# Sea Surface Monostatic and Bistatic EM Scattering Using SSA-1 and UAVSAR Data: Numerical Evaluation and Comparison Using Different Sea Spectra

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## Abstract

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## 1. Introduction

_{0}or NRCS, normalized radar cross-section) from sea clutter is of critical importance. Thus, it is required to develop accurate (theoretical or empirical) models to predict the radar scattering coefficient of the sea background.

## 2. Sea Spectrum

#### 2.1. Omnidirectional Part of Sea Spectra

_{10}) are 5 m/s, 10 m/s and 15 m/s, respectively. For E-spectrum and H-spectrum, the simulations are performed for an inverse wave age of 0.84, corresponding to a fully-developed sea. In Figure 1a, Figure 2a and Figure 3a, one can observe that different spectral models have similar behaviors. For microwave scattering from the rough sea surface, the primary contribution of the scattering is from the small-scale Bragg resonant waves. A common scatterometer typically operates at a moderate incident angle between about 20° and 60°. To better exhibit the differences between the various sea spectra in the small scale range, Figure 1b, Figure 2b and Figure 3b present the sea spectra that accounts for Bragg scattering for incident angles between about 20° and 60° in the C band, corresponding to the curves within the rectangles of Figure 1a, Figure 2a and Figure 3a. Significant discrepancies can be observed among these the spectral models in this range. Moreover, in Figure 1b, Figure 2b and Figure 3b, the effects of wind speed on different spectral models are also different. The F-spectrum presents almost the same as the P-spectrum since the underlying formulations for the two spectra are identical for this range. Additionally, the spectral energies of the F-spectrum and P-spectrum are larger than other spectra in this range.

#### 2.2. Angular Spreading Function

#### 2.3. Slope Variation

_{12.5}is the wind speed at 12.5 m height above sea surface. In the following, the RMS slopes evaluated based on spectral models are compared with the Cox and Munk model.

#### 2.4. Autocorrelation Function

## 3. Models for Scattering Coefficient Estimation

#### 3.1. The First-Order Small Slope Approximation (SSA-1)

_{0}correspond to the polarizations of scattered and incident waves, respectively. $\alpha {\alpha}_{0}\in \left\{\mathrm{HH},\mathrm{HV},\mathrm{VH},\mathrm{VV}\right\}$, where H denotes the horizontal polarization and V denotes the vertical polarization. ${k}_{0}$ and $k$ are horizontal projections of the vector of incident and scattered waves, respectively. ${q}_{0}$ and ${q}_{k}$ are the vertical projections of the incident and scattered wave vectors, respectively.

_{0}(·) denotes the Bessel function of the first kind of zero-order. $M=k\sqrt{{\left(\mathrm{sin}{\theta}_{s}\mathrm{cos}{\varphi}_{s}-\mathrm{sin}{\theta}_{i}\mathrm{cos}{\varphi}_{i}\right)}^{2}+{\left(\mathrm{sin}{\theta}_{s}\mathrm{sin}{\varphi}_{s}-\mathrm{sin}{\theta}_{i}\mathrm{sin}{\varphi}_{i}\right)}^{2}}$. θ

_{i}and θ

_{s}represent the incident and the scattered angles. $\rho \left(r\right)$ is the autocorrelation function, ${\varphi}_{i}$ and ${\varphi}_{s}$ denote incident and scattered azimuth angles. More details about the derivations can be found in Appendix A.

#### 3.2. Empirical Model CMOD5 and PR (Polarization Ratio) Model

## 4. Numerical Simulation and Discussion

#### 4.1. Scattering from the Sea Surface in the Monostatic Configuration

#### 4.1.1. Evaluation with UAVSAR Data in the L Band

#### 4.1.2. Evaluation with CMOD5

#### Incident Angle Variations

_{i}= 0°~20°). In the following, numerical simulations are compared with KA for the specular region and CMOD5 for the moderate region. Here, only the case for U

_{10}= 10 m/s is presented and discussed in detail, and similar situations and conclusions can be obtained for U

_{10}= 5 m/s and U

_{10}= 15 m/s.

_{i}= 0°~20°). For the moderate region (θ

_{i}= 20°~60°), the curves of the E-, H-, R-, and A-spectra exhibit similar results. As for Figure 10b, a similar phenomenon with VV polarization can be observed in the case of the HH polarization in the small incident angle range. Physically, the impacts caused by the polarization effect on the scattering coefficient are very small near the specular region. For the moderate region in the HH polarized channel, it seems that all the models underestimate the scattering coefficient. It is difficult to find a curve that matches well with the empirical model in all incident angle ranges.

#### Wind Speed and Direction Variations

_{i}= 18° are presented in Figure 15. For VV polarization, as observed in Figure 11, the R-spectrum cannot provide a good estimation when the incident angle is smaller than 30°. Therefore, a large difference can be observed between the Romeiser curve and CMOD5 curve in Figure 15a. With respect to θ

_{i}= 40° and θ

_{i}= 58°, the influences of wind speed on Efouhaily, Hwang, Apel, and CMOD5 curves are similar.

_{10}= 10 m/s. As illustrated in Figure 16, Figure 17 and Figure 18, all the curves have their maximum value in both upwind and downwind directions and their minimum at the crosswind direction. This behavior has been verified by many experimental measurements. Significant differences can be observed among the fluctuations (or the difference between peak and valley value) of different curves. These differences are caused by Δ(k) ratios plotted in Figure 4. As for the empirical model, it can be observed that the fluctuation along with wind direction increases with incident angle, while, for approximate results, the increases of fluctuations caused by the incident angle are smaller than CMOD5. It is not easy to find a curve that matches well with the empirical model in all cases. For VV polarization, the R-spectrum matches well with CMOD5 when the incident angle equals 40° and 58° in all wind directions.

_{10}= 5 m/s and U

_{10}= 15 m/s. The fluctuations of CMOD5 under different wind directions are highly dependent on wind speed. None of the spectra could provide accurate predictions for all wind speed cases. For the case of U

_{10}= 5 m/s, the P-spectrum predicts the NRCS well for the HH polarization and θ

_{i}= 58°. The R-spectrum predicts the NRCS well for the VV polarization and θ

_{i}= 58°. For the case of U

_{10}= 15 m/s, the E-spectrum predicts the NRCS well, both for the HH and VV polarizations for θ

_{i}= 18°. The P-spectrum predicts the NRCS well for the HH polarization and θ

_{i}= 40°. The R-spectrum predicts the NRCS well for the VV polarization and θ

_{i}= 40°.

#### 4.2. Scattering from Sea Surface Observed in Bistatic Configuration

#### 4.2.1. Scattering Angle Variation

#### 4.2.2. Scattering Azimuth Angle Variation

## 5. Conclusions and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{i}and θ

_{s}denote incident and scattered angles.

_{0}(·) denotes the Bessel function of the first kind of zero order. Substituting Equations (A7) and (A8) into Equation (A5), the scattering coefficient can be expressed as [20]:

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**Figure 1.**Omnidirectional sea spectra for U

_{10}= 5 m/s. (

**a**) Full range. (

**b**) Bragg scattering wavenumber range in the C band with an incident angle θ

_{i}= 20°~60°.

**Figure 2.**Omnidirectional sea spectra for U

_{10}= 10 m/s. (

**a**) Full range. (

**b**) Bragg scattering wavenumber range in the C band with θ

_{i}= 20°~60°.

**Figure 3.**Omnidirectional sea spectra for U

_{10}= 15 m/s. (

**a**) Full range. (

**b**) Bragg scattering wavenumber range in the C band with θ

_{i}= 20°~60°.

**Figure 4.**Δ(k) ratios given by different authors: (

**a**) U

_{10}= 5 m/s; (

**b**) U

_{10}= 10 m/s; and (

**c**) U

_{10}= 15 m/s.

**Figure 5.**Angular spreading functions given by different authors, k = 135 rad/m: (

**a**) U

_{10}= 5 m/s; (

**b**) U

_{10}= 10 m/s; and (

**c**) U

_{10}= 15 m/s.

**Figure 6.**RMS slopes inferred from spectral and models Cox and Munk model. (

**a**) In the upwind direction. (

**b**) In the crosswind direction.

**Figure 7.**Omnidirectional normalized autocorrelation functions. (

**a**) U

_{10}= 5 m/s; (

**b**) U

_{10}= 10 m/s; and (

**c**) U

_{10}= 15 m/s.

**Figure 10.**NRCSs estimated in relationships to incident angle. U

_{10}= 10 m/s, $\varphi =0\xb0$. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 11.**NRCSs estimated in relationships to incident angle. U

_{10}= 10 m/s, $\varphi =90\xb0$. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 12.**NRCSs estimated in relationship to the wind speed. θ

_{i}= 18°, $\varphi =0\xb0$. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 13.**NRCSs estimated in relationship to the wind speed. θ

_{i}= 40°, $\varphi =0\xb0$. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 14.**NRCSs estimated in relationship to the wind speed. θ

_{i}= 58°, $\varphi =0\xb0$. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 15.**NRCSs estimated in relationship to the wind speed. θ

_{i}= 18°, $\varphi =90\xb0$. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 16.**NRCSs estimated in relationship to the wind direction. U

_{10}= 10 m/s, θ

_{i}= 18°. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 17.**NRCSs estimated in relationship to the wind direction. U

_{10}= 10 m/s, θ

_{i}= 40°. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 18.**NRCSs estimated in relationship to the wind direction. U

_{10}= 10 m/s, θ

_{i}= 58°. (

**a**) VV polarization. (

**b**) HH polarization.

**Figure 20.**NRCSs estimated based on different sea spectra as a function of the scattering angle. U

_{10}= 10 m/s, upwind. (

**a**) VV polarization; (

**b**) HH polarization.

**Figure 21.**NRCSs estimated based on the different sea spectra as functions of the scattering azimuth angle. U

_{10}= 10 m/s. (

**a**) VV polarization; and (

**b**) HH polarization.

Case | Data ID | Time of Acquisition | Incident Angle (°) | Wind Speed U_{10} (m/s) | Wind Direction (°) |
---|---|---|---|---|---|

(a) | 14010 | 20:42 UTC 23 June 2010 | 22–65 | 2.5–5 | 115–126 |

(b) | 32010 | 21:08 UTC 23 June 2010 | 22–65 | 2.5–5 | 115–126 |

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**MDPI and ACS Style**

Zheng, H.; Khenchaf, A.; Wang, Y.; Ghanmi, H.; Zhang, Y.; Zhao, C.
Sea Surface Monostatic and Bistatic EM Scattering Using SSA-1 and UAVSAR Data: Numerical Evaluation and Comparison Using Different Sea Spectra. *Remote Sens.* **2018**, *10*, 1084.
https://doi.org/10.3390/rs10071084

**AMA Style**

Zheng H, Khenchaf A, Wang Y, Ghanmi H, Zhang Y, Zhao C.
Sea Surface Monostatic and Bistatic EM Scattering Using SSA-1 and UAVSAR Data: Numerical Evaluation and Comparison Using Different Sea Spectra. *Remote Sensing*. 2018; 10(7):1084.
https://doi.org/10.3390/rs10071084

**Chicago/Turabian Style**

Zheng, Honglei, Ali Khenchaf, Yunhua Wang, Helmi Ghanmi, Yanmin Zhang, and Chaofang Zhao.
2018. "Sea Surface Monostatic and Bistatic EM Scattering Using SSA-1 and UAVSAR Data: Numerical Evaluation and Comparison Using Different Sea Spectra" *Remote Sensing* 10, no. 7: 1084.
https://doi.org/10.3390/rs10071084