1. Introduction
Surface current measurement using a shore-based high-frequency radar (HFR) is based on the interpretation of Bragg-scattered returns of transmitted radio signals. Bragg signals are backscattered in phase with the transmitted signals, whose wavelengths are twice those of ocean surface gravity waves (e.g., Stewart and Joy 1974; Crombie 1955; Barrick et al. 1977; Paduan and Washburn 2013). A radial velocity map, obtained from multiple steps of the spectral analysis of return signals, consists of a set of radial velocities and bearing angles on a polar coordinate grid. The radial velocity is computed from the shifted amount of Bragg peaks in a Doppler spectrum, and the bearing angle is estimated using either direction finding or beamforming depending on the antenna’s characteristics (e.g., Schmidt 1986; Teague et al. 2001).
Since HFR-derived surface current observations resolve coastal surface circulation from the shoreline (except for the surfzone) to 
However, as archived HFR-derived data are relatively abundant compared to data from other remote sensing and in situ observations, it has been difficult to handle and analyze them. Moreover, the importance of an integrated analysis of high-resolution coastal observations has been raised, including HFR-derived surface currents (e.g., Kim et al. 2011) and submesoscale sea surface heights obtained from satellite missions (e.g., Fu and Ferrari 2008; Uematsu et al. 2013). Thus, the rudimental quality assessment on those high-resolution data has been demanded, which can be aligned with enhanced awareness of building and sustaining regional coastal ocean observing programs (e.g., Malone and Cole 2000; Ocean.US 2002; Stokstad 2006). In this paper, detailed and technical descriptions of HFR data analysis are presented in terms of the quality assurance and quality control (QAQC) of radial velocity data based on the expected geophysical signals and dynamic relationships between driving forces and responses. This work will be beneficial and instructive not only for HFR operators and users within different levels of experience but also for those who work on the analysis of high-resolution geophysical data in time and space by providing systematic and practical guidelines. Although this paper can be incorporated into existing common practice, it is designed to encourage beginners to address HFR-derived data analysis easily and efficiently and to reduce the labor involved in researching techniques scattered among other references. For reference, comprehensive analyses of HFR-derived spectral raw data (prior to the radial data extraction) have been addressed elsewhere (e.g., Kirincich et al. 2012; Flores-Vidal et al. 2013).
The paper is divided into three sections. The temporal and spatial data availability of radials are defined for a systematic organization and analysis of archived radial velocity data (section 2). Geophysical signals in radial velocity data (section 3a) are used to examine spatial consistency, such as spatial coherence in specific frequency bands (section 3b), maps of tidal amplitudes and phases (section 3c), and wind-radial transfer function analysis (section 3d). The uncertainty and signal-to-noise ratio (SNR) of radials are also discussed (section 3e). Finally, the proposed analysis and results are summarized (section 4).
2. An overview
a. Radial velocity data
Figure 1 illustrates the reported radial velocities when a true vector current (black arrows) is measured by a radar located at colored dots. The radial velocities are scalar components projected onto a line connecting a colored grid point and a grid point where the vector current is sampled (examples of the radial velocity map are shown in Figs. 2c and 4a).
Examples of radial velocities (colored arrows) when a vector current (black arrow) is projected onto a line connecting a colored grid point (location of an HFR) and the center where the vector current is sampled.
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
A radial grid consists of range and azimuthal bins on a polar coordinate (Fig. 2a). The range spacing depends on the operating and sweeping frequencies, and the azimuthal spacing varies from 1° to 5°. Figure 2a shows examples of a radial grid having two types of grid spacing, namely, 1.5 km × 1° (green dots) and 4.5 km × 5° (blue or red crosses). A single radial velocity is reported as a scalar value spatially averaged over a polar grid patch, which is the smallest unit in the polar coordinate grid. More details on the spatial spacing of the radial grid and bin averaging of radials will be discussed in section 3c.
(a) An example of HFR radial grids. A radial grid at ARG1 (San Luis Obispo) shows two different grid spacings of 1.5 km × 1° (grid A; green dots) and 4.5 km × 5° (grid B; blue or red crosses). Grid B is a bin-averaged radial grid of grid A. Bin-averaged radials are marked with red dots (no bin-averaged radials are denoted with blue dots). (b),(c) A magnified view of the radial grid and (bin averaged) radial velocities in the black box in (a).
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
In this paper, the radial velocity data are mainly obtained from compact array HFR systems off California (e.g., San Diego and San Luis Obispo) and Oregon (e.g., Manhattan Beach) in the United States, and Yeosu (e.g., Yeosu Bay) in South Korea (see Table 1 for more details). Since the examples presented in the paper are chosen to highlight the proposed techniques, the radial data had to be taken from different regional locations. However, the proposed techniques are applicable to any radial velocity data at the discretion of the user. Additionally, as a compact array system (e.g., SeaSonde) reports two types of radials—radials processed with ideal and measured beam patterns—two sets of radials can be considered simultaneously or separately in the following analyses.
Detailed specifications of high-frequency radars participating in the hindcast analysis are listed with station identification (ID; region), operating frequency (
b. Data availability
An example of the initial treatment of radial velocity data in a hindcast mode. The total number of radial solutions and the number of radial solutions at individual azimuthal and range bins at SDBP (San Diego) for a period of 2 years (2007–08) are used to report the temporal and spatial data availability. (a) Examples of radial velocity maps. (b),(c) Temporal data availability [
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
A radial grid at SDBP (San Diego) consists of 72 azimuthal bins and 40 range bins (Fig. 3a). Hourly radial velocity maps over a period of 2 years (2007–08) are counted as a function of time and space (
A clear definition of the temporal and spatial data availability is useful for communications within the HFR community and for introducing beginners to the organization of archived radial velocity data.
c. Range spacing and azimuthal spacing
In the context of sampling of surface circulation, an optimal spacing of a radial velocity map in the azimuthal and range directions can be determined by the wavenumber energy spectra of radials (Fig. 4). Figure 4a shows a snapshot of radial velocity maps reported at NAM4 (Yeosu Bay), which has 1° azimuthal spacing and 0.75-km range spacing. The energy spectra of hourly radial velocities along a range bin (red) and an azimuthal angle (blue) are averaged over a period of 5 months (March–July 2011), as shown in Figs. 4b and 4c, respectively.
(a) An hourly radial velocity map at NAM4 (Yeosu Bay) 1300 UTC 10 Mar 2011. Radial velocities along a range bin (red) and an azimuthal bin (blue) are chosen to estimate the wavenumber spectra in (b) and (c). Wavenumber spectra are averaged over a period of 5 months (March–July 2011). (b) An averaged wavenumber spectrum of radial velocities along a range bin. (c) An averaged wavenumber spectrum of radial velocities along an azimuthal bin.
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
An optimal sampling spacing can be determined by a wavenumber whose variance is saturated because nearly flat variance beyond a specific wavenumber indicates that there is no new information below that length scale. Figure 4b shows that the saturation of variance or a floor level starts near 0.1 cycles per degree (cpdg), which is equal to the Nyquist wavenumber of data sampled with 5° spacing. Thus, the optimal azimuthal spacing for this site can be higher than 5°. Conversely, an averaged energy spectrum along the azimuthal bin does not show saturation of signals. Thus, an original range spacing of 0.75 km for this site is a reasonable value (Fig. 4c). Moreover, the energy spectra of radial velocities along other azimuthal and range bins show consistent results.
d. Bin averaging of radials
In combining multiple radial velocity maps with different spatial spacing into a vector current map, high-resolution (spacing) radial velocity maps may generate a spatial bias in a mapped vector current field, which is related neither to the beam pattern nor intrinsic radar issues (e.g., Kim et al. 2011). Thus, radial velocity maps may require bin averaging to make their spatial spacing comparable (e.g., 3–5-km range and 5° azimuthal spacing). Figure 2a shows examples of radials reported on a grid of 1° azimuthal spacing and 1.5-km range spacing (green dots) and bin-averaged radials on a grid of 5° azimuthal spacing and 4.5-km range spacing (blue and red crosses) (Figs. 2b and 2c are magnified from Fig. 2a). The radial velocities before and after bin averaging are shown in Fig. 2c. In this bin averaging of radials, a threshold number of radials can be applied to provide statistical significance for spatially averaged radials. Note that methods combining multiple radial velocity maps into a vector current have been discussed elsewhere (e.g., Lipa and Barrick 1983; Kim et al. 2008).
3. Data analysis
a. Geophysical signals
Since a single radial velocity map contains partial information of a true vector current field [Eq. (1)], it includes geophysical signals of ageostrophic and geostrophic currents, barotropic and baroclinic tidal currents, and near-inertial currents (e.g., Kim et al. 2010a, 2011). An averaged energy spectrum of hourly radial velocities at 225 grid points with more than 80% spatial data availability [
A spatially averaged frequency-domain energy spectrum of hourly radial velocities at MAN1 (Manhattan Beach) over 225 grid points with more than 80% temporal data availability for a period of 2 years (2007–08). Barotropic tides (K1, M2, and S2), spring–neap (
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
The geophysical signals of radial velocity data can be evaluated with those in independent observations of currents (e.g., ADCP, current meter, and altimeter data). Additionally, maps with near-inertial variance, tidal amplitudes and phases, and low-frequency variance of radial velocities can reveal where and when the signals are inconsistent. Although radial velocities are sampled on a polar coordinate grid, these geophysical signal maps have a unique spatial structure in a physical space. Thus, discontinuously enhanced and biased features along an azimuthal bin or a range bin can be flagged as nonphysical components and instrumental noise. The following analysis provides more detailed examples.
b. Spatial coherence
Hourly radial velocity maps at MAN1 over 225 grid points for a period of 2 years (2007–08) are analyzed to estimate the spatial coherence of radials between a reference grid point (a white star) and other grid points in a low-frequency band (0 
Spatial coherence of hourly radial velocities between a reference radial grid point (white star) and other radial grid points in two frequency bands. (a),(c) Low-frequency band (0 
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
Spatial inconsistency may result from unfavorable physical environments around the radar system (e.g., interference due to metal structures and landforms), biased or uncalibrated radar beam patterns (section 3f), and footprints of geophysical forces. For instance, the temporal data availability of radials in tide-dominant areas can exhibit dependency on the periodicity of local tides, and the wind direction and fetch can affect the number of radial solutions due to changes in the performance of backscattering associated with the steepness of surface waves (e.g., Mao and Heron 2008). Note that an evaluation based on spatial coherence requires a sufficient number of realizations to capture the variability of interest.
c. Tide-coherent structures
The tidal amplitudes and phases of radials at SDBP, SDPL, and SDCI (San Diego) at the M2 frequency are estimated with a least squares fit to the time series of radials over a period of 2 years (2003–05). Enhanced amplitudes (more than 3 
Tidal amplitudes (cm s–1) and phases (degrees) of hourly radial velocities at SDBP, SDPL, and SDCI (San Diego) at the M2 frequency estimated using harmonic analysis. (a)–(c) Amplitudes (cm s–1). (d)–(f) Phases (°). The phases at SDBP and SDCI are adjusted with bearing angles relative to SDPL. (a),(d) SDPL. (b),(e) SDBP. (c),(f) SDCI. A black arrow in (b),(e) denotes an artifact at the 287°T azimuthal bin (e.g., Fig. 10; Kim et al. 2010a).
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
There are several coastal regions where M2 internal tides have been identified by HFR observations, including Oregon (e.g., Kurapov et al. 2003); Bodega Bay (e.g., Kaplan et al. 2005), off San Francisco Bay (e.g., Gough et al. 2010), and Monterey Bay (e.g., Paduan and Cook 1997; Rosenfeld et al. 2009) in California; and Hawaii (e.g., Zaron et al. 2009; Chavanne et al. 2010a).
d. Wind-coherent structures
Wind-radial transfer functions are estimated from detided radial velocities at MAN1 and the wind stress at three individual NDBC buoys [Cape Elizabeth, Maine (46041); Columbia River Bar (46029); and Stonewall Bank, Oregon (46050)] over a period of 2 years (2007–08). The wind-radial transfer functions at specific frequencies or frequency bands with dominant variance (Fig. 5) can be used to evaluate relevant spatial structures. In this paper, amplitudes averaged over a clockwise near-inertial frequency band (
Amplitudes [(a)–(c); 
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
Figure 8 exhibits results from a single radar and three different wind buoys. When radials obtained from multiple radars are used, the phase of the transfer functions should be adjusted to interpret the results in a consistent manner (section 3c). This approach allows us to identify spatial inconsistencies using independent in situ observations (e.g., wind).
e. Uncertainty
Instead of finding an analytic solution to Eq. (19), a local and unique solution (
When radials face opposite directions and are perfectly matched—that is, 
As a strict criterion for an uncertainty estimate, an area of polar grid patches in two different radar sites can be considered. Since a radar frequency (e.g., operating and sweeping frequencies) is closely related to the area of the polar grid patch, radials derived from radars with a similar order of frequency or radials reported at the radar grid to have a similar order of azimuthal spacing and range spacing are taken into account. However, under this criterion, the paired radials may not be found with sufficient realizations. Thus, in this paper, the paired radials were chosen when they are within a threshold distance (e.g., 200 m) between two radial grid points, defined from different radars.
The uncertainty of radar observations off Yeosu Bay is reported as 6.1 cm s–1 for the 25-MHz system (Fig. 9a) and 12.6 cm s−1 for the 44-MHz system (not shown) based on paired radials obtained from NAM4, HYIL, NHSP, and ODNG (Yeosu Bay) over a period of 2 years (2007–08). The SNR of the 25-MHz system is approximately 4.5 (Fig. 9b). The deviation of the correlation of paired radials obtained from the 25-MHz system is estimated as 0.217. The 44-MHz system has been deployed in a channel, and a high noise level might be caused by interference from the land.
(a) Standard deviation [λ; Eq. (15)] and (b) cross correlation [ρ; Eq. (17)] of paired radial time series at NAM4 and HYIL (Yeosu Bay). Paired time series are obtained from 5° spacing radial velocity maps with more than concurrent 50% spatial data availability. The deviation of the correlation [ξ; Eq. (18)] is 0.217 and the estimated SNR [χ; Eq. (20)] is 4.5.
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
Uncertainty estimates using independent in situ observations have been addressed elsewhere (e.g., Emery et al. 2004; Kaplan et al. 2005; Liu et al. 2010; Paduan et al. 2006). Additionally, the sampling depth, sampling area, and type of signals (e.g., geostrophic or ageostrophic currents) should be taken into account to accurately quantify the uncertainty.
f. Consistency related to antenna patterns
Although radial velocities derived from two radar beam patterns (e.g., ideal and measured beam patterns) may be different from the true current field, the statistics of their difference can be used as a tool to identify spatial sensitivity, including spatial bias and distortions in radial velocity maps (Fig. 10). The radials at the 287°T azimuthal bin appear spurious due to a distorted measured beam pattern at that azimuthal bin, which is visible in Figs. 7b and 7e as well.
Standard deviation [ζ in Eq. (21); cm s–1] of the difference between hourly radial velocities estimated from ideal and measured beam patterns at SDBP for a period of one month for (a) September 2003 and (b) October 2003.
Citation: Journal of Atmospheric and Oceanic Technology 32, 10; 10.1175/JTECH-D-14-00207.1
4. Summary
This technical paper summarizes several ways to conduct quality assessment of the archived surface radial velocities observed from shore-based single or multiple high-frequency radars. As a single radial velocity map contains geophysical signals, their energy spectra exhibit variance associated with surface tides, wind stress, and near-inertial and low-frequency signals. The spatial consistency of radial velocity maps allows us to identify a spurious range and azimuthal bin. In particular, spatial coherence within a frequency band—that is, maps of the amplitude and phase at primary tidal constituents (e.g., harmonic analysis), and wind-radial velocity transfer function analysis—are suggested. The uncertainty of the radar observation itself can be estimated with paired radials obtained at nearby grid points and from two different radar sites. This review paper can be useful to evaluate and to analyze radial velocity data as a part of quality assurance and quality control using statistical and dynamical approaches. Although the examples reported in this technical review are based on radials obtained from a compact array system, the statistical and dynamical analyses presented here can be applicable to the radials observed with a phase array system as well.
As the fundamental data in between spectral raw data (e.g., Kirincich et al. 2012; Flores-Vidal et al. 2013) and vector current maps (e.g., Kim et al. 2008) derived from HFRs, the radial velocity data on polar coordinates contain geophysical signals and corresponding unique spatial structures. The QAQC of radial velocity data is essential for improving the quality of vector current maps and addressing coastal circulation studies along with numerical models (e.g., data assimilation). This review paper clarifies how to analyze HFR-derived radial velocity data and complex geophysical data.
As the proposed techniques require archived data over a time period of at least one year, they may have a limitation with respect to a quick assessment. However, evaluating the periodicity in the radial data and spatial patterns requires multiple realizations to ensure statistical confidence, which leads to reliable determination of spurious data and areas.
Sung Yong Kim is supported by the Basic Science Research Program through the National Research Foundation (NRF), Ministry of Education (NRF-2013R1A1A2057849), and by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), Ministry of Trade, Industry and Energy (20114030200040), South Korea. Surface currents data are provided by Scripps Institution of Oceanography (SIO) at University of California, San Diego; California Polytechnic State University (CalPoly); Oregon State University (OSU; Kim et al. 2011); and the Korea Hydrographic and Oceanographic Administration (KHOA). Wind data are from the National Data Buoy Center (NDBC).
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