Sea Surface Spectrum Research Articles

High-Performance Registration of Sea-Wave Spatial Spectra during the Operational Space Monitoring of Vast Water Areas

In this paper, we describe high-performance methods for recording sea-surface spectra from space images for solving problems of operational oceanography. Algorithms and research software that implement methods for the operational recovery of the characteristics of the sea surface from space images are developed. These algorithms are tested and their performance are estimated using experimental data. The research software is designed to operate with multicore processors. Based on numerical experiments, the software was found to perform within a 1% error spectra reconstruction of slopes and elevations of the sea surface using the high-performance methods that are developed. Computational experiments demonstrated a significant increase in the performance of registering the spectra of slopes and elevations of the sea surface from the spectra of space images due to the parallelization of computations: by 5 times using only the central processor of a standard desktop computer and by more than 12 times using a graphics processor with CUDA technology. Examples of the application of the developed algorithms for monitoring the vast waters of the Black Sea and the Pacific Ocean are given.

Toward real-time optical estimation of ocean waves’ space-time fields

Stereo 3D reconstruction is continuously increasing its popularity in the study of mid-to small-scale sea waves. In the recent past, different approaches have been proposed to reconstruct the space-time sea surface elevation field from synchronized stereo frames. Usually, the reconstruction is performed by first recovering a dense and sparse 3D point cloud from stereo pairs and then by interpolating it into a regular grid. Even considering state-of-the-art methods, with typical image resolutions, it's unlikely to perform the first step in less than dozens of seconds (without paralellization), that can easily doubled if we include the subsequent interpolation step. This will limit the applicability of stereo based wave analysis for all the approaches (like monitoring or data assimilation) in which the time between the raw acquisition and the output of processed data is critical.In this paper, we propose a new method to directly estimate the sea surface spectrum over time from a sequence of stereo frames. We exploit the frequency dispersion relation of gravity waves and the (Non-uniform) Fast Fourier Transform to continuously update the 3D surface and 2D wavenumber spectrum estimations given a sparse set of matching features between the two frames. This effectively combines the two aforementioned steps with a performance gain of more than an order of magnitude while keeping a reconstruction accuracy that is extremely close to the current state-of-the-art approaches. Code is available at https://gitlab.com/fibe/wassfast.

Interactions between barotropic tides and mesoscale processes in deep ocean and shelf regions

The interactions between barotropic tides and mesoscale processes were studied using the results of a numerical model in which tidal forcing was turned on and off. The research area covered part of the East Atlantic Ocean, a steep continental slope, and the European Northwest Shelf. Tides affected the baroclinic fields at much smaller spatial scales than the barotropic tidal scales. Changes in the horizontal patterns of the M2 and M4 tidal constituents provided information about the two-way interactions between barotropic tides and mesoscale processes. The interaction between the atmosphere and ocean measured by the work done by wind was also affected by the barotropic tidal forcing. Tidal forcing intensified the transient processes and resulted in a substantial transformation of the wave number spectra in the transition areas from the deep ocean to the shelf. Tides flattened the sea-surface height spectra down to ~ k−2.5 power law, thus reflecting the large contribution of the processes in the high-frequency range compared to quasi-geostrophic motion. The spectra along sections parallel or normal to the continental slope differ from each other, which indicates that mesoscale turbulence was not isotropic. An analysis of the vorticity spectra showed that the flattening was mostly due to internal tides. Compared with the deep ocean, no substantial scale selectivity was observed on the shelf area. Particle tracking showed that the lengths of the Lagrangian trajectories increased by approximately 40% if the barotropic tidal forcing was activated, which contributed to changed mixing properties. The ratio between the horizontal and vertical scales of motion varied regionally depending on whether barotropic tidal forcing was included. The overall conclusion is that the barotropic tides affect substantially the diapycnal mixing.

Research on Sea Surface Optical Characteristic Detection Based on Spectrum Model

Abstract The study of the optical characteristics of the marine environment and the optical imaging of the marine background by various detection platforms provide an effective way for engineering applications. By analyzing the JONSWAP spectral model, this paper constructs the height data of sea surface spectrum under typical environment, and analyses the difference of sea surface spectrum under different sea conditions. Based on the slope distribution of the sea surface, each part of the infrared radiation on the sea surface is calculated separately and synthesized by using the relationship between the position of the detector and the direction of view of the detection. The simulation model of the infrared radiation characteristics on the sea surface is established, and the distribution characteristics of the infrared radiation characteristics on the sea surface at different detection distances are analyzed.

Quantitative evaluation for variability characteristics of reflected sound waves from sea surface

Many kinds of hydroacoustic devices are used in the field of ocean development of resources and observations. In evaluating the effect of sound propagation in water, it is important to evaluate the characteristics of sound reflection on sea surface. Amplitude and phase of reflected sound waves often fluctuates because of the changing sea surface with waves. In this paper, we evaluated the amplitude and phase variability characteristics of reflected sound waves on sea surface by acoustic simulation with the finite difference time domain method and water tank test. It is revealed that the energy ratio γ for amplitude variability is uniquely determined by Rayleigh roughness parameter when the sea surface is sufficiently random or the number of surface waves included in the irradiation range of sound waves is large. In addition, the standard deviation of phase for the phase variability is determined by regardless of that is, sea surface spectrum.

A Domain Decomposition Finite-Element Method for Modeling Electromagnetic Scattering From Rough Sea Surfaces With Emphasis on Near-Forward Scattering

A high-fidelity full-wave simulator is presented to perform numerical experiments for rough sea scattering problem by considering different polarizations, frequencies, grazing angles, wind speeds, and sea surface spectra. The simulator is based on a novel finite-element domain decomposition (FEDD) method for solving the problem of 2-D electromagnetic scattering over 1-D sea surface. This noniterative method partitions the computational domain into a number of overlapping subdomains and solves each domain individually by employing the locally conformal perfectly matched layer (LC-PML) at the truncation boundaries. LC-PML has a unique feature such that it can be applied to irregular domains on the contrary to standard PML methods, and hence inspired the birth of FEDD. The FEDD method is used at each Monte Carlo realization corresponding to a sample from random rough surfaces and decreases the computational load, especially for electrically large problems. The accuracy and computational efficiency of the method are investigated through several simulations. Using the FEDD method, the statistical behavior of the bistatic radar cross section (RCS) is obtained for both the horizontal and vertical polarizations. A special emphasis is given to forward-scattered RCS and the mean reflection coefficient for sea surface, especially at low grazing angles, and it is shown that the simulator produces results in agreement with the Ament and Miller–Brown approximations, and experimental data, proving the reliability of the simulation approach. The results are also compared with the standard finite-element method and method of moments. Rough sea surfaces are created by using both the Pierson–Moskowitz and Elfouhaily spectra.

Numerical Analysis of Influences From Internal Waves on Electromagnetic Scattering From Sea Surface

A reliable approach based on a two-scale facet-based model and a wave-number spectrum balance equation is presented to analyze the influences from internal waves on electromagnetic scattering from a particular electrically large sea surface. It could be applied to synthetic aperture radar imagery simulation and calculating the scattering coefficients of sea surface with foam, oil film, and ship wake because local scattering coefficients are available. The facet-based model is derived from the Fucks’ first-order small perturbation method function, and then, we give the formula of scattering from arbitrary slope facet taking the two-scale model into consideration. The propagation model of internal waves is established by the Korteweg–de Vries equation, and the mechanism of modulation from internal waves to sea surface spectrum is elucidated on the basis of wave-number spectrum balance equation. Moreover, several examples and theoretical analysis are carried out to investigate the impact of internal waves on scattering characteristics under different parameters. Advisable radar parameters to observe internal waves are suggested based on the results of simulations.

Onto a Skewness Approach to the Generalized Curvature Ocean Surface Scattering Model

The generalized curvature ocean surface scattering model [general curvature model (GCM)] is extended and revisited. Two key steps are addressed in this paper, namely, a necessary sea surface spectrum undressing procedure and the inclusion of a skewness phase-related component. Normalized radar cross-section (NRCS) simulations are generated at C-band for various wind conditions, polarizations, and incidence angles. Results are compared with CMOD5.n. Although the sea surface spectrum undressing procedure is a necessary step, the overall NRCS dynamic is notably affected only in low wind conditions (≤5 m/s). The inclusion of the skewness phase-related component makes the most impact to the NRCS dynamic where the upwind/downwind asymmetry is clearly detectable. A good agreement between the upwind/downwind asymmetry of the extended GCM and CMOD5.n is achieved for moderate winds (≈5–10 m/s) and moderate incidence angles (≈32°–40°). For low incidence angles (<26°), the GCM tends to overestimate the upwind/downwind asymmetry compared with CMOD5.n.

Numerical Computation of the Electromagnetic Bias in GNSS-R Altimetry

In radar altimetry, the electromagnetic (EM) bias is originated by the smaller reflectivity of wave crests than troughs; thus, the average sea surface height is underestimated. Bias uncertainty is currently the largest factor in altimetry error budgets. The EM bias in a bistatic forward-scattering configuration at L-band, such as in Global Navigation Satellite Systems Reflectometry (GNSS-R) altimetry, remains one of the major sources of uncertainty in the altimetry error budget. In this paper, the EM bias is computed using numerical simulations. To do so, a time-dependent synthetic non-Gaussian sea surface is created using the Pierson–Moskowitz and Elfouhaily sea surface height spectra and spreading function. The sea surface is then discretized in facets and “illuminated” using a right-hand circular polarization GNSS signal, previously recorded by an up-looking antenna connected to a data logger. The waves scattered from each facet are then computed using the physical optics method under the Kirchhoff approximation, and the radar cross section of each facet is computed. The scattered electric fields are “collected” by a down-looking left-hand circular polarization antenna, and the EM bias is computed based on its fundamental definition. The numerical model is validated against Millet's model (a combined model of the weakly non-linear and modulation transfer models) with real data at C- and Ku-bands. Then, the numerical model is applied at L-band, for bistatic configurations, including different azimuth angles and different wind speeds. It is found that the EM bias is almost insensitive to the sea surface spectra selected and increases with increasing wind speed and incidence/scattering angle (up to ∼-20 cm at $\theta_{i,s}=45^{\circ}$ and $U_{10}=12 \mbox{m/s}$ ), and it also exhibits a non-negligible azimuthal dependence, which must be accounted for in the error budgets of upcoming GNSS-R altimetry missions.

The measurement of sea surface profile with X-band coherent marine radar

The line-of-sight velocity of scattering facets is related to the Doppler signals of X-band coherent marine radar from the oceanic surface. First, the sign Doppler Estimator is applied to estimate the Doppler shift of each radar resolution cell. And then, in terms of the Doppler shift, a retrieval algorithm extracting the vertical displacement of the sea surface has been proposed. The effects induced by radar look-direction and radar spatial resolution are both taken into account in this retrieval algorithm. The comparison between the sea surface spectrum of buoy data and the retrieved spectrum reveals that the function of the radar spatial resolution is equivalent to a low pass filter, impacting especially the spectrum of short gravity waves. The experimental data collected by McMaster IPIX radar are also used to validate the performance of the retrieval algorithm. The derived significant wave height and wave period are compared with the in situ measurements, and the agreement indicates the practicality of the retrieval technology.

Effect of a roughened sea surface on shallow water propagation with emphasis on reactive intensity obtained with a vector sensor

In this study, sea-surface conditions during the Targets and Reverberation Experiment (TREX) are analyzed. The sea-surface directional spectrum was experimentally measured up to 0.6 Hz with two wave buoys separated by 5 km. The analysis presented here focuses on propagation relating to three canonical sea-surfaces observed during the experiment: calm conditions, and rough conditions with waves either perpendicular or parallel to the primary propagation direction. Acoustic data collected during calm and rough conditions show a significant difference in the amount of out-of-plane scattering. Interference due to this out-of-plane scattering is observed in the component of reactive intensity perpendicular to the propagation direction. These observations are compared with those generated using a model of the sea-surface scattering based on a combination of buoy-measured and modeled directional spectrum. Simulated sea-surfaces are also constructed for this numerical study. A model for wind waves is used to obtain surface wavenumbers greater than those measured by the wave buoys (~1.5 rad/m). Importantly, the spectral peak and it direction are well measured by the buoys and no assumptions on fetch are required, resulting in a more realistic wave spectrum and description of sea-surface conditions for acoustic modeling.

Effects of sea surface roughness on the mid-frequency acoustic pulse decay in shallow water

Recent and ongoing efforts to characterize sea bed parameters from measured acoustic pulse decay have neglected the effects of sea surface roughness. In this paper, these effects are investigated using a rough surface version of RAMPE, RAMSURF, and random rough surface realizations, calculated from a 2D JONSWAP sea surface spectrum with directional spreading. Azimuthal dependence is investigated for sandy bottoms and found that the rate of pulse decay increases when the surface wave fronts are perpendicular to the path of acoustic propagation and higher significant wave height results in higher decay rates. Additionally, the effects from sea surface roughness are found to vary with different waveguide parameters including but not limited to sound speed profile, water depth, and seabed properties. Of particular interest are the combined effects of sea bed properties and rough sea surfaces. It is shown that when clay like sediments are present, higher-order modes are strongly attenuated and effects due to interaction with the rough sea surface are less pronounced. Finally, possible influences of sea-state and 3D out-of-plane propagation effects on the seabed characterization efforts will be discussed. [Work supported by ONR.]

The Two-Scale BPM Scattering Model for Sea Biogenic Slicks Contrast

Sea oil slick observation by means of synthetic aperture radar is still a scientific and operational challenge. In this paper, the sea surface scattering with and without biogenic slicks is analyzed by using the two-scale Boundary Perturbation Method scattering model. The surface slick is supposed to modify both the full-range sea surface spectrum and the slope probability density function by means of the Marangoni damping and by a reduced friction velocity. In this paper, the full-range Universite Catholique de Louvain sea surface spectrum is considered. A new contrast model, which overcomes the drawbacks of the contrast model based on the untilted Small Perturbation Method scattering model, is presented and illustrated in some L- and C-band biogenic slick cases.

Sea surface multispectral index model for estimating chlorophyll a concentration of productive coastal waters in Thailand

Chlorophyll a (Chl a) concentration in water can be estimated using remote sensing methodology. This study uses Chl a high absorption and high reflectance wavelengths to produce indices stable for Chl a monitoring. The relationships between the indices and Chl a are determined and then applied to satellite bands for model development. The sea surface spectrum was measured in situ using a portable spectrometer, and Chl a concentration was analyzed in the laboratory. Satellite images were obtained from Landsat-5 for the day of sampling. The results of a three-band index from the spectrometer composed of wavelengths 435, 488, and 692 nm indicate the most significant correlation with Chl a concentration. The exponential relation was observed with the highest correlation coefficient of r2 = 0.83. The index model was applied to Landsat-5 data, and the observed Chl a dataset was compared with that estimated from Landsat-5. This analysis gave a high correlation of r2 = 0.73.

Doppler Spectra From a Two-Dimensional Ocean Surface at L-Band

An approximate time-harmonic three-dimensional electromagnetic boundary-integral method, the small-slope integral equation, is combined with a series expansion of the Creamer surface representation at second order with respect to the height, denoted by Creamer (2). The resulting model provides at low numerical cost simulations of the nonlinear ocean surface Doppler spectrum at L-band. As a result of approximations, the model is designed for a low-wind speed, typically up to 5 m/s. It is shown that applying directly a second-order model such as Creamer (2) to a semiempirical sea surface spectrum induces an unrealistic magnification of small-scale roughness that is involved in the scattering process at microwave frequencies. This paper thus proposes an undressed version of the Pierson-Moskowitz spectrum that corrects this artifact. Full-polarized Doppler simulations at L-band and 70deg incidence are presented. Effects of the surface nonlinearities are outlined, and the simulated Doppler spectra show correct variations with respect to wind speed and direction

Determining the sea-roughness spectra from an optical image of the sea surface

An optical model of sea-surface imaging based on a two-scale presentation of sea roughness is developed. Using this model, an exact expression for the sea-surface image spectrum in diffuse sky light is obtained, which made it possible to estimate the nonlinear contribution of waves of different scales to the image spectrum. In particular, it is shown that the image spectrum is proportional to the wave tilt spectrum and the coefficient before the tilt spectrum is determined by the modulation of the short-wave contrast by long waves. Accuracy of determination of spectral contrasts of waves in surface-roughness anomalies (film slicks, internal-wave field, etc.) and accuracy of measurement of two-dimensional wave spectra from the sea-surface image spectrum are estimated. Examples of sea-roughness variability in the internal-wave field and examples of two-dimensional sea-roughness spectra are presented. All data were obtained by the optical method under full-scale conditions.

Sea state effect on the sea surface emissivity at l-band

In May 1999, the European Space Agency (ESA) selected the Earth Explorer Opportunity Soil Moisture and Ocean Salinity (SMOS) mission to obtain global and frequent soil moisture and ocean salinity maps. SMOS' single payload is the Microwave Imaging Radiometer by Aperture Synthesis (MIRAS), an L-band two-dimensional aperture synthesis radiometer with multiangular observation capabilities. At L-band, the brightness temperature sensitivity to the sea surface salinity (SSS) is low, approximately 0.5 K/psu at 20/spl deg/C, decreasing to 0.25 K/psu at 0/spl deg/C, comparable to that to the wind /spl sim/0.2 K/(m/s) at nadir. However, at a given time, the sea state does not depend only on local winds, but on the local wind history and the presence of waves traveling from far distances. The Wind and Salinity Experiment (WISE) 2000 and 2001 campaigns were sponsored by ESA to determine the impact of oceanographic and atmospheric variables on the L-band brightness temperature at vertical and horizontal polarizations. This paper presents the results of the analysis of three nonstationary sea state conditions: growing and decreasing sea, and the presence of swell. Measured sea surface spectra are compared with the theoretical ones, computed using the instantaneous wind speed. Differences can be minimized using an effective wind speed that makes the theoretical spectrum best match the measured one. The impact on the predicted brightness temperatures is then assessed using the small slope approximation/small perturbation method (SSA/SPM).

Cloud detection over sea surface by use of autocorrelation functions of upwelling infrared spectra in the 800–900-cm^-1 window region

A new algorithm for cloud detection over sea surface has been developed that makes use of autocorrelation and cross correlation between a real spectrum and either a synthetic or a laboratory spectrum. The scheme is intended for high-spectral-resolution satelliteborne infrared sensors that will measure the Earth's entire emission spectrum rather than the upwelling radiance in a few channels. A new index is defined with which one can determine quantitatively the degree of homogeneity of two spectra in the 800-900-cm(-1) (11.11-12.5 mum) window region. The index makes use of only the observed spectrum along with a reference synthetic spectrum and, therefore, may form the basis for an operational stand-alone cloud-detection algorithm for next-generation high-spectral-resolution infrared sensors. Application both to synthetic spectra obtained in simulation and to sea-surface real spectra recorded through the interferometric monitor for greenhouse gases is considered.

Full-range sea surface spectrum in nonfully developed state for scattering calculations

A new form for the spectrum of the ocean surface vertical displacements is derived for the case of nonfully developed states. The gravity range is expressed as a function of the fetch x and the significant slope /spl conint/ as well. The capillary-gravity range is assumed dependent on the wind friction velocity only. Recent wavenumber spectrum measurements in this spectral domain and ocean conditions are analyzed. Toba's spectral shape is shown to represent correctly these experimental data when updated with an equivalent amplitude factor. An expression for this factor is proposed. It is weakly wind friction velocity dependent, as observed by Mitsuyasu in the late 1970s. The proposed spectrum is then combined with a boundary perturbation model for electromagnetic scattering computations. Empirical scattering models and radar data collocated with assumed ground-truth data are used for comparison. This is shown to give consistent results for both C- and Ku-bands as well as large ranges of wind speeds and incidence angles. Comparisons of backscattering coefficients computed using other sea spectra from the literature are presented. The significant slope is found to be an important factor for scattering at low incidence angles. The proposed spectrum thus constitutes a useful basis for physically based inversion algorithms.

Coherent reflection loss from a Pierson–Moskowitz sea surface using the NLSSA

Numerical results for the incoherent bistatic scattering strength for the nonlocal small-slope approximation (NLSSA) for scattering from rough surfaces [A. G. Voronovich, Waves Random Media 6, 151–167 (1996)], using a Gaussian spectrum, were recently reported [S. L. Broschat and E. I. Thorsos, J. Acoust. Soc. Am. 100, 2702 (1996)]. The cases considered agreed well with exact integral equation results and demonstrated the potential of the NLSSA for accurate modeling of rough surface scattering. In this paper, results for the coherent reflection loss for one-dimensional surfaces are presented. Coherent loss is of particular importance in long-range acoustic propagation when the cumulative effect of multiple interactions with the surface can be significant. The lowest-order NLSSA reflection coefficient is derived, and numerical results are shown for the reflection loss at low grazing angles, using a Pierson–Moskowitz sea surface spectrum. The numerical results are compared with those of other approximate methods and agree well with exact integral equation results. [Work supported by ONR.]