# Retrieval of Internal Solitary Wave Amplitude in Shallow Water by Tandem Spaceborne SAR

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Brief Description of the Experiment

#### 2.2. Processing of the Spaceborne SAR Data and Extraction of ISW Characteristics

#### 2.3. CTD Data and WOA13 V2 Data

^{−1}smaller than that of our in situ measurements. The difference between WOA13 V2 climatological data and in situ measurements may be due to the impacts of weekly synoptic weather events and seasonally/yearly climate signals on the water column condition in shallow water regions. Given the free availability of WOA13 V2 data and the similarity between the WOA13 V2 and the in situ measured buoyancy frequency profile, we also applied the proposed method to derive amplitude by using the WOA13 V2 data in the study area, which is then compared with the derived amplitude by using the in situ stratification data.

#### 2.4. The Conventional Method of ISW Amplitude Estimation Based on the Classic KdV Equation in a Continuously Stratified Ocean Model

#### 2.5. The Proposed Method of ISW Amplitude Estimation Based on the eKdV Equation in a Two-Layer Ocean Model

## 3. Results and Analysis

#### 3.1. The Derived ISW Amplitude Using the Conventional Method

#### 3.2. The Derived ISW Amplitude Using the Proposed Method

## 4. Discussion

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Bathymetric map of southeastern Hainan Island and its adjacent area. The synthetic aperture radar (SAR) image coverages are indicated in the orange dashed line box (GF-3) and the purple box (TS-X). The two locations S1 and S2 where conductivity–temperature–pressure (CTD) measurements were taken are marked by red dots.

**Figure 2.**A portion of (

**a**) the GF-3 SAR image acquired at 22:43 UTC on 10 June 2017 and (

**b**) a TS-X image acquired at 22:32 UTC on 10 June 2017. The yellow arrows superimposed on the GF-3 sub-image show the ERA5 reanalysis sea surface wind vectors (hourly available at 0.25 degree grids) at 23:00 UTC on 10 June 2017.

**Figure 3.**Variations in the pixel backscattering intensity values (averaged and smoothed NRCS) along the transect AA’ corresponding to the red line in Figure 2a.

**Figure 4.**Mean background oceanic profiles of (

**a**) density and (

**b**) buoyancy frequency from CTD casts of S1 (109.8190°E, 18.1596°N) and S2 (109.9268°E, 18.1167°N).

**Figure 5.**Background profiles of (

**a**) density and (

**b**) buoyancy frequency in June obtained from the monthly WOA13 V2 dataset.

**Figure 6.**An example plot of the eKdV solitary wave in SAR images for $A=-1$, $B=0$, $C=0$,$\text{}\gamma =1$, and $b=0.5$.

**Figure 7.**Curve fittings of the theoretical model (Equation (11)) (the black line) to the pixel observation intensity value (red point) of the soliton $\text{}L1$ along transect AA’ in Figure 2a.

**Figure 8.**Curve fittings of the theoretical model (Equation (24)) (the black line) to the pixel observation intensity value (red point) of the soliton $L1$ along transect AA’ in Figure 2a.

SAR | Acquisition Time (UTC) and Date | Imaging Mode | Resolution (m) | Incidence Angle (°) | Polarization |
---|---|---|---|---|---|

TS-X | 22:32 10 June 2017 | ScanSAR | 36 | 34.59–48.75 | VV^{1} |

GF-3 | 22:43 10 June 2017 | Standard stripmap | 8 | 15.23–26.57 | VV-VH^{1} |

^{1}V and H are the vertical and horizontal polarization of the SAR signal, respectively. The first letter denotes polarization of the transmitting signal. The second letter represents polarization of the receiving signal.

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**MDPI and ACS Style**

Jia, T.; Liang, J.; Li, X.-M.; Fan, K.
Retrieval of Internal Solitary Wave Amplitude in Shallow Water by Tandem Spaceborne SAR. *Remote Sens.* **2019**, *11*, 1706.
https://doi.org/10.3390/rs11141706

**AMA Style**

Jia T, Liang J, Li X-M, Fan K.
Retrieval of Internal Solitary Wave Amplitude in Shallow Water by Tandem Spaceborne SAR. *Remote Sensing*. 2019; 11(14):1706.
https://doi.org/10.3390/rs11141706

**Chicago/Turabian Style**

Jia, Tong, Jianjun Liang, Xiao-Ming Li, and Kaiguo Fan.
2019. "Retrieval of Internal Solitary Wave Amplitude in Shallow Water by Tandem Spaceborne SAR" *Remote Sensing* 11, no. 14: 1706.
https://doi.org/10.3390/rs11141706