# Sea Surface Wind Measurement by Airborne Weather Radar Scanning in a Wide-Size Sector

^{1}

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## Abstract

**:**

## 1. Introduction

- (1)
- operational systems, providing continuous, global, or regional observations for forecasting, data assimilation, and model validation;
- (2)
- systems operating with higher temporal and spatial resolution during limited measurement campaigns in order to study the physical processes of wave generation and air/sea interaction.

_{w}consists in defining the principal maximum of a curve of the reflected signal intensity (azimuth of the principal maximum of the NRCS curve ${\mathsf{\psi}}_{{\mathsf{\sigma}}_{\mathrm{max}}^{\circ}}$),

## 2. Materials and Methods

#### 2.1. Airborne Weather Radar Functions and Applications

^{−4}, where λ is the radar wavelength. At the same time, the long-range weather mode is provided in the X-band much more effectively than in the Ku-band. In the ground-mapping mode, the AWR antenna has a wide cosecant-squared elevation beam. A horizontal dimension of the beam is narrow (2° to 6°), while the vertical dimension is relatively wide (10° to 30°). The beam sweeps in an azimuth sector (up to ±100°) [8,9,10]. The scan plane is horizontal because the antenna is stabilized (roll-and-pitch-stabilized). Those AWR features enhance its functionality for its use in the ground-mapping mode as a scatterometer for measuring the water surface backscattering signature and the wind vector over the water surface.

#### 2.2. Wind Vector Retrieval

_{a.v}and horizontal θ

_{a.h}planes (${\mathsf{\theta}}_{a.v}>{\mathsf{\theta}}_{a.h}$), as shown in Figure 1, periodically scan through an azimuth in a sector wider than ±90°, and let a delay selection be used to provide a necessary resolution in the vertical plane. Then, the beam scanning allows for the selection of a power backscattered by the underlying surface for a given incidence angle θ from various directions in a wide azimuth sector. Angular selection (by a narrow horizontal beamwidth) in the horizontal plane along with the delay selection provides angular resolutions in the azimuthal and vertical planes, Δα

_{b}and Δθ, respectively.

_{w}, and the angle between the up-wind direction and the aircraft course ψ be α. Furthermore, let the NRCS model function for medium incidence angles follow Equation (1). Since the selected cell is narrow enough in the vertical plane, the NRCS model function for medium incidence angles Equation (1) can be used without any correction in the wind measurement when the azimuth angular size of a cell is up to 15°–20° [11].

_{s}. NRCS samples obtained from the narrow sector and averaged over all measured values in that sector provide an appropriate NRCS value corresponding to the azimuth angle of the sector. The number of narrow sectors formed in the wide scanning sector equals $N={180}^{\circ}/\Delta {\mathsf{\alpha}}_{s}+1$. Thus, N NRCS values can be obtained from significantly different azimuth angles, and a system of N equations from Equation (1) can be written.

## 3. Results and Discussion

_{L}and an upper wind speed U

_{U}can be found using an averaged 180° azimuth NRSC value ${\mathsf{\sigma}}^{\circ}(U,\mathsf{\theta},\mathsf{\alpha},\Delta {\mathsf{\alpha}}_{w}={180}^{\circ})$ from the following equations:

_{1}and α

_{2}into equations for ${\mathsf{\sigma}}^{\circ}(U,\mathsf{\theta},\mathsf{\alpha}-{90}^{\circ})$ and ${\mathsf{\sigma}}^{\circ}(U,\mathsf{\theta},\mathsf{\alpha}+{90}^{\circ})$ of the system of equations. Finally, the wind direction can be retrieved from Equation (5).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

AWR | airborne weather radar |

NRCS | normalized radar cross section |

SAR | Synthetic Aperture Radar |

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**Figure 1.**Airborne weather radar (AWR) ground looking beam and selected cell geometry. V is the speed of flight; H is the aircraft altitude; θ is the incidence angle of the selected cell; ψ is the aircraft course; θ

_{a.v}is the beamwidth in the vertical plane; θ

_{a.h}is the beamwidth in the horizontal plane; Δα

_{b}is the angular resolution in the azimuthal plane; Δθ is the angular resolution in the vertical plane; ${\mathsf{\sigma}}^{\circ}(U,\mathsf{\theta},\mathsf{\alpha})$ is the current normalized radar cross section (NRCS) value.

**Figure 2.**Azimuth NRCS curve using Equation (1) at the incidence angle of 45°, “true” wind speed of 10 m/s and “true” up-wind direction of 0° (solid line); generated “measured” NRCS after the averaging of 1565 samples in a five-degree azimuth sector (red dots); and azimuth NRCS curve using Equation (1) corresponding to “measured” wind speed of 9.9718 m/s and up-wind direction of 358.7° retrieved from the azimuth sector of [−90°, 90°] (dashed line).

**Figure 3.**Azimuth NRCS curve using Equation (1) at the incidence angle of 45°, “true” wind speed of 10 m/s and “true” up-wind direction of 0° (solid line); generated “measured” NRCS after the averaging of 1565 samples in a five-degree azimuth sector (red dots); and azimuth NRCS curve using Equation (1) corresponding to “measured” wind speed of 10.0071 m/s and up-wind direction of 357.9° retrieved from the azimuth sector of [45°, 225°] (dashed line).

**Figure 4.**Azimuth NRCS curve using Equation (1) at the incidence angle of 45°, “true” wind speed of 10 m/s and “true” up-wind direction of 0° (solid line); generated “measured” NRCS after the averaging of 1565 samples in a five-degree azimuth sector (red dots); and azimuth NRCS curve using Equation (1) corresponding to “measured” wind speed of 9.9975 m/s and up-wind direction of 357.5° retrieved from the azimuth sector of [90°, 270°] (dashed line).

**Figure 5.**Azimuth NRCS curve using Equation (1) at the incidence angle of 45°, “true” wind speed of 10 m/s and “true” up-wind direction of 0° (solid line); generated “measured” NRCS with taking into account the instrumental noise of 0.2 dB after the averaging of 1565 samples in a five-degree azimuth sector (red dots); and azimuth NRCS curve using Equation (1) corresponding to “measured” wind speed of 9.994 m/s and up-wind direction of 357.9° retrieved from the azimuth sector of [−90°, 90°] (dashed line).

**Figure 6.**Azimuth NRCS curve by model Equation (1) at the incidence angle of 45°, “true” wind speed of 10 m/s and “true” up-wind direction of 0° (solid line); generated “measured” NRCS with taking into account the instrumental noise of 0.2 dB after the averaging of 1565 samples in a five-degree azimuth sector (red dots); and azimuth NRCS curve by model Equation (1) corresponding to “measured” wind speed of 10.0258 m/s and up-wind direction of 356.9° retrieved from the azimuth sector of [45°, 225°] (dashed line).

**Figure 7.**Azimuth NRCS curve using Equation (1) at the incidence angle of 45°, “true” wind speed of 10 m/s and “true” up-wind direction of 0° (solid line); generated “measured” NRCS with taking into account the instrumental noise of 0.2 dB after the averaging of 1565 samples in a five-degree azimuth sector (red dots); and azimuth NRCS curve using Equation (1) corresponding to “measured” wind speed of 10.0279 m/s and up-wind direction of 357.3° retrieved from the azimuth sector of [90°, 270°] (dashed line).

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**MDPI and ACS Style**

Nekrasov, A.; Khachaturian, A.; Veremyev, V.; Bogachev, M.
Sea Surface Wind Measurement by Airborne Weather Radar Scanning in a Wide-Size Sector. *Atmosphere* **2016**, *7*, 72.
https://doi.org/10.3390/atmos7050072

**AMA Style**

Nekrasov A, Khachaturian A, Veremyev V, Bogachev M.
Sea Surface Wind Measurement by Airborne Weather Radar Scanning in a Wide-Size Sector. *Atmosphere*. 2016; 7(5):72.
https://doi.org/10.3390/atmos7050072

**Chicago/Turabian Style**

Nekrasov, Alexey, Alena Khachaturian, Vladimir Veremyev, and Mikhail Bogachev.
2016. "Sea Surface Wind Measurement by Airborne Weather Radar Scanning in a Wide-Size Sector" *Atmosphere* 7, no. 5: 72.
https://doi.org/10.3390/atmos7050072