a. The X-band marine radar

The radar is an X-band Racal Decca marine radar fitted with a 1.8-m linear antenna rotating with a 2.4-s period. The horizontal beamwidth at half-power is approximately 1°, producing a 10-m-wide antenna footprint at 500 m. The emitted X-band frequency of 9.4 GHz corresponds to a wavelength of 3.2 cm. As for most marine radars, the polarization is horizontal (HH). The microwave energy is emitted in the form of pulses of varying lengths—short (0.08 μs), medium (0.3 μs), or long (1 μs)—which produce nominal antenna footprints 12, 45, or 150 m long, respectively, in the radial direction. Both the pulse peak power and pulse repetition rate (PRR) are determined by the pulse length setting (Table 1). On reception, the radar signal is log-amplified and displayed on the radar video display unit (VDU).

b. Data capture board

The data capture board is PC based and synchronized with the radar via three links (Fig. 1). The north marker pulse provides the radar heading reference point, the trigger pulse marks each pulse emitted by the magnetron, and the video signal consists of the log-amplified returns from the sea surface. This backscatter signal is extracted by the capture board at the output of the log-amplifier and is unaffected by any signal processing occurring downstream (e.g., rain/sea clutter filtering, sensitivity time control) designed to improve the display of the signal on the VDU.

Various adjustable parameters control the data capture and determine the properties of the digital radar image. The image’s spatial coverage in azimuth can be set to up to 180°. The image’s resolution in azimuth is determined by the number of independent “looks” (or successive echoes returned from the sea surface) averaged by the capture board per pixel in azimuth. In order to reduce speckle, the number of looks is maximized generally to match the image resolution in azimuth with the antenna’s physical horizontal beamwidth. Hence, for a 2.4-s antenna rotation period, a 1° beamwidth, and the PRR values given in Table 1, the number of looks for short, medium, and long pulse settings is equal typically to 16, 8, and 4 pulses, respectively.

The integrated multilook backscatter signal is then sampled at a rate of 20, 10, or 5 MHz, resulting in an image pixel resolution in range equal to 7.5, 15, or 30 m, respectively. The backscatter signal is digitized to 8 bits (256 gray levels) and stored on the PC. The buffer size of the capture board is limited to 512 bytes, each byte corresponding to one pixel in range. Hence, for a sampling rate of 10 MHz, the image’s spatial coverage in range is limited to 7680 m (4.2 nmi).

The data capture board also permits images of the same area to be collected over several antenna rotations. The production of such time series allows the pixel-to-pixel averaging of sequential images into an average backscatter image for which the radar backscatter signal-to-noise ratio is much improved. Similarly, images of higher-order statistical moments can also be computed.

a. Radar equation

The power received at the antenna P_r is related to the NRCS σ⁰ of a target by the radar equation (Ulaby et al. 1982)

View Expanded

where R is the slant range (m) of the target, P_t the transmitted power (W), g(θ, ϕ) the antenna gain pattern in azimuth (θ) and elevation (ϕ), A_e the effective aperture of the antenna (m²), and A_r the physical area of the target (m²). For highly directional marine radar antennas, the gain g(θ, ϕ) can be approximated by the maximum antenna gain, G = g(0, 0). In the present case, G is taken equal to 28 dB, following the manufacturer’s technical specifications. The antenna’s effective aperture A_e is related to the antenna’s physical area A and the antenna efficiency η by A_e = ηA, and represents the performance of the antenna in reception. The antenna’s effective aperture can be related to the maximum gain of the antenna by A_e = Gλ²/4π, where λ is the wavelength of the radar radiation (m). Thus, replacing A_e in (1) leads to the NRCS in decibels:

View Expanded

where the NRCS is a function of received power, target range, physical area of the target, and a scaling factor K characteristic of the properties of the magnetron and antenna, which can be evaluated as K = P_tG²λ²/(4π)³.

b. Sea clutter area A_rs

For distributed targets, the physical area of the target A_r is equivalent to the size of the antenna beam footprint on the sea surface. At high angles of incidence, the footprint of the pulsed radar beam is limited in azimuth by the horizontal beamwidth of the antenna ω and is limited in range by the temporal length of the radiated pulse τ (Fig. 2). The equivalent spatial length of the radar pulse p is given in meters by p = cτ/2, where c is the speed of light (c = 3 × 10⁸ m s⁻¹) and τ is the radar pulse length (s). Assuming a flat earth approximation, Fig. 2 yields the rigorous expression for the pulse-limited vertical beamwidth Φ of the radar beam (rad) as

View Expanded

where h is the height of the radar antenna (m). Hence, the solid angle of the pulsed radar beam Ω (rad²) is given by Ω = Φω, and the area normal to the incident radiation is S_n = R²Ω (m²). Given the expression for the grazing angle, ϕ = sin⁻¹(h/R) in radians, the sea clutter area A_rs (m²) can be written as

View Expanded

For near-grazing angles (Φ small), (4) is equivalent to the classical expression of the clutter cell limited by pulse length (Nathanson 1969):

View Expanded

c. Received power P_r

The signal intensity in the images is related to the received power P_r at the antenna by the radar system transfer function. This relationship includes transmission losses in the radar’s various components, the radar logarithmic amplification, and the digital capture board transfer function. The determination of the system transfer function constitutes the major effort in the normalization of the radar images and is examined in the next section.

a. External calibration approach

1) Formulation

Most modern marine radars are fitted with logarithmic amplifiers designed to increase the dynamic range of the instrument, improve the detectability of targets at far ranges, and reduce the risk of saturation at close ranges. To first approximation, the amplification function may be assumed to be perfectly logarithmic. The relation between received power and intensity is then expressed on a logarithmic scale as a linear function:

XA₁₀P_rB,(6)

where X is the image intensity in digital numbers (DNs) and A and B are two constants defining the amplification function. From (2) and (6), we can write

View Expanded

After equating (7) and (8), we obtain

₁₀R⁴CXD,(9)

with

View Expanded

The numerical values of C and D can then be determined experimentally by plotting 10 log₁₀R⁴ against the echo intensity X for targets of known radar cross section, σ_t = σ⁰_tA_rt, located at different ranges. These empirically determined coefficients will be referred to hereafter as C_t and D_t to indicate that they were obtained from measurements over calibrated point targets. Analytically these coefficients are equal to

View Expanded

Hence, substituting (8) in the expression for the NRCS [(2)] and given the expressions for C_t and D_t [(12) and (13)], the NRCS of the sea surface σ⁰_s can be represented finally in decibels as a function of the pixel intensity X:

σ⁰_s (dB) = C_tXD_t10σ_t10R⁴₁₀A_rs(14)

where C_t and D_t are the coefficients determined empirically from calibrated point targets, σ_t is the radar cross section of the calibrated point target (m²), R is the slant range of the pixel (m), and A_rs is the sea surface area (m²) illuminated by the radar antenna at that range. It should be noted that the traditional R⁻³ dependence of σ⁰_s on range is included implicitly given the quasilinear dependence of A_rs on R at low grazing angles. Hence, the empirical determination of the coefficients C_t and D_t enables the definition of the end-to-end transfer function of the radar system.

b. Internal calibration approach

a. Multiple scattering

Measuring NRCS for targets raised above the sea surface is different from measuring the ocean backscatter coefficient. The radar equation given in (1) is valid only for point targets located in free space. The presence of the air–sea interface between the radar and the target allows for multiple scattering whereby the energy travels not only by the direct path but also by paths that include reflection from the sea surface between the radar and the target. In the case of a perfectly smooth surface and a horizontally polarized X-band radar wave, the magnitude of the reflected component to the backscatter can be of the same order as that of the direct component. Under these particular conditions, the contribution to the received power due to multiple scattering can be estimated and a new expression for the received power can be found as (Skolnik 1980)

View Expanded

where, respectively, h_a and h_t are the heights of the radar antenna and the target above the mean sea level. It follows that the NRCS for a point target in the presence of a reflecting flat surface is given as

σ⁰₁₀P_r10R⁸₁₀A_r10K(18)

where a new scaling coefficient K′ is introduced as

View Expanded

From the expression for the original scaling factor K, the coefficient K′ can be related to K by

View Expanded

b. Basis of a practical procedure for an absolute calibration

If an absolute calibration is to be achieved, the method for the external calibration described in section 4a must be adapted to allow for the multiple scattering discussed above. The assumption of a linear response now leads instead of (9), to

₁₀R⁸CXD(21)

In principle, this enables C′ and D′ to be evaluated empirically as C^′_t and D^′_t from a series of measurements of the signal echo from known targets (σ_t) at various ranges. Then, from (18) and (21), we can write

₁₀P_r−C^′_tX − D^′_t + 10 log₁₀σ_{t 10}K(22)

But 10 log₁₀P_r is described also by the internally derived calibration function f_s,m/l(X). Thus, over the intermediate range in which the linear relationship between the received power in decibels, P_r and image intensity X is valid, we can say

f_s,m/l(X)=−C^′_tX−D^′_t+10 log₁₀σ_t+10 log₁₀K′,(23)

where for short pulse

f_sXX(24)

and for medium–long pulse

f_m/lXX(25)

Thus, C^′_t can be assumed to be equal to the slope coefficient in (24) and (25) determined from the internal calibration, and all that remains is to determine D^′_ts, D^′_tm, and D^′_tl by fitting (21) to measurements of known target echoes. Comparison of (23) with (24) and (25) yields expressions for the new scaling coefficient:

View Expanded

from which the original scaling factor K can be derived using (20).

c. Experimental results

Despite the obvious uncertainty associated with the motion of the buoys, the measurement errors were minimized by carrying out the experiment in very calm wind and sea conditions, thus reducing the pitch-and-roll motion of the buoys and limiting the contribution to the backscatter from the surrounding sea surface. The radar image spatial resolution was optimized to 7.5 m for the accurate measurement of the radar reflectors’ sharp echoes intensities. For each target, a time series of 250 echo intensity measurements was obtained at each pulse setting and was submitted subsequently to statistical analysis.

It was noted from the distorted shape of the buoys’ echoes that the radar receiver presented a low-filter-type response in which a delay is introduced in the time it takes for strong echoes to reach their nominal intensity. The rise time was found to be of the same order as the duration of the medium pulse and therefore was particularly detrimental to the measurement of target echo intensity in short pulse images. The temporal characteristic of the receiver response was estimated from radial transects in the artificial images obtained during the one-step internal calibration. Unfortunately, the maximum 20-MHz sampling rate used in these images proved inadequate to determine the time characteristic of the receiver accurately enough. As a result, only an approximate correction could be applied to the buoy intensities, and it is thought that a pulse-dependent bias may have been introduced at this stage that could question the validity of the empirical K values derived for different pulse settings from these measurements.

After correction of the echo intensities, the histograms for each time series were produced. The intensity associated with the 10 m² radar cross section (RCS) was identified by comparing our results with RCS statistics reported by Trinity House Lighthouse Service for this type of buoy-based radar reflectors. In their latest study (Ward and Vennings 1989), the performance of the Speckter radar reflectors was expressed in statistical terms for various buoy tilt angles. The 16-in. octahedral Speckter radar reflectors were found to behave well, and RCS statistics reported echoes larger or equal to 10 m² for 30% of the time for tilt angles between 0° and 10° from the vertical. In the very calm conditions encountered during our experiment, the buoy motion was assumed to belong to this range of inclinations. The intensity corresponding to the upper 30% of all echo occurrences was therefore determined for each buoy and associated with a 10 m² radar cross section. The range R and the 30% intensity X_30% of the radar reflectors were plotted as 10 log₁₀R⁸ against intensity X_30% in Fig. 8. The intensity of the closest buoy echo unfortunately reached the system saturation level on all pulse lengths and could not be used in the linear function fitting. The offset D^′_t was determined by least square fitting of the data points with a linear function of predetermined slope C^′_t obtained from the one-step internal calibration functions at intermediate intensities expressed in (24) and (25). The coefficient D^′_t was found equal to 323, 325.5, and 326.5 for short, medium, and long pulses respectively. Following the calculation of the intermediate scaling factor K′ from (26) to (28), the original scaling factor K was calculated using (19) for a radar height h_a of 7 m and a reflector height h_t of 3 m above mean sea level. This resulted in values of K equal to 31.3, 35.8, and 36.8 dB for short, medium, and long pulses.

These experimental results are compared in Table 1 with values of K calculated from the manufacturer’s technical specifications for the maximum antenna gain (28 dB) and from laboratory measurements of the emitted power for each pulse setting. The numerical values of the empirically derived scaling factor K are in reasonably good agreement with the calculated values and indicate that the nominal antenna gain figure given by the manufacturer is a realistic estimate of the system’s performances. However, given the uncertainty in the echo intensity correction factor for different pulse lengths, these experimental results are not sufficiently reliable to serve as a basis for the analysis of the radar’s dynamic range capabilities on different pulse settings. Hence, it was deemed safer to perform the absolute calibration of images and the assessment of the system’s NRCS using the calculated values of K. Thus, the final expression of the NRCS in decibels as a function of pixel intensity X (DN) at a range R (m) is

where A_rs is the sea clutter area illuminated by the antenna as defined by (4), f_s and f_m/l are the radar system amplification functions found during the internal calibration of the system for short and medium–long pulse settings, and the last term is the absolute calibration scaling factor calculated from laboratory measurements of the emitted power and the manufacturer’s technical specification of the maximum antenna gain.

a. Errors types

Measurement errors can be divided into systematic or random errors. Systematic errors are caused by incorrect methods of measurement and always bias the results in a particular direction. Usually this type of error does not affect the internal consistency of the measurements, but it becomes critical when comparing measurements with results from other experiments. Random errors are due to unavoidable interference during the measurements and are governed generally by Gaussian statistics. In contrast to systematic errors, random errors can be minimized by averaging over many realizations.

b. Error in pixel intensity

The error in the pixel intensity consists of the error in the received power related to the system noise and stability and to the digitization error introduced during the experimental determination of the instrument transfer function. The high accuracy of the microwave pulse generator used during the internal calibration experiment was found to result in a maximum digitization error less than 1 DN in the artificial images.

The error in the received power was identified as the main source of error in the NRCS, as it consists mostly of the system receiver noise. Receiver noise is a random error related to the thermal agitation of electrons in the instrument, and its statistical characteristics are related directly to the noise temperature of the receiver (Wheeler 1963). The thermal noise characteristics of the present system could be determined experimentally given the ability of the data capture board to collect radar images without prior power transmission. In the absence of transmitted pulses, the signals collected at the amplifier consist of the receiver noise plus the ambient microwave noise. At X-band frequencies and in the absence of other interfering systems in the vicinity, the natural level of microwave energy can be considered negligible in comparison with the instrumental noise. When other systems are present, the disruption of the data is generally sufficiently perceptible to ensure these data are rejected from the analysis.

Experimental measurements of the thermal noise were carried out on several occasions characterized by different environmental conditions to examine the stability of the system with temperature. On each occasion, a time series of 64 “blind” images was collected for all three pulse settings. For each time series, the average and standard deviation images were then produced for a variable number of antenna revolutions. The mean value in the average and standard deviation images was calculated by averaging over the whole image. The results for three different ambient temperatures are presented in Fig. 9 for all three pulse settings. The mean and standard deviation of the receiver noise are expressed in digital numbers between 0 and 255.

The mean receiver noise was found to be largely independent of pulse length setting and the number of revolutions but clearly dependent on temperature. The 5°C temperature difference between the datasets plotted as “×” and “○” in Fig. 9 correspond to a 1.5-count increase in the mean receiver intensity. Thus, the mean receiver noise should in principle be measured for every data capture session but can be assumed safely to be less than 25 counts in most environmental conditions.

The receiver noise standard deviation was found independent of temperature but showed a clear 1/N^1/2 dependence on N, the number of images averaged, in accordance with Gaussian statistics. The variability of the receiver noise appeared larger for long and medium pulse settings, presumably because of the smaller number of independent looks on longer pulse settings. The receiver noise error was then digitized by rounding up to the nearest DN value for a range of N values. The total error in pixel intensity S_x was derived by combining the digitization error and the receiver noise error. The results are summarized in Table 2 for all pulse length settings and a range of N values.

c. Error in emitted power

The transmitted power P_t is affected by a random error linked to the thermal agitation in the magnetron and fluctuations in the power supply. The random pulse-to-pulse fluctuations of the peak power is one of the parameters used to characterize the quality of the magnetron. In the present case, the pulse-to-pulse error is specified by the manufacturer (English Electronic Valves, Chelmsford, United Kingdom) to be less than ±10% of the mean peak power over a wide range of temperature and humidity conditions.

Adopting the rigorous assumption that the manufacturer’s confidence limit represents one standard deviation of the emitted power pulse population, it follows from the laws of random errors that the error in the emitted power for images in which n_i number of independent looks are integrated per pixel in azimuth is

View Expanded

where S₁ is the standard deviation of the single pulse population and P_t is the mean emitted power (W). Similarly, the error in emitted power for radar images collected with n_i number of looks and averaged over N antenna rotations becomes

View Expanded

The error S_Pt in the peak power in radar images can then be calculated for all pulse settings and for a variable number of antenna revolutions N from the values of P_t given in Table 1 and the nominal number of independent looks n_i associated with each pulse setting.

d. Error in range

The error in the range of a given feature is a random error of very small magnitude determined in principle by the accuracy in measuring the time delay between the pulse emission and the reception of the echo. With the digitization of the returned echoes, however, small variations in range can result in a feature appearing alternately on two adjacent pixels. The error in range in a radar image is then a random error with a magnitude determined by the sampling rate used for the digitization. Hence, for short-pulse images collected with a 20-MHz sampling rate, for example, the maximum error in range S_R is 7.5 m.

e. Error in antenna height

The error in the antenna height is a systematic error that biases the results for a given site in a particular direction. It is accountable for the discrepancies between results obtained from different radar locations. In coastal sites, the height of the antenna with respect to the mean sea level is determined whenever possible by direct measurement or visual estimate, taking into account any tidal elevation of the sea surface. When an accurate visual estimation is not available, the antenna height can be obtained from the nearest altitude reading on 1:50 000 Ordnance Survey maps. For much of the U.K. coastline, the Ordnance Survey will guarantee levels to an accuracy of the order of about 10 m (Ordnance Survey 1998, personal communication). Thus, the largest error in antenna height S_h is of the order of 10 m, where high locations such as cliffs are used.

a. Radiometric resolution

The error analysis established that the total relative NRCS error consists of random errors in the pixel intensity X, the emitted peak power P_t, and the range R, as well as a systematic error in the height h of the antenna. Following (32) and the laws of error combination (Boas 1983), the relative NRCS error can be written as

δσ⁰_relativeδW_X²δW_Pt²δW_R^21/2δW_h(35)

where δW_X, δW_Pt, δW_R, and δW_h are the relative errors expressed in decibels associated with pixel intensity, emitted power, range, and antenna height, respectively. The relative error in decibels for each variable is calculated from (32) and from the standard deviation of the variable. For example, the relative error in pixel intensity δW_X expressed in decibels reads

View Expanded

where the overlined symbols indicate the mean value of the variable and S_X is the pixel intensity standard deviation expressed in DN.

From (35) and (32) it follows that the total relative error is a function of range, pixel intensity, antenna height, pulse setting, and the number of images averaged N. Closer examination of the dependence of the individual errors δW_X, δW_Pt, δW_R, and δW_h on these parameters leads to some simplifications. The rapid decay of δW_R and δW_h with range, for example, can be generalized easily by estimating the total error in three image range gates: smaller than 200 m, between 200 and 400 m, and larger than 400 m. Similarly, the dependence on antenna height can be resolved by assimilating the error δW_h to the maximum error as calculated for a range of antenna heights varying between 5 and 100 m above mean sea level.

The dependence of the total error on pixel intensity through δW_X can also be removed by considering the variation of the error δW_X, with intensity. Figure 10 represents δW_X in the form of error bars for a pixel intensity standard deviation S_X of 3 DN. The error appears small and stable throughout the intermediate range of intensities but becomes very large rapidly at low and high intensities. Hence, it is clear that the high slope of the system transfer function at both extremes of the intensity range renders these data unreliable and implies that these data should not be included in the quantitative interpretation of the NRCS. It is therefore possible to remove the dependence of the total error in NRCS on intensity by redefining the system’s dynamic range as the interval of received power levels for which the error δW_X is stable. In terms of intensities, this range corresponds to X values between 30 and 245. The error δW_X can then be represented by the maximum error in that range for given values of S_X. After simplification, the total relative error in NRCS then finally can be estimated from (35) as a function of pulse setting, range gate, and the number of averaged images as presented in Table 3.

b. Dynamic range

The radiometric dynamic range is defined as the range of NRCS values measurable with the present system. In principle, its lower and upper limits are determined, respectively, by the system’s minimum detectable signal (MDS) related to the marine radar noise level and the saturation level of the data capture board. In the present case, however, the high NRCS error found in the previous section at high and low power levels has called for a redefinition of the system’s dynamic range to the intensity interval between 30 and 245, where the major error δW_X is reduced (Fig. 10). Thus, the lower limit of the dynamic range (or MDS equivalent NRCS) is calculated for each pulse setting by introducing X = 30 DN in the normalization equations [(29)–(31)], while the system saturation level (or saturation-equivalent NRCS) is obtained by taking X = 245 DN in the same equations. The MDS and saturation-equivalent NRCS are shown in Fig. 11 for all pulse settings.

a. Calibration methods

For the first time, the radiometric performance of a conventional low-budget marine radar attached to a digital capture board has been investigated. The internal calibration, implemented via a two-step and a one-step method highlighted the importance of treating the composite radar system as a whole to describe the system transfer function with sufficient accuracy for low and high backscatter signals. The one-step calibration method provided results in good agreement with experimental evidence obtained from external measurements on calibrated targets.

The experimental method for the absolute calibration is admittedly questionable, chiefly because of the use of unsteady buoy-based targets. The approach, however, did account for the possibility of multiple scattering, and buoy measurements were obtained statistically over several hundred samples in very calm conditions for which both the buoys’ motion and the contribution to the backscatter from the surrounding sea surface were minimal. Although the empirical results showed reasonable agreement with calculated values of the scaling coefficient K, the lack of accuracy in measuring the receiver’s low-filter temporal characteristics represents a serious problem, as the derived correction factor is likely to include a pulse-length-dependent bias that could misrepresent the performance of the system on different pulse settings. For these reasons, the system performances were evaluated using the more reliable scaling coefficients K calculated from laboratory measurements of the emitted power and the estimate of the nominal antenna gain suggested by the manufacturer.

b. Dynamic range

From the literature, the range of ocean NRCS measured by airborne and shipborne HH-polarized microwave systems at low grazing angles is reported to vary between −60 and −10 dB (Daley et al. 1971; Trizna 1985), while the typical ocean NRCS for a 7 m s⁻¹ wind speed is of the order of −20 to −30 dB. The dynamic range of the marine radar system shown in Fig. 11 spans a 50-dB range, which covers easily these low ocean backscatter values. The widely recognized ability of marine radars to detect low-power echoes at far ranges seems to be further enhanced by the filtering and integrating achieved in the digital capture board. The processing of the returned pulses in the composite system thus results in a reduced signal-to-noise ratio and an extension of the marine radar’s dynamic range toward lower NRCS values. Hence, this ability to measure low-power echoes makes the marine radar system a cheap and simple method to study quantitatively the ocean backscatter at near-horizontal incidence angles.

c. Radiometric resolution

The radiometric resolution of the system shown in Table 3 for various combinations of parameters is seen to improve significantly for ranges beyond 400 m, where it is found to be of the order of 1 dB. Hence, for typically sized radar images, this smaller error applies over more than 90% of the image area and therefore can be considered to represent the overall quality of the digital radar images.

For single-rotation images, the 0.9–1.8-dB error is clearly much poorer than that of traditional research radars, which can claim accuracies better than 0.5 dB (Vogelzang et al. 1992; Meadows and Wright 1994). Nevertheless, this error is better than 1 dB for a short pulse and is therefore of sufficient quality to image the most rapidly changing oceanographic features with reasonable accuracy. The marine radar system offers the additional facility of producing time series of 2D images that may be used to study the spatial and temporal evolution of the sea surface roughness distribution over any period of time, ranging from seconds to minutes to hours, in a manner inaccessible to satellite or airborne systems.

For stationary oceanographic processes, the radiometric resolution in the digital marine radar images can be improved significantly down to 0.6 dB by averaging over several antenna revolutions. On short pulse settings, such low relative errors can be achieved by averaging as few as four successive images. Hence, images from different sites and obtained under different environmental conditions can now be compared with confidence, and most oceanographic processes characterized by radar backscatter signatures over of a few decibels (surfactant slicks, bathymetry–current interactions, fronts, etc.) can be studied quantitatively in space and time with good accuracy using this type of instrument.