Relationships between wind speed and gas transfer, combined with knowledge of the partial pressure difference of CO2 across the air-sea interface are frequently used to determine the CO2 flux between the ocean and the atmosphere. Little attention has been paid to the influence of variability in wind speed on the calculated gas transfer velocities and the possibility of chemical enhancement of CO2 exchange at low wind speeds over the ocean. The effect of these parameters is illustrated using a quadratic dependence of gas exchange on wind speed which is fit through gas transfer velocities over the ocean determined by the natural-14C disequilibrium and the bomb-14C inventory methods. Some of the variability between different data sets can be accounted for by the suggested mechanisms, but much of the variation appears due to other causes. Possible causes for the large difference between two frequently used relationships between gas transfer and wind speed are discussed. To determine fluxes of gases other than CO2 across the air-water interface, the relevant expressions for gas transfer, and the temperature and salinity dependence of the Schmidt number and solubility of several gases of environmental interest are included in an appendix.

Relationship between wind speed and gas exchange over the ocean

A third-generation numerical wave model to compute random, short-crested waves in coastal regions with shallow water and ambient currents (Simulating Waves Nearshore (SWAN)) has been developed, implemented, and validated. The model is based on a Eulerian formulation of the discrete spectral balance of action density that accounts for refractive propagation over arbitrary bathymetry and current fields. It is driven by boundary conditions and local winds. As in other third-generation wave models, the processes of wind generation, whitecapping, quadruplet wave-wave interactions, and bottom dissipation are represented explicitly. In SWAN, triad wave-wave interactions and depth-induced wave breaking are added. In contrast to other third-generation wave models, the numerical propagation scheme is implicit, which implies that the computations are more economic in shallow water. The model results agree well with analytical solutions, laboratory observations, and (generalized) field observations.

/pdf/a-third-generation-wave-model-for-coastal-regions-1-model-37o6uqb942.pdf

A third-generation wave model for coastal regions: 1. Model description and validation

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

/pdf/handbook-of-marine-craft-hydrodynamics-and-motion-control-2qu7epb0pt.pdf

Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

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

A third-generation spectral wave model (Simulating Waves Nearshore (SWAN)) for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases. These verification cases represent an increasing complexity in two- dimensional bathymetry and added presence of currents. In the most complex of these cases, the waves propagate through a tidal gap between two barrier islands into a bathymetry of channels and shoals with tidal currents where the waves are regenerated by a local wind. The wave fields were highly variable with up to 3 orders of magnitude difference in energy scale in individual cases. The model accounts for shoaling, refraction, generation by wind, whitecapping, triad and quadruplet wave-wave interactions, and bottom and depth-induced wave breaking. The effect of alternative formulations of these processes is shown. In all cases a relatively large number of wave observations is available, including observations of wave directions. The average rms error in the computed significant wave height and mean wave period is 0.30 m and 0.7 s, respectively, which is 10% of the incident values for both.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JC900123

A third‐generation wave model for coastal regions: 2. Verification

"Wave spectra were measured along a profile extending 160 kilometers into the North Sea westward from Sylt for a period often weeks in 1968 and 1969. During the main experiment in July 1969, thirteen wave stations were in operation, of which six stations continued measurements into the first two weeks of August. A smaller pilot experiment was carried out in September 1968. Currents, tides, air-sea temperature differences and turbulence in the atmospheric boundary layer were also measured. The goal of the experiment (described in Part 1) was to determine the structure of the source function governing the energy balance of the wave spectrum, with particular emphasis on wave growth under stationary offshore wind conditions (Part 2) and the attenuation of swell in water of finite depth (Part 3). The source functions of wave spectra generated by offshore winds exhibit a characteristic plus-minus signature associated with the shift of the sharp spectral peak towards lower frequencies. The two-lobed distribution of the source function can be explained quantitatively by the nonlinear transfer due to resonant wave-wave interactions (second order Bragg scattering). The evolution of a pronounced peak and its shift towards lower frequencies can also be understood as a selfstabilizing feature of this process. For small fetches, the principal energy balance is between the input by wind in the central region of the spectrum and the nonlinear transfer of energy away from this region to short waves, where it is dissipated, and to longer waves. Most of the wave growth on the forward face of the spectrum can be attributed to the nonlinear transfer to longer waves. For short fetches, approximately (80 ± 20) % of the momentum transferred across the air/sea interface enters the wave field, in agreement with Dobson's direct measurements of the work done on the waves by surface pressures. About 80-90 % of the wave-induced momentum flux passes into currents via the nonlinear transfer to short waves and subsequent dissipation; the rest remains in the wave field and is advected away. At larger fetches the interpretation of the energy balance becomes more ambiguous on account of the unknown dissipation in the low-frequency part of the spectrum. Zero dissipation in this frequency range yields a minimal atmospheric momentum flux into the wave field of the order of (10 to 40) % of the total momentum transfer across the air-sea interface -- but ratios up to 100 % are conceivable if dissipation is important. In general, the ratios (as inferred from the nonlinear energy transfer) lie within these limits over a wide (five-decade) range of fetches encompassing both wave-tank and the present field data, suggesting that the scales of the spectrum continually adjust such that the wave-wave interactions just balance the energy input from the wind. This may explain, among other features, the observed decrease of Phillips' "constant" with fetch. The decay rates determined for incoming swell varied considerably, but energy attenuation factors of two along the length of the profile were typical. This is in order of magnitude agreement with expected damping rates due to bottom friction. However, the strong tidal modulation predicted by theory for the case of a quadratic bottom friction law was not observed. Adverse winds did not affect the decay rate. Computations also rule out wave-wave interactions or dissipation due to turbulence outside the bottom boundary layer as effective mechanisms of swell attenuation. We conclude that either the generally accepted friction law needs to be significantly modified or that some other mechanism, such as scattering by bottom irregularities, is the cause of the attenuation. The dispersion characteristics of the swells indicated rather nearby origins, for which the classical (i event model was generally inapplicable. A strong Doppler modulation by tidal currents was also observed.

/pdf/measurements-of-wind-wave-growth-and-swell-decay-during-the-2esyfu2epg.pdf

Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)

The development of a numerical wave prediction model incorporating a parametrical wind-sea model and a characteristic swell model is described. The parametrical model is an extension of an earlier two-parameter model to the full five Jonswap spectral parameters. An application is presented in which the model is used to hindcast severe wave conditions in the North Sea as part of an engineering study to define long-term extreme wave statistics for the area. The limitations of the model and the needs for future research are discussed.

https://pure.mpg.de/pubman/item/item_3319428_2/component/file_3319429/JC084iC09p05727.pdf

A hybrid parametrical wave prediction model

Three operational shallow water wave models are intercompared for two artificial experiments and verified for a severe storm hindcast, with the objectives of further understanding the effects of the parametrization of shallow water wave processes in numerical models.

The models used are the HYPAS (Max-Planck Institute) and GONO (KNMI) coupled-hybrid models, and the BMO (Meteorological Office) coupled-discrete model which are all briefly described. In the first case, depth-dependent fetch-limited wave growth in a steady wind is examined. In the second case a steady onshore wind is specified over an idealized constant slope coastal shelf, and the stationary wave spectra at various depths are intercompared. For the third case the wind fields for the North Sea storms of 18-26 November 1981 were accurately reconstructed and used by each model in its operational configuration to produce a wave hindcast for this period.

In case 1 the GONO and BMO models exhibit similar behaviour in the evolution of energy and peak frequency, whereas HYPAS displays less depth attenuation and little variation in peak frequency. In case 2 the energy values at different shelf depths are approximately as predicted in case 1 for HYPAS though rather higher for BMO and GONO. However, GONO and HYPAS show little change in peak frequency with depth here whereas BMO wave spectra become double-peaked with a wind-sea peak migrating to higher frequencies in shallower waters. In case 3, the hindcasts, all models produce qualitatively similar results. the time series of wave height and period agree well with measurements, BMO and HYPAS predicting correct energy levels except at storm peaks and GONO generally overpredicting both at lower energy levels and in a duration-limited strong wind case. the r.m.s. error in wave height at the southern shallow water verification site is 0.5 m for all models, and varies between 0.9 m (GONO) and 1.5m (HYPAS) at the northern deep water site. Some wave spectra are presented and the directional relaxation of wind-sea in each model is illustrated.

The results of cases 1 and 2 are readily explained by the formulation of shallow water processes adopted in each model, but it is difficult to isolate and identify these mechanisms in the measured or modelied spectra from the hindcast. It is suggested that future studies involving detailed verification and intercomparison of wave models should be confined to more carefully designed wave-measuring experiments so that less ambiguous results are obtained.

A shallow water intercomparison of three numerical wave prediction models (Swim)

A deep water hybrid parametrical wave model, first discussed in the Joint North Sea Wave Project (Jonswap), has been used to hindcast long-term wave height statistics in the northern North Sea. The wave model was validated against wave measurements at two stations near the British Isles. A representative subset of the vigorous gales over the period 1966–1976 was used as input to the model. Extreme value significant wave height statistics were estimated from the independent storm events, taking into account possible secular changes of the wind field extremes. The results are compared with wave height estimates derived in two other studies.

A Hindcast study of extreme wave conditions in the North Sea

The surface wave environment in the GATE B/C scale is described from wave measurements made from buoys and aircraft during Phase III (September 1974). Particular emphasis is given to the wave measurements made from the pitch-roll buoy deployed in the B-scale array from the ship Gilliss and a similar buoy deployed in the C-scale array from Quadra. Reduction of the pitch-roll buoy measurements provided estimates of the one-dimensional wave spectrum as well as of the mean direction and spread of wave energy as a function of frequency. The data clearly revealed the importance of external forcing on the wave climate in GATE. Most of the wave energy present in the GATE areas was found to be swell imported from the trade wind circulations of both hemispheres and from an intense extratropical cyclone which crossed the North Atlantic at high latitudes early in Phase III. Locally generated waves were clearly evident in the wave spectra, but their energy level way have been modulated significantly by the lo...

/pdf/the-surface-wave-environment-in-the-gate-b-c-scale-phase-iii-9qntug8ijl.pdf

J. A. Ewing

Papers

Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)

A hybrid parametrical wave prediction model

A shallow water intercomparison of three numerical wave prediction models (Swim)

A Hindcast study of extreme wave conditions in the North Sea

The Surface Wave Environment In the GATE B/C Scale—Phase III