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Paul A. Hwang

Abstract

This paper presents a wavenumber spectral model of the surface water waves in the capillary–gravity regime. The database for the analysis consists of spatial and temporal measurements of surface slopes obtained from a scanning slope sensor buoy operating in free-drift mode in the Atlantic Ocean. These data indicate that the contribution of mean square slopes from capillary–gravity waves (wavelengths from 4 mm to 6 cm) is a significant portion of the total mean square slopes. The resulting mean square slopes derived from the proposed spectral model are in excellent agreement with existing field datasets.

The properties of short waves, including the mean square slopes and wind speed dependence of the spectral intensity of individual wave components, derived from optical and microwave sensors are also compared. Significant differences in terms of the magnitudes of the mean square slopes and the exponents of wind speed dependence are found. Some of the possible explanations of the discrepancies are explored.

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Paul A. Hwang

Abstract

This paper describes a technique to measure the spatial structure of short capillary–gravity waves on the water surface. The method is based on optical refraction of a single laser beam crossing the air–water interface to derive the surface slope information. By quickly scanning the laser beam, the spatial and temporal evolution of the surface undulation can be studied in great detail. The spatial measurement of the surface fluctuation also allows direct computation of the wavenumber spectra in the capillary–gravity wave regime. This approach avoids the difficulty of resolving the Doppler frequency shift encountered in the processing of high-frequency spectra derived from a single-point sensor. The modulation of short waves by the orbital velocity of surface long waves is analyzed from the distribution of the wavenumber spectra of short waves along the phase of long waves. Key parameters determining the modulation magnitude are identified to be the slope of wavenumber spectra in the neighborhood of the modulated wave component, the ratio of the group and phase velocities of the modulated wave component, the dimensionless relaxation parameter, and the resonance parameter. Quantitative results on these parameters are obtained from the experimental data.

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Paul A. Hwang

Abstract

In a recent study, the dimensionless surface roughness spectrum has been empirically parameterized as a power-law function of the dimensionless wind speed expressed as the ratio of wind friction velocity and phase speed of the surface roughness wave component. The wave-number-dependent proportionality coefficient, A, and exponent, a, of the power-law function are derived from field measurements of the short-wave spectrum. To extend the roughness spectrum model beyond the wavenumber range of field data, analytical functions are formulated such that A and a approach their asymptotic limits: A 0 and a 0 toward the lowest wavenumber, and A and a toward the highest wavenumber. Of the four asymptotic values, A is considered most questionable for the lack of reference information. When applied to the normalized radar cross-section (NRCS) computation, the results are in good agreement (within about 2 dB) with field data or geophysical model functions (GMFs) for incidence angles between 20° and 40° but significant underestimation occurs for higher incidence angles. The comparison study of NRCS computation offers helpful guidelines for adjusting the asymptotic factors, especially the numerical value of A . Improved agreement between the computed NRCS (vertical polarization) using the new roughness spectrum with GMF is expanded to incidence angles between 20° and 60°. The wind speed range of good agreement between calculation and GMF is below about 15 m s−1 for Ku band and about 30 m s−1 for C band.

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Paul A. Hwang

Abstract

Remote sensing is becoming an important tool for oceanographic research. As the resolution of remote sensors is becoming comparable to the wavelength of dominant ocean surface waves, the usual assumption of homogeneous surface roughness is no longer adequate. In this paper, laboratory data of surface wave displacement and small-scale surface roughness (wavelength 0.004–0.10 m) measured by a scanning slope sensor are analyzed. The results show that higher intensity of surface roughness occurs at the upwind quadrant of the wave crests of background waves. Over a wide wind speed range, the maximum surface roughness is located close to the maximum of surface velocity divergence.

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Paul A. Hwang

Abstract

Transports and net fluxes of surface wave energy and momentum inside tropical cyclones (TCs) are analyzed with wave spectra acquired by hurricane hunters. Previous analyses of dominant wave properties show a primary feature of sinusoidal azimuthal variation. Transports calculated from directional wave spectra are also primarily sinusoidal, which is modeled as a harmonic series. The result reveals that forward transport peaks are in the right-front quarter relative to the TC heading, and somewhat weaker valleys of backward transports are in the left-back quarter. Rightward transport peaks are in the right-back quarter and stronger leftward transport valleys are in the left-front quarter. Net fluxes are derived analytically from the gradients of transports. Their azimuthal variations are primarily biharmonic with forward trend confined in a slightly left-tilted parallel channel about a width two to three radius of maximum wind (RMW) on each side of the TC center. Leftward net fluxes are in a parallel channel of similar size and normal to that of the forward net fluxes. In vectors, the right-back quarter is a region of net influxes of energy and momentum. The TC central region has strong local fluxes that lead to bifurcation of the flux lines into leftward and forward paths. This may play a role in stabilizing the TC propagation. The net fluxes are a small fraction of the expected energy and momentum inputs from local wind except near the eye region. Within about 30 km from the TC center the local wind speed may exceed 30 m s−1 and the net fluxes can exceed 50% of the expected local wind input.

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Paul A. Hwang

Abstract

Wind-wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity functions, the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interpreted as the wave energy evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave-age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind-wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measured and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake.

Significance Statement

This paper presents a growth function and spectrum model to describe wind-wave development in all water depths. Their applicability covers a wide range of wind forcing conditions including steady, accelerating, decelerating, and tropical cyclone events. Support for the unified spectrum model and growth function is presented with field observations and numerical computations.

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Paul A. Hwang

Abstract

Many wind wave spectrum models provide excellent wave height prediction given the input of wind speed and wave age. Their quantification of the surface roughness, on the other hand, varies considerably. The ocean surface roughness is generally represented by the mean square slope, and its direct measurement in open ocean remains a challenging task. Microwave remote sensing from space delivers ocean surface roughness information. Satellite platforms offer global coverage in a broad range of environmental conditions. This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling. The analysis presented in this paper shows that over two orders of magnitude of the wavenumber range (0.3–30 rad m−1), the spectral components follow a power function relating the dimensionless spectrum and the ratio between wind friction velocity and wave phase speed. The power function exponent is about 0.38, which is considerably smaller than unity as expected from the classical equilibrium spectrum function. It may suggest that wave breaking is not only an energy sink but also a source of roughness generation covering a wideband of wavelengths about 20 m and shorter.

Significance Statement

This paper presents low-pass mean square slope (LPMSS) data obtained by spaceborne microwave altimeters and reflectometers operating at L, Ku, and Ka bands (about 1.6, 14, and 36 GHz). The LPMSS data represent the spectrally integrated ocean surface roughness with 11, 95, and 250 rad m−1 upper cutoff wavenumbers, and the maximum wind speeds are 80, 29, and 25 m s−1, respectively. A better understanding of the ocean surface roughness is important to the goal of improving wind wave spectrum modeling that is critical to the investigation of air–sea interaction and ocean remote sensing. The analysis presented in this paper suggests that wave breaking is not only an energy sink but also a generation source of surface roughness covering a wide band of wavelengths about 20 m and shorter.

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Paul A. Hwang

Abstract

Ocean surface roughness and whitecaps are driven by the ocean surface wind stress; thus, their values calculated from the wind speed input may vary significantly depending on the drag coefficient formula applied. Because roughness and whitecaps are critical elements of the ocean surface response in microwave remote sensing, the extensive microwave remote sensing measurements contain the information of the drag coefficient, surface roughness, and whitecap coverage. The scattering radar cross sections from global measurements under calm to tropical cyclone conditions have been used effectively to improve the formulation of the surface roughness spectrum. In this paper, the microwave radiometer measurements in tropical cyclones are exploited to extract information of the drag coefficient and whitecap coverage in high winds. The results show that when expressed as a wind speed power function, the exponent in high winds (greater than about 35 m s−1) is about −1 for the drag coefficient, 0.5 for the wind friction velocity, and 1.25 for the whitecap coverage.

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Paul A. Hwang

Abstract

The 2D wavenumber spectra collected by an airborne scanning radar altimeter in hurricane hunter missions are used to investigate the fetch- and duration-limited nature of wave growth inside hurricanes. Despite the much more complex wind-forcing conditions, the dimensionless growth curves obtained with the wind-wave triplets (reference wind velocity, significant wave height, and dominant wave period) inside hurricanes, except near the eye region, are comparable to the reference similarity counterparts constructed with the wind-wave triplets collected in field experiments conducted under ideal quasi-steady fetch-limited conditions. In dimensionless terms, the youngest waves are in the back quarter of the hurricane. In the Northern Hemisphere, the dimensionless frequency decreases systematically counterclockwise (CCW), and the most mature waves are in the left-hand sector. Except for those waves near the eye region, the dominant wave phase speeds are about 0.32 to 0.71 times of the local wind speed, and they are proper wind seas. Based on the computation of the wind input or energy dissipation in the wave field, a conservative estimate of the air–sea energy exchange over the coverage area of a category one hurricane is about 5 TW. Formulas for the effective fetches and durations in the three hurricane sectors are derived from the data. Using these formulas together with the wave growth functions, the full set of wind-wave triplets can be calculated knowing only one of the three. These results may enhance the capability and scope of monitoring hurricanes from space.

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