
During February and March
$ 2013 $ , an HF radar named Ocean State Measuring and Analyzing Radar, type S (OSMARS) was installed on the west coast of the Taiwan Strait to monitor the sea state. The geographic map is illustrated in Fig. 9. The location of the OSMARS was$ {23.749}^{\circ } $ N,$ {117.597}^{\circ } $ E. The OSMARS is a compact, broadbeam alldigital HF radar system. It adopts a linear FMICW waveform with a center frequency of 13 MHz and a bandwidth of 60 kHz. The range resolution is$ 2.5 $ km correspondingly. The specific radar parameters used for this test are listed in Table 1. The reliability and accuracy in current and wave measurement of the OSMARS have been validated in (Lai et al., 2017a, b). Meanwhile, three insitu waverider buoys, namely, A ($ {23.783}^{\circ } $ N,$ {118.033}^{\circ } $ E), C ($ {23.67}^{\circ } $ N,$ {117.67}^{\circ } $ E) and E ($ {23.417}^{\circ } $ N,$ {117.917}^{\circ } $ E) acquired wind data every halfhour. The distances between the radar station and the three buoys were$ 44 $ km,$ 10.5 $ km, and$ 48 $ km, respectively. During the experiment, the wind predominantly blew from the northeast with speeds that varied between 0 and 16 m/s, as shown in Fig. 10. Buoy E had a relatively high wind speed and a relatively stable wind direction, while Buoy C had a relatively low wind speed. In general, the experimental conditions are ideal because the winds are stable and the effects of wind fetch (infinite wind fetch for northeasterly wind) and water depth (above half of the Bragg wave length as shown in Fig. 9) are negligible.Figure 9. Map of the HF radar deployed on the Fujian coast of the Taiwan Strait. Radar station is marked by the star named XIAN, and the three buoys are marked by dots.
Center frequency/MHz 13 Bandwidth/kHz 60 Transmit antenna monopole Receive antenna crossloop/monopole Sweep period/s 0.38 Average power/W 100 Range resolution/km 2.5 Coherent integration time/min 6.5 Normal direction/(°) 100 Transmitted waveform FMICW pulses Technique of azimuthal resolution direction finding Table 1. Radar parameters of the OSMARS
We built the models based on the radar data collected from February 1 to 28, 2013. To ensure good quality, data with SNR
$ < $ 5 dB are removed as are any data with radial current velocity above the expected maximum (1 m/s) for this region (Lai et al., 2017). The spectral region on the side with a stronger Bragg peak is chosen to estimate the DOA by Multiple Signal Classification (MUSIC) directionfinding algorithm (Schmidt, 1986) using the ideal antenna pattern. Figure 11 shows the times of positive and negative firstorder peaks in each cell for 6 202 frames of data. From Fig. 11, we can see that most DOAs are near the antenna normal direction (100° from the north). The number of viable positive firstorder peaks is more than twice that of the negative ones because the values of the positive FSP are always larger than those of the negative ones. This means that the negative peaks from the southwest are lower in amplitude than the positive peaks from the northwest of each range annulus. To avoid the power difference caused by the distortion of antenna pattern in different directions, the FSP model is only based on the positive FSPs of the monopoleantenna. 
In this section, the actual HF radar propagation attenuation is calculated from onemonth radar data. Figure 12a shows the maximum FSP in different wind speeds and ranges. The maximum FSP is assumed to come from the upwind direction and the effect of WSF can be ignored. From Fig. 12a, we can see that the radar echoes seem to reach the maximum when the wind speed is about 10 m/s. Subsequently, the maximum FSP decreases with the increased wind speed, especially in the far range cell. It results from the increased sea surface roughness. Figure 12b shows the maximum FSP loss (relative to the maximum FSP in range cell 2) under different wind speeds. The maximum FSP loss is the total propagation attenuation and seems to be attenuated linearly with the distance when the wind speed is between 3 m/s and 12 m/s. With the increase of the range cell, the differences between the attenuation under different wind speeds increase gradually. In range cell 23, the attenuation difference between the maximum and the minimum wind speed is up to about 13 dB, which is consistent with the theoretical calculation. Figure 13 shows both the theoretical and the radar extracted propagation attenuation. Basically, the difference is less than 5 dB. We apply the theoretical propagation attenuation model to compensate for the propagation attenuation.

The principle of HF radar wind direction inversion is based on the firstorder Bragg ratios as Eq. (5) shows. The WSF is dependent on wind speed through the parameter
$ s $ . Its compensation is an important part of the FSP attenuation compensation. Hence, we extracted a WSF model by establishing a parameter$ s $ model based on one month’s radar data with the aid of buoy wind data bywhere
$ s $ is the parameter of cosine model as shown in Eq. (4),$ {R}_{{\rm{B}}} $ is the Bragg ratio, and$ {\theta }_{0} $ ,$ {\theta }_{\omega } $ are the DOA and the buoy wind direction, respectively. In Fig. 14, the radar parameter$ s $ is calculated under different buoy wind speeds. When the wind speed is less than$ 13 $ m/s, the parameter$ s $ increases with the growth of wind speed and it decreases when wind speed is greater than$ 13 $ m/s. Compared with$ s $ from the literature (Hasselmann et al., 1980), the variation of radar extracted$ s $ with wind speed is flatter as a function of wind speed. According to this distribution, a secondorder linear fitting is used to fit this distribution, and we get the relationship that$s=0.010\;6{u}^{2}+0.256\;4 $ $ u+1.884\;5$ , where u is the wind speed. The correlation coefficient (R) and root mean square error (RMSE) are 0.76 and 0.21, respectively. As mentioned above, the wind speed in the WSF model is approximated by the wind speed in the previous range cell. 
We apply the secondorder scattering in the initial range cell to obtain the preliminary reference wind speed. The preliminary wind speed can be used to determine whether the firstorder peak is saturated and to initialize the wind vector mapping process when the buoy data are missing. Figure 15a shows the time series of C buoy wind speed and the secondorder spectrum integration at range cell 2. These two variables show a strong correlation with a R of
$ 0.85 $ . We plot it in a scatter plot and fit it by a firstorder linear fitting which has an RMSE of 2.12 m/s and a R of 0.88. The expression of the linear fitting is$ u=0.003\;7*P_s $ $ 27.57 $ where$ P_{\rm{s}} $ is the secondorder spectrum integration and$ u $ is the wind speed. According to the PiersonMoskowitz (PM) nondirectional wave spectrum (Pierson and Moskowitz, 1964) and the radar echo spectrum (Barrick, 1977), a firstorder linear relationship between wind speed and secondorder spectrum integration can also be developed:Figure 15. Wind speed and the secondorder integration versus time (a); scatter plot and linear fitting result (b).
where
$ H_{{\rm{s}}} $ is the significant wave height and$ W\left(\omega \right) $ is a weighting function. Although this relationship is an approximate and depends on a number of assumptions, it demonstrates the reason for the linear relationship between the secondorder integration and the wind speed. It can be seen that the correlation between the two is better at high sea state and worse at low sea state for the absence of secondorder spectrum. 
The FSP model is the key part for wind speed estimation. After the energy compensation for the FSP, the final wind speed can be extracted directly by the FSP model. To avoid the uncertainty caused by WSF, we track the maximum FSP of the monopole at the initial range cell. Because the model is based on the radar echoes at the initial range cell (about
$ 5 $ km from the radar station), the added attenuation of FSP from the rough sea under different wind speeds can be ignored as Fig. 4a shows. According to Eq. (2), the Bragg spectral value is a sample of the directional wave height spectrum at the Bragg frequency. The directional wave height spectrum can be modeled as the product of the nondirectional wave height spectrum and the WSF as Eq. (3) illustrates, which means that the wind speed is closely related to the maximum FSP when the wind speed is below 13 m/s. Figure 16a shows the maximum FSP and the buoy wind speed in time series. To reduce the effect of noise, a fivepoint smoothing filter is applied to the time series of the maximum FSP. These two variables have a strong correlation with a R of 0.88. Their scatter plot shows a power distribution, and it fits the model asFigure 16. Wind speed and the maximum firstorder peak versus time (a); and scatter plot and fitting result (b).
where
$P_{\max} $ is the maximum FSP in dB and$ a $ ,$ b $ and$ c $ are constant parameters that are determined by the training data. The a, b and c are$ 1.096\times{10}^{7} $ , 29 and 119, respectively. The maximum FSP model can provide a good fit to the data with a R of 0.9 and an RMSE of 1.54 m/s as Fig. 16b shows. The fitting results of the model are better when the wind speed is in the range of 4 m/s to 13 m/s. The FSP and wind speed are more relevant at low sea state and irrelevant at high sea state for the saturation of the FSP.
Mapping wind by the firstorder Bragg scattering of broadbeam highfrequency radar
doi: 10.1007/s131310211752z
 Received Date: 20200928
 Accepted Date: 20201031

Key words:
 high frequency radar /
 firstorder Bragg peak /
 broadbeam /
 wind field /
 wind speed
Abstract: Mapping wind with HF radar is still a challenge. The existing secondorder spectrum based wind speed extraction method has the problems of short detection distances and low angular resolution for broadbeam HF radar. To solve these problems, we turn to the firstorder Bragg spectrum power and propose a space recursion method to map surface wind. One month of radar and buoy data are processed to build a wind spreading function model and a firstorder spectrum power model describing the relationship between the maximum of firstorder spectrum power and wind speed in different sea states. Based on the theoretical propagation attenuation model, the propagation attenuation is calculated approximately by the wind speed in the previous range cell to compensate for the firstorder spectrum in the current rangeazimuth cell. By using the compensated firstorder spectrum, the final wind speed is extracted in each cell. The firstorder spectrum and wind spreading function models are tested using one month of buoy data, which illustrates the applicability of the two models. The final wind vector map demonstrates the potential of the method.
Citation:  Yuming Zeng, Hao Zhou, Zhen Tian, Biyang Wen. Mapping wind by the firstorder Bragg scattering of broadbeam highfrequency radar[J]. Acta Oceanologica Sinica. doi: 10.1007/s131310211752z 