This study presents the new airborne Doppler radar Ku-Band Radar for Observation of Surfaces (KuROS), which provides measurements of the normalized radar cross section σ° and of the Doppler velocity over the sea. The system includes two antennas rotating around a vertical axis, although only the results from the lower incidence (14°) antenna are presented here. Also given are the first results from observations performed during two field campaigns held in 2013: the Hydrological Cycle in Mediterranean Experiment (HyMeX) and the Prévision Océanique, Turbidité, Ecoulements, Vagues et Sédimentologie (PROTEVS).
Sea wave directional spectra computed by the radar from tilt modulation of σ° are consistent with those given by the directional wave rider moored in the Mediterranean basin, both in terms of significant wave height Hs and main features of the wavenumber spectrum. As concerns the azimuthal distribution, two methods are tested to remove the 180° ambiguity of the radar-derived directional spectrum. The first method is based on the correlation between the modulations of σ° and Doppler velocity, which reflects the correlation between the sea surface slope and orbital velocity. The second method does not use the Doppler velocity but computes the cross spectrum between the modulations of σ° between two power profiles separated by some time lag ΔT, from which the phase velocity of sea waves is deduced. Comparing the sea wave directional spectra disambiguated by both methods, with the directional spectrum given by the wave rider, it is concluded that the first method (using Doppler velocity) is more efficient to remove the 180° ambiguity and should be preferred to the second method.
Sea-state knowledge is essential for both operational needs (marine meteorology, navigation, offshore and coastal activities,…) and for research needs (better knowledge of hydrodynamics of the waves, interactions between waves and the atmospheric and oceanic boundary layers, coupling of the atmosphere and ocean systems from regional to climatologic scales, interactions between electromagnetic signals and the ocean surface). Although the performance of wave models has significantly improved in the last decades (Cavaleri et al. 2007), improvements are still needed, in particular for high sea-state conditions, extreme events (hurricanes, typhoons), rapidly evolving storms, and for providing accurate prediction not only in terms of wave height but also in terms of peak wavelength and direction (important for swell). Furthermore, numerical models that are presently used to predict the distribution of energy of the ocean surface waves as a function of frequency (or wavenumber) and direction still suffer from various shortcomings (see Cavaleri 2006), among which uncertainties in the parameterization of source and sink terms (dissipation processes, source and sink terms related to turbulent exchanges at the interface), and errors on the prescribed initial state. In addition, because of the limitation in the model discretizations, significant errors in the directional distribution of wave energy may happen in open sea conditions, and this may induce large errors on description of wave evolution when they approach the coasts.
Up to now, the only radar system implemented on spacecraft for measuring ocean wave spectra is the synthetic aperture radar (SAR). Since the pioneering work performed with the SAR mounted on board the Seasat satellite (Gonzalez et al. 1979), it appeared, however, that the SAR systems are expensive to develop and not trivial to use for the estimation of ocean wave directional spectra. In that context, several airborne radars operating without the constraints of SAR have been developed: the Ka-band surface contour radar (SCR) developed by Walsh et al. (1985), the Ku-band Radar Ocean Wave Spectrometer (ROWS) developed by Jackson et al. (1985a,b), the C-band system Radar pour I’Etude du Spectre des Surfaces par Analyse Circulaire (RESSAC; Hauser et al. 1992), the C-band polarimetric Système de Télédétection pour l'Observation par Radar de la Mer (STORM; Hauser et al. 2003), and more recently the X-band coherent real aperture radar (CORAR) system developed by Plant et al. (2005). Such airborne measurements provide directional information with more details than directional buoys (Pettersson et al. 2003).
The China–France Oceanography Satellite (CFOSAT) is a new satellite mission under preparation by the Chinese and French space agencies. It is devoted to the radar observation of directional sea wave spectra and surface winds over the ocean. It will include on the same platform a Ku-band scatterometer (SCAT) for measuring surface winds, developed by the Chinese partner, and a real-aperture Ku-band radar spectrometer [Surface Waves Investigation and Monitoring (SWIM)] for measuring sea waves, developed in France under the support of the Centre National d’Etudes Spatiales (CNES) (Hauser et al. 2010). CFOSAT will be a polar-orbiting satellite at about 520-km altitude. The SWIM instrument will illuminate the surface sequentially with six incidence angles: 0°, 2°, 4°, 6°, 8°, and 10° with an antenna aperture of approximately 2°. To avoid limitations encountered by the SAR systems, the SWIM instrument will use a real-aperture observation technique. But, in order to acquire data in all azimuth orientations, the antenna will be rotating, at a speed rate of 5.6 rpm. The following geophysical parameters will be provided from the SWIM observations: normalized radar cross-section profiles from 0° to 10° incidence (combining all beams); significant wave height and wind speed from the nadir beam, similar to conventional radar altimeter; and directional ocean wave spectra from the combination of the 6°, 8°, 10° beams. Details may be found in Hauser et al. (2010).
In the context of the preparation of the CFOSAT space mission, we developed a new airborne radar, called Ku-Band Radar for Observation of Surfaces (KuROS). The primary aim of KuROS is to optimize the choices made for the implementation of the CFOSAT satellite, and to serve as a tool for the geophysical validation of the CFOSAT sea wave measurements once launched. Another important objective of the KuROS radar is to explore the characteristics of the kinematics of the sea surface. For this purpose, in addition to measuring the normalized radar cross section σ°, KuROS has the ability to measure the Doppler velocity of the radar echo, by means of the pulse-pair technique as described in section 2. Such a Doppler measurement capability was already included in CORAR, developed by Plant et al. (2005), who were able to deduce directional wave spectra from images of surface velocity. However, those were obtained only in the side-looking mode. Here, we use both σ° and Doppler signals simultaneously in the rotating mode at low incidence (around 14°), and we will show that the Doppler information can be used efficiently to remove the 180° ambiguity from the calibrated directional wave spectrum retrieved from the σ° tilt modulation.
To address the question of measuring both wind and waves, the KuROS radar system includes two antennas, one probing a range of incidence angles around 14° to measure waves [called the low incidence (LI) antenna] and another antenna probing incidence angles around 40° to measure wind [medium incidence (MI) antenna]. Both antennas have been tested in an anechoic chamber to determine their radiation patterns. However, when integrated within the body of the aircraft, it turned out that the antenna radiation pattern of the MI antenna obtained from calibration flights over corner reflectors (see section 4 below) did not reproduce the shape of the main lobe pattern expected from anechoic chamber measurements. This is attributed to the presence of a metal collar used to adjust the antenna system within the body of the plane, as will be discussed in section 2. For this reason, the results presented here will be focused on the observations performed with the LI antenna. The field campaigns in which KuROS has been involved will be described in section 3. The results of in-flight calibration of the radar will be briefly reported in section 4, and the first scientific results obtained from the analysis of radar cross section and Doppler velocity will be given in section 5. In particular, two new methods to remove the 180° ambiguity of the measurements of the directional sea wave spectrum will be presented and compared.
2. Description of the instrument
a. General characteristics
The main characteristics of the radar system are given in Table 1. The relatively large antenna beamwidth is required to estimate ocean wave spectra from a real-aperture radar at small incidence (see Hauser et al. 1992; Jackson et al. 1985a). In addition, a Doppler measurement capability has been designed for KuROS. The whole system is mounted in an ATR42 aircraft, operated by the Service des Avions Français Instrumentés pour la Recherche en Environnement (SAFIRE), and the conditions of use of KuROS are specified to allow measurements from flights from about 500 to about 3000 m above the surface.
The block diagram of the instrument is shown in Fig. 1. The overall system is composed of an antenna and radome unit (ARU), a power supply unit (PSU), a radio frequency unit (RFU), a digital processing unit (DPU), and a human interface machine (HIM), and the whole system is controlled by a management and control unit (MCU). Both functions of DPU and MCU are entirely performed by a field-programmable gate array (FPGA) device. A more detailed description of ARU, RFU, and DPU will be briefly given below.
b. Antenna and radome unit
Because of the large range of incidences to be covered, and in order to keep a cost-effective system, two antennas are necessary. We chose a system of two printed antenna arrays, the LI antenna, pointed to 14° incidence with respect to nadir; and the MI antenna, pointed to 40° incidence with respect to nadir (see Fig. 2). The LI antenna operates in the horizontal-transmit horizontal-receive (HH) polarization, and we choose a dual-linear (HH/VV) capability [alternately HH and vertical-transmit vertical-receive (VV)] for the MI antenna to offer comparisons with the CFOSAT-SCAT measurements. This set of two antennas is mounted inside the airplane. The antenna beam points through a 40-mm-thickness quartz window that serves as an interface between the outside and inside of the airplane at its lower part, allowing the whole radar system, including the antennas, to be under cabin pressure. Both antennas are used here through their real aperture, without any synthetic aperture processing. The antenna system can be controlled either to rotate over 360° around the vertical axis at a chosen rotation velocity or to stop at a fixed azimuth angle. The rotation velocity and the flight altitude are determined in order to have an overlap of the ground footprints and to measure a wave spectrum of a few-hundred-meter wavelength. An example of the antenna footprint is shown in Fig. 3. For the sake of legibility, in Fig. 3 the footprint is shown every 300 ms. However, the real-time integration is performed over 1 ms, yielding a displacement of the order of 0.1% of the footprint between successive records.
c. Radio-frequency unit
The transmitted wave is a pulsed chirp whose bandwidth is centered around 13.5 GHz. Because of the large range of distances to be sampled (flight altitudes from 500 to 3500 m, incidences from 0° to 50°), we have defined several chronograms of transmitted pulses, adapted to the flight altitude and the antenna. Table 2 presents these different modes, while Fig. 4 illustrates the time–frequency diagrams of the transmitted pulses. The frequency range (Femin − Femax) of the transmitted chirp has been chosen in order to achieve a high range resolution: (25–125 MHz) for the LI antenna and (30–60 MHz) for the MI antenna, corresponding to a range resolution of 1.5 and 5 m, respectively.
Within the DPU, two chirps in phase quadrature are generated at an intermediate frequency (IF) with the frequency range as given in Table 2. A Tukey window is applied to these two signals before transmission. In RFU, this complex signal is mixed by a single-sideband upconverter with the 13.5-GHz signal generated by a coherent local oscillator (LO), as seen in Fig. 1. After filtering, the signal is sent to a power amplifier. A programmable attenuator in front of the power amplifier enables transmitting a power signal lower than its nominal value, so as to be able to assess the CFOSAT signal-to-noise ratio (SNR) conditions (CFOSAT SNR is ~6 dB per pulse instead of about 11 dB for KuROS in nominal conditions, see below). Then, the signal goes through a passive circulator. A mechanical switch in front of the antennas enables commuting between calibration channels and the LI or MI antenna channels, while a second switch on the MI antenna channel commutes between the H and V polarizations (see Fig. 1).
At the reception, the radar echo is multiplied by a chirp replica, whose highest frequency Frepmax cannot, however, exceed 180 MHz because of the limitation of the FPGA (Virtex-5 XC5VSX95T). We require that the beat signal between echo and replica is integrated over the whole pulse duration TP and, as a consequence, the beat signal is analyzed only over the “analysis band” BA = Frepmax − Femax . The range of distances sampled is D = c(Trep − TP)/2, where c is the velocity of light; and TP and Trep are the pulse and replica durations, respectively, whose values are chosen for each antenna depending upon altitude, as given in Table 2. All these modes are preloaded in the management and control unit and chosen by the operator during flights.
After going through the two switches and the circulator, the received chirps are sent to a low-noise amplifier. They are then filtered to limit the noise band and conserve only the upper band with the received signals. The microwave signal is down converted with the same coherent local oscillator as used in the transmitter part. The signals are then amplified, filtered by an antialiasing filter and sent to the analog-to-digital converter (ADC) of the DPU.
In nominal mode, the wave form is transmitted alternately at low rate (30 s) to the LI and MI antennas (for MI antenna, a switch commutes every 100 ms between the H and V polarizations). It is also possible to use continuously a single antenna (LI or MI antenna) or a single polarization for the MI antenna. All these modes are chosen by the operator during flight.
d. Digital processing unit
The digital processing unit is shown in detail in Fig. 5. After sampling the IF signal at 360 MHz, the first step of the real-time onboard processing is the range compression. The raw signal is poorly resolved because of the long time impulse. Yet, as the transmitted signal is a chirp, a specific signal processing, called the deramping process (simple convolution by a replica signal) delivers the well-resolved signal.
The second step concerns the decimation stage. In Table 2, the analysis band, which corresponds to the maximum beat frequency resulting from the deramping processing, is 54 MHz at most. Therefore, a decimation factor of 6 is applied in order to reduce the complex sampling frequency from 360 to 60 MHz, and the low-pass filter was designed to cut off at 54 MHz.
The third step consists of an FFT processing providing the pulse response, corresponding to the backscattered power as a function of range.
The last step is the coherent integration of the complex samples over 1 ms for each range gate. We choose to use the pulse-pair processing technique (Zrnić 1977), which provides amplitude and phase of the mean signal with an efficient noise reduction. The maximum amplitude of the Doppler velocity that can be measured (corresponding to a phase of the complex signal equal to π is VDmax = λ/(4PRI), where λ is radar wavelength and PRI is pulse repetition interval. From the values of PRI listed in Table 2, it follows that VDmax is at least equal to 103 m s−1, which is always larger than the line-of-sight velocity for the usual velocity of the plane (≈100 m s−1).
The radiometric data [in-phase and quadrature (I&Q) signals integrated on 1 ms] and the ancillary data (aircraft attitudes, GPS time, …) are recorded at the same rate of 1 kHz.
e. Verification and calibration
Internal calibrations and measurements have been performed in a laboratory, involving an internal signal from a noise diode to check the stability of the receiver gain, and an internal 50Ω load to estimate the thermal noise level and to check the stability of the frequency and amplitude of the reflected signal on the load (transfer function restitution). The gain and losses of the complete chain have also been measured, and adequate corrections are deduced from these measurements and applied in ground postprocessing. Such tests involving a noise diode and a 50Ω load are also performed on board to check the stability of the instrument from flight to flight. A specific mode is used for this control (several chirp signals are transmitted and delayed, sweeping all the swath). The transmitted power is measured on board every second and stored in the data frame.
To assess the absolute level of the backscattered power, an external calibration was also performed using corner reflectors (trihedral reflectors) installed on an aircraft runway, overflown by the airplane during specific flights. Those measurements yielded a bias of −0.2 dB when compared to the expected backscatter power levels (see section 4a below).
f. Expected performances on the estimation of the backscattering coefficient
The effective SNRe, corresponding to the inverse of the radiometric resolution Kp, is given by the following relation (e.g., Ulaby et al. 1986):
where Nint is the number of independent samples.
The error δσo on the estimation of the backscattering coefficient (dB) is related to the radiometric resolution through
The signal is integrated coherently over 1 ms through onboard processing. The complex signal can then be integrated over a longer time by postprocessing. The objective is to estimate δσo within a 0.2-dB maximum uncertainty. Table 3 presents the theoretical errors on the estimation of the backscattering coefficient depending on the SNR and the number of independent samples. The results are calculated following different integration times for the two antennas for the 3000-m altitude mode. Those results show that it is necessary to integrate the signal over 30 ms, at least for both antennas to reach the objective of 0.2-dB estimation error.
g. Antenna performances
The antenna design was constrained by the use of a quartz window of 40-mm thickness, which was introduced to allow the whole radar system, including the antennas, to be within the aircraft body under cabin pressure. Efforts have been made through many numerical and laboratory tests to reduce the impact of this window on the antenna pattern. The Institut d’Electronique et de Télécommunications de Rennes (IETR) laboratory in charge of antenna design worked on the optimization of the weighting of each patch using the convex optimization method (Fuchs and Fuchs 2010) to get a main beam with the required specifications (aperture angles and direction). However, after installation on board, the first in-flight measurements on the corner reflectors in February 2012 revealed that for the MI antenna, the radiation pattern is significantly distorted. An external view of the antenna system mounted on the aircraft is shown in Fig. 6. The quartz window is supported by a circular metallic ring, seen in Fig. 6, and is at the origin of a diffraction effect, presumably responsible for this distortion. This drawback prevents us from obtaining reliable results in term of absolute σ° with the MI antenna, even though relative variations of σ° and Doppler measurements are not affected by this problem. Because of this antenna pattern distortion, the results from the MI antenna will not be presented in this paper.
In contrast, the radiation pattern of the LI antenna, whose field of view is nearer to the nadir direction, is not impacted by this metallic ring. This could be checked from the calibration flights over corner reflectors, which yielded radiation patterns of the LI antenna very close to those obtained from laboratory tests, both in terms of shape and absolute level (bias −0.2 dB, rms difference 0.4 dB) as will be seen in section 4a below.
The advantages of this design with a beam pointing through a quartz window are the ease of instrument integration in the airplane, and the fact that the overall instrument is under aircraft pressure. However, the problem encountered with the MI antenna leads us to prepare an upgrading of the radar with a new design where this window will be removed. The modifications are presently under development.
3. Description of the campaigns
The first scientific use of KuROS occurred in March–April 2013 in the context of field campaigns carried out for two meteo-oceanographic programs. The first one is the Hydrological cycle in the Mediterranean Experiment (HyMeX; see Drobinski et al. 2014) in the northern part of Mediterranean Sea, while the second one is the Prévision Océanique, Turbidité, Ecoulements, Vagues et Sédimentologie (PROTEVS) project devoted to observation and modeling of currents, waves, and storm surge with a campaign in the Iroise Sea close to the Brittany coasts of France.
HyMeX is an international cooperative project organized with the aim of improving the understanding and quantification of the hydrological cycle and related processes in the Mediterranean, with emphasis on high-impact weather events. One of the scientific goals is to improve our understanding of intense sea–atmosphere interactions. To address this question, an experimental multiscale strategy has been designed with special observation periods (SOP) imbedded within enhanced observation periods and a long-term observation period. SOP 2 was organized in February–March 2013 in the northwestern part of the Mediterranean Sea to study intense air–sea exchanges and dense water formation. This region is exposed to regional offshore intense winds called mistral (northerly winds) and tramontane (northwesterly winds), usually associated with an anticyclonic system over the western part of France and a cyclonic system over the Gulf of Genova. These situations generate high sea state under fetch-limited conditions, and in winter and at the beginning of spring they also often generate oceanic convection. From 4 March to 15 April 2013, wind blew as mistral and/or tramontane for a total of more than 18 days in periods of 2–3 days of continuous strong (10–25 m s−1) offshore winds. From 4 to 6 March, a cyclonic system located east of Spain generated strong easterly winds (10–20 m s−1) in the northern part of the Gulf of Lion basin.
During this SOP 2 experiment, in situ measurements (from ships, moored buoys, drifters) have been carried out. A meteo-oceanic buoy (called Lion buoy), moored in the Gulf of Lion (northwest of the Mediterranean Sea) provides surface parameters (10-m wind, directional spectra of surface gravity waves, air and sea temperature, atmospheric pressure) in an offshore region. Coastal buoys (Azur, Banyuls, Leucate, etc.) provide additional data of significant wave height, and mean wave period, and for some of them surface wind, and air and sea temperature.
During HyMeX, the French research aircraft ATR42 flight time was shared between two research teams and two types of measurements: in situ measurements in the boundary layer to provide mean and turbulent atmospheric quantities, and remote sensing measurements of the oceanic surface with KuROS. Because the optimal flight levels for KuROS are between 2000 and 3000 m, each flight period was divided in several subperiods, some of them dedicated to KuROS measurements with the 2000- and 3000-m flight levels. A total of 11 flights with KuROS data have been achieved during HyMeX. Table 4 gives the list of flights, the KuROS measurements during these flights, and the corresponding wind and wave conditions at the Lion buoy. An example of the flight plan during a tramontane event (northwesterly flight) is shown in Fig. 7.
The other field experiment during which KuROS was involved is PROTEVS. This experiment was designed and carried out by the French naval service Service Hydrographique et Océanographique de la Marine (SHOM). It is devoted to the study of wave–current interactions and storm surge conditions in the coastal region of Brittany. The goal is to improve the modeling of currents and waves with the Hybrid Coordinate Ocean Model (HYCOM, see http://hycom.org) and the wave model WAVEWATCH III (http://polar.ncep.noaa.gov/waves/index2.shtml), respectively. The area is characterized by very strong tide currents, complex bathymetry, coastal line, as well as frequent occurrence of long swell generated by Atlantic storms. Five Datawell directional waveriders were moored by SHOM in the area as well as several current sensors, which can also provide information on surface waves.
During this experiment, KuROS was flown over the area (see Fig. 8) with two flights on the same day (11 February 2013) separated by about 4 h. The first dataset (1111–1350 UTC) was collected after low tide (which occurred 1047 UTC), with the flight pattern of Fig. 8 described twice (once at 2000 and once at 3000-m altitude). The second dataset (1553–1659 UTC) was collected just before high tide (1650 UTC) with the flight pattern of Fig. 8 at 3000-m altitude. The situation of 11 February 2013 corresponds to a northwest swell with significant wave height of up to 6.8 m, a tide index of 107, and moderate wind (≈6 m s−1).
4. Checks of the performance of the instrument from flight data
a. Calibration flights over corner reflectors
Five trihedral reflectors (40-cm edge, 32.5-dBm2 radar cross section) were installed over a concrete surface, separated by about 50 m in the along-flight direction and 10 m in the across-track direction. Such a layout was chosen to spread the five reflectors over the KuROS footprint while flying at about 450 m above the surface. Several overpasses with KuROS have been carried out, with the KuROS antennas pointed either forward or backward with respect to the aircraft route. During the flight, in coordination with the radar operators on board the plane, ground operators adjust manually the tilt of the trihedral reflectors toward either 14° or 40° depending upon whether the LI or MI antenna is tested. This procedure enables us to assess the antenna radiation pattern and the absolute calibration.
Five overflights of the reflector system were performed during flight 12, but for one of them the flight track was not properly aligned with the system of reflectors, and for another one the aircraft altitude was varying during overflight, rendering the data difficult to interpret. Only the three remaining overflights were quite successful and were therefore retained for analysis. For each of those successful overflights, due to the 10-m across-track separation of the five reflectors, the reflector that is located closest to the flight track yields the highest power backscatter signature and only that one is retained for calibration analysis. The results are shown in Fig. 9. We also display the antenna radiation pattern obtained from the anechoic chamber measurements (blue line) and its Gaussian fit (red dashed line), with maxima coinciding with the 32.5-dBm2 radar cross section of the trihedral reflectors at boresight. It may be seen that the retrieved shape and level of the antenna radiation pattern are remarkably consistent with the two-way radiation pattern obtained from laboratory tests. Over the 3-dB interval (≈7°–20°), the bias and rms difference between in-flight data and laboratory data are −0.2 and 0.4 dB, respectively. For incidence angles above ≈28°, however, the lobe deviates radically from the Gaussian pattern because of the combined effects of secondary lobes, contribution of the ground to the backscattered power, and poor SNR.
The overflights over the trihedral reflectors can also be used to check the consistency of the Doppler velocity measured by the radar. This is illustrated in Fig. 10, where the Doppler velocity measured by the radar is compared with the line-of-sight velocity deduced from the aircraft inertial navigation system. Since the aircraft velocity is different from one overflight to the other, it would be meaningless to compare velocity measurements from different overflights, and therefore the data from only one overflight are displayed in Fig. 10, and only the data from the three most centered trihedrals (those yielding the highest power patterns) are shown. The quality of the retrieval of the Doppler velocity is virtually independent of the incidence angle between 7° and 20°. Over that range of incidences, after averaging over the three overflights reported in Fig. 9, the average bias and rms difference for velocity are 0.4 and 0.5 m s−1, respectively. Below 6°, because of the low altitude used for calibration flights (≈500 m), the uncertainty of the altitude retrieval limits the accuracy of the incidence angle assigned to each range gate, which explains the increased dispersion of the data. Above ≈31° incidence angle, the SNR of the radar signal attains a threshold below which the Doppler velocity retrieval suddenly fails.
b. Assessment of the number of post-integrations to perform
We have seen in section 2d that the signal is integrated coherently over 1 ms by onboard processing, and that the complex signal can then be integrated over a longer time by postprocessing. Tests were performed with coherent and incoherent postprocessing with varying numbers of post-integrations. Figure 11 is an example of the power profile obtained over the sea from an altitude of 2000 m. The power profile integrated coherently over 1 ms is compared with the ones obtained by coherent and incoherent post-integration over 33 ms. Coherent post-integration over N samples should reduce the noise by 5 log10N (dB) while keeping the signal level unaffected. As expected, a comparison of the raw and coherently integrated data displayed in Fig. 11 follows this theoretical behavior. From various tests performed with different integration times, the post-integration time of 33 ms was chosen for the results presented in this paper, providing a reasonable compromise between noise level and effective horizontal resolution (taking into account the displacement of resolution cells). In the worst case of a forward- or backward-viewing direction for an aircraft velocity of 100 m s−1, the footprint displacement during such an integration time is smaller than a range gate. As concerns the azimuthal shift, assuming, for example, a spin rate of the antenna of 4 rpm (equivalent to 24° s−1), over the 33-ms post-integration time the antenna will rotate by 0.79° with respect to the vertical axis. For an incidence angle θ = 14°, in the antenna frame this corresponds to an azimuth displacement of the antenna pattern by 0.79° × sinθ = 0.19°, which is no more than about 3% of the two-way azimuthal antenna beamwidth.
5. First results of σ° and Doppler velocity
a. Analysis of the behavior of the σ° signal
Figure 12 shows an example of the measured σ° averaged over azimuth as a function of incidence angle. The absolute calibration of the data was obtained from laboratory measurements and assessed from the flights over corner reflectors by the method described in section 4a. For this example the wind speed was 9 m s−1 and the significant wave height was Hs ≈ 5.3 m. The standard deviation of σ° over an incidence angle interval of 1° (indicated as error bars in Fig. 12) is on the order of ±1.5 to ±2 dB, depending on incidence angle. This relatively high standard deviation is because σ° is deeply modulated by the sea waves, and those modulations themselves will be used below to retrieve the sea wave spectrum. The average σ° displayed in Fig. 12 may be compared to σ° predicted by empirical geophysical model functions (GMF) that have been produced from satellite data. The GMF by Freilich and Vanhoff (2003) gives a modeled σ° as a function of wind speed, and was built from observations of Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) Ku-band radar for incidence angles between 0° and 18°. This model function is based on the quasi-specular approach in the limit of Gaussian isotropic sea surface slope distribution, which is expected to be accurate for microwave scattering for 0° ≤ θ ≤ 15°. A quadratic multiparameter fit to TRMM PR data sorted according to wind and significant wave height was also performed over the incidence angle range from 5° to 18°, from the large collocated database compiled by Tran et al. (2007), and the result for this wind and wave situation is also indicated in Fig. 12 as plus signs. Finally, the GMF by Wentz and Smith (1999) (thick solid line in Fig. 12) is based on the Ku-band National Aeronautics and Space Administration (NASA) scatterometer (NSCAT) data, which were available only for θ ≥ 18°. Our measurements are consistent with the TRMM models at low incidence angles, although it is ≈1 dB above the NSCAT model near 20° incidence. Such a difference is not significant given the difficulty to perform absolute intercalibrations of GMFs obtained from different satellites, as was shown by Caudal et al. (2005).
The azimuthal variation of σ° can be easily studied because of the rotation of the antenna. Figure 13 shows the azimuthal variation of σ° for the case of flight 18 with an incidence angle of 20°. The display includes 1 min of data, which corresponds to 2.4 rotations of the antenna. A least squares fit to the data is also displayed, involving five parameters (a constant and the phases and amplitudes of the two first harmonics). The azimuthal variation of σ° from Wentz and Smith’s (1999) GMF is also shown for comparison. Apart from the offset of average σ° already identified in Fig. 12, the amplitude of the azimuthal modulation of the KuROS data fitted by two harmonics (±1.1 dB) is fairly close to the amplitude obtained from Wentz and Smith’s (1999) model (±0.9 dB). For this example, the first maximum of the fitted curve occurs for an azimuth of 125°, which differs by no more than 5° from the average wind direction given by the buoy (≈120°). In Fig. 13 note the large variations (±4 dB) of the data around the fitted line. This is due to the small size of the elementary backscattering surface in the range direction, which is determined by the pulse-limited range resolution of the radar (1.5 m), yielding an horizontal resolution of ≈6.2 m for a 14° incidence angle, which is much smaller than the typical wavelength of the dominant sea waves (a few hundred meters). The surface tilt variations due to those large-scale sea waves thus produce the deep modulations of σ° observed in Fig. 13. Such modulations of σ° can be used to measure sea wave directional spectra using the method described in section 5b below.
b. Measurement of the sea wave spectrum
The analysis of the modulations of radar reflectivity as a function of radial distance permits us to compute the directional sea wave spectrum along the direction of observation, while the rotation of the antenna around the vertical axis permits exploring all the azimuthal directions. The theory underlying this measurement technique was given by Jackson et al. (1985a) and is briefly reviewed here. For each azimuthal direction φ of the antenna, positions on the mean sea surface may be defined by their horizontal local coordinates x and y, where x is horizontal distance along the antenna-pointing direction, and y is along the azimuth direction. The elementary backscatter cross section σ is given by σ = σ°A, where A is the area contained within a radar range gate. The presence of the large sea waves produces a tilt modulation of σ given as
where is the surface cross section that would occur if no large-scale wave were present.
The fractional modulation m(x, φ) of the cross section seen by the radar is δσ/σ averaged laterally across the beam:
where G2(y) is the two-way azimuth antenna radiation pattern.
In practice m(x, φ) is obtained by removing a low-order polynomial fit from the measured radar power profile, thus eliminating the trend and retaining only the modulations.
In this expression, k, θ, and φ are the wavenumber, the incidence angle, and the azimuth, respectively. Term Ly is a length related to the azimuthal width of the beam footprint, and Pm(k, φ) is the modulation spectrum, defined as
where FT refers to the Fourier transform operator, and the asterisk (*) stands for the complex conjugate.
As discussed by Jackson et al. (1985a), the speckle noise of the radar technique produces a supplementary modulation of σ°, which is included in the measured modulation spectrum, and this speckle noise must then be removed from the data for precise quantitative studies. To estimate the spectrum of the speckle noise, Hauser et al. (1992) used a semiempirical method based on the comparison between data integrated over different time intervals. Another approach was proposed by Engen and Johnsen (1995) in the context of the processing of SAR images. Those authors proposed to remove the speckle noise by computing image cross spectra between pairs of single-look SAR images separated in time. Following their approach, we replaced here the modulation spectrum Pm(k, φ) from Eq. (6) above with the quantity
The time interval δt should be large enough that the speckle noise of both profiles is decorrelated but small enough that the radar footprint is only marginally displaced during that interval. Also, preliminary post-integration of the raw (1 kHz) data must be sufficient in order to provide a first reduction of the speckle. The interval δt is set to twice the post-integration time to ensure that the speckle noises of both profiles of Eq. (7) are well decorrelated. Here we requested a displacement of the footprint by less than 10% over the time interval δt. From 3000-m altitude with 4 rpm this implies that δt ≤ 80 ms. Several trials were done with δt between 30 and 80 ms, which gave very similar results (the standard deviation of significant wave heights retrieved with those different assumptions was on the order of 3–5 cm for 2000-m flights as well as 3000-m flights). Since the post-integration time used routinely is 33 ms, in this paper we use δt = 66 ms.
Nevertheless, because of imperfect correlation between the sea wave signals at times t and t + δt, the computed P′m(k, φ) happens to be negative on some scarce occurrences. Since the sea wave spectrum should be a positive definite quantity, those values are artificially set to zero. This has virtually no effect on the retrieved significant wave height. The results obtained by this method are fairly consistent with speckle estimates obtained using the approach of Hauser et al. (1992). The results presented below have been obtained by using this cross-spectral approach.
As an example, Fig. 14 shows a comparison between the omnidirectional sea wave spectrum measured by the Lion buoy and by KuROS (corrected from the speckle noise) for the flight of 6 March 2013. The hourly spectrum of the buoy is taken at 1200 UTC (the closest time to the overflight), and the KuROS spectrum just before and just after the overflight is shown. Although the sea wave field was rather inhomogeneous, the radar measurements are consistent with the hourly buoy measurement. The peak frequency observed by both KuROS and the buoy is ≈0.09 Hz. Significant wave height HS is obtained by integrating the directional spectrum F(k, φ) of Eq. (5) over the wavenumber space:
The HS measured by the buoy is 5.3 m, while the HS from the radar is 5.1 and 5.6 m before and after the overflight, respectively.
Figure 15 shows an example of the sea wave directional slope spectrum measured by the radar. Such a spectrum was obtained from a dataset of 30 s, which corresponds to a little more than a rotation of the antenna in that case. Because of the 180° ambiguity of the slope spectrum analysis, only a symmetrized 2D spectrum is presented here. The question of the removal of this 180° ambiguity will be addressed in section 5c below.
A more systematic comparison between KuROS and the sea wave buoy data during overflights has been performed in order to check the ability of KuROS to identify spectral peaks and to refine the calibration of the instrument in terms of HS. The results, including the overflights performed during the HyMeX campaign, which are listed in Table 4, are shown as scatterplots in Fig. 16. As concerns the sea wave peak direction, the 180° ambiguity has been removed by reference to the buoy data. As indicated in Fig. 16, the correlation coefficient C between the buoy and radar measurements are particularly good for Hs (C = 0.93), and the correlation is somewhat weaker for both peak direction (C = 0.81) and peak frequency (C = 0.81). It may be noted that buoys provide sea wave spectra integrated over periods on the order of half an hour at one unique location, and thus the consistency between the wave parameters inferred from buoy and radar in Fig. 16 is quite satisfactory given the spatiotemporal inhomogeneity of the sea wave field. Overall, KuROS is remarkably efficient at identifying spatial inhomogeneities of the wave field occurring in limited fetch situations, which would not be attainable from a unique buoy.
c. Analysis using the Doppler signal
As the KuROS antenna is rotating around a vertical axis, the line-of sight velocity is alternatively positive or negative, depending upon the azimuthal orientation of the antenna. Typical velocities of the aircraft are on the order of 100 m s−1, and thus for incidence angles smaller than 20° the Doppler velocity related to the aircraft motion ranges between −35 and +35 m s−1. An example of the Doppler signal over the sea is shown in Fig. 17. The most important feature is the sinusoidal variation of the Doppler velocity as the antenna is rotating. From the analysis of measurements of Doppler velocities obtained with different orientations of the aircraft with respect to the wind and wave system, the average Doppler velocity signatures that we obtain are consistent with those expected from the aircraft motion, except that we needed to correct the antenna rotation angle by a systematic offset of 4°. This offset, presumably due to a misalignment of the antenna beam, has been systematically corrected from the data presented henceforth in this paper.
To study the velocity signature of the surface, this component related to the aircraft velocity has to be removed by using the ancillary velocity data given by the inertial navigation system (INS) of the plane. The residual Doppler shift or Doppler velocity anomaly, of interest here, is related to the kinematics of the sea surface. Note that the rms errors of the velocity components given by the INS are smaller than 3 cm s−1. Most of this error is related to the low rate of the INS data (25 Hz) while the KuROS data are recorded at a rate of 1 kHz. However, since only the spatial modulations of velocities within each footprint will be used in this paper, those errors will have a negligible effect.
1) Ambiguity removal of the measured sea wave directional spectrum through the orbital velocity of sea waves
Because of the changing orbital velocity along the phase of long surface waves, the front faces (as seen by the radar) of long waves propagating away from the radar have a positive line-of-sight velocity anomaly (orbital velocity directed away from the radar). The front faces of these waves are tilted toward the radar, so that the backscattered power is also greater. The modulations of the normalized radar cross section (NRCS) and Doppler velocity are therefore correlated. In contrast, in a situation of long waves propagating toward the radar, the Doppler anomaly signatures would be inverted and one would thus observe an anticorrelation between the NRCS and Doppler modulations. Thompson et al. (1991) obtained a clear signature of such a correlation between wave orbital velocities and the NRCS for Ku-band radar at an incidence angle of 20°.
Following this approach, we will assume that the orbital velocities dominate the wave-related velocity modulations. The correlations between the σ° and velocity modulations are thus expected to be either positive or negative, depending upon whether the waves are traveling away from or toward the radar, respectively. The sign of this correlation can be obtained for each spectral component by computing the cross spectrum between the fluctuations of σ° and velocity:
where x is the horizontal distance along the direction of observation, FT is the Fourier transform operator along the x dimension, and the asterisk (*) denotes the complex conjugate. Terms δσ° and δV are the σ° and velocity modulations, respectively. To obtain them, one first removes the radial velocity due to airplane from the velocity signal (thus yielding the residual velocity). Then, one computes the smoothed radial profiles of σ° and the residual velocity, which are further removed to yield the modulations δσ° and δV, respectively.
From the computed cross spectrum C1(k, φ), each sea wave Fourier component can be ascribed a propagation direction away from the radar if Real[C1(k, φ)] > 0, or toward the radar if Real[C1(k, φ)] < 0. Figure 18 displays the directional sea wave spectrum disambiguated by this method. It corresponds to the folded spectrum, which was given above in Fig. 15. The main wave train of Fig. 18 is seen clearly to be propagating toward the southwest. This is fully consistent with the direction of propagation of the sea waves as measured by the buoy, as will be shown below in section 5c(2).
2) Comparison with ambiguity removal performed from the phase velocity of sea waves
It may be interesting to compare the method used above to remove the 180° ambiguity of the directional spectra to the approach that is used to retrieve ocean wave spectra from cross spectra of SAR images (Engen and Johnsen 1995). In the same manner as was done above in section 5b, the cross spectrum between two radar power profiles separated by some time lag ΔT can be computed, and the phase velocity of the sea wave can be deduced by analyzing its argument. The cross spectrum may be written as
For each wavenumber k, the phase velocity Vp of the sea wave propagating along the horizontal direction of observation may be obtained through
where δp is the phase difference between the Fourier transforms of δσo/σo at times t and t + ΔT, and VAH is the horizontal component of the aircraft velocity along the direction of observation. From Eq. (10) this may be rewritten as
From the computed cross-spectrum C2(k, φ), each sea wave Fourier component can thus be ascribed a propagation direction away from the radar if VP(k, φ) > 0, or toward the radar if VP(k, φ) < 0 . This method thus permits to remove the direction ambiguity by merely comparing two snapshots of the surface obtained at times t and t + Δt, without the need to use the Doppler measurement.
The choice of the time lag ΔT is rather arbitrary. In section 5b [Eq. (7)], a short time lag of 66 ms was chosen in order to eliminate the speckle noise from two profiles containing virtually the same signal. Here instead we wish to identify the displacements of the wave trains; therefore, the time lag ΔT should be large enough that a significant phase shift is measured between times t and t + ΔT, but small enough that the area illuminated by the radar is only marginally modified over that time interval. The illuminated area is moving under the combined effect of the aircraft velocity and antenna rotation. As a consequence the correlation between radial features obtained at times t and t + ΔT is imperfect, and therefore the cross spectrum C2(k, φ) of Eq. (10) is reduced, rendering the estimation of the sea wave phase velocity more noisy as ΔT is increased. Several trials were performed with different values of ΔT, and the optimum was obtained for ΔT of a few tenths of a second, although the result is only weakly dependent upon the choice made for ΔT between 0.2 and 0.4 s. In this paper we take ΔT = 0.4 s, which yields results that are the closest to the buoy data (see below).
Figure 19 displays the directional sea wave spectrum disambiguated by this method. It corresponds to the same case as Figs. 15 and 18. The overall direction is similar to the one retrieved from the orbital velocity (Fig. 18), with a main component propagating toward the southwest. However, the retrieved directions are more scattered, with an increased number of spectral components propagating along the opposite direction. The question is then whether the scarce components propagating toward the northeast in Fig. 19 are real features or an artifact due to the retrieving process.
To address this question, we compared both retrieved spectra of Figs. 18 and 19 with the ones deduced from the directional Lion buoy. For each wavenumber, however, the data from the directional buoy only consist of a power level and two complex harmonics, and a direct comparison with the much more detailed directional spectra obtained from KuROS is therefore not relevant. We therefore computed the two first harmonics of the spectra obtained from KuROS, and then compared them directly to the buoy data. For each wavenumber, the directional spreading function of the sea wave spectrum may be written as
where φ is the azimuth, while a1, b1, a2, and b2 are real coefficients that are fitted to the data. The sets of coefficients (a1,b1) and (a2,b2) define the first and second complex harmonics, respectively. With respect to a rotation of 180°, the first harmonic is antisymmetric, while the second harmonic is symmetric, and thus the secondary component directed toward the northeast seen in Fig. 19 should correspond to a significant increase of the second harmonic. Validation of the ambiguity removal method will depend upon whether the buoy data show this increased second harmonic. To address this point, Fig. 20 displays the ratio ρ = r2/r1 between the amplitudes of the second and first harmonics, and , respectively. For the set of wavenumbers sampled by the radar (from 0.02 to 0.3 rad m−1), the ratio ρ deduced from orbital velocity (solid line in Fig. 20) exhibits moderate fluctuations, with an average of ρ ≈ 0.61, which is close to the average ratio ρ obtained by the buoy (〈ρ〉 ≈ 0.55). As a comparison, the ratio ρ deduced from the phase velocity in the optimal case (ΔT = 0.4 s, dashed line in Fig. 20) is much more scattered, with a much larger average value (〈ρ〉 ≈ 1.14). This indicates that the secondary northeastern component appearing in Fig. 19 is not confirmed by the buoy data, whereas the spectrum of Fig. 18 is fairly consistent with the buoy data.
We performed such comparisons in a more systematic manner from overflights of the buoy performed on six different days with different wind and sea conditions. For each of those six cases, we computed the difference Δρ(k) between ratios ρ obtained by the radar and by the buoy at each wavenumber k from 0.02 to 0.3 rad m−1. From this we deduced the rms average of Δρ(k) over k (〈Δρ〉). In all six cases studied, the method based on orbital velocity gave smaller 〈Δρ〉 than the method based on phase velocity. The average value of 〈Δρ〉 over the six overflights was found as 0.79 when the orbital velocity method was used, while it was as high as 1.61 when the phase velocity method was used.
The method based on orbital velocity (using the Doppler signature) thus appears to be more efficient at removing the 180° ambiguity on the sea wave directional spectrum retrieved by KuROS, and should be preferred to the method using the phase velocity.
The new airborne Ku-band radar KuROS provides measurements of radial profiles of the normalized radar cross section σ° over the sea surface at low and intermediate incidences. The antenna system is mounted on a platform rotating around a vertical axis in order to explore the different azimuthal directions. The spectrum of ocean waves with wavelengths larger than a few tens of meters is obtained by analyzing the modulations of the radial profiles of σ°. As the antenna is rotating, the different azimuthal directions are explored, allowing for retrieval of the directional spectrum of sea waves. In addition to measuring σ°, KuROS has the ability to measure the Doppler velocity of the radar echo, by means of the pulse-pair technique. This innovative implementation permits exploring the characteristics of the kinematics of the sea surface and removing the 180° ambiguity inherent to the principle of measurements based on the analysis of slope modulations of σ° by a low-incidence real-aperture radar.
To address the question of measuring both wind and waves, the KuROS radar system includes two antennas, one probing a range of incidence angles around 14° [low incidence (LI) antenna] and another antenna probing incidence angles around 40° [medium incidence (MI) antenna]. However, the calibration flights over corner reflectors revealed a significant distortion of the radiation pattern of the MI antenna, presumably due to diffraction by a metal collar used to adjust the antenna system within the body of the plane, and for this reason only the results from the LI antenna have been presented in this paper.
The KuROS radar has participated to two field experiments in 2013: the HyMeX program in the northern part of the Mediterranean Sea and the PROTEVS campaign in the Iroise Sea close to the Brittany coasts of France. We present the implication of KuROS within these field campaigns and give the first results from the observations performed during these campaigns.
Sea wave directional spectra computed from the radar observations during the HyMeX campaign were compared to the sea wave spectra produced by the Lion directional buoy moored in the Mediterranean basin. The speckle noise was removed from the data following the approach by Engen and Johnsen (1995), by computing the cross spectra between radar power profiles separated by some time lag δt taken as 66 ms. The data are consistent both in terms of significant wave height Hs and main features of the wavenumber spectrum. As concerns the azimuthal distribution, two methods were tested in order to remove the 180° ambiguity of the radar-derived directional spectrum. The first method consists of computing the cross spectrum between the modulations of σ° and Doppler velocity, which permits removing the ambiguity by analyzing the sign of the correlation between the sea surface slope and the orbital velocity. The second method consists of computing the cross spectrum between the modulations of σ° between two radar power profiles separated by some time lag ΔT, taken as a few tenths of a second. After removing the velocity of the aircraft, the phase of this cross spectrum permits deducing the phase velocity of sea waves in the terrestrial reference frame, whose sign yields the direction of propagation toward or away from the radar. The sea wave directional spectra disambiguated by both methods are then compared with the directional spectrum produced by the Lion buoy. From this analysis, we conclude that the method based on orbital velocity (using the Doppler signature) is more efficient at removing the 180° ambiguity on the sea wave directional spectrum retrieved by KuROS and should be preferred to the method using the phase velocity.
In the future we intend to use KuROS as a tool for geophysical studies involving the spatiotemporal evolution of the sea wave system in heterogeneous situations. In the context of the preparation of the future CFOSAT space mission, the cross-spectral method that we employed successfully to remove the speckle noise from the sea wave spectrum will permit us to study in more detail the behavior of the speckle noise in various wind and wave conditions, in order to be able to remove it with high accuracy from the satellite data. Other studies will also be devoted to the estimate of the tilt velocity bias, which affects the Doppler signal (Chapron et al. 2005). Although the CFOSAT mission is not intended to have the Doppler measurement capability, the Doppler issues addressed in this paper with airborne radar will hopefully be useful in helping to define future satellite missions for observing the ocean surface.
The authors thank the staff of the radar team at LATMOS for its involvement in the development and operation of KuROS, and in particular Laurent Chardenal, Romain Coulomb, Eric d’Almeida, Laurent Lapauw, Nicolas Pauwels, Jean-Pierre Pineau, and Jean-Paul Vinson, as well as Monique Dechambre, for her active participation to the campaigns. They also wish to thank the staff of the SAFIRE team who operated the ATR42 aircraft. The development and operation of the KuROS radar was funded by the French space agency Centre National d’Etudes Spatiales (CNES). The Lion buoy data were provided by Météo-France in the context of the HyMeX project.