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Modeling of sea spike events with generalized extreme value distribution
... As mentioned above, the normalized reflection symmetry metric will be close to 0 for the sea surface, while it will be expected to be 1 for the metallic targets at sea surface. Therefore, like a sea spike event [34], the presence of ships at sea leads to long-tails in the statistical distribution while describing the normalized reflection symmetry metric statistical distribution of the ocean surface. It has been pointed out that the traditional statistical distribution model including the generalized Gaussian and Gamma distribution cannot fit the long-tails phenomenon well [35][36][37]. ...
... where γ is the normalized reflection symmetry, and k, σ and µ are the shape, scale and location parameters, respectively. These parameters can be estimated by using the maximum likelihood estimation (MLE) method [34]. By the fitting of sea clutter in the wide ocean scene in Figure 2, several statistical distributions are adopted as shown in Figure 3. ...
... where is the normalized reflection symmetry, and k , and are the shape, scale and location parameters, respectively. These parameters can be estimated by using the maximum likelihood estimation (MLE) method [34]. By the fitting of sea clutter in the wide ocean scene in Figure 2, several statistical distributions are adopted as shown in Figure 3. ...
The spaceborne synthetic aperture radar (SAR) is quite powerful in worldwide ocean observation, especially for ship monitoring, as a hot topic in ocean surveillance. The launched Gaofen-3 (GF3) satellite of China can provide C-band and multi-polarization SAR data, and one of its scientific applications is ocean ship detection. Compared with the single polarization system, polarimetric systems can be used for more effective ship detection. In this paper, a generalized extreme value (GEV)-based constant false alarm rate (CFAR) detector is proposed for ship detection in the ocean by using the reflection symmetry metric of dual-polarization. The reflection symmetry property shows big differences between the metallic targets at sea and the sea surface. In addition, the GEV statistical model is employed for reflection symmetry statistical distribution, which fits the reflection symmetry probability density function (pdf) well. Five dual-polarimetric GF3 stripmap ocean data sets are introduced in the paper, to show the contrast in enhancement by using reflection symmetry and to investigate the GEV model fit to the reflection symmetry metric. Additionally, with the detection experiments on the real GF3 datasets, the effectiveness and efficiency of the GEV model for reflection symmetry and the model-based ocean ship detector are verified.
... It is necessary to study and analyze the characteristics of the sea clutter deeply before the accurate reconstruction of sea clutter. For past few decades, many efforts have been devoted to the research of sea clutter characteristics, including the amplitude distribution [2][3][4][5][6], correlation characteristics [7][8][9][10][11], Doppler spectrum [12][13][14][15][16], spikes [17][18][19][20], non-stationarity [21,22], and so on. Among them, amplitude distribution and correlation characteristics get the most attention, and they play an important role in the design of target detection algorithms in a maritime environment. ...
The reconstruction of sea clutter plays an important role in target detection and recognition in a maritime environment. Reproducing the temporal and spatial correlations of real data simultaneously is always a problem in the reconstruction of sea clutter due to the complex coupling between them. In this paper, the spatial–temporal correlated proportional method (STCPM), based on a compound model, is proposed to reconstruct K-distributed sea clutter with correlation characteristics obtained from the real data. The texture component with spatial–temporal correlation is generated by the proportional method and the speckle component with temporal correlation is generated by matrix transformation. Compared with previous methods, the biggest innovation of the STCPM is that it can more accurately generate K-distributed sea clutter with both temporal and spatial correlations. The comparison of the reconstructed and real data demonstrates that the method can reproduce the characteristics of real sea clutter well.
A finales del pasado siglo fue propuesta la detección por radar en el espacio de los momentos estadísticos. Las principales motivaciones para su uso radican en el incremento del poder discriminador de los parámetros y en la disminución de la incertidumbre acerca de su distribución. Sin embargo, la teoría disponible solo considera momentos estadísticamente independientes y carece de procedimientos adaptativos factibles de implementación práctica. La presente investigación contribuye a solucionar las problemáticas anteriores, al incidir en dos aspectos fundamentales: la regla de decisión y el mecanismo de adaptación. Ambos elementos se integran en un novedoso método de detección que consigue mantener la razón de falsa alarma constante cuando los momentos presentan un grado de correlación arbitrario. Mediante experimentos con señales reales se verifica su operación robusta ante escenarios heterogéneos y la mejora en la calidad de la detección respecto a las técnicas con integración no coherente convencionales
At the end of the last century, radar detection in the moments space was proposed. The main motivations for its use are to increase the discriminative ability of the signal parameters and to decrease the uncertainty about their distribution. For achieving detection, it is necessary to determine the decision rules that establish the operations performed by the detector. This work details the obtaining of the optimal decision rule following the Neyman-Pearson criterion and the rule that allows to maintain a constant false alarm rate (CFAR), both for moments with arbitrary correlation degree. The probability densities of the decision statistics are also proposed, which will allow to evaluate the performance of radar detection through statistical moments.
Multitarget detection is very challenging, especially when targets are densely distributed. In conventional constant false alarm rate (CFAR) detection algorithms, the detection threshold is determined based on a pre-estimated background level (BL). However, interfering targets inevitably lead to inaccurate BL estimation, resulting in degraded detection performance. In our previous work, a new solution was developed and verified to be effective; in that solution, compressed sensing (CS)-based detector performs target detection without relying on BL estimation, and a subsequent CFAR regulation processor achieves the desired false alarm rate based on the statistical information of the reduced samples obtained by removing the detected targets and adjacent guard cells from the original samples. However, for scenes with a high target density, the CS-based detector suffers from performance degradation while acquiring the correlation between linear measurements of the signal and the sensing matrix due to the high local signal sparsity. To address this shortcoming, this article proposes a deep neural network (DNN)-based detector that further improves the detection performance by converting the target detection into a problem of peak sequence classification of frequency intensity (FI) measurements from radar. A DNN detector trained on augmented simulated data shows excellent generalization ability for deployment in real scenes. In addition, to achieve better computational efficiency, a Taylor-series-based approximate maximum likelihood estimator with an explicit expression is applied in the CFAR regulation process for the first time. Both simulation and field tests are performed to verify the superiority of the proposed algorithm over conventional algorithms.
Classification of intertidal area in synthetic aperture radar (SAR) images is an important yet challenging issue when considering the complicatedly and dramatically changing features of tidal fluctuation. The difficulty of intertidal area classification is compounded because a high proportion of this area is frequently flooded by water, making statistical modeling methods with spatial contextual information often ineffective. Because polarimetric entropy and anisotropy play significant roles in characterizing intertidal areas, in this paper we propose a novel unsupervised contextual classification algorithm. The key point of the method is to combine the generalized extreme value (GEV) statistical model of the polarization features and the Markov random field (MRF) for contextual smoothing. A goodness-of-fit test is added to determine the significance of the components of the statistical model. The final classification results are obtained by effectively combining the results of polarimetric entropy and anisotropy. Experimental results of the polarimetric data obtained by the Chinese Gaofen-3 SAR satellite demonstrate the feasibility and superiority of the proposed classification algorithm.
Radar backscatter measurements from stationary breaking waves were used to examine how the surface roughness generated by wave breaking affects radar backscatter at moderate incidence angles. Stationary breaking waves were generated by submerging a stationary hydrofoil in a uniform flow. X band radar backscatter measurements were made at numerous streamwise positions along the stationary breaking waves from an incidence angle of 45° for horizontal transmit and receive polarization (HH) and vertical transmit and receive polarization (VV) looking both upwave and downwave. The radar returns increased substantially, and the HH-to-VV polarization ratio approached unity near the breaking crests. This radar signature is consistent with those observed in the field. Detailed optical measurements of the breaking surfaces revealed that the observed radar returns near the breaking crests were the result of increased incoherent backscatter from the small-scale surface roughness generated by the breaking waves, although surface tilt effects also modified the radar return. Scattering models based upon the small perturbation solution performed well in the wake of the stationary breaking crest, but they significantly underestimated the HH-to-VV polarization ratio near the breaking crest. More advanced scattering solutions such as the integral equation method produced more accurate results in regions containing the largest surface roughness. These findings suggest that incoherent backscatter from surface disturbances produced by deep water breaking waves may be the source of the high radar returns and small polarization ratios observed from the ocean at moderate incidence angles.
In recent times, considerable advances have been made on analysing low grazing angle radar sea clutter in the gigahertz frequency range. In this work, a set of coherent and polarimetric sea clutter data is analysed focusing on the statistical and spectral properties of the spikes, whatever is the physical phenomenon that generates them. Using three sea spike defining parameters, the spike amplitude, the minimum spike width and the minimum interval between spikes, it is possible to identify the spiking events from the background. This work shows a sample of results from a statistical and spectral analysis of a set of sea spikes selected from the radar returns, focusing on their Doppler properties, the spike duration and the temporal interval between spikes.
Robust maritime surveillance with radar requires an accurate description of the backscatter from the sea. An estimated probability distribution of the backscatter is commonly used to determine the threshold for separating targets from clutter at a given false alarm rate. Data collected at medium to high grazing angles by the Defence Science Technology Organisation (DSTO) Ingara fully polarimetric X-band radar demonstrate that the commonly used K-distribution is not always adequate for modelling the probability distribution. This is especially the case for the horizontal polarisation and in regions of high backscatter where target detection can be a problem. An alternative proposed as a more accurate model in this region is known as the KK-distribution. The analysis presented in this study describes this model with the addition of multiple looks and a thermal noise component to produce greater accuracy in the mean and underlying shape. The threshold required to achieve a constant false alarm rate is then studied and compared with the K-distribution.
This report studies the spatial distribution of X-band, high resolution and high grazing angle polarimetric sea clutter data. The K distribution usually provides a good fit for the distribution of the VV polarised data. The HH polarised data is spikiest and its distribution exhibits a sudden departure from the K distribution in the tail region, which usually requires the KA or the similar distributions to achieve a better fit in the tail region. Due to drawbacks of the KA distribution, this report proposes the KK and WW distribution models to fit the distribution of sea clutter with spikes. It is found that the KK distribution provides overall the best fit. Distributions of the sum of K and Weibull distributed samples are also presented. DGAD This report contributes to the delivery of Milestone 4.1.1.1.1: High grazing angle sea clutter and target signatures in the AIR 7000 S&T Plan (Annex C – Technical Support Plan). The outcomes of the analysis contained herein will also form a component of the model delivered for Milestone 4.1.1.1.2: Radar modelling capability development – maritime of the Technical Support Plan. These activities are aimed at better understanding the radar performance drivers for operation of High Altitude Long Endurance (HALE) unmanned aerial vehicles (UAVs) in the maritime surveillance role, and therefore reducing risk in any acquisition decision. Sea clutter distributions have been studied for many decades. However most of these studies are based on sea clutter data collected at low grazing angles and for applications of radar mounted on ships or at the coast. Very little analysis of high grazing angle sea clutter has been published in the open literature. The next generation of airborne maritime radar surveillance systems, such as high altitude UAVs, views the sea surface at much higher grazing angles. Sea clutter returns at low grazing angles are often dominated by multipath, shadowing and ducting mechanisms, whereas the Bragg scattering from rough surfaces and scattering from whitecaps often dominate at high grazing angles. These different scattering mechanisms mean that the nature and characteristics of sea clutter at high and low grazing angles are different. In addition, the resolution of the future radar tends to be higher. The finer the radar resolution, the more discrete sea spikes in sea clutter. Understanding and modelling of such spikes are important for the prediction of radar performance and for guidance in developing improved target detection algorithms. Therefore searching for distribution models which provide precise distribution agreement especially in the tail region is necessary in sea clutter distribution studies in order to improve radar performance. In support of Project AIR 7000, DSTO conducted a sea clutter collection trial in the Southern Ocean approximately 100 km south of Port Lincoln in South Australia in 2004 using the DSTO developed X-band, fully polarised airborne radar imaging system, Ingara. Data were collected with incidence angle varying from approximate 45o to 80o, on 8 separate days over an 18-day period. The wind and wave conditions were also recorded using a wave buoy deployed nearby and the information provided by the Royal Australian Navy’s Directorate of Oceanography and Meteorology, and the Australian Government Bureau of Meteorology. The data used in this report are real aperture high range resolution (0.75 m) data with the radar operated in a circular spotlight mode. The radar could therefore be considered to look at the same spot but with different incidence and azimuth angles. Each dataset used in the analysis consists of approximately 106 samples, corresponding to a span of 3.5o to 8o in incidence angle change, depending on nominal incidence angle, and a span of 5o in azimuth angle change. Since the nominal incidence angle is in the plateau region and the span of the azimuth angle is narrow, we can consider the data distribution to be as the spatial distribution. The size of the samples in each dataset provides a reliable data distribution up to 1-cdf equal to the 10-5 level. It is found that the mean clutter varies periodically in azimuth with the maxima and the minima in the upwind and crosswind directions, respectively, and the second peak in the downwind direction. The shape parameter of clutter distributions, however, does not show a noticeable azimuthal pattern correlating to wave/wind directions. The VV polarised data is with the lowest spiky level compared to the HH and HV data. In general the VV data can be fitted by a K distribution with the shape parameter varying from about 4 to 25. The HH polarised data is spikiest and its distribution exhibits a sudden departure from the K distribution in the tail region, often in the region of 1-cdf (cumulative distribution function) equal to 10-3 and beyond. The phenomenon of the sudden departure is believed to be attributed by sea discrete spikes. The finer the radar resolution, the severer is the phenomenon. This observation indicates that the traditional K distribution might not be precise enough to model the distribution of sea clutter with spikes. The KA distribution, which has been more recently proposed in the literature to model the distribution of sea clutter with spikes, has significantly improved the agreement between the data and model distributions in the tail region. However, the KA distribution cannot be expressed in closed form, so it is computationally very expensive. It also imposes a difficulty for the analysis of radar performance, as the analysis often involves the clutter distribution function. Aimed at simplifying the distribution function, this report proposes a KK distribution, which is a mixture of two K distributions of which one representing the distribution of Bragg/whitecap scatterers and the other for the distribution of sea spikes. It shows that the KK distribution is as good as the KA distribution in terms of agreement in the tail region. In addition, the KK distribution introduces the least distortion to the K distribution in the low and mid regions. Mathematically, a KK distribution is simply a sum of two K distributions. Since the Weibull distribution is very close to the K distribution, this report also proposes a WW distribution to improve the agreement between the data pdf and the modelled pdf in the tail region. A WW distribution is a mixture of two Weibull distributions. In general, a Weibull distribution converges a little faster than a K distribution for shape parameters normally found in sea clutter statistics, which often leads to a bigger discrepancy between the data pdf and the Weibull pdf in the tail region. The Weibull fit, even for the VV data is not as good as the K fit. This however can be compensated if a WW distribution is used, as the convergence of the WW distribution is tuneable. The results show that the fitness of the WW distribution in the tail region is comparable to the KK or KA distribution. However, in the low and mid region, the agreement between the data pdf and the WW pdf is not as good as that between the data pdf and the KK (or K) pdf. The use of the KA, KK and WW distributions improves the agreement between the data and fitted distributions in the tail region. It is shown that the difference between the data cdf and the K cdf for the HH polarised data at the 1-cdf equal to 10-5 level can be as big as about −7dB, but the difference can be reduced to about ±1dB if the KK distribution is used to model the data distribution. Since the KK distribution provides the least distortions to the K distribution in the low and mid regions, the fit improvement in the tail region does not worsen the agreement in the low and mid region. The report also proves that a Weibull distribution can be transformed to a Rayleigh or gamma distribution and vice versa through a non-linear but simple mapping. Therefore, in the case where clutter data is modelled as a Weibull distribution, the data may be first transformed accordingly and then treated as a Rayleigh or gamma distribution, as the Rayleigh or gamma distribution is much easier to be dealt with. For simulation, a Weibull distributed dataset can be easily generated from a transform of a Rayleigh distributed dataset. CFAR schemes often employ local statistics of clutter to adaptively set the threshold for target detection. This report also discusses the distribution of the sum of K or Weibull distributed samples. A formula in closed form approaches the distribution of the sum of Weibull distributed samples, which does not have close form, has been proposed. Its correctness has been numerically verified using both the convolution method and simulated data. No noticeable error between the values given by the formula and the values numerically computed from the convolution method or simulated data has been found.
Sea Clutter: Scattering, the K Distribution and Radar Performance, 2nd Edition gives an authoritative account of our current understanding of radar sea clutter. Topics covered include the characteristics of radar sea clutter, modelling radar scattering by the ocean surface, statistical models of sea clutter, the simulation of clutter and other random processes, detection of small targets in sea clutter, imaging ocean surface features, radar detection performance calculations, CFAR detection, and the specification and measurement of radar performance. The calculation of the performance of practical radar systems is presented in sufficient detail for the reader to be able to tackle related problems with confidence. In this second edition the contents have been fully updated and reorganised to give better access to the different types of material in the book. Extensive new material has been added on the Doppler characteristics of sea clutter and detection processing; bistatic sea clutter measurements; electromagnetic scattering theory of littoral sea clutter and bistatic sea clutter; the use of models for predicting radar performance; and use of the K distribution in other fields.
This book examines the statistics of radar scattering from the sea surface in terms of their relevance to radar operating in a maritime environment; including remote sensing, surveillance and targeting appliances. A lot of the work in the book iss based on the compound K-distribution model for the amplitude statistics of sea clutter. In addition, the book addresses the specification of performance required by customers and the measurement of performance of systems supplied to customers.
The compound-Gaussian (CG) distributions have been successfully used for modelling the non-Gaussian clutter measured by high-resolution radars. Within the CG class, the complex K -distribution and the complex t-distribution have been used for modelling sea clutter which is often heavy-tailed or spiky in nature. In this paper, a heavy-tailed CG model with an inverse Gaussian texture distribution is proposed and its distributional properties such as closed-form expressions for its probability density function (p.d.f.) as well as its amplitude p.d.f., amplitude cumulative distribution function and its kurtosis parameter are derived. Experimental validation of its usefulness for modelling measured real-world radar lake-clutter is provided where it is shown to yield better fits than its widely used competitors.
A fundamental characteristic of radar sea clutter, important for radar performance evaluations, is its apparent reflectivity defined a σo (m2/m2). “Apparent” is used as a reminder that any measurement of sea clutter reflectivity includes the effects of propagation and shadowing close to the sea surface. Sea clutter reflectivity depends on many factors, including sea state, wind velocity, grazing angle, polarization, and radar frequency. An empirical sea clutter model proposed by Horst, et al. (1978), the so-called GIT model, has found widespread acceptance in the radar community. However, this model does not always agree with what is the most complete experimental database of sea clutter reflectivity available to the radar systems engineer. The 1991 edition of F. E. Nathanson's book provides seven tables of measured sea clutter reflectivity data summarized from approximately 60 sources. The large deviation between the GIT model and this database, in particular at lower sea states, has prompted NRL to develop an improved model for sea clutter reflectivity based on these tables. The model is a function of radar frequency, polarization, sea state, and grazing angle. The functional form of this empirical model was chosen such that the average absolute deviation (in dB) between the model and the experimental data was minimized.
This Technical Note describes the Osborne Head database, collected at Osborne Head Gunnery Range, OHGR, in November 1993, with the McMaster University IPIX radar, under contract to DSS. Representative examples are worked out for the different operational modes of the radar (staring, scanning, alternate/single polarization, single/multi frequency). Strengths and weaknesses of the database are pointed out as well. The purpose of this Technical Note is to serve as a guide to the database, presenting enough information to allow the extraction of individual datasets from the raw data. These can subsequently be used for sea clutter, target model validation and/or testing of signal processing techniques, leading to enhanced target detection in sea clutter.
Sea clutter refers to the radar backscatter from a patch of ocean surface. To properly characterize radar clutter returns, a lot of effort has been made to fit various distributions to the observed amplitude data of sea clutter. However, the fitting of real sea clutter data using those distributions is not satisfactory. This may be due to the fact that sea clutter data is highly nonstationary. This nonstationarity motivates us to perform distributional analysis on the data obtained by differentiating the amplitude data of sea clutter. By systematically analyzing differentiated data of 280 sea clutter time series measured under various sea and weather conditions, we show that the Tsallis distribution fits sea clutter data much better than commonly used distributions for sea clutter such as the K distribution. We also find that the parameters from the Tsallis distribution are more effective than the ones from the K distribution for detecting low observable targets within sea clutter.
The correct formulation of the likelihood ratio test (LRT)-based detection schemes for a target in the presence of clutter needs a faithful and mathematically tractable clutter model. The state-of-art detection methods usually assume that the land and sea clutter in whose presence a target signal to be detected as K-distributed form of non-Gaussian clutter and uses an LRT detector obtained for the same. However, the macroscopic phenomena of clutter generation in a search radar and also the detailed studies on the measured clutter data show a significant texture fluctuation caused by the continuous antenna scanning motion. Incorporation of the scanning effect in the clutter model introduces challenges in modelling the varying texture and formulating a suitable detection scheme. Here the authors propose a clutter model for such scanning radar applications taking the effect of scanning on the clutter correlation into consideration. A method of fitting the proposed model to measured data and a method of simulating the clutter as per the proposed model are also presented. The proposed model is found to be attractive for an LRT detector design. Further in this study, the proposed clutter model is also validated through a real experimental data which show an excellent match between the simulated and measured data of both sea and land clutters. The close agreement between the model and the measurement clearly illustrates the validity and applicability of the model.
Radar backscatter from the sea surface has a significant effect on radar systems operating in a maritime environment. This study considers the application of modelling sea clutter to the design and development of such systems, and addresses the sensitivity of the predicted performance to the choice of model. The typical phases of the life-cycle of a radar system are described, along with how models are used to support the radar development. Different types of model are reviewed and some examples are given of the comparison of their effect on predicted performance. The conclusion is that the differences are important and continue to warrant further investigation.
This paper presents the statistical analysis of an experimental high-resolution sea-clutter database, collected with a high-resolution Ka-band radar at the south coast of Spain. The main motivation of this paper has been to check the validity of the available theoretical models for high-resolution sea-clutter against data corresponding to a range resolution of centimeters. The overall amplitude probability density function (pdf), the compatibility with a compound representation, and the average spectral behavior of the data are analyzed in detail. Results clearly show the suitability of the compound Gaussian model and, more precisely, that the empirical pdf is well modeled by the generalized K distribution with log-normal texture. A close agreement has also been found between the estimated clutter spectral density and a power-law model.
A 3-GHz Doppler radar has been used to study wave dynamics and
backscatter from the sea surface at low grazing angles. Vertical
polarization results are dominated by Bragg scatter even at low
(˜8°) grazing angles. Horizontal polarization results,
however, show a strong upwind-downwind asymmetry with additional,
high-velocity intermittent scatter in the upwind direction associated
with steep or breaking waves. These characteristics have been exploited
to distinguish spilling breaking events from the background Bragg
scatter. While these "spikes" at a single range may appear random in
time, the combined range and time information reveals a well-determined
propagation pattern. It is shown that for a developing sea in deep
water, group behavior modulates the occurrence of wave breaking. The
frequency-wavenumber spectrum shows a clear separation between the
linear dispersion curve and nonlinear effects related to breaking. The
most important nonlinear feature is a line near the dominant wave group
velocity which is identified with the spectrum of breaking
intermittency. The slope of this line suggests that the wave components
which are most likely to break lie at frequencies significantly above
the dominant wave frequency.
A number of experiments have been carried out in two large wave tanks with three different radar systems. The radar frequency, grazing angle, azimuth angle, water wavelength, wave steepness and the breaking wave strength were all varied systematically. The velocity of the peak Doppler power spectral density was found to depend on the phase velocity of the breaking wave in the radar line of sight, but was independent of the radar frequency. The spectral width depended on the phase velocity of the wave, but not on the grazing angle used. The peak Doppler power and radar cross-section of the breaking waves was found to scale with the radar wavelength (proplambda<sub>r</sub> <sup>1.5</sup>)
An analysis of sea-clutter data obtained in conditions typical of
sea state 2 at X-, S-, L- bands, UHF and VHF is presented. Results show
that sea-clutter exhibits very different spectral characteristics at
higher frequencies compared to those at low frequencies. Experimental
sea-clutter coefficients as a function of grazing angle at various
frequency bands were obtained for upswell and cross-swell conditions.
These results were contrasted with those calculated from two sea-clutter
(the GIT and Sittrop) models, assuming an upwind and a crosswind
condition. The data were quite dissimilar in the low-grazing-angle
regions to those predicted by the two models. Sea-clutter amplitude
statistics provide evidence that the K-distribution serves as a limiting
distribution for sea clutter
This paper deals with the statistical modelling of radar backscattering from sea surface at low-grazing angles in high resolution radar systems. High-resolution polarimetric data at different range resolutions (60, 30, 15, 9 and 3 m) are analysed to highlight the differences in clutter statistical behaviour due to changes of resolution and/or polarisation. The clutter data were recorded by the IPIX radar of McMaster University in Grimsby, Ontario, Canada
In this paper, we deal with the problem of modeling the backscattering from sea surface for low-grazing-angle and high-resolution radar systems. Based on the electromagnetic two-scale model, we analyzed both the amplitude and frequency modulations induced on the small-scale Bragg resonant waves by the large-scale surface tilt and advection due to the swell presence. Evidence of sea-clutter nonstationarity has been verified and the relationship between the variations of clutter spectral features, such as texture, Doppler centroid, and bandwidth, have been studied by processing real sea-clutter data recorded by the IPIX radar of McMaster University, Hamilton, ON, Canada. An autoregressive nonstationary process is proposed and validated to model the physical phenomenon.
In this paper three sets of high-resolution, coherent, and polarimetric radar sea clutter data are analyzed and compared with radar sea clutter models. The nature of the data allows a thorough analysis of the power, polarization and velocity of the sea clutter. It is shown that these quantities, especially the velocity, are good measures of many physical properties of the ocean surface. Furthermore, it is shown that these physical properties match well with the sea clutter models. Sea clutter is found to consist of two components, a diffuse background, characterized by low values of backscattered power, HH/VV polarization ratio and Doppler velocity, and a number of spiking events, which possess higher power, polarization ratio and velocity. The background is reasonably well modeled by tilt-modulated Bragg scattering, whereas the spikes may be associated with the scattering on steepened and/or breaking waves. Moreover, it is shown that the influence of microbreakers has to be taken into account to explain the relatively high polarization ratio. A breaking wave origin for the spikes is supported in two ways. First, by a detailed analysis of the temporal behavior of individual spike backscatter properties, and second, by a statistical analysis of the entire population of spikes.
Backscatter characteristics of 1-4-m-long, mechanically generated
breaking waves have been investigated with a C-band frequency modulated
continuous wave (FMCW) radar (up to 3.77-cm range resolution) in the
large wind-wave tank at the Ocean Engineering Laboratory, University of
California, Santa Barbara. The grazing angle was 6°. Wave breaking
was caused to occur in the test section due to wave group
selfmodulation, just as it has been observed in the ocean. The central
purpose of these experiments was to determine the hydrodynamic sources
of the low grazing angle sea spike and its structure. Using typical,
strong 2.3-m-long breakers, four phases of the breaking process with
distinct hydrodynamic characteristics were identified visually and
correlated with synchronous radar data. These breaking waves yielded a
horizontal copolarization (HH) radar cross section (RCS) of up to 10 m
<sup>2</sup> and concurrent copolarization ratios (HH/vertical
copolarization[VV]) exceeding 40 dB. Synchronous high-speed video images
showed that these peak values appeared just after a plunging jet
developed at the breaker crest, well before it hit the front face of the
wave. Focusing the electromagnetic energy on the jet by the parabolic
front face of the breaking wave is suggested as a mechanism that yields
both high HH returns and high HH/VV ratios. Statistics of HH peak RCS
for the complete range of wavelengths tested show the dependence of
radar backscatter from energetic breaking waves on their wavelength and
implies a scaling law such that the optimum return is obtained when
λ<sub>wave</sub>=40 λ<sub>radar</sub>. Under fixed
conditions of λ<sub>wave</sub> and λ<sub>radar</sub>,
large deviations in HH RCS have been found and have been shown to be
dependent on the strength of the breaker
High-resolution dual-polarization X-band images of the ocean
surface were obtained at a grazing angle of about 3°. Area extensive
imaging allowed us to study the backscatter properties of sea spikes and
to compare radar measurements with visual surface features evident from
video recordings. The vertically polarized radar images consist of
distributed scatter whose amplitude and Doppler velocity are modulated
by larger scale gravity waves consistent with Bragg scattering and
composite surface theory (CST). The horizontally polarized radar images
are dominated by spatially discrete scattering centers (or sea spikes)
moving at velocities comparable to the phase velocities of gravity waves
beyond the spectral peak. These sea spikes also exist in the
corresponding V-pol radar images, but are less prominent due to the
dominant Bragg backscatter. Sea spikes are characterized by polarization
ratios H/V that often exceed unity, typically by about 5 dB. Comparison
of the larger spikes with simultaneous co-registered video recording of
the surface indicates that approximately 30% of observed sea spikes are
associated with actively breaking waves (whitecaps) while the remainder
are identified with “steep” wave features. By classifying
the larger sea spikes according to their corresponding surface features,
we find hat the Doppler velocities for sea spikes due to whitecaps are
noticeably faster (about 50%) than other sea spikes, though the
distributions for both overlap significantly. We also find little
measurable difference in the polarization ratios of the two classes of
sea spikes as observed on the open ocean
Nonlinear dynamics are basic to the characterization of many
physical phenomena encountered in practice. Typically, we are given a
time series of some observable(s) and the requirement is to uncover the
underlying dynamics responsible for generating the time series. This
problem becomes particularly challenging when the process and
measurement equations of the dynamics are both nonlinear and noisy. Such
a problem is exemplified by the case study of sea clutter which refers
to radar backscatter from an ocean surface. After setting the stage for
this case study, the paper presents tutorial reviews of: (1) the
classical models of sea clutter based on the compound K distribution and
(2) the application of chaos theory to sea clutter. Experimental results
are presented that cast doubts on chaos as a possible nonlinear
dynamical mechanism for the generation of sea clutter. Most importantly,
experimental results show that on timescales smaller than a few seconds,
sea clutter is very well described as a complex autoregressive process
of order four or five. On larger timescales, gravity or swell waves
cause this process to be modulated in both amplitude and frequency. It
is shown that the amount of frequency modulation is correlated with the
nonlinearity of the clutter signal. The dynamical model is an important
step forward from the classical statistical approaches, but it is in its
early stages of development