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*Measuring Antenna Patterns for Ocean Surface Current HF Radars with Ships of Opportunity [Journal of Atmospheric and Oceanic Technology](Journal of Atmospheric and Oceanic Technology Via Acquire Media NewsEdge) ABSTRACT HF radars measure ocean surface currents near coastlines with a spatial and temporal resolution that remains unmatched by other approaches. Most HF radars employ direction-finding techniques, which obtain the most accurate ocean surface current data when using measured, rather than idealized, antenna patterns. Simplifying and automating the antenna pattern measurement (APM) process would improve the utility of HF radar data, since idealized patterns are widely used. A method is presented for obtaining antenna pattern measurements for direction-finding HF radars from ships of opportunity. Positions obtained from the Automatic Identification System (AIS) are used to identify signals backscattered from ships in ocean current radar data. These signals and ship position data are then combined to determine the HF radar APM. Data screening methods are developed and shown to produce APMs with low error when compared with APMs obtained with shipboard transponder-based approaches. The analysis indicates that APMs can be reproduced when the signal-to-noise ratio (SNR) of the backscattered signal is greater than 11 dB. Large angular sectors of the APM can be obtained on time scales of days, with as few as 50 ships. (ProQuest: ... denotes formulae omitted.) 1. Introduction Because of their ability to map surface currents with high temporal and spatial resolution, HF radars have become a key component of coastal ocean observing systems. Of the approximately 300 HF radars operating globally, about 130 are funded by the National Oceanic and Atmospheric Administration (NOAA) Integrated Ocean Observing System (IOOS). Typical applications, such as oceanographic research, search and rescue (SAR) operations, and hazardous material spill response, all benefit from accurate HF radar surface current mea- surements. Additionally, precise high-resolution antenna patterns are necessary for successful deployment of emerging bistatic and multistatic HF radar systems. The antenna pattern describes the response of the receive antennas to a signal source as a function of bearing, allowing the bearing to a given signal to be more accurately determined. Several studies have demonstrated improved comparisons between HF radar and in situ ocean current measurements when using a measured antenna pattern (APM) for bearing determination (Barrick and Lipa 1999; Kohut and Glenn 2003; Paduan et al. 2006). Best practices for the operation and maintenance of HF radars prescribe regular measurement of antenna patterns as a neces- sary component of the quality assurance and quality control (QA/QC) of HF radar data (Cook et al. 2008). Therefore, an automated method for determining APMs would assist operators in the QA/QC of HF radar data. The most common type of HF radar is the SeaSonde (manufactured by CODAR Ocean Sensors, Ltd), which uses three collocated receive antennas. This type of HF radar determines the direction to the signal source via direction finding (DF), as opposed to a phased array of receive antennas, which can use beam forming (e.g., Molcard et al. 2009). The SeaSonde receive antennas consist of two orthogonally mounted loop-stick an- tennas (loops) along with one vertical monopole an- tenna (Barrick et al. 1994). Usually the transmit antenna is separated from the receive antennas by at least one radar wavelength (;25 m at 13 MHz), though combined receive-transmit antenna systems are now in use. The receive antenna pattern quantifies the di- rectional sensitivity of the loop antennas in terms of the amplitude and phase of a signal source. The stan- dard method for the measurement of antenna patterns involves a small boat carrying a GPS and a signal source (e.g., transponder) around a site following a circular arc at a range of a few kilometers (Barrick and Lipa 1986). The known direction to the signal source is combined with the received signal to de- termine the antenna pattern. While current measure- ments made with phased array radars may be improved after accounting for nonideal antenna patterns (Graber et al. 1997), and methods described here could be used to determine the APM for these systems, this study primarily addresses SeaSonde DF systems. At HF frequencies, several factors can distort antenna patterns compared with undistorted patterns, typically referred to as ideal patterns (Barrick and Lipa 1986). These factors include flaws in the antennas and con- ductive objects in the antenna near field (i.e., within one wavelength), such as vegetation and fences, soil mois- ture, and variable nearby ocean levels. Based on expe- rience with operating 13 SeaSonde HF radars in the vicinity of Santa Barbara, California, and making about 40 antenna pattern measurements, we have found that moderately distorted patterns are typical. Laws et al. (2010) defined a parameter to quantify the distortion of APMs. Values of the distortion parameter for the transponder-measured patterns in this study were typically less than the average of the 19 measured patterns used by Laws et al. (2010). Antenna pattern measurements at individual sites made over several years show changes through time, though rates of changes are not well constrained due to infrequent measurement. Previous studies have used HF signals backscattered from ships of opportunity to calibrate phased arrays (Fernandez et al. 2003; Fernandez et al. 2006; Flores-Vidal et al. 2013). These approaches differed from APM methods described here, in that the procedures pro- duced relative phase corrections of the array of receive antennas. The methods described were not developed for DF systems that need the relative magnitudes of the three antennas in addition to the phase. Furthermore, the positions of the backscattering ships of opportunity were unknown. The approach for measuring antenna patterns de- scribed here uses commercial ships of opportunity that transmit their positions using the Automatic Identifi- cation System (AIS) (Tetreault 2005). The AIS, de- signed and used primarily for collision avoidance, broadcasts ship identification and position information every 2-10 s while underway. The broadcasts include ship identification [Maritime Mobile Service Identity (MMSI)], latitude, longitude, speed, and heading, and are receivable using low-cost equipment and software. AIS operates in the maritime very high-frequency (VHF) band, with a maximum operational range on the order of 100 km. The AIS supplies critical position data for using ships to derive antenna patterns. This study documents a general method for measuring antenna patterns for DF-type HF radars using ships of opportunity broadcasting with AIS. Section 2 describes how ship signal is identified in HF radar data and the methods used to estimate antenna patterns from ship backscatter. Section 3 shows patterns produced by the method, defines a metric for comparison with transponder- measured patterns, and shows the results of the com- parisons. In section 4 we discuss the implications of these results, and the conclusions are stated in section 5. 2. Methods Data were obtained from four SeaSondes operated by the University of California, Santa Barbara (UCSB), as part of the IOOS surface current mapping network. Three radars used in this study are located along the mainland coastline adjacent to shipping lanes leading to the ports in southern California (Fig. 1). The SeaSondes at Refugio State Beach (RFG), Coal Oil Point (COP), and Mandalay Generating Station (MGS) are located near sea level and operate with stock transmit antennas. The fourth SeaSonde on Santa Cruz Island (SCI) is lo- cated ;450 m above sea level and is set back from the ocean by about 2000 m to the north, ;800 m to the south. It operates with a custom-built dipole transmit antenna that produces more extensive coverage than stock transmit antennas. The receive antenna for each site consists of the standard SeaSonde crossed loops and monopole, separated from the transmit antenna by more than ;25 m. The HF radars operate near 13 MHz with 100-kHz bandwidth, 1.5-km range resolution, and a 2-Hz sweep rate (Table 1). Antenna patterns were measured for each site based on the ship transponder method (hereafter ATRANS) described in Barrick and Lipa (1986), within the time spanned by the AIS data (Table 1). ATRANS then served as ground truth for evaluating antenna patterns derived from backscattering from ships (ASHIP). One difference in our determination of ATRANS compared with the Barrick and Lipa (1986) method was the use of a signal source transmitting a constant signal rather than a tran- sponder. This signal source had a longer range than typical transponders and allowed ATRANS to be de- termined from ranges of 15 km for SCI and 2.5 km for the other sites. a. AIS ship data AIS antennas, receivers, and dedicated computers record the AIS broadcasts at the SCI and COP sites (at approximately 450- and 10-m elevation, respectively). An Icom IC-PCR1500 radio receives the broadcasts and sends the coded signal to a computer running AIS decoding software (Centro de Observaça~o Astrono^mica no Algarve 2012). The resulting files contain ship speed, heading, latitude, longitude, time, and MMSI. From 1 July 2010 through 29 September 2010 (2184 h), AIS data from 1536 individual ships were received and used to generate files with range, bearing, and the radial com- ponent of the ship velocity relative to each of four radars sites. Range and radial velocity are then used to identify ships moving at a nonzero radial velocity within the operating range of each radar. Figure 1 shows locations of ship observations that provided backscattered signals for estimating ASHIP. GPS errors, radial velocity errors due to ship motions (pitch and roll), and aliasing of these motions contribute to errors in the determined bearing. To put an upper bound on the errors from these sour- ces, the standard deviation of the bearings traversed by the ship during the FFT window (256-s time series) is computed (Table 2). Errors in bearings determined from AIS are likely much less than the 28-38 standard deviations. b. HF radar processing Signal processing parameters for the UCSB SeaSon- des are similar to other HF radars operating at these frequencies, which are briefly summarized here. Sea- Sondes use a frequency-modulated interrupted contin- uous wave signal (FMICW), such that each sweep of the entire range (signal transmitted, backscattered, and re- ceived) is completed at 2 Hz. A matrix of the received complex signals is recorded every 256 s for each antenna, with columns corresponding to range, and rows corre- sponding to each sweep (Barrick et al. 1994). For Sea- Sondes these matrices are referred to as range files. FFTs are computed on the columns of this matrix (512 points) and then combined with their complex conju- gates to form autospectra and cross spectra (Lipa and Barrick 1983). Typically, algorithms to remove ship backscatter are applied at this point; thus, the cross spectra from individual FFTs (i.e., with no ensemble averaging) are used in the estimation of ASHIP.For SeaSondes the files containing the unaveraged FFTs of cross spectra are referred to as CSQ files. For pro- cessing spectra to estimate ocean surface currents, the next steps would be ship signal removal (Barrick et al. 1994), ensemble averaging of the cross spectra, and then the application of the multiple signal classi- fication (MUSIC) algorithm (Schmidt 1986). For pro- cessing of ship-based patterns, the ship signal identified in spectra with AIS data is extracted and processed as described below. c. Detecting ship signals in cross spectra AIS broadcasts are used to determine where in the range and Doppler frequency space to look for back- scattered ship signal. As a ship moves through a radar's coverage area, transmitted HF radar waves are back- scattered from the ship and are detected by the receive antenna. Under certain combinations of the ship's range and motion relative to the HF site, the backscattered signal will have power levels comparable to the Bragg peaks from resonant ocean surface waves. Like the Bragg scattered signal, the position of the ship peak in the cross spectra is determined by the ship radial ve- locity and corresponding Doppler shift. Figure 2 shows example HF radar cross spectra from COP containing the backscattered signal and AIS-determined radial velocities of two ships. The x axis was converted from frequency to its Doppler velocity equivalent, given by y 5Dfk021 (where the radar wavenumber k0 is defined as k0 5 2pfc21, c 5 3.00 3 108 ms21 is the speed of light, f is the transmit carrier frequency, and Df is the Doppler shift). The resonant Bragg backscatter peaks (from ocean surface waves) are shown near 6400 cm s21, the deep-water velocity of the ocean surface waves. Figure 2a shows a strong signal associated with a ship centered on ;72 cm s21 along with the AIS-reported radial ve- locities of a second ship expected between 520 and 750 cm s21. Successive plots in time (top to bottom) show changes in the range and radial velocities of the ships, and resulting changes in the backscattered signal power as the ships transit relative to COP. The width of the ship peaks (and Doppler region identified with AIS data) is assumed to result from a combination of changes in the ships' radial velocity and any pitching or rolling motions during the 256-s time series. Processing de- scribed below is applied to each Doppler bin found within the AIS-defined area, such that the combination of one ship and one FFT can yield several estimates of ASHIP at adjacent bearings, along with different signal- to-noise ratios (SNRs). d. Relationship between backscattered signal and antenna patterns The relationship between the signal observations, as found in the HF radar cross spectra, to the antenna pattern is given by Schmidt (1986). Schmidt (1986) models received signal voltages as a linear combination of the incident signals, antenna response, and noise. In the general case, the received complex voltages Xi on antenna i (with i 5 1, 2, ...M, where M 5 3 for SeaSondes) from d incident signals given by Fj ( j 5 1, 2, ...d) plus the assumed uncorrelated noise Wi, are expressed as ... (1) where ai(uj) is the complex response of antenna i to signal Fj arriving fromdirection uj. The columnvector of complex numbers [a1(uj) a2(uj) a3(uj)]T is the antenna pattern at uj. Writing the matrix of ai(uj)asA,Eq.(1) becomes ... (2) {note that A represents the matrix of antenna responses from d incident signals [Eqs. (1) and (2)], while A de- fined previously represents the antenna pattern at all ujg. The covariance matrix S is then obtained from X, ... (3) where the asterisk (*) denotes complex conjugate trans- pose. Assuming the noise variance s2 is equal on each an- tenna, and defining P 5 FF*, we obtain Eq. (4) of Schmidt (1986), ... (4) where I is the identity matrix. Equation (4) expresses the cross-spectra signal power (observed at a given Doppler frequency) as a function of the incident signals, noise, and the antenna pattern. In the special case of a single signal source with a known location, such as backscatter from a ship broad- casting AIS data, Eq. (4) can be used to determine the antenna pattern at the bearing of the ship. In this case, d5 1,and the matrix A becomesa columnvector[a1(uj) a2(uj) a3(uj)]T, with u j given by the bearing to the ship. With d 5 1, P is a scalar, the rank of the matrix APA*is one, and Eq. (4) becomes ... (5) Since P is now a scalar and s2 adds to the diagonals, AA* and S share the same eigenvectors. The 3 3 3matrixAA* has one nonzero eigenvalue and the corresponding eigen- vector is a scalar multiple of A, the antenna pattern vector at uj. These properties result from matrices of the form AA*whenA is a vector (Strang 1988,p.98).Inother words, the vector A becomes the single-basis vector for the matrix AA*. The practical result is that for a known single source, the signal data in the cross-spectra files represented by S are a scalar multiple of the antenna pattern, A 5 [a1(uj) a2(uj) a3(uj)]T at uj. Thus, the antenna pattern A at uj can be derived directly from the elements of the rank 1 matrix S. To recover the antenna pattern, we choose the third column of the matrix S given by sj3 and normalize by s33, ... (6) Note that for SeaSondes, the imaginary part of s33 is zero because the phase f is defined as zero on antenna 3 (the monopole) [where the real and imaginary components are related to the magnitude r and f by Euler's formula, reif 5 r cos(f) 1 ir sin(f)]. Equation (6) shows the an- tenna pattern vector A at bearing uj in terms of the signals observed in the SeaSonde cross spectra. e. Assigning bearing The final step to complete the determination of ASHIP is to associate observations of the antenna pattern in A(uj) to the ship bearing uj. From the AIS latitude and longitude, reported at approximately 10-s intervals, the range to the HF radar site is computed, and from this the time-centered radial velocities and corresponding bearing to the HF radar are computed, producing a time series of ship radial velocity and bearing. These observa- tions form a table during the time of the 256-s FFT (with columns radial velocity and bearing, each row at a new time). The FFT separates the received signals into Dopp- ler frequency bins and their equivalent Doppler radial velocities. The radial velocity of each signal bin is matched with the AIS-determined ship radial velocity, associating a bearing to the ship with each signal bin through a lookup table. The collection of column vectors A(uj)atallob- served values of uj (j 5 1, 2, ...b)isthematrixA, ... (7) For SeaSondes, A is a matrix with three rows, with the third row consisting of all ones, as can be seen from Eq. (6).[Toclarify,A in Eq. (1) is a subset of A defined in Eq. (7).] f. Comparison metric At each bearing, we quantify the difference between the complex quantities ASHIP and ATRANS using the Euclidean distance D between the two at the same bearing. Before computing D, ASHIP and ATRANS are put into an equivalent form consisting of only real numbers. Beginning with Eq. (7), the third row is dropped, and A is rewritten in terms of the real and imaginary components, for example, ... (8) Simplifying the notation, the subscripts R and I desig- nate real and imaginary components, respectively: ... (9) At a given u, Eq. (9) gives the four components of A as a vector of real numbers. For two estimates of the antenna pattern at a given bearing [e.g., ASHIP(u) and ATRANS(u)], the Euclidean distance D is defined, ... (10) where D is the distance between two points in a four- dimensional space. Term D quantifies the difference between the two patterns at given bearing, producing a scalar measure of their similarity. Note that the MUSIC algorithm uses the inverse of D2 in the direction of arrival calculation (Schmidt 1986)andthatD is dimensionless, since both ASHIP and ATRANS have been normalized. g. SNRs for thresholding Four SNRs are defined for thresholding, to separate ship backscatter from other signal sources. Other signal sources include first- and second-order backscatter from the ocean surface, broadband and narrowband noise from other HF radar transmitters, and natural external sources, such as worldwide thunderstorms. These signals typically persist in time, or are broadband, often spread over many Doppler bins and several range cells. When measuring antenna patterns with transponders, the signal is typically characterized by a narrow peak in frequency and range, with power levels well above the noise. Away from the peak, the signal level falls rapidly into background noise in adjacent bins and adjacent range cells. The typical characteristics of transponder signals are also desirable when measuring antenna pat- terns with ship backscatter. Ship backscatter signals are also transient, typically present in a given Doppler bin for only a single FFT. The SNRs described below are designed to exploit the differences in signal character- istics, enabling reliable separation of ship backscatter from other signal sources. Each of the four SNRs is produced according to the equation where SSIGNAL is the power observed (dBm) in the monopole autospectra, in the range cell and the Doppler bin assumed to contain ship backscatter. The term hSNOISE i is the average of bins assumed to contain only noise, as explained below. The four SNRs are deter- mined by varying the method for computing SNOISE. The first SNR, denoted SNRBKGND, is computed from Eq. (11) with hSNOISE i defined as the average power over two frequency ranges, DfBKGND 5 0.701 to 0.960 Hz and 20.701 to 20.960 Hz (Fig. 3a). SeaSonde software typ- ically uses noise levels in the region defined by DfBKGND to compute the SNR of the first-order Bragg scatter peaks. Following the SeaSonde method, an initial hSNOISEi is obtained, and then spectral points more than three standard deviations from the mean are re- moved and hSNOISE i is recomputed on the remaining points. The second SNR, SNRLOCAL, is computed using Eq. (11) after computing hSNOISE i as the mean spectral power spanning a range of Doppler frequency bins (DfLOCAL) adjacent to the ship peak. Here hSNOISE i is the average of 20 Doppler bins found on either side of the spectral region identified by AIS (Fig. 3a). Bragg signals are excluded from this calculation, such that the resulting hSNOISE i may depend on fewer than the 40 Doppler bins. The third SNR, SNRRANGE, is computed using Eq. (11) with hSNOISE i determined from multiple range cells. Unlike SNRBKGND and SNRLOCAL, which are com- puted from single range cells, SNRRANGE is computed using hSNOISE i based on spectra power found in the same Doppler bin (fSHIP) but in several range cells spanning two intervals (Dr). The Dr intervals each span six range cells, beginning two range cells away from SSIGNAL. For example, if the ship SSIGNAL is located in range cell 15 and Doppler bin fSHIP, then hSNOISE i is computed from signals found at fSHIP in the Dr intervals extending be- tween range cells 8-13 and 17-22, as shown in Fig. 3c.The Dr intervals begin two range cells away from SSIGNAL, because the ship backscatter signal may be present in adjacent range cells due to pulse stretching in the receiver (Lipa and Barrick 1983). The fourth SNR, SNRTIME, uses the time domain properties of both SSIGNAL and hSNOISE i to separate short-term signal sources, such as ships, from persistent signal sources, such as currents and waves. Prior to the Eq. (11) calculation, the time-centered, hourly averaged cross spectrum is subtracted from the individual cross spectra containing SSIGNAL. As shown in Fig. 3b, this removes much of the first- and second-order Bragg sig- nal, along with any other signals persisting on hourly or longer time scales. SNRTIME is then computed with Eq. (11) using SSIGNAL from the residual, and hSNOISE i over Doppler regions is defined by DfBKGND as in SNRBKGND. Calculation of SNRTIME is similar to real- time HF radar processing methods, which apply an in- finite impulse response (IIR) filter to remove ship backscatter (Barrick et al. 1994). The above-mentioned methods produce four SNRs for each signal observation that may contain ship backscatter. Low SNR from any of the four methods suggests the presence of contaminating interference or other nonship signal. When applying thresholds to the SNRs, the lowest value of SNR of the four pre- vents the ASHIP point from passing a given SNR threshold. Thus, the minimum of the four methods is found: ... (12) such that each ASHIP observation is associated with one SNR value for use in thresholding. The fraction of points rejected due to a given SNR method is shown in Table 3. The comparisons below show results of ASHIP after re- quiring SNRMIN . 11 dB. Justification for this threshold is described later. h. AIS-based thresholds Three additional metrics are computed from the AIS data for thresholding. Threshold values were de- termined empirically, as discussed below. The first is the standard deviation of the ship radial velocity observed during the 256-s cross-spectra interval (sSHIP). The ASHIP observations obtained from ships when sSHIP . 150 cm s21 were excluded from the analysis. The second metric is the distance between ships and oil platforms (Ddp). ASHIP exhibits large errors when ships are close to these structures, so ships with Ddp , 1500 m were excluded. The third metric, Dds,isdefinedasthe minimum separation in range and Doppler bins be- tween ships. This metric identifies ships that are in nearly the same range cell and traveling at nearly the same radial velocity relative to a site. Ships separated by Dds ,61 range cell and ,620Dopplerbinswere excluded. 3. Results a. Observations Estimates of ASHIP and ATRANS show reasonable agreement for RFG, COP, MGS, and SCI as shown in Figs. 4-7, respectively. At RFG, some bearings exhibit differences, but the overall shape of ATRANS is repro- duced by the 58 bin averages of ASHIP, including a small- scale structure near 1658-1708 (Figs. 4a,b) (bins with N , 5 not shown). A significant difference in the angular coverage is observed, as ATRANS extends angularly from 908 to 2758, while the ASHIP covers 1208-2508 (Fig. 1a). The difference in angular coverage results from the orientation of the shipping lanes relative to the site (Fig. 1a), such that ships at bearings near the edges of ATRANS are at greater range and the backscattered signal levels are low. Figure 8 shows histograms of ASHIP data points versus bearing for each site, illustrating the effect of range on the number of available data points at RFG (Fig. 8a). Figures 8a,b also show low values in histogram bins where most ships pass through the zero Doppler bin, near 1958 for RFG and COP. Background signal levels are consistently high near zero Doppler due to backscatter from stationary objects, for example on land (Long and Trizna 1973), making SNR of the ship back- scatter signal relatively low in this region of the Doppler spectrum. COP has a similar orientation to the shipping lanes as RFG, but the results shown in Fig. 5 have some impor- tant differences from RFG. At COP, ASHIP was pro- duced from about 5 times more observations than at RFG (15 691 data points at COP vs 3043 at RFG; Figs. 8a,b), though these came from only 40% more ships (246 at COP vs 174 at RFG). COP typically has higher levels of transmitted power than RFG (data not shown), and RFG also experiences elevated levels of diurnal back- ground noise (Emery et al. 2004). Lower signal and higher noise levels significantly reduce the number of ships producing antenna pattern estimates at RFG. Differences between Figs. 4 and 5 demonstrate the broader angular coverage obtained at COP, with ob- servations spanning 2008 versus approximately 1308 for RFG. The maps (Figs. 1a,b) and the ship observations versus bearing (Figs. 8a,b) also illustrate this difference. Disagreement between ASHIP and ATRANS observed at COP for bearings ,1408 coincides with the presence of a building and several trees in the near field of the re- ceive antenna at these bearings. Bearings less than 1208 coincide with the presence of a cluster of oil production platforms, suggesting that multipath scatter from these objects may be important even with Ddp . 1500 m. Dis- agreement is also observed between ASHIP and ATRANS for bearings ,2008 in the a2I component (Fig. 5d). Results for MGS loop 1 ASHIP agree with ATRANS between 1908 and 2908 (Fig. 6), while the methods di- verge for bearings less than 1908. Because of the orien- tation of the shipping lanes relative to the site (Fig. 1c), few ship observations are obtained north of 2808, while the transponder pattern continues to 3308. However, several ASHIP observations were obtained at bearings ,;1708 where ATRANS ends, despite the long distances that the HF radar waves must travel over land. The ATRANS from SCI spans approximately 2808 in bearing (Fig. 7) with coverage both north and south of the Santa Cruz Island. Agreement between ASHIP and ATRANS is observed, except between ;308 and ;808, where HF radar waves travel long distances over land. The 58 bin averages of ASHIP reproduce small-scale structure in ATRANS,suchasFig. 7d be- tween 1508 and 2008. A comparable number of ob- servations were obtained within the Santa Barbara Channel as were obtained at RFG (Figs. 8a,d), though a longer time period was covered with the SCI data (Table 1). Backscatter from 422 unique ships pro- duced 29 576 ASHIP observations (Fig. 8d) during the 2 months spanned by the SCI data. Figure 8d shows that most observations originated from south of the island, between 1208 and 2408 (Fig. 1d). Figure 8 also shows the number of individual ship-FFT combinations, providing a lower bound on the number of indepen- dent observations. b. Comparison metric D example and results Prior to comparing ATRANS and ASHIP using D, a simple case is presented to build intuition and to guide interpretation of the results. The range of nominal values of D is illustrated by comparing D between two COP ATRANS measurements from May 2006 and Au- gust 2010 (amplitudes, Fig. 9a; phases, Fig. 9b). Minor differences in the amplitudes and phases, due to minor changes in the site hardware and receive antenna near- field environment, result in D ranging from 0.1 to 0.4 (Fig. 9c). Figure 9c indicates the range of D that can be expected between two antenna patterns that are quali- tatively similar. Figure 10 shows D between the 58 bin averages of ASHIP and ATRANS for each HF radar site, summarizing the comparisons shown in Figs. 4-7. Figure 10a illus- trates the similarity between ASHIP and ATRANS at RFG, with the exception of 1308 and near 2408, where D captures the differences observable in Fig. 4d (at 1308) and Figs. 4b-d (near 2408). For COP, differences be- tween ASHIP and ATRANS at bearings less than 1358 observable in Fig. 5 are shown by D in Fig. 10b, along with the close agreement observed at other bearings with D , 0.1. Figure 10c shows agreement for MGS between 2008 and 2958. Comparing Fig. 10c with Fig. 8c suggests that high D at MGS (outside 2008-2958) may relate to the low N obtained there. Minimum values of D for SCI (Fig. 10d) lie near D 5 0.15, with larger values of D-for example-near 1208 corresponding to differ- ences observed in Figs. 7c,d. Overall, Fig. 10 shows that the lowest values of D, and thus the lowest errors, are observed at COP (Fig. 10b). c. D versus SNRMIN Values and scatter of D decrease rapidly with in- creasing SNRMIN at all four sites (Fig. 11). For SNR greater than 10 dB, the broad scatter in D narrows, such that SNRMIN .;15 dB is associated with low D. SCI is an exception, with some points with SNRMIN . 10 and D ; 1.25. Values of D averaged over bins of width DSNR 5 1 dB are also shown (open circles), along with the number N of points per bin (right-hand y axis) showing that each site has more than 1000 observations with SNRMIN . 10 and more than 100 observations with SNRMIN . 15. 4. Discussion A goal of this research is to evaluate the method as the sole source of antenna pattern measurements. In estimating ASHIP (Figs. 4-7), significant agreement between ASHIP and ATRANS was found (e.g., Fig. 10, with D , 0.2) when the following empirical thresholds were used: ... Figure 11 guided the choice of the SNRMIN threshold, which produces low overall error as measured by D. Limiting the standard deviation of radial velocity (sSHIP) identifies ships with smaller changes in radial velocity during the 256-s integration times of the cross spectra. Both Ddp and Dds thresholds removed multi- source signals, which produced errors in ASHIP. Since each threshold is applied to metrics computed only from the AIS and HF radar data, we suggest the method can serve as an independent source of APMs. While this analysis produced APMs at 58 resolution (Figs. 4-7), with sufficient data density, 18 bins with output every 18 are possible. These results corroborate a theoretical and experi- mental analysis of ship tracking with HF radars (Barrick 2003). Using a SeaSonde with measured antenna pat- terns, the study found a power-law relationship between SNR and the uncertainty in bearing to a target, such that uncertainty decreased with increasing SNR. The analy- sis indicates that uncertainty in the FFT signal power, due to contributions from noise, leads to uncertainty in the MUSIC-determined bearing. Our results similarly show decreased error with increasing SNR (Fig. 11). The results differ, in that the errors here are between two antenna patterns (ASHIP and ATRANS as quantified by D) at a known signal bearing, while the Barrick (2003) results determine the uncertainty in the signal bearing. Barrick (2003) also suggests that contributions from noise (quantified by SNR) explain most of the scatter in ASHIP observed in Figs. 4-7. Both analyses suggest re- jecting data with SNR below 7-10 dB. These combined results demonstrate that SNR is the most important metric for accurate APM determination. Scatter in ASHIP (Figs. 4-7) resulting from errors in the AIS and the GPS positions they report are probably small. Methods used to assign bearings to ASHIP de- scribed in section 2e depend on associating the radial velocity of the received signal with an estimate of the ship position within the FFT time period. As suggested by Table 2, errors in ship positions are likely less than the 28-38 standard deviations of bearings traversed during the FFT time period. Barrick (2003) indicates that SNRMIN 5 11 is equivalent to a bearing uncertainty of about 128. Thus, errors in bearing resulting from GPS or other AIS position errors are likely a small fraction of the errors in estimates of ASHIP. Both of these sources of error and uncertainty are likely reduced through bin averaging of ASHIP. While the Barrick (2003) study associates SNR with bearing uncertainties, the results here associate SNR with a value of D, the difference between ASHIP and ATRANS. Associating a value of D with a bearing un- certainty in the ocean current data is identified as a question for future investigations. This analysis can address two additional questions regarding the generation of patterns from ships. First, how frequently can ASHIP be generated and at what level of error? Figure 12 shows the number of cumula- tive unique bearings u spanned by ASHIP as a function of time [NSHIP(t)] divided by the total number of bearings in ATRANS (NTRANS; both NSHIP and NTRANS at 18 res- olution). Counting observations at 18 resolution enables estimates of the time to produce five points per bin in a58 average. The times required to generate ASHIP(u) for various error levels, set by SNRMIN, are shown by the different lines. For example, Fig. 12a shows that ASHIP at RFG covers about 75% of the 18 bearings of ATRANS with SNRMIN . 10 after 60 days. COP (Fig. 12b) covers about 95% of ATRANS bearings during the same time period. ASHIP covering 75% of ATRANS with SNRMIN . 10 can be generated in approximately 53 days at RFG, 9 days at COP, 12 days at MGS, and 2 days at SCI. Of course these times depend on the level of ship traffic. Applying thresholds such as SNRMIN . 10 sets the error between ASHIP and ATRANS at D 5 0.25 after averaging, as indicated by Fig. 11. Second, how many ships are needed to generate a pattern? This question can be answered by substituting the number of ships n for time t to obtain the ratio NSHIP(n)/NTRANS. Figure 13 shows that ASHIP covering 75% of ATRANS with SNRMIN .10 can be generated from 155 ships at RFG, 50 ships at COP, 48 ships at MGS, and 47 ships at SCI. The results presented here demonstrate the difficultly of using ocean current HF radar for ship detection. Between 500 and 630 ships reporting positions with AIS passed within the coverage areas of the four HF radars. Defining a positive detection as an observation with SNRMIN . 10, between 30% and 85% of the ships were detected. However, these positive detections represent a small fraction of the time (less than about 5%) that the ships were within the coverage area. This result illus- trates the need for modified HF radar processing schemes for ship detection, such as described by Roarty et al. (2010). 5. Conclusions Methods presented here demonstrate the use of ship backscatter to measure antenna patterns for direction- finding HF radars. The Santa Barbara Channel, with shipping lanes within the coverage area of several Sea- Sonde HF radars, provides an ideal testing ground for developing this technology. The analysis supports the following conclusions: * AIS and ship backscatter in cross spectra can be used to independently estimate the receive antenna pattern. * The difference between transponder-measured pat- terns and ship backscatter patterns depends on SNRMIN when SNRMIN .;10 dB. Using SNRMIN . 11 dB as a threshold for ship-based patterns produces low error when these are compared to patterns measured with standard methods. * Significant fractions of the antenna pattern can be measured with as few as 50 ships of opportunity, or on time scales on the order of days depending on the local ship traffic and SNR. Additional questions about HF radar antenna patterns that can be addressed using this method include, How do antenna patterns change through time? What causes them to change? On what time scales do they change? These results suggest that some HF radar deployments will still require transponder calibrations, particularly at bearings near the coast, depending on ship traffic and the geography of the HF site. In unique situations (e.g., HF radar deployed on an island), the methods would cover an equivalent range of bearings. Methods presented here can provide information about APM changes at a site and indicate the need for a transponder calibra- tion. In this way, the method could augment or minimize the need for transponder-based patterns. Given the cost of transponder pattern measurements, it is likely that a software implementation of this method would be a cost-effective way to measure antenna patterns. Be- cause many HF radars operate with idealized patterns, methods for automating antenna pattern measurement would significantly improve surface currents mapped with HF radar. Acknowledgments. We thank Megan McKenna and John Hildebrand, Scripps Institution of Oceanography, for the AIS data. Boat operations by David Salazar, Cristoph Pierre, and Eduardo Romero contributed to ATRANS measurements, and all aspects of this analysis were improved through the work of, and discussions with, Cyril Johnson. We thank the three anonymous reviewers, whose efforts improved the manuscript. This material is based upon work supported by the U.S. Department of Commerce under Contract WC133R10CN0212, and it benefitted from the U.S. Integrated Ocean Observing System program office's HF radar support. 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EMERY Marine Science Institute, and Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California LIBE WASHBURN Department of Geography, University of California, Santa Barbara, Santa Barbara, California CHAD WHELAN AND DON BARRICK CODAR Ocean Sensors, Ltd., Mountain View, California JACK HARLAN National Oceanic and Atmospheric Administration, Silver Spring, Maryland (Manuscript received 30 August 2013, in final form 28 January 2014) Corresponding author address: Brian Emery, Marine Science Institute, University of California, Santa Barbara, Santa Barbara, CA 93106-6150. E-mail: [email protected] DOI: 10.1175/JTECH-D-13-00181.1 (c) 2014 American Meteorological Society |