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 spectrum's 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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JC00467

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

Images of the ocean surface taken with active microwave sensors often contain much information on near-surface and subsurface processes. However, their interpretations may depend on a detailed understanding of the physics of electromagnetic scatter. In scattering theory, the surface hydrodynamics enters the equations via (1) the probability distribution function for either wave heights or slopes, and (2) the two-dimensional wave height/slope autocovariance or its Fourier transform, the wave vector spectrum. This paper advances an improved model for the ocean surface wave vector spectrum based on recent work by M. A. Donelan, by M. L. Banner, and by B. Jahne and their collaborators. The model addresses the range of surface wavelengths from fully developed wind waves to the gravity-capillary region. For gravity-capillary waves, the spectral equation satisfactorily represents the observational data of Jahne et al. taken in tanks at large fetches, in the range from approximately 50 to 1500 rad/m to within the accuracy of the data. From the spectrum, the two-dimensional autocovariance of the sea surface is computed and correlation lengths and curvatures obtained. When used with a modification of Holliday's formulation of microwave radar backscatter from a Gaussian sea, it quantitatively reproduces observational cross section data taken at vertical polarization from aircraft and spacecraft over the open ocean, with differences from the field data having a mean of −0.2 dB and a standard deviation of 1.7 dB, The range of parameters for which satisfactory fits are obtained includes: wind speeds from 1.5 to 24 m/s; frequencies from approximately 5.5 to 35 GHz; and incidence angles from 0° to greater than 60°. For horizontal polarization, the scattering calculations fail rather badly for larger incidence angles, as do all theories based on the Kirchhoff approximation. Additionally, in spite of the incorporation of an anisotropic angular distribution of wave energy, the observed azimuthal variation of radar scatter is not captured, indicating that the source of that variation lies elsewhere.

An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter

An improved composite surface model for the calculation of the normalized radar backscattering cross section (NRCS) of the ocean surface at moderate incidence angles is presented. The model is based on Bragg scattering theory. A Taylor expansion of the NRCS in the two-dimensional surface slope yields nonzero second-order terms which represent a first approximation for the effect of the geometric and hydrodynamic modulation of the Bragg scattering facets by all waves that are long compared to these facets. The corresponding expectation value of the NRCS varies with the wave height spectral density of all these waves, and it depends in a well-defined way on frequency, polarization, incidence angle, and azimuthal look direction of the radar. We show that measured NRCS values at frequencies ranging from 1 GHz (L band) through 34 GHz (Ka band) and wind speeds between 2 and 20 m/s can be well reproduced by the proposed model after some reasonable tuning of the input ocean wave spectrum. Also, polarization effects and upwind/downwind differences of the NRCS appear to be relatively well represented. The model can thus be considered as an advanced wind scatterometer model which is based on physical principles rather than on empirical relationships. The most promising field of application, however, will be the calculation of NRCS variations associated with local distortions of the wave spectrum by surface current gradients or wind effects.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JC00190

An improved composite surface model for the radar backscattering cross section of the ocean surface 1. Theory of the model and optimization/validation by scatterometer data

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 Jiihne 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 spectrum's 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 Unified Directional Spectrum for Long and Short Wind-Driven Waves

We present a passive optical remote sensing technique for recovering shape information about a water surface, in the form of a two-dimensional slope map. The method, known as polarimetric slope sensing (PSS), uses the relationship between surface orientation and the change in polarization of reflected light to infer the instantaneous two-dimensional slope across the field-of-view of an imaging polarimeter. For unpolarized skylight, the polarization orientation and degree of linear polarization of the reflected skylight provide sufficient information to determine the local surface slope vectors. A controlled laboratory experiment was carried out in a wave tank with mechanically generated gravity waves. A second study was performed from a pier on the Hudson River, near Lamont-Doherty Earth Observatory. We demonstrated that the two-dimensional slope field of short gravity waves could be recovered accurately without interfering with the fluid dynamics of the air or water, and water surface features appear remarkably realistic. The combined field and laboratory results demonstrate that the polarimetric camera gives a robust characterization of the fine-scale surface wave features that are intrinsic to wind-driven air‐sea interaction processes.

https://iopscience.iop.org/article/10.1088/0957-0233/19/5/055503/pdf

Retrieval of short ocean wave slope using polarimetric imaging

A detailed study of 2-D wave number spectra of short water surface waves is presented. Using a refraction-based optical technique either the along-wind or the cross-wind slope is visualized in image sectors of up to 30 X 40 cm 2 . The resolution of the images is high enough (down to 1/3 mm) to resolve even the smallest capillary waves. The measurements were performed in the wind/wave facility of the IMST (University of Marseille, France) at 5 through 29 m fetch, the Delft wind wave flume (The Netherlands) from 6 to 100 m fetch, and the 4 m-diameter circular wind/wave facility of the Institute for Environmental Physics at the University of Heidelberg (Germany). A first preliminary analysis of the data is given. The angular dispersion of the waves is most sensitively influenced by the geometry of the facility, especially the width of the water channel. Therefore, it is hardly possible to extrapolate the measured angular dispersion of the waves to the ocean. The unidirectional and along-wind wave number spectra, however, show clear trends which allow for an extrapolation to the ocean. At high fetches and wind speeds, the spectral densities for the wave height are proportional to (kappa) -3.5 well into the capillary wave region until a sharp and almost wind speed independent cutoff occurs at (kappa) approximately equals 1100 m -1 ((lambda) approximately equals 0.6 cm). The increase of the spectral densities with friction velocity depends both on wave number and fetch. While the spectral density for small gravity waves depends only weakly on the friction velocity, it increases strongly at higher wave numbers. Generally, this steepness is smaller at higher fetches.

Two-dimensional wave number spectra of short wind waves: results from wind-wave facilities and extrapolation to the ocean

A thorough understanding of the hydrodynamics of short ocean wave is important for interpreting measurements made by active microwave remote sensing instruments. However, conventional methods for studying the structure of a water surface are not capable of resolving the fine scale structure of the surface, especially in the ultra-gravity and capillary wavelengths. Optical instruments have the potential for resolving the fine-scale structure of the ocean surface, however, methods for calibrating these instruments and verifying the accuracy of the measurements have not been developed. In this paper we describe a multi-faceted approach for verifying the accuracy and calibration of an imaging wave slope gauge (ISG). The first step is a thorough theoretical analysis of the geometrical optics and photometry. A detailed discussion on the relationship between surface slope and observed pixel intensity is presented. This discussion includes second order effects which may tend to bias the results. Secondly, calibration objects formed from thin transparent Perspex sheets with known slope and height profiles are retrieved. The results show that the measurements of the water surface shape are accurate enough to compute 2-D wave number spectra.

Calibration and accuracy of optical slope measurements for short wind waves

Optical techniques to measure the small-scale shape, i.e., the short wind waves of the ocean surface are theoretically reviewed. The well-known `shape from shading' and `shape from stereo' paradigms from computer vision are applied to a specular reflecting surface such as the ocean surface and used to study a variety of techniques with a common and elegant concept. The analysis shows that all techniques which have been used so far to take images of short wind waves such as Stilwell photography and various stereo techniques have significant deficiencies. Techniques based on light reflection (`shape from reflection') are basically only useful to derive wave slope statistics. A technique has been developed -- using an artificial light source to measure the 2-D probability density function of wave slope -- which is an extension of the successful sun glitter technique of Cox and Munk. Stereophotography is plagued by insufficient height resolution for small waves and, even more troublesome, by the problem that features seen in one of the images are not necessarily found in the other (correspondence problem) due to the specular nature of reflection at the water surface. Techniques based on light refraction (`shape from refraction') turn out to be most suitable to take wave slope images. They have been successfully used in the laboratory, but will be applied to the ocean in the near future.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Critical theoretical review of optical techniques for short-ocean-wave measurements

A new optical instrument has been designed for combined slope/height measurements of the small-scale structure of the ocean surface. The compact and rugged sensor head contains two light sources and a short-base CCD stereo camera setup mounted 4 - 6 m above the water surface and looking straight down onto the water surface. It takes stereo images of the specular reflexes on the water surface representing slope zero-crossings in a sector of about 30 X 40 cm2. The height of the reflexes can be determined with a precision of about 2 mm. Experiments have been performed in the wind/wave flume of Delft Hydraulics, at the Scripps pier, and at the Noordwijk research platform in the North Sea. In these campaigns, a total of about half a million stereo images have been taken with continuous time series of up to 8 min at 30 frames/s. Some preliminary results are shown.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Combined slope-height measurements of short wind waves: first results from field and laboratory measurements

: The research was centered around a new experimental technique that uses heat as a proxy tracer to measure the air-sea gas exchange rate. The transfer rate for heat in water is measured by using a known heat flux density and measuring the temperature difference across the aqueous boundary layer. In contrast to geochemical methods that are based on mass balances and that have a slow response time in the order of days to weeks due to the larger vertical scales (typically the depth of the mixed layer), the controlled flux density gives an instantaneous picture' of the transfer process. Hence, direct insight into the transport processes right at the air-water interface is obtained through quantitative analysis of infrared image sequences of the water surface. Together with physical modeling of the underlying transfer processes, this passive infrared radiometry technique allowed the computation of the transfer rates directly from the statistical surface temperature distributions without artificial heating of the water surface. The influence of wind forcing, short wind waves, and surfactants on the air-sea gas transfer in coastal waters was studied in field two experiments. The measurements include the air-sea gas transfer rates with a temporal resolution in order of minutes, the air friction velocity, water currents and turbulence, air and water temperatures, visible and infrared radiative fluxes, the visco-elastic properties of surface films, and wave number-frequency spectra of short wind waves. The measurements of the air-sea gas exchange rates with our instruments were combined with concentration measurements of carbon dioxide and dimethyl sulfide in the sea and the atmosphere, and direct flux measurements of carbon dioxide using the eddy correlation technique.

/pdf/air-water-gas-transfer-in-coastal-waters-4c1i56miaj.pdf

Bernd Jaehne

Papers

Two-dimensional wave number spectra of short wind waves: results from wind-wave facilities and extrapolation to the ocean

Calibration and accuracy of optical slope measurements for short wind waves

Critical theoretical review of optical techniques for short-ocean-wave measurements

Combined slope-height measurements of short wind waves: first results from field and laboratory measurements

Air-Water Gas Transfer in Coastal Waters