# Scattering Properties of Non-Gaussian Ocean Surface with the SSA Model Applied to GNSS-R

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Geometry

#### 2.3. Polarization Synthesis

## 3. Scattering of Non-Gaussian Ocean Surface

#### 3.1. Scattering Model

#### 3.2. Derivation of Non-Gaussian Statistics

#### 3.3. L-Band Forward Scattering Coefficient

## 4. Results

#### 4.1. The Effect of Observation Angle on BRCS

#### 4.2. The Effect of Ocean Wind on NBRCS

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The Elfouhaily non-directional spectrum in the wind speed range of 3–18 m/s. K is the wavenumber corresponding to 1.57 GHz.

**Figure 3.**Trends in cutoff wavenumber and sea surface mean square height with wind speed. Blue dashed line indicates the mean square height ${\sigma}_{z}^{2}$. Red solid line indicates the cutoff wavenumber ${K}_{c}$.

**Figure 4.**Normalized correlation functions for different ocean wind. (

**a**) ${U}_{10}$ = 5 m/s. (

**b**) ${U}_{10}$ = 15 m/s.

**Figure 5.**Comparison of skewness, deviated peakedness, and normalized correlation functions of height for $\varphi ={0}^{\circ}$ and for different wind speed. (

**a**) ${U}_{10}$ = 5 m/s. (

**b**) ${U}_{10}$ = 15 m/s.

**Figure 6.**Comparison of fully polarization non-Gaussian NBRCS and Gaussian NBRCS with specular incidence angle ${\theta}_{i}$, upwind $\varphi ={0}^{\circ}$. (

**a**) ${U}_{10}$ = 5 m/s. (

**b**) ${U}_{10}$ = 15 m/s.

**Figure 8.**Comparison of fully polarization non-Gaussian BRCS and Gaussian NBRCS with specular incidence angle ${\theta}_{s}$. (

**a**) ${\theta}_{i}$ = ${30}^{\circ}$, ${U}_{10}$ = 5 m/s, $\varphi ={90}^{\circ}$ (

**b**) ${\theta}_{i}$ = ${30}^{\circ}$, ${U}_{10}$ = 15 m/s, $\varphi ={90}^{\circ}$ (

**c**) ${\theta}_{i}$ = ${50}^{\circ}$, ${U}_{10}$ = 5 m/s, $\varphi ={0}^{\circ}$ (

**d**) ${\theta}_{i}$ = ${50}^{\circ}$, ${U}_{10}$ = 15 m/s, $\varphi ={0}^{\circ}$.

**Figure 9.**Comparison of non-Gaussian NBRCS and Gaussian NBRCS with wind direction. (

**a**) $SSA-{\sigma}_{RL}^{0}$, ${\theta}_{i}={\theta}_{s}={30}^{\circ}$ (

**b**) $SSA-{\sigma}_{RR}^{0}$, ${\theta}_{i}={\theta}_{s}={30}^{\circ}$ (

**c**) $non-Gaussian\phantom{\rule{3.33333pt}{0ex}}KA-{\sigma}_{RL}^{0}$, ${\theta}_{i}={\theta}_{s}={30}^{\circ}$.

**Figure 11.**Comparison of non-Gaussian, Gaussian NBRCS, and CYGNSS data for wind speed in different wind direction. The wind direction range is (

**a**) $\varphi ={0}^{\circ}$ (

**b**) $\varphi ={30}^{\circ}$ (

**c**) $\varphi ={45}^{\circ}$ (

**d**) $\varphi ={60}^{\circ}$ (

**e**) $\varphi ={90}^{\circ}$.

**Figure 13.**Comparison of non-Gaussian, Gaussian NBRCS, and CYGNSS NBRCS (number of matches = 25,681). (

**a**) Non-Gaussian NBRCS (

**b**) Gaussian NBRCS.

**Figure 14.**Comparison of fully polarization non-Gaussian BRCS in fully bistatic geometry ${\theta}_{i}$ = ${40}^{\circ}$, ${U}_{10}$ = 10 m/s. (

**a**) ${\varphi}_{s}$ = ${30}^{\circ}$, ${\theta}_{s}$ = ${20}^{\circ}$ (

**b**) ${\varphi}_{s}$ = ${30}^{\circ}$, ${\theta}_{s}$ = ${60}^{\circ}$ (

**c**) ${\varphi}_{s}$ = ${60}^{\circ}$, ${\theta}_{s}$ = ${20}^{\circ}$ (

**d**) ${\varphi}_{s}$ = ${60}^{\circ}$, ${\theta}_{s}$ = ${60}^{\circ}$.

**Figure 15.**Comparison of non-Gaussian NBRCS in fully bistatic geometry with scattering azimuth angle. ${\theta}_{i}={40}^{\circ}$, ${U}_{10}$ = 10 m/s, $\varphi ={0}^{\circ}$. (

**a**) ${\theta}_{s}={20}^{\circ}$ (

**b**) ${\theta}_{s}={60}^{\circ}$.

**Figure 16.**Comparison of non-Gaussian NBRCS in fully bistatic geometry with scattering angle. ${\theta}_{i}={40}^{\circ}$, ${U}_{10}$ = 10 m/s. (

**a**) ${\varphi}_{s}={30}^{\circ}$ (

**b**) ${\varphi}_{s}={60}^{\circ}$.

Wind Direction $\mathit{\varphi}$ | $\mathit{RMSE}$ | R | $\mathit{Bias}$ | Number of Matches | |||
---|---|---|---|---|---|---|---|

Non-Gaussian SSA | Gaussian SSA | Non-Gaussian SSA | Gaussian SSA | Non-Gaussian SSA | Gaussian SSA | ||

${0}^{\circ}$ | 1.92 | 2.37 | 0.60 | 0.59 | −1.68 | −2.11 | 307 |

${30}^{\circ}$ | 1.34 | 1.73 | 0.57 | 0.55 | −0.92 | −1.44 | 274 |

${45}^{\circ}$ | 1.22 | 1.85 | 0.65 | 0.64 | −0.62 | −1.56 | 362 |

${60}^{\circ}$ | 1.43 | 1.50 | 0.66 | 0.59 | 0.40 | −0.72 | 326 |

${90}^{\circ}$ | 2.11 | 1.65 | 0.72 | 0.64 | 1.66 | 0.43 | 372 |

Total | 1.60 | 1.82 | 0.64 | 0.60 | −0.23 | −1.08 | 1642 |

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**MDPI and ACS Style**

Sun, W.; Wang, X.; Han, B.; Meng, D.; Wan, W.
Scattering Properties of Non-Gaussian Ocean Surface with the SSA Model Applied to GNSS-R. *Remote Sens.* **2023**, *15*, 3526.
https://doi.org/10.3390/rs15143526

**AMA Style**

Sun W, Wang X, Han B, Meng D, Wan W.
Scattering Properties of Non-Gaussian Ocean Surface with the SSA Model Applied to GNSS-R. *Remote Sensing*. 2023; 15(14):3526.
https://doi.org/10.3390/rs15143526

**Chicago/Turabian Style**

Sun, Weichen, Xiaochen Wang, Bing Han, Dadi Meng, and Wei Wan.
2023. "Scattering Properties of Non-Gaussian Ocean Surface with the SSA Model Applied to GNSS-R" *Remote Sensing* 15, no. 14: 3526.
https://doi.org/10.3390/rs15143526