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Paul A. Hwang and Edward J. Walsh

Abstract

For wind-generated waves, the wind-wave triplets (reference wind speed, significant wave height, and spectral peak wave period) are intimately connected through the fetch- or duration-limited wave growth functions. The full set of the triplets can be obtained knowing only one of the three, together with the input of fetch (duration) information using the pair of fetch-limited (duration limited) wave growth functions. The air–sea energy and momentum exchanges are functions of the wind-wave triplets, and they can be quantified with the wind-wave growth functions. Previous studies have shown that the wave development inside hurricanes follows essentially the same growth functions established for steady wind forcing conditions. This paper presents the analysis of wind-wave triplets collected inside Hurricane Bonnie 1998 at category 2 stage along 10 transects radiating from the hurricane center. A fetch model is formulated for any location inside the hurricane. Applying the fetch model to the 2D hurricane wind field, the detailed spatial distribution of the wave field and the associated energy and momentum exchanges inside the hurricane are investigated. For the case studied, the energy and momentum exchanges display two local maxima resulting from different weightings of wave age and wind speed. Referenced to the hurricane heading, the exchanges on the right half plane of the hurricane are much stronger than those on the left half plane. Integrated over the hurricane coverage area, the right-to-left ratio is about 3:1 for both energy and momentum exchanges. Computed exchange rates with and without considering wave properties differ significantly.

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Paul A. Hwang and Edward J. Walsh

Abstract

Surface wave propagation inside tropical cyclones (TCs) is complicated and multiple wave systems are frequently observed. The directional wave spectra acquired by hurricane hunters are analyzed to quantify its azimuthal and radial variations. Referenced to the hurricane heading, the dominate feature in the front half of the TC coverage area is single wave systems propagating toward left and left-front. Multiple wave systems are generally observed in the back and right quarters outside the radius of maximum wind (RMW). The directional differences and locations of occurrences of multisystem spectra are Gaussian distributed. The directional differences of the secondary and tertiary wave systems from the primary system are centered around 60°–70°. The minor systems are more likely on the left-hand side of the primary system than on the right-hand side by a 3-to-1 ratio. The most likely azimuthal location of multisystem spectra is about 210° counterclockwise from the heading. In the right-front quarter, waves propagate into the advancing wind field and experience extended air–sea exchanges to grow higher and longer; in the left-rear quarter, they propagate away from the advancing wind field and are more likely younger seas. The radial variation of wave propagation is relatively minor except inside the RMW. A model describing the dominant wave propagation direction is presented. The regression statistics between modeled and measured wave directions show consistent agreement in 9 of the 11 datasets available for investigation. Causes for the significantly different statistics of the two remaining datasets include proximity to coast (a landfalling case) and rapid change in the hurricane translation speed or direction.

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Paul A. Hwang and Edward J. Walsh

Abstract

Making use of the fetch- and duration-limited nature of wind-wave growth inside tropical cyclones, an algorithm is developed to estimate the maximum significant wave height and dominant wave period of surface waves generated by tropical cyclone wind fields. The results of the maximum significant wave height and dominant wave period are further approximated by simple power functions of the maximum wind speed. The exponents of the power functions are almost constant, and the proportionality coefficients can be approximated by second-order polynomial functions of the radius of maximum wind speed (RMW). The predicted maximum values agree well with results derived from simultaneous wind and wave measurements obtained during 11 hurricane reconnaissance and research missions in six hurricanes.

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Lynn K. Shay, Edward J. Walsh, and Pen Chen Zhang

Abstract

During the third intensive observational period of the Surface Wave Dynamics Experiment (SWADE), an aircraft-based experiment was conducted on 5 March 1991 by deploying slow-fall airborne expendable current profilers (AXCPs) and airborne expendable bathythermographs (AXBTs) during a scanning radar altimeter (SRA) flight on the NASA NP-3A research aircraft. As the Gulf Stream moved into the SWADE domain in late February, maximum upper-layer currents of 1.98 m s−1 were observed in the core of the baroclinic jet where the vertical current shears were O(10−2 s−1). The SRA concurrently measured the sea surface topography, which was transformed into two-dimensional directional wave spectra at 5–6-km intervals along the flight tracks. The wave spectra indicated a local wave field with wavelengths of 40–60 m propagating southward between 120° and 180°, and a northward-moving swell field from 300° to 70° associated with significant wave heights of 2–4 m.

As the AXCP descended through the upper ocean, the profiler sensed orbital velocity amplitudes of 0.2–0.5 m s−1 due to low-frequency surface waves. These orbital velocities were isolated by fitting the observed current profiles to the three-layer model based on a monochromatic surface wave, including the steady and current shear terms within each layer. The depth-integrated differences between the observed and modeled velocity profiles were typically less than 3 cm s−1. For 17 of the 21 AXCP drop sites, the rms orbital velocity amplitudes, estimated by integrating the wave spectra over direction and frequency, were correlated at a level of 0.61 with those derived from the current profiles. The direction of wave propagation inferred from the AXCP-derived orbital velocities was in the same direction observed by the SRA. These mean wave directions were highly correlated (0.87) and differed only by about 5°.

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Nicholas Scott, Tetsu Hara, Edward J. Walsh, and Paul A. Hwang

Abstract

A new wavelet analysis methodology is proposed to estimate the statistics of steep waves. The method is applied to open ocean wave height data from the Southern Ocean Waves Experiment (1992) and from a field experiment conducted at Duck, North Carolina (1997). Results show that high wave slope crests appear over a wide range of wavenumbers, with a large amount being much shorter than the dominant wave. At low wave slope thresholds, all wave fields have roughly the same amount of wave crests regardless of wind forcing. The steep wave statistic decays exponentially with the square of the wave slope threshold, with a decay rate that is larger for the low wind cases than the high wind cases. Comparison of the steep wave statistic with independent measurements of the breaking wave statistic suggests a breaking wave slope threshold of about 0.12. The steep wave statistic does not scale with the cube of the wind speed, suggesting that other factors besides the wind speed also affect its level. Comparison of the steep wave statistic to the saturation spectrum reveals a reasonable correlation at moderate wave slope thresholds.

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Nicholas Scott, Tetsu Hara, Paul A. Hwang, and Edward J. Walsh

Abstract

A new wavelet analysis methodology is applied to open ocean wave height data from the Southern Ocean Waves Experiment (1992) and from a field experiment conducted at Duck, North Carolina, in 1997 with the aim of estimating the directionality and crest lengths of steep waves. The crest directionality statistic shows that most of the steep wave crests are normal to the direction of the mean wind. This is inconsistent with the Fourier wavenumber spectrum that shows a broad bimodal directional spreading at high wavenumbers. The crest length statistics demonstrate that the wave field is dominated by short-crested waves with small crest length/wavelength ratios. The one-dimensional steep wave statistic obtained from the integration of the directional (two dimensional) steep wave statistic is consistent with the one-dimensional steep wave statistic obtained from the one-dimensional analysis at high wave slope thresholds.

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Edward J. Walsh, C. W. Fairall, and Ivan PopStefanija

Abstract

The airborne NOAA Wide Swath Radar Altimeter (WSRA) is a 16-GHz digital beamforming radar altimeter that produces a topographic map of the waves as the aircraft advances. The wave topography is transformed by a two-dimensional FFT into directional wave spectra. The WSRA operates unattended on the aircraft and provides continuous real-time reporting of several data products: 1) significant wave height; 2) directional ocean wave spectra; 3) the wave height, wavelength, and direction of propagation of the primary and secondary wave fields; 4) rainfall rate; and 5) sea surface mean square slope (mss). During hurricane flights the data products are transmitted in real-time from the NOAA WP-3D aircraft through a satellite data link to a ground station and on to the National Hurricane Center (NHC) for use by the forecasters for intensity projections and incorporation in hurricane wave models. The WSRA is the only instrument that can quickly provide high-density measurements of the complex wave topography over a large area surrounding the eye of the storm.

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Dudley B. Chelton, Edward J. Walsh, and John L. MacArthur

Abstract

With the presently operational altimeter on the U.S. Navy satellite GEOSAT, and three new altimeters soon to be launched by the European, French and U.S. space agencies, satellite altimetry promises to become a standard technique for studying oceanographic variability. Little has been written about the instrumental technique used to determine sea surface height from altimetric measurements. In this paper, we summarize the pulse-compression technique by which a radar altimeter transmits a relatively long pulse and processes the returned signal in a way that is equivalent to transmitting a very short pulse and measuring the time history of the returned power in a sequence of range gates. The effective short pulse enhances the range resolution that would be obtained from the actual long pulse. The method used onboard the satellite to track the point on the returned signal corresponding to the range to mean sea level (spatially averaged over the altimeter footprint) is also summarized. Pulse compression and sea level tracking are important to the overall error budget for altimetric estimates of sea level. The dominant sources of sea level tracking errors are discussed, with particular emphasis on the high degree of accuracy required for the TOPEX altimeter scheduled for launch in mid 1992. Also included here as an appendix is a derivation of the spherical earth correction to altimeter footprint area. It is shown that the flat earth approximation used heretofore in ground-based processing of altimeter data results in a bias of −0.51 dB in estimates of normalized radar cross section from an altitude of 800 km; if not corrected, this bias would increase to −0.83 dB for the TOPEX altitude of 1335 km.

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O. M. Phillips, Daifang Gu, and Edward J. Walsh

Abstract

In a previous paper (Phillips et al.) an approximate theory was developed that predicted that the expected configuration of extreme waves in a random sea (or the average configuration of an ensemble of extreme waves) is proportional to the space-time autocorrelation function of the surface displacement of the wave field as a whole. This result is tested by examination of scanning radar altimeter measurements made during SWADE in four different sea states, including a unimodal mature wave field, a short fetch, a wind-generated sea crossing swell, a very broad directional spectrum, and a fetch-limited wind sea with opposing swell. In each of these, the spatial autocorrelation function was found directly from the SRA data. The highest waves in each dataset were selected and their configurations averaged with respect to the crest. These averaged configurations were in each case found to be consistent with the autocorrelation function.

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Edward J. Walsh, Ivan PopStefanija, Sergey Y. Matrosov, Jian Zhang, Eric Uhlhorn, and Brad Klotz

Abstract

The NOAA Wide-Swath Radar Altimeter (WSRA) uses 80 narrow beams spread over ±30° in the cross-track direction to generate raster lines of sea surface topography at a 10-Hz rate from which sea surface directional wave spectra are produced. A ±14° subset of the backscattered power data associated with the topography measurements is used to produce independent measurements of rain rate and sea surface mean square slope at 10-s intervals. Theoretical calculations of rain attenuation at the WSRA 16.15-GHz operating frequency using measured drop size distributions for both mostly convective and mostly stratiform rainfall demonstrate that the WSRA absorption technique for rain determination is relatively insensitive to both ambient temperature and the characteristics of the drop size distribution, in contrast to reflectivity techniques. The variation of the sea surface radar reflectivity in the vicinity of a hurricane is reviewed. Fluctuations in the sea surface scattering characteristics caused by changes in wind speed or the rain impinging on the surface cannot contaminate the rain measurement because they are calibrated out using the WSRA measurement of mean square slope. WSRA rain measurements from a NOAA WP-3D hurricane research aircraft off the North Carolina coast in Hurricane Irene on 26 August 2011 are compared with those from the stepped frequency microwave radiometer (SFMR) on the aircraft and the Next Generation Weather Radar (NEXRAD) National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE) system.

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