$\end{document}), an SEM was developed where SM (volumetric) predicted values depend on σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document}, σRVo-σRHo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}_{\mathrm{RV}} {-} \sigma ^{\mathrm{o}}_{\mathrm{RH}}$$\end{document}, and RMSheight\documentclass[12pt]{minimal}
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\begin{document}$${\hbox {RMS}}_{\mathrm{height}}$$\end{document}. This SEM showed R2\documentclass[12pt]{minimal}
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\begin{document}$$R^{2}$$\end{document} of 0.87 and adjusted R2\documentclass[12pt]{minimal}
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\begin{document}$$R^{2}$$\end{document} of 0.85, multiple R=0.94 and with standard error of 0.05 at 95% confidence level. Validation of the SM derived from semi-empirical model with observed measurement (SMObserved\documentclass[12pt]{minimal}
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\begin{document}$${\hbox {SM}}_{\mathrm{Observed}}$$\end{document}) showed root mean square error (RMSE) = 0.06, relative-RMSE (R-RMSE) = 0.18, mean absolute error (MAE) = 0.04, normalized RMSE (NRMSE) = 0.17, Nash–Sutcliffe efficiency (NSE) = 0.91 (≈1\documentclass[12pt]{minimal}
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\begin{document}$${\approx } 1$$\end{document}), index of agreement (d) = 1, coefficient of determination (R2)=0.87\documentclass[12pt]{minimal}
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\begin{document}$$(R^{2}) = 0.87$$\end{document}, mean bias error (MBE) = 0.04, standard error of estimate (SEE) = 0.10, volume error (VE) = 0.15, variance of the distribution of differences (Sd2)=0.004\documentclass[12pt]{minimal}
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\begin{document}$$({\hbox {S}}_{\mathrm{d}}^{2}) = 0.004$$\end{document}. The developed SEM showed better performance in estimating SM than Topp empirical model which is based only on σo\documentclass[12pt]{minimal}
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\begin{document}$$\sigma ^{\mathrm{o}}$$\end{document}. By using the developed SEM, top soil SM can be estimated with low mean absolute percent error (MAPE) = 1.39 and can be used for operational applications.
