Radar Image Spectra Research Articles

A Deep Learning Strategy for the Retrieval of Sea Wave Spectra from Marine Radar Data

In the context of sea state monitoring, reconstructing the wave field and estimating the sea state parameters from radar data is a challenging problem. To reach this goal, this paper proposes a fully data-driven, deep learning approach based on a convolutional neural network. The network takes as input the radar image spectrum and outputs the sea wave directional spectrum. After a 2D fast Fourier transform, the wave elevation field is reconstructed, and accordingly, the sea state parameters are estimated. The reconstruction strategy, herein presented, is tested using numerical data generated from a synthetic sea wave simulator, considering the spectral proprieties of the Joint North Sea Wave Observation Project model. A performance analysis of the proposed deep-learning estimation strategy is carried out, along with a comparison to the classical modulation transfer function approach. The results demonstrate that the proposed approach is effective in reconstructing the directional wave spectrum across different sea states.

A simulator of Synthetic Aperture Radar (SAR) image spectra: the applications on oceanswell waves

ABSTRACT The Synthetic Aperture Radar (SAR) carried on-board satellites yields invaluable data of global wave spectra since the early 1990s, with several satellites in orbit at present and more launches scheduled in the near future. However, the retrieval of wave information from SAR images constitutes a complex set of procedures. In this context, we have presented here a methodology to simulate SAR image spectra of ocean swell waves. SAR simulators are important tools for the implementation and evaluation of wave spectra retrieval schemes. The one proposed here is based on the Hasselmann Transform whose Modulation Transfer Functions (MTF’s) account for the main physical processes involved in the imaging of ocean waves. A detailed description of its structure is provided. Through several test cases, we highlight some particularities of the relationship between SAR image spectra and wave spectra. We have evaluated the impact of the parameters settings and input information on the retrieval process, pinpointing possible shortcomings. The results indicated that useful information about the processes involved in the imaging of ocean swells can be derived from the SAR simulator.

On the Nonlinear Mapping of an Ocean Wave Spectrum into a New Polarimetric SAR Image Spectrum

AbstractA new nonlinear transformation relation is derived to describe the mapping of a two-dimensional ocean wave spectrum into a new polarimetric synthetic aperture radar (SAR) image spectrum. It is a further expansion and improvement of Hasselmann’s work. First, the nonlinear mapping relation proposed is derived on the basis of a new polarimetric SAR image instead of the conventional single-polarization SAR image. Second, the nonlinear mapping relation no longer includes the complex hydrodynamic modulation transfer function (MTF). Third, the traditional tilt MTF, which is not accurate enough for the retrieval of sea wave spectrum, is replaced by an empirical tilt MTF derived on the basis of the C-band geophysical model function [i.e., C-band synthetic aperture radar (CSAR) normalized radar cross section (NRCS) model]. A sea wave spectrum retrieval algorithm is then proposed that is based on the new nonlinear mapping and the empirical tilt MTF. The retrieved spectra from C-band polarizedRADARSAT-2SAR images are compared with the results obtained by the ECMWF Ocean Wave Model (ECWAM) and buoy measurements.

A simple method for retrieving significant wave height from Dopplerized X-band radar

Abstract. Retrieving spectral wave parameters such as the peak wave direction and wave period from marine radar backscatter intensity is very well developed. However, the retrieval of significant wave height is difficult because the radar image spectrum (a backscatter intensity variance spectrum) has to be transferred to a wave spectrum (a surface elevation variance spectrum) using a modulation transfer function (MTF) which requires extensive calibration for each individual radar setup. In contrast to the backscatter intensity, the Doppler velocity measured by a coherent radar is induced by the radial velocity (or line-of-sight velocity) of the surface scattering and its periodic component is mainly the contribution of surface waves. Therefore, the variance of the Doppler velocity can be utilized to retrieve the significant wave height. Analyzing approximately 100 days of Doppler velocity measurements of a coherent-on-receive radar operating at X-band with vertical polarization in transmit and receive, a simple relation was derived and validated to retrieve significant wave heights. Comparison to wave measurements of a wave rider buoy as well as an acoustic wave and current profiler resulted in a root mean square error of 0.24 m with a bias of 0.08 m. Furthermore, the different sources of error are discussed and investigated.

Low Wave Number Radar Image Energy Influence on Determining Current

In the radar imaging mechanism different phenomena are present, as a result the radar image is not a direct representation of the sea state. In analyzing radar image spectra, it can be realized that all of these phenomena produce distortions in the wave spectrum. The main effects are more energy for very low frequencies. This work investigates the structure of the sea clutter spectrum, and analysis the low wave number energy influence on determining sea surface current. Then the radar measure current is validated by experiments. By comparing with the in situ data, we know that the radar results reversed by image spectrum without low wave number spectrum have high precision. The low wave number energy influent determining current seriously.

Numerical simulation and validation of ocean waves measured by an Along-Track Interferometric Synthetic Aperture Radar

A new nonlinear integral transform of ocean wave spectra into Along-Track Interferometric Synthetic Aperture Radar (ATI-SAR) image spectra is described. ATI-SAR phase image spectra are calculated for various sea states and radar configurations based on the nonlinear integral transform. The numerical simulations show that the slant range to velocity ratio (R/V), significant wave height to ocean wavelength ratio (H-s/lambda), the baseline (2B) and incident angle (theta) affect ATI-SAR imaging. The ATI-SAR imaging theory is validated by means of Two X-band, HH-polarized ATI-SAR phase images of ocean waves and eight C-band, HH-polarized ATI-SAR phase image spectra of ocean waves. It is shown that ATI-SAR phase image spectra are in agreement with those calculated by forward mapping in situ directional wave spectra collected simultaneously with available ATI-SAR observations. ATI-SAR spectral correlation coefficients between observed and simulated are greater than 0.6 and are not sensitive to the degree of nonlinearity. However, the ATI-SAR phase image spectral turns towards the range direction, even if the real ocean wave direction is 30 degrees. It is also shown that the ATI-SAR imaging mechanism is significantly affected by the degree of velocity bunching nonlinearity, especially for high values of R/V and H-s/lambda.

On the nonlinear integral transform of an ocean wave spectrum into an along‐track interferometric synthetic aperture radar image spectrum

We present a new nonlinear integral transform relating the ocean wave spectrum to the along‐track interferometric synthetic aperture radar (AT‐INSAR) image spectrum. The AT‐INSAR, which is a synthetic aperture radar (SAR) employing two antennas displaced along the platform's flight direction, is considered to be a better instrument for imaging ocean waves than the SAR. This is because the AT‐INSAR yields the phase spectrum and not only the amplitude spectrum as with the conventional SAR. While the SAR and AT‐INSAR amplitude spectra depend strongly on the modulation of the normalized radar cross section (NRCS) by the long ocean waves, which is poorly known, the phase spectrum depends only weakly on this modulation. By measuring the phase difference between the signals received by both antennas, AT‐INSAR measures the radial component of the orbital velocity associated with the ocean waves, which is related to the ocean wave height field by a well‐known transfer function. The nonlinear integral transform derived in this paper differs from the one previously derived by Bao et al. [1999] by an additional term containing the derivative of the radial component of the orbital velocity associated with the long ocean waves. By carrying out numerical simulations, we show that, in general, this additional term cannot be neglected. Furthermore, we present two new quasi‐linear approximations to the nonlinear integral transform relating the ocean wave spectrum to the AT‐INSAR phase spectrum.

Waves at Holderness from X-band radar

During the Holderness Experiment of 1994–1995 and 1995–1996, data were collected by a coastal deployment of an X-band radar with simultaneous deployments of various moored and bottom-mounted wave measurement devices. The radar data consist of sequences of images of the sea surface at intervals of 1.5 h over several months. Three-dimensional wave number-frequency spectra were derived from the sequences of captured images using an analysis method developed by Young et al. [J. Geophys. Res. 90(C1) (1985) 1049]. Some aspects of this analysis were refined. An empirical transfer function was derived relating the radar image spectra to the wave spectra measured by other instruments. A new calibration procedure for obtaining wave height from the radar spectra was also derived. The radar spectra were compared with directional spectra collected by a bottom-mounted InterOcean S4DW directional wave-current meter and with Datawell Waverider data. The capabilities of X-band radar in a coastal situation are discussed including the derivation of water depth required to optimise the analysis.

Ocean wave extraction from RADARSAT synthetic aperture radar inter-look image cross-spectra

This study is concerned with the extraction of directional ocean wave spectra from synthetic aperture radar (SAR) image spectra. The statistical estimation problem underlying the wave-SAR inverse problem is examined in detail in order to properly quantify the wave information content of SAR. As a concrete focus, a data set is considered comprising six RADARSAT SAR images co-located with a directional wave buoy off the east coast of Canada. These SAR data are transformed into inter-look image cross-spectra based on two looks at the same ocean scene separated by 0.4 s. The general problem of wave extraction from SAR is cast in terms of a statistical estimation problem that includes the observed SAR spectra, the wave-SAR transform, and prior spectral wave information. The central role of the weighting functions (inverse of the error covariances) is demonstrated, as well as the consequence of approximate (based on the quasilinear wave-SAR transform) versus exact linearizations on the convergence properties of the algorithm. Error estimates are derived and discussed. This statistical framework is applied to the extraction of spectral wave information from observed RADARSAT SAR image cross-spectra. A modified wave-SAR transform is used to account for case-specific geophysical and imaging effects. Analysis of the residual error of simulated and observed SAR spectra motivates a canonical form for the SAR observation error covariance. Wave estimates are then extracted from the SAR spectra, including wavenumber dependent error estimates and explicit identification of spectral null spaces where the SAR contains no wave information. Band-limited SAR wave information is also combined with prior (buoy) spectral wave estimates through parameterization of the wave spectral shape and use of regularization.

The effect of assimilating ERS‐1 fast delivery wave data into the North Atlantic WAM model

The launch of the European ERS satellites has provided a new source of wave information that is particularly suitable for use in improving wave forecasts in the open ocean. We have implemented and tested a simple system for assimilating corrections to model wave fields produced by the WAM model, where the corrections are derived from inverted synthetic aperture radar (SAR) image spectra from ERS‐1. Corrections are applied to significant wave height, mean period and direction for wave modes that are detectable in both the model and the SAR data. The system has been tested in a storm situation and in moderate conditions using buoy data and altimeter data, as well as SAR observations for verification. Overall, it is demonstrated that the net effect of assimilating SAR data is beneficial but very small. The small impact is due at least partly to relatively small spatial and temporal coverage of the SAR wave mode data. Locally larger impacts were found in the storm situation in individual cases where SAR observations were collocated with independent buoy observations.

An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra

An earlier algorithm for retrieving two‐dimensional wave spectra from synthetic aperture radar (SAR) image spectra is improved by using a modified cost function and introducing an additional iteration loop in which the first‐guess input spectrum is systematically updated. For this purpose a spectral partitioning scheme is applied in which the spectrum is decomposed into a finite number of distinct wave systems. At each iteration step, the individual wave systems of the partitioned nth‐guess wave spectrum are adjusted to agree in mean energy, frequency, and direction with the corresponding mean values of the associated wave systems of the SAR‐inverted wave spectrum. The algorithm retrieves smooth wave spectra, avoiding the discontinuities which tended to arise in the previous algorithm in the transition region near the azimuthal wavenumber cutoff of the SAR image spectrum. The azimuthal cutoff of the SAR spectrum is also reproduced more accurately. The greatest improvement of the new retrieval algorithm is obtained when the discrepancies between the initial first‐guess wave spectrum and the observed SAR spectrum are large. In this case the additional updating loop for the input spectrum enables the retrieved spectrum to adjust such that the simulated SAR spectrum matches more closely the observed SAR spectrum. The overall correlation of a large set of simulated SAR spectra with the measured SAR spectra is found to be significantly higher than with the previous algorithm, indicating that the algorithm not only overcomes isolated shortcomings of the earlier algorithm but also yields retrieved wave spectra which are generally more consistent with the input SAR data. An additional practical advantage of the new algorithm is that it returns spectral partioning parameters which can be used in SAR wave data assimilation schemes.

Comparison of actual and simulated synthetic aperture radar image spectra of ocean waves

We have simulated synthetic aperture radar (SAR) image spectra of ocean waves, which were focused for stationary scenes using three popular formulations of SAR ocean imaging theory: the time‐dependent, velocity‐bunching, and quasi‐linear models. All three models require functional forms for surface wave spectra, modulation transfer functions, and correlation times; these were obtained from data taken during the SAR and X Band Ocean Nonlinearities (SAXON)‐Forschungsplatform Nordsee (FPN) experiment of November 1990. These measurements were made on and near the German research platform Nordsee during the same period of time that SAR images of ocean waves at X, C, and L bands were obtained by aircraft near the tower. We compare the results of our simulations to the actual SAR spectra for a variety of integration times, range‐to‐velocity ratios (R/V), and azimuth angles. We find that all three models reproduce the observed image spectra well when integration times are small and R/V ratios are low to moderate. Some adjustments of the parameters measured on the tower are occasionally necessary in order to produce this agreement, but in most cases these adjustments are small and within measurement errors; in all cases the same parameters suffice for all models. However, we reproduce a result previously obtained by Brüning et al. [1994] that measured modulated transfer functions do not properly account for imagery of range‐traveling waves propagating downwind. We also find that our calculated velocity spreads seem to be too large to reproduce the observations when the significant wave height is above about 1.5 m and R/V is appreciable. For long integration times and high R/V ratios, the velocity‐bunching model smears the spectrum more than the time‐dependent model and more than the observations. We find that the velocity‐bunching formulation is viable up to an integration time that is a function of R/V; for lower ratios, velocity bunching is viable up to longer integration times, and we offer an explanation of why this is so. Finally, we find that for large R/V ratios the quasi‐linear model fails to produce the low‐frequency components observed in actual image spectra and produced by velocity‐bunching and time‐dependent models.

Estimation of the real aperture radar modulation transfer function directly from synthetic aperture radar ocean wave image spectra without a priori knowledge of the ocean wave height spectrum

The phase and amplitude of the real aperture radar (RAR) modulation transfer function (MTF) are, applying both simulated and real synthetic aperture radar (SAR) image spectra, shown to strongly influence the SAR ocean wave imaging of range‐ (or near‐range) traveling wave systems. Conventionally, in situ measurement of the sea state has been used in connection with SAR estimation of the RAR MTF. In most cases, the SAR imaging has been simulated by varying the phase and amplitude of the transfer function until some criterium for best fit between the measured and simulated spectra is met. The main problem with this method is the need for in situ buoy measurements of the underlying ocean wave height spectrum. This paper proposes a new method for estimating the RAR MTF directly from the SAR ocean wave image spectrum. Hence the method differs from previously used methods in that it is independent of in situ measurements of the sea state. The only (weak) restriction is that the observed wave system is range‐ or near‐range traveling. On the basis of three range‐going profiles the RAR MTF phase and amplitude are estimated. Investigations using synthetic data reveal that the SAR image spectrum for realistic sea states is colored by the unknown transfer function to such an extent that the underlying wave spectral form is not critical. Experimentally, the phase and amplitude of the RAR modulation are computed using the Norwegian Continental Shelf Experiment 1988 data. It is shown that the phase is most important for the SAR spectral distribution. Typically, the phase is observed to be in the interval from 60° to 110° and the amplitude to be of the order of 10–18. Furthermore, it is shown from simulation studies that marked changes in real SAR image spectra crossing an atmospheric front are recreated when the measured MTF phase and amplitude are used. Eventually, the hydrodynamic modulation is also extracted from the RAR MTF data. Variations of the hydrodynamic MTF phase across the abovementioned front are focused on. The estimates confirm a consistent wind direction induced modulation on each side of the front. No marked trends are observed for the amplitude. The overall conclusion of the study is that the conformity between simulated and measured spectra is improved when measured RAR MTFs are incorporated in SAR imaging simulation procedures.

Generalizations of the non‐linear ocean‐SAR transform and a simplified SAR inversion algorithm

Abstract It is demonstrated that the non‐linear transform from the ocean wave spectrum to the synthetic aperture radar (SAR) image spectrum may be extended to include point target spreading (dispersive) effects. For practical purposes, the extension amounts to an additional azimuth spectral cut‐off factor applied to the result of the velocity bunching nonlinear transform without point‐target dispersion. The validity of a quasi‐linear approximation is analysed by means of simple Gaussian test spectra, which also reveal the nature of the fully non‐linear velocity bunching transform. The inversion problem is formulated as a constrained functional minimization over non‐negative wave spectra. An iterative solution method that requires an a priori estimate of the wave spectrum is demonstrated. Analysis of the method leads to a simple theory for preparing the necessary weight functions for the observed SAR and the a priori wave spectra. Combined with an optimized quasi‐linear ocean‐SAR transform, the new formula...

Analysis of marine radar image spectra collected during the grand banks ERS‐1 SAR wave experiment

Abstract Remote measurements of wave spectra were made using MacLaren Plansearch's Marine Radar Wave Measuring System (Macrada©) for the duration of the ERS‐1 Grand Banks Experiment (10–27 November 1991). The system consists of a Furuno X‐band marine navigation radar and a personal computer. The system was installed and operated onboard the BIO Research vessel CSS Hudson during the experiment. The radar system provides fully directional wave spectra in real time (within minutes of image acquisition) as well as archiving of the raw images for future analysis. During each of the satellite overpasses, excellent data were collected, covering a variety of wave conditions. This paper describes the data analysis procedures and presents the results of the experiment. In addition, a sensitivity analysis is carried out to study: (1) sensitivity to the number of radar images processed on the resultant spectra, (2) effect of missing one or more images in a dataset, and (3) sensitivity to azimuth angle variation. Fina...

Azimuth smearing in ocean–synthetic aperture radar image spectra: A study of Hasselmann's closed‐form transformation based on Norwegian Continental Shelf Experiment 1988 synthetic aperture radar data

The well‐known along‐track resolution loss in synthetic aperture radar (SAR) ocean wave image spectra is investigated comparing simulations based on Hasselmann's nonlinear integral transform and measurements from the Norwegian Continental Shelf Experiment 1988 experiment. In the literature the resolution loss has often been modeled as a low‐pass filter process, described by the rms azimuth shift width σx, acting within a quasi‐linear SAR transformation. Estimates from real data of σx, as a function the range‐to‐platform velocity (R/V) and incidence angle, are compared to Hasselmann's new nonlinear spectral transformation and the widely used quasi‐linear model. Simulations correlated with real wave data show that the quasi‐linear model, with contributions to σx from the entire spectrum, overestimates σx by roughly 30–40%. The conformity between Hasselmann's model and real data is excellent, however. The numerics also indicate that the degree of nonlinearity in Hasselmann's transform is explicitly related to the surface truth parameters' significant wave height and peak wavelength. Furthermore, the spectral bandwidth, including the subresolution part of the ocean wave spectrum, seems to be of minor importance. It is also shown that the resultant smearing (due to imaging nonlinearities) cannot explicitly be separated from the coherent linear velocity bunching part of the transform. This point is especially discussed since it has led previously to some dissension regarding which ocean spectral components are most essential in the smearing process.

On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion

A new, closed nonlinear integral transformation relation is derived describing the mapping of a two‐dimensional ocean wave spectrum into a synthetic aperture radar (SAR) image spectrum. The general integral relation is expanded in a power series with respect to orders of nonlinearity and velocity bunching. The individual terms of the series can be readily computed using fast Fourier transforms. The convergence of the series is rapid. The series expansion is also useful in identifying the different contributions to the net imaging process, consisting of the real aperture radar (RAR) cross‐section modulation, the nonlinear motion (velocity bunching) effects, and their various interaction products. The lowest term of the expansion with respect to nonlinearity order yields a simple quasi‐linear approximate mapping relation consisting of the standard linear SAR modulation expression multiplied by an additional nonlinear Gaussian azimuthal cutoff factor. The cutoff scale is given by the rms azimuthal (velocity bunching) displacement. The same cutoff factor applies to all terms of the power series expansion. The nonlinear mapping relation is inverted using a standard first‐guess wave spectrum as regularization term. This is needed to overcome the basic 180° mapping ambiguity and the loss of information beyond the azimuthal cutoff. The inversion is solved numerically using an iteration technique based on the successive application of the explicit solution for the quasi‐linear mapping approximation, with interposed corrections invoking the full nonlinear mapping expression. A straightforward application of this technique, however, generally yields unrealistic discontinuities of the best fit wave spectrum in the transition region separating the low azimuthal wave number domain, in which useful SAR information is available and the wave spectrum is modified, from the high azimuthal wave number region beyond the azimuthal cutoff, where the first‐guess wave spectrum is retained. This difficulty is overcome by applying a two‐step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first‐guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine‐scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions.

Azimuth smearing in synthetic aperture radar ocean image spectra from the Norwegian Continental Shelf Experiment of 1988

Along‐track resolution loss in synthetic aperture radar ocean images is investigated using airborne C band data collected at different altitudes. A method is developed for qualifying and quantifying the amount of smearing. The smearing can be described as a low‐pass‐filtering process acting on the image spectra even in a nonlinear region of imaging. The dependency on the ratio of range to platform velocity and the radar incidence angle is presented. An intrinsic value for the subresolution velocity spread (i.e., the rms facet velocity) is estimated to be in the region σu = 0.59–0.73 m/s for the measurements available on March 11, 1988, with significant wave height ≈ 4 m and wind speed ≈ 8 m/s. These values for σu allow a conversion of the smearing to ERS 1 geometry giving a spatial smearing σx in the range 68–84 m which corresponds to a resolution varying between 300 and 370 m in the along‐track direction.

Airborne SAR observations of ocean surface waves penetrating floating ice

The results are presented for a new and improved procedure for estimating the synthetic-aperture radar (SAR) image spectrum of ocean waves. This procedure, the spectral-sum method, involves summing individual image spectra derived from each of the looks of a multilook set. An automatic registration of the per-look spectral information is achieved, accounting for subimage look misregistration due to the wave propagation between looks. Spectral-sum processing is compared with traditional look-sum processing as a function of the radar slant-range. Spectral-sum processing is applied to SAR imagery of waves penetrating the marginal ice zone.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Hindcasts and data assimilation studies with the WAM model during the Seasat period

In the next decade a wealth of ocean surface data will become available through the launch of satellites such as ERS 1. We discuss the problem of how to make optimal use of this data. We have investigated the benefits of having a coupled wind‐wave analysis over the oceans for quality assessment of satellite data, for monitoring the performance of the algorithms (e.g., for the scatterometer), and for producing consistent wind and wave analyses. Using a reliable wave prediction scheme, the WAM model, we show how to cross validate altimeter wave height with scatterometer data and how to construct an analyzed wave model spectrum from the altimeter wave height. The analyzed wave spectrum may be cross validated with the synthetic aperture radar image spectrum. Implications for improvement of, for example, the Seasat scatterometer algorithm are pointed out.