A theoretical model that describes the power of a scattered Global Positioning System (GPS) signal as a function of geometrical and environmental parameters has been developed. This model is based on a bistatic radar equation derived using the geometric optics limit of the Kirchhoff approximation. The waveform (i.e., the time-delayed power obtained in the delay-mapping technique) depends on a wave-slope probability density function, which in turn depends on wind. Waveforms obtained for aircraft altitudes and velocities indicate that altitudes within the interval 5-15 km are the best for inferring wind speed. In some regimes, an analytical solution for the bistatic radar equation is possible. This solution allows converting trailing edges of waveforms into a set of straight lines, which could be convenient for wind retrieval. A transition to satellite altitudes, together with satellite velocities, makes the peak power reduction and the Doppler spreading effect a significant problem for wind retrieval based on the delay-mapping technique. At the same time, different time delays and different Doppler shifts of the scattered GPS signal could form relatively small spatial cells on sea surface, suggesting mapping of the wave-slope probability distribution in a synthetic-aperture-radar (SAR) fashion. This may allow more accurate measurements of wind velocity and wind direction.

Scattering of GPS signals from the ocean with wind remote sensing application

To provide theoretical basis for the connection between observed radar scattering and wind-generated waves, a model for the response of surface waves in the gravity-capillary equilibrium region of the spectrum is proposed on the basis of a local (in wavenumber) balance between wind input and dissipation. The wind input function was constructed on the basis of laboratory observations of short-wave growth, while the dissipation function was developed from ideas of viscous dissipation and wave breaking in response to local accelerations and modified by kinematic effects of phase and group velocity differences. The model was exercised at L, C, X, and Ka bands to demonstrate the differences in wind speed and water temperature sensitivity.

Radar scattering and equilibrium ranges in wind‐generated waves with application to scatterometry

Real and synthetic aperture radars have been used in recent years to image ocean surface waves. Though wavelike patterns are often discernible on radar images, it is still not fully understood how they relate to the actual wave field. The present paper reviews and extends current models on the imaging mechanism. Linear transfer functions that relate the two-dimensional wave field to the real aperture radar (SLAR) image are calculated by using the two-scale wave model. It is noted that a description of the imaging process by these transfer functions can only be adequate for low to moderate sea states. Possible other mechanisms that contribute to the visibility of waves by real aperture radar at higher sea states, such as Bragg scattering from spontaneously generated short waves at peaked crests or in wave breaking regions, and Rayleigh scattering from air bubbles entrained in the water and from water droplets thrown into the air by breaking waves, are discussed in a qualitative way. The imaging mechanism for synthetic aperture radars (SAR's) is strongly influenced by wave motions (i.e., by the orbital velocity and acceleration associated with the long waves). The phase velocity of the long waves does not enter into the imaging process. Focusing of ocean wave imagery is attributed to orbital acceleration effects. The orbital motions lead to a degradation in resolution which causes image smear as well as a SAR inherent imaging mechanism called velocity bunching. The parameter range for which velocity bunching is a linear mapping process is calculated. It is shown that linearity holds only for a relative small range of ocean wave parameters: The likelihood that the transfer function is linear increases as the direction of wave propagation approaches the range direction, as the wavelength increases, and as the wave height decreases. Linearity is required for applying simple linear system theory for calculating the ocean wave spectrum from the gray level intensity spectrum of the image. Although, in general, the full ocean wave spectrum cannot be recovered from the SAR image by applying simple linear inversion techniques, it is concluded that for many cases in which the ocean wave spectrum is relatively narrow the dominant wavelength and direction can still be retrieved from the image even when the mapping transfer function is nonlinear. Finally, we compare our theoretical models for the imaging mechanisms with existing SLAR and SAR imagery of ocean waves and conclude that our theoretical models are in agreement with experimental data. In particular, our theory predicts that swell traveling in flight (azimuthal) direction is not detectable by SLAR but is detectable by SAR.

On the detectability of ocean surface waves by real and synthetic aperture radar

This paper reviews basic synthetic aperture radar (SAR) theory of ocean wave imaging mechanisms, using both known work and recent experimental and theoretical results from the Marine Remote Sensing (MARSEN) Experiment. Several viewpoints that have contributed to the field are drawn together in a general analysis of the backscatter statistics of a moving sea surface. A common focus for different scattering models is provided by the mean image impulse response function, which is shown to be identical to the (spatially varying) frequency variance spectrum of the local complex reflectivity coefficient. From the analysis has emerged a more complete view of the SAR imaging phenomenon than has been previously available. A new, generalized imaging model is proposed.

Theory of synthetic aperture radar ocean imaging: A MARSEN view

A series of spatial wave images recorded by a conventional marine radar is analyzed to determine the three-dimensional E(kx, ky, ω) spectrum. In the absence of a surface current the spectral energy in this three-dimensional wave number frequency space will lie on a shell defined by the dispersion relationship. Any deviation from the expected dispersion relationship can be interpreted as being due to a current induced Doppler shift of the wave frequency. A least squares curve fitting technique is used to determine the surface current required to account for the observed Doppler shift. A comparison of the radar determined spectra and surface currents with ground truth data indicates that the radar system and analysis technique produces results consistent with conventional instrumentation.

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A three-dimensional analysis of marine radar images for the determination of ocean wave directionality and surface currents

This paper reviews analytical methods in electromagnetic scattering theory (i.e., geometrical and physical optics, perturbation, iteration, and integral-equation) which are applicable to the problems of remote sensing of the ocean. In dealing with Earth's surface (in this case, the weakly non-linear ocean), it is not possible to have a complete and exact description of its spatial and temporal statistics. Only the first few moments are generally available; and in the linear approximation the statistics are assumed homogeneous, stationary and Gaussian. For this case, the high-frequency methods (geometrical and physical optics) and perturbation (Rayleigh-Rice), or a combination of them, provide tractable analytical results (i.e., the specular-point, the slightly-rough Bragg scattering and the composite-surface models). The applicability and limitations of these models are discussed. At grazing incidence and for higher frequencies, other scattering mechanisms become significant; and shadowing, diffraction and trapping must be considered. The more exact methods (integral-equation and Green's function) have not been as successful in yielding tractable analytical solutions, although they have the potential to provide improved theoretical scattering results in the future.

Theories for the interaction of electromagnetic and oceanic waves — A review

A review of electromagnetic (e.m.) and hydrodynamic processes pertinent to the backscatter of microwaves from water/ocean waves is presented. The understanding of e.m. scattering from the ocean has increased rapidly in the past two decades. The enhanced knowledge has allowed the probing of ocean waves with radio/microwaves, paving the way for the success of the first oceanographic satellite in 1978, SEASAT. In the future, as the calibration of microwave sensors improve, satellite measurements of the world oceans should become routine. In particular, the forthcoming 1989–1994 World Ocean Circulation Experiment (WOCE) will rely on microwave measurements from space for wind stress and geostrophic currents information.

Microwave Sensing of the Ocean Surface

The M2 tidal currents over Phelps Bank are examined using a fully nonlinear model. Simulations with resolutions of 2’ × 2’ and 0.5’ × 0.5’ were made of the full area covering Nantucket Shoals south of Cape Cod. A fine resolution model (0.125’ × 0.125’) was also run over a limited area surrounding Phelps Bank. Agreement was good in amplitude and phase when compared to surface elevation data. The agreement with current meter data was fair in amplitude and poor in phase with the exception that agreement was good at the one Phelps Bank mooring when compared with models of the full area. The limited area model showed signs of instability that were damped out with a horizontal eddy viscosity. Agreement of this model with data from the one available current meter mooring was worse. Different options are available to go from model predictions to the currents necessary for calibration of microwave data obtained over Phelps Bank.

Determining the currents over phelps bank

A review of the hydrodynamic and electromagnetic processes contributing to radar imaging of ocean waves in the presence of variable currents and nonlinear forcing (input from the wind, energy transfer by resonant nonlinear interactions, and dissipation) is given. Since many of the pertinent processes are quite complex and are areas of active research even today, the review is made as comprehensive as possible, but brief enough so as to bring the reader quickly up to date in the literature and still provide enough insight into the processes involved. Some new results on the development of the gravity-capillary wavenumber spectrum are also given.

SAR Imaging of Ocean Waves in the Presence of Variable Currents

The purpose of this general discussion on e.m. scattering after the formal scientific presentations at the workshop was to ascertain the present state of knowledge in the field, assess the quality of the predictions, and to arrive at some specific recommendations for future research. Frank and active discussions took place in regard to the status of e.m. scattering theories/models for the ocean surface (see Table I). During the formal presentations it was clear that the two-scale model (Wright, 1968; Bass and Fuks, 1979) when properly applied, (Thompson, 1988; Thompson et al., 1988) yields just as good agreement (within a couple of decibels) as the Kirchhoff approximation (Holliday et al., 1986, 1987) when applied to the SARSEX data on SAR imagery (L and X band) for internal waves in the New York Bight. Both of these comparisons only deal with cross section effects, the distortion in the image intensity from wave motion and current variations affecting the phase of the e.m. backscattered fields is not included. To match the theoretical predictions with the measurements, the enhancement in slopes by the internal waves of both the long (greater than 1 m length) and intermediate (of the order of 1 m length) gravity waves should be included in the tilting of the Bragg resonant waves of wave number 2ko sinθ, ko is the wavenumber of the e.m. radiation in free space and θ is the angle of incidence.

Gaspar R. Valenzuela

Papers

Theories for the interaction of electromagnetic and oceanic waves — A review

Microwave Sensing of the Ocean Surface

Determining the currents over phelps bank

SAR Imaging of Ocean Waves in the Presence of Variable Currents

General Discussion on Electromagnetic Scattering