### I. Introduction

*in situ*measured ground-truth datasets. Finally, the new empirical model is verified with independent Sentinel-1 SAR data and the corresponding

*in situ*measured ground-truth data.

### II. Development of a Simple Model

*pq*-polarization,

*pq*-polarized backscattering coefficient of the underlying soil surface,

*A*

*and*

_{pq}*B*

*are unknown constants to be determined for*

_{pq}*pq*-polarization for a given frequency and a vegetation type.

*V*

_{1}and

*V*

_{2}are vegetation parameters, such as vegetation water content (VWC, kg/m

^{2}), biomass

*B*

*(kg/m*

_{m}^{2}), LAI (m

^{2}/m

^{2}), and normalized difference vegetation index (NDVI).

*B*

*(kg/m*

_{m}^{2}) among other parameters for the vegetation parameter

*V*. The transmissivity is

*a*

_{0},

*a*

_{1}, and

*a*

_{2}are constant parameters to be determined for a given frequency and

*pq*-polarized backscattering coefficient of the underlying soil surface.

*p*and

*q*are the co- and cross-polarized ratios,

*k*is the wave number,

*h*

*is the root mean square (RMS) surface height,*

_{rms}*Γ*

*is the reflectivity at the nadir direction*

_{o}*Γ*

*and*

_{v}*Γ*

*are Fresnel reflectivities for*

_{h}*v*- and

*h*-polarizations:

*Γ*

*= |(*

_{v}*ɛ*

_{r}*cosθ*–

*C*

_{1})/(

*ɛ*

_{r}*cosθ*+

*C*

_{1})|

^{2},

*Γ*

*= |(*

_{h}*cosθ*–

*C*

_{1})/(

*cosθ*+

*C*

_{1})|

^{2}with

*Γ*

*= |(*

_{h}*cosθ*–

*C*

_{1})/(

*cosθ*+

*C*

_{1})|

^{2}. The dielectric constant

*ɛ*

*can be obtained using empirical formulas in [14] for a given volumetric soil moisture content*

_{r}*m*

*(cm*

_{v}^{3}/cm

^{3}).

*θ*

*≤ 50°, mainly considering the operating modes of Sentinel-1 SAR and Radarsat-2. Because one of its main applications may be an inversion algorithm for soil moisture retrieval, the biomass range of 0 ≤*

_{i}*B*

*≤ 5 kg/m*

_{m}^{2}is primarily selected in this study, considering the validity regions of soil moisture retrieval for vegetation fields [13].

*B*

*≤ 5 kg/m*

_{m}^{2}with a step of

*B*

*, Δ*

_{m}*B*

*= 0.25 kg/m*

_{m}^{2}, at

*m*

*= 0.03, 0.08, 0.13, 0.18, 0.23, 0.28, and 0.33 cm*

_{v}^{3}/cm

^{3}, and at

*θ*

*= 35°.*

_{i}*a*

_{0},

*a*

_{1}, and

*a*

_{2}by comparing the modified RTM and the simplified WCM at each soil moisture condition. First, by comparing the backscatter from the underlying soil surface with the RTM and the corresponding term of the WCM, the values of the unknown constant

*a*

_{2}were obtained with the best fitting between the RTM and the WCM for various conditions. Second, the unknown constants

*a*

_{0}and

*a*

_{1}were also obtained by comparing between the RTM and the WCM for various conditions. Finally, the unknown constants

*a*

_{0},

*a*

_{1}, and

*a*

_{2}were fitted with the first-order linear polynomials for the soil moisture content

*m*

*.*

_{v}*a*

_{2}= 0.172 for VV-polarization at

*m*

*= 0.18 as an example. The estimated*

_{v}*a*

_{2}values are approximately 0.17 for all polarizations and moisture conditions.

*m*

*= 0.18 cm*

_{v}^{3}/cm

^{3}and

*θ*

*= 35°. For this fitting,*

_{i}*a*

_{0}and

*a*

_{1}are 0.0163 and 0.994 for VV-polarization, 0.0225 and 0.902 for HH-polarization, and 0.0164 and 0.759 for VH-polarization.

*a*

_{0}and

*a*

_{1}over the change of soil moisture is minimal for VV-polarization and maximal for VH-polarization. For example, the ratios of the constant

*a*

_{0}at

*m*

*= 0.33 cm*

_{v}^{3}/cm

^{3}to

*a*

_{0}at

*m*

*= 0.03 cm*

_{v}^{3}/cm

^{3}are about 1.02 for VV-polarization, 1.37 for HH-polarization, and 2.39 for VH-polarization. As an example, Fig. 3 shows the comparison between the estimated values and the best fitting line for the unknown constant

*a*

_{1}for VH-polarization. The best-fitting lines are given by

*a*

_{1 }

*= −0.66*

_{vh}*m*

*+ 0.89 for VH-polarization, as shown in Fig. 3. The other relationships between the unknown constants and the soil moisture content are*

_{v}*a*

_{0,}

*= 0.0013*

_{vv}*m*

*+ 0.0160 and*

_{v}*a*

_{1,}

*= −0.026*

_{vv}*m*

*+ 1.00 for VV-polarization,*

_{v}*a*

_{0,}

*= 0.024*

_{hh}*m*

*+ 0.0181 and*

_{v}*a*

_{1,}

*= −0.32*

_{hh}*m*

*+ 0.96 for HH-polarization, and*

_{v}*a*

_{0,}

*= 0.047*

_{vh}*m*

*+ 0.00814 for VH-polarization. The angular dependency of the direct vegetation layer backscatter term is mainly controlled by cosθ*

_{v}*in (4 ); therefore, the parameters are not sensitive to the incidence angle in a narrow range of incidence angles, 20° ≤*

_{i}*θ*

*≤ 50°.*

_{i}*pq*-polarized backscattering coefficient of the underlying soil surface

*h*

*, the volumetric soil moisture content*

_{rms}*m*

*, the biomass*

_{v}*B*

*, and the radar incidence angle. Therefore, this simple scattering model can be applied to retrieve the soil moisture content and the surface RMS height simultaneously from a dual-polarized SAR dataset for a given incidence angle at 5.4 GHz upon being informed of the vegetation biomass.*

_{m}### III. Verification of the New Simple Model

*m*

*= 0.18 cm*

_{v}^{3}/cm

^{3}.

*B*

*= 0.5 kg/m*

_{m}^{2}for VH-polarization, at

*B*

*= 3 kg/m*

_{m}^{2}for HH-polarization, and at

*B*

*= 3.8 kg/m*

_{m}^{2}for VV-polarization. It was also shown that the cross-polarized backscattering coefficient has a higher sensitivity to the vegetation biomass than co-polarization because the cross-polarized backscatter is significantly influenced by the multiple scattering effect [7], where the vegetation layer causes many different kinds of scatterings.

*θ*

*≤ 50°, as shown in Fig. 5.*

_{i}*in situ*measured groundtruth data. Fig. 6 shows the comparison between the Sentinel-1 SAR datasets and the new simple empirical model for rangelands in Bet Shemesh and Haifa in Israel.

^{2}and 0.43 kg/m

^{2}, the moisture contents were 0.24 cm

^{3}/cm

^{3}and 0.34 cm

^{3}/cm

^{3}, the surface RMS heights were 0.7 cm and 0.6 cm, and the incidence angles were 38.1° and 35.6° for the Bet Shemesh and Haifa sites, respectively. The empirical model again agrees quite well with the independent datasets of Sentinel-1 SAR. The new empirical scattering model is now proven to have good accuracy in predicting multipolarized backscattering coefficients of one-layered vegetation canopies at incidence angles of 20° ≤

*θ*

*≤ 50° at 5.4 GHz, although the model is very simple, with only four input parameters.*

_{i}### IV. Concluding Remarks

*in situ*measured ground-truth data.

*in situ*measured ground-truth data. It was found that the new empirical model agrees well with the experimental data as well as with the RTM. This new empirical model might be good for estimating the backscattering coefficients of one-layered vegetation fields at 5.4 GHz in the range of 20° ≤

*θ*

*≤ 50° for VV-, HH-, and VH-polarizations.*

_{i}