a. Correlation and radial velocity differences

Time series of V_HF and V_m typically showed strong tidal variations as in the 2-week example from FBK– SAMI (Fig. 3a). The time series were clearly similar and exhibited significant correlation for this short interval (r² = 0.81, N = 314; Fig. 3b). Table 1 summarizes the statistical comparisons between V_HF and V_m for all HF radar–mooring pairs over much longer time periods. Variations in lengths of the comparison periods (columns 3 and 4) mainly resulted from changing coverage for some of the radars due to hardware problems. Values of r² fell in the range 0.39–0.77 (column 8), and ΔV_rms ranged from 7 to 19 cm s⁻¹ (column 10). Biases (column 11) were typically less than 2 cm s⁻¹, with a maximum of 6 cm s⁻¹. Slopes m of regression lines were in the range 0.31–0.88 with intercepts b in the range −4.5 to 8.4 cm s⁻¹ (columns 12 and 13).

Good operating conditions and high signal-to-noise ratio (SNR; >25) resulted in ΔV_rms in the range 9–13 cm s⁻¹, and r² in the range 0.59–0.70 for the FBK radar (Table 1). Comparable ΔV_rms (7–10 cm s⁻¹) and r² (0.63–0.77) were found for the PTC radar for the period 1 June 1998–28 January 1999 when unlimited access to the site allowed routine maintenance and repair. Before and after this period, hardware problems reduced the performance of the PTC radar. This is indicated for the PTC–AROF pair by the lower r² (0.58) and greater ΔV_rms (14 cm s⁻¹) for the full time series, 1 August 1997–3 October 1999 (Table 1). Similar results were found using the full time series when PTC was paired with the other moorings of Table 1 (results not shown). The greatest ΔV_rms (11–19 cm s⁻¹) and lowest r² (0.39– 0.62) were observed between the ARG radar and surrounding moorings, most likely due to reduced SNR (occasionally <20) caused by antenna and cable problems.

The longest time series were obtained from the ADCP mooring and the RFG and COP radars (10 186 and 6659 h of overlapping data, respectively). These radars had consistently high signal-to-noise ratios during the mooring deployment period, but with r² (0.50–0.60) and ΔV_rms (11–12 cm s⁻¹) comparable to the other pairs. This may have resulted from the large watch circle of the ADCP mooring (radius ∼750 m). Occasional mooring GPS fixes were adequate enough to determine the mooring watch circle, but too sparse to account for horizontal mooring motion in the ADCP data.

b. Coverage variations

An overall indicator of radar performance is spatial coverage over time. Coverage is defined as the number of sectors returning radials each hour (Figs. 2b–f). Some moorings were near, or just beyond, the range limits of the radars (42 km), or near the edge of angular coverage (e.g., ABOF in Fig. 1). Angular coverage typically extended to within a few degrees of the surrounding coastline. Consistently high coverage obtained at FBK corresponded to high SNRs, low ΔV_rms, and high r². At ARG, low, intermittent coverage corresponded to lower r² and higher ΔV_rms. An increase in coverage at ARG in November 1999, after the comparison period, resulted from antenna and cable replacement. Causes of coverage variability include power outages, antenna collapse, or other hardware failures. For example, at RFG in April 1998 animals bit partially through the transmit cable causing poor transmission, lower signal-to-noise ratios, and frequent signal loss. Transmit and receive cables were then enclosed in electrical conduit. Coverage variations may also result from changing noise sources or variations in the environment around the radar antennas (Prandle et al. 1993).

High-frequency coverage variations were apparent in the time series (Figs. 2b–f). An expanded view of a 2-week period of the RFG time series (Fig. 4a) illustrates a strong diurnal component, which was observed in the coverage time series from all sites. Hourly coverage maps (Figs. 4b, c) show that the diurnal variation resulted from patchiness in coverage, as well as extensions and contractions of range, as observed by Prandle et al. (1993) and Paduan and Rosenfeld (1996). For RFG the diurnal coverage reached a maximum around 1400 local time each day and a minimum about 12 h later (Fig. 4a). No significant squared coherence (γ²) was found between RFG coverage and wind speed from NDBC buoy 46053 (NDBC 53 in Fig. 1), except at a narrow peak centered on 1 cpd, where γ² reached 0.48. This peak may have been coincidental, resulting from the diurnal sea breeze and the diurnal tidal component. In addition to diurnal variations, large fluctuations extending over a range of time scales were evident in the coverage record and often obscured the diurnal pattern.

c. Spectral analysis

To examine variance in the current measurements versus frequency, power spectra were computed for time series of V_HF and V_m, using V_HF from the sector that contained V_m. Rotary spectra (Gonella 1972) of total current vectors were also computed for a selected time series from SAMI, ARG, and FBK, for comparison with previous studies of radar performance. Power spectra of V_HF and V_m for all radar–current meter pairs were computed, but results from SAMI, ARG, and FBK are presented because their time series had the fewest gaps. Other records typically had more missing data (∼30%).

Gaps appear to be a characteristic of direction-finding radars, or the MUSIC algorithm. They may result from the inability of the MUSIC algorithm to resolve all angles at all times for a given range cell, thereby leaving some sectors with no data (Paduan and Rosenfeld 1996). Gaps in time series of V_HF were filled prior to computing spectra. For V_HF time series from FBK measured at the sector coinciding with SAMI, approximately 11% of the data was missing. The same sector observed by ARG had 20% missing. Gaps in V_HF time series were filled by first computing a time series of the spatial mean of surrounding HF radar sectors. Then, a linear least squares fit was computed between this time series and that from the sector nearest the mooring. The fitted line was used to predict the values in the gaps. For the FBK spectra, this procedure reduced missing points from 431 to 13, out of 3758 contiguous hours from 0000 UTC 1 October 1999 to 1300 UTC 5 March 2000. For the ARG spectra, missing points were reduced from 575 to 12 out of 2843 contiguous hours from 0100 UTC 8 November 1999 to 1200 UTC 5 March 2000.

Spectra of V_HF from FBK and V_m from SAMI agree well for frequencies less than 0.1 cycles h⁻¹ (cph), and the diurnal (K₁, 23.93-h period) and semidiurnal (M₂, 12.42-h period) tidal peaks are well resolved (Fig. 5a). Above ∼0.2 cph the V_HF spectrum departs from the V_m spectrum, which has a slope in the range −3 to −2 (mean = −2.6). The flattening of the V_HF spectrum above 0.3 cph, suggesting white noise, is typical of spectra from COP, RFG, and PTC (data not shown). If the white noise level for FBK of ∼70 cm² s⁻² cph⁻¹ (average of FBK V_HF spectrum between 0.3 and 0.5 cph) is extrapolated over the entire bandwidth, about 16% of total variance, the rms level corresponding to the noise is 6 cm s⁻¹. A similar comparison for ARG and SAMI spectra shows separation at about 0.1 cph (Fig. 5b) with a comparable noise level above 0.3 cph. For ARG the extrapolated noise also yields an rms velocity of 6 cm s⁻¹, corresponding to 19% of the total variance. Following Chapman et al. (1997), the contribution of this noise to the tidal band is estimated. For V_HF spectra of Fig. 5a, computed with a 512-point transform, the M₂ tidal peak spreads across 11 frequency bins covering 0.07–0.09 cph. The corresponding rms tidal fluctuation is 7.7 cm s⁻¹. The rms level corresponding to the noise is about 1.2 cm s⁻¹, or about 15% of the M₂ tidal variance.

Gaps were less frequent for total velocity vectors because radials from several sectors were used to compute them. For total vectors using radials from FBK and ARG from 0000 UTC 8 November 1999 to 1200 UTC 5 March 2000, only 11 h of data were missing. Total velocity components U (east) and V (north) were computed from all radials within a 3-km-radius circle centered on a grid point near SAMI, using the least squares fit method of Gurgel (1994).

Clockwise (CW) rotary spectra from SAMI and ARG–FBK show similar levels at the diurnal (K₁) tidal and lower frequencies (Fig. 5c). In the range 0.06–0.25 cph, including the semidiurnal tidal band, the CW spectra for SAMI has somewhat higher variance. This contrasts with counterclockwise (CCW) rotary spectra, which show slightly higher variance in the HF radar time series at the two tidal frequencies. Both CW and CCW spectra from ARG–FBK flatten at about 0.3 cph, consistent with the radial spectra of Figs. 5a and 5b. Above 0.1 cph the slope of the ARG–FBK spectra is flatter than that for SAMI, which trends toward 1 cm² s⁻² cph⁻¹ at 1 cph. This result is similar to the rotary spectra of CODAR data in Fig. 3 of Paduan and Rosenfeld (1996). Flattening above about 1 cph is also evident in rotary spectra reported by Shay et al. (1995), as the OSCR's 1.5-cph Nyquist frequency is approached.

Squared coherence spectra γ² were computed between pairs of time series to examine correlation versus frequency. In Fig. 6a γ² for V_HF from FBK and V_m from SAMI are shown for the same time series used to compute spectra of Fig. 5a. The similar power spectral levels in Figs. 5a and 5b correspond to statistically significant coherent motions up to frequencies of about 0.2 cph, where γ² drops below the 95% threshold. Lower overall γ² is obtained for the ARG–SAMI pair (Fig. 6b), which drops below the 95% threshold at 0.09 cph and briefly at about 0.02 cph. In Fig. 6c, γ² between U and V from ARG–FBK and SAMI were significant below 0.1 cph including the K₁ and M₂ tidal bands. Phase spectra for Figs. 6a–c (not shown) were nearly zero at all frequencies where γ² was above the 95% threshold.

d. Bearing offsets

An example of a large bearing offset, Δθ = −16°, is shown for PTC–SMIN (Fig. 7a). The maximum in r² was broad, but its peak was clearly offset from SMIN as indicated by r² profiles along constant range lines of 4.5, 6.0, and 7.5 km (Figs. 7b,c,d, respectively). The maximum r² occurred in the same range cell as SMIN, such that the offset was in bearing only. A small bearing offset was found for COP–ADCP, with Δθ = −1° (Fig. 8a). Here the sector with maximum r² contained the large mooring watch circle, and a broad maximum extended over bearing and range (Figs. 8b–d). Column 9 of Table 1 shows Δθ for each of the 18 HF radar– mooring pairs; Δθ ranged from −16° to 19° with an average absolute value of 7°, although Δθ could only be determined to within the 5° sector width. Three of the HF radars (PTC, ARG, and FBK) had coverage areas that including more than one mooring (Fig. 1). For these radars, Δθ was not constant, but changed at different locations around the radars (Table 1). For example, at ARG, Δθ was a maximum of Δθ = 19° at 311°, and a minimum of Δθ = 0° at 220°. At FBK, Δθ reached a minimum of −11° at 216° then increased to 16° at 299°. At PTC, with four moorings located at different bearings in its coverage area, Δθ increased roughly monotonically with bearing, from Δθ = −16° at bearing 160° to Δθ = 9° at 291° (Table 1, columns 6 and 9).

a. Coverage variability

Changes in range and azimuthal coverage spanned a range of time scales, with a prominent diurnal variation, consistent with results of Prandle et al. (1993) and Paduan and Rosenfeld (1996). A possible source is the well-known diurnal cycle in the ionosphere's lowest layer, the D region (e.g., Davies 1990), which allows radio waves from great distances (∼10³ to 10⁴ km) to become external noise to coastal HF radars, leading to lower SNR and poor coverage. As an example, an investigation of unusually strong diurnal coverage variations and poor SNR at PTC revealed foreign media broadcasts as the cause. Azimuthal coverage variability has been shown to depend on the distribution of Bragg scattering ocean waves. Laws et al. (2000) used simulated backscatter data for a phased array receive antenna to demonstrated that the MUSIC algorithm produced areas of low coverage when the SNR was 12 dB lower than adjacent areas. Such areas result when the wind direction is perpendicular to the radar look direction, and when the radar coverage area is partially shadowed from the wind by land formations. These regions of decreased sea echo, and lower SNR, are likely a significant source of azimuthal coverage variability for our study region due to the spatial variability in wind speed in the region (Dorman and Winant 2000).

b. Velocity differences

Values of ΔV_rms in Table 1 are comparable in range (7–19 cm s⁻¹) to rms differences in radial and U, V components reported elsewhere. Shay et al. (1995) found rms differences in U, V of 11–15 cm s⁻¹ for a 27-day deployment on the inshore boundary of the Gulf Stream, by comparing 25.4-MHz OSCR (effective sampling depth ∼0.5 m) with current meters at 9.5- and 13.8-m depths. Paduan and Rosenfeld (1996) reported rms differences of 6.2 and 10.8 cm s⁻¹ near Monterey Bay comparing 48-h low-passed U, V components from a CODAR array with ADCP data at 9-m depth. The array consisted of two CODAR SeaSondes operating near 12.5 MHz, and one older CODAR operating at 25.4 MHz. Chapman et al. (1997) found rms U, V differences between 25.4-MHz OSCR and four shipborne current meters in the range 9–16 cm s⁻¹, including measurements made near 5-m depth, where rms differences range from 11 to 15 cm s⁻¹. When combined with the results of Shay et al. (1998), who found rms differences of 7–9 cm s⁻¹ between VMCMs (4- and 6-m depth) and a 25.4-MHz OSCR in a 29-day deployment off the North Carolina coast, these studies suggest an envelope of rms U, V differences between HF radars and ∼5 m currents of 7–15 cm s⁻¹. Similar results for radials were found by Kosro et al. (1997), with 12.6–16.2 cm s⁻¹ from a 7-m ADCP and an OSCR, and Kohut et al. (1999), with 6.7 cm s⁻¹ between a 4.5-m ADCP and a SeaSonde. For comparison, rms differences in U, V between ARG– FBK and SAMI from 1 February 1999 to 14 November 1999 are 10 cm s⁻¹ (U) and 14 cm s⁻¹ (V), while ΔV_rms between FBK and SAMI is 9 cm s⁻¹ for the same period.

Chapman et al. (1997) distinguished between measurement errors resulting from instrument noise, and measurement differences, produced by the subtraction of two current measurements. Measurement differences include errors as well as actual current velocity differences resulting from factors such as different spatial averaging and measurement over different depths. Graber et al. (1997) considered several physical processes contributing to measurement differences. For example, during a summertime period of low winds and waves, they compared currents from an OSCR and a current meter at 5-m depth and attributed 17%–22% of the rms difference to Ekman flow, Stokes drift, and baroclinic currents.

Wind-driven shear in our study area is likely an important contributor to measured differences, especially outside the Santa Barbara Channel. Observations from NDBC 53, located ∼6 km east of the ADCP mooring (Fig. 1), indicate atmospheric conditions comparable to those observed by Graber et al. (1997). NDBC 53 wind speeds averaged 4.8 ± 3.0 m s⁻¹, similar to 4.4 ± 2.1 m s⁻¹ reported in their Table 6. Current shear between ADCP bins at 3.2 and 8.2 m was typically less than 4 × 10⁻⁴ s⁻¹, with occasional episodes in the range 0.5– 1 × 10⁻³ s⁻¹. There are somewhat lower than shear levels observed by Graber et al. (1997). Observations from NDBC buoys near the VMCM moorings outside the Santa Barbara Channel (Fig. 1) show much higher mean wind speeds. NDBC 63 and 54 observed mean wind speeds of 7–8 m s⁻¹ during the study period. Southwest of our study area Richman et al. (1987), using a drifting string of VMCMs, measured near-surface current shears of order 10⁻² s⁻¹ during a high wind event (>12 m s⁻¹). High wind events such as this frequently occur at NDBC 23, 63, and 54. During the study period, winds exceeding 10 m s⁻¹ were observed at these buoys 21%, 17%, and 34% of the time, respectively.

The study region is also subject to substantial swell. Mean wave heights at NDBC 54 during the study were 2.8 ± 0.8 m, with mean dominant periods 11.6 ± 3.7 s. Using available spectral wave data collected with a Datawell Directional Waverider buoy near Point Conception (deployed by the California Data Information Program at CCS/SIO), Stokes drift u_s at depth z was estimated as

View Expanded

where a is the wave amplitude, σ = 2πT⁻¹ is the angular wave frequency, k = g⁻¹ σ² is the wavenumber, and T is wave period. From 19 March 1998 through 30 November 1999, the mean Stokes drift at 1-m depth was 2.2 cm s⁻¹, in the mean wave direction of 290°. This compares well with Stokes drift estimated by Richman et al. (1987) (3 cm s⁻¹), and is larger than estimated by Graber et al. (1997) (∼1 cm s⁻¹). The VMCM measurement may include an error u_m due to wave-induced vertical mooring motions (Pollard 1973),

View Expanded

Over the same time period, u_m was 0.7 cm s⁻¹ using (9). Thus, the net wave-induced velocity difference in the mean wind and wave direction (bearing ∼290°) was 1.5 cm s⁻¹. Wave-induced velocity differences are less important for radials aligned away from this bearing.

Graber et al. (1997) point out that measurements can differ due to horizontal separation between HF radar sectors and current meters locations. Sector sizes increase with range from the radars, which may account for the weak trend of increased ΔV_rms with range (Table 1, Fig. 1). When data from ARG are excluded, r² = 0.32 (N = 16) between ΔV_rms and range. The larger sampling area at greater range increases the likelihood of larger horizontal current variability within the sector. For our radar sites, sectors containing moorings had widths from 0.5 to 3.7 km corresponding to ranges of 5.7–42 km. If a mooring was located near the edge of a given sector, the mooring and the center of the sector could have been as much as ∼2 km apart. Extrapolation from Fig. 10 of Graber et al. (1997) suggests an expected rms difference derived from OSCR total velocity data of about 5–6 cm s⁻¹ resulting from a horizontal separation of 2 km between measurements. Kosro (1987) computed the structure function of horizontal velocity differences using shipboard ADCP data in an upwelling regime. His results suggest an expected difference of 7 cm s⁻¹ for a 2-km separation. These are only rough estimates since horizontal velocity differences are strongly dependent on the flow field.

Limited resolution of the HF radar's Doppler spectra also contributes to ΔV_rms. The length of the time series used to compute Doppler spectra (256 s for these data) sets the radar's spectral resolution. This effectively limits the resolution of V_HF to discrete levels separated by ΔV_HF = 4.3 cm s⁻¹. The conversion of continuous currents into discrete levels produces rms errors of (1/12)^1/2 × ΔV_HF = 1.2 cm s⁻¹ (Bendat and Piersol 2000), assuming the error has a uniform probability distribution. It also produces uncertainty in spectral levels (Fig. 5) corresponding to 3.1 cm² s⁻² (cph)⁻¹, although this is well below observed HF radar noise level at high frequency.

Part of ΔV_rms in Table 1 results from white noise in the HF radar current data, the high-frequency portion of which is evident in V_HF spectra (Figs. 5a,b). The source of this high-frequency noise is the subject of a Ph.D. dissertation by one of the authors (JAH), and preliminary evidence suggests both geophysical and instrument sources. However, results of Laws et al. (2000) suggest at least part of the noise results from the MUSIC algorithm and depends on the transmit frequency. For 13.4-MHz transmit frequency, they estimate 1–2 cm s⁻¹ rms error, compared to the 6 cm s⁻¹ rms error estimated from V_HF spectra in Fig. 5. High-frequency noise in rotary spectra is also observed, despite substantial spatial averaging (Fig. 5c). [An average (standard deviation) of 18 (4) radial velocity measurements went into each hourly total vector data point.] This is coincident with the low γ² at high frequency for U, V components between the radars and mooring (Fig. 6c).

c. Bearing offset

In a previous study comparing OSCR measurements with ADCP data from 7-m depth, Kosro et al. (1997) found that the maximum correlation occurred at a radar cell other than the one lying directly over the mooring. This is consistent with the CODAR SeaSonde bearing offset we observed. Bearing offsets may have several causes, such as antenna pattern distortions, phase calibration of the receive antenna elements, and, in this case, limitations of the MUSIC algorithm. Other easily dismissed explanations include misalignment of the receive antenna and compass errors in the mooring current meters. Misalignment of the receive antenna would result in constant Δθ at each mooring azimuth around a given radar. Table 1 shows that this is not the case: Δθ varies in magnitude and sign for each mooring–radar pair. Also, repeated checks indicated antenna alignments are constant in time to within ∼1°. Similarly, current meter compass error cannot the explain variation of Δθ with bearing. If compass error alone accounted for Δθ, then pairs using the same VMCM would show similar Δθ. Table 1 shows this is not true: for example, for the FBK– SAOF pair Δθ = −8°, but for ARG–SAOF Δθ = 19°.

A possible explanation of nonzero Δθ is given by Barrick and Lipa (1986), who examined the influence of antenna patterns on radial currents. Antenna patterns describe the directional response of the receive antenna to incoming HF radiation. Ideally, only the antenna's design determines the antenna pattern. However, the patterns are also affected by conductors in the near field, the area within about one wavelength of the antenna (∼25 m). These conductors couple with the antenna, distorting the antenna pattern. For example, Barrick and Lipa (1986) found severely distorted antenna patterns during a deployment on an offshore oil platform, with rms bearing errors ∼35°. Antenna pattern distortions can now be accounted for in the MUSIC algorithm; however, during the data collection phase of this study corrections were unavailable and ideal patterns were assumed in processing.

To test the assumption of ideal patterns, antenna patterns at PTC, RFG, and COP were measured by moving a transponder in a small boat along circular arcs within the coverage areas of the radars. Antenna patterns measured at RFG and PTC (data not shown) were typical of patterns found at sites in other regions, exhibiting low levels of distortion, while patterns at COP were moderately distorted (D. Barrick 1999, personal communication).

Measured antenna patterns were compared with Δθ to look for a relationship between distortions in the patterns and nonzero values of Δθ. For example, following a suggestion by J. Paduan (2000, personal communication), a relationship between Δθ and the rate of change of the measured antenna pattern versus bearing was investigated but none was found. Large Δθ occurred both with and without corresponding distortions in antenna patterns.

An important part of the antenna pattern measurement, which may account for nonzero Δθ, is the phase calibration of the three-element receive antenna. Each of the two-loop antenna elements responds to incoming signals with differing voltage phases depending on signal direction. Phase calibrations were initially determined at PTC from sea echo as part of the CODAR data processing procedures (Barrick and Lipa 1986). For comparison, phases were also directly measured with the transponder. Lower Δθ between PTC and SMIN was found when the transponder-derived phases were used (Δθ = 15°), compared with the sea echo–derived phases (Δθ = 30°). The reduction in Δθ indicates a strong link between receive antenna characteristics and Δθ.

Nonzero Δθ may also result from limitations of the MUSIC algorithm. Laws et al. (2000) note that oceanographic application of MUSIC for bearing determination requires assumptions about the flow field. For example, for a three-element receive antenna such as the CODAR SeaSonde's, MUSIC assumes that the same radial velocity occurs in no more than two sectors within a range cell. Flow conditions that invalidate this assumption in the mean may result in Δθ. However, the relative magnitude of this effect compared with the effect of assumed ideal antenna patterns is not clear. Much needs to be learned about how MUSIC is affected by factors such as antenna characteristics and flow conditions.

The effect of Δθ on total velocity vectors, determined from two radars, was examined using simple flow patterns. In one example, a uniform westward flow along a straight coastline was assumed (black arrows, Fig. 9). Here V_HF as functions of range and bearing were computed from the uniform flow at two sites, labeled A and B in Fig. 9. At site A, bearings to sectors on the sea surface were distorted using a linear least squares fit for Δθ observed at the PTC radar. To actual bearings at A, ranging from 90° to 270°, Δθ was added between −18° and 14° as found for PTC (Table 1). Total velocity vectors (gray arrows, Fig. 9) were then computed from V_HF at sites A and B. The mean error in flow speeds between the original vectors (black arrows, Fig. 9) and distorted vectors (gray arrows, Fig. 9) was ∼7% of the original uniform flow speed with a maximum error of ∼15%. The mean error in flow direction was ∼2.5°, with a maximum of ∼9°. Simulations with other simple flow fields produced comparable errors in total velocities (results not shown). These errors illustrate the effect of bearing offsets (Δθ ) on the total velocity data, and the need to understand and correct errors in direction finding.