Sea Surface Wind Correction Using HF Ocean Radar and Its Impact on Coastal Wave Prediction
1. Introduction
Wind estimation and wave prediction are important for coastal oceanography and engineering, and practical applications such as ship navigation, marine construction, and fisheries. High-frequency (HF) ocean radar is a useful tool for measuring coastal ocean currents, and there have been numerous studies of coastal currents measured by HF radar. HF radar can also estimate ocean wave directional spectra by inversion (e.g., Hashimoto and Tokuda 1999; Hashimoto et al. 2003; Hisaki 1996, 2015, 2016a; Lukijanto et al. 2011; Wyatt 1990; Wyatt et al. 2011); however, these studies are very limited because a high signal-to-noise ratio (SNR) of Doppler spectra is required.
HF radar can estimate the sea surface wind direction from the first-order scattering by assuming that the wind direction is the same as the wave direction at the Bragg wave frequency (e.g., Fernandez et al. 1997; Heron and Prytz 2002; Huang et al. 2004, 2012; Chu et al. 2015), although there are differences between them (Hisaki 2002, 2007; Wyatt 2012). The position of the cyclone and atmospheric front can be detected from the HF radar–estimated wind direction (Heron and Rose 1986; Georges et al. 1993; Harlan and Georges 1997; Hisaki 2002). Other applications of only wind direction estimation to meteorology or oceanography are few.
Wind speed is critical for prediction of wave height. Wind direction is also crucial for wave-height prediction near coasts, such as for small islands and complex coastlines, because the fetch is sensitive to wind direction. It may be possible to improve wave prediction near coasts by considering the wind direction estimated from HF radar.
There have been previous studies on wind speed estimation from HF radar. There are three types of methods for estimating wind speed from HF radar. The first method is the estimation of wind-wave energy from the second-order scattering of Doppler spectra (e.g., Dexter and Theodoridis 1982; Heron et al. 1985; Green et al. 2009; Zeng et al. 2016). The advantage of this method is that calibration by other instruments is not required; the drawback is that a high signal-to-noise ratio is required to evaluate wind-wave energy from the second-order scattering of Doppler spectra, and that the contribution of the swell to wave energy must be separated.
The second method involves estimation of wind speed only from first-order scattering using the relationship between wind-wave energy and first-order scattering (Stewart and Barnum 1975; Shen et al. 2012; Kirincich 2016). This method has the advantage that the first-order scattering is robust to noise and that a high SNR is not required as in the first method; however, calibration using other instruments is required.
The third method uses multifrequency radar (Vesecky et al. 2004). Only first-order scattering is used for inferring vertical current shear in this method. However, the cost of a multifrequency radar system is higher than that of a single-frequency radar system, and the relationship between wind speed and vertical current shear is complicated.
Reanalysis wind data are readily available, and wave hindcasting is possible. The spatial resolution of reanalysis wind data is much coarser than that of HF radar–estimated wind and wave parameters. For example, the spatial resolution of National Centers for Environmental Prediction (NCEP) data is approximately 
The objectives of the paper are as follows. The first objective is to describe the method that corrects from the sea surface NCEP winds at low spatial resolution to those at higher spatial resolution using the HF radar. The second objective is to explore the impact of wind correction on wave prediction near the coast of a small island. This method is categorized as one of the second-type methods as described above, but it is easy to obtain wind data for calibration.
Many studies have developed methods to interpolate from HF radar–estimated radial velocities to total vectors on the grid points by the open boundary modal analysis method (e.g., Kaplan and Lekien 2007), or the variational method (e.g., Yaremchuk and Sentchev 2009). The present method is the first attempt to regrid sea surface wind vectors from the first-order scattering level. A method of correcting reanalysis wind data by assimilating HF radar surface currents has also been proposed (Lewis et al. 1998; Barth et al. 2011). The present method is much more simple, and the computer cost is much more lower than that required for the assimilation method.
In sections 2a and 2b the principle is reviewed and the method of estimating wind direction from HF radar is described. A new method for correcting sea surface winds is provided in section 2c. Another method for correcting sea surface winds is described in section 2d. The wind data, wave data, and Doppler spectra are documented in sections 2e and 2f. The wave model is described in section 2g. The results of the corrected winds are explained in section 3a. The comparisons of predicted waves are explored in section 3b. The results of the sensitivity of the wave prediction to the parameters used for correcting winds are presented in section 3c. The results of the other method are provided in section 3d. The conclusions are summarized and discussed in section 4.
2. Method
a. Basic principle
The wavenumber of the swell not generated locally is smaller than the Bragg wavenumber. No previous studies have detected the effect of the swell on the first-order Bragg scattering. It is valid to assume that the impact of nonlocally generated swell on the wind direction estimation by HF radar is small. In contrast, the swell associated with a sudden change in the wind direction affects the wind direction estimation by HF radar, because the wave direction at Bragg wavenumber 
b. Wind direction calculation from HF radar
The Doppler spectra from two radars are used for the analysis. If the ratios R of the two first-order Bragg peaks at a position are obtained from two radars, then we can evaluate 
The Doppler spectra are estimated on radial grids with centers at the radar positions. The wind directions are evaluated at the regular grid points in the 
The parameters 
The HF radar–estimated wind directions satisfying 
c. Wind vector correction from wind direction
d. Error-permitted wind direction method
The value of 
This method is called the error-permitted wind direction method (EPWDM). The EPWDM is similar to the least squares method of HF radar radial-velocity interpolation on the regular grid (e.g., Yaremchuk and Sentchev 2009).
e. Reanalysis wind data
The NCEP Climate Forecast System (CFS) reanalysis wind data are used for hindcasting (http://nomads.ncdc.noaa.gov/data/cfsr/). Hourly forecast data and six-hourly analysis data are used. The hourly forecast data are corrected. The errors of the forecasted wind vectors are evaluated from six-hourly analysis data and forecast data at 6-h intervals. The hourly errors are interpolated with respect to time from the six-hourly errors. The hourly forecast wind data are corrected from the interpolated errors. The spatial resolution of the NCEP CFS reanalysis wind data is approximately 
f. HF radar Doppler spectra
The period of analysis of Doppler spectra by HF radar is from 0000 local standard time (LST) 26 May (1500 UTC 25 May) to 1200 LST 2 July (0300 UTC July 2) in 2001. The observation is also described in Hisaki (2009, 2014). Figure 1a shows the observation area. The radar locations were A (
(a) HF radar observation area. HF wind–corrected area and the wave prediction area at fine spatial resolution (red box). Shown are radar positions A, and B, USW position U, and wind stations N and T. (b) Wave prediction area (blue box) at larger spatial resolution.
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
The 
An ultrasonic wave (USW) gauge is used to observe wave heights and periods. The position of the USW was 
g. Wave model
The configuration of the wave model to predict wave parameters is almost the same as that in Hisaki (2014). The main difference from Hisaki (2014) is the wind data. The objectively analyzed surface winds from the 12-hourly Japan Meteorological Agency (JMA) data were used in Hisaki (2014), whereas hourly NCEP CFS reanalysis wind data were used in the present study. The wave model is explained briefly. The energy balance is used to predict the wave spectrum F 
The wave spectra were predicted by the nested grid. The coarse grid area was from 
3. Results
a. Wind fields
Figure 2 shows an example of sea surface wind vectors (speeds and directions). The surface winds on the shallow reef, which is treated as land in the wave model, are not indicated in Fig. 2. Figure 2a shows winds 
(a) NCEP CFS sea surface wind vectors (
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
An atmospheric front in the area cannot be observed in the JMA synoptic weather chart during the period. The spatial variability of winds at the grid points for which the wind direction is estimated by the HF radar (color vectors) is large in Fig. 2a. The winds changed from southerly to southwesterly during the period, and this variability was due to the small-scale variability associated with the change. The variability of wind vectors also resulted from the HF radar–estimated wind direction error, which is taken into account in the EPWDM.
Figure 3 shows the hourly data acquisition rate of only the HF radar–estimated wind direction 
Hourly data acquisition rate of 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
The data acquisition rate of the dual radar is at most 50% (Fig. 3c). The rate is less than 4% at the USW point. The maximum data acquisition rate of the single or dual radar is approximately 85%. The rate is approximately 70% in the area around 
Figure 4 shows the time series of hourly wind vectors. Figure 4a and 4b show the time series of HF radar–corrected winds and NCEP reanalysis winds at the USW position, respectively. Figure 4c shows the time series of winds at the station on Okinawa Island. The position of the wind station was N (26.21°N, 127.69°E) in Fig. 1a, and the elevation of the station above sea level was 28 m. The elevation of the anemometer from the ground was 48 m. The wind speeds on land are smaller than those on sea, and the wind speed increases with increasing altitude. These time series of winds are similar to each other. The southerly winds are dominant during the analysis period. Fetch-limited conditions frequently occur at the USW position (Fig. 1). The wind directions changed significantly on 31 May, associated with passage of an atmospheric front.
(a) Time series of 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
Figure 5 shows comparisons between 
Comparisons of NCEP winds and HF radar–corrected winds from the EFWDM and for 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
Figure 5b shows the RMSD values of the wind directions of 
b. Comparison of predicted waves
Figure 6 shows comparisons of the wave parameters predicted from HF radar–corrected winds and NCEP reanalysis winds. Figure 6a shows the mean differences in predicted wave heights [
Comparisons of predicted wave parameters from NCEP winds and HF radar–corrected winds from the EFWDM and for 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
Figure 6b shows the RMSD between 
Figure 6c shows the mean differences of predicted wave periods [
Figure 7 shows comparisons of predicted wave heights. The number of two-hourly wave height data is 451. Figures 7a and 7b show the time series and scatterplot of in situ observed wave heights (
Comparisons of USW wave heights, predicted wave heights from NCEP winds, and HF radar–corrected winds from the EFWDM and for 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
Figure 7e shows the time series of differences in predicted wave heights from USW wave heights [
The statistical significance of the improvement at the USW point was investigated by the bootstrap method (e.g., Emery and Thomson 1998), although this was based on comparisons at only one point. The effective sample size 
The predicted wave heights were compared with USW wave heights for the case in which wind directions at the USW position are estimated from the first-order scattering (Fig. 3a) and not from interpolation or extrapolation [Eq. (5)]. The blue symbols in Fig. 7 indicate wave data when the wind directions at the USW position are estimated from the first-order scattering. The number of two-hourly data is 74. The correlations are 
Figure 8 shows comparisons of wave periods. The wave periods in Fig. 8 from the USW are significant wave periods; those from the predicted wave spectra are spectral mean periods [Eq. (16); section 2g], which are different from each other. The correlation between wave periods from NCEP reanalysis winds and USW periods is 
(a) As in Fig. 7a, but for 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
c. Wave prediction for various parameters
The sensitivity of wave prediction to the weight parameter 
Table 1 summarizes the results of comparisons of wave parameters. Case 1-1 in Table 1 is the case of Figs. 7 and 8. The mean 
RMSEs and correlations of USW wave parameters with predicted wave parameters from NCEP winds and HF radar–corrected winds from the EFWDM.
We also predicted the wave parameters from NCEP forecast winds. Case 1-5 is the wave parameter comparisons for HF radar–corrected winds from NCEP forecast winds. Case 1-6 is the wave parameter comparisons for NCEP forecast winds. The accuracies of the predicted wave parameters in case 1-5 are better than those in case 1-6. The correlations of wave parameters in case 1-5 are better than those in case 1-2.
Table 1 shows that the correction of wind directions by HF radar is effective for improving wave prediction at the USW location, in which fetch is sensitive to wind direction. This improvement is not so sensitive to weight 
d. Results of the EPWDM
Figure 9 shows comparisons of wind vectors estimated from the EPWDM with the NCEP winds. Figure 9a shows the RMSD of wind directions for 
(a) As in Fig. 5b, but from the EPWDM and 
Citation: Journal of Atmospheric and Oceanic Technology 34, 9; 10.1175/JTECH-D-16-0249.1
Figure 9b shows the difference of wind speeds. The corrected wind speeds from the EPWDM for 
Figure 9d shows the RMSD of wind directions for 
The wave data are predicted from corrected winds from the EPWDM. Table 2 summarizes the comparison. Cases 2-1 and 2-2 show comparisons of predicted wave parameters for 
The wind speed at the USW point for case 2-1 is the smaller than that in Table 1. The RMSD of wave heights [
4. Discussion and conclusions
New methods to correct sea surface wind using HF radar are developed; these methods are called EFWDM and EPWDM. The wind directions can be estimated from first-order scattering, which is robust to noise. If the first-order scattering from dual radar can be used, then the wave direction at the position is estimated by solving Eq. (3). If the first-order scattering from only single radar can be used, then the wave direction at the position is estimated by solving Eq. (3). The value β in Eq. (3) and the solution close to 
The wind speeds are corrected from reanalysis data. The constraints for estimating wind speeds are that the correction of wind speeds is small and that the correction of horizontal divergence is small in the EFWDM. The constraints are changed to the minimization problem. A method that solves the minimization problem iteratively is developed.
Southerly winds were dominant during the HF radar analysis period (Fig. 4). The fetch is often limited near the western coast of Okinawa Island. The area in which the difference between mean corrected wind speeds and mean reanalysis wind speeds is large is related to the area where the difference 
The RMSD of predicted wave periods {
Figure 7 and Table 1 show that wave prediction near the small island, where the fetch condition is sensitive to wind direction, can be improved by correcting the wind direction using HF radar. The improvement is not as sensitive to the weight parameter 
There are some problems to be improved in the EFWDM in the future. One problem is determining the optimum value of 
We also developed the EPWDM. The EPWDM algorithm is better in principle than the EFWDM, since it includes EFWDM as a particular case. However, we could not verify that the EPWDM is better than the EFWDM from the observation. We could not determine which is the best parameter, 
The absolute values of the complex correlations of in situ observed winds at the station T (Fig. 1a) with NCEP winds (
The Gauss–Seidel method was used to solve the minimization problem. However, the Gauss–Seidel method works well only when the diagonal elements in the matrix of the linear equation [Eq. (12) or (15)] are dominant. The quasi-Newton algorithm (e.g., Gilbert and Lemaréchal 1989) is less restrictive than the Gauss–Seidel method to the structure of the matrix and is more robust for convergence, which should be used to improve the algorithm.
The RMSD between radar-estimated wind direction and NCEP wind direction [
The value of 
There are certain issues that must be explored. One issue is to verify the methods using sea surface wind observation data that are not incorporated into the NCEP reanalysis wind data. The other issue is that the wave prediction was not good when an atmospheric front passed through the study area. Application of the time-interpolation method, which considers the propagation of atmospheric disturbances (Hisaki 2016b), may improve the prediction.
In addition, a possible improvement to the EPWDM is to replace the first term in the right-hand side of Eq. (14) with 
Acknowledgments
This study was supported by a grant-in-aid for scientific research (C-2) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (JSPS 26420504). The GFD DENNOU Library (http://dennou.gaia.h.kyoto-u.ac.jp/arch/dcl/) was used for drawing figures. The Doppler spectra were provided from the Okinawa Electromagnetic Technology Center, National Institute of Information and Communications Technology, Japan (http://okinawa.nict.go.jp/EN/). The wave data were provided from the Coastal Development Institute of Technology, Japan (http://www.cdit.or.jp/). Comments from the reviewers helped to improve the manuscript. In particular, the EPWDM is based on a suggestion from one of the reviewers.
APPENDIX
Gauss–Seidel Algorithm for the EPWDM
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