Tanos Elfouhaily

A unified directional spectrum for long and short wind‐driven waves

Review of several recent ocean surface wave models finds that while comprehensive in many regards, these spectral models do not satisfy certain additional, but fundamental, criteria. We propose that these criteria include the ability to properly describe diverse fetch conditions and to provide agreement with in situ observations of Cox and Munk [1954] and Jahne and Riemer [1990] and Hara et al. [1994] data in the high-wavenumber regime. Moreover, we find numerous analytically undesirable aspects such as discontinuities across wavenumber limits, nonphysical tuning or adjustment parameters, and noncentrosymmetric directional spreading functions. This paper describes a two-dimensional wavenumber spectrum valid over all wavenumbers and analytically amenable to usage in electromagnetic models. The two regime model is formulated based on the Joint North Sea Wave Project (JONSWAP) in the long-wave regime and on the work of Phillips [1985] and Kitaigorodskii [1973] at the high wavenumbers. The omnidirectional and wind-dependent spectrum is constructed to agree with past and recent observations including the criteria mentioned above. The key feature of this model is the similarity of description for the high- and low-wavenumber regimes; both forms are posed to stress that the air-sea interaction process of friction between wind and waves (i.e., generalized wave age, u/c) is occurring at all wavelengths simultaneously. This wave age parameterization is the unifying feature of the spectrum. The spectrums directional spreading function is symmetric about the wind direction and has both wavenumber and wind speed dependence. A ratio method is described that enables comparison of this spreading function with previous noncentrosymmetric forms. Radar data are purposefully excluded from this spectral development. Finally, a test of the spectrum is made by deriving roughness length using the boundary layer model of Kitaigorodskii. Our inference of drag coefficient versus wind speed and wave age shows encouraging agreement with Humidity Exchange Over the Sea (HEXOS) campaign results.

A critical survey of approximate scattering wave theories from random rough surfaces

Abstract This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.

Observation of tropical cyclones by high‐resolution scatterometry

Unprecedented views of surface wind fields in tropical cyclones (hereafter TCs) are provided by the European Remote Sensing Satellite (ERS) C band scatterometer. Scatterometer measurements at C band are able to penetrate convective storms clouds, observing the surface wind fields with good accuracy. However the resolution of the measurements (50x50 km 2) limits the interpretation of the scatterometer signals in such mesoscale events. The strong gradients of the surface wind existing at scales of a few kms are smoothed in the measured features such as the intensity and location of the wind maxima, and the position of the center. Beyond the ERS systems, the scatterometers on-board the ADEOS and METOP satellites, designed by the Jet Propulsion Laboratory and by the European Space Agency, respectively, will be able to produce measurements of the backscattering coefficient at about 25x25 km 2 resolution. A few sets of ERS-1 orbits sampling TC events were produced with an experimental 25x25 km 2 resolution. Enhancing the resolution by a factor of 2 allows location of the wind maxima and minima in a TC with a much better accuracy than at 50 km resolution. In addition, a better resolution reduces the geophysical noise (variability of wind speed within the cell and effect of rain) that dominates the radiometric noise and hence improves the definition of the backscattering measurements. A comprehensive analysis of the backscattering measurements in the case of high winds and high sea states obtained within TCs is proposed in order to refine the interpretation of the wind vector derived from a backscattering model that is currently only calibrated up to moderate winds (< 20 m/s) in neutral conditions. Observations of the TOPEX-POSEIDON dual-frequency altimeter are also used for that purpose. Patterns of the surface winds in TCs are described and characteristic features concerning asymmetries in the maximum winds and in the divergence field are discussed.

Delay-Doppler analysis of bistatically reflected signals from the ocean surface: theory and application

We present a new stochastic theory for delay-Doppler mapping of the ocean surface for bistatic scattering. This stochastic theory should complement nicely the previous theories for the Global Positioning System (GPS) reflected signals from ocean surfaces, especially that of Zavorotny and Voronovich (2000). We quantify the Doppler spread of the reflected signal before interpreting the delay. Our theoretical results compare very well to Doppler spectra computed using data collected during an airborne campaign. The bandwidth of the spectra is linked to the geometry and to the ocean roughness. The bulk of the Doppler spread is caused by the rms slope and not by the surface orbital velocity. Our stochastic theory is generalized to include the delay mapping made possible by the existence of the pseudorandom noise code on the GPS L-band carrier. These results can be seen as a generalization of Woodwards theorem for FM signals to delay-Doppler analysis of more complicated signals. Our formulation is amenable to inversion for the determination of geophysical parameters such as surface wind vector and mean sea level. Another novelty in our approach is the inclusion of the sea state.

Local and non-local curvature approximation: a new asymptotic theory for wave scattering

Abstract We present a new asymptotic theory for scalar and vector wave scattering from rough surfaces which federates an extended Kirchhoff approximation (EKA), such as the integral equation method (IEM), with the first and second order small slope approximations (SSA). The new development stems from the fact that any improvement of the ‘high frequency’ Kirchhoff or tangent plane approximation (KA) must come through surface curvature and higher order derivatives. Hence, this condition requires that the second order kernel be quadratic in its lowest order with respect to its Fourier variable or formally the gradient operator. A second important constraint which must be met is that both the Kirchhoff approximation (KA) and the first order small perturbation method (SPM-1 or Bragg) be dynamically reached, depending on the surface conditions. We derive herein this new kernel from a formal inclusion of the derivative operator in the difference between the polarization coefficients of KA and SPM-1. This new kernel is as simple as the expressions for both Kirchhoff and SPM-1 coefficients. This formal difference has the same curvature order as SSA-1 + SSA-2. It is acknowledged that even though the second order small perturbation method (SPM-2) is not enforced, as opposed to the SSA, our model should reproduce a reasonable approximation of the SPM-2 function at least up to the curvature or quadratic order. We provide three different versions of this new asymptotic theory under the local, non-local, and weighted curvature approximations. Each of these three models is demonstrated to be tilt invariant through first order in the tilting vector.

Improved electromagnetic bias theory

In this paper we describe modifications to a previous theory for the altimeter electromagnetic bias (EM bias) of Srokosz [1986]. A major correction introduces a scaling of Srokoszs model by nonnegligible dimensionless ratios that depend on the slope variance of both long and short waves. With these modifications the EM bias is no longer simply a function of the cross skewness between surface elevation and slope but now depends on the variance ratios that represent the modulation between short and long waves. Inclusion of these ratios can reduce previous EM bias estimates by as much as 50%. Different directions for the longwave and shortwave field are also accounted for in the two-dimensional development of our approach. A radar frequency dependence consistent with observation is also predicted by the new model. Derivation extending our development to the next higher order in wave statistics is also presented and discussed.

Importance of peakedness in sea surface slope measurements and applications

We recall the simple statistical concept that non-Gaussian distribution peakedness results from the compounding of random processes. This idea is applied to observations and analysis of sea surface slopes as inferred using optical and microwave-scattering measurements. Our study emphasizes the importance of identifying and quantifying the distribution variance and kurtosis from observations. Data are shown to indicate consistently non-Gaussian peakedness, to indicate the need to report at least two parameters in an even order analysis, and to indicate near equivalence between radar and optical data. Physical interpretation for observed infrequent steep slopes is given via compounding statistical processes where normally distributed short-scale waves are modulated because of random fluctuations mainly associated with the underlying long wave field. Implications of non-Gaussian peakedness are provided for altimeter backscatter theory and for modeling wave-breaking probability.

An improved geometrical optics model for bistatic GPS scattering from the ocean surface

This paper is concerned with the properties of bistatic microwave scattering from a randomly rough surface, and specifically its application to the study of global positioning system (GPS) satellite signals reflected from the ocean. We present a discussion of some recent refinements of Kirchhoff-type models based on second-order iterations of the surface-current integral equation, and the relationship between these models and their high-frequency (geometric optics) limit. In particular, we show that use of these refinements can extend the domain of applicability of the standard geometrical optics (GO) model. It is found that GO can be nearly as accurate as a Kirchhoff-based model provided that the wavenumber cutoff, at which the surface wave spectrum must be filtered in computing the required slope moments, depends on the roughness of the ocean surface (i.e., wind speed) as well as the incident angle and frequency of the radiation. We use a GO model refined in this way to analyze GPS surface reflection data collected from an aircraft equipped with two down-looking antennas for receiving both left- and right-hand circularly polarized reflections. Concurrent measurements of the local wind and wave conditions were collected from a nearby research vessel. Measured waveforms and mean Doppler widths at both polarizations are compared with predictions from our refined GO model, and discussion is given concerning the sensitivity of the reflected radiation to various geophysical parameters and the utility of GPS reflections for remote sensing applications.

Estimation of wind stress using dual‐frequency TOPEX data

The TOPEX/POSEIDON satellite carries the first dual-frequency radar altimeter. Monofrequency (Ku-band) algorithms are presently used to retrieve surface wind speed from the altimeters radar cross-section measurement (σ0Ku). These algorithms work reasonably well, but it is also known that altimeter wind estimates can be contaminated by residual effects, such as sea state, embedded in the σ0Ku measurement. Investigating the potential benefit of using two frequencies for wind retrieval, it is shown that a simple evaluation of TOPEX data yields previously unavailable information, particularly for high and low wind speeds. As the wind speed increases, the dual-frequency data provides a measurement more directly linked to the short-scale surface roughness, which in turn is associated with the local surface wind stress. Using a global TOPEX σ0° data set and TOPEXs significant wave height (Hs) estimate as a surrogate for the sea states degree of development, it is also shown that differences between the two TOPEX σ0 measurements strongly evidence nonlocal sea state signature. A composite scattering theory is used to show how the dual-frequency data can provide an improved friction velocity model, especially for winds above 7 m/s. A wind speed conversion is included using a sea state dependent drag coefficient fed with TOPEX Hs data. Two colocated TOPEX-buoy data sets (from the National Data Buoy Center (NDBC) and the Structure des Echanges Mer-Atmosphre, Proprietes des Heterogeneites Oceaniques: Recherche Experimentale (SEMAPHORE) campaign) are employed to test the new wind speed algorithm. A measurable improvement in wind speed estimation is obtained when compared to the monofrequency Witter and Chelton [1991] model.

Weakly nonlinear theory and sea state bias estimations

The theory of “weakly” nonlinear (WNL) waves is commonly used in generating higher statistical moments of a random surface wave field. These moments can be used, for example, to estimate the sea state bias (SSB) in radar altimetry under a geometric optical assumption. The present investigation suggests that several previous SSB studies appear to have misapplied this WNL theory by violating its condition of validity. As a result, a pronounced inconsistency appears even for lower-order moments. This inconsistency appears as a difference between the statistical moments of the nonlinear surface generated by the application of the WNL theory and those of the linear input (or bare) spectrum. If measured spectra, which yield measured moments (such as rms elevation and slope), are chosen as an input to WNL theory, then the corresponding moments of resulting output spectra may be severely overestimated. To strictly avoid the inconsistency, WNL theory must only be applied to long gravity waves where the wave-wave interactions are weak, hence the WNL epithet. To further illustrate this problem, we present an inversion scheme that determines the proper input spectrum by forcing the low-order moments of the output spectrum to equal the measured moments. Analytical solutions are given for this inversion based on an explicit formulation of the low-order nonlinear moments and a simplified one-dimensional power law spectrum. The solutions show that the high-frequency portion (wave components shorter than about 10 m) of the input (or bare) spectrum must be significantly less energetic than that of the output spectrum. Our results emphasize the importance of the shorter-scale waves in the SSB mechanism.