# Analysis of Wave Breaking on Gaofen-3 and TerraSAR-X SAR Image and Its Effect on Wave Retrieval

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## Abstract

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## 1. Introduction

## 2. Datasets

#### 2.1. SAR Images and In Situ Data

#### 2.2. Hindcast Data

## 3. Methodology

#### 3.1. NP Estimation

#### 3.2. Radar Backscattering Model

_{0}is the wave number of microwave radar (i.e., ~5 cm for GF-3 and 3 cm for TS-X); θ is the radar incidence angle; ϕ is the satellite’s flight direction; and Sp and St are the Bragg wave-tilted slopes parallel and normal to the direction of the radar beam. ${\mathrm{B}}_{\mathrm{s}}$ is the Bragg scattering coefficient, which is evaluated as follows:

_{i}is the effective incidence angle, and ζ is the sea surface height modulated by the wave and current fields.

_{10}, to produce the wave spectrum E using the well-known wind-sea Joint North Sea Wave Project (JONSWAP) model [46], and to forward calculate the sea surface slopes together with the current. As revealed in [17], the co-polarized NRCS suffers saturation problems at high winds (i.e., >25 m/s), and the simulated Bragg resonant component in NRCS has poor results at such conditions.

#### 3.3. Wave Retrieval Algorithm

_{k}is the first-guess spectrum produced by the JONSWAP model; ${\overline{\mathrm{F}}}_{\mathrm{k}}$ is the SAR-derived wave spectrum obtained in the minimization process; ${\overline{\mathrm{S}}}_{\mathrm{k}}$ is the mapping SAR spectrum obtained using the wave spectrum; ${\mathrm{S}}_{\mathrm{k}}$ is the SAR original intensity spectrum; μ is the weight coefficient; and k is the wave number. The constant B is assumed to be 0.001 so as to ensure convergence of the iteration.

_{s}, which is employed for the division of the SAR intensity spectrum into a linear-mapped wind portion and a nonlinear-mapped swell portion [49]:

^{2}; V = 7600 m/s; R is the distance in the slant direction; U

_{10}is the wind speed; θ is the incidence angle; and φ is the angle of the wave propagation direction relative to the direction of the radar beam.

_{s}, the wave spectrum is initially produced by the JONSWAP, which is treated as a first-guess spectrum in Equation (16), and then, the wind-sea spectrum is inverted from the corresponding SAR portion after minimizing the cost function J. The swell spectrum is simply inverted from the linear-mapped SAR portion, in which the wave number k is less than k

_{s}, without considering the non-linear velocity bunching modulation. It was found that the RMSE of the SWH was about 0.5 m when using the PFSM algorithm for GF-3 [47] and TS-X [46] SAR images.

## 4. Results and Discussion

#### 4.1. Wind and Wave Retrieval

#### 4.2. NP Contribution in Dual-Polarized C-Band and X-Band SAR

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Forcing field | European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data at a 0.25° gird and a time interval of 1-h sea surface current data from HYbrid Coordinate Ocean Model (HYCOM) at a spatial resolution of 0.08° grid and a time interval of 3-h; and water depth data from the General Bathymetric Chart of the Oceans (GEBCO) having a spatial resolution of 0.01° grid |

Other settings | The bins ranged logarithmically between 0.04118 and 0.7186 at an interval of Δf/f = 0.1. The spatial propagation was characterized by 300 s time steps in both the longitudinal and latitudinal directions. |

Resolution | Significant wave height having at a 0.05° gird and temporal resolution of 30-min and the wave spectrum resolved into 24 regular azimuthal directions at a step of 15°. |

Parameterizations | The input/dissipation terms using switches ST2 and STAB2; the wave-wave interactions using the switch GMD |

## Appendix B

_{B}is the wave breaking parameter; g = 9.8 m/s

^{2}; v is the kinematic viscosity of air; u

_{*}is the air friction velocity; C

_{d}is the drag coefficient; U

_{10}is the drag coefficient; β is the wave age; and ${\omega}_{p}$ is the peak angular frequency of the wind-wave. Therefore, the whitecap coverage is conveniently calculated when the wind and wave parameters are known.

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**Figure 1.**Synthetic aperture radar (SAR) measured normalized radar cross sections (NRCSs) of (

**a**) a VV-polarized Gaofen-3 (GF-3) image acquired at 01:58 UTC on 5 May 2017 and (

**b**) a TerraSAR-X (TS-X) image acquired at 16:53 UTC on 3 August 2009. Note that the three buoys located in these images are marked by white crosses.

**Figure 2.**(

**a**) The European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA-5) wind map at 2:00 UTC on 5 May 2017; and (

**b**) The ERA-5 wind map at 17:00 UTC on 3 August 2009. The black rectangle denotes the spatial coverage of two images in Figure 1.

**Figure 3.**(

**a**) The HYbrid Coordinate Ocean Model (HYCOM) sea surface current map at 3:00 UTC on 5 May 2017; and (

**b**) The HYCOM sea surface current map at 18:00 UTC on 3 August 2009. The black rectangle denotes the spatial coverage of two images in Figure 1.

**Figure 4.**The significant wave height (SWH) maps at 09:00 UTC on 20 Sep 2021 from the (

**a**) ERA-5 and (

**b**) WAVEWATCH-III (WW3) data.

**Figure 5.**(

**a**) Validation of WW3-simulated SWHs against ERA-5 for SWHs of 0–4 m; and (

**b**) validation of WW3-simulated whitecap coverage against NDBC buoy data at wind speeds 0–18 m/s.

**Figure 7.**SAR-derived wind maps obtained (

**a**) using CSARMOD-GF from the GF-3 SAR image at 1:58 UTC on 5 May 2017, and (

**b**) using XMOD-2 from the TS-X image at 16:53 UTC on 3 August 2009.

**Figure 8.**The one-dimensional wave spectra obtained using the parameterized first-guess spectrum method (PFSM) scheme: (

**a**) results for a sub-scene of the GF-3 SAR image covering a buoyed area (ID: 46054); and (

**b**) results for a sub-scene on the TS-X image covering a buoyed area (ID: 51001).

**Figure 9.**Validation of SAR-derived SWH against simulation results of the WW3 model in terms of wind speeds between 0 and 25 m/s.

**Figure 10.**The composited NRCS map, including the Bragg resonant and N-P contribution: (

**a**) GF-3 image acquired at 01:58 UTC on 5 May 2017; (

**b**) TS-X image acquired at 16:53 UTC on 3 August 2009.

**Figure 11.**Comparison of composited NRCS with SAR-measured NRCS for wind speeds of 0 to 25 m/s. The blue and red marks illustrate the results for GF-3 and TS-X, respectively.

**Figure 12.**The relations between the ratio (${\mathsf{\sigma}}_{\mathrm{wb}}/{\mathsf{\sigma}}_{0}^{\mathrm{VV}}$ and ${\mathsf{\sigma}}_{\mathrm{wb}}/{\mathsf{\sigma}}_{0}^{\mathrm{HH}}$ ) and the (a,b) SAR-derived wind speed, (c,d) SAR-derived SWH, and (e,f) HYCOM current speed. The blue and red marks illustrate the results for GF-3 and TS-X, respectively.

**Figure 13.**Validation of the SAR-derived SWH against the simulation results of the WW3 model in terms of the whitecap coverage from the WW3 model. The color bar denotes the SAR-derived wind speed.

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## Share and Cite

**MDPI and ACS Style**

Zhong, R.; Shao, W.; Zhao, C.; Jiang, X.; Zuo, J.
Analysis of Wave Breaking on Gaofen-3 and TerraSAR-X SAR Image and Its Effect on Wave Retrieval. *Remote Sens.* **2023**, *15*, 574.
https://doi.org/10.3390/rs15030574

**AMA Style**

Zhong R, Shao W, Zhao C, Jiang X, Zuo J.
Analysis of Wave Breaking on Gaofen-3 and TerraSAR-X SAR Image and Its Effect on Wave Retrieval. *Remote Sensing*. 2023; 15(3):574.
https://doi.org/10.3390/rs15030574

**Chicago/Turabian Style**

Zhong, Ruozhu, Weizeng Shao, Chi Zhao, Xingwei Jiang, and Juncheng Zuo.
2023. "Analysis of Wave Breaking on Gaofen-3 and TerraSAR-X SAR Image and Its Effect on Wave Retrieval" *Remote Sensing* 15, no. 3: 574.
https://doi.org/10.3390/rs15030574